Journal of Physics: Conference Series

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Fault Diagnosis Strategy for Solar Cells Based on Reverse Derivation of

I-V Curve
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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

Fault Diagnosis Strategy for Solar Cells Based on Reverse

Derivation of I-V Curve

Min Sun 1, Huaxing Zhao 2, Bo Chen 1, Wei Zeng 1, Zaineng Yang 3

1
State Grid Jiangxi Electric Power Research Institute, Nanchang Jiangxi 330096;
2
School of Electrical Automation and Information Engineering, Tianjin University,
Tianjin 300000;
3
Chongqing Southwest Integrated Circuit Design company of limited liability,
Chongqing 401332
(Sun Min E-mail: zysyw@163.com), (Zhao Huaxing E-mail: 760945616@qq.com),
(Chen Bo E-mail: 365936179@qq.com), (Zeng Wei E-mail: eric.zengw@gmail.com)
(Yang Zaineng E-mail: 532462384@qq.com)

Abstract: This paper proposes a fault diagnosis strategy for solar cells based on the reverse
derivation of the I-V curve. This strategy does not require real-time monitoring of the surface
irradiance and average temperature of the solar cell during operation. It only needs to
calculate(establish) the I-V curve library under different irradiance and solar cell temperature
in advance, then measure the open circuit voltage and short circuit current of the photovoltaic
module during operation. And the measured voltage and current at the maximum power point
can determine whether the solar cell is faulty. The possible faults of various solar cells are
simulated by setting up experimental equipment, and the method is used for fault diagnosis.
Experimental results show that the proposed method can effectively monitor various faults of
solar cells. The method improves the accuracy of fault detection of the solar cell, enhances the
reliability and economical benefits of the photovoltaic power station, and realizes online fault
detection of the solar cell.

1. Introduction
With the looming global fossil energy shortage and environmental pollution, the demand for
renewable energy is very urgent [1]. As an important form of renewable energy power generation,
solar power generation has developed rapidly in recent years. In a solar generation station, there are
a large number of solar cells, and the failure characteristics are not obvious. If the failure cannot be
inspected and predicted, it will cause the degradation of the performance of the photovoltaic module,
which may also shorten the service life of the module, or even lead to the early scrapping of the
photovoltaic module and then result in a large economic loss [2]. Therefore, it is of great importance
to study the fault detection method of solar cells.
At present, online fault diagnosis methods for solar modules are mainly based on a feature
comparison. That is, comparing the measured values of the components with the calculated values of
the model. If there is a large deviation between the two results, it can be judged that the component
is faulty. There are two main types of component models—numerical models and artificial

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

intelligence models.
The numerical model refers to the model established based on the physical laws of photovoltaic
modules, such as the classic single (double) diode model. The diagnosis method based on the
numerical model mainly measures the real-time temperature and irradiance and substitutes them into
the numerical model formula to obtain the I-V curve of the photovoltaic cell and the corresponding
working maximum power point. The fault can be detected by the difference between the data of the
maximum power point and the measured power. For example, in [8], researchers proposed a method
of simulating solar system power based on the measured temperature and irradiance and used power
loss to analyze faults. In [9], a method for analyzing solar power generation systems based on
measured temperature and irradiance was proposed. The method of fault diagnosis is based on
power loss. In [10], scholars simulate the solar power generation system in real time through the
environmental irradiance and component temperature changes and automatically monitor the faults
of the solar cell array by defining four electrical indicators.
The artificial intelligence model mainly uses intelligent algorithms to model solar modules, and
the subsequent diagnosis process is basically consistent with the algorithm of the numerical model.
In [3] and [4], corresponding photovoltaic array fault diagnosis methods based on different neural
network algorithms were proposed. In [5], the firefly disturbance sparrow search algorithm-extreme
learning machine was used to realize the diagnosis of solar module faults. In [6], scholars proposed
a photovoltaic array intelligent fault diagnosis method based on an optimized nuclear extreme
learning machine and IV characteristic curve. In [7], a solar photovoltaic power plant fault feature
classification method based on RGB image recognition and convolutional neural network was
proposed. Although there are many theoretical studies on the detection method of artificial
intelligence models, it still faces great challenges in large-scale promotion because it requires a large
amount of data for training, and the training data needs to be updated regularly.
However, the theoretical value in the operating state which is calculated based on the battery
numerical model or the artificial intelligence model, both of them depend on the accurate
measurement of the battery operating environment parameters. Photovoltaic power plants cover a
large area and are widely distributed. The components in the same power plant may have large
differences in operating status, while the temperature and irradiance sensors can only monitor data at
a certain location, and cannot cover all components in the station, so they cannot accurately obtain
the operating parameters of each component, eventually resulting in large errors in diagnostic
results.
This paper proposes a fault diagnosis strategy for solar cells based on the inverse I-V curves. It
does not need to measure the temperature and irradiance of the power station, but to test the
short-circuit current and open circuit voltage of the components, and inversely find them in the
preset I-V curve library and matched I-V curves. By comparing the MPPT point on the curve with
the MPPT point measured by the component, it can be judged whether there is a fault.

