Bayat-driven FOPID controller design for biogas-based microgrid with real-time validation

The energy policies of the [Formula: see text] century are increasingly focused on promoting generation solutions with minimal environmental impact. In response to strategic initiatives, the accelerating depletion of fossil fuel reserves has led to integrating renewable sources for power generation. The uncertain nature of solar and wind energy sources, along with fluctuating load demands, leads to frequency instability. This study addresses the challenge of frequency instability by designing a Bayat-tuned fractional-order proportional-integral-derivative (FOPID) controller for a decentralized microgrid [Formula: see text]. The proposed [Formula: see text] model consists of environmentally friendly energy sources such as a biogas turbine generator (BTG), a biodiesel engine generator (BEG), other distributed generation units (DGUs), and energy storage devices (ESDs). The mathematical modeling of [Formula: see text] components is carried out using first-order transfer functions, which are combined to derive the overall transfer function of [Formula: see text] model. This composite model is then approximated as a first-order plus time delay (FOPTD) system to simplify FOPID controller design. The parameters of the FOPID controller are optimized using the Bayat method to achieve robust performance under set-point tracking (SPT) and load disturbance rejection (LDR) scenarios. Based on this approach, three controller variants i.e., FOPID-[Formula: see text], FOPID-[Formula: see text], and FOPID-[Formula: see text], are developed. To validate the effectiveness of the proposed control strategy, various simulation scenarios are considered, including load disturbances and varying levels of solar and wind power penetration. The performance of the controllers is evaluated in terms of frequency deviation, error mitigation, and transient behavior under SPT and LDR conditions. A comparative analysis using error indices, time-domain metrics, control effort, and frequency plots confirms the effectiveness of the Bayat-tuned FOPID designs. Furthermore, real-time validation using the OPAL-RT simulator underscores their practical potential in maintaining frequency stability within [Formula: see text] systems. Owing to the performance analysis, it is justified that discussed FOPID-Bayat controllers consistently ensured controllability with a minimum rise time of [Formula: see text], a nearly constant settling time of [Formula: see text], and reduced control effort down to 0.12. Furthermore, error index evaluation confirmed that FOPID-Bayat[Formula: see text] outperformed other configurations by achieving the lowest IAE (8.737), ITAE (223.0), ITSE (40.39), and ISE (1.706), thereby demonstrating superior efficiency and robustness.