# Integrated Resource Plan

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1 Integrated Resource Plan March 19, 2004 PREPARED FOR KAUA I ISLAND UTILITY COOPERATIVE LCG Consulting 4962 El Camino Real, Suite 112 Los Altos, CA

2 1 IRP

4 regarding the likelihood of different forecasts and the significance of the different risks and opportunities. Due to changing regulatory requirements and higher costs associated with fuel and power plant development, it is important to use a robust methodology to forecast electricity demand. 1.2 Econometric Model of Load Growth For this study, it is assumed that total energy sales over time (Figure 3.1) are predicted based on the following four explanatory variables 1. Resident Population 2. Visitor Population (Average Daily Visitor Census) 3. Average Electricity Price over a (Constant 2004 \$/MWh) 4. Total Personal Income (Constant 2004 M\$) To forecast energy sales, two econometric models were considered: the single equation linear regression model, and the Autoregressive Integrated Moving Average (ARMA) model. The dependent variable (electricity sales or load) and the independent variables all exhibit compound (exponential) growth with respect to time. However, their behavior can be converted to a linear scale by replacing each variable by its natural log, for the regression equation. This guarantees that there is a linear relationship between parameters, and the linear regression coefficients can then be estimated. 4 0 ) + i ln( X it ) i= 1 ln( Y t ) = ln( A β + ut..(3.1) where: Y t - Energy Sales in time period t A 0 - Calculated constant β i - Regression coefficient X it - i th Explanatory (Independent) variable at time period t ut - Error term with the mean 0 in time period t. This type of model assumes that the effect on electric load of changes in any of the four explanatory variables does not change over the entire historical and forecast period. For example, we assume that the customers price elasticity exhibited will remain constant 3 IRP

5 into the future; so that customers are expected to have the same response to future increases in electricity prices as they have shown in the past. Figure 1.1 Electricity Sales for for MWh 450, , , , , , , ,000 50,000 0 Historical Energy Sales (MWh) Over s IRP

6 1.2.1 Limitations of Single Equation Linear Regression Models When forecasting energy sales growth, it is common to use linear regression analysis. However, this approach fails to incorporate the time series behavior within the temporal pattern of load growth itself. In the linear regression analysis described above, variation of the dependent variable (total annual power sales) is explained by variations in four explanatory variables, assuming constant correlations between the dependent and explanatory variables. In reality this may not be true, as other drivers such as policy or environmental changes may also influence the dependent variable, electricity sales. To minimize the errors caused by this possibility, we utilize the time series analysis forecasting methodology, technically known as the ARMA Methodology. Here, the emphasis is not on constructing single equation predictive models, but on analyzing the probabilistic or stochastic property of the time series of the dependent variable itself, letting the data speak for themselves An Autoregressive Moving Average (ARMA) Model In the regression model, the independent variable Y t (electricity sales) is explained by the k independent variables or regressors X 1, X 2,, X k ; (in this study there are k = 4 regressors). In contrast, in the ARMA time series models, Y t may be explained by past or lagged values of Y (electricity sales) itself, plus stochastic error terms. For this reason, such models are sometimes considered a-theoretic models since they cannot be derived from any economic theory. However, we can have the best of both worlds by predicting future variation of the independent variable, electricity sales, based on both its historical relationship to the explanatory variables (the linear regression approach) plus its historical serial autocorrelation (the ARMA approach).. Typically the information that is not explicitly captured in the econometric regression equation lies in the error termu t. We shall apply time series logic to explain part of the variation represented by the error term, achieving better historical explanation for going-forward prediction than achieved with the simple linear regression model. It should be noted that the ARMA model can be implemented using any number of past values for Y and for the linear regression error terms. For this reason, such approaches are typically specified as ARMA(p,q). For example, an ARMA (3,1) model would use the past 3 values of the dependent variable, and the past 1 error term. An important step in applying the ARMA model is to find, by trial-and-error, the number of lagged parameters (p and q) that best explain the dependent variable. To avoid confusion, it should also be noted that there exists a related time-series model, known as ARIMA. This model adds a step before beginning the ARMA model, differencing the historical values of the dependent variable. This step is only necessary 5 IRP

