CN108988320A - Electrical Power System Dynamic element responds characteristic is to Enhancement of Transient Voltage Stability impact analysis method - Google Patents

Electrical Power System Dynamic element responds characteristic is to Enhancement of Transient Voltage Stability impact analysis method Download PDF

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CN108988320A
CN108988320A CN201810682902.6A CN201810682902A CN108988320A CN 108988320 A CN108988320 A CN 108988320A CN 201810682902 A CN201810682902 A CN 201810682902A CN 108988320 A CN108988320 A CN 108988320A
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CN108988320B (en
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杜兆斌
张文倩
黄昌树
夏成军
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South China University of Technology SCUT
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00Circuit arrangements for AC mains or AC distribution networks
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02JCIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention discloses a kind of Electrical Power System Dynamic element responds characteristics to Enhancement of Transient Voltage Stability impact analysis method.In order to study generator, the main influence of HVDC transmission system (HVDC) and induction conductivity on Enhancement of Transient Voltage Stability, from the angle of broad sense branch potential energy, new analysis method is proposed to study influence of the above-mentioned main dynamic element to Enhancement of Transient Voltage Stability.The information of the changing rule and stability margin that are distributed according to transient potential energy in network after failure is basic variable with the idle recovery characteristics of dynamic element each after failure, establishes evaluation index, and then to causing power grid transient voltage instability Mechanism to analyze.Finally, carried out emulation testing using three machines, nine node ac and dc systems on MATLAB and PSAT software platform, the results showed that the feasibility and validity of this method.

Description

电力系统动态元件响应特性对暂态电压稳定性影响分析方法Analysis Method of Influence of Response Characteristics of Power System Dynamic Components on Transient Voltage Stability

技术领域technical field

本发明涉及电网暂态电压稳定性影响分析技术领域,具体涉及包括高压直流输电、发电机、感应电动机等动态元件对电网暂态电压稳定性影响分析,并进一步对电力系统故障后暂态电压失稳机理进行分析。The invention relates to the technical field of impact analysis of power grid transient voltage stability, in particular to the analysis of the influence of dynamic components including high-voltage direct current transmission, generators, induction motors, etc. The stability mechanism is analyzed.

背景技术Background technique

随着以长三角和珠三角为代表的受端电网直流馈入回数不断增加,直流功率馈入比重不断增大,我国电网将不再是单纯的交流电网,而是变为全国范围的交直流互联的大型电网,且复杂程度逐步增大。由于电压失稳或电压崩溃而导致的大面积停电事故陆续发生。国内外电力学者不得不对电压稳定问题越发地关注。晶闸管为核心的高压直流系统相比与传统交流系统,具有很多新动态特性,故障后的无功恢复特性对电压稳定性的影响更为突出,随着直流馈入的比例逐渐增高,系统的电压稳定性将受到更大影响。如何更好的评估包括直流换流器在内的一系列动态元件在故障后对稳定性的影响,并指导优化稳定性能的方法均具有现实意义。传统研究思路中,常利用时域仿真方法,通过改变系统参数来分析动态分量对系统暂态稳定性的影响,但是耗时较长。直接法以其可用于分析稳定性并提供稳定裕度的优点,逐渐步入大众的视野,而其中能量函数成为一种重要的手段。交直流混合系统中,直流受端换流系统的无功恢复特性还是感应电动机失稳导致的整个系统电压失稳,其中的具体原因难以分清。这个问题相关工作成果较少。而其中如何构建相应评估指标来区分不同动态元件带来的影响是一个难题。As the number of DC feed-in loops of the receiving-end power grid represented by the Yangtze River Delta and the Pearl River Delta continues to increase, and the proportion of DC power feed-in continues to increase, my country's power grid will no longer be a pure AC grid, but will become a nationwide AC-DC system. Large interconnected power grids with progressively increasing complexity. Large-scale power outages due to voltage instability or voltage collapse have occurred one after another. Electric power scholars at home and abroad have to pay more and more attention to voltage stability. Compared with the traditional AC system, the high-voltage DC system with the thyristor as the core has many new dynamic characteristics. The influence of the reactive power recovery characteristics after the fault on the voltage stability is more prominent. As the proportion of DC feed-in gradually increases, the voltage of the system Stability will be more affected. How to better evaluate the impact of a series of dynamic components including DC converters on stability after faults, and guide the method of optimizing stability performance are of practical significance. In traditional research ideas, the time-domain simulation method is often used to analyze the influence of dynamic components on the transient stability of the system by changing system parameters, but it takes a long time. The direct method has gradually entered the public's field of vision because it can be used to analyze stability and provide stability margins, and the energy function has become an important method. In the AC/DC hybrid system, whether the reactive power recovery characteristics of the DC receiving end commutation system or the voltage instability of the entire system caused by the instability of the induction motor is difficult to distinguish the specific reasons. There is little work on this issue. However, how to construct corresponding evaluation indicators to distinguish the impact of different dynamic components is a difficult problem.

发明内容Contents of the invention

随着电力网络复杂程度的增加,系统故障后,各种电力设备的动态恢复特性将对电力系统暂态电压稳定性带来不同的影响。故障后系统暂态能量的过度集中是系统不稳定的主要原因,发电机动能的变化将根据系统各部分的参数和特性反映在各种局部电势变化中。受上述思想和暂态电压分析技巧的启发,本发明提出了一种评估不同系统动态元件对暂态电压稳定性影响的评估方法。本发明从广义分支势能的角度出发,提出了新的分析方法来研究发电机、高压直流输电系统(HVDC)、感应电动机等主要动态元件对暂态电压稳定性的影响。根据故障后网络中暂态势能分布的变化规律和稳定裕度的信息,以故障后各电气设备无功的动态恢复特性为基础变量,建立了评估指标,进而对造成电网暂态电压失稳机理进行分析。本方法可以定量权衡各个动态元件的作用,解析系统电压失稳的机理,用以指导系统暂态电压稳定性优化策略。With the increase of the complexity of the power network, the dynamic recovery characteristics of various power equipment will have different impacts on the transient voltage stability of the power system after the system fails. The excessive concentration of system transient energy after a fault is the main cause of system instability, and the change of generator kinetic energy will be reflected in various local potential changes according to the parameters and characteristics of each part of the system. Inspired by the above ideas and transient voltage analysis techniques, the present invention proposes an evaluation method for evaluating the influence of different system dynamic components on the transient voltage stability. From the perspective of generalized branch potential energy, the invention proposes a new analysis method to study the influence of main dynamic elements such as generators, high-voltage direct current transmission systems (HVDC), induction motors, etc. on transient voltage stability. According to the change law of transient potential energy distribution in the network after the fault and the information of the stability margin, the dynamic recovery characteristics of the reactive power of each electrical equipment after the fault are used as the basic variable, and the evaluation index is established, and then the mechanism of the transient voltage instability of the power grid is established. for analysis. This method can quantitatively weigh the role of each dynamic component, analyze the mechanism of system voltage instability, and use it to guide the optimization strategy of system transient voltage stability.

