Multiperiod Energy Market as Adjustable Robust Optimization: Intertemporal Pricing of Dispatchable Generators, Storage Batteries, and Uncertain Renewable Resources.

In this paper, we present modeling and analysis of day-ahead multiperiod energy markets in which each competitive player or aggregator aims at making the highest profit by managing a complex mixture of different energy resources, such as conventional generators, storage batteries, and uncertain renewable resources. First, we develop a multiperiod energy market model in terms of an adjustable robust convex program. This market modeling is novel in the sense that the prosumption cost function of each aggregator, which evaluates the cost or utility to realize an amount of multiperiod energy prosumption, is a multivariable function resulting from a parameterized max-min program, in which the variable of the prosumption cost function is involved as a continuous parameter and the variable of dispatchable resources is involved as an adjustable variable for energy balance. This formulation enables to reasonably evaluate a reward for intertemporal dispatchability enhancement and a penalty for renewable energy uncertainty. In addition, it enables to enforce a market regulation in which every aggregator is responsible for absorbing his renewable energy uncertainty by managing his own dispatchable energy resources. Second, in view of social economy as well as personal economy, we conduct a numerical analysis on the premise of several photovoltaic penetration levels. In this numerical analysis, we demonstrate that renewable generators do not always have priority of energy supply higher than conventional generators due to their uncertainty and limited dispatchability, meaning that the merit order of conventional and renewable generators can reverse. Furthermore, we analyze long-term evolution of competitive energy markets demonstrating that there can be found a social equilibrium of battery penetration levels, at which maximum personal profit with respect to battery system enhancement is attained.