CN103954885B

CN103954885B - The single-ended alignment system of double line down and localization method based on distributed constant

Info

Publication number: CN103954885B
Application number: CN201410213699.XA
Authority: CN
Inventors: 马静; 史宇欣; 高翔; 闫新; 王增平
Original assignee: North China Electric Power University
Current assignee: North China Electric Power University
Priority date: 2014-05-20
Filing date: 2014-05-20
Publication date: 2016-07-06
Anticipated expiration: 2034-05-20
Also published as: CN103954885A

Abstract

The invention discloses a single-end positioning system and a positioning method for double-circuit line faults based on distribution parameters in the technical field of line fault positioning in electric power systems. The system includes a data acquisition module, a compensation voltage solution module, a fault location voltage solution module, and a fault location module; the method includes collecting the voltage phasor and current phasor at any end of the double-circuit fault line, and solving the same-direction zero-sequence compensation of the double-circuit fault line Coefficient function, reverse zero-sequence compensation coefficient function and compensation voltage function of double-circuit fault line; solve the reverse sequence current at the fault, then calculate the voltage phase at the fault according to the reverse sequence current at the fault, and solve the voltage amplitude at the fault, The fault location function is constructed, and the fault location is identified by solving the phase mutation point of the fault location function. The invention is applicable to various double-circuit faults, only needs to collect single-end power information, and does not need information of other substations, is less affected by factors such as fault location and transition resistance, has high positioning accuracy, and is easy to implement.

Description

Single-end location system and location method for double-circuit line fault based on distribution parameters

技术领域technical field

本发明属于电力系统线路故障定位技术领域，尤其涉及一种基于分布参数的双回线故障单端定位系统及定位方法。The invention belongs to the technical field of power system line fault location, and in particular relates to a single-end location system and method for double-circuit line faults based on distribution parameters.

背景技术Background technique

同塔架设的高压双回线输电容量大，且具有显著的经济效益，同时还可以提高电力系统运行的安全性和稳定性，近年来得到了广泛应用。但在现场运行中，双回线故障不可避免，如何精确的定位故障对迅速隔离故障与及时恢复供电具有重要意义。The high-voltage double-circuit line erected on the same tower has a large transmission capacity and has significant economic benefits. At the same time, it can also improve the safety and stability of the power system operation, and has been widely used in recent years. However, in field operation, double circuit faults are unavoidable, and how to accurately locate the fault is of great significance to quickly isolate the fault and restore power supply in time.

目前，双回线故障定位的方法主要分为双端法和单端法。双端法又可分为基于两端同步采样或同步化处理的双端算法，以及无需数据同步采样或同步化处理的双端算法。该类方法采用线路两端电气量，原理上精度高，不受过渡电阻的影响，但其对通信的依赖程度较大，当本端无法获取对端的数据时，算法失效，无法实现故障定位。单端法包括利用单端双回线信息的算法，以及利用单端单回线信息的算法。单端法无需其他站的信息，仅利用本站电压、电流信息即可进行故障定位，对硬件要求低，易于实现。然而，以往的单端法常采用集中参数模型，忽略分布电容影响，随着故障距离的增大，测量精度将无法保证。Currently, fault location methods for double-circuit lines are mainly divided into double-ended methods and single-ended methods. The double-ended method can be further divided into a double-ended algorithm based on simultaneous sampling or synchronous processing at both ends, and a double-ended algorithm that does not require data synchronous sampling or synchronous processing. This type of method uses the electrical quantity at both ends of the line. In principle, it has high precision and is not affected by transition resistance. However, it relies heavily on communication. When the local end cannot obtain the data from the opposite end, the algorithm fails and the fault location cannot be realized. The single-ended method includes an algorithm utilizing information from a single-ended double circuit, and an algorithm utilizing information from a single-ended single circuit. The single-ended method does not need the information of other stations, and can locate the fault only by using the voltage and current information of the station. It has low hardware requirements and is easy to implement. However, the previous single-ended method often adopts a lumped parameter model and ignores the influence of distributed capacitance. As the fault distance increases, the measurement accuracy cannot be guaranteed.

针对以上问题，本发明基于双回线六序网分布参数模型，从双回线跨线故障的电气特性出发，提出一种基于分布参数的双回线故障单端定位系统及定位方法。该发明首先在双回线六序网分布参数模型中计及互感影响，并借助同向零序补偿系数以及反向零序补偿系数，定义精确补偿电压；在此基础上，根据测量端反向序电流与故障处反向序电流相位的关系，推算故障处电压相位及幅值；最后，利用测量电压、电流以及推算的故障处电压构造故障定位函数，通过求解故障定位函数的相位突变点识别故障位置。基于PSCAD的双端系统仿真模型表明，该单端定位系统及方法适用于多种跨线故障，无需其他变电站的信息，且受故障位置、过渡电阻等因素的影响小，定位精度高，易于实现。In view of the above problems, the present invention is based on the distribution parameter model of the six-sequence network of the double-circuit line, starting from the electrical characteristics of the cross-line fault of the double-circuit line, and proposes a single-end positioning system and positioning method for the double-circuit line fault based on the distribution parameters. The invention first takes into account the influence of mutual inductance in the distribution parameter model of the double-circuit six-sequence network, and defines the precise compensation voltage with the help of the same-direction zero-sequence compensation coefficient and the reverse zero-sequence compensation coefficient; on this basis, according to the reverse direction of the measurement terminal According to the relationship between sequence current and reverse sequence current phase at the fault location, the voltage phase and amplitude at the fault location are calculated; finally, the fault location function is constructed by using the measured voltage, current and the estimated voltage at the fault location, and the phase mutation point identification of the fault location function is solved fault location. The simulation model of the double-ended system based on PSCAD shows that the single-ended positioning system and method are suitable for a variety of cross-line faults, do not need information from other substations, and are less affected by factors such as fault location and transition resistance. The positioning accuracy is high and it is easy to implement .

发明内容Contents of the invention

本发明的目的在于，提供一种基于分布参数的双回线故障单端定位系统及定位方法，用于解决现有的双回线故障定位方法存在的不足。The purpose of the present invention is to provide a double-circuit line fault single-end positioning system and positioning method based on distribution parameters, which are used to solve the shortcomings of the existing double-circuit line fault positioning methods.

为了实现上述目的，本发明提出的技术方案是，一种基于分布参数的双回线故障单端定位系统，其特征是所述系统包括：数据采集模块、补偿电压求解模块、故障处电压求解模块和故障定位模块；In order to achieve the above object, the technical solution proposed by the present invention is a single-end positioning system for double-circuit faults based on distributed parameters, which is characterized in that the system includes: a data acquisition module, a compensation voltage solving module, and a fault voltage solving module and fault location module;

其中，所述数据采集模块分别与补偿电压求解模块和故障处电压求解模块相连；所述故障定位模块分别与补偿电压求解模块和故障处电压求解模块相连；Wherein, the data acquisition module is connected to the compensation voltage solving module and the fault voltage solving module respectively; the fault location module is connected to the compensation voltage solving module and the fault voltage solving module respectively;

所述数据采集模块用于采集双回故障线路任意一端的电压相量和电流相量，并将采集的数据分别发送至补偿电压求解模块和故障处电压求解模块；The data acquisition module is used to collect voltage phasors and current phasors at any one end of the double-circuit fault line, and send the collected data to the compensation voltage solving module and the fault voltage solving module respectively;

所述补偿电压求解模块用于根据双回故障线路的六序网分布参数模型，求解双回故障线路的同向零序补偿系数函数和反向零序补偿系数函数，再根据同向零序补偿系数函数和反向零序补偿系数函数确定双回故障线路的补偿电压函数，并将双回故障线路的补偿电压函数发送至故障定位模块；The compensation voltage solving module is used to solve the same-direction zero-sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function of the double-circuit fault line according to the six-sequence network distribution parameter model of the double-circuit fault line, and then according to the same-direction zero-sequence compensation The coefficient function and the reverse zero-sequence compensation coefficient function determine the compensation voltage function of the double-circuit fault line, and send the compensation voltage function of the double-circuit fault line to the fault location module;

所述故障处电压求解模块用于求解故障处反向序电流，再根据故障处反向序电流计算故障处电压相位，并利用采集的电压相量和电流相量求解故障处电压幅值，近而得到故障处电压，然后将所述故障处电压发送至故障定位模块；The voltage solving module at the fault is used to solve the reverse sequence current at the fault, and then calculate the voltage phase at the fault according to the reverse sequence current at the fault, and use the collected voltage phasor and current phasor to solve the voltage amplitude at the fault, nearly and obtain the voltage at the fault, and then send the voltage at the fault to the fault location module;

所述故障定位模块用于根据双回故障线路的补偿电压函数和故障处电压，构造故障定位函数，并通过求解故障定位函数的相位突变点识别故障位置。The fault location module is used to construct a fault location function according to the compensation voltage function of the double-circuit fault line and the voltage at the fault, and identify the fault location by solving the phase mutation point of the fault location function.

一种基于分布参数的双回线故障单端定位方法，其特征是所述方法包括：A single-end positioning method for double-circuit line faults based on distribution parameters, characterized in that the method includes:

步骤1：采集双回故障线路任意一端的电压相量和电流相量；Step 1: Collect the voltage phasor and current phasor at any end of the double-circuit fault line;

步骤2：根据所述双回故障线路的六序网分布参数模型，求解双回故障线路的同向零序补偿系数函数和反向零序补偿系数函数，再根据同向零序补偿系数函数和反向零序补偿系数函数确定双回故障线路的补偿电压函数；Step 2: According to the six-sequence network distribution parameter model of the double-circuit fault line, solve the same-direction zero-sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function of the double-circuit fault line, and then according to the same-direction zero-sequence compensation coefficient function and The reverse zero-sequence compensation coefficient function determines the compensation voltage function of the double-circuit fault line;

步骤3：求解故障处反向序电流；再根据故障处反向序电流计算故障处电压相位，并利用采集的电压相量和电流相量求解故障处电压幅值，近而得到故障处电压；Step 3: Solve the reverse sequence current at the fault; then calculate the voltage phase at the fault according to the reverse sequence current at the fault, and use the collected voltage phasor and current phasor to solve the voltage amplitude at the fault to obtain the voltage at the fault;

步骤4：根据双回故障线路的补偿电压函数和故障处电压，构造故障定位函数，通过求解故障定位函数的相位突变点识别故障位置。Step 4: According to the compensation voltage function of the double-circuit fault line and the voltage at the fault, construct the fault location function, and identify the fault location by solving the phase mutation point of the fault location function.

