**6. The results and discussions**

230 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

In1


Out2 Out1 Filter

z1 z2

y ratio <=


2 ratio

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1 y 1 y

1 y

**Figure 10.** The amplitude comparator block contents

signal

signal

signal rms

signal rms

1 Id1

2 Ia

1 IA

2 z2 1 z1 magnitude angle

magnitude angle

h1

h2

**Figure 11.** The harmonic comparator block contents

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**Figure 12.** The ratio block contents



The results will be given for different cases:

Case 1: magnetizing inrush current,

Case 2: magnetizing inrush with adding load,

Case 3: Three phase to ground fault at loaded transformer,

Case 4: Phase A to ground external fault at loaded transformer,

Other cases of different types of faults and inrush currents such as single line to ground fault, line-to-line fault, line to line to ground fault and three phase fault in both cases loaded and unloaded transformer are illustrated.

Case 1: Magnetizing inrush current:

In this section of simulation, when the primary side CB1 is closed at 0.1 sec, only the inrush current flows in the primary circuit of the power transformer and no current passes through the power transformer to the secondary side as shown in Fig. 13. The harmonic comparator shows in Fig. 14 that the value of the 2nd harmonic is higher than 0.3 of the fundamental component.

**Figure 13.** Inrush currents waveforms of the three phases at the primary side of the power transformer.

**Figure 14.** Harmonic comparator result: the 2nd harmonic and the fundamental component for the 1st case.

**Figure 15.** Amplitude comparator results for the 1st case.

In this case the harmonic calculation part released logic (0) but the amplitude comparator showed in Fig. 15 that the differential current is equal to the inrush current, where both curves are drown over each other, then the amplitude comparator release logic (1). For this logic coordination (0,1) no trip signal is released.

Case 2: Magnetizing inrush with adding load:

232 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**Figure 14.** Harmonic comparator result: the 2nd harmonic and the fundamental component for the 1st

In this case the harmonic calculation part released logic (0) but the amplitude comparator showed in Fig. 15 that the differential current is equal to the inrush current, where both curves are drown over each other, then the amplitude comparator release logic (1). For this

**Figure 15.** Amplitude comparator results for the 1st case.

logic coordination (0,1) no trip signal is released.

case.

This test is carried out after the energization of the power transformer by switching ON the CB1 at 0.1sec and CB2 at 0.3 sec from the beginning of the simulation to see the effect of load excursion on the accuracy of the designed approach. Therefore, a 500W resistive load is added to the system at 0.3 sec. Consequently, the inrush current disappeared and load current started to flow in the primary and secondary circuits of the transformer according to the transformation ratio of the power transformer as shown in Fig. 16. However, the amplitude of the output currents of the primary and secondary CTs are equal due to the proper selection of the transformation ratio of the primary and secondary CTs, which can obviously noticed in Fig. 18. Where, before the time 0.3 sec the differential current was equal to the inrush current, but after the swathing ON of the load the differential current went to zero and the primary and secondary currants became equal.

**Figure 16.** Normal load current starts flowing at 0.3sec.

As shown in Fig. 17, after the switching of CB2, the value of the 2nd harmonic become lower than 0.3 of the fundamental component. Accordingly, the harmonic calculation part released logic (1) but the amplitude comparator released logic (0). Consequently, for this logic coordination (1,0) no trip signal is released. Figure 18 shows the amplitude comparator results.

**Figure 17.** 2nd harmonic and the fundamental component for the 2nd case.

**Figure 18.** Amplitude comparator results for the 2nd case.

Case 3: Three phase to ground fault at loaded transformer:

In this section, a three phase to ground fault is created to test the security of the algorithm. After the switching of CB1 at 0.1sec, an internal fault is created at 0.5 sec at the secondary side of the power transformer by connecting the three phases A, B and C of the secondary side of the power transformer to the ground. In this case, a significant increase of the primary current takes place due to the fault occurrence inside the protected zone at 0.5 sec as shown in Fig. 19. The relay detected this increase using the harmonic and amplitude comparators and realized it as an internal fault. Consequently the transformer is isolated from the grid. Also it is obvious from Fig. 20 that the relay has released a trip signal after 0.57 msec after the occurrence of the fault, which can be considered as a very good speed to isolate the transformer.

