Modelling a solar energy harvester is best way to know the characteristics of the solar energy harvesting technology. Normally, a photovoltaic system (solar panel) is used as a solar energy harvester to directly converter light energy into electricity. The output power of a solar panel highly depends on the environment conditions such as position, light intensity and temperature. The light intensity primarily affects the
amount of current generated and the temperature determines the voltage produced by the solar panel (Dezso et al., 2007). All of these factors need to be taken into consideration when modelling a solar cell. Recently, numerous solar cell models are presented in literature and these models can be roughly classified into a single diode model and a more sophisticated two or more diodes model. The detailed descriptions of these models are summarised in Xiao et al. (2004). The single diode model is the most developed and most common equivalent circuit for a silicon solar cell because of the simple model structure, as shown in Figure 4.1. According to Figure 4.1, five parameters, which are a photocurrent , a dark saturation current , a shunt current
and a shunt resistor and a series resistance , should be determined before modelling a solar cell. But unfortunately, these parameters are not given in the manufactures’ datasheets, which normally provide the open-circuit voltage , the short circuit current , the panel voltage and current at the maximum power point
and . Hence, a straightforward approach, which uses the information provided by the data sheet, to construct a model of a solar cell should be considered.
According to this idea, (Dezso et al., 2007), (Farivar and Asaei, 2010), (Villalva et al., 2009) and (Petreus et al., 2009) have proposed different solar cell’s models to simulate the electrical characteristics of the solar cells. In order to extract parameters easily and to simulate the model rapidly, a solar cell model based on the first empirical model (Petreus et al., 2009), has been adopted in this work. The I-V characteristics of a solar cell can be written as Equations 4.1.
where B and Rs can be expressed by the following equations
{
Figure 4.1 The equivalent circuit of the one diode model
According to Equation 4.1, a solar cell model can be constructed by knowing
, , , , and . Ordinarily, the open circuit voltage
and short circuit current of a solar cell are easily extracted from an experiment. By following two linear relationships between the open circuit voltage and the MPP voltage ( ) of the solar cell, and the short circuit current and MPP current ( ) of the solar cell, the MPP of the solar cell in a certain light condition can be determined (Esram et al., 2007).
(4.4) where is the coefficient of a linear relationship between the MPP voltage and the open circuit voltage of a solar cell, and is the coefficient of a linear relationship between the MPP current and the short circuit current of the solar cell. In this chapter, a SANYO amorphous solar panel AM-5412 (SANY AM-5412, 2008) has been selected to verify the solar cell model. In order to simplify the model description, two fixed coefficients and are employed to estimate the MPP voltage and current of the solar cell. The parameters of the solar panel are illustrated in Table 4.1. The first column is the data when the solar panel is illuminated by a 50kLx standard light. This data is directly provided by the manufacturer. But this is not enough to characterize the solar cell in different situations. Some additional experimental tests should take place to obtain enough information for the model
construction. In this work, three additional tests, which the light intensities are 35kLx, 8.12kLx and 2.93kLx, were tested in the laboratory and the open circuit voltages and the short circuit currents of these three tests were recorded. By using Equations 4.2, 4.3 and 4.4, the other three parameters of the solar cell’s model are determined, as shown in Table 4.1.
Table 4.1 Experimental parameters of the AM-5412 solar cell
50kLx 35kLx 8.12kLx 2.93kLx
Parameter Ratings Rating Rating Rating
3.4 V 3.14V 2.88V 2.61V
19.4mA 13.2mA 2.33mA 0.592mA
44mW 27.4054mW 4.4369mW 1.008mW
16.9mA 11.484mA 2.0271mA 0.515mA
2.6V 2.3864V 2.1888V 1.9575V
By applying these parameters into the simulation model, the I-V and P-V characteristics of the solar panel can be depicted. In order to evaluate the accuracy of the model, an experimental test has been taken place at the laboratory to validate the model. A 100W desk lamp has been used to produce a stable light irradiance in the laboratory. The output voltages and currents of the solar panel have been measured with a variable resistor, which can adjust its resistance from 100 ohms to 1Mohms.
Figure 4.2 (a) and (b) plot the I-V curves and P-V curves of the solar panel in different light conditions for both the simulation and experiments. According to the figures, the accuracy of the model is around 92% at MPPs. Moreover, by analysing the P-V curve of the solar cell, the output power of the solar cell is highly related to the light irradiance levels and the output power of the solar panel is highly related to the output voltage of the solar cell in a fixed light condition. For each light condition, there is a peak power output point, MPP of the solar panel, where the solar panel can provide maximum output power when it operates at this point.
Figure 4.2 (a) I-V characteristic and (b) P-V characteristic of the solar cell