基于GMRES的改进连续潮流算法研究

阐述了一种基于GMRES的改进连续潮流算法,主要针对大型电力系统,在预测环节中采用拉格朗日非线性预测,减少了计算时间;在校正环节中将GMRES方法与牛顿法相结合构成内外双层迭代,并应用ILU分解对系数矩阵进行预处理,从而避免了对修正方程进行直接求解,提高了连续潮流法的计算速度。该算法根据梯度参数变化对步长进行了有效的控制,可以大大提高PV曲线的追踪效率。采用该算法对IEEE300节点测试系统进行仿真计算,取得了良好的计算结果,从而验证了该方法的有效性和快速性。     

基于非线性预测的改进连续潮流算法研究

阐述了一种改进的连续潮流法。该方法预测过程中采用了非线性预测,在功率极限点附近不需要减小步长,校正过程中采用局部参数法求解校正方程,从而减少了绘制PV曲线的时间;潮流计算采用牛拉法,保证了PV曲线绘制过程中的稳定性。通过对IEEE 39和IEEE 118节点测试系统进行仿真计算,取得了良好的计算结果,从而验证了本算法的有效性和快速性。     

基于线性和非线性混合预测的改进连续潮流法

提出了一种改进的连续潮流法求取电力系统的PV曲线。该方法采用线性和非线性的混合预测,解决了常规非线性预测在PV曲线下半支的问题,有效地改善了连续潮流法的性能。采用自动变步长提高了程序的效率。该方法应用于IEEE 39节点测试系统,取得理想的效果,从而验证了该方法的有效性和快速性。     

求取电力系统PV曲线的改进连续潮流算法

连续潮流算法是电压稳定分析的有力工具,能够克服接近稳定极限运行状态时的潮流不收敛的问题.常规的连续潮流算法基于切线预测与牛顿——拉夫逊法校正,求取电力系统PV曲线时所需时间较长.鉴于此,本文提出了一种改进连续潮流算法,它将常规潮流和连续潮流结合起来,可以取得快速和准确的良好效果.从基本工况开始增加负荷,用割线法预测潮流...     

求取电力系统PV曲线的改进连续潮流法

阐述了用改进的连续潮流法求取电力系统的ＰＶ曲线,该方法通过增加一维潮流方程,消除了功率极限点附近的雅可比矩阵奇异的现象,获得精确的电压稳定极限和整支正技术,运算更加快捷精确,同时利用系统左特征矢量的性质获得系统临近崩溃时的最优控制方向,使该方法不但具有理论意义而且有实际应用价值。     

改进连续潮流法追踪PV曲线

本文阐述了用改进连续潮流法求取电力系统的PV曲线。针对常规潮流法在鞍结分岔点附近不收敛,该方法通过增加一维潮流方程,消除了功率极限点附近的雅可比矩阵奇异的现象,获取精确的电压稳定极限和整支PV曲线。算法采用了预估校正技术,相对于以往的预估校正技术,提出了一些改进方法,运算更加快捷精确,更好地解决了常规潮流法在鞍结分岔点附近不收敛的问题,可顺利越过鼻形点,绘制出整枝的PV曲线。并用科学计算软件MATLAB对一个简单电力系统做了仿真验证,证明了该方法的有效性。该方法不但具有理论意义而且有实际应用价值。     

基于几何参数化的连续潮流算法研究

本文提出了一种基于几何参数化求取PV曲线方法。该方法应用预测校正法的连续潮流算法,采用几何参数化,从而消除了在功率极限附近雅可比矩阵奇异的现象,有效地改变了收敛方向,可以精确获得电压稳定极限和完整的PV曲线。应用该算法对IEEE39节点和IEEE118节点的电力系统进行了仿真计算,取得良好的计算结果,证实了该算法的有效性。     

基于改进连续潮流法的电压稳定极限计算方法

针对电压稳定性分析连续潮流法的计算效率、精度及收敛性问题,提出了一种改进型的连续潮流法。该方法在参数化中,有机结合了物理参数化和局部参数化在不同区域的优点,在校正过程引入了一种新的预测-校正法,在步长控制中,提出了变步长控制函数,极大地提高了算法的计算精度、效率和收敛性。最后通过实例证明该方法可以提高连续潮流法分析电压稳定性的效率,并验证了该方法的有效性。     

