Optimization of day-ahead pricing electricity markets based on a simplified methodology for stochastic utility function estimation

Abstract

In the context of smart markets’ popularization, day-ahead pricing of electricity has been deployed more commonly as an attempt to improve the grid’s operation and maximize the socioeconomic welfare. However, estimating the utility function is necessary to maximize the socioeconomic welfare, which is not a trivial task. The utility function models the quality of life added by electricity consumption and depends on several factors, such as the consumer’s class (residential, commercial, industrial, etc.), income, climate conditions, and individual preferences. This paper presents a simplified methodology to estimate the utility function in the context of day-ahead pricing. The main benefit of the proposed method is that its application is straightforward since the modeling is mainly based on simple matrix equations. The demand elasticities (self- and cross-elasticities), which are general concepts in economics, are addressed as input parameters. Due to the inherent uncertainties related to human behavior, a stochastic utility function is proposed to enhance the model’s accuracy/robustness. The proposed model particularly thrives when the effects of cross-elasticities are significant but not massive (although procedures can be applied to mitigate the error if higher cross-elasticities are verified). By applying the proposed model to a hypothetical smart microgrid with 100 consumers and 24 daily periods (hourly prices), results demonstrate that it successfully provides the rates that maximize the socioeconomic welfare created by the market. In the case study, the conventional quadratic utility function implies an error of 73%, whereas the proposed model an error of 10%, highlighting the usefulness of the proposed model.