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Fractional order proportional-integral-derivative(FOPID) controllers have attracted increasing attentions recently due to their better control performance than the traditional integer-order proportional-integral-derivative (PID) controllers. However, there are only few studies concerning the fractional order control of microgrids based on evolutionary algorithms. From the perspective of multi-objective optimization, this paper presents an effective FOPID based frequency controller design method called MOEO-FOPID for an islanded microgrid by using a Multi-objective extremal optimization (MOEO) algorithm to minimize frequency deviation and controller output signal simultaneously in order to improve finally the efficient operation of distributed generations and energy storage devices. Its superiority to nondominated sorting genetic algorithm-II (NSGA-II) based FOPID/PID controllers and other recently reported single-objective evolutionary algorithms such as Kriging-based surrogate modeling and real-coded population extremal optimization-based FOPID controllers is demonstrated by the simulation studies on a typical islanded microgrid in terms of the control performance including frequency deviation, deficit grid power, controller output signal and robustness.

Optimal frequency control of an islanded microgrid has been a challenging issue in the research field of microgrids. Recently, fractional-order calculus theory and some related control methods have attempted to handle this issue. In this paper, a novel fractional-order model predictive control (FOMPC) method is proposed to achieve the optimal frequency control of an islanded microgrid by introducing a fractional-order integral cost function into model predictive control (MPC) algorithm. Firstly, a discrete state-space model is derived for the optimal frequency control problem of an islanded microgrid. Afterward, a fractional-order integral cost function is designed to guide the FOMPC algorithm to obtain optimal control law by borrowing the Grünwald-Letnikov (GL) definition of fractional order calculus. Six simulation studies have been carried out to illustrate the superiority of FOMPC to conventional MPC under dynamical load disturbances, perturbed system parameters and random dynamical power fluctuation of wind turbines.