The Mechanism of the Semi-Transparent Coverings Affecting the Power Generation Capacity of the Photovoltaic Module and Array

Abstract

Shading on photovoltaic (PV) modules due to shadows, covering, dust, etc., usually characterized as semi-transparent, will significantly affect the power generation capacity. No systematic study has considered the impact of semi-transparent coverings on the power generation capacity of PV modules. This paper covers a single cell in the PV module using a covering with a transmittance of 18.55% and systematically investigates its impact on the power generation capacity. The open-circuit voltage (V_oc) of the PV module is nearly unaffected by semi-transparent coverings because the covered cell can be considered as working at a lower irradiance and thus can output a voltage close to that of the uncovered cell. The short-circuit current (I_sc) is significantly affected by coverings because it is co-contributed by the photocurrent (evaluated based on the covering ratio R and transmittance) and the reverse bias current ΔI_sc (the covered cell is in a reverse bias state). The ΔI_sc increases with R because more charge accumulates at the bi-ends of the covered cell; but, it decreases at full covering, which implies that in a partially covered case the uncovered part contributes more to ΔI_sc than the covered part. The fill factor (FF) of the PV module first increases and then decreases with R, as the equivalent resistance of the covered cell increases rapidly with R, which replaces the wire resistance in dominating the series resistance of the PV module when R > 0.6. This work is of great theoretical significance in analyzing the output characteristics of PV modules under real conditions.

1. Introduction

New energy sources, such as photovoltaics (PVs), are rapidly replacing traditional fossils as the dominant energy sources. In 2022, the International Energy Agency (IEA) predicted that global solar-powered electricity supply will increase to 11.5% by 2030 and may reach 24.3% by 2050 [1]. Japan’s RTS Corp predicted that PV power generation in Japan will account for around 15% of the country’s domestic power generation by 2030 [2]. China plans to have 1030 GW of installed solar power capacity by 2030 [3]. As of June 2023, China’s cumulative installed PV capacity reached 470 GW [4]. The cumulative installed capacity of distributed PVs has reached 198.22 GW, accounting for 42.17% of all solar installations [5]. Distributed PVs will be among the most important components of future PV power generation and applications [6]. In the first half of 2023, China’s new installed capacity of distributed PVs amounted to 40.963 GW, accounting for 52.23% of the total installed PV capacity [5].

The most important installation scenarios for distributed PVs are around the electricity users, such as roofs and building surfaces [7,8,9,10,11], which are more prone to being covered than centralized PVs in open and remote areas. Covering from objects such as bird droppings [12,13], leaves [14], dust [15,16], and passing clouds [17,18,19] are often unavoidable. Covered cells not only have a degraded output power but also give significant output power loss over the entire module or even the array through the series-parallel amplification effect [20]. For example, Alonso-García [20] found that fully covering a single cell in a module with by-pass diodes results in a 79% power loss of the module. In addition, the covered cells experience the hot-spot effect, causing localized module heating, which can damage modules and even cause fire [21,22].

There are several existing studies on the large-area covering and energy loss in PV modules. For dust uniformly covering the module, Sulaiman et al. [15] experimentally explored the effect of different dust compositions on the power generation capacity of PV modules and compared the power degradation. The power degradation of the mud-covered modules under 250 W/m² irradiance conditions can be up to 18% or more. Fan et al. [16] proposed a coupling model for dust density, dust particle size, and PV conversion efficiency. They provided a method for evaluating the power generation of PV systems with higher accuracy, and the results demonstrated that dust accumulation significantly inhibits the power output of PV panels. The PV panel performance degradation depends primarily on the dust composition, particle shape, size, and coverage. At 350 W/m² irradiance, the maximum power degradation of PV panels is 65.45% when the cement coverage of the surface is 10.80 g/m².

There are also several existing studies on the localized covering smaller than a single cell area and the behavior of PV modules. It is widely known by researchers who work with the behavior of modules that the covered cell in the PV module is polarized with reverse voltage. In a study on the I–V characteristics of modules under reverse bias, Volker Quaschning et al. [23] introduced an extension term for the avalanche effect to represent the characteristic curves of modules in the negative breakdown region. Tae Hee Jung et al. [24] used a single-diode model, considering the potential difference between partially covered modules and overall low-radiation modules, to express the rapid decrease in current near the open-circuit voltage for partially covered modules and predicted I–V characteristics of modules with partial covering on a single cell.