本发明的目的可以通过采取如下技术方案达到:The purpose of the present invention can be achieved by taking the following technical solutions:

一种电力系统动态元件响应特性对暂态电压稳定性影响分析方法,该分析方法包括下列步骤:A method for analyzing the influence of response characteristics of power system dynamic components on transient voltage stability, the analysis method comprising the following steps:

S1、建立电力系统数学模型,并基于李雅普诺夫理论,构建能够反映该系统模型的能量函数表达式;S1. Establish a mathematical model of the power system, and construct an energy function expression that can reflect the system model based on Lyapunov theory;

S2、暂态电压稳定性判断定。本发明采用通过电力系统分岔条件和启发式电压失稳型主导不稳定平衡点构造的恒定能量面来判断暂态电压稳定性,但不局限于该种方法。该步骤具体如下:S2. Determine the transient voltage stability. The present invention judges the transient voltage stability by adopting the bifurcation condition of the power system and the constant energy surface constructed by the heuristic voltage instability type dominant unstable equilibrium point, but is not limited to this method. The steps are as follows:

S201、构建能量函数;S201, constructing an energy function;

S202、求主导不稳定平衡点;S202, finding the dominant unstable equilibrium point;

S203、求临界能量Ucr;S203, find the critical energy Ucr;

S204、求故障清除时刻能量U;S204. Find the energy U at the moment of fault clearing;

S205、判断故障清除时刻能量U与临界能量Ucr大小,若故障清除时刻能量U大于临界能量Ucr,则判定系统暂态电压失稳;否则,继续转至下一步骤;S205. Determine the magnitude of the energy U and the critical energy Ucr at the time of fault clearing, if the energy U at the time of fault clearing is greater than the critical energy Ucr, then determine that the transient voltage of the system is unstable; otherwise, continue to the next step;

S206、判断是否遇到奇异面,若是,则判定系统暂态电压失稳,否则,判定系统稳定。S206 , judging whether a singular surface is encountered, if so, judging that the transient voltage of the system is unstable, otherwise, judging that the system is stable.

S3、根据步骤S1中构建的能量函数表达式,提取其中与动态电力元件相关的部分,建立各动态元件的势能分量函数,其中,动态元件包括但不限于发电机、高压直流输电系统、感应电动机;S3. According to the energy function expression constructed in step S1, extract the part related to the dynamic power element, and establish the potential energy component function of each dynamic element, wherein the dynamic element includes but not limited to generator, high voltage direct current transmission system, induction motor ;

S4、故障期间,电力系统向电网注入大量能量,发电机转速增加导致动能增大,故障清除后,总能量守恒,动能沿着电力网络逐步转化为各个元件和输电线路的势能。随着动能的振荡变化,各个动态元件的势能逐渐增大并也伴随着一定的振荡。所承受势能增幅最大的动态元件将受到更大的能量冲击,也相应的更容易形成局部能量过冲,进而导致此处更容易发生崩溃,因此可以利用故障后,各个动态元件势能最大值所在势能振荡曲线的前半个周期波的势能增量来简单分析电网脆弱区域。S4. During the fault period, the power system injects a large amount of energy into the grid, and the increase in the generator speed leads to an increase in kinetic energy. After the fault is cleared, the total energy is conserved, and the kinetic energy is gradually converted into the potential energy of each component and transmission line along the power network. With the oscillating change of kinetic energy, the potential energy of each dynamic element increases gradually and is accompanied by certain oscillation. The dynamic element with the largest increase in potential energy will be subject to greater energy impact, and accordingly it is easier to form local energy overshoot, which makes it more prone to collapse here. Therefore, after a fault, the potential energy of the maximum potential energy of each dynamic element can be used The potential energy increment of the first half cycle wave of the oscillation curve is used to simply analyze the vulnerable area of the power grid.

设故障后设备势能分量达到最大值(或极大值)时刻为T2,对应时刻势能分量为U2,在这一周期中,达到最大值前的极小值时刻为T1,对应时刻势能分量为U1,则这一周期中势能差为ΔU=U2-U1Suppose the time when the potential energy component of the equipment reaches the maximum value (or maximum value) after the fault is T 2 , and the potential energy component at the corresponding time is U 2 , in this cycle, the time of the minimum value before reaching the maximum value is T 1 , and the potential energy The component is U 1 , then the potential energy difference in this cycle is ΔU=U 2 -U 1 .

评估指标一:σ1=ΔU/ΔQEvaluation index one: σ 1 = ΔU/ΔQ

评估指标二:σ2=V(T2)/ΔUEvaluation index two: σ 2 =V(T 2 )/ΔU

其中ΔQ为对应时间段内,该电力设备在故障后动态恢复特性影响下的无功变化量。V(T2)为该设备在T2时刻对应接入母线电压幅值。σ1值越大,则意味着这一周期内,该电力设备的无功动态变化使势能增幅越大,即所承受的能量冲击更大,也就越容易超过该处网络能够承受的幅度,继而愈容易在此处导致稳定条件破坏,最后导致系统崩溃;σ2的值越小,即意味着该设备在故障后恢复时,所受到能量冲击较大时刻,其所接入母线节点电压值仍比较低,也就是说此处更容易成为临界支路。因此,可以实现不同系统动态元件对暂态电压稳定性影响的评估。Among them, ΔQ is the reactive power variation of the power equipment under the influence of dynamic recovery characteristics after a fault within the corresponding time period. V(T 2 ) is the corresponding voltage amplitude of the equipment connected to the bus at T 2 time. The larger the value of σ1, it means that in this cycle, the reactive power dynamic changes of the power equipment make the potential energy increase larger, that is, the energy impact suffered is greater, and it is easier to exceed the range that the network can withstand. Then, the easier it is to lead to the destruction of stable conditions here, and finally lead to the collapse of the system; the smaller the value of σ2 , it means that when the equipment is restored after a fault, the voltage value of the connected bus node Still relatively low, that is to say, it is more likely to become a critical branch here. Thus, the evaluation of the influence of different system dynamic elements on the transient voltage stability can be realized.

