# Intelligent Fault Diagnosis in a Power Distribution Network

Authors: Oluleke O. Babayomi; Peter O. Oluseyi
Journal: Advances in Electrical Engineering
 (2016)

---

## Abstract

This paper presents a novel method of fault diagnosis by the use of fuzzy logic and neural network-based techniques for electric power fault detection, classification, and location in a power distribution network. A real network was used as a case study. The ten different types of line faults including single line-to-ground, line-to-line, double line-to-ground, and three-phase faults were investigated. The designed system has 89% accuracy for fault type identification. It also has 93% accuracy for fault location. The results indicate that the proposed technique is effective in detecting, classifying, and locating low impedance faults.


---

## Body

## 1. Introduction

Fault diagnosis and resolution in a power system network are essential for clearing faults that manifest in an electrical power transmission or distribution network. The process of fault resolution comprises three stages: first, the detection and identification or classification of unusual voltage and current characteristics at the affected portions of the network; next, the location of the incidence of the fault to enable quick access and solution to the problems that arise in the power network; and finally, the fault being cleared within the shortest time possible to prevent damage to unaffected parts of the network.


### 1.1. Related Work

Numerous studies have been carried out on the use of intelligent methods for electric fault diagnosis in an electrical system. Some of these methods include expert systems, artificial neural networks, and fuzzy logic. The following review of related literature will be delimited to artificial neural network and fuzzy logic applications.In certain studies, neural network principles were not applied to the power fault diagnostic process. Thus, they lacked the capabilities to learn from data gathered from the electrical network. This was the case in [1], where fuzzy logic-based fault identification in an electric power distribution system was studied and proven to produce accurate classifications of fault types. In addition, the fuzzy logic method was used in combination with discrete wavelet transform and resulted in accurate fault identification [2]. In [3], the data collected by alarms and protection relays in a power network was analyzed with neurofuzzy techniques. A classification based on input signals into faulty component type with a high degree of accuracy was achieved in spite of corrupted alarm signals. Petri net and neurofuzzy methods were used in [4, 5] for fault location in power lines and sections. The adaptive neurofuzzy inference system (ANFIS) was employed in [6] for accurate fault location for transmission lines and underground cables. However, the described procedures in [3–6] are not suitable for power distribution networks.A neurofuzzy means of fault classification, location, and power restoration plan in an electric power distribution system was developed in [7]. Three ANFIS modules were employed for fault type classification, x-coordinates, and y-coordinates of the fault location, respectively. The resulting system performed with a high degree of accuracy. However, it has a shortcoming in the level of accuracy of fault type classification which can be improved upon. The robustness and precision of ANFIS were validated in [8] by testing the characteristics of the system after the addition of white noise to input data.The accuracy of the fuzzy inference system method of fault diagnosis varies with complementary analytical tools employed to enhance the capabilities of the system. Reference [8] reported 78% accuracy in fault type identification when the fuzzy inference was used to analyze data derived by the wavelet transform method. 91% accuracy was reported in [9] for fault detection, while 93% accuracy was achieved for fault location when the first and third harmonic data sets derived from discrete Fourier transform of fault current were applied to intelligent fault diagnosis. In [10], a wavelet multiresolution analysis was used to extract harmonics generated by current transients due to fault incidences. This data was used to develop an ANFIS model that gave accurate fault location with a maximum error of 5%. Furthermore, through a Monte Carlo simulation, the derived algorithm was proven to be immune to the effects of fault impedance, power angle, fault distance, and fault inception angle. While past researchers have focused on the application of either fuzzy logic or ANFIS for fault detection, classification, and location, we propose the use of a fuzzy logic controller for fault identification and ANFIS for fault location for enhanced accuracies.This research work focuses on the detection, identification, and location of faults in the distribution network of a power system. Fault detection is achieved by a fault analysis and the determination of positive, negative, and zero sequence currents and voltages of the power network. Thereafter, a fuzzy controller is included in the network to identify the fault type on the occurrence of a fault. In addition, a neurofuzzy based fault location model is developed. A distribution network in the Nigerian power grid is used as a case study. The ensuing discussion starts with a computational model, describes the methodology employed in the study, and rounds off with insights drawn from the results obtained.


