Dynamic Modelling and Rule-Based Energy Management of a Grid-Connected PV–Hydrogen Microgrid with Transcritical CO₂ Heat Pump Waste Heat Recovery in a Semi-Arid Climate

Solar-hydrogen microgrids dissipate a large share of their input energy as low-grade heat that is rarely exploited. This paper proposes a sector-coupled, battery-free architecture in which the waste heat of a PEM electrolyzer and a PEM fuel cell is recovered by a small-scale (300–500 W) water-to-water transcritical CO₂ (R-744) heat pump charging a domestic hot water (DHW) tank. A multi-physics model combining a temperature-dependent PV model, a PEM electrolyzer voltage model (Nernst, ButlerVolmer, ohmic and concentration terms), hydrogen tank dynamics, a PEM fuel cell model and a transcritical CO₂ cycle with pressure-ratio-dependent isentropic efficiency was implemented in MATLAB/Simulink. A three-mode rule-based energy management strategy (EMS) coordinates electrical and thermal flows. The 3 kW system was simulated for a summer and a winter design day using PVGIS typical meteorological year data for Sidi Bouzid, Tunisia. On the summer day the PV array produced 20.41 kWh and the electrolyzer 265.53 g of H₂; grid import was 1.03 kWh (grid-based selfsufficiency 93%). On the winter day PV output fell to 7.13 kWh, H₂ production to 54.45 g and grid import rose to 7.70 kWh (self-sufficiency 56%). Applying the cycle energy balance, the recovered waste heat (3.85 and 2.45 kWh) yields 5.13 and 3.27 kWh of useful heat, covering about 88% and 31% of the summer and winter DHW demand, and avoiding about 75% of the electricity that resistive heating would require. An inter-seasonal storage scenario (42 kg H₂ at 350 bar, about 1.8 m³ with real-gas correction) lowers the winter grid import to an estimated 3.20 kWh/day. The results demonstrate the technical feasibility of heat-integrated PV-hydrogen systems in semi-arid regions and identify dynamic COP modelling and experimental validation as priorities for future work.