Regular and Irregular Performance Variation of Module String and Occurred Conditions for Potential Induced Degradation-A ﬀ ected Crystalline Silicon Photovoltaic Power Plants

: Potential induced degradation (PID) leads to power degradation, and reduces durability and reliability of solar modules. However, this problem has not been thoroughly solved so far. The results from interlaboratory and ﬁeld study show contradictory fault phenomenon for PID. In this paper, PID of crystalline silicon photovoltaic power plants distributed in various climate conditions was investigated. These photovoltaic power plants consist of two types of crystalline silicon solar modules, which cover almost all kinds of front glass, ethyl vinyl acetate (EVA) and backsheet available commercially. It was found that only a few of power plants were a ﬀ ected by PID. By measuring current voltage characteristics of PID-a ﬀ ected solar modules, the real faults phenomenon was uncovered and classiﬁed into regular and irregular power degradation in a module string. The results obtained in this work show that the negative potential caused by high system voltage and stacking faults are necessary and su ﬃ cient conditions for PID occurrence for the ﬁrst time. The anomalous power degradation is related to the stacking fault, which appears randomly during the crystal growth.


Introduction
Crystalline silicon solar modules have a high reliability and low total number of returns, this is found in the peak power warranty clause supplied by the module producers, which are currently as high as 25 years [1][2][3][4][5]. However, the potential induced degradation caused a remarkable degradation of output power for photovoltaic power plant in recent years [6][7][8]. This has a bad influence on performance ratio and rate of return on investment for photovoltaic power plant. Since Swanson reported significant power loss for SunPower's back-contacted n-type solar modules in the field due to PID, many researchers have devoted their time to solving this problem at solar cells, modules, and systems level [9][10][11][12][13][14]. V. Naumann et al. think that PID is related with sodium decorated stacking faults across the pn junction under high system voltage [15][16][17][18]. S. Koch, K. Mishina and Zhou found that adding two or three layers coatings into crystalline silicon solar cells could reduce the sensitivity of PID [19][20][21]. J. Hylsky et al. deem that crystalline silicon solar cells with the phosphorus silicate glass show properties resistive against PID [22]. J. Kapur and A. Virtuani believe that the encapsulation materials could directly affect the extent of PID [23,24]. S. Hoffmann et al. think that PID could be accelerated by environmental factors such as temperature and humidity [25]. S. Suzuki et al. confirmed that PID in crystalline silicon photovoltaic modules could be accelerated by salt-mist preconditioning [26]. At the photovoltaic system level, some researchers think that the applied negative voltage could remove the sodium ions embedded in the stacking faults, and regain the output power of PID-affected crystalline silicon solar modules [27][28][29][30]. But up to now, the true cause and occurred conditions of PID have not been found thoroughly yet because of complication of PID phenomena. People have not found the sufficient and necessary conditions for PID. In this paper, by investigating the crystalline silicon photovoltaic power plants in various climate conditions, we found that only a few of power plant suffered from PID. These results prove that the potential between crystalline silicon solar cells and the aluminium frame is necessary but is not a sufficient condition for occurrence of PID. The measured photovoltaic power plants consist of two crystalline silicon solar module types, which cover almost all kinds of front glass, EVA and backsheet available commercially. We found that PID is not directly relevant to encapsulation materials. Some proper encapsulation materials of solar modules could only slow PID down. By measuring electrical performance of PID-affected solar modules, the real faults phenomenon were revealed and classified into regular and irregular power degradation in a module string. It was found that the deterioration degree of PID-affected solar modules is not proportional to the applied voltage between solar cells and aluminum frame in some cases in the field, this result agrees with [31]. These findings are a little different from previous study [32]. We think that the anomalous power degradation is related to the stacking fault which appears randomly during the crystal growth. The negative potential and stacking faults are necessary and sufficient conditions for PID occurrence.

