Home Battery Dispatch under a Tiered Peak Power Tariff

Abstract

We consider the problem of operating a battery in a home connected to the grid to minimize electricity cost, which combines an energy charge and a tiered peak power charge based on the average of the $N$ largest daily peak powers in each billing month. With perfect foresight of loads and prices, the minimum cost is the solution of a mixed-integer linear program (MILP), which provides a lower bound on the cost of any implementable policy. We propose a model predictive control (MPC) policy that uses simple forecasts of loads and prices and solves a small MILP at each time step. Numerical experiments on one year of data from a home in Trondheim, Norway, show that the MPC policy attains a cost within $1.7\%$ of the prescient bound, and saves close to three times as much as the best rule-based policy we consider.