电压稳定分析的二阶概率连续潮流法

将概率潮流与二阶连续潮流 (QCPF)相结合 ,在QCPF计算中考虑负荷变化的彼此相关性。节点电压取直角坐标形式 ,确定了二阶概率连续潮流 (PCPF)的相关算式。在正态分布的± 4个标准差下 ,由求得的各点电压的分布特性 ,确定出PV曲线的分布范围。所得算法在IEEE5 7节点的标准算例上进行了分析     

电压稳定分析的二阶概率连续潮流法

将概率潮流与二阶连续潮流(QCPF)相结合,在QCPF计算中考虑负荷变化的彼此相关性.节点电压取直角坐标形式,确定了二阶概率连续潮流(PCPF)的相关算式.在正态分布的±4个标准差下,由求得的各点电压的分布特性,确定出PV曲线的分布范围.所得算法在IEEE57节点的标准算例上进行了分析.     

一种基于自适应步长控制与组合参数化的改进连续潮流计算方法

提出了一种可以完全跟踪光伏(PV)曲线斜率变化的自适应变步长算法,并在理论上比较分析了所提变步长法与常规变步长法的灵敏度特性,通过分析发现,所提变步长法具有更优的自适应性,在保证连续潮流计算精度的同时,大幅降低了计算时间。提出了一种组合参数化法,即在PV曲线的不同区域采用不同的参数化法,同时在PV曲线追踪过程中设置参数化切换断点,并以校正不收敛作为组合切换判据。基于IEEE标准节点系统的计算结果验证了所提自适应变步长算法与组合参数化法的有效性与优越性。     

Solving the nonlinear power flow equations with an inexact Newtonmethod using GMRES

This paper presents a detailed investigation into the effectiveness of iterative methods in solving the linear system subproblem of a Newton power flow solution process. An exact Newton method employing an LU factorization has been one of the most widely used power flow solution algorithms, due to the efficient minimum degree ordering techniques that attempt to minimize fill-in. However, the LU factorization remains a computationally expensive task that can be avoided by the use of an iterative method in solving the linear subproblem. An inexact Newton method with a preconditioned Generalized Minimal Residual (GMRES) linear solver is presented as a promising alternative for solving the power flow equations. When combined with a good quality preconditioner, the Newton-GMRES method achieves a better than 50% reduction in computation, compared to Newton-LU, for two large-scale power systems: one with 3493 buses and 6689 branches, another with 8027 buses and 13765 branches     

Asymptotic numerical method for continuation power flow

In this paper, we use the asymptotic numerical method (ANM) to solve continuation power flow (CPF) problems. ANM can be considered as a higher-order predictor without any corrections. The method has been applied with great success to the areas of fluids, elasticity and structural mechanics. Compared to the general predictor–corrector continuation methods used in power systems, ANM has the following advantages. Firstly, the computation time is smaller. With ANM, the nonlinear problems to be solved are transformed into a recursive sequence of linear systems with the same coefficient matrix, and only one sparse Jacobian matrix factorization is required at each continuation step. Secondly, the computational procedure is automatic. A simple criterion proposed by B. Cochelin et al. can be used to determine the step-length, which makes the continuation easy, and no special step-length control strategy is required. Thirdly, as the solution branch has been expressed into a closed analytical form, the Q-limit points on P–V curves due to reactive power limits violations and other breaking points with the control devices actions can be precisely located with ANM easily. Numerical examples in several power systems were presented to validate the method.     

基于连续潮流和模态分析的电压稳定分析

针对电压稳定分析的连续潮流和模态分析方法进行研究,详细推导了连续潮流和模态分析的具体算法.连续潮流通过局部参数化和预测校正的方法克服其在拐点的奇异性,模态分析则给出节点参与因子和支路参与因子用于标识电压稳定性.结合某省网进行实例分析,证明了节点参与因子和P-U曲线在反映电压稳定性上具有一致性.计算结果表明:连续潮流方法可快速、准确求得系统最大负荷点,判断系统稳定裕度;模态分析方法可以很好定位电压稳定的薄弱区域.     