Materials and Methods
The crystalline silicon photovoltaic power plants studied in this work are distributed in various climate conditions in China. These photovoltaic power plants consist of two crystalline silicon solar module types, i.e., monocrystalline silicon (Mono-Si) solar modules and multicrystalline silicon (Multi-Si) solar modules. The solar modules used in these power plants consist of 60-or 72-piece p-type Mono-Si or Multi-Si solar cells wired in series, respectively. These crystalline silicon solar cells were encapsulated with the classic glass-EVA-cells-EVA-backsheet structure, which cover almost all kinds of front glass, EVA and backsheet available commercially. For every solar module, three bypass diodes were placed in junction box. Also, 20 or 24 crystalline silicon solar cells were serially connected with a bypass diode. The dimensions of crystalline silicon solar cells are 125 × 125 mm 2 or 156×156 mm 2 , and have a conventional H-pattern model and an unpassivated full-area screen-printed aluminium back surface field. Figure 1 gives out the studied photovoltaic power plants and experimental setup. 20~25 • C environmental temperature, 820~900 W/m 2 solar irradiance and 1-2 m/s wind speed were chosen as test conditions in the field. The current-voltage characteristics and output power-voltage characteristics of solar modules were tested by the portable XJTU-10A in the field. The voltages of module strings under open circuit (V oc ) were tested by portable digital multimeter (Fluke Corp., Fluke 15B+). Thermography images (IR images) of crystalline silicon solar modules were acquired by T420 (FLIR Systems, Inc. USA) with a resolution of 320×240 pixels. The spectral range of T420 is 7.5~13µm. And solar modules suffered from PID can be distinguished by its open circuit voltage and the thermography image [14]. The intensity of sunlight was tested by YFJ-10 solar irradiation meter. The working temperature of solar module was tested by thermocouple. The solar modules suffered from PID were labelled in sequence respectively and disassembled from module string, and carried to our laboratory. The current-voltage characteristics of PID-affected solar modules disassembled from photovoltaic array was measured by solar simulator (PASAN Sunsim 3C) under standard test conditions (STC: 1 kW/m 2 irradiation, 25 • C module temperature and AM1.5 global spectrum). The solar simulator was adjusted by the same type standard module. The electroluminescence images (EL images) of the crystalline silicon solar modules were tested by an EL measurement system indoor.
Energies 2019, 12, x FOR PEER REVIEW 3 of 13 electroluminescence images (EL images) of the crystalline silicon solar modules were tested by an EL measurement system indoor.

Probability of PID for Crystalline Silicon Photovoltaic Power Plants Distributed in Various Climate Conditions
In order to find out the reasons for occurrence of PID, the crystalline silicon photovoltaic power plants located in different climate zones were tested. Figure 2 gives out the distribution of the tested photovoltaic power plants. These photovoltaic power plants range from hot to cold and humid to arid.  Figure 3 shows the typical electrical topology of sub-array for the photovoltaic power stations. In Figure 3, 16~18 or 20~22 crystalline silicon solar modules were concatenated into module string. A string box with direct current switch was used to connect the module strings in parallel. The

Probability of PID for Crystalline Silicon Photovoltaic Power Plants Distributed in Various Climate Conditions
In order to find out the reasons for occurrence of PID, the crystalline silicon photovoltaic power plants located in different climate zones were tested. Figure 2 gives out the distribution of the tested photovoltaic power plants. These photovoltaic power plants range from hot to cold and humid to arid.

