Mathematical Modelling of a Static Concentrating Photovoltaic: Simulation and Experimental Validation

For the past twenty years, there has been increasing interest and investment in solar photovoltaic (PV) technology. One particular area of interest is the development of concentrating PV (CPV), especially for use in building integration. Many CPV designs have been developed and investigated. This paper aims at producing a mathematical modelling using MATLAB programme to predict the current-voltage (I-V) and power-voltage (P-V) characteristics of a static CPV. The MATLAB programme could also simulate the angular response of the CPV designs-which has never been explored in the previous literature. In this paper, a CPV known as the rotationally asymmetrical dielectric totally internally reflecting concentrator (RADTIRC) was analysed. A specific RADTIRC design that has an acceptance angle of ±40° was investigated in this paper. A mathematical modelling was used to simulate the angular characteristics of the RADTIRC from −50° to 50° with an increment 5°. For any CPV, we propose that the value of opto-electronic gain, Copto-e needs to be included in the mathematical model, which were obtained from experiments. The range of incident angle (±50°) was selected to demonstrate that the RADTIRC is capable of capturing the sun rays within its acceptance angle of ±40°. In each simulation, the I-V and P-V characteristics were produced, and the short circuit current (Isc), the open-circuit voltage (Voc), the maximum power (Pmax), the fill factor (FF) and the opto-electronic gain (Copto-e) were determined and recorded. The results from the simulations were validated via experiments. It was found that the simulation model is able to predict the I-V and P-V characteristics of the RADTIRC as well as its angular response, with the highest error recorded for the Isc, Voc, Pmax, FF and Copto-e was 2.1229%, 5.3913%, 9.9681%, 4.4231% and 0.0000% respectively when compared with the experiment.

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