An iterative linear programming approach to optimize costs in distributed energy systems by considering nonlinear battery inverter efficiencies

The design and evaluation of a numerical optimization based energy management system for domestic houses comprising photovoltaic energy production and battery electrical storage is considered. The combination of time–variant electricity prices and the option to store generated power for later use introduces the interesting optimization problem of how to optimally operate (charge/discharge) the battery in order to minimize operation costs for the user. In most of the cases, optimization problems consider constant values of the power inverter efficiencies and hence, the optimization problem can be solved by using linear programming methods. The use of constant values of power inverter efficiencies assumes, that changing and discharging energy-flows lie on some most probably operating region of the inverter. We investigate here the validity of this consideration, by modeling an optimization problem, which considers a nonlinear parametrization of the power inverter efficiency curves. This way to model the optimization problem makes the optimization problem itself nonlinear. The main contribution of this paper is the presentation of a method to solve the nonlinear optimization problem generated by the use of nonlinear parametrization of the power inverter efficiency. The proposed method defines and solves a sequence of iterative linear programming optimization problems to solve approximately the original nonlinear optimization problem. Numerical simulations in a realistic simulation setup using measurement data from a photovoltaic installation and load data from a single family house over the time of one entire year are used for evaluating the performance. As the results show, the proposed iterative algorithm is able to achieve lower costs for the user than standard rule-based (non optimization) and frequently used linear optimization approaches not considering the efficiency nonlinearities. It can be concluded that the nonlinear efficiency curves significantly contribute to the overall performance of an energy management system since they vary in a wide range, especially in the part-load range of the inverter.