所述求解双回故障线路的同向零序补偿系数函数采用公式：The formula for solving the same-direction zero-sequence compensation coefficient function of a double-circuit fault line is:

${k k}_{T T} (({l l}_{mf mf})) = = \frac{{z z}_{cT cT 00} sinh sinh (({γ γ}_{T T 00} {l l}_{mf mf})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))} + + \frac{{Z Z}_{mT mT 00} cosh cosh (({γ γ}_{T T 00} {l l}_{mf mf})) - - {Z Z}_{mT mT 00} cosh cosh (({γ γ}_{11} {l l}_{mf mf}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))};;$

其中，l_mf为双回故障线路的六序网中各序网的采集端到故障处的距离；Among them, l _mf is the distance from the acquisition end of each sequence network in the six-sequence network of the double-circuit fault line to the fault location;

z_cT0为双回故障线路的六序网中同向零序网特性阻抗；z _cT0 is the characteristic impedance of the zero-sequence network in the same direction in the six-sequence network of the double-circuit fault line;

γ_T0为双回故障线路的六序网中同向零序网传播系数；γ _T0 is the propagation coefficient of zero-sequence network in the same direction in the six-sequence network of double-circuit fault lines;

z_c1为同向正序网特性阻抗；z _c1 is the characteristic impedance of the positive sequence network in the same direction;

γ₁为同向正序网传播系数；γ ₁ is the propagation coefficient of positive sequence network in the same direction;

Z_mT0为同向零序阻抗；Z _mT0 is the zero-sequence impedance in the same direction;

sinh()为双曲正弦函数；sinh() is a hyperbolic sine function;

cosh()为双曲余弦函数。cosh() is the hyperbolic cosine function.

所述求解双回故障线路的反向零序补偿系数函数采用公式：The formula for solving the reverse zero-sequence compensation coefficient function of the double-circuit fault line is:

${k k}_{F f} (({l l}_{mf mf})) = = \frac{{z z}_{cF f 00} sinh sinh (({γ γ}_{F f 00} {l l}_{mf mf})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))};;$

其中，l_mf为双回故障线路的采集端到故障处的距离；Among them, l _mf is the distance from the collection end of the double-circuit fault line to the fault;

z_cF0为反向零序网特性阻抗；z _cF0 is the characteristic impedance of reverse zero-sequence network;

γ_F0为反向零序网传播系数；γ _F0 is the propagation coefficient of the reverse zero-sequence network;

sinh()为双曲正弦函数。sinh() is the hyperbolic sine function.

所述根据同向零序补偿系数函数和反向零序补偿系数函数确定双回故障线路的补偿电压函数采用公式：The formula used to determine the compensation voltage function of the double-circuit fault line according to the same-direction zero-sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function is:

${\overset{\cdot &Center Dot;}{U u}}_{op op} (({l l}_{mx mx})) = = \overset{\cdot \cdot}{U u} cosh cosh (({γ γ}_{11} {l l}_{mx mx})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mx mx})) {\overset{\cdot &Center Dot;}{I I}}^{' '};;$

其中，为双回故障线路的补偿电压函数，用于计算双回故障线路上距离采集端l_mx处的补偿电压；in, It is the compensation voltage function of the double-circuit fault line, which is used to calculate the compensation voltage at the distance of 1 _mx from the acquisition terminal on the double-circuit fault line;

sinh()为双曲正弦函数；sinh() is a hyperbolic sine function;

为一回线的单相电压同一回线的相间电压或跨线相间电压 is the single-phase voltage of a circuit Phase-to-phase voltage of the same circuit or across-line phase-to-phase voltage

当为一回线的单相电压时， ${\overset{\cdot}{I}}^{'} = {\overset{\cdot}{I}}_{m} + k_{T} (l_{mx}) {\overset{\cdot}{I}}_{mT 0} + k_{F} (l_{mx}) {\overset{\cdot}{I}}_{mF 0};$ when is the single-phase voltage of a circuit hour, ${\overset{&Center Dot;}{I}}^{'} = {\overset{&Center Dot;}{I}}_{m} + k_{T} (l_{mx}) {\overset{\cdot}{I}}_{mT 0} + k_{f} (l_{mx}) {\overset{\cdot}{I}}_{f 0};$

当为同一回线的相间电压时， when is the phase-to-phase voltage of the same circuit hour,

当为跨线相间电压时， when is the phase-to-phase voltage across the line hour,

为采集端相电流； To collect the terminal phase current;

为采集端同一回线相间电流； is the phase-to-phase current of the same loop at the collection end;

为采集端跨线相间电流； is the phase-to-phase current across the collection terminals;

为同向零序网采集端的序电流； is the sequence current at the collection end of the zero-sequence network in the same direction;

为反向零序网采集端的序电流。 is the sequence current at the collection end of the reverse zero-sequence network.

所述求解故障处反向各序电流采用公式：The formula for solving the reverse sequence current at the fault is:

${\overset{\cdot &Center Dot;}{I I}}_{fFi fFi} = = cosh cosh (({γ γ}_{Fi Fi} {l l}_{mf mf})) \cdot \cdot [[11 + + \frac{tanh tanh (({γ γ}_{Fi Fi} {l l}_{mf mf}))}{tanh tanh (({γ γ}_{Fi Fi} (({l l}_{mn mn} - - {l l}_{mf mf}))))}]] \cdot &Center Dot; {\overset{\cdot &Center Dot;}{I I}}_{mFi mFi};;$

其中，i＝0,1,2，分别代表零序、正序和负序；Among them, i=0,1,2, representing zero sequence, positive sequence and negative sequence respectively;

为故障处反向序电流； is the reverse sequence current at the fault;

γ_Fi为反向各序网传播系数；γ _Fi is the propagation coefficient of each reverse sequence network;

l_mn为双回故障线路两端的距离；l _mn is the distance between the two ends of the double-circuit fault line;

l_mf为双回故障线路的采集端到故障处的距离；l _mf is the distance from the collection end of the double-circuit fault line to the fault point;

cosh()为双曲余弦函数；cosh() is the hyperbolic cosine function;

tanh()为双曲正切函数；tanh() is the hyperbolic tangent function;

为反向各序网中采集端的序电流。 is the sequence current at the collecting end in each reverse sequence network.

所述根据故障处反向序电流计算故障处电压相位具体为：The calculation of the voltage phase at the fault according to the reverse sequence current at the fault is specifically:

子步骤A1：根据双回故障线路的故障类型，确定双回故障线路的故障边界电流条件；Sub-step A1: Determine the fault boundary current condition of the double-circuit fault line according to the fault type of the double-circuit fault line;

子步骤A2：根据双回故障线路的故障边界电流条件和故障处反向序电流，计算故障处电压相位。Sub-step A2: Calculate the voltage phase at the fault according to the fault boundary current condition of the double-circuit fault line and the reverse sequence current at the fault.

所述利用采集的电压相量和电流相量求解故障处电压幅值采用公式： The formula used to solve the voltage amplitude at the fault using the collected voltage phasor and current phasor is:

其中，U_f是故障处电压幅值；Among them, U _f is the voltage amplitude at the fault;

为双回故障线路的阻抗角； is the impedance angle of the double-circuit fault line;

θ为与的夹角；θ is and the included angle;

γ为与的夹角；gamma for and the included angle;

当为一回线的单相电压时， ${\overset{\cdot}{I}}^{'} = {\overset{\cdot}{I}}_{m} + k_{T} (l_{mx}) {\overset{\cdot}{I}}_{mT 0} + k_{F} (l_{mx}) {\overset{\cdot}{I}}_{mF 0};$ when is the single-phase voltage of a circuit hour, ${\overset{\cdot}{I}}^{'} = {\overset{\cdot}{I}}_{m} + k_{T} (l_{mx}) {\overset{\cdot}{I}}_{mT 0} + k_{f} (l_{mx}) {\overset{\cdot}{I}}_{f 0};$

为采集端相电流； To collect the terminal phase current;

所述故障定位函数为： $f (l_{mx}) = \frac{{\overset{\cdot}{U}}_{op} (l_{mx}) - {\overset{\cdot}{U}}_{f} \cosh (γ_{1} l_{mx})}{{\overset{\cdot}{I}}^{'}};$ The fault location function is: $f (l_{mx}) = \frac{{\overset{&Center Dot;}{u}}_{op} (l_{mx}) - {\overset{\cdot}{u}}_{f} \cosh (γ_{1} l_{mx})}{{\overset{&Center Dot;}{I}}^{'}};$

其中，为双回故障线路的补偿电压函数；in, is the compensation voltage function of the double-circuit fault line;

是故障处电压； is the fault voltage;

l_mx为与采集端的距离；l _mx is the distance from the acquisition end;

cosh()为双曲余弦函数。cosh() is the hyperbolic cosine function.

所述通过求解故障定位函数的相位突变点识别故障位置具体包括：The identification of the fault location by solving the phase mutation point of the fault location function specifically includes:

子步骤B1：将双回故障线路n等分，n为设定值；Sub-step B1: divide the double-circuit fault line into n equal parts, and n is a set value;

子步骤B2：根据故障定位函数计算每个等分区间两侧端点的故障定位函数的相位，如果等分区间两侧端点的故障定位函数的相位为一个大于零，一个小于零，则判定相位突变点在该等分区间中；Sub-step B2: Calculate the phase of the fault location function of the endpoints on both sides of each equal interval according to the fault location function. If the phases of the fault location functions of the endpoints on both sides of the equal interval are one greater than zero and the other less than zero, then determine the phase mutation the point is in the division interval;

子步骤B3：从相位突变点所在的等分区间左侧端点开始，每隔设定步长Δl，选取一个点并计算选取的点的故障定位函数的相位；Sub-step B3: Starting from the left end point of the equal interval where the phase mutation point is located, select a point every set step size Δl, and calculate the phase of the fault location function of the selected point;

子步骤B4：将第一个故障定位函数的相位小于0的点作为参考点，所述参考点距离采集端l_f+，则故障位置距离采集端为l_f＝l_f+-0.5·Δl。Sub-step B4: Take the point where the phase of the first fault location function is less than 0 as a reference point, and the reference point is far from the collection end l _f+ , then the distance from the fault location to the collection end is l _f =l _f+ -0.5·Δl.

