Keywords

1 Introduction

Fault conditions in the power system can cause a lot of issues and losses. These losses can be fatal too. The condition of a faulty phase if not understood and taken care of quickly would most probably lead to major problems. In order to get to the conclusion of whether the fault is present and if yes, then which type of fault is present in the system needs to be identified as quick as possible. The electrical framework flaws are the best risk to the congruity of power supply. Deficiencies on overhead lines are an unavoidable issue. Thus, an all-around composed protection system must be given to distinguish and disengage faults quickly so that the harm and interruption brought on to the transmission system is minimized. Main part of the fault clearing system is the circuit breaker. Power circuit breakers are used at all voltage levels in a power system, i.e. faults which can either be single phase to ground (LG) or phase to phase (LL) or double phase to ground (LLG) or a three-phase fault (LLLG). Protection of power system using conventional methods is a slightly longer process. The real procedures utilized are fuzzy logic [1,2,3], wavelet strategy [4, 5], artificial neural systems [6, 7], wavelet-fuzzy [8], wavelet-neuro-fuzzy [9], and other latest techniques [10,11,12,13]. The accuracy of wavelet methodology is prevalent in correlation with different strategies and it gives greatly enhanced results.

The essential point of this article is to make sense of the sort of fault and whether the fault is present or not in a power system. The faults in concern are predominantly transmission line faults and all types of these faults are to be covered. This work also looks forward to providing a universal method to recognize faults and also discriminate among the types in case of any power system setup, specifications, parameters, etc. In order to reduce manual switching and calculation, the code tries to show the results of the scenario through minimum manual effort, hence providing results quicker for further measures.

2 Discrete Wavelet Transform (DWT)

A wavelet is a wave-like swaying with plentifulness that starts at zero, increments, and afterward diminishes back to zero. Wavelets can be joined, utilizing an “opposite, shift, duplicate and coordinate” procedure called convolution, with bits of a known signal to concentrate data from the obscure signal.

The DWT can be composed as

$$T_{m,n} = \mathop \smallint \limits_{ - \infty }^{\infty } x\left( t \right)\varphi _{m,n}\left( t \right){\text{d}}t.$$
(1)

The 1-D wavelet transform is given by

$$W_{f}{\left( {a,b} \right)} = \mathop \smallint \limits_{ - \infty }^{\infty } x\left( t \right)\varphi_{a,b}(t){\text{d}}t.$$
(2)

The inverse 1-D wavelet transform is given by

$$x\left( t \right) = (1/c)\mathop \smallint \limits_{0}^{\infty } \mathop \smallint \limits_{ - \infty }^{\infty } W_{f}\left( {a,b} \right)\varphi_{a,b}\left( t \right){\text{d}}b\left( {\frac{{{\text{d}}a}}{{a^{2} }}} \right),$$
(3)
$${\text{where }}c = \mathop \smallint \limits_{ - \infty }^{\infty } \left( {\frac{{\left| {\varphi \omega } \right|^{2} }}{\omega }} \right){\text{d}}\omega < \infty .$$

3 Fault Classification Using DWT

For implementing the proposed method for fault detection and classification, a three-phase simulation model with a source voltage of 400 kV and corresponding zero load angle was used. This identification is based on the DWT energy coefficient of the signal. It generates a high-frequency component to signal. Initially generate the power signal using generator. Then design network power system using three-phase current signal. DWT analysis is performed to identify and classify the fault. Circuit breaker is used to make fault in the signal. Ratio is calculated to find the fault. Fault can be classified based on the ratio. The values of maximum detail coefficient (MDC), energy of the signal (E), and energy ratio (ER) after signal compression in no-fault condition are tabulated in Table 1. These values are used as a reference to compare with respective values in faulty conditions.

Table 1 MDC, E, and ER for no-fault condition
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4 Numerical Simulation Results and Discussion

Output current waveform at no-fault condition is shown in Fig. 1. The detailed coefficients are close to zero in this case of fault. The energy ratios after signal compression can be seen to be similar for all the phases and nearing zero.

Fig. 1
figure 1

Output current waveform at no-fault condition

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In LG, fault condition is shown in Fig. 2. The phase under fault can be identified by the MDC, E, and ER. From Table 2, it is clear that whichever phase the fault occurs in LG fault, that corresponding phase shows in increase in MDC, E, and ER. The other two phases show very little or no change in parameter values.

Fig. 2
figure 2

Output current waveform at LG fault (AG) condition

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Table 2 MDC, E, and ER for LG faults
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When the fault occurs in a LLG fault scenario, the current in both affected phases significantly changes as shown in Fig. 3. The unaffected phase has more or less the same characteristics as the no-fault condition. The faulty phases have maximum or higher values of detail coefficient; energy and energy ratio of the compressed signal are shown in Table 3. Here two of the phases are affected, so naturally those two respective phases have shown in increase in parameter values. The key thing to note here is that although energy ratio has increased for both the concerned phases they are not equal to each other. This is one of the key differentiators between LL and LLG fault.

Fig. 3
figure 3

Output current waveform at LLG fault (BCG) condition

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Table 3 MDC, E, and ER for LLG faults
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In LL fault, the fault incidence in this case will show great amount of change in the faulty phases shown in Fig. 4.

Fig. 4
figure 4

Output current waveform at LL fault (AC) condition

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Unaffected phase has the same current flow as in normal condition and also the values of detail coefficient and ratio after compression. The output values of the faulty phases are more than normal, but they being similar show that they are not in contact with ground. Here two of the phases are affected, so naturally those two respective phases have shown an increase in parameter values as shown in Table 4. The key thing to note here is that energy ratio has increased for both the concerned phases and they are equal or almost equal to each other.

Table 4 MDC, E, and ER for LL faults
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In three-phase fault at fault inception, the current signal of all the three phases change drastically as shown in Fig. 5. The ratios and coefficient values can also be seen to be more than the normal condition. For three-phase fault, it can observe an increase in energy of signal and energy ratio of compressed signal for all three phases which are shown in Table 5.

Fig. 5
figure 5

Output current waveform at LLLG (ABCG) condition

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Table 5 MDC, E, and ER for LLLG fault
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5 Conclusion

The principle point of the work is to identify and classify faults in overhead lines. This is realized using wavelet analysis because it takes into consideration both frequency and time domain. This work uses parameters like MDC, E, and ER after compression to make observations. This is because these parameters are characteristic for a particular type of fault current. Hence, they are optimal for the classification process. Taking the values of the three parameters of no-fault condition as base, we can compare the respective values of the parameters of every type of fault in order to make comparisons and arrive at a conclusion. The outcome signifies that during the no-fault condition all the three parameter values for each phase are comparatively lower. Under fault conditions the value of the respective phase under fault increases and hence shows the result as to which fault is present. Using reverse bi-orthogonal wavelet for transform helps to get the result quicker and the use of this wavelet is helpful to realize the aim. Using wavelet as a method instead of other available toolbox allows faster calculation because wavelet transform considers both frequency and time domain. Using this technique a lot of effects and losses due to faults in transmission lines can be avoided. This will help in reducing damages in electrical systems and potentially help for continuous power supply.