EEI Electric Rate Advanced Course
Wisconsin Public Utility Institute
Demand Rate Design Methodology
Larry Vogt
Manager, Rates
Session Objective
To describe a process for selecting an appropriate
demand rate structure and its component prices
for a commercial/industrial type of rate class, on
the basis of embedded costs.
This process is an extension of the embedded cost
allocation process: it bridges the gap between the
cost-of-service study and rate design.
2
1
Demand Rates
Example Rate
Monthly Rate at Primary
Customer Charge
@
$550.00/Mo.
Demand Charge
@
$5.75/kW
Energy Charges:
First 200 kWh per kW
Next 200 kWh per kW
Next 200 kWh per kW
Over 600 kWh per kW
@
@
@
@
1.750 ¢/kWh
1.399 ¢/kWh
0.981 ¢/kWh
0.505 ¢/kWh
The monthly billing demand shall be the kW
occurring during the 15 minute period of maximum
use, but not less than 85% of the actual demand
occurring in the previous 11 months, nor less than
50% of the contract capacity, and in no case less
than 1,000 kW.
Delivery Voltage Adjustments: An additional
charge of 45¢/kW for secondary service. A credit
of $0.95/kW for transmission service.
Reactive Power Adjustments: An excess kVAR
charge of $1.25/kVAR shall apply in any month in
which the power factor is less than 90%.
 Demand-based rates typically apply
to rate classes having far fewer
customers than classes with nondemand rates, e.g., industrial.
 Individual bill calculations are
typically more complex because of
such billing provisions as:
»
»
»
»
Billing demand ratchets
Rate and contract demand
minimums
Power factor adjustment clauses
Service voltage adjustments
 Rate design is more accurate if rate
modifications are tested on a bill-bybill basis, as if to emulate monthly
billing, as part of the rate design
process.
3
Hopkinson vs. Wright
The Heavyweight Match of the Century
$14.91/kW
0.220¢/kWh
1st 100 kWh/kW
@ 7.50¢/kWh
Next 150 kWh/kW
@ 3.77¢/kWh
Over 250 kWh/kW
@ 1.50¢/kWh
4
2
Session Topics
 Demand rate cost curve development
methodology.
 Fundamental principles and methods of
demand rate design.
 Demand rate provisions for assuring cost
recovery.
5
Cost Curves: An Extension of the
Cost of Service Study
3
Cost Curve Studies
The embedded cost-of-service study allocates customer,
demand, and energy cost components to customer or rate
classes.
A cost curve study is an extension of this cost allocation
process: it bridges the gap between the cost-of-service
study and rate design, i.e., rate structuring and pricing.
The key focus of the cost curve study is the allocation of
the demand-related cost components across the range of
usage. We will assume that fuel is collected outside of the
base rate structure, and we will set the customer-related
costs aside until the end.
7
Cost Analysis Steps
COINCIDENCE FACTOR
VS. LOAD FACTOR
ANALYSIS
HOURS USE OF DEMAND
BILL FREQUENCY
ANALYSIS
UNIT COST
COMPONENT
ANALYSIS
DEMAND
COMPONENT
ALLOCATION
FUNCTIONAL REVENUE
REQUIREMENTS
ANALYSIS
8
4
CF vs. LF Relationship:
The Bary Curve
Average NCP CFs
Plot of Coincidence Factors for Customer Load Factor Groups
100
90
80
70
% CF
60
50
40
30
CF = A × LF3 + B × LF2 + C × LF + D
20
10
0
0
10
20
30
40
50
60
70
80
90
% LF
100
9
Load Factor
The ratio of a customer’s average demand to the customer’s
maximum demand:
LF 
E T
dmax
WHERE:
LF
=
Load factor (%)
E
=
A customer’s monthly energy in kWh
T
=
The number of hours in the month
dmax
=
The customer’s monthly maximum demand in kW
Note: Hours Use of Demand (kWh/kW) = E ÷ dmax
10
5
Coincidence Factor
Conventional Definition
The ratio of the maximum demand of a group of loads as a whole
to the sum of the maximum demands of the individual loads within
the group:
CF 
DMAX
d
max
WHERE:
CF
= Coincidence factor (%)
DMAX = Maximum demand of the group of customers in kW
dmax = d1, d2 , ... dN = The sum of N customer maximum demands in kW
Note: The coincidence factor is the reciprocal of the diversity factor.
