Estimating Dynamic Conditional Spread Densities to Optimise Daily Storage Trading of Electricity

Abstract

This paper formulates dynamic density functions, based upon skewed-t and similar representations, to model and forecast electricity price spreads between different hours of the day. This supports an optimal day ahead storage and discharge schedule, and thereby facilitates a bidding strategy for a merchant arbitrage facility into the day-ahead auctions for wholesale electricity.The four latent moments of the density functions are dynamic and conditional upon exogenous drivers, thereby permitting the mean, variance, skewness and kurtosis of the densities to respond hourly to such factors as weather and demand forecasts. The best specification for each spread is selected based on the Pinball Loss function, following the closed form analytical solutions of the cumulative density functions. Those analytical properties also allow the calculation of risk associated with the spread arbitrages. From these spread densities, the optimal daily operation of a battery storage facility is determined.Whilst day ahead electricity price forecasting has been a topic of substantial and wide ranging research in terms of methods, the focus has mostly been upon price levels for the delivery periods (usually hourly) in the following day. More recently there has been an interest in density forecasts for the hourly prices, motivated by considerations of risk management, see (Weron, 2014;Nowotarski and Weron, 2017) for extensive reviews.In this paper we provide a new formulation with a focus upon price spreads, and specifically we forecast the density functions for the intraday spreads in the day-ahead prices. The optimal operation of storage facilities, e.g. batteries, or load shifting programmes, e.g. demand-side management, over daily cycles depends upon these spreads if they are operated as merchants, arbitraging buying and selling from the wholesale market. Furthermore if risk is a consideration, analysis of the mean-differences in price levels would be inadequate, and we therefore directly estimate the density functions of all hourly spreads in prices at the day-ahead stage. Our specification, estimation and forecasting of these arbitrage spreads is new and computationally-intensive. We then show how these spread densities can support the optimal daily operation of a risk-constrained merchant battery facility.In contrast to the body of work on gas and other storable commodities, e.g. (Boogert and De Jong, 2011;Secomandi, 2018), because of the daily periodicity in electricity prices and the predominance of the day-ahead auctions, which typically set all hourly prices for the following day simultaneously, the operational horizon for storage and load shifting is usually episodic on a daily basis. So the continuous time, dynamic optimisation formulations used for gas and other commodity storage operations are less appropriate for electricity, and furthermore the stochastic simplifications generally required in the analysis of these other models would not meet the requirements of adequate fit to the more complex power price dynamics. Thus...