# Performance Investigation of a Silicon Photovoltaic Module under the Influence of a Magnetic Field

Authors: Dioari Ulrich Combari; Emmanuel Wendsongré Ramde; Idrissa Sourabie; Martial Zoungrana; Issa Zerbo; Dieudonné Joseph Bathiebo
Journal: Advances in Condensed Matter Physics
 (2018)

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## Abstract

Aside from the terrestrial magnetic field that is generated from the earth core, power transmission, and distribution lines, transformers and other equipment do produce a certain amount of magnetic field that could interfere with the performance of photovoltaic modules. This study conducted an experiment and investigated the performance of a silicon photovoltaic module subjected to a magnetic field. The current-voltage and power-voltage characteristics were plotted in the same axis system and allowed us to find, as a function of the magnetic field, the electrical parameters of the photovoltaic module such as maximum electric power, fill factor, conversion efficiency, and charge resistance at the maximum power point. These electrical parameters were then used to calculate the series and shunt resistances of the equivalent circuit of the photovoltaic module. The results have shown that the efficiency of a solar module is affected by the presence of magnetic fields. However, the magnitude of ambient magnetic field generated by power transmissions lines and other equipment is extremely low (in the order of 10−2 mT or less) as compared to the values of the magnetic field used in this study. That made it difficult to conclude as to the impact of such field on solar photovoltaic installations.


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## Body

## 1. Introduction

The performance of a photovoltaic module (PV module) depends on climatic and seasonal parameters but may also depend on the presence of some external factors such as electric field, magnetic field, and electromagnetic field.Various researchers have used theoretical and experimental methods to investigate the effect of climatic and seasonal conditions on photovoltaic modules and arrived at different results.Emetere et al. [1] examined, through experimental tests, the effects of solar radiation irregularities due to climate change on the electrical performance of photovoltaic modules. Koffi et al. [2] experimentally investigated the seasonal variation of the operating temperature of silicon solar modules under tropical atmospheric conditions, including high turbidity (Harmattan dust particles). Their results confirmed that monocrystalline modules have lower temperature coefficient than polycrystalline and amorphous solar modules. Dia et al. [3] studied the degradation of photovoltaic modules under tropical weather conditions. The degradation of the photovoltaic modules, due to exposure to UV radiation, temperature, humidity, and aerosols in a Sahelian environment was investigated. The study showed that the degradation of the photovoltaic modules is more affected by temperature as well as solar irradiation. In the same vain, Kazem et al. [4] investigated the effect of dust on the performance of photovoltaic modules. The authors conducted an experiment to identify the effect of deposition of different pollutants (red soil, ash, sand, calcium carbonate, and silica) on the voltage and power output of photovoltaic modules. The results showed a drop of the voltage and the power output of the photovoltaic module when dust particles are deposited on the photovoltaic module. This drop was noted to be strongly dependent on the type of pollutant and on the level of deposition. The study also noted that ash pollutant affects the most the voltage of photovoltaic modules as compared to the other pollutants.Other researchers used experimental methods to study the effect of magnetic field on the performances of solar cells. Betser et al. [5] used an experimental method to measure the mobility of minority carriers in the base of InP/GaInAs heterojunction bipolar transistor under constant magnetic field. The magnetic field was applied perpendicular to the direction of the current flow. The standard magnetotransport theory was used to establish a relation between the base current with no magnetic field, the change in the base current induced by the magnetic field, the mobility of the electrons, and the intensity of the applied magnetic field. The authors obtained the electron mobility in the base of an NPN InP/GaInAs HBT by measuring the base current as a function of the intensity of applied magnetic field. The result was in agreement with the value of the mobility measured by the zero field time of flight technique. Vardanyan et al. [6] proposed a method for measuring all recombination parameters (diffusion length, diffusion coefficient, carriers mobility, back surface recombination velocity) in the base region of bifacial solar cell illuminated by its rear side and under constant magnetic field applied parallel to the surface of the p-n junction. The bifacial solar cell was illuminated with a monochromatic light and the expression of electron photocurrent and the associated parameters were obtained by solving the continuity equation. By measuring the short circuit photocurrents for two different wavelengths without magnetic field and under applied magnetic field, the authors obtained the recombination parameters of the solar cell. Erel [7] conducted an experiment and studied the effect of electric and magnetic fields on the response of three different types of solar cells (monocrystal, polycrystal, and amorphous Si solar cells). The cells were first illuminated with LEDs of different color and secondly by a lamp, with tungsten filament, of different flux intensity. Erel concluded that the short circuit current and the open circuit voltage decreased in the presence of magnetic the field from red LED to the blue one. For an increasing light flux intensity produced by the lamp with tungsten filament, the short circuit current and the open circuit voltage decreased in the presence of the magnetic field.In a previous work [8] we have shown, by simulation, that within the limits of the study, magnetic fields affect the performance of a photovoltaic module made up of ideal solar cells.The aim of this work was to investigate potential negative impact of magnetic fields on the performance of a commercial silicon photovoltaic module. From experimental measurements of I-V and P-V characteristics of the photovoltaic module, we found the maximum electric power, the fill factor, the conversion efficiency, and the charge resistance at the maximum power point. Then, we calculated the series and shunt resistances of the equivalent circuit of the photovoltaic module.