本发明从双回线故障的电气特性出发，建立基于双回线路分布参数模型的故障定位函数，利用故障定位函数的相位突变性判定故障位置。仿真结果表明，本发明适用于多种双回线故障，只需采集单端电力信息，无需其他变电站的信息，且受故障位置、过渡电阻等因素的影响小，定位精度高，易于实现。The invention starts from the electrical characteristics of double-circuit line faults, establishes a fault location function based on the distribution parameter model of the double-circuit line, and uses the phase mutation of the fault location function to determine the fault location. The simulation results show that the present invention is suitable for various double-circuit faults, only needs to collect single-end power information, and does not need information of other substations, is less affected by factors such as fault location and transition resistance, has high positioning accuracy, and is easy to implement.

附图说明Description of drawings

图1是基于分布参数的双回线故障单端定位系统结构图；Figure 1 is a structural diagram of a single-end location system for double-circuit faults based on distributed parameters;

图2是基于分布参数的双回线故障单端定位方法流程图；Fig. 2 is a flow chart of a double-circuit line fault single-end location method based on distribution parameters;

图3是故障情况下各序网电气量示意图；Figure 3 is a schematic diagram of the electrical quantities of each sequence network under fault conditions;

图4是以相位估算相位误差曲线图；Figure 4 is based on phase estimation Phase error graph;

图5是以相位估算相位误差曲线图；Figure 5 is based on phase estimation Phase error graph;

图6是故障处电压相量图；Figure 6 is the voltage phasor diagram at the fault;

图7是100km处故障时定位函数相位特性图；Figure 7 is a phase characteristic diagram of the positioning function when a fault occurs at 100km;

图8是双回线系统仿真模型图；Fig. 8 is a double circuit system simulation model diagram;

图9是故障位置和故障类型对跨线不接地故障定位影响示意图；Figure 9 is a schematic diagram of the influence of fault location and fault type on the location of cross-line ungrounded faults;

图10是故障位置对跨线两线接地故障定位影响示意图；Figure 10 is a schematic diagram of the influence of the fault location on the location of the two-line ground fault across the line;

图11是故障位置和故障类型对跨线三线接地故障定位影响示意图；Figure 11 is a schematic diagram of the influence of the fault location and fault type on the location of the three-wire ground fault across the line;

图12是故障位置和故障类型对三线故障单相接地定位影响示意图；Figure 12 is a schematic diagram of the impact of fault location and fault type on the location of three-wire fault single-phase ground;

图13是过渡电阻对跨线两线接地故障定位影响示意图；Figure 13 is a schematic diagram of the influence of transition resistance on the location of a two-line ground fault across the line;

图14是过渡电阻和故障类型对跨线三线接地故障定位影响示意图；Figure 14 is a schematic diagram of the impact of transition resistance and fault type on the location of a three-wire ground fault across the line;

图15是过渡电阻和故障类型对三线故障单相接地定位影响示意图。Fig. 15 is a schematic diagram of the influence of transition resistance and fault type on the single-phase-to-ground location of a three-wire fault.

具体实施方式detailed description

下面结合附图，对优选实施例作详细说明。应该强调的是，下述说明仅仅是示例性的，而不是为了限制本发明的范围及其应用。The preferred embodiments will be described in detail below in conjunction with the accompanying drawings. It should be emphasized that the following description is only exemplary and not intended to limit the scope of the invention and its application.

图1是基于分布参数的双回线故障单端定位系统结构图，如图1所示，本发明提供的基于分布参数的双回线故障单端定位系统包括：数据采集模块、补偿电压求解模块、故障处电压求解模块和故障定位模块。其中，数据采集模块分别与补偿电压求解模块和故障处电压求解模块相连，故障定位模块分别与补偿电压求解模块和故障处电压求解模块相连。Fig. 1 is a structural diagram of a double-circuit line fault single-end location system based on distribution parameters, as shown in Figure 1, the double-circuit line fault single-end location system based on distribution parameters provided by the present invention includes: a data acquisition module, a compensation voltage solution module , the voltage solving module at the fault location and the fault location module. Wherein, the data acquisition module is respectively connected with the compensation voltage solution module and the fault location voltage solution module, and the fault location module is connected with the compensation voltage solution module and the fault location voltage solution module respectively.

数据采集模块用于采集双回故障线路任意一端的电压相量和电流相量，并将采集的数据分别发送至补偿电压求解模块和故障处电压求解模块。The data acquisition module is used to collect the voltage phasor and current phasor at any end of the double-circuit fault line, and send the collected data to the compensation voltage solving module and the fault voltage solving module respectively.

补偿电压求解模块用于根据双回故障线路的六序网分布参数模型，求解双回故障线路的同向零序补偿系数函数和反向零序补偿系数函数，再根据同向零序补偿系数函数和反向零序补偿系数函数确定双回故障线路的补偿电压函数，并将双回故障线路的补偿电压函数发送至故障定位模块。The compensation voltage solution module is used to solve the double-circuit fault line's co-direction zero-sequence compensation coefficient function and reverse zero-sequence compensation coefficient function according to the six-sequence network distribution parameter model of the double-circuit fault line, and then according to the and the reverse zero-sequence compensation coefficient function to determine the compensation voltage function of the double-circuit fault line, and send the compensation voltage function of the double-circuit fault line to the fault location module.

故障处电压求解模块用于求解故障处反向序电流，再根据故障处反向序电流计算故障处电压相位，并利用采集的电压相量和电流相量求解故障处电压幅值，近而得到故障处电压，然后将所述故障处电压发送至故障定位模块。The voltage solution module at the fault is used to solve the reverse sequence current at the fault, and then calculate the voltage phase at the fault according to the reverse sequence current at the fault, and use the collected voltage phasor and current phasor to solve the voltage amplitude at the fault, and obtain the voltage at the fault, and then send the voltage at the fault to the fault location module.

故障定位模块用于根据双回故障线路的补偿电压函数和故障处电压，构造故障定位函数，并通过求解故障定位函数的相位突变点识别故障位置。The fault location module is used to construct the fault location function according to the compensation voltage function of the double-circuit fault line and the voltage at the fault, and identify the fault location by solving the phase mutation point of the fault location function.

本发明还提供了一种基于分布参数的双回线故障单端定位方法，如图2所示，该方法包括：The present invention also provides a method for single-ended positioning of double-circuit line faults based on distribution parameters, as shown in Figure 2, the method includes:

步骤1：采集双回故障线路任意一端的电压相量和电流相量。Step 1: Collect the voltage phasor and current phasor at any end of the double-circuit fault line.

数据采集模块采集双回故障线路任意一端的电压相量和电流相量，并发送至补偿电压求解模块和故障处电压求解模块。The data acquisition module collects the voltage phasor and current phasor at any end of the double-circuit fault line, and sends them to the compensation voltage solution module and the fault voltage solution module.

步骤2：在补偿电压求解模块中，根据双回故障线路的六序网分布参数模型，求解双回故障线路的同向零序补偿系数函数和反向零序补偿系数函数，再根据同向零序补偿系数函数和反向零序补偿系数函数，确定双回故障线路的补偿电压与采集端到故障处距离的关系函数，即双回故障线路的补偿电压函数。Step 2: In the compensation voltage solution module, according to the distribution parameter model of the six-sequence network of the double-circuit fault line, solve the same-direction zero-sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function of the double-circuit fault line, and then according to the same-direction zero-sequence The sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function determine the relationship function between the compensation voltage of the double-circuit fault line and the distance from the acquisition terminal to the fault, that is, the compensation voltage function of the double-circuit fault line.

对于对称耦合双回线路的电压和电流相量，经矩阵T实现解耦，得到六序网分布参数模型，如公式(1)所示。For the voltage and current phasors of symmetrically coupled double-circuit lines, decoupling is achieved through the matrix T, and the distributed parameter model of the six-sequence network is obtained, as shown in formula (1).

$T T = = \frac{11}{66} [\begin{matrix} 11 & α α & {α α}^{22} & 11 & α α & {α α}^{22} \\ 11 & {α α}^{22} & α α & 11 & {α α}^{22} & α α \\ 11 & 11 & 11 & 11 & 11 & 11 \\ 11 & α α & {α α}^{22} & - - 11 & - - α α & {- - α α}^{22} \\ 11 & {α α}^{22} & α α & - - 11 & {- - α α}^{22} & - - α α \\ 11 & 11 & 11 & - - 11 & - - 11 & - - 11 \end{matrix}] - - - - - - ((11))$

其中，α＝e^j120°，j为虚数单位。双回线发生故障后，各序网电气量如图3所示，图3中，各序网电压和电流均满足关系式：Wherein, α=e ^j120° , and j is the imaginary unit. After the double-circuit line fails, the electrical quantity of each sequence network is shown in Figure 3. In Figure 3, the voltage and current of each sequence network satisfy the relational expression:

$[\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{mi mi} \\ {\overset{\cdot \cdot}{I I}}_{mi mi} \end{matrix}] = = [\begin{matrix} cosh cosh (({γ γ}_{i i} {l l}_{mf mf})) & {z z}_{ci ci} sinh sinh (({γ γ}_{i i} {l l}_{mf mf})) \\ sinh sinh (({γ γ}_{i i} {l l}_{mf mf})) / / {z z}_{ci ci} & cosh cosh (({γ γ}_{i i} {I I}_{mf mf})) \end{matrix}] [\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{mfi mfi} \\ {\overset{\cdot &Center Dot;}{I I}}_{mfi mfi} \end{matrix}] - - - - - - ((22))$

公式(2)中，i＝T1,T2,T0,F1,F2,F0，分别表示同向正序网、同向负序网、同向零序网、反向正序网、反向负序网和反向零序网。分别为各序网中M端采集的序电压、序电流；为各序网中故障处序电压，为各序网中故障处M端提供的序短路电流，为各序网中故障处序短路电流，l_mf为各序网中M端到故障处的距离。In the formula (2), i=T1, T2, T0, F1, F2, F0, respectively represent the positive sequence network in the same direction, the negative sequence network in the same direction, the zero sequence network in the same direction, the positive sequence network in the reverse direction, and the negative sequence network in the same direction net and reverse zero-sequence net. Respectively, the sequence voltage and sequence current collected by the M terminal in each sequence network; is the fault sequence voltage in each sequence network, is the sequence short-circuit current provided by terminal M at the fault point in each sequence network, is the sequence short-circuit current at the fault point in each sequence network, and l _mf is the distance from the M terminal to the fault point in each sequence network.