进一步地,有n个发电机节点,N个负荷节点,2个直流系统换流站母线节点,且只有1个平衡节点的电力系统动态元件数学模型与能量函数表达式如下所示:Furthermore, there are n generator nodes, N load nodes, two DC system converter station bus nodes, and only one balance node in the power system. The mathematical model and energy function expression of the dynamic components are as follows:

所用四阶发电机模型为:The fourth-order generator model used is:

所用三阶感应电动机模型为:The third-order induction motor model used is:

所述能量函数表达式为:The energy function expression is:

U=UAC+UL1+UL2i+Ug+UR+UI+Ud+UDC U=U AC +U L1 +U L2i +U g +U R +U I +U d +U DC

其中:in:

且有:and have:

其中,下标i和j代表网络母线节点标号,i=1,2,…,n+N+3;j=1,2,…,n+N+3。Wherein, subscripts i and j represent network bus node numbers, i=1, 2, . . . , n+N+3; j=1, 2, . . . , n+N+3.

其中,ρi是为了使Bi -1Ti正定的参数,且对任意不为零的矩阵向量,都有xTBi -1Tix>0,i=1,2,…,n。C=[C1,…,Cn]T,Ci=[0 l];Among them, ρ i is the parameter to make B i -1 T i positive definite, and for any non-zero matrix vector, there is x T B i -1 T i x>0, i=1, 2,...,n . C=[C 1 ,...,C n ] T , C i =[0 l];

UDC=-VIVRBIR cos(θIR);U DC =-V I V R B IR cos(θ IR );

上式中,当i=1,2,…,n时,ωi为发电机转速,δi为发电机转子角度,Mi为发电机惯性时间常数,Pmi为发电机机械功率,Di为阻尼系数,E′qi为q轴暂态电势,Xdi为发电机的暂态电抗,X′di为发电机的次暂态电抗,T‘doi为d轴暂态时间常数,Efdi为励磁电势,Pei为发电机电磁功率,μi为励磁控制器反馈增益系数,Tvi为励磁控制时间常数,ki为励磁电压一阶数学模型中,所接入母线电压相关的线性系数,li为接入母线i的使发电机励磁为正的控制常数;R下标代表整流侧变量,I下标代表逆变侧变量,VR和VI交流母线电压幅值,PdR+jQdR和PdI+jQdI为换流器注入的补偿功率;当i=n+1,n+2,…,n+N+3时,T′doi为定子开路时间常数,Mi为感应电动机惯性时间常数,E′Li为内电势幅值,Xr为转子绕组等值漏抗,Xm为定转子互感抗,Xs为定子绕组漏抗,X′i为暂态电抗,Xi为同步电抗,δi为感应电动机功角,si为感应电动机滑差,Tmi为感应电动机电磁转矩,Tei为机械转矩;UAC为交流网络势能,UL1为静态负荷势能,UL2i为接入i节点感应电动机负荷势能,Ug为系统所有发电机能量和,UR为直流整流侧与交流网络接口势能,UI为直流逆变侧与交流网络接口势能,UDC为直流网络节点间势能,Ud为直流功率交换形成的势能分量,Vi和Vj分别为母线标号i和j的电压幅值,θi和θj分别为母线标号i和j的电压相角,QLi为标号为i的母线所接入静态负荷的无功功率,PLi为标号为i的母线所接入静态负荷的有功功率。In the above formula, when i=1, 2,...,n, ω i is the generator speed, δ i is the generator rotor angle, M i is the generator inertia time constant, P mi is the generator mechanical power, D i is the damping coefficient, E′ qi is the q-axis transient potential, X di is the transient reactance of the generator, X′ di is the sub-transient reactance of the generator, T’ doi is the d-axis transient time constant, E fdi is Excitation potential, P ei is the electromagnetic power of the generator, μ i is the feedback gain coefficient of the excitation controller, T vi is the excitation control time constant, k i is the linear coefficient related to the connected bus voltage in the first-order mathematical model of the excitation voltage, l i is the control constant connected to the bus i to make the excitation of the generator positive; the subscript R represents the variable on the rectifier side, the subscript I represents the variable on the inverter side, and the voltage amplitude of the AC bus of VR and V I , P dR +jQ dR and P dI + jQ dI is the compensation power injected by the converter; when i=n+1, n+2,...,n+N+3, T′ doi is the stator open circuit time constant, Mi is the induction motor Inertial time constant, E′ Li is the amplitude of the internal potential, X r is the equivalent leakage reactance of the rotor winding, X m is the mutual inductance of the stator and rotor, X s is the leakage reactance of the stator winding, X′ i is the transient reactance, and X i is Synchronous reactance, δ i is the power angle of the induction motor, s i is the slip of the induction motor, T mi is the electromagnetic torque of the induction motor, T ei is the mechanical torque; U AC is the AC network potential energy, U L1 is the static load potential energy, U L2i is the load potential energy of the induction motor connected to node i, U g is the energy sum of all generators in the system, U R is the potential energy of the DC rectifier side and the AC network interface, U I is the potential energy of the DC inverter side and the AC network interface, and U DC is the DC Potential energy between network nodes, U d is the potential energy component formed by DC power exchange, V i and V j are the voltage amplitudes of bus labels i and j respectively, θ i and θ j are the voltage phase angles of bus labels i and j, respectively, Q Li is the reactive power of the static load connected to the bus marked i, and P Li is the active power of the static load connected to the bus marked i.

本发明相对于现有技术具有如下的优点及效果:Compared with the prior art, the present invention has the following advantages and effects:

本发明从能量和域的角度,基于电力系统中能量的分布和传播特性,以动态元件无功动态特性为兴趣变量对系统暂态电压失稳影响因素进行分析,该方法相较于时域仿真法,能够提供定量的裕度信息,耗时短,可以超前对暂态电压失稳相关影响因素进行预测分析,并区分了多种动态元件的影响特性。本发明提供了简单的评估指标,将暂态电压、无功和能量结合,以系统的角度综合分析各动态元件对暂态电压稳定性影响,在此基础上可以进一步指导选择电压优化措施,例如,较之传统直接加装无功补偿设备的方法,本实施例还提供了另外一条思路,即可以在电网搭建时通过改进直流系统相关参数来影响其故障后势能变化趋势,进而从根本上提高故障下暂态电压稳定性,同时该方法或许也比配置一定无功补偿设备的经济性更高。From the perspective of energy and domain, based on the distribution and propagation characteristics of energy in the power system, the present invention takes the reactive dynamic characteristics of dynamic components as the variable of interest to analyze the factors affecting the transient voltage instability of the system. Compared with the time-domain simulation The method can provide quantitative margin information, takes a short time, can predict and analyze the factors related to transient voltage instability in advance, and distinguishes the influence characteristics of various dynamic components. The present invention provides a simple evaluation index, combines the transient voltage, reactive power and energy, and comprehensively analyzes the influence of each dynamic element on the transient voltage stability from a systematic point of view. On this basis, it can further guide the selection of voltage optimization measures, such as , compared with the traditional method of directly installing reactive power compensation equipment, this embodiment also provides another idea, that is, the potential energy change trend after a fault can be affected by improving the relevant parameters of the DC system during the construction of the power grid, and then fundamentally improve Transient voltage stability under fault conditions, and this method may also be more economical than configuring certain reactive power compensation equipment.