## 2. Materials and Methods

### 2.1. Experimental Setup

The material used for the experimental study (Figures1 and 2) was as follows:Figure 1
Photography of experimental setup.Figure 2
Experimental setup ((1) inductance in U form; (2) probe; (3) autotransformer.).(i) a monocrystalline silicon photovoltaic module whose characteristics are as follows:(a) maximum electric powerPmax = 5W(b) voltage at maximum power point:Vmax = 17.50V(c) current at maximum power point:Imax = 0.29A(d) open circuit voltage:VOC = 22.05V(e) short circuit current:ISC = 0.32A(f) surface of the photovoltaic module:Smod = 270 cm2(ii) an inductance in U form used for the creation of the magnetic field(iii) a device used for the measurement of the intensity of the magnetic field, made up of a probe and a millivoltmeter(iv) two DC generators: 31.5 V - 2.5 A(v) three rheostats:3300Ω-0.25A, 1000 Ω -0.5A, and 100Ω- 1.5A(vi) a magnetoelectric amperemeter and a magnetoelectric voltmeter(vii) a ferromagnetic voltmeter and a ferromagnetic amperemeter(viii) a ferromagnetic millivoltmeter(ix) an autotransformer: 400 V-13A(x) a pyranometer, Standard ST-1307 to measure the solar irradiance(xi) a Midi Logger GL 200A to measure the temperature T1 at the front side of the photovoltaic module, the temperature T2 at the back side of the photovoltaic module, and the ambient temperature T3The autotransformer was used to vary the intensity of the current through the U inductance located at 1 cm from the photovoltaic module, by varying its supply voltage. Consequently, the intensity of the created magnetic field varied. The variation of the current supplied by the photovoltaic module was obtained by the variation of the charge resistance Rh.It is worth noting that the test was conducted in Ouagadougou located at latitude 12.37°N and longitude 1.52°W.


### 2.2. Magnetic Field Measurement

#### 2.2.1. Device for the Magnetic Field Measurement

The probe used for the measurement of the magnetic field intensity was a coil; this is illustrated by Figure3. This coil is a toroidal inductor whose diameter is 450 mm and it is made up of 10 loops. The loops are made with copper of 1 mm2 of section and protected with an insulator. This probe is positioned at the section of the magnetic circuit of the inductance that creates the magnetic field. The probe is connected to a ferromagnetic millivoltmeter of class 0.5 (Figure 3).Figure 3
Device (probe) used for the measurement of the magnetic field.The method used for the measurement of the magnetic field is the principle of the electromagnetic induction.


#### 2.2.2. Determination of the Teslametric Constant

We suppose that the inductance is not saturated; therefore, it generates a sinusoidal magnetic field whose instantaneous value is given by(1)bt=Bmsin⁡ωtBm is the amplitude of the magnetic field.The sinusoidal magnetic field generated by the inductance in U form produces a magnetic flux through the coil of the probe. The instantaneous value of this magnetic flux is given by(2)ϕt=NSBmsin⁡ωtN is the number of loops of the probe and S is the section of the coil.An electromotive force is induced in the coil and its effective value is measured with a millivoltmeter. The instantaneous value of the electromotive force induced in the coil is expressed in the following:(3)et=-dϕtdt=ωNSBmcos⁡ωt+π(4)et=ωNSB2cos⁡ωt+πThe expression of the amplitude of the electromotive force is given by (5)Em=ωNSB2Thus, we deduced the relation between the effective value of the magnetic field and the one of the electromotive force given by (6)B=1ωNSE=KTEwhere B is effective value of the magnetic field, E is effective value of the electromotive force induced in the coil, and KT is teslametric constant.In this study, the value of the teslametric constant isKT=0.2003(TV-1).Knowing the value of the teslametric constant, we deduced the effective value of the magnetic field from the measured effective value of the electromotive force.The effective values of the magnetic field are given in Table1.Table 1
Effective values of the magnetic field.
E (mV) 0 49.93 74.89 149.76 349.63 499.25 748.88  ΔE (mV) 0 1.00 1.00 2.00 2.00 0.50 5.50  B (mT) 0 10 15 30 50 100 150  ΔB (mT) 0 0.20 0.20 0.40 0.40 0.10 1.10Figure4 is a plot of the effective value of the magnetic field as against the effective value of the electromotive force.Figure 4
Effective value of magnetic field versus effective value of electromotive force.We used Figure4, which is a straight line passing by the origin of the axis, for the determination of the effective value of the magnetic field.


