CN115563921A - Method and system for determining fault transient electric quantity of flexible direct current transmission line - Google Patents

Abstract

The invention discloses a method for determining fault transient electric quantity of a flexible direct current transmission line, which comprises the following steps: constructing an MMC equivalent circuit during interelectrode short circuit according to the MMC converter station circuit parameters; establishing an equivalent model of two ports of the direct current transmission line in a complex frequency domain according to the acquired transmission line parameters; obtaining a direct current fault transient expression under a complex frequency domain according to an MMC equivalent circuit and a direct current transmission line two-port equivalent model when the interelectrode is in short circuit; the method and the device can accurately give the overall trend of the transient process after the fault. The calculation process is simple and convenient, and the complicated modeling simulation process in the traditional simulation method is avoided. Meanwhile, the wave generation process when the overhead line fails can be well reflected. The method can accurately express the overall development trend of fault current flowing through the protection installation position after the fault occurs and before the converter station is locked, and has positive significance on the fault current suppression and protection setting design of the MMC-HVDC system.

Description

Method and system for determining fault transient electrical quantity of flexible direct current transmission line

technical field

The invention belongs to the technical field of flexible direct current transmission, and in particular relates to a method and a system for determining a fault transient electric quantity of a flexible direct current transmission line.

Background technique

At present, the modular multi-level converter (MMC) has the advantages of convenient control, low switching frequency, small harmonics, and modular design, and is one of the commonly used topologies in flexible DC transmission projects. Overhead lines are the main way for high-power electric energy transmission in modular multilevel converter HVDC (MMC-HVDC) systems, but due to long transmission distances and direct exposure to the environment, the use of overhead lines It leads to the increase of the failure probability of the straight line, which seriously threatens the safe and stable operation of the power system.

The switching of the MMC neutron module is nonlinear, and the electromagnetic transient process is complex during a fault. In engineering, simulation software (such as PSCAD/EMTDC) is usually used for simulation. However, the simulation calculation has the following limitations: (1) DC engineering is highly complex , modeling is difficult; (2) The scale of the simulation system is limited, and the simulation is performed separately for different fault types and fault locations, the simulation time is long and the efficiency is low. Therefore, in order to accurately and efficiently analyze the transient process after a fault, the analytical calculation of the fault current has become the focus of attention in the field of control and protection.

In the current research on the calculation of the short-circuit fault current of transmission lines, the lumped parameter model is usually adopted, and the transmission line is equivalent to the RL series branch. And the linear circuit composed of DC power supply, on this basis, solve the equations through circuit theory. However, this ignores the influence of distributed capacitance, and cannot reflect the propagation delay and specific wave process of line faults.

Contents of the invention

In order to solve the problems existing in the prior art, the present invention provides a method for determining the fault transient electric quantity of a flexible direct current transmission line, which can accurately determine the fault transient electric quantity of the direct current transmission line.

The technical problem to be solved by the present invention is achieved through the following technical solutions:

In the first aspect, a method for determining the transient electrical quantity of a flexible direct current transmission line fault is provided, including:

According to the circuit parameters of the MMC converter station, the MMC equivalent circuit is constructed when the poles are short-circuited;

According to the obtained transmission line parameters, an equivalent model of the two ports of the DC transmission line in the complex frequency domain is established;

According to the MMC equivalent circuit and the two-port equivalent model of the DC transmission line when the poles are short-circuited, the transient expression of the DC fault in the complex frequency domain is obtained;

The time domain response is obtained by performing Laplace transform on the DC fault transient expression in the complex frequency domain.

