CN103413032B - Transient stability contingency screening method based on mode excitation degree analyzing - Google Patents

Abstract

The invention discloses a kind of transient stability contingency screening method based on mode excitation degree analyzing, including: use mode excitation degree analyzing method to calculate the significance level index of each node failure；And use maximum difference method to filter out important fault.The method is by system model Taylor expansion at non-equilibrium point, ignore higher order term, calculate fault and each oscillation mode of system is excited degree, using the maximum that excites degree within a cycle of oscillation as the importance index of this fault, finally use maximum difference method to filter out forecast accident.The method does not relies on the experience of operations staff, explicit physical meaning, can filter out forecast accident rapidly.

Description

Translated fromChinese

基于模式激发程度分析的暂态稳定预想事故筛选方法Transient Stability Anticipated Accident Screening Method Based on Mode Excitation Degree Analysis

技术领域technical field

本发明属于电力系统暂态稳定分析领域，具体涉及一种基于模式激发程度分析的暂态稳定预想事故筛选方法。The invention belongs to the field of transient stability analysis of power systems, and in particular relates to a transient stability predictive accident screening method based on mode excitation degree analysis.

背景技术Background technique

大规模新能源发电的接入导致电力系统运行方式的不确定性逐渐增大。在此情况下，在线安全稳定评估将发挥更大的作用。合理地筛选出暂态稳定预想事故是在线安全稳定评估的基础。基于运行人员经验的预想事故筛选方法不适用于在线安全稳定评估，而人工智能方法的物理意义不够明确。The integration of large-scale new energy power generation leads to the gradual increase of uncertainty in the operation mode of the power system. In this case, online security and stability assessment will play a greater role. It is the basis of on-line safety and stability assessment to reasonably screen out transient stability prediction accidents. The predictive accident screening method based on operator experience is not suitable for online safety and stability assessment, and the physical meaning of the artificial intelligence method is not clear enough.

发明内容Contents of the invention

本发明旨在至少在一定程度上解决上述技术问题之一或至少提供一种有用的商业选择。为此，本发明的目的在于提出一种不依赖运行人员经验、筛选效率高的基于模式激发程度分析的暂态稳定预想事故筛选方法。The present invention aims at solving one of the above technical problems at least to a certain extent or at least providing a useful commercial choice. Therefore, the object of the present invention is to propose a transient stability predictive accident screening method based on mode excitation degree analysis that does not rely on operator experience and has high screening efficiency.

为了实现上述目的，本发明实施例的基于模式激发程度分析的暂态稳定预想事故筛选方法，包括以下步骤：S1.采用模式激发程度分析方法计算各个节点故障的重要程度指标；以及S2.采用最大差异法筛选出重要故障。In order to achieve the above-mentioned purpose, the transient stability predictive accident screening method based on the mode excitation degree analysis of the embodiment of the present invention includes the following steps: S1. Using the mode excitation degree analysis method to calculate the importance index of each node fault; and S2. Using the maximum The difference method screens out important faults.

在本发明的一个实施例中，所述步骤S1包括：In one embodiment of the present invention, the step S1 includes:

设系统有n台发电机，对系统进行小干扰稳定性分析，可以得到系统的最大机电振荡周期，记为T_max，设系统有N个节点，依次在每个节点设置三相短路故障，故障时间为0～0.1s，计算各个节点故障的重要程度指标为Assuming that the system has n generators, and analyzing the stability of the system with small disturbances, the maximum electromechanical oscillation period of the system can be obtained, which is denoted as T_max . Assuming that the system has N nodes, a three-phase short-circuit fault is set at each node in turn, and the fault The time is 0-0.1s, and the importance index of each node fault is calculated as

E={E₁,E₂,L,E_N} （1）E={E₁ ,E₂ ,L,E_N } (1)

其中第k(k=1,2,L,N)个节点故障的重要程度指标为Among them, the importance index of the kth (k=1,2,L,N) node failure is

$E_k=\max \left(\right|e_{\mathrm{ij}}^k\left|\right)---\left(2\right)$其中为第j个时间断面时，第k个节点故障对第i个振荡模式的激发程度，i=1,2,L,n-1为系统机电振荡模式的编号；j=t_c,t_c+Δt,t_c+2Δt,L,t_c+T_max，t_c=0.1s为故障消失时间，Δt=0.01s为时域仿真步长，T_max为最大机电振荡周期。在本发明的一个实施例中，所述的计算公式为${\mathrm{E.}}_k=\max \left(\right|e_{\mathrm{ij}}^k\left|\right)---\left(2\right)$ in is the excitation degree of the i-th oscillation mode caused by the k-th node fault at the j-th time section, i=1,2,L,n-1 is the number of the electromechanical oscillation mode of the system; j=t_c ,t_c + Δt,t_c +2Δt,L,t_c +T_max , t_c =0.1s is the fault disappearing time, Δt=0.01s is the time domain simulation step size, and T_max is the maximum electromechanical oscillation period. In one embodiment of the present invention, the The calculation formula is

${\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{<span><span>(</span>(</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>g</span>g</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

的推导过程如下，式(3)中各个符号的含义将在下面的推导过程中给出: The derivation process of is as follows, and the meaning of each symbol in formula (3) will be given in the following derivation process:

发电机采用经典二阶模型，忽略系统阻尼，负荷采用恒阻抗模型，进行网络收缩后，只保留发电机内节点的系统数学模型为The generator adopts the classic second-order model, ignoring the system damping, and the load adopts the constant impedance model. After network contraction, the mathematical model of the system that only retains the internal nodes of the generator is

$\begin{array}{c}\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>M</span>m</span>}\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中ω₀为同步角速度，δ=[δ₁,δ₂,Lδ_n]^T和ω=[ω₁,ω₂,Lω_n]^T分别为各台发电机功角和角速度组成的列向量，1为元素为1的n行列向量，P_m=[P_m1,P_m2,L,P_mn]^T和P_e=[P_e1,P_e2,L,P_en]^T为各机机械功率和电磁功率组成的列向量，M为以各机惯性时间常数为元素的对角矩阵，where ω₀ is the synchronous angular velocity, δ=[δ₁ ,δ₂ ,Lδ_n ]^T and ω=[ω₁ ,ω₂ ,Lω_n ]^T are the column vectors composed of the power angle and angular velocity of each generator respectively, 1 is n row and column vector with element 1, P_m =[P_m1 ,P_m2 ,L,P_mn ]^T and P_e =[P_e1 ,P_e2 ,L,P_en ]^T are the mechanical power and electromagnetic power of each machine A column vector composed of , M is a diagonal matrix with the inertial time constants of each machine as elements,

