Appendix H-1-3 Class Specific Regression Model Statistics

Transcription

1 Appendix H-1- Class Specific Regression Model Statistics EB Page 1 of 1 Delivered: February, A widely used measure of goodness of fit is the Adjusted R-Squared. The Adjusted R-Squared measures how well the estimated model explains actual variation of the monthly sales data. The Adjusted R-Squared can vary from 0 (explains none of data variation) to 1.0 (explains all of the data variation). A model that can explain a high level of the historical sales variation is likely to generate a more accurate sales forecast. The mean absolute percent error (MAPE) measures the average absolute model error (variance between actual sales and predicted sales) on a percent basis. The Durbin-Watson statistic is a test about the presence of first order serial correlation. Serial correlation exists in a regression model when the error in the current period is partly a function of the error in the prior period. A Durbin-Watson statistic around the value of.0 suggests that there is no first order serial correlation. The statistical significance of an explanatory variable in the model is denoted by its T-Statistic value. T-statistic values above.0 (absolute) indicate statistical significance. A P-Value indicates the probability, in percentage, of the coefficient of a given explanatory variable having no impact on sales variation. The closer the P-value to zero, the higher the probability that the variable contributes to explaining historical sales variation and trends. 1

2 Residential Table 1: Residential Sales Forecast Model Statistics EB Page of 1 Delivered: February, 01 Model Statistics Adjusted Observations Deg. of Freedom for Error R-Squared 0. Adjusted R-Squared 0.1 Model Sum of Squares 1,,,1 Sum of Squared Errors 1,1,,1 Mean Squared Error 1,, Std. Error of Regression 1, Mean Abs. Dev. (MAD),00 Mean Abs. % Err. (MAPE).% Durbin-Watson Statistic Variable Coefficient StdErr T-Stat P-Value HDD % CDD1 1, % Pop*PCI*EI_Idx 1,., % Jan-0,1. 1, % Feb-0 -,01.0 1, % Nov- -,.0 1, % Jun-1 -,0.0 1, % Nov - 1,0.0, % Dec 0,., % The Residential model has an Adjusted R-Squared of 0.1 and a MAPE of.%, indicating that the model explains actual sales variation well. The Durbin-Watson Statistic of.0 indicates that serial correlation is not a concern. The primary model variables have T-Statistic values well above.0, indicating that the model drivers are highly statistically significant. The associated P-Values have either a 0 or a low probability indicating that all the variables contribute to explaining historical sales variation and trends. The Residential sales forecast model has tracked historic experience quite well. This can be seen in Figure 1 which shows actual and predicted monthly sales. The Residential sales model is robust and an appropriate tool for forecasting future sales. Figure 1: Residential Sales Actual vs. Predicted Sales kwh

3 EB Page of 1 Delivered: February, 01 1 Forecasted Residential sales derived from the regression model are adjusted downward for expected incremental savings from future residential CDM activity. The assumption is that the impact of all past CDM activity (prior to 01) is embedded in the actual sales data and captured in the regression models. Table shows the annual historical Residential sales with CDM embedded and forecasted Residential sales with and without the CDM adjustment. Table : Historical Weather Normalized Actual and Forecast Sales - Residential (GWh) Weather Normalized before CDM % Change CDM adjustment Weather Normalized after CDM Year % Change 00, -, 00,1 -.% -,1 -.% 0, -1.% -, -1.% 0, 1.1% -, 1.1% 01,.% -,.% 01, 0.% -, 0.% 01, -1.% -, -1.% Average % 0.00% 01 Bridge Year, -0.1%,0-0.% 01 Test Year, 0.% 1,1 0.0% 01 Test Year,1 0.%, -0.% 01 Test Year, 0.% 0, -0.% 01 Test Year, 1.1%, -0.% 00 Test Year, 0.% 1,1-0.% Average % -0.%

4 General Service < 0 kw Table : General Service < 0 kw Sales Forecast Model Statistics EB Page of 1 Delivered: February, 01 Model Statistics Adjusted Observations Deg. of Freedom for Error R-Squared 0. Adjusted R-Squared 0. Model Sum of Squares,,0, Sum of Squared Errors,, Mean Squared Error,01,0 Std. Error of Regression, Mean Abs. Dev. (MAD),0 Mean Abs. % Err. (MAPE).% Durbin-Watson Statistic.0 Variable Coefficient StdErr T-Stat P-Value HDD % CDD % GDP_Idx 1,0.,.. 0.1% CalDays 1, % Jan-0,., % Feb-0 -,0.0, % Oct -,. 1, % Dec,. 1, % The General Service < 0 kw model has an Adjusted R-Squared of 0. and a MAPE of.%, indicating that the model explains actual sales variation well. The Durbin-Watson Statistic of. indicates that serial correlation is not a concern. The model T-Statistic values above.0 indicate that all the model variables are statistically significant at the % and higher level of confidence. This is also shown in P-Values that fall between 0% and 1.0%. The General Service < 0 kw sales forecast model has tracked historic experience quite well. This can be seen in Figure which shows actual and predicted monthly sales. The General Service < 0 kw sales model is robust and an appropriate tool for forecasting future sales. 1 1

