THE USE OF HEAT RATES
IN PRODUCTION COST MODELING
AND MARKET MODELING
April 17, 1998
Joel B. Klein
Electricity Analysis Office
California Energy Commission
[email protected]
(916) 654-4822
DISCLAIMER
“This report was prepared by California Energy Commission staff. Opinions, conclusions, and findings expressed
in this report are those of the author. The report does not represent the official position of the California Energy
Commission until adopted at a public meeting.”
TABLE OF CONTENTS
SECTIONS:
I. OVERVIEW ...........................................................................................…............................ 4
II. INTRODUCTION .................................................................................................................. 5
III. TERMINOLOGY .................................................................................................................. 6
IV. HEAT RATES AS EQUATIONS ........................................................................................ 12
V. HEAT RATES IN PRODUCTION COST MODELING ................................................... 18
VI. HEAT RATES IN MARKET MODELING ....................................................................... 27
APPENDICES
A. SUMMARY OF BLOCK HEAT RATE DATA
B. DATA FOR HEAT RATE EQUATIONS
C. INCREMENTAL HEAT RATE ERRORS
D. AVERAGE TO INCREMENTAL HEAT RATE RATIOS
E. A SIMPLISTIC MARKET MODEL
F. FR 97 NATURAL GAS PRICE FORECAST
HR-DESC.DOC; 4/17/98; PAGE 2
ACKNOWLEDGMENTS OF STAFF PARTICIPATION
A special thank you to the Energy Commission staff for their contributions to this effort.
Pat McAuliffe ..........................................................................
Terry Ewing.............................................................................
Pedro Ramos ...........................................................................
Primary Consultant
Technical Review
Software Consultant
HR-DESC.DOC; 4/17/98; PAGE 3
THE USE OF HEAT RATES
IN PRODUCTION COST MODELING
AND MARKET MODELING
I. OVERVIEW
This is a comprehensive description of heat rates as they have been applied to production cost modeling
in the past and more importantly how they will apply to market modeling in the future. I define the basic
terminology, describe how the data is obtained, and show how it is used in market modeling as opposed
to production cost modeling. I also discuss the inherent difficulties and inaccuracies in the use of heat rate
data. With the possible exceptions of Sections II and III, this is not intended for someone who is looking
for a simplified definition. This report is for someone who requires a comprehensive understanding.
Section II describes the scope of the report and gives an introductory definition of heat rates. Section III
defines the basic terminology of heat rates and gives illustrative examples. It defines Input-Output
Curves, Average Heat Rates, and Incremental Heat Rates – both Average Incremental and Instantaneous
Incremental. It describes how heat rate data is measured and how block heat rate values are calculated
from these measurements. Section IV describes heat rates as equations, as opposed to the block heat
rates that are most typically used by engineers and utility analysts. Section V illustrates how heat rates are
used in production cost modeling. It defines their use in commitment, dispatch and calculating production
costs and marginal costs. It also quantifies the errors produced by using block heat rates of modeling
instead of the equations that actually define these functions in a real utility. Section VI describes how the
use of heat rates will change in the new market, and the modeling of that market. In each Section the
concepts are illustrated using both fictitious, illustrative units and real units.
Appendix A provides a summary of the block heat rate data for the slow-start thermal units for each of
the three IOUs prior to divestiture: PG&E, SCE and SDG&E. This data is referenced in all sections of
this report - and can prove generally useful to engineers and analysts who do work related to heat rates
data. The block data is provided for Input-Output Curve values, Average Heat Rates and Incremental
Heat Rates – both in table and graphical format. Appendix B provides the detailed calculations for
Section IV which describes the development of the heat rate equations that correspond to the block data
heat rates of Appendix A. Appendix C provides the details of the calculations for Section V that
quantifies the errors caused by using block incremental heat rates in modeling, rather than the equations
that more truly characterize the operation of a real utility system. Appendices D, E and F support the
work of Section VI. Appendix D quantifies the differences between Incremental Heat Rates and Average
Heat Rates, in order to characterize and quantify the differences between the marginal cost of the
regulated and market clearing price of the deregulated markets. Appendix E is a simplistic market model,
that is similar to Appendix D in its goal, except that it accomplishes the same thing in a more dynamic
way that allows for a more descriptive and compete characterization of these differences. Appendix F is
a summary of the Energy Commission’s 1997 Fuels Report (FR 97) gas prices that were used in Section
VI that were used to convert the heat rates differences to dollar cost differences.
HR-DESC.DOC; 4/17/98; PAGE 4
II. INTRODUCTION
The fact that you have elected to read this paper suggests that you already have some understanding of
heat rates. Most likely, this is an understanding of Average Heat Rates, whereby a heat rate of 10,000
Btu/kWh is representative of a generating unit requiring 10,000 Btu of fuel to generate one kilowatt-hour
of electricity. It is probable also that you have an understanding that heat rates are a measure of efficiency
whereby a unit that has an Average Heat Rate of 8,000 Btu/kWh is understood to be more efficient than
the previously mentioned unit with an Average Heat Rate of 10,000 Btu/kWh -- and more desirable, all
other things being equal.
And, it is somewhat likely that you have some understanding of Incremental Heat Rates as being used in
the dispatch process of production cost models: the Incremental Heat Rate times the fuel cost equals the
cost of that next increment of power.
It is much less likely that you have an understanding of the difference between Instantaneous Incremental Heat Rate and Average Incremental Heat Rates. This subtlety is not commonly understood but is
essential to a comprehensive understanding of heat rates. It is also unlikely -- unless you are a production
cost modeler -- that you have an understanding of the Input-Output Curve and how it relates to the
Average and Incremental Heat Rates. This paper clarifies all these terms using simple illustrative
examples.
This paper describes how heat rates are used in production cost modeling. More significantly, it also
describes the relevance of the use of heat rates in the new competitive market where a production cost
model is no longer just a production cost model. It now becomes a production cost and market (bidding)
model. The bulk of this paper is devoted to explaining and quantifying the differences in production cost
and market modeling. An important part of this paper is the supporting analytical data which should
prove valuable for future market studies.
HR-DESC.DOC; 4/17/98; PAGE 5
III. TERMINOLOGY
An understanding of heat rates starts with an fundamental understanding of the following terms.
•
•
•
Incremental Costs and Incremental Heat Rates
Average Costs and Average Heat Rates
Input-Output Curves
These terms are most simply explained using an illustrative generator designated “Unit X.” This fictitious
Unit has a maximum output of three-megawatts (3-MW) and a minimum output of one-megawatt (1MW). Unit X is a gas-fired thermal unit with three 1-MW blocks of generation. The heat rates and costs
are shown in Table 1 on a block-by-block basis. The costs as shown in dollars per megawatt-hour
($/MWh) are based on an assumed natural gas cost of $2.50 per million Btu (MMBtu). To further
simplify this explanation, Unit X is assumed to have no variable Operation and Maintenance (O&M)
costs.
TABLE 1: INCREMENTAL VERSUS AVERAGE COSTS FOR UNIT X
INCREMENTAL COSTS
BLOCK
HEAT RATE
COST*
(MW)
(Btu/kWh)
($/MWh)
LEVEL
(MW)
AVERAGE COSTS
HEAT RATE
COST*
(Btu/kWh)
($/MWh)
1
20,000
50
1
20,000
50
1
4,000
10
2
12,000
30
1
6,000
15
3
10,000
25
* Using a natural gas price of 2.50 $/MMBtu
Incremental Costs and Heat Rates
Incremental Heat Rates are a measure of the efficiency of a unit for each block (increment) of power that
it generates. The Incremental heat rate of Unit X for Block 1 is 20,000 Btu/kWh; that is, Unit X requires
20,000 Btu of fuel to produce the first MW. Similarly, Unit X requires 4,000 Btu for the second MW and
6,000 Btu for the third MW.
The Incremental Cost is, very simply, the cost of each block (increment) of generation. Incremental Costs
are derived from Incremental Heat Rates: the Incremental Heat Rate times the fuel cost equals the
Incremental Cost. For Unit X, each increment is one megawatt. The cost of the first MW generated
(Block 1) is 50 $/MWh: 20,000 Btu/kWh x 2.50 $/MMBtu = 50 $/MWh. The cost of the second MW
generated (Block 2) is 10 $/MWh. The cost of the third MW generated (Block 3) is 15 $/MWh.
Average Costs and Heat Rates
The “Average Cost” is subtler than Incremental Cost but is as simple as calculating the average cost of
two oranges bought at different prices. If one orange costs $50 and the second costs $10, you easily
realize that you paid an average of $30 per orange -- and probably also suspect that you’re paying too
much for oranges. Both the Average Heat Rate and the Average Cost are calculated similarly.
HR-DESC.DOC; 4/17/98; PAGE 6
For Block 1, the Average Heat Rate (and Average Cost) is the same as the Incremental Heat Rate (and
Incremental Cost) as they are the same the increment.
The Average Heat Rate at 2-MW (Level 2) is the average of Block 1 and Block 2 Heat Rates:
(20,000+4,000)/2 = 12,000 Btu/kWh. The Average Heat Rate of generating 3-MW is the average of
Blocks 1, 2 and 3: (20,000+4,000+ 6,000)/3 = 10,000 Btu/kWh. In this example, only simple averages
are used since all block sizes are the same. For a unit with unequal block sizes a weighted average would
be used.
The cost of generating at 2-MW is exactly comparable: the average of cost of Block 1 and Block 2 is 30
$/MWh: (50 + 10)/2 = 30 $/MWh – remember the oranges. Similarly, the cost of generating at the level
of 3-MW is 25 $/MWh: (50+10+15)/3 = 25 $/MWh.
Input-Output Curve
In the engineering world, the Input-Output Curve is the mechanism that defines the relationship between
the Incremental and Average Heat Rates. It is also the data that is actually measured in the field. The
Average and Incremental Heat Rates are not measured directly. The Input-Output Curve is measured and
the Average and Incremental Heat Rates are constructed from it. Figure 1 illustrates the Input-Output
Curve for Unit X.
UNIT X
INPUT-OUTPUT CURVE
INPUT (1000 Btu/hr)
30,000
25,000
20,000
15,000
10,000
5,000
0
0
1
2
3
OUTPUT (MW)
Figure 1
The Input-Output Curve is constructed by measuring the fuel (the input) required to maintain various
levels of generation (the output). For Unit X, the engineers would start by measuring the fuel consumed
to maintain an output of 1-MW, finding this to be 20,000 Btu/hr. They would then replicate this
measurement for 2 and 3 MW, and find that Unit X was consuming 24,000 and 30,000 Btu/hr,
respectively. Based on this information, the engineers would construct Figure 1 and could then calculate
the Incremental and Average Heat Rates as follows.
The calculation of Average Heat Rate from the Input-Output Curve it is the simplest to explain. The
Average Heat Rate at a level of generation is equal to the corresponding input in fuel divided by the
HR-DESC.DOC; 4/17/98; PAGE 7
power generated. For Unit X at 1-MW this is 20,000,000 Btu/hr divided by the output of 1 MW:
20,000,000 Btu/hr / 1 MW = 20,000 Btu/kWh. The Average Heat Rate at 2-MW is, again, the fuel
consumed divided by the output power: 24,000,000 Btu/hr / 2 MW = 12,000 Btu/kWh. The Average
Heat Rate at 3-MW is calculated in the same way: 30,000,000 Btu/hr / 3 MW = 10,000 Btu/kWh.
At this point, the reader is better prepared to appreciate that the name “Average Heat Rate” comes from
the measuring of the Input-Output curve. When the engineers measure a generating unit to construct the
Input-Output curve, they note that there are deviations over time in the number of Btu to maintain the
respective output power. They contend with this problem by averaging these different measurements to
ascertain the average Input-Output Curve. Accordingly, they refer to the heat rate that is subsequently
derived from this average value as the Average Heat Rate.
The Incremental Heat Rate is similar but confined to the “increment” in question, only. The first thing
that has to be understood is that our Block 1 Incremental Heat Rate is not truly an Incremental Heat
Rate. It is an Average Heat Rate in “Incremental Heat Rate clothing.” This can be explained using Unit
X. The “so-called” Incremental Heat Rate at Block 1 is shown as 20,000 Btu/kWh -- note that this is
equal in value to the Average Incremental Heat Rate of 20,000 Btu/kWh. It is not just equal in value, it is
the identical quantity. This format facilitates the calculations of heat rates – for example, Tables 1 and 2.
And it is how the data is entered into models. This is all done for convenience but it can not be an
Incremental Heat Rate. Incremental Heat Rates, by definition, are used for dispatch decisions. The 20,000
Btu/kWh Incremental Heat Rate it is never used in a dispatch decision and therefore can never be
considered a true Incremental Heat Rate. This will become clearer in later discussions.
The first real “increment” is between Blocks 1 and 2. This is shown as a Block 2 value, but represents the
Average Incremental Heat Rate from Block 1 to Block 2. Looking at the Input-Output Curve of Unit X,
we see that the input fuel requirement changes from 20,000 to 24,000 Btu/hr in moving from Block 1 to
Block 2. The incremental change to achieve this additional MW of output is an increase of 4,000 Btu/hr:
24,000 - 20,000 = 4,000 Btu/hr. We define the Incremental Heat Rate as the incremental change in input
divided by the incremental change in output: 4,000 Btu/hr / 1 MW = 4,000 Btu/kWh. The calculation for
the Incremental Heat Rate for the increment from Block 2 to Block 3 is similar: (30,000 - 24,000) / 1
MW = 6,000 Btu/kWh.
Table 2 summarizes all these results. Figure 2A, on the following page, shows the data of Table 2
combined with the corresponding figures. This is a format to which we will repeatedly return in
subsequent sections and you need to be completely comfortable with it. Figure 2B shows the corresponding cost data for reference.
TABLE 2: SUMMARY OF HEAT RATE DATA FOR UNIT X
CAPACITY
(MW)
INPUT-OUTPUT
CURVE
(1000 Btu/hr)
INCREMENTAL
HEAT RATE
(Btu/kWh)
AVERAGE
HEAT RATE
(Btu/kWh)
BLOCK 1
1
20,000
20,000
20,000
BLOCK 2
2
24,000
4,000
12,000
BLOCK 3
3
30,000
6,000
10,000
HR-DESC.DOC; 4/17/98; PAGE 8
FIGURE 2A: HEAT RATE PLOTS FOR UNIT X
UNIT X
AVERAGE HEAT RATE
Input-Output Incremental Average
Output
Curve
Heat Rate Heat Rate
(MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
BLOCK 2
BLOCK 3
1
2
3
20,000
24,000
30,000
20,000
4,000
6,000
20,000
12,000
10,000
HEATRATE (Btu/kWh)
20,000
15,000
10,000
5,000
0
0
1
2
3
OUTPUT (MW)
30,000
20,000
25,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
UNIT X
INCREMENTAL HEAT RATE
UNIT X
INPUT-OUTPUT CURVE
20,000
15,000
10,000
5,000
15,000
10,000
5,000
0
0
0
1
2
3
0
1
2
3
OUTPUT (MW)
OUTPUT (MW)
FIGURE 2B: COST PLOTS FOR UNIT X
UNIT X
AVERAGE COST
Output
(MW)
BLOCK 1
BLOCK 2
BLOCK 3
Input-Output Incremental Average
Cost
Cost
Cost
($/hr)
($/MWh)
($/MWh)
1
2
3
50
60
75
50
10
15
50
30
25
COST ($/MWh)
50
40
30
20
10
0
0
1
2
3
OUTPUT (MW)
UNIT X
INPUT-OUTPUT COST
80
UNIT X
INCREMENTAL COST
50
70
40
COST ($/MWh)
COST ($/hr)
60
50
40
30
20
30
20
10
10
0
0
0
1
2
OUTPUT (MW)
3
0
1
2
3
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE 9
Thus far, the examples have been limited solely to the fictitious Unit X. It is now time to examine real
units in order to get a feel for the real thing. I have selected as examples both the most efficient unit in the
PG&E1 system, Moss Landing 7, and the least efficient unit in the PG&E system, Hunters Point 3. These
units are shown below in the same format as Figure 2A.
Figure 3 shows Moss Landing 7 with a full load Average Heat Rate of 8,917 Btu/kWh. Remembering
that a 100 percent efficient generating unit would require 3,413 Btu/kWh, we can calculate the efficiency
of Moss Landing 7 as 38.3 percent: 3,413 / 8,917 = 38.3%.
FIGURE 3: MOSS LANDING 7 HEAT RATES
SUMMARY OF HEAT RATE DATA
UNIT: MOSS LANDING 7
Duke Energy Nov. 1997
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK
BLOCK
BLOCK
BLOCK
BLOCK
1
7%
2 25%
3 50%
4 80%
5 100%
50
185
370
591
739
997,950
1,966,735
3,429,160
5,296,542
6,589,663
19,959
7,176
7,905
8,450
8,737
19,959
10,631
9,268
8,962
8,917
HEAT RATE (Btu/kWh)
INCREMENTAL HEAT RATE
20,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
400
600
800
600
800
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEAT RATE
20,000
HEAT RATE (Btu/kWh)
7,000,000
INPUT (1000 Btu/hr)
200
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
200
400
OUTPUT (MW)
600
800
0
200
400
OUTPUT (MW)
Figure 4 shows Hunter Point 3 with a full load Average Heat Rate of 12,598 Btu/kWh, which corresponds to an efficiency of 27.1 percent: 3,413 / 12,598 = 27.1%. At full load, Hunters Point 3 will
consume 41 percent more fuel to produce a gigawatt-hour (GWh) as Moss Landing 7: 12,598 / 8,917 =
1.41.
1
This unit was announced on November 7, 1998 as divested to Duke Energy, but for the organizational purposes
of this report, it -- and all other IOU divested units -- will be referred to as belonging to the IOU.
HR-DESC.DOC; 4/17/98; PAGE 10
Also, Hunters Point 3 will have a much more expensive incremental cost. Let’s compare the second block
of each unit. The Hunters Point 3 Incremental Heat Rate for Block 2 is 9,883 Btu/kWh. The corresponding Incremental Heat Rate for Moss Landing 7 is 7,176 Btu/kWh. The relative cost for Hunters
Point 3 is therefore 38 percent greater: 9,883 / 7,176 = 1.38.
FIGURE 4: HUNTERS POINT 3 HEAT RATES
SUMMARY HEAT RATE DATA
INCREMENTAL HEAT RATE
UNIT: HUNTERS POINT 3
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK
BLOCK
BLOCK
BLOCK
BLOCK
1
9%
2 25%
3 50%
4 80%
5 100%
10
27
54
86
107
210,370
378,378
671,436
1,063,476
1,347,986
21,037
9,883
10,854
12,251
13,548
21,037
14,014
12,434
12,366
12,598
HEAT RATE (Btu/kWh)
25,000
20,000
15,000
10,000
5,000
0
0
INPUT-OUTPUT CURVE
40
60
80
OUTPUT (MW)
100
120
100
120
AVERAGE HEAT RATE
25,000
1,400,000
1,200,000
HEAT RATE (Btu/kWh)
INPUT (1000 Btu/hr)
20
1,000,000
800,000
600,000
400,000
200,000
0
20,000
15,000
10,000
5,000
0
0
20
40
60
80
OUTPUT (MW)
100
120
0
20
40
60
80
OUTPUT (MW)
Appendix A provides a complete set of these summary heat rate data sheets for all of the slow-start
thermal units for the three IOUs. These can prove useful for future analytical efforts involving heat rates.
HR-DESC.DOC; 4/17/98; PAGE 11
IV. HEAT RATES AS EQUATIONS
The above heat rate definitions are described and illustrated in terms of blocks. Engineers make use of
these blocks as “piece-wise linear representations” of the actual heat rate curves that truly characterize
the units. In the case of Unit X, these “pieces” were 1-MW each. This was useful for our description and
is indeed how the data is typically used by modelers and by engineers in general. This misrepresents the
fact, however, that the heat rates are really continuous -- which is equivalent to saying that the blocks are
infinitely small. It is these continuous equations that are used to dispatch units in a real system -- not the
block data.
Input-Output Curve
The above Input-Output Curve for Unit X is more precisely described by the equation:
y = 1000x2 + 1000x + 18000
Where: x = Output in MW
y = Input in 1000 Btu/hr
Setting x equal to the values of 1, 2 and 3 MW, results in y values of 20,000, 24,000 and 30,000 in 1000
Btu/hr. These points correspond exactly to the points in Table 2 and Figure 2, as would be expected.
Incremental Heat Rate Curve
The Incremental Heat Rate (IHR) Curve is by definition the amount of energy that must be consumed by
the plant in order to achieve an incremental change in output -- in this case, an infinitesimal change in
output. This is mathematically defined as the first derivative of the Input-Output Curve:
IHR = dy/dx = 2000x + 1000
Setting x equal to 1, 2 and 3 MW, results in IHRs of 3,000, 5,000 and 7,000 Btu/kWh. These points are
Instantaneous Incremental Heat Rates and do not correspond directly to any of the above Figures and
Tables that were average values for each block (Average Incremental Heat Rates).
For comparison, the Average Incremental Heat Rates can also be calculated using the Input-Output
Curve. The calculation consists of dividing the incremental Input-Output value (Btu/hr) by the corresponding increment of output (MW).
(y2 - y1)/ (x2-x1) = [(1000 x22 + 1000 x2 + 18000) - (1000 x12 + 1000 x1 + 18000)] / (x2-x1)
= [1000(x22- x12) + 1000(x2-x1)]/ (x2-x1) = 1000[(x22- x12) + (x2 - x1)]/ (x2-x1)
= 1000[(x22- x12)/(x2-x1) + (x2 - x1)/(x2-x1)]
= 1000[(x2+x1)(x2-x1)/(x2-x1) + (x2 - x1)/(x2-x1)]
= 1000(x2 + x1 + 1)
Where: x1 = Minimum Output (MW) of Block
x2 = Maximum Output (MW) of Block
HR-DESC.DOC; 4/17/98; PAGE 12
If values are entered for x2 and x1 for Block 2 and 3, then the appropriate values of 4,000 and 6,000
Btu/kWh in Table 2 result.
For Block 2: x1 = 1MW and x2 = 2 MW.
IHRBlock 2 = 1000(x2 + x1 + 1)
= 1000(2+1+1) = 4,000 Btu/kWh
For Block 3: x1 = 2 MW and x2 = 3 MW.
IHRBlock 2 = 1000(x2 + x1 + 1)
= 1000(3+2+1) = 6,000 Btu/kWh
Average Heat Rate Curve
The Average Heat Rate (AHR) Curve, for Unit X, is defined as the Input-Output Curve divided by the
output capacity at that point:
AHR = y/x = (1000x2 + 1000x + 18000) / x = 1000x + 1000 + 18000/x
Setting x equal to 1, 2 and then 3 MW, results in AHRs of 20,000, 12,000 and 10,000 Btu/kWh. These
points correspond directly to the above Figures and Tables, as expected.
Figure 5 illustrates these equations. This is done at 0.1 MW intervals for convenience, as we can not
reasonably illustrate this for an infinite number of points -- or even 200 points (0.01 MW intervals).
Though limited in this way, the representation is quite adequate to illustrate that these curves (equations)
are much smoother and continuous than the block representation of Figure 2, and therefore more
accurately reflect the real data. Note that the equation describing each curve is show on the respective
graph.
As before, I have included similar data for real units. Figure 6 shows this heat rate data for Moss Landing
7, the most efficient unit in the PG&E system. Figure 7 shows the same data for Hunters Point 3, the
least efficient unit in the PG&E system. Note how differently these curves look from their block counter
parts. Again, I have included the equation that was used to develop each graph.
HR-DESC.DOC; 4/17/98; PAGE 13
FIGURE 5: UNIT X - AS EQUATIONS
(ILLUSTRATED AT 0.1 MW INCREMENTS)
INCREMENTAL
HEAT RATE
(Btu/kWh)
AVERAGE
HEAT RATE
(Btu/kWh)
BLOCK 1
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
20,000
20,310
20,640
20,990
21,360
21,750
22,160
22,590
23,040
23,510
24,000
24,510
25,040
25,590
26,160
26,750
27,360
27,990
28,640
29,310
30,000
3,000
3,200
3,400
3,600
3,800
4,000
4,200
4,400
4,600
4,800
5,000
5,200
5,400
5,600
5,800
6,000
6,200
6,400
6,600
6,800
7,000
20,000
18,464
17,200
16,146
15,257
14,500
13,850
13,288
12,800
12,374
12,000
11,671
11,382
11,126
10,900
10,700
10,523
10,367
10,229
10,107
10,000
BLOCK 2
BLOCK 3
UNIT X
AVERAGE HEAT RATE
20,000
HEATRATE (Btu/kWh)
(MW)
INPUT-OUTPUT
CURVE
(1000 btu/hr)
CAP
15,000
10,000
y/x = 1000x + 1000 + 18000/x
5,000
0
1.0
2.0
OUTPUT (MW)
2.5
3.0
UNIT X
INCREMENTAL HEAT RATE
UNIT X
INPUT-OUTPUT CURVE
30,000
8,000
25,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
1.5
20,000
2
y = 1000x + 1000x + 18000
15,000
10,000
6,000
4,000
dy/dx = 2000x + 1000
2,000
0
1.0
1.5
2.0
OUTPUT (MW)
2.5
3.0
1.0
1.5
2.0
OUTPUT (MW)
2.5
3.0
HR-DESC.DOC; 4/17/98; PAGE 14
FIGURE 6: MOSS LANDING 7 - AS EQUATIONS
CAP
BLOCK 3
BLOCK 4
BLOCK 5
(Btu/kWh)
(Btu/kWh)
7,000,000
50
65
80
95
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
370
385
400
415
430
445
460
475
490
505
520
535
550
565
580
591
606
621
636
651
666
681
696
711
726
739
997,950
1,100,631
1,205,167
1,310,893
1,417,782
1,525,808
1,634,944
1,745,164
1,856,442
1,968,751
2,082,065
2,196,358
2,311,603
2,427,775
2,544,846
2,662,791
2,781,583
2,901,195
3,021,603
3,142,778
3,264,695
3,428,360
3,551,905
3,676,105
3,800,932
3,926,361
4,052,365
4,178,918
4,305,993
4,433,565
4,561,606
4,690,091
4,818,992
4,948,285
5,077,942
5,207,937
5,303,467
5,433,986
5,564,771
5,695,797
5,827,035
5,958,461
6,090,048
6,221,770
6,353,600
6,485,511
6,599,881
6,847
6,929
7,009
7,087
7,164
7,239
7,312
7,384
7,453
7,521
7,587
7,652
7,714
7,775
7,834
7,892
7,947
8,001
8,053
8,103
8,152
8,214
8,258
8,301
8,342
8,381
8,419
8,455
8,489
8,521
8,551
8,580
8,607
8,632
8,655
8,677
8,692
8,710
8,727
8,742
8,756
8,767
8,777
8,785
8,792
8,796
8,799
19,959
16,933
15,065
13,799
12,889
12,206
11,678
11,259
10,920
10,631
10,410
10,216
10,050
9,909
9,788
9,683
9,592
9,512
9,443
9,381
9,328
9,268
9,226
9,190
9,159
9,131
9,106
9,085
9,065
9,048
9,033
9,019
9,007
8,997
8,988
8,979
8,962
8,967
8,961
8,956
8,951
8,947
8,943
8,939
8,936
8,933
8,971
6,000,000
INPUT (1000 Btu/hr)
(1000 Btu/hr)
5,000,000
4,000,000
3,000,000
2,000,000
y = -0.0013x3 + 2.955x2 + 6561.2x + 662025
1,000,000
0
0
100
200
300
400
500
OUTPUT (MW)
600
700
800
700
800
INCREMENTAL HEAT RATE
Moss Landing 7
9,000
HEAT RATE (Btu/kWh)
BLOCK 2
(MW)
INPUT-OUTPUT CURVE
Moss Landing 7
8,500
8,000
7,500
7,000
2
dy/dx = -0.0039x +5.91x + 6561.2
6,500
6,000
0
100
200
300
400
500
OUTPUT (MW)
600
AVERAGE HEAT RATE
Moss Landing 7
20,000
HEAT RATE (Btu/kWh)
BLOCK 1
INPUT-OUTPUT INCREMENTAL AVERAGE
CURVE
HEAT RATES HEAT RATES
18,000
16,000
14,000
y/x = -0.0013x2 + 2.955x + 6561.2 +662025/x
12,000
10,000
8,000
0
100
200
300
400
500
OUTPUT (MW)
600
700
800
HR-DESC.DOC; 4/17/98; PAGE 15
FIGURE 7: HUNTERS POINT 3 - AS EQUATIONS
INPUT-OUTPUT CURVE
Hunters Point 3
INPUT-OUTPUT INCREMENTAL AVERAGE
CAP
CURVE
HEAT RATES HEAT RATES
BLOCK 3
BLOCK 4
BLOCK 5
(Btu/kWh)
10
12
14
16
18
20
22
24
26
27
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
107
210,405
229,503
248,774
268,218
287,836
307,629
327,598
347,742
368,064
378,292
409,241
430,098
451,134
472,351
493,748
515,328
537,090
559,035
581,164
603,477
625,976
648,660
671,531
694,589
717,836
741,271
764,895
788,709
812,714
836,911
861,300
885,881
910,656
935,625
960,789
986,149
1,011,704
1,037,457
1,063,408
1,089,556
1,115,904
1,142,452
1,169,200
1,196,149
1,223,300
1,250,653
1,278,210
1,305,970
1,347,994
9,506
9,592
9,679
9,766
9,853
9,940
10,028
10,117
10,205
10,250
10,384
10,473
10,563
10,654
10,744
10,835
10,927
11,018
11,110
11,203
11,296
11,389
11,482
11,576
11,670
11,765
11,860
11,955
12,050
12,146
12,242
12,339
12,436
12,533
12,631
12,729
12,827
12,926
13,025
13,124
13,224
13,324
13,424
13,525
13,626
13,727
13,829
13,931
14,085
20,037
19,125
17,770
16,764
15,991
15,381
14,891
14,489
14,156
14,014
13,641
13,441
13,269
13,121
12,993
12,883
12,788
12,705
12,634
12,572
12,520
12,474
12,434
12,403
12,376
12,355
12,337
12,324
12,314
12,308
12,304
12,304
12,306
12,311
12,318
12,327
12,338
12,351
12,366
12,381
12,399
12,418
12,438
12,460
12,483
12,507
12,531
12,557
12,598
1,400,000
INPUT (1000 Btu/hr)
(Btu/kWh)
1,200,000
1,000,000
800,000
600,000
400,000
200,000
3
2
Y = 0.0144x + 21.077X + 9080x + 117483
0
0
20
40
60
80
100
120
OUTPUT (MW)
INCREMENTAL HEATRATE
Hunters Point 3
15000
14000
HEATRATE (Btu/kWh)
BLOCK 2
(1000 Btu/hr)
13000
12000
11000
10000
dy/dx = 0.0432x2 + 42.154x + 9080
9000
8000
0
20
40
60
OUTPUT (MW)
80
100
120
AVERAGE HEATRATE
Hunters Point 3
22,000
HEATRATE (Btu/kWh)
BLOCK 1
(MW)
20,000
18,000
y/x = 0.0144x2 + 21.077x + 9080 + 117483/x
16,000
14,000
12,000
10,000
0
20
40
60
80
100
120
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE 16
Appendix B provides a precise description of how to construct the heat rate curves for the real-world
units of the three IOUs, but the following is a brief overview of the process:
Input-Output Curve
The Input-Output Curve is defined by the third order equation:
y= ax3 + bx2+ cx + d
Where: x = Output in MW
y = Input in Btu/hr
a-d = The coefficients that define the equation
Incremental Heat Rate Curve
The Instantaneous Incremental Heat Rate (IHR) is defined as the first derivative of the Input-Output
Curve:
IHR = dy/dx = 3ax2 + 2bx + c
As before, the Average Incremental Heat Rates can also be calculated for comparison, using the InputOutput Curve. The calculation consists of dividing the incremental Input-Output value (Btu/hr) by the
corresponding increment of output (MW).
(y2 - y1)/ (x2-x1) = [(ax23 + bx22 + cx2 + d) - (ax13 + bx12 + cx1 + d)] / (x2-x1)
= [a(x23- x13) + b(x22- x12) + c(x2 - x1)]/ (x2 - x1)
= a(x22 + x2 x1 + x12) + b(x2 + x1) + c
Where: x1 = Minimum Output of Block
x2 = Maximum Output of Block
Average Heat Rate Curve
The Average Heat Rate (AHR) is defined as the Input-Output Curve divided by the output (x).
AHR = y/x = (ax3 + bx2 + cx + d) / x = ax2 + bx + c + d/x
Table B-2 in Appendix B delineates the coefficients, a - d, for constructing each of the above heat rate
curves for all of the three IOU slow-start units.
HR-DESC.DOC; 4/17/98; PAGE 17
V. HEAT RATES IN PRODUCTION COST MODELING
This section discusses heat rates as used in traditional production cost modeling. The next section will
discuss the use of heat rates as related to market modeling.
Most typically, heat rates are provided to the modelers as Average Heat Rates in block form and entered
in that same format. For the Energy Commission, the block sizes are typically 25, 50, 80 and 100 percent
of the maximum capacity, as well as the minimum capacity level. It some instances, however, the data is
provided to the modeler or entered into the model in any of the following forms.
•
•
•
•
Block Average Heat Rates
Average Heat Rates as equations
Block (Average) Incremental Heat Rates
Input-Output Curves
Most models can take Block Average Heat Rates or Block (Average) Incremental Heat Rates (e.g.,
UPLAN and Elfin). A few also have the option to make use of the Input-Output Curve (e.g., Elfin).
Regardless of the form in which the model receives the heat rate data, it will create whatever additional
heat rates it needs to complete its functions.
The heat rate data as provided by the utility is a simplistic representation of the actual measured data. The
original data is a collection of measurements, taken over a period of time. This data must be fit to heat
rate equations, that can only approximate the original data points. In almost all cases the data is provided
as block heat rates which are “piece-wise linear representations” of the heat rate equations. The data
provided to the modelers is therefore a simplification of a curve that approximates the actual data. In
addition, the data can be distorted due to inaccuracies in transcription or errors in the data manipulation.
All data is suspect and should always be inspected for veracity. If the data looks somehow unlikely, try
to obtain the data in a form as close to the original data as possible.
Heat Rates are used in the production cost model for four purposes:
•
•
•
•
Commitment
Dispatch
Marginal Cost
Production Cost
Regardless of the form in which the heat rate data is entered into the model, it is used to create the
necessary Incremental Heat Rates. The Incremental Heat Rates are then used to determine dispatch
(which block of which unit is used next) and marginal cost (the cost of the last unit that was used to meet
load in that hour). Contrary to your intuition, Average Heat Rates as input to the model are not used to
calculate production cost. Incremental Heat Rates are used to construct another set of Average Heat
Rates, that are then used for calculating production costs. The Average Heat Rates as input to the model
are in some models used for commitment (Elfin uses best Average Heat Rate). But other models do not
even use them for this purpose. UPLAN, for example, has a separate entry for this purpose, designated
“Long-Run Average Heat Rate” which is the modeler’s best estimate as to how the unit will perform over
the period being modeled.
HR-DESC.DOC; 4/17/98; PAGE 18
Input-Output Curves
As described above, this curve most closely represents the original measured data. It is typically a slightly
sloping upward curve, that looks almost like a straight line, and it can therefore be easily and accurately
fit to an equation: typically a third-order equation. Figure 8 shows the Input-Output Curve for Unit X in
equation form (from Figure 5) superimposed over the block form (from Figure 2). Due to the almost
linear nature of this curve, the differences are quite small -- and even difficult to see in the graph. The
Modeling representation is two straight lines. The Actual data is an equation.
UNIT X
INPUT-OUTPUT CURVE
INPUT (1000 Btu/hr)
30,000
28,000
MODELING
26,000
24,000
ACTUAL
22,000
20,000
1
1.5
2
OUTPUT (MW)
2.5
3
Figure 8
If the Input-Output Curve is used directly in the model, it is entered as a third order equation, as
described above. The model will then use this Curve (“Actual” in Figure 8) to create the necessary block
Incremental Heat Rates (“Modeling” in Figure 8), which provide the very same results as if the
Incremental Heat Rate blocks had been entered directly.
Incremental Heat Rates
In the model, the Incremental Heat Rates are used in block form, designated Average Incremental Heat
Rates. The block form is used, rather than the continuous curves of the equations, to make the
computational time reasonable. As the number of blocks is increased, the computational time increases. If
continuous curves are used, the block size goes to zero, and the number of calculations tends towards
infinity.
Average Incremental Heat Rates are generally drawn as shown in Figure 2A, which is reiterated here as
Figure 9. But this is not a correct representation of the Average Incremental Heat Rate. They should
really be drawn as shown Figure 10. This confusion arises from the fact that modelers are accustomed to
using and manipulating data as shown in Tables 1 and 2. The representation of Figure 9 seems like the
likely representation of this data -- and it is convenient for most uses -- but it is not precise. Figure 10 in
the more accurate representation of Average Incremental Heat Rate.
HR-DESC.DOC; 4/17/98; PAGE 19
UNIT X
INCREMENTAL HEAT RATE
TYPICAL
UNIT X
INCREMENTAL HEAT RATE
CORRECTED
HEATRATE (Btu/kWh)
HEATRATE (Btu/kWh)
20,000
15,000
10,000
5,000
15,000
10,000
5,000
0
0
1
Figure 9
20,000
1.5
2
OUTPUT (MW)
2.5
1
3
1.5
2
OUTPUT (MW)
2.5
3
Figure 10
As previously explained, the model does not use the 20,000 Btu/kWh as an Incremental Heat Rate, as it
is not used in dispatch decisions. Unit X is committed at its minimum generation level (Block 1 level of 1MW) and only the values of 4,000 Btu/kWh (from 1 to 2 MW) and 6,000 Btu/kWh (from 2 to 3 MW)
are used in the dispatch decisions.
Although Figure 10 is an accurate representation of the Average Incremental Heat Rates as used in
models, it is not the true representation of the Incremental Heat Rate used in the dispatch of the units in a
real system, as explained in the previous section. The continuous Incremental Heat Rate equations are the
true representation that is used in the dispatch of a real system. The block Incremental Heat Rates of
Figure 10 used in modeling are known more precisely as Average Incremental Heat Rates, as they
represent the average value over the block. The Incremental Heat Rates of the equations are used in the
actual dispatch of real units are known as the Instantaneous Incremental Heat Rates. Figure 11
compares the “Modeling” representation (Average Incremental Heat Rate) to the “Actual” heat rates
used in dispatch (Instantaneous Incremental Heat Rate).
The inherent assumption in using the modeling heat rate data is that on average it will emulate the actual
heat rate data. That is, over time, the modeling approximation will be sometimes low and sometimes high
but will average out. Unfortunately, this is not strictly true for Incremental Heat Rates data. There are
two areas of concern: (1) the dispatch decision (2) the calculation of marginal cost.
If the blocks are small and are of comparable size, the dispatch error is probably reasonably small.
Unfortunately, the block sizes are commonly different since the unit sizes are different. In PG&E, for
example, unit sizes vary from 52 MW to 739 MW. A block size that is set at 25 percent, is 13 MW in one
case and 185 MW in the second case.
In the case of marginal cost, errors will commonly occur and will be most pronounced at the edges of the
blocks. Figure 11 illustrates these errors for our Unit X, comparing the block representation to the
continuous representation (which for computational convenience is sampled as 0.1 MW blocks). The
applicable errors are 33 % at 1-MW, -20% at 2-MW and -14.3% at 3-MW.
