# Chaotic Extension Neural Network-Based Fault Diagnosis Method for Solar Photovoltaic Systems

Authors: Kuo-Nan Yu; Her-Terng Yau; Jian-Yu Li
Journal: Mathematical Problems in Engineering
 (2014)

---

## Abstract

At present, the solar photovoltaic system is extensively used. However, once a fault occurs, it is inspected manually, which is not economical. In order to remedy the defect of unavailable fault diagnosis at any irradiance and temperature in the literature with chaos synchronization based intelligent fault diagnosis for photovoltaic systems proposed by Hsieh et al., this study proposed a chaotic extension fault diagnosis method combined with error back propagation neural network to overcome this problem. It used the nn toolbox of matlab 2010 for simulation and comparison, measured current irradiance and temperature, and used the maximum power point tracking (MPPT) for chaotic extraction of eigenvalue. The range of extension field was determined by neural network. Finally, the voltage eigenvalue obtained from current temperature and irradiance was used for the fault diagnosis. Comparing the diagnostic rates with the results by Hsieh et al., this scheme can obtain better diagnostic rates when the irradiances or the temperatures are changed.


---

## Body

## 1. Introduction

This study focused on solar photovoltaic fault diagnosis. Solar energy is generated from the sunlight, which is an inexhaustible renewable energy, as compared to other green energies. At present, the solar photovoltaic system has been used in many fields, and current research focuses are the use of this technology, such as efficient storage, environmental issues, and subsequent maintenance. The analysis based on fault diagnosis technology can save labor cost greatly.Many studies have proposed fault diagnosis technologies for photovoltaic system. Most of traditional fault diagnosis technologies are based on intelligent algorithms including neural network [1–3]. For example, in 2009, Wu et al. used BP neural network for fault diagnosis, the diagnostic rate was very high, but a large amount of data was required for learning and training. The convergence of samples was time consuming [4]. In 2011, Syafaruddin et al. used three-layer artificial neural network for fault diagnosis and provided more accurate diagnostic result than one-layer fault diagnosis. However, this method was also time consuming [5]. In 2011, Shimakage et al. discussed photovoltaic system fault diagnosis and used measurement and observation for diagnosis. They recorded the power generated by the faulted photovoltaic system and compared it with the presently measured power. However, the data for comparison were required and time was required to create the database [6]. In 2012, Zhao et al. proposed a decision tree-based diagnostic method for photovoltaic cell. The diagnostic rate of this method was as high as 99.8%, but more than 1,000 times of intercomparison were required in the course of diagnosis [7]. In 2014, Tadj et al. proposed a GISTEL (gisement solaire par télédetection: solar radiation by teledetection) model to improve the photovoltaic cell diagnosis on fuzzy logic estimated satellite image. The method was difficult to be implemented [8]. In 2014, Hsieh et al. used chaotic extension theory for diagnosis, and the accuracy rate was very high. However, due to the limitation of extension theory, the diagnostic rate decreased greatly when the temperature and irradiance changed. This study aims to remedy the defects in the literature [9].In the literature [9], 10-series 2-parallel solar photovoltaic array was used as the model of fault diagnosis. Chaotic synchronization system was combined with extenics for fault diagnosis. However, the classical domain cannot identify the fault state accurately as long as the irradiance and temperature have changed. This study uses BP neural network, so as to remedy the defect of unavailable diagnosis when the irradiance and temperature change, and uses the center of error dynamic trajectories of two chaotic subsystems as eigenvalue, to overcome the decrease in diagnostic rate that resulted from undervoltage at low light level.


## 2. Architecture of Solar Power System

The fault diagnosis module used in this paper is 10-series 2-parallel photovoltaic, as shown in Figure1, and MPPT, the system architecture, is shown in Figure 2; the matlab 2010 is used for simulation. The specifications of SM1611 photovoltaic cell are shown in Table 1 [9].Table 1
Solar panel model and specifications.
Solar panel model
SM 1611
Maximum power (P
MAX)
1.65 W
Open-circuit voltage (V
OC)
3.0 V
Short-circuit current (I
SC)
0.8 AFigure 1
10-series 2-parallel schematic diagram.Figure 2
MPPT control system schematic diagram.The photovoltaic cell is set as short circuit to simulate nine fault states to be illustrated by Table2, and the I-V and P-V characteristic curves at different irradiances and temperatures are observed.Table 2
Solar photovoltaic system fault category.
Fault category
Fault condition (short circuit set in faulted solar cell)
Case  1(C1)
There is no fault in two-series connected photovoltaic cells.
Case  2(C2)
One solar cell fault occurs in any series branch of two-series branch photovoltaic system.
Case  3(C3)
Two solar cells have faults in any series branch of two-series branch photovoltaic system.
Case  4(C4)
Three solar cells have faults in any series branch of two-series branch photovoltaic system.
Case  5(C5)
One solar cell fault occurs in both of the two-series branches of two-series branch photovoltaic system.
Case  6(C6)
Two solar cells have faults in both of the two-series branches of two-series branch photovoltaic system.
Case  7(C7)
In the two-series branch photovoltaic system, one solar cell has fault in one-series branch and two solar cells have faults in the other branch.
Case  8(C8)
In the two-series branch photovoltaic system, one solar cell has fault in one-series branch and four solar cells have faults in the other branch.
Case  9(C9)
In the two-series branch photovoltaic system, two solar cells have faults in one-series branch and three solar cells have faults in the other branch.