11
CF vs. LF Relationship
Low Load Factor Customers
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Low Coincidence of Load
21
High Load Factor Customers
22
23
24
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
High Coincidence of Load
12
6
Coincidence of Load
Throughout the System
Coincidence
Factor
100% Load Factor
1.0
Low Load Factor
Numbers of Customers
13
Relationship of the CF
to the Cost-of-Service Study
 Since the Bary Curve is based on the coincidence factors of different groups
(i.e., subsets of the total commercial and industrial customer base that have
been differentiated by load factor); and
 Since the maximum demand (DMAX) of any group can occur at any time;
 Then DMAX is similar to a non-coincident demand of a cost-of-service study
customer or rate class.
 So let us refer to this coincidence factor as the “CFNCP:”
CFNCP 
DMAX
DMAX
d
max
Group Load
 Often primary distribution and sometimes distribution substations are
allocated to customer or rate classes using a class NCP allocation factor.
14
7
Bary Curve Analysis
Developing the Demand Cost Allocation Model
Average NCP CFs
100
90
80
70
% CF
60
50
40
30
20
10
CF = A × LF3 + B × LF2 + C × LF + D
0
0
10
20
30
40
50
60
70
80
90
100
% LF
15
A More Diverse Bary Curve
 An NCP type of allocation factor is generally not a good fit for the production
and transmission levels of the system as it does not represent very well the
high degree of load diversity that exists at those levels.
 So let us define a different coincidence factor that is more representative of
upper system load diversity that we will refer to as the “CFCP:”
CFCP 
D SYS
d
max
DSYS
Group Load
 “DSYS ” is a load factor group’s demand at the hour of system peak.
 Note that CFCP ≤ CFNCP at the same load factor.
 We can now plot another Bary Curve based on the CFCP data points.
16
8
Calibrated Bary Curves
CP Basis vs. NCP Basis
100%
90%
80%
70%
% CF
60%
50%
40%
30%
20%
10%
0%
0
50
100 150 200 250 300 350 400 450 500 550 600 650 700
CP-CF
NCP-CF
MAX
kWh/kW
17
Hours Use of Demand
20
kW
15
Hours use of demand (HUD) is
another way of expressing load
factor:
MAX kW
10
5
0
6
12
18
HOURS
24
20
15
HUD = kWh  kWMAX
LF = HUD  Hr
10
5
0
6
12
20
15
18
24
HUD is expressed as kWh per kW
20 kW Maximum
Demand Used For
12 Out of 24 Hours
10
5
0
6
12
18
24
18
9
Cost Analysis Steps
COINCIDENCE FACTOR
VS. LOAD FACTOR
ANALYSIS
HOURS USE OF DEMAND
BILL FREQUENCY
ANALYSIS
DEMAND
COMPONENT
ALLOCATION
UNIT COST
COMPONENT
ANALYSIS
FUNCTIONAL REVENUE
REQUIREMENTS
ANALYSIS
19
Hours Use of Demand
Bill Frequency
kW
35,000
Customer Actual Maximum Demands
Large C&I Rate
133 Bills
30,000
105,522 MWh
d
25,000
max
 238,558 kW
442 kWh/kW
20,000
60.5% Load Factor
15,000
10,000
5,000
kWh/kW
72
0
69
0
66
0
63
0
60
0
57
0
54
0
51
