CN103795058B

CN103795058B - The air extract analysis of electric power system and system failure sort method

Info

Publication number: CN103795058B
Application number: CN201410049147.XA
Authority: CN
Inventors: 周前; 胡泽春; 汪成根; 赵静波; 赵博石
Original assignee: Tsinghua University; State Grid Corp of China SGCC; State Grid Jiangsu Electric Power Co Ltd; Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
Current assignee: Tsinghua University; State Grid Corp of China SGCC; State Grid Jiangsu Electric Power Co Ltd; Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
Priority date: 2014-02-12
Filing date: 2014-02-12
Publication date: 2015-10-28
Anticipated expiration: 2034-02-12
Also published as: CN103795058A

Abstract

The present invention proposes a static voltage stability margin analysis and system fault sorting method of a power system, including: determining the static voltage collapse point based on the optimal multiplier-based Newton iterative method; judging the type of the voltage collapse point according to the characteristics of the iterative convergence; According to the requirement of stability margin, the dangerous situation of system failure is checked and the ranking of stability faults is given; the faults are parameterized and the severity ranking of instability faults is given by iterative method. The invention can quickly provide the voltage stability margin of the power system online, and monitor the voltage stability effectively in real time; the comprehensive sorting of stability faults and instability faults can guide the generator adjustment and operation online when the system fails. The switching of reactive power compensation equipment can also be used to guide the adjustment of branch parameters, line increase or decrease, and configuration of FACTS equipment offline, which is of great significance to the operation and planning of the power system.

Description

Static Voltage Stability Margin Analysis and System Fault Sorting Method of Power System

技术领域technical field

本发明涉及电力系统监测、分析及控制的技术领域，具体地说是一种电力系统的静态电压稳定裕度分析及系统故障排序方法。The invention relates to the technical field of power system monitoring, analysis and control, in particular to a static voltage stability margin analysis and system fault sorting method of a power system.

背景技术Background technique

电力系统的电压稳定问题研究起步晚于频率稳定问题的研究，起步于上世纪四十年代，直到上世纪七十年代后，电压稳定问题才开始作为一个专门的领域受到关注，随着现代电力系统的发展，输电领域的发展可能滞后于系统负荷增长和发电水平的增长，电力网络往往运行在高负荷水平下，面临电压稳定临界限制，引发了一系列重大的电压稳定事故。The research on the voltage stability of the power system started later than the research on the frequency stability. It started in the 1940s. It was not until the 1970s that the voltage stability problem began to receive attention as a specialized field. With the modern power system The development of the power transmission field may lag behind the growth of system load and power generation level. The power network often operates at a high load level and faces a critical limit of voltage stability, which leads to a series of major voltage stability accidents.

静态电压稳定问题有诸多分析方法。利用系统PV曲线，给出在一定负荷增长方向上负荷节点的电压稳定裕度，是最为常用的静态电压稳定分析方法，该方法有明确的物理背景，分析效果直观，有着连续潮流等成熟的分析方法，如图1所示，由下式定义电压稳定裕度λ，There are many analysis methods for the static voltage stability problem. Using the system PV curve to give the voltage stability margin of the load node in a certain load growth direction is the most commonly used static voltage stability analysis method. This method has a clear physical background, the analysis effect is intuitive, and it has mature analysis such as continuous power flow. method, as shown in Fig. 1, the voltage stability margin λ is defined by the following formula,

$λ λ = = \frac{{P P}_{max max c c} - - {P P}_{initial initial}}{{P P}_{initial initial}}$

图1中，P_maxc是指电压崩溃点时系统的有功功率水平，P_initial是指系统初始运行点有功功率水平，P_maxI是指系统运行满足一定裕度要求下系统的最大无功功率水平，V_I是指系统运行满足一定裕度要求下系统最低电压水平，V_C是指电压崩溃点时的电压水平。In Fig. 1, P _maxc refers to the active power level of the system at the voltage collapse point, P _initial refers to the active power level at the initial operating point of the system, and P _maxI refers to the maximum reactive power level of the system when the system operation meets a certain margin requirement, V _I refers to the minimum voltage level of the system when the system operation meets a certain margin requirement, and V _C refers to the voltage level at the voltage collapse point.

系统故障如发电机、并联无功补偿器等注入型设备的退出和系统线路、变压器等支路型设备的退出对于系统的电压稳定水平会产生直接的影响，一般故障的发生均会造成电压稳定裕度λ的减小，若λ大于0时，可认为故障后系统仍保持稳定，若λ小于0，则故障后系统将失去稳定，称为失稳故障。System faults, such as the withdrawal of injection-type equipment such as generators and parallel reactive power compensators, and the withdrawal of branch-type equipment such as system lines and transformers, will have a direct impact on the voltage stability of the system. The occurrence of general faults will cause voltage stability. With the reduction of margin λ, if λ is greater than 0, it can be considered that the system remains stable after the fault; if λ is less than 0, the system will lose stability after the fault, which is called an unstable fault.

中国发明专利（申请号201010140847.1）输电网严重故障后的电压稳定裕度实时评估与最优控制方法，通过判断迭代求解潮流步骤中计算得到的解点是真实解还是最优解来判断故障后系统的电压稳定性，利用阻尼牛顿法求解，增加了一次迭代过程，再利用连续潮流求解稳定裕度，迭代次数较多、时间较长，且没有实现对故障严重程度的排序。Chinese Invention Patent (Application No. 201010140847.1) Real-time evaluation and optimal control method of voltage stability margin after severe fault of transmission network, by judging whether the solution point calculated in the step of iteratively solving the power flow is the real solution or the optimal solution to judge the system after the fault The voltage stability of the voltage stability is solved by the damped Newton method, which adds an iterative process, and then uses the continuous power flow to solve the stability margin. The number of iterations is large and the time is long, and the ranking of the severity of the fault is not realized.

中国发明专利（申请号201110368041.2）一种电力系统故障严重程度评价方法，根据仿真过程信息判断系统是否发生了功角、电压、频率失稳；分别按照功角、电压、频率三个指标计算出该故障的严重系数，将前述得到的三个严重系数进行加权组合得出综合严重系数，该故障严重程度排序方法涉及电压稳定和频率稳定，并不是针对性地解决电压稳定故障排序名问题，且故障排序的依据是故障结果，是对故障对系统产生的影响进行排序，没有讨论解决故障的难易程度，同时无法给出解决故障的运行调度方法。Chinese invention patent (application number 201110368041.2) is a method for evaluating the severity of power system faults. According to the simulation process information, it is judged whether the power angle, voltage, and frequency instability have occurred in the system; The severity coefficient of the fault, the comprehensive severity coefficient is obtained by weighting the three severity coefficients obtained above. The basis of the sorting is the fault result, which is to sort the impact of the fault on the system. It does not discuss the difficulty of solving the fault, and cannot give the operation scheduling method to solve the fault.