In combination with the first aspect, further, the MMC equivalent circuit constructed according to the circuit parameters of the MMC converter station when interpole short circuit includes:

Obtain the MMC circuit parameters, including bridge arm resistance R _arm , bridge arm inductance L _arm , smoothing reactor inductance L _fw , sub-module on-resistance R _on and sub-module capacitance C _SM ;

Construct the RCL series circuit according to the obtained circuit parameters of the MMC converter station, and use it as the MMC equivalent circuit when the poles are short-circuited, where the resistance is R _eq , the inductance is L _eq , and the capacitance is C _eq ;

Wherein, N is the number of sub-modules connected in series on the upper and lower bridge arms of each phase of the MMC.

In combination with the first aspect, further, the establishment of the two-port equivalent model of the DC transmission line in the complex frequency domain according to the obtained transmission line parameters includes:

Obtain transmission line parameters, including transmission line resistance per unit length R ₀ , unit length inductance L ₀ , unit length conductance G ₀ , unit length capacitance C ₀ and transmission line distance L;

According to the parameters of the transmission line, the DC transmission line model in the complex frequency domain is expressed by ordinary differential equations as follows:

Solve formula (2) to get

x为位置变量，s为拉布拉斯算子，γ为传播系数，Z₁为波阻抗，U_f、U_b分别为传输线电压前行波和反行波；I_f、I_b分别为传输线电流前行波和反行波，U、I分别表示复频域下直流传输线的电压电流；in,

x is the position variable, s is the Laplace operator, γ is the propagation coefficient, Z ₁ is the wave impedance, U _f and U _b are the forward wave and reverse wave of the transmission line voltage respectively; _{If and I b are} the transmission line Current forward wave and reverse wave, U and I respectively represent the voltage and current of the DC transmission line in the complex frequency domain;

Taking x=0 and x=L respectively, the DC transmission line is equivalent to a two-port equivalent model, and the port characteristics of the two-port equivalent model are expressed as follows:

Among them, U _m and U _n respectively represent the voltages of the nodes at both ends of the transmission line, I _m and In represent the currents of the nodes at both ends of the transmission line respectively, and U _is the node voltage vector;

The two-port equivalent model is expressed by the current admittance matrix Y as:

Combined with the first aspect, further, the DC fault transient expression in the complex frequency domain includes:

Laplace transformation is performed on the inductance and capacitance in the MMC equivalent circuit when the poles are short-circuited to obtain the inductance voltage and capacitance current in the complex frequency domain, as shown in the following formula:

V _L (s)＝ _Leq sI _L (s) _-Leq i _L (0 _- ) (6)

I _C (s)＝C _eq sV _C (s)-C _eq v _C (0 _- ) (7)

Among them, V _L (s), I _L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; V _C (s), I _C (s) are the capacitor voltage and current in the complex frequency domain, respectively; L _eq , C _eq are the inductance and capacitance of the MMC equivalent circuit when the poles are short-circuited; i _L (0-), v _C (0-) are the steady-state DC current and voltage, respectively;

Construct the equivalent circuit of the transmission line pole-to-pole fault in the complex frequency domain;

On the basis of the single transmission line admittance matrix in the transmission line interpole fault equivalent circuit, the nodal admittance matrix is established for the transmission line interpole fault equivalent circuit;

The relationship between the current and voltage at both ends of the transmission line in the complex frequency domain is obtained based on the node admittance matrix established by the equivalent circuit of the transmission line interpole fault equivalent model and the two-port equivalent model of the DC transmission line in the complex frequency domain. relationship, actual circuit information, and the termination of the transmission line to obtain the equation of the relationship between the voltage of each node and the current of the branch;

Solve the equations of the relationship between the voltage of each node and the branch current to obtain the DC fault transient expression F(s) in the complex frequency domain.

