Coincident Peak
Forecasting Example
Load Forecast Workshop
August 22, 2013
overview
• This slide deck will provide an example of the estimation
of equations, calculations, supporting data, and results
for a hypothetical load serving entity (LSE) preparing a
coincident peak load forecast for the resource adequacy
process.
• The NCP forecast has already been prepared.
• The data is real.
• The purpose is to provide LSEs with a basic
understanding of the ideas in action – not to provide
a prescriptive, compulsory approach.
• Please ask questions as we proceed.
2
glossary
• CP
• NCP
• CF
• DF
Coincident Peak Demand: LSE peak at the
time of MISO’s expected or actual peak
Non-Coincident Peak Demand: LSE peak
whenever it occurs during the month or year
Coincidence Factor: CP/NCP
Must be between 0 and 1, inclusively.
Diversity Factor: 1 – CF
3
theoretical approach
• The LSE desires a forecast of its peak, coincident with
the expected MISO peak.
• The primary explanatory factor for the difference in load
between the NCP hour and the CP hour is the
temperature.
• The difference in these temperatures, whether positive or
negative, causes the loads to differ.
• There are other causal factors, but they are believed to be
relatively minor.
• We assume that the values have been increased as
necessary to reflect all LMRs that were in operation
during the hours affected.
4
data
Month
Year
Jun
Jul
Aug
Sep
Jun
Jul
Aug
Sep
Jun
Jul
Aug
Sep
Jun
Jul
Aug
Sep
Jun
Jul
Aug
Sep
Jun
Jul
Aug
Sep
2005
2005
2005
2005
2006
2006
2006
2006
2007
2007
2007
2007
2008
2008
2008
2008
2009
2009
2009
2009
2010
2010
2010
2010
MISOCP kW
918,320
934,884
1,090,203
740,151
755,396
1,215,007
820,727
768,011
1,095,477
1,098,992
1,002,019
1,045,020
889,373
999,966
875,147
717,578
929,495
723,403
859,063
820,326
964,741
902,436
911,958
749,824
NCP kW
1,070,877
1,105,691
1,137,329
952,352
1,017,800
1,215,007
985,244
810,405
1,095,477
1,170,021
1,138,503
1,055,006
934,779
1,046,810
1,007,662
977,592
1,046,503
911,383
1,028,962
847,419
988,473
1,040,124
1,078,117
791,789
MISOCP °F
NCP °F
DF
ABS(Temp Diff)
81
82
91
76
79
100
79
83
84
88
86
89
82
90
85
67
88
73
81
79
90
84
88
74
95
91
87
81
90
100
85
75
84
95
92
87
88
93
79
80
93
88
86
80
90
93
80
73
0.1425
0.1545
0.0414
0.2228
0.2578
0.0000
0.1670
0.0523
0.0000
0.0607
0.1199
0.0095
0.0486
0.0447
0.1315
0.2660
0.1118
0.2063
0.1651
0.0320
0.0240
0.1324
0.1541
0.0530
14
9
4
5
11
0
6
8
0
7
6
2
6
3
6
13
5
15
5
1
0
9
8
1
Note: This data ends with 2010; you will have 2011 and 2012 data as well.
5
step #1: equation #1: explaining diversity
ABS(Temp Diff)
Linear (ABS(Temp Diff))
0.3000
0.2500
0.2000
Regression Statistics
Multiple R
0.7615
R Square
0.5799
Adjusted R Square
0.5608
Standard Error
0.054
Observations
24
DF
SUMMARY OUTPUT
0.1500
0.1000
y = 0.0141x + 0.0235
R² = 0.5799
0.0500
0.0000
0
2
4
6
8
10
ABS(Temp Diff)
12
14
16
ANOVA
df
Regression
Residual
Total
Intercept
ABS(Temp Diff)
SS
MS
F
Significance F
1 0.086957721 0.086957721 30.36863642 1.5441E-05
22 0.062994922 0.002863406
23 0.149952643
Coefficients
0.0235
0.0141
Standard
Error
0.0189
0.0026
t Stat
1.25
5.51
Is it
reasonable?
P-value
Lower 95%
0.22574
-0.0156
0.00002
0.0088
Upper
95%
0.0626
0.0194
Is it statistically
significant?
6
step 2: getting forecast input values
• Equation 1 requires the absolute value of the temperature
difference between the two peak hours.
• Perhaps by examining the relationship between the NCP
temperature and the CP temperature, we could answer
this question.
• If so, we could then use the temperature assumed in the
NCP “50/50” forecast to determine the CP temperature,
which would then provide us with the temperature
difference.
NCP
TEMP
CP
TEMP
NCP – CP
TEMP
D.F.
7
equation #2: NCP to CP temperatures
MISO CP Temperature
Temperatures
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.5463
R Square
0.2985
Adjusted R Square
0.2666
Standard Error
5.97
Observations
24
Linear (Temperatures)
105
100
95
90
85
80
75
70
65
y = 0.5596x + 34.677
R² = 0.2985
65
70
75
80
85
90
NCP Temperature
95
100
105
ANOVA
df
Regression
Residual
Total
Intercept
NCP Temp
Significanc
SS
MS
F
eF
1 334.0066 334.0066 9.361269 0.005741
22 784.9518 35.67963
23 1118.958
Coefficient Standard
s
Error
34.7
15.9
0.560
0.183
t Stat
P-value
2.18
0.0406
3.06
0.0057
Is it
reasonable?
Lower
Upper
95%
95%
1.6
67.7
0.180
0.939
Is it statistically
significant?
8
step 3: determining CP temperature
MISO CP Temperature
• Let’s assume that 91° was used as the “50/50” temperature for
the NCP submitted.
• Using Eq.2, input “91” as the NCP Temperature.
• Result?
Temperatures
FCST
Linear (Temperatures)
86° is the estimated
105
CP Temperature.
100
95
• And?
90
85
The temperature
80
difference (for use in
75
70
Eq.1) is 91-86 = 5.
65
65
75
85
NCP Temperature
95
105
9
step 4: determining the coincident peak
DF
• From Step 3, the temperature difference is “5”.
• From Eq.1, with an input of “5”, the resulting DF is .0941
• If the DF is .0941, the
ABS(Temp Diff)
Fcst
Linear (ABS(Temp Diff))
CF is .9059, and the
0.3000
Coincident Peak
0.2500
forecast is
0.2000
.9059 x NCP forecast
0.1500
0.1000
y = 0.0141x + 0.0235
R² = 0.5799
0.0500
0.0000
0
5
10
ABS(Temp Diff)
15
20
10
questions?
Contact:
• Ted Kuhn ([email protected] )
or
• Mike Robinson ([email protected] )
11