## 3. Research Method

### 3.1. Chaos Synchronization Theory

The chaos synchronization theory designs a slave system to synchronize a master system. The chaos synchronization system consists of two subsystems, a master system and a slave system, representing the relation between master and servant. This paper uses Lorenz chaos synchronization system, which is highly sensitive to parametric variation, to capture the voltage signal of photovoltaic system and extract the kinematic trajectory of dynamic error. The center of this kinematic trajectory is used as the eigenvalue of fault. The architecture of Lorenz chaos synchronization system is expressed as follows [10]:
(1)
Master:
{
x
˙
1
=
α
(
x
2
-
x
1
)
x
˙
2
=
β
x
1
-
x
1
x
3
-
x
2
x
˙
3
=
x
1
x
2
-
γ
x
3
,
Slave:
{
y
˙
1
=
α
(
y
2
-
y
1
)
y
˙
2
=
β
y
1
-
y
1
y
3
-
y
2
y
˙
3
=
y
1
y
2
-
γ
y
3
,
where α, β, and γ are system parameters and x and y are the state variables. The master-slave system error state can be expressed as e
1
=
x
1
-
y
1, e
2
=
x
2
-
y
2, and e
3
=
x
3
-
y
3; the dynamic error system is expressed as follows [10]:
(2)
[
e
˙
1
e
˙
2
e
˙
3
]
=
[
-
α
α
0
β
-
1
0
0
0
-
γ
]
[
e
1
e
2
e
3
]
+
[
0
-
x
1
x
3
+
y
1
y
3
x
1
x
2
-
y
1
y
2
]
.This paper uses the final dynamic errorse
˙
1, e
˙
2, and e
˙
3 to draw the dynamic error trajectory diagram for observation.


### 3.2. Extension Theory

The extension theory solves contradiction problem quantitatively and qualitatively to change it into compatibility problem. The difference between extension theory and fuzzy theory is that the range of fuzzy set is〈
0,1
〉, whereas the extension is a real number extended from 〈
0,1
〉 to 〈
-
∞
,
∞
〉 [11]. The extension theory is characterized by a small amount of calculation and simplicity, and it has high accuracy rate in evaluating multiple parameters and complex construction. This paper uses this feature to judge the eigenvalue captured by Lorenz chaos synchronization system to identify the fault category of photovoltaic system.


#### 3.2.1. Matter-Element Theory

In the extension theory, the matter-element is the basic element describing things. The general matter-element model is the mathematical model applied to extension, defined as follows [12]:
(3)
R
(
P
,
C
,
V
)
=
[
P
c
1
v
1
c
2
v
2
⋮
⋮
c
n
v
n
]
,
where R is the matter-element, P is the name of the matter-element, C is the eigenvector, and V is the magnitude vector corresponding to C.


#### 3.2.2. Extension Set

The extension set means the range of set is extended from-
∞ to ∞ to represent the extensibility of thing characteristics, the correlation function is defined as (4), and the correlation grade of extension set can be expressed as Figure 3 [13].Figure 3
Extension set correlation function.Consider(4)
K
(
n
)
=
ρ
(
n
,
N
o
)
D
(
n
,
N
o
,
N
p
)
D
(
n
,
N
o
,
N
p
)
=
{
ρ
(
n
,
N
p
)
-
ρ
(
n
,
N
o
)
,
n
∉
N
o
-
1
,
n
∈
N
o
ρ
(
n
·
N
o
)
=
|
n
-
a
+
b
2
|
-
b
-
a
2
ρ
(
n
·
N
p
)
=
|
n
-
d
+
e
2
|
-
e
-
d
2
,
where K is the correlation grade, N
o is the classical domain, N
s is the neighborhood domain, and N
o
∈
N
s.


### 3.3. Neural Network

The neural network is a computational theory derived from human brain structure, and it consists of many layers of neurons. The neural network is capable of calculation, memorization, reasoning, and logical decision and readjustment. The forward error backpropagation algorithm proposed by Rvomelhart and Mcclelland (1986) has excellent effect on computing nonlinear system. This paper uses this feature to calculate the eigenvalue changed at different temperatures and irradiances and uses BP neural network to determine the classical domain and neighborhood domain of extension theory.The neural network consists of multiple layers of neurons; the input end is called input layer and the output end is called output layer. The hidden layer is between the output layer and input layer. The input layer and the output layer are the basic structures forming the neural network; the hidden layer is dispensable. The basic structure is shown in Figure4 [14].Figure 4
Neural network architecture.


### 3.4. Chaotic Extension Neural Network Diagnosis System and Process

Figure5 shows the system diagnosis process of chaotic extension neural network. First, the measured irradiance, temperature, and V
MPPT are recorded, and the recorded irradiance and temperature are imported into the BP neural network system to obtain the extension classical domain range of chaos center eigenvalue at current irradiance and temperature, and then the recorded voltage is imported into the chaos synchronization system to obtain a kinematic trajectory of chaotic dynamic system. The center point of kinematic trajectory is taken as the basis of diagnosis. Finally, the fault category of photovoltaic system can be identified as long as the obtained signal is imported into the diagnostic system of chaotic extension neural network.Figure 5
System diagnosis process of chaotic extension neural network.


## 3.1. Chaos Synchronization Theory

The chaos synchronization theory designs a slave system to synchronize a master system. The chaos synchronization system consists of two subsystems, a master system and a slave system, representing the relation between master and servant. This paper uses Lorenz chaos synchronization system, which is highly sensitive to parametric variation, to capture the voltage signal of photovoltaic system and extract the kinematic trajectory of dynamic error. The center of this kinematic trajectory is used as the eigenvalue of fault. The architecture of Lorenz chaos synchronization system is expressed as follows [10]:
(1)
Master:
{
x
˙
1
=
α
(
x
2
-
x
1
)
x
˙
2
=
β
x
1
-
x
1
x
3
-
x
2
x
˙
3
=
x
1
x
2
-
γ
x
3
,
Slave:
{
y
˙
1
=
α
(
y
2
-
y
1
)
y
˙
2
=
β
y
1
-
y
1
y
3
-
y
2
y
˙
3
=
y
1
y
2
-
γ
y
3
,
where α, β, and γ are system parameters and x and y are the state variables. The master-slave system error state can be expressed as e
1
=
x
1
-
y
1, e
2
=
x
2
-
y
2, and e
3
=
x
3
-
y
3; the dynamic error system is expressed as follows [10]:
(2)
[
e
˙
1
e
˙
2
e
˙
3
]
=
[
-
α
α
0
β
-
1
0
0
0
-
γ
]
[
e
1
e
2
e
3
]
+
[
0
-
x
1
x
3
+
y
1
y
3
x
1
x
2
-
y
1
y
2
]
.This paper uses the final dynamic errorse
˙
1, e
˙
2, and e
˙
3 to draw the dynamic error trajectory diagram for observation.