发明内容Contents of the invention

本发明提供一种电力系统的静态电压稳定裕度分析及系统故障排序方法，能够在线较快速地给出系统的电压稳定裕度，对电力系统的电压稳定性进行实时有效的监测；稳定性故障和失稳性故障的综合排序可以在系统发生故障时在线指导发电机出力调整和无功补偿设备的投切，也可以离线指导支路参数调整、线路增减、FACTS设备的配置等，对电力系统的运行与规划均有重要的意义。The invention provides a static voltage stability margin analysis and system fault sorting method of a power system, which can quickly provide the voltage stability margin of the system online, and monitor the voltage stability of the power system effectively in real time; stability faults The comprehensive sorting of faults and instability faults can guide the adjustment of generator output and the switching of reactive power compensation equipment online when the system fails, and can also guide the adjustment of branch parameters, line increase and decrease, and FACTS equipment configuration offline. The operation and planning of the system are of great significance.

本发明所采用的技术手段如下：The technical means adopted in the present invention are as follows:

电力系统的静态电压稳定裕度分析及系统故障排序方法，包括以下步骤：The static voltage stability margin analysis of the power system and the system fault sorting method include the following steps:

（1）根据对电力系统的监测结果，判断电力系统是否发生故障，如果电力系统未发生故障，即在正常运行方式下，则从可行域外出发进行基于最优乘子的牛顿迭代法，求取电力系统在预定负荷增长方向上的电压稳定裕度以及确定电压崩溃临界点，然后转入步骤2）；如果电力系统发生故障，则直接进入步骤3）；(1) According to the monitoring results of the power system, it is judged whether the power system is faulty. If the power system is not faulty, that is, in the normal operation mode, the Newton iteration method based on the optimal multiplier is carried out from outside the feasible region to obtain The voltage stability margin of the power system in the predetermined load growth direction and the determination of the critical point of voltage collapse, and then go to step 2); if the power system fails, go directly to step 3);

（2）根据牛顿迭代法收敛情况分析电压稳定裕度，并区分电压崩溃点类型；(2) Analyze the voltage stability margin according to the convergence of the Newton iterative method, and distinguish the types of voltage collapse points;

（3）如果电力系统发生故障，仍然按照从可行域外出发进行基于最优乘子的牛顿迭代法，求取电压稳定裕度以及确定电压崩溃临界点，在迭代过程中，迭代初始点选择所述步骤（1)正常运行方式下求取的电压崩溃临界点裕度；(3) If the power system fails, still follow the Newton iterative method based on the optimal multiplier starting from outside the feasible region to obtain the voltage stability margin and determine the critical point of voltage collapse. During the iterative process, the initial point of the iterative selection is Step (1) The voltage collapse critical point margin obtained under the normal operation mode;

（4）分析所述步骤（3）求取的电压稳定裕度，若电压稳定裕度不小于0，则为稳定性故障，根据电压稳定裕度大小对稳定性故障进行严重程度排序，电压稳定裕度值越小，故障越严重；若电压稳定裕度小于0，则为失稳故障，首先对故障进行参数化，然后按照从可行域外出发的基于最优乘子的牛顿迭代方法求取电压崩溃临界点，在迭代过程中，迭代初始点选择故障参数为0时的电压稳定裕度；(4) Analyze the voltage stability margin obtained in the above step (3). If the voltage stability margin is not less than 0, it is a stability fault. The severity of the stability fault is sorted according to the voltage stability margin. The voltage stability The smaller the margin value, the more serious the fault; if the voltage stability margin is less than 0, it is an unstable fault. First, the fault is parameterized, and then the voltage is calculated according to the Newton iterative method based on the optimal multiplier starting from outside the feasible region The critical point of collapse, in the iterative process, the voltage stability margin when the fault parameter is 0 is selected as the initial point of the iterative;

（5）计算所述步骤（4）求取的电压崩溃临界点故障参数，根据故障参数大小对失稳故障进行严重程度排序，故障参数越大，故障越严重；(5) Calculate the fault parameters at the critical point of voltage collapse obtained in the step (4), and sort the severity of instability faults according to the size of the fault parameters. The larger the fault parameter, the more serious the fault;

（6）综合步骤（4）和步骤（5）的两种排序，按照电压稳定裕度值从大到小，然后故障参数从小到大的顺序，给出故障统一排序，指导电力系统运行。(6) Combining the two sorts of steps (4) and (5), according to the order of voltage stability margin from large to small, and then fault parameters from small to large, a unified fault ranking is given to guide the operation of the power system.

前述的步骤（1）中，从可行域外出发进行基于最优乘子的牛顿迭代法，求取电压稳定裕度以及确定电压崩溃临界点的具体方法为：In the aforementioned step (1), the Newton iterative method based on the optimal multiplier is carried out from outside the feasible region, and the specific methods for obtaining the voltage stability margin and determining the critical point of voltage collapse are as follows:

负荷和发电机的增长方向由下式定义：The increasing direction of load and generator is defined by:

P_Li＝P_Li0+λb_Pi P _Li ＝P _Li0 +λb _Pi

Q_Li＝Q_Li0+λb_Qi Q _Li ＝Q _Li0 +λb _Qi

P_Gi＝P_Gi0+λb_Gi P _Gi ＝P _Gi0 +λb _Gi

其中，λ为电压稳定裕度，P_Li0，Q_Li0分别为节点i在基准状态下注入的有功功率和无功功率，P_Li，Q_Li分别为节点i在当前状态下注入的有功功率和无功功率，P_Gi0，P_Gi为节点i发电机在基准状态下和当前状态下注入的有功功率，b_Pi，b_Qi，b_Gi分别为节点i的负荷有功出力，无功出力和发电机出力的变化方向向量；Among them, λ is the voltage stability margin, P _Li0 , Q _Li0 are the active power and reactive power injected by node i in the reference state, respectively, P _Li , Q _Li are the active power and reactive power injected by node i in the current state, respectively Active power, P _Gi0 , P _Gi is the active power injected by the node i generator in the reference state and the current state, b _Pi , b _Qi , b _Gi are the load active output, reactive output and generator output of node i respectively The change direction vector of

带参数的潮流方程表示为：The power flow equation with parameters is expressed as:

f(x,λ)＝f(x)-S＝0f(x,λ)=f(x)-S=0

S＝S₀+λbS＝S ₀ +λb

其中，S₀，S分别为基准状态下和当前状态下节点和发电机注入功率向量，S₀=(P_Li0,Q_Li0,P_Gi0)，S=(P_Li,Q_Li,P_Gi)，b为节点和发电机注入功率变化方向向量，b＝(b_Pi,b_Qi,b_Gi)，x为状态变量；Among them, S ₀ , S are the injected power vectors of nodes and generators in the reference state and current state respectively, S ₀ =(P _Li0 ,Q _Li0 ,P _Gi0 ), S=(P _Li ,Q _Li ,P _Gi ), b is the direction vector of node and generator injection power change, b=(b _Pi ,b _Qi ,b _Gi ), x is the state variable;