附图说明Description of drawings

图1是本发明中公开的电力系统动态元件响应特性对暂态电压稳定性影响分析方法的流程示意图;Fig. 1 is a schematic flow chart of the method for analyzing the influence of the response characteristics of power system dynamic components on transient voltage stability disclosed in the present invention;

图2是包含直流的三机九节点系统示意图;Figure 2 is a schematic diagram of a three-machine nine-node system including DC;

图3是故障清除时刻为1.18s部分母线节点电压图;Fig. 3 is a part of the bus node voltage diagram when the fault is cleared at 1.18s;

图4是1.178s清除故障后感应电动机、直流势能变化曲线图;Figure 4 is a curve diagram of the induction motor and DC potential energy change after the fault is cleared in 1.178s;

图5是1.178s清除故障后发电机势能变化曲线图;Fig. 5 is a curve diagram of generator potential energy change after 1.178s to clear the fault;

图6是1.178s清除故障时发电机功角图;Figure 6 is the power angle diagram of the generator when the fault is cleared in 1.178s;

图7是1.18s清除故障后失稳情况下感应电动机滑差图。Figure 7 is the slip diagram of the induction motor under the condition of instability after clearing the fault in 1.18s.

具体实施方式Detailed ways

为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

实施例Example

如图1所示的电力系统动态元件响应特性对暂态电压稳定性影响分析方法流程图,本实施例公开的电力系统动态元件响应特性对暂态电压稳定性影响分析方法包括下列步骤:As shown in FIG. 1 , the flow chart of the method for analyzing the influence of the response characteristics of the dynamic components of the power system on the transient voltage stability, the method for analyzing the influence of the response characteristics of the dynamic components of the power system on the transient voltage stability disclosed in this embodiment includes the following steps:

步骤S1、建立电力系统数学模型,并基于李雅普诺夫理论,构建能够反映该系统模型的能量函数表达式。得到的能量函数表达式如下所示:Step S1, establishing a mathematical model of the power system, and constructing an energy function expression that can reflect the system model based on Lyapunov theory. The obtained energy function expression is as follows:

U=UAC+UL1+UL2i+Ug+UR+UI+Ud+UDC U=U AC +U L1 +U L2i +U g +U R +U I +U d +U DC

其中:in:

且有:and have:

其中,ρi是为了使Bi -1Ti正定的参数,且对任意不为零的矩阵向量,都有xTBi -1Tix>0,i=1,2,3;Among them, ρ i is a parameter to make B i -1 T i positive definite, and for any non-zero matrix vector, x T B i -1 T i x>0, i=1, 2, 3;

C=[C1,…,Cn]T,Ci=[0 l];C=[C 1 ,...,C n ] T , C i =[0 l];

上式下标i和j代表网络母线节点标号,本实施例中,i和j=1,2,3,…,9,i=1,2,3时,即接入了发电机的母线,i=6时,即接入了感应电动机负荷母线,下标i和j代表网络母线节点标号。当i=1,2,3时,ωi为发电机转速,δi为发电机转子角度,Mi为发电机惯性时间常数,Pmi为发电机机械功率,Di为阻尼系数,E′qi为q轴暂态电势,Xdi为发电机的暂态电抗,X′di为发电机的次暂态电抗,T‘doi为d轴暂态时间常数,Efdi为励磁电势,Pei为发电机电磁功率,μi为励磁控制器反馈增益系数,Tvi为励磁控制时间常数,ki为励磁电压一阶数学模型中,所接入母线电压相关的线性系数,li为接入母线i的使发电机励磁为正的控制常数;R下标代表整流侧变量,I下标代表逆变侧变量,VR和VI交流母线电压幅值,PdR+jQdR和PdI+jQdI为换流器注入的补偿功率;当i=6时,T′doi为定子开路时间常数,Mi为感应电动机惯性时间常数,ELi为内电势幅值,Xr为转子绕组等值漏抗,Xm为定转子互感抗,Xs为定子绕组漏抗,X′i为暂态电抗,Xi为同步电抗,δi为感应电动机功角,si为感应电动机滑差,Tmi为感应电动机电磁转矩,Tei为机械转矩;UAC为交流网络势能,UL1为静态负荷势能,UL2i为接入i节点感应电动机负荷势能,Ug为系统所有发电机能量和,UR为直流整流侧与交流网络接口势能,UI为直流逆变侧与交流网络接口势能,UDC为直流网络节点间势能,Ud为直流功率交换形成的势能分量,Vi和Vj分别为母线标号i和j的电压幅值,θi和θj分别为母线标号i和j的电压相角,QLi为标号为i的母线所接入静态负荷的无功功率,PLi为标号为i的母线所接入静态负荷的有功功率。The subscripts i and j represent the network bus node labels. In the present embodiment, i and j=1, 2, 3, ..., 9, when i=1, 2, 3, the bus bar of the generator is connected, When i=6, the induction motor load bus is connected, and the subscripts i and j represent the node numbers of the network bus. When i=1, 2, 3, ω i is the generator speed, δ i is the rotor angle of the generator, Mi is the inertia time constant of the generator, P mi is the mechanical power of the generator, D i is the damping coefficient, E′ qi is the q-axis transient potential, X di is the transient reactance of the generator, X′ di is the sub-transient reactance of the generator, T’ doi is the d-axis transient time constant, E fdi is the excitation potential, P ei is Generator electromagnetic power, μ i is the feedback gain coefficient of the excitation controller, T vi is the excitation control time constant, k i is the linear coefficient related to the connected bus voltage in the first-order mathematical model of the excitation voltage, l i is the connected bus i is the control constant that makes the generator excitation positive; R subscript represents the variable on the rectifier side, I subscript represents the variable on the inverter side, V R and V I AC bus voltage amplitude, P dR +jQ dR and P dI +jQ dI is the compensation power injected by the converter; when i=6, T′ doi is the stator open-circuit time constant, M i is the inertia time constant of the induction motor, E Li is the amplitude of the internal potential, X r is the rotor winding, etc. X m is the mutual inductance of the stator and rotor, X s is the leakage reactance of the stator winding, X′ i is the transient reactance, X i is the synchronous reactance, δ i is the power angle of the induction motor, s i is the slip of the induction motor, T mi is the electromagnetic torque of the induction motor, T ei is the mechanical torque; U AC is the potential energy of the AC network, U L1 is the static load potential energy, U L2i is the load potential energy of the induction motor connected to node i, and U g is the energy of all generators in the system and, U R is the potential energy of the DC rectifier side and the AC network interface, U I is the potential energy of the DC inverter side and the AC network interface, U DC is the potential energy between the DC network nodes, U d is the potential energy component formed by the DC power exchange, V i and V j is the voltage amplitude of the bus labels i and j respectively, θ i and θ j are the voltage phase angles of the bus labels i and j respectively, Q Li is the reactive power of the static load connected to the bus labeled i, P Li is the active power of the static load connected to the bus marked i.