The most common types of covering in distributed PVs, such as shadows from power wires and bird droppings, do not completely cover the cell. That is to say, some coverings on the PV modules are semi-transparent. Therefore, the cell surface can still receive some irradiance, and the covered cell has a certain output capacity. Despite the prevalence of sub-cell-sized semi-transparent localized coverings within PV modules, there is a notable paucity of research focusing on the mechanisms by which such coverings detrimentally impact module performance. Present-day investigations into the output characteristics of modules subjected to localized covering often overlook the distinct effects of different parts of the covered cell. This oversight can result in imprecise forecasts of the photovoltaic module’s current–voltage (I–V) curves and thermal dynamics. A systematic study of the mechanisms of semi-transparent coverings affecting the power generation capacity of PV cells, modules, and arrays is important for analyzing and evaluating the power output characteristics of PV modules.

This paper uses an obstruction with 18.55% light transmittance as the semi-transparent covering material to simulate the common covering situation of distributed PVs where a single cell in the module is covered. This study explores the mechanism of how coverings affect the power generation capacity of PV cells, modules, strings, and arrays under different covering ratios Most notably, the different contributions of the covered and uncovered parts to the solar cell reverse bias current were first revealed. This work is of great theoretical importance for siting, fault diagnosis, operation, maintenance, and power generation predictions of distributed PVs.

2. Research Processes and Methodologies

2.1. Experimental Design

Eighty polycrystalline silicon solar cells, using PERC technology with an area of 15.6 × 15.6 cm² and I_sc = 8.353 A, V_oc = 0.570 V, and P_max = 2.272 W under standard test conditions, were series-welded to form four modules, labeled modules 1–4, (as shown in Figure 1a). Modules 1 and 2 are connected in series to form the PV string 12, modules 3 and 4 are connected in series to form PV string 34, and the PV array is formed by connecting PV strings 12 and 34 in parallel (as shown in Figure 1b). Material with a transmittance of 18.55% was used to simulate obstruction in a distributed PV array.

The I–V characteristics of each module, string, and array were measured. The effects of covering on the power loss of modules, strings, and arrays when a cell (as shown in Figure 1c) in module 1 was covered was explored, and the effect of power loss by the covering was examined. The micro-mechanisms by which semi-transparent covering affected the I–V characteristics of the modules, strings, and arrays were investigated.

2.2. Research Processes

Figure 2 shows the whole research processes in this work. At first, we investigated the mechanism of a semi-transparent covering on the output characteristics of a single cell. The output power and I–V characteristics of the cell were measured under different covering ratios and irradiances, and the relationships between them were analyzed.

We then measured the output powers and I–V characteristics of the PV module and investigated the mechanisms of the semi-transparent covering on the output characteristics of PV module. (1) The mechanisms of the current, voltage, and FF of the module were analyzed under different covering scenarios. (2) The I–V characteristics of the module under different covering ratios were investigated using the I–V of a single cell as a standard to reveal the mechanism for the series mismatch loss incurred when connecting single cells in series to form a module.

Finally, we measured the output powers and I–V characteristics of the PV strings and the PV array and investigated the mechanism of a semi-transparent covering affecting the output characteristics of the PV string and array.

The I–V curve acquisition equipment comprised a DC electronic load (ITECH IT8813B) and an automatic data acquisition system (ITECH IT9380). The irradiator from lailx New energy technology Co., Ltd., Suzhou, China, was used to measure the sunlight irradiance. The experiments were performed outdoors with an environmental temperature of 25 °C (±1 °C). The angle of the modules was adjusted so that the solar cells received irradiances of 250 W/m², 500 W/m², and 750 W/m². The following outputs were measured as shown in Figure 2: (1) the I–V curves of a cell under various covering ratios from 0 to 1 with an interval of 1/5; (2) the I–V curves of PV module 1 when a certain cell was covered by ratios from 0 to 1 with an interval of 1/5; and (3) the I–V curves of the PV string and array when a certain cell was covered by ratios from 0 to 1 with an interval of 1/5.

