**1. Introduction**

Renewable energy, including photovoltaic power generation, has steadily increased globally through [1,2] continuous cost-cutting efforts based on eco-friendly elements and low maintenance costs [3,4], despite the high costs and relatively low economy in the early stages of its implementation [5]. Owing to economic security and increased supply of renewable energy [6,7], the achievement of grid parity has recently accelerated [8,9], with a certain percentage of fossil fuel usage steadily being replaced by renewable energy

**Citation:** Lee, K.; Cho, S.; Yi, J.; Chang, H. Prediction of Power Output from a Crystalline Silicon Photovoltaic Module with Repaired Cell-in-Hotspots. *Electronics* **2022**, *11*, 2307. https://doi.org/10.3390/ electronics11152307

Academic Editors: Luis Hernández-Callejo, Jesús Armando Aguilar Jiménez and Carlos Meza Benavides

Received: 23 June 2022 Accepted: 22 July 2022 Published: 24 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

usage, and hence, the total use of renewable energy has increased over the past decade [10]. Expanding the solar energy supply may reduce carbon dioxide emissions and achieve a healthy mix of energy sources to overcome the climate crisis [11,12]. However, the increasing demand for solar energy may cause shortages of the resources used in the advanced production of solar modules [13–15]. In particular, owing to the scarcity of resources such as silver, indium, and bismuth, target material consumptions of 2, 0.38, and 1.8 mg/Wp [16,17], respectively, have been proposed; thus, a significant reduction in material consumption is required to expand renewable energy supply [18].

The large-scale installation of photovoltaic modules results in the problems of economic use of resources during production and processing of waste modules after use [19,20]. By 2050, 80 million tons of accumulated photovoltaic modules are expected to reach their service life worldwide, with 10 million tons in the US alone [21]. With the rapid increase in the installation of photovoltaic modules in countries such as China, the collection and recycling of end-of-life photovoltaic modules is becoming an important task, and various methods of building efficient recycling systems are being investigated [22]. According to previous studies, the predicted accumulated waste that will be generated from 2020 to 2080 in existing solar power plants varies in proportion to solar installations, and is expected to peak at 130,000 tons in 2051 and 141,297 tons in 2054 [23]. Currently, the life of a photovoltaic module is approximately 20–30 years; therefore, the life of photovoltaic modules installed in the early 2000s will expire on a large scale, and the disposal of waste modules will increase rapidly. Photovoltaic modules consist of expensive materials, such as aluminum, silver, copper, tin, and silicon wafers. In addition, they can be used as highly attractive recycled materials in terms of the environmental charges imposed when filling landfills. In the recycling process of a general photovoltaic module, research has primarily focused on recycling by collecting silicon wafers and refabricating them into optimized silicon solar cells [24,25], pyrolyzing organic materials such as ethylene vinyl acetate (EVA) [26], and removing organic materials such as glass and ribbon metals [27,28]. As a research example on recovering the performance of photovoltaic modules, a technology for recovering the insulation resistance of aging modules by injecting coatings based on polyurethane, epoxy, silicone, and synthetic rubber of crystalline photovoltaic modules was introduced [29,30]. However, recycling or reuse technology generally involves removal of frames, junction boxes, or cables, etc., from crystalline photovoltaic modules, followed by thermal or chemical decomposition of the laminated module to collect glass, silicon, metal, and polymer [31,32].

This recycling technology is not currently widely used because it is expensive and the return on investment (ROI) is less than approximately −0.25 as of 2022 [33]. In addition, the recycling method, which involves collecting the raw materials separately, is not applicable to the recovery of damaged modules in an operating power plant because the failure of a part of the module results in the crushing of other usable parts. Accordingly, this paper proposes a technology to recover photovoltaic modules at the same or a higher level of the initial power value by replacing cells at a safety risk, such as power loss and hotspots, owing to damage to some cells of an aged silicon photovoltaic module. Most commercial solar power plants receive subsidies from the government. In this case, only certified modules of a particular model should be used during the generation period. If the module fails, it cannot be replaced by another model. Moreover, owing to the rapid improvement in cell efficiency every year [34,35], the module model continues to change. In commercial power plants, restoring the output of a module by cell replacement is very useful. Technological advancements in the restoration of the module result in a power deviation between the initial and new cell [36,37]. Therefore, when replacing a cell with a new cell having a higher power, the possibility of an electrical mismatch loss occurring should be considered, and the long-term power degradation of the initial cell should be confirmed. Hence, the purpose of the experiment was to determine the extent to which the output improvement of the new cell is reflected in the output of the module to be restored. Previous studies have shown that the prediction of power mainly includes power

degradation in modules with hotspots or how much power decreases as a result of EL in modules with potential-induced degradation (PID) [38,39]. However, the purpose of this study was to predict the improvement to power through replacement of damaged cells in a module, which has not been attempted before. The results of this study suggest that the energy and environmental costs of recycling modules can be significantly reduced by reusing waste modules in more diverse states.

#### **2. Experiments**

#### *2.1. Methods and Procedures*

The overall experiment was conducted in the following order: module power output and defect verification, calculation of grade of originally applied cells, grade verification of replacement cells, power prediction, module power recovery, comparison of predicted power output and experimental results, and application of correction values. First, the defects and power output of the module to be recovered were checked via electroluminescence (EL) measurement and a sun-simulator. EL measurements are used to identify internal defects that cannot be visually identified using EL in solar cells. Table 1 provides the nomenclature for the electrical characteristics of the module.