非平衡点(δ⁽⁰⁾,ω⁽⁰⁾)处的线性化模型为$\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&delta;}}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&omega;}}\end{array}\right]=\left[\begin{array}{c}f\left({\mathrm{\&omega;}}^{\left(0\right)}\right)\\ g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)\end{array}\right]+A\left[\begin{array}{c}\mathrm{\&Delta;\&delta;}\\ \mathrm{\&Delta;\&omega;}\end{array}\right]$（5）The linearization model at the non-equilibrium point (δ⁽⁰⁾ , ω⁽⁰⁾ ) is$\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&delta;}}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&omega;}}\end{array}\right]=\left[\begin{array}{c}f\left({\mathrm{\&omega;}}^{\left(0\right)}\right)\\ g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)\end{array}\right]+A\left[\begin{array}{c}\mathrm{\&Delta;\&delta;}\\ \mathrm{\&Delta;\&omega;}\end{array}\right]$ (5)

$<span><span>=</span>=</span>\left[\begin{array}{c}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>\\ {\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>\end{array}\right]<span><span>+</span>+</span>\left[\begin{array}{cc}\mathrm{<span><span>0</span>0</span>}& {\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}\mathrm{<span><span>I</span>I</span>}\\ <span><span>-</span>-</span>{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>J</span>J</span>}& \mathrm{<span><span>0</span>0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span><span>\&Delta;\&delta;</span>\&Delta;\&delta;</span>}\\ \mathrm{<span><span>\&Delta;\&omega;</span>\&Delta;\&omega;</span>}\end{array}\right]$

其中0和I分别为n阶零矩阵和n阶单位阵，J为P_e对δ变化的雅克比矩阵，将式(5)化为二阶微分方程形式得$\mathrm{\&Delta;}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_{0}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)+\tilde{A}\mathrm{\&Delta;\&delta;}$（6）Among them, 0 and I are n-order zero matrix and n-order unit matrix, respectively, and J is the Jacobian matrix of P_e changing with respect to δ. Transforming Equation (5) into a second-order differential equation, we get$\mathrm{\&Delta;}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_{0}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)+\tilde{A}\mathrm{\&Delta;\&delta;}$ (6)

$<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>J\&Delta;\&delta;</span>J\&Delta;\&delta;</span>}$

设和为的特征值和右特征矩阵，则A的特征值和右特征矩阵为$\mathrm{\&Lambda;}=\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_1& 0\\ 0& {\mathrm{\&Lambda;}}_2\end{array}\right]$（7）Assume and for The eigenvalues and right eigenmatrix of A, then the eigenvalues and right eigenmatrix of A are$\mathrm{\&Lambda;}=\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_1& 0\\ 0& {\mathrm{\&Lambda;}}_2\end{array}\right]$ (7)

其中$\begin{array}{cc}{\mathrm{\&Lambda;}}_1=\mathrm{diag}\{j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|},j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,j\sqrt{\left|{\mathrm{\&lambda;}}_n\right|}\},& {\mathrm{\&Lambda;}}_2=\mathrm{diag}\{-j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|}-j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,-j\sqrt{\left|{\mathrm{\&lambda;}}_n\right|}\},\end{array},$做如下变换in$\begin{array}{cc}{\mathrm{\&Lambda;}}_1=\mathrm{diag}\{j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|},j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,j\sqrt{\left|{\mathrm{\&lambda;}}_{\mathrm{no}}\right|}\},& {\mathrm{\&Lambda;}}_2=\mathrm{diag}\{-j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|}-j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,-j\sqrt{\left|{\mathrm{\&lambda;}}_{\mathrm{no}}\right|}\},\end{array},$ Do the following transformation

$\mathrm{<span><span>\&Delta;\&delta;</span>\&Delta;\&delta;</span>}<span><span>=</span>=</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}}\mathrm{<span><span>Z</span>Z</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

代入式(6)可得Substitute into formula (6) to get

$\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span><span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>Z</span>Z</span>}}<span><span>=</span>=</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}\mathrm{<span><span>E</span>E.</span>}<span><span>+</span>+</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}\mathrm{<span><span>Z</span>Z</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$

其中定义为模式激发程度矩阵，为的左特征矩阵，且则故障对模式λ_i的激发程度为in Defined as the mode excitation degree matrix, for The left eigenmatrix of , and Then the excitation degree of the fault to the mode λ_i is

${\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>10</span>10</span>}<span><span>)</span>)</span>$

求解式(9)得Solve formula (9) to get

${\mathrm{<span><span>z</span>z</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>=</span>=</span><span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>il</span>il</span>}}\mathrm{<span><span>cos</span>cos</span>}<span><span>(</span>(</span>\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>sin</span>sin</span>}<span><span>(</span>(</span>\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

代入初始条件得Substitute the initial conditions to get

$\begin{array}{c}{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>+</span>+</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&Delta;\&delta;</span>\&Delta;\&delta;</span>}<span><span>(</span>(</span>\text{<span><span>0</span>0</span>}<span><span>)</span>)</span>\\ {\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&Delta;\&omega;</span>\&Delta;\&omega;</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>12</span>12</span>}<span><span>)</span>)</span>$

其中in

f(ω⁽⁰⁾)=ω₀(ω⁽⁰⁾-1)f(ω⁽⁰⁾ )=ω₀ (ω⁽⁰⁾ -1)