2. On-line measurement of electrical parameters of a single component

Since the electrical parameters are easy to measure and the measurement accuracy is high, this study
first realized the online measurement of open circuit voltage, MPPT current, short circuit current,
and other parameters on the photovoltaic panel, and then used the reverse deduction method of I/V
curve to carry out fault identification.
The monitoring circuit used in this study is shown in Figure 1. In the working state, the solar
battery charges the energy storage circuit (a large capacitor, equivalent to a small battery) through a
diode, and at the same time supplies power to the power circuit, and the microcontroller works
normally. When we are monitoring, we first read the voltage and current of the MPPT point. When
we are measuring the short-circuit current, the switch circuit is closed, the solar cell is
short-circuited, and the microcontroller reads the short-circuit current. Because of the energy storage
circuit and anti-reverse diode, the post-stage circuit can work normally without power down. After
the current test, the switch circuit is closed, and the solar cell outputs normally. The open circuit

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

voltage can be measured by stopping the inverter for a short time.

PV+ PV-OUT+

Power
Supply
Circuit
micro Switch
Energy controller circuit
storage
Circuit
PV- PV-OUT-
Current
detection
circuit
Figure 1. Monitoring circuit

3. IV curve library modeling method

3.1 Modeling method of the solar cell module

Due to the photoelectric loss inside the solar cell, the current behavior of the actual solar cell will
deviate from the ideal [11]. To characterize these deviations, researchers have proposed a variety of
photovoltaic cell models, among which the single-diode model is widely used in practical
engineering because of its simplicity and precision.
In the single-diode model, only one diode is connected in parallel with the photogenerated
current source. The calculation formula of its output current I is:
  (V + IRs )   V + IRs
I = I pv − I 0 exp   − 1 −
  Vt n   Rp
(1)
where Vt = N s kT / q is the thermal voltage of the solar cell array, q = 1.602 10 −19
is the electron
charge, k = 1.38110−23 is the Boltzmann constant, T is the Kelvin temperature of the solar cell,
N s is the number of battery groups connected in series, and n is the ideality factor of the diode, I pv ,
I 0 , Rs , R p are respectively the photogenerated current and the diode saturation Current, series
resistance, parallel resistance. The photogenerated current is linearly dependent on irradiance and
also affected by temperature. So, its calculation formula is:
G
I pv = I pv ,n   1 + K I (T − Tn )
 Gn  (2)
where I pv , n , Gn , Tn are the photogenerated current, irradiance, and temperature under the standard
working conditions, respectively, and K I the current temperature coefficient. The diode saturation
current is mainly related to temperature. When matching the open circuit voltage of the model with
the experimental data with a very large temperature range [12], the calculation formula is:
I sc ,n + K I T
I0 =
exp((Voc ,n + KV T ) / nVt ) − 1
(3)
T = T − Tn
(4)
where I sc , n , Voc ,n are the short-circuit current and open-circuit voltage under standard working
conditions, respectively, and KV is the voltage temperature coefficient. Parallel resistance is
mainly related to irradiance, and its calculation formula is:
Rp G
=
Rp ,n Gn
(5)

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

where R p ,n is the parallel resistance under standard working conditions.

