Introduction

The generating stations are located near the coal fields, which are generally far away from the electrical load centers, i.e., end user of the electricity. The electrical power in bulk is produced in these generating stations. This power is transmitted from these generating stations to the load centers by means of three-phase transmission lines. The length of the power system transmission lines may vary from few kilometers to thousands of kilometers, and they are directly exposed to the external environment. Hence, the overhead transmission lines are very prone to the faults, i.e., ten different types of fault can occur anywhere, any time on the transmission lines. As the transmission lines carry huge amount of power, even a slight disturbance may lead to the blackout of a substantial geographical area. These disturbances may lead to deterioration of quality of power supplied to the consumers. Therefore, a reliable and accurate method for fault detection, classification and isolation of the faulty section is required so that the supply can be restored as early as possible. Several techniques have been proposed by the researchers about the said problem, in last two decades.

The various methods have been published in the research literature by researchers, which are based upon Fourier transform, wavelet transforms, S-transform, Z-transform, etc. The Fourier transform-based methods of fault classification utilize the Fourier transform for analysis of the signals. Abdel Aziz et al. [1] proposed a Fourier transform-based method, which employs the third-harmonic components only, and based upon third-harmonic components, three different models have been developed. Samantaray [2] presented an S-transform and fuzzy logic-based fault classification method. The concept of S-transform uses the concept of wavelet transform. The phase space information of the phase current signal is adopted. The method suffers inherent disadvantages of the transform and fuzzy logic. Dasgupta et al. [3] presented a method which is based upon wavelet entropy and artificial neural network (ANN). But, the ANN takes a longer duration in conversing, if the data set is huge. Majid Jamil et al. [4] presented a wavelet spectral energy and GNN-based method of fault location. Pradhan et al. [5] proposed a discrete wavelet transform-fuzzy logic-based approach for series capacitor-compensated transmission line, but this method is complex and not accurate for boundary line cases, where the difference in between two faults data is very near to each other. The various hybrid techniques based upon fuzzy logic, soft computing, neural network, adaptive network, etc, are discussed in [6,7,8,9,10]. Moravejb et al. proposed an idea for fault detection and fault classification of a power system transmission line, which is based upon the combination of hyperbolic S-transform and learning machine (i.e., ANN) using one cycle current and voltage signals of three phases. The method is complicated as the numbers of input samples is doubled because both the current and the voltage are required for fault classification [10]. Jayabharata Reddy et al. [11] presented a model of fault detection and location, which is based upon wavelet transform and fuzzy logic. Rizwan et al. [12] discussed the method of feed forward neural network, which is combined with wavelet transform in fault location calculations. Alanzi et al. [13] proposed a method, which is based upon comparison of phase shift angle of measured voltage signal, but the algorithm is not as effective as, when the numbers of fault cases is more. The multi-resolution analysis (MRA) of wavelet transform is adopted for capturing the information about the nature of fault and location of fault. One end three-phase current of transmission line is measured and sampled. The error in the classification and location of the fault increased with overlapping of zones, which makes the proposed scheme very complex.

This paper is broadly classified into five parts: The first part gives the brief introduction and description of the related research work which has been already done. The second part deals with brief introduction of the projected algorithm. The second part also elaborates about the use of Clarke transform in detection of ground and Fourier transform and its application in calculation of phase shift angle. Third part deals with the generation of data set and development of fuzzy inference system (FIS) for segregation of faults on the basis of the ground. The GA-generalized neural network (GNN) is discussed in the fourth part. In the fifth part, model under consideration and its outcome are discussed, and the sixth part is conclusion. The results obtained by developed algorithm establish the authenticity of the proposed method. The flow of the algorithm is shown in Fig. 1.

Fig. 1
figure 1

Flow of fault classification system

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Signal Processing and Information Gathering

The first step in the process of fault categorization is to acquire the appropriate signals, which gives the required information about the faults and is used in the process of fault detection and categorization. The unclassified information received from the analysis should be proper and precise enough for declaring exact nature of fault. Three-phase power transmission system has only two signals, which can be considered and analyzed. The first quantity is voltage, and the second quantity is current. In this paper, only the voltage signal of respective three phases is acquired at generating bus location and analyzed.