动态连续潮流与改进粒子群优化算法相结合的静态电压稳定分析

建立了静态电压稳定分析的优化数学模型,同时用精确罚函数的形式处理节点电压和发电机无功功率这两个状态变量的不等式约束.提出了一种动态连续潮流(Dynamic Continuation Power Flow,DCPF)与自适应混沌聚焦粒子群算法(Adaptive Chaotic Focusing Particle Swarm Optimization,ACFPSO)相结合求取最大静态电压稳定裕度的方法.该方法以静态电压稳定裕度最大为目标函数,用DCPF计算每一组控制变量对应的静态电压稳定裕度,将混沌算法引入到自适应聚焦粒子群算法中组成ACFPSO,利用ACFPSO进行最优控制变量组合的搜索.通过分析控制变量组合和静态电压稳定裕度的对应关系,找到提高静态电压稳定裕度的措施.对IEEE6、IEEE30节点系统的仿真计算验证了该算法的有效性.     

基于连续潮流的配电网供电能力评估

随着非全相运行的分布式电源大量接入配电网,配电网固有的三相不平衡特征更加突出,传统配电网供电能力评估因忽略配电网三相不平衡特征导致结果不准确。为了准确分析三相不平衡特征对配电网最大供电能力评估的影响,建立了以配电网供电负荷参数最大为目标函数,考虑了支路热约束和节点电压等状态变量和分布式电源的有功和无功功率等控制变量的含分布式电源三相不平衡配电网供电能力评估模型。选择电压跌落情况最严重的相作为连续参数,确保预测-校正过程的的连续潮流法求解的结果更加精确。最后,采用拓展的IEEE33节点配电系统进行仿真验证,表明文中所提的模型和求解方法是有效的。     

An efficient geometric parameterization technique for the continuation power flow

Continuation methods have been shown as efficient tools for solving ill-conditioned cases, with close to singular Jacobian matrices, such as the maximum loading point of power systems. Some parameterization techniques have been proposed to avoid matrix singularity and successfully solve those cases. This paper presents a new geometric parameterization scheme that allows the complete tracing of the P–V curves without ill-conditioning problems. The proposed technique associates robustness to simplicity and, it is of easy understanding. The Jacobian matrix singularity is avoided by the addition of a line equation, which passes through a point in the plane determined by the total real power losses and loading factor. These two parameters have clear physical meaning. The application of this new technique to the IEEE systems (14, 30, 57, 118 and 300 buses) shows that the best characteristics of the conventional Newton's method are not only preserved but also improved.     

Application of continuation power flow method in radial distribution systems

The paper presents a set of equations (SOE) comprising voltage magnitude and nodal real/reactive power balance equations to model a radial distribution system (RDS). The voltage equations in the SOE have dual roots. Then a Newton–Raphson (NR) method is presented to solve the SOE to determine the voltage solution of an RDS. This NR method is extended using the continuation technique to trace the P–V curves and to determine the maximum loading point of an RDS. Implementation of the proposed method on some common RDS and a 5002-bus RDS is demonstrated. An interesting characteristic of the path traced by the minimum singular value of the system Jacobian during the application of the continuation method for a system with shunt capacitors is reported. An analysis of a simple 4-bus system with and without a capacitor demonstrates that the presence of capacitive load creates multiple positive regions of σ_min. One positive region exists when the system is healthy (before collapse). The second region exists in between collapse point and the point where an increase in the load creates reactive power flow reversal on the source line.     

基于连续潮流法的交直流系统可利用传输能力的计算

提出并建立了交直流系统可利用传输能力(ATC)模型.该模型采用两端直流混合系统,考虑电压稳定性、节点电压水平、热稳定、N-1故障等安全约束条件.应用连续潮流法求解过程中,将交流和直流系统方程分解计算,通过直流网络状态量与换流器交流母线电压和给定直流控制量之间关系方程组来简捷地计及交直流系统间耦合关系.对IEEE30节点系统进行的仿真计算证明了所提出模型和算法的有效性.     

Development of nonlinear predictor with a set of predicted points for continuation power flow

In this paper, a new continuation power flow method is proposed to speed up computational time for drawing P– V curves in power systems. The continuation power flow calculation aims at successively evaluating power flow solutions in changing the nodal specified value of power flow calculation. The P– V curves are useful for static voltage instability. The conventional continuation power flow calculation methods are based on the predictor– corrector method. This paper proposes a new nonlinear predictor in the predictor– corrector method. The proposed method simultaneously evaluates a set of solution candidates through the nonlinear predictor. The effectiveness of the proposed method is demonstrated in sample systems. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(4): 30–41, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20297