Confidence Interval on Marginal Price and Capacity Adequacy of Power System with Price-Elastic Demand Using a Negative Binomial Random Variable of High Dispersion

Abstract

Based upon the Bernstein's inequality or the Gamma and Chi-square distributions as alternatives to the standard methods, we paraphrased a negative binomial distribution of high dispersion and transformed to a weibull distribution for probability evaluation. An increasing deployment of smart grid technologies and demand response programs has enabled demands to be more elastic in response to electricity prices, actively contributing to power system operation. However, demand-price elasticity could potentially impact accuracy of electricity price forecasting and generation capacity adequacy evaluation, which have not been thoroughly explored in literature. To this end, a confidence interval is developed to evaluate marginal electricity price and capacity adequacy of power systems with elastic demand, while considering uncertainties of both demand and supply sides (e.g., random outages of generating units with multi-bidding-segments as well as variability of renewable energy outputs). Specifically, based on the concept of marginal bidding segment, the probability of a bidding segment being marginal is computed via the probabilistic production simulation approach. Accordingly, the discrete probability distribution of marginal electricity price can be obtained, which is further used to calculate mean and variance of marginal electricity price with elastic demand. Moreover, considering the interaction between elastic demands and uncertain electricity prices, the loss-of-load probability and the expected unsaved energy are further estimated. Numerical studies are presented to validate effectiveness of the proposed method.