Journal of Electrical Engineering
Vol. 07  No. 02 ( 2019 ), Article ID: 30920 , 8 pages
10.12677/JEE.2019.72017

Analysis of the Mechanism of Electromechanical Oscillations for Power System under Random Excitation

Jintao Jiang

School of Electrical Engineering, Northeast Dianli University, Jilin Jilin

Received: June 2nd, 2019; accepted: June 17th, 2019; published: June 24th, 2019

ABSTRACT

There is a wealth of dynamic information hidden in system responses which are subject to the random excitations. On the basis of the stochastic differential algebraic equations and features of random excitations, by linearizing the equations, this paper derivates the analytical expressions of the power system dynamic response under random excitation. So we mathematically prove the presence of power oscillation characteristics in power ambient data. It reveals the basic mechanism of system oscillation characteristics by using ambient signals. Based on the case of small fluctuations caused by random changes of loads of IEEE-four generators two areas system, comparing the identified parameters with theoretical characteristic parameters and analysis of the results of probability distributions, we conclude that it is feasible and effective to identify the oscillation characteristics by using the ambient data. Our work further reinforces the theoretical basis of the oscillation characteristics identification on the basis of the ambient signal.

Keywords:Random Excitation, Low Frequency Oscillation, Ambient Signal, Mode Parameters

1. 引言

2. 电力系统动态响应

Figure 1. Power system response type

3. 随机激励下电力系统响应的数学解析

$\left\{\begin{array}{l}\stackrel{˙}{x}=f\left(x,y\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(1\right)\\ 0=g\left(x,y\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(2\right)\end{array}$

$\stackrel{˙}{u}=-Cu+\delta \xi$ (5)

$\Delta y=\left[\begin{array}{cc}-{g}_{y}^{-1}{g}_{x}& -{g}_{y}^{-1}{g}_{u}\end{array}\right]\left[\begin{array}{l}\Delta x\\ \Delta u\end{array}\right]$ (6)

$\left[\begin{array}{l}\Delta \stackrel{˙}{x}\\ \Delta \stackrel{˙}{u}\end{array}\right]=\left[\begin{array}{l}{f}_{x}-{f}_{y}{g}_{y}^{-1}{g}_{x}-{f}_{y}{g}_{y}^{-1}{g}_{u}\\ 0-C\end{array}\right]\left[\begin{array}{l}\Delta x\\ \Delta u\end{array}\right]+\delta \left[\begin{array}{l}0\\ {I}_{{n}_{u}}\end{array}\right]\xi$ (7)

$\stackrel{˙}{z}=Az+\delta B\xi$ (8)

$|A-\lambda I|=0$ ，可计算出系统n个振荡模式对应的特征值 ${\lambda }_{i}={\sigma }_{i}+j{\omega }_{i}\left(i=1,2,\cdots ,n\right)$ ，则系统状态变量的时域解析表达式为：

$z\left(t\right)=\underset{i=1}{\overset{n}{\sum }}{v}_{i}{u}_{i}^{\text{T}}z\left(0\right){\text{e}}^{{\sigma }_{i}t}\mathrm{sin}\left({\omega }_{i}t+{\phi }_{i}\right)+\delta B\xi$ (9)

4. 实验结果与分析

Figure 2. The one-line diagram of four generators two area

Table 1. The characteristic results of four generators two area

Figure 3. Modal graph of four generators two area

Figure 4. The response and probability distribution of active power of generator 1

Figure 5. The response and probability distribution of active power of inter area connected line

Table 2. The statistical results of active power of four generators and connected line

Table 3. The identification results of four generators two area

Figure 6. The probability distributions of identification results of interarea mode

Figure 7. The probability distributions of identification results of local mode

Figure 8. The probability distributions of identification results of local mode

5. 结论

1) 随机激励下系统基本运行方式维持不变，在无新设备投运的前提下系统保持原有动态特征；

2) 采用合适的辨识技术能够从随机相应数据中提取出系统机电振荡参数，所提取参数及各机电振荡模态表征与基础运行方式吻合；

3) 实测数据分析结果表明基于随机响应数据的机电振荡特征识别对电力系统小干扰稳定在线量化评估具有重要的指导意义；

Figure 9. Mode shape identification results of four generators two area

Analysis of the Mechanism of Electromechanical Oscillations for Power System under Random Excitation[J]. 电气工程, 2019, 07(02): 136-143. https://doi.org/10.12677/JEE.2019.72017

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