Optimal Power Usage by Stochastic Programming

Power usage optimization by two stage stochastic programming is studied for a single smart house equipped with a solar power generator and a rechargeable battery, and also for a power transfer network composed of smart houses. Optimization is defined as the minimization of the total power purchase over a certain period with decision variables which describe the power purchase, charge/discharge and mutual transfer. Linear programming model (LP) is extended to a stochastic programming model (SP) when power generation and consumption are given not as fixed values but as stochastic variables under a certain distribution. Two types of recourse variables are introduced to express the power purchase and the charge to and discharge from a battery. Numerical experiments are executed to compare the optimal plans obtained by LP, 1-variable SP and 2-variables SP using measurement data obtained by survey researches. The first experiment is for a community which shares the power generator and battery. The second experiment is for a small network of two smart houses which mutually transfer the generated power. Both experiments show the effectiveness of 2-variables SP with charge/discharge recourses. Obtained global optimality for a whole network is compared with a local optimality for each house under a certain power price. Price adjustment is discussed for the global optimality based on the local optimality.