The Use of Extreme Value Theory for Forecasting Long-Term Substation Maximum Electricity Demand

Abstract

Substation annual maximum electricity demand events are extreme, as customers respond to infrequent and extreme weather. Despite the extreme nature of annual maximum demand, the statistical theory of extreme values has only rarely, if ever, been applied. To support long-term planning, utilities typically complete energy consumption and maximum demand forecasts, which are often conducted separately through two different process, leading to inconsistent trends and messages. To address these shortcomings, a point process approach from extreme value theory is proposed to model substation maximum demand as a function of trends in three common factors already required by utilities including customer count, average demand, and installed photovoltaic capacity. The point process model can be parameterized as a nonstationary generalized extreme value distribution with location and scale parameters dependent on the trends of these factors. As the generalized extreme value distribution governs the behaviors of block maxima (annual maximum demand) with forecast trends of three common factors, substation maximum demand can be estimated as per quantiles required by planning standards. Therefore, the proposed approach is not only realistic and flexible to forecast maximum demand but also ensures consistent outcomes and messaging between the two outputs from energy consumption and maximum demand forecasts.