Optimal the tilt angles for photovoltaic modules in Taiwan

A particle-swarm optimization method with nonlinear time-varying evolution (PSO-NTVE) is employed in determining the tilt angle of photovoltaic (PV) modules in Taiwan. The objective is to maximize the output electrical energy of the modules. In this study, seven Taiwanese cities were selected for analysis. First, the position of the Sun at any time and location was predicted by the mathematical procedure of Julian dating; then, the solar irradiation was obtained at each site under a clear sky. By combining the temperature effect, the PSO-NTVE method is adopted to calculate the optimal tilt angles for fixed south-facing PV modules. In this method, the parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments have an effect that approximates the full factorial experiments. A comparison of the measurement results in electrical energy between the four PSO methods and the PV modules set a six tilt angles. The results indicated that the annual solar radiation has a maximum value of 2658.69 kW h/m2 in Hengchun, and the conversion efficiency of the modules ranges from 13.14% for Taitung to 13.39% for Hengchun. Also, it should be noticed that the annual efficiency for Hengchun is higher than that for Kaohsiung because the average monthly PV-module temperature of Kaohsiung is higher than of Hengchun at this time. The results show that the annual optimal angle for the Taipei area is 18.16°18.16°; for Taichung, 17.3°17.3°; for Tainan, 16.15°16.15°; for Kaosiung, 15.79°15.79°; for Hengchung, 15.17°15.17°; for Hualian, 17.16°17.16°; and for Taitung, 15.94°15.94°.