Application of Clarke Transform in Detection of Ground in Faults

The Clarke transformation (CT) is also known as αβγ transformation. This transform is generally used for analyzing three-phase quantities, which is similar to the symmetrical component analysis. The Clarke transformation of any three-phase quantity can be calculated as follows:

$$ \left[ {\begin{array}{*{20}l} {V_{\alpha } } \hfill \\ {V_{\beta } } \hfill \\ {V_{\gamma } } \hfill \\ \end{array} } \right] = \frac{2}{3}\left[ {\begin{array}{*{20}l} 1 \hfill & { - \frac{1}{2}} \hfill & { - \frac{1}{2}} \hfill \\ 0 \hfill & {\frac{\sqrt 3 }{2}} \hfill & { - \frac{\sqrt 3 }{2}} \hfill \\ {\frac{1}{2}} \hfill & {\frac{1}{2}} \hfill & {\frac{1}{2}} \hfill \\ \end{array} } \right]\left[ {\begin{array}{*{20}l} {V_{a} } \hfill \\ {V_{b} } \hfill \\ {V_{c} } \hfill \\ \end{array} } \right] $$
(1)

where Va, Vband Vc are any three-phase signal, and in the present case, they are voltages of three phases a, b and c, respectively. Vα, Vβand Vγ are three model components of Clarke transformation.

$$ T = \frac{2}{3}\left[ {\begin{array}{*{20}l} 1 \hfill & { - \frac{1}{2}} \hfill & { - \frac{1}{2}} \hfill \\ 0 \hfill & {\frac{\sqrt 3 }{2}} \hfill & { - \frac{\sqrt 3 }{2}} \hfill \\ {\frac{1}{2}} \hfill & {\frac{1}{2}} \hfill & {\frac{1}{2}} \hfill \\ \end{array} } \right] $$
(2)

where T is Clarke transformation matrix. The matrix T is unitary in nature, i.e., its inverse is identical to its transpose.

The three model components of Clarke transformation provide the very useful information about the nature of fault. The first two components, i.e., α-model component and β-model component, are related to the phase only and are known as real components. The last one, i.e., γ-model component, is related to the ground only and hence known as ground mode component. These components can be obtained easily with the help of Clarke transformation matrix as expressed in (1). The ground mode component of Clarke transformation is very identical to the symmetrical zero sequence component of three-phase voltages. This feature of Clarke transformation is effectively utilized in the detection of involvement of ground when any type of fault occurs.

In the present paper, the voltage signal of respective three phases is measured and first analyzed with the help of Clarke transformation. The three-phase measured voltage signals are then fed through the Clarke transformation block of MATLAB. Here, only the ground mode component Vγ is analyzed and used as an important input. The extensive study by simulating the model of transmission line shows that the magnitude of Vγ is very significant, whenever the ground is involved in any type of fault. The magnitude of Vγ is easily detectable and measurable, and this feature is adopted by the paper for segregation of ground-related faults from the phase-to-phase faults. The input matrix is formed by having the one dedicated row of the Vγ. The value of Vγ is obtained directly from the block available in the MATLAB. The mean of vector of Vγ generated in MATLAB is taken for each different value of transmission line parameters and different operating situations of power system. Hence, the phases-to-ground faults are easily distinguished by phase-to-phase faults.

Application of Fourier Transform in Calculating Phase Angle

The value of phase angle is an essential quantity associated with any of the electrical power system signal, whether voltage or current. Whenever any disturbance occurs in power system, phase angle also changes accordingly. The value of phase shift angle varies substantially from healthy power system to faulty power system. This holds true for all three phases of electrical power transmission system. The phase angle of voltage also changes with any fault or any disturbance on the transmission line. The change in phase angle of voltage or current of electrical power transmission system occurs because with any fault, the electrical topology of transmission network changes. This leads to an immediate change in X/R ratio of the transmission network, and hence, the phase angle changes accordingly.

