摘要
电压稳定问题是电力系统分析的重要课题之一。随着电力系统的发展,电力负荷增长迅速,电网间连接日益紧密。近年来已经有多起电压崩溃事件发生。人们对电压稳定越发重视。
最大功率法是静态电压稳定分析的主要方法之一,确定电压稳定极限是最大功率法的重点。雅克比矩阵在鞍节点附近奇异的问题是确定电压稳定极限的难点。为解决该问题,人们提出了连续潮流法,负荷导纳模型法,非线性规划法等大量方法。
本文以静态电压稳定为研究课题,在总结前人研究的文献后,介绍了电压稳定问题的定义和分类,罗列了各种电压稳定的分析计算方法。针对鞍节点附近潮流方程雅克比矩阵奇异的问题,本文对负荷导纳模型法进行了研究。
文本介绍了传统的负荷导纳模型法,陈述了雅克比矩阵的特征根分布和矩阵奇异之间的关系。本文中证明了以下结论:将负荷无功转化为电纳形式,可以减缓雅克比矩阵特征根向坐标原点的移动,从而改善潮流方程收敛性。。
传统负荷导纳模型法对部分节点潮流方程收敛性的改善有限。针对该问题,本文对负荷导纳模型法加以改进。在负荷无功转化之后,再将负荷有功转化为电导形式,使得雅克比矩阵特征根向坐标原点的移动再次被减速,鞍节点附近潮流方程收敛性得到进一步的提升。
本文采用编程语言Python调用电力系统仿真软件PSS/E(Power System Simulation for Engneering)的模块,对IEEE-30节点系统进行了演算,绘制了系统中的多个节点的PV曲线。由数据可见,相比传统的负荷导纳模型法,改进的负荷导纳模型法拥有更好的潮流方程收敛性。
Power system voltage stability has been recognized as one of the most import topics in the analysis of the power system.For the development of the power system and load,the grid interconnections become much more closer.Several voltage collapse accidents has been taken place recently.More attention has been paid to the problem of voltage stabiliy.
The maximum power method is one of the main methods in the static voltage stability analysis area,and its focus is the determination of the steady state voltage stability limit.The singular problem of Jacobian matrix around SNB(Saddle Node Bifurcation) is the difficulty of the maximum power method.Continuation power flow algorithm,load admittance model method, nonlinear programming method have been introduced to solve the porblem.
This paper concentrates on the static voltage stability.After the summary of the predecessors' literature,the definition and classification of the voltage stability is introduced,and the Algorithms of the voltage stability are listed.In accordance with the singularity of the Jacobian matrix near the SNB,this paper deals with the load admittance model algorithm.
The traditional load addmittance model algorithm is introduced.The relationship between the character roots’distribution of the the Jacobian matrix and the matrix singularity is stated.It has improved that transforming the load’s reactive power into suscepitance form can slow the movement of the character roots of the Jacobian matrix to the coordinate origin,and improve the convergence of the power flow equation.
In terms of some node’s convergence of the power flow equation which is not effective with the traditional load addmittance model algorithm,the traditional load addmittance model algorithm has been improved.After transforming the load’s reactive power into suscepitance form, load’s active power can be turned into the conductance form.It can slow movement of the character roots of the Jacobian matrix to the coordinate origin again,and make the convergence of the power flow equation better.
Python and PSS/E have been used to calculate the IEEE-30 node network,draw the PV curve of several nodes has been drawn.This paper's conclusion authenticated that load addmittance model algorithm is better than the traditional one.
