CN104362642A

CN104362642A - Dynamic reactive reserved optimizing method for improving long-term voltage stabilization in AC/DC (Alternating Current/Direct Current) power grid

Info

Publication number: CN104362642A
Application number: CN201410584184.0A
Authority: CN
Inventors: 王�琦; 张健; 刘丽平; 刘明松; 林伟芳
Original assignee: State Grid Corp of China SGCC; China Electric Power Research Institute Co Ltd CEPRI
Current assignee: State Grid Corp of China SGCC; China Electric Power Research Institute Co Ltd CEPRI
Priority date: 2014-10-27
Filing date: 2014-10-27
Publication date: 2015-02-18
Anticipated expiration: 2034-10-27
Also published as: CN104362642B

Abstract

The present invention provides a dynamic reactive power backup optimization method for improving medium- and long-term voltage stability of an AC-DC power grid, comprising the following steps: determining a set of key faults affecting medium- and long-term voltage stability of an AC-DC power grid; adjusting reactive power output of dynamic reactive power compensation equipment, And calculate the sensitivity of the dynamic reactive power compensation equipment; sort the m dynamic reactive power compensation equipment, and calculate the weight coefficient of the dynamic reactive power compensation equipment; calculate the dynamic reactive power compensation equipment reserve capacity, establish a dynamic reactive power reserve optimization model, and Solve the dynamic reactive power reserve optimization model. The invention provides auxiliary decision-making support for improving the medium- and long-term voltage stability level of the multi-DC power grid, improves the medium- and long-term voltage stability margin of the large-scale AC-DC power grid, establishes a smooth power transmission channel between the sending and receiving ends, and improves the AC-DC power grid. It is of great significance to improve the transmission capacity of transmission channels and improve the economy and power quality of power grid operation.

Description

Dynamic reactive power reserve optimization method for improving medium and long-term voltage stability of AC and DC power grids

技术领域technical field

本发明属于电力系统技术领域，具体涉及一种提高交直流电网中长期电压稳定的动态无功备用优化方法。The invention belongs to the technical field of electric power systems, and in particular relates to a dynamic reactive power reserve optimization method for improving medium- and long-term voltage stability of AC and DC power grids.

背景技术Background technique

电压稳定问题被国内外学者重视以来，已经发展为多个研究分支，对电压稳定也有了明确合理的定义，经过多年研究努力，电力学者们已经在电压稳定问题的某些领域中取得了丰硕的成果,如对静态电压稳定分析、动态电压稳定中的小干扰电压稳定及暂态电压稳定分析中，都已形成了一套较为完善的研究理论和分析方法，在电力系统调度运行及监测控制等方面都发挥着不可替代的作用。然而目前国内对中长期电压稳定问题的研究尚不够深入，没有形成较为统一的认识，人们对中长期电压失稳机理及过程不能进行详细严谨的分析，因此，研究中长期电压稳定问题具有非常重要的理论意义。Since the problem of voltage stability has been valued by scholars at home and abroad, it has developed into multiple research branches, and there is a clear and reasonable definition of voltage stability. After years of research efforts, electric power scholars have achieved fruitful results in some fields of voltage stability. Achievements, such as static voltage stability analysis, small disturbance voltage stability in dynamic voltage stability, and transient voltage stability analysis, have formed a relatively complete set of research theories and analysis methods, which can be used in power system dispatching operation and monitoring control. play an irreplaceable role. However, at present, domestic research on medium and long-term voltage stability is not deep enough, and no unified understanding has been formed. People cannot conduct detailed and rigorous analysis on the mechanism and process of medium and long-term voltage instability. Therefore, it is very important to study medium and long-term voltage stability. theoretical significance.

电力系统遭受大扰动后，由于负荷的电压灵敏性可能暂时保持电压稳定，然而电力系统中很多影响电压稳定性的元件都存在慢动态动作过程，随着有载调压变压器分接头的换接，以及具有负荷恢复特性的元件功率恢复，经过一个较长的时间过程后，系统仍然存在发生电压崩溃的可能，这就是中长期电压稳定问题，中长期电压稳定分析所研究时域范围为几分钟甚至几十分钟。负荷恢复特性对中长期电压失稳有极大影响，具有恢复特性的元件主要有感应电动机和恒温负荷，同时有载调压变压器分接头换接是造成负荷恢复的重要原因。由于上述3种动态元件的响应时间常数长短不一，从而形成快慢动态结合的中长期电压失稳过程。After the power system suffers a large disturbance, due to the voltage sensitivity of the load, it may temporarily maintain voltage stability. However, many components in the power system that affect voltage stability have a slow dynamic action process. As well as the power recovery of components with load recovery characteristics, after a long period of time, the system still has the possibility of voltage collapse, which is the problem of medium and long-term voltage stability. dozens of minutes. Load recovery characteristics have a great impact on medium and long-term voltage instability. The components with recovery characteristics mainly include induction motors and constant temperature loads. At the same time, the tap change of on-load tap changer transformers is an important reason for load recovery. Since the response time constants of the above three kinds of dynamic elements are different in length, a mid- to long-term voltage instability process combining fast and slow dynamics is formed.

当前，缺乏有效、快速、适应性强的电压稳定控制方法也是引发大停电事故的重要原因之一。我国虽然未曾发生由电压稳定问题引起的大停电事故，但随着“西电东送，南北互供”电力系统联网格局的形成，负荷中心水平不断增长，大容量远距离输电不断增加，我国电力系统的电压稳定性问题日益突出，发生电压失稳事故的几率也越来越大。由于电压稳定问题具有隐蔽性和突发性，事故期间难以察觉，一旦发生电压崩溃，在我国当前电网实际情况下，势必造成极其巨大的损失。因此，研究提高中长期电压稳定的动态无功备用优化问题，有效防止电压失稳和电压崩溃事故发生，具有重要的理论价值和实际意义。At present, the lack of effective, rapid and adaptable voltage stability control methods is also one of the important reasons for causing blackouts. Although my country has never had a major power outage caused by voltage stability problems, with the formation of the "West-to-East Power Transmission, North-South Mutual Supply" power system network pattern, the level of load centers has continued to increase, and large-capacity long-distance transmission has continued to increase. The problem of voltage stability of the system is becoming more and more prominent, and the probability of voltage instability accidents is also increasing. Due to the concealment and suddenness of the voltage stability problem, it is difficult to detect it during the accident. Once a voltage collapse occurs, it will inevitably cause extremely huge losses in the actual situation of my country's current power grid. Therefore, it is of great theoretical value and practical significance to study the optimization problem of dynamic reactive power reserve to improve medium and long-term voltage stability and effectively prevent voltage instability and voltage collapse accidents.

发明内容Contents of the invention

为了克服上述现有技术的不足，本发明提供一种提高交直流电网中长期电压稳定的动态无功备用优化方法，为提高多直流落点电网中长期电压稳定水平提供了辅助决策支持，对提高大规模交直流电网中长期电压稳定裕度，建立送、受端之间畅通的电力传输通道，提升交直流输电通道输送能力，改善电网运行的经济性和电能质量，均具有重大意义。In order to overcome the deficiencies of the above-mentioned prior art, the present invention provides a dynamic reactive power reserve optimization method for improving the medium- and long-term voltage stability of the AC-DC power grid, which provides auxiliary decision-making support for improving the medium- and long-term voltage stability level of the multi-DC power grid, and is useful for improving It is of great significance to establish a medium- and long-term voltage stability margin for large-scale AC and DC power grids, establish a smooth power transmission channel between sending and receiving ends, improve the transmission capacity of AC and DC transmission channels, and improve the economy and power quality of power grid operation.

为了实现上述发明目的，本发明采取如下技术方案：In order to realize the above-mentioned purpose of the invention, the present invention takes the following technical solutions:

本发明提供一种提高交直流电网中长期电压稳定的动态无功备用优化方法，所述方法包括以下步骤：The present invention provides a dynamic reactive power backup optimization method for improving medium and long-term voltage stability of an AC-DC power grid. The method includes the following steps:

步骤1：确定影响交直流电网中长期电压稳定的关键故障集合；Step 1: Determine the key fault sets that affect the long-term voltage stability of the AC-DC grid;

步骤2：调整动态无功补偿设备的无功出力，并计算动态无功补偿设备的灵敏度；Step 2: Adjust the reactive power output of the dynamic reactive power compensation equipment, and calculate the sensitivity of the dynamic reactive power compensation equipment;

步骤3：对m个动态无功补偿设备进行排序，并计算动态无功补偿设备的权重系数；Step 3: sort the m dynamic reactive power compensation equipment, and calculate the weight coefficient of the dynamic reactive power compensation equipment;

步骤4：计算动态无功补偿设备备用容量，建立动态无功备用优化模型，并求解该动态无功备用优化模型。Step 4: Calculate the reserve capacity of dynamic reactive power compensation equipment, establish a dynamic reactive power reserve optimization model, and solve the dynamic reactive power reserve optimization model.

