The Effects of Nonuniform Illumination on the Electrical Performance of a Single Conventional Photovoltaic Cell

2.1. Physical and Electrical Characteristics of the PV Cell

To study the effects of nonuniform flux distribution on the performance parameters of a single PV cell, a series of indoor experimental tests were conducted using a multipurpose mobile solar simulator [10]. This multipurpose mobile solar simulator produces illumination with a good spectral match to AM 1.5 reference spectrum, uniformity of 95%, and an average collimation of 83% [10]. The PV cell used in this study was Bosch M 2BB monocrystalline PV cell with physical and electrical properties listed in Table 1 [11]. The effect of nonuniform illumination on the performance parameters of this cell was investigated at two different energy flux concentration ratios: low and medium, as described in detail in Sections 2.2.1 and 2.2.2, respectively.

2.2. Experimental Test Procedure

2.2.1. Experimental Test at Low Energy Flux Concentration

The objective of this experiment was to investigate the effect of nonuniform illumination and its geometrical orientations on a single standard PV cell at low energy flux concentration ratios. Nonuniform illumination over the cell surface was created by using a black opaque material to cover a fraction of the cell while the rest of the surface remained uncovered. The experimental tests were performed in two different stages. First, a full cell was uniformly illuminated (Figure 1(a)) at a selected irradiance and then 25% the total cell area was covered by an opaque material. The remaining fraction (75% of the total cell area as shown in Figure 1(b)) was exposed to irradiance which had equal energy as the cell exposed to uniform illumination (i.e., Figure 1(a)). The irradiation intensity on uncovered cell fraction (G_uncovered) that produced the same amount of energy as the full illuminated cell was calculated as

$$ (1)

For evaluating the effect of nonuniform illumination orientations on the performance of a PV cell, an opaque material equal to 25% of the total cell area was placed across the grids of the PV cell as shown in Figure 1(c). The result from this experiment was compared with the result from Figure 1(b), when an opaque material (of the same area) was placed along the grids. Table 2 shows the amount of irradiance and energy flux incident on the active cell area for both uniform and nonuniform illumination conditions. The incident energy on the active PV cell area (E_PV  cell) was calculated from (2) [12]:

$$ (2)

where G_PV  cell is the irradiance incident on the active area of a PV cell and A_{PV cell} is the active area of a PV cell.

Table 2. Irradiance and energy flux incident on the active cell area for uniform and nonuniform illumination profiles.

Illuminated cell area (m2)	Irradiance on the active cell area (±20 W/m2)	Energy incident on the active cell area (W)
Full cell (uniform) (0.02347)	804	18.87
75% along the grids (0.01760)	1070	18.83
75% across the grids (0.01760)	1070	18.83

During the experimental tests, irradiance on the surface of a PV cell, open-circuit voltage (V_OC), short-circuit current (I_SC), intermediate current and voltage, ambient temperature, and cell temperature were measured. The measurements for these parameters followed the same procedures as that described in [4], with the exception of irradiance that has to be adjusted for every experiment to ensure equal amount of incident energy. The illumination intensity on the surface of a PV cell was measured by a CM4 high temperature pyranometer with an error of ±20 W/m² at 1000 W/m² [4] while open-circuit voltage, short-circuit current, and intermediate current and voltage were measured by a Keithley 2430 Model SourceMeter with the voltage and current error of ±0.0080 V and ±0.0034 A [4], respectively.

From the current and voltage measurements, the I-V characteristic of each test was plotted. These curves were used to extract the current and voltage at maximum power point (I_MPP and V_MPP), respectively, for fill factor (FF) and cell efficiency (η) calculations. The cell fill factor and efficiency were calculated using (3) [13] and (4) [13, 14], respectively:

$$ (3)

$$ (4)

2.2.2. Experimental Test at Medium Energy Flux Concentration

Results from experiment test one (effect of nonuniform illumination at low energy concentration ratio), as presented in Section 3.1, indicated that the performance of single conventional PV cell, at low energy flux concentration ratio and constant cell temperature, does not depend on the way the energy flux is distributed on the surface of a single standard PV cell. Thus, to examine if a PV cell at medium energy concentration ratio behaves in a different way, a second experimental test was conducted.