## 1.1. Related Work

Numerous studies have been carried out on the use of intelligent methods for electric fault diagnosis in an electrical system. Some of these methods include expert systems, artificial neural networks, and fuzzy logic. The following review of related literature will be delimited to artificial neural network and fuzzy logic applications.In certain studies, neural network principles were not applied to the power fault diagnostic process. Thus, they lacked the capabilities to learn from data gathered from the electrical network. This was the case in [1], where fuzzy logic-based fault identification in an electric power distribution system was studied and proven to produce accurate classifications of fault types. In addition, the fuzzy logic method was used in combination with discrete wavelet transform and resulted in accurate fault identification [2]. In [3], the data collected by alarms and protection relays in a power network was analyzed with neurofuzzy techniques. A classification based on input signals into faulty component type with a high degree of accuracy was achieved in spite of corrupted alarm signals. Petri net and neurofuzzy methods were used in [4, 5] for fault location in power lines and sections. The adaptive neurofuzzy inference system (ANFIS) was employed in [6] for accurate fault location for transmission lines and underground cables. However, the described procedures in [3–6] are not suitable for power distribution networks.A neurofuzzy means of fault classification, location, and power restoration plan in an electric power distribution system was developed in [7]. Three ANFIS modules were employed for fault type classification, x-coordinates, and y-coordinates of the fault location, respectively. The resulting system performed with a high degree of accuracy. However, it has a shortcoming in the level of accuracy of fault type classification which can be improved upon. The robustness and precision of ANFIS were validated in [8] by testing the characteristics of the system after the addition of white noise to input data.The accuracy of the fuzzy inference system method of fault diagnosis varies with complementary analytical tools employed to enhance the capabilities of the system. Reference [8] reported 78% accuracy in fault type identification when the fuzzy inference was used to analyze data derived by the wavelet transform method. 91% accuracy was reported in [9] for fault detection, while 93% accuracy was achieved for fault location when the first and third harmonic data sets derived from discrete Fourier transform of fault current were applied to intelligent fault diagnosis. In [10], a wavelet multiresolution analysis was used to extract harmonics generated by current transients due to fault incidences. This data was used to develop an ANFIS model that gave accurate fault location with a maximum error of 5%. Furthermore, through a Monte Carlo simulation, the derived algorithm was proven to be immune to the effects of fault impedance, power angle, fault distance, and fault inception angle. While past researchers have focused on the application of either fuzzy logic or ANFIS for fault detection, classification, and location, we propose the use of a fuzzy logic controller for fault identification and ANFIS for fault location for enhanced accuracies.This research work focuses on the detection, identification, and location of faults in the distribution network of a power system. Fault detection is achieved by a fault analysis and the determination of positive, negative, and zero sequence currents and voltages of the power network. Thereafter, a fuzzy controller is included in the network to identify the fault type on the occurrence of a fault. In addition, a neurofuzzy based fault location model is developed. A distribution network in the Nigerian power grid is used as a case study. The ensuing discussion starts with a computational model, describes the methodology employed in the study, and rounds off with insights drawn from the results obtained.


## 2. Computational Model

### 2.1. Fault Analysis

Electric power faults in a distribution system occur randomly and their severity varies in intensity. There are four major types of faults: namely, three-phase fault, single line-to-ground fault (LG), line-to-line fault (LL), and double line-to-ground fault (LLG). Amongst these, the three-phase fault is the most severe when it occurs in a power grid, while the line-to-ground fault arises most commonly. LG, LL, and LLG faults cause unbalanced currents to flow through the network and sequence diagrams are employed in the analysis of unbalanced fault incidents in electric networks. The fault currents due to three-phase LG, LL, and LLG faults are given by (1) to (4), respectively. Z
f represents the fault impedance, Z
k
k represents the impedance at bus k, I
f
a
(
0
)
,
I
f
a
(
1
)
,
I
f
a
(
2
) are the zero, positive, and negative sequence fault currents in Phase A, respectively, and V
f is the per unit voltage at the fault point:(1)
I
f
a
1
=
V
f
Z
k
k
1
+
Z
f
,
(2)
I
f
a
0
=
I
f
a
1
=
I
f
a
2
=
V
f
Z
k
k
1
+
Z
k
k
2
+
Z
k
k
3
+
3
Z
f
,
(3)
I
f
a
1
=
I
f
a
2
=
V
f
Z
k
k
1
+
Z
k
k
2
+
Z
f
,
(4)
I
f
a
1
=
V
f
Z
k
k
1
+
Z
k
k
2
Z
k
k
0
+
3
Z
f
/
Z
k
k
2
+
Z
k
k
0
+
3
Z
f
,
I
f
a
2
=
-
I
f
a
1
Z
k
k
0
+
3
Z
f
Z
k
k
2
+
Z
k
k
0
+
3
Z
f
,
I
f
a
0
=
-
I
f
a
1
Z
k
k
2
Z
k
k
2
+
Z
k
k
0
+
3
Z
f
.