## 3.2. Extension Theory

The extension theory solves contradiction problem quantitatively and qualitatively to change it into compatibility problem. The difference between extension theory and fuzzy theory is that the range of fuzzy set is〈
0,1
〉, whereas the extension is a real number extended from 〈
0,1
〉 to 〈
-
∞
,
∞
〉 [11]. The extension theory is characterized by a small amount of calculation and simplicity, and it has high accuracy rate in evaluating multiple parameters and complex construction. This paper uses this feature to judge the eigenvalue captured by Lorenz chaos synchronization system to identify the fault category of photovoltaic system.


### 3.2.1. Matter-Element Theory

In the extension theory, the matter-element is the basic element describing things. The general matter-element model is the mathematical model applied to extension, defined as follows [12]:
(3)
R
(
P
,
C
,
V
)
=
[
P
c
1
v
1
c
2
v
2
⋮
⋮
c
n
v
n
]
,
where R is the matter-element, P is the name of the matter-element, C is the eigenvector, and V is the magnitude vector corresponding to C.


### 3.2.2. Extension Set

The extension set means the range of set is extended from-
∞ to ∞ to represent the extensibility of thing characteristics, the correlation function is defined as (4), and the correlation grade of extension set can be expressed as Figure 3 [13].Figure 3
Extension set correlation function.Consider(4)
K
(
n
)
=
ρ
(
n
,
N
o
)
D
(
n
,
N
o
,
N
p
)
D
(
n
,
N
o
,
N
p
)
=
{
ρ
(
n
,
N
p
)
-
ρ
(
n
,
N
o
)
,
n
∉
N
o
-
1
,
n
∈
N
o
ρ
(
n
·
N
o
)
=
|
n
-
a
+
b
2
|
-
b
-
a
2
ρ
(
n
·
N
p
)
=
|
n
-
d
+
e
2
|
-
e
-
d
2
,
where K is the correlation grade, N
o is the classical domain, N
s is the neighborhood domain, and N
o
∈
N
s.


## 3.2.1. Matter-Element Theory

In the extension theory, the matter-element is the basic element describing things. The general matter-element model is the mathematical model applied to extension, defined as follows [12]:
(3)
R
(
P
,
C
,
V
)
=
[
P
c
1
v
1
c
2
v
2
⋮
⋮
c
n
v
n
]
,
where R is the matter-element, P is the name of the matter-element, C is the eigenvector, and V is the magnitude vector corresponding to C.


## 3.2.2. Extension Set

The extension set means the range of set is extended from-
∞ to ∞ to represent the extensibility of thing characteristics, the correlation function is defined as (4), and the correlation grade of extension set can be expressed as Figure 3 [13].Figure 3
Extension set correlation function.Consider(4)
K
(
n
)
=
ρ
(
n
,
N
o
)
D
(
n
,
N
o
,
N
p
)
D
(
n
,
N
o
,
N
p
)
=
{
ρ
(
n
,
N
p
)
-
ρ
(
n
,
N
o
)
,
n
∉
N
o
-
1
,
n
∈
N
o
ρ
(
n
·
N
o
)
=
|
n
-
a
+
b
2
|
-
b
-
a
2
ρ
(
n
·
N
p
)
=
|
n
-
d
+
e
2
|
-
e
-
d
2
,
where K is the correlation grade, N
o is the classical domain, N
s is the neighborhood domain, and N
o
∈
N
s.


## 3.3. Neural Network

The neural network is a computational theory derived from human brain structure, and it consists of many layers of neurons. The neural network is capable of calculation, memorization, reasoning, and logical decision and readjustment. The forward error backpropagation algorithm proposed by Rvomelhart and Mcclelland (1986) has excellent effect on computing nonlinear system. This paper uses this feature to calculate the eigenvalue changed at different temperatures and irradiances and uses BP neural network to determine the classical domain and neighborhood domain of extension theory.The neural network consists of multiple layers of neurons; the input end is called input layer and the output end is called output layer. The hidden layer is between the output layer and input layer. The input layer and the output layer are the basic structures forming the neural network; the hidden layer is dispensable. The basic structure is shown in Figure4 [14].Figure 4
Neural network architecture.


## 3.4. Chaotic Extension Neural Network Diagnosis System and Process

Figure5 shows the system diagnosis process of chaotic extension neural network. First, the measured irradiance, temperature, and V
MPPT are recorded, and the recorded irradiance and temperature are imported into the BP neural network system to obtain the extension classical domain range of chaos center eigenvalue at current irradiance and temperature, and then the recorded voltage is imported into the chaos synchronization system to obtain a kinematic trajectory of chaotic dynamic system. The center point of kinematic trajectory is taken as the basis of diagnosis. Finally, the fault category of photovoltaic system can be identified as long as the obtained signal is imported into the diagnostic system of chaotic extension neural network.Figure 5
System diagnosis process of chaotic extension neural network.


## 4. Simulation Results and Comparison

This study aims to remedy the defect of unavailable diagnosis at varying irradiance and temperature in the literature [9], so the BP neural network is adopted. Figure 6 is the schematic diagram of system diagnosis.Figure 6
Schematic diagram of system diagnosis of chaotic extension neural network.


