如今由於分散式發電的比重越來越高，配電系統虛功控制的作用變得至關重要。適當的虛功控制，可調節電壓並降低電力系統中的實功率損耗。然而，間歇性特徵的分散式發電機，例如可再生能源的風能和太陽能發電等，會在電力系統中產生發電的不確定性。因此，本論文提出了一種基於Gram-Charlier級數展開的新型快速機率潮流法，以應對這種不確定性。此外，快速機率潮流只處理隨機變數中關於預期值的變化，從而減少迭代的次數。
本論文還提出了一種結合平均數-變異數和粒子群的演算法，稱為平均數-變異數粒子群演算法。模擬結果證明，在解決幾個複雜數學函數快速機率潮流最佳解下，其準確性和收斂率方面有良好的表現。此外，採用平均數-變異數粒子群演算法獲得最佳的發電機電壓、變壓器分接頭和靜態補償，來盡量減少實功率損耗，同時其隨機電壓會滿足限制，並透過使用獨立的25-Bus(澎湖)系統的模擬驗證所提出的方法的實用性。最後和考慮傳統的機率潮流進行比較。

The role of reactive power control in a distribution system becomes essential due to the high penetration of distributed generations (DGs) nowadays. Proper reactive power control can regulate the voltage profile and reduce real power losses in a power system. However, intermittent characteristics of distributed generations (e.g., renewable energies from wind and solar power) impose uncertainty of power generation on operators in the power system. Therefore, this thesis presents a novel fast probabilistic power flow (FPPF) method based on the Gram-Charlier series expansion to deal with such uncertainty. The FPPF method, in which PV and PQ buses are considered, is presented. In addition, the FPPF method only deals with variations of random variables with respect to the expected values, thus reducing the number of iterations.
This thesis also proposes a combination of mean-variance and particle swarm optimization algorithm, named mean-variance particle swarm optimization (MVPSO). In solving the optimal solutions of several complex mathematical functions, the excellent performance of MVPSO in accuracy and convergence rate can be shown by simulated results. Moreover, MVPSO is adopted to obtain the optimal values of generator voltages, transformer taps and static compensators to minimize the real power losses while the stochastic voltages satisfy the operational limits. Applicability of the proposed method is verified through simulation using an autonomous 25-bus (Penghu) system. Comparative studies considering traditional probabilistic power flow (TPPF) are performed as well.

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