電力系統的慣量決定了電力系統在短期電力不平衡情况下保持同步的能力。它對系統的暫態穩定性、頻率穩定性、電驛保護等動態行為具有無可比擬的作用。隨著風力發電、太陽能發電等可再生能源的普及率增加，電網頻率擾動的風險增大，系統慣性水准的評估已成為電力系統頻率穩定性的重要研究方向。隨著同步相量測量單元（PMU）的大量設備，使得利用擾動後數據評估系統慣量成為可能。

本文利用ESPRIT訊號擬合技術以獲得系統發生大擾動事件時的頻率響應曲線方程式，且在計算搖擺方程式和調速機出力的動態方程式所產生的解析解。藉由頻率響應曲線方程式和解析解的關係，以便我們可以通過非線性最小二乘法估計相應的電力系統頻率響應參數。並分別在不同程度的發電損失，不同的再生能源滲透率和不同的負載模型之件進行比較。

Power system inertia determines the ability of the power system to keep synchronization in the case of short-term power imbalance. It plays an unparalleled role in the transient stability, frequency stability, protection relay, and other dynamic behaviors of the system due to the increased penetration of renewable energy such as wind power and solar photovoltaic (SPV) generation of frequency disturbance in power grid increases. The evaluation of system inertia level has become an important research direction of power system frequency stability. A large number of equipment of synchronous phasor measurement unit (PMU) make it possible to evaluate system inertia by using post-disturbance data.

In this paper, a method of inertia estimation based on PMU synchronous measurement is proposed. Using the frequency signal fitting method ESPRIT to obtain the equation of the frequency deviation curve and the analytical solution through swing equation and governor power dynamic equation, we derived to find the relationship between the equation of the frequency deviation curve and analytical solution, so that we can estimate the corresponding parameters through the nonlinear least square method.

Contents
Acknowledgements
摘要i
Abstract ii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Influence of Inertia on Power System . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Different signal fitting method analysis . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Pisarenko Harmonic Decomposition . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Prony Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 MUSIC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 ESPRIT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 LSESPRIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 TLSESPRIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Choice of Model Order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Inertia Estimation 19
3.1 Principle of applying the swing equation for disturbance event estimation . . . 19
3.2 Frequency Response Regulation . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Analytical Solution of frequency and governor power . . . . . . . . . . . . . . 23
3.4 Proposed Method to Obtain Frequency Deviation Signal Equation . . . . . . . 25
3.5 Inertia Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Case Study 33
4.1 Case 1: IEEE 39 bus with general disturbance event . . . . . . . . . . . . . . . 33
4.1.1 Scenario 1 : 230 MW Loss of Generation . . . . . . . . . . . . . . . . 35
4.1.2 Scenario 2 : 540 MW Loss of Generation . . . . . . . . . . . . . . . . 37
4.1.3 Scenario 3 : 720 MW Loss of Generation . . . . . . . . . . . . . . . . 39
4.1.4 Scenario 4 : 1000MW Loss of Generation . . . . . . . . . . . . . . . 41
4.2 Case 2: IEEE 39 bus with different penetration of renewable energy source . . 43
4.2.1 Scenario 1 : 230 MW Loss of Generation . . . . . . . . . . . . . . . . 44
4.2.2 Scenario 2 : 540 MW Loss of Generation . . . . . . . . . . . . . . . . 45
4.2.3 Scenario 3 : 720 MW Loss of Generation . . . . . . . . . . . . . . . . 46
4.2.4 Scenario 4 : 1000 MW Loss of Generation . . . . . . . . . . . . . . . 48
4.3 Case 3: IEEE 39 bus with different load modeling . . . . . . . . . . . . . . . . 49
4.3.1 Scenario 1 : ZIP load model : Constant active power . . . . . . . . . . 50
4.3.2 Scenario 2 : ZIP load model : Constant current . . . . . . . . . . . . . 52
4.3.3 Scenario 3 : ZIP load model : Constant impedance . . . . . . . . . . . 53
4.4 Case 4: IEEE 39 bus consider both Renewable Energy Source and Load Model 56
4.4.1 Scenario 1 : ZIP load model : Constant active power with Different
Penetration of Renewable Energy Source . . . . . . . . . . . . . . . . 56
4.4.2 Scenario 2 : ZIP load model : Constant current with Different Penetration
of Renewable Energy Source . . . . . . . . . . . . . . . . . . . . 58
4.4.3 Scenario 3 : ZIP load model : Constant impedance with Different Penetration
of Renewable Energy Source . . . . . . . . . . . . . . . . . . 59
4.5 Case 5: Taipower Disturbance Event in Peak time and Offpeak time . . . . . . 61
4.5.1 Scenario 1 : Peak Time . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5.2 Scenario 2 : Offpeak Time . . . . . . . . . . . . . . . . . . . . . . . . 62
4.6 Chapter Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.6.1 Comparison of different weight of nonlinear least square estimation . . 64
4.6.2 Comparison of different frequency deviation signal fitting Method . . . 65
5 Summary and Future work . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

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