Probability of PID for Crystalline Silicon Photovoltaic Power Plants Distributed in Various Climate Conditions
In order to find out the reasons for occurrence of PID, the crystalline silicon photovoltaic power plants located in different climate zones were tested. Figure 2 gives out the distribution of the tested photovoltaic power plants. These photovoltaic power plants range from hot to cold and humid to arid.  Figure 3 shows the typical electrical topology of sub-array for the photovoltaic power stations. In Figure 3, 16~18 or 20~22 crystalline silicon solar modules were concatenated into module string. A string box with direct current switch was used to connect the module strings in parallel. The  Figure 3 shows the typical electrical topology of sub-array for the photovoltaic power stations. In Figure 3, 16~18 or 20~22 crystalline silicon solar modules were concatenated into module string. A string box with direct current switch was used to connect the module strings in parallel. The string box was directly concatenated to solar inverter. The Al frame of solar module was grounded for the sake of preventing electric shock. string box was directly concatenated to solar inverter. The Al frame of solar module was grounded for the sake of preventing electric shock. Figure 3. Typical electrical topology of sub-array for the studied photovoltaic power stations. 16~18 or 20~22 crystalline silicon solar modules were concatenated into module string. A string box with direct current switch was used to connect the module strings in parallel. The string box was directly concatenated to solar inverter. The aluminium frame of solar module was grounded for the sake of preventing electric shock. Table 1 gives out the information of the studied power plants, and a certain power plant is or not affected by PID. From Table 1, it was found that only multicrystalline silicon solar modules in Quyang, monocrystalline silicon solar modules in Dingbian and Zhanjiang suffered from PID. The probability of PID for multicrystalline silicon photovoltaic power plants is 6.28%, and the probability of PID for monocrystalline silicon photovoltaic power plants is 6.81%. In these power plants, some solar modules exposed to negative potential show an abnormal power degradation caused by PID, but other solar modules exposed to negative potential are PID-free. So this result confirms that negative potential is necessary condition for PID, and negative potential is not sufficient condition for PID. Some of findings agree with many published papers [33][34][35].  Table 1, the photovoltaic power plants located in Quyang and Dingbian suffered from PID, so high temperature and humid are not the necessary prerequisite to occurrence of PID, but the high temperature and humid could aggravate the extent of PID [10].
In these power plants, the solar modules used almost all of the front glass, EVA and backsheet available commercially. It was also not found that occurrence of PID is related with EVA, backsheet, monocrystalline or multicrystalline silicon solar cells from Table 1. . Typical electrical topology of sub-array for the studied photovoltaic power stations. 16~18 or 20~22 crystalline silicon solar modules were concatenated into module string. A string box with direct current switch was used to connect the module strings in parallel. The string box was directly concatenated to solar inverter. The aluminium frame of solar module was grounded for the sake of preventing electric shock. Table 1 gives out the information of the studied power plants, and a certain power plant is or not affected by PID. From Table 1, it was found that only multicrystalline silicon solar modules in Quyang, monocrystalline silicon solar modules in Dingbian and Zhanjiang suffered from PID. The probability of PID for multicrystalline silicon photovoltaic power plants is 6.28%, and the probability of PID for monocrystalline silicon photovoltaic power plants is 6.81%. In these power plants, some solar modules exposed to negative potential show an abnormal power degradation caused by PID, but other solar modules exposed to negative potential are PID-free. So this result confirms that negative potential is necessary condition for PID, and negative potential is not sufficient condition for PID. Some of findings agree with many published papers [33][34][35].  Table 1, the photovoltaic power plants located in Quyang and Dingbian suffered from PID, so high temperature and humid are not the necessary prerequisite to occurrence of PID, but the high temperature and humid could aggravate the extent of PID [10].
In these power plants, the solar modules used almost all of the front glass, EVA and backsheet available commercially. It was also not found that occurrence of PID is related with EVA, backsheet, monocrystalline or multicrystalline silicon solar cells from Table 1. Figure 4 shows the potential distribution of crystalline silicon solar module between solar cells and an aluminium frame for two types of module strings. Figure 4a shows the potential of module string made up of 17 solar modules with 72 pieces solar cells in series, Figure 4b gives out the potential of module string made up of 22 solar modules with 60 pieces solar cells in series. The potential of the aluminium frame is zero because it is grounded. For crystalline silicon solar modules situated on the front half module string, the potential of solar cells is positive relative to aluminium frame. For solar modules located in the rear half module string, the potential of solar cells is negative relative to the aluminium frame. The potential is caused by high voltage formed by the series connection of solar modules. The potential that each solar module sustains is directly proportional to the serial number of the modules in working conditions [36]. For a certain PID-affected power plant, the encapsulated materials of all solar modules are the same, and the working conditions, such as illumination, temperature, relative humidity, soil, rain, and etc. are also the same except the potential that solar module endures. If the viewpoint of surface polarization effect for PID mechanism is correct, out of question, the degradation rate of power is relevant to the location of each module in module string, i.e., the closer the solar module approaches the negative pole of module string, the more serious the deterioration of maximum power for the solar module is. If the standpoint of sodium-decorated stacking faults across n + -p junctions for PID mechanism is correct, the deterioration degree of solar module will increase with the increasing of module sequence number only when the density of stacking faults on all solar cells in a certain module string is nearly equal.  Figure 4 shows the potential distribution of crystalline silicon solar module between solar cells and an aluminium frame for two types of module strings. Figure 4a shows the potential of module string made up of 17 solar modules with 72 pieces solar cells in series, Figure 4b gives out the potential of module string made up of 22 solar modules with 60 pieces solar cells in series. The potential of the aluminium frame is zero because it is grounded. For crystalline silicon solar modules situated on the front half module string, the potential of solar cells is positive relative to aluminium frame. For solar modules located in the rear half module string, the potential of solar cells is negative relative to the aluminium frame. The potential is caused by high voltage formed by the series connection of solar modules. The potential that each solar module sustains is directly proportional to the serial number of the modules in working conditions [36]. For a certain PID-affected power plant, the encapsulated materials of all solar modules are the same, and the working conditions, such as illumination, temperature, relative humidity, soil, rain, and etc. are also the same except the potential that solar module endures. If the viewpoint of surface polarization effect for PID mechanism is correct, out of question, the degradation rate of power is relevant to the location of each module in module string, i.e., the closer the solar module approaches the negative pole of module string, the more serious the deterioration of maximum power for the solar module is. If the standpoint of sodium-decorated stacking faults across n + -p junctions for PID mechanism is correct, the deterioration degree of solar module will increase with the increasing of module sequence number only when the density of stacking faults on all solar cells in a certain module string is nearly equal.  The relationship between open circuit voltages of crystalline silicon solar modules and module sequence in PID-affected solar module strings corresponding to Figure 4 respectively for the two PID-affected power plants is shown in Figure 5. In Figure 5, the open circuit voltages of solar modules were measured in the field and translated to STC by XJTU-10A.