采用最优乘子的牛顿迭代法，迭代初始点选取满足潮流在可行域外的电压稳定裕度值，在潮流第k次迭代求出状态变量x^(k)的修正量Δx^(k)，Δx^(k)＝J^(k)-1f(x^(k))，其中，J^(k)为第k次迭代的雅克比矩阵，f(x^(k))为将第k次迭代求出状态变量x^(k)代入潮流方程组，雅克比矩阵的具体形式为：Using the Newton iterative method of the optimal multiplier, the initial point of the iteration is selected to satisfy the voltage stability margin value outside the feasible region of the power flow, and the correction amount Δx ^(k) of the state variable x ^(k) is obtained in the kth iteration of the power flow, Δx ^{( k)} =J ^(k)-1 f(x ^(k) ), where J ^(k) is the Jacobian matrix of the kth iteration, and f(x ^(k) ) is the state variable obtained from the kth iteration Substituting x ^(k) into the power flow equations, the specific form of the Jacobian matrix is:

以一个标量乘子β乘以修正量Δx^(k)，再来修正状态变量x^(k)，其中标量乘子β由以下目标函数求得：Multiply the correction amount Δx ^(k) by a scalar multiplier β, and then correct the state variable x ^(k) , where the scalar multiplier β is obtained by the following objective function:

$min min F f ((β β)) = = \frac{11}{22} {Σ Σ}_{i i = = 11}^{22 n no} {f f}_{i i}^{22} (({x x}^{((k k))} + + βΔ βΔ {x x}^{((k k))}))$

f_i(·)表示方程组f(x,λ)＝f(x)-S＝0中的第i个方程，2n为方程的个数，通过求取F(β)极值获得标量乘子β，方程如下式：f _i (·) represents the i-th equation in the equation system f(x,λ)=f(x)-S=0, 2n is the number of equations, the scalar multiplier is obtained by finding the extreme value of F(β) β, the equation is as follows:

$\frac{dF f ((β β))}{dβ dβ} = = 00;;$

标量乘子β为0时对应的状态变量x^*为潮流方程的最小二乘解，β为0时的电压稳定裕度λ_critical即为电压崩溃临界点对应的裕度值。When the scalar multiplier β is 0, the corresponding state variable x ^* is the least squares solution of the power flow equation, and the voltage stability margin λ _critical when β is 0 is the margin value corresponding to the critical point of voltage collapse.

前述的步骤（2）的具体实现过程为：The specific implementation process of the aforementioned step (2) is:

若在步骤（1）的迭代中，出现某个节点反复发生PV/PQ类型转换的情况,则电压崩溃点的类型为约束诱导型，此节点为电压崩溃点；If during the iteration of step (1), a node repeatedly undergoes PV/PQ type conversion, the type of voltage collapse point is a constraint-induced type, and this node is a voltage collapse point;

若在步骤（1）的迭代中，出现某几个节点反复发生PV/PQ类型转换的情况,则电压崩溃点的类型为约束诱导型，记录这些节点，每次选1个节点i，按所述步骤（1）计算潮流，潮流收敛后，根据最终的雅克比矩阵计算灵敏度，若满足以下条件：If in the iteration of step (1), some nodes repeatedly undergo PV/PQ type conversion, then the type of voltage collapse point is the constraint-induced type, record these nodes, select one node i each time, press the The above step (1) calculates the power flow. After the power flow converges, the sensitivity is calculated according to the final Jacobian matrix, if the following conditions are met:

$\{\begin{matrix} \frac{dλ dλ}{d d {V V}_{Gi Gi}} > > 00 \\ \frac{dλ dλ}{d d {Q Q}_{Gi Gi}} > > 00 \end{matrix}$

则节点i为电压崩溃点，其中，V_Gi为节点i发电机电压，Q_Gi为节点i发电机注入的无功功率，Then node i is the voltage collapse point, where V _Gi is the generator voltage of node i, Q _Gi is the reactive power injected by the generator of node i,

若在步骤（1）的迭代中，电压稳定裕度的修正量小于预设精度，则电压崩溃点的类型为鞍结型，则得到最小二乘解后，需要进一步修正电压稳定裕度λ，搜寻电压崩溃点，即搜寻对应电压崩溃点的电压稳定裕度λ_critical，具体为：If in the iteration of step (1), the correction amount of the voltage stability margin is less than the preset accuracy, the type of the voltage collapse point is saddle junction type, and after obtaining the least squares solution, the voltage stability margin λ needs to be further corrected, Search for the voltage collapse point, that is, search for the voltage stability margin λ _critical corresponding to the voltage collapse point, specifically:

定义∑为介于潮流方程有解和无解区域之间的边界，节点净注入功率向量S组成一个空间，S^λ，S′，S^m三者均为空间中功率向量，S′为当前功率向量，定义S^m为∑在状态变量x^*处的切平面上距当前功率向量S′欧氏距离最近的点，定义S^λ为切平面与节点注入功率变化方向向量b的交点，S^λ与S^critical重合，S^critical表示电压崩溃临界点对应的功率向量，定义电压稳定裕度的修正量Δλ为S′与S^λ间负荷参数差值，则S^λ可表示为下式：Define ∑ as the boundary between the solution and non-solution areas of the power flow equation, the net injected power vector S of the node forms a space, S ^λ , S′, S ^m are all power vectors in the space, and S′ is the current power vector, define S ^m as Σ on the tangent plane at the state variable x ^* and the point with the closest Euclidean distance to the current power vector S′, define S ^λ as the intersection point between the tangent plane and the node injection power change direction vector b, and S ^λ and S ^critical coincides, S ^critical represents the power vector corresponding to the critical point of voltage collapse, and the correction value Δλ of the voltage stability margin is defined as the load parameter difference between S′ and S ^λ , then S ^λ can be expressed as the following formula:

S^λ＝S′-ΔλbS ^λ = S'-Δλb

$Δλ Δλ = = \frac{{| | | | {S S}^{' '} - - f f (({x x}^{* *})) | | | |}_{22} cos cos {θ θ}_{11}}{{| | | | b b | | | |}_{22} cos cos {θ θ}_{22}}$

其中，θ₁表示功率向量S^m与最小二乘解处的潮流方程f(x^*)之间的夹角，θ₂表示功率向量S^m和S^λ之间的夹角，Among them, θ ₁ represents the angle between the power vector S ^m and the power flow equation f(x ^* ) at the least squares solution, θ ₂ represents the angle between the power vector S ^m and S ^λ ,

∑为凸曲面时，电压稳定裕度λ的修正式为：When ∑ is a convex surface, the correction formula of voltage stability margin λ is:

λ^(k+1)＝λ^(k)-Δλ^(k+1) λ ^(k+1) = λ ^{(k) -} Δλ ^(k+1)

∑为凹曲面时，When Σ is a concave surface,

若Δλ^(k)大于预设精度，则电压稳定裕度λ的修正式为：If Δλ ^(k) is greater than the preset accuracy, the correction formula of the voltage stability margin λ is:

${λ λ}^{((k k + + 11))} = = {λ λ}^{((k k))} + + \frac{Δ Δ {λ λ}^{((k k))}}{22}$

若θ₁＝90°或θ₂＝90°且θ₁≠90°时，则根据下式计算电压稳定裕度的修正量Δλ：If θ ₁ =90° or θ ₂ =90° and θ ₁ ≠90°, then calculate the correction value Δλ of the voltage stability margin according to the following formula:

$Δλ Δλ = = \frac{{| | | | {S S}^{' '} - - f f (({x x}^{* *})) | | | |}_{22}}{{| | | | b b | | | |}_{22}}$

电压稳定裕度λ的修正式为：λ^(k+1)＝λ^(k)-Δλ^(k+1)。The correction formula of the voltage stability margin λ is: λ ^(k+1) = λ ^{(k) -} Δλ ^(k+1) .