Since the maximum irradiance achievable by the solar simulator used in the first experiments was about 1300 W/m² (at 1.45 m above the target), to obtain medium energy flux concentration on the PV cell, a symmetric 2-dimensional CPC and V-trough collectors were fabricated. The CPC had an acceptance half-angle (θ_a), entrance (A_a), and exit (A_r) apertures areas of 30^°, 109 mm, and 218 mm, respectively, making a geometric concentration ratio (C_g) of 2.0. The CPC was truncated to a height of about 212 mm to reduce fabrication material cost [15]. For direct performance comparison, a choice was made to fabricate a V-trough with the same geometrical concentration ratio and aperture area as that of the symmetric CPC. Therefore, a V-trough with trough angle, ψ = 10^°, was chosen to provide large acceptance at comparable size to the CPC. The V-trough collector had maximum height, slope height, entrance width (w_a), and exit width (w_r) of 296.7 mm, 301.3 mm, 109.0 mm, and 213.6 mm, respectively. Both concentrators were fabricated with high reflectivity anodised aluminium sheets with reflectivity of 0.90 [4].

Due to the nature of the illumination profiles in the CPC collector [3], the CPC was used to obtain nonuniform energy flux and medium energy concentration ratio whilst the V-trough collector was used to obtain low energy concentration ratio and uniform energy flux. For these experiments, the width of a PV cell used in experiment one was cut into 109 mm (using the FB1500 Laser Cutting Machine) to accommodate the base dimension of the CPC and V-trough collector. Figure 2 shows the photographs of the fabricated collectors (CPC and V-trough) and the PV cell under experimental test.

Although both collectors (CPC and V-trough) had the same concentration ratio (1.96), they differ in reflecting surface geometry, optical efficiency, energy flux illumination, and maximum height. For direct comparison of the PV cell performance parameters, therefore, care was taken to ensure that the PV cell under both concentrators had the same amount of incident energy. Thus, the intensity on the aperture of a V-trough collector at normal incidence angle G_aperture(V-trough,  θ_in = 0^°) that produced the same amount of energy on the PV cell as the CPC at θ_in was calculated from

$$ (5)

where G_aperture(CPC, θ_in) is the intensity on the aperture of the CPC collector at θ_in incidence angle.

In (5), $$ is experimental optical efficiency of the CPC or V-trough at θ_in incidence angle, calculated as

$$ (6)

E_{PV cell} is the energy incident on the PV cell and E_aperture is the energy incident on the aperture of a collector given by

$$ (7)

where A_aperture is the aperture area of the collector defined by

$$ (8)

For comparison, the experimental test at medium concentration level was performed for two different energy concentration ratios. The first experiment was carried out when the peak energy concentration ratio for the CPC was 3 at θ_in   = 0^° and the second was performed when the peak energy concentration ratio for the CPC was 6 at θ_in   = 20^° (it should be noted that 20° incident angle was chosen because this is the incidence angle with the maximum CPC energy concentration ratio). Under both experiments, the V-trough collector was maintained at normal incidence angle to obtain uniform energy flux on the PV cell as illustrated in Figure 2(b).

Using (5) and the values of G_aperture(CPC), η_exp(CPC), and η_exp(V-trough, θ_in   = 0^°), the intensity on the aperture of a V-trough collector for the first and second experiments (medium energy concentration level) was determined. Table 3 shows the irradiance and energy flux at the aperture of the concentrator and on the surface of a PV cell for the CPC and V-trough collector for the two experiments.

Table 3. Incident irradiance and energy flux at the aperture and on the surface of a PV cell for the CPC and V-trough collector for the two experimental test conditions.

Type of the experiment	System description	Intensity on the aperture (±20 W/m2)	Energy on the aperture (W)	Intensity on the PV cell (±20 W/m2)	Energy at the PV cell (W)
Experiment number 1 (concentration ratio = 3)	CPC at θin = 0°	600	20.00	541	18.46
	V-trough at θin = 0°	595	19.83	541	18.75
Experiment number 2 (concentration ratio = 6)	CPC at θin = 20°	551	18.36	506	17.76
	V-trough at θin = 0°	557	18.56	506	17.76

The experimental set-up and test procedures for the two experiments in this section were the same as those described in [4]. From the current and voltage measurements, the I-V characteristic of the PV cell under each test condition was plotted. These curves were used to extract V_OC, I_SC, V_MPP, and I_MPP for FF and η calculations. The FF and η (with concentrator) were calculated using (3) and (9) [16], respectively:

$$ (9)

3.1. PV Cell Performances at Low Energy Concentration

Figure 3 shows a comparison of the I-V characteristics for a PV cell illuminated uniformly and nonuniformly. It can be seen that there are no significant differences between the two curves. The small discrepancy between the two curves is related to the repeatability of the measurements, especially setting the “current compliance limit” in each measurement to ensure that the measuring device (the Keithley 2430 SourceMeter) measures the correct value of I_SC. It can be concluded, therefore, that, at low energy concentration ratio, nonuniform illumination does not have any effect on the I-V characteristic of a single standard PV cell. This can be explained by the fact that, at low energy flux concentration, the effect of shunt and series resistance, which results from nonuniform illumination, is negligible [17–19].

