This paper presents a real-time model predictive control (MPC) framework for a grid-connected PV system integrated with a hybrid energy storage system (HESS) composed of a redox flow battery (RFB) and a supercapacitor (SC). The control architecture consists of two layers: a genetic algorithm (GA) performs a six-hour rolling-horizon optimization at hourly resolution to schedule the RFB for electricity-cost minimization, while a minute-level supervisory layer executes the schedule in real time and coordinates the SC to compensate fast power mismatches, ramp-rate violations and short-timescale deviations. The framework accounts for grid interconnection limits and storage constraints, and its modular design enables adaptation to other storage technologies, alternative control objectives and various systems.The method is evaluated using field data from the Technology Center for Energy at Landshut University (TZE) and compared with a stand-alone RFB and a rule-based benchmark under practical-forecast and perfect-foresight conditions. Results show that SC support reduces battery-limited tracking periods from about 60% to 18%, as the SC absorbs fast mismatches and improves RFB tracking real-time feasibility. In addition, the GA-based controller increases arbitrage profit by about 10% compared to the rule-based benchmark. Overall, coordinated RFB–SC operation enhances both economic performance and constraint-compliant real-time energy management.