Lexicographic multi-objective optimization for the unit commitment problem and economic dispatch in a microgrid

In this paper, we present a multi-objective approach for the optimal control of dispatchable loads and bi-directional energy storages in a microgrid, commonly referred as the unit commitment problem and economic dispatch problem. We consider two different and possibly conflicting objectives: the minimization of the end user energy bill price and the maximization of the system stability as a function of the overall system´s load. We propose a lexicographic ordering of the objectives so that the end user´s energy cost is considered as the primary objective and the system´s stability is the secondary objective. In order to evaluate the performances, we provide a comprehensive micro-simulation environment used to study different demand response (DR) price profiles. The proposed multi-objective approach mitigates the network instability effects introduced by static DR programs with high price volatility. We conclude that almost flat DR price profiles with higher rates during high-peak periods should be preferred instead of high volatile profiles. With flat DR price profiles, both the end user and the utility company can benefit from smart-control algorithms adopting a lexicographic multi-objective optimization scheme.