5 Figure : General Service < 0 kw Sales Actual vs. Predicted Sales kwh EB Page of 1 Delivered: February, 01 Forecasted General Service < 0 kw sales derived from the regression model is then downward adjusted for expected incremental savings from future General Service < 0 kw CDM activity. The assumption is that the impact of all past CDM activity (prior to 01) is embedded in the actual sales data and captured in the regression models. Table shows the annual historical General Service < 0 kw sales with CDM embedded and forecasted General Service < 0 kw sales with and without the CDM adjustment. Table : Historical Weather Normalized Actual and Forecast Sales - General Service < 0 kw (GWh) 1 Weather Normalized before CDM % Change CDM adjustment Weather Normalized after CDM Year % Change 00 1,0-1,0 00 1,00 -.0% - 1,00 -.0% 0 1,01 0.% - 1,01 0.% 0 1,0 0.% - 1,0 0.% 01 1,00 0.% - 1,00 0.% 01 1,0 0.% - 1,0 0.% 01 1,0 0.% - 1,0 0.% Average % 0.% 01 Bridge Year 1,0 0.% 1,01 0.% 01 Test Year 1,0 0.% 1 1,00-0.1% 01 Test Year 1,01 0.% 1,0-0.% 01 Test Year 1,0 0.% 1,0-0.% 01 Test Year 1,0 0.% 1,0-0.% 00 Test Year 1,0 1.0% 1,01-0.% Average % -0.% General Service > 0 kw

6 Table : General Service > 0 kw Sales Forecast Model Statistics EB Page of 1 Delivered: February, 01 Model Statistics Adjusted Observations Deg. of Freedom for Error R-Squared 0. Adjusted R-Squared 0. Model Sum of Squares,,0,1 Sum of Squared Errors,,,0 Mean Squared Error 1,1,1 Std. Error of Regression, Mean Abs. Dev. (MAD), Mean Abs. % Err. (MAPE).0% Durbin-Watson Statistic 1. 1 Variable Coefficient StdErr T-Stat P-Value HDD % CDD % ManGDP_Idx 1,0., % CalDays, % Jan-0-1,0.0, % Feb-0,.1, % Sep- -,1., % May-,., % Jun- - 0,. 1, % Dec-1 1,01.00, % Nov-1 1,0.,1.. 0.% Jun 1,.1,..1 0.% The General Service > 0 kw model has an Adjusted R-Squared of 0. and a MAPE of.0% indicating that the model explains actual sales variation well. The Durbin-Watson Statistic of 1. indicates that serial correlation is not a concern. The explanatory variables have T-Statistic values above.0, indicating that all the model variables are statistically significant at the % and higher level of confidence. This is also supported by P-Values that fall between 0% and 1.0%. Forecasted sales are consistent with historical sales trend. This can be seen in Figure which depicts actual and predicted General Service > 0 kw sales. The General Service > 0 kw sales model is robust and an appropriate tool for forecasting future sales. Figure : General Service > 0 kw Sales Actual vs. Predicted Sales kwh

7 EB Page of 1 Delivered: February, 01 1 Forecasted General Service > 0 kw sales derived from the regression model is then adjusted downward for expected incremental savings from future General Service > 0 kw CDM activity. The assumption is that the impact of all past CDM activity (prior to 01) is embedded in the actual sales data and captured in the regression models. Table shows the annual historical General Service > 0 kw sales with CDM embedded and forecasted General Service > 0 kw sales with and without the CDM adjustment. Table shows the annual historical General Service > 0 kw demand and forecasted General Service > 0 kw demand Table : Historical Weather Normalized Actual and Forecast Sales - General Service > 0 kw (GWh)

