直流潮流与交流潮流算法的综合比较研究

发布时间：2018-05-22 12:59

本文选题：高斯-赛德尔法 + 牛顿-拉夫逊法　；参考：《南昌大学》2015年硕士论文

【摘要】：本文对电力系统潮流计算的几种常规算法进行了新的探索和尝试。作为线性方程组求解潮流计算的重要环节,文中首先对高斯消元、高斯-约当消元以及三种三角分解法进行了比较详细的介绍并做了相关的分析与比较;其次,文中对元件的等值电路以及节点导纳矩阵的形成与修改进行了系统的归纳,提出了节点导纳矩阵中稀疏性和对称性的应用,并通过实例验证了该方法的有效性;针对潮流计算问题的数学模型,文中从变量、类型、功能以及越界条件四个方面着手,将系统各类节点分为PQ、PV和平衡节点,针对高斯-赛德尔法迭代次数多、收敛速度慢的特点,将加速因子引入其中可以有效减少其迭代次数、加快收敛速度,此外,文中还提出了一种基于导纳矩阵直角坐标形式的新高斯-赛德尔法,并详细推导了基于阻抗矩阵直角坐标形式的高斯-赛德尔法,针对牛顿-拉夫逊法潮流计算,文中重点介绍了对称稀疏性在形成雅可比矩阵中的应用并作了对比分析;文中最后对潮流计算的特殊解法—PQ分解法和直流潮流进行了详细的介绍,提出了PQ分解法的简化算法并对其进行了验算,结果证明该简化算法能够保证其收敛性、计算精度以及原特性不变,而使其修正方程式更为简单;当系统要求计算速度快而允许计算精度有一定误差时,用直流潮流或许是最好的选择。
[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.
【学位授予单位】：南昌大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TM744

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