Pricing Power,
Energy and Capacity
METU
Pricing Power, Energy and Capacity
Basic Principles of
Electricity Markets
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 1
Pricing Power, Energy and Capacity
METU
Symbols
Generation - Load
Generator
Supply - Demand
470 MW
Four plants supplying two loads
Generator Feeder
Gen (step-up) Transformer
Generator Bus
4000 MW
1600 MW
Generator Circuit Breaker
900 MW
Load Feeder
730 MW
Load Bus
770 MW
TEIAS
Turkish
Electricity
Transmission
Company
Load (Step-down) Transf.
Load
300 MW
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 2
METU
Pricing Power, Energy and Capacity
Electrical Power
Electrical Power
Electrical Power is the rate of flow of
energy (Watt)
Electrical Power is the energy flowing in a
unit time interval (one hour or one sec)
Power = Energy / Time
(Watt)
(Watt)
(kWatt)
Generator
Power = Energy / Time
Load
+
(Watt-second) (second)
(Watt-hour)
(hour)
(kWatt-hour) (hour)
Unit time interval is generally one second
or one hour
1 kW = 1000 Watts (kilo = 103)
1 MW = 1000 kWatts (Mega = 106)
1 GW = 1000 Mwatts (Giga = 109)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 3
METU
Pricing Power, Energy and Capacity
Electrical Energy
Energy is the flow of power within a certain
period of time (Watt-Second, Ws)
Energy =
Power x Time
(Watt-second, Ws) (Watt-sec) (Watt)
(second)
Afşin Elbistan-A Plant (4x340 MW)
Generator
Energy
Load
+
Energy = Power x Time
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 4
METU
Pricing Power, Energy and Capacity
Commercial Units for Electrical Energy
Electrical Energy
Commercial measure for energy is kiloWatt-hour (kWh)
Energy = Power x Time (Watt-second, Ws)
(Watt-sec) (Watt) (second)
Energy
= Power x Time (kWh)
(KiloWatt-hour) (KiloWatt) (hour)
Energy
Generator
+
1 Kilo Watt = 1000 Watts
1 Hour = 3600 seconds
Load
Energy = Power x Time
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 5
METU
Pricing Power, Energy and Capacity
Price of Energy
Electrical Energy
Definition:
Energy is the flow of power over a
certain period of time
Hence, price of energy is expressed in
terms of $ per hour per MW of power
flow, i.e.
Price of energy is measured in terms of
either;
• $ / ( MW per hour),
• $ / MWh or
• Cent / (kW per hour) ,
• Cent / kWh
Energy
Generator
+
Load
Energy = Power x Time
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 6
METU
Pricing Power, Energy and Capacity
Rating of a Plant
Definition
Installation of a Birecik HPP (672 MW) Turbine
Power Rating (rated power)
of a generating plant is the
highest electrical power
allowed to generate under
normal operating conditions
Power rating of a plant is
determined by the size of
the plant, i.e. the maximum
power that can be
generated
Power rating of a plant is
measured in terms of MW
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 7
METU
Pricing Power, Energy and Capacity
Capacity of a Plant
Capacity of a Plant
Yamula HPP Kayseri, (2 x 50 MW)
Capacity of a plant is the overall
electrical energy (not power !) that can
be generated during the lifetime of the
plant
Capacity of a plant is determined by;
• Overall lifetime (service duration) of
the plant, in which electrical energy
is produced (years),
• Power rating (MW),
• Annual Duration of Availability (ADA)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 8
METU
Pricing Power, Energy and Capacity
Capacity of a Plant
Definition
Sugözü (Isken) Coal Plant 1210 MW
Capacity of a plant is a term that
involves a time dimension (years) as
well as power rating
(Please note that the term; “being available
for service” is used, instead of “being in
service”)
In other words, a plant may be “available for
service”, in a certain period, but may not
actually be “in service”, i.e. may not be
“operated or committed” within this period
due to commercial conditions in the
contract
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 9
METU
Pricing Power, Energy and Capacity
Annual Duration of Availability (ADA)
Definition
Karkey Şırnak, Silopi - 120 MW
Karadeniz Enerji
Annual Duration of Availability (ADA) is the
duration in which the plant will be available for
service within one year period
Annual Percentage of Availability (APA) is the
percentage of the duration in which the plant is
available within a year
(i.e. percentage of duration obtained by excluding
the period in which the plant is not available for
one year period)
APA = (8760 h -Tunavailable ) / 8760 x 100 (%)
= 1 – Tunavailable / 8760 x 100 (%)
ADA = 8760 h x APA / 100
= 8765 x Annual Percentage of Availability / 100
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 10
METU
Pricing Power, Energy and Capacity
Annual Duration of Availability (ADA)
Reasons for a Plant being Unavailable
Plant;
• may not always have continuously supplied, regular,
sufficient fuel, i.e. water flow or wind, (APA for most
hydroelectric and wind plants in Turkey are 43 %, and
33 %, respectively),
• is taken out of service due to some unexpected failures
or scheduled (regular) repair and maintanence
activities, such as plant or line failure etc.
• is not allowed to operate beyond a certain duration,
due to conditions in the commercial contracts.
Unexpected outages, machine and/or system failures are
not regarded as terms in calculating the Annual
Percentage of Availability (APA)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 11
METU
Pricing Power, Energy and Capacity
Annual Capacity (s)
Annual Capacity
Afşin Elbistan Group-A (4 x 340 MW)
Annual Capacity is the total energy that
can be supplied within the period of
“Annual Duration of Availability” by
considering all the physical and other
real constraints
Annual capacity can be written as;
s = Prated x ADA (kWh/year)
where, ADA is the Annual Duration
of Availability (Hours)
Annual capacity is measured in terms of
MWy (MW-year) or MWh/year or kWh/year,
Annual capacity has the same units as
energy
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 12
METU
Pricing Power, Energy and Capacity
Annual Capacity (s) - Example
Example
Birecik HPP (672 MW)
Calculate the Annual Capacity (in kWh) of
Birecik Hydroelectric Power Plant with
670 MW rated power and 41 % Annual
Percentage of Availability
s = Prated x ADA
ADA = 8760 x APA / 100
= 8760 x 0.41 = 3593.6 hours
s = Prated x ADA
= 670 x 1000 x 3593.6
= 2.407 billion kWh
Production agreed in ESA
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 13
METU
Pricing Power, Energy and Capacity
Capacity of a Plant
Capacity of a Plant
Capacity of a plant is the total electrical
energy that can be supplied within the overall
lifetime of plant, by considering all the
physical and other real constraints
Capacity can be written as;
C = Prated x ADA x T
=sxT
Where, C is the capacity of plant in MWh,
P is the power rating of plant (MW),
ADA is Annual Duration of Availability,
s is Annual Capacity,
T is the overall lifetime of the plant (years)
Dimension of capacity is MWh, kWy or kWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 14
METU
Pricing Power, Energy and Capacity
Difference between Capacity and Rated Power
Rated Power and Capacity
Rated power of a plant;
• is the ability of generating electrical
energy within unit period of time, such
as hour, under normal operating
conditions, regardless of the time and
duration
• is measured in terms of kW or MW,
Capacity of a plant, on the other hand,
• is the total amount of electrical energy
to be generated in terms of the rating
of the plant, within Annual Duration of
Availability (ADA)
• is measured in terms of kWy or MWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 15
METU
Pricing Power, Energy and Capacity
Difference between Capacity and Rated Power
Rated Power and Capacity
Bores, Wind Power Plant
Bozcaada, 10.2 MW
Why the price of a used plant is half of that of
a new plant, although the rated powers of both
plants are the same ?