The difference in the phase angle of voltage at different time intervals, i.e., the pre-fault voltage and during-fault voltage, can be used for detection of fault. Hence, the changing pattern of phase angle alone can be used for the classification and detection of the faults. The value of phase angle may be negative or positive depending upon the time of sampling of the signal, which is three-phase voltage in the present case. The value of phase angle can be calculated in degrees, radians or in seconds, depending upon our convenience. This can be achieved simply by changing the settings of the MATLAB model of three-phase transmission line system. There are so many methods available for finding the phase angle, but the presented paper takes the help of fast Fourier transform (FFT) for calculating the phase angle. The FFT method of finding phase shift is very easy and suitable for sampled three-phase voltage signals.

The FFT of any signal y with n element is given by

$$ Y_{k} = \sum\limits_{j = 0}^{n - 1} {w^{jk} y_{j} } $$
(3)

where ω is a complex nth root of unity, i.e.,

$$ w = {\text{e}}^{ - 2\pi i/n} $$
(4)

The FFT can also be expressed with the help of matrix,

$$ Y = Fy $$
(5)

The elements of F are given by the below equation:

$$ f_{k,j} = \omega^{jk} $$
(6)

The nature of FFT matrix Y is complex for complex y.

Figure 2 shows the typical FFT windows (in red color) of phase voltage of phases A, B and C, respectively, for phase-to-ground fault, on phase A of the transmission line. Figure 3 shows the FFT analysis of all the waveforms, shown in Fig. 1 for all three-phase voltage signals. Table 1 shows the FFT parameters used for FFT analysis in the proposed research work. These waveforms are obtained by simulating the transmission line model developed in the MATLAB/Simulink environment for one combination of fault resistance and fault initiation angle. The FFT analysis of other voltages for different faults and different values of fault resistance and fault initiation angle is also carried out, but they are not shown here because of space constraint.

Fig. 2
figure 2

FFT windows (in red color) for AG fault on three-phase transmission line. a Phase A voltage signal. b Phase B voltage signal. c Phase C voltage signal (color figure online)

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Fig. 3
figure 3

FFT analysis of different phase voltages under AG fault on three-phase transmission line. a FFT of phase A voltage signal. b FFT of phase B voltage signal. c FFT of phase C voltage signal

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Table 1 FFT parameters for FFT analysis
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Fuzzy Decision System (FDS) for Segregation of the Ground Faults

The proposed research work has adopted the fuzzy logic for differentiating the faults which have ground involvement and which do not have involvement of the ground. The fuzziness in the data makes an effective implementation of the fuzzy logic in this method.

The fuzzy decision system mainly consists of the following components.

Fuzzification of the Analyzed Data

Fuzzification is a technique in which the input variables are mapped onto linguistic variables. These linguistic variables are then used by the fuzzy decision system (FDS) to make decisions of ground and non-ground fault classification. The output of Clark transformation (i.e., ground mode component Vγ) is used as input to fuzzification block of FDS. The fuzzification process uses the membership functions to accomplish the task of fuzzification. Figure 4 shows the deployment of membership function for input variables.

Fig. 4
figure 4

Fuzzy membership functions for input variables

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Inference from the DATA

After fuzzification of the ground mode component, Vγ is mapped onto linguistic variables. The control decisions now can be made based on these linguistic variables in order to get the output in linguistic form. The input, i.e., the ground mode component Vγ, is mapped in to three linguistic variables. The fuzzy input variable Vγ now consists of three linguistic variables, namely zero, positive and negative [i.e., zero (Z), positive (P) or negative (N)] depending upon the value of Vγ. Three simple fuzzy rules for fuzzy decision system formed are given as follows:

  1. 1.

    If Vγ is Z, then Fault Non-Ground

  2. 2.

    If Vγ is P, then Fault Ground

  3. 3.