$\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

Δδ(0)=δ(0)-δ⁽⁰⁾Δδ(0)=δ(0)-δ⁽⁰⁾

Δω(0)=ω(0)-ω⁽⁰⁾Δω(0)=ω(0)-ω⁽⁰⁾

因为是非平衡点处线性化，(δ⁽⁰⁾,ω⁽⁰⁾)中包含了扰动因素，所以Δδ(0)=Δω(0)=0，假设暂态过程中角速度变化不大，则ω⁽⁰⁾=1，f(ω⁽⁰⁾)=0，所以式(12)变为Because it is linearized at the non-equilibrium point, (δ⁽⁰⁾ , ω⁽⁰⁾ ) contains disturbance factors, so Δδ(0)=Δω(0)=0, assuming that the angular velocity does not change much during the transient process, then ω⁽⁰⁾ =1, f(ω⁽⁰⁾ )=0, so formula (12) becomes

c_i1=e_i （14）c_i1 =e_i (14)

c_i2=0c_i2 =0

代入式(11)得Substitute into formula (11) to get

由式(8)与式(15)可知，扰动对振荡模式的激发程度越大，系统的振荡越剧烈，From formula (8) and formula (15), it can be seen that the greater the excitation degree of the disturbance to the oscillation mode, the more severe the oscillation of the system,

式(10)为扰动对振荡模式λ_i的激发程度，若扰动为第k(k=1,2,L,N)个节点故障，且非平衡点为时域仿真的第j个时间断面，即(δ⁽⁰⁾,ω⁽⁰⁾)=(δ^(j),ω^(j))，则式(10)变为式(3)的形式。在本发明的一个实施例中，的特征值中有一个零特征值，将各机功角转化为相对坐标可以消除零特征值，采用相对坐标系后，降了一阶，若采用相对于最后一台发电机的情况，此时做以下处理：将的前n-1行元素减去最后一行，再去掉第n行和第n列，g(δ⁽⁰⁾)的前n-1行元素减去最后一行，再去掉第n行。Equation (10) is the excitation degree of the disturbance to the oscillation mode λ_i . If the disturbance is the kth (k=1,2,L,N) node failure, and the imbalance point is the jth time section of the time domain simulation, That is (δ⁽⁰⁾ , ω⁽⁰⁾ )=(δ^(j) , ω^(j) ), then formula (10) becomes the form of formula (3). In one embodiment of the invention, There is a zero eigenvalue in the eigenvalue of , and the zero eigenvalue can be eliminated by transforming the power angles of each machine into relative coordinates. After using the relative coordinate system, If the situation relative to the last generator is adopted, the following processing should be done at this time: The first n-1 rows of elements minus the last row, and then remove the nth row and nth column, the first n-1 row elements of g(δ⁽⁰⁾ ) minus the last row, and then remove the nth row.

在本发明的一个实施例中，所述步骤S2包括：In one embodiment of the present invention, the step S2 includes:

将各个节点故障的重要程度指标按照由小到大的顺序排序，排序后将前一个指标与后一个指标做比值运算，当这个比值达到最小值时，就找到了非重要故障与重要故障的界线，假设排序后的各节点故障的重要程度指标为E₁E₂...E_N，且Sort the importance indicators of each node fault in ascending order, and perform a ratio operation between the previous index and the latter index after sorting. When the ratio reaches the minimum value, the boundary between non-important faults and important faults is found. , assuming that the importance index of each node failure after sorting is E₁ E₂ ... E_N , and

${\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>r</span>r</span>}}<span><span>/</span>/</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>r</span>r</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1,2</span>1,2</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>min</span>min</span>}}<span><span>|</span>|</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>/</span>/</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}<span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>16</span>16</span>}<span><span>)</span>)</span>$

则重要节点故障为第r+1,r+2,L,N个故障。Then the important node faults are the r+1, r+2, L, Nth faults.

根据本发明实施例的基于模式激发程度分析的暂态稳定预想事故筛选方法，将系统模型在非平衡点处泰勒展开，忽略高阶项，计算故障对系统各个振荡模式的激发程度，将激发程度在一个振荡周期内的最大值作为该故障的重要性指标，最后采用最大差异法筛选出预想事故。该方法不依赖于运行人员的经验，物理意义明确，可以快速地筛选出预想事故。According to the transient stability predictive accident screening method based on the mode excitation degree analysis of the embodiment of the present invention, the system model is expanded by Taylor at the non-equilibrium point, the higher-order terms are ignored, and the excitation degree of the fault to each oscillation mode of the system is calculated, and the excitation degree The maximum value in an oscillation cycle is used as the importance index of the fault, and finally the maximum difference method is used to screen out the expected accidents. This method does not depend on the experience of the operator, has clear physical meaning, and can quickly screen out anticipated accidents.

本发明的附加方面和优点将在下面的描述中部分给出，部分将从下面的描述中变得明显，或通过本发明的实践了解到。Additional aspects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.

附图说明Description of drawings

本发明的上述和/或附加的方面和优点从结合下面附图对实施例的描述中将变得明显和容易理解，其中：The above and/or additional aspects and advantages of the present invention will become apparent and comprehensible from the description of the embodiments in conjunction with the following drawings, wherein:

图1是本发明实施例的基于模式激发程度分析的暂态稳定预想事故筛选方法的流程图；Fig. 1 is the flow chart of the transient stability anticipation accident screening method based on the pattern excitation degree analysis of the embodiment of the present invention;

图2是IEEE三机九节点系统的结构示意图；Figure 2 is a schematic structural diagram of an IEEE three-machine nine-node system;

图3是E指标柱状图；和Figure 3 is a histogram of the E indicator; and

图4是S指标柱状图。Figure 4 is a histogram of the S index.

具体实施方式detailed description

下面详细描述本发明的实施例，所述实施例的示例在附图中示出，其中自始至终相同或类似的标号表示相同或类似的元件或具有相同或类似功能的元件。下面通过参考附图描述的实施例是示例性的，旨在用于解释本发明，而不能理解为对本发明的限制。Embodiments of the present invention are described in detail below, examples of which are shown in the drawings, wherein the same or similar reference numerals designate the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the figures are exemplary and are intended to explain the present invention and should not be construed as limiting the present invention.

如图1所示，本发明实施例的基于模式激发程度分析的暂态稳定预想事故筛选方法包括以下两个步骤：As shown in Figure 1, the transient stability predictive accident screening method based on the mode excitation degree analysis of the embodiment of the present invention includes the following two steps:

步骤1：step 1:

采用模式激发程度分析方法计算各个节点故障的重要程度指标。The importance degree index of each node fault is calculated by using the mode excitation degree analysis method.