The series resistance and diode ideality factor are independent of temperature and irradiance,
namely:
Rs = Rs , n
(6)
n = nn
(7)
where Rs , n , nn are the series resistance and the ideality factor of the diode under standard
working conditions, respectively.
Since it can be determined I 0 by Formula (3), the determination of the output formula first
requires the determination of nn , I pv , n , Rs , n and under standard operating conditions R p ,n . The
output formula is an implicit transcendental formula, and the unknown model parameters cannot be
directly obtained according to the public elementary functions. At the same time, these parameters to
be obtained have a strong correlation, and the values of the parameters vary greatly, so the solution
of the model parameters becomes difficult, extremely difficult [13].
In recent years, researchers have developed many parameter identification methods, among
which the iterative method is widely used in parameter identification. In this paper, the iterative
method is chosen to obtain the model parameters of solar cells.
Since the series resistance of the solar cell is small but the parallel resistance is large, when we
are selecting the initial value, it can be considered I pv ,n  I sc ,n and the value of nn is usually
selected as 1  nn  1.5 . The relationship Rs between and R p is obtained by matching the
maximum power calculated by the model with the actual maximum power [5], and the calculation
formula is:
R p ,n = Vmp,n (Vmp,n + Rs,n I mp,n ) /
  
 Vmp.n + Rs,n I mp,n 

V I − V I e nVt 
 mp,n pv,n mp,n 0, n 
+Vmp,n I 0,n − Pmax,e,n 
  (8)
The initial value is set to [14]:
Rs ,n = 0
(9)
10Voc ,n
R p ,n =
I sc ,n
(10)
[10]
It is constantly corrected in the iterative process I pv , n , and the calculation method is:
Rp,n + Rs,n
I pv,n = I sc,n
Rp,n
(11)
After determining the parameters, the maximum power can be solved by the perturbation and
observation methods. That is, the output voltage is continuously changed according to the power
variation trend until the power decreases when the voltage is changed in both directions, and the
power is the maximum power at this time. The maximum power is compared with the panel
parameters, and when the difference between the two is lower than the threshold, the iteration is
completed, and the parameters at this time are the parameters of the single diode model of the solar
cell.
In summary, the IV curve modeling process is shown in Figure 2:

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

Start

Rs=0
Calculate Rp=Rp, min by formula
(10)
Calculate I0 through formula(3)
Solving Pmax by perturbation
observation method
ΔP=|Pmax-Pmax.e |

ΔP>threshold

Yes

No
Quantitative increase of Rs
Calculate Ipv, n by formula (11)
Calculate Rp, n by formula (8)
Solving Pmax by perturbation
observation method
ΔP=|Pmax -Pmax.e|

End

Figure 2. Flow chart of IV curve library modeling

3.2 IV curve library calculation method

As for the IV curve under standard working conditions, changing the temperature and irradiance,
calculating I pv , I 0 and R p , and building a library of IV curves under a certain range of
temperature and irradiance. A series of IV curves of different irradiance and temperature are shown
in Figure 3(a) and Figure 3(b):

Figure 3. (a) I V Curves under different irradiance

6

4
Current (A)

Cells Temp =30°C，Pmax=174W

Cells Temp =40°C，Pmax=165W
2
Cells Temp =50°C，Pmax=155W
Cells Temp =60°C，Pmax=146W
Cells Temp =70°C，Pmax=136W
1
Cells Temp =80°C，Pmax=126W

0
0 5 10 15 20 25 30 35 40 45
Voltage (V)

Figure 3. (b) I V Curves at different temperatures

These curves have four characteristic parameters: open circuit voltage Voc , short circuit current
I sc , and MPPT point voltage Vmppt and current I mppt . As long as these four parameters are
determined, the approximate shape of this curve can be determined. According to the panel

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

parameters of solar cells, the IV curves under different temperatures and different irradiances can be
obtained by calculation, and then a series of [ Voc , I sc , Vmppt , I mppt ] can be obtained to form an IV
curve library. Through the photovoltaic cell online monitoring module shown above, you can
' ' '
measure V oc , I 'sc , V mppt , find the I mppt same data pair I sc in the IV curve library Voc , and
'
locate the corresponding IV curve Through the actual measurement of V mppt and the curve I mppt ,
'
the corresponding measured maximum power P mppt and theoretical maximum power Pmppt are
obtained and compared. If the difference between the two exceeds the preset threshold value, it can
be determined that the fault exists.