所述步骤1中，对交直流电网进行故障扫描，计算负荷母线i的电压稳定裕度K_MVSi，有：In the step 1, a fault scan is performed on the AC/DC power grid, and the voltage stability margin K _MVSi of the load bus i is calculated, as follows:

${K K}_{MVSi MVSi} = = \frac{| | {Z Z}_{Li Li} | | - - | | {Z Z}_{Ti Ti} | |}{| | {Z Z}_{Li Li} | |}$

其中，Z_Li为负荷母线i处的负荷等值阻抗，Z_Ti为系统戴维南等值阻抗；Among them, Z _Li is the load equivalent impedance at load bus i, and Z _Ti is the Thevenin equivalent impedance of the system;

选取K_MVSi最小值为交直流电网的电压稳定裕度，记为K_MVSI，根据交直流电网的电压稳定裕度值确定故障的严重情况，得到关键故障，从而得到关键故障集合。The minimum value of K _MVSi is selected as the voltage stability margin of the AC-DC grid, which is denoted as K _MVSI . According to the voltage stability margin value of the AC-DC grid, the seriousness of the fault is determined, and the key faults are obtained, thereby obtaining the key fault set.

所述步骤2中，动态无功补偿设备包括发电机、静止无功补偿器和静止同步补偿器。In the step 2, the dynamic var compensation equipment includes a generator, a static var compensator and a static synchronous compensator.

所述步骤2具体包括以下步骤：Described step 2 specifically comprises the following steps:

步骤2-1：分别调整各动态无功补偿设备的无功出力，并对关键故障再次进行时域仿真；Step 2-1: Adjust the reactive power output of each dynamic reactive power compensation device separately, and conduct time domain simulation again for key faults;

步骤2-2：在中长期时间尺度下，针对某故障l，计算动态无功补偿设备j的灵敏度SI_l,j；Step 2-2: Calculate the sensitivity SI _l ,j of dynamic reactive power compensation equipment j for a certain fault l on the medium and long-term time scale;

步骤2-3：在中长期时间尺度下，针对多个故障，计算动态无功补偿设备j的灵敏度SI_j。Step 2-3: Calculate the sensitivity SI _j of the dynamic reactive power compensation device j for multiple faults on a medium and long-term time scale.

所述步骤2-2中，针对某故障l，动态无功补偿设备j的灵敏度SI_l,j表示为：In the step 2-2, for a certain fault l, the sensitivity SI _{l,j of the dynamic reactive power compensation device j} is expressed as:

${SI Si}_{l l,, j j} = = \frac{{k k}_{MVSI MVSI,, l l} (({Q Q}_{j j 00} + + {ΔQ ΔQ}_{j j})) - - {k k}_{MVSI MVSI,, l l} (({Q Q}_{j j 00}))}{{ΔQ ΔQ}_{Rj Rj}}$

其中，Q_j0为动态无功补偿设备j的初始无功出力；ΔQ_j为调整动态无功补偿设备j的无功功率变化量；ΔQ_Rj为调整动态无功补偿设备j的无功备用变化量；k_MVSI,l(Q_j0+ΔQ_j)为调整动态无功补偿设备j的无功出力后，在故障F_l下，交直流电网的负荷裕度值；k_MVSI,l(Q_j0)为调整动态无功补偿设备j的无功出力前，在故障F_l下，交直流电网的负荷裕度值。Among them, Q _j0 is the initial reactive power output of dynamic reactive power compensation equipment j; ΔQ _j is the reactive power variation of adjusting dynamic reactive power compensation equipment j; ΔQ _Rj is the reactive power reserve variation of adjusting dynamic reactive power compensation equipment j ; k _MVSI,l (Q _j0 +ΔQ _j ) is the load margin value of the AC/DC power grid under fault F _l after adjusting the reactive output of dynamic reactive power compensation equipment j; k _MVSI,l (Q _j0 ) is Before adjusting the reactive power output of the dynamic reactive power compensation equipment j, the load margin value of the AC and DC power grid under the fault F _l .

所述步骤2-3中，针对多个故障，动态无功补偿设备j的灵敏度SI_j表示为：In the step 2-3, for multiple faults, the sensitivity SI _j of the dynamic reactive power compensation device j is expressed as:

${SI Si}_{j j} = = {Σ Σ}_{l l = = 11}^{{N N}_{l l}} {SI Si}_{l l,, j j}$

其中，N_l为关键故障总数。Among them, N _l is the total number of critical faults.

所述步骤3具体包括以下步骤：Described step 3 specifically comprises the following steps:

步骤3-1：根据SI_j对m个动态无功补偿设备进行排序，SI_j最大值表征该动态无功补偿设备对中长期电压稳定的贡献程度最大，贡献程度大的动态无功补偿设备留出更多无功备用量；Step 3-1: sort the m dynamic reactive power compensation equipment according to SI _j , the maximum value of SI _j indicates that the dynamic reactive power compensation equipment contributes the most to the medium and long-term voltage stability, and the dynamic reactive power compensation equipment with a large contribution is reserved Generate more reactive power reserves;

步骤3-2：以SI_j最大值SI_max为基准，归一化处理SI_j，计算动态无功补偿设备的权重系数p_j，有p_j＝SI_j/|SI_max|。Step 3-2: Based on the maximum value of SI _j SI _max , normalize SI _j and calculate the weight coefficient p _j of the dynamic reactive power compensation equipment, p _j = SI _j /|SI _max |.

所述步骤4具体包括以下步骤：Described step 4 specifically comprises the following steps:

步骤4-1：计算动态无功补偿设备的备用容量Q_RM；Step 4-1: Calculate the reserve capacity Q _RM of the dynamic reactive power compensation equipment;

步骤4-2：以提高Q_RM作为动态无功备用优化目标，建立动态无功备用优化模型；Step 4-2: Taking improving Q _RM as the optimization goal of dynamic reactive power reserve, establishing a dynamic reactive power reserve optimization model;

步骤4-3：采用遗传算法求解该动态无功备用优化模型。Step 4-3: The genetic algorithm is used to solve the dynamic reactive power reserve optimization model.

所述步骤4-1中，动态无功补偿设备的备用容量Q_RM表示为：In the step 4-1, the reserve capacity Q _RM of the dynamic reactive power compensation equipment is expressed as:

${Q Q}_{RM RM} = = {Σ Σ}_{j j = = 11}^{m m} {p p}_{j j} (({Q Q}_{gj gj max max} - - {Q Q}_{gj gj}))$

其中，Q_gjmax为中长期电压稳定中动态无功补偿设备j的无功出力上限，Q_gj为动态无功补偿设备j的当前无功出力。Among them, Q _gjmax is the upper limit of reactive power output of dynamic reactive power compensation device j in medium and long-term voltage stability, and Q _gj is the current reactive power output of dynamic reactive power compensation device j.

所述步骤4-2中，动态无功备用优化模型的目标函数为：In the step 4-2, the objective function of the dynamic reactive power reserve optimization model is:

$max max {Q Q}_{RM RM} = = {Σ Σ}_{j j = = 11}^{m m} {p p}_{j j} (({Q Q}_{gj gj max max} - - {Q Q}_{gj gj}))$

动态无功备用优化模型的约束条件包括潮流方程约束和变量约束；所述变量约束为控制变量约束和状态变量约束；The constraints of the dynamic reactive power reserve optimization model include power flow equation constraints and variable constraints; the variable constraints are control variable constraints and state variable constraints;

(1)潮流方程约束：(1) Power flow equation constraints:

在动态无功备用优化模型中，各个节点的有功出力和无功出力都满足以下潮流方程，有：In the dynamic reactive power reserve optimization model, the active output and reactive output of each node satisfy the following power flow equations, which are:

$\{\begin{matrix} {P P}_{Gi Gi} - - {P P}_{Li Li} - - {P P}_{ti ti ((dc dc))} - - {V V}_{i i} {Σ Σ}_{r r = = 11}^{n no} {V V}_{r r} (({G G}_{ir ir} cos cos {δ δ}_{ir ir} + + {B B}_{ir ir} sin sin {δ δ}_{ir ir})) = = 00 \\ {Q Q}_{Gi Gi} + + {Q Q}_{Ci Ci} - - {Q Q}_{Li Li} - - {Q Q}_{ti ti ((dc dc))} - - {V V}_{i i} {Σ Σ}_{r r = = 11}^{n no} {V V}_{r r} (({G G}_{ir ir} sin sin {δ δ}_{ir ir} - - {B B}_{ir ir} cos cos {δ δ}_{ir ir})) = = 00 \end{matrix}$