### 4.1. Simulation Results

This study uses matlab 2010 and nn toolbox for simulation. The fault category is the short circuit in the solar panel of photovoltaic array, so as to simulate one normal state and eight fault states (i.e., C1~C9), as shown in Table2.The P-V and I-V characteristic curves are different in different states. The additional noise makes the kinematic trajectory of chaos system easier to be identified. Figure7 is the three-dimensional diagram of chaotic dynamic error in the normal state of 500 W/m2 40°C; the chaos center points in various states are taken as the range of extension classical domain, and the BP neural network is used to decide the chaos center points at different temperatures and irradiances. The sunshine intensity is about 400 W/m2~1000 W/m2 during 8:00~16:00 in Taiwan, as shown in Table 3 [15], and the temperature is about 25°C~50°C; the simulation is based on the conditions [9]. Figures 8(a), 8(b), 9(a), and 9(b) show the P-V and I-V characteristic curves at 1000 W/m2 25°C and 500 W/m2 40°C.Table 3
Sunshine intensity in different time intervals.
Time interval (UTC + 08:00)
Irradiance value (W/m2)
7:00~8:00
158~395
8:00~9:00
395~656
9:00~10:00
656~730
10:00~11:00
730~870
11:00~12:00
870~932
12:00~13:00
870~914
13:00~14:00
870~913
14:00~15:00
870~912
15:00~16:00
632~870
16:00~17:00
158~280Figure 7
Three-dimensional diagram of normal chaotic dynamic error at 500 W/m2 40°C.P-V and I-V characteristic curves at 1000 W/m2 25°C.
(a)
P-V
(b)
I-VP-V and I-V characteristic curves at 500 W/m2 40°C.
(a)
I-V
(b)
P-VFirst, the irradiance of 400 W/m2~1000 W/m2 is divided into intervals of 100 irradiance; the temperature is divided into 25°C, 30°C, 40°C, and 50°C intervals as the input ends of BP neural network. The voltage of each interval is taken for chaos signal extraction; the obtained signal center point is used as the output end of neural network. Figures 10 and 11 show the e
˙
1
-
e
˙
3 dynamic error plane and center of different faults at 1000 W/m2 25°C and 500 W/m2 40°C. The data of e
˙
3 center point of each interval are obtained. Table 4 shows the center point values at various irradiances and temperatures. The data are imported into the BP neural network of nn tool for training to calculate the center point of chaotic kinematic trajectory generated in different conditions. In Table 3, the center point adds ±0.5 as the range of extension classical domain, and then the fault voltage signal is imported for fault diagnosis.Table 4
Center point values at different irradiances and temperatures.
Data
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
1000 W/m2 25°C
510.4643
466.6346
403.0097
336.9965
440.9046
367.1505
392.7802
270.0989
318.5866
1000 W/m2 30°C
423.9461
384.2504
331.8281
279.6135
360.4166
296.4365
319.305
223.3225
257.5316
1000 W/m2 40°C
303.6795
273.2271
238.4073
203.3484
253.9672
205.7853
224.6499
162.0302
179.1338
1000 W/m2 50°C
423.9461
384.2504
331.8281
279.6135
360.4166
296.4365
319.305
223.3225
257.5316
900 W/m2 25°C
457.1445
423.7284
371.5272
308.6055
403.0104
340.6735
362.7715
247.7087
296.5857
900 W/m2 30°C
386.6972
353.5165
306.1361
256.1142
333.0595
276.7268
297.0517
204.9426
240.1221
900 W/m2 40°C
280.6887
253.7645
218.3704
186.4827
236.5171
192.9238
209.3046
148.5407
167.4806
900 W/m2 50°C
210.7214
189.524
165.4722
141.7511
144.5628
141.4557
154.9977
112.7255
122.8688
800 W/m2 25°C
391.5921
370.5262
333.048
280.6498
356.0653
308.557
326.1221
223.9556
272.0152
800 W/m2 30°C
341.6574
316.5865
278.4199
231.5121
300.314
253.4934
270.7338
185.3674
221.2131
800 W/m2 40°C
253.9414
231.2014
200.1783
168.4703
216.3469
178.0942
192.5487
134.2771
154.3977
800 W/m2 50°C
192.0345
173.5387
150.5305
127.9922
161.1028
130.758
142.5223
101.6299
113.2707
700 W/m2 25°C
314.5517
304.8765
284.1958
248.2921
297.1806
267.8527
279.592
199.9536
241.466
700 W/m2 30°C
286.7018
271.0453
244.428
207.0795
259.892
225.1551
238.491
164.6638
199.2278
700 W/m2 40°C
222.272
204.5738
179.3767
149.4428
192.5778
160.7518
172.9791
119.1263
140.088
700 W/m2 50°C
170.4388
155.0974
134.6042
113.3157
118.4572
118.4572
128.6777
89.93955
102.556
600 W/m2 25°C
233.7565
230.7093
223.2524
205.8939
227.9525
215.5746
221.084
174.1138
201.5134
600 W/m2 30°C
222.609
215.5159
201.5031
177.5427
209.7437
189.2676
197.7411
144.0344
171.6018
600 W/m2 40°C
184.113
172.3014
154.2809
130.2548
163.7463
139.8199
149.3071
103.04
123.3908
600 W/m2 50°C
145.0369
133.3973
117.3126
97.81224
125.1117
104.0237
112.428
77.50333
90.74045
500 W/m2 25°C
159.2883
158.5788
156.8393
152.0567
157.8894
154.6332
156.2005
138.8777
150.2812
500 W/m2 30°C
156.1902
154.0336
149.3204
139.0552
152.0642
144.0444
147.6893
119.561
135.6136
500 W/m2 40°C
139.2521
133.2785
123.1959
107.7763
128.4807
113.8041
119.9614
86.82071
102.6594
500 W/m2 50°C
114.9432
107.4587
96.52619
81.99123
101.7915
86.67798
92.8941
64.3971
76.65465
400 W/m2 25°C
97.18495
97.04757
96.744
95.95195
96.91125
96.31457
96.61014
93.35858
95.54372
400 W/m2 30°C
96.67736
96.20672
95.20266
92.80305
95.74832
49.29442
49.44406
48.24918
48.96747
400 W/m2 40°C
91.52255
89.52814
85.85849
79.17138
87.73116
81.62739
84.39876
67.59447
76.26249
400 W/m2 50°C
80.47037
76.90738
71.29433
62.91227
73.94753
65.43214
69.12599
51.00417
59.25853Figure 10
e
˙
1
-
e
˙
3 dynamic error plane and center of different faults at 1000 W/m2 25°C.Figure 11
e
˙
1
-
e
˙
3 dynamic error plane and center of different faults at 500 W/m2 40°C.