0
48
0
45
0
42
0
39
0
36
0
33
0
30
0
27
0
24
0
21
0
18
0
15
0
90
12
0
60
0
30
100%
Load Factor
20
10
Diversified Demands by HUD
kW
kW
Customer Actual Maximum Demands
35,000
Customer Diversified Maximum Demands
35,000
MAX kW
30,000
30,000
25,000
25,000
20,000
20,000
NCP kW
CP kW
15,000
 238,558 kW
kWh PER kW
72
0
69
0
66
0
63
0
60
0
57
0
54
0
51
0
48
0
45
0
42
0
39
0
36
0
33
0
30
0
27
0
24
0
21
0
18
0
90
0
72
0
69
0
66
0
63
0
60
0
57
0
54
0
51
0
48
0
45
0
42
0
39
0
36
0
33
0
30
0
27
0
24
0
21
0
18
0
90
15
0
12
0
0
60
5,000
30
5,000
15
0
10,000
12
0
max
60
d
10,000
30
15,000
kWh PER kW
100%
90%
MAX kW =
80%
238,558
70%
CFNCP
60%
Results of Bary Curve Applications:
NCP kW =
207,638
CP kW =
180,104
50%
40%
CFCP
30%
20%
10%
0%
0
50
100
150
200
250
300
CP-CF
350
400
NCP-CF
450
500
550
600
650
21
700
MAX
Cost Analysis Steps
COINCIDENCE FACTOR
VS. LOAD FACTOR
ANALYSIS
HOURS USE OF DEMAND
BILL FREQUENCY
ANALYSIS
UNIT COST
COMPONENT
ANALYSIS
DEMAND
COMPONENT
ALLOCATION
FUNCTIONAL REVENUE
REQUIREMENTS
ANALYSIS
22
11
Functional Revenue Requirements
For an Example C&I Rate Class
Cost
Revenue
Cost-of-Service
Component
Requirements
Allocation Basis
$105,888
BILLS
CUSTOMER
DEMAND:
 PRODUCTION

TRANSMISSION
P&T TOTAL

$1,637,638
12-CP kW
478,584
12-CP kW
$2,116,222
DISTRIBUTION
1,135,780
NCP kW
305,354
MAX kW


TRANSFORMERS
TOTAL DEMAND
$3,557,356
ENERGY:
 VARIABLE O&M

FUEL
TOTAL ENERGY
$232,148
MWh
2,616,942
MWh
$2,849,090
TOTAL
$6,512,334
23
Cost Analysis Steps
COINCIDENCE FACTOR
VS. LOAD FACTOR
ANALYSIS
HOURS USE OF DEMAND
BILL FREQUENCY
ANALYSIS
UNIT COST
COMPONENT
ANALYSIS
DEMAND
COMPONENT
ALLOCATION
FUNCTIONAL REVENUE
REQUIREMENTS
ANALYSIS
24
12
Unit Cost Development
For an Example C&I Rate Class
Cost
Revenue
Rate Class Billing
Unit
Component
Requirements
Determinants
Costs
CUSTOMER
$105,888
DEMAND:
 PRODUCTION

TRANSMISSION
P&T TOTAL

DISTRIBUTION
133 BILLS
$1,637,638
180,104 kW (CP)
478,584
180,104 kW (CP)
$2,116,222
180,104 kW (CP)
$796.15
$9.093
$2.657
$11.75
1,135,780
207,638 kW (NCP)
305,354
238,558 kW (MAX)
$5.47
$1.28
$3,557,356
238,558 kW (MAX)
$14.912*


TRANSFORMERS
TOTAL DEMAND
* NON-DIVERSIFIED
ENERGY:
 VARIABLE O&M

FUEL
TOTAL ENERGY
$232,148
105,522 MWh
0.220¢/kWh
2,616,942
105,522 MWh
2.480¢/kWh
$2,849,090
TOTAL
$6,512,334
25
Cost Analysis Steps
COINCIDENCE FACTOR
VS. LOAD FACTOR
ANALYSIS
HOURS USE OF DEMAND
BILL FREQUENCY
ANALYSIS
UNIT COST
COMPONENT
ANALYSIS
DEMAND
COMPONENT
ALLOCATION
FUNCTIONAL REVENUE
REQUIREMENTS
ANALYSIS
26
13
Demand Cost Allocation
HUD
CF-CP
$/CP-kW
CF-NCP
$/NCP-kW
$/MAX-kW
$/kW
0
0.0000
$0.00
0.0000
$0.00
$0.00
$0.00
20
0.0442
0.52
0.1669
0.91
1.28
2.71
50
0.1193
1.40
0.3596
1.97
1.28
4.65
100
0.2571
3.02
0.5592
3.06
1.28
7.36
200
0.5061
5.95
0.7264
3.97
1.28
11.20
300
0.6603
7.76
0.8177
