On the Observability of Solar Energy Systems

This paper considers the problems of observability and the design of a sequential state estimator for estimating the fluid temperature in a flat plate solar collector in the presence of measurement error. The collector is modeled by a first order, bilinear partial differential equation which describes the fluid temperature profile as a function of distance and time. The observability question is put into the framework of investigating certain conditions under which an initial temperature profile can be uniquely determined from a set of measurements of the fluid temperature from fixed sensor positions. In addition, the estimator equations represent the analog of the well known extended Kalman filter equations for lumped parameter systems. Numerical examples are given to demonstrate the implementation of the state estimator, on-line, using experimental data taken from the active solar energy system at Colorado State Universities Solar House III.