## 2.1. Experimental Setup

The material used for the experimental study (Figures1 and 2) was as follows:Figure 1
Photography of experimental setup.Figure 2
Experimental setup ((1) inductance in U form; (2) probe; (3) autotransformer.).(i) a monocrystalline silicon photovoltaic module whose characteristics are as follows:(a) maximum electric powerPmax = 5W(b) voltage at maximum power point:Vmax = 17.50V(c) current at maximum power point:Imax = 0.29A(d) open circuit voltage:VOC = 22.05V(e) short circuit current:ISC = 0.32A(f) surface of the photovoltaic module:Smod = 270 cm2(ii) an inductance in U form used for the creation of the magnetic field(iii) a device used for the measurement of the intensity of the magnetic field, made up of a probe and a millivoltmeter(iv) two DC generators: 31.5 V - 2.5 A(v) three rheostats:3300Ω-0.25A, 1000 Ω -0.5A, and 100Ω- 1.5A(vi) a magnetoelectric amperemeter and a magnetoelectric voltmeter(vii) a ferromagnetic voltmeter and a ferromagnetic amperemeter(viii) a ferromagnetic millivoltmeter(ix) an autotransformer: 400 V-13A(x) a pyranometer, Standard ST-1307 to measure the solar irradiance(xi) a Midi Logger GL 200A to measure the temperature T1 at the front side of the photovoltaic module, the temperature T2 at the back side of the photovoltaic module, and the ambient temperature T3The autotransformer was used to vary the intensity of the current through the U inductance located at 1 cm from the photovoltaic module, by varying its supply voltage. Consequently, the intensity of the created magnetic field varied. The variation of the current supplied by the photovoltaic module was obtained by the variation of the charge resistance Rh.It is worth noting that the test was conducted in Ouagadougou located at latitude 12.37°N and longitude 1.52°W.


## 2.2. Magnetic Field Measurement

### 2.2.1. Device for the Magnetic Field Measurement

The probe used for the measurement of the magnetic field intensity was a coil; this is illustrated by Figure3. This coil is a toroidal inductor whose diameter is 450 mm and it is made up of 10 loops. The loops are made with copper of 1 mm2 of section and protected with an insulator. This probe is positioned at the section of the magnetic circuit of the inductance that creates the magnetic field. The probe is connected to a ferromagnetic millivoltmeter of class 0.5 (Figure 3).Figure 3
Device (probe) used for the measurement of the magnetic field.The method used for the measurement of the magnetic field is the principle of the electromagnetic induction.


### 2.2.2. Determination of the Teslametric Constant

We suppose that the inductance is not saturated; therefore, it generates a sinusoidal magnetic field whose instantaneous value is given by(1)bt=Bmsin⁡ωtBm is the amplitude of the magnetic field.The sinusoidal magnetic field generated by the inductance in U form produces a magnetic flux through the coil of the probe. The instantaneous value of this magnetic flux is given by(2)ϕt=NSBmsin⁡ωtN is the number of loops of the probe and S is the section of the coil.An electromotive force is induced in the coil and its effective value is measured with a millivoltmeter. The instantaneous value of the electromotive force induced in the coil is expressed in the following:(3)et=-dϕtdt=ωNSBmcos⁡ωt+π(4)et=ωNSB2cos⁡ωt+πThe expression of the amplitude of the electromotive force is given by (5)Em=ωNSB2Thus, we deduced the relation between the effective value of the magnetic field and the one of the electromotive force given by (6)B=1ωNSE=KTEwhere B is effective value of the magnetic field, E is effective value of the electromotive force induced in the coil, and KT is teslametric constant.In this study, the value of the teslametric constant isKT=0.2003(TV-1).Knowing the value of the teslametric constant, we deduced the effective value of the magnetic field from the measured effective value of the electromotive force.The effective values of the magnetic field are given in Table1.Table 1
Effective values of the magnetic field.
E (mV) 0 49.93 74.89 149.76 349.63 499.25 748.88  ΔE (mV) 0 1.00 1.00 2.00 2.00 0.50 5.50  B (mT) 0 10 15 30 50 100 150  ΔB (mT) 0 0.20 0.20 0.40 0.40 0.10 1.10Figure4 is a plot of the effective value of the magnetic field as against the effective value of the electromotive force.Figure 4
Effective value of magnetic field versus effective value of electromotive force.We used Figure4, which is a straight line passing by the origin of the axis, for the determination of the effective value of the magnetic field.