4. Fault monitoring algorithm

I ' sc , I 'mppt , and V 'mppt are measured in real time V ' oc , the measured value of the solar cell with the
'
curve in the I sc , IV curve library locates the corresponding I - V curve according to the measured
' '
value. Therefore, the process of locating the IV curve is that V oc finds I sc the closest point to the
actual measurement in a group of ( I sc , Voc ), that is, to calculate the point distance in
'
two-dimensional space V oc .
In order to correctly reflect the influence of different types of photovoltaic cells and different
environmental parameters, the weighted vector distance method can be used to calculate the spatial
distance. First calculating I =| I sc − I sc | , U =| U oc − U oc | , and then calculating the weighted
' '

error X = I  I +U  U , where  I and are  U the weights corresponding to and U

respectively. For I X , if it is less than the threshold, the corresponding curve can be located,
and if it is greater than the threshold, we need to continue to judge.
Locating the IV curve, we calculate the power deviation between the maximum power point on
the curve and the measured maximum power point. If the power deviation is less than the threshold,
the solar cell is working normally. And if it is greater than the threshold, the solar cell is faulty.
To sum up, the fault monitoring process is shown in Figure 4:
Start

i=1

i=i+1 i>threshold Yes

ΔI=|Isci-I sc|

ΔU=|Uoci-U oc|

calculationΔ
X

The output cannot

Yes ΔX>threshol find the
d corresponding
No curve, which may
Output be faulty
Correspondence
Uoc、IscUmppt、Imppt

P mppt=Vmppt*I mppt
P ,mppt=V ,mppt*I ,mpp

calculationΔP

ΔP>threshold No
Yes

normal
fault
operation

End

Figure 4. Flow chart of fault monitoring

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

5 Results and Discussion

5.1 Experimental platform

The solar power generation system under test is composed of 8 solar panels with a maximum output
power of 400 W and a total capacity of 3200 Wp, which are installed on the roof, as shown in Figure
5. The parameters of the solar panels are shown in Table 1. Installing a monitoring unit on each solar
panel, simulating and monitoring the normal operation status of solar modules, shadow shading
faults, aging faults, short-circuit faults, and short-circuit faults.
Table 1 Parameters of the solar array under standard working conditions
Parameter name numerical value
V oc (V) 53.1
I sc (A) 9.73
V mppt (V) 44.5
I mppt (A) 9.32
P max (W) 414.74
K V (V/K) -0.0028
K I (A/K) 0.0004
NS _ 72

Figure 5. Experimental platform

5.2 I V curve library and I V curve data in normal operation

In order to match the formed I-V curve library data with the minimum precision of the instrument
and the experimental environment, the irradiance of the I-V curve library is constructed according to
the temperature coefficient of the open circuit voltage of the battery panel, the temperature of the
short-circuit current and the temperature irradiance variation range of the experimental area. The
range is set as 1 00-1200 W/m2. With a difference of 10 W/m2, the temperature range is set at
5-60 °C, with a difference of 5 °C. A total of 1332 IV curves were generated. The data of part of the
IV curve library is shown in Table 2.
Table 2 Partial data of IV curve library
V oc (V) I sc (A) V mppt (V) I mppt (A)
51.91 0.97 44.84 0.92
50.82 0.97 43.73 0.92
49.74 0.97 42.62 0.92
48.64 0.97 41.50 0.92
47.55 0.97 40.39 0.91
46.46 0.97 39.29 0.91
45.36 0.98 38.18 0.91
44.26 0.98 37.08 0.91
43.16 0.98 35.98 0.91

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

In order to determine the error range set by the threshold method, the operating data of the solar
cell during the normal operation was collected under different temperatures and irradiances, the
corresponding IV curve was located and the power error was calculated. Some results are shown in
Table 3 and Table 4:
Table 3 Measured data during normal operation
measured
V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W)
value
1 38.78 6.71 48.13 7.29 260.21
2 38.72 6.83 48.14 7.33 264.46
3 38.76 6.77 48.04 7.31 262.41
4 39.07 6.94 48.09 7.51 271.15

Table 4 Data of IV curve during normal operation

curve value V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W) error
1 38.43 6.75 47.28 7.25 259.31 0.0035
2 39.46 6.85 48.33 7.34 270.24 0.0214
3 39.46 6.85 48.33 7.34 270.24 0.0290
4 39.48 7.03 48.37 7.44 277.58 0.0232
According to the experimental results, the maximum power error between measured data and
theoretical data is 3.5 %, so 3.5% is used as the power error threshold.
In order to verify the accuracy of the method for fault discrimination, experiments were carried
out on the shadow occlusion fault, aging fault open circuit, and short circuit fault of the solar system
at different times.

