## 2 Reverse Bias Characteristic of a PV Module Due to Voltage Mismatch Conditions
### The Failure of Bypass Diodes
From the experimental results, it is estimated that the non-uniformity of irradiance and the operation of the bypass diode by partial shading cause a small decrease in the open-circuit voltage of a PV module. For this reason, the reverse current hardly flows or is insignificant. In this chapter, a simulation was conducted to confirm the flow of reverse current due to the voltage mismatch in the PV arrays of dozens of PV modules, connected in series and in parallel. The DC array circuit of a general PV system is shown in Figure 9. The PV string has dozens of PV modules connected in series, and fuses are installed in the \(+\) and \(-\) poles of the string. Each string is connected in parallel and connected to the DC side of the inverter. The simulation tool was used with Matlab-Simulink, and the modeling is reflected in Figure 9. PV strings and arrays were constructed using Matlab-Simulink's PV module blocks. PV module specifications (Pmax: 320 W, Voc: 45.5 V, Vmp: 36.7 V, Isc: 9.25 A, Imp: 8.72 A) were set to be identical to the PV modules used for the reverse current measurement in Section 4. Even if three bypass diodes are inserted into the PV module, it was assumed that one bypass diode is embedded in each PV module for a smooth simulation. Inverter failure is assumed to be open-circuit state of the DC array. However, in the simulation, if the circuit is open, an error occurs. Thus, it is equalized using a capacitor. The simulation schematic is shown in Figure 10.  
Figure 8: I–V characteristics of a PV module due to the failure of bypass diodes. Figure 9: Schematic of the DC (Direct current) array of PV system for simulation. The simulation conditions were as follows. First, the voltage mismatch conditions in the simulation were set to the operation of the bypass diodes and the failure of the bypass diodes. Second, the installation of blocking diodes in the combiner box was not recommended, according to the current combiner box standard. Thus, blocking diodes were excluded from the PV array configuration. Third, the operating state of the inverter was set to be a stop state, which is one of the common failure factors of the inverter. The parallel circuit of PV arrays was assumed to be a four-loop circuit. The environmental conditions of the simulation were assumed to be STC conditions, in which the irradiance is 1000 W/m\({}^{2}\), and the PV module temperature is 25 \({}^{\circ}\)C. The variables in the simulation were set to increase the number of parallel circuits to 2, 3, and 4 loop circuits and to increase the number of PV modules, with the operation or failure of bypass diodes, to 1, 2, and 3 ea. The operation of bypass diodes by partial shading was simulated by lowering the irradiance to about 0 W/m\({}^{2}\). The reverse current was measured, on the side of the PV string, with the operation or failure of the bypass diode. Additionally, the failure of the bypass diode was assumed to be a minute resistance of about 0.05 \(\Omega\) or less, in reference to Equation (1), shown below. Equation (1) is the current equation of a PV module with a bypass diode failure. The output of the PV module with the bypass diode failure was analyzed by equalizing it with a minute resistor [22]:  
Figure 5:0  
The simulation results are as follows. First, the simulation is a condition under which the bypass diode operates. In Table 1, the reverse current ranged from \(-0.01\) A to \(-0.02\) A, even if the number of parallel circuits or operations of bypass diodes of PV modules increased. As shown in the experimental results in Section 2.3, it can be seen that the operation of bypass diodes does not cause a large potential difference between PV strings. Therefore, it was confirmed that the reverse current rarely flows as a consequence of the operation of the bypass diode. Next, the simulation is a condition under which the bypass diode fails.