Optimal Time-Dependent Operation of Open Loop Solar Collector Systems

Abstract

Closed loop flat-plate solar collector systems are considered. The water storage tank operates in fully mixed regime. An indirect optimal control technique based on Pontryagin’s maximum principle is implemented. The optimal operation strategy involves two-steps 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. 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: \( V_{s} /A \approx 33.3\;\text{L/m}^{2} \). The optimal control strategy does not exhibit such an optimum: the thermal energy supply to the user (slightly) decreases by increasing the ratio \( V_{s} /A \). Storage units are usually included in solar energy conversion systems designed for direct thermal energy utilization. Closed loop should be preferred to open loop configurations in this case. This chapter refers to optimal operation strategies for energy gain maximization by using closed loop flat plate solar collector systems. Both stratified and fully mixed water storage tanks are considered. The fluid mass flow rate in the collectors is the control parameter. Section 17.1 presents a simplified approach by Kovarik and Lesse (Sol Energy 18:431–435, 1976), covering uniform and stratified water storage tanks. Section 17.2 describes a more involved approach by Badescu (Energy Convers Manag 49:169–184, 2008) which refers to fully mixed storage tanks.