7 when the dependent variable is not stationary over the historical period. However, the dependent variable in our ARMA model the error term from the linear regression equation is stationary. Therefore the simple ARMA model is used, not the ARIMA model. Improving on the model represented by equation 3.1, the ARMA model used in this study explain the linear regression error term u t for any time period (year) t, based on both an autoregressive term ( ρ u t 1 ) and moving average term for the error term ( θε t 1 ), plus, of course the remaining unexplained errorε t. The original error term is thus modeled as shown in Equation 3.2. u t = ρ u t 1 + θε t 1 + ε t..(3.2) 1.3 Data Collection For deriving the predictive model, data for the explanatory and dependent variables (except for Total Income) for the period of 1970 until 1991 was obtained from the previous IRP study done by LCG Consulting 2 prepared for Citizens Utilities. For the remaining data, a variety of sources were used as summarized below Resident Population Historical resident population data for were obtained from LCG s 1993 IRP report. Corresponding data for years were obtained from Hawaii County population estimates Visitor Population Historical visitor population data for were obtained from LCG s 1993 IRP report. For , visitors population data were obtained from the Department of Business, Economic Development and Tourism (DBEDT) 4. For , visitor population data were obtained from the Hawaii State Department of Business 5. It should 2 Integrated Resource Plan, October LCG Consulting, Los Altos, CA 3 Source: Population Division, U.S. Census Bureau. Release Date: April 17, 2003, Table CO-EST Hawaii County Population Estimates: April 1, 2000 to July 1, Department of Business, Economic Development and Tourism (DBEDT): Summary of County Tourism, Hawaii State Department of Business, Economic Development and Tourism, Research and Economic Analysis Division, 2001 Annual Visitor Research Report; Historical Visitor Data, spreadsheet (http://www.state.hi.us/dbedt/monthly/historical-r.xls) 6 IRP

8 be noted that in 2001, the anticipated visitor population growth was adversely affected by the events of 9/11 and was below normal. Therefor, the 2002 visitor population was estimated as the average of the year 2000 and year 2001 visitor populations Total Income Total Income ( ) data were obtained from The State of Hawaii Data Book, The total income is assumed to be highly dependent on the levels of tourist activity. In 2001 and 2002, tourism was adversely affected by the events of 9/11 and was below normal. Assuming that the year of 2000 was a normal year, year 2002 total income was calculated as the average of year 2000 and year 2001 total income Electricity Sales (Dependent Variable) and Average Electricity Price Data for electricity sales and average electricity price for were obtained from LCG s 1993 IRP report. For , Energy Sales ( Power Sold ) and Sales Revenues data were obtained from The State of Hawaii Data Book 7. These data were used to calculate the Average Electricity Price, as shown in Table 3.1. Table 1.1 Calculation of Average Electricity Price for for years ENERGY SALES (MWh) ENERGY REV (nom 1000\$) Average Price (\$/MWh) ,955 62, ,737 73, ,112 77, ,029 72, ,781 77, ,922 94, ,521 91, ,487 90, For the intervening years , total generation data provided by KIUC were used with the appropriate adjustments for losses to estimate the energy sales for these years. 6 Hawaii State Department of Commerce and Consumer Affairs, Division of Consumer Advocacy, records- 7 From the tables Electric Utilities, By Islands 7 IRP

9 To estimate the average electricity price for those years, sales revenue was first estimated as follows. Since year 1995 data were available for both Hawaii and of sales, the ratio of Kaua I revenue to total Hawaii revenue could be calculated as 6.06%. When applied to the sales revenue for Hawaii 8 this produced estimated total sales revenues for for years (Table 3.2). Finally, using total generation adjusted for losses (to give sales) and the estimated sales revenue, the average energy price was derived for years (Table 3.2). Table 1.2 Estimation of Average Electricity Price for, Hawaii Kauai Actual Total Rev Actual Rev (\$000 nom) (\$000 nom) ,037,702 62,928 weight(%) : 6.06% Actual Revenue Estimated Rev Total Gen (MWh) Aver Energy Price ,525 49, , ,797 55, , ,907 57, , The complete set of input data used for regression analysis is presented in Table Energy Resources Coordinator s Annual Report IRP