Answer:
Although the rated powers are the same, the
used plant has exhausted a certain period of its
lifetime, hence its capacity, i.e. its life for
supplying energy is reduced by that amount
Price of a used plant is determined by its
remaining capacity, not by its rated power
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 16
METU
Pricing Power, Energy and Capacity
Daily Loading Curve
A basic characteristics of
electrical loads is that the
demand is not constant, but
varies in time. In other words,
demand varies with respect to
hours, days, weeks and
seasonal conditions
As seen from the figure, the
peak level of demand in winter
season is about 40 MW, while
the off-peak level is 26 MW,
which is 0.65 of the peak level
Peak level
Total Demand (MW)
Daily Loading Curve
Winter
Summer
Off-Peak level
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 17
METU
Pricing Power, Energy and Capacity
Daily Loading Curve
Daily Loading Curve
This situation creates serious
difficulties in system
operation, as electricity cannot
be stored, hence the total
supply must always be
matching the total demand and
losses in in the system
Daily Loading Curve of the Spanish System
October 09, 2007
The system operator therefore,
spends a considarable amount
of care and effort to follow the
balance between the total
supply and demand
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 18
METU
Pricing Power, Energy and Capacity
Daily Loading Curve
Weekday and Saturday Daily Loading Curves for Domestic and Industrial Loads
Weekday Total
Saturday Total
Weekday Industrial
Saturday Industrial
Demand (MW)
Ref: Electric Power Systems, B.M. Weedy, pp.4
80
70
60
50
40
30
20
23:00
0:00
22:00
21:00
20:00
18:00
19:00
17:00
16:00
15:00
14:00
13:00
12:00
11:00
10:00
8:00
9:00
7:00
6:00
5:00
03:00
04:00
0:00
1:00
0
02:00
10
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 19
METU
Pricing Power, Energy and Capacity
Daily Energy Consumption
Vertical and horizontal axes of the
daily load curve are power and time,
respectively
In case that power demand is regular
(flat) in time, then the rectangular
area under the curve would represent
the total energy consumption of the
load
Then, the daily energy consumption,
Energy consumed = P x ∆t
= 25 MW x 24 h
= 600 MWh
Please note that Daily Capacity is the area of the
overall rectangle, i.e.
Daily Capacity = Pmax x Duration = 40 MW x 24 h.
Total Demand P(t) (MW)
Daily Energy Consumption
40
35
Daily Loading Curve (Flat)
30
25
20
15
Energy consumed
10
5
0
0 2
4
6
8
10
12
14
16
18
20
22
24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 20
METU
Pricing Power, Energy and Capacity
Daily Energy Consumption
However, the actual daily loading
curve is nonlinear, hence,
the energy consumption is
calculated by evaluating the integral
of the daily loading curve, i.e. the
area under the curve
Total Demand P(t) (MW)
Daily Energy Consumption
40
Daily Loading Curve (Nonlinear)
35
30
25
20
15
24
Energy consumed / day = ∫ P(t) dt (MWh)
Energy consumed
10
0
5
0
0
2
4
6
8
10
12
14
16
18
20
22 24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 21
METU
Pricing Power, Energy and Capacity
Unconsumed Energy
Unconsumed energy is the area
on upper part of the Daily Loading
Curve, which corresponds to the
energy that could have been
generated, but cannot be
consumed by the consumer, due to
the Daily Loading Characteristics
of the Consumption
Please note that Full Capacity is the overall
area of the rectangle, i.e. 40 MW x 24 hours
Total Demand P(t) (MW)
Unconsumed Energy = Full Capacity - ∫ P(t) dt = Pmax x Duration - ∫ P(t) dt
40
Unconsumed Energy
35
30
25
Daily Loading Curve (Nonlinear)
20
15
10
5
0
2
4
6
8
10
12
14
16
18
20
22
24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 22
METU
Pricing Power, Energy and Capacity
Demand and Consumption
Demand:
is the electrical power required to
operate customer's facilities.
Demand is power (kW),
Consumption:
is the amount of electrical energy
consumed and is measured in
kilowatt-hours (kWh).
Consumption is energy (kWh)
Peak demand
Total Demand P(t) (MW)
Difference between Demand and Consumption
40
35
30
25
20
16
15
Energy consumed
10
5
Average demand
0
0
2
4
6
8
10 12
14 16 18
20
22 24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 23
METU
Pricing Power, Energy and Capacity
Capacity Factor (c)
Capacity Factor (c) is the percentage
utilization of the capacity by a load
which is defined as the ratio of the
area under the load duration curve to
the overall area
Capacity of plant is the area of the
overall rectangle, i.e. 40 MW x 24 h
Energy consumed on the other hand,
is the area under the curve
c = Area under the Curve / Overall Area
= ∫ P(t) dt / Overall Area
Capacity Factor is unitless
Capacity Factor (c)
Total Demand P(t) (MW)
Definition
40
35
30
25
20
15
Energy consumed
10
5
0
0
2
4
6
8
10 12 14 16 18 20 22 24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 24
METU
Pricing Power, Energy and Capacity
Capacity Factor (c)
Capacity Factor (c)
Capacity Factor for the load shown on the
right hand side may be expressed as;
c = Energy consumed / Capacity allocated
= Energy consumed / Total energy that can be
supplied
= ∫ P(t) dt / (α x rated power x duration)
= Area under the curve / overall rectangular area
= Area under the curve / 40 MW x 24 hours
Area under the curve = Average demand x duration
where, ∫ P(t) dt is the energy consumed during the
allocated service period,
Capacity allocated = α x rated power x duration
Total Demand P(t) (MW)
Definition
40
35
30
25
Energy consumed
20
16
15
10
Average Demand
5
0
0
2
4
6
8
10
12
14
16
18
20
22 24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 25
METU
Pricing Power, Energy and Capacity
Capacity Factor (c)
Example
Solution
Capacity Factor = c
c = Energy consumed / Capacity of plant
= ∫ P(t) dt / Capacity of plant
= Area under the curve / Overall rectangular area
Please note that;
Area under the curve = Average power x Duration
c = 16 x 24 MWh / 40 x 24
= 384 MWh / 960 MWh
= 0.4
(i.e. 40 %)
Total Demand P(t) (MW)
Rated power of the plant supplying load = 40 MW,
Average demand of the load
= 16 MW
Average demand = 16 MW
Calculate the Capacity Factor of the load
with the following figures;
Capacity Factor (c)
40
35
30
25
20
16
15
Energy consumed
10
5
0
0
2
4
6
8
10
12
14
16
18
20
22
24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 26
METU
Pricing Power, Energy and Capacity
Question
Calculate the Capacity Factor of the
demand shown on the RHS
Answer
c = ∫ P(t) dt / Capacity of plant
= ( P / Pr ) x ( t / T ) (unitless)
where, c is the capacity factor,
P is the power allocated to customer,
Pr is the total rated power of the
plant,
t is the total duration of allocation
(hours),
T is the overall duration of the availability
of plant (hours)
c = ( 20 / 40 ) x ( 0.60 / 1.0 ) = 30.0 %
Total Demand P(t) (MW)
Example
40
35
Duration of Allocation
30
25
20
15
Allocated
Capacity
10
P = Allocated
Power
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6 0.7
0.8
0.9 1.0
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 27
Pricing Power, Energy and Capacity
METU
A Note
Please note that the approach which calculates the Capacity Factor by
using the integral of the Loading Curve is more general
40
Daily Loading Curve (Nonlinear)
35
30
25
20
15
Allocated Capacity
10
c = ( P / Pr ) x ( t / T )
Total Demand P(t) (MW)
Total Demand P(t) (MW)
c = Area under the Curve / Overall Area
= ∫ P(t) dt / Overall Area
40
35
25
20
15
5
0
0
2
4
6
8
10 12 14 16 18 20
22 24
Time (Hours)
P = Allocated
Power
Allocated Capacity
10
5
0
Duration of Allocation
30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 28
METU
Pricing Power, Energy and Capacity
Commercial Meaning of Capacity Factor
Capacity Factor is a measure of Utilization
Karakaya HEPP (1800 MW)
• Supplier simply allocates the ordered and
committed portion of the capacity of the plant,
• Supplier is not interested whether this portion is
properly utilized or not by the consumer, i.e.