**Table 1.** Nomenclature for the electrical characteristics of the module.


The current corresponding to the cell *I*sc and the voltage at the same level as the module *V*oc were applied for the measurement. EL images of the module were captured in several parts of a darkroom, recollected, and displayed on a screen. The EL equipment manufactured by MC Science in Korea was used for the measurements. The simulator measures the module's *Isc*, *Voc*, *Pmax*, etc., under the standard test condition (STC) at 25 ◦C, 1 Sun (1000 W/m2), and air mass 1.5, and corrects the actual temperature to output the calculated value to the screen. The equipment used in this study was a Spire-Nissinbo Sun Simulator. The equipment was calibrated for proper use in the certification test of the photovoltaic module by receiving the AAA in three evaluation items: uniformity, stability, and spectrum. Measurements of power output from equipment are displayed in various ways, i.e., 1–4 digits after the decimal point; however, in this study, the third digit after the decimal point was rounded to two digits to maintain consistency. The CTM (cell to module) factor calculation method was applied to the power analysis of the cells used at the time of manufacturing the target samples and the review of the cells to be replaced [40]. The grade of the applied cell was inversely calculated based on the initial power output of the module disclosed on the Internet by the manufacturer. The module power after cell replacement was predicted after checking the grade of the cell to be replaced.

The CTM coefficient k-factor calculation method was used to analyze the power of the original cell of the target samples and review the replacement cell. Manufacturing modules from cells, models, and formulas for classifying the CTM coefficient k-factor, which affects efficiency or power, and analyzing loss or acquisition mechanisms have been presented in previous research [41,42]. If the dimension data and rated power of a module released by the module manufacturer are the initial power outputs of the module, the module efficiency is calculated to be 13.6%. Because the module power output is calculated from the sum of the CTM coefficient k factor and the initial solar cell power in the module power output calculation model, the power output of the module can be calculated using Equations (1) and (2) [41,43]. The factors *i* and *m* in Equations (1) and (2) are variables of the routinely used pie function, and refer to the extension of the CTM factor. The CTM k-factor consisted of 15 types: *k*<sup>1</sup> (module margin), *k*<sup>2</sup> (cell spacing), *k*<sup>3</sup> (cover reflection), *k*<sup>4</sup> (cover absorption), *k*<sup>5</sup> (cover/encapsulant reflection), *k*<sup>6</sup> (encapsulant absorption), *k*<sup>7</sup> (interconnection shading), *k*<sup>8</sup> (cell/encapsulant coupling), *k*<sup>9</sup> (finger coupling), *k*<sup>10</sup> (interconnector coupling), *k*<sup>11</sup> (cover coupling), *k*<sup>12</sup> (cell interconnection), *k*<sup>13</sup> (string interconnection), *k*<sup>14</sup> (electrical mismatch), and *k*<sup>15</sup> (junction box and cabling). The meaning of *I* = 3−*m* in the ∏-function of Equation (1) means CTM k-factor from k3 to k15. Then, the sum of the cell power outputs from *j* = 1−*n* from the ∑-function is the number *n* of cells applied to the module.

$$P\_{module} = \prod\_{i=3}^{m} k\_i \cdot \sum\_{i=1}^{n} P\_{cell,i} \tag{1}$$

$$\text{CTM}\_{power} = \prod\_{i=3}^{m} k\_i \tag{2}$$

In terms of module efficiency, factors affecting the entire area of a gap module between modules are important; however, when a module is produced from a cell, a design margin (*k*1) to ensure an electrical insulation distance and a loss factor (*k*2) owing to the cell interval are not related to a power change. The module efficiency can be expressed by Equations (3) and (4) [41].

$$\eta\_{module} = \frac{P\_{module}}{E\_{STC} \cdot (A\_{module} + A\_{cell\ spacing} + A\_{cells})} \tag{3}$$

$$
\eta\_{modulc} = \overline{\eta\_c} \cdot (k\_1 + k\_2 - 1) \cdot \prod\_{i=3}^{m} k\_i \tag{4}
$$

Therefore, according to this model, the module efficiency is proportional to the average efficiency of the cell rather than being dominantly affected by the lowest efficiency. The average efficiency of the cell was calculated by considering the electrical mismatch loss (*k*14) of the cell to predict the power output of the module to be restored. For the loss caused by the electrical mismatch of cells, studies were published prior to research on the CTM factor, and the widely known definition of RPL is expressed as the difference between the maximum power (*Pmpc*) of *n* individual cells connected in series to form a cell string or module. RPL can be expressed as Equation (5) from the difference between the sum of the maximum power of all cells and the maximum power of the module.

$$RPL = \frac{\sum\_{i=1}^{n} \cdot P\_{mpii} - P\_{module}}{\sum\_{i=1}^{n} \cdot P\_{mpii}} \tag{5}$$

In theory, when individual cells operate completely independently, the maximum power output is denoted as *P max*, and when the average cell power output value in a group is *Pmax*, the calculation of RPLB (relative power loss of a module using Bucciarelli's equation) is as shown in Equation (6).

$$RPL\_B = \frac{P\_{\max}^{\prime} - P\_{module}}{n \cdot I\_{mp}^{-} V\_{mp}^{-}} \tag{6}$$

The power output after cell replacement and the state inside the module were also confirmed using the EL and Sun simulators. The cell replacement process is discussed in the next section. After cell replacement, the gain factor (power increment of the replacement cell), loss factor (long-term degradation, electrical mismatch), and unidentified tolerance parts of the module track the experimental results and apply the same to the two samples, correct the power predictions, and finally compare them with the results.
