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):

I_PV=I_PC﹣I_o{exp[(q/n_ck_cT)(V_PV＋R_SI_PV)]﹣1}﹣(V_PV＋R_SI_PV/R_sh) （1）

In the formula, I_o is the PN junction reverse saturation current of the equivalent diode inside the photovoltaic cell, and the mathematical expression of I_o is expressed by formula (2):
I_o =I_0r[T/T_r]exp{[qE_g/n_ck_c][(1/T_r)﹣(1﹣T)]} (2)
I_pc 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):
I_o = [I_SC＋K_ic(T﹣T_r)](s/1000) (3)
R_sh 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:
R_s 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:
n_c is the diode characteristic factor, when the thermodynamic temperature T=300K, the nc value is about 2.8:
k_c 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:
I_pv is the output current of the photovoltaic cell;
V_pv is the output voltage of the photovoltaic cell;
T_r is the standard temperature for photovoltaic cell testing specified by IEC 60904-1, Tr -300K;
I_0r is the reverse saturation current of the equivalent diode PN junction inside the photovoltaic cell under Tr conditions;
E_g is the band gap of the semiconductor in photovoltaic cells, and the band gap of different materials is different (E_g=0.2~3.7eV);
I_sc is the short-circuit current at the output of the photovoltaic cell:
k_ic 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 R_sh and R_s 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.
I_PV=I_PC﹣I_o{exp[(q/n_ck_cT)V_PV]﹣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, V_oc is the open circuit voltage at the output of the photovoltaic cell:
P_pv is the output power of the photovoltaic cell;
I_mpp 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;
V_mpp 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;
P_mpp 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. .