Forecasting residual demand curves of the day-ahead electricity market with a Hilbertian ARMAX model

Abstract

The offering or bidding strategy of an agent operating in a day-ahead electricity market may be optimized by modeling the competitive behavior of its competitors. This can be done using residual demand curves. For every auction, the residual demand is defined as the clearing price of the market expressed as a function of the amount of energy the agent is able to buy or sell. Forecasting residual demand curves is the first and essential step in the design of optimal bidding strategies. Residual demand curves can be considered as a functional time series defined as the realization of a stochastic process where each observation is a continuous function defined on a finite interval. In order to forecast these curves, a functional Hilbertian ARMAX model is presented in this paper using functional integral operators in the L2 space. The kernels of the operators are modeled as linear combinations of sigmoid functions, where the parameters of each sigmoid are estimated using a Quasi-Newton algorithm which minimizes the sum of squared functional errors. This functional model allows forecasting the time series of hourly residual demand curves taking into account time dependencies, seasonality as well as exogenous variables. An empirical study is presented for the hourly residual demand curves of the Spanish day?ahead electricity market.