In combination with the first aspect, further, the time domain response obtained by performing Laplace transform on the DC fault transient expression in the complex frequency domain includes:

The following formula is used to perform Laplace transform on the DC fault transient expression in the complex frequency domain

Among them, f(t) is the DC fault transient expression in the time domain; s=σ+jω is the Laplacian operator; j is an imaginary number, ω is the frequency, σ is any normal number, z=st, t for time;

Use the rational function ξ _β.α (z) to perform Pade approximation on the function e ^z , so that the first α+β+1 terms of the two Taylor expansions are equal, and the expression of ξ _β.α (z) is as follows:

Among them, P _β (z) and Q _α (z) are polynomials of order β and α respectively, and α-β>2;

如下式所示：Substitute ξ _β.α (z) for e ^z to get the approximate expression of f(t)

As shown in the following formula:

进行积分计算，得到直流故障暂态的时域响应如下式所示：According to the remainder theorem

Carrying out integral calculation, the time-domain response of DC fault transient is obtained as follows:

Among them, z _i is the pole of ξ _β.α (z), and k _i is the residue corresponding to the pole.

In the second aspect, a system for determining the transient electrical quantity of a flexible direct current transmission line fault is provided, including:

The MMC equivalent circuit building block for short circuit between poles is used to construct the equivalent circuit of MMC for short circuit between poles according to the circuit parameters of the MMC converter station;

The two-port equivalent model building block of the DC transmission line in the complex frequency domain is used to establish the two-port equivalent model of the DC transmission line in the complex frequency domain according to the obtained transmission line parameters;

The DC fault transient expression acquisition module in the complex frequency domain is used to obtain the DC fault transient expression in the complex frequency domain according to the MMC equivalent circuit and the DC transmission line two-port equivalent model when the poles are short-circuited;

The line fault transient electrical quantity determination module is used to perform Laplace transform on the DC fault transient expression in the complex frequency domain to obtain the time domain response.

In conjunction with the second aspect, further, the operations performed by the MMC equivalent circuit building block during the short circuit between the poles include:

Obtain the MMC circuit parameters, including bridge arm resistance R _arm , bridge arm inductance L _arm , smoothing reactor inductance L _fw , sub-module on-resistance R _on and sub-module capacitance C _SM ;

Construct the RCL series circuit according to the obtained circuit parameters of the MMC converter station, and use it as the MMC equivalent circuit when the poles are short-circuited, where the resistance is R _eq , the inductance is L _eq , and the capacitance is C _eq ;

Wherein, N is the number of sub-modules connected in series on the upper and lower bridge arms of each phase of the MMC.

In combination with the second aspect, further, the operations performed by the two-port equivalent model building module of the DC transmission line in the complex frequency domain include:

Obtain transmission line parameters, including transmission line resistance per unit length R ₀ , unit length inductance L ₀ , unit length conductance G ₀ , unit length capacitance C ₀ and transmission line distance L;

According to the parameters of the transmission line, the DC transmission line model in the complex frequency domain is expressed by ordinary differential equations as follows:

Solve formula (2) to get

x为位置变量，s为拉布拉斯算子，γ为传播系数，Z₁为波阻抗，U_f、U_b分别为传输线电压前行波和反行波；I_f、I_b分别为传输线电流前行波和反行波；in,

x is the position variable, s is the Laplace operator, γ is the propagation coefficient, Z ₁ is the wave impedance, U _f and U _b are the forward wave and reverse wave of the transmission line voltage respectively; _{If and I b are} the transmission line Current forward and backward waves;

Taking x=0 and x=L respectively, the DC transmission line is equivalent to a two-port equivalent model, and the port characteristics of the two-port equivalent model are expressed as follows:

Among them, U _m and U _n respectively represent the voltages of the nodes at both ends of the transmission line, I _m and In represent the currents of the nodes at both ends of the transmission line respectively, and U _is the node voltage vector;

The two-port equivalent model is expressed by the current admittance matrix Y as:

In combination with the second aspect, further, the operations performed by the DC fault transient expression acquisition module in the complex frequency domain include:

Laplace transformation is performed on the inductance and capacitance in the MMC equivalent circuit when the poles are short-circuited to obtain the inductance voltage and capacitance current in the complex frequency domain, as shown in the following formula:

