當分析一信號時，必須先考慮信號為平穩信號或非平穩信號。當信號為平穩信號時，利用傅立葉轉換即可求出其頻域的資訊。但是，當信號為非平穩信號時，我們則需要以時間-頻率表現法來同時說明信號的時間和頻率的資訊。故當處理的信號為非平穩信號時，就必須以時頻分析法來處理。時頻分析除了解析信號中隱含的頻率，還提供了頻率隨時間變化的情形。
電力系統低頻振盪的時域信號為非平穩信號，主要為多種振盪模式的總和響應，難以直接分析信號的各種特性。本論文以希爾伯特-黃轉換中的經驗模態分解搭配小波轉換，來分析電力系統功率響應波形。透過經驗模態分解將波形展開成多個內建模態函數中，並利用小波轉換繪出以三維的時間-頻率-能量表示的時頻圖，經由所繪得的時頻圖可觀察到低頻振盪頻率及其能量隨時間變化之特性，並找出低頻振盪頻率的振盪參與能量較高的機組。透過與頻域分析結果比對得知在低頻振盪模式之頻率的振盪參與能量較高的機組，其頻域分析的參與因數亦較高。研究結果顯示，在低頻振盪模式參與能量較高的機組裝設電力系統穩定器，電力系統低頻振盪阻尼可獲得改善。

When a signal is to be analyzed, we must consider first whether the signal is stationary or non-stationary. If the signal is stationary, we can use the Fourier transform to derive its frequency-domain information. However, when the signal is non-stationary, we need to apply the time-frequency expression to obtain both the time and the frequency information. The time-frequency analysis is able to figure out the frequency and its variation with time for the signal.
Power system low frequency oscillations are non-stationary time-domain signals which are the sum of responses of various oscillation modes and it is not easy to analyze directly the characteristics of the oscillations. This thesis aims to utilize the empirical mode decomposition (EMD) and wavelet transform for analyzing the signals of power system low frequency oscillations. The EMD method is a technique to decompose a signal into a number of intrinsic mode function (IMF) components with time varying amplitudes and frequencies, and depicts the three dimensional time-frequency diagram via time-frequency-energy expression by using the wavelet transformation. The time characteristics of frequency and energy associated with low frequency oscillation mode can be obtained from the time-frequency graphs and then the generating unit with higher participation energy in low frequency oscillation model can be found. It is found the generator having higher participation energy in time-frequency analysis will own higher participation factor with the low frequency oscillation mode in frequency domain analysis. Simulation results show that the damping of power system low frequency oscillation can be improved with the power system stabilizer installed on the generator with higher participation energy.

摘要 I
Abstract II
圖目錄 VI
表目錄 XII
第一章 緒論 1
1.1 研究動機及目的 1
1.2 文獻回顧 2
1.3 研究方法 3
1.4 研究軟體 4
1.5 分章內容 4
第二章 電力系統低頻振盪分析與電力系統穩定器 6
2.1 電力系統低頻振盪介紹 6
2.2 系統振盪之類型 7
2.3 頻域分析 8
2.4 時域模擬 12
2.5 電力系統穩定器 12
第三章 時頻分析理論與方法 15
3.1 前言 15
3.2 希爾伯特-黃轉換 16
3.3 短時傅立葉轉換與小波轉換 21
3.4 經驗模態分解搭配小波轉換 23
第四章 雙區域電力系統分析 26
4.1 雙區域電力系統架構概述 26
4.2 雙區域電力系統之時頻分析 27
4.2.1 系統未裝設電力系統穩定器 28
4.2.2 發電機裝設電力系統穩定器 44
4.3 系統分析之結果 58
第五章 大型電力系統分析 60
5.1 研究系統架構概述 60
5.2 大型電力系統之時頻分析 65
5.3 系統分析之結果 105
第六章 結論 107
6.1 總結 107
6.2 未來研究方向 108
參考文獻 109

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