4.47
1.28
13.51
400
0.7482
8.79
0.8694
4.76
1.28
14.83
500
0.8042
9.45
0.9007
4.93
1.28
15.66
600
0.8629
10.14
0.9309
5.09
1.28
16.51
700
0.9588
11.27
0.9791
5.36
1.28
17.91
730
1.0000
$11.75
1.0000
$5.47
$1.28
$18.50
27
Allocated Total Demand Cost
As a Function of the Hours Use of Demand
$/kW
$18.00
$16.50
$15.00
$13.50
$12.00
$10.50
$9.00
$7.50
$6.00
$4.50
$3.00
$1.50
$0
50
100 150 200 250 300 350 400 450 500 550 600 650 700
kWh/kW
28
14
Conversion of $/kW to ¢/kWh
Development of a Diversified Cost Structure
$/kW
$18.00
$16.50
$15.00
$13.50
$12.00
$10.50
$9.00
$7.50
$6.00
EXAMPLE FOR 50 TO 100 kWh/kW RANGE:
$4.50
$7.36  $4.65
 100  5.420¢/kWh
100  50
$3.00
$1.50
$0
50
100 150 200 250 300 350 400 450 500 550 600 650 700
kWh/kW
29
Equivalent Cost Structures
Diversified vs. Non-diversified
kWh/kW
DEMAND
$/kW
¢/kWh
ENERGY*
¢/kWh
TOTAL
¢/kWh
0
$0.00
0.000
0.000
0.000
20
2.71
13.550
0.220
13.770
50
4.65
6.467
0.220
6.687
100
7.36
5.420
0.220
5.640
200
11.20
3.840
0.220
4.060
300
13.51
2.310
0.220
2.530
400
14.83
1.320
0.220
1.540
500
15.66
0.830
0.220
1.050
NON-DIVERSIFIED
600
16.51
0.850
0.220
1.070
COST STRUCTURE
700
17.90
1.400
0.220
1.620
$14.912/kW
730
$18.50
1.967
0.220
2.187
* VO&M
CUSTOMER
$796.15/MO
0.220¢/kWh
CUSTOMER
$796.15/MO
30
15
Equivalent Cost Structures
Diversified vs. Non-diversified
LOAD FACTOR
10%
¢/kWh
25%
∞
50%
75%
100%
∞
28
CURVES ARE PLOTTED WITHOUT
THE CUSTOMER COMPONENT
26
24
22
20
NON-DIVERSIFIED
$14.912/kW
0.220¢/kWh
18
16
14
12
10
8
6
HUD DIVERSIFIED
COST STRUCTURE
4
2
20
30
40
50
100
150
200
250
400
600
730
kWh/kW
31
Fundamental Principles of
Demand Rate Design
16
Equivalent Cost Structures
Applied Rate Tilt
LOAD FACTOR
10%
¢/kWh
25%
∞
50%
75%
100%
∞
28
CURVES ARE PLOTTED WITHOUT
THE CUSTOMER COMPONENT
26
24
22
20
Tilted
Hopkinson
$7.038/kW
2.00¢/kWh
18
16
NON-DIVERSIFIED
$14.912/kW
0.220¢/kWh
14
12
10
8
6
HUD DIVERSIFIED
COST STRUCTURE
4
2
20
30
40
50
100
150
200
250
400
600
730
kWh/kW
33
Application of Rate Tilt
The non-diversified structures yielded by the cost-of-service study for all customer or rate
classes will have high unit demand costs ($/kW). In other words, the energy unit costs
contain no demand cost elements. Consider applying the non-diversified cost structure
to both of these customers:
$14.92/kW
0.220¢/kWh
kW
kW
100 kW
Customer A
3.591¢/kWh
(100% tilted)
Customer B
34
17
Equivalent Cost Structures
An Alternative HUD Rate
LOAD FACTOR
10%
¢/kWh
25%
∞
50%
75%
100%
∞
28
CURVES ARE PLOTTED WITHOUT
THE CUSTOMER COMPONENT
26
24
22
20
NON-DIVERSIFIED
$14.912/kW
0.220¢/kWh
Tilted
Hopkinson
$7.038/kW
2.00¢/kWh
18
16
Wright Hours Use of Demand
FIRST 100 kWh/kW @ 7.50¢/kWh
NEXT 150 kWh/kW @ 3.77¢/kWh
OVER 250 kWh/kW @ 1.50¢/kWh
14
12
10
8
6
HUD DIVERSIFIED
COST STRUCTURE
4
2
20
30
40
50
100