将式(2)各序网中M端采集的六序电压相加可得：The six-sequence voltage collected by the M terminal in each sequence network of formula (2) Add up to get:

$\begin{matrix} {\overset{\cdot &Center Dot;}{U u}}_{m m} = = \frac{{\overset{. .}{U u}}_{mfT f 11}}{cosh cosh (({γ γ}_{T T 11} {l l}_{mf mf}))} + + {z z}_{cT cT 11} tanh tanh (({γ γ}_{T T 11} {l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mT mT 11} + + \frac{{\overset{\cdot \cdot}{U u}}_{mfT f 22}}{cosh cosh (({γ γ}_{T T 22} {l l}_{mf mf}))} + + {z z}_{cT cT 22} tanh tanh (({γ γ}_{T T 22} {l l}_{mf mf})) {\overset{. .}{I I}}_{mT mT 22} + + \\ \frac{{\overset{. .}{U u}}_{mfT f 00}}{cosh cosh (({γ γ}_{T T 00} {l l}_{mf mf}))} + + {z z}_{cT cT 00} tanh tanh (({γ γ}_{T T 00} {l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mT mT 00} + + \frac{{\overset{\cdot &Center Dot;}{U u}}_{mfF f 11}}{cosh cosh (({γ γ}_{F f 11} {l l}_{mf mf}))} + + {z z}_{cF f 11} tanh tanh (({γ γ}_{F f 11} {l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mF f 11} + + \\ \frac{{\overset{\cdot &Center Dot;}{U u}}_{mfF f 22}}{cosh cosh (({γ γ}_{F f 22} {l l}_{mf mf}))} + + {z z}_{cF f 22} tanh tanh (({γ γ}_{F f 22} {l l}_{mf mf})) {\overset{\cdot \cdot}{I I}}_{mF f 22} + + \frac{{\overset{\cdot &Center Dot;}{U u}}_{mfF f 00}}{cosh cosh (({γ γ}_{F f 00} {l l}_{mf mf}))} + + {z z}_{cF f 00} tanh tanh (({γ γ}_{F f 00} {l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mF f 00} \\ = = \frac{{\overset{\cdot \cdot}{U u}}_{mf mf}}{cosh cosh (({γ γ}_{11} {l l}_{mf mf}))} + + {z z}_{c c 11} tanh tanh (({γ γ}_{11} {l l}_{mf mf})) [[{\overset{\cdot \cdot}{I I}}_{m m} + + {k k}_{T T} (({l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mT mT 00} + + {k k}_{F f} (({l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mF f 00}]] \end{matrix} - - - - - - ((33))$

其中，分别为采集端M的相电压及相电流，为故障处相电压，z_c1、γ₁分别为同向正序网特性阻抗和传播系数，k_T(l_mf)、k_F(l_mf)分别为同向零序补偿系数函数及反向零序补偿系数函数，两者分别表示为：in, are the phase voltage and phase current of the acquisition terminal M respectively, is the phase voltage at the fault, z _c1 and γ ₁ are the characteristic impedance and propagation coefficient of the positive sequence network in the same direction, respectively, k _T (l _mf ), k _F (l _mf ) are the zero sequence compensation coefficient function in the same direction and the reverse zero Sequence compensation coefficient function, both of which are expressed as:

${k k}_{T T} = = (({l l}_{mf mf})) = = \frac{{z z}_{cT cT 00} sinh sinh (({γ γ}_{T T 00} {l l}_{mf mf})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))} + + \frac{{Z Z}_{mT mT 00} cosh cosh (({γ γ}_{T T 00} {l l}_{mf mf})) - - {Z Z}_{mT mT 00} cosh cosh (({γ γ}_{11} {l l}_{mf mf}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))} - - - - - - ((44))$

${k k}_{F f} (({l l}_{mf mf})) = = \frac{{z z}_{cF f 00} sinh sinh (({γ γ}_{F f 00} {l l}_{mf mf})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mf mf}))} - - - - - - ((55))$

公式(4)和(5)中，z_cT0为双回故障线路的六序网中同向零序网特性阻抗，γ_T0为双回故障线路的六序网中同向零序网传播系数，z_c1为同向正序网特性阻抗，γ₁为同向正序网传播系数，z_cF0为反向零序网特性阻抗，γ_F0为反向零序网传播系数，Z_mT0为同向零序阻抗，sinh()为双曲正弦函数，cosh()为双曲余弦函数。In formulas (4) and (5), _zcT0 is the characteristic impedance of the same-direction zero-sequence network in the six-sequence network of the double-circuit fault line, and γ _T0 is the propagation coefficient of the same-direction zero-sequence network in the six-sequence network of the double-circuit fault line, z _c1 is the characteristic impedance of the positive sequence network in the same direction, γ ₁ is the propagation coefficient of the positive sequence network in the same direction, z _cF0 is the characteristic impedance of the reverse zero sequence network, γ _F0 is the propagation coefficient of the reverse zero sequence network, Z _mT0 is the zero sequence network in the same direction Sequence impedance, sinh() is hyperbolic sine function, cosh() is hyperbolic cosine function.

由式(3)可知，若一回线上两个相电压相减，则同向零序电流及反向零序电流均抵消，因此该回线相间电压与故障处相间电压以及相间电流之间的关系为：It can be seen from formula (3) that if the two phase voltages on a loop line are subtracted, the zero-sequence current in the same direction and the zero-sequence current in the reverse direction will all cancel out, so the phase-to-phase voltage of the loop line Phase to fault voltage and phase-to-phase current The relationship between is:

同理，若跨线的两个相电压相减，仅同向零序电流抵消，则跨线相间电压与故障处跨线相间电压以及跨线相间电流之间的关系为：Similarly, if the two phase voltages across the line are subtracted, only the zero-sequence current in the same direction cancels out, and the phase-to-phase voltage across the line Phase-to-phase voltage across line at fault and the phase-to-phase current across the lines The relationship between is:

定义距M端l_mx处的补偿电压函数为：Define the compensation voltage function at l _mx from M terminal for:

${\overset{\cdot \cdot}{U u}}_{op op} (({l l}_{mx mx})) = = \overset{\cdot &Center Dot;}{U u} cosh cosh (({γ γ}_{11} {l l}_{mx mx})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{mx mx})) {\overset{\cdot &Center Dot;}{I I}}^{' '} - - - - - - ((88))$

其中，的取值与电压的类型有关，如式(9)所示：in, value and voltage is related to the type, as shown in formula (9):

若为一回线的单相电压则为该回线的单相电流同向零序电流以及反向零序电流之和；若为同一回线的相间电压则为相间电流若为跨线相间电压则为跨线相间电流与反向零序电流之和。like is the single-phase voltage of a circuit but is the single-phase current of the return line The sum of the zero-sequence current in the same direction and the zero-sequence current in the reverse direction; if is the phase-to-phase voltage of the same circuit but is the phase-to-phase current like is the phase-to-phase voltage across the line but is the phase-to-phase current across the line and the sum of the reverse zero-sequence current.

步骤3：在故障处电压求解模块中，求解故障处反向序电流；再根据故障处反向序电流计算故障处电压相位，并利用采集的电压相量和电流相量求解故障处电压幅值，近而得到故障处电压。Step 3: In the fault location voltage solution module, solve the reverse sequence current at the fault location; then calculate the voltage phase at the fault location according to the reverse sequence current at the fault location, and use the collected voltage phasor and current phasor to solve the voltage amplitude at the fault location , to obtain the voltage at the fault.

(i)首先，求解故障处反向序电流。(i) First, solve the reverse sequence current at the fault.

根据反向网可求出M端(采集端)反向正/负/零序电流与故障处反向正/负/零序电流的关系：According to the reverse network, the reverse positive/negative/zero-sequence current of the M terminal (acquisition terminal) can be obtained Reverse positive/negative/zero sequence current with fault Relationship:

$\frac{{\overset{\cdot &Center Dot;}{I I}}_{fF f 012012}}{{\overset{\cdot &Center Dot;}{I I}}_{mF f 012012}} = = cosh cosh (({γ γ}_{F f 012012} {l l}_{mf mf})) \cdot \cdot {{11 + + \frac{tanh tanh (({γ γ}_{F f 012012} {l l}_{mf mf}))}{tanh tanh [[{γ γ}_{F f 012012} (({l l}_{mn mn} - - {l l}_{mf mf}))]]}}} - - - - - - ((1010))$

由公式(10)可知，故障处反向序电流为 ${\overset{\cdot}{I}}_{fFi} = \cosh (γ_{Fi} l_{mf}) \cdot [1 + \frac{\tanh (γ_{Fi} l_{mf})}{\tanh [γ_{Fi} (l_{mn} - l_{mf})]}] \cdot {\overset{\cdot}{I}}_{mFi} .$ From formula (10), it can be seen that the reverse sequence current at the fault is ${\overset{&Center Dot;}{I}}_{fFi} = \cosh (γ_{Fi} l_{mf}) \cdot [1 + \frac{\tanh (γ_{Fi} l_{mf})}{\tanh [γ_{Fi} (l_{mn} - l_{mf})]}] &Center Dot; {\overset{&Center Dot;}{I}}_{mFi} .$

其中，i＝0,1,2，分别代表零序、正序和负序，为故障处反向序电流，γ_Fi为反向各序网传播系数，l_mn为双回故障线路两端的距离，l_mf为双回故障线路的采集端到故障处的距离，cosh()为双曲余弦函数，tanh()为双曲正切函数，为反向各序网中采集端的序电流。以相位估算的相位误差曲线如图4所示，考虑到负序网与正序网具有相同参数，因此以相位估算相位误差曲线与正序网相同。同理，以相位估算相位误差曲线如图5所示，可以看出，最大误差不超过0.2°。Among them, i=0,1,2 represent zero sequence, positive sequence and negative sequence respectively, is the reverse sequence current at the fault location, γ _Fi is the propagation coefficient of each reverse sequence network, l _mn is the distance between two ends of the double-circuit fault line, l _mf is the distance from the collection end of the double-circuit fault line to the fault location, cosh() is Hyperbolic cosine function, tanh() is hyperbolic tangent function, is the sequence current at the collecting end in each reverse sequence network. by phase estimation The phase error curve of is shown in Figure 4, considering that the negative sequence network and the positive sequence network have the same parameters, so the phase estimation The phase error curve is the same as that of the positive sequence network. In the same way, with phase estimation The phase error curve is shown in Figure 5. It can be seen that the maximum error does not exceed 0.2°.