### 2.2. Fuzzy Inference System

Fuzzy logic involves reasoning algorithms that mimic human thinking in a manner describable as a kind of gray logic, as opposed to binary logic that uses only two values. Therefore, fuzzy logic associates input data with a range of values between 0 and 1. The data is thus processed by a fuzzy controller in three stages: namely, fuzzification, fuzzy processing, and defuzzification. Fuzzification translates input data into a fuzzy form with the aid of input membership functions. Common membership functions include the triangular-shaped, bell-shaped, S-shaped, and Z -shaped functions. Fuzzy processing associates the fuzzified inputs via a set of IF…THEN rules to determine how the input membership functions will associate. Finally, defuzzification converts the value from the processing stage into an output using methods such as the centre of gravity method and the maximum value method. There are two common fuzzy inference systems (FIS): namely, Sugeno-type FIS and Madami-type FIS. The Sugeno FIS is efficient and works well with mathematical, linear, optimization, and adaptive techniques. On the other hand, the Mandami FIS is intuitive and suitable for human input.


### 2.3. Adaptive Neurofuzzy Inference System

The difference between the adaptive neurofuzzy inference system (ANFIS) and the FIS is that, with the FIS, only fixed membership functions that are chosen arbitrarily are used. However, ANFIS membership functions are adapted to a historical data set. FIS modeling relies heavily on the user’s interpretation of the relationship between the input and output data. On the other hand, ANFIS improves the process by adapting the input and output membership functions to the relationship of a sample set of input/output data. This adaptation for bespoke membership functions is attained through neuroadaptive learning. The learning process works similarly to that of neural networks and calculates membership function parameters that optimally permit the fuzzy inference system to track the input/output data according to the following steps:(1)
Postulate a model structure that relates inputs to outputs through membership functions and fuzzy rules using the Sugeno-type FIS.
(2)
Collect input/output data for training by ANFIS.
(3)
Train the initial model with the data provided constrained by an error criterion.


### 2.4. Case Study

Nigeria’s electricity transmission grid is at a voltage of 330 kV, while the distribution network is a 33 kV/11 kV system managed by eleven distribution companies across the country. The test network shown in Figure1 is an extract from Orile District distribution system, under Eko Electricity Distribution Company (EKEDC).Figure 1
One-line diagram of distribution network.


## 2.1. Fault Analysis

Electric power faults in a distribution system occur randomly and their severity varies in intensity. There are four major types of faults: namely, three-phase fault, single line-to-ground fault (LG), line-to-line fault (LL), and double line-to-ground fault (LLG). Amongst these, the three-phase fault is the most severe when it occurs in a power grid, while the line-to-ground fault arises most commonly. LG, LL, and LLG faults cause unbalanced currents to flow through the network and sequence diagrams are employed in the analysis of unbalanced fault incidents in electric networks. The fault currents due to three-phase LG, LL, and LLG faults are given by (1) to (4), respectively. Z
f represents the fault impedance, Z
k
k represents the impedance at bus k, I
f
a
(
0
)
,
I
f
a
(
1
)
,
I
f
a
(
2
) are the zero, positive, and negative sequence fault currents in Phase A, respectively, and V
f is the per unit voltage at the fault point:(1)
I
f
a
1
=
V
f
Z
k
k
1
+
Z
f
,
(2)
I
f
a
0
=
I
f
a
1
=
I
f
a
2
=
V
f
Z
k
k
1
+
Z
k
k
2
+
Z
k
k
3
+
3
Z
f
,
(3)
I
f
a
1
=
I
f
a
2
=
V
f
Z
k
k
1
+
Z
k
k
2
+
Z
f
,
(4)
I
f
a
1
=
V
f
Z
k
k
1
+
Z
k
k
2
Z
k
k
0
+
3
Z
f
/
Z
k
k
2
+
Z
k
k
0
+
3
Z
f
,
I
f
a
2
=
-
I
f
a
1
Z
k
k
0
+
3
Z
f
Z
k
k
2
+
Z
k
k
0
+
3
Z
f
,
I
f
a
0
=
-
I
f
a
1
Z
k
k
2
Z
k
k
2
+
Z
k
k
0
+
3
Z
f
.


