大规模电力系统中的等值算法研究
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摘要
随着我国互联电力系统的发展,各个区域之间的联系加强,本区域内发生的一些扰动,很有可能引发相邻区域内电网的失稳。因此,进行电网安全分析时,必须将整个互联电网都考虑在内。这样考虑的结果,一方面提高了电网分析的精度和准确度,但另一方面却降低了分析计算速度,这在目前所追求的实时安全分析的大环境下显然是不能允许的。
网络等值是指保留研究区域不变,而对外部区域在保证其对研究系统的影响不变的前提下,进行简化的过程。这对大规模电力系统进行稳态潮流分析、暂态稳定分析以及实时安全分析等方面都有很重要的意义。
同调等值法是研究大规模电力系统的离线暂态(大扰动)稳定分析时常用的一种目前比较成熟的等值方法,它主要由三大步组成:同调机群的判别、母线和网络的化简、等值机的聚合。同调机群的判别目前主要采用时域仿真法或人为判别同调组的方法;母线和网络的化简主要采用恒功率变换技术,在具体的实现中主要采用Ward等值法或者REI等值法中的节点消去规则;等值机的聚合则根据等值机传递函数与各单机传递函数的集合函数有最接近的频域特性。
动态等值效果的好坏,取决于聚合过程中等值发电机的模型确定以及参数的求取。对于发电机内部,尽可能选取那些阶数比较高的模型,如暂态、次暂态模型;对于励磁模型,虽然有多种模型可供选择,但是在实际应用中,只要将重要特征区分开来(如BPA模型中的E-模型、F-模型),模型的选择对等值结果不会有太大的影响;对于原动机、调速系统,由于等值发电机的转动惯量比较大,调速系统对等值的效果影响不大,可以近似忽略。
在进行节点消去以及发电机的暂态仿真中,需要进行大量的矩阵运算,加之大规模电力系统的维数比较大,需要采用稀疏矩阵存储技术,在矩阵的运算中,采用LU分解方法对稀疏矩阵进行分解,形成L、D、U因子表。这样一来,既可以求解右端向量为一列时的方程组,又可以求解右端向量为多列时的矩阵求逆运算或者灵敏度计算。
基于天津电力局2005年冬季全国联网数据的算例表明了同调等值技术在进行网络化简上的有效性。
With the trend of inter-connection and deregulation among the power systems, the relationship among the different areas is intensified. When fault occurs in one area, it is likely to lead to other areas’instability. So, the impact from the external power systems has to be taken into consideration when conducting security assessment on its own. This results in two aspects, one is improving the precision and the accuracy of the analysis, the other is slowing the calculating speed, which is unbearable in the recent aspiration of real-time security analysis.
Network reduction is the process of reducing the dimension of the power system, while keep the researched area unchanged and preserve the external networks’influence on the researched area. The large-scale power system equivalence is very important for the steady state power flow analysis, transient stability analysis, and the real-time security analysis.
Coherent equivalent algorithm is a classical equivalent method in the large-scale power system off-line transient stability analysis. It is typically done in the next three steps: identification of the groups of coherent generators, reduction of the external network, and aggregation of the coherent generators. In the first step, coherent generators are identified using linear simulation or manual identification; in the second step, the network reduction is based on the constant megavolt ampere (MVA) technology, in this process we often use Ward equivalent method or REI equivalent method to reduce the nodes in the external network; in the last step, we keep the equivalent generator’s transfer function identical with the set function of the single generator’s transfer function in the frequency domain.
The effectiveness of the dynamic equivalent method is based on the model of the equivalent generators and its’parameters. For generators we try to select the model with most possible high order, such as transient model and sub-transient model. For exciter model, in the practical application, we only need to classify the major aspect (such as E- model and F- model in the BPA software), and the result is mostly acceptable. For primer mover and its controller, they can be neglected because the equivalent generator’s moment of inertia is always great.
In the process of the network reduction and the generators’transient simulation, we have to solve great amount of matrix calculation. Besides, the dimension of the matrix of the power system is always high, it is important to use the sparse matrix technique. When solving the sparse matrix, we conduct LU decomposition to form L, D, U matrix. Finally we can use the L, D, U matrix to solve the linear function and the inverse matrix, even the sensitivity calculation.
The simulation results on the inter-connected power system (the data given by the Tianjin power grid in the winter, 2005) validate the efficiency of the coherent equivalence.