proper utilization of this portion is merely a
problem of the consumer,
• On the other hand, customer is not interested
whether the plant is fully utilized or not, i.e. full
utilization of plant is a problem of supplier
Low capacity factor means;
• For plant owner: under-utilization of the plant and
hence slower rate of return,
• For customer: Increase in fixed costs and hence
increase in the overall tariff
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 29
METU
Pricing Power, Energy and Capacity
Definition
Load (Diversity) Factor is defined as
the ratio of Average Demand (Pavg) to
Peak Demand (Pavg)
Load Factor = Pavg / Ppeak
where, Pavg = Energy consumed /
duration (hours)
= ∫ P(t) dt / duration (hours)
Total Demand P(t) (MW)
Load (Diversity) Factor
40
35
30
25
20
16
15
10
5
0
0
Peak demand
Average demand
2
4
6
8
10
12
14
16
18
20
22 24
Time (Hours)
Load (Diversity) Factor is a measure of
the effective utilization of the load and
distribution equipment, i.e. higher load
factor means better utilization of the
transformer, line or cable
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 30
METU
Pricing Power, Energy and Capacity
Proof
Load Factor is defined as;
Load Factor = Pavg / Ppeak
Multiplying numerator and denominator by
the overall duration of operation,
∆t = 24 hours
Load Factor = Pavg ∆t / Ppeak ∆t
= ∫ P(t) dt / Overall Area
= Energy Consumed / Capacity
Allocated
= Capacity Factor
Total Demand P(t) (MW)
Capacity and Load Factors are Identical
40
35
30
25
20
16
15
10
Peak demand
5
Average demand
0
0
2
4
6
8
10
12
14
16
18
20
22
24
Time (Hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 31
Pricing Power, Energy and Capacity
METU
Example: Capacity Factor of Çamlıca HEPP
Water Flow Statistics of Çamlıca HPP
Artvin, Arhavi, 85 MW
İstasyon No
: 22-79,
Suyun Adı : Kapistre Deresi,
Yılı
Ocak
Şubat
Mart
1989
6,66
8,05
17,41
23,51
29,83
22,62
10,49
1990
8,23
8,04
14,51
19,87
39,06
23,14
1991
5,81
7,57
16,89
21,65
25,00
1992
3,81
1,45
24,20
41,20
1993
6,70
17,50
26,60
1994
6,80
6,73
1995
12,00
1996
Nisan
Mayıs
İstasyonun Adı: Çamlıca,
Haziran
Temm.
Yağış Alanı:
Agust.
89.7 Km2,
Eylül
Ekim
7,18
10,86
29,54
11,16
18,45
23,73
37,50
20,10
25,70
35,20
18,30
29,90
5,85
9,66
4,18
9,15
1997
12,43
1998
Birim:
Hm3
Kasım
Aralık
Yıllık Top.
14,88
14,66
8,56
174,72
19,20
9,97
10,79
12,13
205,63
17,78
11,53
13,39
6,01
4,79
172,61
22,30
16,40
14,90
18,10
8,24
7,64
215,84
24,00
20,90
23,50
31,40
28,40
19,70
10,30
269,90
14,50
9,21
4,91
2,40
4,09
15,40
20,10
14,80
147,14
14,20
20,00
10,30
9,04
7,92
16,80
17,80
13,30
12,10
148,97
6,39
9,08
16,82
17,56
6,79
9,60
13,69
15,63
5,74
6,04
120,66
7,89
7,39
24,03
29,17
19,79
22,77
13,39
28,05
19,12
8,30
10,57
202,90
7,06
9,82
12,50
25,52
22,62
18,75
11,83
8,16
16,59
14,06
11,01
7,29
165,22
1999
6,15
9,31
9,15
13,41
22,92
10,73
9,64
3,22
10,57
17,14
12,18
9,68
134,09
2000
4,68
6,77
11,79
26,29
19,87
19,41
7,08
5,79
8,48
15,54
22,69
10,33
158,71
2001
6,01
6,46
15,87
14,05
17,85
12,80
6,95
8,86
10,17
17,42
7,77
8,15
132,35
2002
9,28
11,30
17,70
20,20
17,50
25,80
8,73
4,90
10,30
26,20
36,20
21,70
209,81
2003
13,30
4,91
6,03
25,10
12,70
9,51
7,43
10,90
13,60
16,30
7,14
4,64
131,56
2004
5,39
10,40
20,20
25,56
21,50
19,34
7,80
12,77
14,96
20,81
18,78
10,98
188,48
Ortalama
7,83
8,59
14,39
20,35
21,39
15,94
11,80
9,47
12,06
15,99
12,92
9,58
160,27
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 32
METU
Pricing Power, Energy and Capacity
Example: Annual Flow Curve for Çamlıca HEPP
Capacity Factor
Area under the curve is the total annual energy generated
Area under the Annual Flow Curve
Overall Area
= 37 x 0.1 x 4 / (24 x 1.0) x 100
= 61.67 %
Average Flow Rate (m3/sec)
c =
Annual Flow Curve for Çamlıca HPP
24,00
20,00
16,00
12,00
8,00
4,00
0,00
Ocak Şubat
Mart
Nisan Mayıs Hazır. Temm. Agust. Eylül
Ekim Kasım Aralık
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 33
METU
Pricing Power, Energy and Capacity
Example: Flow Duration Curve for Çamlıca HEPP
Capacity Factor
Overall Area
= 37 x 0.1 x 4 / (24 x 1.0) x 100
= 61.67 %
Flow Rate (m3/sec)
c =
Area under the Annual Flow Curve
Flow Duration Curve for Çamlıca HPP
24,00
20,00
16,00
12,00
8,00
4,00
0,00
Ocak Şubat
Mart
Nisan Mayıs Hazır. Temm. Agust. Eylül
Ekim Kasım Aralık
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 34
METU
Pricing Power, Energy and Capacity
Example: Flow Duration Curve of Çamlıca HEPP
Scaling of Time Axis
Then, divide the resulting hours
by 8765, scaling the horizontal
axis to yield a range varying
between 0 and one.
Flow Rate (m3/sec)
Now, convert months on the
horizontal axis, to 30 days x 24
hours / day, making; 8765 hours
in total, i.e. 30 x 24 + 5 = 8765
hours
Flow Duration Curve for Çamlıca HPP
24,00
Please note that capacity factor
for these parts is quite low, i.e.
These units of plant remain
idle for most of the time
20,00
16,00
12,00
8,00
4,00
0,00
0
0.1
0.2
0.3
0.4
0.5
0.8
0.9 1.0
0.6 0.7
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 35
Pricing Power, Energy and Capacity
METU
Example: Capacity Factor of Çamlıca HEPP
Rated Power
Height (head)
P = 9.81 x q x h x 
= 9.81 x 22 m3 x 402.18 x 0.90 (kW)
= 78120 kW = 78.12 MW
Height (Head) = 402.18 (m)
Flow Rate (m3/sec)
where, P is the rated power of the plant
expressed in kW
q is flow rate = 35 (m3/sec)
h is height = 402.18 m
 is efficiency factor = 0.90
24,00
20,00
16,00
12,00
8,00
4,00
0,00
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 36
METU
Pricing Power, Energy and Capacity
Example: Capacity Factor of Çamlıca HEPP
Flow Duration Curve for Çamlıca HPP
Now, assume that only a certain
part of flow, with a rate below a
given limit (16 m3/sec) is let to
pass through turbine to generate
electricity and the remaing part is
thrown out on the spillway
P = 9.81 x q x h x 
= 9.81 x 16 m3 / sec x
402.18 m x 0.90
= 56813 kW
= 56.8 MW
where, q is flow rate (m3/sec)
h is height (m),
 is efficiency factor
Flow Rate (m3/sec)
Rated Power
24,00
20,00
Energy wasted due to water
thrown out on the spillway
16,00
12,00
8,00
Rated Power = 56.8 MW
4,00
0,00
0
0.1
0.2
0.3
0.4
0.5
0.8
0.9 1.0
0.6 0.7
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 37
METU
Pricing Power, Energy and Capacity
Example: Capacity Factor of Çamlıca HEPP
Capacity factor is now
determined in terms of the blue
area under the curve
c =
Blue Area under the Curve
Flow Duration Curve for Çamlıca HPP
Flow Rate (m3/sec)
Capacity Factor
24,00
20,00
Energy wasted due to water
thrown out on the spillway
16,00
Rectangular Area : (16 - 0) x (1 - 0)
= 34.5 x 0.1 x 4 / (16 x 1.0)
= 86.25 %
Capacity factor is now higher,
implying faster rate of return for
plant investment, but with the
expense of wasting some
generation capacity
12,00
8,00
Rated Power = 56.8 MW
4,00
0,00
0
0.1
0.2
0.3
0.4
0.5
0.8
0.9 1.0
0.6 0.7
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 38
METU
Pricing Power, Energy and Capacity
Firm and Secondary Energies of an HEPP
Firm Power:
is the power that the plant can
maintain at a constant level during
the overall period of operation within
one year, i.e.