Regular and Irregular Degradation of Open Circuit Voltage of Module Strings under Field Conditions
From Figure 5a, it was found that the open circuit voltages of crystalline silicon solar modules from module 1 to module 9 are almost equal for all monocrystalline silicon module strings, and there is almost no degradation. But the open circuit voltages of modules from module 10 to module The relationship between open circuit voltages of crystalline silicon solar modules and module sequence in PID-affected solar module strings corresponding to Figure 4 respectively for the two PID-affected power plants is shown in Figure 5. In Figure 5, the open circuit voltages of solar modules were measured in the field and translated to STC by XJTU-10A.
From Figure 5a, it was found that the open circuit voltages of crystalline silicon solar modules from module 1 to module 9 are almost equal for all monocrystalline silicon module strings, and there is almost no degradation. But the open circuit voltages of modules from module 10 to module 17 decrease gradually with the increasing module number for the module string 1 to 5. This finding seems to give us some hints that there is a relationship between the extent of PID and the potential of solar modules in some cases. This result agrees with [32,37]. But for module string 6, 7 and 8, the voltages of solar modules from No. 10  17 decrease gradually with the increasing module number for the module string 1 to 5. This finding seems to give us some hints that there is a relationship between the extent of PID and the potential of solar modules in some cases. This result agrees with [32,37]. But for module string 6, 7 and 8, the voltages of solar modules from No. 10