5.3 Shadow occlusion failure experiment

The measured data and curve data corresponding to the shadow occlusion fault experiment are
shown in Table 5 and Table 6:
Table 5 Measured data of shadow occlusion failure
measured
V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W)
value
1 11.78 4.13 45.88 4.49 48.65
2 12.5 4.01 45.72 4.44 50.13
3 11.06 4.63 45.91 4.75 51.21
4 9.46 7.34 46.97 7.45 69.44
5 10.11 4.33 46.4 4.55 43.78

Table 6 Data of IV curve of shadow occlusion failure

curve
V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W) error
value
1 37.85 4.20 46.04 4.51 207.54 0.7656
2 37.85 4.20 46.04 4.51 207.54 0.7585
3 37.94 4.47 46.20 4.80 221.86 0.7692
4 38.46 7.02 47.38 7.55 357.50 0.8058
5 37.88 4.29 46.09 4.61 212.31 0.7938

When a shadow occlusion fault occurs, the power error between the measured data and the

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

corresponding I V curve data is extremely large, both greater than 75 %, far exceeding the set
threshold of 3.5%, which can accurately determine the existence of a fault. This result fully
demonstrates the correctness of the method.

5.4 Aging failure experiment

The main manifestation of aging failure is the increase of series resistance, so the series resistance of
solar modules is simulated. The corresponding measured data and curve data are shown in Table 7
and Table 8:
Table 7 Measured data of aging failure
Resistance (Ω) V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W)
1 38.78 6.71 48.13 7.29 260.21
3 38.25 6.77 48.04 7.31 258.95
5 38.07 6.94 48.09 7.51 264.21

Table 8 Data of IV curve of aging failure

Resistance
V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W) error
(Ω)
1 39.46 6.85 48.33 7.34 270.24 0.0385
3 39.46 6.85 48.33 7.34 270.24 0.0436
5 39.48 7.03 48.40 7.53 277.58 0.0506
When a 1 Ω resistor is connected in series, the power loss is only about 2% of the total power due
to the small power change caused by it. Therefore, after fitting with the curve in the I-V curve
library, the error is only 3.8%. A certain threshold is used to determine the existence of a fault. When
3 Ω and 5 Ω resistors are connected in series, due to the increase of power loss and the error after
fitting increases correspondingly, it is judged that there is a fault.
In summary, when an aging fault occurs, the method proposed in this paper can accurately
determine the existence of a fault.

5.5 Short-circuit and open-circuit fault experiments

Short-circuit and open-circuit faults have more obvious characteristics than the first two faults.
Since the photovoltaic arrays in this paper are connected in series when an open-circuit fault occurs,
the maximum power point current and the short-circuit current are 0, and the corresponding I-V
curve cannot be located at this time, and it is determined that there is a fault. When a short-circuit
fault occurs, the maximum power point voltage and open circuit voltage are 0, and the
corresponding I-V curve cannot be located at this time, and it is determined that there is a fault. The
corresponding measured data are shown in Table 9 and Table 10.
Table 9 Measured data of short circuit fault
Measured V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W)
value
1 0 7.27 0 7.27 0
2 0 6.94 0 6.94 0

Table 10 Measured data of open circuit fault

Measured V mppt (V) Im ppt (A) V OC (V) I sc (A) P max (W)
value
1 48.52 0 48.52 0 0
2 48.68 0 48.68 0 0

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2023 2nd International Conference on Power System and Power Engineering IOP Publishing
Journal of Physics: Conference Series 2564 (2023) 012018 doi:10.1088/1742-6596/2564/1/012018

6. Conclusions
This paper proposes a method for online monitoring of solar module failures and proposes a method
based on an iterative method to calculate IV curves under different working conditions and form a
library of IV curves. By comparing the open-circuit voltage and short-circuit current of the
measured data with the open-circuit voltage and short-circuit current in the I V curve library, the
corresponding I V curve is located. Finally, the threshold method is used to monitor the fault, and
the measured maximum power is compared with the maximum power corresponding to the IV curve.
And if the threshold is exceeded, it is judged that there is a fault. The research method in this paper
is verified by the actual 3200 Wp solar power generation system. Compared with the 5% threshold
of power error used in [15], the power error is reduced and the range of faults that can be identified
is expanded. Compared with the method proposed by predecessors to calculate the theoretical value
by online monitoring of the operating environment of solar modules, this method eliminates the
error caused by monitoring the operating environment and improves the accuracy of fault
monitoring.

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