## 2.2.1. Device for the Magnetic Field Measurement

The probe used for the measurement of the magnetic field intensity was a coil; this is illustrated by Figure3. This coil is a toroidal inductor whose diameter is 450 mm and it is made up of 10 loops. The loops are made with copper of 1 mm2 of section and protected with an insulator. This probe is positioned at the section of the magnetic circuit of the inductance that creates the magnetic field. The probe is connected to a ferromagnetic millivoltmeter of class 0.5 (Figure 3).Figure 3
Device (probe) used for the measurement of the magnetic field.The method used for the measurement of the magnetic field is the principle of the electromagnetic induction.


## 2.2.2. Determination of the Teslametric Constant

We suppose that the inductance is not saturated; therefore, it generates a sinusoidal magnetic field whose instantaneous value is given by(1)bt=Bmsin⁡ωtBm is the amplitude of the magnetic field.The sinusoidal magnetic field generated by the inductance in U form produces a magnetic flux through the coil of the probe. The instantaneous value of this magnetic flux is given by(2)ϕt=NSBmsin⁡ωtN is the number of loops of the probe and S is the section of the coil.An electromotive force is induced in the coil and its effective value is measured with a millivoltmeter. The instantaneous value of the electromotive force induced in the coil is expressed in the following:(3)et=-dϕtdt=ωNSBmcos⁡ωt+π(4)et=ωNSB2cos⁡ωt+πThe expression of the amplitude of the electromotive force is given by (5)Em=ωNSB2Thus, we deduced the relation between the effective value of the magnetic field and the one of the electromotive force given by (6)B=1ωNSE=KTEwhere B is effective value of the magnetic field, E is effective value of the electromotive force induced in the coil, and KT is teslametric constant.In this study, the value of the teslametric constant isKT=0.2003(TV-1).Knowing the value of the teslametric constant, we deduced the effective value of the magnetic field from the measured effective value of the electromotive force.The effective values of the magnetic field are given in Table1.Table 1
Effective values of the magnetic field.
E (mV) 0 49.93 74.89 149.76 349.63 499.25 748.88  ΔE (mV) 0 1.00 1.00 2.00 2.00 0.50 5.50  B (mT) 0 10 15 30 50 100 150  ΔB (mT) 0 0.20 0.20 0.40 0.40 0.10 1.10Figure4 is a plot of the effective value of the magnetic field as against the effective value of the electromotive force.Figure 4
Effective value of magnetic field versus effective value of electromotive force.We used Figure4, which is a straight line passing by the origin of the axis, for the determination of the effective value of the magnetic field.


## 3. Results and Discussion

### 3.1. Experimental I-V Characteristics

The experimental setup of Figure1 allowed us to measure the intensity provided by the photovoltaic module to a variable charge resistance and its voltage for four constant values of magnetic field intensity. The results of the measurement are presented in Table 2.Table 2
Values of current and voltage of the photovoltaic module against the intensity of the magnetic field and for a solar irradiance of 600 W/m2.
B (mT) 0 15 30 50 Temperature at front side Temperature at back side Ambient temperature V m o d (V) I m o d 1(mA) I m o d 2(mA) I m o d 3(mA) I m o d 4(mA) T1 (°C) T2 (°C) T3 (°C) 0 205 176.12 137 90.4 38.9 37.7 52.6 2 201 174.49 136.2 90.16 43.9 41.3 54.5 4 198.35 172.38 135 89.7 43.7 41.5 53.5 6 193.25 170.79 132.85 87.8 42 41.6 54.7 8 187 168 130 85.2 43 41.4 54.6 10 176.42 160.65 127.75 82.9 43.6 41.2 53.6 12 164.69 150.62 123 79.7 44.2 41 52.8 14 148.03 134.79 117 77 44.3 41.2 52.9 16 120.29 113 102 71.88 44 41.3 52.8 18 57 65.05 66.67 63.44 43.4 41 52.7 18.45 42.96 52 55.83 59 43.8 41.4 54 18.94 27 37 44.88 51 43.8 41 55.5 20 0 7 14 24.2 41.6 40.3 54.4 20.91 0 0 0 2 41.4 40.8 55 21.5 0 0 0 0 42.1 41.4 54.6The results in Table2 show that, from short circuit to open circuit, the intensity of the electric current decreases when the intensity of the applied magnetic field increases.We noticed that the ambient temperatures T3 are higher than the temperatures T1 measured at the front side of the photovoltaic module. The temperatures T1 are also higher than the temperatures T2 measured at the back side of the photovoltaic module.Figure5 is a plot of the experimental I-V curves of the photovoltaic module for different values of the magnetic field.Figure 5
Experimental I-V characteristics at different intensity of the magnetic field.The experimental I-V curves have the same shape as the theoretical I-V curves obtained through modelling in a previous study by Combari et al. [8]. As the intensity of the magnetic field in milliTesla (mT) was varied from 0 to 15, 0 to 30, and 0 to 50, the short circuit current decreased by 14%, 22%, and 34%, respectively, while the open circuit voltage slightly increased by 5%, 5%, and 8%, respectively.