其中，P_Gi和Q_Gi分别为电力系统中发电机节点的有功出力和无功出力；P_Li和Q_Li分别为负荷节点的有功出力和无功出力；Q_Ci为节点的无功补偿容量；G_ir和B_ir分别为节点i、r之间的电导和电纳；V_i和V_r分别为节点i、r的电压；δ_ir为节点i、r之间的电压相角差；n为节点总数；P_ti(dc)和Q_ti(dc)分别为直流节点的有功输入和无功输入，分为以下两种情况：Among them, P _Gi and Q _Gi are the active power output and reactive power output of the generator node in the power system, respectively; P _Li and Q _Li are the active power output and reactive power output of the load node, respectively; Q _Ci is the reactive power compensation capacity of the node; G _ir and B _ir are the conductance and susceptance between nodes i and r respectively; V _i and V _r are the voltages of nodes i and r respectively; δ _ir is the voltage phase angle difference between nodes i and r; n is The total number of nodes; P _ti(dc) and Q _ti(dc) are the active input and reactive input of DC nodes respectively, which are divided into the following two cases:

1)节点i在整流侧换流母线上，P_ti(dc)和Q_ti(dc)分别表示为：1) Node i is on the commutation bus on the rectifier side, P _ti(dc) and Q _ti(dc) are expressed as:

$\{\begin{matrix} {P P}_{ti ti ((dc dc))} = = {k k}_{p p} {U u}_{dR d} {I I}_{d d} \\ {Q Q}_{ti ti ((dc dc))} = = {k k}_{p p} {I I}_{d d} \sqrt{{((\frac{33 \sqrt{22}}{{πK πK}_{dR d}} {bV v}_{R R}))}^{22} - - {U u}_{dR d}^{22}} \end{matrix}$

其中，k_p为换流器的极数；U_dR为整流侧直流电压；I_d为直流线路电流；K_dR为整流侧换流变压器变比；b为每极的6脉波串联桥数；V_R为整流侧的交流母线电压幅值；Among them, k _p is the number of poles of the converter; U _dR is the DC voltage on the rectification side; I _d is the DC line current; K _dR is the conversion ratio of the converter transformer on the rectification side; b is the number of 6-pulse series bridges for each pole; _VR is the amplitude of the AC bus voltage on the rectifier side;

2)节点i在逆变侧换流母线上，P_ti(dc)和Q_ti(dc)分别表示为：2) Node i is on the inverter side commutation bus, P _ti(dc) and Q _ti(dc) are expressed as:

$\{\begin{matrix} {P P}_{ti ti ((dc dc))} = = - - {k k}_{p p} {U u}_{dI iGO} {I I}_{d d} \\ {Q Q}_{ti ti ((dc dc))} = = {k k}_{p p} {I I}_{d d} \sqrt{{((\frac{33 \sqrt{22}}{{πK πK}_{dI iGO}} {bV v}_{I I}))}^{22} - - {U u}_{dI iGO}^{22}} \end{matrix}$

其中，U_dI为逆变侧直流电压；K_dI为逆变侧换流变压器变比；V_I为逆变侧的交流母线电压幅值；Among them, _UdI is the DC voltage of the inverter side; _KdI is the conversion ratio of the converter transformer on the inverter side; V _I is the AC bus voltage amplitude on the inverter side;

(2)控制变量约束：(2) Control variable constraints:

$\{\begin{matrix} {V V}_{Gi Gi min min} \leq \leq {V V}_{Gi Gi} \leq \leq {V V}_{Gi Gi max max},, i i = = 1,2 1,2,, . . . . . .,, {N N}_{G G} \\ {V V}_{SVCg SVC min min} \leq \leq {V V}_{SVCg SVC} \leq \leq {V V}_{SVCg SVC max max},, g g = = 1,2 1,2,, . . . . . .,, {N N}_{SVC SVC} \\ {V V}_{SVGh wxya min min} \leq \leq {V V}_{SVGh wxya} \leq \leq {V V}_{SVGh wxya max max},, h h = = 1,2 1,2,, . . . . . .,, {N N}_{SVG SVG} \\ {Q Q}_{Cu Cu min min} \leq \leq {Q Q}_{Cu Cu} \leq \leq {Q Q}_{Cu Cu max max},, u u = = 1,2 1,2,, . . . . . .,, {N N}_{C C} \\ {T T}_{k k min min} \leq \leq {T T}_{k k} \leq \leq {T T}_{k k max max},, k k = = 1,2 1,2,, . . . . . .,, {N N}_{T T} \\ {U u}_{dl dl min min} \leq \leq {U u}_{dl dl} \leq \leq {U u}_{dl dl max max},, l l = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {I I}_{dm dm min min} \leq \leq {I I}_{dm dm} \leq \leq {I I}_{dm dm max max},, m m = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {P P}_{dn dn min min} \leq \leq {P P}_{dn dn} \leq \leq {P P}_{dn dn max max},, n no = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {θ θ}_{dr dr min min} \leq \leq {θ θ}_{dr dr} \leq \leq {θ θ}_{dr dr max max},, r r = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \end{matrix}$

其中，N_G、N_SVC、N_SVG、N_C、N_T和N_dc分别为发电机节点数、静止无功补偿器节点数、静止同步补偿器节点数、并联电容器节点数、变压器可调分接头数和直流网络节点数；V_Gi为发电机节点的端电压，V_Gimin和V_Gimax分别为V_Gi的下限值和上限值；V_SVCg为静止无功补偿器节点的端电压，V_SVCgmin和V_SVCgmax分别为V_SVCg的下限值和上限值；V_SVGh为静止同步补偿器节点的端电压，V_SVGhmin和V_SVGhmax分别为V_SVGh下限值和上限值；Q_Cu为并联电容器组的补偿容量，Q_Cumin和Q_Cumax分别为Q_Cu下限值和上限值；T_k为变压器可调分接头，T_kmin和T_kmax分别为T_k下限值和上限值；U_dl、I_dm、P_dn和θ_dr分别为换流器控制电压、控制电流、控制功率以及控制角，U_dlmin和U_dlmax、I_dmmin和I_dmmax、P_dnmin和P_dnmax、θ_drmin和θ_drmax分别表示相应的下限值和上限值；Among them, N _G , N _SVC , _NSVG , N _C , _NT and N _dc are respectively the number of generator nodes, the number of static var compensator nodes, the number of static synchronous compensator nodes, the number of shunt The number of joints and the number of DC network nodes; V _Gi is the terminal voltage of the generator node, V _Gimin and V _Gimax are the lower limit and upper limit of V _Gi respectively; V _SVCg is the terminal voltage of the static var compensator node, V _SVCgmin and V _SVCgmax are the lower limit and upper limit of V _SVCg respectively; V _SVGh is the terminal voltage of the static synchronous compensator node, V _SVGhmin and V _SVGhmax are the lower limit and upper limit of V _SVGh respectively; Q _Cu is the parallel The compensation capacity of the capacitor bank, Q _Cumin and Q _Cumax are the lower limit and upper limit of Q _Cu respectively; T _k is the transformer adjustable tap, T _kmin and T _kmax are the lower limit and upper limit of T _k respectively; U _dl , I _dm , P _dn and θ _dr are the converter control voltage, control current, control power and control angle respectively, U _dlmin and U _dlmax , I _dmmin and I _dmmax , P _dnmin and P _dnmax , θ _drmin and θ _drmax Respectively represent the corresponding lower limit and upper limit;

(3)状态变量约束：(3) State variable constraints:

$\{\begin{matrix} {Q Q}_{Gi Gi min min} \leq \leq {Q Q}_{Gi Gi} \leq \leq {Q Q}_{Gi Gi max max},, i i = = 1,2 1,2,, . . . . . .,, {N N}_{G G} \\ {B B}_{SVCg SVC min min} \leq \leq {B B}_{SVCg SVC} \leq \leq {B B}_{SVCg SVC max max},, g g = = 1,2 1,2,, . . . . . .,, {N N}_{SVC SVC} \\ {I I}_{SVGh wxya min min} \leq \leq {I I}_{SVGh wxya} \leq \leq {I I}_{SVGh wxya max max},, h h = = 1,2 1,2,, . . . . . .,, {N N}_{SVG SVG} \\ {V V}_{Lp LP min min} \leq \leq {V V}_{Lp LP} \leq \leq {V V}_{Lp LP max max},, p p = = 1,2 1,2,, . . . . . .,, {N N}_{L L} \end{matrix}$

其中，N_L为负荷节点数；Q_Gi为发电机节点无功出力，Q_Gimin和Q_Gimax分别为Q_Gi的下限值和上限值；B_SVCg为静止无功补偿器电纳，B_SVCgmin和B_SVCgmax分别为B_SVCg的下限值和上限值；I_SVGh为静止同步补偿器电流幅值，I_SVGhmin和I_SVGhmax分别为I_SVGh的下限值和上限值；V_Lp为负荷节点电压幅值，V_Lpmin和V_Lpmax分别为V_Lp的下限值和上限值。Among them, N _L is the number of load nodes; Q _Gi is the reactive power output of generator nodes, Q _Gimin and Q _Gimax are the lower limit and upper limit of Q _Gi respectively; B _SVCg is the susceptance of static var compensator, B _SVCgmin and B _SVCgmax are the lower limit and upper limit of B _SVCg respectively; _ISVGh is the current amplitude of the static synchronous compensator, _ISVGhmin and _ISVGhmax are the lower limit and upper limit of _ISVGh respectively; V _Lp is the load node The voltage amplitude, V _Lpmin and V _Lpmax are the lower limit and upper limit of V _Lp respectively.