网络等值是指保留研究区域不变,而对外部区域在保证其对研究系统的影响不变的前提下,进行简化的过程。这对大规模电力系统进行稳态潮流分析、暂态稳定分析以及实时安全分析等方面都有很重要的意义。
同调等值法是研究大规模电力系统的离线暂态(大扰动)稳定分析时常用的一种目前比较成熟的等值方法,它主要由三大步组成:同调机群的判别、母线和网络的化简、等值机的聚合。同调机群的判别目前主要采用时域仿真法或人为判别同调组的方法;母线和网络的化简主要采用恒功率变换技术,在具体的实现中主要采用Ward等值法或者REI等值法中的节点消去规则;等值机的聚合则根据等值机传递函数与各单机传递函数的集合函数有最接近的频域特性。
动态等值效果的好坏,取决于聚合过程中等值发电机的模型确定以及参数的求取。对于发电机内部,尽可能选取那些阶数比较高的模型,如暂态、次暂态模型;对于励磁模型,虽然有多种模型可供选择,但是在实际应用中,只要将重要特征区分开来(如BPA模型中的E-模型、F-模型),模型的选择对等值结果不会有太大的影响;对于原动机、调速系统,由于等值发电机的转动惯量比较大,调速系统对等值的效果影响不大,可以近似忽略。
在进行节点消去以及发电机的暂态仿真中,需要进行大量的矩阵运算,加之大规模电力系统的维数比较大,需要采用稀疏矩阵存储技术,在矩阵的运算中,采用LU分解方法对稀疏矩阵进行分解,形成L、D、U因子表。这样一来,既可以求解右端向量为一列时的方程组,又可以求解右端向量为多列时的矩阵求逆运算或者灵敏度计算。
基于天津电力局2005年冬季全国联网数据的算例表明了同调等值技术在进行网络化简上的有效性。
With the trend of inter-connection and deregulation among the power systems, the relationship among the different areas is intensified. When fault occurs in one area, it is likely to lead to other areas’instability. So, the impact from the external power systems has to be taken into consideration when conducting security assessment on its own. This results in two aspects, one is improving the precision and the accuracy of the analysis, the other is slowing the calculating speed, which is unbearable in the recent aspiration of real-time security analysis.
Network reduction is the process of reducing the dimension of the power system, while keep the researched area unchanged and preserve the external networks’influence on the researched area. The large-scale power system equivalence is very important for the steady state power flow analysis, transient stability analysis, and the real-time security analysis.
Coherent equivalent algorithm is a classical equivalent method in the large-scale power system off-line transient stability analysis. It is typically done in the next three steps: identification of the groups of coherent generators, reduction of the external network, and aggregation of the coherent generators. In the first step, coherent generators are identified using linear simulation or manual identification; in the second step, the network reduction is based on the constant megavolt ampere (MVA) technology, in this process we often use Ward equivalent method or REI equivalent method to reduce the nodes in the external network; in the last step, we keep the equivalent generator’s transfer function identical with the set function of the single generator’s transfer function in the frequency domain.
The effectiveness of the dynamic equivalent method is based on the model of the equivalent generators and its’parameters. For generators we try to select the model with most possible high order, such as transient model and sub-transient model. For exciter model, in the practical application, we only need to classify the major aspect (such as E- model and F- model in the BPA software), and the result is mostly acceptable. For primer mover and its controller, they can be neglected because the equivalent generator’s moment of inertia is always great.
In the process of the network reduction and the generators’transient simulation, we have to solve great amount of matrix calculation. Besides, the dimension of the matrix of the power system is always high, it is important to use the sparse matrix technique. When solving the sparse matrix, we conduct LU decomposition to form L, D, U matrix. Finally we can use the L, D, U matrix to solve the linear function and the inverse matrix, even the sensitivity calculation.
The simulation results on the inter-connected power system (the data given by the Tianjin power grid in the winter, 2005) validate the efficiency of the coherent equivalence.
引文
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[4]邱晓燕,李兴源,王建等,电力系统实时等值及电压稳定性分析,电网技术,2004,28(7):7-10.
[5]万国成,任震,田翔,配电网可靠性评估的网络等值法模型研究,中国电机工程学报,2003,23(5):48-52.
[6]李娟,刘修宽,曹国臣等,一种面向节点的电网等值参数跟踪估计方法的研究,中国电机工程学报,2003,23(3):30-33.
[7]王婷,王大光,邓超平等,用RTDS建立省级电力系统等值模型的初步研究,福建电力与电工,2005,25(3):1-4.
[8]赵勇,苏毅,陈峰等,福建电网在线稳定控制系统中华东电网的实时动态等值研究,电网技术,2005,29(4):18-22.
[9]陈礼义,孙丹峰,电力系统动态等值中发电机组详细模型的参数集合,中国电机工程学报,1989,9(5):30-39.
[10] Ourari, M.L,Dessaint, L.A,Do, V.Q. Generating units aggregation for dynamic equivalent of large power systems. Power Engineering Society General Meeting,2004, 2(1):1535-1541.
[11] Sung-K Joo, Chen-Ching Liu,Jong-Woong Cheo. Enhancement of Coherency Identification Techniques for Power System Dynamic Equivalents. Power Engineering Society Summer Meeting,IEEE,2001, 3(2):1811-1816.
[12]国家电网公司,电网公司电力系统安全稳定计算规定,2006.3.
[13]宋文南,李树鸿,张尧,电力系统潮流计算.
[14]赵遵廉,REI等值法在电力系统暂态稳定计算中的应用,武汉水利电力学院学报,1981,2:105-108.
[15]邓长虹,陈允平,张俊潇,REI法在动态等值中的应用于改进,高电压技术,2005,31(7):55-60.
[16]倪以信,陈寿孙,张宝霖,动态电力系统的理论和分析,北京:清华大学出版社,2002.
[17]姚良忠,倪以信,李凌霞,大规模电力系统分区动态等值的快速直接暂态稳定分析,电力系统自动化,1993,17(3):20-25.
[18]杭乃善,李如琦,同调机组群的不对称Y阵动态等值法,电网技术,2000,24(6):34-36.
[19]康义,周献林,谢国恩,用NETOMAC程序进行电力系统动态等值研究,电网技术,1998,22(5):21-24.
[20]王锡凡,方万良,杜正春,现代电力系统分析,北京:科学出版社,2003.
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[23] Miah, A.M, Simple dynamic equivalent for fast online transient stability assessment. Generation, Transmission and Distribution, IEE Proceedings, 1998, 145(1):49-55.
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