8 Weather Normalized before CDM % Change CDM adjustment EB Page of 1 Weather Normalized Delivered: February, 01 after CDM % Change Year 00, -, 00,0 -.% -,0 -.% 0,1 1.0% -,1 1.0% 0, 1.% -, 1.% 01,0 1.1% -,0 1.1% 01, -0.% -, -0.% 01,1 0.1% -,1 0.1% Average % -0.% 01 Bridge Year,0 0.% 1,1 0.0% 01 Test Year, 1.%, 0.% 01 Test Year, 0.%, 0.0% 01 Test Year,1 0.% 1, -0.1% 01 Test Year,0 0.% 0, -0.% 00 Test Year,0 1.0% 0, -0.1% Average % 0.0% Table : Historical Weather Normalized Actual and Forecast Demand - General Service > 0 kw (MW) Weather Normalized before CDM % Change CDM adjustment Weather Normalized after CDM Year % Change 00 1,1-1,1 00, -.% -, -.% 0,0 0.% -,0 0.% 0 1,0 1.% - 1,0 1.% 01 1, 0.% - 1, 0.% 01 1,0 0.% - 1,0 0.% 01 1,0-1.0% - 1,0-1.0% Average % -0.% 01 Bridge Year 1,0 1.0% 0 1, 0.% 01 Test Year 1, 1.% 1 1,1 0.% 01 Test Year 1, 0.% 1,1 0.0% 01 Test Year 1, 0.% 1,00-0.1% 01 Test Year 1,0 0.% 1,1-0.% 00 Test Year 1, 1.0% 1,1-0.1% Average % 0.1%

9 Sentinel Lighting Sales EB Page of 1 Delivered: February, 01 Table : Sentinel Lighting Sales Forecast Model Statistics Model Statistics Iterations 1 Adjusted Observations Deg. of Freedom for Error R-Squared 0. Adjusted R-Squared 0. Model Sum of Squares 1,1. Sum of Squared Errors 1. Mean Squared Error.1 Std. Error of Regression 1.1 Mean Abs. Dev. (MAD) 1.1 Mean Abs. % Err. (MAPE).0% Durbin-Watson Statistic 1. Variable Coefficient StdErr T-Stat P-Value SentinelCusts % Apr % Oct % Jan % Mar % May % Jul % Aug % Oct % Nov % Dec % The primary explanatory variable for the Sentinel Lighting sales model is the Sentinel customer counts within PowerStream s territory. The Sentinel Lighting model has an Adjusted R-Squared of 0. and a MAPE of.0%, indicating that the model explains actual sales variation well. The Durbin-Watson Statistic of 1. indicates that serial correlation is not a concern. The explanatory variables have T-Statistic values above.0, indicating that the model variables are statistically significant at the % and higher level of confidence. This is also supported by P-Values that fall between 0% and 1.%.

10 Table shows the annual historical and forecasted Sentinel Lighting sales. Table shows the annual historical and forecasted Sentinel Lighting demand. Table : Historical Actual and Forecast Sales - Sentinel Lighting (MWh) EB Page of 1 Delivered: February, 01 Year % Change % 0 -.1% 0 -.0% % 01-0.% 01 -.% 01 Bridge Year.% 01 Test Year -0.% 01 Test Year -0.1% 01 Test Year 0.0% 01 Test Year 0.0% 00 Test Year 0.0% Table : Historical Actual and Forecast Demand - Sentinel Lighting (kw) Year % Change 00 1, 00 1,1 -.1% 0 1,.% 0 1, -.1% 01 1,01 -.% 01 1,0-0.% 01 -.% 01 Bridge Year.% 01 Test Year -0.% 01 Test Year -0.1% 01 Test Year 0.0% 01 Test Year 0.0% 00 Test Year 0.0% Street Lighting

11 Table : Street Lighting Sales Forecast Model Statistics EB Page of 1 Delivered: February, 01 Model Statistics Iterations 1 Adjusted Observations Deg. of Freedom for Error R-Squared 0. Adjusted R-Squared 0.0 Model Sum of Squares 1,,. Sum of Squared Errors 0,,.1 Mean Squared Error,. Std. Error of Regression. Mean Abs. Dev. (MAD). Mean Abs. % Err. (MAPE).% Durbin-Watson Statistic. 1 Variable Coefficient StdErr T-Stat P-Value CONST % HrLight % Nov % Apr % Feb % Nov % Dec % Jan % Apr % May % Aug % Dec % The primary independent variable for the Street Lighting sales model is Hours of Light. The Street Lighting model has an Adjusted R-Squared of 0.0, indicating that the model explains actual sales variation well. The Durbin-Watson Statistic of. indicates that serial correlation is not a concern. The explanatory variables have T-Statistic values above.0, indicating statistical significance. This is also supported by P-Values that fall between 0% and.%. In developing the load forecast for Street Lighting sales, PowerStream has taken into account the LED streetlight conversion planned by the municipalities in its service areas. Over a -year period of time, starting in 01, the existing HPS streetlights owned by the City of Vaughan, Markham and Barrie will be fully converted to the LED streetlights.