150
200
250
400
600
730
kWh/kW
35
Hopkinson vs. Wright
The Bout Begins
1st 100 kWh/kW
@ 7.50¢/kWh
Next 150 kWh/kW
@ 3.77¢/kWh
Over 250 kWh/kW
@ 1.50¢/kWh
$14.91/kW
0.220¢/kWh
36
18
Hopkinson vs. Wright
A Mathematical Comparison
A mathematical analysis of the Hopkinson and Wright rate forms yields
an additional perspective of how these structures operate.
Hopkinson
Wright
$14.91/kW
1st 100 kWh/kW
@ 7.50¢/kWh
0.220¢/kWh
Next 150 kWh/kW
@ 3.77¢/kWh
Over 250 kWh/kW
@ 1.50¢/kWh
Note that the Customer cost component of $796.15 will be included but fuel
cost will be excluded from this analysis.
37
Rate Formulization
Hopkinson Rate
Since a rate is applied to determinants to calculate a bill, it
can be expressed as an equation (or a series of equations)
using e as the variable representing monthly kWh usage
and d as the variable representing the monthly maximum
demand. Fixed charges, such as the Customer Charge,
are represented by a constant.
The example Hopkinson rate is thus expressed simply as:
Bill = 14.91d + 0.00220e + 796.15
38
19
Rate Structure Graph
Hopkinson Rate
kWh
100,000
Monthly Rate
90,000
730 kWh/kW or
100% Load Factor
$796.15/Bill
$14.91/kW
0.220¢/kWh
80,000
70,000
60,000
50,000
40,000
30,000
14.91d + 0.00220e + 796.15
20,000
10,000
0
0
25
50
75
100
125
kW
39
Rate Structure Graph
Wright Rate
kWh
100,000
Monthly Rate
90,000
$796.15/Bill
80,000
First 100 kWh/kW @ 7.50¢/kWh
70,000
Next 150 kWh/kW @ 3.77¢/kWh
Over 250 kWh/kW @ 1.50¢/kWh
60,000
1.50¢/kWh
50,000
40,000
30,000
20,000
3.77¢/kWh
10,000
7.50¢/kWh
0
0
25
50
kW
75
100
125
40
20
Rate Formulization
Wright Rate
Formulization of the example Wright rate is more involved:
From 0 to 100 kWh/kW
Bill = 0.0750e + 796.15
From 100 to 250 kWh/kW
Bill = [(e – 100d) × 0.0377] + [100d × 0.0750] + 796.15
Bill = 3.73d + 0.0377e + 796.15
41
Rate Formulization
Wright Rate
Over 250 kWh/kW
Bill = [(e – 250d) × 0.0150] + [150d × 0.0377]
[100d × 0.0750] + 796.15
Bill = 9.405d + 0.0150e + 796.15
42
21
Rate Structure Graph
Wright Rate
kWh
100,000
Monthly Rate
90,000
$796.15
First 100 kWh/kW @ 7.50¢/kWh
80,000
Next 150 kWh/kW @ 3.77¢/kWh
70,000
Over 250 kWh/kW @ 1.50¢/kWh
60,000
50,000
9.405d + 0.0150e + 796.15
40,000
30,000
20,000
3.73d + 0.0377e + 796.15
10,000
0.0750e + 796.15
0
0
25
50
kW
75
100
125
43
Hopkinson vs. Wright
Decision
$14.91/kW
0.220¢/kWh
1st 100 kWh/kW
@ 7.50¢/kWh
Next 150 kWh/kW
@ 3.77¢/kWh
Over 250 kWh/kW
@ 1.50¢/kWh
44
22
Rate Structure Selection
Distributions of Monthly Customer Demands
Scatter Plots of kW Demand vs. kWh/kW for Different Rate Classes
18,000
14,000
16,000
12,000
14,000
10,000
12,000
10,000
8,000
8,000
6,000
6,000
4,000
4,000
2,000
2,000
0
0
0
73 146 219 292 365 438 511 584 657 730
This type of dispersion supports a
tilted Hopkinson rate structure.