Parametric Analysis of Solar Modules Dismounted from PID-Affected Power Plants under STC
The PID-affected monocrystalline and multicrystalline silicon solar modules from different power plants were labelled in order respectively and disassembled from module strings, and carried to lab for degradation investigation under STC. Figure 6 gives out the current-voltage and power-voltage curves of 17 monocrystalline silicon modules dismounted from the module string 1 corresponding to Figure 5a. From Figure 6, it was found that the maximum output powers of module 1 to 9 almost have no degradation. But the solar module 10 to 17 exhibit different degrees of power degradation with the increasing module number, even if these solar modules suffered from an even growth of potential with the increasing module number, i.e., it was not found that the larger negative potential induce more serious PID in proportion.

Parametric Analysis of Solar Modules Dismounted from PID-Affected Power Plants under STC
The PID-affected monocrystalline and multicrystalline silicon solar modules from different power plants were labelled in order respectively and disassembled from module strings, and carried to lab for degradation investigation under STC. Figure 6 gives out the current-voltage and power-voltage curves of 17 monocrystalline silicon modules dismounted from the module string 1 corresponding to Figure 5a. From Figure 6, it was found that the maximum output powers of module 1 to 9 almost have no degradation. But the solar module 10 to 17 exhibit different degrees of power degradation with the increasing module number, even if these solar modules suffered from an even growth of potential with the increasing module number, i.e., it was not found that the larger negative potential induce more serious PID in proportion. 17 decrease gradually with the increasing module number for the module string 1 to 5. This finding seems to give us some hints that there is a relationship between the extent of PID and the potential of solar modules in some cases. This result agrees with [32,37]. But for module string 6, 7 and 8, the voltages of solar modules from No. 10

Parametric Analysis of Solar Modules Dismounted from PID-Affected Power Plants under STC
The PID-affected monocrystalline and multicrystalline silicon solar modules from different power plants were labelled in order respectively and disassembled from module strings, and carried to lab for degradation investigation under STC. Figure 6 gives out the current-voltage and power-voltage curves of 17 monocrystalline silicon modules dismounted from the module string 1 corresponding to Figure 5a. From Figure 6, it was found that the maximum output powers of module 1 to 9 almost have no degradation. But the solar module 10 to 17 exhibit different degrees of power degradation with the increasing module number, even if these solar modules suffered from an even growth of potential with the increasing module number, i.e., it was not found that the larger negative potential induce more serious PID in proportion.    Figure 7, it was found that the electrical parameters of module 1 to 9 show a normal degradation caused by light-induced degradation. But the maximum output powers of module 10 to 17 show an irregular degradation with the increasing module number. The deterioration degree of Module 14 in Figure 7 is more serious than that of module 15 and module 16. This is different from that of Module string 1 of Figure 6. In other words, even if module 14 of module string 7 underwent a lower negative potential than that of module 15 and module 16 in the field, module 14 shows more power degradation than module 15 and module 16. Thus, it is proved that there is another important factor about the extent of PID in addition to this potential.  Figure 7, it was found that the electrical parameters of module 1 to 9 show a normal degradation caused by light-induced degradation. But the maximum output powers of module 10 to 17 show an irregular degradation with the increasing module number. The deterioration degree of Module 14 in Figure 7 is more serious than that of module 15 and module 16. This is different from that of Module string 1 of Figure 6. In other words, even if module 14 of module string 7 underwent a lower negative potential than that of module 15 and module 16 in the field, module 14 shows more power degradation than module 15 and module 16. Thus, it is proved that there is another important factor about the extent of PID in addition to this potential.      Figure 7 is more serious than that of module 15 and module 16. This is different from that of Module string 1 of Figure 6. In other words, even if module 14 of module string 7 underwent a lower negative potential than that of module 15 and module 16 in the field, module 14 shows more power degradation than module 15 and module 16. Thus, it is proved that there is another important factor about the extent of PID in addition to this potential.     Figure 9 shows the change of maximum power of modules from 3 different PID-affected module strings, which are monocrystalline silicon module strings 1 and 7 of Figure 5a, and multicrystalline silicon module string 1 of Figure 5b, respectively. From Figure 9, it was found that the solar modules located in the front half-string shows a normal power degradation caused by light-induced degradation, and the deterioration degrees of solar modules located in the rear half-string do not increase with the increasing negative potential except for partial monocrystalline silicon module strings. From Figure 9 and Table 1, it was also found that the negative potential relative to the aluminium frame is not sufficient, but is a necessary condition for PID. The severity of PID is not necessarily related to the magnitude of negative potential in the field. But in laboratory, the higher applied negative voltage induces more severe PID for a certain PID-susceptible solar modules. The positive potential does not induce PID. This result agrees with [37]. multicrystalline silicon module string 1 of Figure 5b, respectively. From Figure 9, it was found that the solar modules located in the front half-string shows a normal power degradation caused by light-induced degradation, and the deterioration degrees of solar modules located in the rear half-string do not increase with the increasing negative potential except for partial monocrystalline silicon module strings. From Figure 9 and Table 1, it was also found that the negative potential relative to the aluminium frame is not sufficient, but is a necessary condition for PID. The severity of PID is not necessarily related to the magnitude of negative potential in the field. But in laboratory, the higher applied negative voltage induces more severe PID for a certain PID-susceptible solar modules. The positive potential does not induce PID. This result agrees with [37]. Figure 9. The change of the maximum output power for three module strings, which are monocrystalline silicon module string 1 and 7 of Figure 5a, and multicrystalline silicon module string 1 of Figure 5b, respectively.

