Optimal Control of a Network of Power Microgrids Using the Pontryagin´s Minimum Principle

The optimal control of the power flows in a network of microgrids (MGs) is presented. The problem is solved using the mathematical formalization of the optimal control based on the Pontryagin´s minimum principle (PMP). The objective is to deliver an optimal control strategy for the minimization of the power flows among MGs, and to maintain the storage system operating around a given reference value. This study proposes an original formulation based on the PMP that may be viewed as a preliminary continuous time attempt to model and control the exchange of power in a network of MGs. Its main originality is the use and the exchange of information and forecast of energy production and consumption on the whole set of MGs, to improve the overall quality of the power management, and energy storage. A method based on the PMP is developed to solve the corresponding constrained optimal control problem in an almost exclusively analytical way and thus, to calculate the optimal control. To prove the viability of the proposed approach, an example has been solved for the case of four MGs collaborating in a network.