HR-DESC.DOC; 4/17/98; PAGE 20
FIGURE 11: UNIT X - COMPARING INCREMENTAL HEAT RATES
BLOCK 1
BLOCK 2
BLOCK 3
INCREMENTAL HEAT RATES
ACTUAL MODELING ERROR
(MW)
(Btu/kWh)
(Btu/kWh)
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
3,000
3,200
3,400
3,600
3,800
4,000
4,200
4,400
4,600
4,800
5,000
5,200
5,400
5,600
5,800
6,000
6,200
6,400
6,600
6,800
7,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
MODELING vs. ACTUAL
INCREMENTAL HEAT RATES
(%)
33.3%
25.0%
17.6%
11.1%
5.3%
0.0%
-4.8%
-9.1%
-13.0%
-16.7%
-20.0%
15.4%
11.1%
7.1%
3.4%
0.0%
-3.2%
-6.3%
-9.1%
-11.8%
-14.3%
10,000
9,000
ACTUAL HEAT RATE
(Instantaneous incremental)
8,000
HEAT RATES (Btu/kWh)
OUTPUT
7,000
6,000
5,000
4,000
3,000
MODELING HEAT RATE
(Average Incremental)
2,000
1,000
0
1.0
1.5
2.0
2.5
3.0
OUPTPUT (MW)
Figures 12 and 13 show this same data for our previously identified real illustrative units, Moss Landing 7
and Hunters Point 3. Figure 12 compares the Modeling data of Figure 3 to the Actual equations of Figure
6. Figure 13 compares the Modeling data of Figure 4 to the Actual equations of Figure 7.
Table 3 summarizes these results for Unit X, Moss Landing 7 and Hunters Point 3 along with comparable
data for the units in the IOU systems (pre-divestiture). The supporting data and calculations for the IOU
system are shown in Appendix C. The Table shows both the most positive and most negative errors for
each case. Ignoring the errors for Unit X, which are for illustrative purposes only, the largest errors are
still significant. PG&E shows maximum errors of +6.0 and -8.6 percent. SCE shows a maximum errors of
+3.4 and -5.4 percent. An examination of the data in Appendix C, however, shows that for the most part
the errors are only a few percent.
TABLE 3: SUMMARY OF INCREMENTAL HEAT RATE ERRORS
PG&E
SCE
SDG&E
Moss Landing 7
Hunters Point 3
UNIT X
POSITIVE
6.0%
3.4%
0.9%
4.8%
5.8%
33.3%
MAXIMUM ERRORS (%)
NEGATIVE
-8.6%
-5.4%
-5.4%
-4.6%
-5.9%
-20.0%
HR-DESC.DOC; 4/17/98; PAGE 21
FIGURE12: MOSS LANDING 7 - COMPARING INCREMENTAL HEAT RATES
CAP
ACTUAL HEAT RATE CURVE
INSTANTANEOUS INCREMENTAL HEATRATE
INCREMENTAL HEAT RATES
ACTUAL MODELING ERROR
(MW) (Btu/kWh)
(Btu/kWh)
(%)
BLOCK 4
BLOCK 5
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,737
8,737
8,737
8,737
8,737
8,737
8,737
8,737
8,737
8,737
4.8%
3.6%
2.4%
1.2%
0.2%
-0.9%
-1.9%
-2.8%
-3.7%
-4.6%
4.2%
3.3%
2.5%
1.7%
0.9%
0.2%
-0.5%
-1.2%
-1.8%
-2.4%
-3.0%
-3.8%
2.3%
1.8%
1.3%
0.8%
0.4%
-0.1%
-0.5%
-0.8%
-1.2%
-1.5%
-1.8%
-2.1%
-2.4%
-2.6%
-2.8%
0.3%
0.1%
-0.1%
-0.2%
-0.3%
-0.5%
-0.6%
-0.6%
-0.7%
-0.7%
8,500
8,000
7,500
2
dy/dx = -0.0039x +5.91x + 6561.2
7,000
6,500
6,000
0
100
200
300
400
500
OUTPUT (MW)
600
700
800
700
800
MODELING HEAT RATE BLOCKS
AVERAGE INCREMENTAL HEATRATE
9,000
HEATRATE (Btu/kWh)
BLOCK 3
6,847
6,929
7,009
7,087
7,164
7,239
7,312
7,384
7,453
7,521
7,587
7,652
7,714
7,775
7,834
7,892
7,947
8,001
8,053
8,103
8,152
8,214
8,258
8,301
8,342
8,381
8,419
8,455
8,489
8,521
8,551
8,580
8,607
8,632
8,655
8,677
8,692
8,710
8,727
8,742
8,756
8,767
8,777
8,785
8,792
8,796
8,799
8,500
8,000
7,500
7,000
6,500
6,000
0
100
200
300
400
500
OUTPUT (MW)
600
MODELING vs. ACTUAL
Moss Landing 7
9,000
HEATRATE (Btu/kwh)
BLOCK 2
50
65
80
95
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
370
385
400
415
430
445
460
475
490
505
520
535
550
565
580
591
606
621
636
651
666
681
696
711
726
739
HEATRATE (Btu/kWh)
9,000
BLOCK 1
ACTUAL HEAT RATE
(Instantaneous Incremental)
8,500
8,000
7,500
MODELING HEAT RATE
(Average Incremental)
7,000
6,500
6,000
0
100
200
300
400
500
OUTPUT (MW)
600
700
800
HR-DESC.DOC; 4/17/98; PAGE 22
FIGURE13: HUNTERS POINT 3 - COMPARING INCREMENTAL HEAT RATES
BLOCK 3
BLOCK 4
BLOCK 5
(Btu/kWh)
(Btu/kWh)
(%)
15,000
10
12
14
16
18
20
22
24
26
27
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
106
107
9,506
9,592
9,679
9,766
9,853
9,940
10,028
10,117
10,205
10,250
10,384
10,473
10,563
10,654
10,744
10,835
10,927
11,018
11,110
11,203
11,296
11,389
11,482
11,576
11,670
11,765
11,860
11,955
12,050
12,146
12,242
12,339
12,436
12,533
12,631
12,729
12,827
12,926
13,025
13,124
13,224
13,324
13,424
13,525
13,626
13,727
13,829
13,931
14,034
14,085
9,883
9,883
9,883
9,883
9,883
9,883
9,883
9,883
9,883
9,883
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
4.0%
3.0%
2.1%
1.2%
0.3%
-0.6%
-1.4%
-2.3%
-3.2%
-3.6%
4.5%
3.6%
2.8%
1.9%
1.0%
0.2%
-0.7%
-1.5%
-2.3%
-3.1%
-3.9%
-4.7%
-5.5%
5.8%
5.0%
4.1%
3.3%
2.5%
1.7%
0.9%
0.1%
-0.7%
-1.5%
-2.3%
-3.0%
-3.8%
-4.5%
-5.2%
-5.9%
3.5%
2.7%
2.0%
1.2%
0.4%
-0.3%
-1.0%
-1.8%
-2.5%
-3.2%
-3.6%
14,000
HEATRATE(Btu/KWh)
(MW)
13,000
12,000
11,000
10,000
2
dy/dx = 0.0432x +42.154x + 9080
9,000
0
20
40
60
OUTPUT (MW)
80
100
120
MODELING HEAT RATE BLOCKS
AVERAGE INCREMENTAL HEAT RATE
14,000
13,500
HEATRATE (Btu/kWh)
BLOCK 2
CAP
13,000
12,500
12,000
11,500
11,000
10,500
10,000
9,500
9,000
0
20
40
60
80
100
120
OUTPUT (MW)
MODELING vs. ACTUAL
HUNTERS POINT 3
15,000
ACTUAL HEAT RATE
(Instantaneous Incremental)
14,000
HEATRATE (Btu/kWh)
BLOCK 1
ACTUAL HEAT RATE CURVE
INSTANTANEOUS INCREMENTAL HEAT RATE
INCREMENTAL HEAT RATES
ACTUAL MODELING ERROR
13,000
12,000
11,000
10,000
MODELING HEAT RATE
(Average Incremental)
9,000
0
20
40
60
OUTPUT (MW)
80
100
120
HR-DESC.DOC; 4/17/98; PAGE 23
Average Heat Rate
Figure 14 shows the typical representation of the block Average Heat Rate for Unit X, repeated from
Figure 2A. As with the Input-Output and the Incremental Heat Rate Curves, this is not strictly correct.
As previously explained, Figure 14 is really a piece-wise linear representation of the actual Average Heat
Rate curve, which is shown in Figure 15.
UNIT X
AVERAGE HEAT RATE
TYPICAL
20,000
HEATRATE (Btu/kWh)
20,000
HEATRATE (Btu/kWh)
UNIT X
AVERAGE HEAT RATE
ACTUAL
15,000
10,000
5,000
0
15,000
10,000
5,000
0
1
2
3
1
OUTPUT (MW)
Figure 14
2
OUTPUT (MW)
3
Figure 15
This error is of no particular importance, however. As explained above, the Average Heat Rate block
data plays a very small role in modeling. Other than its possible use for commitment, it has no direct
function. The Average Heat Rate data is entered into the model primarily to be used in the development
of the Incremental Heat Rate block data -- and the model is only using the block point so that the linear
nature of the data does not compromise the modeling. It is the Incremental Heat Rate block data that is
used to calculate the Average Heat Rates and the corresponding production costs. This may seem
somewhat “round-about” but this will become clearer as we continue.
As demand increases, the model looks at the various blocks of power available to it and decides which
block is the least expensive. In the case of Unit X, its offering would be 10 $/MWh (4,000 Btu/kWh) for
Block 2 and 15 $/MWh (6,000 Btu/kWh) for Block 3. Unit X’s production cost turns out to be the very
same as if it were based on its Average Heat Rate, 30 $/MWh at 2 MW and 25 $/MWh as 3 MW. Based
on this description, it would appear that the model would actually be using the above Average Heat Rate
Curve as previously defined. Actually, this is only a coincidence and only seems to work because I used
cases where the output was precisely 1, 2 or 3 MW.
Take the subtler case where the output is 1.5 MW. The model calculates the production cost using block
Incremental Heat Rates as follows. It notes that the heat rate of block 1 as 20,000 Btu/kWh and
calculates the corresponding cost of the one MWh as $50. It then notes that Unit X has provided 1/2
MW from Block 2 at 4,000 Btu/kWh and calculates the cost of that as one-half of a MWh as $5: 4,000
Btu/kWh x 2.5 $/MMBtu x 1/2 MWh = $5. The production cost for this hour is simply the sum of the
two costs: $50 + $5 = $55. The average cost of generation is equal to the total production cost ($55)
divided by the total generation (1.5 MWh): 36.67 $/MWh.
HR-DESC.DOC; 4/17/98; PAGE 24
The Average Heat Rate can be calculated as 14,667 Btu/kWh: 36.67 $/MWh / 2.5 $/MMBtu = 14,667
Btu/kWh. The actual Average Heat Rate predicted by the Average Heat Rate equation is 14,500
Btu/kWh. We see that the error is 1.1 percent: 14,667/14,500 - 1 = 1.1%.
Figure 16 compares the Average Heat Rate as would be calculated in the model against the actual data at
0.1 MW intervals. It is clear that even in this simplistic Unit X case, the effect of this error is small: of the
order of 1 percent or less.
FIGURE 16: UNIT X
CALCULATED vs. ACTUAL AVERAGE HEAT RATES
INCREMENTAL
AVERAGE HEAT RATES
OUTPUT HEAT RATE CALCULATED ACTUAL ERROR
(MW)
(Btu/kWh)
(Btu/kWh)
(Btu/kWh)
(%)
BLOCK 1
BLOCK 2
BLOCK 3
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.0
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
4,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
6,000
20,000
18,545
17,333
16,308
15,429
14,667
14,000
13,412
12,889
12,421
12,000
11,714
11,455
11,217
11,000
10,800
10,615
10,444
10,286
10,138
10,000
20,000
18,464
17,200
16,146
15,257
14,500
13,850
13,288
12,800
12,374
12,000
11,671
11,382
11,126
10,900
10,700
10,523
10,367
10,229
10,107
10,000
0.0%
0.4%
0.8%
1.0%
1.1%
1.1%
1.1%
0.9%
0.7%
0.4%
0.0%
0.4%
0.6%
0.8%
0.9%
0.9%
0.9%
0.8%
0.6%
0.3%
0.0%
Figure 17 shows the comparable calculations for our two real units: Moss Landing 7 and Hunters Point 3.
The error is even smaller: in all cases less than one percent. I have not provided the corresponding graphs
as the lines would track so closely together that it would make this representation meaningless.
I find the error to be surprisingly small given the apparent grossness of the block Incremental Heat Rate
representation. It is clear that this is not something to bother ourselves about. But it is important to
know this for a fact.
HR-DESC.DOC; 4/17/98; PAGE 25
FIGURE 17: COMPARING INCREMENTAL HEAT RATES
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
MOSS LANDING 7
HUNTERS POINT 3
INCR. HR
AVERAGE HEAT RATES
CAP MODELING CALCULATED ACTUAL ERROR
INCR. HR
AVERAGE HEAT RATES
CAP MODELING CALCULATED ACTUAL ERROR
(MW)
(Btu/kWh)
(Btu/kWh)
(Btu/kWh)
(%)
(MW)
(Btu/kWh)
(Btu/kWh)
(Btu/kWh)
(%)
50
65
80
95
110
125
140
155
170
185
200
215
230
245
260
275
290
305
320
335
350
365
370
380
395
410
425
440
455
470
485
500
515
530
545
560
575
590
591
605
620
635
650
665
680
695
710
725
739
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,176
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
7,905
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,450
8,737
8,737
8,737
8,737
8,737
8,737
8,737
8,737
8,737
8,737
19,959
17,009
15,165
13,904
12,986
12,289
11,741
11,300
10,936
10,631
10,426
10,251
10,098
9,963
9,845
9,739
9,644
9,558
9,481
9,410
9,346
9,268
9,214
9,246
9,216
9,188
9,162
9,138
9,115
9,094
9,074
9,055
9,038
9,021
9,005
8,990
8,976
8,963
8,962
8,957
8,952
8,946
8,942
8,937
8,933
8,928
8,924
8,920
8,917
19,959
16,933
15,065
13,799
12,889
12,206
11,678
11,259
10,920
10,642
10,410
10,216
10,050
9,909
9,788
9,683
9,592
9,512
9,443
9,381
9,328
9,266
9,239
9,239
9,202
9,169
9,140
9,114
9,092
9,071
9,054
9,038
9,024
9,011
9,000
8,991
8,982
8,974
8,974
8,967
8,961
8,956
8,951
8,947
8,943
8,940
8,936
8,933
8,931
0.0%
0.5%
0.7%
0.8%
0.8%
0.7%
0.5%
0.4%
0.1%
-0.1%
0.2%
0.3%
0.5%
0.5%
0.6%
0.6%
0.5%
0.5%
0.4%
0.3%
0.2%
0.0%
-0.3%
0.1%
0.2%
0.2%
0.2%
0.3%
0.3%
0.2%
0.2%
0.2%
0.2%
0.1%
0.1%
0.0%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.1%
-0.2%
10
12
14
16
18
20
22
24
26
27
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
100
102
104
107
9,883
9,883
9,883
9,883
9,883
9,883
9,883
9,883
9,883
9,883
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
10,854
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
12,251
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
13,584
21,037
19,178
17,850
16,854
16,080
15,460
14,953
14,531
14,173
14,014
13,698
13,520
13,364
13,224
13,099
12,987
12,886
12,793
12,709
12,632
12,560
12,495
12,434
12,428
12,421
12,416
12,410
12,405
12,401
12,396
12,392
12,388
12,385
12,381
12,378
12,375
12,372
12,369
12,366
12,394
12,420
12,445
12,470
12,493
12,515
12,536
12,557
12,577
12,605
21,037
19,125
17,770
16,764
15,991
15,381
14,891
14,489
14,156
14,011
13,641
13,441
13,269
13,121
12,993
12,883
12,788
12,705
12,634
12,572
12,520
12,474
12,436
12,403
12,376
12,355
12,337
12,324
12,314
12,308
12,304
12,304
12,306
12,311
12,318
12,327
12,338
12,351
12,365
12,381
12,399
12,418
12,438
12,460
12,483
12,507
12,531
12,557
12,598
0.0%
0.3%
0.5%
0.5%
0.6%
0.5%
0.4%
0.3%
0.1%
0.0%
0.4%
0.6%
0.7%
0.8%
0.8%
0.8%
0.8%
0.7%
0.6%
0.5%
0.3%
0.2%
0.0%
0.2%
0.4%
0.5%
0.6%
0.7%
0.7%
0.7%
0.7%
0.7%
0.6%
0.6%
0.5%
0.4%
0.3%
0.1%
0.0%
0.1%
0.2%
0.2%
0.3%
0.3%
0.3%
0.2%
0.2%
0.2%
0.1%
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
HR-DESC.DOC; 4/17/98; PAGE 26
VI. HEAT RATES IN MARKET MODELING
The previous section described the use of heat rates in production cost modeling. In this section, I
describe their role in the competitive market -- which is a much more complex role.
In the market model, it is the bids that determine the dispatch of the units -- not their costs of operation.
Bidding data is entered into market models in one of two ways, and most models allow for both of these.
One way requires that the bid is determined outside of the model and entered into the model as a unit cost
($/MWh), in which case heat rates play no direct role in setting the Market Clearing Price (MCP). It is
not to be forgotten, however, that the heat rates in the model must continue to play the role of emulating
operating costs -- operating costs by definition depend on heat rates.
The other way of developing bids is to let the model estimate the bid -- generally as some function of
operating costs. One method is to assume that the bid is based on variable costs -- the economists’
favorite. That is, the bid is based on the fuel cost associated with Average Heat Rate (plus O&M and
start-up costs). Unfortunately, most models have not been able to make this transition, and model
designers are allowing their models to dispatch as they always have, based on incremental cost
(Incremental Heat Rate) -- also known as marginal or nodal cost. This proxy for the real mechanism
inevitably leads to questionable results. The models then find some way to emulate the actual MCP by
adding on some additional amount to the incremental cost so that the overall revenue will be adequate to
ensure a viable market.
The comprehensive solution to this problem requires that the model do both methods of dispatch.
Members of the market will bid based on Average Cost because they must rely on the market for all of
their revenue. If they bid their incremental cost and set the market clearing price (MCP), they would lose
the difference between their Average and Incremental Costs -- otherwise known as no-load cost
(described below). Participants who are not members can bid their Incremental Cost because their other
costs (no-load costs) are captured through other sales.
The Relationship Between Average and Incremental Heat Rates
What now becomes apparent is that we have those who can bid based on Incremental Heat Rates
competing against those who must by necessity bid based on Average Heat Rates -- a strange paradigm
by anyone’s standards. In this same vein, we have an IOU who is used to dispatching based on
Incremental Costs (Incremental Heat Rates) constructing bids based on Average Costs (Average Heat
Rates). For markets that require one-part bidding, this is further complicated by the need for monotonically increasing bids: each subsequent capacity block is bid at a price higher than the last. The market
members find themselves with the laborious task of trying to construct monotonically increasing bids
from decreasing Average Costs (Average Heat Rates) -- a formidable task.
It should now become clear why it is important to understand and quantify the differences between
Average and Incremental Costs. I have attempted to quantify these differences as ratios of Average Heat
Rate (AHR) to Incremental Heat Rate (IHR).
Figure 18 shows the ratio of the AHR to the IHR for Moss Landing 7, the most efficient unit in the
PG&E system (pre-divestiture). At maximum output, the difference between AHR and IHR is insignificant. But at minimum output, AHR/IHR is 2.9. The average over all generation levels is 1.26.
HR-DESC.DOC; 4/17/98; PAGE 27
FIGURE 18
MOSS LANDING 7
RATIO OF AVERAGE TO INCREMENTAL HEAT RATES
3.0
2.9
2.5
AHR/IHR
2.0
1.5
1.02
1.0
0.5
0.0
0
100
200
300
400
500
600
700
800
OUTPUT (MW)
Figure 19 shows the corresponding ratio for Hunters Point 2, the least efficient unit in the PG&E system.
At full output AHR/IHR is 0.9. At minimum output it is 2.2. The average value is 1.16.
FIGURE 19
HUNTERS POINT 3
RATIO OF AVERAGE TO INCREMENTAL HEAT RATES
2.5
2.2
AHR/IHR
2.0
1.5
1.0
0.9
0.5
0.0
0
20
40
60
80
100
120
OUTPUT (MW)
Table 5 shows these same values for all of the subject IOU units. R(x1) is the value of AHR/IHR at
minimum power output. R(x2) is the corresponding value at maximum power output. RAVE is the average
value for the entire range of output. The supporting data and calculations are provided in Appendix D,
but the procedure is briefly described below.
HR-DESC.DOC; 4/17/98; PAGE 28
TABLE 5: AVERAGE TO INCREMENTAL HEAT RATE RATIOS (R)
OUTPUT (MW)
X1
X2
AVERAGE/INCREMENTAL
R(X1)
R(X2)
Rave
PG&E UNITS
Contra Costa 6
Contra Costa 7
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 3
Morro Bay 4
Moss Landing 6
Moss Landing 7
Pittsburg 1&2
Pittsburg 3&4
Pittsburg 5
Pittsburg 6
Pittsburg 7
Potrero 3
Averages
46
46
10
10
10
62
62
46
46
50
50
62
62
46
46
120
47
340
340
105
107
107
326
326
338
338
739
739
326
326
325
325
720
207
1.46
1.58
1.95
2.13
2.21
1.37
1.35
1.46
1.48
2.87
2.91
1.54
1.43
1.54
1.67
1.62
1.20
1.68
0.92
0.94
0.84
0.96
0.89
1.00
1.00
1.05
1.01
1.05
1.02
0.95
0.86
1.03
0.97
0.97
0.89
0.98
1.13
1.14
1.18
1.19
1.16
1.10
1.11
1.14
1.12
1.25
1.26
1.17
1.13
1.14
1.16
1.20
1.05
1.17
SCE UNITS
Alamitos 1&2
Alamitos 3&4
Alamitos 5&6
Cool Water 1
Cool Water 2
Cool Water 3&4
El Segundo 1&2
El Segundo 3&4
Etiwanda 1&2
Etiwanda 3&4
Highgrove 1&2
Highgrove 3&4
Huntington Beach 1&2
Long Beach 8&9
Mandalay 1&2
Ormond Beach 1
Ormond Beach 2
Redondo Beach 5&6
Redondo Beach 7&8
San Bernardino 1&2
Averages
20
40
260
17
19
140
20
40
20
40
8
10
40
70
40
250
50
20
260
14
350
640
960
65
81
512
350
670
264
640
66
89
430
560
430
750
750
350
960
126
3.19
3.02
1.42
1.30
1.31
2.02
3.04
2.96
2.72
2.75
5.87
8.51
1.96
1.31
1.90
1.35
2.46
3.54
1.32
3.24
1.83
1.04
1.04
1.00
1.01
1.02
1.10
1.05
1.03
1.00
1.02
1.58
1.73
1.01
1.02
0.95
1.00
0.99
1.09
1.02
1.15
1.03
1.34
1.33
1.12
1.10
1.11
1.43
1.32
1.31
1.30
1.28
2.41
2.99
1.20
1.08
1.16
1.13
1.23
1.41
1.12
1.54
1.27
SDG&E UNITS
Encina 1
Encina 2
Encina 3
Encina 4
Encina 5
South Bay 1
South Bay 2
South Bay 3
South Bay 4
Averages
20
20
20
20
20
30
30
30
45
107
104
110
300
330
143
150
175
150
1.47
1.34
1.32
1.87
2.07
1.43
1.33
1.40
1.30
1.47
0.91
0.94
0.98
0.97
0.95
0.93
0.99
0.96
1.01
0.96
1.10
1.08
1.09
1.13
1.15
1.10
1.10
1.10
1.12
1.12
HR-DESC.DOC; 4/17/98; PAGE 29
The minimum and maximum Ratios, R(x1) and R(x2), were calculated using the equations for the Average
Heat Rate (AHR) and Incremental Heat Rate (IHR), for each unit, as follows:
The Input-Output Curve is typically defined by the third order equation:
y = ax3 + bx2+ cx + d
Where: x = Output in MW
y = Input in Btu/hr
a-d = The coefficients that define the equation
The Average Heat Rate (AHR) is defined as the Input-Output Curve (y) divided by the output (x):
AHR = y/x = (ax3 + bx2 + cx + d) / x
The Incremental Heat Rate (IHR) is defined as the first derivative of the Input-Output Curve:
IHR = dy/dx = 3ax2 + 2bx + c
The Ratio of Average Heat Rate to Incremental Heat Rate (R) is therefore:
R = AHR/IHR = (y/x) / dy/dx = [(ax3+bx2+cx+d)/x] / (3ax2+2bx+c)
The minimum output ratio, R(x1), and maximum output ratio, R(x2), are then developed by setting x
equal to the minimum output (x1) and maximum output (x2) values, respectively.
R(x1) = [(a x13+b x12+c x1+d)/ x1] / (3a x12+2b x1+c)
R(x2) = [(a x23+b x22+c x2+d)/ x2] / (3a x22+2b x2+c)
The average value, RAVE, is found by integrating R from the minimum output (x1) to the maximum output
(x2), and then dividing this result by the difference between the minimum and maximum outputs (x2 - x1):
RAVE = [ò
ò R dx {from x1
to x2 } ]
/ (x2 - x1)
= [ò
ò AHR/IHR dx {from x1
to x2 } ]
/ (x2 - x1)
Where: x1 = Minimum Operating Level(MW)
x2 = Maximum Operating Level (MW)
The integration of R, (ò
ò R dx), is:
ò R dx =[(x/3) +(d×Ln(x)/c) +(bG/18a) - (dG/2c) + (2cE/3F) - (bdE/cF) - (Eb2/9aF)]
HR-DESC.DOC; 4/17/98; PAGE 30
Where: E = ATan((3ax+b)/F)
F = (3ab-x2)1/2
G = Ln(3ax2+2bx+c)
Ln = Natural Log
ATan = Arc Tangent
Substituting the coefficients of Table B-2 in Appendix B into the above equations gives the results shown
in Table 5. Using the now familiar Moss Landing 7 unit to illustrate this gives:
a = -0.0013
b = 2.955
c = 6561.2
d = 662025
•
x1 = 50 MW
x2 = 739 MW
The AHR/IHR at minimum generation: R(x1)
R(x1) = AHR/IHR = (ax3+bx2+cx+d)/x] / (3ax2+2bx+c): x1 = 50 MW
R(50) = AHR/IHR = [(-0.0013×503+2.955×502+6561.2×50+662025)/50]
/ (3×-0.0013×502+2×2.955×50+662025)
R(50) = AHR/IHR = 2.91
•
The AHR/IHR at maximum generation: R(x2)
R(x2)= AHR/IHR = (y/x)/y′= [(ax3+bx2+cx+d)/x] / (3ax2+2bx+c): x2 = 739 MW
R(739) = AHR/IHR = [(-0.0013×7393+2.955×7392+6561.2×739+662025)/739]
/ (3× -0.0013×7392+2×2.955×739+662025)
R(739) = AHR/IHR = 1.02
•
The average AHR/IHR: RAVE
RAVE = [ò
ò R dx {from x1
to x2 } ]
/ (x2 - x1)
ò R dx =[(x/3) +(d×Ln(x)/c) +(bG/18a) - (dG/2c) + (2cE/3F) - (bdE/cF) - (Eb2/9aF)]
Where: E = ATan((3ax+b)/F)
F = (3ab-x2)1/2
G = Ln(3ax2+2bx+c)
R(739) = (739/3)+(662025ln(739)/6561.2)+(2.955G/18/-0.0013)-(662025G/2/6561.2)
+(2×6561.2E/3F) -(2.955×662025E/6561.2F)-(2.9552E/9×-0.0013F)
Where: E = ATan((3×-0.0013×739+2.955)/F)
F = (3×-0.0013×2.955-7392)1/2
G = Ln(3×-0.0013×7392+2×2.955×739+6561.2)
HR-DESC.DOC; 4/17/98; PAGE 31
R(50) = (50/3)+(662025ln(50)/6561.2)+(2.955G/18/-0.0013)-(662025G/2/6561.2)
+(2×6561.2E/3F) -(2.955×662025E/6561.2F)-(2.9552E/9×-0.0013F)
Where: E = ATan((3×-0.0013×50+2.955)/F)
F = (3×-0.0013×2.955-502)1/2
G = Ln(3×-0.0013×502+2×2.955×50+6561.2)
RAVE = [R(739) - R(50)] / (739 - 50) = 1.2596.
At the bottom of each set of IOU values in Table 5 is an average value that is calculated as the weighted
average using the relevant capacity for each R(x) value:
Average R(x) = [å
å R(x) ×x] / åx for all x in an IOU
•
•
•
System average R(x1) is weighted by x1.
System average R(x2) is weighted by x2 .
System average RAVE is weighted by x2 - x1.
Table 5 can be better visualized in graphical form. Figures 20A, B and C present the data of Table 5 in
graphical form, except this time system ratios of AHR/HR are arranged in terms of increasing values of
R(x1).
HR-DESC.DOC; 4/17/98; PAGE 32
FIGURE 20A
AHR/IHR RATIOS
PG&E UNITS
3.0
AHR/IHR
2.5
R(X1)
Rave
2.0
1.5
1.0
0.5
R(X2)
mos7
mos6
hnp3
hnp2
hmb1&2
pit6
pit7
con7
pit1&2
pit5
mor4
con6
mor3
pit3&4
hnp4
pot3
mor1&2
0.0
PLANT
FIGURE 20B
AHR/IHR RATIOS
SCE UNITS
9.0
8.0
AHR/IHR
7.0
R(X1)
6.0
5.0
4.0
3.0
Rave
2.0
1.0
R(X2)
hig3&4
hig1&2
red5&6
sbr1&2
ala1&2
els1&2
ala3&4
els3&4
eti3&4
eti1&2
orb2
cw34
hun1&2
man1&2
ala5&6
orb1
red7&8
lb8&9
cw02
cw01
0.0
PLANT
FIGURE 20C
AHR/IHR RATIOS
SDG&E UNITS
2.5
R(X1)
AHR/IHR
2.0
Rave
1.5
1.0
0.5
0.0
sba4
R(X2)
enc3
sba2
enc2
sba3
sba1
enc1
enc4
enc5
PLANT
Table 6 summarizes the ranges of the unit data found in the Table 5 (and Figures 20A, B & C). Table 7
summarizes the system average values for each IOU (pre-divestiture).
HR-DESC.DOC; 4/17/98; PAGE 33
TABLE 6: UNIT RATIOS OF AHR/IHR
RATIOS OF AHR/IHR
UTILITY
PG&E
SCE
SDG&E
R(x1)
R(x2)
RAVE
1.20 - 2.91
1.30 - 8.51
1.30 - 2.07
0.84 - 1.05
0.95 - 1.73
0.91 - 1.01
1.05 - 1.26
1.08 - 2.99
1.08 - 1.15
It is apparent from Table 6 that the minimum output values, R(x1), vary dramatically and are typically
large. But the maximum outputs, R(x2), vary slightly and are typically small in magnitude. The average
values, RAVE, which would be the most representative of the operation of the units over time, do not vary
as dramatically or are as large as the R(x1) values but are nonetheless significantly large in range and
magnitude -- suggesting the potential for large differences between the incremental cost and the average
cost.
The system average ratios of Table 7 are probably more useful than the ranges of Table 6, in that it is a
more average representation of the effect on market clearing price (MCP). Considering that the PG&E
and SCE units will set the MCP much more often than SDG&E, it appears that on average the Average
Heat Rate, RAVE, will tend to be in the range of 17 to 27 percent higher than the Incremental Heat Rate
(IHR) -- during those hours that the IOU units set the MCP.
TABLE 7: SYSTEM RATIOS OF AHR/IHR
RATIOS OF AHR/IHR
UTILITY
PG&E
SCE
SDG&E
R(x1)
R(x2)
RAVE
1.68
1.83
1.47
0.98
1.03
0.96
1.17
1.27
1.12
The 17 to 27 percent values are meaningful if one is willing to accept the simplifying assumption that over
the long run all units will be used equally and each unit will experience all levels of generation an equal
number of hours. This is of course simplistic, but useful for this simplistic characterization.
In actual practice, the more efficient units will be used more than the less efficient units and all units will
tend to generate more at their lower levels than their higher levels. In general, both of these realities will
increase the ratio (R) of Average Heat Rate (AHR) to Incremental Heat Rate (IHR). This is very difficult
to quantify, but nevertheless I attempt to so in the next section, A Simplistic Market Model.
A Simplistic Market Model
This section presents a Simplistic Market Model that is a more comprehensive emulation of the ratio (R)
of Average Heat Rate (AHR) to Incremental Heat Rate (IHR). This model uses the above heat rate data
but combines the data into an emulation of the competitive market, which allows us to look at the system
R values throughout various levels of generation, rather than the system average (RAVE) values described
above. The calculations and methodology are provided in Appendix E for those who would like to
replicate this process in detail, but the following adequately describes the method and results.
Traditional production cost modeling consists of commitment and dispatch. The commitment process
consists of identifying the most economic set of plants necessary to meet the daily peak. The dispatch of
HR-DESC.DOC; 4/17/98; PAGE 34
these plants is based on the incremental cost of each plant’s capacity blocks. The Incremental Cost is
determined by the fuel cost (the IHR times dispatch gas price) plus variable O&M, on a $/MWh basis.
The available capacity block with the least Incremental Cost at the moment of increased load is
dispatched to meet that load.
In the California market, the PX and the ISO disavow responsibility for commitment and assign that
responsibility to the bidder. The PX and the ISO rely solely on dispatch. They dispatch the system based
on the lowest bid offered, indifferent to the actual cost of dispatch.
For the case of non-members, who have other means of capturing revenue and are just offering
increments of surplus power to the market, their bids will probably continue to be based on their
Incremental Costs. But for the members of the market (IOUs and those who will depend on the market
for all their revenue), their bids must reflect all costs, not just Incremental Costs. Their variable O&M
costs will not change, but their fuel related bid must now reflect their average cost (AHR times total gas
price) as well as their start-up costs.
The Simplistic Market Model ignores the effects of variable O&M and start-up costs -- as well as the
effects of commitment. It concentrates solely on the differences in heat rates between the AHR, which is
representative of MCP, and IHR, which is representative of traditional dispatch (that is, MC). Figures
21A, B & C compare AHR to IHR on a graphical basis. These heat rate curves are for the IOU slowstart gas-fired units (steam units and combined cycle units), ignoring the fast-start units (CTs), as CTs do
not in general set the MCP.2 Units other than the IOU units are ignored under the simplifying assumption
that the IOU units will set the market clearing price most of the time -- although this is only approximately true.3 The heat rate curves are shown separately for each IOU in order to make the presentation
more legible. In actual practice, the three curves would be combined -- and would include all units and
not just the slow-start gas-fired units.
The process for deriving the AHR and IHR curves of the Figure 21 series is burdensome but conceptually quite simple. To facilitate this understanding, you should imagine that this data is simply the sorting
of the block heat rate data provided in Appendix A. Then realize that this data can not be used directly as
AHR and IHR are not directly comparable.
Each Incremental Heat Rate (IHR) value is an average for its block. Each Average Heat Rate (AHR)
value is the point values at the end of the block. To make these values comparable requires that AHR
values also be characterized as an average for the same block. This is done using the equations of
Appendix B. This new value is delineated as AHRAVE to differentiate it from the traditional AHR value.
IHR is then recalculated using the corresponding equation, so that AHR and IHR will be completely
comparable. As with all previous analyses, in cases where two units have the same size capacity blocks,
they are combined into one equivalent unit in order to make the computation and representation simpler.
2
Although CTs can bid into the PX market and set the MCP, it is expected that in general CTs will bid into the
non-spin market and will not set the MCP.
3
Various simulations suggest that the slow-start gas-fired IOU units will only set the market clearing price
approximately 50 to 70 percent of the time, depending on the particular set of assumptions.
HR-DESC.DOC; 4/17/98; PAGE 35
FIGURE 21A,B&C
PG&E
AHRave vs IHR
18,000
HEAT RATE (Btu/kWh)
16,000
AHR ave
14,000
12,000
10,000
8,000
6,000
IHR
4,000
2,000
0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
OUTPUT (MW)
SCE
AHRave vs IHR
45,000
HEAT RATE (Btu/kWh)
40,000
35,000
AHR ave
30,000
25,000
20,000
15,000
10,000
5,000
IHR
0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
OUTPUT (MW)
SDG&E
AHRave vs IHR
14,000
AHR ave
HEAT RATE (Btu/kWh)
12,000
10,000
8,000
IHR
6,000
4,000
2,000
0
0
200
400
600
800
1,000
1,200
1,400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE 36
The IHR curves of the Figure 21 series are constructed to emulate the dispatch of the regulated system.
Each slow-start gas-fired unit is represented by four IHR blocks.4 These heat rate blocks are then sorted
by increasing IHRs.
The AHRAVE curves of Figure 21 are constructed to emulate the dispatch of the competitive market.
These values are sorted similar to those of IHR except the AHRAVE blocks can not simply be ordered by
increasing AHRAVE value, as was done with the IHR values. This would lead to the physical impossibility
of less expensive upper blocks being dispatched before more expensive lower blocks. To represent this
physical limitation, the units are first sorted based on their first block heat rates (Block 2). When the first
unit with the lowest expensive first block AHRAVE is identified, it is logical that all of its upper blocks will
then be dispatched before going on to the first block (Block 2) of any other unit; as at that point, no other
unit’s first block can compete with this unit’s upper blocks. Thus, we see the saw-tooth nature of the
AHRAVE curves in the Figure 21 series. The downward sloping arc of each “tooth” represents the
AHRAVE curve of that unit, starting at the highest heat rate block (first block) and ending at the minimum
point (last block).
The two curves of Figure 21 series clearly illustrate the fact that the AHRAVE dispatch is inherently more
costly than the IHR dispatch -- without even accounting for the difference between the dispatch price of
gas and the total price of gas. We can also see from these same figures that the AHRAVE curve is not flat,
as is the IHR curve. This suggests that the typical statements about there not being much variance in the
MCP bids between units is perhaps too simplistic.
At the same time, these AHRAVE curves can not be truly representative of the California market, as the
market requires 1-Part monotonic bidding, such that each unit’s bid price series must increase with each
block of power. That is, the AHRAVE must look similar to the IHR curve. The knowledge of this paradox
allows us to understand the dilemma of the plant owner in bidding a unit’s costs into the market -- or the
modeler in modeling the market. Each unit has declining (downward sloping) costs that must be
converted to monotonically increasing (upward sloping) costs. These curves can be equal at one point,
only. This means that if the plant owner wants to bid its unit’s costs in any one hour, the owner must
know the exact generation level -- that one point where the curves are equal. Herein lies the difficulty for
the plant owner -- and the modeler. If the exact capacity level (block heat rate) can be determined, the
correct unit is dispatched. Otherwise, the incorrect unit is selected resulting in inefficient dispatch and the
concomitant shift in revenues to an alternative bidder.
We can not hope to emulate the actual dispatch of the system with this simplistic model. Nevertheless, we
can develop a crude proxy for the system by rearranging the IHR and AHRAVE data into weighted
averages. The Figure 22 series uses the same data of the Figure 21 series except that it is a running
weighted average -- as each unit is added, a weighted system average is calculated based on the
cumulative capacity (MW) of the blocks. This is done for both the IHR and the AHRAVE data. The
respective curves are system values of IHR and the AHRAVE, and are designated SIHR and the
SAHRAVE, respectively.
4
Appendix A provides five blocks of average heat rate data but the first block does not qualify as an incremental
heat rate. It is an average heat rate.
HR-DESC.DOC; 4/17/98; PAGE 37
FIGURE 22A,B&C
PG&E
SYSTEM AVERAGE HEAT RATES
HEAT RATE (Btu/kWh)
12,000
11,000
10,000
SAHR ave
9,000
8,000
SIHR
7,000
6,000
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
OUTPUT (MW)
SCE
SYSTEM AVERAGE HEAT RATES
HEAT RATE (Btu/kWh)
12,000
SAHR ave
11,000
10,000
9,000
8,000
SIHR
7,000
6,000
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
OUTPUT (MW)
SDG&E
SYSTEM AVERAGE HEAT RATES
12,000
HEAT RATE (Btu/kWh)
SAHRave
11,000
10,000
9,000
SIHR
8,000
7,000
6,000
0
200
400
600
800
OUTPUT (MW)
1,000
1,200
1,400
HR-DESC.DOC; 4/17/98; PAGE 38
The weighted average data shown in the Figure 22 series can be considered as representative of an
average value that could be expected over time at various levels of generation -- looking at individual
IOUs, one at a time. These Figures show that the ratio of SAHRAVE to SIHR does increase at lower
generation levels, but not as dramatically as we might have thought -- assuming that we’re looking at
reasonably to be expected values of output.
These results can be made to conform to our results in the previous section by taking the end point in
each curve. Table 8 summarizes the heat rate data for the last point in each curve and calculates the
SAHRAVE / SIHR values for each utility. These SAHRAVE / SIHR values are very close to the Table 7
values but do not match exactly. This is to be expected since mathematically they are not exactly
equivalent.
