多运行方式下的概率暂态稳定分析
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摘要
基于数值积分法的传统暂态稳定计算通常基于单一的系统运行方式,即确定性的网络结构、网络参数和系统运行参数,因而得到的功角摇摆曲线也是确定性的。电力系统在实际运行过程中,存在着许多随机扰动,例如节点注入功率或网络结构的变化。在电力系统暂态稳定计算中,当考虑负荷波动影响时,发电机状态变量具有分布特性。变量的分布特性由其数字特征来描述,例如均值与协方差。
由于暂态稳定分析中涉及到大量的微分方程和代数方程,表达复杂,清晰明了的系统化解析表达有利于概率暂态稳定模型的建立与计算。本文以节点注入功率和PV电压运行曲线为基础,形成多运行方式。先利用全系统微分方程和代数方程,在稳态条件下形成系统化的线性化解析表达,确定多运行方式下的发电机初始运行状态的分布特性。进而利用小干扰稳定分析中的系统矩阵,系统化表达暂态稳定数值计算中相邻时刻间的变量关系,实现多系统运行方式下的概率暂态稳定分析,得到发电机功角摇摆曲线的分布特性。
由于初始运行状态的线性化表达与小干扰稳定分析中的A阵类似,相邻两时刻之间变量的解析关系式中的A阵与小干扰分析中的A阵一致,因此借用小干扰稳定分析中成熟的“插入式”建模技术形成相应的系数矩阵。
所述算法在一个8机系统上进行了试算。计算所得功角摇摆曲线也不再是单一的一条线,而是具有分布特性的带状范围。
因目前研究方法尚未保留高阶项,在计算过程中不断采用线性化模型,造成计算误差上升。若保留高阶项应该能提高变量均值与协方差的计算精度。
The traditional transient stability calculation based on numerical integration method is usually under single system operating conditions with deterministic network configuration, network parameters and system operating parameters, thus the obtained power angle swing curve is deterministic. In the actual operation of power systems, there are many random disturbances and uncertainties, such as the changes of nodal injection power or network configuration, as well as measurement and estimation error. In the calculation of power system transient stability, generator state variables will possess of distribution characteristic when effect of load variation is considered. The distribution characteristic of variables can be described by their numerical characteristics, such as expectation and covariance.
Expressions for transient stability analysis are complex because it involves a large number of differential equations and algebraic equations. Clear and systematical expressions benefit the foundation and calculation of the probability transient stability model. Based on operating curves of PV nodal voltages and nodal injection powers, multi-operation conditions are formed. Firstly, total system differential equations and algebraic equations are used to form the linearization expressions under steady state conditions. The distribution property of generators in initial operating state is determined under system multi-operation conditions. Then the coefficient matrix used in small signal stability analysis is applied to systematically describe the variable relationship between adjacent time periods in the transient stability calculation. So the probabilistic transient stability analysis under multi-operation conditions is achieved. Obtained results are the distribution characteristics of generator power-angle swing curves.
Due to the similarity between linear expressions of initial operating state and the A matrix used in small signal stability analysis, as well as the A matrix used to describe the variable relationship between adjacent time periods is the same with that A matrix used in small signal stability analysis, the mature "plug-in" modeling technology used in small signal stability analysis is applied to form the corresponding coefficient matrix.
Proposed approach is examined on an eight-machine system. Calculated power angle swing curve is no longer a single line, but the band with distribution property.
Because the higher order items have not been retained in the methods currently and linear model is continuously used in the calculation process, the calculation error increases. If the higher order items are maintained, the calculation accuracy could be raised.
由于暂态稳定分析中涉及到大量的微分方程和代数方程,表达复杂,清晰明了的系统化解析表达有利于概率暂态稳定模型的建立与计算。本文以节点注入功率和PV电压运行曲线为基础,形成多运行方式。先利用全系统微分方程和代数方程,在稳态条件下形成系统化的线性化解析表达,确定多运行方式下的发电机初始运行状态的分布特性。进而利用小干扰稳定分析中的系统矩阵,系统化表达暂态稳定数值计算中相邻时刻间的变量关系,实现多系统运行方式下的概率暂态稳定分析,得到发电机功角摇摆曲线的分布特性。
由于初始运行状态的线性化表达与小干扰稳定分析中的A阵类似,相邻两时刻之间变量的解析关系式中的A阵与小干扰分析中的A阵一致,因此借用小干扰稳定分析中成熟的“插入式”建模技术形成相应的系数矩阵。
所述算法在一个8机系统上进行了试算。计算所得功角摇摆曲线也不再是单一的一条线,而是具有分布特性的带状范围。
因目前研究方法尚未保留高阶项,在计算过程中不断采用线性化模型,造成计算误差上升。若保留高阶项应该能提高变量均值与协方差的计算精度。
The traditional transient stability calculation based on numerical integration method is usually under single system operating conditions with deterministic network configuration, network parameters and system operating parameters, thus the obtained power angle swing curve is deterministic. In the actual operation of power systems, there are many random disturbances and uncertainties, such as the changes of nodal injection power or network configuration, as well as measurement and estimation error. In the calculation of power system transient stability, generator state variables will possess of distribution characteristic when effect of load variation is considered. The distribution characteristic of variables can be described by their numerical characteristics, such as expectation and covariance.
