Sequential circle criterion approach for robustly stabilizing individual generators with SVC

Absolute stability with the spatially defined linear time‐invariant (LTI) state‐space modelings is scrutinized by means of what we call the sequential Lyapunov approach, which possesses independent significance in stabilization when gain‐scheduling control laws are adopted. Then, this theoretical result is exploiting for stabilization of individual generators via SVC actions. More precisely, by remodeling the perturbed swing equations of synchronous generators in multimachine networks through spatially defined LTI state‐space expressions subjected to uncertainties and power disturbance, which are viewed as sector nonlinearities, we introduce frequency responses for coping with nonlinear power swing dynamics of individual generators. By sequentially relating the frequency responses to the circle criterion (substantially, the KYP theorem or the positive real lemma) claimed for LTI systems subject to sector disturbances, output feedback control laws for static VAR compensators are worked out to stabilize individual generators. The frequency‐domain approach is also useful in steady‐state specification besides stabilization in individual generators. Examples show efficacy of the suggested stabilization and steady‐state specification technique. Copyright © 2014 John Wiley & Sons, Ltd.

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