10 Table 1.3 Input data for regression analysis Visitor Population (ADVC) Total Average Price Income (Nom\$/MWh) (Nom \$M) Resident Population Sales (MWh) ,800 2, , ,900 3, , ,900 3, , ,900 4, , ,600 4, , ,400 4, , ,900 5, , ,500 5, , ,800 6, , ,100 7, , ,400 7, , ,600 6, , ,900 6, , ,000 7, , ,100 10, , ,300 10, , ,200 14, , ,900 14, , ,300 15, , ,000 18, , ,600 18, , ,100 19, , ,003 13, , ,864 8, , ,627 13, , ,983 14, , ,435 15, , ,539 15, , ,603 17, , ,264 18, , ,463 18, , ,223 16, , ,946 17, , Regression Analysis Before conducting the regression analysis, some adjustments have been made to the data. First, all values for explanatory and dependent variables such as average electricity price and total income were transformed using the natural logarithmic (nlog or Ln) values. Transforming to the natural log is necessary because all of the dependent and independent variables grow at a compound rate (just like a bank account growing at a fixed percent interest rate.) The log function transforms this compound growth into linear growth, which in turn makes it possible for the variables relationships to be estimated using linear regression. Total sales (MWh) was the dependent variable, while the four dependent variables were: resident population, visitor population, average retail electricity price, and total personal income. Finally, regression coefficients were 9 IRP

11 estimated using the OLS algorithm, and the error terms (residuals) were calculated for each period t. The resulting single equation linear regression model explaining electricity sales (demand) was as follows: Ln (Sales) = * Ln (Resident Population) * Ln (Visitor Population) 0.070* Ln (Average Price) * Ln (Total Income) The adjusted R-squared value for the model is extremely high ( ), indicating that nearly all of the variability in electricity demand can be explained using the independent variables selected. It should be noted that both the dependent variable (sales) and at least one of the independent variables (resident population) contain a growth rate that is inherently very similar. It is a well-known econometric principle that this can result in spurious correlation, where the R -squared value is estimated to be much higher than its true value. However, for several reasons we have chosen not to eliminate this effect through the standard data-detrending process: 1) Unlike textbook examples of spurious correlation where two variables share the same growth rate by coincidence (spuriously), we believe that the similar growth rates of population and electricity demand do in fact reflect a causal relationship, and therefore have predictive power. 2) Even where spurious correlation is present, the resulting regression coefficients are not biased per se. The worst problem is an overestimation of the model s explanatory power (overestimation of precision, not accuracy). 3) A high priority was placed on maintaining ease of use and intuitive understandability in our regression model. Detrending the data would undermine both of these goals. The signs of the coefficients (Table 3.4) indicate that as both resident and visitor populations increase, Electricity Sales also increase. The absolute value of the tstatistic greater than 2.33 indicates that the Resident Population and Visitor Population are significant predictors of Electricity Sales. To be precise, these two population parameters are statistically different from zero at the 99% confidence interval or certainty level. The negative coefficient and high t-statistic for the third independent variable, price, allow us to conclude at a 95% confidence level that demand is price elastic (As the average price of electricity increases, energy sales decrease.) Likewise, we conclude at the 95% confidence interval that electricity demand is income-elastic (as income increases, so does electricity consumption). Figure 3.2 displays how the regression equation accurately explains variation in the dependent variable, actual historical electricity sales. Table 3.5 provides the underlying actual and predicted sales for each year. 10 IRP

12 Table 1.4 Coefficients in Single Equation Regression Variable Coefficients (betas) t Stat Intercept Ao Resident Population Visitor Population Average Price 2003 \$/MW Total Income 2003 \$M The model suggests that each percentage increase in resident population has historically been associated with a % increase in energy sales, while a one percent increase in visitor population is associated with a 0.086% increase in energy sales. On the other hand, a one percent increase in electricity price is associated with a 0.07% decrease in sales. Finally, a one percent increase in total income is associated with a % increase in electricity demand. Figure 1.2 Predicted vs. Actual Sales over the historical period MWh 450, , , , , , , ,000 50, Forecasted by Regression vs Actual Sales (MWh) Pred Sales (MWh) Actual Sales (MWh) IRP

13 Table 1.5 Actual Historical Sales vs. Sales Predicted by Regression Actual Sales Pred Sales (MWh) (MWh) , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Results of ARMA Model To further improve explanatory power, the ARMA 9 model was applied, under the following six (6) combinations of AR (autoregressive) and MA (moving average) processes: ARMA(1,1), ARMA(1,2), ARMA(2,1), ARMA(2,2), ARMA(2,3), ARMA(3,3). For each year 1970 through 2002, Table 3.6 compares actual historical sales with sales predicted by each the six regression/arma models. To aid evaluation of the 9 Statistical software called Intercooled Stata was used for analysis 12 IRP