设系统有n台发电机，对系统进行小干扰稳定性分析，可以得到系统的最大机电振荡周期，记为T_max。设系统有N个节点，依次在每个节点设置三相短路故障，故障时间为0～0.1s，计算各个节点故障的重要程度指标为Assuming that the system has n generators, the small disturbance stability analysis of the system can obtain the maximum electromechanical oscillation period of the system, denoted as T_max . Assuming that the system has N nodes, a three-phase short-circuit fault is set on each node in turn, and the fault time is 0-0.1s, and the importance index of each node fault is calculated as

E={E₁,E₂,L,E_N} （1）其中第k(k=1,2,L,N)个节点故障的重要程度指标为E={E₁ ,E₂ ,L,E_N } (1) The importance index of the kth (k=1,2,L,N) node failure is

${\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>=</span>=</span>\mathrm{<span><span>max</span>max</span>}<span><span>(</span>(</span><span><span>|</span>|</span>{\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>|</span>|</span><span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>2</span>2</span>}<span><span>)</span>)</span>$

其中为第j个时间断面时，第k个节点故障对第i个振荡模式的激发程度，i=1,2,L,n-1为系统机电振荡模式的编号；j=t_c,t_c+Δt,t_c+2Δt,L,t_c+T_max，t_c=0.1s为故障消失时间，Δt=0.01s为时域仿真步长，T_max为最大机电振荡周期。的计算公式为in is the excitation degree of the i-th oscillation mode caused by the k-th node fault at the j-th time section, i=1,2,L,n-1 is the number of the electromechanical oscillation mode of the system; j=t_c ,t_c + Δt,t_c +2Δt,L,t_c +T_max , t_c =0.1s is the fault disappearing time, Δt=0.01s is the time domain simulation step size, and T_max is the maximum electromechanical oscillation period. The calculation formula is

${\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{<span><span>(</span>(</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>)</span>)</span>}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>ij</span>ij</span>}}^{\mathrm{<span><span>k</span>k</span>}}{\mathrm{<span><span>g</span>g</span>}}^{\mathrm{<span><span>k</span>k</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>j</span>j</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>3</span>3</span>}<span><span>)</span>)</span>$

的推导过程如下，式(3)中各个符号的含义将在下面的推导过程中给出。 The derivation process of is as follows, and the meaning of each symbol in formula (3) will be given in the following derivation process.

发电机采用经典二阶模型，忽略系统阻尼，负荷采用恒阻抗模型，进行网络收缩后，只保留发电机内节点的系统数学模型为The generator adopts the classic second-order model, ignoring the system damping, and the load adopts the constant impedance model. After network contraction, the mathematical model of the system that only retains the internal nodes of the generator is

$\begin{array}{c}\stackrel{<span><span>.</span>.</span>}{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>(</span>(</span>\mathrm{<span><span>\&omega;</span>\&omega;</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>\\ \mathrm{<span><span>M</span>m</span>}\stackrel{<span><span>\&CenterDot;</span>\&Center\; Dot;</span>}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>4</span>4</span>}<span><span>)</span>)</span>$

其中ω₀为同步角速度，δ=[δ₁,δ₂,Lδ_n]^T和ω=[ω₁,ω₂,Lω_n]^T分别为各台发电机功角和角速度组成的列向量，1为元素为1的n行列向量，P_m=[P_m1,P_m2,L,P_mn]^T和P_e=[P_e1,P_e2,L,P_en]^T为各机机械功率和电磁功率组成的列向量，M为以各机惯性时间常数为元素的对角矩阵。where ω₀ is the synchronous angular velocity, δ=[δ₁ ,δ₂ ,Lδ_n ]^T and ω=[ω₁ ,ω₂ ,Lω_n ]^T are the column vectors composed of the power angle and angular velocity of each generator respectively, 1 is n row and column vector with element 1, P_m =[P_m1 ,P_m2 ,L,P_mn ]^T and P_e =[P_e1 ,P_e2 ,L,P_en ]^T are the mechanical power and electromagnetic power of each machine The column vector composed of M is a diagonal matrix with the inertial time constants of each machine as elements.

非平衡点(δ⁽⁰⁾,ω⁽⁰⁾)处的线性化模型为The linearization model at the non-equilibrium point (δ⁽⁰⁾ , ω⁽⁰⁾ ) is

$\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&delta;}}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&omega;}}\end{array}\right]=\left[\begin{array}{c}f\left({\mathrm{\&omega;}}^{\left(0\right)}\right)\\ g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)\end{array}\right]+A\left[\begin{array}{c}\mathrm{\&Delta;\&delta;}\\ \mathrm{\&Delta;\&omega;}\end{array}\right]$（5）$\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&Center\; Dot;}{\mathrm{\&delta;}}\\ \mathrm{\&Delta;}\stackrel{\&Center\; Dot;}{\mathrm{\&omega;}}\end{array}\right]=\left[\begin{array}{c}f\left({\mathrm{\&omega;}}^{\left(0\right)}\right)\\ g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)\end{array}\right]+A\left[\begin{array}{c}\mathrm{\&Delta;\&delta;}\\ \mathrm{\&Delta;\&omega;}\end{array}\right]$ (5)

$<span><span>=</span>=</span>\left[\begin{array}{c}{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>\\ {\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>\end{array}\right]<span><span>+</span>+</span>\left[\begin{array}{cc}\mathrm{<span><span>0</span>0</span>}& {\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}\mathrm{<span><span>I</span>I</span>}\\ <span><span>-</span>-</span>{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>J</span>J</span>}& \mathrm{<span><span>0</span>0</span>}\end{array}\right]\left[\begin{array}{c}\mathrm{<span><span>\&Delta;\&delta;</span>\&Delta;\&delta;</span>}\\ \mathrm{<span><span>\&Delta;\&omega;</span>\&Delta;\&omega;</span>}\end{array}\right]$

