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Optimal control of a solar collector loop using a distributed-lumped model

1981; Elsevier BV; Volume: 17; Issue: 3 Linguagem: Inglês

10.1016/0005-1098(81)90010-8

1873-2836

Abraham Orbach, Chris Rorres, R. Fischl,

Photovoltaic System Optimization Techniques

This paper considers the optimal control of a solar collector loop described by a bilinear distributed parameter model for the collector fluid temperature and a bilinear lumped parameter model for the storage fluid temperature. The objective is to control the collector fluid velocity so as to maximize the net energy collected over a fixed time period. Necessary conditions for optimality, given by a set of equations whose solution yields the optimal control, are derived. It is shown that the optimal control is an open-loop, bang-bang control which depends on two terms: a measurable quantity which depends on the state of the collector fluid, and a quantity which depends on a future knowledge of the weather data. It is also shown that for the case in which only two switches occur during the period of operation, the optimal control depends only on the temperature difference across the collector. Thus, one can construct a feedback on/off controller for the system provided that it is known a priori that only two switches will occur during the time interval under consideration.