Continuous-time robust frequency regulation in isolated microgrids with decentralized fixed structure μ-synthesis and comparative analysis with PID and FOPID controllers

www.nature.com/scientificreports OPEN Continuous‑time robust frequency regulation in isolated microgrids with decentralized fixed structure μ‑synthesis and comparative analysis with PID and FOPID controllers Abdallah Mohammed , Ahmed Kadry *, Maged Abo‑Adma , Adel El Samahy & Rasha Elazab Isolated microgrids, which are crucial for supplying electricity to remote areas using local energy sources, have garnered increased attention due to the escalating integration of renewable energy sources in modern microgrids. This integration poses technical challenges, notably in mitigating frequency deviations caused by non-dispatchable renewables, which threaten overall system stability. Therefore, this paper introduces decentralized fixed structure robust μ-synthesis controllers for continuous-time applications, surpassing the limitations of conventional centralized controllers. Motivated by the increasing importance of microgrids, this work contributes to the vital area of frequency regulation. The research challenge involves developing a controller that not only addresses the identified technical issues but also surpasses the limitations of conventional centralized controllers. In contrast to their centralized counterparts, the proposed decentralized controllers prove more reliable, demonstrating enhanced disturbance rejection capabilities amidst substantial uncertainties, represented through normalized co-prime factorization. The proposed controllers are designed using the D-K iteration technique, incorporating performance weight filters on control actions to maintain low control sensitivity and ensure specific frequency band operation for each sub-system. Importantly, the design considers unstructured uncertainty up to 40%, addressing realworld uncertainties comprehensively. Rigorous robust stability and performance tests underscore the controller’s superiority, demonstrating its robustness against elevated uncertainty levels. Robust stability is verified for all controllers, with the proposed controller showing robust stability against up to 171% of the modeled uncertainty. Notably, the controller boasts a fixed structure with lower order compared to other H-infinity controllers, enhancing its practical implementation. Comparative analyses against Coronavirus Herd Immunity Optimizer tuned Proportional-Integral-Derivative (CHIO-PID) controller and CHIO tuned Fractional-Order Proportional-Integral-Derivative (CHIO-FOPID) controller further validate the superior performance of the proposed solution, offering a significant step towards ensuring the stability and reliability of microgrid systems in the face of evolving energy landscapes. Keywords Microgrid, Frequency regulation, Decentralized controller, Fixed structure μ-synthesis, Robust frequency control Recently, isolated microgrids have become a focal point for researchers due to their potential to fulfill the energy needs of remote areas. Despite the attractiveness of renewable energy sources in modern microgrids, the escalating integration of renewables introduces technical challenges, including low inertia and output power fluctuations resulting from the stochastic behavior of these sources. Such challenges lead to high frequency deviations and voltage instabilities1. These issues can be mitigated by incorporating traditional energy sources such as diesel Faculty of Engineering, Helwan University, Cairo, Egypt. *email: Scientific Reports | (2024) 14:20800 | https://doi.org/10.1038/s41598-024-70405-7 1 Vol.:(0123456789) www.nature.com/scientificreports/ generators, batteries, flywheels, superconducting magnetic energy storage systems, and ultra-capacitors2–4. However, each energy storage system has its drawbacks, with energy storage systems suffering from high frequency response and maintenance problems, flywheels and superconducting magnetic energy storage systems facing energy density issues, and ultra-capacitors standing out with fast power response5. Microgrids often employ both centralized and decentralized control systems6. While centralized control is straightforward, it faces reliability issues, as any interruption in the central controller affects the system’s stability, and expanding or scaling this form of control is challenging. In contrast, decentralized control, with separate and adaptable local controllers, offers a more dependable, flexible, and extendable s olution7. Droop control has emerged as a decentralized technique with a key advantage—it does not rely on communication but instead focuses on regional measurements. However, droop control approaches tend to overlook the dynamics of generators, impacting the control response and performance. To guarantee dynamic stability in the presence of a high level of disturbance, consideration and analysis of generator dynamics become i mperative8. Existing literature explores various control strategies such as model predictive control (MPC)9 and modified model predictive control (MMPC)10. However, these approaches often face limitations due to challenges in practical implementation. While MPC and MMPC can offer improved performance in theory, their practical application is hindered by computational complexity and the need for precise modeling, which can be difficult to achieve in real-world s cenarios11. Additionally, Proportional-Integral-Derivative (PID) controllers12,13 and Fractional Order PID (FOPID) controllers14,15 are widely used in practice due to their simplicity and effectiveness in many applications. However, these controllers also have limitations. PID controllers can struggle with system uncertainties and nonlinearities16, leading to suboptimal performance under certain conditions. FOPID controllers, while offering better tuning flexibility and robustness than traditional PID controllers, still face challenges related to parameter tuning and implementation c omplexity17. Thus, while these control strategies are extensively employed in practice, their limitations, including system uncertainties, lack of a systematic framework, and practical implementation challenges, must be acknowledged and addressed to enhance their effectiveness in ensuring dynamic stability and optimal performance. In18,19, the H∞ control method was illustrated as a centralized controller. However, system uncertainties were not addressed. The decentralized H∞ loop shaping controllers for frequency regulation in the microgrid are presented in16. However, each controller was shaped for each generation unit separately; therefore, interconnections between distributed generation units were not taken into consideration. Furthermore, they did not have a framework for loop shaping that was systematic. Additionally, it is difficult to implement the designed controller because the order of the designed H∞ controller is equal to the order of the plant. The designed controller should have a fixed-structure controller, satisfy robust stability and performance requirements, and have (...truncated)