其中0和I分别为n阶零矩阵和n阶单位阵，J为P_e对δ变化的雅克比矩阵，将式(5)化为二阶微分方程形式得Among them, 0 and I are n-order zero matrix and n-order unit matrix, respectively, and J is the Jacobian matrix of P_e changing with respect to δ. Transforming Equation (5) into a second-order differential equation, we get

$\mathrm{\&Delta;}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_{0}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)+\tilde{A}\mathrm{\&Delta;\&delta;}$（6）$\mathrm{\&Delta;}\stackrel{\&Center\; Dot;\&Center\; Dot;}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_{0}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)+\tilde{A}\mathrm{\&Delta;\&delta;}$ (6)

$<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>J\&Delta;\&delta;</span>J\&Delta;\&delta;</span>}$

设和为的特征值和右特征矩阵。则A的特征值和右特征矩阵为$\mathrm{\&Lambda;}=\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_1& 0\\ 0& {\mathrm{\&Lambda;}}_2\end{array}\right]$（7）Assume and for The eigenvalues and right eigenmatrix of . Then the eigenvalues and right eigenmatrix of A are$\mathrm{\&Lambda;}=\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_1& 0\\ 0& {\mathrm{\&Lambda;}}_2\end{array}\right]$ (7)

其中$\begin{array}{cc}{\mathrm{\&Lambda;}}_1=\mathrm{diag}\{j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|},j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,j\sqrt{\left|{\mathrm{\&lambda;}}_n\right|}\},& {\mathrm{\&Lambda;}}_2=\mathrm{diag}\{-j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|}-j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,-j\sqrt{\left|{\mathrm{\&lambda;}}_n\right|}\}.\end{array},$做如下变换in$\begin{array}{cc}{\mathrm{\&Lambda;}}_1=\mathrm{diag}\{j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|},j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,j\sqrt{\left|{\mathrm{\&lambda;}}_{\mathrm{no}}\right|}\},& {\mathrm{\&Lambda;}}_2=\mathrm{diag}\{-j\sqrt{\left|{\mathrm{\&lambda;}}_1\right|}-j\sqrt{\left|{\mathrm{\&lambda;}}_2\right|},...,-j\sqrt{\left|{\mathrm{\&lambda;}}_{\mathrm{no}}\right|}\}.\end{array},$ Do the following transformation

$\mathrm{<span><span>\&Delta;\&delta;</span>\&Delta;\&delta;</span>}<span><span>=</span>=</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&Phi;</span>\&Phi;</span>}}\mathrm{<span><span>Z</span>Z</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>8</span>8</span>}<span><span>)</span>)</span>$

代入式(6)可得Substitute into formula (6) to get

$\stackrel{<span><span>\&CenterDot;</span>\&CenterDot;</span><span><span>\&CenterDot;</span>\&CenterDot;</span>}{\mathrm{<span><span>Z</span>Z</span>}}<span><span>=</span>=</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}\mathrm{<span><span>E</span>E.</span>}<span><span>+</span>+</span>\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&Lambda;</span>\&Lambda;</span>}}\mathrm{<span><span>Z</span>Z</span>}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>9</span>9</span>}<span><span>)</span>)</span>$

其中定义为模式激发程度矩阵，为的左特征矩阵，且故障对模式λ_i的激发程度为in Defined as the mode excitation degree matrix, for The left eigenmatrix of , and The excitation degree of the fault to the mode λ_i is

${\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>10</span>10</span>}<span><span>)</span>)</span>$

求解式(9)得Solve formula (9) to get

${\mathrm{<span><span>z</span>z</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>=</span>=</span><span><span>-</span>-</span>{\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>+</span>+</span>{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>1</span>1</span>}}\mathrm{<span><span>cos</span>cos</span>}<span><span>(</span>(</span>\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>2</span>2</span>}}\mathrm{<span><span>sin</span>sin</span>}<span><span>(</span>(</span>\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>11</span>11</span>}<span><span>)</span>)</span>$

代入初始条Substitute the initial

$\begin{array}{c}{\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>+</span>+</span>{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&Delta;\&delta;</span>\&Delta;\&delta;</span>}<span><span>(</span>(</span>\text{<span><span>0</span>0</span>}<span><span>)</span>)</span>\\ {\mathrm{<span><span>c</span>c</span>}}_{\mathrm{<span><span>i</span>i</span>}\mathrm{<span><span>2</span>2</span>}}<span><span>=</span>=</span>{\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>+</span>+</span>{\mathrm{<span><span>\&omega;</span>\&omega;</span>}}_{\mathrm{<span><span>0</span>0</span>}}{\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\stackrel{<span><span>~</span>~</span>}{\mathrm{<span><span>\&psi;</span>\&psi;</span>}}}_{\mathrm{<span><span>i</span>i</span>}}\mathrm{<span><span>\&Delta;\&omega;</span>\&Delta;\&omega;</span>}<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>\end{array}<span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>12</span>12</span>}<span><span>)</span>)</span>$

其中in

f(ω⁽⁰⁾)=ω₀(ω⁽⁰⁾-1)f(ω⁽⁰⁾ )=ω₀ (ω⁽⁰⁾ -1)

$\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>\&delta;</span>\&delta;</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>M</span>m</span>}}^{<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>m</span>m</span>}}<span><span>-</span>-</span>{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>e</span>e</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>0</span>0</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>13</span>13</span>}<span><span>)</span>)</span>$

Δδ(0)=δ(0)-δ⁽⁰⁾Δδ(0)=δ(0)-δ⁽⁰⁾

Δω(0)=ω(0)-ω⁽⁰⁾Δω(0)=ω(0)-ω⁽⁰⁾

因为是非平衡点处线性化，(δ⁽⁰⁾,ω⁽⁰⁾)中包含了扰动因素，所以Δδ(0)=Δω(0)=0。假设暂态过程中角速度变化不大，则ω⁽⁰⁾=1，f(ω⁽⁰⁾)=0，所以式(12)变为Because it is linearized at the non-equilibrium point, (δ⁽⁰⁾ , ω⁽⁰⁾ ) contains disturbance factors, so Δδ(0)=Δω(0)=0. Assuming that the angular velocity does not change much during the transient process, then ω⁽⁰⁾ = 1, f(ω⁽⁰⁾ ) = 0, so the formula (12) becomes

c_i1=e_i （14）c_i1 =e_i (14)

c_i2=0c_i2 =0

代入式(11)得Substitute into formula (11) to get

${\mathrm{<span><span>z</span>z</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>=</span>=</span>{\mathrm{<span><span>e</span>e</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>[</span>[</span>\mathrm{<span><span>cos</span>cos</span>}<span><span>(</span>(</span>\sqrt{<span><span>|</span>|</span>{\mathrm{<span><span>\&lambda;</span>\&lambda;</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>|</span>|</span>}\mathrm{<span><span>t</span>t</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}<span><span>]</span>]</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>15</span>15</span>}<span><span>)</span>)</span>$