TABLE 8: SUMMARY OF SYSTEM HEAT RATES
SIHR HEAT RATE (Btu/kWh)
SAHRAVE HEAT RATE (Btu/kWh)
SAHRAVE / SIHR
PG&E
SCE
SDG&E
9,057
10,522
1.16
8,943
11,217
1.25
9,830
10,944
1.11
This same data also suggests that units will have a different competitive status under the restructured
market than they do now. For example, under regulation and traditional dispatch (IHR), the SCE units
would seem to have the most favorable position -- absent consideration of gas prices -- since SCE has the
lowest SHIR (8,943 Btu/kWh). But based on the market dispatch (AHRAVE), PG&E would appear to
have the most favorable position -- since PG&E has the lowest SAHRAVE (10,522 Btu/kWh).
My heat rate analysis up to this point has ignored costs, which is clearly a short coming which will now
be corrected. Table 9 presents estimated 1998 gas prices, which were taken from the Energy Commission’s 1997 Fuels Forecast (FR 97) approved on March 18, 1998.
TABLE 9: SUMMARY OF 1998 GAS PRICES (FR 97)
FORECAST YEAR = 1998
PG&E
Cool Water
SCE OTHER
SDG&E
DISPATCH
($/MMBtu)
2.31
2.24
2.43
2.34
TOTAL
($/MMBtu)
2.51
2.34
2.61
2.91
Figures 23A, B & C provide the comparable cost data for each IOU based on the above 1998 gas prices.
Figure 24 combines the Figure 23 series into one graph, and for the first time we have a representation of
the total system -- IOUs only. In Figure 24, SAHRAVE times the total price of gas can be considered a
proxy for MCP and SHIR times the dispatch price of gas can be considered a proxy for MC. The
distances between these two curves allow us to appreciate the difference between MCP and MC that is
due to the combination of heat rate and gas price differences.
HR-DESC.DOC; 4/17/98; PAGE 39
FIGURE 23A,B&C
PG&E
MCP & MC PROXIES
35
MCP = AHR @ TOTAL GAS PRICE
COST ($/MWh)
30
25
20
15
MC = IHR @ DISPATCH GAS PRICE
10
5
0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
OUTPUT (MW)
SCE
MCP & MC PROXIES
35
MCP = AHR @ TOTAL GAS PRICE
COST ($/MWh)
30
25
20
MC = IHR @ DISPATCH GAS PRICE
15
10
5
0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
OUTPUT (MW)
SDG&E
MCP & MC PROXIES
35
COST ($/MWh)
30
MCP = AHR @ TOTAL GAS PRICE
25
20
MC = IHR @ DISPATCH GAS PRICE
15
10
5
0
0
200
400
600
800
1,000
1,200
1,400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE 40
FIGURE 24
COLLECTIVE IOUs
MCP & MC PROXIES
UNIT COST ($/MWh)
30
25
MCP = SAHRave @ TOTAL GAS PRICE
20
MC = SIHR @ DISPATCH GAS PRICE
15
10
5
0
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
OUTPUT (MW)
Figure 25 is a curve that is the ratio of the two curves in Figure 24. It is the ratio of the MCP proxy to
the MC proxy for selected points: at 1000 MW intervals. The curve shows values in the range of 1.26 to
1.45 depending on the output level. These are very significant differences to be sure, but perhaps not as
large as we might have expected given that in any one hour the difference can be much higher than this –
as high as 8.5:1 as we have already shown.
FIGURE 25
COLLECTIVE IOUs
AHR/IHR (MCP/MC)
AHR/IHR
1.5
1.4
1.3
1.2
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
OUTPUT(MW)
The Figure 25 curve implies that given an extended period of time where each unit is allowed to
experience all of its various levels, the average will be as shown. Remembering our earlier conclusion that
this is probably simplistic because units will tend to operate more at their lower levels, we have to
conclude that the 1.26 to 1.45 range is probably low. At the same time, we must recognize that the
lowest and highest portions of the curve will tend to be used the least. The least that we can say here is
that this ratio will undoubtedly be 1.26 -- or higher. That is, the MCP should exceed traditional MC
by something greater than 26 percent.
Figure 26 is the same as Figure 25 except that the difference due to the gas price differential has been
removed. This Figure represents the difference between Average and Incremental Heat Rates, only. The
HR-DESC.DOC; 4/17/98; PAGE 41
range is now 1.17 to 1.36, as opposed to the 1.26 to 1.45 of Figure 25. The effect of using Average
instead of Incremental Heat Rates is in the range is something greater than 17 percent. The effect of the
gas prices is therefore about 9 percentage points. Compared to earlier Natural Gas Price Forecasts, this
differential is small. For example, there were years in earlier forecasts where PG&E had dispatch gas
prices that were 25 percent lower than the total gas price. At the same time, Energy Commission Staff
expects that the 9 percentage points probably overstate the differential in the future as there are
indications that the fixed cost component of contract gas prices will become smaller and smaller. It is also
expected that utilities and others will probably bid their total price of gas in order to receive reasonable
remuneration from the competitive market. Figure 26 is therefore probably the more accurate estimate.
FIGURE 26
COLLECTIVE IOUs
AHR/IHR (MCP/MC)
HEAT RATES ONLY
AHR/IHR
1.4
1.3
1.2
1.1
0
2,000
4,000
6,000
8,000
OUTPUT(MW)
10,000
12,000
14,000
It is important to keep in mind that these representations are exceedingly simplistic. First, they are based
on IOU (pre-divestiture) slow-start gas-fired units, only. Second, the IHR and the AHRAVE values are
based on a simplistic averaging system. Third, all system generation and transmission constraints are
ignored. Finally, these calculations are for one year, only. There is no reason to believe that these
representations are anything but illustrative.
No-Load Heat Rates
No-Load Heat Rates relate to the concept of No-Load Costs which were conceived at a time when the
California competitive market was proposed to be based on three-part bidding. Although this concept is
no longer relevant in the California market, it continues to be a subject of discussion. In addition, the NoLoad Cost concept may still prove viable in other competitive markets. For these reasons, it is included
within this paper.
The three components to 3-parts bidding are:
•
•
•
No-Load Bid
Monotonic Energy Bid
Start-Up Costs
Only the first two items are germane to our present discussion -- the Start-Up costs will be ignored in this
paper. As already explained, the market participants need to bid their Average Costs; but bidding
HR-DESC.DOC; 4/17/98; PAGE 42
Average Costs, which are declining costs, does not allow for bidding monotonic bids. Before the decision
was made to go to one-part bidding, the market designers decided to solve this problem using the NoLoad Cost component. When this No-Load Cost is subtracted from the Average Cost, Monotonic Energy
Bids remain.
The No-Load Heat Rate is defined as the extrapolation of the Input-Output Curve back to the vertical
axis (Input). This can most easily be illustrated by returning to our Unit X. The Unit X Input-Output
Curve is shown in Figure 27, using the equation developed for Figure 5: y = 1000x2 + 1000x + 18000,
where x = Output in MW and y = Input in 1000 Btu/hr. Extrapolating back to the Input axis creates an
intercept point of 18,000,000 Btu/hr which defines the No-Load quantity. Note that this same value can
be obtained by setting x = 0 in the Input-Output equation.
FIGURE 27
UNIT X
INPUT-OUTPUT CURVE
INPUT (1000 Btu/kWh)
30,000
28,000
26,000
24,000
22,000
20,000
No-Load = 18,000Btu/hr
18,000
16,000
0
1
2
3
OUTPUT (MW)
Multiplying this 18,000,000 Btu/hr by our fuel cost of 2.5 $/MMBtu provides the hourly bid quantity of
$45 per hour. This is by definition a fixed cost in each hour that is independent of the output. At the same
time, its effect on the calculation of the Monotonic Energy Bid is not a constant amount. This is
illustrated in Table 10.
TABLE 10: CALCULATION OF MONOTONIC ENERGY BIDS FOR UNIT X
UNIT X
MONOTONIC ENERGY BID
NO-LOAD BID
TOTAL ENERGY BID
BLOCK 1
(HEAT RATE)
5 $/MWh
(2,000 Btu/kWh)
45 $/MWh
(18,000 Btu/kWh)
50 $/MWh
(20,000 Btu/kWh)
BLOCK 2
(HEAT RATE)
7.5 $/MWh
(3,000 Btu/kWh)
22.5 $/MWh
(9,000 Btu/kWh)
30 $/MWh
(12,000 Btu/kWh)
BLOCK 3
(HEAT RATE)
10 $/MWh
(4,000 Btu/kWh)
15 $/MWh
(6,000 Btu/kWh)
25 $/MWh
(10,000 Btu/kWh)
The Monotonic Energy Bids are calculated as the difference between the Total Energy Bid and the NoLoad Bid. For Block 1, the total cost is 50 $/MWh (20,000 Btu/kWh) and the No-Load is 45 $/MWh
(18,000 Btu/kWh). The monotonic bid is therefore 5 $/MWh (2,000 Btu/kWh): 50 $/MWh (20,000
Btu/kWh) - 45 $/MWh (18,000 Btu/kWh). For Block 2 the No-Load Cost has to be spread across twice
as many MW so its cost (and heat rate) is divided by two and the Monotonic Energy Bid is 30 $/MWh HR-DESC.DOC; 4/17/98; PAGE 43
22.5 $/MWh = 7.5 $/MWh. Similarly for the Block 3 the No-Load Cost is spread across three times as
many MW and is divided by 3 and the Monotonic Energy Bid is calculated as 10 $/MWh.
This can be illustrated with graphs. Figure 28 shows the hourly costs for Unit X, which show No-Load as
being constant at $45 per hour. It is the monotonic energy bid that varies from $5 at 1-MW to $10 at 3MW.
FIGURE 28
HOURLY COSTS ($)
UNIT X
HOURLY COST COMPONENTS
80
70
60
50
40
30
MONOTONIC COSTS
NO-LOAD
20
10
0
1
2
3
OUTPUT (MW)
Figure 29 shows the costs per unit energy varying as illustrated in Table 10. It shows the No-Load Costs
decreasing as they are spread over more MWh, and the monotonic costs increasing as required by 3-part
bidding. The total of these two costs represent the Average Cost, corresponding to the Average Heat
Rate.
FIGURE 29
UNIT X
COST PER MWh
COST ($/MWh)
50
MONOTONIC COSTS
40
NO-LOAD
30
20
10
0
1
2
3
OUTPUT (MW)
As with past efforts I provide a real unit to illustrate No-Load Costs for real units: Moss Landing 7.
Figure 30 shows No-Load calculation using the Input-Output Curve. As before, the no-load value can be
found as the d coefficient of the Input-Output Curve (Table B-2 in Appendix B.)
HR-DESC.DOC; 4/17/98; PAGE 44
FIGURE 30
MOSS LANDING 7
INPUT-OUTPUT CURVE
INPUT (1000 Btu/hr)
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
No-Load = 662,025,000 Btu/hr
0
0
100
200
300
400
500
600
700
800
OUTPUT (MW)
Figure 31 shows the No-Load Costs for Moss Landing 7 on an hourly basis. Figure 32 shows these same
costs on $/MWh basis.
FIGURE 31
HOURLY COSTS ($)
MOSS LANDING 7
HOURLY COSTS
9,000
8,000
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
MONOTONIC
COSTS
NO- L OAD
COSTS
62
82
164
260
326
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE 45
FIGURE 32
MOSS LANDING 7
COSTS PER MWh
40
MONOTONIC
COSTS ($/MWh)
35
COSTS
NO- L OAD
COSTS
30
25
20
15
10
5
0
62
82
164
260
326
OUTPUT (MW)
I have calculated and summarized the No-Load Heat Rates for all the IOU units, using the “d” coefficient
of the heat rate equations as the No-Load Heat Rate. The supporting data is provided in Appendix D.
Using this data, I made what I consider to be an important correlation. Figures 33A, B and C show
AHR/IHR ratios as a function of these No-Load Heat Rates. I expected to find a very high correlation
between the AHR/IHR ratios and No-Load Heat Rates, since they both reflect the difference between
AHR and IHR. But in fact, they do not seem to correlate at all.
This correlation is bad enough that I have to wonder about the viability of the proposed concept for
market bidding. In Figures 33 the situation becomes ludicrous in that there is a negative value for NoLoad Heat Rate. It is possible, however, that if the equations were completely reworked, going back to
the original Input-Output field measurements, that much of the heat rate data would change and perhaps
change the nature of the correlation so that the No-Load Heat Rates would make sense.
HR-DESC.DOC; 4/17/98; PAGE 46
1,000,000
662,025
657,281
632,496
0.5
1,000,000
737,960
293,691
223,144
R(X1)
193,103
164,658
727,238
677,108
219,614
218,209
205,948
200,714
194,590
190,385
180,146
177,052
117,483
115,531
99,926
70,409
AHR/IHR
2.5
162,660
590,522
588,318
585,227
2.00
109,919
3.00
453,856
7.00
397,249
1.00
327,238
326,693
315,310
302,880
301,952
267,439
230,091
56,315
48,471
-694,407
ahr/ihr
8.00
107,907
102,533
100,850
91,919
66,695
AHR/IHR
FIGURE 33A,B&C
AHR/IHR vs NO-LOAD HEAT RATE
PG&E
3.0
2.0
Rave
1.5
1.0
R(X2)
0.0
NO-LOAD HEAT RATE (Btu/kWh)
AHR/IHR vs NO-LOAD HEAT RATE
SCE
9.00
R(X1)
6.00
5.00
4.00
Rave
0.00
R(X1)
NO-LOAD HEAT RATE (Btu/kWh)
AHR/IHR vs NO-LOAD HEAT RATE
SDG&E
2.5
2.0
1.5
1.0
0.5
0.0
NO-LOAD HEAT RATE Btu/kWh)
HR-DESC.DOC; 4/17/98; PAGE 47
APPENDICES A - E
FOR
THE USE OF HEAT RATES
IN PRODUCTION COST MODELING
AND MARKET MODELING
HR-DESC.DOC; 4/17/98; PAGE 48
APPENDIX A
SUMMARY OF BLOCK HEAT RATE DATA
This appendix provides a summary of all the known heat rate data for the slow-start thermal units owned
by the IOUs -- prior to divestiture. For those units that have been divested, they are still grouped by the
IOU that formerly owned them but the new owner is noted. Each summary includes the Input-Output
Curve, the (Average) Incremental Heat Rates and the Average Heat Rates, as well as the corresponding
plots of that data.
The sources of this data is as follows:
• PG&E: ER 96 CFM Filing dated April 1996 except for Moss Landing 6 & 7
which are taken from 1994 CPUC Rate Case
• SCE: ER 94 CFM Filing dated June 1993
• SDG&E: April 28, 1997 FAX from Pat Harner of SDG&E
During the review of this data I noticed a number of anomalies. In some cases I changed the data in order
to make it appear more reasonable. In the remainder of the cases, I elected to use the data as it was
provided by the IOU but noted my concerns.
In attempting to use the ER 96 CFM heat rate data for PG&E, I noticed that there were four instances
when some of a unit’s heat rate blocks were changed from the previously used data (1994 Rate Case)
but not others -- which is physically impossible. Figures A-1 through A-4 summarize these instances.
Morro Bay 4 shows a revised Block 2 heat rate but none of its other heat rate blocks were revised. Moss
Landing 6 shows only Blocks 1 and 2 being revised from ER 94 numbers. Moss Landing 7 shows Blocks
1, 2 and 5 being revised but not Blocks 3 and 4. Pittsburg 7 showed only Block 5 being revised. For
Morro Bay 4 and Pittsburg 7, I elected to use the ER 96 CFM data as is because the effects on the heat
rate characteristics appeared to be insignificant. For Moss Landing 6 and 7, I reverted to the 1994 Rate
Case data as the ER 96 data was producing serious anomalies in the Instantaneous Incremental Heat Rate
curves; Figure A-5 illustrates this for Moss Landing 7 -- the curve should not be turning down on the
end. This decision was based on a conversation with Mark Meldgin of PG&E and Jim Hoffsis of the
Northern California Unit.
FIGURE A-1
UNIT: MORRO BAY 4 - PG&E 1994 RATE CASE
OUTPUT
(%)
(MW)
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
14%
25%
50%
80%
100%
UNIT: MORRO BAY 4 - ER 96 CFM
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
(1000 Btu/hr) (Btu/kWh)
46 590,364
85 930,495
169 1,672,931
270 2,591,190
338 3,224,520
12,834
8,721
8,839
9,092
9,314
OUTPUT
(%)
(MW)
(Btu/kWh)
12,834
10,947
9,899
9,597
9,540
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
14%
25%
50%
80%
100%
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
(1000 Btu/hr) (Btu/kWh)
46 590,364
85 921,995
169 1,672,931
270 2,591,190
338 3,224,520
12,834
8,503
8,940
9,092
9,314
(Btu/kWh)
12,834
10,847
9,899
9,597
9,540
HR-DESC.DOC; 4/17/98; PAGE A-1
FIGURE A-2
UNIT: MOSS LANDING 6 - PG&E 1994 RATE CASE
Duke Energy Nov. 1997
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
OUTPUT
(%)
(MW)
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
7%
25%
50%
80%
100%
UNIT: MOSS LANDING 6 - ER 96 CFM
Duke Energy Nov. 1997
(1000 Btu/hr) (Btu/kWh)
50
185
370
591
739
997,950
1,985,975
3,503,900
5,409,423
6,704,208
19,959
7,319
8,205
8,622
8,749
OUTPUT
(%)
(MW)
(Btu/kWh)
19,959
10,735
9,470
9,153
9,072
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
7%
25%
50%
80%
100%
50
185
370
591
739
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
(1000 Btu/hr) (Btu/kWh)
990,900
1,933,435
3,503,900
5,409,423
6,704,208
19,818
6,982
8,489
8,622
8,749
(Btu/kWh)
19,818
10,451
9,470
9,153
9,072
FIGURE A-3
UNIT: MOSS LANDING 7 - PG&E 1994 RATE CASE
Duke Energy Nov. 1997
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
OUTPUT
(%)
(MW)
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
7%
25%
50%
80%
100%
UNIT: MOSS LANDING 7 - ER 96 CFM
Duke Energy Nov. 1997
(1000 Btu/hr) (Btu/kWh)
50
185
370
591
739
997,950
1,966,735
3,429,160
5,296,542
6,589,663
19,959
7,176
7,905
8,450
8,737
OUTPUT
(%)
(MW)
(Btu/kWh)
19,959
10,631
9,268
8,962
8,917
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
7%
25%
50%
80%
100%
50
185
370
591
739
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
(1000 Btu/hr) (Btu/kWh)
990,900
1,924,185
3,429,160
5,296,542
6,561,581
19,818
6,913
8,135
8,450
8,548
(Btu/kWh)
19,818
10,401
9,268
8,962
8,879
FIGURE A-4
UNIT: PITTSBURG 7 - PG&E 1994 RATE CASE
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
OUTPUT
(%)
(MW)
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
17%
25%
50%
80%
100%
UNIT: PITTSBURG 7 - ER 96 CFM
(1000 Btu/hr) (Btu/kWh)
120
180
360
576
720
1,686,000
2,194,020
3,725,640
5,615,424
6,981,840
14,050
8,467
8,509
8,749
9,489
OUTPUT
(%)
(MW)
(Btu/kWh)
14,050
12,189
10,349
9,749
9,697
BLOCK 1
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
17%
25%
50%
80%
100%
120
180
360
576
720
Input-Output
Incremental Average
Curve Heat Rate Heat Rate
(1000 Btu/hr) (Btu/kWh)
1,686,000
2,194,020
3,725,640
5,615,424
6,993,360
14,050
8,467
8,509
8,749
9,569
(Btu/kWh)
14,050
12,189
10,349
9,749
9,713
FIGURE A-5
INCREMENTAL HEATRATE
Moss Landing 7
HEATRATE (Btu/kWh)
9,000
8,500
8,000
7,500
dy/dx = -0.009x2 +9.586x + 6044.8
7,000
6,500
6,000
0
200
400
600
800
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-2
The SCE data was taken from ER 94 CFM filings, as SCE did not file CFM data for ER 96. The only
exception is the data for Cool Water 3&4, which I considered to be questionable. Figure A-6 shows the
heat rate summary data for this unit as provided for ER 94 CFM filing. Note the irregular shape of the
heat rate data, particularly the highly unlikely shape of the Incremental Heat Rate data.
I felt that something was probably wrong with this data and took the liberty to changing it. Looking at
the Input-Output data, it appears that Block 3 is an erroneous point. I fixed this data by ignoring this
unlikely value, fitting an equation to the remaining 4 points of the Input-Output Curve and reconstructing
the heat rate values as shown in Figure A-7.
FIGURE A-6
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1 27%
BLOCK 2 35%
BLOCK 3 47%
BLOCK 4 74%
BLOCK 5 100%
140
180
240
380
512
1,983,800
2,264,400
2,980,560
3,716,400
4,776,960
14,170
7,015
11,936
5,256
8,035
14,170
12,580
12,419
9,780
9,330
HEATRATE (Btu/kWh)
16,000
UNIT: COOL WATER 3&4
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
400
500
600
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
16,000
HEATRATE (Btu/kWh)
5,000,000
INPUT (1000 Btu/hr)
100
4,000,000
3,000,000
2,000,000
1,000,000
0
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
400
OUTPUT (MW)
600
0
200
400
600
OUTPUT (MW)
My decision on this is arguable as a combined cycle unit is a combination of a steam unit and a CT. One
would expect therefore some irregularity in the heat rate curves. Nevertheless, I have elected to stay with
my proposed revision until the Cool Water 3 and 4 heat rate data can be verified.
The SDG&E data was taken from a 4/28/97 FAX from Pat Harner. SDG&E did not file ER 96 CFM heat
rate data and there ER 94 data appeared to be unreasonable in some cases.
HR-DESC.DOC; 4/17/98; PAGE A-3
FIGURE A-7
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 27%
BLOCK 2 35%
BLOCK 3 47%
BLOCK 4 74%
BLOCK 5 100%
140
180
240
380
512
1,983,721
2,264,236
2,688,080
3,714,898
4,773,296
(Btu/kWh)
14,169
7,013
7,064
7,334
8,018
(Btu/kWh)
14,169
12,579
11,200
9,776
9,323
HEATRATE (Btu/kWh)
16,000
UNIT: COOL WATER 3&4
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
500
600
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
16,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
400
OUTPUT (MW)
600
0
200
400
600
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-4
PG&E
SUMMARY HEAT RATE DATA
(SOURCE: ER 96 CFM FILING)
HR-DESC.DOC; 4/17/98; PAGE A-5
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: CONTRA COSTA 6
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 14%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
46
85
170
272
340
600,944
936,870
1,670,930
2,570,944
3,240,540
(Btu/kWh)
(Btu/kWh)
13,064
8,613
8,636
8,824
9,847
13,064
11,022
9,829
9,452
9,531
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
OUTPUT (MW)
0
400
SUMMARY HEAT RATE DATA
100
200
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: CONTRA COSTA 7
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 14%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
46
85
170
272
340
621,046
950,045
1,675,690
2,584,544
3,248,700
(Btu/kWh)
(Btu/kWh)
13,501
8,436
8,537
8,910
9,767
13,501
11,177
9,857
9,502
9,555
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
400
300
400
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
14,000
HEATRATE (Btu/kWh)
3,500,000
INPUT (1000 Btu/hr)
100
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-6
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 10%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
10
26
53
84
105
211,645
376,350
662,050
1,010,184
1,296,803
(Btu/kWh)
(Btu/kWh)
21,165
10,294
10,581
11,230
13,649
21,165
14,475
12,492
12,026
12,351
HEATRATE (Btu/kWh)
25,000
UNIT: HUMBOLDT 1&2
20,000
15,000
10,000
5,000
0
0
40
60
80
100
120
100
120
100
120
100
120
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
25,000
HEATRATE (Btu/kWh)
1,400,000
INPUT (1000 Btu/hr)
20
1,200,000
1,000,000
800,000
600,000
400,000
200,000
20,000
15,000
10,000
5,000
0
0
0
20
40
60
80
OUTPUT (MW)
100
0
120
SUMMARY HEAT RATE DATA
20
40
60
80
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: HUNTERS POINT 2
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
9%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
10
27
54
86
107
215,510
391,824
688,122
1,067,862
1,334,504
21,551
10,371
10,974
11,867
12,697
21,551
14,512
12,743
12,417
12,472
HEATRATE (Btu/kWh)
25,000
20,000
15,000
10,000
5,000
0
0
40
60
80
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
25,000
HEATRATE (Btu/kWh)
1,400,000
INPUT (1000 Btu/hr)
20
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
20,000
15,000
10,000
5,000
0
0
20
40
60
80
OUTPUT (MW)
100
120
0
20
40
60
80
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-7
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: HUNTERS POINT 3
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
9%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
10
27
54
86
107
210,370
378,378
671,436
1,063,476
1,347,986
21,037
9,883
10,854
12,251
13,548
21,037
14,014
12,434
12,366
12,598
HEATRATE (Btu/kWh)
25,000
20,000
15,000
10,000
5,000
0
0
40
60
80
100
120
100
120
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
25,000
1,400,000
1,200,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
20
1,000,000
800,000
600,000
400,000
200,000
0
20,000
15,000
10,000
5,000
0
0
20
40
60
80
OUTPUT (MW)
100
0
120
SUMMARY HEAT RATE DATA
20
40
60
80
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: HUNTERS POINT 4
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 19%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
62
82
164
260
326
748,092
926,108
1,667,060
2,567,240
3,208,166
(Btu/kWh)
(Btu/kWh)
12,066
8,901
9,036
9,377
9,711
12,066
11,294
10,165
9,874
9,841
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
3,500,000
INPUT (1000 Btu/hr)
100
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-8
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 19%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
62
82
164
260
326
786,408
974,201
1,748,568
2,676,700
3,341,500
(Btu/kWh)
(Btu/kWh)
12,684
9,390
9,444
9,668
10,073
12,684
11,881
10,662
10,295
10,250
HEATRATE (Btu/kWh)
14,000
UNIT: MORRO BAY 1&2
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
3,500,000
INPUT (1000 Btu/hr)
100
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-9
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: MORRO BAY 3
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 14%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
46
85
169
270
338
606,924
960,670
1,721,096
2,640,060
3,261,700
(Btu/kWh)
(Btu/kWh)
13,194
9,070
9,053
9,099
9,142
13,194
11,302
10,184
9,778
9,650
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
300
OUTPUT (MW)
0
400
SUMMARY HEAT RATE DATA
100
200
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: MORRO BAY 4
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 14%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
46
85
169
270
338
590,364
921,995
1,672,931
2,591,190
3,224,520
(Btu/kWh)
(Btu/kWh)
12,834
8,503
8,940
9,092
9,314
12,834
10,847
9,899
9,597
9,540
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-10
SUMMARY HEAT RATE DATA
UNIT: MOSS LANDING 6
Duke Energy Nov. 1997
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
7%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
50
185
370
591
739
997,950
1,985,975
3,503,900
5,409,423
6,704,208
19,959
7,319
8,205
8,622
8,749
19,959
10,735
9,470
9,153
9,072
HEATRATE (Btu/kWh)
INCREMENTAL HEATRATE
20,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
600
800
600
800
AVERAGE HEATRATE
20,000
7,000,000
HEATRATE (Btu/kWh)
18,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
200
400
600
800
0
200
OUTPUT (MW)
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
50
185
370
591
739
997,950
1,966,735
3,429,160
5,296,542
6,589,663
19,959
7,176
7,905
8,450
8,737
19,959
10,631
9,268
8,962
8,917
HEATRATE (Btu/kWh)
INCREMENTAL HEATRATE
UNIT: MOSS LANDING 7
Duke Energy Nov. 1997
BLOCK 1
7%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
400
OUTPUT (MW)
SUMMARY OF HEAT RATE DATA
20,000
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
400
600
800
600
800
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
20,000
7,000,000
18,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
400
OUTPUT (MW)
INPUT-OUTPUT CURVE
INPUT (1000 Btu/hr)
200
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
200
400
OUTPUT (MW)
600
800
0
200
400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-11
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: PITTSBURG 1&2
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 19%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
62
82
164
260
326
873,642
1,052,798
1,793,094
2,692,950
3,374,752
(Btu/kWh)
(Btu/kWh)
14,091
8,958
9,028
9,374
10,330
14,091
12,839
10,934
10,358
10,352
HEATRATE (Btu/kWh)
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
16,000
3,500,000
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
100
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
0
400
100
SUMMARY HEAT RATE DATA
200
OUTPUT (MW)
300
400
INCREMENTAL HEATRATE
UNIT: PITTSBURG 3&4
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 19%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
62
82
164
260
326
836,256
1,017,005
1,757,998
2,670,200
3,411,264
(Btu/kWh)
(Btu/kWh)
13,488
9,037
9,037
9,502
11,228
13,488
12,403
10,720
10,270
10,464
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-12
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
14,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 14%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
46
81
163
260
325
615,664
920,970
1,651,679
2,537,080
3,144,700
(Btu/kWh)
(Btu/kWh)
13,384
8,723
8,911
9,128
9,348
13,384
11,370
10,133
9,758
9,676
12,000
HEATRATE (Btu/kWh)
UNIT: PITTSBURG 5
10,000
8,000
6,000
4,000
2,000
0
0
100
300
400
300
400
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
3,500,000
12,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
200
OUTPUT (MW)
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
400
0
100
SUMMARY HEAT RATE DATA
200
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: PITTSBURG 6
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 14%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
46
81
163
260
325
660,284
960,174
1,683,464
2,583,620
3,232,125
(Btu/kWh)
(Btu/kWh)
14,354
8,568
8,821
9,280
9,977
14,354
11,854
10,328
9,937
9,945
HEATRATE (Btu/kWh)
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
16,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-13
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
16,000
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1 17%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
120
180
360
576
720
1,686,000
2,194,020
3,725,640
5,615,424
6,993,360
14,050
8,467
8,509
8,749
9,569
14,050
12,189
10,349
9,749
9,713
12,000
10,000
8,000
6,000
4,000
2,000
0
0
INPUT-OUTPUT CURVE
7,000,000
400
OUTPUT (MW)
600
800
600
800
14,000
HEATRATE (Btu/kWh)
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
200
400
OUTPUT (MW)
600
800
0
200
SUMMARY HEAT RATE DATA
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 23%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
47
52
104
166
207
514,697
559,520
1,023,880
1,598,746
2,022,597
(Btu/kWh)
(Btu/kWh)
10,951
8,965
8,930
9,272
10,338
10,951
10,760
9,845
9,631
9,771
HEATRATE (Btu/kWh)
UNIT: POTRERO 3
10,000
8,000
6,000
4,000
2,000
0
0
INPUT-OUTPUT CURVE
HEATRATE (Btu/kWh)
1,000,000
500,000
0
100
150
200
250
200
250
AVERAGE HEATRATE
12,000
1,500,000
50
OUTPUT (MW)
2,500,000
2,000,000
400
OUTPUT (MW)
INCREMENTAL HEATRATE
12,000
INPUT (1000 Btu/hr)
200
AVERAGE HEATRATE
16,000
6,000,000
INPUT (1000 Btu/hr)
HEATRATE (Btu/kWh)
14,000
UNIT: PITTSBURG 7
10,000
8,000
6,000
4,000
2,000
0
0
50
100
150
OUTPUT (MW)
200
250
0
50
100
150
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-14
SCE
SUMMARY HEAT RATE DATA
(SOURCE: ER 94 CFM FILING)
HR-DESC.DOC; 4/17/98; PAGE A-15
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: ALAMITOS 1&2
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
6%
BLOCK 2 26%
BLOCK 3 51%
BLOCK 4 77%
BLOCK 5 100%
20
90
180
270
350
577,980
1,216,755
2,057,760
2,927,610
3,732,050
(Btu/kWh)
28,899
9,125
9,345
9,665
10,056
(Btu/kWh)
28,899
13,520
11,432
10,843
10,663
HEATRATE (Btu/kWh)
30,000
25,000
20,000
15,000
10,000
5,000
0
0
100
300
400
300
400
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
30,000
HEATRATE (Btu/kWh)
4,000,000
INPUT (1000 Btu/hr)
200
OUTPUT (MW)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
25,000
20,000
15,000
10,000
5,000
0
0
100
200
300
OUTPUT (MW)
0
400
100
SUMMARY HEAT RATE DATA
200
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: ALAMITOS 3&4
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
6%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 75%
BLOCK 5 100%
40
160
320
480
640
1,011,300
2,024,880
3,407,680
4,840,320
6,334,400
(Btu/kWh)
(Btu/kWh)
25,283
8,447
8,643
8,954
9,338
25,283
12,656
10,649
10,084
9,898
HEATRATE (Btu/kWh)
30,000
25,000
20,000
15,000
10,000
5,000
0
0
400
600
800
600
800
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
30,000
HEATRATE (Btu/kWh)
7,000,000
INPUT (1000 Btu/hr)
200
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
25,000
20,000
15,000
10,000
5,000
0
0
200
400
OUTPUT (MW)
600
800
0
200
400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-16
