Operational scheduling of microgrids via parametric programming

We present a parametric programming based approach for energy management in microgrids. An operational planning problem for a grid-connected microgrid with energy sources including solar photovoltaic, wind turbine and battery energy storage system, in addition to a household load demand, is captured as a parametric mixed-integer linear programming problem (p-MILP) through parameterizations of the uncertain coordinates of wind and solar energy resources. Thus, the energy management problem - typically nonlinear - is transformed into a linear bi-level optimization problem, where choice of the parameterization scheme is made at the upper level while system operation decisions are made at the lower level. The p-MILP formulation leads to significant improvements in uncertainty handling, solution quality and computational ease; by removing dependency of the solution on meteorological forecasts and avoiding the multiple computational cycles of the traditional online optimization techniques. The problem is solved offline on a flexible time-scale basis, allowing online implementation to be achievable on real-time system state updates. The proposed parametric programming approach extends the state-of-the-art in microgrid energy management methods and the results from various case studies are used to demonstrate the feasibility of our method.