**3. Experimental**

In this section, the faults that occur in transmission lines and transformers are tested by using the experimental setup. The difference current signals and transients generated from the experimental setup are detected and recorded for analysis with a wavelet. The experimental model is shown in Figure 2.

**Figure 2.** Characteristic signal of the mother wavelet.

Figure 2 shows the fault simulation circuit in the case of transmission lines connected to a transformer. The 40 km 115 kV transmission lines are calculated to be resistor, inductor and capacitor (RLC) parameters that are connected to a nominal pi model and a 15 kVA, 440/220 V transformer. The transformer is designed to accept internal short-circuiting. The design of the transformer permits a tap change every 10% of both the primary and secondary sides to test internal faults in the transformer. Moreover, the faults occurring in the transmission lines are tested by following these conditions:


The experimental setup is shown in Figure 3.

**Figure 3.** Experimental setup.

After recording the di fferential current from the transformer, the di fferential current is obtained through the wavelet transform method. The current signal is transformed using the DWT to extract high-frequency components at scales 1–3 with di fferent mother wavelets, such as the Daubechies (db), symlets (sym), biorthogonal (bior), and Coiflets (coif) wavelets. The coe fficient from the DWT is varied depending on various factors, and this coe fficient is squared to emphasize the change in coe fficient. The four mother wavelets are utilized to decompose the di fferential current signals. The DWT coe fficients of the phase faults are larger than those of the phase unfaults.

The example of di fferential current obtained from the transformer (relay 1) in case of internal fault and the coe fficient after using di fferent mother wavelets is shown in Figure 4. From the figure, it can be seen that the DWT signals at scale 1 generate much noise compared with those at scales 2–3. The coe fficients at scales 2–3 are notable when faults occur, and at scale 3, a lower frequency can be detected compared to that at scale 2. Thus, this research chose the coe fficients at scale 2 for analysis of the fault types.

**Figure 4.** *Cont.*

**Figure 4.** Differential current signals from the wavelet transform in the case of internal faults at phases in each mother wavelet: (**a**) Daubechies (db2); (**b**) symlets (sym2); (**c**) biorthogonal (bior3.1); (**d**) Coiflets (coif1).

(**d**)

#### **4. Fault Classification**

The fault classification algorithm using in this research was designed based on the DWT methodology as described in the flowchart in Figure 5. The operation of the algorithm detecting the fault on the power system consists of a transmission line and a transformer by first checking the status of relay 1 (at the transformer). Relay 1 obtains the di fferential current signals from the transformer and extracts the coe fficient value using DWT. This algorithm considers the maximum coe fficients at scale 2 every 5 ms (1/4 cycle). When the coe fficients changes more than five times and attains values larger than 5 × <sup>10</sup>−3, an internal fault occurs. This status will signal the relay 1 to trip. Otherwise, it is an external fault and will send a signal for relay 2 (at the transmission line).

For the relay 2, the required signals from the transmission line are the positive sequence of the three-phase current signal. These signals will input through DWT to extract the coe fficient value. The fault classification conditions in relay 2 are the maximum coe fficients at scale 2 of the positive sequence every 5 ms (1/4 cycle). When the coe fficients change more than 2 times and attain values larger than 1 × <sup>10</sup>−2, a fault occurs. This status will signal the relay 2 to trip.

The designed fault classification algorithm and testing of the proposed algorithm consists of testing of the experimental setup to obtain the signal from both relays 1 and 2. The number of case studies was varied with the di fferent conditions to obtain a number of data points, as shown in Table 1. The data were divided into three sets with a total number of data points of 1776; the first set of data was used for algorithm design—50% (888 data points), the second set of data was used for algorithm testing—25% (444 data points), and the last set of data was used for a case study—25% (444 data points). The first set was used to design the condition within the algorithm with an accuracy of more than 95%. The second set of data, di fferent from the first set, was used to test the accuracy of the algorithm. The third set of the data, the newer data di fferentiated from the first two sets, was used as the case study to evaluate the performance of the proposed algorithm.

**Table 1.** Number of data points used in the case study.


The four di fferent mother wavelets were used to decompose the current signals to obtain the coe fficient value from the high-frequency component. The extraction from the DWT of a di fferential current showed that the coe fficients of the internal faults changed more than those of the external faults. However, the results of the four mother wavelets were similar, as shown in Figure 6. This characteristic was used to design the condition in a fault classification algorithm for relay 1 (transformer). External faults can be analyzed by using coe fficients of transmission line systems. The coe fficient characteristics between faulty and normal conditions when applied di fferent mother wavelets are shown in Figure 7. The extraction from the DWT of three-phase and positive sequence signals showed a similar trend with the fault condition having a higher coe fficient than the normal condition. However, there was a di fference in the coe fficient value between di fferent mother wavelets. The above behavior was used to design algorithms for fault classification.

The algorithm was operated by using the maximum coe fficients, as shown in Figure 8, for the transformer (relay 1) and Figure 9 for the transmission line (relay 2). From Figure 8 it can be seen that the result from DWT of di fferential current in scale 2 provided a higher maximum coe fficient during the transient condition compared to the normal condition. In Figure 9, a similar trend was also shown with the maximum coe fficient from scale 2 in the case of an external fault higher than the normal case. The normal case only consisted of noise due to no significant transient state in the signal. This characteristic was used to indicate fault status, and the di fferent mother wavelet provided di fferent maximum coe fficient values, which could impact the design algorithm.

**Figure 5.** Algorithms for fault classification.

**Figure 6.** Differential current signals from wavelet transform in scale 2 obtained from relay 1: (**a**) internal fault; (**b**) external fault.

**Figure 8.** *Cont.*

**Figure 8.** Maximum values of the coefficients from the wavelet transform at scale 2 used in classifying the faults in relay 1: (**a**) Daubechies (db2); (**b**) symlets (sym2); (**c**) biorthogonal (bior3.1); (**d**) Coiflets (coif1).

**Figure 9.** Maximum values of the coefficients from the wavelet transform at scale 2 used in classifying the faults in relay 2: (**a**) Daubechies (db2); (**b**) symlets (sym2); (**c**) biorthogonal (bior3.1); (**d**) Coiflets (coif1).