故障处相位分别利用相位估算，记为：Troubleshooting phase separation Phase estimation, denoted as:

${\overset{\cdot &Center Dot;}{I I}}_{fF f 11} \approx \approx {k k}_{11} (({l l}_{mf mf})) {\overset{\cdot \cdot}{I I}}_{mF f 11},, {\overset{\cdot \cdot}{I I}}_{fF f 22} \approx \approx {k k}_{22} (({l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mF f 22} - - - - - - ((1111))$

其中，由式(11)可得，故障处反向正负序电流的相位可由采集端M的反向正负序电流相位估算：in, From formula (11), it can be obtained that the phase of the reverse positive and negative sequence current at the fault can be estimated from the phase of the reverse positive and negative sequence current at the acquisition terminal M:

$\begin{matrix} arg arg (({a a}_{11} {\overset{\cdot &Center Dot;}{I I}}_{fF f 11} + + {a a}_{22} {\overset{\cdot &Center Dot;}{I I}}_{fF f 22})) \approx \approx arg arg [[{a a}_{11} {k k}_{11} (({l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mF f 11} + + {a a}_{22} {k k}_{22} (({l l}_{mf mf})) {\overset{\cdot &Center Dot;}{I I}}_{mF f 22}]] \\ = = arg arg [[{k k}_{11} (({l l}_{mf mf})) (({a a}_{11} {\overset{\cdot \cdot}{I I}}_{mF f 11} + + {a a}_{22} {\overset{\cdot &Center Dot;}{I I}}_{mF f 22}))]] \\ = = arg arg [[(({a a}_{11} {\overset{\cdot \cdot}{I I}}_{mF f 11} + + {a a}_{22} {\overset{\cdot &Center Dot;}{I I}}_{mF f 22}))]] \end{matrix} - - - - - - ((1212))$

其中，a₁、a₂为任意实数。Wherein, a ₁ and a ₂ are any real numbers.

(ii)其次，根据双回线跨线故障的边界条件与双回线路电流的六序分量，利用故障处反向序电流计算故障处电压相位。(ii) Secondly, according to the boundary conditions of double-circuit line cross-line faults and the six-sequence components of double-circuit line current, the voltage phase at the fault is calculated by using the reverse sequence current at the fault.

在本例中，选取IA(I回线的A相)为特殊相，故障边界六相电流I_fAT,F经T阵解耦为六序分量I_fAI,II：In this example, IA (phase A of the I circuit) is selected as the special phase, and the six-phase current I _fAT,F at the fault boundary is decoupled into six-sequence components I _fAI,II by the T array:

I_fAT,F＝TI_fAI,II(13)I _fAT,F =TI _fAI,II (13)

其中， $I_{fAT, F} = {[\begin{matrix} {\overset{\cdot}{I}}_{fAT 1} & {\overset{\cdot}{I}}_{fAT 2} & {\overset{\cdot}{I}}_{fAT 0} & {\overset{\cdot}{I}}_{fAT 1} & {\overset{\cdot}{I}}_{fAF 2} & {\overset{\cdot}{I}}_{fAF 0} \end{matrix}]}^{T};$ $I_{fAI, II} = {[\begin{matrix} {\overset{\cdot}{I}}_{fAI} & {\overset{\cdot}{I}}_{fBI} & {\overset{\cdot}{I}}_{fCI} & {\overset{\cdot}{I}}_{fAII} & {\overset{\cdot}{I}}_{fBII} & {\overset{\cdot}{I}}_{fCII} \end{matrix}]}^{T} .$ in, $I_{f, f} = {[\begin{matrix} {\overset{\cdot}{I}}_{f 1} & {\overset{\cdot}{I}}_{f 2} & {\overset{\cdot}{I}}_{f 0} & {\overset{\cdot}{I}}_{f 1} & {\overset{&Center Dot;}{I}}_{f 2} & {\overset{&Center Dot;}{I}}_{f 0} \end{matrix}]}^{T};$ $I_{f, II} = {[\begin{matrix} {\overset{\cdot}{I}}_{f} & {\overset{&Center Dot;}{I}}_{fB} & {\overset{&Center Dot;}{I}}_{f} & {\overset{\cdot}{I}}_{wxya} & {\overset{&Center Dot;}{I}}_{wxya} & {\overset{\cdot}{I}}_{wxya} \end{matrix}]}^{T} .$

根据两线两相故障、三线两相故障和三线三相故障情况下的边界条件以及式(13)，可推导故障处电压的相位与反向序电流相位的关系。According to the boundary conditions in the case of two-line two-phase fault, three-line two-phase fault and three-line three-phase fault and formula (13), the relationship between the phase of the voltage at the fault and the phase of the reverse sequence current can be deduced.

(A)对于两线两相跨线相间故障：(A) For two-line two-phase cross-line fault:

当发生IBIIC(I回线的B相和II回线的C相)跨线不接地故障时，故障边界的电流条件为：When an IBIIC (phase B of the I loop and phase C of the II loop) cross-line non-ground fault occurs, the current condition of the fault boundary is:

${I I}_{fAI f,, II II} {[\begin{matrix} 00 & {\overset{\cdot \cdot}{I I}}_{fBI fB} & 00 & 00 & 00 & {\overset{\cdot \cdot}{I I}}_{fBI fB} \end{matrix}]}^{T T} - - - - - - ((1414))$

将式(14)代入式(13)，可得故障处反向正序电流与相电流的关系：Substituting Equation (14) into Equation (13), the relationship between the reverse positive sequence current and the phase current at the fault can be obtained:

${\overset{\cdot \cdot}{I I}}_{fAF f 11} = = \frac{11}{66} ((α α {\overset{\cdot \cdot}{I I}}_{fBI fB} - - {α α}^{22} {\overset{\cdot \cdot}{I I}}_{fCII wxya})) = = \frac{11}{66} ((α α {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} + + {α α}^{22} {\overset{\cdot &Center Dot;}{I I}}_{fBI fB})) = = - - \frac{11}{66} {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} - - - - - - ((1515))$

根据故障类型，可得故障两相(I回线B相以及II回线C相)相间电压的相位与反向正序电流相位之间的关系：According to the type of fault, the phase-to-phase voltage of the faulty two phases (phase B of the I loop and phase C of the II loop) can be obtained The phase and reverse positive sequence current The relationship between the phases:

(B)对于两线两相跨线接地故障：(B) For two-wire two-phase cross-line ground fault:

当发生IBIIC(I回线的B相和II回线的C相)跨线接地故障时，故障边界的电流条件为：When an IBIIC (phase B of the I loop and phase C of the II loop) cross-line ground fault occurs, the current condition of the fault boundary is:

${I I}_{fAI f,, II II} {[\begin{matrix} 00 & {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} & 00 & 00 & 00 & {\overset{\cdot &Center Dot;}{I I}}_{fCII wxya} \end{matrix}]}^{T T} - - - - - - ((1717))$

将式(17)代入式(13)，可得故障处反向零序电流与相电流的关系：Substituting Equation (17) into Equation (13), the relationship between the reverse zero-sequence current and the phase current at the fault can be obtained:

${\overset{\cdot &Center Dot;}{I I}}_{fAF f 00} = = \frac{11}{66} (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB} - - {\overset{\cdot &Center Dot;}{I I}}_{fCII wxya})) - - - - - - ((1818))$

根据故障类型，可得故障两相相间电压相位与反向零序电流相位的关系：According to the type of fault, the fault two-phase phase-to-phase voltage can be obtained Phase and Reverse Zero Sequence Current Phase relationship:

$arg arg (({\overset{\cdot \cdot}{U u}}_{fBICII wxya})) = = arg arg (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB} - - {\overset{\cdot &Center Dot;}{I I}}_{fCII wxya})) = = arg arg (({\overset{\cdot &Center Dot;}{I I}}_{fAF f 00})) - - - - - - ((1919))$

(C)对于三线两相跨线相间故障：(C) For three-wire two-phase cross-line faults:

当发生IBCIIC(I回线的BC相和II回线的C相)跨线不接地故障时，故障边界的电流条件为：When an IBCIIC (phase BC of the I loop and phase C of the II loop) cross-line non-ground fault occurs, the current condition of the fault boundary is:

$\{\begin{matrix} {I I}_{fAI f,, II II} = = {[\begin{matrix} {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} & 00 & {\overset{\cdot &Center Dot;}{I I}}_{fCI f} & 00 & 00 & {\overset{\cdot &Center Dot;}{I I}}_{fCII wxya} \end{matrix}]}^{T T} \\ {\overset{\cdot \cdot}{I I}}_{fBI fB} + + {\overset{\cdot &Center Dot;}{I I}}_{fCI f} + + {\overset{\cdot &Center Dot;}{I I}}_{fCII wxya} = = 00 \end{matrix} - - - - - - ((2020))$

将式(20)代入式(13)，可得故障处反向正序电流及反向负序电流的表达式：Substituting formula (20) into formula (13), the reverse positive sequence current at the fault can be obtained and reverse negative sequence current expression for:

$\{\begin{matrix} {\overset{\cdot \cdot}{I I}}_{fAF f 11} = = \frac{11}{66} ((α α {\overset{\cdot \cdot}{I I}}_{fBI fB} + + {α α}^{22} {\overset{\cdot \cdot}{I I}}_{fCI f} - - {α α}^{22} {\overset{\cdot &Center Dot;}{I I}}_{fAII wxya})) \\ {\overset{\cdot \cdot}{I I}}_{fAF f 22} = = \frac{11}{66} (({α α}^{22} {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} + + α α {\overset{\cdot \cdot}{I I}}_{fCI f} - - α α {\overset{\cdot \cdot}{I I}}_{fAII wxya})) \end{matrix} - - - - - - ((21 twenty one))$

消去式(21)中的可得故障处反向正负序电流与相电流的关系：In the elimination formula (21) The relationship between the reverse positive and negative sequence current and the phase current at the fault can be obtained:

${\overset{\cdot &Center Dot;}{I I}}_{fAF f 11} - - α α {\overset{\cdot \cdot}{I I}}_{fAF f 22} = = \frac{11}{66} ((α α - - 11)) {\overset{\cdot \cdot}{I I}}_{fBI fB} - - - - - - ((22 twenty two))$

根据故障类型，可得故障处I回线相间电压的相位与反向正负序电流相位的关系：According to the fault type, the phase-to-phase voltage of the I circuit at the fault can be obtained The relationship between the phase of and the reverse positive and negative sequence current phase:

$arg arg (({\overset{\cdot \cdot}{U u}}_{fBCI f})) = = arg arg (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB})) = = arg arg ((\frac{{\overset{\cdot \cdot}{I I}}_{fAF f 11} - - α α {\overset{\cdot \cdot}{I I}}_{fAF f 22}}{α α - - 11})) - - - - - - ((23 twenty three))$

(D)对于三线两相跨线接地故障：(D) For three-wire two-phase cross-line ground fault:

