Robust Stability Region of PI Controllers for an Interval Time Delayed Load Frequency Control

Transmission delays, load fluctuations, and intermittent output power of renewable energy sources will all have a substantial impact on frequency stability in microgrids (MGs). In response, various types of advanced control techniques were employed to improve the performance of the load frequency control (LFC) systems. Notwithstanding this, the fragility of the current techniques makes LFC systems vulnerable to parametric (interval) uncertainties associated with communication time delay. Inspired by recent breakthroughs in robust control, in this study, we device a novel graphical tuning method of the PI controller for tackling this issue. First, we determine the shape of the value set for the characteristic function of uncertain LFC system. Then, the exposed edges are constructed to the boundary of this set under interval uncertainties. To accomplish this step and thanks to the D-decomposition method, the robust stability region in the parameter space of the controllers are determined. Our devised methodology contributes a family of robust stabilizing controllers, instead of just one, where it enables a more flexible choice for the controller parameters. The efficacy of the proposed methodology is indicated on a given single-area MG.