Electroluminescence Images and Thermography Images for Monocrystalline and Multicrystalline Silicon Solar Modules Suffered from PID
In some cases, the electroluminescence images and thermography images of monocrystalline silicon solar modules from the same PID-affected module string present a regular change, as shown in Figure 10. From Figure 10, it was found that the solar cells near the aluminium frame exhibit higher temperatures than the middle solar cells in module 17; this has been proven by [36]. But in other cases, the EL image and IR image of PID-affected monocrystalline silicon solar module dismounted from the module string present an irregular change, as shown in Figure 11. From Figure 11, it was found that the solar cells near the aluminium frame do not exhibit high temperature than middle solar cells in module 14, even if the solar cells near to the aluminium frame sustain larger negative potential [32]. This finding is different from Figure 10.  Figure 10a is electroluminescence image for module 1, the right in Figure 10a is electroluminescence image for module 17. The left in Figure 10b is thermography image for module 1, the right in Figure 10b is thermography image for module 17. The solar cells near to the aluminium frame exhibit higher temperatures than the middle solar cells in module 17. Reprint from [33]. Copyright 2017, Elsevier.

Electroluminescence Images and Thermography Images for Monocrystalline and Multicrystalline Silicon Solar Modules Suffered from PID
In some cases, the electroluminescence images and thermography images of monocrystalline silicon solar modules from the same PID-affected module string present a regular change, as shown in Figure 10. From Figure 10, it was found that the solar cells near the aluminium frame exhibit higher temperatures than the middle solar cells in module 17; this has been proven by [36]. But in other cases, the EL image and IR image of PID-affected monocrystalline silicon solar module dismounted from the module string present an irregular change, as shown in Figure 11. From Figure 11, it was found that the solar cells near the aluminium frame do not exhibit high temperature than middle solar cells in module 14, even if the solar cells near to the aluminium frame sustain larger negative potential [32]. This finding is different from Figure 10. multicrystalline silicon module string 1 of Figure 5b, respectively. From Figure 9, it was found that the solar modules located in the front half-string shows a normal power degradation caused by light-induced degradation, and the deterioration degrees of solar modules located in the rear half-string do not increase with the increasing negative potential except for partial monocrystalline silicon module strings. From Figure 9 and Table 1, it was also found that the negative potential relative to the aluminium frame is not sufficient, but is a necessary condition for PID. The severity of PID is not necessarily related to the magnitude of negative potential in the field. But in laboratory, the higher applied negative voltage induces more severe PID for a certain PID-susceptible solar modules. The positive potential does not induce PID. This result agrees with [37].