当发生IBCIIC(I回线的BC相和II回线的C相)跨线接地故障时，式(22)所表示的B相故障电流与反向正负序电流的关系仍然满足，此时故障处I回线的B相电压的相位可由相位表示：When an IBCIIC (phase BC of circuit I and phase C of circuit II) cross-line grounding fault occurs, the relationship between the fault current of phase B and the reverse positive and negative sequence current expressed in formula (22) is still satisfied, and the fault Phase B voltage of return line I The phase of Phase means:

$arg arg (({\overset{\cdot &Center Dot;}{U u}}_{fBI fB})) = = arg arg (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB})) = = arg arg ((\frac{{\overset{\cdot &Center Dot;}{I I}}_{fAF f 11} - - α α {\overset{\cdot &Center Dot;}{I I}}_{fAF f 22}}{α α - - 11})) - - - - - - ((24 twenty four))$

(E)对于三线两相非跨线单相接地故障：(E) For three-wire two-phase non-cross-line single-phase ground fault:

I回线的BC相间发生不接地故障的同时，II回线的C相发生接地故障(IBC-IICG)，式(22)所示的关系仍然满足，此时故障处I回线相间电压的相位可由相位表示：When a non-ground fault occurs between BC phases of the I circuit, a ground fault occurs on the C phase of the II circuit (IBC-IICG), and the relationship shown in formula (22) is still satisfied. At this time, the phase-to-phase voltage of the I circuit at the fault The phase of Phase means:

$arg arg (({\overset{\cdot &Center Dot;}{U u}}_{fBCI f})) = = arg arg (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB})) = = arg arg ((\frac{{\overset{\cdot &Center Dot;}{I I}}_{fAF f 11} - - α α {\overset{\cdot &Center Dot;}{I I}}_{fAF f 22}}{α α - - 11})) - - - - - - ((2525))$

(F)对于三线两相跨线单相接地故障：(F) For three-wire two-phase cross-line single-phase ground fault:

当发生IBIIC跨线不接地故障且I回线的C相发生接地故障(IBIIC-ICG)时，式(22)所示关系仍满足，此时故障处相间电压(I回线B相和II回线C相)的相位可由相位表示为：When an IBIIC cross-line non-ground fault occurs and a ground fault occurs on phase C of the I return line (IBIIC-ICG), the relationship shown in equation (22) is still satisfied, and the phase-to-phase voltage at the fault is (I circuit B phase and II circuit C phase) phase can be determined by The phase is expressed as:

$arg arg (({\overset{\cdot \cdot}{U u}}_{fBICII wxya})) = = arg arg (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB})) = = arg arg ((\frac{{\overset{\cdot &Center Dot;}{I I}}_{fAF f 11} - - α α {\overset{\cdot &Center Dot;}{I I}}_{fAF f 22}}{α α - - 11})) - - - - - - ((2626))$

(G)对于三线三相跨线相间故障：(G) For three-wire three-phase cross-line faults:

当发生IBCIIA跨线不接地故障时，故障边界的电流条件为：When an IBCIIA cross-line non-ground fault occurs, the current condition of the fault boundary is:

${I I}_{fAI f,, II II} = = {[\begin{matrix} 00 & {\overset{\cdot \cdot}{I I}}_{fBI fB} & {\overset{\cdot \cdot}{I I}}_{fCI f} & {\overset{\cdot \cdot}{I I}}_{fAII wxya} & 00 & 00 \end{matrix}]}^{T T} - - - - - - ((2727))$

将式(27)代入式(13)，可得故障处反向正序电流及反向负序电流表达式：Substituting equation (27) into equation (13), the expressions of reverse positive sequence current and reverse negative sequence current at the fault can be obtained:

$\{\begin{matrix} {\overset{\cdot \cdot}{I I}}_{fAF f 11} = = \frac{11}{66} ((α α {\overset{\cdot \cdot}{I I}}_{fBI fB} + + {α α}^{22} {\overset{\cdot \cdot}{I I}}_{fCI f} - - {\overset{\cdot &Center Dot;}{I I}}_{fAII wxya})) \\ {\overset{\cdot &Center Dot;}{I I}}_{fAF f 22} = = \frac{11}{66} (({α α}^{22} {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} + + α α {\overset{\cdot &Center Dot;}{I I}}_{fCI f} - - {\overset{\cdot &Center Dot;}{I I}}_{fAII wxya})) \end{matrix} - - - - - - ((2828))$

消去式(28)中的可得故障处反向正负序电流与相电流的关系：In the elimination formula (28) The relationship between the reverse positive and negative sequence current and the phase current at the fault can be obtained:

${\overset{\cdot &Center Dot;}{I I}}_{fAF f 11} - - {\overset{\cdot &Center Dot;}{I I}}_{fAF f 22} = = \frac{11}{66} ((α α - - {α α}^{22})) (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB} - - {\overset{\cdot &Center Dot;}{I I}}_{fCI f})) = = \frac{11}{66} j j \sqrt{33} (({\overset{\cdot &Center Dot;}{I I}}_{fBI fB} - - {\overset{\cdot &Center Dot;}{I I}}_{fCI f})) - - - - - - ((2929))$

(H)对于三线三相跨线接地故障：(H) For three-wire three-phase cross-line ground fault:

当发生IBCIIA跨线接地故障时，在IBCIIA三线三相跨线相间故障中推导的相位关系式(30)仍然成立。When an IBCIIA cross-line ground fault occurs, the phase relationship (30) derived in the IBCIIA three-wire three-phase cross-line fault still holds.

(I)对于三线三相非跨线单相接地故障：(I) For three-wire three-phase non-cross-line single-phase ground fault:

当I回线的BC相发生相间不接地故障且II回线的A相发生接地故障(IBC-IIAG)时，除满足式(27)以外，同时满足：When phase-to-phase non-ground fault occurs on phase BC of circuit I and ground fault occurs on phase A of circuit II (IBC-IIAG), in addition to satisfying formula (27), it also satisfies:

${\overset{\cdot \cdot}{I I}}_{fBI fB} + + {\overset{\cdot &Center Dot;}{I I}}_{fCI f} = = 00 - - - - - - ((3131))$

将式(31)代入(12)，可得故障处反向正负序电流与相电流的关系：Substituting formula (31) into (12), the relationship between the reverse positive and negative sequence current and the phase current at the fault can be obtained:

${\overset{\cdot \cdot}{I I}}_{fAF f 11} - - {\overset{\cdot &Center Dot;}{I I}}_{fAF f 22} = = \frac{11}{33} ((α α - - {α α}^{22})) {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} = = \frac{11}{33} j j \sqrt{33} {\overset{\cdot &Center Dot;}{I I}}_{fBI fB} - - - - - - ((3232))$

应当说明的是，上述(A)-(I)给出了以IA为特殊相，根据不同类型的双回故障线路，计算故障处电压相位的具体实例。对于相同的故障类型，发生故障的线相不同，选取的特殊相会不同，故障边界的电流条件也会不同。比如，当(A)中的两线两相跨线相间故障发生在I回线的A相和II回线的C相之间，即当发生IAIIC跨线不接地故障时，选取以IB为特殊相，故障边界条件的电流条件为 $I_{fI, II} = {[\begin{matrix} {\overset{\cdot}{I}}_{fAI} & 0 & 0 & 0 & 0 & - {\overset{\cdot}{I}}_{fAI} \end{matrix}]}^{T}$ 代入式(13)可得故障处反向序电流与相电流的关系 ${\overset{\cdot}{I}}_{fBF 1} = \frac{1}{6} (α^{2} {\overset{\cdot}{I}}_{fAI} - α {\overset{\cdot}{I}}_{fCII}) = \frac{1}{6} (α^{2} {\overset{\cdot}{I}}_{fAI} + α {\overset{\cdot}{I}}_{fAI}) = - \frac{1}{6} {\overset{\cdot}{I}}_{fAI},$ 根据故障类型，可得故障两相(I回线A相以及II回线C相)相间电压的相位与反向正序电流相位之间的关系：再比如，上述(C)中的三线两相跨线相间故障中，当发生IACIIC跨线不接地故障时，以IB为特殊相，故障边界的电流条件为 $\{\begin{matrix} I_{fI, II} = {[\begin{matrix} {\overset{\cdot}{I}}_{fAI} & 0 & {\overset{\cdot}{I}}_{fCI} & 0 & 0 & {\overset{\cdot}{I}}_{fCII} \end{matrix}]}^{T} \\ {\overset{\cdot}{I}}_{fAI} + {\overset{\cdot}{I}}_{fCI} + {\overset{\cdot}{I}}_{fCII} = 0 \end{matrix},$ 代入式(13)可得故障处反向序电流与相电流的关系为可得故障相间电压与反向序电流相位之间的关系在获得故障类型后，根据故障类型确定故障边界的电流条件以及选取相应的特殊相，再利用双回线路电流的六序分量推导得到故障电压相位与反向序电流的关系，是本领域技术人员常用的技术，由于篇幅所限，本发明仅对各种故障类型中，以IA为特殊相推导了故障电压相位与反向序电流的关系，其他情况下的推导过程不再赘述。It should be noted that the above (A)-(I) give a specific example of calculating the voltage phase at the fault according to different types of double-circuit fault lines with IA as the special phase. For the same fault type, the fault line phase is different, the selected special phase will be different, and the current conditions of the fault boundary will also be different. For example, when the phase-to-phase fault of two lines and two phases in (A) occurs between phase A of circuit I and phase C of circuit II, that is, when an IAIIC non-ground fault occurs, select IB as the special fault. phase, the current condition of the fault boundary condition is $I_{f, II} = {[\begin{matrix} {\overset{&Center Dot;}{I}}_{f} & 0 & 0 & 0 & 0 & - {\overset{&Center Dot;}{I}}_{f} \end{matrix}]}^{T}$ Substituting into equation (13), the relationship between the reverse sequence current and the phase current at the fault can be obtained ${\overset{\cdot}{I}}_{f 1} = \frac{1}{6} (α^{2} {\overset{&Center Dot;}{I}}_{f} - α {\overset{&Center Dot;}{I}}_{wxya}) = \frac{1}{6} (α^{2} {\overset{&Center Dot;}{I}}_{f} + α {\overset{&Center Dot;}{I}}_{f}) = - \frac{1}{6} {\overset{&Center Dot;}{I}}_{f},$ According to the fault type, the phase-to-phase voltage of the faulty two phases (phase A of the I loop and phase C of the II loop) can be obtained The phase and reverse positive sequence current The relationship between the phases: For another example, in the three-wire two-phase cross-line fault in the above (C), when an IACIIC cross-line non-ground fault occurs, IB is the special phase, and the current condition of the fault boundary is $\{\begin{matrix} I_{f, II} = {[\begin{matrix} {\overset{&Center Dot;}{I}}_{f} & 0 & {\overset{&Center Dot;}{I}}_{f} & 0 & 0 & {\overset{\cdot}{I}}_{wxya} \end{matrix}]}^{T} \\ {\overset{&Center Dot;}{I}}_{f} + {\overset{&Center Dot;}{I}}_{f} + {\overset{&Center Dot;}{I}}_{wxya} = 0 \end{matrix},$ Substituting into equation (13), the relationship between the reverse sequence current and the phase current at the fault can be obtained as Available fault phase-to-phase voltage The relationship between the reverse sequence current phase After obtaining the fault type, determine the current condition of the fault boundary and select the corresponding special phase according to the fault type, and then use the six-sequence component of the double-circuit line current to derive the relationship between the fault voltage phase and the reverse sequence current. Commonly used technologies, due to space limitations, the present invention only deduces the relationship between fault voltage phase and reverse sequence current for various fault types, taking IA as a special phase, and the derivation process in other cases will not be repeated.