3. Results and Discussion

3.1. Output of a Single Cell under Semi-Transparent Covering

We first examined and determined the mechanism by which the output power of a single cell is affected by the covering ratio with a semi-transparent partial covering. The results are the basis for subsequent investigations of the I–V characteristics for PV module, string, and array.

Table 1. Output power, power loss, and loss ratio of a single PV cell at different irradiances and covering ratios.

Covering Ratio	P (W/m2)	Ideal Power (W)	Power (W)	Power Loss (W)	Loss Ratio	Theoretical Loss Ratio
0	250		0.775	-	-	0%
	500		1.507	-	-
	750		2.159	-	-
1/5	250	0.775	0.664	0.111	14.32%	16.29%
	500	1.507	1.248	0.259	17.19%
	750	2.159	1.848	0.311	14.40%
2/5	250	0.775	0.519	0.256	33.03%	32.58%
	500	1.507	1.037	0.470	31.19%
	750	2.159	1.507	0.652	30.20%
3/5	250	0.775	0.388	0.387	49.94%	48.87%
	500	1.507	0.772	0.735	48.77%
	750	2.159	1.117	1.042	48.26%
4/5	250	0.775	0.276	0.499	64.39%	65.16%
	500	1.507	0.548	0.959	63.64%
	750	2.159	0.797	1.362	63.08%
1	250	0.775	0.154	0.621	80.13%	81.45%
	500	1.507	0.324	1.183	78.50%
	750	2.159	0.459	1.700	78.74%

gives the output power, power loss, and power loss ratio of single PV cells with covering ratios from 1/5 to 1 and irradiances of 250–750 W/m². In the table “Ideal power” means the measured power output without a covering; “Power” is the actual measured power output; “Power loss” is the difference between “Ideal power” and “Power”; and “Loss ratio” is defined as the ratio of “Power loss” to “Ideal power”. The theoretical power loss ratio of a single solar cell is calculated based on the covering ratio and transmittance as covering ratio × (1 − transmittance) = covering ratio × (1 − 18.55%) = covering ratio × 81.45%.

The “Loss ratio” of a single cell is approximately proportional to the theoretical power loss ratio. The second-to-last column of Table 1 indicates that under different covering ratios, the “Loss ratio” of a single cell is not strongly related to the irradiance. This suggests that in covered cells, the covered and uncovered portions have a parallel connection, consistent with Smokler’s description [25].

Figure 3a provides the output I_sc of an uncovered single cell with irradiance. Although the output I_sc of the cell is nearly linear with the irradiance, the degree of deviation from linearity gradually increases with irradiance (Figure 3a). Even with the three-row probe testing process (Figure 3c), it is still difficult to circumvent the series resistance in the measurement circuit. According to Figure 3b, higher irradiance leads to a larger current I, which in turn leads to a greater voltage drop across the series resistance. Thus, a smaller voltage was measured by the I–V meter, affecting the test results (higher irradiance gives smaller FF).

Based on Figure 3b, it is inferred that the effect of the wire resistance (series resistance) gradually weakens as the irradiance decreases. This inference can be confirmed by the proportion of power loss of a single cell in the case of full covering.

Based on the transmittance, the power loss ratio of the cell under full covering is about 100 − 18.55% = 81.45%. From Table 1, the power loss ratios are 80.13%, 78.50%, and 78.74% for irradiances of 250 W/m², 500 W/m², and 750 W/m², respectively. The 250 W/m² irradiance “Loss ratio” is closer to the estimated value based on the transmittance. Therefore, we used the irradiance condition of 250 W/m² throughout this study. In addition, with 20 cells in series in the module, the reliability of test results can be further ensured. This is because if we assume the wire resistance remains constant, the share of its voltage drop V_s = R_s·I in the output voltage of the module will be weakened to about 1/20 of that in a single cell case.

3.2. Output of PV Module under Semi-Transparent Covering

3.2.1. Output of the PV Module When One Cell Is Fully Covered

A PV module is the basic unit for PV power generation, in which single cells are connected in series/parallel to meet the higher output voltage and current. According to the theory of Wenham et al. [25], when a cell in a PV module is covered, the output voltage of the module is unaffected. However, the output current will be limited by the current of the covered cell. Figure 4 shows the current–voltage curves and power–voltage curves of PV module 1, where one cell is covered by various ratios, as denoted in Figure 1c, under irradiance of 250 W/m². For quantitative description, the I_sc, V_oc, FF, and actual power of PV module 1 are listed in

Table 2. Outputs of PV module 1 at irradiance 250 W/m², where a cell is covered by various ratios.

