Simulation Results Comparison Between LS and TLS Algorithm

Both LS and TLS algorithms are using the same 9 cases to test the performance. In order to compare the two algorithms, we will use the TVE results.

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Table 5.26 LS and TLS Algorithms TVE Results Comparison Cases Conditions

SNR/dB, /s

TVE (%)

LS TLS

Case 1 Without Noise 0.0503 0.0405

SNR=20 0.0582 0.0490 SNR=40 0.0482 0.0448 SNR=60 0.0504 0.0457 Case 2 _5.1 5  M Without Noise 0.2554 0.1696 SNR=20 0.2688 0.1728 SNR=40 0.2564 0.1704 SNR=60 0.2554 0.1698 5 . 5 5 M Without Noise 0.4862 0.3422 SNR=20 0.4927 0.3497 SNR=40 0.4846 0.3431 SNR=60 0.4863 0.3422 Case 3 _5.1 5  M Without Noise 0.0502 0.0460 SNR=20 0.0765 0.0501 SNR=40 0.0565 0.0470 SNR=60 0.0503 0.0460 5 . 5 5 M Without Noise 0.0502 0.0460 SNR=20 0.0639 0.0568 SNR=40 0.0535 0.0522 SNR=60 0.0503 0.0460 Case 4 Without Noise 0.8092 0.5582

SNR=20 0.8281 0.5610

SNR=40 0.8099 0.5583

SNR=60 0.8091 0.5582

Case 5 Without Noise 0.0504 0.0401

SNR=20 0.0755 0.0633

SNR=40 0.0583 0.0465

SNR=60 0.0507 0.0460

Case 6 Without Noise 0.2783 0.2198

SNR=20 0.2907 0.2209

SNR=40 0.2785 0.2200

SNR=60 0.2784 0.2199

Case 7 Without Noise 0.0507 0.0145

SNR=20 0.0670 0.0182

SNR=40 0.0530 0.0151

SNR=60 0.0509 0.0146

58 05 . 0   0.1548 0.1469 1 . 0   0.0928 0.0739 Case 9  0.0265 0.0502 0.0460 05 . 0   0.0083 0.0070 1 . 0   0.0011 0.0009

In Table 5.26, all the TVE simulation results have been compared together. The first column are the cases that were tested in both LS and TLS algorithms. Case 1 is a voltage signal with only integer harmonic components. Case 2 is a voltage signal with unknown frequency and only one non-integer harmonic component. Case 3 has the same signal with case 2 except that the frequency is given. Case 4 is a voltage signal with unknown frequency and several non-integer harmonic components. Case 5 has the same signal with case 4 except that the frequency is given. Case 6 is a voltage signal with unknown frequency, decaying d.c. component, fundamental component and a non-integer harmonic component. Case 7 has the same signal with case 6 except that the frequency is given. Case 8 is a voltage signal with unknown frequency and a non-integer harmonic component. The different time constants have been tested in this case. Case 9 has the same signal with case 8 except that the frequency is given. The second column shows the different conditions of the cases, such as different SNR or time constants. The third and the fourth columns are the TVE results of LS and TLS algorithms separately.

From the table, we can see that for all the cases, the TVEs of the TLS algorithms are smaller than that of the LS algorithms. We can conclude that the TLS algorithm performs better than the LS algorithm when frequency of non-integer harmonic components are given.

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5.4 Conclusion

This chapter presents how TLS algorithm works and has used Matlab to test the performance of the TLS algorithm. After that, the performance of the LS algorithm and TLS algorithm has been provided by comparing the TVE results.

From the simulation results, we can find that the TLS algorithm gives an accurate estimation on phasor when the frequency of the harmonic components are given. When there are non-integer harmonic components in the signal and the frequency are not given, the LS algorithm fails to extract the parameters of the non-integer harmonic components. However, the estimation of the decaying d.c. component and the fundamental component are still accuracy. When the time constant is becoming larger, the TLS algorithm can provide a more accurate estimation.

The comparison result between LS algorithm and TLS algorithm shows that the TLS algorithm performs better when frequency of non-integer harmonic components are given.

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Chapter 6 Conclusion

The frequency tracking and the phasor estimation has been important issues for decades in the electric power system. The LS and TLS algorithms are both widely used in such areas.

This thesis firstly investigates the performance of the LS algorithm used on the frequency tracking. The LS algorithm gives an accurate estimation when the frequency on has a small deviation from the expected value. The estimation value may have a great sudden change when the actual frequency steps up and down. The sudden change can be regarded as a symbol when the actual frequency changes. When the decaying d.c. component is involved in the signal, there will be a delay of the LS algorithm before it gives an accurate estimation on the frequency.

The paper then focused on phasor estimation using both the LS algorithm and the TLS algorithm. The signal is supposed to have a decaying d.c. component, several harmonic components and the Gaussian White Noise. With the frequency of the harmonic components given, both algorithms can precisely estimate the phasor. When the frequency of the harmonic components are not given, both algorithms fail to extract the parameters of the non-integer harmonic components. However, the estimation of the decaying d.c. component and the fundamental component are still accurate. Both LS and TLS algorithms works well with noise added. The signal with different time constants have also been tested, and the estimation becomes more accurate with the time constants becoming larger. The comparison of the TVE result between the LS algorithm and the TLS algorithm shows that the TLS algorithm has a better performance than the LS algorithm.

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VITA

Hengdao Guo was born in Xuzhou, China in 1989. In 2008, he attended China University of Mining and Technology for the first two years, and then transferred to University of Kentucky and finished another two years as an undergraduate student. He got the Bachelor of Science degrees in Electrical Engineering of both two universities. After that, he pursued his degree of Master of Science in Electrical Engineering again in University of Kentucky. He will graduate in December 2014. He got E.ON U.S. Endowed Scholarship, Transfer Scholarship, William C Parker Scholarship and Power and Energy Scholarship during his study in University of Kentucky.