234 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**Figure 17.** 2nd harmonic and the fundamental component for the 2nd case.

**Figure 18.** Amplitude comparator results for the 2nd case.

Case 3: Three phase to ground fault at loaded transformer:

In this section, a three phase to ground fault is created to test the security of the algorithm. After the switching of CB1 at 0.1sec, an internal fault is created at 0.5 sec at the secondary side of the power transformer by connecting the three phases A, B and C of the secondary side of the power transformer to the ground. In this case, a significant increase of the As shown in Fig. 21, after the occurrence of the fault at time 0.5 sec, the value of the 2nd harmonic increased during the transient time and then decreased rapidly to a value lower than 0.3 of the fundamental component once the steady state is achieved. Accordingly, the harmonic calculation part released logic (1). Also from Fig. 22 which shows the result of the amplitude comparator the value of the differential current is no longer equal to zero. Accordingly the amplitude comparator released logic (1). Therefore, for this logic coordination (1,1) a trip signal is released in order to isolate the power transformer from the grid.

**Figure 19.** Increase of phase A, B & C currents due to the occurrence of the fault at 0.5 sec for loaded transformer

**Figure 20.** Zoomed trip signal, trip time is around 0.57 msec

**Figure 21.** 2nd harmonic and the fundamental component for the case of three phase to ground fault at loaded transformer.

**Figure 22.** Amplitude comparator result for the 3rd case.

Case 4: Phase A to ground external fault at loaded transformer.

This case is similar to case 2, where the occurrence of the fault current outside the protected zone leaded to the increase of fault currents in both sides of the power transformer. Therefore the relay considered this case as a sever increase in load currents. Fig. 23 shows the increase in phase A currant and no trip signal is released

**Figure 21.** 2nd harmonic and the fundamental component for the case of three phase to ground fault at

This case is similar to case 2, where the occurrence of the fault current outside the protected zone leaded to the increase of fault currents in both sides of the power transformer. Therefore the relay considered this case as a sever increase in load currents. Fig. 23 shows

loaded transformer.

**Figure 22.** Amplitude comparator result for the 3rd case.

Case 4: Phase A to ground external fault at loaded transformer.

the increase in phase A currant and no trip signal is released

**Figure 23.** Increase of phase A current due to the occurrence of the fault at 0.5 sec for loaded transformer

**Figure 24.** 2nd harmonic and the fundamental component for the Case for the 4th case.

As illustrated in Fig. 24, after the occurrence of the external fault at 0.5 sec, the value of the 2nd harmonic decreased to a value less than 0.3 of the fundamental component. Accordingly, the harmonic calculation part released logic (1) but the amplitude comparator released logic (0) because the differential current is almost zero as it can be seen from Fig. 25. Consequently, for this logic coordination (1,0) no trip signal is released.

**Figure 25.** Amplitude comparator result for the 4th case.

Similarly, the relay is tested for all other cases of different types of faults such as single line to ground, line to line, line to line to ground and three phase faults in both cases loaded and unloaded transformer. In all cases the relay has successfully released a trip signal in each case. The results of some of these different types of faults are shown in Figs (26 - 30).

**Figure 26.** Increase of phase A & B currents due to the occurrence of the fault at 0.5 sec, for unloaded transformer

Similarly, the relay is tested for all other cases of different types of faults such as single line to ground, line to line, line to line to ground and three phase faults in both cases loaded and unloaded transformer. In all cases the relay has successfully released a trip signal in each

case. The results of some of these different types of faults are shown in Figs (26 - 30).

**Figure 26.** Increase of phase A & B currents due to the occurrence of the fault at 0.5 sec, for unloaded

**Figure 25.** Amplitude comparator result for the 4th case.

transformer

**Figure 27.** Increase of phase A , B & C currents due to the occurrence of the fault at 0.5 sec, for unloaded transformer

**Figure 28.** Increase of phase A current due to the occurrence of the fault at 0.5 sec for loaded transformer

**Figure 29.** Increase of phase B & C currents due to the occurrence of the fault at 0.5 sec for loaded transformer

**Figure 30.** Increase of phase A current due to the occurrence of the fault at 0.5 sec, for unloaded transformer

