Stability analysis and stabilization of delayed reduced-order model of large electric power system

This paper discusses stability analysis using spectral discretization of time-delayed electric power system. The stability assessment is discussed in terms of influence of time delays on inter-area oscillation modes of the power system models: well-known 4-generator and 14-generator Southeast Australian power system. The three dominant inter-area modes available in full-order power system are retained in its equivalent representation, i.e., reduced-order model, obtained with the input-output variables of the generator that participates actively to low-frequency oscillation modes. The pseudospectrum analysis suggests the most dominant modes to be sensitive against time delay. The rightmost characteristic roots and the robust spectral abscissa are computed over a wide range of time delays in the input-output variables. The approach applied in study computes all the characteristic roots in the right half s-plane with the number of discretization points selected in such a way that rational approximation of the exponential functions remains accurate in this region. The effect of time delays on the computation of spectral abscissa is also investigated. Further, reduced-order time-delayed model is also used to design the wide-area controller by optimizing (minimizing) the robust spectral abscissa.