A Renewable-Penetration-Adaptive PID Gain-Scheduling Strategy with a Robustness Index for Load Frequency Control of Low-Inertia Power Systems

Abstract

The increasing penetration of inverter-interfaced renewable energy sources (RESs) reduces the effective rotational inertia of power systems, degrading the transient performance of conventional fixed-gain Load Frequency Control (LFC). This paper proposes a renewable-penetration-adaptive PID gain-scheduling strategy for single-area LFC, in which the proportional and derivative gains are scheduled as explicit functions of a renewable penetration factor that also drives an analytic reduction of the effective system inertia time constant. Unlike fuzzy- or optimization-based gain-scheduled controllers reported in the literature, the proposed law is closed-form and computationally lightweight, making it suitable for embedded governor implementation. A second contribution is a composite Renewable Robustness Index (RRI) that aggregates the normalized degradation of the Integral of Squared Error (ISE) and settling time across a sweep of penetration levels into a single comparative score. The proposed scheme is evaluated in MATLAB against a conventional fixed-gain PID controller for penetration levels of 0, 20, 40 and 60 percent. The results are expected to show that the adaptive scheme maintains a smaller peak frequency deviation and a higher Renewable Robustness Index than the fixed-gain controller as the renewable share increases, indicating improved resilience of the proposed low-complexity controller to reduced-inertia operating conditions.