### 3.2. Experimental Power-Voltage Characteristics

The experimental values in Table2 allowed us to compute the electric power that the photovoltaic module can provide to an external charge. The results are in Table 3.Table 3
Electric power and voltage of the photovoltaic module against the intensity of the magnetic field for a solar irradiance of 600 W/m2.
B (mT) 0 15 30 50 Temperature at front side Temperature at back side Ambient temperature V m o d (V) P m o d 1(W) P m o d 2 (W) P m o d 3 (W) P m o d 4 (W) T1 (°C) T2 (°C) T3 (°C) 0 0 0 0 0 38.9 37.7 52.6 2 0.402 0.349 0.272 0.18 43.9 41.3 54.5 4 0.793 0.67 0.54 0.359 43.7 41.5 53.5 6 1.16 1.025 0.797 0.527 42 41.6 54.7 8 1.496 1.344 1.04 0.682 43 41.4 54.6 10 1.764 1.607 1.278 0.829 43.6 41.2 53.6 12 1.976 1.807 1.476 0.956 44.2 41 52.8 14 2.072 1.887 1.638 1.078 44.3 41.2 52.9 16 1.925 1.802 1.632 1.152 44 41.3 52.8 18 1.026 1.171 1.2 1.142 43.4 41 52.7 18.45 0.793 0.96 1.03 1.089 43.8 41.4 54 18.94 0.511 0.701 0.85 0.966 43.8 41 55.5 20 0 0.14 0.28 0.048 41.6 40.3 54.4 20.91 0 0 0 0.042 41.4 40.8 55 21.5 0 0 0 0 42.1 41.4 54.6The results show that the electric power decreases with an increase of the magnetic field, except for points close to the open circuit voltage. The decrease of the electric power means that, as the magnetic field increases, the decrease in current is much more important than the increase in voltage.Figure6 is a plot of the electric power versus the voltage at different intensity of the magnetic field.Figure 6
Experimental power versus voltage at different intensity of the magnetic field.Figure6 is also in accordance with the theoretical power-voltage characteristics which were obtained through modelling in a previous study by Combari et al. [8]. It can be observed that, as the intensity of the magnetic field increases, the electric power at the maximum power point decreases. Also, as intensity of the magnetic field increases, the curves get less steep and shift to the right towards the open circuit voltage region. Consequently, the maximum power point moves towards large values of the voltage but lower values of the current, hence decreasing the electric power. In fact, as the intensity of the magnetic field in milliTesla (mT) was varied from 0 to 15, 0 to 30, and 0 to 50, the electric power at the maximum power point decreased by about 9%, 21%, and 48%, respectively.


### 3.3. Characteristic Values of the Photovoltaic Module

We present in this section the characteristics of the photovoltaic module under the influence of the magnetic field. The characteristics include current, voltage, and charge resistance at the maximum power point (MPP), series and shunt resistances, maximum electric power, fill factor, and conversion efficiency.


#### 3.3.1. Electrical Parameters of the Photovoltaic Module

The electrical parameters (current and voltage at maximum power point, maximum electric power, fill factor, conversion efficiency, and charge resistance at the maximum power point) of the photovoltaic module under magnetic field are found using the method proposed in previous works [8, 10].During the test, while measuring the characteristics I-V and P-V, the solar irradiance was also simultaneously measured alongside. The retained values were those corresponding to a measured solar irradiance of 600 W. The incident irradiance falling on the photovoltaic module was calculated through the formulaPincSmod and found to be 16.20 W; Smod is the surface of the photovoltaic module, as defined in Section 2.1. The above calculated incident irradiance was used for the calculation of the conversion efficiency.The results are presented in Table4.Table 4
Electrical parameters of the photovoltaic module against the intensity of the magnetic field and for a solar irradiance of 600 W/m2.
B(mT) P m a x(W) V m a x(V) I m a x(A) V o c(V) I s c(A) R M P P(Ω) FF (%) ɳ (%) 0 2.075 13.65 0.152 20.00 0,205 89.80 50.61 12.81 15 1.931 14.41 0.134 20.50 0,176 107.54 53.49 11.91 30 1.694 15.40 0.11 20.91 0.137 140.00 59.13 10.46 50 1.152 16.00 0.072 21.50 0.090 222.22 59.59 7.12On one hand, these results show that the maximum electric power and the related conversion efficiency decrease with an increase of the magnetic field; on the other hand the fill factor and the resistance at the maximum power point increase with an increase of the magnetic field. These experimental results are in agreement with the findings of the studies conducted on a silicon solar cell [10, 11] and on a silicon photovoltaic module [8, 11].Within the limits of this study, it is clear that the efficiency of a solar module is affected by the presence of a magnetic field. However, the magnitude of ambient magnetic field generated by power transmissions lines and other equipment is extremely low (in the order of 10−2 mT or less as illustrated in Table 5) as compared to the values of the magnetic field used in this study. That makes it difficult to conclude as to the impact of such field on solar photovoltaic installations.Table 5
Magnetic field from high voltage power transmission lines [9].
Voltage (kV) Magnitude of the magnetic field from high voltage power transmission lines according to distance to the source (mT) 0 m 30 m 100 m 400 0.03 0.012 0.001 225 0.02 0.003 0.0003 90 0.01 0.001 0.0001


