Optimal design of stationary flat-plate solar collectors : deterministic and probabilistic approaches

Abstract

Paper presented to the 3rd Southern African Solar Energy Conference, South Africa, 11-13 May, 2015.

Because of the soaring energy prices, many countries have shown an increased interest in the utilization of solar energy. The optimization of the solar energy collector design plays a critical role in the efficient collection of solar energy. Flat-plate collectors can be designed in applications that require energy delivery at moderate temperatures (up to 100◦C above ambient temperature). These collectors use both beam and diffuse solar radiation, and do not need to track the sun. They are simple to manufacture and install with relatively low maintenance cost which make this kind of solar collectors more popular. The design of a flat-plate solar collector embraces many relationships among the collector parameters, field parameters and solar radiation data at any given location. The shading decreases the incident energy on collector plane of the field. The multi-objective optimum design of stationary flat-plate solar collectors is presented in this work. The clear day solar beam radiation and diffuse radiation at the location of the solar collector (Miami) are estimated. The maximization of the annual average incident solar energy, maximization of the lowest month incident solar energy and minimization of the cost are considered as objectives.. The game theory methodology is used for the solution of the three objective problems to find the best compromise solution. The sensitivity analysis with respect to the design variables and the solar constant are conducted to find the relative influence of the parameters on the design. The multi-objective optimum design of stationary flat-plate solar collectors under probabilistic uncertainty is also considered. The three objectives stated earlier are considered in the optimization problem. The solar constant, altitude, typical day of each month and most of the design variables have been treated as probabilistic variables following normal distribution. The game theory methodology is used for the solution of the three objective constrained optimization problems to find a balanced solution. A parametric study is conducted with respect to changes in the standard deviation of the mean values of design variables and probability of constraint satisfaction. This work represents a novel application of the multi-objective optimization strategy, including probabilistic approach, for the solution of the solar collector design problem. The present study is expected to help designers in creating optimized solar collectors based on any specified requirements.