Mixed integer non-linear programming via the cross-entropy approach for power system stabilisers location and tuning

Mixed integer non-linear programming (MINLP) via the cross-entropy approach for the optimal location and tuning of power system stabiliser (PSS) is presented. The considered problem is to maximise the damping ratio of the global system under a minimum number of PSS and simultaneously to find out the best candidate machines to be equipped with PSSs. The damping ratio objective is achieved by tuning the controllers to shift the lightly damped and undamped electromechanical modes of all plants to a prescribed zone in the s-plane. This problem of tuning and location of PSS over a wide range of system configurations is formulated as a MINLP problem where the objective is the aggregation of the two objectives on the damping ratio and on the PSS's number. The mixed optimisation problem, with a great combinatory aspect, is solved by an extension of the cross-entropy approach from the rare event framework. The performance of this technique for damping the oscillations in multimachine power systems is confirmed through eigenvalues analysis over many scenarios. For comparative purpose the Monte Carlo simulation and the classical approach have been used to show the effectiveness of the proposed approach.