8765 x 0.95 = 8236 hours
Here, Firm Power = 8 MW
Firm Energy:
is the total energy generated at firm
power, during the overall period of
operation within one year
Secondary Energy:
is the energy other than firm energy
Firm and Secondary Energies
Flow Rate (m3/sec)
Definitions
24,00
20,00
16,00
12,00
8,00
4,00
0,00
0
0.1
0.2
Firm Power
0.3
0.4
0.5
0.8
0.9 1.0
0.6 0.7
Duration (100 % = 8765 hours)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 39
METU
Pricing Power, Energy and Capacity
Approximation on Firm Energy
Approximate Firm Energy:
Since water flow statistics
involves some uncertainity at
about 5 % level, Firm Energy
may be assumed to be the
energy generated at power
available not during the overall
period of operation, but during
95 % of the overall period of
operation, i.e.
8765 x 0.95 = 8326 hours
Here, Firm Power = 10 MW
Firm and Secondary Energies
Flow Rate (m3/sec)
Approximation
24,00
20,00
16,00
12,00
8,00
4,00
0,00
0
0.1
Firm Power
0.2
0.3
0.4
0.5
0.8
0.9 1.0
0.6 0.7
Duration (100 % = 8765 hours)
95 % of overall duration = 8326 hours
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 40
METU
Pricing Power, Energy and Capacity
Firm and Secondary Energies on the Flow Duration Curve
Definitions
Firm Energy:
is the integral of the energies
generated during 95 % of the
overall duration,
i.e. 8765 x 0.95 = 8236 hours
Firm Power:
is the power used to generate
firm energy
Secondary Energy:
is the remaining energy
generated
Firm and Secondary Energies
24,00
Flow Rate (m3/sec)
Wasted
Power
20,00
Energy wasted due to
water thrown out on the
spillway
16,00
Secondary energy
Secondary
Power
Firm energy
12,00
8,00
Firm Power
4,00
0,00
0
0.1
0.2
0.3
0.4
0.5
0.6 0.7 0.8 0.9 1.0
Duration (100 % = 8765 hours)
95 % of overall duration = 8236 hours
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 41
Pricing Power, Energy and Capacity
METU
Price of Rated Power
Electrical Power
Energy
Generator
+
Energy = Power x Time
Load
Definition:
Price of rated power is the investment made for
each MW of the plant, usually expressed in
terms of USD
Since power is measured in terms of MW,
price of rated power is expressed in terms of
USD per MW, i.e. $ / MW
Total investment made for plant
Price of rated Power = --------------------------------------------Rated power of plant
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 42
METU
Pricing Power, Energy and Capacity
Overnight Cost (OC) of a Plant
Overnight Cost of a Plant
Overnight cost of a plant is the present-value
of the investment made for the construction
of the plant
Overnight cost of a plant is the amount that
would have to be invested as lump sum up
front to pay completely for its construction
until it is turned-on into service
Financial Costs are NOT included in the
Overnight Cost
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 43
METU
Pricing Power, Energy and Capacity
Components of Overnight Cost (OC)
Classification of Overnight Costs
Direct Investments (EPC(*) Costs)
Investments made for;
o
Engineering;
o
Surveying of the site area,
o
Project,
o
Control
o
Equipment,
o
Construction,
o
Installation,
o
Test and Commissioning
o
of the plant
--------------------------------------------------(*) EPC: Engineering, Procurement,
Overnight Costs
Direct
Investments
Indirect
Investments
Construction
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 44
METU
Pricing Power, Energy and Capacity
Components of Overnight Cost (OC)
Classification of Overnight Costs
Indirect Investments
Indirect investments made for;
o Licensing and expropriation of the site area,
o Licensing of the plant,
o Construction of the service roads / harbour,
o Infrastructure for the transportation of the
cooling and service water,
o Fuel storage and waste disposal facilities,
o Transformer and switching substation(s),
o Cables and transmission lines connecting
plant to grid,
o Site for personnel residence and social
activities
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 45
METU
Pricing Power, Energy and Capacity
Overnight Cost (OC)
Definition
Overnight Cost
is the sum of all fixed costs as lump sum up
front to pay (present value) during the
installation of plant, until it is turned-on
into service
Overnight Cost includes
•
•
•
Installation Cost,
Tax and Insurance premiums,
All other expenditures spent during the
construction period, except financial
costs
Overnight Costs of Various
Plants ($/MW)(*)
Plant
Doğalgaz Kombine çevrim
Konvansiyonel kömür
Geliştirilmiş (advanced) kömür
Kömür gazifikasyon (IGCC)
Nükleer
Gaz türbini - merkezi
Gaz türbini - dağınık (distributed)
Diesel generatör - dağınık
Yakıt pili (Fuel cell) - dağınık
Rüzgâr - karasal
Rüzgâr - denizüstü
Fotovoltaik - dağınık
Fotovoltaik - merkezi
Biyoyakıt
Jeotermal
Hidroelektrik
Overnight Costs
(Million $ / 1000 MW)
400 - 600
800 - 1 300
1 100 – 1 300
1 300 – 1 600
1 700 - 2 150
350 - 450
700 - 800
400 - 500
3 000 - 4 000
1 600 - 1 800
2 200 – 2 500
6 000 - 7 000
4 000 - 5 000
1 500 - 2 500
1 800 - 2 600
1 900 - 2 600
----------------------------(*) 2003 Invesment Outlook-IEA, Financial costs are not included
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 46
METU
Pricing Power, Energy and Capacity
Annual Capacity Cost (A Rough Formula)
Annual Capacity Cost
Annual Capacity cost of a plant is the Overnight Cost per MW,
per year
Overnight Cost of Plant ($)
Annual Capacity Cost (*) = ------------------------------------------------------------------- ($ /MWy)
Rated Power (MW) x Lifetime of the Plant (year)
Overnight Cost of Plant ($)
= ---------------------------------------------------- ($ /MWy)
Overall Capacity of the Plant (MWy)
------------------------------------(*) This is a rough formula, since depreciation is ignored here (Actually it must be considered)
Annual capacity cost of a plant is a quantity, like energy,
measured in terms of $ / MWy
Annual Capacity cost is expressed as $ / MW-year
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 47
METU
Pricing Power, Energy and Capacity
Alternative Units for Capacity Cost
Conversion
Conversion factor between $ / MWh and Cent / kWh is 0.1
i.e.
1 $ = 100 Cent,
1 MW = 1000 kW,
Hence,
1 $ / MWh = 100 Cent / 1000 kWh
= 100 / 1000 Cent / kWh = 0.1 Cent / kWh
or
1 Cent / kWh = 10 $ / MWh
Example
12.5 Cent / kWh = 10 x 12.5 $ / MWh = 125 $ / MWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 48
METU
Pricing Power, Energy and Capacity
Alternative Units for Capacity Cost
Conversion
Conversion factor between $ / kWy and $ / MWh is
8.76
i.e.
1 MW = 1000 kW
1 Year = 8765 Hours
Hence,
1 $ / MWh = 1 $ / (1000 kW x Year / 8765)
= 8765 $ / 1000 kWy
= 8.765 $ / kWy
Example
125 $ / MWh = 8.765 x 125 $ / kWy = 1095.6 $ / kWy
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 49
METU
Pricing Power, Energy and Capacity
Rental Rate of a Plant
Rental Rate (Cost) of a Plant
Definition:
Rental rate (cost) of a plant is the cost of renting the
overall plant for a certain period of time, such as,
one year with all the variable costs are excluded.
