Optimal Design of Proportional–Integral Controllers for Grid-Connected Solid Oxide Fuel Cell Power Plant Employing Differential Evolution Algorithm

This paper proposes the application of differential evolution (DE) algorithm for the optimal tuning of proportional–integral controller designed to improve the small signal dynamic response of a grid-connected solid oxide fuel cell (SOFC) system. The small signal model of the study system is derived and considered for the controller design as the target here is to track small variations in SOFC load current. The proposed proportional–integral (PI) controllers are incorporated in the feedback loops of hydrogen and oxygen partial pressures, grid current d–q components and dc voltage with an aim to improve the small signal dynamic responses. The controller design problem is formulated as the minimization of an eigenvalue-based objective function where the target is to find out the optimal gains of the PI controllers in such a way that the discrepancy between the obtained and desired eigenvalues is minimized. Eigenvalue and time domain simulations are presented for both open-loop and closed-loop systems. To test the efficacy of DE over other optimization tools, the results obtained with DE are compared with those obtained by particle swarm optimization (PSO) algorithm and invasive weed optimization (IWO) algorithm. Three different types of load disturbances are considered for the time domain-based results to investigate the performances of different optimizers under different sorts of load variations. Moreover, nonparametric statistical analyses, namely one-sample Kolmogorov–Smirnov (KS) test and paired sample t test, are used to identify the statistical advantage of DE algorithm over the other two. The presented results suggest the supremacy of DE over PSO and IWO in finding the optimal solution.