In the present paper, the stability of inverter-based microgrids is considered. A decentralized state-feedback control approach for inverter-based microgrids with a linear matrix inequality (LMI) stability condition is proposed. Controller gains for inverters are designed by solving the LMI optimization problem. The resulting controller stabilizes the system, guaranteeing zero steady-state frequency deviations. | Journal of Computer Science and Cybernetics, , (2015), 55–69 DOI: ON THE STABILITY OF INVERTER-BASED MICROGRIDS VIA LMI OPTIMIZATION TRUONG DUC TRUNG AND MIGUEL PARADA CONTZEN Control systems group, Technical University Berlin {trung,parada-contzen}@ Abstract. The implementation of a number of individual small distributed energy resources forms the new generation of power systems - the microgrid. For an isolated operating condition of microgrids, the classical stabilizing approaches for control of large power systems are no longer applicable, as the characteristics of microgrids differ significantly from conventional power systems. Therefore, a new control approach must be investigated in order to robustly stabilize microgrids during disturbances, which are caused by load changes and the intermittent nature of alternative energy sources. In the present paper, the stability of inverter-based microgrids is considered. A decentralized state-feedback control approach for inverter-based microgrids with a linear matrix inequality (LMI) stability condition is proposed. Controller gains for inverters are designed by solving the LMI optimization problem. The resulting controller stabilizes the system, guaranteeing zero steady-state frequency deviations. The control approach is then validated via an academical example. Keywords. decentralized control, distributed energy resource, LMI, microgrids, quasi-block diagonal dominance, voltage-source inverters. 1. INTRODUCTION The widespread implementation of renewable energy sources, . wind, solar energy, biogas, etc., leads to an increasing amount of distributed energy resources (DERs), . windturbines, photovoltaics, fuel cells, etc., which are connected to the transmission network at the low-voltage (LV) level next to the consumption point. Most of DERs are natively direct current (DC) or unregulated alternative current (AC) resources, while conventional power .