前述的步骤（5）对故障进行参数化是指，设反映系统故障参数为μ，且参数范围为：The parameterization of the fault in the aforementioned step (5) means that the parameter reflecting the system fault is μ, and the parameter range is:

0＜μ＜10<μ<1

故障参数μ为0时表示故障未发生，为1时表示故障彻底发生。When the fault parameter μ is 0, it means that the fault has not occurred, and when it is 1, it means that the fault has completely occurred.

前述的步骤（5）中，对于不同的故障，故障参数μ的计算按下述参数化潮流方程求出：In the aforementioned step (5), for different faults, the fault parameter μ is calculated according to the following parameterized power flow equation:

（1）单个发电机退出的参数化潮流方程(1) Parametric power flow equation for a single generator exit

$\{\begin{matrix} μ μ {P P}_{Gi Gi} - - {P P}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) - - {V V}_{i i}^{22} {G G}_{ii i} = = 00 \\ μ μ {Q Q}_{G G min min U u} \leq \leq {Q Q}_{Gi Gi} \leq \leq μ μ {Q Q}_{G G max max U u} \end{matrix}$

（2）单个并联电容器或电抗器退出的参数化潮流方程(2) Parametric power flow equation for a single shunt capacitor or reactor exit

$μ μ {Q Q}_{Si Si} - - {Q Q}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} - - {B B}_{ij ij} sin sin {θ θ}_{ij ij})) + + {V V}_{i i}^{22} {B B}_{ii i} = = 00$

（3）单个负荷退出的参数化潮流方程(3) Parametric power flow equation for single load withdrawal

$\{\begin{matrix} {P P}_{Gi Gi} - - μ μ {P P}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) {- - V V}_{i i}^{22} {G G}_{ii i} = = 00 \\ {Q Q}_{Si Si} - - μ μ {Q Q}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) + + {V V}_{i i}^{22} {B B}_{ii i} = = 00 \end{matrix}$

（4）单个支路退出的参数化潮流方程(4) Parametric power flow equation for single branch exit

$\{\begin{matrix} {P P}_{Gi Gi} - - {P P}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I,, j j &NotEqual; &NotEqual; m m}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) - - {V V}_{i i} {V V}_{m m} ((μ μ {G G}_{im im} cos cos {θ θ}_{im im} + + μ μ {B B}_{im im} sin sin {θ θ}_{im im})) - - {V V}_{i i}^{22} {G G}_{iinew inew} = = 00 \\ {Q Q}_{Ri Ri} - - {Q Q}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) - - {V V}_{i i} {V V}_{m m} ((μ μ {G G}_{im im} cos cos {θ θ}_{im im} + + μ μ {B B}_{im im} sin sin {θ θ}_{im im})) - - {V V}_{i i}^{22} {G G}_{iinew inew} + + {V V}_{i i}^{22} {B B}_{ii i} new new = = 00 \end{matrix}$

如果出现多重故障，则参数化潮流方程为该多重故障中各单个故障参数化潮流方程的线性叠加；If multiple faults occur, the parameterized power flow equation is the linear superposition of the parameterized power flow equations of each single fault in the multiple faults;

其中，P_Di节点i的负荷吸收的有功功率；P_Gi为节点i发电机注入的有功功率；Q_Gi为节点i发电机注入的无功功率；Q_Di为节点i负荷吸收的无功功率；Q_Si为并联电容器容量，Q_GmaxU，Q_GminU为发电机无功输出的上、下限；Q_Ri为故障后无功补偿电容器的容量；V_i为节点i的电压幅值；I为所有节点集合；θ_ij为节点i、j之间的相角差；B_ij为导纳矩阵中节点i、j之间的电纳；G_ij为导纳矩阵中节点i、j之间的电导；G_ii为节点i的自电导；B_ii为节点i的自电纳；G_iinew为支路i-m发生故障后系统导纳矩阵中的自导；B_iinew为支路i-m发生故障后系统导纳矩阵中的自电纳。Among them, P _Di is the active power absorbed by the load of node i; P _Gi is the active power injected by the generator of node i; Q _Gi is the reactive power injected by the generator of node i; Q _Di is the reactive power absorbed by the load of node i; Q _Si is the capacity of the shunt capacitor, Q _GmaxU and Q _GminU are the upper and lower limits of the reactive power output of the generator; Q _Ri is the capacity of the reactive power compensation capacitor after a fault; V _i is the voltage amplitude of node i; I is the set of all nodes ; θ _ij is the phase angle difference between nodes i and j; B _ij is the susceptance between nodes i and j in the admittance matrix; G _ij is the conductance between nodes i and j in the admittance matrix; G _ii is the self-conductance of node i; B _ii is the self-conductance of node i; G _iinew is the self-conductance in the system admittance matrix after the branch im fails; B _iinew is the system admittance matrix after the branch im fails Self-supply.

通过采用上述技术手段，本发明具有的有益效果为：By adopting above-mentioned technical means, the beneficial effect that the present invention has is:

1）操作简单易行，步骤清晰，在线分析可以通过系统SCADA或PMU获得的数据进行直接分析，离线分析易于通过仿真工具完成；1) The operation is simple and easy, the steps are clear, the online analysis can be directly analyzed through the data obtained by the system SCADA or PMU, and the offline analysis is easy to complete through the simulation tool;

2）计算简单、快速，使用从可行域外出发的基于最优乘子潮流迭代分析方法避免了连续潮流求解电压崩溃临界点在接近崩溃点时不易收敛的情况，潮流迭代初始点明确，减少了迭代次数，受系统规模影响少；2) The calculation is simple and fast. Using the optimal multiplier power flow iterative analysis method starting from outside the feasible region avoids the situation that the continuous power flow solution voltage collapse critical point is not easy to converge when it is close to the collapse point. The initial point of power flow iteration is clear, which reduces the number of iterations The number of times is less affected by the system scale;

3）对系统发生故障进行参数化，利用没有物理意义的0-1之间的故障参数进行故障严重程度排序，用于排序的参数不仅仅是对故障后果严重程度的排序，更多是故障发生过程或在线运行解决难度的排序情况；3) Parameterize the failure of the system, and use the failure parameters between 0 and 1 that have no physical meaning to sort the severity of the failure. The parameters used for sorting are not only the ranking of the severity of the consequences of the failure, but also the occurrence of the failure Process or online operation to solve the order of difficulty;

4）将故障严重程度由故障后是否失稳分成两大类，并在两个步骤中对两类步骤分别进行了排序，分别进行的排序结果进行了统一的排序分析，统一的排序结果可以指导系统的运行和规划，通过前期规划和现场运行，降低可能发生故障的严重程度排序。4) The severity of the fault is divided into two categories by whether it is unstable after the fault, and the two types of steps are sorted in the two steps, and the sorting results are analyzed in a unified way. The unified sorting results can guide System operation and planning, through preliminary planning and on-site operation, reduce the severity of possible failures.