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
12,000
UNIT: ALAMITOS 5&6
AES 1/1/98
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 27%
BLOCK 2 44%
BLOCK 3 63%
BLOCK 4 81%
BLOCK 5 100%
260
420
600
780
960
(Btu/kWh)
(Btu/kWh)
11,713
8,203
8,514
9,113
9,223
11,713
10,376
9,818
9,655
9,574
3,045,380
4,357,920
5,890,500
7,530,900
9,191,040
HEATRATE (Btu/kWh)
10,000
8,000
6,000
4,000
2,000
0
0
200
400
600
OUTPUT (MW)
800
1000
800
1000
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
12,000
10,000,000
9,000,000
8,000,000
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
INPUT (1000 Btu/hr)
HEATRATE (Btu/kWh)
10,000
8,000
6,000
4,000
2,000
0
0
200
400
600
OUTPUT (MW)
800
1000
0
200
SUMMARY HEAT RATE DATA
400
600
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: COOL WATER 1
Houston Industries Inc. 1/1/98
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 26%
BLOCK 2 46%
BLOCK 3 66%
BLOCK 4 86%
BLOCK 5 100%
17
30
43
56
65
203,048
324,240
448,318
575,904
666,575
(Btu/kWh)
(Btu/kWh)
11,944
9,322
9,544
9,814
10,075
11,944
10,808
10,426
10,284
10,255
HEATRATE (Btu/kWh)
12,000
10,000
8,000
6,000
4,000
2,000
0
0
20
40
OUTPUT (MW)
60
80
60
80
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
12,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
700,000
600,000
500,000
400,000
300,000
200,000
100,000
0
10,000
8,000
6,000
4,000
2,000
0
0
20
40
OUTPUT (MW)
60
80
0
20
40
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-17
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: COOL WATER 2
Houston Industries Inc. 1/1/98
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 23%
BLOCK 2 43%
BLOCK 3 63%
BLOCK 4 83%
BLOCK 5 100%
19
35
51
67
81
(Btu/kWh)
(Btu/kWh)
12,181
9,368
9,540
9,741
9,960
12,181
10,895
10,470
10,296
10,238
231,439
381,325
533,970
689,832
829,278
HEATRATE (Btu/kWh)
14,000
10,000
8,000
6,000
4,000
2,000
0
0
20
40
60
80
100
80
100
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
12,200
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
0
12,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
12,000
11,800
11,600
11,400
11,200
11,000
10,800
10,600
10,400
10,200
19
35
51
OUTPUT (MW)
67
0
81
SUMMARY HEAT RATE DATA
20
40
60
OUTPUT (MW)
INCREMENTAL HEATRATE
16,000
UNIT: COOL WATER 3&4
Houston Industries Inc. 1/1/98
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1 27%
BLOCK 2 35%
BLOCK 3 47%
BLOCK 4 74%
BLOCK 5 100%
Summer Rate
140
180
240
380
512
482
1,983,660
2,264,220
2,688,000
3,714,880
4,773,376
14,169
7,014
7,063
7,335
8,019
14,169
12,579
11,200
9,776
9,323
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
400
OUTPUT (MW)
500
600
AVERAGE HEATRATE
16,000
5,000,000
4,500,000
4,000,000
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
INPUT-OUTPUT CURVE
100
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
OUTPUT (MW)
500
600
0
100
200
300
400
OUTPUT (MW)
500
600
HR-DESC.DOC; 4/17/98; PAGE A-18
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: EL SEGUNDO 1&2
NRG/ Destec Consortium
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
6%
BLOCK 2 26%
BLOCK 3 51%
BLOCK 4 77%
BLOCK 5 100%
20
90
180
270
350
556,760
1,202,400
2,048,040
2,914,785
3,706,850
(Btu/kWh)
(Btu/kWh)
27,838
9,223
9,396
9,631
9,901
27,838
13,360
11,378
10,796
10,591
HEATRATE (Btu/kWh)
30,000
25,000
20,000
15,000
10,000
5,000
0
0
100
200
OUTPUT (MW)
300
400
300
400
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
30,000
HEATRATE (Btu/kWh)
4,000,000
INPUT (1000 Btu/hr)
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
25,000
20,000
15,000
10,000
5,000
500,000
0
0
0
100
200
OUTPUT (MW)
300
0
400
100
SUMMARY HEAT RATE DATA
200
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: EL SEGUNDO 3&4
NRG/ Destec Consortium
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
6%
BLOCK 2 24%
BLOCK 3 48%
BLOCK 4 72%
BLOCK 5 100%
40
160
320
480
670
985,120
1,991,920
3,364,160
4,777,920
6,526,135
24,628
8,390
8,577
8,836
9,201
24,628
12,450
10,513
9,954
9,741
HEATRATE (Btu/kWh)
25,000
20,000
15,000
10,000
5,000
0
0
200
400
OUTPUT (MW)
600
800
600
800
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
25,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
20,000
15,000
10,000
5,000
0
0
200
400
OUTPUT (MW)
600
800
0
200
400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-19
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: ETIWANDA 1&2
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
8%
BLOCK 2 30%
BLOCK 3 53%
BLOCK 4 76%
BLOCK 5 100%
20
80
140
200
264
496,960
1,052,680
1,630,580
2,236,700
2,923,008
24,848
9,262
9,632
10,102
10,724
24,848
13,159
11,647
11,184
11,072
HEATRATE (Btu/kWh)
25,000
20,000
15,000
10,000
5,000
0
0
50
150
200
250
300
250
300
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
25,000
HEATRATE (Btu/kWh)
3,000,000
INPUT (1000 Btu/hr)
100
2,500,000
2,000,000
1,500,000
1,000,000
500,000
20,000
15,000
10,000
5,000
0
0
0
50
100
150
200
OUTPUT (MW)
250
0
300
SUMMARY HEAT RATE DATA
50
100
150
200
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: ETIWANDA 3&4
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
6%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 75%
BLOCK 5 100%
40
160
320
480
640
919,180
1,931,360
3,313,280
4,741,200
6,227,840
22,980
8,435
8,637
8,925
9,292
22,980
12,071
10,354
9,878
9,731
HEATRATE (Btu/kWh)
25,000
20,000
15,000
10,000
5,000
0
0
200
600
800
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
25,000
HEATRATE (Btu/kWh)
7,000,000
INPUT (1000 Btu/hr)
400
OUTPUT (MW)
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
20,000
15,000
10,000
5,000
0
0
200
400
OUTPUT (MW)
600
800
0
200
400
600
800
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-20
SUMMARY HEAT RATE DATA
INCREMENTAL HEAT RATE
UNIT: HIGHGROVE 1&2
Thermo Ecotek 1/1/98
HEATRATE (Btu/kWh)
50,000
45,000
40,000
35,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 12%
BLOCK 2 27%
BLOCK 3 58%
BLOCK 4 85%
BLOCK 5 100%
8
18
38
56
66
394,428
478,563
647,333
799,811
884,766
(Btu/kWh)
(Btu/kWh)
49,304
8,414
8,439
8,471
8,496
49,304
26,587
17,035
14,282
13,406
30,000
25,000
20,000
15,000
10,000
5,000
0
0
20
INPUT-OUTPUT CURVE
60
80
60
80
AVERAGE HEAT RATE
800,000
700,000
45,000
INPUT (1000 Btu/hr)
HEATRATE (Btu/kWh)
900,000
50,000
600,000
500,000
400,000
300,000
200,000
100,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
0
0
0
20
40
OUTPUT (MW)
60
80
0
20
SUMMARY OF HEAT RATE DATA
BLOCK 1 11%
BLOCK 2 27%
BLOCK 3 56%
BLOCK 4 90%
BLOCK 5 100%
10
24
50
80
89
666,030
776,602
987,124
1,237,224
1,313,607
(Btu/kWh)
(Btu/kWh)
66,603
7,898
8,097
8,337
8,487
66,603
32,358
19,742
15,465
14,760
HEATRATE (Btu/kWh)
70,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
40
OUTPUT (MW)
INCREMENTAL HEAT RATE
UNIT: HIGHROVE 3&4
Thermo Ecotek 1/1/98
60,000
50,000
40,000
30,000
20,000
10,000
0
0
20
40
60
80
100
80
100
OUTPUT (MW)
AVERAGE HEAT RATE
INPUT-OUTPUT CURVE
70,000
HEATRATE (Btu/kWh)
1,400,000
INPUT (1000 Btu/hr)
40
OUTPUT (MW)
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
60,000
50,000
40,000
30,000
20,000
10,000
0
0
20
40
60
OUTPUT (MW)
80
100
0
20
40
60
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-21
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
18,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
9%
BLOCK 2 33%
BLOCK 3 56%
BLOCK 4 79%
BLOCK 5 100%
40
140
240
340
430
664,240
1,519,420
2,396,520
3,301,570
4,146,060
(Btu/kWh)
(Btu/kWh)
16,606
8,552
8,771
9,051
9,383
16,606
10,853
9,986
9,711
9,642
HEATRATE (Btu/kWh)
16,000
UNIT: HUNTINGTON BEACH 1&2
AES Corp. 1/1/98
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
OUTPUT (MW)
400
500
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
18,000
4,500,000
4,000,000
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
16,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
100
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
OUTPUT (MW)
400
500
0
100
SUMMARY HEAT RATE DATA
200
300
OUTPUT (MW)
400
500
INCREMENTAL HEATRATE
14,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 13%
BLOCK 2 32%
BLOCK 3 54%
BLOCK 4 73%
BLOCK 5 100%
70
180
300
410
560
882,000
1,938,600
3,096,000
4,163,550
5,636,400
(Btu/kWh)
(Btu/kWh)
12,600
9,605
9,645
9,705
9,819
12,600
10,770
10,320
10,155
10,065
HEATRATE (Btu/kWh)
UNIT: LONG BEACH 8&9
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
500
600
500
600
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
200
300
400
OUTPUT (MW)
500
600
0
100
200
300
400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-22
SUMMARY HEAT RATE DATA
INCREMENTAL HEAT RATE
16,000
UNIT: MANDALAY 1&2
Houston Industries Inc. 1/1/98
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
9%
BLOCK 2 33%
BLOCK 3 56%
BLOCK 4 79%
BLOCK 5 100%
40
140
240
340
430
629,380
1,491,280
2,379,000
3,300,380
4,166,055
15,735
8,619
8,877
9,214
9,619
15,735
10,652
9,913
9,707
9,689
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
200
300
OUTPUT (MW)
400
500
400
500
AVERAGE HEAT RATE
INPUT-OUTPUT CURVE
16,000
4,500,000
14,000
HEATRATE (Btu/kWh)
4,000,000
INPUT (1000 Btu/hr)
100
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
12,000
10,000
8,000
6,000
4,000
2,000
500,000
0
0
0
100
200
300
OUTPUT (MW)
400
500
0
100
SUMMARY HEAT RATE DATA
200
300
OUTPUT (MW)
INCREMENTAL HEAT RATE
UNIT: ORMOND BEACH 1
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 33%
BLOCK 2 49%
BLOCK 3 67%
BLOCK 4 83%
BLOCK 5 100%
250
370
500
620
750
2,713,000
3,692,970
4,788,500
5,836,060
7,019,250
(Btu/kWh)
(Btu/kWh)
10,852
8,166
8,427
8,730
9,101
10,852
9,981
9,577
9,413
9,359
HEATRATE (Btu/kWh)
12,000
8,000
6,000
4,000
2,000
0
0
200
400
600
800
600
800
OUTPUT (MW)
AVERAGE HEAT RATE
INPUT-OUTPUT CURVE
8,000,000
12,000
7,000,000
10,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
10,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
8,000
6,000
4,000
2,000
0
0
0
200
400
OUTPUT (MW)
600
800
0
200
400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-23
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
20,000
UNIT: ORMOND BEACH 2
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
7%
BLOCK 2 30%
BLOCK 3 53%
BLOCK 4 77%
BLOCK 5 100%
50
225
400
575
750
993,850
2,427,075
3,907,200
5,448,125
7,067,250
(Btu/kWh)
(Btu/kWh)
19,877
8,190
8,458
8,805
9,252
19,877
10,787
9,768
9,475
9,423
HEATRATE (Btu/kWh)
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
400
600
800
600
800
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
20,000
8,000,000
18,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
200
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
200
400
OUTPUT (MW)
600
800
0
SUMMARY HEAT RATE DATA
200
400
OUTPUT (MW)
INCREMENTAL HEATRATE
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
6%
BLOCK 2 26%
BLOCK 3 51%
BLOCK 4 77%
BLOCK 5 100%
20
90
180
270
350
632,340
1,261,755
2,083,770
2,922,750
3,685,325
(Btu/kWh)
(Btu/kWh)
31,617
8,992
9,134
9,322
9,532
31,617
14,020
11,577
10,825
10,530
HEATRATE (Btu/kWh)
35,000
UNIT: REDONDO BEACH 5&6
AES Corp. 1/1/98
30,000
25,000
20,000
15,000
10,000
5,000
0
0
200
300
400
300
400
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
35,000
HEATRATE (Btu/kWh)
4,000,000
INPUT (1000 Btu/hr)
100
3,500,000
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
30,000
25,000
20,000
15,000
10,000
5,000
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-24
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 27%
BLOCK 2 38%
BLOCK 3 69%
BLOCK 4 83%
BLOCK 5 100%
260
360
660
800
960
2,917,070
3,772,260
6,395,730
7,655,600
9,128,640
(Btu/kWh)
11,220
8,552
8,745
8,999
9,207
(Btu/kWh)
11,220
10,479
9,691
9,570
9,509
HEATRATE (Btu/kWh)
12,000
UNIT: REDONDO BEACH 7&8
AES Corp. 1/1/98
10,000
8,000
6,000
4,000
2,000
0
0
400
600
800
1000
800
1000
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
12,000
10,000,000
9,000,000
8,000,000
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
200
10,000
8,000
6,000
4,000
2,000
0
0
200
400
600
OUTPUT (MW)
800
0
1000
200
400
600
OUTPUT (MW)
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: SAN BERNARDINO 1&2
Thermo Ecotek 1/1/98
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1 11%
BLOCK 2 33%
BLOCK 3 56%
BLOCK 4 78%
BLOCK 5 100%
14
42
70
98
126
384,727
627,249
881,895
1,143,611
1,414,854
27,481
8,662
9,095
9,347
9,687
27,481
14,935
12,599
11,670
11,229
HEATRATE (Btu/kWh)
30,000
25,000
20,000
15,000
10,000
5,000
0
0
100
150
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
30,000
1,600,000
1,400,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
50
1,200,000
1,000,000
800,000
600,000
400,000
200,000
25,000
20,000
15,000
10,000
5,000
0
0
0
50
100
OUTPUT (MW)
150
0
50
100
150
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-25
SDG&E
SUMMARY HEAT RATE DATA
(SOURCE: April 28, 1997 FAX)
HR-DESC.DOC; 4/17/98; PAGE A-26
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: ENCINA 1
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 19%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
20
27
54
86
107
266,060
327,367
577,533
903,080
1,142,760
(Btu/kWh)
(Btu/kWh)
13,303
9,082
9,352
10,142
11,200
13,303
12,238
10,795
10,550
10,680
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
INPUT-OUTPUT CURVE
20
40
60
80
OUTPUT (MW)
100
120
AVERAGE HEATRATE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
1,200,000
1,000,000
800,000
600,000
400,000
200,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
20
40
60
80
OUTPUT (MW)
100
0
120
20
SUMMARY HEAT RATE DATA
40
60
80
OUTPUT (MW)
100
120
100
120
100
120
INCREMENTAL HEATRATE
UNIT: ENCINA 2
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 19%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
20
26
52
83
104
257,200
314,990
570,232
893,734
1,124,864
(Btu/kWh)
(Btu/kWh)
12,860
9,632
9,817
10,369
11,112
12,860
12,115
10,966
10,742
10,816
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
20
40
60
80
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
14,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
12,000
10,000
8,000
6,000
4,000
2,000
0
0
20
40
60
80
OUTPUT (MW)
100
120
0
20
40
60
80
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-27
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
UNIT: ENCINA 3
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1 18%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
20
28
55
88
110
258,720
332,530
606,540
947,232
1,185,030
12,936
9,841
9,964
10,324
10,809
12,936
12,092
11,028
10,764
10,773
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
20
60
80
100
120
100
120
OUTPUT (MW)
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
HEATRATE (Btu/kWh)
1,200,000
INPUT (1000 Btu/hr)
40
1,000,000
800,000
600,000
400,000
200,000
12,000
10,000
0
8,000
6,000
4,000
2,000
0
0
20
40
60
80
OUTPUT (MW)
100
0
120
20
SUMMARY HEAT RATE DATA
40
60
80
OUTPUT (MW)
INCREMENTAL HEATRATE
UNIT: ENCINA 4
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
7%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
20
75
150
240
300
353,480
874,500
1,596,300
2,495,520
3,124,500
(Btu/kWh)
(Btu/kWh)
17,674
9,473
9,624
9,991
10,483
17,674
11,660
10,642
10,398
10,415
HEATRATE (Btu/kWh)
18,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
150
200
250
300
250
300
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
18,000
HEATRATE (Btu/kWh)
3,500,000
INPUT (1000 Btu/hr)
50
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
0
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
50
100
150
200
OUTPUT (MW)
250
300
0
50
100
150
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-28
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
20,000
18,000
HEATRATE (Btu/kWh)
16,000
UNIT: ENCINA 5
14,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1
6%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
20
83
165
264
330
372,640
941,967
1,695,870
2,652,144
3,330,030
(Btu/kWh)
(Btu/kWh)
18,632
9,037
9,194
9,659
10,271
18,632
11,349
10,278
10,046
10,091
12,000
10,000
8,000
6,000
4,000
2,000
0
0
INPUT-OUTPUT CURVE
200
OUTPUT (MW)
300
400
300
400
AVERAGE HEATRATE
20,000
3,500,000
18,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
100
3,000,000
2,500,000
2,000,000
1,500,000
1,000,000
500,000
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
100
200
OUTPUT (MW)
300
400
0
100
200
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-29
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
14,000
10,000
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 21%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
30
36
72
114
143
HEATRATE (Btu/kWh)
12,000
UNIT: SOUTH BAY 1
369,180
418,954
736,236
1,145,830
1,444,872
(Btu/kWh)
(Btu/kWh)
12,306
8,656
8,875
9,548
10,456
12,306
11,719
10,297
10,016
10,104
8,000
6,000
4,000
2,000
0
0
50
150
AVERAGE HEATRATE
INPUT-OUTPUT CURVE
14,000
1,600,000
1,400,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
100
OUTPUT (MW)
1,200,000
1,000,000
800,000
600,000
400,000
200,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
0
50
100
OUTPUT (MW)
150
0
50
SUMMARY HEAT RATE DATA
100
OUTPUT (MW)
150
INCREMENTAL HEATRATE
UNIT: SOUTH BAY 2
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
BLOCK 1 20%
BLOCK 2 25%
BLOCK 3 50%
BLOCK 4 80%
BLOCK 5 100%
30
38
75
120
150
353,970
426,322
758,025
1,175,520
1,465,200
(Btu/kWh)
(Btu/kWh)
11,799
9,044
8,965
9,278
9,656
11,799
11,219
10,107
9,796
9,768
HEATRATE (Btu/kWh)
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
150
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
12,000
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
50
10,000
8,000
6,000
4,000
2,000
0
0
50
100
OUTPUT (MW)
150
0
50
100
150
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-30
SUMMARY HEAT RATE DATA
INCREMENTAL HEATRATE
14,000
10,000
Input-Output Incremental Average
OUTPUT
Curve
Heat Rate Heat Rate
(%) (MW) (1000 Btu/hr) (Btu/kWh) (Btu/kWh)
BLOCK 1
17%
BLOCK 2
25%
BLOCK 3
50%
BLOCK 4
80%
BLOCK 5 100%
30
44
88
140
175
HEATRATE (Btu/kWh)
12,000
UNIT: SOUTH BAY 3
374,430
497,350
895,038
1,394,400
1,747,200
12,481
8,940
9,090
9,512
10,080
12,481
11,368
10,229
9,960
9,984
8,000
6,000
4,000
2,000
0
0
50
150
200
AVERAGE HEATRATE
1,800,000
14,000
1,600,000
12,000
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
INPUT-OUTPUT CURVE
100
OUTPUT (MW)
1,400,000
1,200,000
10,000
1,000,000
800,000
600,000
400,000
200,000
0
8,000
6,000
4,000
2,000
0
0
50
100
OUTPUT (MW)
150
0
200
50
SUMMARY HEAT RATE DATA
100
OUTPUT (MW)
150
200
INCREMENTAL HEATRATE
UNIT: SOUTH BAY 4
Input-Output Incremental Average
Curve
Heat Rate Heat Rate
OUTPUT
(%) (MW) (1000 Btu/hr)
(Btu/kWh)
(Btu/kWh)
BLOCK 1
30%
45
618,615
13,747
13,747
BLOCK 2
50%
75
937,500
10,630
12,500
BLOCK 3
80% 120
1,430,520
10,956
11,921
BLOCK 4 100% 150
1,773,300
11,426
11,822
Note: Only 4 blocks because minimum block > 25% block.
HEATRATE (Btu/kWh)
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
0
100
150
OUTPUT (MW)
INPUT-OUTPUT CURVE
AVERAGE HEATRATE
14,000
1,800,000
1,600,000
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
HEATRATE (Btu/kWh)
INPUT (1000 Btu/hr)
50
12,000
10,000
8,000
6,000
4,000
2,000
0
0
50
100
OUTPUT (MW)
150
0
50
100
150
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE A-31
APPENDIX B
DATA FOR HEAT RATE EQUATIONS
This Appendix describes my method for developing the heat rate equations, as well as providing the
parameters that define these equations. The heat rate curves are:
•
•
•
Input-Output Curve
Incremental Heat Rate Curve
Average Heat Rate Curve
Input-Output Curve
The Input-Output Curve is typically defined by the third order equation:
y = ax3 + bx2+ cx + d
Where: x = Output in MW
y = Input in Btu/hr
a-d = coefficients that define the equation
Incremental Heat Rate Curve
The Incremental Heat Rate (IHR) is defined as the first derivative of the Input-Output Curve:
IHR = dy/dx = 3ax2 + 2bx + c
Average Heat Rate Curve
The Average Heat Rate (AHR) is defined as the Input-Output Curve divided by the output (x).
AHR = y/x = (ax3 + bx2 + cx + d) / x
The complete step-by-step process of constructing these heat rate curves is as follows. Enter the block
heat rate data of Appendix A into an Excel spreadsheet, as is shown in Table B-1 for the illustrative case
of Moss Landing 7. “I/O Curve” is the input-output block data. “IHR” is the Incremental Heat Rate
block data. “AHR” is the Average Heat Rate block data. Actually, only the I/O curve data is necessary
for this process -- the rest of the data is provided herein for completeness.
HR-DESC.DOC; 4/17/98; PAGE B-1
TABLE B-1: ELFIN HEAT RATE DATA FOR MOSS LANDING 7.
OUTPUT
I/O
IHR
AHR
CURVE
(%)
(MW)
(Btu/hr)
(Btu/kWh)
(Btu/kWh)
1 6.8%
50
997,950
19,959
19,959
2 25.0%
185
1,966,735
7,176
10,631
3 50.1%
370
3,429,160
7,905
9,268
4 80.0%
591
5,296,542
8,450
8,962
5 100.0%
739
6,589,663
8,737
8,917
Using the I/O Curve (Btu/hr) and Output (MW) data of Table B-1, prepare an Excel graph as shown in
Figure B-1.
MOSS LANDING 7 I/O CURVE
INPUT (1000Btu/hr)
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
0
200
400
600
800
OUTPUT(MW)
Figure B-1
Next, use the Excel feature of “insert trendline” to identify a third order equation to fit the data points -and select the option that prints the equation on the graph, as shown in Figure B-2.
HR-DESC.DOC; 4/17/98; PAGE B-2
MOSS LANDING 7 I/O CURVE
INPUT (1000Btu/hr)
y = -0.0013x3 + 2.955x2 + 6561.2x + 662025
7,000,000
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
0
0
200
400
600
800
OUTPUT(MW)
Figure B-2
Copy the coefficients, a - d, into the above equations. These equations along with the values of X1 and X2
define the curves. For Moss Landing 7:
a = -0.0013
b = 2.955
c = 6561.2
d = 662,025
x1 = 50 MW
x2 = 739 MW
Using these coefficients, the Input-Output (I/O), Incremental Heat Rate (IHR) and Average Heat Rate
(AHR) Curves can be developed, as follows:
I/O = y= ax3 + bx2+ cx + d = -0.0013x3 + 2.955x2 + 6561.2x + 662025
IHR = dy/dx = 3ax2 + 2bx + c = -0.0039x3 + 5.91x2 + 6561.2
AHR = y/x = (ax3 + bx2 + cx + d) / x = (-0.0013x3 + 2.955x2 + 6561.2x + 662025) /x
Table B-2 summarizes the coefficients (a - d) and the minimum (x1) and maximum (x2) output values for
each of the IOU units. Note that these curves can never fit the I/O data of Appendix A exactly, so that
the I/O equation points – as well as the other heat rate equation points – will never match the original
data exactly. But they will be close enough for all practical purposes.
HR-DESC.DOC; 4/17/98; PAGE B-3
TABLE B-2: SUMMARY HEAT RATE DATA
a
COEFICIENTS
b
c
PG&E UNITS
Contra Costa 6
Contra Costa 7
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 3
Morro Bay 4
Moss Landing 6
Moss Landing 7
Pittsburg 1&2
Pittsburg 3&4
Pittsburg 5
Pittsburg 6
Pittsburg 7
Potrero 3
0.0148 -6.0775
0.0099 -2.9176
0.2946 -30.3370
0.0116 12.9790
0.0144 21.0770
0.0010
1.3752
0.0049 -1.1685
0.0006 -0.1178
0.0004
1.0588
-0.0021
3.6945
-0.0013
2.9550
0.0148 -5.3036
0.0300 -12.1140
-0.0001
1.3632
0.0056 -0.0515
0.0023 -1.8450
0.0468 -11.9850
SCE UNITS
Alamitos 1&2
Alamitos 3&4
Alamitos 5&6
Cool Water 1
Cool Water 2
Cool Water 3&4
El Segundo 1&2
El Segundo 3&4
Etiwanda 1&2
Etiwanda 3&4
Highgrove 1&2
Highgrove 3&4
Huntington 1&2
Long Beach 8&9
Mandaly 1&2
Ormond Beach 1
Ormond Beach 2
Redondo 5&6
Redondo 7&8
San Bernardino 1&2
0.0018
0.0005
-0.0006
0.0293
0.0203
0.0035
0.0010
0.0004
0.0053
0.0005
0.0004
-0.0086
0.0011
0.0004
0.0022
0.0006
0.0005
0.0007
0.0002
-0.0099
0.0806
0.0597
0.0349
0.0048
0.0049
0.0386
0.0147
0.0162
0.0182
SDG&E UNITS
Encina 1
Encina 2
Encina 3
Encina 4
Encina 5
South Bay 1
South Bay 2
South Bay 3
South Bay 4
d
OUTPUT (MW)
MIN
MAX
9356.2
8746.7
11330.0
9870.6
9080.0
8659.0
9498.3
9063.6
8559.2
6598.2
6561.2
9610.6
10551.0
8752.4
8550.1
8951.1
9908.0
180,146
223,144
99,926
115,531
117,483
205,948
200,714
190,385
194,590
657,281
662,025
293,691
219,614
218,209
266,012
632,496
70,409
46
46
10
10
10
62
62
46
46
50
50
62
62
46
46
120
47
340
340
105
107
107
326
326
338
338
739
739
326
326
325
325
720
207
0.8174
0.4401
2.2408
6.1850
3.2256
-1.4482
0.7726
0.4377
1.7528
0.4642
0.8061
5.6470
0.6180
-0.0512
0.8052
0.3588
0.4250
0.6815
0.2479
7.9479
9018.2
8338.1
6843.4
8979.5
9148.4
7206.1
9129.0
8294.0
9044.1
8328.1
8392.3
7715.1
8411.7
9600.9
8238.8
7773.3
8043.1
8910.0
8345.6
8260.7
397,249
677,108
1,000,000
48,471
56,315
993,648
373,847
652,689
315,310
585,227
327,238
588,318
326,693
210,025
301,952
737,960
590,522
453,856
727,238
267,439
20
40
260
17
19
140
20
40
20
40
8
10
40
70
40
250
50
20
260
14
350
640
960
65
81
512
360
670
264
640
66
89
430
560
430
750
750
350
960
126
-0.0003
0.0023
0.0034
0.0010
0.0010
0.0094
-0.0041
0.0004
-0.0052
8949.0
9535.0
9780.0
9437.0
8975.0
8528.0
8850.0
8873.0
10430.0
86,430
66,030
62,840
164,700
193,100
112,300
88,070
107,800
147,600
20
20
20
20
20
30
30
30
45
107
104
110
300
330
143
150
175
150
HR-DESC.DOC; 4/17/98; PAGE B-4
APPENDIX C
INCREMENTAL HEAT RATE ERRORS
This Appendix shows the method used to quantify the magnitude of the errors caused by using the
Average Incremental Heat Rate block data of modeling in place of the Incremental Heat Rate data used
in the actual dispatch of the generation system.
I evaluated only the block data end points assuming that the maximum errors would occur at these points.
The Actual heat rates (Instantaneous Incremental Heat Rates) were developed using the heat rate curve
data from Appendix B. It might appear that the Block heat rates (Average Incremental Heat Rates) could
be taken directly from Appendix A. But since equations had to be developed for the Instantaneous Heat
Rate values, I used those same equations to develop the Block heat rates in order to make the two
quantities more comparable. The differences are small but it does make the data appear more reasonable.
INSTANTANEOUS INCREMENTAL HEAT RATES - ACTUAL DATA
The Instantaneous Incremental Heat Rates are developed from the basic Input-Output Curve, which is
typically defined by the third order equation:
y = ax3 + bx2+ cx + d
Where: x = Output in MW
y = Input in Btu/hr
a-d = The coefficients that define the equation
The Instantaneous Incremental Heat Rate (IIHR) is defined as the first derivative of the Input-Output
Curve:
IIHR = dy/dx = 3ax2 + 2bx + c
AVERAGE INCREMENTAL HEAT RATE - BLOCK DATA
The Average Incremental Heat Rates (AIHR) can also be calculated using the Input-Output Curve. The
calculation consists of dividing the incremental Input-Output value (Btu/hr) by the corresponding
increment of output (MW).
AIHR = (y2 - y1)/ (x2-x1)
= [(ax23 + bx22 + cx2 + d) - (ax13 + bx12 + cx1 + d)] / (x2-x1)
= [a(x23- x13) + b(x22- x12) + c(x2 - x1)]/ (x2 - x1)
= a(x22 + x2 x1 + x12) + b(x2 + x1) + c
HR-DESC.DOC; 4/17/98; PAGE C-1
Where: x1 = Minimum Output of Block
x2 = Maximum Output of Block
ILLUSTRATIVE EXAMPLE
The complete step-by-step process of constructing this heat rate data is done using the first block of
Moss Landing 7. The coefficients (a-d) and the x1 and x2 values for Moss Landing 7 are taken from Table
B-2 in Appendix B:
a = -0.0013
b = 2.955
c = 6561.2
d = 662025
x1 = 50 MW
x2 =185 MW
Instantaneous Incremental Heat Rates
IIHR = 3a x12 + 2bx1 + c
IIHR(50) = 3(-0.0013)502 + 2(2.955)50 + 6561.2 = 6847.95 = 6847
IIHR(185) = 3(-0.0013)1852 + 2(2.955)185 + 6561.2 = 6847.95 = 7521
Average Incremental Heat Rates
AIHR = a(x22 + x2 x1 + x12) + b(x2 + x1) + c
= -0.0013(1852 + 185x50 + 502) + 2.955(185 + 50) + 6561.2 = 7195.86 =7196
Errors
Error = (AIHR - IIHR) / IIHR
Error (50) = (7196 - 6847) / 6847 = 5.1%
Error (185) = (7196 - 7521) / 7521 = -4.3%
Using AIHR for estimating IIHR causes results in a values that is 5.1 percent too high at 50 MW and 4.3 percent too low at 185 MW.
The corresponding errors between IIHR and AIHR are calculated for the 50 and 185 MW points.
Table C-1 shows the results of similar calculations for PG&E. Tables C-2 and C-3 show the resulting
values for SCE and SDG&E, respectively. The columns delineated as “ACTUAL” are the Instantaneous
Heat Rate (IIHR) values, and the columns delineated as “BLOCKS” are the Average Incremental Heat
Rate (AIHR) values. The “ERROR” column is calculated as the percent difference between these two
values relative to the “ACTUAL” value. Table C-4 summarizes the percent errors of Tables C-1 through
C-3 and sorts them from high to low. This is the data that provides the maximum error numbers in Table
3 of the main report. The errors range from 6.9 to -8.6 percent but most are a few percent or less.
HR-DESC.DOC; 4/17/98; PAGE C-2
TABLE C-1: INCREMENTAL HEAT RATE ERRORS
PG&E UNITS
PLT
Name
Blk
#
con6
con6
con6
con6
con6
1
2
3
4
5
INCREMENTAL HEAT RATES
CAPACITY COEFICIENTS ACTUAL BLOCKS ERROR
(%) (MW)
(Btu/kWh) (Btu/kWh)
(%)
a = 0.0148
14%
46
b = -6.0775
8,891
8,756
-1.5%
25%
85
c = 9356.2
8,644
8,756
1.3%
50% 170
d = 180146
8,573
8,555
-0.2%
80% 272 X1 = 46
9,335
8,877
-4.9%
100% 340 X2 = 340
10,356
9,811
-5.3%
mos6
mos6
mos6
mos6
mos6
1
2
3
4
5
INCREMENTAL HEAT RATES
CAPACITY COEFICIENTS ACTUAL BLOCKS ERROR
(%) (MW)
(Btu/kWh) (Btu/kWh)
(%)
a = -0.0021
7%
50 b = 3.6945
6,952
7,370
6.0%
25% 185 c = 6598.2
7,750
7,370
-4.9%
50% 370 d = 657281
8,470
8,146
-3.8%
80% 591 X1 = 50
8,765
8,668
-1.1%
100% 739 X2 = 739
8,618
8,714
1.1%
con7
con7
con7
con7
con7
1
2
3
4
5
14%
25%
50%
80%
100%
46
85
170
272
340
a=
b=
c=
d=
X1 =
X2 =
0.0099
-2.9176
8746.7
223144
46
340
8,541
8,465
8,613
9,357
10,196
8,496
8,496
8,503
8,933
9,754
-0.5%
0.4%
-1.3%
-4.5%
-4.3%
mos7
mos7
mos7
mos7
mos7
1
2
3
4
5
7%
25%
50%
80%
100%
a=
50 b =
185 c =
370 d =
591 X1 =
739 X2 =
-0.0013
2.955
6561.2
662025
50
739
6,847
7,521
8,214
8,692
8,799
7,196
7,196
7,890
8,485
8,760
5.1%
-4.3%
-3.9%
-2.4%
-0.4%
hmb1&2
hmb1&2
hmb1&2
hmb1&2
hmb1&2
1
2
3
4
5
10%
25%
50%
80%
100%
10
26
53
84
105
a=
b=
c=
d=
X1 =
X2 =
0.2946
-30.337
11330
99926
10
105
10,812
10,350
10,597
12,469
14,703
10,543
10,543
10,366
11,392
13,521
-2.5%
1.9%
-2.2%
-8.6%
-8.0%
pit1&2
pit1&2
pit1&2
pit1&2
pit1&2
1
2
3
4
5
19%
25%
50%
80%
100%
a=
62 b =
82 c =
164 d =
260 X1 =
326 X2 =
0.0148
-5.3036
9610.6
293691
62
326
9,124
9,039
9,065
9,854
10,871
9,079
9,079
9,003
9,391
10,331
-0.5%
0.4%
-0.7%
-4.7%
-5.0%
hnp2
hnp2
hnp2
hnp2
hnp2
1
2
3
4
5
9%
25%
50%
80%
100%
10
27
54
86
107
a=
b=
c=
d=
X1 =
X2 =
0.0116
12.979
9870.6
115531
10
107
10,134
10,597
11,374
12,360
13,047
10,364
10,364
10,981
11,861
12,701
2.3%
-2.2%
-3.5%
-4.0%
-2.6%
pit3&4
pit3&4
pit3&4
pit3&4
pit3&4
1
2
3
4
5
19%
25%
50%
80%
100%
a=
62 b =
82 c =
164 d =
260 X1 =
326 X2 =
0.03
-12.114
10551
219614
62
326
9,395
9,169
8,998
10,336
12,218
9,276
9,276
8,983
9,529
11,211
-1.3%
1.2%
-0.2%
-7.8%
-8.2%
hnp3
hnp3
hnp3
hnp3
hnp3
1
2
3
4
5
9%
25%
50%
80%
100%
10
27
54
86
107
a=
b=
c=
d=
X1 =
X2 =
0.0144
21.077
9080
117483
10
107
9,506
10,250
11,482
13,025
14,085
9,876
9,876
10,861
12,246
13,552
3.9%
-3.6%
-5.4%
-6.0%
-3.8%
pit5
pit5
pit5
pit5
pit5
1
2
3
4
5
14%
25%
50%
80%
100%
a=
46 b =
81 c =
163 d =
260 X1 =
325 X2 =
-0.0001
1.3632
8572.4
218209
46
325
8,697
8,791
9,009
9,261
9,427
8,744
8,744
8,900
9,135
9,344
0.5%
-0.5%
-1.2%
-1.4%
-0.9%
hnp4
hnp4
hnp4
hnp4
hnp4
1
2
3
4
5
19%
25%
50%
80%
100%
62
82
164
260
326
a=
b=
c=
d=
X1 =
X2 =
0.001
1.3752
8659
205948
62
326
8,841
8,905
9,191
9,577
9,874
8,873
8,873
9,044
9,379
9,724
0.4%
-0.4%
-1.6%
-2.1%
-1.5%
pit6
pit6
pit6
pit6
pit6
1
2
3
4
5
14%
25%
50%
80%
100%
a=
46 b =
81 c =
163 d =
260 X1 =
325 X2 =
0.0056
-0.0515
8550.1
266012
46
325
8,581
8,652
8,980
9,659
10,291
8,613
8,613
8,797
9,293
9,963
-0.1%
-1.0%
-1.8%
-3.9%
-3.1%
mor1&2
mor1&2
mor1&2
mor1&2
mor1&2
1
2
3
4
5
19%
25%
50%
