Optimization of Frequency Regulation Using a PID Controller Tuned via the Grey Wolf Optimizer Applied to the Isolated Limbani Microgrid (#1636)

Authors

Ramos Yapo, Aquiles Taylor

Mayta Lampa, Steven Alex

Quispe Esperilla, Yamil

Quispe Cruz, Eduardo Anddré

Ramos Cutipa, Jose Manuel

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.