Optimal control of flow in solar collector systems with fully mixed water storage tanks

Abstract

The paper deals with optimal flow control in closed loop flat plate solar collector systems. The water storage tank operates in the fully mixed regime. Two design configurations were considered: (A) one serpentine in the tank (for the secondary circuit) and (B) two serpentines in the tank (for both primary and secondary circuits). An indirect optimal control technique based on Pontryagin’s maximum principle was implemented. A detailed collector model and realistic meteorological data from both cold and warm seasons were used in applications. Configuration (A) gives better performance than configuration (B) but cannot be used during the cold season at higher geographical latitudes. The optimal operation strategy involves two step up and down jumps between zero and a maximum allowable fluid flow rate in the primary circuit. During days with overcast sky, the pump in the primary circuit operates almost continuously. During days with cloudy or clear sky, the pump often stops. Heat provided to the user increases when the maximum fluid flow rate increases. This applies to both configurations (A) and (B). In the case of configuration (B), the heat provided to the user becomes rather constant at higher flow rates. When a constant flow rate strategy is adopted, there is an optimum ratio between the volume of the storage tank and the area of the solar energy collection surface: V s/ A ≈ 33.3 L/m 2. The optimal control strategy does not exhibit such an optimum: the thermal energy supply to the user (slightly) decreases by increasing the ratio V s/ A.