本文選題：高斯-賽德爾法 + 牛頓-拉夫遜法��； 參考：《南昌大學(xué)》2015年碩士論文

【摘要】：本文對(duì)電力系統(tǒng)潮流計(jì)算的幾種常規(guī)算法進(jìn)行了新的探索和嘗試。作為線性方程組求解潮流計(jì)算的重要環(huán)節(jié),文中首先對(duì)高斯消元、高斯-約當(dāng)消元以及三種三角分解法進(jìn)行了比較詳細(xì)的介紹并做了相關(guān)的分析與比較;其次,文中對(duì)元件的等值電路以及節(jié)點(diǎn)導(dǎo)納矩陣的形成與修改進(jìn)行了系統(tǒng)的歸納,提出了節(jié)點(diǎn)導(dǎo)納矩陣中稀疏性和對(duì)稱性的應(yīng)用,并通過(guò)實(shí)例驗(yàn)證了該方法的有效性;針對(duì)潮流計(jì)算問(wèn)題的數(shù)學(xué)模型,文中從變量、類型、功能以及越界條件四個(gè)方面著手,將系統(tǒng)各類節(jié)點(diǎn)分為PQ、PV和平衡節(jié)點(diǎn),針對(duì)高斯-賽德爾法迭代次數(shù)多、收斂速度慢的特點(diǎn),將加速因子引入其中可以有效減少其迭代次數(shù)、加快收斂速度,此外,文中還提出了一種基于導(dǎo)納矩陣直角坐標(biāo)形式的新高斯-賽德爾法,并詳細(xì)推導(dǎo)了基于阻抗矩陣直角坐標(biāo)形式的高斯-賽德爾法,針對(duì)牛頓-拉夫遜法潮流計(jì)算,文中重點(diǎn)介紹了對(duì)稱稀疏性在形成雅可比矩陣中的應(yīng)用并作了對(duì)比分析;文中最后對(duì)潮流計(jì)算的特殊解法—PQ分解法和直流潮流進(jìn)行了詳細(xì)的介紹,提出了PQ分解法的簡(jiǎn)化算法并對(duì)其進(jìn)行了驗(yàn)算,結(jié)果證明該簡(jiǎn)化算法能夠保證其收斂性、計(jì)算精度以及原特性不變,而使其修正方程式更為簡(jiǎn)單;當(dāng)系統(tǒng)要求計(jì)算速度快而允許計(jì)算精度有一定誤差時(shí),用直流潮流或許是最好的選擇。
[Abstract]:In this paper, several conventional algorithms for power flow calculation are explored and tried. As an important part of power flow calculation for solving linear equations, this paper first introduces Gao Si elimination, Gao Si Jordan elimination and three triangular decomposition methods in detail, and makes relative analysis and comparison. In this paper, the equivalent circuit of the element and the formation and modification of the node admittance matrix are systematically summarized, and the application of sparsity and symmetry in the node admittance matrix is proposed, and the effectiveness of the method is verified by an example. Aiming at the mathematical model of power flow calculation problem, this paper starts from four aspects of variables, types, functions and crossing conditions, divides all kinds of nodes of the system into PQPV and balanced nodes, and aims at the high number of iterations by Gauss-Seedel method. Because of the slow convergence rate, introducing the acceleration factor into it can effectively reduce the number of iterations and accelerate the convergence speed. In addition, a new Gauss-Seder method based on the rectangular coordinate form of admittance matrix is proposed in this paper. The Gauss-Seidel method based on the rectangular coordinate form of impedance matrix is deduced in detail. Aiming at the power flow calculation of Newton-Raphson method, the application of symmetry sparsity in the formation of Jacobian matrix is introduced and compared. In the end of the paper, the special solution of power flow calculation-PQ decomposition method and DC power flow method are introduced in detail, and the simplified algorithm of PQ decomposition method is put forward and verified. The result shows that the simplified algorithm can ensure its convergence. The calculation accuracy and the original characteristics are invariable, which makes the correction equation simpler. When the system requires fast calculation speed and allows a certain error in the calculation accuracy, using DC power flow may be the best choice.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TM744

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本文編號(hào)：1922170