V _L (s)＝ _Leq sI _L (s) _-Leq i _L (0 _- ) (6)

I _C (s)＝C _eq sV _C (s)-C _eq v _C (0 _- ) (7)

Among them, V _L (s), I _L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; V _C (s), I _C (s) are the capacitor voltage and current in the complex frequency domain, respectively; L _eq , C _eq are the inductance and capacitance of the MMC equivalent circuit when the poles are short-circuited; i _L (0-), v _C (0 _- ) are the steady-state DC current and voltage, respectively;

Construct the equivalent circuit of the transmission line pole-to-pole fault in the complex frequency domain;

On the basis of the single transmission line admittance matrix in the transmission line interpole fault equivalent circuit, the nodal admittance matrix is established for the transmission line interpole fault equivalent circuit;

The relationship between the current and voltage at both ends of the transmission line in the complex frequency domain is obtained based on the node admittance matrix established by the equivalent circuit of the transmission line interpole fault equivalent model and the two-port equivalent model of the DC transmission line in the complex frequency domain. relationship, actual circuit information, and the termination of the transmission line to obtain the equation of the relationship between the voltage of each node and the current of the branch;

Solve the equations of the relationship between the voltage of each node and the branch current to obtain the DC fault transient expression F(s) in the complex frequency domain.

With reference to the second aspect, further, the operations performed by the line fault transient electrical quantity determination module include:

The following formula is used to perform Laplace transform on the DC fault transient expression in the complex frequency domain

Among them, f(t) is the DC fault transient expression in the time domain; s=σ+jω is the Laplacian operator; j is an imaginary number, ω is the frequency, σ is any normal number, z=st, t for time;

Use the rational function ξ _β.α (z) to perform Pade approximation on the function e ^z , so that the first α+β+1 terms of the two Taylor expansions are equal, and the expression of ξ _β.α (z) is as follows:

Among them, P _β (z) and Q _α (z) are polynomials of order β and α respectively, and α-β>2;

如下式所示：Substitute ξ _β.α (z) for e ^z to get the approximate expression of f(t)

As shown in the following formula:

进行积分计算，得到直流故障暂态的时域响应如下式所示：According to the remainder theorem

Carrying out integral calculation, the time-domain response of DC fault transient is obtained as follows:

Among them, z _i is the pole of ξ _β.α (z), and k _i is the residue corresponding to the pole.

Beneficial effects of the present invention: the present invention can more accurately give the overall trend of the transient process after a fault. The calculation process is simple, avoiding the cumbersome and complicated modeling and simulation process in the traditional simulation method. At the same time, it can well reflect the occurrence wave process when the overhead line is faulty. The proposed method can more accurately express the overall development trend of the fault current flowing through the protection installation after the fault occurs and before the converter station is blocked, which has positive significance for the fault current suppression and protection setting design of the MMC-HVDC system.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is a schematic structural diagram of the main circuit of the MMC-HVDC system applicable to the present invention;

Fig. 3 is the MMC equivalent circuit diagram when short circuit between poles among the present invention;

4 is a schematic diagram of an equivalent model of two ports of a DC transmission line in the complex frequency domain in the present invention;

Fig. 5 is a schematic diagram of an equivalent circuit of a fault between poles of a transmission line of an MMC-HVDC system in a complex frequency domain according to the present invention.

detailed description

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. the embodiment. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

In order to better understand the present invention, the related technologies in the technical solution of the present invention will be described below.

