*3.2. Predicting the Power Output of the Restore Module When Applying A Replacement Cell*

The following are the considerations for predicting the power of a module to be recovered when a new cell is installed: the first element is the deviation between the actual power output of the initial module and rated power output. This part was expected to be within the initial tolerance range, and after module recovery, the results and discussion were verified. Next, the power increase of the replacement cell should be added and the value of the field-aged power degradation rate from the initial power of the existing cell should be deducted. Moreover, the loss from the electrical mismatch between the cells should also be considered. The increase in the power of the replacement cell can be easily calculated using Equations (2) and (4). The next part to be considered is the loss caused by the electrical mismatch. A recent study reported that the result of power loss from the electrical mismatch of cells within a module was difficult to determine; however, when the direct parallel configuration of modules was different, the relative power loss (RPL) of the array due to electrical mismatch was 1.3–2.6% [45]. In previous studies, the power loss caused by the electrical mismatch of cells was reported to be approximately 0.009–0.19% [46]; thus, it is already reflected as −0.19% in the CTM factor; therefore, it should be applied conservatively. In the prediction of the power output, the final part to be considered is the loss from power degradation owing to the field aging factor of the existing cell. In general, the rate of power output degradation guaranteed by a module manufacturer is 0.7%/year, which is a guaranteed limit design considering the power

degradation caused by the failure of some modules in PV power plants. Referring to the results reported in a previous study, the actual power output degradation rate of more than 80% for crystalline PV modules in PV power plants that have been operated for more than 10 years is approximately 0.27%/year on average [47]. This figure is significantly lower than the limit guaranteed by manufacturers. In this study, we applied this figure to calculate the power output prediction. Table 5 lists the power output predictions for the recovered modules.


**Table 5.** Power output prediction for recovered modules.

For 190 A, 10 broken cells were replaced; thus, (10 × 4.28 Wp) + (44 × 3.58 Wp) = 42.8 + 157.52 = 200.32 Wp is the total power output value of the cell. In 190 B, six cells were replaced: (6 × 4.28 Wp) + (48 × 3.58 Wp) = 25.68 + 171.84 = 197.52 Wp. The results are presented in Table 4. Through the calculation, the predicted power output values of 190 A and 190 B were calculated as 196.40 Wp and 193.50 Wp, respectively. The CTM factor *ki* values ranging from *k*<sup>1</sup> to *k*15, and *k*<sup>3</sup> to *k*<sup>15</sup> are shown in the table; however, *k*<sup>1</sup> and *k*<sup>2</sup> values are not shown in the table nor described here. The CTM factor *k*<sup>1</sup> is the module margin, which is approximately −2.03% in a typical module, and *k*<sup>2</sup> is the cell spacing, which is also generally −0.53%. This value is a design factor for the module area and depends on module dimensions. However, the module margin or cell interval for insulation distance affects only the area efficiency of the module and does not produce power by itself; therefore, the calculation of CTM power was excluded from previous research.

#### *3.3. Results of Power Recovery by Cell Replacement of 190 A and 190 B Samples*

Figure 4 shows a comparison of the EL images of the modules before and after repair. In Figure 4c,d, the relatively bright cells are the newly replaced cells. In Figure 4a, when replacing cells of the 190 A sample, one more cell was replaced by damaging adjacent cells while removing the cells from the hot plate, and as the cell replacement operation was repeated, the same mistake was not repeated. Some small cracks not shown in Figure 4a are observed in Figure 4b, which are defects occurring during manual cell removal. However, the result shown in Figure 4d is not much different from that in Figure 4c because cell replacement has become familiar and cell removal progressed much more easily. For an easy recovery process, care should be taken to prevent additional cell cracks when collecting and reinstalling the modules to be repaired.

**Figure 4.** EL images in modules before and after recovery. (190 A, 190 B). (**a**) Among a total of 54 cells from 190 A, 10 cells with a severe crack degree were removed and (**b**) replaced with a new cell to recover. (**c**) Sample 190 B exhibited severe power degradation in approximately six cells, and hot spots due to pore soldering also occurred in the busbar–interconnector connection. (**d**) However, both the power and FF were recovered after cell replacement and pore soldering repair.

Table 6 lists the electrical characteristics of the module before and after recovery. The module power increased by approximately 4.50% to 198.60 Wp from the rated power for 190 A, and by approximately 5.10% to 199.70 Wp for 190 B. We verified that, considering the loss of electrical mismatch between the existing cell and the new cell, the higher power of individual cells had a greater effect on the power of the module.


**Table 6.** Electrical data of modules before and after recovery.

As mentioned in Section 3.2, when the difference in cell mismatch is not large, the loss due to mismatch is insignificant in the range 0.10–0.19%, and most (>80%) of crystalline photovoltaic modules are only approximately 0.27%/year on average. Therefore, it matches well with the result that predicted that the gain factor would have a greater impact on the final power output of the module than the loss factor [46,47].

