A Complete Control-Oriented Model for Hydrogen Hybrid Renewable Microgrids with High-Voltage DC Bus Stabilized by Batteries and Supercapacitors

The growing penetration of renewable energy sources requires resilient microgrids capable of providing stable and continuous operation. Hybrid energy storage systems (HESS), which integrate hydrogen-based storage systems (HBSS), battery storage systems (BSS), and supercapacitor banks (SCB), are essential to ensuring the flexibility and robustness of these microgrids. Accurate modelling of these microgrids is crucial for analysis, controller design, and performance optimization, but the complexity of HESS poses a significant challenge: simplified linear models fail to capture the inherent nonlinear dynamics, while nonlinear approaches often require excessive computational effort for real-time control applications. To address this challenge, this study presents a novel state space model with linear variable parameters (LPV), which effectively balances accuracy in capturing the nonlinear dynamics of the microgrid and computational efficiency. The research focuses on a high-voltage DC bus microgrid architecture, in which the BSS and SCB are connected directly in parallel to provide passive DC bus stabilization, a configuration that improves system resilience but has received limited attention in the existing literature. The proposed LPV framework employs recursive linearisation around variable operating points, generating a time-varying linear representation that accurately captures the nonlinear behaviour of the system. By relying exclusively on directly measurable state variables, the model eliminates the need for observers, facilitating its practical implementation. The developed model has been compared with a reference model validated in the literature, and the results have been excellent, with average errors, MAE, RAE and RMSE values remaining below 1.2% for all critical variables, including state-of-charge, DC bus voltage, and hydrogen level. At the same time, the model maintains remarkable computational efficiency, completing a 24-h simulation in just 1.49 s, more than twice as fast as its benchmark counterpart. This optimal combination of precision and efficiency makes the developed LPV model particularly suitable for advanced model-based control strategies, including real-time energy management systems (EMS) that use model predictive control (MPC). The developed model represents a significant advance in microgrid modelling, as it provides a general control-oriented approach that enables the design and operation of more resilient, efficient, and scalable renewable energy microgrids.