在智慧電網開始發展之前，用戶所使用的電量是依照一般傳統電表的讀數做為依據，有心人士便將電表改造，使得讀數失準，即為竊電，竊電至今是一項待解決的問題，未來將有賴於智慧電表之監控，透過智慧電網，得到即時的運轉數據，掌握電網之用電，以確保運轉數據的正確性。
利用即時的運轉數據，進行狀態估計來偵測竊電，以求解最小化加權最小平方之狀態估計為目的，為了得到相較於以往的牛頓法還要更好的狀態估計解，本文提出了以半正定規劃之問題型式，加上半正定放鬆將非凸問題放寬為凸問題，利用半正定規劃來達到全域最佳解，並利用一輸電系統及配電系統來驗證此方法之效能。在狀態估計之後，利用歷史資料來比對用戶用電異常之可能性，基於機率模型假設，利用變異數分析來判定用戶是否竊電。
本文整合了狀態估計以及機率模型，利用所接收到的量測值與歷史資料，發展出一流程，包含竊電偵測，竊電戶確認，最後再修正，以達到智慧電網克服竊電問題之目的。

Before starting the development of smart grid, the users’ power consumption is collected by the traditional mechanical meter reading. People with bad intention remodel the mechanical meters to make the readings inaccurate. When the power company charges for the electric bill, they get the wrong reading, and thus people can achieve the goal of stealing electric power. Stealing electric power also called non-technical loss. The stealing of electric power is a critical issue to be solved. In the future, a smart meter can immediately monitoring the whole system and get the instant operating data. By properly using the data from smart meters, the correctness of the operation data can be guaranteed.
In this thesis, we consider state estimation to detect tampering data. Conventionally, weighted least-squared error based state estimation is used. In order to obtain better state estimation solution, we use semi-definite programming to solve this problem. The convex semi-definite relaxation (SDR) technique is further pursued to render the nonconvex R-SE problem efficiently solvable. Compared with the conventional Newton's method, the semi-definite programming can achieve the global optimal solution rather than local optimal solutions. A transmission system and distribution system are performed to validate the effectiveness of this method. After the detection, the historical data is used to verify the possibility of anomalies. The integration of state estimation using on the received measured value and probability model using on the historical data can give a good trace of the users. The proposed process that involves stealing detection, confirm suspect, and data correction can solve the non-technical loss problem.

誌謝 i
摘要 ii
Abstract iii
目錄 v
表次 vii
圖次 ix
第一章 緒論 1
1.1 研究背景與動機 1
1.1.1 關於線路損失 1
1.1.2 非技術性損失 2
1.1.3 竊電的罪刑 3
1.2 國內外相關研究 4
1.2.1 支撐向量機模型(SVM) 4
1.2.2 智慧型電阻來確認用戶電力使用 6
1.2.3 狀態估計分析 8
1.3 論文大綱 9
第二章 電力系統狀態估計與半正定規劃理論 10
2.1 電力系統的狀態估計 10
2.1.1 狀態估計介紹 10
2.1.2 狀態估計的統計估測 11
2.2 半正定規劃(Semidefinite Programming) 12
2.2.1 凸問題介紹(Convex) 12
2.2.2 矩陣的半正定特性(Positive Semidefinite) 14
2.2.3 半正定規劃解線性規劃問題(Linear Programming) 16
2.2.4 半正定規劃解二次規劃(Quadratric Programming) 17
第三章 配電竊電偵測數學模型 20
3.1 配電系統數學模型 20
3.1.1 系統資料 20
3.1.2 配電線路模型 21
3.1.3 發電機模型 26
3.1.4 變壓器模型 26
3.2 半正定規劃求解狀態估計數學模型 27
3.2.1 最佳化數學模型 27
3.3 竊電偵測數學模型 32
3.4 竊電資料定位數學模型 39
3.5 竊電資料之修正 42
3.6 計算流程 42
第四章 測試結果及討論 46
4.1 測試系統 46
4.1.1 6-bus網狀輸電測試系統 46
4.1.2 三相8-bus輻射狀配電測試系統 49
4.2 半正定規劃解狀態估計之效能測試 52
4.2.1 6-bus網狀輸電系統之狀態估計測試 52
4.2.2 8-bus輻射狀配電系統之狀態估計測試 58
4.3 定位異常用戶 67
4.3.1 6-bus輸電系統之情境測試 67
4.3.2 8-bus配電系統之情境測試 68
4.4 嫌疑戶之歷史資料比對 69
4.5 修正數據 73
第五章 結論與未來研究方向 77
參考文獻 79

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