Covering Ratio	Isc (A)	Voc (V)	FF	Ideal Power (W)	Actual Power (W)	Power Loss (W)	Loss Ratio
0	2.258	11.255	0.607	15.495	15.278	0.217	1.40%
1/5	2.102	11.125	0.632	15.495	14.816	0.679	4.38%
2/5	1.967	11.165	0.648	15.495	14.200	1.295	8.36%
3/5	1.618	11.120	0.651	15.495	11.731	3.764	24.29%
4/5	1.293	11.187	0.600	15.495	8.679	6.816	43.99%
1	0.675	11.223	0.352	15.495	2.666	12.829	82.79%

. Here, the “Ideal power” is calculated by multiplying the ideal power of a single cell (as listed in Table 1) by the number of cells in series, which is 20.

From Figure 4 and Table 2, it can be observed that the open-circuit voltage (V_oc) of the module with a semi-transparent covering is approximately 11.223 V. Compared to the module without a covering, whose V_oc is around 11.255 V, they are nearly equal. This is consistent with the findings of Wenham et al. [25]. This is because the covered cells with a semi-transparent covering operate equivalently to uncovered cells operating at 18.55% irradiance, and their V_oc values are nearly identical. If the effect of reverse bias on the current of the covered cell is not considered, the I_sc of the module can be evaluated as I_sc-uncovered × transmittance = 2.258 × 18.55% = 0.419 A, where I_sc-measured is the measured short-circuit current. However, the measured I_sc of the module, 0.675 A, is higher than the evaluated value and 1.615 times the theoretical estimate. Such a phenomenon can be attributed to the fact that the uncovered cells in series provide a sufficiently large reverse bias voltage to the covered cell. This causes the covered cell to approach a reverse breakdown state, resulting in a reverse bias current that is greater than the reverse saturation current.

Table 2 indicates that the FF of the module decreases dramatically (from 60.71% to 35.20%) when the cell is completely covered. This is because the covered cell can be equivalent to introducing a large series resistance into the module (allowing the uncovered cell to operate at a low current), decreasing I_sc while dramatically decreasing FF. Comprehensively, when a cell in the module is completely covered, the V_oc is nearly the same as that of the uncovered case, and the I_sc is 1.615 times higher than that calculated based on the transmittance, while the FF decreases from 60.71% to 35.20%. Therefore, the output power of the module is lower than that theoretically predicted according to the transmittance (15.495 W × 18.55% ≈ 2.874 W vs. 2.666 W).

3.2.2. Impact of Covering Ratio on the Output of the PV Module

When the cell denoted in Figure 1c is partially covered, as shown in Table 2, the V_oc of PV module 1 is generally stable around 11.26 V, having no apparent correlation with the covering ratio, as mentioned above. The I_sc and FF of the module exhibit complex variations with changes in the covering ratio. To analyze the impact of the covering ratio on the I_sc of the PV module, we first define a physical quantity, called the reverse bias current ΔI_sc, to represent the current flowing through the covered cell caused by the reverse bias voltage provided by the uncovered cells in series. This term is calculated as

$$\Delta I_{sc}=I_{\mathit{sc-measured}}-I_{\mathit{sc-evaluated}}$$

(1)

where I_sc-measured is the measured short-circuit current, and I_sc-evaluated is the short-circuit current evaluated based on the covering ratio, R, and transmittance of 18.55%.

$$I_{\mathit{sc-evaluated}}=I_{\mathit{sc-uncovered}}\times \left(1-R\right)+I_{\mathit{sc-uncovered}}\times R\times 18.55\%$$

(2)

where I_sc-uncovered is the short-circuit current of the PV module measured for the uncovered condition. Equation (2) implies that the covered and uncovered parts in covered cells are in parallel [24].

The trends of I_sc and ΔI_sc with the covering ratio are given in Figure 5. The ΔI_sc increases gradually with the covering ratio but decreases rapidly at full covering. This is because the increased covering ratio creates more charge accumulation at the bi-ends of the covered cell, resulting in a larger reverse bias voltage and a larger ΔI_sc. Whereas, the rapid decrease in ΔI_sc at full covering implies that the uncovered part of the cell also provides the reverse bias current and contributes more than the covered area. This is because illumination increases the carrier concentration in the uncovered part of the cell, and the p–n junction is more susceptible to reverse breakdown.