与现有技术相比，本发明的有益效果在于：Compared with prior art, the beneficial effect of the present invention is:

1.目前尚无适用于多馈入直流电网特征的提高中长期电压稳定的动态无功备用优化技术，本发明创新性地提出了一种适用于多馈入直流电网特征提高中长期电压稳定的动态无功备用优化方法；1. At present, there is no dynamic reactive power backup optimization technology suitable for the characteristics of multi-infeed DC grids to improve medium- and long-term voltage stability. Dynamic reactive power reserve optimization method;

2.与基于静态的传统无功备用优化方法相比，本方法详细考虑了系统的动态特性，能够更加准确地确定动态无功补偿设备备用容量，为电网的优化运行提供基础；2. Compared with the static-based traditional reactive power reserve optimization method, this method considers the dynamic characteristics of the system in detail, can more accurately determine the reserve capacity of dynamic reactive power compensation equipment, and provides a basis for the optimal operation of the power grid;

3.通过时域仿真分析，可快捷、方便、准确地确定各无功源的参与因子，可应用于大规模电力系统的动态无功备用优化，克服了传统电力系统动态无功优化的算法只能应用于小系统的缺点。3. Through the time-domain simulation analysis, the participation factors of each reactive power source can be quickly, conveniently and accurately determined, which can be applied to the dynamic reactive power reserve optimization of large-scale power systems, overcoming the traditional power system dynamic reactive power optimization algorithm only Disadvantages that can be applied to small systems.

附图说明Description of drawings

图1是本发明实施例中提高交直流电网中长期电压稳定的动态无功备用优化方法流程图；Fig. 1 is a flowchart of a dynamic reactive power backup optimization method for improving long-term voltage stability of an AC-DC power grid in an embodiment of the present invention;

图2是本发明实施例中采用遗传算法求解动态无功备用优化模型流程图；Fig. 2 is the flow chart of adopting genetic algorithm to solve dynamic reactive standby optimization model in the embodiment of the present invention;

图3是本发明实施中3机10节点修正测试交直流系统示意图；Fig. 3 is a schematic diagram of a 3-machine 10-node correction test AC/DC system in the implementation of the present invention;

图4是本发明实施例中发电机相对功角变化曲线图；Fig. 4 is a curve diagram of relative power angle changes of generators in an embodiment of the present invention;

图5是本发明实施例中发电机2和发电机3的励磁电流曲线图；Fig. 5 is the exciting current graph of generator 2 and generator 3 in the embodiment of the present invention;

图6是本发明实施例中节点9和节点10电压变化曲线图；Fig. 6 is a curve diagram of voltage changes at node 9 and node 10 in an embodiment of the present invention;

图7是本发明实施例中优化前后节点3(发电机G3机端)电压曲线图；Fig. 7 is a voltage curve diagram of node 3 (generator G3 machine terminal) before and after optimization in the embodiment of the present invention;

图8是本发明实施例中优化前后节点10电压曲线图。Fig. 8 is a curve diagram of the voltage of node 10 before and after optimization in the embodiment of the present invention.

具体实施方式Detailed ways

下面结合附图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.

${K K}_{MVSi MVSi} = = \frac{| | {Z Z}_{Li Li} | | - - | | {Z Z}_{Ti Ti} | |}{| | {Z Z}_{Li Li} | |} - - - - - - ((11))$

步骤2-2：在中长期时间尺度下，针对某故障l，计算动态无功补偿设备j的灵敏度SI_l,j；Step 2-2: Calculate the sensitivity SI _l,j of the dynamic reactive power compensation equipment j for a certain fault l under the medium and long-term time scale;

${SI Si}_{l l,, j j} = = \frac{{k k}_{MVSI MVSI,, l l} (({Q Q}_{j j 00} + + {ΔQ ΔQ}_{j j})) - - {k k}_{MVSI MVSI,, l l} (({Q Q}_{j j 00}))}{{ΔQ ΔQ}_{Rj Rj}} - - - - - - ((22))$

${SI Si}_{j j} = = {Σ Σ}_{l l = = 11}^{{N N}_{l l}} {SI Si}_{l l,, j j} - - - - - - ((33))$

${Q Q}_{RM RM} = = {Σ Σ}_{j j = = 11}^{m m} {p p}_{j j} (({Q Q}_{gj gj max max} - - {Q Q}_{gj gj})) - - - - - - ((44))$

$max max {Q Q}_{RM RM} = = {Σ Σ}_{j j = = 11}^{m m} {p p}_{j j} (({Q Q}_{gj gj max max} - - {Q Q}_{gj gj})) - - - - - - ((55))$

(1)潮流方程约束：(1) Power flow equation constraints:

$\{\begin{matrix} {P P}_{Gi Gi} - - {P P}_{Li Li} - - {P P}_{ti ti ((dc dc))} - - {V V}_{i i} {Σ Σ}_{r r = = 11}^{n no} {V V}_{r r} (({G G}_{ir ir} cos cos {δ δ}_{ir ir} + + {B B}_{ir ir} sin sin {δ δ}_{ir ir})) = = 00 \\ {Q Q}_{Gi Gi} + + {Q Q}_{Ci Ci} - - {Q Q}_{Li Li} - - {Q Q}_{ti ti ((dc dc))} - - {V V}_{i i} {Σ Σ}_{r r = = 11}^{n no} {V V}_{r r} (({G G}_{ir ir} sin sin {δ δ}_{ir ir} - - {B B}_{ir ir} cos cos {δ δ}_{ir ir})) = = 00 \end{matrix} - - - - - - ((66))$

$\{\begin{matrix} {P P}_{ti ti ((dc dc))} = = {k k}_{p p} {U u}_{dR d} {I I}_{d d} \\ {Q Q}_{ti ti ((dc dc))} = = {k k}_{p p} {I I}_{d d} \sqrt{{((\frac{33 \sqrt{22}}{{πK πK}_{dR d}} {bV v}_{R R}))}^{22} - - {U u}_{dR d}^{22}} \end{matrix} - - - - - - ((77))$

$\{\begin{matrix} {P P}_{ti ti ((dc dc))} = = - - {k k}_{p p} {U u}_{dI iGO} {I I}_{d d} \\ {Q Q}_{ti ti ((dc dc))} = = {k k}_{p p} {I I}_{d d} \sqrt{{((\frac{33 \sqrt{22}}{{πK πK}_{dI iGO}} {bV v}_{I I}))}^{22} - - {U u}_{dI iGO}^{22}} \end{matrix} - - - - - - ((88))$

(2)控制变量约束：(2) Control variable constraints:

$\{\begin{matrix} {V V}_{Gi Gi min min} \leq \leq {V V}_{Gi Gi} \leq \leq {V V}_{Gi Gi max max},, i i = = 1,2 1,2,, . . . . . .,, {N N}_{G G} \\ {V V}_{SVCg SVC min min} \leq \leq {V V}_{SVCg SVC} \leq \leq {V V}_{SVCg SVC max max},, g g = = 1,2 1,2,, . . . . . .,, {N N}_{SVC SVC} \\ {V V}_{SVGh wxya min min} \leq \leq {V V}_{SVGh wxya} \leq \leq {V V}_{SVGh wxya max max},, h h = = 1,2 1,2,, . . . . . .,, {N N}_{SVG SVG} \\ {Q Q}_{Cu Cu min min} \leq \leq {Q Q}_{Cu Cu} \leq \leq {Q Q}_{Cu Cu max max},, u u = = 1,2 1,2,, . . . . . .,, {N N}_{C C} \\ {T T}_{k k min min} \leq \leq {T T}_{k k} \leq \leq {T T}_{k k max max},, k k = = 1,2 1,2,, . . . . . .,, {N N}_{T T} \\ {U u}_{dl dl min min} \leq \leq {U u}_{dl dl} \leq \leq {U u}_{dl dl max max},, l l = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {I I}_{dm dm min min} \leq \leq {I I}_{dm dm} \leq \leq {I I}_{dm dm max max},, m m = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {P P}_{dn dn min min} \leq \leq {P P}_{dn dn} \leq \leq {P P}_{dn dn max max},, n no = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {θ θ}_{dr dr min min} \leq \leq {θ θ}_{dr dr} \leq \leq {θ θ}_{dr dr max max},, r r = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \end{matrix} - - - - - - ((99))$

