Principios de la evaluación

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Figure 4.45 shows that the DFT fault voltage magnitude is larger than FFT pre-fault magnitude for points 2 and 3 only, but equal with FFT pre-pre-fault for points 0 and 1.

It is also the same in figure 4.46, where the DFT pre-fault current for all the points are larger than that of FFT by 1.0pu, 2.6pu, 3.4pu and 7.8pu for points 0, 1, 2 and 3 respectively.

However in figure 4.47, DFT and FFT pre-fault impedance, FFT pre-fault impedance for point 3 is larger than that of DFT by 6.5pu.

In figure 4.48, it shows that DFT and FFT three phase fault voltage magnitude are equal for points 0 and 1, but for points 2 and 3, the DFT three phase fault voltage is larger than that of FFT by 2.4pu and 2.0pu respectively.

Figure 4.49 show that for points 0, 2 and 3, the DFT and FFT three phase current magnitudes are equal, while for point 1, the DFT is larger than FFT BY 7.0pu.

Also, the impedance of DFT and FFT for points 0 and 1 are equal, while for 2 and 3 the DFT three phase impedance is larger than that of FFT by 28pu.

4.5 Comparative Analysis between the Results of the Application of the

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% Error = Nigerian (Mathematical) value –IEEE 14−Bus value

IEEE 14−Bus value 𝑥 100 (4.2)

Table 4.22: DFT Pre-fault VoltagePercentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS DFT V(n) Nigerian

DFT V(n) IEEE

Error Difference

1 0 -0.6191 0.1067 480.00

2 1 1.6733 -3.1580 47.00

3 2 0.3385 -4.3590 92.00

4 3 1.7460 -7.5000 77.00

Table 4.23: DFT Three Phase Fault Voltage Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS DFT V(n) Nigerian

DFT V(n) IEEE

Error Difference

1 0 -0.1087 1.5330 92.90

2 1 0.2941 -2.8250 89.60

3 2 0.0691 -4.4280 98.40

4 3 0.3061 -8.6210 96.40

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Table 4.24: FFT Pre-fault Voltage Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS FFT V(n) Nigerian

FFT V(n) IEEE

Error Difference

1 0 -0.6191 0.1067 480.00

2 1 1.6183 -3.1580 48.80

3 2 0.8099 -0.0449 1703.80

4 3 1.6183 -5.9290 72.70

Table 4.25: FFT Three Phase Fault Voltage Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS FFT V(n) Nigerian

FFT V(n) IEEE

Error Difference

1 0 4.0848 1.5330 166.46

2 1 -0.0463 -2.8250 98.36

3 2 -0.0446 1.4500 96.90

4 3 -0.0463 -6.5240 99.30

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Table 4. 26: DFT Pre-fault Current Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS DFT I(n) Nigerian

DFT I(n) IEEE

Error Difference

1 0 -0.1670 0.8193 79.62

2 1 0.6433 -0.3559 80.77

3 2 0.0812 -0.7883 89.69

4 3 0.6461 -0.1919 236.69

Table 4. 27: DFT Three Phase Fault Current Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS DFT V(n) Nigerian

DFT V(n) IEEE

Error Difference

1 0 -1.1077 9.6370 88.50

2 1 2.9899 -4.1860 28.57

3 2 0.7053 4.2730 83.50

4 3 3.1239 -22.57 86.16

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Table 4. 28: FFT Pre-fault Current Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS FFT I(n) Nigerian

FFT I(n) IEEE

Error Difference

1 0 -0.3503 0.8193 57.24

2 1 0.1521 -0.3559 52.64

3 2 0.3371 -0.7971 57.71

4 3 0.5902 -1.3540 56.41

Table 4. 29: FFT Three Phase Fault Current Percentage Error Difference between Nigerian (Mathematical Approach) and IEEE 14 – Bus Networks

S/N N - POINTS FFT I(n) Nigerian

FFT I(n) IEEE

Error Difference

1 0 5.5992 9.6370 41.89

2 1 -0.1116 -4.1860 97.00

3 2 -0.0290 9.3750 99.70

4 3 -0.1116 -15.92 99.30

According to the power system transmission line fault characteristics, when fault such as three phase fault occurs on the transmission line, the line voltage decreases

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very lower than the pre-fault value. At same time, the current on the line drastically increased more than its pre-fault value.

Therefore, considering Tables 4.22 to 4.29, DFT Nigerian (mathematical approach) has its lowest pre-fault voltage magnitude as 0.3395pu while IEEE 14-bus has 0.1067pu. In the same vein, FFT Nigerian (mathematical approach) has its lowest pre-fault voltage magnitude as 0.6191pu while IEEE 14-bus has 0.0449pu.

Also, the DFT Nigerian (mathematical approach) has its largest three phase fault current magnitude as 0.6461pu while IEEE 14-bus has 0.8193pu. In the same vein, FFT Nigerian (mathematical approach) has its largest three phase fault current magnitude as 5.5992pu while IEEE 14-bus has 15.92pu.

However, the difference between the DFT mathematical approach lowest pre-fault voltage and its largest current magnitudes is only 0.3066pu and that of FFT is 4.9801pu which is large enough.

Also, the difference between the DFT IEEE 14 – bus network lowest pre-fault voltage and its largest current magnitudes is 0.7126pu and that of FFT is 15.88pu which is significantly large enough.

With these results above, three phase fault has been successfully detected and cleared using DFT and FFT signal processing techniques since the results conforms to the power system transmission line fault characteristics.

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CHAPTER FIVE CONCLUSION 5.1 Summary of the work

This dissertation has been able to develop and implement a fault detection modelbased on Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT) for fault detection on the any transmission line. These fault detection models are developed, implemented using mathematical and computer simulation approaches.

They were validated using Matlab/Simulink R2017a and IEEE 14 – bus System networks.

Considering the performance of the two models, the output results obtained and the difficulties encountered, we conclude that, the DFT and FFT produced time – and frequency – domain waveforms and spectrum diagramsrespectively. These diagrams illustrates the faulty conditions of the transmission line and the low and large magnitude of DFT and FFT parameters (voltage and current) respectively against that of no faults are evidence that fault occurred and were detected on the transmission line.

One of the disadvantages of using DFT in diagnosing the fault is it inability to carry detailed fault information about the signals but give a better result than the FFT.

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