### 4.2. Comparison

The literature [9] simulated fault diagnosis at 1000 W/m2 25°C, so this study used 1000 W/m2 25°C, 1000 W/m2 30°C, and 900 W/m2 25°C for comparison, as shown in Tables 5(a), 5(b), 6(a), 6(b), 7(a), and 7(b).Table 5
1000 W/m2 25°C diagnostic result.
(a)
Original literature
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
0.71277
-
0.82783
-
0.98066
-
0.76204
-
0.8813
-
0.84332
-
1
-
0.94555
C2
-
0.72198
1
-
0.77112
-
0.97482
-
0.68079
-
0.84335
-
0.79216
-
1
-
0.92876
C3
-
0.97026
-
0.91917
1
-
0.9819
-
0.88336
-
0.88328
-
0.8429
-
1
-
0.94815
C4
-
1
-
0.95903
-
0.88299
1
-
0.93033
-
0.8293
-
0.86864
-
0.88656
-
0.81035
C5
-
0.89264
-
0.83442
-
0.85419
-
0.98472
1
-
0.90089
-
0.86786
-
1
-
0.95529
C6
-
1
-
0.93853
-
0.82443
-
0.91072
-
0.89546
1
-
0.80291
-
0.93911
-
0.85451
C7
-
0.98944
-
0.92881
-
0.81628
-
0.97739
-
0.88633
-
0.84873
1
-
1
-
0.93314
C8
-
1
-
0.92787
-
0.79398
-
0.75559
-
0.87732
-
0.69945
-
0.76872
1
-
0.53752
C9
-
1
-
0.94868
-
0.85341
-
0.8261
-
0.91271
-
0.78616
-
0.83544
-
0.78829
1
(b)
This paper
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
1
-
0.98248
-
0.97801
-
0.98897
-
0.97954
-
0.98146
-
0.976
-
0.97732
C2
-
0.47293
1
-
0.62539
-
0.88383
-
0.25053
-
0.79562
-
0.68466
-
1
-
0.92394
C3
-
0.89219
-
0.62946
1
-
0.64614
-
0.40071
-
0.37748
-
0.0395
-
1
-
0.76833
C4
-
1
-
0.89251
-
0.60889
1
-
0.80349
-
0.28261
-
0.5355
-
0.61376
-
0.1127
C5
-
0.62227
-
0.20589
-
0.35382
-
0.79961
1
-
0.64747
-
0.45607
-
1
-
0.8688
C6
-
1
-
0.82528
-
0.36424
-
0.29859
-
0.68056
1
-
0.24494
-
0.81261
-
0.48768
C7
-
0.97836
-
0.73257
-
0.07283
-
0.59351
-
0.52725
-
0.28489
1
-
1
-
0.73387
C8
-
0.97527
-
0.97663
-
0.98023
-
0.99133
-
0.97776
-
0.98436
-
0.98115
1
-
1
C9
-
1
-
0.9291
-
0.74203
-
0.16318
-
0.87039
-
0.52683
-
0.69363
-
0.52549
1Table 6
1000 W/m2 30°C diagnostic result.
(a)
Original literature
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
-
0.12676
0.535734
0.893778
-
0.16441
1
0.280185
0.713481
-
1
-
0.42615
C2
-
1
-
0.37627
0.781551
0.200473
0.060822
0.796451
1
-
0.88258
-
0.1439
C3
-
1
-
0.63702
0.036782
1
-
0.38265
0.512455
0.163909
0.131216
0.844341
C4
-
1
-
0.75659
-
0.30474
0.341188
-
0.58601
0.014244
-
0.21949
1
0.560711
C5
-
1
-
0.52001
0.370992
0.683991
-
0.18365
1
0.539099
-
0.35383
0.350138
C6
-
1
-
0.68808
-
0.10905
0.718689
-
0.46948
0.29972
0.000199
0.927234
1
C7
-
1
-
0.93896
-
0.82566
-
0.66369
-
0.89619
-
0.74567
-
0.80428
-
0.75234
1
C8
-
1
-
0.79017
-
0.40065
0.156169
-
0.64312
-
0.12567
-
0.32716
1
0.345408
C9
-
1
-
0.79017
-
0.40065
0.156169
-
0.64312
-
0.12567
-
0.32716
1
0.345408
(b)
This paper
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
1
-
0.98075
-
0.97562
-
0.98721
-
0.97681
-
0.97904
-
0.9731
-
0.97443
C2
-
0.50963
1
-
0.62158
-
0.87545
-
0.30151
-
0.81663
-
0.7059
-
1
-
0.93444
C3
-
0.91719
-
0.63621
1
-
0.63327
-
0.37768
-
0.46009
-
0.13406
-
1
-
0.80697
C4
-
1
-
0.87978
-
0.58433
1
-
0.77377
-
0.14027
-
0.46523
-
0.61615
-
0.22971
C5
-
0.67223
-
0.26196
-
0.32826
-
0.77891
1
-
0.6745
-
0.47794
-
1
-
0.88363
C6
-
1
-
0.83391
-
0.42575
-
0.16331
-
0.68747
1
-
0.26122
-
0.74861
-
0.46405
C7
-
1
-
0.75352
-
0.1478
-
0.51948
-
0.5362
-
0.30847
1
-
0.95434
-
0.72744
C8
-
0.96412
-
0.96588
-
0.97019
-
0.9827
-
0.96743
-
0.97668
-
0.97193
1
-
1
C9
-
1
-
0.93576
-
0.77789
-
0.32037
-
0.87912
-
0.54062
-
0.71426
-
0.48932
1Table 7
900 W/m2 25°C diagnostic result.
(a)
Original literature
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
0.39087
1
0.35864
-
0.39016
0.900709
-
0.07243
0.23286
-
1
-
0.57939
C2
-
0.13222
0.533484
0.909789
-
0.15757
1
0.290808
0.727889
-
1
-
0.42149
C3
-
1
-
0.69818
-
0.1379
-
0.17831
-
0.48667
1
-
0.03219
-
0.76564
-
0.36617
C4
-
1
-
0.68808
-
0.10905
0.718689
-
0.46948
0.29972
0.000199
0.555377
1
C5
-
0.97245
-
0.92459
1
-
0.92894
-
0.89105
-
0.89051
-
0.85263
-
1
-
0.95137
C6
-
1
-
0.87885
-
0.65397
1
-
0.79396
-
0.49521
-
0.61154
-
0.695
-
0.47851
C7
-
1
-
0.76003
-
0.31456
-
0.19902
-
0.59186
1
-
0.23051
-
0.70642
-
0.36204
C8
-
1
-
0.79017
-
0.40065
0.156169
-
0.64312
-
0.12567
-
0.32716
1
0.345408
C9
-
1
-
0.68808
-
0.10905
0.718689
-
0.46948
0.29972
0.000199
0.921613
1
(b)
This paper
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
1
-
0.97775
-
0.97193
-
0.98589
-
0.9741
-
0.97647
-
0.96965
-
0.97134
C2
-
0.42441
1
-
0.60899
-
0.88998
-
0.21619
-
0.7852
-
0.67089
-
1
-
0.91837
C3
-
0.81912
-
0.57699
1
-
0.66532
-
0.35669
-
0.34659
0.00116
-
1
-
0.75167
C4
-
1
-
0.90157
-
0.64017
1
-
0.81906
-
0.34539
-
0.5728
-
0.6241
-
0.0134
C5
-
0.56918
-
0.16613
-
0.32758
-
0.8108
1
-
0.63062
-
0.43403
-
1
-
0.85962
C6
-
1
-
0.82945
-
0.37656
-
0.38985
-
0.68651
1
-
0.25984
-
0.88577
-
0.52306
C7
-
0.89864
-
0.67586
-
0.03513
-
0.61682
-
0.48165
-
0.25189
1
-
1
-
0.71569
C8
-
0.97645
-
0.97778
-
0.98132
-
0.99383
-
0.9789
-
0.9853
-
0.98223
1
-
1
C9
-
1
-
0.92758
-
0.73526
-
0.05418
-
0.86688
-
0.51838
-
0.6857
-
0.56027
1Table8 compares the diagnostic rates and shows the diagnostic method of the literature [9]. When the irradiance is unchanged and the temperature rises by 5°C, the diagnostic rate decreases to 22.23% as the range of chaotic kinematic trajectory is changed. When the irradiance decreases to 1000 W/m2 and the temperature is unchanged, the diagnostic rate is only 11.11%. The diagnostic rate will decrease greatly if the temperature or irradiance changes.Table 8
Comparison of diagnostic rates.
State
Category
Diagnostic rate in literature [9]
Diagnostic rate in this paper
1000 W/m2 25°C
100%
100%
1000 W/m2 30°C
11.11%
100%
900 W/m2 25°C
22.23%
100%