(iii)最后，由M端电压和电流推算故障处电压幅值。根据图6所示的相量关系，可得故障处电压幅值表达式：(iii) Finally, calculate the voltage amplitude at the fault from the voltage and current at terminal M. According to the phasor relationship shown in Figure 6, the voltage amplitude expression at the fault can be obtained:

其中，U_f为故障处单相电压或相间电压或跨线相间电压为线路阻抗角，θ为与的夹角，γ为与的夹角。Among them, U _f is the single-phase voltage at the fault or phase-to-phase voltage or across-line phase-to-phase voltage is the line impedance angle, θ is and The included angle of , γ is and angle.

步骤4：故障定位模块根据双回故障线路的补偿电压函数和故障处电压，构造故障定位函数，通过求解故障定位函数的相位突变点识别故障位置。Step 4: The fault location module constructs a fault location function according to the compensation voltage function of the double-circuit fault line and the voltage at the fault, and identifies the fault location by solving the phase mutation point of the fault location function.

根据补偿电压函数以及推算的故障处电压由式(3)和式(6)可得如下关系式：According to the compensation voltage function and the estimated fault voltage From formula (3) and formula (6), the following relationship can be obtained:

$\frac{{\overset{\cdot &Center Dot;}{U u}}_{op op} (({l l}_{mx mx})) - - {\overset{\cdot &Center Dot;}{U u}}_{f f} cosh cosh (({γ γ}_{11} {l l}_{mx mx}))}{{\overset{\cdot &Center Dot;}{I I}}^{' '}} = = {z z}_{c c 11} sinh sinh [[{γ γ}_{11} (({l l}_{mf mf} - - {l l}_{mx mx}))]] - - - - - - ((3535))$

构造故障定位函数f(l_mx)：Construct the fault location function f(l _mx ):

$f f (({l l}_{mx mx})) = = \frac{{\overset{\cdot &Center Dot;}{U u}}_{op op} (({l l}_{mx mx})) - - {\overset{\cdot &Center Dot;}{U u}}_{f f} cosh cosh (({γ γ}_{11} {l l}_{mx mx}))}{{\overset{\cdot &Center Dot;}{I I}}^{' '}} - - - - - - ((3636))$

设故障距离l_mf为100km，该故障定位函数的相位特性如图7所示。Assuming that the fault distance l _mf is 100km, the phase characteristics of the fault location function are shown in Figure 7.

由图7可看出，当l_mx<l_mf时，故障定位函数的相位在90°附近，当l_mx>l_mf时，故障定位函数的相位在-90°附近，当l_mx＝l_mf时，故障定位函数的相位为0。因此，故障定位函数相位在故障距离l_mf处发生突变，且突变点仅有一个，故可通过求解故障定位函数的相位突变点识别故障位置，具体子步骤如下：It can be seen from Fig. 7 that when l _mx <l _mf , the phase of the fault location function is around 90°; when l _mx >l _mf , the phase of the fault location function is around -90°; when l _mx =l _mf When , the phase of the fault location function is 0. Therefore, the phase of the fault location function changes abruptly at the fault distance l _mf , and there is only one mutation point, so the fault location can be identified by solving the phase mutation point of the fault location function, and the specific sub-steps are as follows:

子步骤B1：将双回故障线路n等分，n为设定值。Sub-step B1: Divide the double-circuit fault line into n equal parts, where n is a set value.

子步骤B2：根据故障定位函数计算每个等分区间两侧端点的故障定位函数的相位。如果等分区间两侧端点的故障定位函数的相位为一个大于零，一个小于零，则判定相位突变点在该等分区间中。Sub-step B2: Calculate the phase of the fault location function of the endpoints on both sides of each equal interval according to the fault location function. If one of the phases of the fault location functions of the endpoints on both sides of the equal interval is greater than zero and the other is less than zero, then it is determined that the phase mutation point is in the equal interval.

子步骤B3：从相位突变点所在的等分区间左侧端点开始，每隔设定步长Δl，选取一个点并计算选取的点的故障定位函数的相位。Sub-step B3: Starting from the left end point of the equal interval where the phase mutation point is located, a point is selected every set step size Δl, and the phase of the fault location function of the selected point is calculated.

合理选取子步骤B1中的等分区个数n，只需在缩小后的某一等分区内搜索相位突变点即可。因此在不影响故障测距精度的前提下，该故障定位算法所需的运算时间缩短为原来的1/n，求解速度较快。To reasonably select the number n of equal partitions in sub-step B1, it is only necessary to search for phase mutation points in a certain reduced equal partition. Therefore, under the premise of not affecting the accuracy of fault location, the operation time required by the fault location algorithm is shortened to 1/n of the original, and the solution speed is faster.

实施例1Example 1

图8所示为利用PSCAD软件搭建的一电压等级为330kV、长为300km的双端系统仿真模型。Figure 8 shows a simulation model of a double-terminal system with a voltage level of 330kV and a length of 300km built using PSCAD software.

线路MN两端等效电源相角差为δ，二者电源幅值分别为1.05和1pu。两侧系统参数为：Z_M1＝1.0515+j43.1749Ω，Z_M0＝0.6+j29.0911Ω，Z_N1＝26+j44.9185ΩΩ，Z_N0＝20+j37.4697Ω。The phase angle difference of the equivalent power supply at both ends of the line MN is δ, and the amplitudes of the two power supplies are 1.05 and 1pu respectively. The system parameters on both sides are: Z _M1 =1.0515+j43.1749Ω, Z _M0 =0.6+j29.0911Ω, Z _N1 =26+j44.9185ΩΩ, Z _N0 =20+j37.4697Ω.

单回线正(负)序参数为：R₁＝0.05468Ω/km，L₁＝1.0264mH/km，C₁＝0.01095μF/km。The positive (negative) sequence parameters of the single circuit line are: R ₁ =0.05468Ω/km, L ₁ =1.0264mH/km, C ₁ =0.01095μF/km.

单回线零序参数为：R₀＝0.2931Ω/km，L₀＝3.9398mH/km，C₀＝00.05473μF/km。The zero sequence parameters of the single circuit line are: R ₀ =0.2931Ω/km, L ₀ =3.9398mH/km, C ₀ =00.05473μF/km.

双回线零序互阻抗参数为：R_m0＝0.2385Ω/km，L_m0＝2.6274mH/km，C_m0＝0.00026μF/km。The zero-sequence mutual impedance parameters of double-circuit line are: R _m0 =0.2385Ω/km, L _m0 =2.6274mH/km, C _m0 =0.00026μF/km.

定义故障定位相对误差：Define the relative error of fault location:

两线两相跨线不接地故障、三线两相跨线不接地故障以及三线三相跨线不接地故障情况下，不同故障位置对故障定位精度的影响程度如图9所示，可以看出，相对测距误差在290km处达到最大，最大相对误差分别为0.055％、0.0517％和0.055％，均不超过0.1％。In the case of two-line two-phase cross-line ungrounded fault, three-line two-phase ungrounded fault and three-wire three-phase ungrounded fault, the degree of influence of different fault locations on fault location accuracy is shown in Figure 9. It can be seen that, The relative ranging error reaches the maximum at 290km, and the maximum relative errors are 0.055%, 0.0517% and 0.055%, respectively, all of which do not exceed 0.1%.

图10为两线两相跨线接地故障情况下，不同故障位置对故障定位精度的影响程度。图11为三线两相跨线接地故障以及三线三相跨线接地故障情况下，不同故障位置对故障定位精度的影响程度。由图10和图11可以看出，各故障情况下相对测距误差均随故障距离增大而增大，最大相对测距误差的绝对值分别为0.2283％、0.0783％和0.125％，均不超过0.3％。Figure 10 shows the degree of influence of different fault locations on fault location accuracy in the case of a two-line two-phase cross-line ground fault. Figure 11 shows the influence of different fault locations on fault location accuracy in the case of a three-wire two-phase cross-line ground fault and a three-wire three-phase cross-line ground fault. It can be seen from Figure 10 and Figure 11 that the relative ranging error increases with the increase of the fault distance under each fault condition, and the absolute values of the maximum relative ranging error are 0.2283%, 0.0783% and 0.125%, respectively, which do not exceed 0.3%.

三线两相非跨线单相接地故障、三线两相跨线单相接地故障以及三线三相非跨线单相接地故障情况下，故障位置对故障定位精度的影响程度如图12所示，由图12可以看出，最大相对测距误差分别为0.0783％、0.0783％和0.055％，均不超过0.1％。In the case of a three-wire two-phase non-cross-line single-phase ground fault, a three-wire two-phase single-phase ground fault and a three-wire three-phase non-cross-line single-phase ground fault, the influence of the fault location on the fault location accuracy is shown in Figure 12. It can be seen from Fig. 12 that the maximum relative ranging errors are 0.0783%, 0.0783% and 0.055%, respectively, all of which do not exceed 0.1%.

在距测量(采集)处290km，发生两线两相跨线接地故障，过渡电阻对故障定位精度的影响程度如图13所示，可以看出，当过渡电阻为300Ω时，相对测距误差最大，其绝对值为2.7717％。At 290km away from the measurement (acquisition), a two-line two-phase cross-line grounding fault occurs. The degree of influence of the transition resistance on the fault location accuracy is shown in Figure 13. It can be seen that when the transition resistance is 300Ω, the relative ranging error is the largest , and its absolute value is 2.7717%.

