Influences on Solar Cell Performance

Abstract

Solar cell performance is affected greatly by a variety of factors. Major factors include heat, irradiation and parasitic resistances as demonstrated in this experiment. Changing the conditions for the solar module and plotting the I-V curves illustrated how each condition influenced certain performance characteristics.

Introduction

Understanding the characteristics of a solar cell is vital to establish what factors affect its performance. Environmental parameters need to be accounted for in real world conditions so understanding how these parameters impact the performance of solar cells is imperative. I-V curves demonstrate these performance characteristics visually.

When a solar cell is under illumination, photons with energy higher than the bandgap can be absorbed giving an electron enough energy to break free from its covalent bond, allowing it to roam free in the conduction band (creating a hole in its place)[1]. Conductor contacts connected to each side of the p-n junction collect these electrons as electrical current. Resistance between the two contacts controls the trade-off between voltage and current for the output.

In the dark, the I-V curve of a solar cell portrays the same shape as a diode but when photons are absorbed, the curve is transformed down vertically as there will be a negative current produced[2]. This is shown for an ideal solar cell in the by:

$I={I_L–I}_0\left[\exp \left(\frac{\mathit{qV}}{\mathit{nkT}}\right)–1\right]$

     (1)

where ${\mathrm{I}}_{\mathrm{L}}$

is the light generated, ${\mathrm{I}}_0$

is the saturation current density, $\mathrm{q}$

is the electron charge, V is the voltage, k is Boltzmann’s constant, T is the temperature, n is ideality factor.

Fig. 1 – Equivalent circuit for a solar cell and an I-V curve for a solar cell in the dark and under illumination

Temperature impacts the characteristics of silicon in terms of its bandgap which affects the I_SC and conversely has a major impact on the V_OC which is influenced by the I­­­₀ [Eq. 1].[3]

There are parasitic effects caused by a series resistance (R_S) and parallel resistance (R_Sh) which are a source for a reduction in efficiency by losing the power in the resistances.

Image from: https://urjart.wordpress.com/2008/10/10/solar-cell-equivalent-circuit/[4]

Methodology

According to Ohm’s law (V=IR), a resistor has a linear relationship for its current and voltage so using a source-measuring unit, a resistor’s current output was tested manually at different voltages to show this relationship.

A silicon diode in forward bias was measured at selected voltages following the same process as was done for the resistor to produce an I-V curve. As the relationship for a diode isn’t linear, at a threshold voltage current began to pass through.

Due to probe inconsistencies, a 4-wire configuration a PV module was set up with the source-measuring unit. Using a halogen lamp and a solarimeter, the PV module was set to receive irradiances of 250W/m², 500W/m² and 750W/m² by adjusting the distance. As the light from a halogen light isn’t very uniform, the irradiance was checked at multiple points on the PV module.

Screens and filters could be used to prevent any indirect light and improve the uniformity of the light. Due to the infrared light emitted from the halogen lamp, a cooling fan was used to attempt to keep the temperature of the module regulated at 30℃ (measured using a thermocouple) however there was a limitation for consistency of the temperature when using this equipment. This could be improved by using an automatic temperature control system. When checking the irradiances, the thickness of the solarimeter had to be accounted for as marginal distances errors impact the irradiance readings considerably. On the source-measuring unit, a suitable stop voltage was chosen (0.6V × 8 = 4.8V) with source limit set at 200mA for an automatic linear sweep with 100 points. The unit then plotted the 100 current outputs for each voltage on an I-V graph which was reformatted on Excel.

Using the same settings on the source-measuring unit, the PV module was set at a distance in which it received 500W/m² irradiance. Using the fan as a cooler and heater, the output was measured at temperatures of 40℃ and 50℃ (30℃ values were produced previously) and the I-V curves were generated.

From the equivalent circuit for the solar cell, the effect of changing the values of the series and shunt resistor were tested. At test conditions of 30℃ and 500W/m², a high value resistor (680Ω) was added to the circuit in parallel to the solar module to simulate a large shunt resistance and the I-V curve was generated with the same settings as previously. This was repeated but with a lower value resistor (156Ω) to create a comparison which demonstrated the effect this parallel resistor has on the performance. Using this 156Ω resistor but changing to a series configuration with the solar cell, the I-V curve was generated again. Repeating this process again with the 680Ω resistor established the effect on performance that the series resistor has with varying values.