## 2.2. Fuzzy Inference System

Fuzzy logic involves reasoning algorithms that mimic human thinking in a manner describable as a kind of gray logic, as opposed to binary logic that uses only two values. Therefore, fuzzy logic associates input data with a range of values between 0 and 1. The data is thus processed by a fuzzy controller in three stages: namely, fuzzification, fuzzy processing, and defuzzification. Fuzzification translates input data into a fuzzy form with the aid of input membership functions. Common membership functions include the triangular-shaped, bell-shaped, S-shaped, and Z -shaped functions. Fuzzy processing associates the fuzzified inputs via a set of IF…THEN rules to determine how the input membership functions will associate. Finally, defuzzification converts the value from the processing stage into an output using methods such as the centre of gravity method and the maximum value method. There are two common fuzzy inference systems (FIS): namely, Sugeno-type FIS and Madami-type FIS. The Sugeno FIS is efficient and works well with mathematical, linear, optimization, and adaptive techniques. On the other hand, the Mandami FIS is intuitive and suitable for human input.


## 2.3. Adaptive Neurofuzzy Inference System

The difference between the adaptive neurofuzzy inference system (ANFIS) and the FIS is that, with the FIS, only fixed membership functions that are chosen arbitrarily are used. However, ANFIS membership functions are adapted to a historical data set. FIS modeling relies heavily on the user’s interpretation of the relationship between the input and output data. On the other hand, ANFIS improves the process by adapting the input and output membership functions to the relationship of a sample set of input/output data. This adaptation for bespoke membership functions is attained through neuroadaptive learning. The learning process works similarly to that of neural networks and calculates membership function parameters that optimally permit the fuzzy inference system to track the input/output data according to the following steps:(1)
Postulate a model structure that relates inputs to outputs through membership functions and fuzzy rules using the Sugeno-type FIS.
(2)
Collect input/output data for training by ANFIS.
(3)
Train the initial model with the data provided constrained by an error criterion.


## 2.4. Case Study

Nigeria’s electricity transmission grid is at a voltage of 330 kV, while the distribution network is a 33 kV/11 kV system managed by eleven distribution companies across the country. The test network shown in Figure1 is an extract from Orile District distribution system, under Eko Electricity Distribution Company (EKEDC).Figure 1
One-line diagram of distribution network.


## 3. Methodology

### 3.1. Fuzzy Fault Controller Design

The model for a two-input-one-output ANFIS is illustrated in Figure2. The diagram outlines the entire structure of the neurofuzzy inference system. The fuzzy diagnostic controller of interest in Figure 3 has six inputs: namely, I
a
,
I
b
,
I
c
,
V
a
,
V
b, and V
c. These are the phase currents and phase voltages, respectively. The inputs are processed by the fuzzy diagnostic controller and the output is a number representing the particular fault incidence in the distribution network.Figure 2
Basic ANFIS model for a two-input-one-output system.Figure 3
Block diagram of 6-input fuzzy inference system.For the fuzzy inference system (FIS) being designed, the membership functions employed for both input and output are triangular-shaped. Each input has two membership functions labelled LW (low) and HI (high), while the output has eleven membership functions labelled O0 to O10, as illustrated in Figure 4.Figure 4
(a) Fuzzy input membership functions. (b) Fuzzy output membership functions.
(a)
(b)In addition, Table1 shows the sixty-four rules applicable to the 6-input FIS. However, only ten of these define the fault types of interest. The remaining are designed to give outputs of O0, implying that they are nonapplicable situations.Table 1
Fuzzy inference rules for 6-input fault system.
Rule
I
a
I
b
I
c
V
a
V
b
V
c
Output
Fault type
1
HI
LW
LW
LW
HI
HI
1
LG fault, Phase A
2
LW
HI
LW
HI
LW
HI
2
LG fault, Phase B
3
LW
LW
HI
HI
HI
LW
3
LG fault, Phase C
4
HI
HI
LW
HI
HI
HI
4
LL fault, Phases A-B
5
LW
HI
HI
HI
HI
HI
5
LL fault, Phases B-C
6
HI
LW
HI
HI
HI
HI
6
LL fault, Phases A-C
7
HI
HI
LW
LW
LW
HI
7
LLG fault, Phases A-B
8
LW
HI
HI
HI
LW
LW
8
LLG fault, Phases B-C
9
HI
LW
HI
LW
HI
LW
9
LLG fault, Phases A-C
10
HI
HI
HI
LW
LW
LW
10
3-phase fault
11 to 64
All other input combinations
0
N/AFigures5(a) and 5(b) are plots of Load 1 three-phase currents and voltages, respectively, under normal conditions. The calibration of the Mandami-type fuzzy fault controller involved the use of no-load RMS values of current (994 A) and voltage (18.56 kV) as the base design. Values of current and voltage for each of the 10 faults were recorded. Generally, any value of current and voltage 1% above the base values was set as high (HI) and values from 0 to 1.0 pu were low (LW). Table 1 was drawn by recording the characteristics of each phase current and voltage at the incidence of the faults. In Figure 6, the characteristics of currents and voltages are shown for four types of faults that affect Phase A. These plots corroborate the information in Table 1: for example, an LG fault on Phase A results in a high Phase A current, relatively low Phases B and C currents, low Phase A voltage, and relatively high Phases B and C voltages.Figure 5
Load current and voltage during normal conditions: (a) phase currents and (b) phase voltages.
(a)
(b)Figure 6
Plots of Phase A current and voltage during different faults.