Dimension of rental rate generally $ / year
The ratio of rental rate to the rated power of the plant
yields capacity cost
i.e. Rental Rate ($/year)
----------------------------- = Capacity Cost ($/MWy)
Rated Power (MW)
= Capacity Cost (Cent/kWh)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 50
METU
Pricing Power, Energy and Capacity
Units
Electrical Energy
Measurement Units
Quantity
Measurement
Unit
Price Unit
Energy
MWh or kWh
$ / MWh or $ /kWy
Power
MW or kW
$ / MW or $ /kW
Capacity MWh or kWh
$ / MWh or $ /kWy
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 51
METU
Pricing Power, Energy and Capacity
Annual Capacity Cost or Annual Revenue
Annual Capacity Cost
Annual Capacity Cost
is the cost, corresponding to the annual return of the “Overnight
Cost” of a plant for each MW
Annual Capacity Cost (*)
Overnight Cost of plant ($)
= -------------------------------------------------------------------- ($ /MWy)
Rated Power (MW) x Lifetime of the Plant (year)
Overnight Cost of plant ($)
= ---------------------------------------------------- ($ /MWy)
Annual Capacity of the Plant (MWy)
-----------------------------------(*) This is a rough formula, since depreciation is ignored here (Actually it must be considered)
Unit for Annual Capacity Cost is $ / MW-year
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 52
METU
Pricing Power, Energy and Capacity
Fixed Capacity Cost
Definition
Fixed Capacity Cost
of a plant is the cost dependent only on the
capacity, not on the system operating
conditions and percentage of Availability, i.e.
(capacity factor)
Fixed Capacity Cost is the cost charged for
each MWh sold in terms of $ / MWh dependent
only on the capacity
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 53
METU
Pricing Power, Energy and Capacity
Components of Fixed Capacity Cost
Components of Fixed Capacity Cost
Fixed capacity cost includes;
• Investment costs concerning all
infrastructure, land and real properties,
• Financial costs of credits, loans, etc,
• Regular repair and maintenance
expenditures,
• Salaries of the permanently employed
personnel
Unit for Fixed Capacity Cost / MWh is
$ / MWh or $ / kWy or Cent / kWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 54
METU
Pricing Power, Energy and Capacity
The Need for Fixed Capacity Cost
Meaning of Fixed Capacity Cost
Bares (Bandırma) 30 MW
The main reason for imposing fixed capacity
cost is that the customers with zero
consumption would otherwise pay nothing,
although they have allocated the plant, if
only variable cost were imposed
If only variable cost were imposed, it would
be perfectly possible for these customers
without making any consumption, to make
agreement with plants for receving only
operating reserve services with no obligation
of buying electricity and paying no charge
for this service
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 55
METU
Pricing Power, Energy and Capacity
Fixed Capacity Cost
Fixed Capacity Cost / MWh - FCC
Fixed Capacity Cost / MWh – FCC is the capacity
cost for each MWh sold by that plant
Sugözü (Isken) 1210 MW
Annual Capacity Cost ($)
Fixed Capacity Cost / kWh = -----------------------------------------Rated Power (MW) * ADA (h)
Annual Capacity Cost ($)
= -------------------------------------Annual Capacity (MWh)
Annual Capacity Cost ($)
= ------------------------------------s (MWh)
Unit for Fixed Capacity Cost / MWh is
$ / MWh or $ / kWy or Cent / kWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 56
METU
Pricing Power, Energy and Capacity
Variable Capacity Cost (VCC)
Variable Capacity Cost
(VCC)
Akenerji
Kemalpaşa (İzmir) Power Plant 127 MW
Variable Capacity Cost (VCC) is the
component of the capacity cost,
charged in proportion with the
amount of consumption
This component of cost is variable,
and depends on every MWh of
energy consumed in terms of $/ MWh
Unit for Variable Capacity Cost (VCC) is
$ / MWh or $ / kWy or Cent / kWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 57
METU
Pricing Power, Energy and Capacity
The Need for Variable Capacity Cost
Meaning of Variable Capacity Cost
Variable Capacity Cost is the component of the
capacity cost, charged in $ / MWh for every
MWh of energy consumed
The main reason for imposing variable capacity
cost is that all customers regardless of their
consumption would otherwise pay the same
amount of capacity charge, if only fixed cost
were imposed
In other words, if only fixed cost were imposed,
a customer with no consumption would pay the
same annual fixed cost as the customer with
large consumption
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 58
METU
Pricing Power, Energy and Capacity
Variable Capacity Cost
Variable Capacity Cost - VCC
Variable Capacity Cost of a plant is the
component of the capacity cost charged for every
MWh of energy consumed
Another term used for Variable Capacity Cost of a
plant is “Operation Cost”
Terms in Variable Capacity Cost;
• Internal electricity consumption; Electricity
consumptions of the machines and equipment
in the plant,
• Consumption of all other consumables, such
as “Limestone” used for preventing air
pollution,
• All other similiar “operation dependent”
expenditures
Please note that salaries Paid to
Personnel Responsible for Regular
Operation is included in “Fixed Costs”
not in variable Costs.
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 59
METU
Pricing Power, Energy and Capacity
Total Variable Cost (VC) of a Plant
Total Variable Cost - VC
Total Variable Cost of a plant - VC includes;
• Fuel Cost – FUC in $ / MWh,
• Variable Capacity Cost – VCC in $ / MWh
Hence, Total Variable Cost is the sum of the two
terms;
VC = FUC + VCC
where, VCC is the Variable Capacity Cost,
FUC is the Fuel Cost
Unit for Total Variable Cost (VC) is $ / MWh or $ / kWy
or Cent / kWh
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 60
METU
Pricing Power, Energy and Capacity
Fixed and Variable Costs of Electricity
Investment for Plant Installation
Investment for Plant Connection to System
Total Investment Cost / kWh
Investment for Air Pollution Preventation System
Expenditures for Regular Repair and Maintanence (R/M) Activities
Fixed Capacity Cost / kWh
Total R/M Cost / kWh
Expenditures for Regular R/M for Air Pollution Preventation System
Salaries Paid to Personnel Responsible for Regular Operation
Total Personnel Cost / kWh
Salaries Paid to Personnel Responsible for Air Pollution
Preventation System
Payments for Operational Material Consumed
Payments for Operational Air Pollution Prevetion System Material
Consumed
Payments for Fuel
Total Cost for Consumables /
kWh
Variable Capacity Cost /
kWh
+
Total Fuel Cost / kWh
Combined Capacity Cost
(CCC)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 61
METU
Pricing Power, Energy and Capacity
Overnight
Cost-OC
(Million $/MW)
Gas Turbine
(Simplex)
Coal
0,550
1,050
Fixed
Cost-FCC
($/MWh)
4.62
12.21
($/kWy)
40.48
106.96
Variable
Cost-VC
($/MWh)
35.00
10.00
($/kWy)
306.60
87.60
30
25
Total Variable Cost-VC
Plant
Fixed Cost-FCC
Fixed and Variable Costs
Combined Capacity Cost ($/MWh)