Electroluminescence Images and Thermography Images for Monocrystalline and Multicrystalline Silicon Solar Modules Suffered from PID
In some cases, the electroluminescence images and thermography images of monocrystalline silicon solar modules from the same PID-affected module string present a regular change, as shown in Figure 10. From Figure 10, it was found that the solar cells near the aluminium frame exhibit higher temperatures than the middle solar cells in module 17; this has been proven by [36]. But in other cases, the EL image and IR image of PID-affected monocrystalline silicon solar module dismounted from the module string present an irregular change, as shown in Figure 11. From Figure 11, it was found that the solar cells near the aluminium frame do not exhibit high temperature than middle solar cells in module 14, even if the solar cells near to the aluminium frame sustain larger negative potential [32]. This finding is different from Figure 10.   Figure 12 gives out the typical EL image and IR image of PID-affected multicrystalline silicon solar module from the module string. From Figure 12, it was found that there is not a regular change in PID-affected multicrystalline silicon solar module, i.e., the solar cells adjacent to the aluminium frame do not exhibit higher temperature than the middle cells in the multicrystalline silicon solar module. According to the measured results from the field, we did not also find the regular change of IR images and EL images for PID-affected multicrystalline silicon module string in the photovoltaic power plants. The above results prove that there are regular and irregular electroluminescence images and thermography images of monocrystalline silicon modules that suffered from PID in the field, and it was not found that there are the regular electroluminescence images and thermography images of multicrystalline silicon solar modulesthat suffered from PID, as far as we know.

Discussion
According to the aforementioned results, the probability of PID for monocrystalline and multicrystallinesilicon photovoltaic power plants is very small for the installed power plants in China. There are regular and irregular electroluminescence images and thermography images for monocrystalline silicon solar modules that suffered from PID in the field. It was not found that there were regular electroluminescence images and thermography images for multicrystalline silicon solar modules that suffered from PID. These results could be explained by preparation process of monocrystalline and multicrystallinesilicon solar modules.  Figure 12 gives out the typical EL image and IR image of PID-affected multicrystalline silicon solar module from the module string. From Figure 12, it was found that there is not a regular change in PID-affected multicrystalline silicon solar module, i.e., the solar cells adjacent to the aluminium frame do not exhibit higher temperature than the middle cells in the multicrystalline silicon solar module. According to the measured results from the field, we did not also find the regular change of IR images and EL images for PID-affected multicrystalline silicon module string in the photovoltaic power plants.   Figure 12 gives out the typical EL image and IR image of PID-affected multicrystalline silicon solar module from the module string. From Figure 12, it was found that there is not a regular change in PID-affected multicrystalline silicon solar module, i.e., the solar cells adjacent to the aluminium frame do not exhibit higher temperature than the middle cells in the multicrystalline silicon solar module. According to the measured results from the field, we did not also find the regular change of IR images and EL images for PID-affected multicrystalline silicon module string in the photovoltaic power plants. The above results prove that there are regular and irregular electroluminescence images and thermography images of monocrystalline silicon modules that suffered from PID in the field, and it was not found that there are the regular electroluminescence images and thermography images of multicrystalline silicon solar modulesthat suffered from PID, as far as we know.

