Abstract
In this dissertation, a methodology integrating an enhanced Newton OptimalPower Flow (OPE) method and the generalized Benders decomposition theoryis proposed to solve the long term VAR planning problem. The problemcovers the questions of where, when and how much VAR compensators shouldbe installed in a power system. Important contributions of thisdissertation may be summarized below in sequence:First, the author enhances Newton OPF on several aspects to render themcthod more efficient and stable numerically. This includes: (1) New indexfor enforcing variables outside boundaries, threshold for releasingbinding inequality constraints, and strategy for releasing some inequalityconstraints initially are proposed such that the binding/releasinginequality constraints can be more efficiently determined. (2) Whilesolving the algebraic equations of the necessary condition for optimality,values and signs of pivoted terms are modified properly under someconditions to avoid numerical oscillation, (3) Necessary and sufficientconditions are presented for one to judge whether the OPF solution isfeasible or infeasible. In addition, the theoretical basis may provide onewith good guidance to achieve a desired infeasible solution. (4)Mathematical analysis of convergence speed of Newton OPF under differentcases is made. This clarifies some puzzling numerical results about theconvergent speed while running Newton OPF.Next, by integrating the above enhanced Newton OPF with the generalizedBenders decomposition theory, an efficient methodology is presented forlong term VAR planning. This method decomposes the original complicatedproblem into master problem and slave level such that discrete andcontinuous variables can be handled separately. Furthermore, eachsubproblem of various base and contingency cases can be decoupledcompletely in the slave level. This not only simplifies greatly theoriginal very large scale nonlinear programming problem but also, for thefirst time, enables one to find a complete reactive compensatorinstallation pattern for each period. Finally, a heuristic scheme forproviding fast and good approximate discrete solution in the masterproblem together with an application of relaxed convergent tolerance inthe slave level makes the proposed method more efficient.Third, in view of the power system security, in addition to correctivecontrol, concept of preventive control is further covered in the proposedlong term VAR planning methodology. Major contributions in this aspectinclude (1) presentation of a formula for predicting the post-contingencyvoltage magnitudes. This enables one to eliminate a lot of contingencypower flow equations and reduces greatly the computational burden. (2) Analgorithm based on the infeasibility condition is proposed for one todetermine which mode (preventive and corrcctive) should be adopted forcach contingency. (3) Clear solution comparison between the preventive andcorrective modes for the same contingency. This provides the planner withclear choice for making a decision.Finally, based on the optimality conditions of Kuhn-Tucker theorem and theauthou's experience in running the Newton OPF program, an expert systemmodule is proposed to interpret the Newton OPF result for inexperiencedusers. This expert system moddule is developed in an expert system shellcalled OPS83, which supplies a fast inference enging and convenientinterface with Fortran programs. Through the help of this expert system,cnormous amount of OPF output is reduced greatly. Only the criticalinformation as well as important data are listed to assist users moreefficiently figure out the results. In addition, the proposed expertsystem is able ot suggest the users take proper actions such asrescheduling generations and/or adding extra compensators depending on thecauses of the system weakness. In fact, due to the fast speed, the expertsystem incorporating with OPF can be applied to on-line reactive powerdispatch.本文提出一個結合強化牛頓最佳電力潮流法和廣義邊德斯分割定理的方法，以解長期無效電力規劃問題，這個方法解決了應該在那裡、在什麼時候、以及安裝多少無效電力設備的問題。本文的主要貢獻可分述如下：首先，作者改進原有牛頓最佳電力潮流法，使其更有效率，在數值計算方面更穩定，這包括（１）針對超限變數提出限制的新指標，定出臨界值以作為不等式之釋放標準，並提出如何於起始階段放寬某些不等式限制的策略，使得不等式限制能更有效的處理；（２）當解最佳解之必要條件的代數式時，提出支軸項在某些條件下，於數值及符號上之修定標準，以避免數值方面的振盪；（３）提出辨別牛頓最佳電力潮流法是否有解的充分必要條件，利用這些理論基礎，亦可提供吾人就無解情況下，如何獲取一最佳近似解；（４）分析牛頓最佳電力潮流法在不同狀況下之收斂特性，這可以澄清吾人在執行程式時，常會碰到一些不同數值收斂速率之奇怪現象。其次，在本論文中更提出一有效方法，藉綜合上述強化牛頓最佳電力潮流法與廣義邊德斯分割定理，以做長期無效電力規劃：這個方法將原有的問題分割成主問題與僕層，使得離散和連續變數可以分開來解，並且在僕層中，每個不同的基載或偶發事件可以分別獨立處理，這不僅大大簡化原有超大型非線性問題，並且也是文獻上，第一次能完滿解決同時考慮多期間之無效電力規劃問題。最後，並提出一個快速而有效的方法，以獲取問題之近似離散解，及在僕層中建議使用較寬的收斂容忍度，使整個方法更有效率。第三，以系統安全為觀點，本論文除了能處理一般更正式控制外，並更進一步考慮預防式，主要的貢獻如下：（１）提出一個跳線後電壓大小的預估公式，以大量減少電力潮流方程式，增加求解效率；（２）文中並基於無解條件，提出一個計算法則，對於每一偶發事件，決定是否該採用更正式或預防式控制；（３）可對同一偶發事件，提供預防式和更正式的解，以為規劃師比較參考，俾方便決策。最後，根據肯塔克最佳化定理(Kuhn-Tucker optimization Theorem)和作者執行牛頓最佳電力潮流程式的經驗，本論文針對沒有經驗的使用者發展出一套解釋牛頓最佳電力潮流解的專家系統，這個專家系統是用一個OPS83 的專家系統殼所發展出來，它能提供與福傳程式相接的介面，並具有快速的推理機構；經由此專家系統的幫助，可以減少大量的潮流解輸出，而只輸出一些較重要訊息和資料，俾使使用者能更有效的瞭解其結果；此外，此專家系統能依據系統的弱點原因，建議使用者採取適當行動，如重調發電機輸出、添裝無效電力設備等。事實上，由於本系統推理之速度極快，可結合最佳電力潮流法以應用於電力系統無效電力之線上調度。