由式(8)与式(15)可知，扰动对振荡模式的激发程度越大，系统的振荡越剧烈。From formula (8) and formula (15), it can be seen that the greater the excitation degree of the disturbance to the oscillation mode, the more severe the oscillation of the system.

式(10)为扰动对振荡模式λi的激发程度，若扰动为第k(k=1,2,L,N)个节点故障，且非平衡点为时域仿真的第j个时间断面，即(δ⁽⁰⁾,ω⁽⁰⁾)=(δ^(j),ω^(j))，则式(10)变为式(3)的形式。Equation (10) is the excitation degree of the disturbance to the oscillation mode λi, if the disturbance is the kth (k=1,2,L,N) node failure, and the imbalance point is the jth time section of the time domain simulation, that is (δ⁽⁰⁾ ,ω⁽⁰⁾ )=(δ^(j) ,ω^(j) ), then formula (10) becomes the form of formula (3).

另外，的特征值中有一个零特征值，将各机功角转化为相对坐标可以消除零特征值。采用相对坐标系后，降了一阶，若采用相对于最后一台发电机的情况。需要做以下处理：将的前n-1行元素减去最后一行，再去掉第n行和第n列。g(δ⁽⁰⁾)的前n-1行元素减去最后一行，再去掉第n行。in addition, There is a zero eigenvalue in the eigenvalue of , and the zero eigenvalue can be eliminated by transforming the power angles of each machine into relative coordinates. After using the relative coordinate system, Down by one order, if the situation relative to the last generator is used. The following processing is required: the Subtract the last row from the first n-1 rows of elements, and then remove the nth row and nth column. Subtract the last row from the first n-1 row elements of g(δ⁽⁰⁾ ), and then remove the nth row.

步骤2：Step 2:

采用最大差异法筛选出重要故障。Important faults are screened out using the maximum difference method.

首先将各个节点故障的重要程度指标按照由小到大的顺序排序，排序后将前一个指标与后一个指标做比值运算，当这个比值达到最小值时，就找到了非重要故障与重要故障的界线。假设排序后的各节点故障的重要程度指标为E₁E₂...E_N，且Firstly, the importance index of each node fault is sorted from small to large, and after sorting, the ratio operation of the previous index and the latter index is performed. When the ratio reaches the minimum value, the non-important fault and the important fault are found. boundaries. Suppose the importance index of each node failure after sorting is E₁ E₂ ... E_N , and

${\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>r</span>r</span>}}<span><span>/</span>/</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>r</span>r</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}<span><span>=</span>=</span>\underset{\mathrm{<span><span>k</span>k</span>}<span><span>=</span>=</span>\mathrm{<span><span>1,2</span>1,2</span>}<span><span>,</span>,</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>.</span>.</span><span><span>,</span>,</span>\mathrm{<span><span>N</span>N</span>}<span><span>-</span>-</span>\mathrm{<span><span>1</span>1</span>}}{\mathrm{<span><span>min</span>min</span>}}<span><span>|</span>|</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>k</span>k</span>}}<span><span>/</span>/</span>{\mathrm{<span><span>E</span>E.</span>}}_{\mathrm{<span><span>k</span>k</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}}<span><span>|</span>|</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>-</span>-</span><span><span>(</span>(</span>\mathrm{<span><span>16</span>16</span>}<span><span>)</span>)</span>$

则重要节点故障为第r+1,r+2,L,N个故障。Then the important node faults are the r+1, r+2, L, Nth faults.

由上可知，根据本发明实施例的基于模式激发程度分析的暂态稳定预想事故筛选方法，将系统模型在非平衡点处泰勒展开，忽略高阶项，计算故障对系统各个振荡模式的激发程度，将激发程度在一个振荡周期内的最大值作为该故障的重要性指标，最后采用最大差异法筛选出预想事故。该方法不依赖于运行人员的经验，物理意义明确，可以快速地筛选出预想事故。As can be seen from the above, according to the transient stability predictive accident screening method based on mode excitation degree analysis in the embodiment of the present invention, the system model is expanded at the non-equilibrium point by Taylor, and the high-order terms are ignored to calculate the excitation degree of each oscillation mode of the system. , the maximum value of the excitation degree in one oscillation cycle is taken as the importance index of the fault, and finally the maximum difference method is used to screen out the expected accidents. This method does not depend on the experience of the operator, has clear physical meaning, and can quickly screen out anticipated accidents.

为使本领域技术人员更好地理解本发明，下面结合图2-图4，以美国电气和电子工程师协会（Institute of Electrical and Electronics Engineers，IEEE）三机九节点系统为例，说明该方法的具体实施方式。In order for those skilled in the art to better understand the present invention, the following uses the Institute of Electrical and Electronics Engineers (Institute of Electrical and Electronics Engineers, IEEE) three-machine nine-node system as an example to illustrate the method in conjunction with Figures 2-4 detailed description.

IEEE三机九节点系统的结构示意图如图2所示，依次计算各个节点故障的重要程度指标和极限切除时间，结果如表1所示。将节点故障重要程度指标记为E指标，将极限切除时间的倒数记为S指标，两种指标的柱状图如图3和图4所示，可见两种指标判断出的各个节点故障的重要程度趋势相同。最后依据E指标，采用最大差异法筛选出重要故障，为节点2和节点7的故障。The structural diagram of the IEEE three-machine nine-node system is shown in Figure 2, and the importance index and limit cut-off time of each node fault are calculated in turn, and the results are shown in Table 1. The importance index of node failure is marked as E index, and the reciprocal of the limit cut-off time is recorded as S index. The histograms of the two indexes are shown in Figure 3 and Figure 4. It can be seen that the importance of each node failure judged by the two indexes The trend is the same. Finally, according to the E index, the maximum difference method is used to screen out the important faults, which are the faults of node 2 and node 7.

