Optimal Frequency Control in Isolated Microgrids Integrating Renewable Energy and PHEVs Using a Modified Ziegler–Nichols-Based Multistage PID Controller

Abstract

Maintaining frequency stability in islanded microgrids (MGs) has become increasingly challenging due to the growing penetration of renewable energy sources, particularly photovoltaic systems, wind turbine generators (WTGs), and plug-in hybrid electric vehicles (PHEVs). The intermittent nature of renewable generation and continuous load variations introduces significant power imbalances, resulting in frequency deviations and degraded system stability. Although the classical Ziegler–Nichols (ZN) tuning method is attractive because of its simplicity and ease of implementation, it is generally limited to conventional proportional–integral–derivative (PID) controllers and is often inadequate for renewable-dominated MGs. To overcome these limitations, this paper proposes a modified ZN-based tuning strategy for a novel multistage PID (MPID) controller. Unlike the conventional ZN method, the proposed approach extends its applicability to the MPID structure by introducing an additional proportional gain (KPP), enabling the tuning of five controller parameters while preserving low computational complexity and practical implementation. The proposed controller is implemented and validated using a detailed MATLAB/Simulink model of an isolated MG comprising PV systems, WTG, diesel generators, and PHEVs. Its performance is comprehensively evaluated under multi-step load disturbances, renewable power fluctuations, combined disturbances, and different PHEV charging/discharging modes and battery state-of-charge levels. Furthermore, the proposed controller is benchmarked against conventional ZN-PID, ZN-FOPID, and both PID- and MPID-based controllers tuned using Particle Swarm Optimization, Cuckoo Search Algorithm, Moth–Flame Optimization, and Grasshopper Optimization Algorithm. Simulation results demonstrate that the proposed ZN-MPID controller achieves the best overall dynamic performance, with a settling time of 4.109 s, zero overshoot, a maximum frequency undershoot of 1.801 × 10−4 Hz, and the lowest error indices (ISE = 3.073 × 10−6, ITSE = 0.697 × 10−6, and ITAE = 3.40 × 10−4). Compared with the investigated metaheuristic-based PID controllers, the proposed controller reduces the settling time by up to 86.1% and the error indices by up to 95.5%. It also consistently outperforms all investigated MPID tuning methods, confirming the effectiveness of the proposed modified ZN tuning strategy. Overall, the proposed methodology provides an efficient, low-complexity, and practical solution for frequency regulation in renewable-dominated isolated MGs.