Optimal Control of Energy Storage in a Microgrid by Minimizing Conditional Value-at-Risk

This paper presents two methods for online rolling horizon optimal control of an energy storage unit in a grid-connected microgrid, subject to uncertainty in demand and electricity pricing. The proposed methods are based on the concept of rolling horizon control, where battery charge/discharge activities are determined by repeatedly solving a linear optimization problem over a moving control window. The predicted values of the microgrid net electricity demand and electricity prices over the control horizon are assumed to be uncertain. The first formulation of the control is based on the scenario-based stochastic conditional value at risk (CVaR) optimization, where the cost function includes electricity usage cost, battery operation costs, and grid signal smoothing objectives. Multivariate Gaussian distribution is used to model the variations of electricity prices and net demand power around their predicted nominal values. The second formulation of the control reduces the computations by taking a worst-case CVaR stochastic optimization approach. In this case, the uncertainty in demand is still stochastic but the problem constraints are made robust with respect to price variations in a range. Simulation results under different scenarios are presented to demonstrate the effectiveness of the proposed methods.