14 different models, for each model error measure was calculated as (predicted value actual value) 2, summed over all 33 years ( ), then divided by the 33-year sum of the actual values. A plot of this error measure for all six regression/arma models and for the single regression equation model (Figure 3.3) shows he predictive advantage of the ARMA(2,2) model. The ARMA(2,2) model incorporates the impact on the dependent variable, energy sales, of not only the four explanatory variables on the energy sales, but also captures the time series (autocorrelation) of the energy sales in successive years, giving added explanatory power. The error measures in all but one of the tested ARMA models are lower than in the single equation model. 13 IRP

15 Table 1.6 Sales Over the Historical Period: Actual vs. Predicted Under Different Regression/ARMA Models Predicted Sales (MWh) Actual Sales (MWh) ARMA (1,1) ARMA (1,2) ARMA (2,1) ARMA (2,2) ARMA (3,2) ARMA (3,3) , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , IRP

16 Figure 1.3 Error Measures for Different Models Error Minimizing Model Level of Inaccuracy ARMA (1,1) ARMA (1,2) ARMA (2,1) ARMA (2,2) ARMA (3,2) ARMA (3,3) Single Equation Model The regression coefficient for the four explanatory variables in the ARMA(2,2) model are similar to those in the single equation regression modeling; and take the following form. Ln (Sales) = * Ln (Resident Population) * Ln (Visitor Population) 0.031* Ln (Average Price) * Ln (Total Income) However, additional predictive power is provided by the serial correlation and moving average terms in the ARMA model. Furthermore, when the ARMA(2,2) model is used, the average electricity price as an explanatory variable is not significant, even at a 90% confidence interval. Resident Population is the most significant explanatory variable, followed by Visitor Population and Total Income. Table 3.7 shows the ARMA model coefficients. Table 1.7 ARMA Model Coefficients Variable Coefficients (betas) t Stat Intercept Ao Resident Population Visitor Population Average Price 2003 \$/MW Total Income 2003 \$M IRP

17 1.5 Electricity Sales Forecast for s The final step is to develop a forecast of electricity demand for the years using the ARMA regression model with a second order autoregressive process and first order moving average process. This required development of a forecast for each of the independent (explanatory) variables for Forecast values for resident population, visitor population and total income are based on population and economic projections 10 for the State of Hawaii for years 2005, 2010, 2015, 2020 and 2025, with linear interpolation for the intervening years. Average electricity price is forecast based on an escalation rate of 2.5%. 11 Forecast values for all four explanatory variables are shown in the Table 3.8. Using the regression/arma(2,2) model, this produces the projected electricity sales trend shown in Figure The values for these projections for five distinct years were obtained from the report entitled, Population and Economic Projections for the State of Hawaii to The escalation rate was assumed to be equal to the Consumer Price Index of 2.5% for the first half of 2003, as reported by the Bureau of Labor Statistics, US Department of Labor. 16 IRP

18 Table 1.8 Projected Values of Explanatory Variables, Forecast of the Annual Peak and Energy Sales, and Electricity Growth Rate for Resident Population Visitor Population Average Price (2004 \$/MWh) Total Income (2004 \$M) Annual Energy Sales (MWh) Annual Peak Sales (MW) Sales Growth Rate (%) ,946 17, , , ,131 20, , , ,315 20, , , ,500 21, , , ,560 22, , , ,620 23, , , ,680 23, , , ,740 24, , , ,800 24, , , ,040 25, , , ,280 25, , , ,520 26, , , ,760 26, , , ,000 27, , , ,340 28, , , ,680 28, , , ,020 29, , , ,360 29, , , ,700 30, , , ,040 31, , , ,380 31, , , ,720 32, , , ,060 33, , , ,400 33, , , IRP

19 Figure 1.4 Actual ( ) and Most-likely Case Forecast Electricity Sales ( ) 900, , ,000 Forecasted Sales (MWh) 600, , , ,000 Actual Forecast 200, , For the forecast period, annual peak loads are projected by assuming that the peak load/annual load ratio reported for 2002 continues to be experienced in the future, and applying this ratio to projected annual sales. (Sales were adjusted for losses to obtain load met by generation.) For each forecast year, each monthly peak loads was calculated to be the same fraction of the annual peak as it was in 2002 (Table 3.7). Table 1.9 Monthly Peaks as Fractions of Annual Peak Month Fraction (%) January February March April May June July August September October November December IRP

