Sophisticated solar heating controllers: Are they cost effective

Abstract

This paper describes the results of a study to investigate the value of applying sophisticated controls to solar heating systems. A residential solar heating system utilizing a heat pump operating in the series-storage mode is considered and optimal control theory is used to derive a control strategy. The basic question addressed is how much of an improvement in efficiency can be gained, relative to a conventionally designed controller, if an unrestricted control strategy is applied in an optimal fashion. The efficiency comparison is made on the basis of the amount of auxiliary energy required to attain an acceptable level of room temperature regulation. The second-order model for the system is derived using basic energy balance techniques and 4 control inputs are employed overall. The optimal control inputs are determined using Pontryagin's Maximum Principle which requires solution of a two-point boundary value problem. This is solved numerically using an iterative technique.