#### 3.3.2. Series and Shunt Resistances of the Equivalent Circuit of the Photovoltaic Module

The experimental values of the series and shunt resistances of the equivalent circuit of the photovoltaic module were calculated using equations suggested by Combari et al. [8].Table6 gives the series and shunt resistances of the equivalent circuit of the photovoltaic module.Table 6
Series and shunt resistance of the equivalent circuit of the photovoltaic module as a function of the magnetic field and for a solar irradiance of 600 W/m2.
B(mT) 0 15 30 50  R s (Ω) 7.76 9.90 12.20 17.70  R s h (Ω) 257.547 363.430 562.590 888.889The values of the series and shunt resistances of the equivalent circuit of the photovoltaic module increase with the intensity of the magnetic field. This is in line with the results achieved by the theoretical study [8].


## 3.1. Experimental I-V Characteristics

The experimental setup of Figure1 allowed us to measure the intensity provided by the photovoltaic module to a variable charge resistance and its voltage for four constant values of magnetic field intensity. The results of the measurement are presented in Table 2.Table 2
Values of current and voltage of the photovoltaic module against the intensity of the magnetic field and for a solar irradiance of 600 W/m2.
B (mT) 0 15 30 50 Temperature at front side Temperature at back side Ambient temperature V m o d (V) I m o d 1(mA) I m o d 2(mA) I m o d 3(mA) I m o d 4(mA) T1 (°C) T2 (°C) T3 (°C) 0 205 176.12 137 90.4 38.9 37.7 52.6 2 201 174.49 136.2 90.16 43.9 41.3 54.5 4 198.35 172.38 135 89.7 43.7 41.5 53.5 6 193.25 170.79 132.85 87.8 42 41.6 54.7 8 187 168 130 85.2 43 41.4 54.6 10 176.42 160.65 127.75 82.9 43.6 41.2 53.6 12 164.69 150.62 123 79.7 44.2 41 52.8 14 148.03 134.79 117 77 44.3 41.2 52.9 16 120.29 113 102 71.88 44 41.3 52.8 18 57 65.05 66.67 63.44 43.4 41 52.7 18.45 42.96 52 55.83 59 43.8 41.4 54 18.94 27 37 44.88 51 43.8 41 55.5 20 0 7 14 24.2 41.6 40.3 54.4 20.91 0 0 0 2 41.4 40.8 55 21.5 0 0 0 0 42.1 41.4 54.6The results in Table2 show that, from short circuit to open circuit, the intensity of the electric current decreases when the intensity of the applied magnetic field increases.We noticed that the ambient temperatures T3 are higher than the temperatures T1 measured at the front side of the photovoltaic module. The temperatures T1 are also higher than the temperatures T2 measured at the back side of the photovoltaic module.Figure5 is a plot of the experimental I-V curves of the photovoltaic module for different values of the magnetic field.Figure 5
Experimental I-V characteristics at different intensity of the magnetic field.The experimental I-V curves have the same shape as the theoretical I-V curves obtained through modelling in a previous study by Combari et al. [8]. As the intensity of the magnetic field in milliTesla (mT) was varied from 0 to 15, 0 to 30, and 0 to 50, the short circuit current decreased by 14%, 22%, and 34%, respectively, while the open circuit voltage slightly increased by 5%, 5%, and 8%, respectively.


