Robust Stability Region for Load Frequency Control with Inverter Air Conditioner using Kharitonov’s Theorem

The widespread use of inverter based air conditioners (IACs) as a controllable load makes them a promising tool in the frequency regulation of power systems. However, utilization an open communication network in the aggregation and control of several IACs introduces time delays which adversely affect the frequency stability. Moreover, uncertainties in system parameters makes the stability issue as challenging problem together with time delays. Time delays and uncertainties degrade the controller performance cause undesirable fluctuation in system frequency and may even lead to instability. Therefore, a robust controller design is essential to maintain stability under disturbances considering both delays and parametric uncertainties. This work proposes a novel utilization of Kharitonov’s Theorem with stability boundary locus approach—to determine robust all stabilizing controller gains constituting a stable region. The influences of parametric uncertainties, the number of IACs and time delays on stability regions are comprehensively analyzed. Results clearly show that increase in time delay and uncertainty reduces the size of the robust stability, indicating diminished stability robustness. Finally, the accuracy of theoretical results is verified by using MATLAB Simulink and quasi-polynomial mapping-based root finder algorithm.