Fixed and Variable Cost of Thermal Plants
20
15
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 62
Pricing Power, Energy and Capacity
METU
Fixed and Variable Cost of Various Plants
Fixed and Variable Costs
Plant
Overnight
Cost-OC
Fixed
Cost -FCC
Variable
Cost –VC
Fuel
Cost-FUC
Heat
Rate
(Million$/MW)
($/MWh)
($/MWh)
($/MBtu)
(Btu/kWh)
Advanced Nuclear
1.729
23.88
4.16
0.40
10400
Coal
1.021
14.10
11.77
1.25
9419
Wind Turbine
0.919
13.85
5.0
0.0
0.0
Gas Turbine (Comb. Cycle)
0.533
7.36
20.78
3.00
6927
Gas Turbine (Simplex)
0.315
4.75
34.40
3.00
11467
Hydroelectric
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 63
Pricing Power, Energy and Capacity
METU
Unit Commitment - Example
Screening Curves
Problem
Fixed and Variable Costs
Plant
Hydroelectric
Fixed
Cost -FCC
Variable
Cost –VC
($/MWh)
($/MWh)
17.0
6.0
Advanced Nuclear
23.88
4.16
Coal
14.10
11.77
Gas Turbine (Comb. Cycle)
7.36
20.78
Gas Turbine (Simplex)
4.75
34.40
13.85
5.0
Wind Turbine
45
Combined Capacity Cost ($/MWh)
Now, plot the fixed and variable costs of the
plants on the same scale
40
35
30
25
20
15
10
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 64
METU
Pricing Power, Energy and Capacity
An ideal and fair solution is to assume neither the
fixed, nor the variable costs alone, but assume a
combination of these costs with a proper linear
combination coefficient
• Fixed Capacity Cost ($ / MWh), which is
independent of consumption,
• Variable Cost ($ / MWh), depending on the amount
of consumption, i.e. depending on Capacity
Factor
30
25
20
15
Variable Cost ($/MWh)
Total Variable Cost ($/MWh)
A possible and fair solution is that each customer
must pay for his electricity consumption with
respect to;
Fixed Cost ($/MWh)
Most customers consume only a small
portion of the overall capacity of plant, hence
their capacity factor is much less than unity
Total Cost ($/MWh)
Combining Fixed and Variable Costs
10
Fixed Cost ($/MWh)
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
Capacity Factor, C = 0.3
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 65
METU
Pricing Power, Energy and Capacity
Combined Capacity Cost (CCC)
CCC = FCC + VC x c ($/MWh)
or
y = b + a
where,
in
x
x
CCC is the Combined Capacity Cost of the plant
$ / MWh or in $ / kWy,
FCC is the Fixed Capacity Cost,
VC is the Total Variable Cost,
c is the combination coefficient, called
“Capacity Factor”
30
10
25
Slope = Variable Cost-VC
Total Variable Cost-VC
Combined Capacity Cost = (Fixed Capacity Cost) +
c x (Variable Capacity Cost)
where, c is a linear combination coefficient called
Capacity Factor. Thus,
Combined Capacity Cost ($/MWh)
In other words;
Fixed Cost-FCC
Assuming a combination of fixed and variable capacity costs
20
15
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 66
METU
Pricing Power, Energy and Capacity
Example
Combined Capacity Cost
Question:
Calculate the Combined Capacity Cost
a thermal (coal) plant with fixed and
variable cost as shown below at a
capacity factor of 1/3
Fixed
Cost-VC
Variable
Cost-FCC
($/MWh)
($/kWy)
($/MWh)
($/kWy)
12.21
106.96
10.0
87.60
CCC = FCC + VC x c
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 67
METU
Pricing Power, Energy and Capacity
Example
CCC = FCC + VC x c
= 12.21 + (1/3) x 10.00
= 15.54 $ / MWh
or
= 15.54 x 8.76 = 136.15 $ / kWy
20
15
Fixed Cost-FCC
CCC
Slope = Variable Cost-VC
25
Total Variable Cost-VC
Substituting the given parameters in
the formula:
Combined Capacity Cost ($/MWh)
Answer
30
10
5
0
0
0.1 0.2
0.3
0.4
0.5 0.6
0.7
0.8 0.9
1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 68
METU
Pricing Power, Energy and Capacity
AR = CCC x s = FCC x s + c x VC x s
= FAR + c x VAR
($/year)
where, AR is the is the overall annual income to
be earned from a plant called Annual
Revenue,
FAR = FCC x s is Fixed Annual Revenue
VAR = VC x s is Variable Annual Revenue
s is the “Annual Capacity” as defined
earlier
30
25
20
VAR
Combined Capacity Cost (CCC) in the above
equation may be multiplied by the “Annual
Capacity” s, yielding “Annual, Fixed and
Variable Revenues”; AR, FAR and VAR
15
10
AR (c = 1)
FAR
Definition
Annual Revenue (AR) ($/year)
Fixed and Variable Annual Revenues
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 69
METU
Pricing Power, Energy and Capacity
Please note that;
• Dimension of Annual Revenue is $ / year,
• Annual Revenue becomes maximum when
the Capacity Factor is unity, i.e. c = 1 (full
capacity)
30
25
20
VAR
Annual Revenue (AR)
AR = CCC x s
= FAR + c x VAR
Annual Revenue (AR) ($/year)
Fixed and Variable Annual Revenues
15
10
FAR
AR (c = 1)
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 70
METU
Pricing Power, Energy and Capacity
AR = FAR + 0.6 x VAR
25
20
15
10
AR ( c = 0.6 )
5
0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
Capacity Factor c = 0.6
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 71
VAR
In practice, it may not always be
possible to commit a plant at full
capacity factor, i.e. at unity capacity
factor, (c = 1.0)
In this case, the fixed and variable
annual revenues must be combined by
taking into account the actual capacity
factor, which is a number between zero
and unity, ( c = 0.6 )
30
VAR x c
AR = FAR + c x VAR
FAR
Annual Revenue (AR)
Annual Revenue (AR) ($/year)
Annual Revenue (AR)
METU
Pricing Power, Energy and Capacity
Example
Solution
Variable Capacity
Cost-VC
($/MWh)
($/kWy)
($/MWh)
($/kWy)
12.21
106.96
10.0
87.60
Fixed Annual Revenue (FAR)
FAR = FCC x s
= FCC x Prated x ADA
= 12.21 $ / MWh x 70 MW x 0.85 x 8765
= 6,367,728.65 $
30
25
Variable Annual Revenue
Fixed
Cost-FCC
20
15
Fixed Annual Revenue
Calculate Fixed and Variable Annual
Revenues (FAR) and (VAR) of a coal plant,
with 70 MW power rating, operated at 0.85
Annual Duration of Availability (ADA)
Annual Revenue (AR) ($/year)
Example
10
Variable Annual Rrevenue
Fixed Annual Revenue
5
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 0.9
1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 72
METU
Pricing Power, Energy and Capacity
Example
Solution
Please note that Variable
Annual Revenue is
calculated at full Capacity
Factor, i.e. c = 1.0
30
25
Variable Annual Revenue
VAR = 10.0 $/MWh x 70 MW x 0.85 x 8765
= 5,215,175.00 $
20
15
Fixed Annual Revenue
Variable Annual Revenue (VAR)
Annual Revenue (AR) ($/year)
Example
10
Variable Annual Rrevenue
Fixed Annual Revenue
5
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 73
METU
Pricing Power, Energy and Capacity
Example
FACC = FAR (unchanged)
VAC = VAR x c
c
= 0.238
FACC = 6,367,728,65 (unchanged)
VAC = 5,215,175.00 x 0.238
= 1,241,211 $
30
25
20
VAR
Calculate the “Fixed and Variable Annual
Capacity Costs” of a 70 MW coal plant
with a capacity factor of 0.238. The
annual revenues are the same as given in
the previous example
Hence,
Annual Revenue (AR) ($/year)
Question
15
VAR x c
FAR
10
AR ( c = 0.238 )
5
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 74
METU
Pricing Power, Energy and Capacity
Fixed and Variable Annual Costs
Fixed and Variable Costs
Example
Plant
30
25
Total Variable Cost-VC
Fixed Cost-FCC
Combined Capacity Cost ($/MWh)