步骤S2、暂态电压稳定性判断定。本发明采用通过电力系统分岔条件和基于启发式得到电压失稳型主导不稳定平衡点构造的恒定能量面来判断暂态电压稳定性,但不局限于该种方法。Step S2, determining transient voltage stability. The present invention judges the transient voltage stability by using the bifurcation condition of the power system and the constant energy surface constructed based on the heuristically obtained voltage instability type dominant unstable equilibrium point, but is not limited to this method.

本实施案例中,母线5处于1s时刻设置三相短路故障,1.18s时刻清除,PSAT在进行时域仿真时中断,即如图3可得,在该故障下,故障后暂态运行轨迹碰到奇异面,导致微分代数方程组(DAE)模型下的时域仿真无法运算,此时故障清除后瞬刻能量值为0.36,小于主导不稳定平衡点所求得的临界能量,但在该故障下,故障后暂态运行轨迹碰到奇异面,导致DAE模型下的时域仿真无法运算,由于奇异分叉现象与暂态电压失稳紧密相关,因此,本实施例也视为发生暂态电压失稳。In this implementation case, a three-phase short-circuit fault is set at 1s on busbar 5 and cleared at 1.18s. PSAT is interrupted during time-domain simulation, as shown in Figure 3. Under this fault, the transient operation track after the fault encounters The singular surface makes it impossible to calculate the time domain simulation under the differential algebraic equation (DAE) model. At this time, the instantaneous energy value after the fault is cleared is 0.36, which is less than the critical energy obtained from the dominant unstable equilibrium point. However, under the fault , after the fault, the transient operation trajectory encounters a singular surface, which makes the time domain simulation under the DAE model impossible to calculate. Since the singular bifurcation phenomenon is closely related to the transient voltage instability, this embodiment is also regarded as the occurrence of transient voltage instability. stable.

步骤S3、根据步骤S1中构建的能量函数表达式,提取其中与动态电力元件相关的部分,建立各动态元件的势能分量函数,其中,动态元件包括但不限于发电机、高压直流输电系统、感应电动机。Step S3, according to the energy function expression constructed in step S1, extract the part related to the dynamic power components, and establish the potential energy component function of each dynamic component, wherein the dynamic components include but not limited to generators, high-voltage direct current transmission systems, induction electric motor.

由步骤S1得到的各个动态元件势能分量函数表达如下:The potential energy component function of each dynamic element obtained by step S1 is expressed as follows:

发电机势能:Generator potential energy:

感应电动机势能分量:Induction motor potential energy components:

直流输电系统势能分量:Potential energy components of DC transmission system:

各符号表征变量见步骤S1。由时域仿真结果可以求得每个时步各个势能分量值和变化曲线。See step S1 for each symbolic representation variable. The value and change curve of each potential energy component at each time step can be obtained from the time domain simulation results.

步骤S4、故障期间,电力系统向电网注入大量能量,发电机转速增加导致动能增大,故障清除后,总能量守恒,动能沿着电力网络逐步转化为各个元件和输电线路的势能。随着动能的振荡变化,各个动态元件的势能逐渐增大并也伴随着一定的振荡。所承受势能增幅最大的动态元件将受到更大的能量冲击,也相应的更容易形成局部能量过冲,进而导致此处更容易发生崩溃,因此可以利用故障后,各个动态元件势能最大值所在势能振荡曲线的前半个周期波的势能增量来简单分析电网脆弱区域。Step S4. During the fault period, the power system injects a large amount of energy into the grid, and the increase in the generator speed leads to an increase in kinetic energy. After the fault is cleared, the total energy is conserved, and the kinetic energy is gradually converted into the potential energy of each component and transmission line along the power network. With the oscillating change of kinetic energy, the potential energy of each dynamic element increases gradually and is accompanied by certain oscillation. The dynamic element with the largest increase in potential energy will be subject to greater energy impact, and accordingly it is easier to form local energy overshoot, which makes it more prone to collapse here. Therefore, after a fault, the potential energy of the maximum potential energy of each dynamic element can be used The potential energy increment of the first half cycle wave of the oscillation curve is used to simply analyze the vulnerable area of the power grid.

设故障后设备势能分量达到最大值(或极大值)时刻为T2,对应时刻势能分量为U2,在这一周期中,达到最大值前的极小值时刻为T1,对应时刻势能分量为U1,则这一周期中势能差为ΔU=U2-U1Suppose the time when the potential energy component of the equipment reaches the maximum value (or maximum value) after the fault is T 2 , and the potential energy component at the corresponding time is U 2 , in this cycle, the time of the minimum value before reaching the maximum value is T 1 , and the potential energy The component is U 1 , then the potential energy difference in this cycle is ΔU=U 2 -U 1 .

评估指标一:σ1=ΔU/ΔQEvaluation index one: σ 1 = ΔU/ΔQ

评估指标二:σ2=V(T2)/ΔUEvaluation index two: σ 2 =V(T 2 )/ΔU

其中ΔQ为对应时间段内,该电力设备在故障后动态恢复特性影响下的无功变化量。V(T2)为该设备在T2时刻对应接入母线电压幅值。σ1值越大,则意味着这一周期内,该电力设备的无功动态变化使势能增加速度更快,增幅越大,即所承受的能量冲击更大,也就越容易超过该处网络能够承受的幅度,继而愈容易在此处导致稳定条件破坏,最后导致系统崩溃;σ2的值越小,即意味着该设备在故障后恢复时,所受到能量冲击较大时刻,其所接入母线节点电压值仍比较低,也就是说此处更容易成为临界支路。Among them, ΔQ is the reactive power variation of the power equipment under the influence of dynamic recovery characteristics after a fault within the corresponding time period. V(T 2 ) is the corresponding voltage amplitude of the equipment connected to the bus at T 2 time. The larger the value of σ1, it means that in this cycle, the dynamic change of reactive power of the power equipment makes the potential energy increase faster, and the greater the increase, that is, the greater the energy impact it bears, the easier it is to exceed the power of the network. The range that can be tolerated is more likely to lead to the destruction of stable conditions here, and finally lead to the collapse of the system; the smaller the value of σ 2 , it means that when the equipment receives a greater energy impact when recovering from a fault, the The voltage value of the input bus node is still relatively low, which means that it is more likely to become a critical branch.