## 4.1. Simulation Results

This study uses matlab 2010 and nn toolbox for simulation. The fault category is the short circuit in the solar panel of photovoltaic array, so as to simulate one normal state and eight fault states (i.e., C1~C9), as shown in Table2.The P-V and I-V characteristic curves are different in different states. The additional noise makes the kinematic trajectory of chaos system easier to be identified. Figure7 is the three-dimensional diagram of chaotic dynamic error in the normal state of 500 W/m2 40°C; the chaos center points in various states are taken as the range of extension classical domain, and the BP neural network is used to decide the chaos center points at different temperatures and irradiances. The sunshine intensity is about 400 W/m2~1000 W/m2 during 8:00~16:00 in Taiwan, as shown in Table 3 [15], and the temperature is about 25°C~50°C; the simulation is based on the conditions [9]. Figures 8(a), 8(b), 9(a), and 9(b) show the P-V and I-V characteristic curves at 1000 W/m2 25°C and 500 W/m2 40°C.Table 3
Sunshine intensity in different time intervals.
Time interval (UTC + 08:00)
Irradiance value (W/m2)
7:00~8:00
158~395
8:00~9:00
395~656
9:00~10:00
656~730
10:00~11:00
730~870
11:00~12:00
870~932
12:00~13:00
870~914
13:00~14:00
870~913
14:00~15:00
870~912
15:00~16:00
632~870
16:00~17:00
158~280Figure 7
Three-dimensional diagram of normal chaotic dynamic error at 500 W/m2 40°C.P-V and I-V characteristic curves at 1000 W/m2 25°C.
(a)
P-V
(b)
I-VP-V and I-V characteristic curves at 500 W/m2 40°C.
(a)
I-V
(b)
P-VFirst, the irradiance of 400 W/m2~1000 W/m2 is divided into intervals of 100 irradiance; the temperature is divided into 25°C, 30°C, 40°C, and 50°C intervals as the input ends of BP neural network. The voltage of each interval is taken for chaos signal extraction; the obtained signal center point is used as the output end of neural network. Figures 10 and 11 show the e
˙
1
-
e
˙
3 dynamic error plane and center of different faults at 1000 W/m2 25°C and 500 W/m2 40°C. The data of e
˙
3 center point of each interval are obtained. Table 4 shows the center point values at various irradiances and temperatures. The data are imported into the BP neural network of nn tool for training to calculate the center point of chaotic kinematic trajectory generated in different conditions. In Table 3, the center point adds ±0.5 as the range of extension classical domain, and then the fault voltage signal is imported for fault diagnosis.Table 4
Center point values at different irradiances and temperatures.
Data
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
1000 W/m2 25°C
510.4643
466.6346
403.0097
336.9965
440.9046
367.1505
392.7802
270.0989
318.5866
1000 W/m2 30°C
423.9461
384.2504
331.8281
279.6135
360.4166
296.4365
319.305
223.3225
257.5316
1000 W/m2 40°C
303.6795
273.2271
238.4073
203.3484
253.9672
205.7853
224.6499
162.0302
179.1338
1000 W/m2 50°C
423.9461
384.2504
331.8281
279.6135
360.4166
296.4365
319.305
223.3225
257.5316
900 W/m2 25°C
457.1445
423.7284
371.5272
308.6055
403.0104
340.6735
362.7715
247.7087
296.5857
900 W/m2 30°C
386.6972
353.5165
306.1361
256.1142
333.0595
276.7268
297.0517
204.9426
240.1221
900 W/m2 40°C
280.6887
253.7645
218.3704
186.4827
236.5171
192.9238
209.3046
148.5407
167.4806
900 W/m2 50°C
210.7214
189.524
165.4722
141.7511
144.5628
141.4557
154.9977
112.7255
122.8688
800 W/m2 25°C
391.5921
370.5262
333.048
280.6498
356.0653
308.557
326.1221
223.9556
272.0152
800 W/m2 30°C
341.6574
316.5865
278.4199
231.5121
300.314
253.4934
270.7338
185.3674
221.2131
800 W/m2 40°C
253.9414
231.2014
200.1783
168.4703
216.3469
178.0942
192.5487
134.2771
154.3977
800 W/m2 50°C
192.0345
173.5387
150.5305
127.9922
161.1028
130.758
142.5223
101.6299
113.2707
700 W/m2 25°C
314.5517
304.8765
284.1958
248.2921
297.1806
267.8527
279.592
199.9536
241.466
700 W/m2 30°C
286.7018
271.0453
244.428
207.0795
259.892
225.1551
238.491
164.6638
199.2278
700 W/m2 40°C
222.272
204.5738
179.3767
149.4428
192.5778
160.7518
172.9791
119.1263
140.088
700 W/m2 50°C
170.4388
155.0974
134.6042
113.3157
118.4572
118.4572
128.6777
89.93955
102.556
600 W/m2 25°C
233.7565
230.7093
223.2524
205.8939
227.9525
215.5746
221.084
174.1138
201.5134
600 W/m2 30°C
222.609
215.5159
201.5031
177.5427
209.7437
189.2676
197.7411
144.0344
171.6018
600 W/m2 40°C
184.113
172.3014
154.2809
130.2548
163.7463
139.8199
149.3071
103.04
123.3908
600 W/m2 50°C
145.0369
133.3973
117.3126
97.81224
125.1117
104.0237
112.428
77.50333
90.74045
500 W/m2 25°C
159.2883
158.5788
156.8393
152.0567
157.8894
154.6332
156.2005
138.8777
150.2812
500 W/m2 30°C
156.1902
154.0336
149.3204
139.0552
152.0642
144.0444
147.6893
119.561
135.6136
500 W/m2 40°C
139.2521
133.2785
123.1959
107.7763
128.4807
113.8041
119.9614
86.82071
102.6594
500 W/m2 50°C
114.9432
107.4587
96.52619
81.99123
101.7915
86.67798
92.8941
64.3971
76.65465
400 W/m2 25°C
97.18495
97.04757
96.744
95.95195
96.91125
96.31457
96.61014
93.35858
95.54372
400 W/m2 30°C
96.67736
96.20672
95.20266
92.80305
95.74832
49.29442
49.44406
48.24918
48.96747
400 W/m2 40°C
91.52255
89.52814
85.85849
79.17138
87.73116
81.62739
84.39876
67.59447
76.26249
400 W/m2 50°C
80.47037
76.90738
71.29433
62.91227
73.94753
65.43214
69.12599
51.00417
59.25853Figure 10
e
˙
1
-
e
˙
3 dynamic error plane and center of different faults at 1000 W/m2 25°C.Figure 11
e
˙
1
-
e
˙
3 dynamic error plane and center of different faults at 500 W/m2 40°C.