## 3.2. Experimental Power-Voltage Characteristics

The experimental values in Table2 allowed us to compute the electric power that the photovoltaic module can provide to an external charge. The results are in Table 3.Table 3
Electric power and voltage of the photovoltaic module against the intensity of the magnetic field for a solar irradiance of 600 W/m2.
B (mT) 0 15 30 50 Temperature at front side Temperature at back side Ambient temperature V m o d (V) P m o d 1(W) P m o d 2 (W) P m o d 3 (W) P m o d 4 (W) T1 (°C) T2 (°C) T3 (°C) 0 0 0 0 0 38.9 37.7 52.6 2 0.402 0.349 0.272 0.18 43.9 41.3 54.5 4 0.793 0.67 0.54 0.359 43.7 41.5 53.5 6 1.16 1.025 0.797 0.527 42 41.6 54.7 8 1.496 1.344 1.04 0.682 43 41.4 54.6 10 1.764 1.607 1.278 0.829 43.6 41.2 53.6 12 1.976 1.807 1.476 0.956 44.2 41 52.8 14 2.072 1.887 1.638 1.078 44.3 41.2 52.9 16 1.925 1.802 1.632 1.152 44 41.3 52.8 18 1.026 1.171 1.2 1.142 43.4 41 52.7 18.45 0.793 0.96 1.03 1.089 43.8 41.4 54 18.94 0.511 0.701 0.85 0.966 43.8 41 55.5 20 0 0.14 0.28 0.048 41.6 40.3 54.4 20.91 0 0 0 0.042 41.4 40.8 55 21.5 0 0 0 0 42.1 41.4 54.6The results show that the electric power decreases with an increase of the magnetic field, except for points close to the open circuit voltage. The decrease of the electric power means that, as the magnetic field increases, the decrease in current is much more important than the increase in voltage.Figure6 is a plot of the electric power versus the voltage at different intensity of the magnetic field.Figure 6
Experimental power versus voltage at different intensity of the magnetic field.Figure6 is also in accordance with the theoretical power-voltage characteristics which were obtained through modelling in a previous study by Combari et al. [8]. It can be observed that, as the intensity of the magnetic field increases, the electric power at the maximum power point decreases. Also, as intensity of the magnetic field increases, the curves get less steep and shift to the right towards the open circuit voltage region. Consequently, the maximum power point moves towards large values of the voltage but lower values of the current, hence decreasing the electric power. In fact, as the intensity of the magnetic field in milliTesla (mT) was varied from 0 to 15, 0 to 30, and 0 to 50, the electric power at the maximum power point decreased by about 9%, 21%, and 48%, respectively.


## 3.3. Characteristic Values of the Photovoltaic Module

We present in this section the characteristics of the photovoltaic module under the influence of the magnetic field. The characteristics include current, voltage, and charge resistance at the maximum power point (MPP), series and shunt resistances, maximum electric power, fill factor, and conversion efficiency.


### 3.3.1. Electrical Parameters of the Photovoltaic Module

The electrical parameters (current and voltage at maximum power point, maximum electric power, fill factor, conversion efficiency, and charge resistance at the maximum power point) of the photovoltaic module under magnetic field are found using the method proposed in previous works [8, 10].During the test, while measuring the characteristics I-V and P-V, the solar irradiance was also simultaneously measured alongside. The retained values were those corresponding to a measured solar irradiance of 600 W. The incident irradiance falling on the photovoltaic module was calculated through the formulaPincSmod and found to be 16.20 W; Smod is the surface of the photovoltaic module, as defined in Section 2.1. The above calculated incident irradiance was used for the calculation of the conversion efficiency.The results are presented in Table4.Table 4
Electrical parameters of the photovoltaic module against the intensity of the magnetic field and for a solar irradiance of 600 W/m2.
B(mT) P m a x(W) V m a x(V) I m a x(A) V o c(V) I s c(A) R M P P(Ω) FF (%) ɳ (%) 0 2.075 13.65 0.152 20.00 0,205 89.80 50.61 12.81 15 1.931 14.41 0.134 20.50 0,176 107.54 53.49 11.91 30 1.694 15.40 0.11 20.91 0.137 140.00 59.13 10.46 50 1.152 16.00 0.072 21.50 0.090 222.22 59.59 7.12On one hand, these results show that the maximum electric power and the related conversion efficiency decrease with an increase of the magnetic field; on the other hand the fill factor and the resistance at the maximum power point increase with an increase of the magnetic field. These experimental results are in agreement with the findings of the studies conducted on a silicon solar cell [10, 11] and on a silicon photovoltaic module [8, 11].Within the limits of this study, it is clear that the efficiency of a solar module is affected by the presence of a magnetic field. However, the magnitude of ambient magnetic field generated by power transmissions lines and other equipment is extremely low (in the order of 10−2 mT or less as illustrated in Table 5) as compared to the values of the magnetic field used in this study. That makes it difficult to conclude as to the impact of such field on solar photovoltaic installations.Table 5
Magnetic field from high voltage power transmission lines [9].
Voltage (kV) Magnitude of the magnetic field from high voltage power transmission lines according to distance to the source (mT) 0 m 30 m 100 m 400 0.03 0.012 0.001 225 0.02 0.003 0.0003 90 0.01 0.001 0.0001


### 3.3.2. Series and Shunt Resistances of the Equivalent Circuit of the Photovoltaic Module

The experimental values of the series and shunt resistances of the equivalent circuit of the photovoltaic module were calculated using equations suggested by Combari et al. [8].Table6 gives the series and shunt resistances of the equivalent circuit of the photovoltaic module.Table 6
Series and shunt resistance of the equivalent circuit of the photovoltaic module as a function of the magnetic field and for a solar irradiance of 600 W/m2.
B(mT) 0 15 30 50  R s (Ω) 7.76 9.90 12.20 17.70  R s h (Ω) 257.547 363.430 562.590 888.889The values of the series and shunt resistances of the equivalent circuit of the photovoltaic module increase with the intensity of the magnetic field. This is in line with the results achieved by the theoretical study [8].