0
73 146 219 292 365 438 511 584 657 730
This type of dispersion supports a
Wright rate structure.
45
Demand Rates:
Assuring Cost Recovery
23
Determination of Billing Demand
The monthly billing demand is often determined by
computing and selecting the greatest of:
 The current month metered demand,
 A percentage of prior month metered demands,
 A percentage of the contract capacity, and
 The rate schedule minimum demand.
47
Impacts of Billing Demand
Determination on the Demand Charge
Example: LGS Rate Class
Demand Component Revenue Requirement = $8,381,900
Billing kW
838,190
Demand Charge
$10.00 per kW
+ 8,939 Ratchet kW
847,129
$9.89 per kW
+ 17,115 Contract kW
864,244
$9.70 per kW
+ 3,184 Minimum kW
867,244
$9.67 per kW
Actual metered kW only
48
24
Power Component Relationships
The three power components are vectors and thus can not be added
algebraically.
kVA  kW 2  kVAR 2
kVA = 1,250
kVAR = 750
 = 36.87°
Power Factor = kW ÷ kVA
Power Factor = 0.8 or 80%
kW = 1,000
SINE  = kVAR  kVA
COSINE  = kW  kVA
TANGENT  = kVAR  kW
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Cost Impacts of Power Factor
CUSTOMER A: 2,185 kW
@ 95% PF
2,300 kVA
CUSTOMER B: 2,185 kW
@ 78% PF
2,800 kVA
480Y/277 V
480Y/277 V
1 × 2,500 kVA
2 × 1,500 kVA
12.47Y/7.2 kV
$54,258
TRANSFORMER COSTS
$74,152
∆ = $19,894
50
25
Present Rate Comparison
Analysis Based on 95% Power Factor
Rate MGS
Customer Charge
@
$1.00/Day ($30.42/Mo.)
Demand Charge
@
$1.20/kW
Energy Charges:
First 200 kWh per kW
First 31,000 kWh
Over 31,000 kWh
Next 200 kWh per kW
Over 400 kWh per kW
@
@
@
@
kWh
5.901¢/kWh
4.031 ¢/kWh
1.828 ¢/kWh
0.602 ¢/kWh
LGS Lower
Minimum Demand = 5 kW
Rate LGS
Customer Charge
@ $700.00/Mo.
Demand Charge
@
Energy Charges:
First 200 kWh per kVA
Next 200 kWh per kVA
Over 400 kWh per kVA
@
@
@
MGS Lower
$5.70/kVA
1.718 ¢/kWh
1.395 ¢/kWh
0.598 ¢/kWh
kW
Minimum Demand = 500 kVA
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Scenario 1: Increase Rate MGS,
While Holding Rate LGS Constant
LGS Lower
MGS Lower
LGS Lower
MGS Lower
Possible migrations
from MGS to LGS.
52
26
Scenario 2: Increase Rate LGS,
While Holding Rate MGS Constant
MGS Lower
MGS Lower
Possible migrations
from LGS to MGS.
53
Rate Profitability View
Price vs. Cost Differential Chart
kW
54
27
Summary of Key Points
• Coincidence of load, and its relationship with
load factor, is a major cost-causation driver.
• A cost curve serves as a means for development
of a rate structure and its unit prices, since it
yields the average cost per kWh across the
whole range of usage.
• Rate schedule provisions, including various
methods to determine monthly billing demand
and power factor, help mitigate the risks
associated with cost recovery.
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