附图说明Description of drawings

图1为连续潮流方法和电压稳定裕度定义示意图；Figure 1 is a schematic diagram of the continuous power flow method and the definition of voltage stability margin;

图2为从可行域外进行基于最优乘子牛顿迭代的示意图；Fig. 2 is a schematic diagram of Newton iteration based on optimal multiplier from outside the feasible domain;

图3为从可行区域外找寻电压崩溃点的迭代几何模型示意图；Fig. 3 is a schematic diagram of an iterative geometric model for finding a voltage breakdown point from outside the feasible region;

图4为描述稳定性故障和失稳故障的统一排序示意图；Figure 4 is a schematic diagram of a unified sequence describing stability faults and instability faults;

图5为本发明的电力系统的静态电压稳定裕度分析及系统故障排序方法流程图。Fig. 5 is a flow chart of the static voltage stability margin analysis and system fault sorting method of the power system according to the present invention.

具体实施方式Detailed ways

下面结合附图和具体实施方式，对本发明作进一步详细说明。The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

本发明利用从可行域外出发进行迭代的最优乘子牛顿迭代方法，该方法迭代目标为找到电压崩溃临界点，即可分析出系统电压稳定裕度，该方法避免了常规连续潮流计算在接近崩溃点时产生的收敛困难的问题，减少了迭代次数，提高了求解速度，还可根据收敛特征识别电压崩溃类型。The present invention utilizes the optimal multiplier Newton iterative method starting from outside the feasible region. The iterative goal of this method is to find the critical point of voltage collapse, and then the system voltage stability margin can be analyzed. This method avoids the conventional continuous power flow calculation when it is close to collapse It reduces the number of iterations, improves the solution speed, and can also identify the type of voltage collapse according to the convergence characteristics.

如图5所示，本发明方法包括以下步骤：As shown in Figure 5, the inventive method comprises the following steps:

1、首先根据对电力系统的监测结果，判断电力系统是否发生故障，如果电力系统未发生故障，即在正常运行方式下，则从可行域外出发进行基于最优乘子的牛顿迭代法，求取电力系统在预定负荷增长方向上的电压稳定裕度以及确定电压崩溃临界点，然后转入步骤2；如果电力系统发生故障，则直接进入步骤3；1. First, according to the monitoring results of the power system, it is judged whether the power system is faulty. If the power system is not faulty, that is, in the normal operation mode, the Newton iteration method based on the optimal multiplier is carried out from outside the feasible region to obtain The voltage stability margin of the power system in the predetermined load growth direction and the determination of the critical point of voltage collapse, and then go to step 2; if the power system fails, go directly to step 3;

正常运行方式下，In normal operation mode,

负荷和发电机的增长方向可以由下式定义：The increasing direction of load and generator can be defined by:

P_Li＝P_Li0+λb_Pi P _Li ＝P _Li0 +λb _Pi

Q_Li＝Q_Li0+λb_Qi Q _Li ＝Q _Li0 +λb _Qi

P_Gi＝P_Gi0+λb_Gi P _Gi ＝P _Gi0 +λb _Gi

其中，λ为电压稳定裕度，P_Li0，Q_Li0分别为节点i在基准状态下注入的有功功率和无功功率，P_Li，Q_Li分别为节点i在当前状态下注入的有功功率和无功功率，P_Gi0，P_Gi为节点i发电机在基准状态下和当前状态下注入的有功功率，b_Pi，b_Qi，b_Gi分别为节点i的负荷有功出力，无功出力和发电机出力的变化方向向量。以上节点功率可代入潮流方程，Among them, λ is the voltage stability margin, P _Li0 , Q _Li0 are the active power and reactive power injected by node i in the reference state, respectively, P _Li , Q _Li are the active power and reactive power injected by node i in the current state, respectively Active power, P _Gi0 , P _Gi is the active power injected by the node i generator in the reference state and the current state, b _Pi , b _Qi , b _Gi are the load active output, reactive output and generator output of node i respectively The change direction vector of . The above node power can be substituted into the power flow equation,

带参数的潮流方程可以表示为：The power flow equation with parameters can be expressed as:

f(x,λ)＝f(x)-S＝0f(x,λ)=f(x)-S=0

S＝S₀+λbS＝S ₀ +λb

其中，S₀，S分别为基准状态下和当前状态下节点和发电机注入功率向量，S₀=(P_Li0,Q_Li0,P_Gi0)，S=(P_Li,Q_Li,P_Gi)，b为节点和发电机注入功率变化方向向量，b＝(b_Pi,b_Qi,b_Gi)，x为状态变量。Among them, S ₀ , S are the injected power vectors of nodes and generators in the reference state and current state respectively, S ₀ =(P _Li0 ,Q _Li0 ,P _Gi0 ), S=(P _Li ,Q _Li ,P _Gi ), b is the change direction vector of node and generator injection power, b=(b _Pi ,b _Qi ,b _Gi ), x is the state variable.

如图2所示，采用最优乘子的牛顿迭代法，迭代初始点选取满足潮流在可行域外的电压稳定裕度值λ₀，沿着如图所示逼近方向，找到电压崩溃临界点对应的裕度λ_critical；As shown in Figure 2, the Newton iterative method with the optimal multiplier is adopted, the initial point of the iteration is selected to satisfy the voltage stability margin value λ ₀ outside the feasible region of the power flow, and along the approaching direction as shown in the figure, find the voltage corresponding to the critical point of voltage collapse Margin λ _critical ;

最优乘子潮流利用直角坐标下功率方程为二次函数的特性，在潮流第k次迭代求出状态变量的修正量Δx^(k)，Δx^(k)＝J^(k)-1f(x^(k))，其中，J^(k)为第k次迭代的雅克比矩阵，f(x^(k))为将第k次迭代求出状态变量x^(k)代入潮流方程组，雅克比矩阵的具体形式为：The optimal multiplier power flow uses the characteristic that the power equation is a quadratic function in Cartesian coordinates, and obtains the correction amount Δx ^(k) of the state variable in the k-th iteration of the power flow, Δx ^(k) = J ^(k)-1 f(x ^(k) ), where J ^(k) is the Jacobian matrix of the k-th iteration, f(x ^(k) ) is the state variable x ^(k) obtained in the k-th iteration and substituted into the power flow equations, and the Jacobian matrix The specific form is:

$\frac{dF f ((β β))}{dβ dβ} = = 00$

在找到崩溃临界点之前，随迭代进行，β越来越小，直至为0，此时目标函数维持在一个正值上，对应的状态变量x^*为潮流的最小二乘解，对应的雅克比矩阵J(x^*)奇异。Before the critical point of collapse is found, as the iteration proceeds, β becomes smaller and smaller until it is 0. At this time, the objective function is maintained at a positive value, and the corresponding state variable x ^* is the least squares solution of the power flow, and the corresponding Jacobian The matrix J(x ^* ) is singular.