80%
100%
62
82
164
260
326
a=
b=
c=
d=
X1 =
X2 =
0.0049
-1.1685
9498.3
200714
62
326
9,410
9,406
9,510
9,884
10,299
9,407
9,407
9,441
9,675
10,081
0.0%
0.0%
-0.7%
-2.1%
-2.1%
pit7
pit7
pit7
pit7
pit7
1
2
3
4
5
17%
25%
50%
80%
100%
a=
120 b =
180 c =
360 d =
576 X1 =
720 X2 =
0.0023
-1.845
8951.1
632496
120
720
8,608
8,510
8,517
9,115
9,871
8,555
8,555
8,476
8,762
9,469
-0.6%
0.5%
-0.5%
-3.9%
-4.1%
mor3
mor3
mor3
mor3
mor3
1
2
3
4
5
14%
25%
50%
80%
100%
46
85
169
270
338
a=
b=
c=
d=
X1 =
X2 =
0.0006
-0.1178
9063.6
190385
46
338
9,057
9,057
9,075
9,131
9,190
9,056
9,056
9,064
9,100
9,159
0.0%
0.0%
-0.1%
-0.3%
-0.3%
pot3
pot3
pot3
pot3
pot3
1
2
3
4
5
23%
25%
50%
80%
100%
a=
47 b =
52 c =
104 d =
166 X1 =
207 X2 =
0.0468
-11.985
9908
70409
47
207
9,092
9,041
8,934
9,798
10,962
9,066
9,066
8,924
9,276
10,341
-0.3%
0.3%
-0.1%
-5.3%
-5.7%
mor4
mor4
mor4
mor4
mor4
1
2
3
4
5
14%
25%
50%
80%
100%
46
85
169
270
338
a=
b=
c=
d=
X1 =
X2 =
0.0004
1.0588
8559.2
194590
46
338
8,659
8,748
8,951
9,218
9,412
8,703
8,703
8,848
9,083
9,314
0.5%
-0.5%
-1.2%
-1.5%
-1.0%
PLT
Blk
Name #
HR-DESC.DOC; 4/17/98; PAGE C-3
TABLE C-2: INCREMENTAL HEAT RATE ERRORS
SCE UNITS
PLT
Name
Blk
#
ala1&2
ala1&2
ala1&2
ala1&2
ala1&2
1
2
3
4
5
ala3&4
ala3&4
ala3&4
ala3&4
ala3&4
1
2
3
4
5
ala5&6
ala5&6
ala5&6
ala5&6
ala5&6
1
2
3
4
5
cw01
cw01
cw01
cw01
cw01
1
2
3
4
5
cw02
cw02
cw02
cw02
cw02
1
2
3
4
5
cw34
cw34
cw34
cw34
cw34
1
2
3
4
5
els1&2
els1&2
els1&2
els1&2
els1&2
1
2
3
4
5
els3&4
els3&4
els3&4
els3&4
els3&4
1
2
3
4
5
eti1&2
eti1&2
eti1&2
eti1&2
eti1&2
1
2
3
4
5
eti3&4
eti3&4
eti3&4
eti3&4
eti3&4
1
2
3
4
5
INCREMENTAL HEAT RATES
CAPACITY COEFICIENTS ACTUAL BLOCKS ERROR
(%) (MW)
(Btu/kWh) (Btu/kWh)
(%)
a = 0.0018
6%
20 b = 0.8174
9,053
9,127
0.8%
26%
90 c = 9018.2
9,209
9,127
-0.9%
51% 180 d = 397249
9,487
9,341
-1.5%
77% 270 X1 = 20
9,853
9,663
-1.9%
100% 350 X2 = 350
10,252
10,047
-2.0%
a = 0.0005
6%
40 b = 0.4401
8,376
8,443
0.8%
25% 160 c = 8338.1
8,517
8,443
-0.9%
50% 320 d = 677108
8,773
8,639
-1.5%
75% 480 X1 = 40
9,106
8,933
-1.9%
100% 640 X2 = 640
9,516
9,305
-2.2%
a = -0.0006
27% 260 b = 2.2408
7,887
8,155
3.4%
44% 420 c = 6843.4
8,408
8,155
-3.0%
63% 600 d = 1.00E+06
8,884
8,656
-2.6%
81% 780 X1 = 260
9,244
9,074
-1.8%
100% 960 X2 = 960
9,487
9,375
-1.2%
a = 0.0293
26%
17 b = 6.185
9,215
9,320
1.1%
46%
30 c = 8979.5
9,430
9,320
-1.2%
66%
43 d = 48471
9,674
9,549
-1.3%
86%
56 X1 = 17
9,948
9,808
-1.4%
100%
65 X2 = 65
10,155
10,050
-1.0%
a = 0.0203
23%
19 b = 3.2256
9,293
9,368
0.8%
43%
35 c = 9148.4
9,449
9,368
-0.9%
63%
51 d = 56315
9,636
9,540
-1.0%
83%
67 X1 = 19
9,854
9,742
-1.1%
100%
81 X2 = 81
10,071
9,960
-1.1%
a = 0.0035
27% 140 b = -1.4482
7,006
7,013
0.1%
35% 180 c = 7206.1
7,025
7,013
-0.2%
47% 240 d = 993648
7,116
7,064
-0.7%
74% 380 X1 =
140
7,622
7,334
-3.8%
100% 512 X2 =
512
8,476
8,018
-5.4%
a = 0.0010
6%
20 b = 0.7726
9,161
9,224
0.7%
26%
90 c = 9129.0
9,292
9,224
-0.7%
51% 180 d = 373847
9,504
9,394
-1.2%
77% 270 X1 = 20
9,765
9,631
-1.4%
100% 350 X2 = 360
10,037
9,898
-1.4%
a=
0.0004
6%
40 b =
0.4377
8,331
8,395
0.8%
24% 160 c =
8294.0
8,465
8,395
-0.8%
48% 320 d =
652689
8,697
8,576
-1.4%
72% 480 X1 =
40
8,991
8,839
-1.7%
100% 670 X2 =
670
9,419
9,198
-2.4%
a = 0.0053
8%
20 b = 1.7528
9,121
9,264
1.6%
30%
80 c = 9044.1
9,426
9,264
-1.7%
53% 140 d = 315310
9,847
9,627
-2.2%
76% 200 X1 = 20
10,381
10,104
-2.7%
100% 264 X2 = 264
11,078
10,719
-3.2%
a = 0.0005
6%
40 b = 0.4642
8,368
8,438
0.8%
25% 160 c = 8328.1
8,515
8,438
-0.9%
50% 320 d = 585227
8,779
8,641
-1.6%
75% 480 X1 = 40
9,119
8,943
-1.9%
100% 640 X2 = 640
9,537
9,322
-2.3%
PLT
Name
Blk
#
hig1&2
hig1&2
hig1&2
hig1&2
hig1&2
1
2
3
4
5
hig3&4
hig3&4
hig3&4
hig3&4
hig3&4
1
2
3
4
5
hun1&2
hun1&2
hun1&2
hun1&2
hun1&2
1
2
3
4
5
lbc8&9
lbc8&9
lbc8&9
lbc8&9
lbc8&9
1
2
3
4
5
man1&2
man1&2
man1&2
man1&2
man1&2
1
2
3
4
5
orb1
orb1
orb1
orb1
orb1
1
2
3
4
5
orb2
orb2
orb2
orb2
orb2
1
2
3
4
5
red5&6
red5&6
red5&6
red5&6
red5&6
1
2
3
4
5
red7&8
red7&8
red7&8
red7&8
red7&8
1
2
3
4
5
sbr1&2
sbr1&2
sbr1&2
sbr1&2
sbr1&2
1
2
3
4
5
INCREMENTAL HEAT RATES
CAPACITYCOEFICIENTS ACTUAL BLOCKS ERROR
(%) (MW)
(Btu/kWh) (Btu/kWh)
(%)
a = 0.0004
12%
8 b = 0.8061
8,405
8,413
0.1%
27%
18 c = 8392.3
8,422
8,413
-0.1%
58%
38 d = 327238
8,455
8,438
-0.2%
85%
56 X1 = 8
8,486
8,471
-0.2%
100%
66 X2 = 66
8,504
8,495
-0.1%
a = -0.0086
11%
10 b = 5.647
7,825
7,899
0.9%
27%
24 c = 7715.1
7,971
7,899
-0.9%
56%
50 d = 588318
8,215
8,096
-1.4%
90%
80 X1 = 10
8,454
8,338
-1.4%
100%
89 X2 = 89
8,516
8,485
-0.4%
a= 0.0011
9%
40 b = 0.618
8,466
8,552
1.0%
33% 140 c = 8411.7
8,649
8,552
-1.1%
56% 240 d = 326693
8,898
8,768
-1.5%
79% 340 X1 = 40
9,213
9,050
-1.8%
100% 430 X2 = 430
9,553
9,379
-1.8%
a= 0.0004
11%
70 b = -0.0512
9,600
9,608
0.1%
33% 180 c = 9600.9
9,621
9,608
-0.1%
56% 300 d = 210025
9,678
9,647
-0.3%
78% 410 X1 = 70
9,761
9,717
-0.4%
100% 560 X2 = 560
9,920
9,836
-0.8%
a = 0.0022
9%
40 b = 0.8052
8,314
8,443
1.6%
33% 140 c = 8238.8
8,594
8,443
-1.8%
56% 245 d = 301952
9,030
8,799
-2.5%
79% 340 X1 = 40
9,549
9,279
-2.8%
100% 430 X2 = 430
10,152
9,842
-3.1%
a = 0.0006
33% 250 b = 0.3588
8,065
8,171
1.3%
49% 370 c = 7773.3
8,285
8,171
-1.4%
67% 500 d = 737960
8,582
8,429
-1.8%
83% 620 X1 = 250
8,910
8,742
-1.9%
100% 750 X2 = 750
9,324
9,112
-2.3%
a = 0.0005
7%
50 b = 0.4250
8,089
8,192
1.3%
30% 225 c = 8043.1
8,310
8,192
-1.4%
53% 400 d = 590522
8,623
8,459
-1.9%
77% 575 X1 = 50
9,028
8,818
-2.3%
100% 750 X2 = 750
9,524
9,268
-2.7%
a = 0.0007
6%
20 b = 0.6815
8,938
8,992
0.6%
26%
90 c = 8910
9,050
8,992
-0.6%
51% 180 d = 453856
9,223
9,134
-1.0%
77% 270 X1 = 20
9,431
9,324
-1.1%
100% 350 X2 = 350
9,644
9,535
-1.1%
a = 0.0002
27% 260 b = 0.2479
8,515
8,557
0.5%
38% 360 c = 8345.6
8,602
8,557
-0.5%
69% 660 d = 727238
8,934
8,759
-2.0%
83% 800 X1 = 260
9,126
9,028
-1.1%
100% 960 X2 = 960
9,375
9,248
-1.4%
a = -0.0099
11%
14 b = 7.9479
8,477
8,681
2.4%
33%
42 c = 8260.7
8,876
8,681
-2.2%
56%
70 d = 267439
9,228
9,056
-1.9%
78%
98 X1 = 14
9,533
9,384
-1.6%
100% 126 X2 = 126
9,792
9,667
-1.3%
HR-DESC.DOC; 4/17/98; PAGE C-4
TABLE C-3: INCREMENTAL HEAT RATE ERRORS
SDG&E UNITS
PLT
Name
Blk
#
CAPACITY
(%)
(MW)
COEFICIENTS
INCREMENTAL HEAT RATES
ACTUAL BLOCKS ERROR
(Btu/kWh) (Btu/kWh)
(%)
enc1
enc1
enc1
enc1
enc1
1 18.7%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
20
27
54
86
107
a=
b=
c=
d=
X1 =
X2 =
0.0806
-0.0003
8949.0
86,430
20
107
9,046
9,122
9,641
10,722
11,719
9,082
9,082
9,353
10,140
11,202
0.40%
-0.44%
-2.99%
-5.42%
-4.41%
enc2
enc2
enc2
enc2
enc2
1 19.2%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
20
26
52
83
104
a=
b=
c=
d=
X1 =
X2 =
0.0597
0.0023
9535.0
66,030
20
104
9,607
9,656
10,020
10,775
11,473
9,630
9,630
9,818
10,368
11,111
0.25%
-0.27%
-2.01%
-3.78%
-3.15%
enc3
enc3
enc3
enc3
enc3
1 18.2%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
20
28
55
88
110
a=
b=
c=
d=
X1 =
X2 =
0.0349
0.0034
9780.0
62,840
20
110
9,822
9,859
10,097
10,590
11,046
9,840
9,840
9,965
10,325
10,810
0.18%
-0.20%
-1.31%
-2.51%
-2.14%
enc4
enc4
enc4
enc4
enc4
1
6.7%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
20
75
150
240
300
a=
b=
c=
d=
X1 =
X2 =
0.0048
0.0010
9437.0
164,700
20
300
9,443
9,518
9,759
10,261
10,724
9,473
9,473
9,625
9,991
10,484
0.32%
-0.47%
-1.37%
-2.63%
-2.24%
enc5
enc5
enc5
enc5
enc5
1
6.1%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
20
83
165
264
330
a=
b=
c=
d=
X1 =
X2 =
0.0049
0.0010
8975.0
193,100
20
330
8,981
9,075
9,373
9,994
10,567
9,018
9,018
9,207
9,660
10,270
0.42%
-0.62%
-1.77%
-3.34%
-2.81%
sba1
sba1
sba1
sba1
sba1
1 21.0%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
30
36
72
114
143
a=
b=
c=
d=
X1 =
X2 =
0.0386
0.0094
8528.0
112,300
30
143
8,633
8,677
9,121
10,046
10,899
8,654
8,654
8,874
9,548
10,456
0.25%
-0.26%
-2.71%
-4.95%
-4.06%
sba2
sba2
sba2
sba2
sba2
1 20.0%
2 25.0%
3 50.0%
4 80.0%
5 100.0%
30
38
75
120
150
a=
b=
c=
d=
X1 =
X2 =
0.0147
-0.0041
8850.0
88,070
30
150
8,890
8,912
9,098
9,485
9,843
8,900
8,900
8,995
9,277
9,658
0.12%
-0.13%
-1.14%
-2.20%
-1.88%
sba3
sba3
sba3
sba3
sba3
1 17.1%
2 25.0%
3 50.3%
4 80.1%
5 100.0%
30
44
88
140
175
a=
b=
c=
d=
X1 =
X2 =
0.0162
0.0004
8873.0
107,800
30
175
8,917
8,966
9,244
9,823
10,357
8,940
8,940
9,089
9,511
10,080
0.26%
-0.29%
-1.67%
-3.17%
-2.67%
sba4
sba4
sba4
sba4
1 30.0%
2 50.0%
3 80.0%
5 100.0%
45
75
120
150
10,540
10,736
11,214
11,656
10,630
10,630
10,957
11,427
10,838
0.85%
-0.99%
-2.30%
-1.96%
a=
b=
c=
d=
X1 =
X2 =
0.0182
-0.0052
10430.0
147,600
45
150
HR-DESC.DOC; 4/17/98; PAGE C-5
TABLE C-4: SUMMARY OF INCREMENTAL HEAT RATE ERRORS
----- CONTINUED ----PG&E UNITS
UNIT
ERROR
SCE UNITS
UNIT
ERROR
SDG&E UNITS
PG&E UNITS
UNIT
ERROR UNIT
ERROR
SCE UNITS
UNIT
ERROR
mos6
mos7
hnp3
hnp2
hmb1&2
con6
pit3&4
mos6
pit5
pit7
mor4
pit1&2
con7
hnp4
pot3
mor1&2
mor3
mor3
mor1&2
pot3
mor3
pit6
pit3&4
con6
pot3
mor3
mor3
hnp4
mos7
pit7
pit1&2
mor4
con7
pit5
pit7
pit1&2
mor1&2
pit5
pit6
mor4
mos6
mor4
pit5
pit3&4
con7
pit5
mor4
con6
hnp4
hnp4
ala5&6
sbr1&2
eti1&2
man1&2
orb1
orb2
cw01
hun1&2
hig3&4
eti3&4
ala1&2
cw02
ala3&4
els3&4
els1&2
red5&6
red7&8
hig1&2
cw34
lbc8&9
hig1&2
hig1&2
lbc8&9
cw34
hig1&2
hig1&2
lbc8&9
hig3&4
lbc8&9
red7&8
red5&6
cw34
els1&2
els3&4
lbc8&9
cw02
ala3&4
ala1&2
hig3&4
eti3&4
red5&6
cw02
cw01
red7&8
cw02
hun1&2
red5&6
red5&6
cw02
els1&2
sba4
enc5
enc1
enc4
sba3
sba1
enc2
enc3
sba2
sba2
enc3
sba1
enc2
sba3
enc1
enc4
enc5
sba4
sba2
enc3
enc4
sba3
enc5
sba2
sba4
enc2
enc3
sba2
enc4
sba4
enc3
enc4
sba3
sba1
enc5
enc1
enc2
sba3
enc5
enc2
sba1
enc1
sba1
enc1
cw01
ala5&6
sbr1&2
cw01
red7&8
hig3&4
els1&2
orb1
els1&2
els3&4
cw01
orb2
hig3&4
hun1&2
ala3&4
ala1&2
sbr1&2
eti3&4
els3&4
eti1&2
man1&2
hun1&2
orb1
hun1&2
ala5&6
sbr1&2
orb1
ala3&4
orb2
ala1&2
eti3&4
red7&8
ala1&2
sbr1&2
ala3&4
eti1&2
eti3&4
orb1
orb2
els3&4
man1&2
ala5&6
eti1&2
orb2
man1&2
ala5&6
man1&2
eti1&2
cw34
cw34
6.0%
5.1%
3.9%
2.3%
1.9%
1.3%
1.2%
1.1%
0.5%
0.5%
0.5%
0.4%
0.4%
0.4%
0.3%
0.0%
0.0%
0.0%
0.0%
-0.1%
-0.1%
-0.1%
-0.2%
-0.2%
-0.3%
-0.3%
-0.3%
-0.4%
-0.4%
-0.5%
-0.5%
-0.5%
-0.5%
-0.5%
-0.6%
-0.7%
-0.7%
-0.9%
-1.0%
-1.0%
-1.1%
-1.2%
-1.2%
-1.3%
-1.3%
-1.4%
-1.5%
-1.5%
-1.5%
-1.6%
3.4%
2.4%
1.6%
1.6%
1.3%
1.3%
1.1%
1.0%
0.9%
0.8%
0.8%
0.8%
0.8%
0.8%
0.7%
0.6%
0.5%
0.1%
0.1%
0.1%
-0.1%
-0.1%
-0.1%
-0.2%
-0.2%
-0.2%
-0.3%
-0.4%
-0.4%
-0.5%
-0.6%
-0.7%
-0.7%
-0.8%
-0.8%
-0.9%
-0.9%
-0.9%
-0.9%
-0.9%
-1.0%
-1.0%
-1.0%
-1.1%
-1.1%
-1.1%
-1.1%
-1.1%
-1.1%
-1.2%
0.9%
0.4%
0.4%
0.3%
0.3%
0.2%
0.2%
0.2%
0.1%
-0.1%
-0.2%
-0.3%
-0.3%
-0.3%
-0.4%
-0.5%
-0.6%
-1.0%
-1.1%
-1.3%
-1.4%
-1.7%
-1.8%
-1.9%
-2.0%
-2.0%
-2.1%
-2.2%
-2.2%
-2.3%
-2.5%
-2.6%
-2.7%
-2.7%
-2.8%
-3.0%
-3.2%
-3.2%
-3.3%
-3.8%
-4.1%
-4.4%
-5.0%
-5.4%
pit6
hnp4
mor1&2
mor1&2
hmb1&2
hnp2
mos7
hmb1&2
hnp2
pit6
hnp2
hnp3
hnp3
mos6
pit7
pit6
mos7
hnp2
pit7
mos7
con7
con7
pit1&2
mos6
con6
pit1&2
con6
pot3
hnp3
pot3
hnp3
pit3&4
hmb1&2
pit3&4
hmb1&2
-1.8%
-2.1%
-2.1%
-2.1%
-2.2%
-2.2%
-2.4%
-2.5%
-2.6%
-3.1%
-3.5%
-3.6%
-3.8%
-3.8%
-3.9%
-3.9%
-3.9%
-4.0%
-4.1%
-4.3%
-4.3%
-4.5%
-4.7%
-4.9%
-4.9%
-5.0%
-5.3%
-5.3%
-5.4%
-5.7%
-6.0%
-7.8%
-8.0%
-8.2%
-8.6%
-1.2%
-1.2%
-1.3%
-1.3%
-1.4%
-1.4%
-1.4%
-1.4%
-1.4%
-1.4%
-1.4%
-1.4%
-1.4%
-1.5%
-1.5%
-1.5%
-1.6%
-1.6%
-1.7%
-1.7%
-1.8%
-1.8%
-1.8%
-1.8%
-1.8%
-1.9%
-1.9%
-1.9%
-1.9%
-1.9%
-1.9%
-2.0%
-2.0%
-2.2%
-2.2%
-2.2%
-2.3%
-2.3%
-2.3%
-2.4%
-2.5%
-2.6%
-2.7%
-2.7%
-2.8%
-3.0%
-3.1%
-3.2%
-3.8%
-5.4%
HR-DESC.DOC; 4/17/98; PAGE C-6
APPENDIX D
AVERAGE TO INCREMENTAL HEAT RATE RATIOS
This Appendix provides the detailed description for the calculation of Average Heat Rate (AHR) to
Incremental Heat Rate (IHR) presented in Section VI of the main body of this report. These Ratios, R(x),
are calculated using the equations described in Appendix B and are done for three cases:
•
•
•
The AHR/IHR at minimum generation: R(x1)
The AHR/IHR at maximum generation: R(x2)
The average AHR/IHR: RAVE
The minimum generation ratio, R(x1), and maximum generation ratio, R(x2), are calculated using the
equations for the Average Heat Rate (AHR) and Incremental Heat Rate (IHR) curves for each unit, as
follows.
The Input-Output Curve is defined by the third order equation:
y = ax3 + bx2+ cx + d
Where: x = Output in MW
y = Input in Btu/hr
a-d = The coefficients that define the equation
The Average Heat Rate (AHR) is defined as the Input-Output Curve (y) divided by the output (x):
AHR = y/x = (ax3 + bx2 + cx + d) / x
The Incremental Heat Rate (IHR) is defined as the first derivative of the Input-Output Curve:
IHR = dy/dx = 3ax22 + 2bx + c
The Ratio (R) of Average Heat Rate (AHR) to Incremental Heat Rate (IHR) is therefore:
R = AHR/IHR = (y/x) / dy/dx = [(ax3+bx2+cx+d)/x] / (3ax2+2bx+c)
The minimum and maximum generation values of the R are then developed by setting x equal to the
minimum (x1) and maximum (x2) output capacities of the units.
HR-DESC.DOC; 4/17/98; PAGE D-1
The average value, RAVE, is found by integrating R from the minimum capacity (x1) to the maximum
capacity (x2), and then dividing this result by the difference between the minimum and maximum outputs
(x2 - x1):
RAVE = [ò
ò R dx {from x1
to x2 } ]
/ (x2 - x1)
= [ò
ò AHR/IHR dx {from x1
to x2 } ]
/ (x2 - x1)
Where: x1 = Minimum Operating Level(MW)
x2 = Maximum Operating Level (MW)
The integration of R, (ò
ò R dx), is:
ò R dx =[(x/3) +(d×Ln(x)/c) +(bG/18a) - (dG/2c) + (2cE/3F) - (bdE/cF) - (Eb2/9aF)]
Where: E = ATan((3ax+b)/F)
F = (3ab-x2)1/2
G = Ln(3ax2+2bx+c)
Ln = Natural Log
ATan = Arc Tangent
Moss Landing 7, once again, provides the necessary step-by-step illustration. The above equations can be
evaluated using the values in Table B-2, of Appendix B: the coefficients (a-d) and the x1 and x2 values.
a = -0.0013
b = 2.955
c = 6561.2
d = 662025
x1 = 50 MW
x2 = 739 MW
The R(x) values are now calculated as follows:
•
The AHR/IHR at minimum generation: R(x1)
R(x1) = AHR/IHR = (ax3+bx2+cx+d)/x] / (3ax2+2bx+c): for x1 = 50 MW
R(50) = AHR/IHR = (-0.0013*503+2.955*502+6561.2*50+662025)/50]
/ (3* -0.0013*502+2*2.955*50+662025) = 2.91
•
The AHR/IHR at maximum generation: R(x2)
R(x2)= AHR/IHR = (y/x)/y′= [(ax3+bx2+cx+d)/x] / (3ax2+2bx+c): x2 = 739 MW
R(739) = AHR/IHR = (-0.0013*7393+2.955*7392+6561.2*739+662025)/739]
/ (3* -0.0013*7392+2*2.955*739+662025) = 1.02
HR-DESC.DOC; 4/17/98; PAGE D-2
•
The average AHR/IHR: RAVE
RAVE = [ò
ò R dx {from x1
to x2 } ]
/ (x2 - x1)
The integration of R, (ò
ò R dx), is:
ò R dx =[(x/3) +(d×Ln(x)/c) +(bG/18a) - (dG/2c) + (2cE/3F) - (bdE/cF) - (Eb2/9aF)]
Where: E = ATan((3ax+b)/F)
F = (3ab-x2)1/2
G = Ln(3ax2+2bx+c)
Ln = Natural Log
ATan = Arc Tangent
R(739) = (739/3)+(662025ln(739)/6561.2)+(2.955G/18/-0.0013)-(662025G/2/6561.2)
+(2×6561.2E/3F) -(2.955×662025E/6561.2F)-(2.9552E/9×-0.0013F)
Where: E = ATan((3×-0.0013×739+2.955)/F)
F = (3×-0.0013×2.955-7392)1/2
G = Ln(3×-0.0013×7392+2×2.955×739+6561.2)
R(50) = (50/3)+(662025ln(50)/6561.2)+(2.955G/18/-0.0013)-(662025G/2/6561.2)
+(2×6561.2E/3F) -(2.955×662025E/6561.2F)-(2.9552E/9×-0.0013F)
Where: E = ATan((3×-0.0013×50+2.955)/F)
F = (3×-0.0013×2.955-502)1/2
G = Ln(3×-0.0013×502+2×2.955×50+6561.2)
RAVE = [R(739) - R(50)] / (739 - 50) = 1.26
This is prohibitive to do as a hand calculation and an attempt to use an Excel spreadsheet failed due to
imaginary numbers being part of the solution. This required that Math Lab be used directly.
Table D-2 shows the results of calculating the R(x) values for the IOU units. Table D-2CALCS shows
the calculation of the system average values for each of the R(x) values:
•
•
•
System average R(x1) is weighted by x1.
System average R(x2) is weighted by x2 .
System average RAVE is weighted by x1 - x2.
Table D-3 is the same as Table D-2 except that the data has been sorted by R(x1).The Figure D-1 series
shows this same data graphically.
HR-DESC.DOC; 4/17/98; PAGE D-3
TABLE D-2: SUMMARY OF R(X) VALUES
OUTPUT (MW)
X1
X2
AVERAGE/INCREMENTAL
R(X1)
R(X2)
Rave
PG&E UNITS
Contra Costa 6
Contra Costa 7
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 3
Morro Bay 4
Moss Landing 6
Moss Landing 7
Pittsburg 1&2
Pittsburg 3&4
Pittsburg 5
Pittsburg 6
Pittsburg 7
Potrero 3
Averages
46
46
10
10
10
62
62
46
46
50
50
62
62
46
46
120
47
340
340
105
107
107
326
326
338
338
739
739
326
326
325
325
720
207
1.46
1.58
1.95
2.13
2.21
1.37
1.35
1.46
1.48
2.87
2.91
1.54
1.43
1.54
1.67
1.62
1.20
1.68
0.92
0.94
0.84
0.96
0.89
1.00
1.00
1.05
1.01
1.05
1.02
0.95
0.86
1.03
0.97
0.97
0.89
0.98
1.13
1.14
1.18
1.19
1.16
1.10
1.11
1.14
1.12
1.25
1.26
1.17
1.13
1.14
1.16
1.20
1.05
1.17
SCE UNITS
Alamitos 1&2
Alamitos 3&4
Alamitos 5&6
Cool Water 1
Cool Water 2
Cool Water 3&4
El Segundo 1&2
El Segundo 3&4
Etiwanda 1&2
Etiwanda 3&4
Highgrove 1&2
Highgrove 3&4
Huntington Beach 1&2
Long Beach 8&9
Mandalay 1&2
Ormond Beach 1
Ormond Beach 2
Redondo Beach 5&6
Redondo Beach 7&8
San Bernardino 1&2
Averages
20
40
260
17
19
140
20
40
20
40
8
10
40
70
40
250
50
20
260
14
350
640
960
65
81
512
350
670
264
640
66
89
430
560
430
750
750
350
960
126
3.19
3.02
1.42
1.30
1.31
2.02
3.04
2.96
2.72
2.75
5.87
8.51
1.96
1.31
1.90
1.35
2.46
3.54
1.32
3.24
1.83
1.04
1.04
1.00
1.01
1.02
1.10
1.05
1.03
1.00
1.02
1.58
1.73
1.01
1.02
0.95
1.00
0.99
1.09
1.02
1.15
1.03
1.34
1.33
1.12
1.10
1.11
1.43
1.32
1.31
1.30
1.28
2.41
2.99
1.20
1.08
1.16
1.13
1.23
1.41
1.12
1.54
1.27
SDG&E UNITS
Encina 1
Encina 2
Encina 3
Encina 4
Encina 5
South Bay 1
South Bay 2
South Bay 3
South Bay 4
Averages
20
20
20
20
20
30
30
30
45
107
104
110
300
330
143
150
175
150
1.47
1.34
1.32
1.87
2.07
1.43
1.33
1.40
1.30
1.47
0.91
0.94
0.98
0.97
0.95
0.93
0.99
0.96
1.01
0.96
1.10
1.08
1.09
1.13
1.15
1.10
1.10
1.10
1.12
1.12
HR-DESC.DOC; 4/17/98; PAGE D-4
TABLE D-2CALCS: CALCULATIONS OF R(X) VALUES
X1
PG&E UNITS
Contra Costa 6
Contra Costa 7
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 3
Morro Bay 4
Moss Landing 6
Moss Landing 7
Pittsburg 1&2
Pittsburg 3&4
Pittsburg 5
Pittsburg 6
Pittsburg 7
Potrero 3
Totals/Averages
SCE UNITS
Alamitos 1&2
Alamitos 3&4
Alamitos 5&6
Cool Water 1
Cool Water 2
Cool Water 3&4
El Segundo 1&2
El Segundo 3&4
Etiwanda 1&2
Etiwanda 3&4
Highgrove 1&2
Highgrove 3&4
Huntington Beach 1&2
Long Beach 8&9
Mandalay 1&2
Ormond Beach 1
Ormond Beach 2
Redondo Beach 5&6
Redondo Beach 7&8
San Bernardino 1&2
Totals/Averages
SDG&E UNITS
Encina 1
Encina 2
Encina 3
Encina 4
Encina 5
South Bay 1
South Bay 2
South Bay 3
South Bay 4
Totals/Averages
OUTPUT (MW)
X2
X2-X1
46
46
10
10
10
62
62
46
46
50
50
62
62
46
46
120
47
821
AVERAGE/INCREMENTAL
R(X1)
R(X2)
Rave
X1*R(X1)
WEIGHTED
X2*R(X2) (X2-X1)*Rave
340
340
105
107
107
326
326
338
338
739
739
326
326
325
325
720
207
6,034
294
294
95
97
97
264
264
292
292
689
689
264
264
279
279
600
160
5,213
1.46
1.58
1.95
2.13
2.21
1.37
1.35
1.46
1.48
2.87
2.91
1.54
1.43
1.54
1.67
1.62
1.20
1.68
0.92
0.94
0.84
0.96
0.89
1.00
1.00
1.05
1.01
1.05
1.02
0.95
0.86
1.03
0.97
0.97
0.89
0.98
1.13
1.14
1.18
1.19
1.16
1.10
1.11
1.14
1.12
1.25
1.26
1.17
1.13
1.14
1.16
1.20
1.05
1.17
67.38
72.62
19.47
21.27
22.13
84.64
83.56
67.04
68.20
143.29
145.66
95.65
88.81
70.76
76.89
194.87
56.59
1,378.84
312.90
318.64
88.15
102.29
95.70
325.04
324.58
355.14
342.54
777.84
750.09
310.53
279.21
333.60
314.02
701.06
184.54
5,915.85
331.05
335.53
112.12
115.01
112.14
291.36
293.52
332.86
327.98
863.32
867.86
310.16
297.84
318.42
323.98
719.37
168.72
6,121.23
20
350
40
640
260
960
17
65
19
81
140
512
20
350
40
670
20
264
40
640
8
66
10
89
40
430
70
560
40
430
250
750
50
750
20
350
260
960
14
126
1,378 9,043
330
600
700
48
62
372
330
630
244
600
58
79
390
490
390
500
700
330
700
112
7,665
3.19
3.02
1.42
1.30
1.31
2.02
3.04
2.96
2.72
2.75
5.87
8.51
1.96
1.31
1.90
1.35
2.46
3.54
1.32
3.24
1.83
1.04
1.04
1.00
1.01
1.02
1.10
1.05
1.03
1.00
1.02
1.58
1.73
1.01
1.02
0.95
1.00
0.99
1.09
1.02
1.15
1.03
1.34
1.33
1.12
1.10
1.11
1.43
1.32
1.31
1.30
1.28
2.41
2.99
1.20
1.08
1.16
1.13
1.23
1.41
1.12
1.54
1.27
63.84
120.75
370.26
22.03
24.90
283.13
60.78
118.27
54.49
109.84
46.93
85.11
78.45
91.88
76.13
336.39
122.85
70.75
342.61
45.37
2,524.77
363.93
664.66
959.64
65.62
82.35
563.18
369.00
693.30
263.83
653.94
104.04
154.26
433.93
568.63
410.62
753.21
742.61
382.18
975.45
144.47
9,348.82
441.73
798.01
782.81
53.02
68.80
531.03
436.30
824.97
316.85
767.97
139.63
236.14
466.24
531.22
451.86
566.67
861.31
466.05
783.35
172.40
9,696.34
87
84
90
280
310
113
120
145
105
1.47
1.47
1.34
1.32
1.87
2.07
1.43
1.33
1.40
1.30
1.47
0.91
0.94
0.98
0.97
0.95
0.93
0.99
0.96
1.01
0.96
1.10
1.08
1.09
1.13
1.15
1.10
1.10
1.10
1.12
1.12
97.52
98.04
107.28
291.36
315.13
132.57
148.86
168.69
152.15
95.76
90.64
97.66
317.74
356.79
124.51
132.03
159.63
117.77
20
20
20
20
20
30
30
30
45
107
104
110
300
330
143
150
175
150
29.41
26.77
26.34
37.43
41.49
42.77
39.82
41.99
58.69
HR-DESC.DOC; 4/17/98; PAGE D-5
TABLE D-3: SORTED BY R(X1) VALUES
OUTPUT (MW)
X1
X2
PG&E UNITS
Potrero 3
Morro Bay 1&2
Hunters Point 4
Pittsburg 3&4
Morro Bay 3
Contra Costa 6
Morro Bay 4
Pittsburg 5
Pittsburg 1&2
Contra Costa 7
Pittsburg 7
Pittsburg 6
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Moss Landing 6
Moss Landing 7
Averages
AVERAGE/INCREMENTAL
R(X1)
R(X2)
Rave
ABREV,
pot3
mor1&2
hnp4
pit3&4
mor3
con6
mor4
pit5
pit1&2
con7
pit7
pit6
hmb1&2
hnp2
hnp3
mos6
mos7
47
62
62
62
46
46
46
46
62
46
120
46
10
10
10
50
50
207
326
326
326
338
340
338
325
326
340
720
325
105
107
107
739
739
1.20
1.35
1.37
1.43
1.46
1.46
1.48
1.54
1.54
1.58
1.62
1.67
1.95
2.13
2.21
2.87
2.91
1.68
0.89
1.00
1.00
0.86
1.05
0.92
1.01
1.03
0.95
0.94
0.97
0.97
0.84
0.96
0.89
1.05
1.02
0.98
1.05
1.11
1.10
1.13
1.14
1.13
1.12
1.14
1.17
1.14
1.20
1.16
1.18
1.19
1.16
1.25
1.26
1.17
SCE UNITS
Cool Water 1
Cool Water 2
Long Beach 8&9
Redondo Beach 7&8
Ormond Beach 1
Alamitos 5&6
Mandalay 1&2
Huntington Beach 1&2
Cool Water 3&4
Ormond Beach 2
Etiwanda 1&2
Etiwanda 3&4
El Segundo 3&4
Alamitos 3&4
El Segundo 1&2
Alamitos 1&2
San Bernardino 1&2
Redondo Beach 5&6
Highgrove 1&2
Highgrove 3&4
Averages
cw01
cw02
lb8&9
red7&8
orb1
ala5&6
man1&2
hun1&2
cw34
orb2
eti1&2
eti3&4
els3&4
ala3&4
els1&2
ala1&2
sbr1&2
red5&6
hig1&2
hig3&4
17
19
70
260
250
260
40
40
140
50
20
40
40
40
20
20
14
20
8
10
65
81
560
960
750
960
430
430
512
750
264
640
670
640
350
350
126
350
66
89
1.30
1.31
1.31
1.32
1.35
1.42
1.90
1.96
2.02
2.46
2.72
2.75
2.96
3.02
3.04
3.19
3.24
3.54
5.87
8.51
1.83
1.01
1.02
1.02
1.02
1.00
1.00
0.95
1.01
1.10
0.99
1.00
1.02
1.03
1.04
1.05
1.04
1.15
1.09
1.58
1.73
1.03
1.10
1.11
1.08
1.12
1.13
1.12
1.16
1.20
1.43
1.23
1.30
1.28
1.31
1.33
1.32
1.34
1.54
1.41
2.41
2.99
1.27
SDG&E UNITS
South Bay 4
Encina 3
South Bay 2
Encina 2
South Bay 3
South Bay 1
Encina 1
Encina 4
Encina 5
Averages
sba4
enc3
sba2
enc2
sba3
sba1
enc1
enc4
enc5
45
20
30
20
30
30
20
20
20
150
110
150
104
175
143
107
300
330
1.30
1.32
1.33
1.34
1.40
1.43
1.47
1.87
2.07
1.47
1.01
0.98
0.99
0.94
0.96
0.93
0.91
0.97
0.95
0.96
1.12
1.09
1.10
1.08
1.10
1.10
1.10
1.13
1.15
1.12
HR-DESC.DOC; 4/17/98; PAGE D-6
FIGURE D-1A,B&C (TABLE D-3)
AHR/IHR RATIOS
PG&E UNITS
3.0
AHR/IHR
2.5
R(X1)
Rave
2.0
1.5
1.0
0.5
R(X2)
mos7
mos6
hnp3
hnp2
hmb1&2
pit6
pit7
con7
pit1&2
pit5
mor4
con6
mor3
pit3&4
hnp4
pot3
mor1&2
0.0
PLANT
AHR/IHR RATIOS
SCE UNITS
9.0
8.0
AHR/IHR
7.0
R(X1)
6.0
5.0
4.0
3.0
Rave
2.0
1.0
R(X2)
hig3&4
hig1&2
red5&6
sbr1&2
ala1&2
els1&2
ala3&4
els3&4
eti3&4
eti1&2
orb2
cw34
hun1&2
man1&2
ala5&6
orb1
red7&8
lb8&9
cw02
cw01
0.0
PLANT
AHR/IHR RATIOS
SDG&E UNITS
2.5
R(X1)
AHR/IHR
2.0
Rave
1.5
1.0
R(X2)
0.5
0.0
sba4
enc3
sba2
enc2
sba3
sba1
enc1
enc4
enc5
PLANT
Since AHR/IHR is simply a function of AHR and IHR, it is of interest to see what their relative roles are
in this regard. Looking at R(x1), for example, we see some very large values, which obviously must be
driven by large AHR, small IHR or both. Figures D-2A, B and C show the R values as a function of
HR-DESC.DOC; 4/17/98; PAGE D-7
AHR(x1). Although not entirely consistent, the AHR appears to be a significant driver in setting the high
values of R(x1) -- but not particularly for RAVE or R(x2), with the possible exception of SCE. The data for
Figures D-2 is tabulated in Table D-4.
FIGURE D-2A,B&C (TABLE D-4)
AHR/IHR vs MINIMUM BLOCK AHR
PG&E
3.0
R(X1)
AHR/IHR
2.5
Rave
2.0
1.5
1.0
R(X2)
0.5
21,551
21,165
21,037
19,959
19,959
14,354
14,091
14,050
13,501
13,488
13,384
13,194
13,064
12,834
12,684
12,066
10,951
0.0
MIN BLOCK AHR (Btu/kWh)
AHR/IHR vs MINIMUM BLOCK AHR
SCE
9.0
8.0
R(X1)
AHR/IHR
7.0
6.0
5.0
Rave
4.0
3.0
2.0
1.0
R(X2)
66,603
49,304
31,617
28,899
27,838
27,481
25,283
24,848
24,628
22,980
19,877
16,606
15,735
14,169
12,600
12,181
11,944
11,713
11,220
10,852
0.0
MIN BLOCK AHR (Btu/kWh)
AHR/IHR vs MINIMUM BLOCK AHR
SDG&E
2.50
R(X1)
AHR/IHR
2.00
Rave
1.50
1.00
0.50
0.00
11,799
R(X2)
12,306
12,481
12,860
12,936
13,303
13,747
17,674
18,632
MIN BLOCK AHR (Btu/kWh)
HR-DESC.DOC; 4/17/98; PAGE D-8
TABLE D-4: SORTED BY AHR(X1)
OUTPUT (MW)
X1
X2
AHR
X1
ABREV,
pot3
hnp4
mor1&2
mor4
con6
mor3
pit5
pit3&4
con7
pit7
pit1&2
pit6
mos6
mos7
hnp3
hmb1&2
hnp2
47
62
62
46
46
46
46
62
46
120
62
46
50
50
10
10
10
207
326
326
338
340
338
325
326
340
720
326
325
739
739
107
105
107
10,951
12,066
12,684
12,834
13,064
13,194
13,384
13,488
13,501
14,050
14,091
14,354
19,959
19,959
21,037
21,165
21,551
1.20
1.37
1.35
1.48
1.46
1.46
1.54
1.43
1.58
1.62
1.54
1.67
2.87
2.91
2.21
1.95
2.13
1.68
0.89
1.00
1.00
1.01
0.92
1.05
1.03
0.86
0.94
0.97
0.95
0.97
1.05
1.02
0.89
0.84
0.96
0.98
1.05
1.10
1.11
1.12
1.13
1.14
1.14
1.13
1.14
1.20
1.17
1.16
1.25
1.26
1.16
1.18
1.19
1.17
SCE UNITS
Ormond Beach 1
Redondo Beach 5&6
Alamitos 5&6
Cool Water 1
Cool Water 2
Long Beach 8&9
Cool Water 3&4
Mandalay 1&2
Huntington Beach 1&2
Ormond Beach 2
Etiwanda 3&4
El Segundo 3&4
Etiwanda 1&2
Alamitos 3&4
San Bernardino 1&2
El Segundo 1&2
Alamitos 1&2
Redondo Beach 7&8
Highgrove 1&2
Highgrove 3&4
Averages
orb1
red5&6
ala5&6
cw01
cw02
lb8&9
cw34
man1&2
hun1&2
orb2
eti3&4
els3&4
eti1&2
ala3&4
sbr1&2
els1&2
ala1&2
red7&8
hig1&2
hig3&4
250
20
260
17
19
70
140
40
40
50
40
40
20
40
14
20
20
260
8
10
750
350
960
65
81
560
512
430
430
750
640
670
264
640
126
350
350
960
66
89
10,852
11,220
11,713
11,944
12,181
12,600
14,169
15,735
16,606
19,877
22,980
24,628
24,848
25,283
27,481
27,838
28,899
31,617
49,304
66,603
1.35
3.54
1.42
1.30
1.31
1.31
2.02
1.90
1.96
2.46
2.75
2.96
2.72
3.02
3.24
3.04
3.19
1.32
5.87
8.51
1.83
1.00
1.09
1.00
1.01
1.02
1.02
1.10
0.95
1.01
0.99
1.02
1.03
1.00
1.04
1.15
1.05
1.04
1.02
1.58
1.73
1.03
1.13
1.41
1.12
1.10
1.11
1.08
1.43
1.16
1.20
1.23
1.28
1.31
1.30
1.33
1.54
1.32
1.34
1.12
2.41
2.99
1.27
SDG&E UNITS
South Bay 2
South Bay 1
South Bay 3
Encina 2
Encina 3
Encina 1
South Bay 4
Encina 4
Encina 5
Averages
sba2
sba1
sba3
enc2
enc3
enc1
sba4
enc4
enc5
30
30
30
20
20
20
45
20
20
150
143
175
104
110
107
150
300
330
1.33
1.43
1.40
1.34
1.32
1.47
1.30
1.87
2.07
1.47
0.99
0.93
0.96
0.94
0.98
0.91
1.01
0.97
0.95
0.96
1.10
1.10
1.10
1.08
1.09
1.10
1.12
1.13
1.15
1.12
PG&E UNITS
Potrero 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 4
Contra Costa 6
Morro Bay 3
Pittsburg 5
Pittsburg 3&4
Contra Costa 7
Pittsburg 7
Pittsburg 1&2
Pittsburg 6
Moss Landing 6
Moss Landing 7
Hunters Point 3
Humboldt 1&2
Hunters Point 2
Averages
11,799
12,306
12,481
12,860
12,936
13,303
13,747
17,674
18,632
AVERAGE/INCREMENTAL
R(X1)
R(X2)
Rave
HR-DESC.DOC; 4/17/98; PAGE D-9
Figures D-3A, B and C are similar to Figures D-2A, B, and C except that we are looking at the
correlation with IHR, rather than the AHR. In this case the results are much more ambiguous. A low or
a high IHR seems to go with a high AHR/IHR ratio equally well. It appears that only AHR shows any
correlation. The tabulated numbers for Figures D-3A, B and C are provided in Table D-5.
FIGURE D-3A,B&C (TABLE D-5)
AHR/IHR vs IHR
PG&E
3.0
R(X1)
AHR/IHR
2.5
2.0
Rave
1.5
1.0
R(X2)
0.5
10,371
10,294
9,883
9,390
9,070
9,037
8,965
8,958
8,901
8,777
8,723
8,721
8,613
8,467
8,436
7,319
7,176
0.0
BLOCK 2 IHR (Btu/kWh)
AHR/IHR vs IHR
SCE
9.0
AHR/IHR
8.0
R(X1)
7.0
6.0
5.0
Rave
4.0
3.0
2.0
1.0
R(X2)
9,605
9,368
9,322
9,262
9,223
9,125
8,992
8,662
8,619
8,552
8,552
8,447
8,435
8,414
8,390
8,203
8,190
8,166
7,898
7,014
0.0
BLOCK 2 IHR (Btu/kWh)
AHR/IHR vs IHR
SDG&E
2.5
R(X1)
AHR/IHR
2.0
Rave
1.5
1.0
R(X2)
0.5
0.0
8,656
8,940
9,037
9,044
9,082
9,473
BLOCK 2 IHR (Btu/kWh)
9,632
9,841
10,630
HR-DESC.DOC; 4/17/98; PAGE D-10
TABLE D-5: SORTED BY IHR(X1)
OUTPUT (MW)
X1
X2
PG&E UNITS
Moss Landing 7
Moss Landing 6
Contra Costa 7
Pittsburg 7
Contra Costa 6
Morro Bay 4
Pittsburg 5
Pittsburg 6
Hunters Point 4
Pittsburg 1&2
Potrero 3
Pittsburg 3&4
Morro Bay 3
Morro Bay 1&2
Hunters Point 3
Humboldt 1&2
Hunters Point 2
Averages
ABREV,
mos7
mos6
con7
pit7
con6
mor4
pit5
pit6
hnp4
pit1&2
pot3
pit3&4
mor3
mor1&2
hnp3
hmb1&2
hnp2
IHR
X1
AVERAGE/INCREMENTAL
R(X1)
R(X2)
Rave
50
50
46
120
46
46
46
46
62
62
47
62
46
62
10
10
10
739
739
340
720
340
338
325
325
326
326
207
326
338
326
107
105
107
7,176
7,319
8,436
8,467
8,613
8,721
8,723
8,777
8,901
8,958
8,965
9,037
9,070
9,390
9,883
10,294
10,371
2.91
2.87
1.58
1.63
1.46
1.48
1.54
1.44
1.37
1.54
1.20
1.43
1.46
1.35
2.21
1.95
2.13
1.67
1.02
1.05
0.94
0.98
0.92
1.01
1.03
0.98
1.00
0.95
0.89
0.86
1.05
1.00
0.89
0.84
0.96
0.98
1.26
1.25
1.14
1.20
1.13
1.12
1.14
1.12
1.10
1.17
1.05
1.13
1.14
1.11
1.16
1.18
1.19
1.17
SCE UNITS
Cool Water 3&4
cw34
Highgrove 3&4
hig3&4
Ormond Beach 1
orb1
Ormond Beach 2
orb2
Alamitos 5&6
ala5&6
El Segundo 3&4
els3&4
Highgrove 1&2
hig1&2
Etiwanda 3&4
eti3&4
Alamitos 3&4
ala3&4
Huntington Beach 1&2hun1&2
Redondo Beach 7&8 red7&8
Mandalay 1&2
man1&2
San Bernardino 1&2 sbr1&2
Redondo Beach 5&6 red5&6
Alamitos 1&2
ala1&2
El Segundo 1&2
els1&2
Etiwanda 1&2
eti1&2
Cool Water 1
cw01
Cool Water 2
cw02
Long Beach 8&9
lb8&9
Averages
140
10
250
50
260
40
8
40
40
40
260
40
14
20
20
20
20
17
19
70
512
89
750
750
960
670
66
640
640
430
960
430
126
350
350
350
264
65
81
560
7,014
7,898
8,166
8,190
8,203
8,390
8,414
8,435
8,447
8,552
8,552
8,619
8,662
8,992
9,125
9,223
9,262
9,322
9,368
9,605
2.02
8.51
1.35
2.46
1.42
2.96
5.87
2.75
3.02
1.96
1.32
1.90
3.24
3.54
3.19
3.04
2.72
1.30
1.31
1.31
1.83
1.10
1.73
1.00
0.99
1.00
1.03
1.58
1.02
1.04
1.01
1.02
0.95
1.15
1.09
1.04
1.05
1.00
1.01
1.02
1.02
1.03
1.43
2.99
1.13
1.23
1.12
1.31
2.41
1.28
1.33
1.20
1.12
1.16
1.54
1.41
1.34
1.32
1.30
1.10
1.11
1.08
1.27
SDG&E UNITS
South Bay 1
South Bay 3
Encina 5
South Bay 2
Encina 1
Encina 4
Encina 2
Encina 3
South Bay 4
Averages
30
30
20
30
20
20
20
20
45
143
175
330
150
107
300
104
110
150
8,656
8,940
9,037
9,044
9,082
9,473
9,632
9,841
10,630
1.43
1.40
2.07
1.33
1.47
1.87
1.34
1.32
1.30
1.47
0.93
0.96
0.95
0.99
0.91
0.97
0.94
0.98
1.01
0.96
1.10
1.10
1.15
1.10
1.10
1.13
1.08
1.09
1.12
1.12
sba1
sba3
enc5
sba2
enc1
enc4
enc2
enc3
sba4
G100
HR-DESC.DOC; 4/17/98; PAGE D-11
APPENDIX E
A SIMPLISTIC MARKET MODEL
This Appendix describes the development of the Simplistic Market Model described in Section VI, of the
main body of this report. This model is a very simplified characterization of the market that does not
pretend to have the accuracy of a model such as UPLAN but is, at the same time, more useful in
visualizing the competitive market as it compares to the existing regulated market. It does this by making
a pseudo comparison of the Marginal Cost (MC) of the regulated market to the Market Clearing Price
(MCP) of the competitive market. It does this using the heat rate and fuel cost data of the IOU slowstart gas-fired units for the three IOUs: PG&E, SCE and SDG&E -- all at pre-divestiture ownership.