Question
Calculate the fixed and variable
annual costs with 70 MW power
rating, operated at 0.85 Annual
Duration of Availability
20
15
10
5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
Overnight
Cost-OC
Fixed
Cost-FCC
Variable
Cost-VC
(Million
$/MW)
($/MWh)
($/kWy)
($/MWh)
Gas Turbine
0,550
7.26
40.48
35.00
306.60
Coal
1,050
12.21 106.96
10.00
87.60
($/kWy)
Answer
Fixed Annual Capacity Cost (FACC) of the plant
FACC = 12.21 $ / MWh x 70 MW x 8760 hours x 0.85
= 6,367,728.65 $
Variable Annual Capacity Cost (VAC) of the plant
VAC = 10.00 $/MWh x 70 MW x 8760 hours x 0.85
= 5,215,175.00 $
The same as previously calculated
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 75
METU
Pricing Power, Energy and Capacity
Example
Cost Components
for a BOT Plant (*)
---------------------------------(*) A foreign investment
made in a Middle East
Country
20 year
payment plan
Date
(Year)
Duration
(Years)
Annual
Generation
(kWh)
Cost
Fixed
Variable
(Cent/kWh)
(Cent/kWh)
Gas
Price
Total
Price
(Cent/kWh)
(Cent/kWh)
1999
-
2.596.979.788
4.677
1.128
3.089
8.894
2000
1
3.410.213.896
4.677
1.142
4.392
10.212
2001
2
3.683.816.410
4.677
1.180
4.637
10.494
2002
3
3.368.217.170
4.677
1.199
3.938
9.814
2003
4
3.701.172.090
4.677
1.223
3.938
9.838
2004
5
3.683.816.410
4.677
1.248
3.938
9.863
2005
6
3.368.217.170
3.159
1.273
3.938
8.370
2006
7
3.796.563.120
3.159
1.298
3.938
8.395
2007
8
3.683.816.410
3.159
1.324
3.938
8.421
2008
9
3.368.217.170
3.159
1.350
3.938
8.448
2009
10
3.701.172.090
3.159
1.377
3.938
8.475
2010
11
3.683.816.410
0.045
1.405
3.938
5.389
2011
12
3.368.217.170
0.045
1.433
3.938
5.417
2012
13
3.796.563.120
0.045
1.462
3.938
5.445
2013
14
3.683.816.410
0.267
1.491
3.938
5.696
2014
15
3.368.217.170
0.210
1.521
3.938
5.480
2015
16
3.701.172.090
0.207
1.551
3.938
5.696
2016
17
3.683.816.410
0.207
1.582
3.938
5.727
3.938
5.759
3.938
5.791
3.938
5.824
2017
2018
2019
Total Production
18
0.207 in this 1.614
Please
note3.368.217.170
that gas price figures
column
are3.796.563.120
included in the tariff
–
19
0.207as “Pass 1.646
Through
Term”
20
3.683.816.410
0.207
1.679
70.899.437.416
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 76
METU
Pricing Power, Energy and Capacity
Annual Capacity Cost
Annual Fixed Capacity Cost Formula
Annual Fixed Capacity Cost - (FCC) of
plant may be written in terms of the
Overnight + Financial Costs (OC) as;
Karkey Şırnak, Silopi - 120 MW
Karadeniz Enerji
r
FCC = ---------------- x OC
1-1/( 1+r )T
r x ( 1+r )T
= ---------------- x OC ($ / kWy)
( 1+r )T -1
where, r is annual discount or depreciation
rate of the investment (% / 100),
OC is the Overnight Cost (million
$/MW),
T is the lifetime of the plant (years)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 77
METU
Pricing Power, Energy and Capacity
Annual Capacity Cost
Annual Capacity Cost Formula
The ratio
r x ( 1+r )T
------------( 1+r )T-1
represents the fraction of capital paid
annually in order to return it with
interests, at the end of the project
Please note that, the approximate
exponential formula given in the book is
quite inaccurate particularly for the
cases, where the time period T is shorter
than 10 years, hence it is neither much
applicable, nor useful
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 78
METU
Pricing Power, Energy and Capacity
Annual Capacity Cost
Example
Find the Annual Fixed Capacity
Cost of a plant with 300 million
USD overnight cost and 25 years
lifetime
Assume 8 % depreciation rate
Annual Fixed Capacity Cost Formula
r x ( 1+r )T
FCC = ---------------- x OC
( 1+r )T -1
0.08 x (1 + 0.08)25
= ------------------------ x OC
(1 + 0.08)25 -1
= (9.365 %) x 300
= 28.095 million USD / year
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 79
METU
Pricing Power, Energy and Capacity
A Rough Formula for Fixed Capacity Cost
Combined Capacity Cost (million $/year)
30
Fixed Cost-FCC
Annual Fixed Capacity Cost Formula
10
r x ( 1+r )T
FCC = ---------------- x OC ($ / kWy)
( 1+r )T -1
Total Variable Cost-VC
25
20
15
A rough form of the above formula may be
obtained for the case, where, r is set to zero.
The formula then reduces to
FCC = OC / T
which is the same as the Rough Formula given
previously
5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Homework: Derive the above result (Hint: use
L’Hopital’s Rule).
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 80
METU
Pricing Power, Energy and Capacity
A Rough Formula for Fixed Capacity Cost
Annual Fixed Capacity Cost
Formula
Homework: Derive the above result
(Hint: use L’Hopital’s Rule).
r x ( 1+r )T
FCC = ---------------- x OC ($ / kWy)
( 1+r )T -1
where, r is annual discount or depreciation rate
of the investment (% / 100),
OC is the Overnight Cost (million $/MW),
T is the lifetime of the plant (years)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 81
METU
Pricing Power, Energy and Capacity
Example
Calculate the fixed cost of a natural gas fired thermal
plant with 20 year life and Overnight Cost (OC) of
0.550 million $ / MW by assuming 10 % annual
depreciation rate
r x ( 1+r )T
FCC = ---------------- x OC ($ / kWy)
( 1+r )T -1
(1+0.1)20
0.1 x
= ------------------- 0.550 * 1 000 000 = 63.61 $ / kWy
(1+0.1)20 – 1
= 63.61 / 8.76 $ / MWh = 7.26 $ / MWh
30
25
Total Variable Cost-VC
OC and FCC have the same dimension, i.e. when OC
is given in $/MWh, FCC also comes out to be in $/MWh
20
15
Fixed Cost-FCC
Example
Combined Capacity Cost ($/MWh)
Fixed Capacity Cost / MWh
10
5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 82
METU
Pricing Power, Energy and Capacity
Calculation of Fixed Capacity Cost by using Excel
Example
Calculate the annual fixed cost of a
200 MW gas fired plant with 20 year
life and Overnight Cost (OC) of 0.550
million $ / MW by assuming 10 %
annual depreciation rate
Solution
• Open Excel in Windows,
• Bring cursor on the tab labelled
“Sheet1” at the bottom of the
spreadsheet and press (Right Click),
• “Insert” press (Left Click)
• “Spreadsheet Solutions” press (Left
Click)
• “Loan Amortization” press (Left Click)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 83
METU
Pricing Power, Energy and Capacity
Calculation of Fixed Capacity Cost by using Excel
Solution
Now enter the spaces as follows;
•
•
•
•
•
•
•
Loan Amount: 200 MW x 0.55 106 USD/MW
= 110 000 000 USD
Annual Interest Rate: 10,0 %
Loan Period (in Years): 20
Number of payments/Year: 1
Starting date of the Loan: 1
Optional Extra payments: (Leave blank)
110000000
10,0 %
20
1
1
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 84
METU
Pricing Power, Energy and Capacity
Calculation of Fixed Capacity Cost by using Excel
Result
Annual Payment = 12,92 million USD
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 85
METU
Pricing Power, Energy and Capacity
Nükleer Santral Kurulum Birim Bedelleri(*)
(Finansman Giderleri hariç)
Diablo Canyon Nuclear Power
Plant
Bilgi Kaynağı
Birim
Bedel
/kW
Bedel/
kW
(USD)
Massachusset Institute of Technology
(USD)
2000
2000,00
DGEMP (Reference Costs for Power Generation)
(Euro)
1280
1520,13
T&L (Tarjanne R & Loustarinen K.)