To better illustrate that the current of the module is affected by the joint influence of the covered and uncovered portions of a single cell, we give the relationship between ΔI_sc and the covering ratio R based on the basic assumption that the covered and uncovered parts in the cell are connected in parallel [26]:

$$\begin{array}{l}\Delta I_{sc}=R\times A_1\times \{\exp \left[q\cdot t\cdot \left(R+B_1\right)/\left(K_{B}T\right)\right]+C_1\}\\ +\left(1-R\right)\times A_2\times \{\exp \left[q\cdot t\cdot \left(R+B_2\right)/\left(K_{B}T\right)\right]+C_2\}\end{array}$$

(3)

where the first and second terms on the right side represent the reverse bias currents due to the covered and uncovered parts, respectively. We fit the equation for the reverse breakdown current of the p–n junction using an exponential form. The parameter A is the reverse saturation current with respect to the carrier concentration. t·R denotes the magnitude of the reverse bias voltage, t·B denotes the required reverse breakdown voltage, and C ensures that the curve crosses the 0 point. We then fit the parameters A, B, t, and C with the relationships between ΔI_sc and covering ratio R under 250 W/m² irradiance. The fitting results are

$$\begin{array}{l}\Delta I_{sc}=R\times 0.142\times \{\exp \left[q\cdot 0.026\cdot \left(R-0.500\right)/\left(K_{B}T\right)\right]-0.046\}\\ +\left(1-R\right)\times 0.601\times \{\exp \left[q\cdot 0.026\cdot \left(R+0.044\right)/\left(K_{B}T\right)\right]-1.073\}\end{array}$$

(4)

It should be noted that in this paper the fitting equation for ΔI_sc is specific to the modules used. Therefore, for commercial photovoltaic modules, targeted system measurements and data fitting are required to give ΔI_sc versus covering ratio of cell for a specific commercial module. The mechanism of Equations (3) and (4) are applicable to all crystalline silicon solar cells, albeit with potentially different specific values.

The uncovered part has a greater impact on the ΔI_sc, as shown in Figure 5, consistent with the previous inference.

The FF of the module has a complex relationship with the covering ratio, as shown in Figure 6, which tends to increase and then decrease with the covering ratio. The FF of the module changes with the covering ratio because it is affected primarily by the series resistance and the module current. The increased covering ratio leads to a decreased module current. Thus, the voltage drop of the wire resistance (series resistance) of the uncovered cell decreases [proportional to (1 − R)], causing the FF to increase. However, an increased covering ratio leads to a corresponding increase in the charge accumulation at the bi-ends of the covered cells. An increased reverse bias voltage [proportional to R] corresponds to a greater equivalent resistance of the covered cells, causing FF to decrease. When the covering ratio is larger than a certain value, maybe 0.6 for a silicon solar cell, the dominant factor for FF seems to change: the equivalent resistive voltage drop accelerates for the covered cell with an increased covering ratio, resulting in the FF of the module to decrease with the covering ratio. When the cell is fully covered, the “preferred channel” for its reverse bias current (high carrier concentration region that is not covered) disappears. Therein, the module series resistance is the largest, and the FF is the smallest.

3.3. Output of PV String and Array under Semi-Transparent Covering

The cell connection method of the PV string is similar to that of the PV module (Figure 1), except it is formed by connecting more cells in series. Therefore, the mechanism of its I–V characteristics with the proportion of cell covering are similar to those of the PV module. As shown in

Table 3. The output parameters of PV module 1 and PV string 12 at irradiance 250 W/m².

Covering Ratio	Isc (A)		Voc (V)		FF
	Module	String	Module	String	Module	String
0	2.258	2.221	11.255	22.040	0.601	0.607
1/5	2.102	2.184	11.125	22.039	0.634	0.612
2/5	1.967	2.109	11.165	22.037	0.647	0.612
3/5	1.618	2.286	11.120	22.034	0.652	0.519
4/5	1.293	1.465	11.187	22.033	0.600	0.389
1	0.675	1.460	11.223	22.030	0.352	0.181

, the V_oc of PV string 12 is approximately equal to twice the voltage of module 1 in all cases. The current is larger than that of module 1 as the series connection of more cells provides a greater reverse bias voltage for the covered cells. The FF decreases compared with that of module 1, likely because the output characteristics of modules 1 and 2 are dissimilar due to detuning of the output characteristics.