## 4.2. Comparison

The literature [9] simulated fault diagnosis at 1000 W/m2 25°C, so this study used 1000 W/m2 25°C, 1000 W/m2 30°C, and 900 W/m2 25°C for comparison, as shown in Tables 5(a), 5(b), 6(a), 6(b), 7(a), and 7(b).Table 5
1000 W/m2 25°C diagnostic result.
(a)
Original literature
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
0.71277
-
0.82783
-
0.98066
-
0.76204
-
0.8813
-
0.84332
-
1
-
0.94555
C2
-
0.72198
1
-
0.77112
-
0.97482
-
0.68079
-
0.84335
-
0.79216
-
1
-
0.92876
C3
-
0.97026
-
0.91917
1
-
0.9819
-
0.88336
-
0.88328
-
0.8429
-
1
-
0.94815
C4
-
1
-
0.95903
-
0.88299
1
-
0.93033
-
0.8293
-
0.86864
-
0.88656
-
0.81035
C5
-
0.89264
-
0.83442
-
0.85419
-
0.98472
1
-
0.90089
-
0.86786
-
1
-
0.95529
C6
-
1
-
0.93853
-
0.82443
-
0.91072
-
0.89546
1
-
0.80291
-
0.93911
-
0.85451
C7
-
0.98944
-
0.92881
-
0.81628
-
0.97739
-
0.88633
-
0.84873
1
-
1
-
0.93314
C8
-
1
-
0.92787
-
0.79398
-
0.75559
-
0.87732
-
0.69945
-
0.76872
1
-
0.53752
C9
-
1
-
0.94868
-
0.85341
-
0.8261
-
0.91271
-
0.78616
-
0.83544
-
0.78829
1
(b)
This paper
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
1
-
0.98248
-
0.97801
-
0.98897
-
0.97954
-
0.98146
-
0.976
-
0.97732
C2
-
0.47293
1
-
0.62539
-
0.88383
-
0.25053
-
0.79562
-
0.68466
-
1
-
0.92394
C3
-
0.89219
-
0.62946
1
-
0.64614
-
0.40071
-
0.37748
-
0.0395
-
1
-
0.76833
C4
-
1
-
0.89251
-
0.60889
1
-
0.80349
-
0.28261
-
0.5355
-
0.61376
-
0.1127
C5
-
0.62227
-
0.20589
-
0.35382
-
0.79961
1
-
0.64747
-
0.45607
-
1
-
0.8688
C6
-
1
-
0.82528
-
0.36424
-
0.29859
-
0.68056
1
-
0.24494
-
0.81261
-
0.48768
C7
-
0.97836
-
0.73257
-
0.07283
-
0.59351
-
0.52725
-
0.28489
1
-
1
-
0.73387
C8
-
0.97527
-
0.97663
-
0.98023
-
0.99133
-
0.97776
-
0.98436
-
0.98115
1
-
1
C9
-
1
-
0.9291
-
0.74203
-
0.16318
-
0.87039
-
0.52683
-
0.69363
-
0.52549
1Table 6
1000 W/m2 30°C diagnostic result.
(a)
Original literature
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
-
0.12676
0.535734
0.893778
-
0.16441
1
0.280185
0.713481
-
1
-
0.42615
C2
-
1
-
0.37627
0.781551
0.200473
0.060822
0.796451
1
-
0.88258
-
0.1439
C3
-
1
-
0.63702
0.036782
1
-
0.38265
0.512455
0.163909
0.131216
0.844341
C4
-
1
-
0.75659
-
0.30474
0.341188
-
0.58601
0.014244
-
0.21949
1
0.560711
C5
-
1
-
0.52001
0.370992
0.683991
-
0.18365
1
0.539099
-
0.35383
0.350138
C6
-
1
-
0.68808
-
0.10905
0.718689
-
0.46948
0.29972
0.000199
0.927234
1
C7
-
1
-
0.93896
-
0.82566
-
0.66369
-
0.89619
-
0.74567
-
0.80428
-
0.75234
1
C8
-
1
-
0.79017
-
0.40065
0.156169
-
0.64312
-
0.12567
-
0.32716
1
0.345408
C9
-
1
-
0.79017
-
0.40065
0.156169
-
0.64312
-
0.12567
-
0.32716
1
0.345408
(b)
This paper
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
1
-
0.98075
-
0.97562
-
0.98721
-
0.97681
-
0.97904
-
0.9731
-
0.97443
C2
-
0.50963
1
-
0.62158
-
0.87545
-
0.30151
-
0.81663
-
0.7059
-
1
-
0.93444
C3
-
0.91719
-
0.63621
1
-
0.63327
-
0.37768
-
0.46009
-
0.13406
-
1
-
0.80697
C4
-
1
-
0.87978
-
0.58433
1
-
0.77377
-
0.14027
-
0.46523
-
0.61615
-
0.22971
C5
-
0.67223
-
0.26196
-
0.32826
-
0.77891
1
-
0.6745
-
0.47794
-
1
-
0.88363
C6
-
1
-
0.83391
-
0.42575
-
0.16331
-
0.68747
1
-
0.26122
-
0.74861
-
0.46405
C7
-
1
-
0.75352
-
0.1478
-
0.51948
-
0.5362
-
0.30847
1
-
0.95434
-
0.72744
