# Analysis of Parallel Characteristics of Photovoltaic Modules

Photovoltaic modules of the same type are connected in parallel to form a parallel photovoltaic array, as shown in Figure 1. m(m≥2) battery modules are connected in parallel, the voltages on the battery modules are Vz1, Vz2, .. ., Vzm, the output currents are lz1, Iz2, …, Izm, and the output voltage of the parallel photovoltaic array is Vb , The output current is Ib, so there is:

Suppose the equivalent photo-generated current of the photovoltaic cell module is (Iph1, Iph2,…, Iphm), by formula (1) and formula (2)
Available formula (3).

From equations (2) and (3), the output current expression (4) of the parallel photovoltaic array can be obtained, and the output power expression (5) of the parallel photovoltaic array can be obtained.

Through the analysis of equations (4) and (5), the characteristic expressions of the parallel photovoltaic array can be obtained as equations (6) to (9), where Voc.a is the open circuit voltage of the parallel photovoltaic array. When m=1, it is the characteristic expression of a single battery module. Comparing formula (10), formula (11), formula (12), formula (13) and formula (6) ~ formula (9) respectively, it can be seen that the characteristics of parallel photovoltaic array are similar to those of monolithic battery modules.

From equations (6) to (9), it can be seen that the maximum power point voltage Vmpp.b of the parallel photovoltaic array satisfies the relationship described in equation (14), and there is O<Vmpp.b<Voc.a.

Therefore, the parallel photovoltaic array still has the current monotonously decreasing with the increase of the output voltage within its working voltage range, and the output power also has the characteristic of single peak value.
When the illumination is uneven, assuming Iph1≥Iph2≥…≥Iphm, there is △Iph1=Iph1﹣Iph2≥0, △Iph2=Iph2﹣Iph3≥0,…,△Iph(m﹣1)= Iph(m﹣1)﹣Iphm≥0 and other relations, then can be obtained by formula (3):

According to equations (6) and (15), it can be seen that the unbalanced illumination will cause the operating voltage range of each battery module in the parallel photovoltaic array to be inconsistent, and there is a difference between the output current of each battery module, which may cause some The open circuit voltage Voc.z of the battery components is smaller than the open circuit voltage Voc.a of the array, which causes these battery components to be in a negative current working state, which in turn leads to the hot spot effect. The usual solution to this problem is to use the reverse blocking characteristic of the diode to connect the diode in series with the battery assembly to prevent the photovoltaic battery assembly from working in a negative current state, as shown in Figure 2. When the voltage at the array terminal is greater than the voltage at the parallel branch terminal, the diodes of the corresponding branch are in a blocking state, preventing negative current from flowing through the corresponding battery assembly, thereby protecting the battery assembly.

Under the condition of series diode, when m=2, and there is △Iph=Iph1-Iph2>0, the above analysis can get formula (16).

According to equation (10), it can be known that the open circuit voltage of the photovoltaic cell module that receives weaker light is expressed by equation (17).

In addition, it can be seen from equation (14) that when there is no series diode, the maximum power point voltage Vmpp.b of the parallel photovoltaic array satisfies equation (18). The maximum power point voltage Vmpp.z1 of the photovoltaic module itself that receives strong light satisfies equation (19). Suppose the expression of g(Vb) is as shown in equation (20), then it is easy to know its derivative g(Vb)’>0.

Substitute Voc.z2 into equation (19), and perform the transformation shown in equation (21) and equation (22).

From the above analysis and combining formula (21) and formula (22), it can be seen that if lph2 and △Iph have a relationship as shown in formula (23), then Voc.z2<Vmpp.b. At this time, for a parallel photovoltaic array with diodes connected in series and uneven light reception, there will be a discontinuous operating point in the output power curve, which is on the left side of the maximum power point voltage of the parallel photovoltaic array and is at There is no peak power point with dPb/dVb=0 on the left side of this discontinuity point. Because the diode is connected in series, when the output voltage of the array is greater than Voc.z.2, it is equivalent to only PV1 is working, so the maximum power point voltage of the array is Vmpp.z1.

If there is a relationship between Iph2 and △Iph as shown in formula (24), then Vmpp.b<Voc.z2<Vmpp.z1. At this time, the discontinuity point is on the right side of the maximum power point voltage of the parallel photovoltaic array, so there is a peak power point of dPb/dVb=0 on the left side of the discontinuity point. In addition, when the output voltage of the array is greater than Voc.z2, it is equivalent to that only PV1 is working, and Voc.z2<Vmpp.z1, so there is also a peak power point of dPb/dVb=0 on the right side of the discontinuity point. The voltage is Vmpp.z1.

If Iph2 and △Iph have the relationship shown in formula (25), then Vmpp.z1<Voc.z2. At this time, the discontinuity point is on the right side of Vmpp.z1, so there is no peak power point of dPb/dVb=0 in the range where the output voltage of the photovoltaic array is greater than Voc.z2. At this time, there is only one PV curve that satisfies the output of the photovoltaic array. The peak power point of dPb/dVb=0, the voltage at this point is Vmpp.b.

Suppose Iph1=5A, ε=10﹣3, Figure 3 shows the change of related parameters in equations (21) and (22) during the change of lph2 from 0A to 5A. In the figure, area I satisfies formula (23), area II satisfies formula (24), and area III satisfies formula (25). It can be seen that only when Iph2 is in zone II, the output power of the photovoltaic array will have two peak points, and at this time, the light received by the two photovoltaic cell modules is seriously uneven. When the unevenness of illumination is not serious, the parallel photovoltaic array formed by two photovoltaic modules under the condition of series diodes has only one extreme point of output power within the operating voltage range.

Figure 4 shows that two photovoltaic modules with uneven illumination are connected in series with diodes to form a parallel photovoltaic array. Although there is a discontinuity point in the operating voltage range, there is only one extreme power point that satisfies dPb/dVb=0.

In the same way, the following conclusions can be drawn: the parallel photovoltaic array formed by the parallel connection of photovoltaic modules with m series diodes, if there is Iph1≥Iph2≥…≥Iphm, when Iphm satisfies the formula (26), the photovoltaic array only exists An extreme power point that satisfies dPb/dVb=0.

It can be seen that, compared with the series-connected photovoltaic array, the parallel photovoltaic array has only one extreme point when the unevenness of the illumination is not serious, and it is easy to realize the maximum power point tracking.