基于图2系统,并在母线5处于1s时刻设置三相短路故障,并分别于1.05s、1.1s、1.14s、1.178s清除故障。Based on the system in Figure 2, a three-phase short-circuit fault is set when bus 5 is in 1s, and the faults are cleared at 1.05s, 1.1s, 1.14s, and 1.178s respectively.

对比同一故障清除时刻下,故障后势能振荡增幅曲线(以图4、图5为例)可以明显发现:直流系统、2号发电机在达到势能最大值的这一周期中,由极小值到最大值的振荡幅度最大,其次为感应电动机负荷,最后为1号发电机和3号发电机。同时也可以发现,随着离故障点电气距离的增大,各个电气设备在能量冲击下,势能振荡的最大幅值出现的时间逐步推移,这也侧面反映了能量在网络中的传播特性以及暂态电压失稳有可能发生在多摆的情况。Comparing the post-fault potential energy oscillation amplitude curves (take Fig. 4 and Fig. 5 as examples) at the same time when the fault is cleared, it can be clearly found that in the period when the DC system and No. The oscillation amplitude of the maximum value is the largest, followed by the induction motor load, and finally by generators 1 and 3. At the same time, it can also be found that with the increase of the electrical distance from the fault point, the time for the maximum amplitude of potential energy oscillation of each electrical equipment under the energy impact gradually passes, which also reflects the propagation characteristics of energy in the network and the temporary State voltage instability may occur in the case of multiple swings.

表1.指标一σ1 Table 1. Index σ 1

表2.指标二σ2 Table 2. Index two σ 2

表1中,直流系统的指标一σ1对应值远高于其他设备,其次是2号发电机和感应电动机负荷,而距故障点电气距离最远的3号发电机则最小。说明在各个电气设备的恢复特性作用下,直流受端换流系统动态无功的变化导致在受到最大能量冲击时,直流系统势能振荡幅度和增幅速度更容易变大,即在这一摆更容易使得局部能量过大,超出该处承受能力而发生系统稳定性破坏,进而加速系统暂态电压崩溃。因此,直流受端换流系统的无功恢复特性在该系统暂态电压失稳中占主导地位。In Table 1, the corresponding value of index σ 1 of the DC system is much higher than that of other equipment, followed by No. 2 generator and induction motor load, while No. 3 generator whose electrical distance from the fault point is the farthest is the smallest. It shows that under the influence of the recovery characteristics of each electrical equipment, the change of dynamic reactive power of the DC receiving-end commutation system leads to the potential energy oscillation amplitude and the increase speed of the DC system are easier to become larger when the maximum energy impact is received, that is, it is easier in this pendulum The local energy is too large, and the system stability is destroyed beyond the bearing capacity of the place, thereby accelerating the transient voltage collapse of the system. Therefore, the reactive power recovery characteristics of the DC receiving-end commutation system play a dominant role in the transient voltage instability of the system.

随着故障清除时间的增大,感应电动机负荷与2号发电机指标一σ1的绝对值逐渐增大,而直流系统的σ1值有小幅度的变小。因此,故障清除时间越长,故障时系统各个节点电压跌落幅度越大,感应电动机的负荷特性对暂态电压稳定性的影响逐渐增大。而三台发电机中,2号发电机受到能量冲击时,在直流恢复特性、感应电机负荷特性以及输电网络的传输特性作用下,为支撑网络节点电压形成的无功动态变化对自身势能振荡幅值和频率影响高于其他两台发电机,说明在故障清除后,三台发电机中,2号发电机处更容易发生局部能量变化过大,再若发生暂态电压失稳,2号发电机应该会比其他两台机组早出现功角失稳。由于其所接入的2号母线与直流系统相连,同时,表2中,2号发电机、高压直流系统和感应电动机负荷的指标二σ2对应值远远低于1号发电机和3号发电机,因此2号发电机、直流系统、感应电动机负荷形成了该电力系统的电压脆弱点。With the increase of fault clearing time, the absolute value of induction motor load and No. 2 generator index σ 1 increases gradually, while the value of σ 1 of DC system decreases slightly. Therefore, the longer the fault clearing time, the larger the voltage drop of each node of the system when the fault occurs, and the influence of the load characteristics of the induction motor on the transient voltage stability gradually increases. Among the three generators, when Generator No. 2 is impacted by energy, under the action of the DC recovery characteristics, the load characteristics of the induction motor and the transmission characteristics of the transmission network, the dynamic change of reactive power formed to support the network node voltage will affect the oscillation amplitude of its own potential energy. The value and frequency are higher than those of the other two generators, indicating that after the fault is cleared, among the three generators, generator No. 2 is more prone to excessive local energy changes. The generator should experience power angle instability earlier than the other two generators. Because the No. 2 bus connected to it is connected to the DC system, and at the same time, in Table 2, the index 2 σ 2 corresponding value of No. 2 generator, high-voltage DC system and induction motor load is far lower than that of No. 1 generator and No. 3 Generator, so No. 2 generator, DC system, induction motor load form the voltage vulnerability point of this power system.

另外由表1和上述两个表中数据可以明显看出,随着故障清除时间的增加,故障时电压跌落幅值越大,故障期间向系统注入的能量值越大,则故障后系统各个动态元件受到的能量冲击也越大,2号发电机、直流系统、感应电动机负荷处所积聚的局部能量值也将越大,暂态电压稳定性越低。In addition, it can be clearly seen from the data in Table 1 and the above two tables that with the increase of the fault clearing time, the greater the amplitude of the voltage drop during the fault, the greater the value of energy injected into the system during the fault, and the dynamics of the system after the fault. The greater the energy impact on the components, the greater the local energy value accumulated at the No. 2 generator, the DC system, and the load of the induction motor, and the lower the transient voltage stability.

稳定情况下(图6为例),2号发电机的相对功角摆开幅度远远超过其他两台机组,且功角超前。发生暂态电压失稳时,虽然由于遇到奇异面,受DAE模型的限制,PSAT无法继续仿真下去,然而从图7可以看出1.2s时,感应电机的滑差达到峰值并有降低的趋势,即感应电动机负荷转子已经开始加速,说明遇到奇异面时,并非由于感应电动机不能正常加速而发生堵转,引起感应电机负荷电压失稳,才导致的整个系统电压崩溃,故也侧面说明了直流受端换流系统无功恢复特性对该系统暂态电压失稳影响的主导性。In a stable situation (Figure 6 as an example), the relative power angle swing range of No. 2 generator is far greater than that of the other two units, and the power angle is ahead. When the transient voltage instability occurs, although PSAT cannot continue to simulate due to the limitation of the DAE model due to the encounter with the singular surface, it can be seen from Figure 7 that the slip of the induction motor reaches a peak value and tends to decrease at 1.2s , that is, the load rotor of the induction motor has begun to accelerate, indicating that when encountering a singular surface, it is not because the induction motor cannot accelerate normally and the rotor is blocked, which causes the load voltage of the induction motor to become unstable, which leads to the voltage collapse of the entire system, so it also explains from the side The dominance of the reactive power recovery characteristics of the DC receiving-end converter system on the influence of transient voltage instability on the system.