Block Incremental Heat Rates (IHR) are used for characterizing the MC, and block Average Heat Rates
(AHR) are used for characterizing MCP. This would be simply a matter of comparing the IHR and AHR
block values from Appendix A except for the fact that they are no directly comparable to one another, as
will be explained below. It therefore becomes necessary to characterize the IHR and AHR values in
equation form, as described in Appendix B. The block IHR values would be the same as the block values
of Appendix A except for the fact that equations cannot fit the data points of the block data exactly. The
AHR values must be converted to AHR average block values (AHRAVE), as will be explained below.
From this data, system IHRs (SIHR) and system AHRAVE (SAHRAVE) are developed. Finally, using the
FR 97 Gas Price Forecast described in Appendix F, the corresponding costs are developed which can
stand as proxies for MC and MCP.
BLOCK INCREMENTAL HEAT RATES
The equations developed in Appendix B are used to develop the block Incremental Heat Rates (IHRs).
These IHRs would be the same as those in Appendix A except for the fact that the equations of Appendix
B can never fit the block data of Appendix A exactly. The block IHR values are reconstructed in the
format of Appendix A.
Moss Landing 7 is used to illustrate this process. The relevant heat rate data from Appendix A is
summarized in Table E-1. It is necessary to understand that the block 1 IHR is not really a IHR as it
represents the heat rate for the minimum block, which can not be used in a dispatch decision. Therefore,
only blocks 2-5 are applicable.
TABLE E-1: MOSS LANDING 7 DATA FROM APPENDIX A
BLOCK
CAPACITY
AHR
I/O
IHR
#
Curve
(%)
(MW) (Btu/kWh) (1000 Btu/hr) (Btu/kWh)
1
6.8%
50
19,959
997,950
19,959
2
25.0%
185
10,631
1,966,735
7,176
3
50.1%
370
9,268
3,429,160
7,905
4
80.0%
591
8,962
5,296,542
8,450
5
100.0% 739
8,917
6,589,663
8,737
HR-DESC.DOC; 4/17/98; PAGE E-1
The necessary IHR block data for each unit is constructed from the respective Input-Output Curve
(Btu/hr) of Appendix B which is a third order equation:
y=ax3+bx2+cx+d
Where: y = Input fuel (Btu/hr)
x = Output generation (MW)
a - d = The coefficients defined by Table B-2 in Appendix B.
The block Average Incremental Heat Rates can then be calculated from the Input-Output curve:
(y2 - y1)/ (x2-x1) = [(ax23 + bx22 + cx2 + d) - (ax13 + bx12 + cx1 + d)] / (x2-x1)
= [a(x23- x13) + b(x22- x12) + c(x2 - x1)]/ (x2 - x1)
= a(x22 + x2 x1 + x12) + b(x2 + x1) + c
Where: x1 = Minimum Output of the Block
x2 = Maximum Output of the Block
For Block 1 of Moss Landing 7, the following coefficients and output values are applicable:
a = -0.0013
b = 2.955
c = 6561.2
d = 662,025
x1 = 50 MW
x2 = 185 MW
The corresponding Block 1 Average Incremental Heat Rate is:
(y2 - y1)/ (x2-x1) = a(x22 + x2 x1 + x12) + b(x2 + x1) + c
= -0.0013(1852+185*50+502) + 2.955(185+50) + 6561.2 = 7,196 Btu/kWh
The remaining IHR values can be constructed similarly and are summarized in Table E-2. The rest of the
values can then be constructed from the IHR values, as was done in Table E-1. But only the IHR values
are of interest here since the necessary AHRAVE values must be calculated as is explained below.
TABLE E-2: MOSS LANDING 7 DATA BASED ON EQUATION.
BLOCK
CAPACITY
AHR
I/O
IHR
#
Curve
(%)
(MW) (Btu/kWh) (1000 Btu/hr) (Btu/kWh)
1
6.8%
50
19,946
997,310
19,946
2
25.0%
185
10,642
1,968,751
7,196
3
50.1%
370
9,266
3,428,360
7,890
4
80.0%
591
8,974
5,303,467
8,485
5
100.0% 739
8,931
6,599,881
8,760
The IHR values for the other units are calculated similarly and are summarized in Table E-3.
HR-DESC.DOC; 4/17/98; PAGE E-2
TABLE E-3: BLOCK INCREMENTAL HEAT RATES (IHRs)
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
INC
INC
INC
INC
IHR
IHR
IHR
IHR
MW Btu/kWh MW Btu/kWh MW Btu/kWh MW Btu/kWh
PG&E UNITS
Contra Costa 6
Contra Costa 7
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 3
Morro Bay 4
Moss Landing 6
Moss Landing 7
Pittsburg 1&2
Pittsburg 3&4
Pittsburg 5
Pittsburg 6
Pittsburg 7
Potrero 3
39
39
16
17
17
20
20
39
39
135
135
20
20
35
35
60
5
8,756
8,496
10,543
10,364
9,876
8,873
9,407
9,056
8,703
7,370
7,196
9,079
9,276
8,744
8,613
8,555
9,066
85
85
27
27
27
82
82
84
84
185
185
82
82
82
82
180
52
8,555
8,503
10,366
10,981
10,861
9,044
9,441
9,064
8,848
8,146
7,890
9,003
8,983
8,900
8,797
8,476
8,924
102
102
31
32
32
96
96
101
101
221
221
96
96
97
97
216
62
8,877
8,933
11,392
11,861
12,246
9,379
9,675
9,100
9,083
8,668
8,485
9,391
9,529
9,135
9,293
8,762
9,276
68
68
21
21
21
66
66
68
68
148
148
66
66
65
65
144
41
9,811
9,754
13,521
12,701
13,552
9,724
10,081
9,159
9,314
8,714
8,760
10,331
11,211
9,344
9,963
9,469
10,341
SCE UNITS
Alamitos 1&2
Alamitos 3&4
Alamitos 5&6
Cool Water 1
Cool Water 2
Cool Water 3&4
El Segundo 1&2
El Segundo 3&4
Etiwanda 1&2
Etiwanda 3&4
Highgrove 1&2
Highgrove 3&4
Huntington 1&2
Long Beach 8&9
Mandaly 1&2
Ormond Beach 1
Ormond Beach 2
Redondo 5&6
Redondo 7&8
San Bernardino 1&2
70
120
160
13
16
40
70
120
60
120
10
14
100
110
100
120
175
70
100
28
9,127
8,443
8,155
9,320
9,368
7,013
9,224
8,395
9,264
8,438
8,413
7,899
8,552
9,608
8,443
8,171
8,192
8,992
8,557
8,681
90
160
180
13
16
60
90
160
60
160
20
26
100
120
105
130
175
90
300
28
9,341
8,639
8,656
9,549
9,540
7,064
9,394
8,576
9,627
8,641
8,438
8,096
8,768
9,647
8,799
8,429
8,459
9,134
8,759
9,056
90
160
180
13
16
140
90
160
60
160
18
30
100
110
95
120
175
90
140
28
9,663
8,933
9,074
9,808
9,742
7,334
9,631
8,839
10,104
8,943
8,471
8,338
9,050
9,717
9,279
8,742
8,818
9,324
9,028
9,384
80
160
180
9
14
132
80
190
64
160
10
9
90
150
90
130
175
80
160
28
10,047
9,305
9,375
10,050
9,960
8,018
9,898
9,198
10,719
9,322
8,495
8,485
9,379
9,836
9,842
9,112
9,268
9,535
9,248
9,667
7
6
8
55
63
6
8
14
-
9,082
9,630
9,840
9,473
9,019
8,654
8,900
8,940
-
27
26
28
75
82
36
38
44
30
9,353
9,818
9,965
9,625
9,208
8,874
8,995
9,089
10,630
32
31
33
90
99
43
45
53
45
10,140
10,368
10,325
9,991
9,660
9,548
9,277
9,511
10,957
21
21
22
60
66
29
30
35
30
11,202
11,111
10,810
10,484
10,270
10,456
9,658
10,080
11,427
SDG&E UNITS
Encina 1
Encina 2
Encina 3
Encina 4
Encina 5
South Bay 1
South Bay 2
South Bay 3
South Bay 4
HR-DESC.DOC; 4/17/98; PAGE E-3
BLOCK AVERAGE HEAT RATES
At first blush, it might appear that the AHR is calculated similarly but this is not possible because the
AHR and IHR data in Table E-2 are not directly comparable. The Moss Landing 7 IHR of 7,196
Btu/kWh for block 2, for example, is an average for the Block 2, for the range from 50 MW to 185 MW.
But the corresponding AHR of 10,642 Btu/kWh is the heat rate at the point of 185 MW. In order to
make these values comparable, an average AHR value for the range of 50 MW to 185 MW has to be
calculated. This value is designated as AHRAVE herein, and calculated using calculus. The AHR curve is
integrated over each of its blocks and that value is divided by the number of megawatts associated with
the respective block. The process is as follows.
The Input-Output Curve (Btu/hr) is as before represented by the third order equation:
y = ax3+bx2+cx+d
Where: y = Input fuel (Btu/hr)
x = Output generation (MW)
a - d = The coefficients defined by Table B-2 in Appendix B.
And the Average Heat Rate curve (AHR) is by definition equal to the Input-Output curve (y) divided by
the respective capacity, x:
AHR = y/x = (ax3+bx2+cx+d)/x
The average AHR, AHRAVE, is the integral of AHR from x1 to x2 divided by the quantity x2 - x1:
AHRAVE = [ò
ò AHR dx {from X1
to X2 } ]
/ (x2 - x1)
Where: x1 = Minimum operating level of the block (MW)
x2 = Maximum operating level of the block (MW)
The integration of AHR, (ò
ò AHR dx), is as follows:
ò AHR dx = ò [(ax
[ 3+bx2+cx+d)/x]dx = a/3 ·x3+ b/2 ·x2 + c ·x + d · Ln(x)
Where: Ln(x) = Natural Log of x
Or in spreadsheet language:
ò AHR
AH dx = ò [(a*X^3+b*X^2+c*X+d)/X]dx
[
= a/3*X^3+b/2*X^2+c*X+d*ln(X)
The coefficients, a - d, along with the values of x1 and x2 for each block is copied onto a spreadsheet. The
formula for òAHR dx is entered onto the Excel spreadsheet in two places: once for calculating the value
of òAHR dx for x1 and once for x2. For the first block (from 50 MW to 185 MW) this would be:
HR-DESC.DOC; 4/17/98; PAGE E-4
a = -0.0013
b = 2.955
c = 6561.2
d = 662,025
x1 = 50 MW
x2 = 185 MW
ò AHR(x1) dx = 1/3*a*x1^3+1/2*b*x1^2+c*x1+d*ln(x1)
ò AHR(x2) dx = 1/3*a*x2^3+1/2*b*x2^2+c*x2+d*ln(x2)
Finally, the two values of ò AHR dx are subtracted from one another and the resulting value is divided by
the difference of the x2 - x1 values:
AHRAVE = [ò
ò AHR(x2) dx - ò AHR(x1) dx ] / (x2 - x1)
Excel then makes the following calculations:
ò AHR(x2) dx = a/3*x2^3+b/2*x2^2+c*x2+d*ln(x2)
= -0.0013/3×1853 + 2.955/2×1852 + 6561.2×185 + 662025×Ln(185) = 4,717,651.8
ò AHR(x1) dx = a/3*x1^3+b/2*x1^2+c*x1+d*ln(x1)
= -0.0013/3×503 + 2.955/2×502 + 6561.2 × 50 + 662025×Ln(50) = 2,921,556.6
AHRAVE = (4,717,651.8 - 2,921,556.6) / (185 - 50) = 1,796,095.2 / 135 = 13,304 Btu/kWh
Table E-4 provides the resulting block AHRAVE values for each block of each slow-start IOU unit.
HR-DESC.DOC; 4/17/98; PAGE E-5
TABLE E-4: BLOCK AVERAGES OF AVERAGE HEAT RATES (AHRAVE)
BLOCK 2
BLOCK 3
BLOCK 4
BLOCK 5
INC
INC
INC
INC
AHR
AHR
AHR
AHR
MW Btu/kWh MW Btu/kWh MW Btu/kWh MW Btu/kWh
PG&E UNITS
Contra Costa 6
Contra Costa 7
Humboldt 1&2
Hunters Point 2
Hunters Point 3
Hunters Point 4
Morro Bay 1&2
Morro Bay 3
Morro Bay 4
Moss Landing 6
Moss Landing 7
Pittsburg 1&2
Pittsburg 3&4
Pittsburg 5
Pittsburg 6
Pittsburg 7
Potrero 3
39
39
16
17
17
20
20
39
39
135
135
20
20
35
35
60
5
11,860
12,112
16,853
16,865
16,339
11,642
12,246
12,056
11,694
13,370
13,304
13,412
12,905
12,186
12,870
13,001
10,853
85
85
27
27
27
82
82
84
84
185
185
82
82
82
82
180
52
10,300
10,361
13,245
13,382
12,974
10,585
11,128
10,616
10,292
9,918
9,758
11,673
11,388
10,598
10,899
11,062
10,207
102
102
31
32
32
96
96
101
101
221
221
96
96
97
97
216
62
9,579
9,622
12,142
12,517
12,336
9,985
10,438
9,950
9,714
9,273
9,079
10,573
10,408
9,907
10,075
9,977
9,689
68
68
21
21
21
66
66
68
68
148
148
66
66
65
65
144
41
9,479
9,517
12,167
12,433
12,471
9,854
10,266
9,712
9,561
9,115
8,949
10,339
10,341
9,712
9,929
9,705
9,686
SCE UNITS
Alamitos 1&2
Alamitos 3&4
Alamitos 5&6
Cool Water 1
Cool Water 2
Cool Water 3&4
El Segundo 1&2
El Segundo 3&4
Etiwanda 1&2
Etiwanda 3&4
Highgrove 1&2
Highgrove 3&4
Huntington 1&2
Long Beach 8&9
Mandaly 1&2
Ormond Beach 1
Ormond Beach 2
Redondo 5&6
Redondo 7&8
San Bernardino 1&2
70
120
160
13
16
40
70
120
60
120
10
14
100
110
100
120
175
70
100
28
17,605
16,210
10,532
11,259
11,401
13,307
17,208
15,882
16,432
15,141
34,940
44,598
12,570
11,404
12,114
10,354
13,188
18,702
10,808
18,968
90
160
180
13
16
60
90
160
60
160
20
26
100
120
105
130
175
90
300
28
12,222
11,407
9,810
10,587
10,650
11,822
12,131
11,251
12,244
11,005
20,641
24,520
10,331
10,506
10,087
9,753
10,168
12,511
9,995
13,553
90
160
180
13
16
140
90
160
60
160
18
30
100
110
95
120
175
90
140
28
11,084
10,311
9,560
10,343
10,370
10,361
11,038
10,188
11,371
10,078
15,481
17,262
9,822
10,230
9,706
9,486
9,595
11,144
9,633
12,072
80
160
180
9
14
132
80
190
64
160
10
9
90
150
90
130
175
80
160
28
10,734
9,960
9,491
10,264
10,262
9,506
10,678
9,825
11,106
9,798
13,820
15,100
9,666
10,107
9,664
9,382
9,442
10,661
9,548
11,426
7
6
8
55
63
6
8
14
-
12,717
12,454
12,468
13,407
13,352
11,995
11,487
11,853
-
27
26
28
75
82
36
38
44
30
11,323
11,390
11,426
11,022
10,671
10,821
10,526
10,653
13,010
32
31
33
90
99
43
45
53
45
10,611
10,808
10,857
10,482
10,120
10,099
9,912
10,051
12,147
21
21
22
60
66
29
30
35
30
10,601
10,769
10,761
10,399
10,060
10,047
9,774
9,963
11,860
SDG&E UNITS
Encina 1
Encina 2
Encina 3
Encina 4
Encina 5
South Bay 1
South Bay 2
South Bay 3
South Bay 4
HR-DESC.DOC; 4/17/98; PAGE E-6
SYSTEM INCREMENTAL HEAT RATES
If the block IHRs are sorted by increasing values for each IOU, they can be considered to be a simplified
representation of the dispatch in the existing regulated system -- and is therefore a simplistic representation of MC for the respective IOU. These sorted values are shown under the heading IHR in Table E-5
series: Table E-5-PGE for PG&E, Table E-5-SCE for SCE and Table E-5-SDG for SDG&E. The only
restraint is that the Block order can not be violated. That is, Block 2 must be taken before Block 3, Block
3 must be taken before Block 4, and Block 4 must be taken before Block 5. Since IHRs should always
have increasing values, maintaining this restraint is not a problem. The Figure E-1 series show this same
data graphically, along with corresponding AHRAVE data which is described in the next section.
The column designated IHR x MW is the product of each MW increment and its corresponding IHR,
which represents the number of Btu that the respective unit can produce in any one hour. The next
column is a running sum of these products, which represents the total Btu that the system to that point
can generate in one hour. The last column, designated “Cumulative SIHR” is the running sum values
divided by the cumulative MW. These SIHR values are shown in Figure series E-2, along with similar
AHR data which is also described in the next section.
Since IHR values set the MC in the regulated system – along with variable O&M costs, they can be
thought of a proxy for MC. Accordingly, SIHR values can be thought of as a system MC for the blocks
being used at that point, which corresponds to the average MC which could be expected if all these same
blocks contributed to the marginal cost equal amounts of time. That is, we will consider SIHR to be our
proxy for MC in a traditional regulated system.
SYSTEM AVERAGE HEAT RATES
The System AHRAVE, SAHRAVE, values are calculated similarly to SIHR but the sorting is more complex,
intended to be representative of the dispatch in a competitive market with one part bidding. The AHRAVE
data is sorted such that blocks are taken in economic order, with the same provision that blocks can not
be taken out of physical order. As it turns out, once the first block (Block 2) is taken, its upper blocks are
so economic that there is no other Block 2 that can compete. Accordingly, the graphical emulation of this
dispatch of heat rates, Figures E-1, show a saw tooth shape where each downward sloping arc (of four
blocks) is a unit’s heat rate curve. This is a very different shape than that of the conventional IHR curve.
The SAHRAVE values are calculated similar to the SIHR values and are also shown in Tables E-5. The
SAHRAVE values are the cumulative weighted average of these individual unit AHRAVE values. The
corresponding graphs are shown in Figure E-2.
HR-DESC.DOC; 4/17/98; PAGE E-7
TABLE E-5-PGE: PG&E SYSTEM IHR AND AHRAVE CALCULATIONS
SUMMARY IHR DATA
UNIT
BLK INC
IHR
CUM
PLANT # MW Btu/kWh MW
IHR*MW
1000Btu
mos7
mos6
mos7
mos6
pit7
mos7
con7
con7
pit7
con6
pit6
mos6
mor4
mos6
pit5
con6
mos7
pit7
pit6
mor4
hnp4
con6
pit5
pot3
con7
pit3&4
pit1&2
hnp4
mor3
mor3
pot3
pit1&2
mor4
mor3
pit5
mor3
pot3
pit3&4
pit6
mor4
pit5
hnp4
pit1&2
mor1&2
mor1&2
pit7
pit3&4
mor1&2
hnp4
con7
con6
hnp3
pit6
mor1&2
pit1&2
pot3
hnp2
hmb1&2
hmb1&2
hnp3
hnp2
pit3&4
hmb1&2
hnp2
hnp3
hnp2
hmb1&2
hnp3
971,441
994,931
1,459,609
1,506,925
1,525,759
1,875,107
331,331
722,789
513,295
727,171
301,456
1,915,722
339,425
1,289,726
306,050
341,490
1,296,414
1,892,651
721,354
743,248
177,454
905,452
729,832
464,057
911,212
736,606
738,207
741,638
353,189
761,357
45,329
181,571
917,368
919,114
886,132
622,813
575,101
185,523
901,420
633,373
607,366
900,405
901,583
188,135
774,202
1,363,571
914,759
928,783
641,751
663,242
667,170
167,886
647,610
665,338
681,813
423,968
176,181
279,882
168,689
293,239
296,490
739,944
353,140
379,557
391,877
266,719
283,948
284,586
2
2
3
3
3
4
2
3
2
3
2
4
2
5
2
2
5
4
3
3
2
4
3
3
4
3
3
3
2
3
2
2
4
4
4
5
4
2
4
5
5
4
4
2
3
5
4
4
5
5
5
2
5
5
5
5
2
3
2
3
3
5
4
4
4
5
5
5
135
135
185
185
180
221
39
85
60
85
35
221
39
148
35
39
148
216
82
84
20
102
82
52
102
82
82
82
39
84
5
20
101
101
97
68
62
20
97
68
65
96
96
20
82
144
96
96
66
68
68
17
65
66
66
41
17
27
16
27
27
66
31
32
32
21
21
21
7,196
7,370
7,890
8,146
8,476
8,485
8,496
8,503
8,555
8,555
8,613
8,668
8,703
8,714
8,744
8,756
8,760
8,762
8,797
8,848
8,873
8,877
8,900
8,924
8,933
8,983
9,003
9,044
9,056
9,064
9,066
9,079
9,083
9,100
9,135
9,159
9,276
9,276
9,293
9,314
9,344
9,379
9,391
9,407
9,441
9,469
9,529
9,675
9,724
9,754
9,811
9,876
9,963
10,081
10,331
10,341
10,364
10,366
10,543
10,861
10,981
11,211
11,392
11,861
12,246
12,701
13,521
13,552
135
270
455
640
820
1,041
1,080
1,165
1,225
1,310
1,345
1,566
1,605
1,753
1,788
1,827
1,975
2,191
2,273
2,357
2,377
2,479
2,561
2,613
2,715
2,797
2,879
2,961
3,000
3,084
3,089
3,109
3,210
3,311
3,408
3,476
3,538
3,558
3,655
3,723
3,788
3,884
3,980
4,000
4,082
4,226
4,322
4,418
4,484
4,552
4,620
4,637
4,702
4,768
4,834
4,875
4,892
4,919
4,935
4,962
4,989
5,055
5,086
5,118
5,150
5,171
5,192
5,213
SUMMARY AHR DATA
Cumulative
IHR*MW
SIHR
1000Btu Btu/kWh
971,441
1,966,372
3,425,981
4,932,906
6,458,665
8,333,772
8,665,104
9,387,893
9,901,188
10,628,359
10,929,814
12,845,537
13,184,962
14,474,688
14,780,738
15,122,229
16,418,642
18,311,293
19,032,647
19,775,896
19,953,349
20,858,801
21,588,633
22,052,690
22,963,902
23,700,507
24,438,714
25,180,352
25,533,541
26,294,897
26,340,226
26,521,797
27,439,165
28,358,279
29,244,411
29,867,224
30,442,325
30,627,848
31,529,268
32,162,641
32,770,007
33,670,412
34,571,995
34,760,130
35,534,331
36,897,902
37,812,661
38,741,444
39,383,196
40,046,438
40,713,607
40,881,494
41,529,104
42,194,442
42,876,255
43,300,223
43,476,404
43,756,286
43,924,976
44,218,215
44,514,705
45,254,649
45,607,789
45,987,346
46,379,222
46,645,941
46,929,889
47,214,476
7,196
7,283
7,530
7,708
7,876
8,006
8,023
8,058
8,083
8,113
8,126
8,203
8,215
8,257
8,267
8,277
8,313
8,358
8,373
8,390
8,394
8,414
8,430
8,440
8,458
8,474
8,489
8,504
8,511
8,526
8,527
8,531
8,548
8,565
8,581
8,592
8,604
8,608
8,626
8,639
8,651
8,669
8,686
8,690
8,705
8,731
8,749
8,769
8,783
8,798
8,812
8,816
8,832
8,850
8,870
8,882
8,887
8,895
8,901
8,911
8,923
8,952
8,967
8,985
9,006
9,021
9,039
9,057
UNIT
BLK INC
AHR CUM
AHR*MW
PLANT
# MW Btu/kWh
MW 1000Btu
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
15
15
15
15
16
16
16
16
17
17
17
17
pot3
pot3
pot3
pot3
hnp4
hnp4
hnp4
hnp4
mor4
mor4
mor4
mor4
con6
con6
con6
con6
mor3
mor3
mor3
mor3
con7
con7
con7
con7
pit5
pit5
pit5
pit5
mor1&2
mor1&2
mor1&2
mor1&2
pit6
pit6
pit6
pit6
pit3&4
pit3&4
pit3&4
pit3&4
pit7
pit7
pit7
pit7
mos7
mos7
mos7
mos7
mos6
mos6
mos6
mos6
pit1&2
pit1&2
pit1&2
pit1&2
hnp3
hnp3
hnp3
hnp3
hmb1&2
hmb1&2
hmb1&2
hmb1&2
hnp2
hnp2
hnp2
hnp2
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
5
52
62
41
20
82
96
66
39
84
101
68
39
85
102
68
39
84
101
68
39
85
102
68
35
82
97
65
20
82
96
66
35
82
97
65
20
82
96
66
60
180
216
144
135
185
221
148
135
185
221
148
20
82
96
66
17
27
32
21
16
27
31
21
17
27
32
21
10,853
10,207
9,689
9,686
11,642
10,585
9,985
9,854
11,694
10,292
9,714
9,561
11,860
10,300
9,579
9,479
12,056
10,616
9,950
9,712
12,112
10,361
9,622
9,517
12,186
10,598
9,907
9,712
12,246
11,128
10,438
10,266
12,870
10,899
10,075
9,929
12,905
11,388
10,408
10,341
13,001
11,062
9,977
9,705
13,304
9,758
9,079
8,949
13,370
9,918
9,273
9,115
13,412
11,673
10,573
10,339
16,339
12,974
12,336
12,471
16,853
13,245
12,142
12,167
16,865
13,382
12,517
12,433
5
57
119
160
180
262
358
424
463
547
648
716
755
840
942
1,010
1,049
1,133
1,234
1,302
1,341
1,426
1,528
1,596
1,631
1,713
1,810
1,875
1,895
1,977
2,073
2,139
2,174
2,256
2,353
2,418
2,438
2,520
2,616
2,682
2,742
2,922
3,138
3,282
3,417
3,602
3,823
3,971
4,106
4,291
4,512
4,660
4,680
4,762
4,858
4,924
4,941
4,968
5,000
5,021
5,037
5,064
5,095
5,116
5,133
5,160
5,192
5,213
54,266
530,763
600,716
397,135
232,845
867,947
958,544
650,366
456,063
864,561
981,103
650,147
462,528
875,488
977,042
644,582
470,181
891,770
1,004,983
660,441
472,386
880,708
981,468
647,154
426,514
869,041
960,937
631,257
244,911
912,503
1,002,050
677,577
450,461
893,708
977,237
645,407
258,107
933,821
999,204
682,485
780,062
1,991,242
2,154,948
1,397,580
1,796,095
1,805,199
2,006,352
1,324,404
1,804,959
1,834,901
2,049,296
1,349,026
268,231
957,189
1,014,964
682,388
277,769
350,302
394,742
261,888
269,651
357,616
376,412
255,499
286,706
361,311
400,547
261,103
Cumulative
AHR*MW
SAHR
1000Btu
Btu/kWh
54,266
585,029
1,185,744
1,582,880
1,815,724
2,683,671
3,642,216
4,292,582
4,748,644
5,613,206
6,594,309
7,244,456
7,706,983
8,582,471
9,559,513
10,204,095
10,674,276
11,566,046
12,571,029
13,231,470
13,703,857
14,584,564
15,566,033
16,213,187
16,639,701
17,508,742
18,469,679
19,100,936
19,345,848
20,258,351
21,260,402
21,937,979
22,388,440
23,282,147
24,259,384
24,904,791
25,162,898
26,096,719
27,095,923
27,778,408
28,558,470
30,549,713
32,704,661
34,102,241
35,898,336
37,703,535
39,709,887
41,034,291
42,839,250
44,674,150
46,723,446
48,072,472
48,340,703
49,297,892
50,312,855
50,995,243
51,273,012
51,623,314
52,018,056
52,279,943
52,549,594
52,907,211
53,283,622
53,539,122
53,825,827
54,187,139
54,587,685
54,848,789
10,853
10,264
9,964
9,893
10,087
10,243
10,174
10,124
10,256
10,262
10,176
10,118
10,208
10,217
10,148
10,103
10,176
10,208
10,187
10,162
10,219
10,228
10,187
10,159
10,202
10,221
10,204
10,187
10,209
10,247
10,256
10,256
10,298
10,320
10,310
10,300
10,321
10,356
10,358
10,357
10,415
10,455
10,422
10,391
10,506
10,467
10,387
10,333
10,433
10,411
10,355
10,316
10,329
10,352
10,357
10,356
10,377
10,391
10,404
10,412
10,433
10,448
10,458
10,465
10,486
10,501
10,514
10,522
HR-DESC.DOC; 4/17/98; PAGE E-8
TABLE E-5-SCE: SCE SYSTEM IHR AND AHRAVE CALCULATIONS
SUMMARY IHR DATA
UNIT
BLK INC
IHR
CUM
PLANT # MW Btu/kWh MW
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
cw34
cw34
cw34
hig3&4
cw34
hig3&4
ala5&6
orb1
orb2
hig3&4
els3&4
hig1&2
orb1
eti3&4
hig1&2
man1&2
ala3&4
orb2
hig1&2
hig3&4
hig1&2
hun1&2
red7&8
els3&4
ala3&4
eti3&4
ala5&6
sbr1&2
orb1
red7&8
hun1&2
man1&2
orb2
els3&4
ala3&4
eti3&4
red5&6
red7&8
hun1&2
sbr1&2
ala5&6
orb1
ala1&2
red5&6
els3&4
els1&2
red7&8
eti1&2
orb2
man1&2
ala3&4
cw01
eti3&4
red5&6
ala1&2
cw02
ala5&6
hun1&2
sbr1&2
2
3
4
2
5
3
2
2
2
4
2
2
3
2
3
2
2
3
4
5
5
2
2
3
3
3
3
2
4
3
3
3
4
4
4
4
2
4
4
3
4
5
2
3
5
2
5
2
5
4
5
2
5
4
3
2
5
5
4
40
60
140
14
132
26
160
120
175
30
120
10
130
120
20
100
120
175
18
9
10
100
100
160
160
160
180
28
120
300
100
105
175
160
160
160
70
140
100
28
180
130
70
90
190
70
160
60
175
95
160
13
160
90
90
16
180
90
28
7,013
7,064
7,334
7,899
8,018
8,096
8,155
8,171
8,192
8,338
8,395
8,413
8,429
8,438
8,438
8,443
8,443
8,459
8,471
8,485
8,495
8,552
8,557
8,576
8,639
8,641
8,656
8,681
8,742
8,759
8,768
8,799
8,818
8,839
8,933
8,943
8,992
9,028
9,050
9,056
9,074
9,112
9,127
9,134
9,198
9,224
9,248
9,264
9,268
9,279
9,305
9,320
9,322
9,324
9,341
9,368
9,375
9,379
9,384
40
100
240
254
386
412
572
692
867
897
1017
1027
1157
1277
1297
1397
1517
1692
1710
1719
1729
1829
1929
2089
2249
2409
2589
2617
2737
3037
3137
3242
3417
3577
3737
3897
3967
4107
4207
4235
4415
4545
4615
4705
4895
4965
5125
5185
5360
5455
5615
5628
5788
5878
5968
5984
6164
6254
6282
IHR*MW
1000Btu
280,515
423,843
1,026,818
110,589
1,058,398
210,501
1,304,836
980,508
1,433,628
250,148
1,007,398
84,135
1,095,717
1,012,529
168,768
844,270
1,013,150
1,480,332
152,474
76,365
84,951
855,242
855,746
1,372,124
1,382,232
1,382,483
1,558,076
243,056
1,049,016
2,627,705
876,842
923,941
1,543,113
1,414,195
1,429,341
1,430,826
629,452
1,263,956
905,042
253,562
1,633,296
1,184,559
638,866
822,033
1,747,566
645,700
1,479,652
555,834
1,621,972
881,550
1,488,738
121,160
1,491,457
839,196
840,686
149,892
1,687,520
844,104
262,764
SUMMARY AHR DATA
Cumulative
IHR*MW
SIHR
1000Btu Btu/kWh
280,515
704,358
1,731,177
1,841,766
2,900,164
3,110,665
4,415,501
5,396,009
6,829,637
7,079,785
8,087,183
8,171,318
9,267,035
10,279,564
10,448,332
11,292,602
12,305,752
13,786,084
13,938,558
14,014,923
14,099,874
14,955,116
15,810,862
17,182,986
18,565,218
19,947,700
21,505,776
21,748,832
22,797,847
25,425,553
26,302,395
27,226,335
28,769,448
30,183,643
31,612,984
33,043,810
33,673,262
34,937,218
35,842,260
36,095,822
37,729,117
38,913,677
39,552,542
40,374,575
42,122,141
42,767,841
44,247,493
44,803,327
46,425,299
47,306,849
48,795,587
48,916,747
50,408,203
51,247,400
52,088,086
52,237,979
53,925,499
54,769,602
55,032,367
7,013
7,044
7,213
7,251
7,513
7,550
7,719
7,798
7,877
7,893
7,952
7,956
8,010
8,050
8,056
8,083
8,112
8,148
8,151
8,153
8,155
8,177
8,196
8,225
8,255
8,280
8,307
8,311
8,330
8,372
8,385
8,398
8,420
8,438
8,459
8,479
8,488
8,507
8,520
8,523
8,546
8,562
8,570
8,581
8,605
8,614
8,634
8,641
8,661
8,672
8,690
8,692
8,709
8,719
8,728
8,730
8,748
8,758
8,760
PLANT
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
15
15
15
orb1
orb1
orb1
orb1
ala5&6
ala5&6
ala5&6
ala5&6
red7&8
red7&8
red7&8
red7&8
cw01
cw01
cw01
cw01
cw02
cw02
cw02
cw02
lbc8&9
lbc8&9
lbc8&9
lbc8&9
man1&2
man1&2
man1&2
man1&2
hun1&2
hun1&2
hun1&2
hun1&2
orb2
orb2
orb2
orb2
cw34
cw34
cw34
cw34
eti3&4
eti3&4
eti3&4
eti3&4
els3&4
els3&4
els3&4
els3&4
ala3&4
ala3&4
ala3&4
ala3&4
eti1&2
eti1&2
eti1&2
eti1&2
els1&2
els1&2
els1&2
UNIT
BLK INC
AHR CUM
AHR*MW
#
MW Btu/kWh
MW 1000Btu
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
120
130
120
130
160
180
180
180
100
300
140
160
13
13
13
9
16
16
16
14
110
120
110
150
100
105
95
90
100
100
100
90
175
175
175
175
40
60
140
132
120
160
160
160
120
160
160
190
120
160
160
160
60
60
60
64
70
90
90
10,354
9,753
9,486
9,382
10,532
9,810
9,560
9,491
10,808
9,995
9,633
9,548
11,259
10,587
10,343
10,264
11,401
10,650
10,370
10,262
11,404
10,506
10,230
10,107
12,114
10,087
9,706
9,664
12,570
10,331
9,822
9,666
13,188
10,168
9,595
9,442
13,307
11,822
10,361
9,506
15,141
11,005
10,078
9,798
15,882
11,251
10,188
9,825
16,210
11,407
10,311
9,960
16,432
12,244
11,371
11,106
17,208
12,131
11,038
120
250
370
500
660
840
1,020
1,200
1,300
1,600
1,740
1,900
1,913
1,926
1,939
1,948
1,964
1,980
1,996
2,010
2,120
2,240
2,350
2,500
2,600
2,705
2,800
2,890
2,990
3,090
3,190
3,280
3,455
3,630
3,805
3,980
4,020
4,080
4,220
4,352
4,472
4,632
4,792
4,952
5,072
5,232
5,392
5,582
5,702
5,862
6,022
6,182
6,242
6,302
6,362
6,426
6,496
6,586
6,676
1,242,460
1,267,892
1,138,317
1,219,663
1,685,114
1,765,810
1,720,773
1,708,324
1,080,843
2,998,470
1,348,586
1,527,641
146,369
137,631
134,456
92,374
182,415
170,402
165,923
143,666
1,254,487
1,260,742
1,125,296
1,516,118
1,211,366
1,059,098
922,045
869,785
1,256,984
1,033,061
982,224
869,928
2,307,837
1,779,318
1,679,122
1,652,347
532,296
709,297
1,450,505
1,254,776
1,816,911
1,760,748
1,612,465
1,567,706
1,905,889
1,800,080
1,630,072
1,866,701
1,945,196
1,825,110
1,649,777
1,593,579
985,907
734,610
682,273
710,761
1,204,540
1,091,829
993,454
Cumulative
AHR*MW
SAHR
1000Btu
Btu/kWh
1,242,460
2,510,352
3,648,669
4,868,332
6,553,446
8,319,256
10,040,029
11,748,353
12,829,196
15,827,666
17,176,252
18,703,893
18,850,262
18,987,893
19,122,349
19,214,723
19,397,138
19,567,541
19,733,464
19,877,130
21,131,618
22,392,360
23,517,655
25,033,773
26,245,140
27,304,238
28,226,283
29,096,067
30,353,051
31,386,112
32,368,336
33,238,264
35,546,102
37,325,420
39,004,542
40,656,889
41,189,186
41,898,483
43,348,988
44,603,764
46,420,675
48,181,424
49,793,888
51,361,595
53,267,484
55,067,564
56,697,636
58,564,337
60,509,533
62,334,643
63,984,420
65,577,999
66,563,907
67,298,517
67,980,790
68,691,551
69,896,091
70,987,920
71,981,374
10,354
10,041
9,861
9,737
9,929
9,904
9,843
9,790
9,869
9,892
9,871
9,844
9,854
9,859
9,862
9,864
9,876
9,883
9,887
9,889
9,968
9,997
10,008
10,014
10,094
10,094
10,081
10,068
10,152
10,157
10,147
10,134
10,288
10,282
10,251
10,215
10,246
10,269
10,272
10,249
10,380
10,402
10,391
10,372
10,502
10,525
10,515
10,492
10,612
10,634
10,625
10,608
10,664
10,679
10,685
10,690
10,760
10,779
10,782
- Continued on Next Page -
HR-DESC.DOC; 4/17/98; PAGE E-9
TABLE E-5-SCE: SCE SYSTEM IHR AND AHRAVE CALCULATIONS - CONTINUED
SUMMARY IHR DATA
UNIT
BLK INC
IHR
CUM
PLANT
# MW Btu/kWh MW
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
els1&2
red5&6
cw02
cw01
lbc8&9
eti1&2
els1&2
lbc8&9
ala1&2
sbr1&2
lbc8&9
cw02
cw01
lbc8&9
man1&2
els1&2
cw02
ala1&2
cw01
eti1&2
eti1&2
3
5
3
3
2
3
4
3
4
5
4
4
4
5
5
5
5
5
5
4
5
90
80
16
13
110
60
90
120
90
28
110
16
13
150
90
80
14
80
9
60
64
9,394
9,535
9,540
9,549
9,608
9,627
9,631
9,647
9,663
9,667
9,717
9,742
9,808
9,836
9,842
9,898
9,960
10,047
10,050
10,104
10,719
6372
6452
6468
6481
6591
6651
6741
6861
6951
6979
7089
7105
7118
7268
7358
7438
7452
7532
7541
7601
7665
IHR*MW
1000Btu
845,487
762,837
152,635
124,142
1,056,887
577,613
866,751
1,157,626
869,675
270,663
1,068,869
155,877
127,510
1,475,363
885,739
791,833
139,444
803,745
90,452
606,260
685,992
SUMMARY AHR DATA
Cumulative
IHR*MW
SIHR
1000Btu
Btu/kWh
55,877,854
56,640,691
56,793,326
56,917,468
57,974,354
58,551,967
59,418,718
60,576,344
61,446,019
61,716,682
62,785,550
62,941,427
63,068,937
64,544,300
65,430,039
66,221,872
66,361,316
67,165,061
67,255,513
67,861,772
68,547,765
PLANT
8,769
8,779
8,781
8,782
8,796
8,803
8,815
8,829
8,840
8,843
8,857
8,859
8,860
8,881
8,892
8,903
8,905
8,917
8,919
8,928
8,943
15
16
16
16
16
17
17
17
17
18
18
18
18
19
19
19
19
20
20
20
20
els1&2
ala1&2
ala1&2
ala1&2
ala1&2
red5&6
red5&6
red5&6
red5&6
sbr1&2
sbr1&2
sbr1&2
sbr1&2
hig1&2
hig1&2
hig1&2
hig1&2
hig3&4
hig3&4
hig3&4
hig3&4
UNIT
BLK INC
AHR CUM
#
MW Btu/kWh
MW
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
80
70
90
90
80
70
90
90
80
28
28
28
28
10
20
18
10
14
26
30
9
10,678
17,605
12,222
11,084
10,734
18,702
12,511
11,144
10,661
18,968
13,553
12,072
11,426
34,940
20,641
15,481
13,820
44,598
24,520
17,262
15,100
6,756
6,826
6,916
7,006
7,086
7,156
7,246
7,336
7,416
7,444
7,472
7,500
7,528
7,538
7,558
7,576
7,586
7,600
7,626
7,656
7,665
AHR*MW
1000Btu
854,229
1,232,347
1,099,983
997,572
858,733
1,309,127
1,125,960
1,002,955
852,893
531,107
379,489
338,005
319,940
349,396
412,821
278,651
138,196
624,373
637,514
517,867
135,898
Cumulative
AHR*MW
SAHR
1000Btu
Btu/kWh
72,835,602
74,067,949
75,167,933
76,165,504
77,024,237
78,333,364
79,459,324
80,462,279
81,315,172
81,846,279
82,225,769
82,563,773
82,883,714
83,233,109
83,645,930
83,924,581
84,062,777
84,687,150
85,324,663
85,842,530
85,978,428
10,781
10,851
10,869
10,871
10,870
10,947
10,966
10,968
10,965
10,995
11,005
11,009
11,010
11,042
11,067
11,078
11,081
11,143
11,189
11,212
11,217
TABLE E-5-SDG: SDG&E SYSTEM IHR AND AHRAVE CALCULATIONS
SUMMARY IHR DATA
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
UNIT
BLK INC
IHR
PLANT # MW Btu/kWh
CUM
MW
IHR*MW
1000Btu
sba1
sba1
sba2
sba3
sba2
enc5
enc1
sba3
enc5
sba2
enc1
enc4
sba3
sba1
enc4
enc2
sba2
enc5
enc2
enc3
enc3
enc4
sba3
enc1
enc5
enc3
enc2
sba1
enc4
sba4
enc3
sba4
enc2
enc1
sba4
6
42
49
63
100
163
170
214
296
341
368
423
475
518
593
599
629
728
754
761
789
879
914
946
1,012
1,045
1,076
1,105
1,165
1,195
1,217
1,262
1,283
1,304
1,334
49,761
317,258
66,752
122,921
337,295
568,178
61,304
397,663
755,067
417,453
250,190
521,012
499,334
409,609
721,861
57,782
289,727
956,313
255,261
73,797
274,033
899,145
352,798
325,492
677,814
340,712
323,495
299,053
629,024
318,894
237,817
493,050
231,114
239,716
342,800
2
3
2
2
3
2
2
3
3
4
3
2
4
4
3
2
5
4
3
2
3
4
5
4
5
4
4
5
5
3
5
4
5
5
5
6
36
8
14
38
63
7
44
82
45
27
55
53
43
75
6
30
99
26
8
28
90
35
32
66
33
31
29
60
30
22
45
21
21
30
8,654
8,874
8,900
8,940
8,995
9,019
9,082
9,089
9,208
9,277
9,353
9,473
9,511
9,548
9,625
9,630
9,658
9,660
9,818
9,840
9,965
9,991
10,080
10,140
10,270
10,325
10,368
10,456
10,484
10,630
10,810
10,957
11,111
11,202
11,427
SUMMARY AHR DATA
Cumulative
IHR*MW
SIHR
1000Btu Btu/kWh
49,761
367,019
433,771
556,691
893,986
1,462,164
1,523,468
1,921,131
2,676,198
3,093,651
3,343,841
3,864,854
4,364,188
4,773,796
5,495,657
5,553,440
5,843,167
6,799,479
7,054,740
7,128,538
7,402,570
8,301,716
8,654,514
8,980,006
9,657,820
9,998,533
10,322,028
10,621,080
11,250,104
11,568,999
11,806,816
12,299,866
12,530,980
12,770,695
13,113,496
8,654
8,844
8,852
8,872
8,918
8,957
8,962
8,988
9,049
9,079
9,099
9,148
9,188
9,218
9,269
9,273
9,291
9,341
9,358
9,362
9,383
9,446
9,470
9,493
9,543
9,568
9,591
9,614
9,658
9,683
9,703
9,748
9,770
9,793
9,830
PLANT
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
8
8
8
8
9
9
9
9
sba2
sba2
sba2
sba2
sba3
sba3
sba3
sba3
sba1
sba1
sba1
sba1
enc2
enc2
enc2
enc2
enc3
enc3
enc3
enc3
enc1
enc1
enc1
enc1
sba4
sba4
sba4
enc5
enc5
enc5
enc5
enc4
enc4
enc4
enc4
UNIT
BLK INC AHR CUM
# MW Btu/kWh
MW
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
4
5
2
3
4
5
2
3
4
5
8
38
45
30
14
44
53
35
6
36
43
29
6
26
31
21
8
28
33
22
7
27
32
21
30
45
30
63
82
99
66
55
75
90
60
11,487
10,526
9,912
9,774
11,853
10,653
10,051
9,963
11,995
10,821
10,099
10,047
12,454
11,390
10,808
10,769
12,468
11,426
10,857
10,761
12,717
11,323
10,611
10,601
13,010
12,147
11,860
13,352
10,671
10,120
10,060
13,407
11,022
10,482
10,399
8
45
90
120
134
178
230
265
271
307
349
378
384
410
441
462
470
497
530
552
559
586
618
639
669
714
744
807
889
988
1,054
1,109
1,184
1,274
1,334
AHR*MW
1000Btu
86,153
394,724
446,038
293,222
162,982
466,072
527,667
348,692
68,970
386,850
433,231
287,355
74,725
296,130
337,196
223,992
93,511
314,203
358,269
236,737
85,839
302,896
340,628
226,864
390,293
546,615
355,796
841,146
875,006
1,001,886
663,934
737,388
826,635
943,351
623,912
Cumulative
AHR*MW
SAHR
1000Btu Btu/kWh
86,153
480,877
926,915
1,220,138
1,383,119
1,849,191
2,376,858
2,725,550
2,794,520
3,181,370
3,614,601
3,901,956
3,976,681
4,272,810
4,610,006
4,833,998
4,927,509
5,241,712
5,599,981
5,836,718
5,922,557
6,225,453
6,566,081
6,792,945
7,183,238
7,729,853
8,085,648
8,926,794
9,801,800
10,803,686
11,467,620
12,205,008
13,031,642
13,974,993
14,598,905
11,487
10,686
10,299
10,168
10,341
10,418
10,334
10,285
10,321
10,380
10,345
10,323
10,356
10,421
10,449
10,463
10,495
10,547
10,566
10,574
10,600
10,633
10,632
10,631
10,737
10,826
10,868
11,062
11,026
10,935
10,880
11,005
11,006
10,969
10,944
HR-DESC.DOC; 4/17/98; PAGE E-10
FIGURE E-1-PGE
PG&E
AHR ave vs IHR
18,000
HEAT RATE (Btu/kWh)
16,000
AHR ave
14,000
12,000
10,000
8,000
6,000
IHR
4,000
2,000
0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
OUTPUT (MW)
FIGURE E-1-SCE
SCE
AHRave vs IHR
45,000
40,000
HEAT RATE (Btu/kWh)
35,000
AHR ave
30,000
25,000
20,000
15,000
10,000
5,000
IHR
0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
OUTPUT (MW)
FIGURE E-1-SDG
SDG&E
AHRave vs IHR
14,000
AHR ave
HEAT RATE (Btu/kWh)
12,000
10,000
8,000
IHR
6,000
4,000
2,000
0
0
200
400
600
800
1,000
1,200
1,400
OUTPUT (MW)
HR-DESC.DOC; 4/17/98; PAGE E-11
FIGURE E-2-PGE
PG&E
SYSTEM AVERAGE HEAT RATES
HEAT RATE (Btu/kWh)
12,000
11,000
10,000
SAHR ave
9,000
8,000
SIHR
7,000
6,000
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
OUTPUT (MW)
FIGURE E-2-SCE
SCE
SYSTEM AVERAGE HEAT RATES
12,000
SAHR ave
HEAT RATE (Btu/kWh)
11,000
10,000
9,000
8,000
SIHR
7,000
6,000
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
OUTPUT (MW)
FIGURE E-2-SDG
SDG&E
SYSTEM AVERAGE HEAT RATES
12,000
HEAT RATE (Btu/kWh)
SAHRave
11,000
10,000
9,000
SIHR
8,000
7,000
6,000
0
200
400
600
800
OUTPUT (MW)
1,000
1,200
1,400
HR-DESC.DOC; 4/17/98; PAGE E-12
SYSTEM COSTS
The System Costs are calculated as the SIHR and the SAHRAVE values multiplied by the relevant fuel
costs. SCE must be handled differently as it has two gas prices: one for the Cool Water units and another
for the other SCE units. The Cool Water gas price is significantly lower than SCE’s general gas price,
which gives the Cool Water units a considerable economic advantage raising them higher up in the
economic dispatch order.