*link to theory

Results

Measuring the I-V curve of the 220Ω resistor shows a linear relationship as R=V/I according to Ohm’s law [Fig.2(A)].

Fig.  2- I-V curve for a 220Ω resistor (a) and I-V curve for a diode in forward bias (b)

Looking at Fig.2(B), the diode outputs no current until the knee voltage of around 600-700mV.

At 750W/m² the solar module has the highest V_OC and the highest I_SC as the curve has been shifted up vertically from the lower irradiances [Fig.3(A)].

At 50℃ the I_SC is increased slightly compare to lower temperatures however the V_OC is decreased by a much greater amount [Fig.3(B)].

Fig.  3- I-V curve for different irradiances at 30℃ (a) and J-V curve for different temperatures at 500W/m² (b)

Table 1 – Performance values for tests at different irradiance and temperatures

The effect of the different conditions on the solar modules is displayed in Table 1.

Fig.4(A) demonstrates the impact of having a low shunt resistance on the V_OC. The 156Ω resistor has a V_OC difference to the 680Ω resistor of 3V.

With the 156Ω series resistor the curve [Fig.4(B)] isn’t too dissimilar to the curve in Fig.3(A) with the 500W/m² but with higher resistance values, the I_SC is lower by almost 90%.

Fig.  4- Effect of different parallel resistor values (a) and Effect of different series resistor values (B)

Analysis

Irradiation:

I-V graph represent Ohm’s law when the relationship is linear as: V=IR. When testing the current at different voltages for the resistor it’s possible to check the resistance [Fig.2(A)]. As it’s linear relationship, any point on the line can be used to find the resistance: 1000mv/4.548mA=219.893Ω.

Silicon diodes in forward bias with a positive voltage start with minimal current but once it reaches the knee point at around 0.6-0.7V then there is a considerable increase of current for just a small increment of voltage. At this voltage, there is enough holes supplied to the P region and free electrons supplied to the N region for the electrons and holes to be attracted across the depletion region conversely. This creates a current flow in one direction.

In the dark, the solar module doesn’t generate any current as there’s no photons being absorbed by the solar cells for photogeneration to occur. With more irradiance, there are more photons being absorbed meaning more current is generated. From Fig.3(A) the curve is transformed vertically with the highest irradiance (750W/m²) producing the highest I_SC of 104mA whereas 250W/m² irradiance only produced an I_SC of 3mA. As the light from the halogen lamp isn’t uniform, the irradiance throughout the surface of the PV module varies meaning these results won’t be entirely accurate for the specific irradiance values. In real systems the tilt and orientation of the PV modules should be considered to gain the optimal irradiation for the system.

Temperature:

Testing the solar module at different temperatures shows a change in I_SC. At 30℃ the I_SC is 66.6mA but at 50℃ the I_SC is 70.3mA [Table 1]. With higher temperatures there is a reduction in the semiconductors bandgap.[5] More light can be absorbed as less energy will be needed to raise charge carriers to the conduction band, therefore I_SC increases[6]. The decrease in bandgap causes an increase in intrinsic carrier concentration (n_i²) which is correlated to the reverse saturation current by:

$I_0=\mathit{qA}\frac{D{n}_i^2}{L{N}_D}$

      (2)

Where D is the minority carrier diffusion coefficient, L is the minority carrier diffusion length.

The open circuit voltage (V_OC) then decreases due to the inverse relationship to the saturation current (I₀):

$V_{\mathit{OC}}=\frac{\mathit{kT}}{q}\ln \left(\frac{I_{\mathit{sc}}}{I_0}\right)$

     (3)

V_OC affects the maximum power, the fill factor and the efficiency. Temperature has a significant impact on the V_OC so even though there is an increase in I_SC, there is an overall loss in efficiency (η):

$\eta =\frac{V_{\mathit{OC}}{J}_{\mathit{SC}}\mathit{FF}}{P_{\mathit{in}}}$

      (4)

where FF is the fill factor, P_in is the input power J_SC is the short circuit current density.

For the current density of each cell, the current is multiplied by the area of $5.4\times {10}^{–4}{m}^2$

which is shown in the J-V curve for the temperature dependence in Fig. 3(B).

