電力系統(tǒng)低頻振蕩非線性模態(tài)分析方法及分析軟件開發(fā)

1、電力系統(tǒng)低頻振蕩非線性模態(tài)分析方法及分析軟件開發(fā)        【中文摘要】我國電力產(chǎn)業(yè)正處于高速發(fā)展時(shí)期,電網(wǎng)的規(guī)模日漸龐大,“重負(fù)荷、弱聯(lián)系、快速勵(lì)磁、低阻尼”的情況日趨明顯。這使得當(dāng)今的電力系統(tǒng)成了一個(gè)極其復(fù)雜的強(qiáng)非線性系統(tǒng),它時(shí)常表現(xiàn)出如狀態(tài)變量和模式交互作用等非線性現(xiàn)象。而這些非線性作用已成為影響系統(tǒng)穩(wěn)定性的重要因素。傳統(tǒng)的線性化分析方法,即使是全模型數(shù)值仿真,都很難計(jì)及系統(tǒng)內(nèi)部非線性動(dòng)態(tài)結(jié)構(gòu)信息,并揭示這些非線性奇異現(xiàn)象的實(shí)質(zhì)。目前,研究這類非線性的理論依據(jù)主要有正規(guī)形理論和模態(tài)級(jí)數(shù)法。前者的2階解析解

2、對(duì)電力系統(tǒng)2階非線性特性的分析和應(yīng)用已經(jīng)相當(dāng)成熟,而后者相對(duì)較少?；谀B(tài)級(jí)數(shù)法的3階解析解因其表達(dá)式十分復(fù)雜而不利于編程實(shí)現(xiàn)?？梢?對(duì)電力系統(tǒng)更高階非線性特性的分析和應(yīng)用仍處于亟待研究的階段。如何方便、可靠地對(duì)這些非線性特性進(jìn)行分析,已日益成為電力領(lǐng)域?qū)W者的一項(xiàng)重要工作。本文從電力系統(tǒng)小信號(hào)分析的算法和軟件兩個(gè)方面進(jìn)行了研究:1.高階模態(tài)分析方法的研究本文基于正規(guī)形理論推導(dǎo)了形式更加簡潔的電力系統(tǒng)3階解析解表達(dá)式,并定義了模態(tài)交互作用指標(biāo),如3階非線性參與因子、非線性度指標(biāo)和非線性相互作用指標(biāo)等。通過3個(gè)系統(tǒng)的仿真,驗(yàn)證了該3階解析解的有效性。并導(dǎo)出了基于該3階解析解的振蕩分析表達(dá)式,進(jìn)行了

3、振蕩機(jī)理仿真分析。同時(shí),應(yīng)用正規(guī)形理論的2、3階解析解分析3機(jī)9母線系統(tǒng)的非線性相互作用。結(jié)果表明,非線性相互作用極其復(fù)雜,模態(tài)的高階交互作用具有多樣性,在電力系統(tǒng)模態(tài)分析中考慮2階以上的更高階項(xiàng)的影響是非常必要的。2.電力系統(tǒng)高階模態(tài)分析程序的開發(fā)目前國內(nèi)外廣泛使用的電力仿真軟件無一例外的只提供了小信號(hào)穩(wěn)定分析(又稱小干擾穩(wěn)定分析)功能,這一功能只能進(jìn)行線性模態(tài)分析,不具備2階及以上的高階模態(tài)分析功能。針對(duì)此空缺,本文使用Matlab?編寫電力系統(tǒng)高階分析程序和操縱界面,同時(shí)集成正規(guī)形理論和模態(tài)級(jí)數(shù)法。針對(duì)求取系統(tǒng)狀態(tài)方程的高階偏導(dǎo)數(shù)矩陣的關(guān)鍵和難點(diǎn),采用了數(shù)值微分法來解決。針對(duì)高階偏導(dǎo)數(shù)矩

4、陣維數(shù)高、稀疏性大的特點(diǎn),采用現(xiàn)有的稀疏技術(shù)保證了計(jì)算分析的速度和效率,盡可能減少對(duì)內(nèi)存的占用。同時(shí),該工具采用Java編寫了一個(gè)接口類來實(shí)現(xiàn)了與PSASP的接口,其輸進(jìn)數(shù)據(jù)由PSASP提供,包括系統(tǒng)數(shù)據(jù)、潮流和暫態(tài)結(jié)果數(shù)據(jù),并提供m文件格式存儲(chǔ)這些輸進(jìn)數(shù)據(jù),輸出結(jié)果采用報(bào)表或繪圖的形式給出。該分析程序采用界面化操縱,可以方便地使用正規(guī)形理論和模態(tài)級(jí)數(shù)法進(jìn)行電力系統(tǒng)振蕩等模態(tài)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