表1.各个节点故障的重要程度指标和极限切除时间Table 1. The importance index and limit cut-off time of each node failure

节点编号node number重要程度指标importance index极限切除时间cut-off time110.4520.4520.2870.287220.9050.9050.2080.208330.5660.5660.2370.237440.5200.5200.2670.267550.4760.4760.3130.313660.4040.4040.3270.327770.9440.9440.2100.210880.6790.6790.2580.258990.6720.6720.2240.224

流程图中或在此以其他方式描述的任何过程或方法描述可以被理解为，表示包括一个或更多个用于实现特定逻辑功能或过程的步骤的可执行指令的代码的模块、片段或部分，并且本发明的优选实施方式的范围包括另外的实现，其中可以不按所示出或讨论的顺序，包括根据所涉及的功能按基本同时的方式或按相反的顺序，来执行功能，这应被本发明的实施例所属技术领域的技术人员所理解。Any process or method descriptions in flowcharts or otherwise described herein may be understood to represent modules, segments or portions of code comprising one or more executable instructions for implementing specific logical functions or steps of the process , and the scope of preferred embodiments of the invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including substantially concurrently or in reverse order depending on the functions involved, which shall It is understood by those skilled in the art to which the embodiments of the present invention pertain.

在本说明书的描述中，参考术语“一个实施例”、“一些实施例”、“示例”、“具体示例”、或“一些示例”等的描述意指结合该实施例或示例描述的具体特征、结构、材料或者特点包含于本发明的至少一个实施例或示例中。在本说明书中，对上述术语的示意性表述不一定指的是相同的实施例或示例。而且，描述的具体特征、结构、材料或者特点可以在任何的一个或多个实施例或示例中以合适的方式结合。In the description of this specification, descriptions referring to the terms "one embodiment", "some embodiments", "example", "specific examples", or "some examples" mean that specific features described in connection with the embodiment or example , structure, material or characteristic is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

尽管上面已经示出和描述了本发明的实施例，可以理解的是，上述实施例是示例性的，不能理解为对本发明的限制，本领域的普通技术人员在不脱离本发明的原理和宗旨的情况下在本发明的范围内可以对上述实施例进行变化、修改、替换和变型。Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and cannot be construed as limitations to the present invention. Variations, modifications, substitutions, and modifications to the above-described embodiments are possible within the scope of the present invention.

Claims (2)

1. A transient stability forecast accident screening method based on mode excitation degree analysis is characterized by comprising the following steps:

s1, calculating an importance degree index of each node fault by adopting a mode excitation degree analysis method;

the step S1 includes:

the system is provided with n generators, small interference stability analysis is carried out on the system, and the maximum electromechanical oscillation period of the system can be obtained and recorded as T_maxThe system is provided with N nodes, each node is provided with a three-phase short-circuit fault in sequence,the fault time is 0-0.1 s, and the importance degree index of each node fault is calculated as

E＝{E₁,E₂,..,E_N} (1)

Wherein the k-th node failure has an importance level index of

$E_k=max\left(\right|e_{ij}^k\left|\right)---\left(2\right)$

WhereinWhen the number is j, the degree of excitation of the k node fault to the ith oscillation mode is 1,2, …, N; 1,2, …, and n-1 is the number of the electromechanical oscillation mode of the system; j ═ t_c，t_c+Δt，t_c+2Δt，…，t_c+T_max，t_c0.1s is failure vanishing time, 0.01s is time domain simulation step length, T_maxIs the maximum electromechanical oscillation period;

wherein, theIs calculated by the formula

$e_{ij}^k={\mathrm{\&omega;}}_0{\left({\mathrm{\&lambda;}}_{ij}^k\right)}^{-1}{\widetilde{\mathrm{\&psi;}}}_{ij}^k{g}^k\left({\mathrm{\&delta;}}^{\left(j\right)}\right)---\left(3\right)$

The derivation process of (3) is as follows, and the meaning of each symbol in the formula (3) will be given in the derivation process below:

the generator adopts a classical second-order model, neglects system damping, adopts a constant impedance model for load, and only a system mathematical model of an internal node of the generator is reserved after network contraction

$\stackrel{\&CenterDot;}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_0(\mathrm{\&omega;}-1)$

$M\stackrel{\&CenterDot;}{\mathrm{\&omega;}}=P_m-P_e---\left(4\right)$

Wherein ω is₀Is synchronous angular velocity ═ 2₁，₂，…,_n]^TAnd ω ═ ω [ ω ]₁，ω₂，…,ω_n]^TColumn vectors consisting of power angle and angular velocity of each generator, 1 is n-row column vector with element 1, P_m＝[P_m1，P_m2，…，P_mn]^TAnd P_e＝[P_e1，P_e2，…，P_en]^TIs a column vector formed by mechanical power and electromagnetic power of each machine, M is a diagonal matrix taking inertia time constant of each machine as an element,

point of non-equilibrium (⁽⁰⁾,ω⁽⁰⁾) Is linearized by a model of

$\begin{array}{c}\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&delta;}}\\ \mathrm{\&Delta;}\stackrel{\&CenterDot;}{\mathrm{\&omega;}}\end{array}\right]=\left[\begin{array}{c}f\left({\mathrm{\&omega;}}^{\left(0\right)}\right)\\ g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)\end{array}\right]+A\left[\begin{array}{c}\mathrm{\&Delta;}\mathrm{\&delta;}\\ \mathrm{\&Delta;}\mathrm{\&omega;}\end{array}\right]\\ =\left[\begin{array}{c}{\mathrm{\&omega;}}_0({\mathrm{\&omega;}}^{\left(0\right)}-1)\\ M^{-1}(P_m-P_e^{\left(0\right)})\end{array}\right]+\left[\begin{array}{cc}0& {\mathrm{\&omega;}}_{0}I\\ -M^{-1}J& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}\mathrm{\&delta;}\\ \mathrm{\&Delta;}\mathrm{\&omega;}\end{array}\right]\end{array}---\left(5\right)$