21 Average price seems to have the least significant impact on the loads and for this reason we decided not to model it separately from the base case in high/low scenarios. These projected energy sales forecasts are net of the transmission and distribution losses. They are scaled up to account for losses, producing the electricity load to be served by the KIUC system that is the focus of this supply-side IRP study. 20 IRP

22 Figure 1.5 Forecast Population (Low, Most-likely and High Growth Scenarios) Low Growth Scenario 140, ,000 Low Visitor Population Low Resident Population 100,000 80,000 60,000 40,000 20, Base Scenario 140, ,000 Base Visitor Population Base Resident Population 100,000 Population 80,000 60,000 40,000 20, High Growth Scenario 140, ,000 High Visitor Population High Resident Population 100,000 Population 80,000 60,000 40,000 20, IRP

23 Table 1.10 Forecast of Scenario Drivers Low Resident Population Base Resident Population High Resident Population Low Visitor Population Base Visitor Population High Visitor Population Average Price (2003 \$/MWh) Low Total Income (2003 \$M) Base Total Income (2003 \$M) High Total Income (2003 \$M) ,066 60,131 61,031 17,748 18,221 18, ,571 1,576 1, ,186 60,315 62,136 18,066 19,041 19, ,626 1,636 1, ,306 60,500 63,261 18,389 19,898 20, ,675 1,692 1, ,625 61,560 64,407 18,719 20,794 21, ,725 1,750 1, ,945 62,620 65,573 19,054 21,731 22, ,777 1,809 1, ,266 63,680 66,760 19,395 22,709 23, ,830 1,871 1, ,589 64,740 67,969 19,743 23,731 24, ,885 1,935 1, ,914 65,800 69,199 20,096 24,800 25, ,942 2,001 2, ,241 67,040 70,452 20,456 25,340 26, ,984 2,060 2, ,569 68,280 71,728 20,822 25,880 27, ,028 2,119 2, ,900 69,520 73,027 21,195 26,420 29, ,073 2,179 2, ,232 70,760 74,349 21,575 26,960 30, ,118 2,238 2, ,565 72,000 75,695 21,962 27,500 32, ,165 2,297 2, ,901 73,340 77,065 22,355 28,100 33, ,212 2,364 2, ,238 74,680 78,461 22,755 28,700 35, ,261 2,432 2, ,577 76,020 79,881 23,163 29,300 36, ,311 2,499 2, ,917 77,360 81,328 23,578 29,900 38, ,362 2,567 2, ,260 78,700 82,800 24,000 30,500 40, ,414 2,634 2, ,043 80,040 84,299 24,430 31,160 42, ,467 2,705 2, ,869 81,380 85,825 24,867 31,820 44, ,521 2,776 3, ,705 82,720 87,379 25,313 32,480 46, ,577 2,847 3, ,551 84,060 88,961 25,766 33,140 48, ,633 2,918 3, ,408 85,400 90,572 26,228 33,800 51, ,691 2,989 3,441 IRP 22

24 1.5.2 Comparison of Alternative Load Growth Scenarios The trends in annual energy sales under the Low, Most Likely and High load growth scenarios are shown in both tabular and plotted format in Figure 3.6. Scaled up to account for 6% losses, the corresponding load projections to be met by system generation are shown in Figure 3.7. Finally, the corresponding annual peak load projections (including losses) are shown in Figure 3.8. Under the Most Likely load growth scenario, peak load grows from 71.3 MW in 2003 to 132 MW in Under the Low and High load growth scenarios, the projected 2025 peak load reaches 94MW and 154 MW respectively. On a percentage basis, the range in projected energy growth across the three scenarios is similar to the range in projected peak load growth. Clearly, over the 20-year planning horizon, load growth uncertainty can have a large impact on the magnitude and composition of a desirable supply plan, as well as on the underlying financial and reliability risks. Figure 1.6 Forecast Annual Energy Sales (High, Most-likely and Low Growth Scenarios) Forecasted Energy Sales (GWh) Low Base High Energy Sales (GWh) Low 800 Base High IRP 23

25 Figure 1.7 Forecasted Total Generation (High, Most-likely and Low Growth Scenarios) Total Generation (GWh) Low Base High Total Generation (GWh) Low Base 900 High Figure 1.8 Forecasted Peak Generation (High, Most-likely and Low Growth Scenarios) Peak Generation (GWh) Low Base High Peak Generation (MW) Low 125 Base High IRP 24

26 IRP 25

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