Robust stabilization of power systems subject to a series of lightning strokes modeled by Markov jumps: Attracting ellipsoids approach

Power systems are subject to stochastic faults and process random noise. The faults (due to e.g. lightning strokes) can be temporary or permanent. When a lightning stroke hits a transmission line, the circuit breakers open to clear the fault and reclose. The resulting parameters changes are modelled as a discrete-time Markov jumps in this paper using the practical statistical failure rates. System parameters are also subject to random noise e.g. line reactance’s depend on the conductors spacing which in turn depends on stochastic wind speeds. This paper presents a novel power system excitation control robust against such stochastic uncertainties. The design is based on a derived sufficient condition in the framework of linear matrix inequalities (LMI), and the attracting ellipsoid approach. The effectiveness of the proposed control is tested on a multi-machine power system.