## 3.3.1. Electrical Parameters of the Photovoltaic Module

The electrical parameters (current and voltage at maximum power point, maximum electric power, fill factor, conversion efficiency, and charge resistance at the maximum power point) of the photovoltaic module under magnetic field are found using the method proposed in previous works [8, 10].During the test, while measuring the characteristics I-V and P-V, the solar irradiance was also simultaneously measured alongside. The retained values were those corresponding to a measured solar irradiance of 600 W. The incident irradiance falling on the photovoltaic module was calculated through the formulaPincSmod and found to be 16.20 W; Smod is the surface of the photovoltaic module, as defined in Section 2.1. The above calculated incident irradiance was used for the calculation of the conversion efficiency.The results are presented in Table4.Table 4
Electrical parameters of the photovoltaic module against the intensity of the magnetic field and for a solar irradiance of 600 W/m2.
B(mT) P m a x(W) V m a x(V) I m a x(A) V o c(V) I s c(A) R M P P(Ω) FF (%) ɳ (%) 0 2.075 13.65 0.152 20.00 0,205 89.80 50.61 12.81 15 1.931 14.41 0.134 20.50 0,176 107.54 53.49 11.91 30 1.694 15.40 0.11 20.91 0.137 140.00 59.13 10.46 50 1.152 16.00 0.072 21.50 0.090 222.22 59.59 7.12On one hand, these results show that the maximum electric power and the related conversion efficiency decrease with an increase of the magnetic field; on the other hand the fill factor and the resistance at the maximum power point increase with an increase of the magnetic field. These experimental results are in agreement with the findings of the studies conducted on a silicon solar cell [10, 11] and on a silicon photovoltaic module [8, 11].Within the limits of this study, it is clear that the efficiency of a solar module is affected by the presence of a magnetic field. However, the magnitude of ambient magnetic field generated by power transmissions lines and other equipment is extremely low (in the order of 10−2 mT or less as illustrated in Table 5) as compared to the values of the magnetic field used in this study. That makes it difficult to conclude as to the impact of such field on solar photovoltaic installations.Table 5
Magnetic field from high voltage power transmission lines [9].
Voltage (kV) Magnitude of the magnetic field from high voltage power transmission lines according to distance to the source (mT) 0 m 30 m 100 m 400 0.03 0.012 0.001 225 0.02 0.003 0.0003 90 0.01 0.001 0.0001


## 3.3.2. Series and Shunt Resistances of the Equivalent Circuit of the Photovoltaic Module

The experimental values of the series and shunt resistances of the equivalent circuit of the photovoltaic module were calculated using equations suggested by Combari et al. [8].Table6 gives the series and shunt resistances of the equivalent circuit of the photovoltaic module.Table 6
Series and shunt resistance of the equivalent circuit of the photovoltaic module as a function of the magnetic field and for a solar irradiance of 600 W/m2.
B(mT) 0 15 30 50  R s (Ω) 7.76 9.90 12.20 17.70  R s h (Ω) 257.547 363.430 562.590 888.889The values of the series and shunt resistances of the equivalent circuit of the photovoltaic module increase with the intensity of the magnetic field. This is in line with the results achieved by the theoretical study [8].


## 4. Conclusions

This experimental study shows that the maximum electric power output of a photovoltaic module, hence its conversion efficiency, decreases when the intensity of the magnetic field increases. On the contrary, the fill factor and the resistance at the maximum power point do increase with the intensity of the magnetic field. The increase of the experimental values of the series and shunt resistances of the equivalent circuit of the photovoltaic module under magnetic field confirm its resistive behaviour called magnetoresistance.Thus, the maximum electric power and the conversion efficiency are two electrical parameters extremely dependent on the intensity of the applied magnetic field. Consequently, the presence of relatively important magnetic fields in the neighborhood of a photovoltaic module decreases its performance.However, it is difficult to conclude as to whether ambient magnetic field generated by power transmissions lines and other equipment have noticeable impact on solar photovoltaic installations, since the magnitude of such field is extremely lower compared to the values of the magnetic field used in this study.The authors then recommend further studies that will narrow into magnetic fields in the order of those generated by power transmissions lines, transformers, and other equipment.



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