Pareto-Efficient Capacity Planning for Residential Photovoltaic Generation and Energy Storage with Demand-Side Load Management

Abstract

Optimal sizing of residential photovoltaic (PV) generation and energy storage (ES) systems is a timely issue since government polices aggressively promote installing renewable energy sources in many countries, and small-sized PV and ES systems have been recently developed for easy use in residential areas. We in this paper investigate the problem of finding the optimal capacities of PV and ES systems in the context of home load management in smart grids. Unlike existing studies on optimal sizing of PV and ES that have been treated as a part of designing hybrid energy systems or polygeneration systems that are stand-alone or connected to the grid with a fixed energy price, our model explicitly considers the varying electricity price that is a result of individual load management of the customers in the market. The problem we have is formulated by a D-day capacity planning problem, the goal of which is to minimize the overall expense paid by each customer for the planning period. The overall expense is the sum of expenses to buy electricity and to install PV and ES during D days. Since each customer wants to minimize his/her own monetary expense, their objectives look conflicting, and we first regard the problem as a multi-objective optimization problem. Additionally, we secondly formulate the problem as a D-day noncooperative game between customers, which can be solved in a distributed manner and, thus, is better fit to the pricing practice in smart grids. In order to have a converging result of the best-response game, we use the so-called proximal point algorithm. With numerical investigation, we find Pareto-efficient trajectories of the problem, and the converged game-theoretic solution is shown to be mostly worse than the Pareto-efficient solutions.