### 3.2. ANFIS Model Design

The given distribution network was modeled and simulated with SIMULINK for Load 1 (50 MW, 30 MVar) and Load 2 (60 MW). At Load 1 and Load 2, each of the 10 faults was simulated over a range of values of the fault impedance from 0.001 Ω to 10 Ω for 150 ms. The resulting values of phase currents and voltages were recorded and this data (3,454 data points) was later used to train the FIS. Data for checking the model results was collected at a fault resistance of 6.5 Ω and this set of data was not used in training the FIS. Fault samples were taken 25 ms after the incidence of the fault.The initial Sugeno fuzzy inference system which has six inputs, namely,I
a
,
I
b
,
I
c
,
V
a
,
V
b, and V
c, was chosen to have 3 membership functions of the generalized bell type for each of the inputs. The use of three input membership functions resulted in lower errors than when two membership functions were applied. The output membership function was set as constant, while for optimization hybrid combination of least-squares estimation with back propagation was employed. The initial input membership functions prior to training and after training are illustrated in Figures 7(a) and 7(b). As shown, the training process significantly altered the voltage membership functions. The resulting ANFIS model has 1,503 nodes, 729 linear parameters, 53 nonlinear parameters, and 783 total parameters. 2,570 data points were used for training, while 884 data points were used for checking the model. A parameter-to-training data pair ratio of 3.3 indicates that the training data was sufficient to capture the general characteristics of the physical system.Figure 7
(a) Initial input membership functions. (b) Trained input membership functions.
(a)
(b)The ANFIS designed has twenty outputs. Outputs 10 to 19 represent ten fault types at Load 1, while outputs 20 to 29 represent ten fault types that occur at Load 2. The interpretations of the twenty different outputs are highlighted in Table2.Table 2
Interpretation of ANFIS model output.
ANFIS output
Fault type
10
LG, Ph. A (Load 1)
11
LG, Ph. B (Load 1)
12
LG, Ph. C (Load 1)
13
LL, Ph. A-B (Load 1)
14
LL, Ph. B-C (Load 1)
15
LL, Ph. A-C (Load 1)
16
LLG, Ph. A-B (Load 1)
17
LLG, Ph. B-C (Load 1)
18
LLG, Ph. A-C (Load 1)
19
3-Ph. fault (Load 1)
20
LG, Ph. A (Load 2)
21
LG, Ph. B (Load 2)
22
LG, Ph. C (Load 2)
23
LL, Ph. A-B (Load 2)
24
LL, Ph. B-C (Load 2)
25
LL, Ph. A-C (Load 2)
26
LLG, Ph. A-B (Load 2)
27
LLG, Ph. B-C (Load 2)
28
LLG, Ph. A-C (Load 2)
29
3-Ph. fault (Load 2)