Figures 5 and 6 show the I–V curves before and after power recovery for 190 A and 190 B, respectively. The results in Figures 5 and 6 show that Isc and Voc do not change significantly before and after module restoration and that the V–P curve is deformed by cell breakage, the FF is recovered, and the power of the module is restored.

**Figure 5.** I–V and V–P curves before and after power recovery for sample 190 A.

**Figure 6.** I–V and V–P curves before and after power recovery for sample 190 B.

As shown in Figures 5 and 6, both the cell-in-hotspot-specific stepped I–V and multipeak-shaped V–P curves are recovered.

Figures 7 and 8 show a brief circuit diagram of module 190 A before and after recovery, respectively. In the figures, *Iph* represents the solar irradiance and *Ipv* represents the power

output current. *D*1, *D*2, and *D*<sup>3</sup> denote bypass diodes #1–#3, respectively, and *Rs* denotes the series resistance.

**Figure 7.** Sub-circuit diagram of 190 A before recovery.

**Figure 8.** Sub-circuit diagram of module 190 A after recovery.

In the EL image of Figure 7, nine cells were cracked, resulting in resistance loss. In this case, the ratio of shaded (or inactive) areas causing hot spots in the cell increased proportionally with the range of inactive areas between 20% and 50%. If the resistance becomes excessively large over a greater range or if the bypass diode is short-circuited [48], it causes 100% power loss to the entire connected string [49,50]. A part looks relatively brighter around the interconnector immediately next to the dark area of the damaged cell, and the current is concentrated on a part of a cell with relatively low resistance owing to cracks; thus, power loss occurs in the shaded and connected cells.

Figure 8 shows the EL of the module whose power was recovered after the cell replacement of the 190 A sample and its diagram. The picture for 190 B is repeated, so I omit it.

#### *3.4. Comparative Analysis of Power Recovery Results and Predicted Values*

Table 7 shows the difference between the predicted power output value obtained using the CTM analysis before module recovery and the value measured after cell replacement.


**Table 7.** Comparison of predicted and experimental values.

Even when applying the power deviation when manufacturing a module, both cases exhibited a positive deviation; therefore, the loss, such as electrical mismatch, in the CTM factor was considered conservative among the possible ranges. The CTM power analysis results at 190 A are shown in Figure 9.

**Figure 9.** CTM power analysis for a recovered module (190 A).

The sum of the power of the initial and replacement cells was defined as 200.32 Wp using the values calculated in Equation (1) and Table 4, and when CTM factors were applied, the predicted value of 198.60 Wp was determined. Here, if 2.20 Wp, i.e., the difference from the experimental results, was reflected, it was analyzed, as shown in Figure 9. The difference between the predicted and experimental result for 190 A was 1.12%, which fell within 3% of the power output tolerance value of the initial module. The analysis result of sample 190 B indicated that the error was larger. Figure 10 shows the CTM power analysis of the recovered module (190 B).

Sample 190 B was of the same grade as 190 A, and because there were fewer replacement cells (six), the power acquisition from the replacement cell was smaller than that at 190 A; therefore, the total power output of the cell was calculated as 197.52 Wp. In addition, the numbers of remaining cells in 190 A and 190 B were 44 and 48 cells, respectively; thus, the long-term degradation was then calculated to be −0.47 Wp, which is greater than −0.34 Wp for 190 A. The experimental value was 199.70 Wp, i.e., 6.20 Wp higher than the predicted value of 193.50 Wp. This is approximately 3.20% higher than the predicted value of 3% or more, which is the power output tolerance value of the initial module.

**Figure 10.** CTM power analysis for a recovered module (190 B).

#### *3.5. Analysis of Prediction Error and Correction of Prediction Value Reflecting Initial Tolerance*

The error begins with the sum of the cell power output values. The final power value was 199.70 Wp, and the sum of the calculated cell power values was 197.52 Wp, which began with a difference of 2.18 Wp even if the CTM was assumed to be "0." The value 2.18 Wp was 1.15% of the initial rated power value of 190 Wp, which was within the allowable tolerance range of the module. Therefore, assuming that the initial use cells of 190 A and 190 B were the same, sample 190 B corrected the experimental deviation of 2.18 Wp. Those of 190 A were calculated by adjusting the number of cells to calculate the correction value of 2.00 Wp. Accordingly, the predicted power output values of 190 A and 190 B could be recalculated as listed in Table 8. The initial power output prediction value of sample 190 A was 196.4 Wp. For the power correction value of 1.998 Wp within the tolerance shown in the experimental result, the correction prediction value was 198.4 Wp. Additionally, the error decreased to 0.10% with the final experiment result of 198.6 Wp. When the initial power output prediction value of 193.5 Wp was corrected for 190 B, the corrected prediction value was 195.68 Wp, which was approximately 2.13% lower than the experimental result for 199.7 Wp.

**Table 8.** Analysis of predicted and experimental values.


When the tolerance value calculated above was added to the initial rated power, the initial power of the module was approximately 192.45 Wp. Based on this, the power before and after module recovery owing to cell damage and the recovery trend of the *FF* are shown in Figure 11.

