LMI Approach to Decentralized H∞ Control of Facts Devices in a Large Power System: Polytopic Representation of Operating Conditions

Abstract

A polytopic representation of uncertainties in the operating conditions is introduced for a sequential design of decentralized Flexible AC Transmission Systems (FACTS) controllers for a multi-machine power system. An H∞-output feedback design procedure using Linear Matrix Inequality (LMI) is applied. Two different types of uncertainties are considered in the design. One uncertainty is due to the interaction from the undesigned loop when evaluating performance, which is bounded in the design of controller using mixed-sensitivity. Another source of uncertainty is considered in the design due to changing in operating point, which is treated by Polytopic Linear Differential Inclusion (PLDI) where various operating conditions are used in the model. The performance of the controllers is verified through non-linear simulations under large disturbances.