本研究旨在探討改良型變異數矩陣之建構方法，並應用於提升電力系統狀態估計之效能。這是由於現行加權最小平方法在構建量測變異數矩陣時，常假設各量測數據相互獨立，並採用對角矩陣形式，未能考慮量測數據之間的統計關聯性，進而可能導致狀態估計結果產生偏差。為解決此問題，本文提出一套改良型變異數矩陣建構方法，結合點估計法與矩陣稀疏化最佳化技術，不僅透過點估計法推估電力系統中具有不確定性的參數，用以反映量測數據之間的統計關聯性，並且導入稀疏化技術，以構建具有關聯性之共變異數矩陣，並提升其在狀態估計中的實用性與準確性。而為驗證本文所提方法之可行性，本文針對不同電力系統及多種模擬情境進行測試。模擬結果顯示，所提方法確實有助於提升匯流排電壓與相角的估測準確度，同時可作為電力工程人員監控系統運轉時之施行參考。

This study aims to explore a method for constructing an improved variance matrix and its application in enhancing the performance of power system state estimation. In conventional weighted least squares methods, the measurement variance matrix is often assumed to be diagonal, under the premise that all measurement data are statistically independent. However, this assumption neglects the correlations among measurements, potentially leading to biased state estimation results. To address this issue, this thesis proposes a method for constructing an improved variance matrix that integrates point estimation and sparse matrix optimization techniques. The proposed approach utilizes point estimation to infer uncertain parameters within the power system, thereby capturing the statistical correlations among measurements. Meanwhile, sparse optimization is employed to construct a correlated covariance matrix, enhancing both the practicality and accuracy of the method in state estimation applications. To verify the feasibility of the proposed method, this study conducts tests on various power systems under multiple simulation scenarios. The simulation results indicate that the proposed approach effectively improves the estimation accuracy of bus voltages and phase angles. The proposed approach can also serve as a practical reference for power engineers in monitoring system operations.

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