**Figure 11.** Result of module recovery via cell replacement (power and *FF*).

Table 9 summarizes the initial, failed (before recovery), and recovered (after recovery) values of the power degradation module owing to cell cracking.


**Table 9.** Electrical data deviation of initial, faulty, and recovered module.

The characteristic of the recovery of the cell in the hotspot module by cell replacement is that the *Voc* value hardly changes step-by-step but decreases within the error range by step. The largest negative mismatch factor in the phase of the power drop to the cell in the hotspot was *Imp*, exhibiting a 29.43% decrease at 190 A compared with the initial value, which had the greatest impact on the power decrease of −21.69%. Even in sample 190 B, *Imp* degradation caused a −22.48% decrease in the cell in the hot spot stage, and a power degradation of −26.47% was also the largest factor. For a positive mismatch with a high power, the *Isc* and *Imp* values both increased, and the *Vmp* value decreased step-by-step at 190 A; thus, the factor that most affected the positive mismatch was the increase in Isc and *Imp*; the increase in *Imp*, in particular, was the largest factor. Figure 12 shows the EL images of samples (**a**) 190 A and (**b**) 190 B recovered by cell replacement, and (**c**) IR images measuring whether the module generated heat by installing them again in the power plant.

**Figure 12.** Images of the recovered module (190 A, 190 B). (**a**) is an EL image of the repaired 190A module, and (**b**) is an EL image of the repaired 190B module. (**c**) is an IR image of 190A and 190B re-installed at the plant.

A difference in brightness was observed between the replaced and existing cells in the EL images shown in Figure 12a,b, but in Figure 12c, no significant heat generation was observed in the IR image at the installation site. The IR camera used to measure cell heat generation was a Ti400 FLUKE equipment.

Thus, we confirmed the restoration potential of modules that are underpowered by cells in hotspots in commercial power plants. When some cells are damaged in a crystalline PV module, the module can be restored by replacing those cells instead of discarding the entire module. Assuming that this method restores more than 180 sheets per day on a 200-Wp module basis, the cost of restoring the module is approximately 0.17 \$/Wp. This is slightly more than half of the recent crystalline module price of 0.30 \$/Wp. However, for commercial use, a long-term reliability test of a module repaired using this method must be performed to confirm the results. Accordingly, reuse of modules instead of recycling will be an economical and eco-friendly alternative.

#### **4. Conclusions**

In this study, the power loss caused by the damage of a cell in a module was determined through EL images and I–V and V–P curves of the module, and research was conducted to recover only the damaged cells to be equal to or higher than the initial power of the module. The recovery of modules is important in the electrical serial–parallel design and application of existing structures in PV power plants. Therefore, the grade of the cell applied at the time of module production was calculated using the CTM factor analysis method and applied considering the dimensions and tolerance of the specification sheet of the module presented by the manufacturer. To predict the power of the recovered module, the power degradation factor from the aging factor of the module, not in the existing CTM formula, and the mismatch loss of the cell were checked again and recalculated. The results of the power output prediction calculated using the formula and the power output of the recovered module measured as the experimental result had an error of 1.12% in sample 190 A and 3.20% in sample 190 B. This was determined to be an error, assuming that the rated power output was the initial power output, because the accurate power output of the initial module was unknown. As a result of calibrating the power of approximately 2 Wp by feeding back the initial tolerance from the recovered module power output, the revised prediction was calculated as 198.40 Wp in 190 A and 195.68 Wp in 190 B, and the experimental results indicated error rates of 0.10% and 2.01%, respectively. This study confirmed that even when a replacement cell applied to the recovered module had an average power output of approximately 19.60% (4.28 Wp) higher than that of the existing cell, and Isc had an average value of approximately 8.98% higher (8.62 A), the loss of

electrical mismatch did not significantly affect the power, and heat generation of existing normal cells was not observed. In addition, even for modules operated for a long time (>10 years), the power reduction rate is significantly smaller than the 0.70%/year suggested by the module manufacturers. Even if a degradation of approximately 2.40% over 10 years was applied, there was no significant error in the power prediction. As the life of a PV module increases, the recovery technology for discontinued modules becomes a very important economic factor for PV power plants with a considerable remaining operating period. Module recovery technology through cell replacement is useful as an economical reuse and high-value-added technology to prevent power degradation in an operating power plant. A technology to recover a module function by selectively replacing only the necessary cells and recovering a module function, even when it has expired commercially, would be significantly more economical than decomposing and collecting it as raw material. We believe that in future studies, work should continue to verify the effect of electrical mismatch in a wider range of cells on modules as well as the long-term reliability to predict the lifetime of restored modules.

**Author Contributions:** Conceptualization, formal analysis, writing—original draft preparation, K.L.; investigation, data curation, S.C.; project administration, J.Y.; supervision, project administration, H.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study received no external funding.

**Acknowledgments:** This research was supported by grants from the New and Renewable Energy Technology Development Program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korean Ministry of Trade, Industry, and Energy (MOTIE) (Project No. 20203030010060 and 20213030010400).

**Conflicts of Interest:** The authors declare no conflict of interest.