引文
[1] C. Taylor.电力系统电压稳定.王壁译.北京:中国电力出版社,2002.23~26
[2] Thierry Van Custsem,Costas Vournas.电力系统电压稳定性.胡祥译.北京:电子工业出版社,2007.56~69
[3]王正风.电力系统电压稳定的综述.电气时代,2007:102~104
[4]刘鹏,吴刚.世界范围内两起典型电压崩溃事故分析.电网技术,2003,Vol.7(5):35~37
[5]余逸鑫,董存.美加“8.14大停电“过程中的电压崩溃.电气设备,2004,Vol.5(3):26～27
[6]印永华,郭剑波,赵剑军.美加“8.14”大停电事故初步分析以及应吸取的教训.电网技术,2003,Vol.27(10):8~11
[7]赵松立,曹一家,程时杰.电力系统电压稳定性问题综述(一).电力系统自动化,1994,Vol.18(6):66～68
[8]徐泰山,薛宇胜,韩祯翔.关于电力系统电压稳定性方法的综述.电力系统自动化,1996,Vol.20(5):62~67
[9]李国庆,李小军,彭晓洁.计及发电报价等影响因素的静态电压稳定分析.中国电机工程学报,2008, Vol.28(22):35~40
[10] Y.Tamura,H.Mori, S.Iwamoto.Relationship Between Voltage Instability and Multiple Load Flow Solutions in Electric Power Systems.IEEE Transactions on Power Apparatus and Systems,1983, Vol.102(5) :1115~1125
[11] T.J.Overbye and R.P.Klump.Effective Calculation of Power System Low-Voltage Solutions.IEEE Transactions on PWRS,1996,Vol.11(1):75~82
[12] V.A.Venikov,V.A.Stroev,V.I.Idelchick.Estimation of Electric Power System Steady-state Stability in Load Flow Calculation.IEEE Trans.on Power Apparatus and System,1975,PAS-94:1034~1041
[13] A. Tiranuchit.Towards a Computationally Feasible On-Line Voltage Instability in Electric Power System.IEEE Trans.PWRS,1988,Vol.3(2):259~264
[14]冯治鸿,刘取,倪以信等.多机电力系统电压静态稳定分析—奇异值分解法.中国电机工程学报,1992,Vol.12(3):59~64
[15] Gao B,Morison K,Kundur P.Voltage Stability Evaluation Using Model Analysis.IEEE Transactions on Power Systems,1992,Vol.7(4):1529~1542
[16]张尧,宋文南,贺家李.临近电压稳定极限的潮流和静稳极限算法.中国电机工程学报,1993,Vol.13(6):40~45
[17]张尧,宋文南.节点电压稳定临界状态和弱节点的确定.中国电机工程学报,1993,Vol.13(6):40~45
[18]郭瑞鹏,韩祯祥.电压稳定分析的改进连续潮流法.电力系统自动化,1999,Vol.23(14):13~16
[19]王锡凡,方万良,杜正春.现代电力系统分析北京:中国电力出版社,2003,96~99
[20] C.A.Canizarcs,F.L.Alvarado.Point of Collapse and Continuation Methods for large AC/DC Systems.IEEE Transactions on Power Systems,February 1993,Vol.8(1):1~8
[21] Byongjun Lee , Hwachang Song , sae-hyuk Kwon , et al . A Study on Determination of Interface Flow Limits in the KEPCO System Using Modified Continuation Power Flow.IEEE Transactions on Power Systems,2002,Vol.17(3):557~564
[22]葛维春.电力系统电压稳定性与电压崩溃问题的研究: [博士学位论文].哈尔滨:哈尔滨工业大学,1992. 31～37
[23] M. Z Sadek .Voltage Instability Subsequent to Short Circuit Recoveries.Electric Power System Research,1991,(21):162~167
[24]韩学军,游振华.基于FVSI线稳定指标计算母线最大承载负荷确定电力系统弱母线的方法.广东电力,2006,Vol.19(11):18~21
[25]冯治鸿,刘取,倪以信,等.多机电力系统电压动态稳定性分析研究.中国电机工程学报,1992,Vol.12(3):37~43
[26] Kurita A,Okubo H,Price W.Multiple Time Scale Power System Dynamic Simulations.IEEE Trans on PWRS 1993,Vol.8(1):378~383
[27] T.J.Overbye.Use of Energy Methods for On-line Assessment of Power System Voltage Security.IEEE Transactions on Power Systems,1993,Vol.8(2):452~458
[28]彭志炜,胡国根,韩祯翔.基于分叉理论的电力系统电压稳定性分析.北京:人民电力出版社,2005.21~26
[29] Jarjis J.,Galiana F. D..Quantitative Analysis of Strady State Stability in Power Networks.IEEE PAS,1981,100:318~326
[30] Carpaneto E. G.,Chicco G. et al.A Newton– Raphson Method for Steady State Voltage Stability Assessment.Proc.Bulk Power Syst.,1991,42:341~345
[31] I.Dobson,H.D.Chiang.On Voltage Collapse in Electric Power System.IEEE Trans On Power System 1990,Vol.5(2):689~693
[32]邓集祥.电力系统分歧浅谈.控制与决策,1993,Vol.8(2):56~61
[33]古以熹.矩阵特征根的分布.应用数学学报,1994,Vol.17(4):501~511
[34]梁景伟.分块矩阵特征值的圆盘估计.中国石油大学学报,2006,Vol.30(1):154~156
[35]蔡晔.基于PSS/E的电力系统静态电压稳定分析:[硕士学位论文].杭州:浙江大学,2003. 25~37
[36]江全元,彭旬东,张宝形.PSS/E——一种先进的电力系统仿真软件.高电压技术,2005,Vol.31(1):61~62
[37]程华,徐政.PSASP与PSS/E稳定计算的模型与结果比较.电网技术,2004,Vol.28(5):1~4
[38]廖晓晖,张沛超.基于Python开发PSS/E高级应用程序.继电器,2008,Vol.36(11):9~12
[39] Pilgrim,Mark.Dive Into Python. Springer-Verlag New York Inc,2006. 152～156
[40]陈儒.Python源码剖析.北京:电子工业出版设,2008. 16～21