The Table E-6 series, on the next page, gives the cost calculations for each of the three IOUs. In each
case, SAHRAVE is multiplied by the total price of gas and SIHR is multiplied by the dispatch price of gas.
Table E-7 gives the cost calculations for the three IOUs combined into a single system. Figures E-3 and
E-4 give the graphical representations for Tables E-6 and E-7, respectively.
Figure E-4 (Table E-7) can be thought of as a proxy for the entire system. The SIHR at the dispatch
price of gas curve is a proxy for the MC of the regulated system, and SAHRAVE at the total price of gas
curve is a proxy for the MCP of the competitive market.
Figure E-5 is a curve that is the ratio of the two curves in Figure 4 (Table E-7). It is the ratio of the MCP
proxy to the MC proxy for selected points: at 1000 MW intervals. The curve shows values in the range of
1.26 to 1.45 depending on the output level. These are very significant differences to be sure, but it is
important to keep in mind that in any one hour the difference can be much higher than this – as high as
8.5:1 as we have already shown.
The Figure E-5 curve implies that given an extended period of time where each unit is used equally and is
allowed to experience all of its various levels equally, the average will be as shown. Remembering our
earlier conclusion that this is unlikely since units will tend to operate more at their lower levels, we have
to conclude that the 1.26 to 1.45 range is probably low. At the same time, we must recognize that the
lowest and highest portions of the curve will tend to be used the least. The least that we can say here is
that this ratio will undoubtedly be higher than 1.26 – that is, MCP will no doubt exceed traditional MC by
something greater than 26 percent. Based on knowledge of computer simulations, not provided herein,
the estimate is easily 30 percent or more.
Figure E-6 is the same as Figure E-5 except that the difference due to the gas price differential has been
removed. This Figure represents the difference between Average and Incremental Heat Rates, only. The
range is now 1.17 to 1.36, as opposed to the 1.26 to 1.45 of Figure E-5. The effect of using Average
instead of Incremental Heat Rates is in the range of something greater than 17 percent. The effect of the
gas prices is therefore about 9 percent.
HR-DESC.DOC; 4/17/98; PAGE E-13
TABLE E-6-PGE: PG&E SYSTEM AVERAGE COST CALCULATIONS
SUMMARY IHR DATA
BLK INC
IHR
PLANT
#
MW
Btu/kWh
CUM
MW
mos7
mos6
mos7
mos6
pit7
mos7
con7
con7
pit7
con6
pit6
mos6
mor4
mos6
pit5
con6
mos7
pit7
pit6
mor4
hnp4
con6
pit5
pot3
con7
pit3&4
pit1&2
hnp4
mor3
mor3
pot3
pit1&2
mor4
mor3
pit5
mor3
pot3
pit3&4
pit6
mor4
pit5
hnp4
pit1&2
mor1&2
mor1&2
pit7
pit3&4
mor1&2
hnp4
con7
con6
hnp3
pit6
mor1&2
pit1&2
pot3
hnp2
hmb1&2
hmb1&2
hnp3
hnp2
pit3&4
hmb1&2
hnp2
hnp3
hnp2
hmb1&2
hnp3
2
2
3
3
3
4
2
3
2
3
2
4
2
5
2
2
5
4
3
3
2
4
3
3
4
3
3
3
2
3
2
2
4
4
4
5
4
2
4
5
5
4
4
2
3
5
4
4
5
5
5
2
5
5
5
5
2
3
2
3
3
5
4
4
4
5
5
5
135
135
185
185
180
221
39
85
60
85
35
221
39
148
35
39
148
216
82
84
20
102
82
52
102
82
82
82
39
84
5
20
101
101
97
68
62
20
97
68
65
96
96
20
82
144
96
96
66
68
68
17
65
66
66
41
17
27
16
27
27
66
31
32
32
21
21
21
7,196
7,370
7,890
8,146
8,476
8,485
8,496
8,503
8,555
8,555
8,613
8,668
8,703
8,714
8,744
8,756
8,760
8,762
8,797
8,848
8,873
8,877
8,900
8,924
8,933
8,983
9,003
9,044
9,056
9,064
9,066
9,079
9,083
9,100
9,135
9,159
9,276
9,276
9,293
9,314
9,344
9,379
9,391
9,407
9,441
9,469
9,529
9,675
9,724
9,754
9,811
9,876
9,963
10,081
10,331
10,341
10,364
10,366
10,543
10,861
10,981
11,211
11,392
11,861
12,246
12,701
13,521
13,552
135
270
455
640
820
1041
1080
1165
1225
1310
1345
1566
1605
1753
1788
1827
1975
2191
2273
2357
2377
2479
2561
2613
2715
2797
2879
2961
3000
3084
3089
3109
3210
3311
3408
3476
3538
3558
3655
3723
3788
3884
3980
4000
4082
4226
4322
4418
4484
4552
4620
4637
4702
4768
4834
4875
4892
4919
4935
4962
4989
5055
5086
5118
5150
5171
5192
5213
Disp.
2.31
$/MWh
16.6
17.0
18.2
18.8
19.6
19.6
19.6
19.6
19.8
19.8
19.9
20.0
20.1
20.1
20.2
20.2
20.2
20.2
20.3
20.4
20.5
20.5
20.6
20.6
20.6
20.8
20.8
20.9
20.9
20.9
20.9
21.0
21.0
21.0
21.1
21.2
21.4
21.4
21.5
21.5
21.6
21.7
21.7
21.7
21.8
21.9
22.0
22.3
22.5
22.5
22.7
22.8
23.0
23.3
23.9
23.9
23.9
23.9
24.4
25.1
25.4
25.9
26.3
27.4
28.3
29.3
31.2
31.3
IHR*MW
Block
Cumul.
971441
994931
1459609
1506925
1525759
1875107
331331
722789
513295
727171
301456
1915722
339425
1289726
306050
341490
1296414
1892651
721354
743248
177454
905452
729832
464057
911212
736606
738207
741638
353189
761357
45329
181571
917368
919114
886132
622813
575101
185523
901420
633373
607366
900405
901583
188135
774202
1363571
914759
928783
641751
663242
667170
167886
647610
665338
681813
423968
176181
279882
168689
293239
296490
739944
353140
379557
391877
266719
283948
284586
971441
1966372
3425981
4932906
6458665
8333772
8665104
9387893
9901188
10628359
10929814
12845537
13184962
14474688
14780738
15122229
16418642
18311293
19032647
19775896
19953349
20858801
21588633
22052690
22963902
23700507
24438714
25180352
25533541
26294897
26340226
26521797
27439165
28358279
29244411
29867224
30442325
30627848
31529268
32162641
32770007
33670412
34571995
34760130
35534331
36897902
37812661
38741444
39383196
40046438
40713607
40881494
41529104
42194442
42876255
43300223
43476404
43756286
43924976
44218215
44514705
45254649
45607789
45987346
46379222
46645941
46929889
47214476
SUMMARY AHR DATA
SIHR
Disp.
2.31
Btu/kWh
$/MWh
PLANT
#
MW
Btu/kWh
CUM
MW
7,196
7,283
7,530
7,708
7,876
8,006
8,023
8,058
8,083
8,113
8,126
8,203
8,215
8,257
8,267
8,277
8,313
8,358
8,373
8,390
8,394
8,414
8,430
8,440
8,458
8,474
8,489
8,504
8,511
8,526
8,527
8,531
8,548
8,565
8,581
8,592
8,604
8,608
8,626
8,639
8,651
8,669
8,686
8,690
8,705
8,731
8,749
8,769
8,783
8,798
8,812
8,816
8,832
8,850
8,870
8,882
8,887
8,895
8,901
8,911
8,923
8,952
8,967
8,985
9,006
9,021
9,039
9,057
16.6
16.8
17.4
17.8
18.2
18.5
18.5
18.6
18.7
18.7
18.8
18.9
19.0
19.1
19.1
19.1
19.2
19.3
19.3
19.4
19.4
19.4
19.5
19.5
19.5
19.6
19.6
19.6
19.7
19.7
19.7
19.7
19.7
19.8
19.8
19.8
19.9
19.9
19.9
20.0
20.0
20.0
20.1
20.1
20.1
20.2
20.2
20.3
20.3
20.3
20.4
20.4
20.4
20.4
20.5
20.5
20.5
20.5
20.6
20.6
20.6
20.7
20.7
20.8
20.8
20.8
20.9
20.9
pot3
pot3
pot3
pot3
hnp4
hnp4
hnp4
hnp4
mor4
mor4
mor4
mor4
con6
con6
con6
con6
mor3
mor3
mor3
mor3
con7
con7
con7
con7
pit5
pit5
pit5
pit5
mor1&2
mor1&2
mor1&2
mor1&2
pit6
pit6
pit6
pit6
pit3&4
pit3&4
pit3&4
pit3&4
pit7
pit7
pit7
pit7
mos7
mos7
mos7
mos7
mos6
mos6
mos6
mos6
pit1&2
pit1&2
pit1&2
pit1&2
hnp3
hnp3
hnp3
hnp3
hmb1&2
hmb1&2
hmb1&2
hmb1&2
hnp2
hnp2
hnp2
hnp2
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
5
52
62
41
20
82
96
66
39
84
101
68
39
85
102
68
39
84
101
68
39
85
102
68
35
82
97
65
20
82
96
66
35
82
97
65
20
82
96
66
60
180
216
144
135
185
221
148
135
185
221
148
20
82
96
66
17
27
32
21
16
27
31
21
17
27
32
21
10,853
10,207
9,689
9,686
11,642
10,585
9,985
9,854
11,694
10,292
9,714
9,561
11,860
10,300
9,579
9,479
12,056
10,616
9,950
9,712
12,112
10,361
9,622
9,517
12,186
10,598
9,907
9,712
12,246
11,128
10,438
10,266
12,870
10,899
10,075
9,929
12,905
11,388
10,408
10,341
13,001
11,062
9,977
9,705
13,304
9,758
9,079
8,949
13,370
9,918
9,273
9,115
13,412
11,673
10,573
10,339
16,339
12,974
12,336
12,471
16,853
13,245
12,142
12,167
16,865
13,382
12,517
12,433
5
57
119
160
180
262
358
424
463
547
648
716
755
840
942
1010
1049
1133
1234
1302
1341
1426
1528
1596
1631
1713
1810
1875
1895
1977
2073
2139
2174
2256
2353
2418
2438
2520
2616
2682
2742
2922
3138
3282
3417
3602
3823
3971
4106
4291
4512
4660
4680
4762
4858
4924
4941
4968
5000
5021
5037
5064
5095
5116
5133
5160
5192
5213
BLK INC
AHR
Total
2.51
$/MWh
27.2
25.6
24.3
24.3
29.2
26.6
25.1
24.7
29.4
25.8
24.4
24.0
29.8
25.9
24.0
23.8
30.3
26.6
25.0
24.4
30.4
26.0
24.2
23.9
30.6
26.6
24.9
24.4
30.7
27.9
26.2
25.8
32.3
27.4
25.3
24.9
32.4
28.6
26.1
26.0
32.6
27.8
25.0
24.4
33.4
24.5
22.8
22.5
33.6
24.9
23.3
22.9
33.7
29.3
26.5
26.0
41.0
32.6
31.0
31.3
42.3
33.2
30.5
30.5
42.3
33.6
31.4
31.2
AHR*MW
Block
Cumul.
54266
530763
600716
397135
232845
867947
958544
650366
456063
864561
981103
650147
462528
875488
977042
644582
470181
891770
1004983
660441
472386
880708
981468
647154
426514
869041
960937
631257
244911
912503
1002050
677577
450461
893708
977237
645407
258107
933821
999204
682485
780062
1991242
2154948
1397580
1796095
1805199
2006352
1324404
1804959
1834901
2049296
1349026
268231
957189
1014964
682388
277769
350302
394742
261888
269651
357616
376412
255499
286706
361311
400547
261103
54266
585029
1185744
1582880
1815724
2683671
3642216
4292582
4748644
5613206
6594309
7244456
7706983
8582471
9559513
10204095
10674276
11566046
12571029
13231470
13703857
14584564
15566033
16213187
16639701
17508742
18469679
19100936
19345848
20258351
21260402
21937979
22388440
23282147
24259384
24904791
25162898
26096719
27095923
27778408
28558470
30549713
32704661
34102241
35898336
37703535
39709887
41034291
42839250
44674150
46723446
48072472
48340703
49297892
50312855
50995243
51273012
51623314
52018056
52279943
52549594
52907211
53283622
53539122
53825827
54187139
54587685
54848789
SAHR
Total
2.5
Btu/kWh
$/MWh
10,853
10,264
9,964
9,893
10,087
10,243
10,174
10,124
10,256
10,262
10,176
10,118
10,208
10,217
10,148
10,103
10,176
10,208
10,187
10,162
10,219
10,228
10,187
10,159
10,202
10,221
10,204
10,187
10,209
10,247
10,256
10,256
10,298
10,320
10,310
10,300
10,321
10,356
10,358
10,357
10,415
10,455
10,422
10,391
10,506
10,467
10,387
10,333
10,433
10,411
10,355
10,316
10,329
10,352
10,357
10,356
10,377
10,391
10,404
10,412
10,433
10,448
10,458
10,465
10,486
10,501
10,514
10,522
27.1
25.7
24.9
24.7
25.2
25.6
25.4
25.3
25.6
25.7
25.4
25.3
25.5
25.5
25.4
25.3
25.4
25.5
25.5
25.4
25.5
25.6
25.5
25.4
25.5
25.6
25.5
25.5
25.5
25.6
25.6
25.6
25.7
25.8
25.8
25.7
25.8
25.9
25.9
25.9
26.0
26.1
26.1
26.0
26.3
26.2
26.0
25.8
26.1
26.0
25.9
25.8
25.8
25.9
25.9
25.9
25.9
26.0
26.0
26.0
26.1
26.1
26.1
26.2
26.2
26.3
26.3
26.3
HR-DESC.DOC; 4/17/98; PAGE E-14
TABLE E-6-SCE: SCE SYSTEM AVERAGE COST CALCULATIONS
SUMMARY IHR DATA
Disp.
2.24
DISPATCH
PLANT BLK INC
IHR
CUM 2.43
Unit Cost * MW
# MW Btu/kWh MW $/MWh Unit
Cumul.
cw34
cw34
cw34
cw34
cw01
cw02
cw02
cw01
cw02
cw01
cw02
cw01
hig3&4
hig3&4
ala5&6
orb1
orb2
hig3&4
els3&4
hig1&2
orb1
eti3&4
hig1&2
man1&2
ala3&4
orb2
hig1&2
hig3&4
hig1&2
hun1&2
red7&8
els3&4
ala3&4
eti3&4
ala5&6
sbr1&2
orb1
red7&8
hun1&2
man1&2
orb2
els3&4
ala3&4
eti3&4
red5&6
red7&8
hun1&2
sbr1&2
ala5&6
orb1
ala1&2
red5&6
els3&4
els1&2
red7&8
eti1&2
orb2
man1&2
ala3&4
eti3&4
2
3
4
5
2
2
3
3
4
4
5
5
2
3
2
2
2
4
2
2
3
2
3
2
2
3
4
5
5
2
2
3
3
3
3
2
4
3
3
3
4
4
4
4
2
4
4
3
4
5
2
3
5
2
5
2
5
4
5
5
40 7,013
60 7,064
140 7,334
132 8,018
13 9,320
16 9,368
16 9,540
13 9,549
16 9,742
13 9,808
14 9,960
9 10,050
14 7,899
26 8,096
160 8,155
120 8,171
175 8,192
30 8,338
120 8,395
10 8,413
130 8,429
120 8,438
20 8,438
100 8,443
120 8,443
175 8,459
18 8,471
9 8,485
10 8,495
100 8,552
100 8,557
160 8,576
160 8,639
160 8,641
180 8,656
28 8,681
120 8,742
300 8,759
100 8,768
105 8,799
175 8,818
160 8,839
160 8,933
160 8,943
70 8,992
140 9,028
100 9,050
28 9,056
180 9,074
130 9,112
70 9,127
90 9,134
190 9,198
70 9,224
160 9,248
60 9,264
175 9,268
95 9,279
160 9,305
160 9,322
40
100
240
372
385
401
417
430
446
459
473
482
496
522
682
802
977
1007
1127
1137
1267
1387
1407
1507
1627
1802
1820
1829
1839
1939
2039
2199
2359
2519
2699
2727
2847
3147
3247
3352
3527
3687
3847
4007
4077
4217
4317
4345
4525
4655
4725
4815
5005
5075
5235
5295
5470
5565
5725
5885
15.7
15.8
16.4
18.0
20.9
21.0
21.4
21.4
21.8
22.0
22.3
22.5
19.2
19.7
19.8
19.9
19.9
20.3
20.4
20.4
20.5
20.5
20.5
20.5
20.5
20.6
20.6
20.6
20.6
20.8
20.8
20.8
21.0
21.0
21.0
21.1
21.2
21.3
21.3
21.4
21.4
21.5
21.7
21.7
21.9
21.9
22.0
22.0
22.0
22.1
22.2
22.2
22.4
22.4
22.5
22.5
22.5
22.5
22.6
22.7
628
949
2,300
2,371
271
336
342
278
349
286
312
203
269
512
3,171
2,383
3,484
608
2,448
204
2,663
2,460
410
2,052
2,462
3,597
371
186
206
2,078
2,079
3,334
3,359
3,359
3,786
591
2,549
6,385
2,131
2,245
3,750
3,436
3,473
3,477
1,530
3,071
2,199
616
3,969
2,878
1,552
1,998
4,247
1,569
3,596
1,351
3,941
2,142
3,618
3,624
628
1,578
3,878
6,249
6,520
6,856
7,198
7,476
7,825
8,111
8,423
8,626
8,894
9,406
12,577
14,959
18,443
19,051
21,499
21,703
24,366
26,826
27,236
29,288
31,750
35,347
35,718
35,903
36,110
38,188
40,267
43,602
46,960
50,320
54,106
54,697
57,246
63,631
65,762
68,007
71,757
75,193
78,666
82,143
83,673
86,744
88,944
89,560
93,529
96,407
97,960
99,957
104,204
105,773
109,368
110,719
114,660
116,803
120,420
124,044
Disp.
2.24 =Cool Water
2.43
PLANT
$/MWh
15.7
15.8
16.2
16.8
16.9
17.1
17.3
17.4
17.5
17.7
17.8
17.9
17.9
18.0
18.4
18.7
18.9
18.9
19.1
19.1
19.2
19.3
19.4
19.4
19.5
19.6
19.6
19.6
19.6
19.7
19.7
19.8
19.9
20.0
20.0
20.1
20.1
20.2
20.3
20.3
20.3
20.4
20.4
20.5
20.5
20.6
20.6
20.6
20.7
20.7
20.7
20.8
20.8
20.8
20.9
20.9
21.0
21.0
21.0
21.1
O
O
O
O
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
15
15
15
15
cw01
cw01
cw01
cw01
cw02
cw02
cw02
cw02
orb1
orb1
orb1
orb1
ala5&6
ala5&6
ala5&6
ala5&6
red7&8
red7&8
red7&8
red7&8
lbc8&9
lbc8&9
lbc8&9
lbc8&9
cw34
cw34
cw34
cw34
man1&2
man1&2
man1&2
man1&2
hun1&2
hun1&2
hun1&2
hun1&2
orb2
orb2
orb2
orb2
eti3&4
eti3&4
eti3&4
eti3&4
els3&4
els3&4
els3&4
els3&4
ala3&4
ala3&4
ala3&4
ala3&4
eti1&2
eti1&2
eti1&2
eti1&2
els1&2
els1&2
els1&2
els1&2
BLK INC
#
MW
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
13
13
13
9
16
16
16
14
120
130
120
130
160
180
180
180
100
300
140
160
110
120
110
150
40
60
140
132
100
105
95
90
100
100
100
90
175
175
175
175
120
160
160
160
120
160
160
190
120
160
160
160
60
60
60
64
70
90
90
80
SUMMARY AHR DATA
Total
2.34
TOTAL
AHR
CUM
2.61
Unit Cost * MW
Btu/kWh
MW $/MWh Unit
Cumul.
11,259
10,587
10,343
10,264
11,401
10,650
10,370
10,262
10,354
9,753
9,486
9,382
10,532
9,810
9,560
9,491
10,808
9,995
9,633
9,548
11,404
10,506
10,230
10,107
13,307
11,822
10,361
9,506
12,114
10,087
9,706
9,664
12,570
10,331
9,822
9,666
13,188
10,168
9,595
9,442
15,141
11,005
10,078
9,798
15,882
11,251
10,188
9,825
16,210
11,407
10,311
9,960
16,432
12,244
11,371
11,106
17,208
12,131
11,038
10,678
13
26
39
48
64
80
96
110
230
360
480
610
770
950
1,130
1,310
1,410
1,710
1,850
2,010
2,120
2,240
2,350
2,500
2,540
2,600
2,740
2,872
2,972
3,077
3,172
3,262
3,362
3,462
3,562
3,652
3,827
4,002
4,177
4,352
4,472
4,632
4,792
4,952
5,072
5,232
5,392
5,582
5,702
5,862
6,022
6,182
6,242
6,302
6,362
6,426
6,496
6,586
6,676
6,756
26.3
24.8
24.2
24.0
26.7
24.9
24.3
24.0
27.0
25.5
24.8
24.5
27.5
25.6
25.0
24.8
28.2
26.1
25.1
24.9
29.8
27.4
26.7
26.4
31.1
27.7
24.2
22.2
31.6
26.3
25.3
25.2
32.8
27.0
25.6
25.2
34.4
26.5
25.0
24.6
39.5
28.7
26.3
25.6
41.5
29.4
26.6
25.6
42.3
29.8
26.9
26.0
42.9
32.0
29.7
29.0
44.9
31.7
28.8
27.9
343
322
315
216
427
399
388
336
3,243
3,309
2,971
3,183
4,398
4,609
4,491
4,459
2,821
7,826
3,520
3,987
3,274
3,291
2,937
3,957
1,246
1,660
3,394
2,936
3,162
2,764
2,407
2,270
3,281
2,696
2,564
2,271
6,023
4,644
4,383
4,313
4,742
4,596
4,209
4,092
4,974
4,698
4,254
4,872
5,077
4,764
4,306
4,159
2,573
1,917
1,781
1,855
3,144
2,850
2,593
2,230
343
665
979
1,195
1,622
2,021
2,409
2,745
5,988
9,297
12,268
15,452
19,850
24,459
28,950
33,409
36,230
44,056
47,575
51,563
54,837
58,127
61,064
65,021
66,267
67,927
71,321
74,257
77,419
80,183
82,590
84,860
88,140
90,837
93,400
95,671
101,694
106,338
110,721
115,033
119,776
124,371
128,580
132,671
137,646
142,344
146,598
151,470
156,547
161,311
165,617
169,776
172,349
174,267
176,047
177,903
181,046
183,896
186,489
188,718
Total
2.34
2.61
$/MWh
26.3
25.6
25.1
24.9
25.3
25.3
25.1
25.0
26.0
25.8
25.6
25.3
25.8
25.7
25.6
25.5
25.7
25.8
25.7
25.7
25.9
25.9
26.0
26.0
26.1
26.1
26.0
25.9
26.0
26.1
26.0
26.0
26.2
26.2
26.2
26.2
26.6
26.6
26.5
26.4
26.8
26.9
26.8
26.8
27.1
27.2
27.2
27.1
27.5
27.5
27.5
27.5
27.6
27.7
27.7
27.7
27.9
27.9
27.9
27.9
- Continued on Next Page -
HR-DESC.DOC ; 4/17/98: PAGE E-15
TABLE E-6-SCE: SCE SYSTEM AVERAGE COST CALCULATIONS - CONTINUED
SUMMARY IHR DATA
Disp.
2.24
DISPATCH
PLANT BLK INC
IHR
CUM 2.43
Unit Cost * MW
# MW Btu/kWh MW $/MWh Unit
Cumul.
red5&6
ala1&2
ala5&6
hun1&2
sbr1&2
els1&2
red5&6
lbc8&9
eti1&2
els1&2
lbc8&9
ala1&2
sbr1&2
lbc8&9
lbc8&9
man1&2
els1&2
ala1&2
eti1&2
eti1&2
4
3
5
5
4
3
5
2
3
4
3
4
5
4
5
5
5
5
4
5
90 9,324
90 9,341
180 9,375
90 9,379
28 9,384
90 9,394
80 9,535
110 9,608
60 9,627
90 9,631
120 9,647
90 9,663
28 9,667
110 9,717
150 9,836
90 9,842
80 9,898
80 10,047
60 10,104
64 10,719
5975
6065
6245
6335
6363
6453
6533
6643
6703
6793
6913
7003
7031
7141
7291
7381
7461
7541
7601
7665
22.7
22.7
22.8
22.8
22.8
22.8
23.2
23.3
23.4
23.4
23.4
23.5
23.5
23.6
23.9
23.9
24.1
24.4
24.6
26.0
2,039
2,043
4,101
2,051
639
2,055
1,854
2,568
1,404
2,106
2,813
2,113
658
2,597
3,585
2,152
1,924
1,953
1,473
1,667
Disp.
2.24 =Cool Water
2.43
PLANT
$/MWh
126,084
128,127
132,227
134,278
134,917
136,971
138,825
141,393
142,797
144,903
147,716
149,829
150,487
153,085
156,670
158,822
160,746
162,699
164,172
165,839
21.1
21.1
21.2
21.2
21.2
21.2
21.2
21.3
21.3
21.3
21.4
21.4
21.4
21.4
21.5
21.5
21.5
21.6
21.6
21.6
16
16
16
16
17
17
17
17
18
18
18
18
19
19
19
19
20
20
20
20
BLK INC
#
MW
ala1&2
ala1&2
ala1&2
ala1&2
red5&6
red5&6
red5&6
red5&6
sbr1&2
sbr1&2
sbr1&2
sbr1&2
hig1&2
hig1&2
hig1&2
hig1&2
hig3&4
hig3&4
hig3&4
hig3&4
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
70
90
90
80
70
90
90
80
28
28
28
28
10
20
18
10
14
26
30
9
SUMMARY AHR DATA
Total
2.34
TOTAL
AHR
CUM
2.61
Unit Cost * MW
Btu/kWh
MW $/MWh Unit
Cumul.
17,605
12,222
11,084
10,734
18,702
12,511
11,144
10,661
18,968
13,553
12,072
11,426
34,940
20,641
15,481
13,820
44,598
24,520
17,262
15,100
6,826
6,916
7,006
7,086
7,156
7,246
7,336
7,416
7,444
7,472
7,500
7,528
7,538
7,558
7,576
7,586
7,600
7,626
7,656
7,665
45.9
31.9
28.9
28.0
48.8
32.7
29.1
27.8
49.5
35.4
31.5
29.8
91.2
53.9
40.4
36.1
116.4
64.0
45.1
39.4
3,216
2,871
2,604
2,241
3,417
2,939
2,618
2,226
1,386
990
882
835
912
1,077
727
361
1,630
1,664
1,352
355
Total
2.34
2.61
$/MWh
191,935
194,806
197,410
199,651
203,068
206,006
208,624
210,850
212,236
213,227
214,109
214,944
215,856
216,933
217,661
218,021
219,651
221,315
222,667
223,021
28.1
28.2
28.2
28.2
28.4
28.4
28.4
28.4
28.5
28.5
28.5
28.6
28.6
28.7
28.7
28.7
28.9
29.0
29.1
29.1
SHAR
Total
2.91
TABLE E-6-SDG: SDG&E SYSTEM AVERAGE COST CALCULATIONS
SUMMARY IHR DATA
BLK INC CUM
PLANT
# MW MW
IHR
Disp.