其中，N_G、N_SVC、N_SVG、N_C、N_T和N_dc分别为发电机节点数、静止无功补偿器节点数、静止同步补偿器节点数、并联电容器节点数、变压器可调分接头数和直流网络节点数；V_Gi为发电机节点的端电压，V_Gimin和V_Gimax分别为V_Gi的下限值和上限值；V_SVCg为静止无功补偿器节点的端电压，V_SVCgmin和V_SVCgmax分别为V_SVCg的下限值和上限值；V_SVGh为静止同步补偿器节点的端电压，V_SVGhmin和V_SVGhmax分别为V_SVGh下限值和上限值；Q_Cu为并联电容器组的补偿容量，Q_Cumin和Q_Cumax分别为Q_Cu下限值和上限值；T_k为变压器的变比，T_kmin和T_kmax分别为T_k下限值和上限值；U_dl、I_dm、P_dn和θ_dr分别为换流器控制电压、控制电流、控制功率以及控制角，U_dlmin和U_dlmax、I_dmmin和I_dmmax、P_dnmin和P_dnmax、θ_drmin和θ_drmax分别表示相应的下限值和上限值；Among them, N _G , N _SVC , _NSVG , N _C , _NT and N _dc are respectively the number of generator nodes, the number of static var compensator nodes, the number of static synchronous compensator nodes, the number of shunt The number of joints and the number of DC network nodes; V _Gi is the terminal voltage of the generator node, V _Gimin and V _Gimax are the lower limit and upper limit of V _Gi respectively; V _SVCg is the terminal voltage of the static var compensator node, V _SVCgmin and V _SVCgmax are the lower limit and upper limit of V _SVCg respectively; V _SVGh is the terminal voltage of the static synchronous compensator node, V _SVGhmin and V _SVGhmax are the lower limit and upper limit of V _SVGh respectively; Q _Cu is the parallel The compensation capacity of the capacitor bank, Q _Cumin and Q _Cumax are the lower limit and upper limit of Q _Cu respectively; T _k is the transformation ratio of the transformer, T _kmin and T _kmax are the lower limit and upper limit of T _k respectively; U _dl , I _dm , P _dn and θ _dr are the converter control voltage, control current, control power and control angle respectively, U _dlmin and U _dlmax , I _dmmin and I _dmmax , P _dnmin and P _dnmax , θ _drmin and θ _drmax respectively Indicates the corresponding lower limit value and upper limit value;

(3)状态变量约束：(3) State variable constraints:

$\{\begin{matrix} {Q Q}_{Gi Gi min min} \leq \leq {Q Q}_{Gi Gi} \leq \leq {Q Q}_{Gi Gi max max},, i i = = 1,2 1,2,, . . . . . .,, {N N}_{G G} \\ {B B}_{SVCg SVC min min} \leq \leq {B B}_{SVCg SVC} \leq \leq {B B}_{SVCg SVC max max},, g g = = 1,2 1,2,, . . . . . .,, {N N}_{SVC SVC} \\ {I I}_{SVGh wxya min min} \leq \leq {I I}_{SVGh wxya} \leq \leq {I I}_{SVGh wxya max max},, h h = = 1,2 1,2,, . . . . . .,, {N N}_{SVG SVG} \\ {V V}_{Lp LP min min} \leq \leq {V V}_{Lp LP} \leq \leq {V V}_{Lp LP max max},, p p = = 1,2 1,2,, . . . . . .,, {N N}_{L L} \end{matrix} - - - - - - ((1010))$

步骤4-3中，采用遗传算法求解该动态无功备用优化模型；In step 4-3, a genetic algorithm is used to solve the dynamic reactive power reserve optimization model;

遗传算法的基本思想是，在某特定环境下的一群个体，由于环境限制，只有适应性强的可生存，而弱者被淘汰，它们适应环境的优良性状会遗传给后代。GA应用于无功备用优化问题时可以理解为：电力系统下的一组初始潮流解，受各种约束条件约束，通过目标函数评价其优劣，评价值低的被抛弃，只有评价值高的有机会将其特征迭代至下一轮解，最后趋向最优。The basic idea of genetic algorithm is that in a group of individuals in a specific environment, due to environmental constraints, only those with strong adaptability can survive, while the weak are eliminated, and their excellent traits for adapting to the environment will be passed on to future generations. When GA is applied to the optimization problem of reactive power reserve, it can be understood as: a group of initial power flow solutions under the power system are constrained by various constraints, and their advantages and disadvantages are evaluated by the objective function. Those with low evaluation values are discarded, and only those with high evaluation values There is an opportunity to iterate its features to the next round of solutions, and finally tend to be optimal.

具体过程如下：The specific process is as follows:

(1)首先，根据下式随机产生第一代母体，有：(1) First, the first-generation matrix is randomly generated according to the following formula:

X_i＝INT(RND(X_imax-X_iimn))+X_imin (11)X _i =INT(RND(X _imax -X _iimn ))+X _imin (11)

其中，RND为随机数，且0<RND<1；INT(*)为取整；Among them, RND is a random number, and 0<RND<1; INT(*) is rounding;

X_i若为V_Gi，则X_imax、X_imax分别表示发电机节点的端电压上下限；If X _i is V _Gi , then X _imax and X _imax represent the upper and lower limits of the terminal voltage of the generator node respectively;

X_i若为V_SVCg，则X_imax、X_imax分别表示静止无功补偿器节点的端电压上下限；If X _i is V _SVCg , then X _imax and X _imax respectively represent the upper and lower limits of the terminal voltage of the static var compensator node;

X_i若为V_SVGh，则X_imax、X_imax分别表示静止同步补偿器节点的端电压上下限；If X _i is V _SVGh , then X _imax and X _imax respectively represent the upper and lower limits of the terminal voltage of the static synchronous compensator node;

X_i若为Q_Cu，则X_imax、X_imax分别表示并联电容器组的补偿容量上下限；If X _i is Q _Cu , then X _imax and X _imax represent the upper and lower limits of the compensation capacity of the parallel capacitor bank respectively;

X_i若为T_k，则X_imax、X_imax分别表示变压器的变比上下限。If X _i is T _k , then X _imax and X _imax represent the upper and lower limits of the transformation ratio of the transformer respectively.

式(11)使变量的约束方程可转化为整数变量的约束方程。如1+5×0.025％的变压器其YT的取值范围为1～11。编码采用二进制数，每五位顺序表示Y_Vgi、Y_Vsvcg、Y_Vsvgh、Y_Qcu、Y_Tk的值：Equation (11) makes the constraint equation of variable can be transformed into the constraint equation of integer variable. Such as 1+5×0.025% transformer, its value range of YT is 1～11. The encoding adopts binary numbers, and every five bits sequentially represent the values of Y _Vgi , Y _Vsvcg , Y _Vsvgh , Y _Qcu , and Y _Tk :

H＝[…,b_5i-4,…,b_5i,…,b_5g-4,…b_5g,…,b_5h-4,…b_5h,…,b_5u-4,…,b_5u,…,b_5k-4,…,b_5k,…] (12)H＝[…,b _5i-4 ,…,b _5i ,…,b _5g-4 ,…b _5g ,…,b _5h-4 ,…b _5h ,…,b _5u-4 ,…,b _5u ,… ,b _5k-4 ,…,b _5k ,…] (12)

(2)对A中的每个个体根据式(13)进行解码，修改原始潮流数据中对应的值，再开始潮流计算，本发明的潮流计算程序采用的是N-R法；(2) decode each individual in A according to formula (13), modify the corresponding value in the original power flow data, and then start the power flow calculation, and the power flow calculation program of the present invention adopts the N-R method;

$\{\begin{matrix} {V V}_{Gi Gi} = = {V V}_{Gi Gi max max} + + ((11 + + {Y Y}_{Vgi Vgi})) {ΔV ΔV}_{Gi Gi} \\ {V V}_{SVCg SVC} = = {V V}_{SVCg SVC max max} + + ((11 - - {Y Y}_{Vsvcg Vsvcg})) {ΔV ΔV}_{SVCg SVC} \\ {V V}_{SVGh wxya} = = {V V}_{SVGh wxya max max} + + ((11 - - {Y Y}_{Vsvgh Vsvgh})) {ΔV ΔV}_{SVGh wxya} \\ {Q Q}_{Cu Cu} = = {Y Y}_{Qcu Qcu} \times \times {ΔQ ΔQ}_{Cu Cu} \\ {T T}_{k k} = = {T T}_{k k max max} + + ((11 - - {Y Y}_{Tk Tk})) {ΔT ΔT}_{k k} \end{matrix} - - - - - - ((1313))$