    If Vγ is N, then Fault Ground

GA-Generalized Neural Network and Its Application in Fault Classification

The genetic algorithm-generalized neural network (GA-GNN) is a recent development in the field of intelligent tools, which is helpful in making meaningful decision from raw and unclassified data. Artificial neural network (ANN) was just one step earlier available for the same purpose. The ANN establishes a linear/nonlinear relationship in between input and output data or a universal function approximation to establish the relation in between input and output data. The aggregator functions used in developing ANN model is crisp in nature, which is not suitable for decision making, when we do not have input data in crisp form. Hence, the concept of GNN is developed which uses the compensatory operators which are fuzzy in nature and results are better as compared to ANN. Since the input data are fuzzy/vague in nature, the GNN uses the combination of sum and multiplication in order to deal with the vagueness of the input data.

Model of the GA-GNN

The presented paper has adopted two functions for developing the GA-GNN algorithm. The first is sigmoid function, and the second is Gaussian function. The combination of both provides the ability to deal with the nonlinearity involved in the problem. The typically developed GA-GNN model processes the output by summing up the output of sigmoid function and Gaussian function, and the proposed model is known as summation-type neural model.

The final output of the GA-GNN is a function of two outputs OΣ and Oπ, where Σ is summation function and π is aggregation function. The output of summation part is given by

$$ O_{\Sigma} = \frac{1}{{1 + {\text{e}}^{{ - \lambda_{s} *s\_{\text{net}}}} }} $$
(7)

where \( s\_{\text{net}} = \Sigma W_{i} X_{i} + X_{o\Sigma} \) and λs = parameter of summation function.

The output of the product aggregation part can be represented as

$$ O_{ \Pi } = {\text{e}}^{{ - \lambda_{\text{p}} * p\_{\text{net}}^{2} }} $$
(8)

where \( p\_{\text{net}} = \Pi W_{i} X_{i} * X_{o \Pi } \) and λp = parameter of product function, and the final output of the GA-GNN is given by following equation:

$$ {\text{GA-GNNoutput}} = O_{\varSigma} *W + O_{\varPi } *(1 - W) $$
(9)

This GA-GNN output is depending on weights factor (W). In this case, the weights are W and (1 − W) for summation function and aggregation function, respectively.

Error Minimization Using GA

The output of the GA-GNN will contain error, and this error is calculated and minimized by comparing it with the desired output. The GA technique is adopted to minimize this error. Basically, the sum squared error for convergence of model is used. The sum squared error Ep is given by

$$ E_{p} = \Sigma E_{i}^{2} $$
(10)

where Ei is error, i.e.,\( E_{i}^{2} = (Y_{i} - O_{i} ) \) between input Yi and output Oi.

The change in weights (\( \Delta W_{\Sigma} \)) with summation function and change in weights (\( \Delta W_{ \Pi } \)) with product function are find out using genetic algorithm.

The data matrix obtained by Clarke transforms and FFT is then used as input to the GA-GNN for various faults to train using GA. The GA-GNN model will then give the precise information about the kind of fault.

Modeling and Simulation of Three-Phase Transmission System

A three-phase transmission system model is created in the MATLAB for studying the diverse nature of the faults. The system under consideration has two generators connected at both the ends of the transmission line for energizing the line. The voltage of each phase is measured at the bus B1, as shown in Fig. 5. Clarke transformation is obtained with the help of Clarke transform block, instead of command line for detection of involvement of ground in the fault. Phase shift angle is also measured directly by using fast Fourier transform (FFT) block, which is readily available in the MATLAB. All of these blocks can be seen in Fig. 5. The value of ground fault resistance for all respective three phases is varied from 15 to 60 Ω, and for line faults, the fault resistance is varied from 0.10 to 0.75 Ω, respectively. These values provide a wide range of data over different operating conditions, and these data are utilized for generating the input matrix. The generated input matrix is then used for fuzzy logic and for training the GA-GNN model. The Fault commencement angle is very important factor as it plays a crucial role in deciding the magnitude of voltage at the time of fault, which also affects the during-fault voltage waveform. Hence, the value of fault commencement angle is varied from 0° to 90° so that all the possible situations can be taken into account. The sampling time taken is 80e−6 s, which covers all the signals of our interests.