Example 1

As shown in Figure 1-5, Figure 1 shows the main circuit structure diagram of the MMC-HVDC system. It should be noted that the MMC-HVDC system is the sum of the AC system at both ends, the MMC converter station, and the DC transmission line. The equipment in the station mainly includes converter transformers, AC filters, smoothing reactors and converters. The MMC-HVDC system converts the three-phase alternating current into direct current through the rectification of the converter station, and then the MMC converter station sends it to another converter station through the direct current transmission line for inversion into three-phase alternating current. The upper and lower bridge arms of each phase of the MMC flow station are respectively composed of N half-bridge sub-modules connected in series with the bridge arm reactance, and each half-bridge SM includes two IGBTs, freewheeling diode groups and an energy storage capacitor; both ends of the DC line Connect the smoothing reactor. During normal operation, the total number of input SMs in the upper and lower bridge arms of each phase in the MMC at any time remains unchanged and is N (half of all SMs in each phase), and the DC voltage remains stable. And the corresponding output AC voltage can be obtained by controlling the distribution of N input SMs between the upper and lower bridge arms.

Please refer to Fig. 2, a method for calculating the fault transient electrical quantity of flexible direct current transmission lines based on numerical Laplace inverse transform provided by the present invention, including:

Step S1: According to the circuit parameters of the MMC converter station in the MMC-HVDC system, the MMC equivalent circuit is established when the poles are short-circuited and the parameters of the equivalent circuit are determined. The specific process is as follows:

Step S1.1: Obtain the MMC circuit parameters, including bridge arm resistance R _arm , bridge arm inductance L _arm , smoothing reactor inductance L _fw , sub-module on-resistance R _on , and sub-module capacitance C _SM . The sub-module groups of the upper and lower bridge arms of each phase of the MMC are obtained by connecting N sub-modules in series, and N is a positive integer greater than 1.

Step S1.2: Establish the MMC equivalent circuit and determine the parameters of the equivalent circuit when there is a short circuit between electrodes. The equivalent circuit model is an RLC series circuit, in which the resistance is R _eq , the inductance is L _eq , and the capacitance C _eq .

It is understandable that after a short circuit occurs between the poles of the transmission line in the MMC-HVDC system, the power transmission between the sending end and the receiving end converter station stops, and the SM capacitor in the input state discharges to the fault point through the bridge arm, which is equivalent to a three-phase short circuit Fault. For a period of time before the converter station is locked, the number of input SMs in the converter station remains unchanged at N, and the control system has little effect on the short-circuit current. The MMC can be equivalent to an RLC series circuit.

It should be noted that the equivalent resistance R _eq , equivalent inductance L _eq , and equivalent capacitance C _eq in the equivalent circuit of the MMC converter station can be calculated from the MMC circuit parameters as follows:

Step S2: Establish the equivalent two-port network model of the DC transmission line in the complex frequency domain, the specific process is as follows:

Step S2.1: Obtain transmission line parameters, including unit length resistance R ₀ , unit length inductance L ₀ , unit length conductance G ₀ , unit length capacitance C ₀ and transmission line distance L. m and n are the serial numbers of the end nodes at both ends of the transmission line (first and last ends).

Step S2.2: In the complex frequency domain, a transmission line model is established and expressed by an ordinary differential equation.

The transmission line is represented by the following system of partial differential equations in the time domain:

Among them, u and i respectively represent the voltage and current of the transmission line in the time domain.

Laplace transform is performed on the partial differential equations in the time domain, and the transmission line model in the complex frequency domain can be expressed as an ordinary differential equation as follows:

U and I represent the voltage and current of the transmission line in the complex frequency domain, respectively.

Step S2.3: Solve the ordinary differential equation of the transmission line model in the complex frequency domain to obtain its general solution as follows:

为传播系数；,

为波阻抗。U_f、U_b分别为传输线电压前行波和反行波；I_f、I_b分别为传输线电流前行波和反行波；x为位置变量。In the formula,

is the propagation coefficient;

is the wave impedance. U _f , U _b are forward wave and reverse wave of transmission line voltage respectively; _{If , I b are} forward wave and reverse wave of transmission line current respectively; x is position variable.

Step S2.4: Take x=0, x=L, that is, the first and last nodes m and n of the transmission line. The transmission line in the complex frequency domain is equivalent to a two-port network, and its port characteristics are described by admittance matrix.

