An Empirical Approach to Optimize Nonlinear Problems of Domestic Energy Management Systems

Numerical optimization methods are used to reduce the operative costs and emissions of domestic houses comprising photovoltaic energy production and battery electrical storage combined with time-variant electricity prices. The modelling of the system comprises the different involved devices, energy flows and their constraints, and an objective function, which parametrizes the object of the optimization. The solution of the optimization problem defines the most adequate charging and discharging strategy of the battery into the future (prediction horizon). Power inverter efficiencies are usually modelled by assuming that they have constant values, and hence, that charging and discharging energy-flows lie on the most probably operating region of the inverter. A more realistic modelling of the power inverter efficiencies should consider a nonlinear parametrization of the efficiency curves. This consideration converts the optimization problem into a nonlinear one. It this paper, we modify a method to solve nonlinear optimization problems means iterations of linear optimization problems. The first iteration uses as seed values the solution of an optimization problem, which considers constant efficiencies of the battery inverter provided by the manufacturer of the battery. With the values of the solution of the optimization problem and with help of measured (dis)charging power curves and the optimized (dis)charging, new values of the efficiencies of the inverter of the battery will be determined, and the optimization problem will be with these values again computed. If a certain number of iterations is achieved or the values of the efficiencies converge, then the process stops.