式中：ΔV_Gi、ΔV_SVCg、ΔV_SVGh、ΔQ_Cu、ΔT_k对应变量有级调节单元值；In the formula: ΔV _Gi , ΔV _SVCg , ΔV _SVGh , ΔQ _Cu , ΔT _k correspond to variables with step-by-step adjustment unit values;

Y_Vgi、Y_Vsvcg、Y_Vsvgh、Y_Qcu、Y_Tk代表控制变量开关位置的整数变量；Y _Vgi , Y _Vsvcg , Y _Vsvgh , Y _Qcu , Y _Tk represent the integer variables of the position of the control variable switch;

Y_Vgi＝1，表示第i个发电机节点端电压调到最大；Y _Vgi = 1, indicating that the i-th generator node terminal voltage is adjusted to the maximum;

Y_Vsvcg＝1，表示第g个静止无功补偿器节点端电压调到最大；Y _Vsvcg = 1, indicating that the node terminal voltage of the gth static var compensator is adjusted to the maximum;

Y_Vsvgh＝1，表示第h个静止同步补偿器节点端电压调到最大；Y _Vsvgh = 1, indicating that the node terminal voltage of the hth static synchronous compensator is adjusted to the maximum;

Y_Qcu＝1，表示第j个电容器投入一组电容量；Y _Qcu = 1, which means that the jth capacitor is put into a group of capacitance;

Y_Tk＝1，表示第k个变压器分接头置于变比最大位置；Y _Tk = 1, indicating that the kth transformer tap is placed at the maximum transformation ratio position;

(3)经过潮流计算，获得了各节点的电压、无功和动态无功备用容量等数据，并将其由大到小排序；(3) After power flow calculation, the data of voltage, reactive power and dynamic reactive power reserve capacity of each node are obtained, and they are sorted from large to small;

(4)依据适应值大小对各个体进行排序，保留亲和力大的个体组成个体群B，同时对B内的个体进行交叉变异操作，保留操作后整体适应值大的个体，组成个体群C；依据适应值大小对B、C进行排列组成个体群D；(4) Sort the individuals according to the size of the fitness value, keep the individuals with high affinity to form the individual group B, and at the same time carry out the cross-mutation operation on the individuals in B, keep the individuals with the large overall fitness value after the operation, and form the individual group C; according to The size of the fitness value is arranged to form the individual group D by arranging B and C;

(5)检查迭代结束条件，如果达到则结束，否则转下一步；(5) Check the iteration end condition, if it is reached, it will end, otherwise go to the next step;

(6)随机产生一组新的个体群E，与D共同组成新一代迭代计算个体群F，转步骤(2)，重新开始计算。(6) Randomly generate a new set of individual groups E, together with D to form a new generation of iterative calculation individual group F, go to step (2), and restart the calculation.

实施例Example

如图3所示，针对3机10节点系统，500kV母线(Bus6)向负荷区域的两个负荷供电，其中的工业负荷(节点Bus7)通过OLTC变压器与500kV负荷母线连接，而居民负荷与商业负荷(节点Bus10)则通过两台OLTC变压器和一段代表次级输电系统的阻抗接在500kV负荷母线。负荷地区有一台1600MVA的等值发电机(节点Bus3)，并采用了大量的并联补偿装置，节点8上分别配置了容量为±240Mvar的静止无功补偿器(SVC)和容量为600Mvar的电容器组，该电容器组每组容量为100Mvar，共6组。两台远方的发电机通过4条500kV线路和1回双极直流输电线路向负荷区域输送功率。仿真所采用的主要模型：变压器(Bus9～Bus10)为OLTC变压器，其它分接头保持不变；节点Bus7上的负荷为恒功率模型，其它负荷为恒阻抗模型；发电机2和3(节点Bus2和Bus3)上的发电机有过励磁限制装置，发电机1(节点Bus1)为无穷大发电机。As shown in Figure 3, for the 3-machine 10-node system, the 500kV bus (Bus6) supplies power to two loads in the load area, and the industrial load (node Bus7) is connected to the 500kV load bus through an OLTC transformer, while the residential load and the commercial load (Node Bus10) is connected to the 500kV load bus through two OLTC transformers and a section of impedance representing the secondary transmission system. There is a 1600MVA equivalent generator (node Bus3) in the load area, and a large number of parallel compensation devices are used. Node 8 is equipped with a static var compensator (SVC) with a capacity of ±240Mvar and a capacitor bank with a capacity of 600Mvar. , each group of capacitors has a capacity of 100Mvar, a total of 6 groups. Two remote generators transmit power to the load area through four 500kV lines and one bipolar DC transmission line. The main model used in the simulation: transformers (Bus9~Bus10) are OLTC transformers, and other taps remain unchanged; the load on node Bus7 is a constant power model, and other loads are constant impedance models; generators 2 and 3 (nodes Bus2 and The generator on Bus3) has an over-excitation limiting device, and generator 1 (node Bus1) is an infinite generator.

对此系统进行故障扫描，确定威胁系统中长期电压稳定的关键故障集合。为了方便地说明TSI指标的有效性，本算例只考察最严重的N-1故障，故障形式为t＝0.1s时节点5～节点6间的一回交流联络线在节点6侧发生三相永久性短路故障，故障后0.09s跳开故障线路节点6侧开关，0.1s跳开故障线路节点5侧开关。Fault scanning is performed on this system to determine the key fault sets that threaten the long-term voltage stability of the system. In order to illustrate the effectiveness of the TSI index conveniently, this example only examines the most serious N-1 fault, and the fault form is that when t=0.1s, a three-phase AC connection line between node 5 and node 6 occurs on the side of node 6 For permanent short-circuit faults, the switch on the 6 side of the faulty line node is tripped 0.09s after the fault, and the switch on the 5th side of the faulty line node is tripped 0.1s.

图4表示发电机2、发电机3分别与发电机1之间相对功角摇摆曲线。由图4可见，这个扰动引起的初始快速暂态过程会很快消失，表明系统是可以保持暂态功角稳定的，后续的中长期过程中功角虽有摇摆，但角度都比较小，表明系统也可以保持中长期功角稳定。FIG. 4 shows relative power angle swing curves between generator 2 , generator 3 and generator 1 respectively. It can be seen from Figure 4 that the initial fast transient process caused by this disturbance will disappear quickly, indicating that the system can maintain the stability of the transient power angle. The system can also maintain medium and long-term power angle stability.

图5中过励磁限制器的励磁电流表明了发电机2和发电机3电动势E_q的响应，这个电动势正比于励磁电流。如图所示，扰动之后，发电机2和发电机3的励磁电流会突然上升，如果超过了转子电流限制，就会启动过励磁限制器的反时间机制。扰动后，OLTC变压器的运行对发电机强加了一个非常重的无功需求。这个需求进一步恶化了转子过负荷，直到最终过励磁限制器被激励，致使励磁电流回到其额定值。注意，这个过励限制器是积分型的，以至于E_q被强迫到E_q ^lim。随后的分接头变换导致暂态励磁电流升高，这个升高的励磁电流很快被过励磁限制器所检测(如图5中发电机2、3励磁电流的最大值点)，并给予校正。The excitation current of the overexcitation limiter in Fig. 5 shows the response of generator 2 and generator 3 electromotive force _Eq , which is proportional to the excitation current. As shown in the figure, after the disturbance, the excitation current of generator 2 and generator 3 will suddenly rise, and if the rotor current limit is exceeded, the inverse time mechanism of the overexcitation limiter will be activated. After the disturbance, the operation of the OLTC transformer imposes a very heavy reactive power demand on the generator. This requirement further exacerbates the rotor overload until eventually the overexcitation limiter is energized causing the field current to return to its rated value. Note that this overexcitation limiter is of the integral type so that E _q is forced to E _q ^lim . Subsequent tap changes lead to an increase in the transient excitation current, which is quickly detected by the over-excitation limiter (as shown in Figure 5 at the maximum value of the excitation currents of generators 2 and 3) and corrected.

