電力系統的經濟運轉主要包含兩個層面，即虛功調度與實功調度。理論上，虛功調度與實功調度存在耦合關係，亦即二者在調度過程中會相互影響，但由於一般輸電線存在很高的X/R 比值，在此情況下，可利用解耦觀念將虛功與實功調度分割成兩個獨立的子問題，即P問題與Q 問題，以利於問題的求解。為同時求解此虛功與實功調度問題，本計畫提出混合差分演化法，在固定實功條件下求取虛功調度問題，以獲得最低實功損失下各匯流排電壓與變壓器分接頭設定的最佳解。當完成最佳虛功調度，接著求取虛功固定不變條件下之多目標實功調度問題，以獲得滿足環保與經濟條件下之最佳發電輸出排程。混合差分演化法是一種多點搜尋、以群體演化為基礎之最佳化方法，主要在傳統差分演化法中加入遷移與加速運算子，以在過早收斂與整體搜尋的取捨間獲得平衡。由於混合差分演化法為一極優之最佳化搜尋工具，當應用於求解此虛功與實功調度問題時，能獲得良好的調度結果。本計畫所提出的方法測試於IEEE 30 個匯流排及台電345kV 簡化系統，結果顯示，所提出之HDE 方法在解的品質及執行時間上均優於DE 及PSO 方法 Power system economical operation consists of two aspects: reactive power dispatch and active power dispatch. Theoretically, there has the coupling relation between reactive and active power dispatch. That means they will influence each other. However, due to a high X/R ratio exists in the transmission line, the problem of reactive and active power dispatch can then be decomposed into two individual sub-problems by the decoupling concept, i.e., P problem and Q problem, which would be beneficial for the problem resolution. To simultaneously solve the optimal reactive and active power dispatch problem, a hybrid differential evolution (HDE) algorithm is presented in this project. Based on the minimization of active power transmission losses, the optimal solutions of each bus voltage and tap setting of each transformer can then be obtained. After finishing the optimal reactive power dispatch, the active power dispatch is performed accordingly while the reactive power remains unchanged. The optimal generation schedule satisfying both environmental and economic objectives is then obtained by the proposed HDE method. HDE is a multi-point search and population-based optimization method. To have the population holds the diversity characteristic, a migrating phase and an accelerated phase are embedded into the original version of DE. Due to the superiority in optimization, the HDE method can acquires better results when applied to the reactive and active power dispatch problem. The proposed approach has been verified on the IEEE 30-bus and Taipower 345kv simplified systems. Testing results indicate that the proposed HDE has high-quality solution and shorter computation time than DE and PSO methods.