In addition to investigating the effect of nonuniform illumination on various cell performance parameters, the effect of nonuniform illumination location on cell performance parameters was also studied. This was done by placing an opaque material across the grids of the PV cell as shown in Figure 1(c). The result from this experiment was compared with the results from another nonuniform illumination location (of the same area) but introduced along the grids of the PV cell as in Figure 1(b). Table 4 shows the results from these experiments.

It can be seen that the location of nonuniform illumination (along or across the cell grids) in a single cell has no significant effect on the cell performance parameters. For cell performance parameters which are linearly dependent on the irradiance such as I_SC and P_MPP, the results observed in Table 4 can be explained by equal amount of energies that were received in both cases whilst for those parameters which are affected by series resistance (I_SC and P_MPP, FF, and η), equal values of nonillumination along the grids and across the grids were due to the fact that, at low energy concentration ratio, nonuniform illumination had very low series resistance which mean negligible effect on the parameters. For the V_OC, the same values were measured for nonuniform illumination along and across the cell grids because the PV cell used in both experiments had the same physical properties. According to Andreev et al. [9], the V_OC depends on the saturation current and light generated current which are controlled by the majority carrier concentration and electrophysical parameters (mobility and diffuse lengths) of the cell.

The results from these experiments regarding the effect of nonuniform illumination on different cell performance parameters contradict the previous published works of Pfeiffer and Bihler [5] and Franklin and Coventry [8]. In order to find out if increasing nonuniform illumination area may have an effect on the cell performance parameters, similar experiments as those in Table 2 were carried out. However, in this case the area covered by a black opaque material along and across the PV cell grids was increased to 50%. In each experiment, a full cell (illuminated uniformly) and a cell in which 50% of its area was uncovered by an opaque material had equal incident energy as shown in Table 5.

Figure 5 shows the I-V characteristics for the PV cell under uniform and nonillumination. It can be seen that both I-V characteristics are the same, specifically in the low voltage region, implying that increasing nonuniform illumination area does not have any effect on the I-V curve of a single standard cell. The same conclusion can be made for the V_OC, I_SC, P_MPP, FF, and η in Figure 6. This is in agreement with the results in Figure 4 when a nonuniform illumination occupied only 25% of the total cell area.

Table 6 shows the results of the experiments which were carried out to compare the performance of the PV cell under two different nonuniform illumination geometries (a square and a rectangle). The area covered by each geometrical shape was 50% of the total cell area. The square opaque material was place at the centre of the cell whilst the rectangular shape was placed along the grids of the PV cell. Since the energy incident on the PV cell under both cases was the same and the effect of series resistance was negligible (due to low energy flux concentration), it can be seen that there is no significant difference between V_OC, I_SC, P_MPP, FF, and η for a square and a rectangular nonuniform illumination shape. The small difference observed in the cell performance parameters between the two geometrical shapes was attributed to imperfection in producing a square opaque material with exactly the required dimension of 110.3085 mm each side.

Furthermore, the effect of nonuniform illumination locations on the PV cell performance parameters of a single cell was studied in detail. The study was done by using two different geometry opaque materials: a square and rectangles. In each case, the area covered by a geometrical shape was 50% of the total cell area. The square opaque material was place at the centre of the cell whilst the rectangular shapes were placed along and across the grids of the PV cell at various positions as illustrated in Table 7. These combinations were chosen so that the results represent any type of nonuniform profile that occurs in real situation. It can be seen (from Table 7) that there is no significant different in V_OC, I_SC, P_MPP, FF, and η for each of the investigated nonuniform illumination locations.

Table 7. The effect of nonuniform illumination locations on the PV cell performance parameters. In each case, the level of nonuniform illumination was 50% of the total cell area.