图6给出了节点9和节点10的电压，即给负荷供电的OLTC的高压侧母线9电压和负荷侧节点10电压。由图可见，暂态过程中，节点9能够在0.87p.u.处稳定运行。OLTC变压器通过降低变比T_k，设法恢复负荷侧节点10电压。经过30秒的初始时间延迟后，OLTC转换器开始运行，约55秒，经过5次分接头调整之后，母线电压上升到0.915pu，非常接近事故前水平，发电机2和3的励磁电流输出也随之增加以满足系统对无功功率的需求(图5)。但是到了347秒时，由于发电机3的过励磁限制装置开始动作，限制了其输出电流，使得该机的无功功率输出也随之下降，导致负荷节点10的电压再次下降。为保证电压，变压器分接头继续动作了18次。在442秒时，发电机2的过励磁限制装置也开始动作，系统的无功功率缺口大大增加，导致了电压崩溃的发生。Figure 6 shows the voltages of nodes 9 and 10, that is, the voltage of the bus 9 on the high-voltage side of the OLTC supplying power to the load and the voltage of the node 10 on the load side. It can be seen from the figure that during the transient process, node 9 can run stably at 0.87pu. The OLTC transformer tries to restore the load-side node 10 voltage by reducing the transformation ratio T _k . After an initial time delay of 30 seconds, the OLTC converter started to operate, and after about 55 seconds, after 5 tap adjustments, the bus voltage rose to 0.915pu, which was very close to the level before the accident, and the excitation current output of generators 2 and 3 also decreased. Then increase to meet the system's demand for reactive power (Figure 5). But at 347 seconds, because the overexcitation limiting device of the generator 3 started to act, limiting its output current, the reactive power output of the generator also decreased, causing the voltage of the load node 10 to drop again. In order to ensure the voltage, the transformer tap continued to operate 18 times. At 442 seconds, the over-excitation limiting device of generator 2 also started to act, and the reactive power gap of the system increased greatly, resulting in voltage collapse.

在用本发明求出无功备用容量优化问题各控制变量后，利用时域仿真验证分析所提方法的有效性。After using the present invention to obtain the control variables of the reactive power reserve capacity optimization problem, the effectiveness of the proposed method is verified and analyzed by time domain simulation.

节点5～节点6间的一回交流联络线在节点6侧发生三相永久性短路故障，故障后0.09s跳开故障线路节点6侧开关，0.1s跳开故障线路节点5侧开关。图7和图8分别为发电机G3机端电压和节点10电压曲线，从图中可以看出，优化后系统的中长期电压稳定性比优化前要好，这说明采用本发明提出的优化算法能有效提高电网的中长期电压稳定性。A three-phase permanent short-circuit fault occurred on the node 6 side of the primary AC tie line between node 5 and node 6. After the fault, the switch on the node 6 side of the faulty line was tripped 0.09s, and the switch on the node 5 side of the faulty line was tripped 0.1s. Fig. 7 and Fig. 8 are generator G3 machine terminal voltage and node 10 voltage curves respectively, as can be seen from the figure, the medium and long-term voltage stability of the system after optimization is better than before optimization, this shows that adopting the optimization algorithm proposed by the present invention can Effectively improve the medium and long-term voltage stability of the power grid.

最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，所属领域的普通技术人员参照上述实施例依然可以对本发明的具体实施方式进行修改或者等同替换，这些未脱离本发明精神和范围的任何修改或者等同替换，均在申请待批的本发明的权利要求保护范围之内。Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Those of ordinary skill in the art can still modify or equivalently replace the specific implementation methods of the present invention with reference to the above embodiments. Any modifications or equivalent replacements departing from the spirit and scope of the present invention are within the protection scope of the claims of the pending application of the present invention.

Claims

1. improve the dynamic reactive power reserve optimization method of medium and long-term voltage stability of AC-DC power grid, it is characterized in that: described method comprises the following steps:

Step 1: Determine the key fault sets that affect the long-term voltage stability of the AC-DC grid;

Step 2: Adjust the reactive power output of the dynamic reactive power compensation equipment, and calculate the sensitivity of the dynamic reactive power compensation equipment;

Step 3: sort the m dynamic reactive power compensation equipment, and calculate the weight coefficient of the dynamic reactive power compensation equipment;

Step 4: Calculate the backup capacity of dynamic reactive power compensation equipment, establish a dynamic reactive power backup optimization model, and solve the dynamic reactive power backup optimization model.

2. The dynamic reactive power backup optimization method for improving long-term voltage stability of the AC-DC power grid according to claim 1, characterized in that: in the step 1, the AC-DC power grid is scanned for faults, and the voltage stability of the load bus i is calculated The margin K _MVSi , has:

{K K}_{MVSi MVSi} = = \frac{| | {Z Z}_{Li Li} | | - - | | {Z Z}_{Ti Ti} | |}{| | {Z Z}_{Li Li} | |}

Among them, Z _Li is the load equivalent impedance at load bus i, and Z _Ti is the Thevenin equivalent impedance of the system;

The minimum value of K _MVSi is selected as the voltage stability margin of the AC-DC grid, which is denoted as K _MVSI . According to the voltage stability margin value of the AC-DC grid, the seriousness of the fault is determined, and the key faults are obtained, thereby obtaining the key fault set.

3. The dynamic reactive power backup optimization method for improving long-term voltage stability in AC and DC power grids according to claim 1, characterized in that: in the step 2, the dynamic reactive power compensation equipment includes generators, static var compensators and Static synchronous compensator.

4. The dynamic reactive power backup optimization method for improving medium and long-term voltage stability of AC-DC power grid according to claim 1, characterized in that: said step 2 specifically comprises the following steps:

Step 2-1: Adjust the reactive power output of each dynamic reactive power compensation equipment separately, and conduct time domain simulation again for key faults;

Step 2-2: Calculate the sensitivity SI _l,j of the dynamic reactive power compensation equipment j for a certain fault l under the medium and long-term time scale;

Step 2-3: Calculate the sensitivity SI _j of the dynamic reactive power compensation device j for multiple faults on a medium and long-term time scale.

5. The dynamic reactive power backup optimization method for improving long-term voltage stability in the AC-DC power grid according to claim 4, characterized in that: in the step 2-2, for a certain fault l, the sensitivity of the dynamic reactive power compensation device j SI _l,j is expressed as:

{SI Si}_{l l,, j j} = = \frac{{k k}_{MVSI MVSI,, l l} (({Q Q}_{j j 00} + + Δ Δ {Q Q}_{j j})) - - {k k}_{MVSI MVSI,, l l} (({Q Q}_{j j 00}))}{Δ Δ {Q Q}_{Rj Rj}}

Among them, Q _j0 is the initial reactive power output of dynamic reactive power compensation equipment j; ΔQ _j is the reactive power variation of adjusting dynamic reactive power compensation equipment j; ΔQ _Rj is the reactive power reserve variation of adjusting dynamic reactive power compensation equipment j ; k _MVSI,l (Q _j0 +ΔQ _j ) is the load margin value of the AC/DC power grid under fault F _l after adjusting the reactive output of dynamic reactive power compensation equipment j; k _MVSI,l (Q _j0 ) is Before adjusting the reactive power output of the dynamic reactive power compensation equipment j, the load margin value of the AC and DC power grid under the fault F _l .

6. The dynamic reactive power backup optimization method for improving the long-term voltage stability of the AC-DC power grid according to claim 4, characterized in that: in the step 2-3, for multiple faults, the sensitivity of the dynamic reactive power compensation device j _SIj is expressed as:

{SI Si}_{j j} = = {Σ Σ}_{l l = = 11}^{{N N}_{l l}} {SI Si}_{l l,, j j}

Among them, N _l is the total number of critical faults.

7. The dynamic reactive power backup optimization method for improving medium and long-term voltage stability of AC-DC power grid according to claim 4, characterized in that: said step 3 specifically comprises the following steps:

Step 3-1: sort the m dynamic reactive power compensation equipment according to SI _j , the maximum value of SI _j indicates that the dynamic reactive power compensation equipment contributes the most to the medium and long-term voltage stability, and the dynamic reactive power compensation equipment with a large contribution is reserved Generate more reactive power reserves;

Step 3-2: Based on the maximum value of SI _j SI _max , normalize SI _j and calculate the weight coefficient p _j of the dynamic reactive power compensation equipment, p _j = SI _j /|SI _max |.

8. The dynamic reactive power backup optimization method for improving medium and long-term voltage stability of AC-DC power grid according to claim 1, characterized in that: said step 4 specifically comprises the following steps:

Step 4-1: Calculate the reserve capacity Q _RM of the dynamic reactive power compensation equipment;

Step 4-2: Taking improving Q _RM as the optimization goal of dynamic reactive power reserve, establishing a dynamic reactive power reserve optimization model;

Step 4-3: The genetic algorithm is used to solve the dynamic reactive power reserve optimization model.

9. according to claim 8, improve the dynamic reactive power reserve optimization method of long-term voltage stability of AC-DC power grid, it is characterized in that: in described step 4-1, the reserve capacity Q _RM of dynamic reactive power compensation equipment is expressed as:

{Q Q}_{RM RM} = = {Σ Σ}_{j j = = 11}^{m m} {p p}_{j j} (({Q Q}_{gj gj max max} - - {Q Q}_{gj gj}))

Among them, Q _gjmax is the upper limit of reactive power output of dynamic reactive power compensation device j in medium and long-term voltage stability, and Q _gj is the current reactive power output of dynamic reactive power compensation device j.