The PV array consists of PV strings 12 and 34 in parallel. Based on

Table 4. The output parameters of the PV array with respect to string 12 and string 34 at 250 W/m².

Covering Ratio	Isc (A)			Voc (V)			FF
	Array	String 12	String 34	Array	String 12	String 34	Array	String 12	String 34
0	4.450	2.221	2.150	22.103	22.040	22.244	0.642	0.607	0.686
1/5	4.419	2.184	2.150	22.102	22.039	22.244	0.638	0.612	0.686
2/5	4.297	2.109	2.150	22.099	22.037	22.244	0.629	0.612	0.686
3/5	4.073	2.286	2.150	22.097	22.034	22.244	0.594	0.519	0.686
4/5	3.910	1.465	2.150	22.088	22.033	22.244	0.560	0.389	0.686
1	3.814	1.460	2.150	22.085	22.030	22.244	0.477	0.181	0.686

, it is apparent that the output current of the PV array is nearly identical to the combined output currents of PV strings 12 and 34, and the output voltage of the PV array closely approximates the average of PV strings 12 and 34. However, the FF of the PV array is better than that of PV string 12. This is because there is no covering in string 34, so the FF is better than that in the presence of covering. The parallel relationship indicates that the FF of the array should be between the values of the two strings.

4. Conclusions

This paper considers semi-transparent coverings that often occur in distributed PV installations. By welding 80 polycrystalline silicon solar cells into four modules and covering a single cell in one of the PV modules with a semi-transparent obstruction, the mechanism of how the covering affects the power generation capacity of PV modules was systematically investigated.

At first, the output characteristics of a single cell under the semi-transparent covering were investigated. It is found that the power loss ratio of a single cell is approximately proportional to the “covering ratio × (1 − transmittance)”. The relationship between irradiance and power loss ratio is small: when 3/5 of the area of the single cell is covered, its power loss rate is 48.77% under 500 W/m² irradiance conditions; under 750 W/m² irradiance conditions, its power loss rate is 48.26%. This indicates that the covered and uncovered parts of the cell are connected in parallel. Then, the influence of semi-transparent covering on the output characteristics of a module is studied. If one cell is fully covered in the module, the V_oc will be approximately equal to that without covering; however, the I_sc is larger than that of the PV module calculated based on the transmittance of the covering. This is because the uncovered cells in series provide a sufficiently large reverse bias voltage to the covered one, causing the covered cell to approach a reverse breakdown state and resulting in a reverse bias current. As the covered cell corresponds to introducing a large series resistance in the module, the FF of the module decreases substantially. Comprehensively, the actual output power of the module, 2.666 W, is lower than the theoretical prediction based on the transmittance, 2.874 W. When a cell in the PV module is partially covered, the V_oc shows little relationship with the covering ratio; however, the reverse bias current ΔI_sc caused by the reverse bias voltage increases gradually as the covering ratio increases but decreases rapidly at full covering. This is due to the uncovered part contributing larger than the covered part for the reverse bias current. The module FF increases and then decreases with the covering ratio of the single cell. This is because the FF is affected by the wire resistance and the equivalent series resistance simultaneously, and when the covering ratio is greater than 0.6, the dominant factor changes from the wire resistance to the equivalent series resistance. Finally, the influences of semi-transparent covering on the output characteristics of a PV string and array were investigated. The ΔI_sc of the covered cell in the PV string and PV array is larger than that in the PV module because more cells are connected in series to provide a larger reverse bias voltage. The V_oc and FF of the PV string and array satisfy the series/parallel relationship of the modules.

This paper simulates scenarios in distributed PVs with a semi-transparent covering and investigates the mechanism of how coverings affect the power generation capacity of PV cells, modules, strings, and arrays under different covering ratios. Most notably, the different contributions of the covered and uncovered parts to the solar cell reverse bias current were first revealed. The results are important for analyzing the output characteristics of PV modules under real conditions.