12 Delivered: February, 01 Inevitably, the efficiency and economics of LED lighting system will lead to reduction in energy consumption. Research and case studies suggested that the LED lighting technology reduced energy use by anywhere between 1% - 0%, depending on the quality of the LEDs deployed. A recent case study on Mississauga LED streetlights conversion revealed that the energy use was reduced by %. Table 1 references LED Streetlights case studies and energy use reduction in Canada and the United States. Table 1: LED Streetlights Studies EB Page 1 of 1 Reference sissauga%0case%0study%0cinal.pdf land%0case%0study.pdf th%0bay%0case%0study.pdf monton%0case%0study.pdf Comment In Mississauga case study (largest in Canada), energy use reduced % In Welland case study, energy use reduced % In North Bay case study, energy use reduced % In Edmonton case study, energy use reduced 0% //led-streetlights-already-paying-off /0/doe-gateway-report-compares-ledstreetlights-with-hps.html Welland's LED streetlights using,000 kwh/month compared with 0,000 kwh/month for HPS LED street lights use 0-0% less electricity and have at least times the life expectancy than HPS fixtures Based on system efficiency (which is more relevant than source efficiency) HID is around 0 lumens/w, LED at least 0 ln/w In Kansas City, MO, LED streetlights reduced energy use by 1-1% compared with HPS. Although the LEDs emitted 1% less light, it was higher quality and better directed (less light spill) For the purpose of forecasting Street Lighting sales, PowerStream assumed that 1) 1/ of the streetlights in scope will be converted to the LED streetlights each year over the -year window commencing in 01; and that ) the converted LED streetlights will reduce the energy use by 0%. PowerStream manually adjusted the Street Lighting load from the regression model by these reduced energy use. Table 1 shows the annual historical and forecasted Street Lighting sales. Table 1 shows the annual historical and forecasted Street Lighting demand. Table 1: Historical Actual and Forecast Sales - Street Lighting (MWh)

13 Year before LED Adjustment LED Adjustment after LED Adjustment % Change 00, -, 00, -, 1.% 0, -,.% 0,1 -,1 1.% 01 0, - 0,.% 01 1,0-1,0 0.% 01 0,1-0,1-1.% 01 Bridge Year 0, - 0, -0.1% 01 Test Year, -,,00 -.% 01 Test Year 0, - 1,1,1-1.% 01 Test Year 0, - 1,0,0-1.% 01 Test Year 0, - 1,, -1.0% 00 Test Year, -,, -1.% Table 1: Historical Actual and Forecast Demand - Street Lighting (MW) EB Page 1 of 1 Delivered: February, 01 Year before LED Adjustment LED Adjustment after LED Adjustment % Change % % % % % % 01 Bridge Year % 01 Test Year % 01 Test Year % 01 Test Year % 01 Test Year % 00 Test Year % Large Use There are two customers in the Large Use class LU1 and LU. LU was classified as Large Use in 01. The load forecast was developed individually for each customer based on historical averages and then consolidated to derive the total load for the Large Use class. The three year average is used for each Large Use customer. Table 1 provides the annual historical and forecasted Large Use sales. Table 1: Historical Actual and Forecast Sales Large Use (MWh)

14 EB Page 1 of 1 Delivered: February, 01 Year LU 1 % Change LU % Change Total % Change 00 0,01,,0 00, -.%,1.%,1 -.% 0, 1.% 1,.%,1.% 0, -1.%,.%,0 0.% 01,0-1.%,0 1.% 0,0 0.% 01,0-0.%,1-1.0%,1-0.% 01, -1.% 1,1 -.%, -.0% 01 Bridge Year, -1.% 1, -0.%, -0.% 01 Test Year,1-1.% 1,0-0.%, -0.% 01 Test Year,1-1.% 1,0-0.%, -0.% 01 Test Year,1-1.% 0, -0.%, -0.% 01 Test Year,0-1.% 0, -0.%, -0.% 00 Test Year,00-1.% 0,1-0.%, -0.%

15 Unmetered Scattered Load EB Page 1 of 1 Delivered: February, 01 Similar to the Large Use, the load forecast for Unmetered Scattered Load (USL) was developed based on historical averages. The three year average is used to forecast USL class sales. Table 1 provides the annual historical and forecasted USL sales. Table 1: Historical Actual and Forecast Sales Unmetered Scattered Load (MWh) Year % Change 00, , 1.% 0 1,00 0.% 0 1, 0.% 01 1,.% 01 1,1 1.% 01 1,.% 01 Bridge Year 1,0.% 01 Test Year 1,.% 01 Test Year 1,.% 01 Test Year 1,.% 01 Test Year 1,1.% 00 Test Year 1,0.%