2、根据牛顿迭代法收敛情况分析电压稳定裕度，并区分电压崩溃点类型；2. Analyze the voltage stability margin according to the convergence of the Newton iterative method, and distinguish the types of voltage collapse points;

若在步骤1的迭代中，出现某个节点反复发生PV/PQ类型转换的情况,此节点无功出力约束是导致系统发生电压崩溃起作用的约束，发生约束诱导型电压崩溃，此节点为电压崩溃点；If in the iteration of step 1, a node repeatedly undergoes PV/PQ type conversion, the reactive power output constraint of this node is a constraint that causes voltage collapse to occur in the system, and a constraint-induced voltage collapse occurs, and this node is a voltage crash point;

若在步骤1的迭代中，出现某几个节点反复发生PV/PQ类型转换的情况,其机理与单节点反复转换类似，则记录这些节点，每次选1个节点i，按所述步骤1计算潮流，潮流收敛后，根据最终的雅克比矩阵计算灵敏度，若满足以下条件：If in the iteration of step 1, some nodes repeatedly undergo PV/PQ type conversion, the mechanism is similar to that of a single node, then record these nodes, select one node i each time, and follow the step 1 Calculate the power flow, after the power flow converges, calculate the sensitivity according to the final Jacobian matrix, if the following conditions are met:

则节点i即为引起约束诱导型电压崩溃的节点，其中，V_Gi为节点i发电机电压，Q_Gi为节点i发电机注入的无功功率，Then node i is the node that causes the constraint-induced voltage collapse, where V _Gi is the generator voltage of node i, Q _Gi is the reactive power injected by the generator of node i,

若在步骤1的迭代中，电压稳定裕度的修正量小于预设精度，预设精度视计算精确度要求而定，本发明中取0.001，则电压崩溃点的类型为鞍结型，则得到最小二乘解后，需要进一步修正电压稳定裕度λ，搜寻电压崩溃点，即搜寻对应电压崩溃点的电压稳定裕度λ_critical，具体为：If in the iteration of step 1, the correction amount of the voltage stability margin is less than the preset accuracy, the preset accuracy depends on the calculation accuracy requirements. In the present invention, if it is 0.001, the type of the voltage collapse point is the saddle junction type, and then we get After the least squares solution, it is necessary to further modify the voltage stability margin λ to search for the voltage collapse point, that is, to search for the voltage stability margin λ _critical corresponding to the voltage collapse point, specifically:

如图3所示，定义∑为介于潮流方程有解和无解区域之间的边界，所得的最小二乘解x^*满足（1）f(x^*)位于∑上，对应的雅克比矩阵J(x^*)奇异；（2）J(x^*)的零特征值对应的左特征向量ω^*与∑在f(x^*)处正交。节点净注入功率向量S组成一个空间，S^λ，S′，S^m三者均为空间中功率向量，定义S′为当前功率向量，定义S^m为∑在状态变量x^*处的切平面上距当前功率向量S′欧氏距离最近的点，定义S^λ为切平面与节点注入功率变化方向向量b的交点，S^λ与S^critical重合，S^critical表示电压崩溃临界点对应的功率向量，定义电压稳定裕度的修正量Δλ为S′与S^λ间负荷参数差值，则S^λ可表示为下式：As shown in Figure 3, ∑ is defined as the boundary between the solution and non-solution regions of the power flow equation. The obtained least squares solution x ^* satisfies (1) f(x ^* ) is located on ∑, and the corresponding Jacobian matrix J(x ^* ) is singular; (2) The left eigenvector ω ^* and ∑ corresponding to the zero eigenvalue of J(x ^* ) are orthogonal at f(x ^* ). The net injected power vector S of the node forms a space, S ^λ , S′, and S ^m are all power vectors in the space, define S′ as the current power vector, and define S ^m as ∑ on the tangent plane at the state variable x ^* The point with the closest Euclidean distance to the current power vector S′, define S ^λ as the intersection point of the tangent plane and the node injection power change direction vector b, S ^λ coincides with S ^critical , and S ^critical represents the power vector corresponding to the critical point of voltage collapse, defined The correction amount Δλ of the voltage stability margin is the load parameter difference between S′ and S ^λ , then S ^λ can be expressed as the following formula:

S^λ＝S′-ΔλbS ^λ = S'-Δλb

∑为凸曲面时，电压稳定裕度λ的修正式为：When Σ is a convex surface, the correction formula of the voltage stability margin λ is:

λ^(k+1)＝λ^(k)-Δλ^(k+1) λ ^(k+1) = λ ^{(k) -} Δλ ^(k+1)

∑为凹曲面时，When Σ is a concave surface,

3、如果电力系统发生故障，仍然按照从可行域外出发进行基于最优乘子的牛顿迭代法，求取电压稳定裕度以及确定电压崩溃临界点，在迭代过程中，迭代初始点选择所述步骤1正常运行方式下求取的电压崩溃临界点裕度，即λ_critical；3. If the power system fails, still follow the Newton iterative method based on the optimal multiplier starting from outside the feasible region to obtain the voltage stability margin and determine the critical point of voltage collapse. During the iterative process, select the initial point of the iterative step 1 The voltage collapse critical point margin calculated under normal operation mode, namely λ _critical ;

4、分析步骤3求取的电压稳定裕度，若电压稳定裕度不小于0，则为稳定性故障，根据电压稳定裕度大小对稳定性故障进行严重程度排序，电压稳定裕度值越小，故障越严重；若电压稳定裕度小于0，则为失稳故障，首先对故障进行参数化，设反映系统故障参数为μ，且参数范围为：0＜μ＜1，4. Analyze the voltage stability margin obtained in step 3. If the voltage stability margin is not less than 0, it is a stability fault. The severity of the stability fault is sorted according to the voltage stability margin. The smaller the voltage stability margin value is , the fault is more serious; if the voltage stability margin is less than 0, it is an unstable fault. First, the fault is parameterized, and the parameter reflecting the system fault is set to μ, and the parameter range is: 0<μ<1,

故障参数μ为0时表示故障未发生，为1时表示故障彻底发生，对于一个失稳故障来说，故障彻底发生后潮流方程无解，因此通过从可行域外基于最优乘子的牛顿迭代方法，从μ＝0这一潮流可行域外出发，即在迭代过程中，迭代初始点选择故障参数为0时的电压稳定裕度，随着μ逐渐增加，找到电压崩溃临界点，对应的μ值即作为故障排序的参数。μ值越大，故障越严重，μ＝1对应的最严重故障。When the fault parameter μ is 0, it means that the fault has not occurred, and when it is 1, it means that the fault has completely occurred. For an unstable fault, the power flow equation has no solution after the fault completely occurs. Therefore, the Newton iteration method based on the optimal multiplier from outside the feasible region , starting from outside the power flow feasible region of μ = 0, that is, in the iterative process, the initial point of the iteration selects the voltage stability margin when the fault parameter is 0, and as μ gradually increases, the critical point of voltage collapse is found, and the corresponding μ value is as a parameter for fault sorting. The larger the value of μ, the more serious the fault, and μ=1 corresponds to the most serious fault.