10. according to claim 8, improve the dynamic reactive power reserve optimization method of long-term voltage stability of AC-DC power grid, it is characterized in that: in described step 4-2, the objective function of dynamic reactive power reserve optimization model is:

max max {Q Q}_{RM RM} = = {Σ Σ}_{j j = = 11}^{m m} {p p}_{j j} (({Q Q}_{gj gj max max} - - {Q Q}_{gj gj}))

The constraints of the dynamic reactive power reserve optimization model include power flow equation constraints and variable constraints; the variable constraints are control variable constraints and state variable constraints;

(1) Power flow equation constraints:

In the dynamic reactive power reserve optimization model, the active output and reactive output of each node satisfy the following power flow equations, which are:

\{\begin{matrix} {P P}_{Gi Gi} - - {P P}_{Li Li} - - {P P}_{ti ti ((dc dc))} - - {V V}_{i i} {Σ Σ}_{r r = = 11}^{n no} {V V}_{r r} (({G G}_{ir ir} cos cos {δ δ}_{ir ir} + + {B B}_{ir ir} sin sin {δ δ}_{ir ir})) = = 00 \\ {Q Q}_{Gi Gi} + + {Q Q}_{Ci Ci} - - {Q Q}_{Li Li} - - {Q Q}_{ti ti ((dc dc))} - - {V V}_{i i} {Σ Σ}_{r r = = 11}^{n no} {V V}_{r r} (({G G}_{ir ir} sin sin {δ δ}_{ir ir} - - {B B}_{ir ir} cos cos {δ δ}_{ir ir})) = = 00 \end{matrix}

Among them, P _Gi and Q _Gi are the active power output and reactive power output of the generator node in the power system, respectively; P _Li and Q _Li are the active power output and reactive power output of the load node, respectively; Q _Ci is the reactive power compensation capacity of the node; G _ir and B _ir are the conductance and susceptance between nodes i and r respectively; V _i and V _r are the voltages of nodes i and r respectively; δ _ir is the voltage phase angle difference between nodes i and r; n is The total number of nodes; P _ti(dc) and Q _ti(dc) are the active input and reactive input of DC nodes respectively, which are divided into the following two cases:

1) Node i is on the commutation bus on the rectifier side, P _ti(dc) and Q _ti(dc) are expressed as:

\{\begin{matrix} {P P}_{ti ti ((dc dc))} = = {k k}_{p p} {U u}_{dR d} {I I}_{d d} \\ {Q Q}_{ti ti ((dc dc))} = = {k k}_{p p} {I I}_{d d} \sqrt{{((\frac{33 \sqrt{22}}{π π {K K}_{dR d}} b b {V V}_{R R}))}^{22} - - {U u}_{dR d}^{22}} \end{matrix}

Among them, k _p is the number of poles of the converter; U _dR is the DC voltage on the rectification side; I _d is the DC line current; K _dR is the conversion ratio of the converter transformer on the rectification side; b is the number of 6-pulse series bridges for each pole; _VR is the amplitude of the AC bus voltage on the rectifier side;

2) Node i is on the inverter side commutation bus, P _ti(dc) and Q _ti(dc) are expressed as:

\{\begin{matrix} {P P}_{ti ti ((dc dc))} = = {- - k k}_{p p} {U u}_{dI iGO} {I I}_{d d} \\ {Q Q}_{ti ti ((dc dc))} = = {k k}_{p p} {I I}_{d d} \sqrt{{((\frac{33 \sqrt{22}}{π π {K K}_{dI iGO}} b b {V V}_{I I}))}^{22} - - {U u}_{dI iGO}^{22}} \end{matrix}

Among them, _UdI is the DC voltage of the inverter side; _KdI is the conversion ratio of the converter transformer on the inverter side; V _I is the AC bus voltage amplitude on the inverter side;

(2) Control variable constraints:

\{\begin{matrix} {V V}_{Gi Gi min min} \leq \leq {V V}_{Gi Gi} \leq \leq {V V}_{Gi Gi max max},, i i = = 1,2 1,2,, . . . . . .,, {N N}_{G G} \\ {V V}_{SVCg SVC min min} \leq \leq {V V}_{SVCg SVC} \leq \leq {V V}_{SVCg SVC max max},, g g = = 1,2 1,2,, . . . . . .,, {N N}_{SVC SVC} \\ {V V}_{SVGh wxya min min} \leq \leq {V V}_{SVGh wxya} \leq \leq {V V}_{SVGh wxya max max},, h h = = 1,2 1,2,, . . . . . .,, {N N}_{SVG SVG} \\ {Q Q}_{Cu Cu min min} \leq \leq {Q Q}_{Cu Cu} \leq \leq {Q Q}_{Cu Cu max max},, u u = = 1,2 1,2,, . . . . . .,, {N N}_{C C} \\ {T T}_{k k min min} \leq \leq {T T}_{k k} \leq \leq {T T}_{k k max max},, k k = = 1,2 1,2,, . . . . . .,, {N N}_{T T} \\ {U u}_{dl dl min min} \leq \leq {U u}_{dl dl} \leq \leq {U u}_{dl dl max max},, l l = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {I I}_{dm dm min min} \leq \leq {I I}_{dm dm} \leq \leq {I I}_{dm dm max max},, m m = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {P P}_{dn dn min min} \leq \leq {P P}_{dn dn} \leq \leq {P P}_{dn dn max max},, n no = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \\ {θ θ}_{dr dr min min} \leq \leq {θ θ}_{dr dr} \leq \leq {θ θ}_{dr dr max max},, r r = = 1,2 1,2,, . . . . . .,, {N N}_{dc dc} \end{matrix}

Among them, N _G , N _SVC , _NSVG , N _C , _NT and N _dc are respectively the number of generator nodes, the number of static var compensator nodes, the number of static synchronous compensator nodes, the number of shunt The number of joints and the number of DC network nodes; V _Gi is the terminal voltage of the generator node, V _Gimin and V _Gimax are the lower limit and upper limit of V _Gi respectively; V _SVCg is the terminal voltage of the static var compensator node, V _SVCgmin and V _SVCgmax are the lower limit and upper limit of V _SVCg respectively; V _SVGh is the terminal voltage of the static synchronous compensator node, V _SVGhmin and V _SVGhmax are the lower limit and upper limit of V _SVGh respectively; Q _Cu is the parallel The compensation capacity of the capacitor bank, Q _Cumin and Q _Cumax are the lower limit and upper limit of Q _Cu respectively; T _k is the transformer adjustable tap, T _kmin and T _kmax are the lower limit and upper limit of T _k respectively; U _dl , I _dm , P _dn and θ _dr are the converter control voltage, control current, control power and control angle respectively, U _dlmin and U _dlmax , I _dmmin and I _dmmax , P _dnmin and P _dnmax , θ _drmin and θ _drmax Respectively represent the corresponding lower limit and upper limit;

(3) State variable constraints:

\{\begin{matrix} {Q Q}_{Gi Gi min min} \leq \leq {Q Q}_{Gi Gi} \leq \leq {Q Q}_{Gi Gi max max},, i i = = 1,2 1,2,, . . . . . .,, {N N}_{G G} \\ {B B}_{SVCg SVC min min} \leq \leq {B B}_{SVCg SVC} \leq \leq {B B}_{SVCg SVC max max},, g g = = 1,2 1,2,, . . . . . .,, {N N}_{SVC SVC} \\ {I I}_{SVGh wxya min min} \leq \leq {I I}_{SVGh wxya} \leq \leq {I I}_{SVGh wxya max max},, h h = = 1,2 1,2,, . . . . . .,, {N N}_{SVG SVG} \\ {V V}_{Lp LP min min} \leq \leq {V V}_{Lp LP} \leq \leq {V V}_{Lp LP max max},, p p = = 1,2 1,2,, . . . . . .,, {N N}_{L L} \end{matrix}

Among them, N _L is the number of load nodes; Q _Gi is the reactive power output of generator nodes, Q _Gimin and Q _Gimax are the lower limit and upper limit of Q _Gi respectively; B _SVCg is the susceptance of static var compensator, B _SVCgmin and B _SVCgmax are the lower limit and upper limit of B _SVCg respectively; _ISVGh is the current amplitude of the static synchronous compensator, _ISVGhmin and _ISVGhmax are the lower limit and upper limit of _ISVGh respectively; V _Lp is the load node The voltage amplitude, V _Lpmin and V _Lpmax are the lower limit and upper limit of V _Lp respectively.