Location of nonuniform illumination on the PV cell	PV cell performance parameters
	VOC (±0.0080 V)	ISC (±0.0034 A)	PMPP (W)	FF	η (%)
	0.5455	4.8831	1.8693	0.7018	13.2744
	0.5546	4.8847	1.8783	0.6933	13.3383
	0.5637	4.8808	1.9063	0.6929	13.5371
	0.5455	4.8831	1.8693	0.7018	13.2744
	0.5546	4.8865	1.9065	0.7035	13.5386
	0.5546	4.8847	1.8783	0.6933	13.3383
	0.5546	4.8865	1.9065	0.7035	13.5386

3.2. PV Cell Performances at Medium Energy Concentration

Figures 7 and 8 illustrate the I-V characteristics of the PV cell under uniform and nonuniform illumination when the peak energy flux concentration was 3 and 6, respectively. Although the PV cell under uniform and nonuniform illumination had the same energy in each experiment and the cell temperature was kept constant, it can be seen that the I-V curve for uniform illumination was higher than that of nonuniform illumination in both experiments. This was attributed to series resistance effect which is higher under nonuniform illumination condition [20].

As shown in both Figures 7 and 8, there is a significant decrease in the I-V curve “sharpness” around the maximum power point for uniform and nonuniform illumination. This was due to voltage and current drop around the maximum power point. The voltage drop was due to the distributed diodes being at higher potential than the potential at the terminal while the current decrease was due to series resistance [17, 20]. The series resistance also reduced the maximum power output and this reduction increases with the increase in energy concentration ratio as illustrated in the inserted table in Figures 7 and 8. The nonuniform illumination for the PV module is illustrated in Figure 1(a) where there are two sharp energy peaks in the PV cell while the PV cell in the V-trough collector (Figure 1(b)), with the same amount energy, was uniformly illuminated. The sharp energy concentrations in Figure 1(a) resulted in higher current drops for a PV cell under nonuniform illumination than a PV cell under uniform illumination as illustrated in the inserted table in Figures 7 and 8.

Table 8 shows the variation in the PV cell performance parameters with energy illumination profiles for the two experiments. It can be seen that there is no difference in V_OC for uniform and nonuniform illumination when the peak energy concentration was 3. However, the V_OC slightly decreased (by about 1.3%) when the peak energy concentration in the nonuniform illumination increased from 3 to 6. This result can be explained as follows: under uniform illumination, V_OC does not change even if the series resistance (R_S) varies, because at short-circuit condition (I_SC   = 0) there are no current flows through the R_S, which means that the voltage measured at the contacts equals the voltage at the diode junction. However, for the nonuniform illumination, there is an internal current flow from the highly illuminated region to the least-illuminated region [6]. This internal current flow produces a voltage drop across the series resistance of the cell which significantly affects the V_OC. The decrease in V_OC increases with increase in internal series resistance, increase in nonuniformity peak energy concentration, and increase in energy illumination level [6].

At low series resistance, the short-circuit current increases linearly with radiation intensity because it is a linear function of the light generated current which is proportional to the photon flux incident on the cell [17]. However, at sufficiently energy concentration (high current), the effect of R_S becomes nonnegligible and the effect of nonuniform illumination becomes noticeable because the high local currents in part of the cell created by the peak intensity generate resistive losses. The short-circuit current loss as a result of series resistance increases with energy illumination level and peak energy flux concentration [18]. This is illustrated in Table 8 in which I_SC for nonuniform illumination decreased by 0.8% and 2.3% when the peak concentration ratio increased from 3 to 6, respectively.

It can be observed from Table 8 that a PV cell under uniform illumination had higher power output and efficiency than a similar cell with nonuniform illumination, despite the fact that the cell had the same amount of energy under both cases (see Table 5). For example, at a peak energy flux concentration equal to 6, a reduction in P_MPP of about 80 mW for nonuniform illumination was observed whilst the cell efficiency was observed to drop significantly, from about 9.25% to 8.82% for nonuniform illumination. The reason is that, at medium energy concentration, a PV cell under nonuniform illumination had higher internal series resistance than a similar cell under uniform illumination [18].

Similarly to I_SC and P_MPP, series resistance should reduce the FF of a cell under nonuniform illumination much more than a cell under uniform illumination. However, as shown in Table 8, the FF for a cell illuminated uniformly was only 2.4% higher than a similar PV cell under nonuniform illumination. The reason for this small difference is not clearly understood from this experiment. Further investigations are required to establish if this could be due to another factor(s).