C8
-
0.96412
-
0.96588
-
0.97019
-
0.9827
-
0.96743
-
0.97668
-
0.97193
1
-
1
C9
-
1
-
0.93576
-
0.77789
-
0.32037
-
0.87912
-
0.54062
-
0.71426
-
0.48932
1Table 7
900 W/m2 25°C diagnostic result.
(a)
Original literature
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
0.39087
1
0.35864
-
0.39016
0.900709
-
0.07243
0.23286
-
1
-
0.57939
C2
-
0.13222
0.533484
0.909789
-
0.15757
1
0.290808
0.727889
-
1
-
0.42149
C3
-
1
-
0.69818
-
0.1379
-
0.17831
-
0.48667
1
-
0.03219
-
0.76564
-
0.36617
C4
-
1
-
0.68808
-
0.10905
0.718689
-
0.46948
0.29972
0.000199
0.555377
1
C5
-
0.97245
-
0.92459
1
-
0.92894
-
0.89105
-
0.89051
-
0.85263
-
1
-
0.95137
C6
-
1
-
0.87885
-
0.65397
1
-
0.79396
-
0.49521
-
0.61154
-
0.695
-
0.47851
C7
-
1
-
0.76003
-
0.31456
-
0.19902
-
0.59186
1
-
0.23051
-
0.70642
-
0.36204
C8
-
1
-
0.79017
-
0.40065
0.156169
-
0.64312
-
0.12567
-
0.32716
1
0.345408
C9
-
1
-
0.68808
-
0.10905
0.718689
-
0.46948
0.29972
0.000199
0.921613
1
(b)
This paper
Status
Case
C1
C2
C3
C4
C5
C6
C7
C8
C9
C1
1
-
1
-
0.97775
-
0.97193
-
0.98589
-
0.9741
-
0.97647
-
0.96965
-
0.97134
C2
-
0.42441
1
-
0.60899
-
0.88998
-
0.21619
-
0.7852
-
0.67089
-
1
-
0.91837
C3
-
0.81912
-
0.57699
1
-
0.66532
-
0.35669
-
0.34659
0.00116
-
1
-
0.75167
C4
-
1
-
0.90157
-
0.64017
1
-
0.81906
-
0.34539
-
0.5728
-
0.6241
-
0.0134
C5
-
0.56918
-
0.16613
-
0.32758
-
0.8108
1
-
0.63062
-
0.43403
-
1
-
0.85962
C6
-
1
-
0.82945
-
0.37656
-
0.38985
-
0.68651
1
-
0.25984
-
0.88577
-
0.52306
C7
-
0.89864
-
0.67586
-
0.03513
-
0.61682
-
0.48165
-
0.25189
1
-
1
-
0.71569
C8
-
0.97645
-
0.97778
-
0.98132
-
0.99383
-
0.9789
-
0.9853
-
0.98223
1
-
1
C9
-
1
-
0.92758
-
0.73526
-
0.05418
-
0.86688
-
0.51838
-
0.6857
-
0.56027
1Table8 compares the diagnostic rates and shows the diagnostic method of the literature [9]. When the irradiance is unchanged and the temperature rises by 5°C, the diagnostic rate decreases to 22.23% as the range of chaotic kinematic trajectory is changed. When the irradiance decreases to 1000 W/m2 and the temperature is unchanged, the diagnostic rate is only 11.11%. The diagnostic rate will decrease greatly if the temperature or irradiance changes.Table 8
Comparison of diagnostic rates.
State
Category
Diagnostic rate in literature [9]
Diagnostic rate in this paper
1000 W/m2 25°C
100%
100%
1000 W/m2 30°C
11.11%
100%
900 W/m2 25°C
22.23%
100%


## 5. Conclusion

The chaotic extension neural network diagnosis proposed in this paper is integrated with error backpropagation neural network. It can remedy the defect of large decrease in diagnostic rate when the irradiance and temperature have changed in the original literature effectively. The defect in the original literature is remedied, and the high diagnostic rate in the original literature is maintained. In comparison to the original neural network diagnosis, the addition of extension theory reduces the time of repeated training. In addition, as the chaos synchronization theory is used, when the diagnosis is difficult due to undervoltage caused by the environment, the signal can be amplified by using the advantages of chaos theory for diagnosis.



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*Source: 280520-2014-05-13.xml*