## 3.1. Fuzzy Fault Controller Design

The model for a two-input-one-output ANFIS is illustrated in Figure2. The diagram outlines the entire structure of the neurofuzzy inference system. The fuzzy diagnostic controller of interest in Figure 3 has six inputs: namely, I
a
,
I
b
,
I
c
,
V
a
,
V
b, and V
c. These are the phase currents and phase voltages, respectively. The inputs are processed by the fuzzy diagnostic controller and the output is a number representing the particular fault incidence in the distribution network.Figure 2
Basic ANFIS model for a two-input-one-output system.Figure 3
Block diagram of 6-input fuzzy inference system.For the fuzzy inference system (FIS) being designed, the membership functions employed for both input and output are triangular-shaped. Each input has two membership functions labelled LW (low) and HI (high), while the output has eleven membership functions labelled O0 to O10, as illustrated in Figure 4.Figure 4
(a) Fuzzy input membership functions. (b) Fuzzy output membership functions.
(a)
(b)In addition, Table1 shows the sixty-four rules applicable to the 6-input FIS. However, only ten of these define the fault types of interest. The remaining are designed to give outputs of O0, implying that they are nonapplicable situations.Table 1
Fuzzy inference rules for 6-input fault system.
Rule
I
a
I
b
I
c
V
a
V
b
V
c
Output
Fault type
1
HI
LW
LW
LW
HI
HI
1
LG fault, Phase A
2
LW
HI
LW
HI
LW
HI
2
LG fault, Phase B
3
LW
LW
HI
HI
HI
LW
3
LG fault, Phase C
4
HI
HI
LW
HI
HI
HI
4
LL fault, Phases A-B
5
LW
HI
HI
HI
HI
HI
5
LL fault, Phases B-C
6
HI
LW
HI
HI
HI
HI
6
LL fault, Phases A-C
7
HI
HI
LW
LW
LW
HI
7
LLG fault, Phases A-B
8
LW
HI
HI
HI
LW
LW
8
LLG fault, Phases B-C
9
HI
LW
HI
LW
HI
LW
9
LLG fault, Phases A-C
10
HI
HI
HI
LW
LW
LW
10
3-phase fault
11 to 64
All other input combinations
0
N/AFigures5(a) and 5(b) are plots of Load 1 three-phase currents and voltages, respectively, under normal conditions. The calibration of the Mandami-type fuzzy fault controller involved the use of no-load RMS values of current (994 A) and voltage (18.56 kV) as the base design. Values of current and voltage for each of the 10 faults were recorded. Generally, any value of current and voltage 1% above the base values was set as high (HI) and values from 0 to 1.0 pu were low (LW). Table 1 was drawn by recording the characteristics of each phase current and voltage at the incidence of the faults. In Figure 6, the characteristics of currents and voltages are shown for four types of faults that affect Phase A. These plots corroborate the information in Table 1: for example, an LG fault on Phase A results in a high Phase A current, relatively low Phases B and C currents, low Phase A voltage, and relatively high Phases B and C voltages.Figure 5
Load current and voltage during normal conditions: (a) phase currents and (b) phase voltages.
(a)
(b)Figure 6
Plots of Phase A current and voltage during different faults.


## 3.2. ANFIS Model Design

The given distribution network was modeled and simulated with SIMULINK for Load 1 (50 MW, 30 MVar) and Load 2 (60 MW). At Load 1 and Load 2, each of the 10 faults was simulated over a range of values of the fault impedance from 0.001 Ω to 10 Ω for 150 ms. The resulting values of phase currents and voltages were recorded and this data (3,454 data points) was later used to train the FIS. Data for checking the model results was collected at a fault resistance of 6.5 Ω and this set of data was not used in training the FIS. Fault samples were taken 25 ms after the incidence of the fault.The initial Sugeno fuzzy inference system which has six inputs, namely,I
a
,
I
b
,
I
c
,
V
a
,
V
b, and V
c, was chosen to have 3 membership functions of the generalized bell type for each of the inputs. The use of three input membership functions resulted in lower errors than when two membership functions were applied. The output membership function was set as constant, while for optimization hybrid combination of least-squares estimation with back propagation was employed. The initial input membership functions prior to training and after training are illustrated in Figures 7(a) and 7(b). As shown, the training process significantly altered the voltage membership functions. The resulting ANFIS model has 1,503 nodes, 729 linear parameters, 53 nonlinear parameters, and 783 total parameters. 2,570 data points were used for training, while 884 data points were used for checking the model. A parameter-to-training data pair ratio of 3.3 indicates that the training data was sufficient to capture the general characteristics of the physical system.Figure 7
(a) Initial input membership functions. (b) Trained input membership functions.
(a)
(b)The ANFIS designed has twenty outputs. Outputs 10 to 19 represent ten fault types at Load 1, while outputs 20 to 29 represent ten fault types that occur at Load 2. The interpretations of the twenty different outputs are highlighted in Table2.Table 2
Interpretation of ANFIS model output.
ANFIS output
Fault type
10
LG, Ph. A (Load 1)
11
LG, Ph. B (Load 1)
12
LG, Ph. C (Load 1)
13
LL, Ph. A-B (Load 1)
14
LL, Ph. B-C (Load 1)
15
LL, Ph. A-C (Load 1)
16
LLG, Ph. A-B (Load 1)
17
LLG, Ph. B-C (Load 1)
18
LLG, Ph. A-C (Load 1)
19
3-Ph. fault (Load 1)
20
LG, Ph. A (Load 2)
21
LG, Ph. B (Load 2)
22
LG, Ph. C (Load 2)
23
LL, Ph. A-B (Load 2)
24
LL, Ph. B-C (Load 2)
25
LL, Ph. A-C (Load 2)
26
LLG, Ph. A-B (Load 2)
27
LLG, Ph. B-C (Load 2)
28
LLG, Ph. A-C (Load 2)
29
3-Ph. fault (Load 2)


