Appropriate sampling procedures for load research

Abstract

The Public Utilities Regulatory Policies Act (PURPA) requires electric utility companies with annual sales exceeding 500 million kilowatt-hours of electricity to report specific types of load research data to the Federal Energy Regulatory Committee and the state Public Utility Commissions. One of the key requirements is the reporting of the estimated customer demand for electricity. PURPA also specifies that, in estimating the customer demand for electricity, the level of confidence must be at least 90% and the level of reliability must be 0.1 or less. In order to estimate the customer demand for electricity, electric utility companies must sample a group of its customer population. The Load Research Manual (1980), published by the United States Department of Energy, outlines a sampling procedure that could be used in load research. The procedure outlined by the manual assumes that the sampling distribution of the average annual demand for electricity is normally distributed. However, there is research evidence to indicate that the annual demand for electricity, scaled by the average annual demand, is best described by the Gamma, Weibull, or Log-Normal distribution (Liittschwager, 1971). Hence, for relatively small sample sizes, the assumption of normality of the sampling distribution of the sample mean will not be satisfied. Further, the procedure suggested by the Load Research Manual (1980) also fails to address the reliability requirement. The objective of this research is to provide an appropriate sampling procedure that can be used by electric utility companies to estimate the customer demand for electricity and to satisfy the requirements of PURPA. Specifically, using simulated distributions of electrical demand, the following key issues in estimating the customer demand for electricity were addressed: (1) The determination of the sample size necessary to satisfy the requirements of PURPA, (2) The determination of the effectiveness of stratified sampling procedures, (3) The determination of the effectiveness of using data transformations to normality and then using "normal theory" principles to determine sample size, and (4) The determination of the effectiveness of a statistical technique called bootstrapping to monitor changes in the customer population over time. The results indicate that the methodologies suggested by this study will indeed provide the electrical utility companies with a sampling procedure that is appropriate in estimating the customer demand for electricity according to PURPA requirements.