(Euro)
1900
2256,44
RAE (Royal Academy of Engineering)
(Pound)
1150
2006,41
Univ. of Chicago
(USD)
1500
1500,00
CERI (Canadian Energy Research Institute)
(Can $)
2347
2059,02
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 86
METU
Pricing Power, Energy and Capacity
Nükleer Santral İşletme Birim Bedelleri
Nuclear Power Plant in Bushehr, İran
(Under construction, February 26, 2006)
Yıllar İşletme ve
Bakım
Maliyeti
Yakıt
Maliyeti
Toplam
(Cent/kWh) (Cent/kWh) (Cent/kWh)
1981
1,41
1,06
2,47
1985
1,93
1,28
3,21
1990
2,07
1,01
3,08
1005
1,73
0,69
2,42
2000
1,37
0,52
1,89
2003
1,28
0,44
1,72
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 87
METU
Pricing Power, Energy and Capacity
Nükleer Santral için Enerji Maliyeti(*)
Beznau Nuclear Power Plant, Switzerland
Kurulu güç
1000
Yıl
8760
Emreamadelik Oranı
0,9
Yıllık Çalışma Süresi
7884
Bakım Onarım Süresi (%)
10
Net Çalışma Süresi (Hour)
7095,6
Amortisman Süresi (Yıl)
8
63.072.000
Amortisman süresi içinde Çalışma Süresi (Hour)
1 MW için Yatırım (Cent)
300.000.000
1 KWh için amortisman yükü (Cent/kWh)
İşletme Bakım Onarım Yükü (%)
4,76
10
Toplam amortisman yükü (Cent/kWh)
5,23
Yakıt Bedeli (Cent/kWh)
1,72
Toplam Birim Enerji Bedeli (Cent/kWh)
6,95
------------------------------------------------(*) Decommissioning cost is ignored
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 88
Pricing Power, Energy and Capacity
METU
Load Duration Curve
40
Total Demand P(t) (MW)
Total Demand P(t) (MW)
Load Duration Curve is the sorted form of the Daily Loading Curve
35
30
25
20
15
Sorted
wrt power
10
5
0
40
35
30
25
20
15
10
5
0
2
4
6
8
10 12 14 16 18 20 22 24
Time (hours)
0
0
2
4
6
8 10 12 14 16 18 20 22 24
Duration (hours)
Areas (Energy consumptions) are the same
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 89
METU
Pricing Power, Energy and Capacity
Total Energy Supplied
Total energy supplied to the load is the
vertical integral of the demand curve,
over the vertical interval: P(t)  0, 40 ;
 Duration (P) dP = Total energy supplied
Total Demand P(t) (MW)
Capacity Factor is the same as Duration of the Load Slice
40
30
30
25
20
15
10
5
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Duration (%)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 90
METU
Pricing Power, Energy and Capacity
Now, consider a plant supplying a
load slice with thickness ∆P and
duration d
Duration of the load slice is the
same as Capacity Factor of that
plant
Justification
Total energy that can be supplied
by the plant for a load slice ∆P is
the overall hatched area (blue area
+ red area ) in the rectangular load
slice
Energy actually supplied by the
plant, on the other hand, is only the
blue hatched area
Total Demand P(t) (MW)
Capacity Factor is the same as Duration of the Load Slice
40
30
30
∆P
25
20
15
Duration = d
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Duration (%)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 91
METU
Pricing Power, Energy and Capacity
Proof of Claim
Capacity Factor may then be
written as;
Capacity Factor = Actual energy supplied/
overall energy that can be supplied
(Capacity) of the plant;
or
c = Blue area / (Red area + Blue area)
= ∆P x d / ∆P x Overall duration
= ∆P x d / ∆P x 1
=d/1
=d
Conclusion;
Capacity Factor is the same as duration
of operation i.e.;
d=c
Total Demand P(t) (MW)
Capacity Factor is the same as Duration of the Load Slice
40
30
30
∆P
25
20
15
Duration = d
10
5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Duration (%)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 92
METU
Pricing Power, Energy and Capacity
Energy Supplied in Load Slice
Load Slice
Load Duration Curve
Assume that this load slice; Pslice
represents a particular plant operating
within duration d
Total energy supplied by this load
slice to the load within duration d may
then be written as;
E = ∆Px d
=∆Pxc
where,
∆ P is the rated power of plant (MW),
d is the duration of supply,
c is the capacity factor of supply
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 93
METU
Pricing Power, Energy and Capacity
Combined Energy Cost
“Combined Capacity Cost (CCC), may be
divided by “Capacity Factor (c)”, resulting
“Combined Energy Cost (CEC)”
CEC = CCC / c
= FCC / c + VC
where, CEC is known as the “Combined
Energy Cost”
Combined Energy Cost Curve
Combined Energy Cost ($MWh)
Combined Energy Cost
250.0
225.0
200.0
175.0
150.0
Coal Plant
125.0
100.0
75.0
Gas Plant
50.0
25.0
0.0
0.0 0.1 0.2
0.3 0.4
0.5
0.6 0.7
0.8 0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 94
METU
Pricing Power, Energy and Capacity
Combined Energy Cost
Combined Energy Cost
CEC = CCC / c
comes out again in $ / MWh
Combined Energy Cost ($MWh)
Hyperbolic characteristics showing
“Combined Energy Cost” of the Gas
and coal plants given in the previous
examples are shown in the graph on
th RHS
As c is unitless, unit of division:
Combined Energy Cost Curve
250.0
225.0
200.0
175.0
Coal Plant
150.0
125.0
100.0
75.0
Gas Plant
50.0
25.0
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 95
METU
Pricing Power, Energy and Capacity
Combined Energy Cost
Combined Energy Cost Curve
As expected, Combined Energy Cost
for:
• Gas Plant alternative is preferable
for capacity factors within the
range:
0 ≤ c ≤ 0.3
and
• Coal plant alternative is preferable
for capacity factors within the
range:
0.3 ≤ c ≤ 1.0
Combined Energy Cost ($MWh)
Combined Energy Cost
250.0
225.0
200.0
175.0
Coal Plant
150.0
125.0
100.0
75.0
Gas Plant
50.0
25.0
0.0
0.0 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 96
METU
Pricing Power, Energy and Capacity
Combined Energy Cost
Combined Energy Cost Curve
Combined Energy Cost Curves on
the RHS show that;
• Gas Plant alternative is preferable
for capacity factors:
0 ≤ c ≤ 0.3
and
• Coal plant alternative is preferable
for capacity factors:
0.3 ≤ c ≤ 1.0
Combined Energy Cost ($MWh)
Combined Energy Cost
250.0
225.0
200.0
175.0
150.0
125.0
Gas Plant
100.0
75.0
50.0
Coal Plant
25.0
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 97
METU
Pricing Power, Energy and Capacity
Example
Combined Energy Cost Curve
Question
Calculate the average energy cost a
thermal (coal) plant with fixed and
variable capacity costs as shown in
the following table at a capacity factor
of 1/3
Fixed
Cost-FCC
Variable
Cost-VC
Combined Energy Cost ($MWh)
Combined Energy Cost
250.0
225.0
200.0
175.0
150.0
Coal Plant
125.0
100.0
75.0
($/MWh)
12.21
($/kWy)
106.96
($/MWh)
10.00
($/kWy)
87.60
Gas Plant
50.0
25.0
0.0
CEC = FCC / c + VC
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 98
METU
Pricing Power, Energy and Capacity
Example
Answer:
Substitute the given parameters in the
formula:
CEC = FCC / c + VC
CEC
= 12.21 / (1/3) + 10.00
= 46.63 $ / MWh
or
Combined Energy Cost Curve
Combined Energy Cost ($MWh)
Combined Energy Cost
250.0
225.0
200.0
175.0
150.0
Coal Plant
125.0
100.0
75.0
= 46.63 x 8.76 = 408.48 $ / kWy
= 408.48 x 100 Cent / kW x 8760 h
= 4.66 Cent / kWh
Gas Plant
50.0
25.0
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1.0
Capacity Factor (c)
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 99
METU
Pricing Power, Energy and Capacity
Total Cost of Supplying Demand
Application
Load Duration Curve
Total cost of supplying the load by this
plant within duration d may then be
written as;
Total cost of energy = E x CEC
= ∆ P x c x CEC
= ∆ P x CCC
where,
or
E is the total energy supplied,
CEC is the Combined Energy Cost,
defined as;
CEC
= FCC / c + VC,
CCC is the Combined Capacity Cost
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 100
METU
Pricing Power, Energy and Capacity
Equivalence of Average Capacity and Energy Costs
Load Duration Curve
Application
Therefore, it is shown that the total
cost of energy calculated in both
ways are the same, i.e.
E x CEC = ∆ P x CCC
where,
CCC is Combined Capacity Cost defined as;
CCC = FCC + c x VC
CEC is Combined Energy Cost defined as;
CEC = FCC / c + VC
In fact, the two formulations are equivalent
Main disadvantage of the latter formulation
is that the characteristics of CEC are
nonlinear and hence they tend to be
unbounded as c is reaches to zero.
EE 710 Electricity Trading, Electrical and Electronics Eng. Dept., METU, Spring 2007, Prof. Dr. Osman SEVAIOGLU, Page 101