Optimization of Frequency Regulation Using a PID Controller Tuned via the Grey Wolf Optimizer Applied to the Isolated Limbani Microgrid

Abstract

The isolated hydropower plant of Limbani, located in Puno, operates in a non-interconnected system with low inertia and high sensitivity to load disturbances and variability in renewable generation. This work evaluates, through simulation, the hydro–photovoltaic hybridization of the system and proposes a frequency regulation strategy based on a PID controller tuned offline using the Grey Wolf Optimizer (GWO), comparing its performance with the classical Ziegler–Nichols tuning. The dynamic model incorporates the turbine–penstock interaction, including water-hammer effects, and uses an aggregated inertia representative of high renewable penetration; photovoltaic power is modeled as injected power with a first-order dynamic delay. The tuning is formulated as an optimization problem that minimizes the ITAE index and introduces penalties for frequency band violations, implemented under a simulation framework with the controller embedded in the model loop. Validation considers a 20% load increase, loss of photovoltaic generation, and continuous 24-hour operation with a demand peak between 18:00 and 21:00. Compared with Ziegler–Nichols, the GWO-tuned PID reduces ITAE by 47.5%, control effort by 34.3%, and settling time by 62%, improves the frequency nadir from 58.80 to 59.35 Hz, and reduces maximum overshoot, maintaining 60 ± 0.05 Hz during daily operation.