Continuous optimal control approaches to microgrid energy management

Abstract

We propose a novel method for the microgrid energy management problem by introducing a nonlinear, continuous-time, rolling horizon formulation. The method is linearization-free and gives a global optimal solution with closed loop controls. It allows for the modelling of switches. We formulate the energy management problem as a deterministic optimal control problem (OCP). We solve (OCP) with two classical approaches: the direct method and Bellman’s Dynamic Programming Principle (DPP). In both cases we use the optimal control toolbox Bocop for the numerical simulations. For the DPP approach we implement a semi-Lagrangian scheme adapted to handle the optimization of switching times for the on/off modes of the diesel generator. The DPP approach allows for accurate modelling and is computationally cheap. It finds the global optimum in less than one second, a CPU time similar to the time needed with a Mixed Integer Linear Programming approach used in previous works. We achieve this result by introducing a ‘trick’ based on the Pontryagin Maximum Principle. The trick reduces the computation time by several orders and improves the precision of the solution. For validation purposes, we performed simulations on datasets from an actual isolated microgrid located in northern Chile. The result shows that the DPP method is very well suited for this type of problem.