## 4. Results

Figure8 illustrates the per-unit RMS phase currents and voltages at the occurrence of line-to-line and double line-to-ground faults on lines B and C. The fuzzy fault controller accurately deciphered the fault numbers as 5 and 8, respectively. For line-to-ground faults on Phases A and C, Figure 9 shows that the outputs of the controller are 1 and 3, respectively, which are accurate codes for the respective fault types.Figure 8
Fuzzy fault controller output for (a) LL fault on Phases B-C and (b) LLG fault on Phases B-C.
(a)
(b)Figure 9
Fuzzy fault controller output for (a) LG fault on Phase A and (b) LG fault on Phase C.
(a)
(b)Training of the ANFIS fault locator and identifier was carried out in 120 epochs. Figure10(a) indicates that the ANFIS training error reduced as the number of epochs increased. The curve shows the training error declining over 40 epochs (the third 40 epochs of training; epochs 80–120).Figure 10
(a) Error curve for ANFIS model training process. (b) Plots of ANFIS output and error. (c) Plots of ANFIS output and error for multiple simultaneous faults.
(a)
(b)
(c)Model validation is an important part of the entire design process. The validation of the developed ANFIS model was done by testing the trained FIS model with input-out data set that was not used in the neurofuzzy training process. This was achieved with 884 pairs of input/output vectors. Figure10(b) illustrates the ANFIS output and actual expected output for 884 data points of the checking data. From the resulting plots, we can deduce that the ANFIS model has 51% accuracy for identification of fault type and 93% accuracy for the location of faults that occur at either Load 1 or Load 2. Furthermore, the system was tested for situations when similar faults occur at both loads simultaneously. 3,188 data points were collected for this purpose. In this case, the results shown in Figure 10(c) indicate that the ANFIS correctly identified the fault type in 27% of cases and accurately reported one location of the fault in 78% of the cases.Thus, the ANFIS model has a high accuracy of fault location when the fault occurs at a single point. However, the fault location accuracy is significantly reduced when the same fault occurs at multiple points in the distribution network. Furthermore, for the developed ANFIS model, fault type identification is relatively low for both single and multiple-point fault locations in the distribution network. Hence, for fault type identification, the fuzzy fault controller afore-described, which has 89% accuracy, is better suited for the purpose. In comparison with the ANFIS reported in [9, 10], our designed ANFIS has similar levels of accuracies of fault location without the extraction of additional features like harmonics from the input signals. In addition, the accuracy of our fuzzy logic fault classification has similar levels of performance with the designs in [9, 10].


## 5. Conclusion

In this paper, an adaptive neurofuzzy method of achieving fault diagnosis in a power distribution system was presented. Data was first obtained from the network for ten types of faults. The data collated was utilized in training the fuzzy inference system for both fault identification and fault location. The output of the neurofuzzy model is represented with integers from 10 to 19 and 20 to 29, representing fault types for Loads 1 and 2 in the distribution system, respectively. The accuracy of fault location was high when only one type of fault occurs in the power system network. However, when the same fault type occurs simultaneously at more than one point in the power system, the fault location accuracy is significantly reduced. Therefore, complementing the ANFIS with a fuzzy logic-based fault identifier improves the accuracy of fault identification.



---

*Source: 8651630-2016-10-19.xml*