Optimum Integration of Solar Energy With Battery Energy Storage Systems

This article discusses optimum designs of photovoltaic (PV) systems with battery energy storage system (BESS) by using real-world data. Specifically, we identify the optimum size of PV panels, the optimum capacity of BESS, and the optimum scheduling of BESS charging/discharging, such that the long-term overall cost, including both utility bills and the PV system, is minimized. The optimization is performed by considering a plethora of parameters, such as energy usage, energy cost, weather, geographic location, inflation, and the cost, efficiency, and aging effects of solar panels and BESS. To capture the impacts of long-term factors such as aging effects, inflation, and discounted economic returns, the problem is formulated as a mixed integer nonlinear programming (MINLP) problem over the time horizon covering the entire life cycles of solar panels and BESS of the order of ten years or longer, whereas almost all existing works on PV system designs consider much shorter time horizons of the order of days or weeks. The MINLP is transformed into mixed integer linear programming (MILP) and solved by branch-and-bound (B&B) algorithm. The complexity of MILP is high due to the long time horizon. A new low-complexity algorithm is then proposed by using dynamic programming, where it is shown that the MINLP problem can be transformed into one that satisfies Bellman’s principal of optimality. Applying the newly developed algorithms on real-world data from a commercial user in San Francisco reveals that the system achieves the break-even point at the 66th month and achieves a 29.3% reduction in total system cost.