Using (2), the efficiency for each cell is calculated [Table 1] given that each cell is working equally demonstrating that the cell is more efficient at lower temperatures.

Parasitic resistances:

Manufacturing defects can cause power loss in form of shunt resistance (R_Sh) which offers the light-generated current a diversion path. With low values of R_Sh there is a reduced amount of load current due to this path and the voltage from the solar cell becomes less.[7]

With a resistor in parallel representing shunt resistance, the I_SC isn’t altered compared to that without the resistor however the V_OC and the FF are. The smaller the value of shunt resistance, the more current which will take the alternative path which reduces the voltage from the solar cell. Including this shunt resistance into Equation (1) gives:

$I=I_L–I_0\exp \left[\frac{\mathit{qV}}{\mathit{nkT}}\right]–\frac{V}{R_{\mathit{Sh}}}$

          (5)

This is demonstrated with the I-V curves in Fig. 4(A) with the different resistance values of 680Ω, 220Ω and 156Ω. As P=IV and there is a reduction in current, the power will also face significant losses. As there are losses in V_OC this affects the MPP and the FF[8].

Contributing factors for the series resistance (R_S) in the equivalent circuit for a solar cell include: movement of the current across the p-n junction, the resistance of the contacts and the resistance between the connection of the silicon and contacts[9].

Series resistance impacts the current from the solar cell. The higher the series resistance, the less light-generated current based on the relationship of V=IR. The short circuit current is reduced only at very high values of R_S as established in Fig.4(B) where the I_SC is 63mA for the 156Ω resistor but 1mA for 680Ω resistor. When you compare the I_SC for the 156Ω series resistor to when there’s no series resistor [Fig.3(A)] there isn’t much of a change however there is a reduction in FF. Including this series resistance into Equation (1) gives:

$I=I_L–I_0\exp \left[\frac{q\left(V+I{R}_S\right)}{\mathit{nkT}}\right]$

         (6)

Conclusions

From testing the solar cell at varying irradiances, it shows how imperative it is for the performance of the system to be receiving as much irradiance as possible to maximise the amount of light-generated current. Temperature plays a key role in changing the output voltage which influences the efficiency; a photovoltaic system in cooler conditions will perform better than that at hotter temperatures. The importance in minimising the parasitic effects is established by the results for both series and shunt resistances otherwise there is a result in power loss. 

References

[1] G. Knier, “How do Photovoltaics Work?,” Nasa, 2002. [Online]. Available: https://science.nasa.gov/science-news/science-at-nasa/2002/solarcells. [Accessed: 31-Oct-2018].

[2] “Part II – Photovoltaic Cell I-V Characterization Theory and LabVIEW Analysis Code – National Instruments,” 2012.

[3] S. Chander, A. Purohit, A. Sharma, Arvind, S. P. Nehra, and M. S. Dhaka, “A study on photovoltaic parameters of mono-crystalline silicon solar cell with cell temperature,” Energy Reports, vol. 1, pp. 104–109, Nov. 2015.

[4] P. Sidi, D. Sukoco, W. Purnomo, H. Sudibyo, and D. Hartanto, “Electric Energy Management and Engineering in Solar Cell System,” in Solar Cells – Research and Application Perspectives, InTech, 2013.

[5] T. Tayagaki, Y. Hoshi, and N. Usami, “Investigation of the open-circuit voltage in solar cells doped with quantum dots,” Sci. Rep., vol. 3, no. 1, p. 2703, Dec. 2013.

[6] B. V Chikate, Y. A. Sadawarte, and B. D. C. O. E. Sewagram, “The Factors Affecting the Performance of Solar Cell,” 2015.

[7] A. D. Dhass, E. Natarajan, and L. Ponnusamy, “Influence of shunt resistance on the performance of solar photovoltaic cell,” in 2012 International Conference on Emerging Trends in Electrical Engineering and Energy Management (ICETEEEM), 2012, pp. 382–386.

[8] S. Wenham, Applied photovoltaics, 2nd ed. Earthscan, 2007.

[9] M. Wolf and H. Rauschenbacht, “SERIES RESISTANCE EFFECTS ON SOLAR CELL MEASUREMENTS *,” Pergamon Press, 1963.