2.34
Btu/kWh
$/MWh
Block
Cumul.
sba1
sba1
sba3
enc5
sba3
sba2
enc5
sba2
sba1
enc3
enc4
sba3
enc5
enc4
enc3
enc1
enc2
sba2
enc1
enc2
enc4
sba3
enc5
sba1
enc1
enc2
sba4
sba4
enc3
sba2
enc4
sba4
enc2
enc1
enc3
sba4
8,560
8,764
8,937
9,016
9,082
9,127
9,190
9,287
9,368
9,374
9,472
9,487
9,605
9,617
9,635
9,736
9,763
9,763
9,815
9,889
9,966
10,027
10,163
10,169
10,231
10,258
10,268
10,278
10,375
10,407
10,437
10,741
10,760
10,909
11,377
11,797
20.0
20.5
20.9
21.1
21.3
21.4
21.5
21.7
21.9
21.9
22.2
22.2
22.5
22.5
22.5
22.8
22.8
22.8
23.0
23.1
23.3
23.5
23.8
23.8
23.9
24.0
24.0
24.0
24.3
24.4
24.4
25.1
25.2
25.5
26.6
27.6
59923
324271
116177
531917
390525
73019
725985
343637
412176
74995
502013
483825
902838
711654
260155
68155
58577
439331
265009
257107
867054
340914
640257
294911
327393
318009
369663
10278
342383
312208
615781
483358
225956
229081
250290
353905
59923
384194
500371
1032288
1422813
1495832
2221817
2565454
2977630
3052625
3554638
4038464
4941301
5652955
5913110
5981265
6039842
6479174
6744183
7001290
7868344
8209258
8849515
9144426
9471819
9789828
10159491
10169769
10512151
10824359
11440141
11923498
12149455
12378536
12628826
12982730
2
3
2
2
3
2
3
3
4
2
2
4
4
3
3
2
2
4
3
3
4
5
5
5
4
4
3
2
4
5
5
4
5
5
5
5
7
37
13
59
43
8
79
37
44
8
53
51
94
74
27
7
6
45
27
26
87
34
63
29
32
31
36
1
33
30
59
45
21
21
22
30
7
44
57
116
159
167
246
283
327
335
388
439
533
607
634
641
647
692
719
745
832
866
929
958
990
1021
1057
1058
1091
1121
1180
1225
1246
1267
1289
1319
IHR*MW
SUMMARY AHR DATA
SHIR
Total
2.91
Btu/kWh
$/MWh
8,560
8,732
8,778
8,899
8,949
8,957
9,032
9,065
9,106
9,112
9,161
9,199
9,271
9,313
9,327
9,331
9,335
9,363
9,380
9,398
9,457
9,480
9,526
9,545
9,567
9,588
9,612
9,612
9,635
9,656
9,695
9,733
9,751
9,770
9,797
9,843
24.9
25.4
25.5
25.9
26.0
26.1
26.3
26.4
26.5
26.5
26.7
26.8
27.0
27.1
27.1
27.2
27.2
27.2
27.3
27.3
27.5
27.6
27.7
27.8
27.8
27.9
28.0
28.0
28.0
28.1
28.2
28.3
28.4
28.4
28.5
28.6
BLK INC CUM
PLANT # MW MW
AHR
Total
2.91
Btu/kWh
$/MWh
Block
Cumul.
Btu/kWh
$/MWh
sba1
sba1
sba1
sba1
sba3
sba3
sba3
sba3
sba2
sba2
sba2
sba2
enc1
enc1
enc1
enc1
enc3
enc3
enc3
enc3
enc4
enc4
enc4
enc4
enc5
enc5
enc5
enc5
enc2
enc2
enc2
enc2
sba4
sba4
sba4
sba4
11,778
10,613
9,922
9,857
11,880
10,680
10,062
9,961
12,099
11,007
10,352
10,259
12,632
11,483
10,831
10,737
13,155
11,675
10,933
10,891
13,472
11,055
10,494
10,398
13,485
10,741
10,144
10,055
14,131
12,451
11,406
11,135
14,726
13,382
12,128
11,847
34.3
30.9
28.9
28.7
34.6
31.1
29.3
29.0
35.2
32.0
30.1
29.9
36.8
33.4
31.5
31.2
38.3
34.0
31.8
31.7
39.2
32.2
30.5
30.3
39.2
31.3
29.5
29.3
41.1
36.2
33.2
32.4
42.9
38.9
35.3
34.5
82446
392666
436553
285863
154440
459244
513141
338664
96795
407264
465856
307762
88422
310038
346586
225480
105243
315230
360797
239600
714007
818074
912936
613474
795593
848535
953543
633474
84783
323726
353600
233841
14726
481746
545765
355406
82446
475112
911665
1197528
1351968
1811212
2324353
2663017
2759812
3167077
3632933
3940695
4029117
4339155
4685741
4911221
5016464
5331694
5692491
5932091
6646098
7464172
8377108
8990582
9786176
10634711
11588254
12221728
12306511
12630237
12983837
13217677
13232404
13714149
14259914
14615320
11,778
10,798
10,360
10,235
10,400
10,469
10,377
10,322
10,375
10,452
10,439
10,425
10,465
10,532
10,553
10,562
10,606
10,663
10,680
10,688
10,931
10,945
10,894
10,858
11,033
11,009
10,932
10,883
10,900
10,935
10,948
10,951
10,954
11,024
11,063
11,081
34.3
31.4
30.1
29.8
30.3
30.5
30.2
30.0
30.2
30.4
30.4
30.3
30.5
30.6
30.7
30.7
30.9
31.0
31.1
31.1
31.8
31.8
31.7
31.6
32.1
32.0
31.8
31.7
31.7
31.8
31.9
31.9
31.9
32.1
32.2
32.2
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
7
37
44
29
13
43
51
34
8
37
45
30
7
27
32
21
8
27
33
22
53
74
87
59
59
79
94
63
6
26
31
21
1
36
45
30
7
44
88
117
130
173
224
258
266
303
348
378
385
412
444
465
473
500
533
555
608
682
769
828
887
966
1060
1123
1129
1155
1186
1207
1208
1244
1289
1319
AHR*MW
HR-DESC.DOC ; 4/17/98: PAGE E-16
FIGURE E-3-PGE
PG&E
MCP & MC PROXIES
35
MCP = AHR @ TOTAL GAS
PRICE
COST ($/MWh)
30
25
20
15
MC = IHR @ DISPATCH GAS PRICE
10
5
0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
5,500
OUTPUT (MW)
FIGURE E-3-SCE
SCE
MCP & MC PROXIES
35
MCP = AHR @ TOTAL GAS PRICE
COST ($/MWh)
30
25
20
MC = IHR @ DISPATCH GAS PRICE
15
10
5
0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
OUTPUT (MW)
FIGURE E-3-SDG
SDG&E
MCP & MC PROXIES
35
COST ($/MWh)
30
MCP = AHR @ TOTAL GAS PRICE
25
20
MC = IHR @ DISPATCH GAS PRICE
15
10
5
0
0
200
400
600
800
1,000
1,200
1,400
OUTPUT (MW)
HR-DESC.DOC ; 4/17/98: PAGE E-17
TABLE E-7: ALL IOUs SYSTEM AVERAGE COST CALCULATIONS
SUMMARY IHR DATA (Dispatch Gas Price)
BLK INC
IHR
PLANT
#
MW Btu/kWh
cw34
cw34
cw34
mos7
cw34
mos6
cw01
cw02
cw02
cw01
mos7
cw02
cw01
mos6
cw02
cw01
pit7
mos7
con7
con7
pit7
con6
mos6
mor4
mos6
pit5
con6
mos7
pit7
pit6
mor4
pit6
hnp4
con6
pit5
pot3
con7
pit3&4
pit1&2
hnp4
mor3
mor3
pot3
pit1&2
mor4
mor3
pit6
pit5
mor3
pot3
pit3&4
mor4
pit5
sba1
hnp4
pit1&2
mor1&2
mor1&2
pit7
pit3&4
pit6
2
3
4
2
5
2
2
2
3
3
3
4
4
3
5
5
3
4
2
3
2
3
4
2
5
2
2
5
4
2
3
3
2
4
3
3
4
3
3
3
2
3
2
2
4
4
4
4
5
4
2
5
5
2
4
4
2
3
5
4
5
40 7,013
60 7,064
140 7,334
135 7,196
132 8,018
135 7,370
13 9,320
16 9,368
16 9,540
13 9,549
185 7,890
16 9,742
13 9,808
185 8,146
14 9,960
9 10,050
180 8,476
221 8,485
39 8,496
85 8,503
60 8,555
85 8,555
221 8,668
39 8,703
148 8,714
35 8,744
39 8,756
148 8,760
216 8,762
35 8,821
84 8,848
82 8,868
20 8,873
102 8,877
82 8,900
52 8,924
102 8,933
82 8,983
82 9,003
82 9,044
39 9,056
84 9,064
5 9,066
20 9,079
101 9,083
101 9,100
97 9,135
97 9,135
68 9,159
62 9,276
20 9,276
68 9,314
65 9,344
7
8,560
96 9,379
96 9,391
20 9,407
82 9,441
144 9,469
96 9,529
65 9,579
SUMMARY AHR DATA (Total Gas Price)
Unit
Unit*MW System
CUM
Cost
Unit Cumul. Cost
MW $/MWh $/hr
$/hr $/MWh
40
100
240
375
507
642
655
671
687
700
885
901
914
1099
1113
1122
1302
1523
1562
1647
1707
1792
2013
2052
2200
2235
2274
2422
2638
2673
2757
2839
2859
2961
3043
3095
3197
3279
3361
3443
3482
3566
3571
3591
3692
3793
3890
3987
4055
4117
4137
4205
4270
4277
4373
4469
4489
4571
4715
4811
4876
15.7
15.8
16.4
16.6
18.0
17.0
20.9
21.0
21.4
21.4
18.2
21.8
22.0
18.8
22.3
22.5
19.6
19.6
19.6
19.6
19.8
19.8
20.0
20.1
20.1
20.2
20.2
20.2
20.2
20.4
20.4
20.5
20.5
20.5
20.6
20.6
20.6
20.8
20.8
20.9
20.9
20.9
20.9
21.0
21.0
21.0
21.1
21.1
21.2
21.4
21.4
21.5
21.6
20.0
21.7
21.7
21.7
21.8
21.9
22.0
22.1
628
949
2300
2244
2371
2298
271
336
342
278
3372
349
286
3481
312
203
3525
4331
765
1670
1186
1680
4425
784
2979
707
789
2995
4372
713
1717
1680
410
2092
1686
1072
2105
1702
1705
1713
816
1759
105
419
2119
2123
2047
2047
1439
1328
429
1463
1403
140
2080
2083
435
1788
3150
2113
1438
628
1578
3878
6122
8493
10791
11062
11398
11740
12018
15390
15739
16025
19506
19818
20021
23545
27877
28642
30312
31497
33177
37602
38386
41366
42073
42862
45856
50228
50941
52658
54338
54748
56840
58526
59598
61702
63404
65109
66822
67638
69397
69502
69921
72040
74163
76210
78257
79696
81025
81453
82916
84319
84459
86539
88622
89057
90845
93995
96108
97546
15.7
15.8
16.2
16.3
16.8
16.8
16.9
17.0
17.1
17.2
17.4
17.5
17.5
17.7
17.8
17.8
18.1
18.3
18.3
18.4
18.5
18.5
18.7
18.7
18.8
18.8
18.8
18.9
19.0
19.1
19.1
19.1
19.1
19.2
19.2
19.3
19.3
19.3
19.4
19.4
19.4
19.5
19.5
19.5
19.5
19.6
19.6
19.6
19.7
19.7
19.7
19.7
19.7
19.7
19.8
19.8
19.8
19.9
19.9
20.0
20.0
BLK INC
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
14
15
15
15
15
16
AHR
PLANT
#
MW
Btu/kWh
cw01
cw01
cw01
cw01
cw02
cw02
cw02
cw02
orb1
orb1
orb1
orb1
pot3
pot3
pot3
pot3
ala5&6
ala5&6
ala5&6
ala5&6
red7&8
red7&8
red7&8
red7&8
hnp4
hnp4
hnp4
hnp4
mor4
mor4
mor4
mor4
pit6
pit6
pit6
pit6
hun3
hun3
hun3
hun3
con6
con6
con6
con6
hun4
hun4
hun4
hun4
mor3
mor3
mor3
mor3
con7
con7
con7
con7
pit5
pit5
pit5
pit5
mor1&2
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
13
13
13
9
16
16
16
14
120
130
120
130
5
52
62
41
160
180
180
180
100
300
140
160
20
82
96
66
39
84
101
68
35
82
97
65
30
30
30
35
39
85
102
68
30
30
30
45
39
84
101
68
39
85
102
68
35
82
97
65
20
11,259
10,587
10,343
10,264
11,401
10,650
10,370
10,262
10,354
9,753
9,486
9,382
10,853
10,207
9,689
9,686
10,532
9,810
9,560
9,491
10,808
9,995
9,633
9,548
11,642
10,585
9,985
9,854
11,694
10,292
9,714
9,561
11,709
10,352
9,751
9,625
11,342
10,862
10,602
10,474
11,860
10,300
9,579
9,479
11,407
10,926
10,661
10,474
12,056
10,616
9,950
9,712
12,112
10,361
9,622
9,517
12,186
10,598
9,907
9,712
12,246
Unit
Unit*MW System
CUM Total Unit Cumul.
Total
MW $/MWh $/hr
$/hr
$/MWh
13
26
39
48
64
80
96
110
230
360
480
610
615
667
729
770
930
1110
1290
1470
1570
1870
2010
2170
2190
2272
2368
2434
2473
2557
2658
2726
2761
2843
2940
3005
3035
3065
3095
3130
3169
3254
3356
3424
3454
3484
3514
3559
3598
3682
3783
3851
3890
3975
4077
4145
4180
4262
4359
4424
4444
26.3
24.8
24.2
24.0
26.7
24.9
24.3
24.0
27.0
25.5
24.8
24.5
27.2
25.6
24.3
24.3
27.5
25.6
25.0
24.8
28.2
26.1
25.1
24.9
29.2
26.6
25.1
24.7
29.4
25.8
24.4
24.0
29.4
26.0
24.5
24.2
29.6
28.4
27.7
27.3
29.8
25.9
24.0
23.8
29.8
28.5
27.8
27.3
30.3
26.6
25.0
24.4
30.4
26.0
24.2
23.9
30.6
26.6
24.9
24.4
30.7
343
322
315
216
427
399
388
336
3243
3309
2971
3183
136
1332
1508
997
4398
4609
4491
4459
2821
7826
3520
3987
584
2179
2406
1632
1145
2170
2463
1632
1029
2131
2374
1570
888
851
830
957
1161
2197
2452
1618
893
855
835
1230
1180
2238
2523
1658
1186
2211
2463
1624
1071
2181
2412
1584
615
343
665
979
1195
1622
2021
2409
2745
5988
9297
12268
15452
15588
16920
18428
19425
23823
28432
32923
37382
40203
48029
51548
55536
56120
58299
60704
62337
63482
65652
68114
69746
70775
72905
75280
76850
77738
78588
79419
80375
81536
83734
86186
87804
88697
89553
90387
91618
92798
95036
97559
99216
100402
102613
105076
106700
107771
109952
112364
113949
114563
26.3
25.6
25.1
24.9
25.3
25.3
25.1
25.0
26.0
25.8
25.6
25.3
25.3
25.4
25.3
25.2
25.6
25.6
25.5
25.4
25.6
25.7
25.6
25.6
25.6
25.7
25.6
25.6
25.7
25.7
25.6
25.6
25.6
25.6
25.6
25.6
25.6
25.6
25.7
25.7
25.7
25.7
25.7
25.6
25.7
25.7
25.7
25.7
25.8
25.8
25.8
25.8
25.8
25.8
25.8
25.7
25.8
25.8
25.8
25.8
25.8
- Continued on Next Page -
HR-DESC.DOC ; 4/17/98: PAGE E-18
TABLE E-7: ALL IOUs SYSTEM AVERAGE COST CALCULATIONS - CONTINUED
SUMMARY IHR DATA (Dispatch Gas Price)
BLK INC
IHR
PLANT
#
MW Btu/kWh
sba1
mor1&2
hnp4
con7
sba3
con6
enc5
hnp3
hig3&4
sba3
sba2
enc5
mor1&2
sba2
hig3&4
sba1
enc3
pit1&2
pot3
ala5&6
enc4
orb2
hnp2
hmb1&2
orb1
sba3
enc5
enc4
enc3
hig3&4
hmb1&2
enc1
enc2
sba2
hig1&2
orb1
eti3&4
hig1&2
man1&2
ala3&4
enc1
orb2
hig1&2
hig3&4
hig1&2
enc2
hnp3
hun1&2
red7&8
enc4
sba3
ala3&4
hnp2
eti3&4
ala5&6
sbr1&2
els1-4
orb1
enc5
sba1
red7&8
3
4
5
5
2
5
2
2
2
3
2
3
5
3
3
4
2
5
5
2
2
2
2
3
2
4
4
3
3
4
2
2
2
4
2
3
2
3
2
2
3
3
4
5
5
3
3
2
2
4
5
3
3
3
3
2
2
4
5
5
3
37
96
66
68
13
68
59
17
14
43
8
79
66
37
26
44
8
66
41
160
53
175
17
27
120
51
94
74
27
30
16
7
6
45
10
130
120
20
100
120
27
175
18
9
10
26
27
100
100
87
34
160
27
160
180
28
190
120
63
29
300
8,764
9,675
9,724
9,754
8,937
9,811
9,016
9,876
7,899
9,082
9,127
9,190
10,081
9,287
8,096
9,368
9,374
10,331
10,341
8,155
9,472
8,192
10,364
10,366
8,171
9,487
9,605
9,617
9,635
8,338
10,543
9,736
9,763
9,763
8,413
8,429
8,438
8,438
8,443
8,443
9,815
8,459
8,471
8,485
8,495
9,889
10,861
8,552
8,557
9,966
10,027
8,639
10,981
8,641
8,656
8,681
8,715
8,742
10,163
10,169
8,759
SUMMARY AHR DATA (Total Gas Price)
Unit
Unit*MW System
CUM
Cost
Unit Cumul. Cost
MW $/MWh $/hr
$/hr $/MWh
4913
5009
5075
5143
5156
5224
5283
5300
5314
5357
5365
5444
5510
5547
5573
5617
5625
5691
5732
5892
5945
6120
6137
6164
6284
6335
6429
6503
6530
6560
6576
6583
6589
6634
6644
6774
6894
6914
7014
7134
7161
7336
7354
7363
7373
7399
7426
7526
7626
7713
7747
7907
7934
8094
8274
8302
8492
8612
8675
8704
9004
20.5
22.3
22.5
22.5
20.9
22.7
21.1
22.8
19.2
21.3
21.4
21.5
23.3
21.7
19.7
21.9
21.9
23.9
23.9
19.8
22.2
19.9
23.9
23.9
19.9
22.2
22.5
22.5
22.5
20.3
24.4
22.8
22.8
22.8
20.4
20.5
20.5
20.5
20.5
20.5
23.0
20.6
20.6
20.6
20.6
23.1
25.1
20.8
20.8
23.3
23.5
21.0
25.4
21.0
21.0
21.1
21.2
21.2
23.8
23.8
21.3
759
2145
1482
1532
272
1541
1245
388
269
914
171
1699
1537
804
512
964
175
1575
979
3171
1175
3484
407
647
2383
1132
2113
1665
609
608
390
159
137
1028
204
2663
2460
410
2052
2462
620
3597
371
186
206
602
677
2078
2079
2029
798
3359
685
3359
3786
591
4024
2549
1498
690
6385
98305
100450
101933
103465
103737
105278
106523
106911
107179
108093
108264
109963
111500
112304
112815
113780
113955
115530
116510
119680
120855
124339
124746
125392
127775
128907
131020
132685
133294
133902
134291
134451
134588
135616
135820
138483
140943
141353
143405
145867
146487
150084
150455
150640
150847
151448
152126
154204
156284
158312
159110
162469
163154
166513
170299
170890
174914
177463
178961
179651
186036
20.0
20.1
20.1
20.1
20.1
20.2
20.2
20.2
20.2
20.2
20.2
20.2
20.2
20.2
20.2
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.3
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.4
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.5
20.6
20.6
20.6
20.6
20.6
20.6
20.6
20.6
20.7
BLK INC
16
16
16
17
17
17
17
18
18
18
18
19
19
19
19
20
20
20
20
21
21
21
21
22
22
22
22
23
23
23
23
24
24
24
24
25
25
25
25
26
26
26
26
27
27
27
27
28
28
28
28
29
29
29
29
30
30
30
30
31
31
AHR
PLANT
#
MW
Btu/kWh
mor1&2
mor1&2
mor1&2
cw34
cw34
cw34
cw34
man1&2
man1&2
man1&2
man1&2
pit3&4
pit3&4
pit3&4
pit3&4
pit7
pit7
pit7
pit7
hun1&2
hun1&2
hun1&2
hun1&2
mos7
mos7
mos7
mos7
mos6
mos6
mos6
mos6
pit1&2
pit1&2
pit1&2
pit1&2
sba1
sba1
sba1
sba1
orb2
orb2
orb2
orb2
sba3
sba3
sba3
sba3
sba2
sba2
sba2
sba2
enc1
enc1
enc1
enc1
enc3
enc3
enc3
enc3
enc4
enc4
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
82
96
66
40
60
140
132
100
105
95
90
20
82
96
66
60
180
216
144
100
100
100
90
135
185
221
148
135
185
221
148
20
82
96
66
7
37
44
29
175
175
175
175
13
43
51
34
8
37
45
30
7
27
32
21
8
27
33
22
53
74
11,128
10,438
10,266
13,307
11,822
10,361
9,506
12,114
10,087
9,706
9,664
12,905
11,388
10,408
10,341
13,001
11,062
9,977
9,705
12,570
10,331
9,822
9,666
13,304
9,758
9,079
8,949
13,370
9,918
9,273
9,115
13,412
11,673
10,573
10,339
11,778
10,613
9,922
9,857
13,188
10,168
9,595
9,442
11,880
10,680
10,062
9,961
12,099
11,007
10,352
10,259
12,632
11,483
10,831
10,737
13,155
11,675
10,933
10,891
13,472
11,055
Unit*MW System
CUM Total Unit Cumul.
Total
MW $/MWh $/hr
$/hr
$/MWh
4526
4622
4688
4728
4788
4928
5060
5160
5265
5360
5450
5470
5552
5648
5714
5774
5954
6170
6314
6414
6514
6614
6704
6839
7024
7245
7393
7528
7713
7934
8082
8102
8184
8280
8346
8353
8390
8434
8463
8638
8813
8988
9163
9176
9219
9270
9304
9312
9349
9394
9424
9431
9458
9490
9511
9519
9546
9579
9601
9654
9728
27.9
26.2
25.8
31.1
27.7
24.2
22.2
31.6
26.3
25.3
25.2
32.4
28.6
26.1
26.0
32.6
27.8
25.0
24.4
32.8
27.0
25.6
25.2
33.4
24.5
22.8
22.5
33.6
24.9
23.3
22.9
33.7
29.3
26.5
26.0
34.3
30.9
28.9
28.7
34.4
26.5
25.0
24.6
34.6
31.1
29.3
29.0
35.2
32.0
30.1
29.9
36.8
33.4
31.5
31.2
38.3
34.0
31.8
31.7
39.2
32.2
2290
2515
1701
1246
1660
3394
2936
3162
2764
2407
2270
648
2344
2508
1713
1958
4998
5409
3508
3281
2696
2564
2271
4508
4531
5036
3324
4530
4606
5144
3386
673
2403
2548
1713
240
1143
1270
832
6023
4644
4383
4313
449
1336
1493
986
282
1185
1356
896
257
902
1009
656
306
917
1050
697
2078
2381
116854
119369
121070
122315
123975
127369
130305
133467
136231
138638
140908
141556
143900
146408
148121
150079
155077
160486
163994
167274
169971
172534
174805
179313
183844
188880
192204
196735
201340
206484
209870
210543
212946
215493
217206
217446
218589
219859
220691
226714
231358
235741
240054
240503
241839
243333
244318
244600
245785
247141
248036
248293
249196
250204
250860
251167
252084
253134
253831
255909
258289
25.8
25.8
25.8
25.9
25.9
25.8
25.8
25.9
25.9
25.9
25.9
25.9
25.9
25.9
25.9
26.0
26.0
26.0
26.0
26.1
26.1
26.1
26.1
26.2
26.2
26.1
26.0
26.1
26.1
26.0
26.0
26.0
26.0
26.0
26.0
26.0
26.1
26.1
26.1
26.2
26.3
26.2
26.2
26.2
26.2
26.2
26.3
26.3
26.3
26.3
26.3
26.3
26.3
26.4
26.4
26.4
26.4
26.4
26.4
26.5
26.6
- Continued on Next Page -
HR-DESC.DOC ; 4/17/98: PAGE E-19
TABLE E-7: ALL IOUs SYSTEM AVERAGE COST CALCULATIONS - CONTINUED
SUMMARY IHR DATA (Dispatch Gas Price)
SUMMARY AHR DATA (Total Gas Price)
PLANT
#
MW Btu/kWh
Unit
Unit*MW System
CUM
Cost
Unit Cumul. Cost
MW $/MWh $/hr
$/hr $/MWh
hun1&2
man1&2
enc1
orb2
pit3&4
enc2
sba4
sba4
enc3
ala3&4
eti3&4
sba2
els1-4
hmb1&2
enc4
red5&6
red7&8
hun1&2
sbr1&2
ala5&6
orb1
hun3
ala1&2
red5&6
hun4
sba4
red7&8
enc2
els1-4
eti1&2
orb2
man1&2
ala3&4
hun3
eti3&4
red5&6
hnp2
ala1&2
ala5&6
hun1&2
sbr1&2
enc1
hun4
red5&6
hun4
els1-4
hun3
eti1&2
hnp3
ala1&2
sbr1&2
hun4
enc3
man1&2
hnp2
ala1&2
hun3
eti1&2
sba4
hmb1&2
hnp3
eti1&2
3
3
4
4
5
4
3
2
4
4
4
5
3
4
5
2
4
4
3
4
5
2
2
3
2
4
5
5
4
2
5
4
5
3
5
4
4
3
5
5
4
5
3
5
4
5
4
3
4
4
5
5
5
5
5
5
5
4
5
5
5
5
100
105
32
175
66
31
36
1
33
160
160
30
250
31
59
70
140
100
28
180
130
30
70
90
30
45
160
21
250
60
175
95
160
30
160
90
32
90
180
90
28
21
30
80
30
270
30
60
32
90
28
45
22
90
21
80
35
60
30
21
21
64
9104
9209
9241
9416
9482
9513
9549
9550
9583
9743
9903
9933
10183
10214
10273
10343
10483
10583
10611
10791
10921
10951
11021
11111
11141
11186
11346
11367
11617
11677
11852
11947
12107
12137
12297
12387
12419
12509
12689
12779
12807
12828
12858
12938
12968
13238
13268
13328
13360
13450
13478
13523
13545
13635
13656
13736
13771
13831
13861
13882
13903
13967
BLK INC
IHR
8,768
8,799
10,231
8,818
11,211
10,258
10,268
10,278
10,375
8,933
8,943
10,407
8,963
11,392
10,437
8,992
9,028
9,050
9,056
9,074
9,112
9,126
9,127
9,134
9,137
10,741
9,248
10,760
9,259
9,264
9,268
9,279
9,305
9,309
9,322
9,324
11,861
9,341
9,375
9,379
9,384
10,909
9,387
9,535
9,568
9,583
9,606
9,627
12,246
9,663
9,667
9,695
11,377
9,842
12,701
10,047
10,057
10,104
11,797
13,521
13,552
10,719
21.3
21.4
23.9
21.4
25.9
24.0
24.0
24.0
24.3
21.7
21.7
24.4
21.8
26.3
24.4
21.9
21.9
22.0
22.0
22.0
22.1
22.2
22.2
22.2
22.2
25.1
22.5
25.2
22.5
22.5
22.5
22.5
22.6
22.6
22.7
22.7
27.4
22.7
22.8
22.8
22.8
25.5
22.8
23.2
23.3
23.3
23.3
23.4
28.3
23.5
23.5
23.6
26.6
23.9
29.3
24.4
24.4
24.6
27.6
31.2
31.3
26.0
2131
2245
766
3750
1709
744
865
24
801
3473
3477
731
5445
816
1441
1530
3071
2199
616
3969
2878
665
1552
1998
666
1131
3596
529
5625
1351
3941
2142
3618
679
3624
2039
877
2043
4101
2051
639
536
684
1854
698
6287
700
1404
905
2113
658
1060
586
2152
616
1953
855
1473
828
656
657
1667
188167
190412
191178
194928
196638
197382
198247
198271
199072
202545
206022
206753
212198
213014
214454
215984
219055
221255
221871
225840
228718
229383
230936
232933
233600
234731
238326
238855
244480
245830
249772
251914
255532
256210
259834
261874
262750
264793
268894
270945
271584
272120
272804
274658
275355
281642
282343
283746
284652
286765
287423
288483
289068
291221
291837
293790
294645
296119
296947
297603
298260
299927
20.7
20.7
20.7
20.7
20.7
20.7
20.8
20.8
20.8
20.8
20.8
20.8
20.8
20.9
20.9
20.9
20.9
20.9
20.9
20.9
20.9
20.9
21.0
21.0
21.0
21.0
21.0
21.0
21.0
21.1
21.1
21.1
21.1
21.1
21.1
21.1
21.2
21.2
21.2
21.2
21.2
21.2
21.2
21.2
21.2
21.3
21.3
21.3
21.3
21.3
21.3
21.3
21.3
21.4
21.4
21.4
21.4
21.4
21.4
21.4
21.5
21.5
BLK INC
31
31
32
32
32
32
33
33
33
33
34
34
34
34
35
35
35
35
36
36
36
36
37
37
37
37
38
38
38
38
39
39
39
39
40
40
40
40
41
41
41
41
42
42
42
42
43
43
43
43
44
44
44
44
45
45
45
45
46
46
46
46
AHR
PLANT
#
MW
Btu/kWh
enc4
enc4
enc5
enc5
enc5
enc5
eti3&4
eti3&4
eti3&4
eti3&4
hnp3
hnp3
hnp3
hnp3
enc2
enc2
enc2
enc2
els1-4
els1-4
els1-4
els1-4
hmb1&2
hmb1&2
hmb1&2
hmb1&2
ala3&4
ala3&4
ala3&4
ala3&4
hnp2
hnp2
hnp2
hnp2
sba4
sba4
sba4
sba4
eti1&2
eti1&2
eti1&2
eti1&2
ala1&2
ala1&2
ala1&2
ala1&2
red5&6
red5&6
red5&6
red5&6
sbr1&2
sbr1&2
sbr1&2
sbr1&2
hig1&2
hig1&2
hig1&2
hig1&2
hig3&4
hig3&4
hig3&4
hig3&4
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
2
3
4
5
87
59
59
79
94
63
120
160
160
160
17
27
32
21
6
26
31
21
190
250
250
270
16
27
31
21
120
160
160
160
17
27
32
21
1
36
45
30
60
60
60
64
70
90
90
80
70
90
90
80
28
28
28
28
10
20
18
10
14
26
30
9
10,494
10,398
13,485
10,741
10,144
10,055
15,141
11,005
10,078
9,798
16,339
12,974
12,336
12,471
14,131
12,451
11,406
11,135
16,141
11,525
10,517
10,188
16,853
13,245
12,142
12,167
16,210
11,407
10,311
9,960
16,865
13,382
12,517
12,433
14,726
13,382
12,128
11,847
16,432
12,244
11,371
11,106
17,605
12,222
11,084
10,734
18,702
12,511
11,144
10,661
18,968
13,553
12,072
11,426
34,940
20,641
15,481
13,820
44,598
24,520
17,262
15,100
Unit*MW System
CUM Total Unit Cumul.
Total
MW $/MWh $/hr
$/hr
$/MWh
9815 30.5
9874 30.3
9933 39.2
10012 31.3
10106 29.5
10169 29.3
10289 39.5
10449 28.7
10609 26.3
10769 25.6
10786 41.0
10813 32.6
10845 31.0
10866 31.3
10872 41.1
10898 36.2
10929 33.2
10950 32.4
11140 42.1
11390 30.1
11640 27.4
11910 26.6
11926 42.3
11953 33.2
11984 30.5
12005 30.5
12125 42.3
12285 29.8
12445 26.9
12605 26.0
12622 42.3
12649 33.6
12681 31.4
12702 31.2
12703 42.9
12739 38.9
12784 35.3
12814 34.5
12874 42.9
12934 32.0
12994 29.7
13058 29.0
13128 45.9
13218 31.9
13308 28.9
13388 28.0
13458 48.8
13548 32.7
13638 29.1
13718 27.8
13746 49.5
13774 35.4
13802 31.5
13830 29.8
13840 91.2
13860 53.9
13878 40.4
13888 36.1
13902 116.4
13928 64.0
13958 45.1
13967 39.4
2657
1785
2315
2469
2775
1843
4742
4596
4209
4092
697
879
991
657
247
942
1029
680
8005
7520
6862
7179
677
898
945
641
5077
4764
4306
4159
720
907
1005
655
43
1402
1588
1034
2573
1917
1781
1855
3216
2871
2604
2241
3417
2939
2618
2226
1386
990
882
835
912
1077
727
361
1630
1664
1352
355
260946
262731
265046
267516
270291
272134
276876
281472
285680
289772
290469
291348
292339
292996
293243
294185
295214
295895
303899
311419
318281
325461
326137
327035
327980
328621
333698
338462
342768
346927
347646
348553
349559
350214
350257
351659
353247
354281
356854
358772
360552
362408
365624
368495
371099
373340
376757
379695
382313
384539
385925
386916
387798
388633
389545
390622
391350
391710
393340
395004
396356
396710
26.6
26.6
26.7
26.7
26.7
26.8
26.9
26.9
26.9
26.9
26.9
26.9
27.0
27.0
27.0
27.0
27.0
27.0
27.3
27.3
27.3
27.3
27.3
27.4
27.4
27.4
27.5
27.6
27.5
27.5
27.5
27.6
27.6
27.6
27.6
27.6
27.6
27.6
27.7
27.7
27.7
27.8
27.9
27.9
27.9
27.9
28.0
28.0
28.0
28.0
28.1
28.1
28.1
28.1
28.1
28.2
28.2
28.2
28.3
28.4
28.4
28.4
HR-DESC.DOC ; 4/17/98: PAGE E-20
FIGURE E-4-ALL
COLLECTIVE IOUs
MCP & MC PROXIES
25
MCP = SAHR @ TOTAL GAS PRICE
20
MC = SIHR @ DISPATCH GAS PRICE
15
10
5
0
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
OUTPUT (MW)
FIGURE E-5
COLLECTIVE IOUs
AHR/IHR (MCP/MC)
AHR/IHR
1.5
1.4
1.3
1.2
0
2,000
4,000
6,000
8,000
10,000
12,000
14,000
10,000
12,000
14,000
OUTPUT(MW)
FIGURE E-6
COLLECTIVE IOUs
AHR/IHR (MCP/MC)
HEAT RATES ONLY
1.4
AHR/IHR
UNIT COST ($/MWh)
30
1.3
1.2
1.1
0
2,000
4,000
6,000
8,000
OUTPUT(MW)
HR-DESC.DOC ; 4/17/98: PAGE E-21
APPENDIX F
FR 97 GAS PRICE FORECAST
This Appendix summarizes the Energy Commission’s 1997 Gas Price Forecast (FR 97), which was
approved by the Commissioners at their March 18, 1998 Business Meeting. The 1998 dispatch and total
gas prices were used in Section VI in demonstrating the difference between traditional marginal cost and
the market clearing price of the new competitive market.
Table F-1 summarizes the dispatch and total gas prices in both nominal and real 1998 dollars. The
dispatch gas price reflects the variable costs of gas, only. Total gas price also includes the fixed
component of gas. Although both of these are provided, Energy Commission Staff expects that the
electric utilities will no longer use the dispatch price of gas in the new competitive market and will base
all their bidding on the total price of gas.
TABLE F-1: FR 97 GAS PRICE FORECAST
FR 97 GAS PRICE FORECAST (MARCH 18, 1998)
Nominal $/MMBtu
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
PG&E
Disp Total
2.31 2.51
2.04 2.24
1.98 2.19
2.07 2.28
2.17 2.38
2.28 2.50
2.40 2.62
2.53 2.75
2.66 2.89
2.80 3.03
2.94 3.18
3.09 3.34
3.25 3.51
3.44 3.70
3.64 3.91
3.86 4.13
4.08 4.36
4.30 4.59
4.54 4.83
SCE
Disp Total
2.43 2.61
2.08 2.27
1.97 2.17
2.09 2.29
2.20 2.40
2.34 2.55
2.48 2.69
2.63 2.85
2.78 3.00
2.95 3.17
3.15 3.38
3.33 3.57
3.45 3.69
3.65 3.90
3.87 4.12
4.09 4.35
4.32 4.59
4.55 4.83
4.81 5.10
Cool Water SDG&E
Disp Total Disp Total
2.24 2.34 2.34 2.91
1.90 2.00 2.04 2.56
1.98 2.08 2.07 2.61
2.08 2.18 2.18 2.73
2.17 2.27 2.29 2.85
2.28 2.38 2.42 2.98
2.41 2.51 2.56 3.13
2.55 2.65 2.70 3.28
2.70 2.80 2.84 3.43
2.85 2.95 3.01 3.61
3.01 3.11 3.21 3.81
3.18 3.28 3.38 3.99
3.34 3.44 3.51 4.14
3.52 3.62 3.72 4.36
3.70 3.80 3.94 4.58
3.89 3.99 4.16 4.82
4.09 4.19 4.39 5.06
4.30 4.40 4.63 5.31
4.51 4.61 4.89 5.59
1998 $/MMBtu
Apr 16, 1997
Deflators
1998 1.00
1999 1.02
2000 1.05
2001 1.08
2002 1.11
2003 1.15
2004 1.18
2005 1.22
2006 1.27
2007 1.31
2008 1.36
2009 1.41
2010 1.46
2011 1.51
2012 1.56
2013 1.62
2014 1.68
2015 1.74
2016 1.80
Year
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
PG&E
Disp Total
2.31 2.51
1.99 2.19
1.88 2.08
1.91 2.11
1.95 2.14
1.99 2.18
2.03 2.21
2.06 2.25
2.10 2.28
2.13 2.31
2.16 2.34
2.19 2.37
2.23 2.41
2.28 2.45
2.33 2.50
2.38 2.55
2.43 2.60
2.48 2.64
2.52 2.69
SCE
Disp Total
2.43 2.61
2.03 2.21
1.88 2.06
1.93 2.11
1.98 2.16
2.04 2.22
2.10 2.28
2.15 2.32
2.19 2.36
2.25 2.42
2.32 2.49
2.36 2.53
2.37 2.53
2.42 2.59
2.47 2.64
2.53 2.69
2.58 2.74
2.62 2.78
2.67 2.83
Cool Water
Disp Total
2.24 2.34
1.85 1.95
1.88 1.98
1.92 2.01
1.95 2.04
1.98 2.07
2.04 2.12
2.09 2.17
2.13 2.21
2.17 2.25
2.22 2.29
2.26 2.33
2.29 2.36
2.33 2.40
2.37 2.43
2.40 2.47
2.44 2.50
2.47 2.53
2.51 2.56
SDG&E
Disp Total
2.34 2.91
1.99 2.49
1.96 2.48
2.01 2.52
2.05 2.56
2.11 2.59
2.16 2.64
2.20 2.68
2.25 2.71
2.29 2.75
2.36 2.81
2.40 2.84
2.41 2.84
2.47 2.89
2.52 2.93
2.57 2.98
2.62 3.02
2.67 3.06
2.72 3.10
After 1998, gas prices drop and do not return to their 1998 level in real dollars until around 2010 and
beyond, depending on the utility. This drop is due to vast gas resources in the Gulf of Mexico becoming
available.
HR-DESC.DOC ; 4/17/98: PAGE F-1
Figures F-1 through F-4 provide the data of Table F-1 graphically. Figures F-1 and F-2 present the gas
prices in nominal (current) dollars; F-1 presents the dispatch price of gas and F-2 presents the total price
of gas. Figures F-3 and F-4 present the comparable data in real 1998 dollars.
FIGURE F-1
FR 97 DISPATCH GAS PRICES
IN NOMINAL $/MMBtu
GAS PRICE($/MMBtu)
5.0
4.5
4.0
PG&E
3.5
SCE
3.0
C.W.
2.5
SDG&E
2.0
1.5
1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
YEAR
FIGURE F-2
GAS PRICE($/MMBtu)
FR 97 TOTAL GAS PRICES
IN NOMINAL $/MMBtu
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
PG&E
SCE
C.W.
SDG&E
YEAR
HR-DESC.DOC ; 4/17/98: PAGE F-2
FIGURE F-3
FR 97 DISPATCH GAS PRICES
IN REAL 1998 $/MMBtu
GAS PRICE ($/MMBtu)
2.8
2.6
PG&E
2.4
SCE
2.2
CW
SDG&E
2.0
1.8
1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
YEAR
FIGURE F-4
GAS PRICE ($/MMBtu)
FR 97 TOTAL GAS PRICE IN REAL 1998 $/MMBtu
3.2
3.0
2.8
PG&E
2.6
SCE
2.4
CW
2.2
SDG&E
2.0
1.8
1998 2000 2002 2004 2006 2008 2010 2012 2014 2016
YEAR
HR-DESC.DOC ; 4/17/98: PAGE F-3