综上所述,本发明为了研究发电机,高压直流输电系统(HVDC)和电动机对暂态电压稳定性的主要影响,从广义分支势能的角度出发,提出了新的分析方法来研究上述主要动态元件对暂态电压稳定性的影响。根据故障后网络中暂态势能分布的变化规律和稳定裕度的信息,以故障后各电气设备无功的动态恢复特性为基础变量,建立了评估指标,进而对造成电网暂态电压失稳机理进行分析。时域仿真的结果与本发明方法分析结果基本一致,验证了该方法的有效性。In summary, in order to study the main influences of generators, high-voltage direct current transmission systems (HVDC) and motors on transient voltage stability, the present invention proposes a new analysis method to study the above-mentioned main dynamics from the perspective of generalized branch potential energy Effect of components on transient voltage stability. According to the change law of transient potential energy distribution in the network after the fault and the information of the stability margin, the dynamic recovery characteristics of the reactive power of each electrical equipment after the fault are used as the basic variable, and the evaluation index is established, and then the mechanism of the transient voltage instability of the power grid is established. for analysis. The time-domain simulation results are basically consistent with the analysis results of the method of the present invention, which verifies the effectiveness of the method.

上述实施例为本发明较佳的实施方式,但本发明的实施方式并不受上述实施例的限制,其他的任何未背离本发明的精神实质与原理下所作的改变、修饰、替代、组合、简化,均应为等效的置换方式,都包含在本发明的保护范围之内。The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (4)