Wherein 0 and I are respectively an n-order zero matrix and an n-order unit matrix, and J is P_eFor the varying Jacobian matrix, the equation (5) is converted into a second order differential equation form

$\begin{array}{c}\mathrm{\&Delta;}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&delta;}}={\mathrm{\&omega;}}_{0}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)+\tilde{A}\mathrm{\&Delta;}\mathrm{\&delta;}\\ ={\mathrm{\&omega;}}_0{M}^{-1}(P_m-P_e^{\left(0\right)})-{\mathrm{\&omega;}}_0{M}^{-1}J\mathrm{\&Delta;}\mathrm{\&delta;}\end{array}---\left(6\right)$

Is provided withAndis composed ofThe eigenvalue and the right eigenmatrix of A are then

$\mathrm{\&Lambda;}=\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_1& 0\\ 0& {\mathrm{\&Lambda;}}_2\end{array}\right]---\left(7\right)$

$\mathrm{\&Phi;}=US=\left[\begin{array}{cc}\widetilde{\mathrm{\&Phi;}}& 0\\ 0& 1/{\mathrm{\&omega;}}_0\widetilde{\mathrm{\&Phi;}}\end{array}\right]\left[\begin{array}{cc}1& 2\\ {\mathrm{\&Lambda;}}_1& {\mathrm{\&Lambda;}}_2\end{array}\right]$

Wherein

Make the following changes

$\mathrm{\&Delta;}\mathrm{\&delta;}=\widetilde{\mathrm{\&Phi;}}Z---\left(8\right)$

Can be substituted by formula (6)

$\stackrel{\&CenterDot;\&CenterDot;}{Z}=\widetilde{\mathrm{\&Lambda;}}E+\widetilde{\mathrm{\&Lambda;}}Z---\left(9\right)$

Wherein,is defined as a matrix of the degree of mode excitation,is composed ofA left feature matrix of, andthen the fault is to mode lambda_iHas an excitation degree of

$e_i={\mathrm{\&omega;}}_0{\mathrm{\&lambda;}}_i^{-1}{\widetilde{\mathrm{\&Psi;}}}_{i}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)---\left(10\right)$

Solving the formula (9)

$z_i\left(t\right)=-e_i+c_{i1}cos\left(\sqrt{\left|{\mathrm{\&lambda;}}_i\right|t}\right)+c_{i2}sin\left(\sqrt{\left|{\mathrm{\&lambda;}}_i\right|t}\right)---\left(11\right)$

Substituting into the initial condition to obtain

$c_{i1}={\mathrm{\&omega;}}_0{\mathrm{\&lambda;}}_i^{-1}{\widetilde{\mathrm{\&Psi;}}}_{i}g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)+{\widetilde{\mathrm{\&Psi;}}}_i\left({\mathrm{\&delta;}}^{\left(0\right)}\right)$

$c_{i2}={\sqrt{\left|{\mathrm{\&lambda;}}_i\right|}}^{-1}{\widetilde{\mathrm{\&Psi;}}}_{i}f\left({\mathrm{\&omega;}}^{\left(0\right)}\right)+{\mathrm{\&omega;}}_0{\sqrt{\left|{\mathrm{\&lambda;}}_i\right|}}^{-1}{\widetilde{\mathrm{\&Psi;}}}_i\mathrm{\&Delta;}\mathrm{\&omega;}\left(0\right)---\left(12\right)$

Wherein

f(ω⁽⁰⁾)＝ω₀(ω⁽⁰⁾-1)

$g\left({\mathrm{\&delta;}}^{\left(0\right)}\right)=M^{-1}(P_m-P_e^{\left(0\right)})$

Δ(0)＝(0)-⁽⁰⁾(13)

Δω(0)＝ω(0)-ω⁽⁰⁾

Because of linearization at the point of non-equilibrium, (⁽⁰⁾,ω⁽⁰⁾) Because a disturbance factor is included, Δ (0) ═ Δ ω (0) ═ 0, and ω is calculated assuming that the angular velocity does not change much during the transient process⁽⁰⁾＝1，f(ω⁽⁰⁾) When it is equal to 0, the formula (12) is changed to

$\begin{array}{c}{c}_{i1}=e_i\\ c_{i2}=0\end{array}---\left(14\right)$

Is substituted by formula (11)

$z_i\left(t\right)=e_i\&lsqb;cos\sqrt{\left|{\mathrm{\&lambda;}}_i\right|t}-1\&rsqb;---\left(15\right)$

As can be seen from equations (8) and (15), the larger the excitation degree of the disturbance to the oscillation mode, the more intense the oscillation of the system,

equation (10) is perturbation-to-oscillation mode λ_iIf the disturbance is the kth node fault and the unbalanced point is the jth time section of the time domain simulation, that is

(⁽⁰⁾,ω⁽⁰⁾)＝(^(j),ω^(j)) Then formula (10) becomes the form of formula (3);

and

s2, screening out important faults by adopting a maximum difference method;

the step S2 includes:

sorting the importance degree indexes of the node faults according to a sequence from small to large, performing ratio operation on the former index and the latter index after sorting, finding a boundary line between the non-important fault and the important fault when the ratio reaches the minimum value, and assuming that the importance degree index of each node fault after sorting is E₁E₂...E_NAnd is and

$E_r/E_{r+1}=\underset{k=1,2,...,N-1}{\min }|E_r/E_{r+1}|---\left(16\right)$

the important node failures are the r +1, r +2, …, N failures.

2. The method for transient stability prognosis accident screening based on pattern excitation degree analysis according to claim 1,the characteristic value of the computer has a zero characteristic value, the zero characteristic value can be eliminated by converting the machine angles into relative coordinates, and after a relative coordinate system is adopted,the first step is reduced, if the situation relative to the last generator is adopted, the following treatment is carried out at the moment: will be provided withThe first n-1 row of elements minus the last row, the nth row and the nth column, g: (⁽⁰⁾) The first n-1 row elements minus the last row and then the nth row is eliminated.