Forecasting of power distribution produced in a photovoltaic power plant based on forecasted distribution of global solar radiation

This work deals with the forecasting of power distribution produced in a photovoltaic (PV) power plant. Since the power produced in such a power plant depends on the global solar radiation, a new method for forecasting of global solar radiation distribution during the day is proposed. The expression for calculating extraterrestrial solar radiation G in the time interval t is an element of [t0, t0+ Delta t] is given by (4), where the orbital eccentricity factor e(t) and declination angle d are given by (5) and (7), respectively. The solar constant Gsc is defined by (3), M (1) is the Sun surface power density while Ts (2) is the temperature on the Sun surface. The global solar radiation that reaches the Earth surface Ggl depends on the extraterrestrial radiation G, the path of sunbeams through the atmosphere and the weather conditions in the atmosphere. In this work the impact of the weather conditions in the atmosphere is neglected. The spherical surfaces of the Earth and the Earth's atmosphere are approximated by two planes as shown in Fig. 1. In this way the length of the sunbeams path through the atmosphere l can be calculated by (8) where h=50 to 80 km is the atmosphere height, while the solar- altitude angle a s is defined by (6). When the extraterrestrial radiation G and the global radiation Ggl are known, the relation between them k(l) (9) can be given as a function of the sunbeam path length in the atmosphere l if the impact of weather conditions is neglected (clear sky). In this work function k(l) is approximated by a sum of exponential functions (10) whose parameters are determined by applying a stochastic search algorithm called Differential Evolution [10]. The approximation function parameters A(.) and B-. are given in Table 1 while the approximation function k(l) is shown in Fig. 2. The approximation function k(l) is applied to calculate global solar radiation Ggl- f that reaches the Earth's atmosphere (11). A comparison of the measured and by (11) forecasted global radiation distribution during a day is shown in Figs. 3 and 4. The forecasted global solar radiation distribution from Figs. 3 and 4 is used together with the PV power-plant model based on the solar-cell model, Fig. 5, equations (12) and (13), for calculation of the forecasted PV power plant output power distribution. The PV power-plant data are given in Table 2 while the comparison of measured and forecasted output power distribution is shown in Figs. 6 and 7.