1.一种电力系统动态元件响应特性对暂态电压稳定性影响分析方法,其特征在于,所述的分析方法包括下列步骤:1. a kind of power system dynamic element response characteristic is to transient voltage stability influence analysis method, it is characterized in that, described analysis method comprises the following steps: S1、建立电力系统数学模型,并基于李雅普诺夫理论,构建能够反映该系统模型的能量函数表达式;S1. Establish a mathematical model of the power system, and construct an energy function expression that can reflect the system model based on Lyapunov theory; S2、暂态电压稳定性判断,通过电力系统分岔条件和基于启发式求得的电压失稳型主导不稳定平衡点构造的恒定能量面来判断暂态电压稳定性;S2. Judging transient voltage stability, judging transient voltage stability through power system bifurcation conditions and a constant energy surface constructed based on heuristically obtained voltage instability-type dominant unstable equilibrium points; S3、根据步骤S1中构建的能量函数表达式,提取其中与动态电力元件相关的部分,建立各动态元件的势能分量函数,其中,所述的动态元件包括发电机、高压直流输电系统、感应电动机;S3. According to the energy function expression constructed in step S1, extract the part related to the dynamic power element, and establish the potential energy component function of each dynamic element, wherein the dynamic element includes a generator, a high-voltage direct current transmission system, and an induction motor ; S4、故障期间,电力系统向电网注入大量能量,发电机转速增加导致动能增大,故障清除后,总能量守恒,动能沿着电力网络逐步转化为各个元件和输电线路的势能,随着动能的振荡变化,各个动态元件的势能逐渐增大并也伴随着一定的振荡,所承受势能增幅最大的动态元件将受到更大的能量冲击,利用各个动态元件势能最大值所在势能振荡曲线的前半个周期波的势能增量来分析电网脆弱区域。S4. During the fault period, the power system injects a large amount of energy into the grid, and the increase in the generator speed leads to an increase in kinetic energy. After the fault is cleared, the total energy is conserved, and the kinetic energy is gradually converted into the potential energy of each component and transmission line along the power network. With the increase of kinetic energy Oscillation changes, the potential energy of each dynamic element gradually increases and is accompanied by a certain oscillation, the dynamic element with the largest increase in potential energy will receive a greater energy impact, and use the first half of the potential energy oscillation curve where the maximum potential energy of each dynamic element is located. The potential energy increment of the wave is used to analyze the vulnerable areas of the power grid. 2.根据权利要求1所述的电力系统动态元件响应特性对暂态电压稳定性影响分析方法,其特征在于,所述的步骤S2过程如下:2. the power system dynamic element response characteristic according to claim 1 influences analysis method on transient voltage stability, it is characterized in that, described step S2 process is as follows: S201、构建能量函数;S201, constructing an energy function; S202、求主导不稳定平衡点;S202, finding the dominant unstable equilibrium point; S203、求临界能量Ucr;S203, find the critical energy Ucr; S204、求故障清除时刻能量U;S204. Find the energy U at the moment of fault clearing; S205、判断故障清除时刻能量U与临界能量Ucr大小,若故障清除时刻能量U大于临界能量Ucr,则判定系统暂态电压失稳;否则,继续转至下一步骤;S205. Determine the magnitude of the energy U and the critical energy Ucr at the time of fault clearing, if the energy U at the time of fault clearing is greater than the critical energy Ucr, then determine that the transient voltage of the system is unstable; otherwise, continue to the next step; S206、判断是否遇到奇异面,若是,则判定系统暂态电压失稳,否则,判定系统稳定。S206 , judging whether a singular surface is encountered, if so, judging that the transient voltage of the system is unstable, otherwise, judging that the system is stable. 3.根据权利要求1所述的电力系统动态元件响应特性对暂态电压稳定性影响分析方法,其特征在于,所述的步骤S4中各个动态元件势能最大值所在势能振荡曲线的前半个周期波的势能增量来分析电网脆弱区域,通过以下评估指标实现不同系统动态元件对暂态电压稳定性影响的评估,具体如下:3. The method for analyzing the influence of response characteristics of power system dynamic components on transient voltage stability according to claim 1, wherein in the step S4, the first half period wave of the potential energy oscillation curve where the potential energy maximum value of each dynamic component is located The potential energy increment is used to analyze the vulnerable areas of the power grid, and the impact of different system dynamic components on the transient voltage stability can be evaluated through the following evaluation indicators, as follows: 设故障后设备势能分量达到最大值或极大值的时刻为T2,对应时刻势能分量为U2,在这一个势能波动周期中,达到最大值前的极小值时刻为T1,对应时刻势能分量为U1,则这一个势能波动周期中势能差为ΔU=U2-U1,定义评估指标如下:Suppose the moment when the potential energy component of the equipment reaches the maximum value or the maximum value after the fault is T 2 , and the potential energy component at the corresponding time is U 2 , in this potential energy fluctuation cycle, the minimum value time before reaching the maximum value is T 1 , and the corresponding time The potential energy component is U 1 , then the potential energy difference in this potential energy fluctuation cycle is ΔU=U 2 -U 1 , and the evaluation index is defined as follows: 评估指标一:σ1=ΔU/ΔQEvaluation index one: σ 1 = ΔU/ΔQ 评估指标二:σ2=V(T2)/ΔUEvaluation index two: σ 2 =V(T 2 )/ΔU 其中,ΔQ为对应时间段内,该电力设备在故障后动态恢复特性影响下的无功变化量,V(T2)为该设备在T2时刻对应接入母线电压幅值。Among them, ΔQ is the reactive power variation of the power equipment under the influence of dynamic recovery characteristics after a fault within the corresponding time period, and V(T 2 ) is the voltage amplitude of the equipment connected to the bus at time T 2 . 4.根据权利要求1所述的电力系统动态元件响应特性对暂态电压稳定性影响分析方法,其特征在于,电力系统的动态元件数学模型与能量函数表达式如下所示:4. The method for analyzing the influence of the dynamic element response characteristics of the power system on transient voltage stability according to claim 1, wherein the dynamic element mathematical model and the energy function expression of the power system are as follows: 所用四阶发电机模型为:The fourth-order generator model used is: 所用三阶感应电动机模型为:The third-order induction motor model used is: 所述有n个发电机节点,N个负荷节点,2个直流系统换流站母线节点,且只有1个平衡节点的电力系统能量函数表达式为:The energy function expression of the power system with n generator nodes, N load nodes, two DC system converter station bus nodes, and only one balance node is: U=UAC+UL1+UL2i+Ug+UR+UI+Ud+UDC U=U AC +U L1 +U L2i +U g +U R +U I +U d +U DC 其中:in: 且有:and have: E=[E1,…,En]T,Ei=[E′qi Efdi];T=blockdiag[T1,…,Tn],A=blockdiag[A1,…,An],B=blockdiag[B1,…,Bn], E=[E 1 ,…,E n ] T , E i =[E′ qi E fdi ]; T=blockdiag[T 1 ,…,T n ], A=blockdiag[A 1 ,...,A n ], B=blockdiag[B 1 ,...,B n ], 其中,下标i和j代表网络母线节点标号,i=1,2,…,n+N+3,j=1,2,…,n+N+3,ρi是为了使Bi -1Ti正定的参数,且对任意不为零的矩阵向量,都有xTBi -1Tix>0,i=1,2…,n;Among them, the subscripts i and j represent the network bus node labels, i=1, 2,..., n+N+3, j=1, 2,..., n+N+3, ρ i is to make B i -1 T i is a positive definite parameter, and for any non-zero matrix vector, there is x T B i -1 T i x>0, i=1, 2..., n; C=[C1,…,Cn]T,Ci=[0 l];C=[C 1 ,...,C n ] T , C i =[0 l]; UDC=-VIVRBIR cos(θIR);U DC =-V I V R B IR cos(θ IR ); 上式中,当i=1,2,…,n时,ωi为发电机转速,δi为发电机转子角度,Mi为发电机惯性时间常数,Pmi为发电机机械功率,Di为阻尼系数,E′qi为q轴暂态电势,Xdi为发电机的暂态电抗,X′di为发电机的次暂态电抗,T′doi为d轴暂态时间常数,Efdi为励磁电势,Pei为发电机电磁功率,μi为励磁控制器反馈增益系数,Tvi为励磁控制时间常数,ki为励磁电压一阶数学模型中,所接入母线电压相关的线性系数,li为接入母线i的使发电机励磁为正的控制常数;R下标代表整流侧变量,I下标代表逆变侧变量,VR和VI交流母线电压幅值,PdR+jQdR和PdI+jQdI为换流器注入的补偿功率;当i=n+1,n+2,…,n+N+3时,T′doi为定子开路时间常数,Mi为感应电动机惯性时间常数,E′Li为内电势幅值,Xr为转子绕组等值漏抗,Xm为定转子互感抗,Xs为定子绕组漏抗,X′i为暂态电抗,Xi为同步电抗,δi为感应电动机功角,si为感应电动机滑差,Tmi为感应电动机电磁转矩,Tei为机械转矩;UAC为交流网络势能,UL1为静态负荷势能,UL2i为接入i节点感应电动机负荷势能,Ug为系统所有发电机能量和,UR为直流整流侧与交流网络接口势能,UI为直流逆变侧与交流网络接口势能,UDC为直流网络节点间势能,Ud为直流功率交换形成的势能分量,Vi和Vj分别为母线标号i和j的电压幅值,θi和θj分别为母线标号i和j的电压相角,QLi为标号为i的母线所接入静态负荷的无功功率,PLi为标号为i的母线所接入静态负荷的有功功率。In the above formula, when i=1, 2,...,n, ω i is the generator speed, δ i is the generator rotor angle, M i is the generator inertia time constant, P mi is the generator mechanical power, D i is the damping coefficient, E′ qi is the q-axis transient potential, X di is the transient reactance of the generator, X′ di is the sub-transient reactance of the generator, T′ doi is the d-axis transient time constant, E fdi is Excitation potential, P ei is the electromagnetic power of the generator, μ i is the feedback gain coefficient of the excitation controller, T vi is the excitation control time constant, k i is the linear coefficient related to the connected bus voltage in the first-order mathematical model of the excitation voltage, l i is the control constant connected to the bus i to make the excitation of the generator positive; the subscript R represents the variable on the rectifier side, the subscript I represents the variable on the inverter side, and the voltage amplitude of the AC bus of VR and V I , P dR +jQ dR and P dI + jQ dI is the compensation power injected by the converter; when i=n+1, n+2,...,n+N+3, T′ doi is the stator open circuit time constant, Mi is the induction motor Inertial time constant, E′ Li is the amplitude of the internal potential, X r is the equivalent leakage reactance of the rotor winding, X m is the mutual inductance of the stator and rotor, X s is the leakage reactance of the stator winding, X′ i is the transient reactance, and X i is Synchronous reactance, δ i is the power angle of the induction motor, s i is the slip of the induction motor, T mi is the electromagnetic torque of the induction motor, T ei is the mechanical torque; U AC is the AC network potential energy, U L1 is the static load potential energy, U L2i is the load potential energy of the induction motor connected to node i, U g is the energy sum of all generators in the system, U R is the potential energy of the DC rectifier side and the AC network interface, U I is the potential energy of the DC inverter side and the AC network interface, and U DC is the DC Potential energy between network nodes, U d is the potential energy component formed by DC power exchange, V i and V j are the voltage amplitudes of bus labels i and j respectively, θ i and θ j are the voltage phase angles of bus labels i and j, respectively, Q Li is the reactive power of the static load connected to the bus marked i, and P Li is the active power of the static load connected to the bus marked i.
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