Regressionbased Approach for Calculating CBL

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Regression-based Approachfor Calculating CBL
Dr. Sunil Maheshwari Dominion Virginia Power
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Benefits of Regression Approach

• This approach can be used to calculate CBL for
  both weather-sensitive and non-weather-sensitive
  loads.
• The science of regression theory is well
  developed.
• Most statistical packages such as SAS, STATA,
  SPSS, etc. can perform regression analysis.
• Regression equations can be easily updated on a
  periodic basis (perhaps annually).

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Description of Regression Approach

• The idea is to treat load as a function of
  explanatory factors such as weather, time of day,
  day of the week, etc.
• Estimate the relationship between load and
  explanatory variables using a variety of
  functional forms.
• Pick the functional form that gives the highest
  R-sq adjusted or the lowest Root Mean Squared
  Error (RMSE)

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Functional Forms for Weather-Sensitive Loads

• Form 1 Load a bCDD cHDD
• Form 2 Load a S (bi CDDi) S (cj HDDj)
  
• Temperature breakpoints to be established based
  on Regression Analysis
• Form 3 Load a S (bi CDDi) S (cj HDDj)
  S (dk hourk)
• In addition to weather, each hour impacts the
  load as well.

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Functional Forms for Non-Weather Sensitive Loads

• The following forms may do a good job of
  estimating CBL for Industrial loads
• Form 4 Load a S (bk hourk) S (cj
  monthj)
• Form 5 Load a b TimeTrend S (ck hourk)
  S (dj monthj)

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Applying Theory into Practice

• For one of our DSR participants (a Building
  Complex), we estimated the relationship between
  2006 hourly Load and Weather using Functional
  Form 3
• Load a S (bi CDDi) S (cj HDDj) S (dk
  hourk)
• Following temperature breakpoints were used
• For Heating Degree Days (HDD) 65, 55, 40, 25
• For Cooling Degree Days (CDD) 65, 80, 90, 100

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Applying Theory into Practice

• We further sliced the data by
• Day type
• Weekdays
• Weekends and Holidays
• Season
• Winter December - March
• Summer June - September
• Shoulder April, May, October, November

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Partial Regression Output (Summer, Weekday)

• regress load cdd_65to80 cdd_80to90 cdd_90to100
  cdd_over100 hdd hddsq hour2-hour24 if
  year2006 weekdayflag1 holiday0
  season"Summer"
• Source SS df MS
  Number of obs 2040
• -------------------------------------------
  F( 28, 2011) 518.86
• Model 339127510 28 12111696.8
  Prob gt F 0.0000
• Residual 46942715.2 2011 23342.9713
  R-squared 0.8784
• -------------------------------------------
  Adj R-squared 0.8767
• Total 386070225 2039 189342.925
  Root MSE 152.78
• --------------------------------------------------
  ----------------------------
• load Coef. Std. Err. t
  Pgtt 95 Conf. Interval
• -------------------------------------------------
  ----------------------------
• cdd_65to80 33.08646 .9634143 34.34
  0.000 31.19707 34.97586
• cdd_80to90 31.6024 .5931229 53.28
  0.000 30.4392 32.7656
• cdd_90to100 32.58845 .68489 47.58
  0.000 31.24528 33.93162
• cdd_over100 (dropped)
• hdd -104.137 6.194134 -16.81
  0.000 -116.2846 -91.98941
• hddsq 4.866126 .6342737 7.67
  0.000 3.622224 6.110028
• hour2 -33.26744 23.44299 -1.42
  0.156 -79.24253 12.70765

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Predicted Load (CBL) based on 2006 data applied
to 2007 data

• Using regression parameters from previous slide,
  predict the load for 2007.
• Compare predicted load (CBL) to actual load.
• Absolute average deviation between Actual and
  Predicted Load was less than 5.
• Regression Equations will be re-estimated every
  year

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Actual vs Predicted (CBL) - 2007
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Actual Load vs Predicted (CBL) - Summer,
Weekday(Absolute Average Deviation 3)
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Actual Load vs Predicted (CBL) - Winter,
Weekday(Absolute Average Deviation 3.6)
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Actual Load vs Predicted (CBL) - Shoulder,
Weekday(Absolute Average Deviation 3.7)
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Actual Load vs Predicted (CBL) -
Weekend/Holiday(Absolute Average Deviation
4.7)
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Conclusions

• 4 Equations with single variable hourly
  temperature
• Summer, Weekday
• Winter, Weekday
• Shoulder, Weekday
• Weekends / Holidays
• Good fit (R-sq adjusted gt 78 in all cases).
• Simplified calculations, and the regression
  equations can be easily updated.