Maximising revenue via optimal control of a concentrating solar thermal power plant with limited storage capacity

Concentrating solar thermal power plants with thermal energy storage is a potential source of clean electrical power. This work has the same four optimal control modes established in a previous paper where Pontryagin's principle demonstrated that to maximise revenue from a plant with unlimited storage the optimal modes were to: (i) store all collected power, without generating; (ii) generate using collected power only; (iii) generate at maximum capacity using both collected and stored power; (iv) generate a maximum capacity, storing any surplus power. This paper presents an expanded analysis to cover a more realistic case where there is limited storage capacity, introducing 2 differences. First, it is sometimes necessary to discard power if the store is full. Second, the critical prices used to determine the optimal control can change whenever the store becomes full or empty. Again we use Pontragin's principle to derive necessary conditions for an optimal control and present an algorithm to find the sequence of critical prices required to construct it. The analysis gives more insight into the nature of the optimal control than mathematical programming or probabilistic search techniques, and the calculation is fast‐finding the optimal control for a yearlong operation in about 30 seconds.