Fig. 5
figure 5

Simulink model of the three-phase transmission line in MATLAB

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The typical values of both the voltage sources are as follows:

  • Phase-to-phase RMS voltage: 220 kV

  • Number of phases: 3

  • Phase angle of phase at source A: 0°

  • Phase angle of phase at source A: 35°

  • Frequency: 50 Hz

  • Internal connection: Yg

The length of transmission line is 400 km, and distribution types of parameters are taken so that the needed accuracy can be obtained. Therefore, the given method can also be utilized for fault detection of long transmission line.

The fault resistances and fault inception angles are varied step by step. The model is simulated for each value of fault inception angle for extensive study of the phase voltage waveforms. Mean values of third component of Clarke transform and phase shift angle are arranged in the matrix form. The matrix is normalized with respect to its own column so that the relative difference can be analyzed properly. The accuracy of the algorithm depends upon the training of the GA-GNN, which depends upon the size of the input data, i.e., the more the size of input data, the better the accuracy of GA-GNN. The model is simulated for all possible ten types of fault for different parameters to generate the data set for training purpose of the GA-GNN. Figure 6 depicts the graph of GA-GNN training between generation and fitness of offspring. The graph represented in Fig. 7 shows the robustness of the proposed GA-GNN method for different types of faults. A GA-GNN and a typical ANN model structure are also compared here to show the simplicity of the proposed method shown in Table 2. The table shows the superiority of the proposed method.

Fig. 6
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Graph representing GA-GNN training

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Fig. 7
figure 7

Testing of GA-GNN for different types of faults

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Table 2 Comparison of network complexity involved in ANN and GA-GNN
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Results and Discussion

After training, the GA-GNN fault detector (FD) has been tested for different faulty conditions and different parameters. These conditions included different fault locations, different commencement angles from (i.e., 0° to 90°) and different fault resistances (i.e., 0 Ω to 60 Ω). Table 3 shows the variation in Clarke components and variation in phase angle for single-line-to-ground faults. It is clear that the value of Vγ for the ground-related fault is nonzero and is greater than values of Vγ for line-to-line faults. Table 4 shows the variation in Clarke components and variation in phase angle for double-line-to-ground faults, and Table 5 shows the variation in Clarke components and variation in phase angle for line-to-line faults. It is again clear that the value of Vγ for the faults, where the ground is not involved, is almost zero. The careful observation of the given tables can be concluded in the form that for each type of fault a unique pattern of data is generated. These unique patterns can be used for classification of faults. Based upon these data, an artificial intelligent network is developed.

Table 3 Changing patterns of Clarke component and phase angle variation for different values of fault resistances and fault commencement angle for single-phase-to-ground faults
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Table 4 Changing patterns of Clarke component and phase angle variation for different values of fault resistances and fault commencement angle for double-phase-to-ground faults
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Table 5 Patterns of Clarke component and phase angle variation for different values of fault resistances and fault commencement angle for line-to-line fault
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Conclusion

This paper proposed a GA-GNN method for fault categorization of a three-phase transmission system. The paper has adopted the Clarke transform, phase shift angle, fuzzy logic and GA-GNN efficiently for categorization of faults of a three-phase transmission system. The voltage signals at one bus of the transmission system are used for fault categorization, and this makes the adaption and realistic implementation of the algorithm effortless. The effectiveness and preciseness of the presented method have been increased by synergizing the qualities of both fuzzy logic and GA-GNN. The training data set of GA-GNN for diverse realistic conditions, e.g., fault commencement angle, fault resistance and ten different types of faults GA-GNN, made the method more robust. The training time taken for the GA-GNN is comparatively less. The results obtained show that the presented scheme is very effective and robust in classification of the different types of fault. All efforts have been made in the modeling of the three-phase transmission system to match with the real-life transmission system.