# Analysis of the electrical characteristics of photovoltaic cells

① Equivalent mathematical model of photovoltaic cell
A typical equivalent circuit of a photovoltaic cell is shown in Figure 1, and its output characteristic equation can be described by equation (1):

IPV=IPC﹣Io{exp[(q/nckcT)(VPV＋RSIPV)]﹣1}﹣(VPV＋RSIPV/Rsh) （1）

In the formula, Io is the PN junction reverse saturation current of the equivalent diode inside the photovoltaic cell, and the mathematical expression of Io is expressed by formula (2):
Io =I0r[T/Tr]exp{[qEg/nckc][(1/Tr)﹣(1﹣T)]} (2)
Ipc is the photo-generated current, which is proportional to the temperature of the photovoltaic cell and the effective light intensity received by the photovoltaic cell. It is described by formula (3):
Io = [ISC＋Kic(T﹣Tr)](s/1000) (3)
Rsh is the equivalent parallel resistance of photovoltaic cells, generally in kiloohm level. Because of its large value, it has little effect on the characteristics of photovoltaic cells:
Rs is the equivalent series resistance of the photovoltaic cell, and its resistance is generally less than 1Ω;
q is the amount of electronic charge, q=1.6×10-19C/m2:
nc is the diode characteristic factor, when the thermodynamic temperature T=300K, the nc value is about 2.8:
kc is Boltzmann’s constant, kc=1.38×10-23J/K;
T is the thermodynamic temperature of the photovoltaic cell, T-273.15+t, t is the temperature in Celsius:
Ipv is the output current of the photovoltaic cell;
Vpv is the output voltage of the photovoltaic cell;
Tr is the standard temperature for photovoltaic cell testing specified by IEC 60904-1, Tr -300K;
I0r is the reverse saturation current of the equivalent diode PN junction inside the photovoltaic cell under Tr conditions;
Eg is the band gap of the semiconductor in photovoltaic cells, and the band gap of different materials is different (Eg=0.2~3.7eV);
Isc is the short-circuit current at the output of the photovoltaic cell:
kic is the temperature coefficient of the short-circuit current.
Since the equivalent series resistance resistance of photovoltaic cells is very small, and the equivalent parallel resistance resistance is relatively large, the influence of Rsh and Rs on photovoltaic characteristics is usually ignored in engineering, and the engineering approximate mathematical model of photovoltaic cells is obtained as formula (4 ), this greatly simplifies the analysis of the electrical characteristics of photovoltaic cells.
IPV=IPC﹣Io{exp[(q/nckcT)VPV]﹣1} (4)

②Classic electrical characteristics of photovoltaic cells
The electrical characteristics of photovoltaic cells are usually described by P-V (power-voltage) or I-V (current-voltage) characteristic curves. Typical P-V and I-V characteristic curves of photovoltaic cells are shown in Figure 2.

In the figure, Voc is the open circuit voltage at the output of the photovoltaic cell:
Ppv is the output power of the photovoltaic cell;
Impp is the maximum power point current, the working current of the photovoltaic cell at the time when the photovoltaic cell outputs the maximum power under the given light and temperature conditions;
Vmpp is the maximum power point voltage, the working voltage of the photovoltaic cell at the moment when the photovoltaic cell outputs the maximum power under the given light and temperature conditions;
Pmpp is the maximum power that a photovoltaic cell can output under given light and temperature conditions.

Figure 2 shows that the output power of the photovoltaic cell first increases and then decreases with the increase of the output voltage. The output current basically remains unchanged and then decreases rapidly with the increase of the output voltage. The PV and IV characteristic curves have obvious non-linear characteristics. .
According to formula (4), the characteristic curves of photovoltaic cells under different light conditions and different temperature conditions can be drawn, as shown in Figure 3. Among them, Figure 3 (a) and (b) are the P-V and I-V characteristic curves of photovoltaic cells under different light conditions. When the temperature is constant, as the light intensity changes from weak to strong, the peak power of the photovoltaic cell increases significantly, the open circuit voltage increases only slightly, and the short-circuit current increases greatly. Therefore, the light intensity mainly affects the short-circuit current at a constant temperature. size. Figure 3 (c) and (d) are the P-V and L-V characteristic curves of photovoltaic cells under different temperature conditions. When the light intensity is constant, as the temperature drops, the short-circuit current of the photovoltaic cell decreases slightly, and the open circuit voltage increases significantly, so its peak power also increases significantly, which means that under the same lighting conditions, the output power of the photovoltaic cell is larger when the temperature is lower. .