图14为距离测量处290km，发生三线两相跨线接地故障以及三线三相跨线接地故障情况下，过渡电阻对定位精度的影响程度。同样，当过渡电阻为300Ω时，相对测距误差绝对值也为最大，分别为1.2683％和1.6183％。Figure 14 shows the degree of influence of transition resistance on positioning accuracy in the case of a three-wire two-phase cross-line ground fault and a three-wire three-phase cross-line ground fault at a distance of 290km from the measurement location. Similarly, when the transition resistance is 300Ω, the absolute value of the relative ranging error is also the largest, which are 1.2683% and 1.6183% respectively.

在距保护测量处290km，发生三线两相非跨线单相接地故障、三线两相跨线单相接地故障以及三线三相非跨线单相接地故障情况下，过渡电阻对故障定位精度的影响程度如图15所示，由图15可知，最大相对测距误差分别为0.095％、0.215％和0.055％。因此，各种经过渡电阻接地的故障中，最大相对误差绝对值仅为2.7717％，不超过3％。Influence of transition resistance on fault location accuracy in the case of three-wire two-phase non-cross-line single-phase ground fault, three-wire two-phase single-phase ground fault and three-wire three-phase non-cross-line single-phase ground fault at 290km away from the protection measurement place The degree is shown in Figure 15, and it can be seen from Figure 15 that the maximum relative ranging errors are 0.095%, 0.215% and 0.055%, respectively. Therefore, the absolute value of the maximum relative error is only 2.7717%, not more than 3%, among various faults grounded through the transition resistance.

以上所述，仅为本发明较佳的具体实施方式，但本发明的保护范围并不局限于此，任何熟悉本技术领域的技术人员在本发明揭露的技术范围内，可轻易想到的变化或替换，都应涵盖在本发明的保护范围之内。因此，本发明的保护范围应该以权利要求的保护范围为准。The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the present invention can easily think of changes or Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims

1. A double-circuit fault single-ended location system based on distributed parameters, characterized in that said system includes: data acquisition module, compensation voltage solution module, fault place voltage solution module and fault location module;

Wherein, the data acquisition module is connected to the compensation voltage solving module and the fault voltage solving module respectively; the fault location module is connected to the compensation voltage solving module and the fault voltage solving module respectively;

The data acquisition module is used to collect voltage phasors and current phasors at any one end of the double-circuit fault line, and send the collected data to the compensation voltage solving module and the fault voltage solving module respectively;

The compensation voltage solving module is used to solve the same-direction zero-sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function of the double-circuit fault line according to the six-sequence network distribution parameter model of the double-circuit fault line, and then according to the same-direction zero-sequence compensation The coefficient function and the reverse zero-sequence compensation coefficient function determine the compensation voltage function of the double-circuit fault line, and send the compensation voltage function of the double-circuit fault line to the fault location module;

The voltage solving module at the fault is used to solve the reverse sequence current at the fault, and then calculate the voltage phase at the fault according to the reverse sequence current at the fault, and use the collected voltage phasor and current phasor to solve the voltage amplitude at the fault, nearly and obtain the voltage at the fault, and then send the voltage at the fault to the fault location module;

The fault location module is used to construct a fault location function according to the compensation voltage function of the double-circuit fault line and the voltage at the fault, and identify the fault location by solving the phase mutation point of the fault location function.

2. A double-circuit fault single-ended location method based on distribution parameters, characterized in that said method comprises:

Step 1: Collect the voltage phasor and current phasor at any end of the double-circuit fault line;

Step 2: According to the six-sequence network distribution parameter model of the double-circuit fault line, solve the same-direction zero-sequence compensation coefficient function and the reverse zero-sequence compensation coefficient function of the double-circuit fault line, and then according to the same-direction zero-sequence compensation coefficient function and The reverse zero-sequence compensation coefficient function determines the compensation voltage function of the double-circuit fault line;

Step 3: Solve the reverse sequence current at the fault; then calculate the voltage phase at the fault according to the reverse sequence current at the fault, and use the collected voltage phasor and current phasor to solve the voltage amplitude at the fault to obtain the voltage at the fault;

Step 4: According to the compensation voltage function of the double-circuit fault line and the voltage at the fault, construct the fault location function, and identify the fault location by solving the phase mutation point of the fault location function.

3. method according to claim 2, it is characterized in that the same direction zero-sequence compensation coefficient function of said solving double-circuit fault line adopts formula:

{k k}_{T T} (({l l}_{m m f f})) = = \frac{{z z}_{c c T T 00} sinh sinh (({γ γ}_{T T 00} {l l}_{m m f f})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{m m f f}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{m m f f}))} + + \frac{{Z Z}_{m m T T 00} cosh cosh (({γ γ}_{T T 00} {l l}_{m m f f})) - - {Z Z}_{m m T T 00} cosh cosh (({γ γ}_{11} {l l}_{m m f f}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{m m f f}))};;

Among them, l _mf is the distance from the acquisition end of each sequence network in the six-sequence network of the double-circuit fault line to the fault location;

z _cT0 is the characteristic impedance of the zero-sequence network in the same direction in the six-sequence network of the double-circuit fault line;

γ _T0 is the propagation coefficient of zero-sequence network in the same direction in the six-sequence network of double-circuit fault lines;

z _c1 is the characteristic impedance of the positive sequence network in the same direction;

γ ₁ is the propagation coefficient of positive sequence network in the same direction;

Z _mT0 is the zero-sequence impedance in the same direction;

sinh() is a hyperbolic sine function;

cosh() is the hyperbolic cosine function.

4. method according to claim 3, it is characterized in that the reverse zero-sequence compensation coefficient function of described solving double-circuit fault line adopts formula:

{k k}_{F f} (({l l}_{m m f f})) = = \frac{{z z}_{c c F f 00} sinh sinh (({γ γ}_{F f 00} {l l}_{m m f f})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{m m f f}))}{{z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{m m f f}))};;

Among them, z _cF0 is the characteristic impedance of reverse zero-sequence network;

γ _F0 is the propagation coefficient of the reverse zero-sequence network.

5. method according to claim 4, it is characterized in that described according to zero-sequence compensation coefficient function in the same direction and the compensation voltage function of reverse zero-sequence compensation coefficient function to determine the compensation voltage function of double-circuit fault line adopts formula:

{\overset{\cdot &Center Dot;}{U u}}_{o o p p} (({l l}_{m m x x})) = = \overset{\cdot &Center Dot;}{U u} cosh cosh (({γ γ}_{11} {l l}_{m m x x})) - - {z z}_{c c 11} sinh sinh (({γ γ}_{11} {l l}_{m m x x})) {\overset{\cdot \cdot}{I I}}^{' '};;

in, It is the compensation voltage function of the double-circuit fault line, which is used to calculate the compensation voltage at the distance of 1 _mx from the acquisition terminal on the double-circuit fault line;

is the single-phase voltage of a circuit Phase-to-phase voltage of the same circuit or across-line phase-to-phase voltage

when is the single-phase voltage of a circuit hour,

{\overset{\cdot}{I}}^{'} = {\overset{\cdot}{I}}_{m} + k_{T} (l_{m x}) {\overset{&Center Dot;}{I}}_{m T 0} + k_{f} (l_{m x}) {\overset{&Center Dot;}{I}}_{m f 0};

when is the phase-to-phase voltage of the same circuit hour,

when is the phase-to-phase voltage across the line hour,

To collect the terminal phase current;

is the phase-to-phase current of the same loop at the collection end;

is the phase-to-phase current across the collection terminals;

is the sequence current at the collection end of the zero-sequence network in the same direction;

is the sequence current at the collection end of the reverse zero-sequence network.

6. method according to claim 5, it is characterized in that described solution fault place reverse each sequence current adopts formula:

{\overset{\cdot \cdot}{I I}}_{f f F f i i} = = cosh cosh (({γ γ}_{F f i i} {l l}_{m m f f})) \cdot \cdot [[11 + + \frac{tanh tanh (({γ γ}_{F f i i} {l l}_{m m f f}))}{tanh tanh [[{γ γ}_{F f i i} (({l l}_{m m n no} - - {l l}_{m m f f}))]]}]] \cdot \cdot {\overset{\cdot &Center Dot;}{I I}}_{m m F f i i};;

Among them, i=0,1,2, representing zero sequence, positive sequence and negative sequence respectively;

is the reverse sequence current at the fault;

γ _Fi is the propagation coefficient of each reverse sequence network;

l _mn is the distance between the two ends of the double-circuit fault line;

tanh() is the hyperbolic tangent function;

is the sequence current at the collecting end in each reverse sequence network.

7. The method according to claim 6, wherein the calculation of the voltage phase at the fault according to the reverse sequence current at the fault is specifically:

Sub-step A1: Determine the fault boundary current condition of the double-circuit fault line according to the fault type of the double-circuit fault line;

Sub-step A2: Calculate the voltage phase at the fault according to the fault boundary current condition of the double-circuit fault line and the reverse sequence current at the fault.

8. The method according to claim 7, characterized in that the voltage phasor and current phasor that utilizes the collection to solve the voltage amplitude at the fault adopts the formula:

Among them, U _f is the voltage amplitude at the fault;

is the impedance angle of the double-circuit fault line;

θ is and the included angle;

gamma for and angle, is the fault voltage.

9. The method according to claim 8, characterized in that the fault location function is:

f f (({l l}_{m m x x})) = = \frac{{\overset{\cdot &Center Dot;}{U u}}_{o o p p} (({l l}_{m m x x})) - - {\overset{\cdot &Center Dot;}{U u}}_{f f} cosh cosh (({γ γ}_{11} {l l}_{m m x x}))}{{\overset{\cdot &Center Dot;}{I I}}^{' '}} . .

10. The method according to claim 9, characterized in that the phase mutation point identification fault location by solving the fault location function specifically includes:

Sub-step B1: divide the double-circuit fault line into n equal parts, and n is a set value;

Sub-step B2: Calculate the phase of the fault location function of the endpoints on both sides of each equal interval according to the fault location function. If the phases of the fault location functions of the endpoints on both sides of the equal interval are one greater than zero and the other less than zero, then determine the phase mutation the point is in the division interval;

Sub-step B3: Starting from the left end point of the equal interval where the phase mutation point is located, select a point every set step size Δl and calculate the phase of the fault location function of the selected point;

Sub-step B4: Take the point where the phase of the first fault location function is less than zero as a reference point, and the reference point is far from the collection end l _f+ , then the distance from the fault location to the collection end is l _f =l _f+ -0.5·Δl.