Optimal probabilistic design of multi-band power system stabilizers using the two-point estimate method

This paper introduces an optimization approach for the probabilistic design of multi-band power system stabilizers, considering demand uncertainties. The primary objective is to minimize the sum of central gains for each multi-band structure. The approach incorporates inequality constraints to manage parameter bounds and to ensure the probabilities of achieving security (based on the minimum damping ratio) and stability (based on the spectral abscissa). To address this complex problem, particle swarm optimization is proposed in conjunction with the two-point estimate method (2PEM) for probabilistic small-signal analysis. The 2PEM facilitates the use of a limited set of samples, enhancing efficiency. The efficacy of this approach is demonstrated through results obtained for a Brazilian test system and the New England test system, validated using Monte Carlo simulation. These results confirm both the accuracy and computational efficiency of the proposed method. Additionally, time-domain nonlinear simulations affirm the system’s stability under large perturbations.