1 Regression-based Approach for Calculating CBL Dr. Sunil Maheshwari Dominion Virginia Power

2 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).

3 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)

4 Functional Forms for Weather-Sensitive Loads Form 1: Load = a + b*CDD + c*HDD Form 2: Load = a + Σ (b i * CDD i ) + Σ (c j * HDD j ); Temperature breakpoints to be established based on Regression Analysis Form 3: Load = a + Σ (b i * CDD i ) + Σ (c j * HDD j ) + Σ (d k * hour k ); In addition to weather, each hour impacts the load as well.

5 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 + Σ (b k * hour k ) + Σ (c j * month j ); Form 5: Load = a + b * TimeTrend + Σ (c k * hour k ) + Σ (d j * month j );

6 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 + Σ (b i * CDD i ) + Σ (c j * HDD j ) + Σ (d k * hour k ); Following temperature breakpoints were used: – For Heating Degree Days (HDD) – 65, 55, 40, 25 – For Cooling Degree Days (CDD) – 65, 80, 90, 100

7 We further sliced the data by: –Day type Weekdays Weekends and Holidays –Season Winter – December - March Summer – June - September Shoulder – April, May, October, November Applying Theory into Practice…

8 Partial Regression Output (Summer, Weekday) regress load cdd_65to80 cdd_80to90 cdd_90to100 cdd_over100 hdd hddsq hour2-hour24 if year==2006 & weekdayflag==1 & holiday==0 & season=="Summer" Source | SS df MS Number of obs = F( 28, 2011) = Model | Prob > F = Residual | R-squared = Adj R-squared = Total | Root MSE = load | Coef. Std. Err. t P>|t| [95% Conf. Interval] cdd_65to80 | cdd_80to90 | cdd_90to100 | cdd_over100 | (dropped) hdd | hddsq | hour2 | hour3 | hour4 |

9 Predicted Load (CBL) based on 2006 data applied to 2007 data Using regression parameters from previous slide, predict the load for 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

10 Actual vs Predicted (CBL)

11 Actual Load vs Predicted (CBL) - Summer, Weekday (Absolute Average % Deviation = 3%)

12 Actual Load vs Predicted (CBL) - Winter, Weekday (Absolute Average % Deviation = 3.6%)

13 Actual Load vs Predicted (CBL) - Shoulder, Weekday (Absolute Average % Deviation = 3.7%)

14 Actual Load vs Predicted (CBL) - Weekend/Holiday (Absolute Average % Deviation = 4.7%)

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