电力系统低频振荡非线性模态分析方法及分析软件开发

1、电力系统低频振荡非线性模态分析方法及分析软件开发        【中文摘要】我国电力产业正处于高速发展时期,电网的规模日渐庞大,“重负荷、弱联系、快速励磁、低阻尼”的情况日趋明显。这使得当今的电力系统成了一个极其复杂的强非线性系统,它时常表现出如状态变量和模式交互作用等非线性现象。而这些非线性作用已成为影响系统稳定性的重要因素。传统的线性化分析方法,即使是全模型数值仿真,都很难计及系统内部非线性动态结构信息,并揭示这些非线性奇异现象的实质。目前,研究这类非线性的理论依据主要有正规形理论和模态级数法。前者的2阶解析解

2、对电力系统2阶非线性特性的分析和应用已经相当成熟,而后者相对较少。基于模态级数法的3阶解析解因其表达式十分复杂而不利于编程实现。可见,对电力系统更高阶非线性特性的分析和应用仍处于亟待研究的阶段。如何方便、可靠地对这些非线性特性进行分析,已日益成为电力领域学者的一项重要工作。本文从电力系统小信号分析的算法和软件两个方面进行了研究:1.高阶模态分析方法的研究本文基于正规形理论推导了形式更加简洁的电力系统3阶解析解表达式,并定义了模态交互作用指标,如3阶非线性参与因子、非线性度指标和非线性相互作用指标等。通过3个系统的仿真,验证了该3阶解析解的有效性。并导出了基于该3阶解析解的振荡分析表达式,进行了

3、振荡机理仿真分析。同时,应用正规形理论的2、3阶解析解分析3机9母线系统的非线性相互作用。结果表明,非线性相互作用极其复杂,模态的高阶交互作用具有多样性,在电力系统模态分析中考虑2阶以上的更高阶项的影响是非常必要的。2.电力系统高阶模态分析程序的开发目前国内外广泛使用的电力仿真软件无一例外的只提供了小信号稳定分析(又称小干扰稳定分析)功能,这一功能只能进行线性模态分析,不具备2阶及以上的高阶模态分析功能。针对此空缺,本文使用Matlab?编写电力系统高阶分析程序和操纵界面,同时集成正规形理论和模态级数法。针对求取系统状态方程的高阶偏导数矩阵的关键和难点,采用了数值微分法来解决。针对高阶偏导数矩

4、阵维数高、稀疏性大的特点,采用现有的稀疏技术保证了计算分析的速度和效率,尽可能减少对内存的占用。同时,该工具采用Java编写了一个接口类来实现了与PSASP的接口,其输进数据由PSASP提供,包括系统数据、潮流和暂态结果数据,并提供m文件格式存储这些输进数据,输出结果采用报表或绘图的形式给出。该分析程序采用界面化操纵,可以方便地使用正规形理论和模态级数法进行电力系统振荡等模态分析。');【Abstract】 With the growth of interconnected power system, the power system is characterized by the c

5、onditions such asheavily loaded, weakly connected, fast excitation, low damping. Nowadays, the power system becomes a complex nonlinear system, in which the nonlinear interaction phenomenon, such as the interaction of the state variables and the modes, generally happens. These nonlinear interactions

6、 have become one of the most significant factors affecting the stability of system.The linear analysis methods, even the full model numerical simulation, are not able to explain the essence of some nonlinear singularity phenomenon, because those methods are difficult to consider the internal nonline

7、ar structural dynamics. Currently, the Normal Form theory and the Modal Series method in vector fields are the basic tools to study the dynamic characteristic of nonlinear power systems. The 2nd-order analytical solutions of the former are widely applied to analyze the 2nd-order nonlinear characteri

8、stic of power system, while the later is a little less used. Moreover, the expressions of the 3rd-order analytical solutions based on Modal Series method are so complex that it is not convenient to implement it in programs. It is shown that the further higher order nonlinear analysis of power system

9、 and applications should be developed, and methods for convenient and reliable analysis should be found.The thesis studied the algorithms and software tool of power system small-signal analysis, including two aspects:1. Study on the higher-order modal analysis methodsBased on the theory of Normal Fo

10、rms, the much *r 3rd-order analytical solutions of power systems dynamical equation were deduced, and modal interaction indices, such as the 3rd-order nonlinear participation factors, the nonlinearity index and the nonlinear interaction index, were also defined. The validity of the solutions was pro

11、ved through the simulations of three power system cases. The expression of oscillation analysis based on the 3rd-order analytical solutions is deduced, and used to analyze the mechanism of oscillation. The nonlinear interaction of 3-generator 9-bus system was analyzed by the 2nd- and 3rd-order analy

12、tical solutions based on Normal Form theory. It is shown that the higher-order modal interaction is so complicated that the effect of terms higher than 2nd-order should be considered in power system modal analysis.2. Development of the power system higher order analysis toolNowadays, the widely used

13、 power system simulation tools only give the small-signal stability analysis which is linear modal analysis, lacking the function of nonlinear modal analysis. In this thesis, the“power system higher order analysis tool”and its operation inte*ce are developed using Matlab?. Both the Normal Form metho

14、d and Modal Series method are implemented in this tool set. The numerical differentiation algorithm is used to obtain the higher order partial derivatives of the system state space equation. In order to compress the memory requirements and lower the dimension of the matrices, sparse technology is us

15、ed in the development of the program. An inte*ce class, which is programmed with Java, is developed to interchange data with PSASP. The input data supplied by PSASP include the system parameters, the power flow and transient stability data. The tool provides a mechanism to store these data, and present the results eit