Home Energy Management with Dynamic Tariffs and Tiered Peak Power Charges

Manuscript, June, 2023.

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We consider a simple home energy system consisting of a (net) load, an energy storage device, and a grid connection. We focus on minimizing the cost for grid power that includes a time-varying usage price and a tiered peak charge that depends on the average of the largest N daily powers over a month. When the loads and prices are known, the optimal operation of the storage device can be found by solving a mixed-integer linear program (MILP). This prescient charging policy is not implementable in practice, but it does give a bound on the best performance possible. We propose a simple model predictive control (MPC) method that relies on simple forecasts of future prices and loads. The MPC problem is also an MILP, but it can be solved directly as a linear program (LP) using simple enumeration of the tiers for the current and next months, and so is fast and reliable. Numerical experiments on real data from a home in Trondheim, Norway, show that the MPC policy achieves a cost that is only 1.7% higher than the prescient performance bound.