Expressions for transient stability analysis are complex because it involves a large number of differential equations and algebraic equations. Clear and systematical expressions benefit the foundation and calculation of the probability transient stability model. Based on operating curves of PV nodal voltages and nodal injection powers, multi-operation conditions are formed. Firstly, total system differential equations and algebraic equations are used to form the linearization expressions under steady state conditions. The distribution property of generators in initial operating state is determined under system multi-operation conditions. Then the coefficient matrix used in small signal stability analysis is applied to systematically describe the variable relationship between adjacent time periods in the transient stability calculation. So the probabilistic transient stability analysis under multi-operation conditions is achieved. Obtained results are the distribution characteristics of generator power-angle swing curves.
Due to the similarity between linear expressions of initial operating state and the A matrix used in small signal stability analysis, as well as the A matrix used to describe the variable relationship between adjacent time periods is the same with that A matrix used in small signal stability analysis, the mature "plug-in" modeling technology used in small signal stability analysis is applied to form the corresponding coefficient matrix.
Proposed approach is examined on an eight-machine system. Calculated power angle swing curve is no longer a single line, but the band with distribution property.
Because the higher order items have not been retained in the methods currently and linear model is continuously used in the calculation process, the calculation error increases. If the higher order items are maintained, the calculation accuracy could be raised.
引文
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[6]韩祯祥,曹一家.电力系统的安全性及防治措施[J].电网技术,2004,28(9):1-6
[7]周孝信,郑健超,沈国荣等.从美加东北电网大面积停电事故中吸取教训[J].电网技术,2003,27(9):1-6
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[13]郭志忠,柳焯.快速高阶Taylor级数法暂态稳定计算[J].中国电机工程学报,1991,11(3):9-15
[14]Pai M A,Sauer P W,Dobraca F.A New Trajectory Approximation Technique for Transient Stability Studies[J],International Electrical Power & Energy Systems,1991,13(5):249-254
[15]Kulkarni,Pai M A.Parallel Computation of Power System Dynamic Using Multi-step Methods[J].Electrical Power & Energy Systems,1992,14(1):33-38
[16]汪宗芳,陈德树,何仰赞.大规模电力系统暂态稳定性实时仿真及快速判断[J].中国电机工程学报,1993,13(6):13-19
[17]Athay T A.Practical Method for the Direct Analysis of Transient Stability[J].IEEE Transactions on Power Apparatus and Systems,1979,98(2):573-584
[18]Chung T S,Fang D Z.A Fast Approach to Transient Stability Estimation Using an improved Potential Energy Boundary Surface Method[J].Electric Power System Reaserch,1995,34(1):47-55
[19]Xue Y,Van Custem T,Ribbens-Pavella M.Extended Equal Area Criterion Justifications,Generalizations,Applications[J].IEEE Transactions on Power Systems,1989,4(1):44-52
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[21]Burchett R C,Heydt G.T,Probabilistic Methods for Power System Dynamic Stability Studies[J].IEEE Transactions on Power Apparatus and Systems,1978,97(3):695-702
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[23]Billinton R,Kurugant P R S.A probabilistic Index for Transient Stability[J].IEEE Transactions on Power Apparatus and Systems,1980,99(1):195-206
[24]Billinton R,Kurugant P R S.Probabilistic Evaluation of Transient Stability in a Multi-machine Power System[J].Proceeding IEE,1979,126(4):321-326
[25]鞠平,马大强.电力系统的概率稳定性分析[J].电力系统自动化,19190,14(3):18-23
[26]鞠平,吴耕扬,李扬.电力系统概率稳定的基本定理及算法[J].中国电机工程学报,1991,11(6):17-25
[27]Aboreshaid S,Billinton R.and Firuzabad M.F.Probabilistic Transient Stability Studies Using the Method of Bisection[J].IEEE Transactions on Power Systems,1996,11(4):1990-1995
[28]Chiodo E.,Gagliardi F.and Lauria D.Probabilistic Approach to Transient Stability Evaluation[J].IEE Proc.-Generation,Transmission and Distribution,1994,141(5):537-543
[29]甘德强,王锡凡,王小路.电力系统暂态概率稳定性的分析[J].中国电力,1994(4):32-35
[30]曹一家,陈文振,程时杰.电力系统暂态稳定性的概率分析[J].海军工程学 院院报,1994(2):44-49
[31]Guo Yongji,Xi yongjian,Xiao Kai.Composite system reliability evaluation based on monte-earle simulation combined with outages screening[J].IEEE Trans on PWRS,1999,14(2):785-790
[32]宋云亭,郭永基,鲁宗相.改进的概率稳定评估方法及其应用[J].电网技术,2003,27(3):23-27
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