Keywords

1 Introduction

The protection of power networks from unpredictable events as well as boosting their reliability in solid performance has always been a critical concern in the end-to-end delivery of energy [1]. In this situation, removing potential mistakes can go a long way toward preventing similar unpleasant incidents and so preserving the power system’s reliability [2]. Electrical arcing in sections of electrical wires with closure abnormalities is most likely to blame for the first faults. Re-emerging with an equally elevated aspect of frequency occurring, initial errors over time can damage cable overhaul and can become a permanent flaw in the system. As a result, a precise system is crucial for rapid detection and detection of a recent fault in the system among comparable possible events [3]. Nascent defects are most noticeable in their short duration, as well as low electrical amplitude compared to other system defects, considering which conventional protective transmission can detect these errors [4]. The nascent flaw is recalled by a distorted waveform, similar to square surgery, rather than an error. With the detection of emerging errors, a permanent network error can be predicted [1]. Radial basis work networks are often used by the ANN type for performance measurement problems [5]. RBFNN is differentiated from other neural networks due to its better speculation and faster learning speed. The RBFNN-dependent model [1] uses the output data of the model simulated data as a target and then [6] trains the neural network using it [7]. In Sect. 2, the simulation behind the sensing and categorization in case of [8] wavelet-based transmission line fault is briefly discussed. Further, to overcome the constraints of this method, RBFNN has been proposed in Sect. 3. Its detailed methodology followed by experimental results has been briefly mentioned in Sect. 4. At last, in Sect. 5, the research has been concluded.

2 Wavelet-Based Transmission Line Fault Detection

Electromagnetic transients in energy systems are characterized by the most common short-term factors, such as errors, which are very important. These defects cause serious damage to the electrical system and the problem. Therefore, there is a need to find the error, its type, where it is formed in the line as well as to rectify the error at the earliest so as not to cause the same damage [9]. Wavelet modification is largely created by this strategy, which could be effectively implemented by using two filters HP and LP [10]. HPF was derived after applying the wavelet function while the measured details of the input with the LPF, which brings a smooth translation of the input signal and is taken from the mathematical function associated with the prominent mother wavelet. In this analysis, the results are controlled using db4 as the mother wavelet (prime wavelet) for signal analysis [1]. Basic electrical power and current phasors are calculated using an algorithm based on [11] discrete Fourier transform that minimizes the effects of DC decay significantly. The system is modeled on the MATLAB SimPowerSystems site. The results shown in the proposed system are secure, fast, and very accurate. The frequency has been set to 50 Hz with voltage of 220 V and transmission line of length 120 km. Making amplification of current signals using a threshold power level, the primary power of all current signals by keeping the balance without change to calculate the limit of the change in power, if any power exceeds this level, this means that there is an error condition at that section of the line [12]. The error is generated by selecting combination of different phases of lines from fault generation box (Fig. 1).

Fig. 1
Two line graphs. Graph 1 represents voltage V versus time in seconds. The plotted data peaks at about (2, 0.046). Graph 2 represents current in milliamperes versus seconds. The plotted data peaks at about (4, 0.03).

a Voltage output waveform, b current output waveform

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3 Radial Basis Function Neural Network (RBFNN)

RBFNNs are used to compare advanced functions straight from output data to a simple topology [1]. They have a better overall performance compared to most neural feed-forward networks. The most widely used basic function is the Gaussian exp function. In successional learning, the neural network is trained to measure activity while a sequence of training sample dice is randomly drawn, introduced into a network and are read by each network [13]. RBFNN has a special two-layered structure one hidden layer and one output. The input layer does not process the information; it only works to distribute input data between nodes. Each node in the hidden layer is an RBF [1]. The output from jth Gaussian node of the xi input object is calculated, where the vector xi captures the ith input data, and vector cj represents the central point of the jth Gaussian function. ‖xi − cj‖ is the calculated [6] Euclidean distance, and width σ is a criterion that controls the smoothness of the function. The output is calculated by a combination of linear radial functions and bias w0 [7].

4 Experiment and Result

Accuracy of artificial neural network depends upon the input and output data. Larger the data, higher will be the accuracy and vice-versa. The simulation is run for 138 times. The maximum coefficient of all simulations is stored in form of a table. In order to classify all types of faults, we need output signal for each phase current as well as for ground current. There are 4 variables which represents phase A, B, C, and ground. In normal condition, the output is encountered as “0” and during fault it is “1” (Table 1).

Table 1 Maximum coefficient of different phases in different types of faults
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We have obtained 138 cases by applying all 12 fault conditions before the transmission line as well as after the transmission line position and by changing the fault ground resistance in the form of a table as shown here (Table 2).

Table 2 Output values of different phases in different types of faults
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Normal output condition is represented by assigning “0” and that of fault condition is represented by “1”. At this stage, we have defined the input and output data for the RBFNN. We have a total of 138 cases. The normal proportion for division of data into training and testing is 70% and 30%, respectively. However, as a rough estimate, we have chosen 30 cases for testing purpose and remaining 108 cases for training purpose. After successful training, the performance of the RBFNN is tested for these unseen 30 cases. If neural network classifies correctly, its efficiency will be 100% (Table 3).

Table 3 Comparison of RBFNN output with actual output
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RBFNN has provided the output of all 30 cases, which was compared with the actual output of all the 30 cases (Fig. 2).

Fig. 2
A line graph represents performance versus 100 Epochs. The plotted line is in a downward trend, where the train starts at about (10 superscript 0, 0) until (10 superscript minus 3, 71), falls abruptly to (10 superscript negative 1, 71), and is almost stable until (10 superscript negative 31, 100).

Performance of RBFNN training data

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Radial basis function neural network is very fast and has completed its training within short period of time. With 100 neurons, it has provided highest successful training with error equal to 1.99829e−31.

5 Conclusion

RBFNN has successfully and accurately detected the output of all the 30 cases. This shows that it has accuracy of 99.16%. RBFNN is much faster from the traditional wavelet method. Wavelet transform depends on the threshold value to classify the different types of faults in power system, which is not generalized and cannot be used for all types of power system, leading to lack of directional selectivity. Therefore, to overcome this limitation, RBFNN method has been used. We can see this from the graph where 108 cases have been trained in very short period of time.