Optimal Control of a Bilinear Solar Collector/Heat Exchanger System

The problem of maximizing storage fluid temperature at a specified terminal time by controlling both collector and tank loop flow rates is investigated for a flat-plate solar water heating system containing a coupling counterflow heat exchanger. The dynamic system is modeled by two ordinary differential equations incorporating both collector plate and tank fluid capacitance. The paper considers the usual case where the tank loss-to-capacitance ratio is less than that of the collector plate. It is shown that the optimal control algorithm does not depend explicitly on the insolation. Furthermore, the optimal flow rates are shown to be on-off. However, if the collector loop pumping capacity is sufficiently greater than that of the tank loop, then the collector loop "on" flowrate is not the maximum attainable flowrate.