Discussion
According to the aforementioned results, the probability of PID for monocrystalline and multicrystallinesilicon photovoltaic power plants is very small for the installed power plants in China. There are regular and irregular electroluminescence images and thermography images for monocrystalline silicon solar modules that suffered from PID in the field. It was not found that there were regular electroluminescence images and thermography images for multicrystalline silicon solar modules that suffered from PID. These results could be explained by preparation process of monocrystalline and multicrystallinesilicon solar modules. The above results prove that there are regular and irregular electroluminescence images and thermography images of monocrystalline silicon modules that suffered from PID in the field, and it was not found that there are the regular electroluminescence images and thermography images of multicrystalline silicon solar modulesthat suffered from PID, as far as we know.

Discussion
According to the aforementioned results, the probability of PID for monocrystalline and multicrystallinesilicon photovoltaic power plants is very small for the installed power plants in China. There are regular and irregular electroluminescence images and thermography images for monocrystalline silicon solar modules that suffered from PID in the field. It was not found that there were regular electroluminescence images and thermography images for multicrystalline silicon solar modules that suffered from PID. These results could be explained by preparation process of monocrystalline and multicrystallinesilicon solar modules.
Usually, the monocrystalline silicon ingots are produced by Czochralski technology. In recent years, the length of silicon ingot has reached 3.5 m or so, and the growth speed of monocrystalline silicon ingot has been improved from 0.8 mm/min to 1.6 mm/min so as to reducing process costs. The stacking faults that emerged in semiconductor-grade silicon may go back to solar-grade silicon. Because the rate of rotation and pulling could be controlled accurately, the stacking faults may be formed uniformly. During subsequent automatic production, the similar monocrystallinesilicon solar modules were installed in a module string. Thus, it is likely to present a regular degradation in monocrystalline silicon power plants. Multicrystalline silicon ingots are usually produced by a directional solidification technique; the length and width of multicrystalline silicon ingot are nearly 1 m, but the height of multicrystalline silicon ingot is only less than 0.4 m. Stacking faults is not likely well-distributed on bricks cut from a multicrystalline silicon ingot. Compared with monocrystalline silicon ingot, such a growth characteristic for multicrystalline silicon leads to a higher probability of irregular degradation in multicrystalline silicon power plants.
In summary, in terms of the outcome, we think the negative potential and stacking faults are necessary and sufficient conditions for PID occurrence [34,[38][39][40]. Because sodium ions exist in every material of solar module besides rain and soil, some encapsulation materials with a low sodium ion concentration only alleviate PID of the solar module for a period of time. The high temperature and humidity are beneficial to migration of sodium ion, so the high temperature and humid could aggravate the extent of PID [41][42][43][44][45]. Because of the complication of stacking faults, it is nearly impossible to calculate power degradation as a function of negative system bias, stress time, module temperature and relative humidity.

Conclusions
In this paper, PID of crystalline silicon photovoltaic power plants distributed in various climate conditions was investigated. It was found that only a few power plants suffered from PID. In our study, the probability of PID for multicrystalline silicon photovoltaic power plants is 6.28%, and the probability of PID for monocrystalline silicon photovoltaic power plants is 6.81%. By measuring electrical characteristics of solar modules suffered from PID, the real faults phenomenon was revealed and classified into regular and irregular power degradation in the field for the first time. Owing to occasional stacking faults, it was found that there is no a general relationship between the degradation rate of open circuit voltage and applied negative potential for PID-affected solar modules, and there is also no a general relationship between the degradation rate of output power and applied negative potential for PID-affected solar modules. EL and IR images prove that there are regular and irregular electroluminescence images and thermography images for monocrystalline silicon solar modules suffered from PID in the field. It was not found that there were regular electroluminescence images and thermography images for multicrystalline silicon solar modules. These phenomena are explained by a preparation process of monocrystalline silicon and multicrystalline silicon solar modules. The analysis of the results underlines the fact that the negative potential and stacking faults are necessary and sufficient conditions for PID occurrence.