Controller for a solar heating system with an electrical backup

Abstract

This paper describes the mathematical modeling and optimization of a solar heating system that stores reserve energy from the electric power network. The paper focuses on the design of a controller which minimizes use of electric energy, uses that energy at times when its cost is low, and maximizes human comfort.

The mathematical model has identifiable state vari ables, control input variables, disturbance input variables, and system parameters. The state vari ables are temperatures in the solar collector, in the first storage tank, in the second storage tank, and in the room and walls. Electric power input to the heating coils, heat pump, and circulating pump form the control input vector. Ambient temperatures and solar radiation are treated as uncontrollable input variables.

The objectives of the optimization scheme are

(1) maximizing the use of solar energy, (2) minimi zing the cost of electricity, and (3) maximizing human comfort. These are combined into an overall system performance index. A suboptimal feedback con troller based on this index uses an extension of Pearson's method ⁶; it involves (1) linearizing the system about an equilibrium point which shifts with time, (2) employing on-line computer control of the linearized system, and (3) changing the control strategy frequently.

Results of computer simulations show that the formu lated controller acceptably achieved the design objectives.