5、计算步骤4）求取的电压崩溃临界点故障参数，根据故障参数大小对失稳故障进行严重程度排序，故障参数越大，故障越严重；故障参数μ的计算按下述参数化潮流方程求出：5. Calculation step 4) Calculate the fault parameters at the critical point of voltage collapse, and sort the severity of the instability faults according to the size of the fault parameters. The larger the fault parameter, the more serious the fault; the fault parameter μ is calculated according to the following parameterized power flow equation find:

$\{\begin{matrix} {P P}_{Gi Gi} - - μ μ {P P}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} cos cos {θ θ}_{ij ij} + + {B B}_{ij ij} sin sin {θ θ}_{ij ij})) - - {V V}_{i i}^{22} {G G}_{ii i} = = 00 \\ {Q Q}_{Si Si} - - μ μ {Q Q}_{Di Di} - - {V V}_{i i} \underset{j j &Element; &Element; I I}{Σ Σ} {V V}_{j j} (({G G}_{ij ij} sin sin {θ θ}_{ij ij} - - {B B}_{ij ij} cos cos {θ θ}_{ij ij})) + + {V V}_{i i}^{22} {B B}_{ii i} = = 00 \end{matrix}$

当出现多重故障时，多重复杂故障的系统参数化潮流方程是以上几种情形的线性叠加，仅仅采用一个参数μ，多重故障以一定的参数水平发生，并进行衡量，When multiple faults occur, the system parameterized power flow equation of multiple complex faults is a linear superposition of the above situations. Only one parameter μ is used, and multiple faults occur at a certain parameter level and are measured.

6、如图4所示，综合步骤4和步骤5的两种排序，按照电压稳定裕度值从大到小，然后故障参数从小到大的顺序，给出故障统一排序，指导电力系统运行。6. As shown in Figure 4, combining the two sorts of steps 4 and 5, according to the voltage stability margin value from large to small, and then the order of fault parameters from small to large, a unified fault ranking is given to guide the operation of the power system.

Claims

1. the air extract analysis of electric power system and system failure sort method, is characterized in that, comprise the following steps:

(1) according to the monitoring result to electric power system, judge whether electric power system breaks down, if electric power system is not broken down, namely under normal operating mode, then carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for the voltage stability margin of electric power system on predetermined load growing direction and determine voltage collapse critical point, then proceeding to step 2); If electric power system is broken down, then directly enter step 3);

(2) according to Newton iteration method convergence situation analysis voltage stability margin, and voltage collapse vertex type is distinguished;

(3) if electric power system is broken down, still according to the Newton iteration method of carrying out from feasible zone outside based on Optimal Multiplier, ask for voltage stability margin and determine voltage collapse critical point, in an iterative process, the voltage stability margin asked under selecting described step (1) normal operating mode of iteration initial point and voltage collapse critical point;

(4) voltage stability margin that described step (3) is asked for is analyzed, if voltage stability margin is not less than 0, is then stable fault, according to voltage stability margin size, order of severity sequence is carried out to stable fault, voltage stability margin value is less, and fault is more serious; If voltage stability margin is less than 0, be then unstability fault, first parametrization carried out to fault, then ask for voltage collapse critical point according to the Newton iteration method based on Optimal Multiplier from feasible zone outside, in an iterative process, voltage stability margin when iteration initial point selects fault parameter to be 0;

(5) calculate the voltage collapse critical point fault parameter that described step (4) is asked for, carry out order of severity sequence according to fault parameter size to unstability fault, fault parameter is larger, and fault is more serious;

(6) two kinds of sequences of combining step (4) and step (5), according to voltage stability margin value from big to small, then fault parameter order from small to large, to unified sequence of being out of order, instructs power system operation.

2. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, in described step (1), carry out the Newton iteration method based on Optimal Multiplier from feasible zone outside, ask for voltage stability margin and determine that the concrete grammar of voltage collapse critical point is:

The growing direction of load and generator is defined by following formula:

P _Li＝P _Li0+λb _Pi

Q _Li＝Q _Li0+λb _Qi

P _Gi＝P _Gi0+λb _Gi

Wherein, λ is voltage stability margin, P _li0, Q _li0be respectively active power and reactive power that node i injects under normal condition, P _li, Q _libe respectively active power and reactive power that node i injects under current state, P _gi0, P _gifor the active power that node i generator injects under normal condition and under current state, b _pi, b _qi, b _gibe respectively that the load of node i is meritorious exerts oneself, idlely exert oneself and the change direction vector of generator output;

Power flow equation with parameter is expressed as:

f(x,λ)＝f(x)-S＝0

S＝S ₀+λb

Wherein, S ₀, S is respectively under normal condition and current state lower node and generator injecting power vector, S ₀=(P _li0, Q _li0, P _gi0), S=(P _li, Q _li, P _gi), b is node and generator injecting power change direction vector, b=(b _pi, b _qi, b _gi), x is state variable;

Adopt the Newton iteration method of Optimal Multiplier, iteration initial point is chosen and is met the voltage stability margin value of trend outside feasible zone, obtains state variable x in trend kth time iteration ^(k)correction amount x ^(k),

Δ x ^(k)=J ^(k)-1f (x ^(k)), wherein, J ^(k)for the Jacobian matrix of kth time iteration, f (x ^(k)) for kth time iteration is obtained state variable x ^(k)substitute into power flow equation group, the concrete form of Jacobian matrix is:

J = [\begin{matrix} \frac{&PartialD; f_{1}}{&PartialD; x_{1}} & \frac{&PartialD; f_{1}}{&PartialD; x_{2}} & . . . & \frac{&PartialD; f_{1}}{&PartialD; x_{n}} \\ \frac{&PartialD; f_{2}}{&PartialD; x_{1}} & \frac{&PartialD; f_{2}}{&PartialD; x_{2}} & . . . & \frac{&PartialD; f_{2}}{&PartialD; x_{n}} \\ . . . \\ \frac{&PartialD; f_{n}}{&PartialD; x_{1}} & \frac{&PartialD; f_{n}}{&PartialD; x_{2}} & . . . & \frac{&PartialD; f_{n}}{&PartialD; x_{n}} \end{matrix}]

Correction amount x is multiplied by with a scalar multiplier β ^(k), then revise state variable x ^(k), the sub-β of its Scalar Multiplication is tried to achieve by following target function:

\min F (β) = \frac{1}{2} Σ_{i = 1}^{2 n} {f_{i}}^{2} (x^{(k)} + βΔ x^{(k)})

F _i() represents i-th equation in equation group f (x, λ)=f (x)-S=0, and 2n is the number of equation, obtains scalar multiplier β by asking for F (β) extreme value, equation as shown in the formula:

\frac{dF (β)}{dβ} = 0;

The state variable x that scalar multiplier β is corresponding when being 0 ^*for the least square solution of power flow equation, voltage stability margin λ when β is 0 _criticalbe the margin value that voltage collapse critical point is corresponding.

3. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, the specific implementation process of described step (2) is:

If in the iteration of step (1), occur that the situation of PV/PQ type conversion occurs certain node repeatedly, then the type of voltage collapse point is constraint induction type, and this node is voltage collapse point;

If in the iteration of step (1), occur that the situation of PV/PQ type conversion occurs certain several node repeatedly, then the type of voltage collapse point is constraint induction type, record these nodes, select 1 node i at every turn, calculate trend by described step (1), after trend convergence, according to final Jacobian matrix meter sensitivity, if meet the following conditions:

\{\begin{matrix} \frac{dλ}{d V_{Gi}} > 0 \\ \frac{dλ}{d Q_{Gi}} > 0 \end{matrix}

Then node i is voltage collapse point, wherein, and V _gifor node i generator voltage, Q _gifor the reactive power that node i generator injects,

If in the iteration of step (1), the correction of voltage stability margin is less than default precision, then the type of voltage collapse point is saddle junction type, after then obtaining least square solution, need to revise voltage stability margin λ further, search voltage collapse point, namely search the voltage stability margin λ of corresponding voltage collapse point _critical, be specially:

Definition Σ has between power flow equation to separate and without the border of separating between region, node clean injecting power vector S forms a space, S ^λ, S', S ^mthree is vector power in space, and S' is current power vector, definition S ^mfor Σ is at state variable x ^*point nearest apart from current power vector S' Euclidean distance on the section at place, definition S ^λfor section and node injecting power change direction vector b intersection point, S ^λwith S ^criticaloverlap, S ^criticalrepresent the vector power that voltage collapse critical point is corresponding, the correction amount λ of definition voltage stability margin is S' and S ^λbetween load parameter difference, then S ^λcan following formula be expressed as:

S ^λ＝S'-Δλb

Δλ = \frac{{| | S^{'} - f (x^{*}) | |}_{2} \cos θ_{1}}{{| | b | |}_{2} \cos θ_{2}}

Wherein, θ ₁represent vector power S ^mwith the power flow equation f (x at least square solution place ^*) between angle, θ ₂represent vector power S ^mand S ^λbetween angle,

When Σ is convex surface, the amendment type of voltage stability margin λ is:

λ ^(k+1)＝λ ^(k)-Δλ ^(k+1)

When Σ is concave curved surface,

If Δ λ ^(k)be greater than default precision, then the amendment type of voltage stability margin λ is:

λ^{(k + 1)} = λ^{(k)} + \frac{Δ λ^{(k)}}{2}

If θ ₁=90 ° or θ ₂=90 ° and θ ₁when ≠ 90 °, then according to the correction amount λ of following formula calculating voltage stability margin:

Δλ = \frac{{| | S^{'} - f (x^{*}) | |}_{2}}{{| | b | |}_{2}}

The amendment type of voltage stability margin λ is: λ ^(k+1)=λ ^(k)-Δ λ ^(k+1).

4. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, described step (5) is carried out parametrization to fault and is referred to, if reflection system failure parameters is μ, and parameter area is:

0＜μ＜1

Fault parameter μ represents that fault does not occur when being 0, represents that fault thoroughly occurs when being 1.

5. the air extract analysis of electric power system according to claim 1 and system failure sort method, it is characterized in that, in described step (5), for different faults, the calculating of fault parameter μ is obtained by following parametrization power flow equation:

(1) the parametrization power flow equation that exits of single generator

\{\begin{matrix} μ P_{Gi} - P_{Di} - V_{i} \underset{j &Element; I}{Σ} V_{j} (G_{ij} \cos θ_{ij} + B_{ij} \sin θ_{ij}) - {V_{i}}^{2} G_{ii} = 0 \\ μ Q_{G \min U} \leq Q_{Gi} \leq μ Q_{G \max U} \end{matrix}

(2) the parametrization power flow equation that exits of single shunt capacitor or reactor

μ Q_{Si} - Q_{Di} - V_{i} \underset{j &Element; I}{Σ} V_{j} (G_{ij} \cos θ_{ij} - B_{ij} \sin θ_{ij}) + {V_{i}}^{2} B_{ii} = 0

(3) the parametrization power flow equation that exits of single load

\{\begin{matrix} P_{Gi} - μ P_{Di} - V_{i} \underset{j &Element; I}{Σ} V_{j} (G_{ij} \cos θ_{ij} + B_{ij} \sin θ_{ij}) - {V_{i}}^{2} G_{ii} = 0 \\ Q_{Si} - μ Q_{Di} - V_{i} \underset{j &Element; I}{Σ} V_{j} (G_{ij} \sin θ_{ij} - B_{ij} \cos θ_{ij}) + {V_{i}}^{2} B_{ii} = 0 \end{matrix}

(4) the parametrization power flow equation that exits of single branch road

\{\begin{matrix} P_{Gi} - P_{Di} - V_{i} \underset{j &Element; I, j &NotEqual; m}{Σ} V_{j} (G_{ij} \cos θ_{ij} + B_{ij} \sin θ_{ij}) - V_{i} V_{m} (μ G_{im} \cos θ_{im} + μ B_{im} \sin θ_{im}) - {V_{i}}^{2} G_{iinew} = 0 \\ Q_{Ri} - Q_{Di} - V_{i} \underset{j &Element; I}{Σ} V_{j} (G_{ij} \sin θ_{ij} - B_{ij} \cos θ_{ij}) - V_{i} V_{m} (μ G_{im} \cos θ_{im} + μ B_{im} \sin θ_{im}) - {V_{i}}^{2} G_{iinew} + {V_{i}}^{2} B_{ii} new = 0 \end{matrix}

If there is multiple faults, then parametrization power flow equation is the linear superposition of each single fault parameter power flow equation in this multiple faults;

Wherein, P _dithe active power of the load absorption of node i; P _gifor the active power that node i generator injects; Q _gifor the reactive power that node i generator injects; Q _difor the reactive power of node i load absorption; Q _sifor shunt capacitor capacity, Q _gmaxU, Q _gminUfor the upper and lower limit that generator reactive exports; Q _rifor the capacity of reactive-load compensation capacitor after fault; V _ifor the voltage magnitude of node i; I is all node set; θ _ijfor the phase angle difference between node i, j; B _ijfor the susceptance between admittance matrix interior joint i, j; G _ijfor the conductance between admittance matrix interior joint i, j; G _iifor the self-conductance of node i; B _iifor node i from susceptance; G _iinewfor branch road i-m break down after self-conductance in system admittance matrix; B _iinewfor branch road i-m break down after in system admittance matrix from susceptance.