Specifically, taking x=0 and x=L respectively, the relationship between the two ends of the transmission line in the complex frequency domain can be expressed as:

Concerned about the electrical characteristics at both ends of the transmission line, the transmission line in the complex frequency domain is regarded as a two-port network, and its port characteristics can be expressed in the form of a transmission parameter matrix as:

According to the above formula, when the transmission parameter matrix adopts the admittance matrix, the port characteristics of the two-port network are expressed as:

In the formula, u _m and u _n are the voltages of the first and last nodes m and _n of the transmission line respectively, i _m and in are the currents of the first and last nodes m and n of the transmission line respectively, and the equivalent model of the two ports of the DC transmission line passes through the current admittance of the transmission line The matrix Y is expressed as:

Step S3: Calculate the DC fault transient state in the complex frequency domain. The specific process is as follows:

Step S3.1: After the MMC equivalent circuit is established in step S1 when the poles are short-circuited, the Laplace transform is performed on the inductance L _eq and the capacitance C _eq in the equivalent circuit to obtain the expressions in the complex frequency domain as follows:

V _L (s)＝ _Leq sI _L (s) _-Leq i _L (0 _- ) (9)

I _C (s)＝C _eq sV _C (s)-C _eq v _C (0 _- ) (10)

where V _L (s), I _L (s) are the inductance, voltage, and current of the transmission line in the complex frequency domain, respectively; V _C (s), I _C (s) are the voltage and current of the transmission line capacitance in the complex frequency domain, respectively. i _L (0 _- ), v _C (0 _- ) are steady-state DC current and voltage, which can be expressed as:

Where U _dc and I _dc are MMC DC voltage and current in steady state, respectively.

In the complex frequency domain, the inductance is represented by the Norton equivalent circuit; the capacitance is represented by the Thevenin equivalent circuit.

Step S3.2: Establish the equivalent circuit of the fault between poles of the transmission line of the MMC-HVDC system in the complex frequency domain, see Figure 4 for the circuit diagram. Each node of the circuit in the figure is numbered (node-1 to node-6). The voltage of each node is denoted as U _n (s), the subscript n is the node number; the current of each branch is denoted as I _nm (s), and n and m in the subscript are the node numbers of the two ends of the branch respectively.

Step 3.3: On the basis of the single transmission line admittance matrix Y _nm , the node admittance matrix is established for the DC system transmission line interpole fault equivalent circuit, as follows:

Y _nm,k in the matrix Y _Trans is the kth element in the transmission line admittance matrix Y _nm .

Step S3.4: The equivalent two-port network model of the transmission line obtained in step S2 reflects the relationship between current and voltage at both ends of the transmission line in the complex frequency domain through the admittance matrix. According to the actual circuit information and the termination of the transmission line, the node analysis method is used to obtain the equation representing the relationship between the voltage of each node and the branch current as follows:

Step S3.5: According to the MMC equivalent circuit obtained in step S1 and the inductance and capacitance expressions in the complex frequency domain obtained in step S3.1, the boundary conditions are introduced as follows:

In the formula, Z _eq,L =R _eq,L +L _eq,L s+1/C _eq,L s, Z _eq.R =R _eq.R +L _eq.R s+1/C _eq.R s. Req,L , _Leq , _L , C _eq,L and _Req.R , Leq, _R , C _eq,R are the equivalent resistance, inductance and capacitance in the equivalent circuit of the left and right converter stations respectively. Step S3.6: Solve the equation (Equation (13)) representing the relationship between the voltage of each node and the branch current to obtain the DC fault transient expression F(s) in the complex frequency domain.

Step S4: After the DC fault transient expression in the complex frequency domain is obtained, the conversion from the frequency domain to the time domain is realized by numerical inverse Laplace transform, and the corresponding time domain response is obtained. The specific process is as follows:

Step S4.1: After calculating the DC fault transient expression F(s) in the complex frequency domain by step S3, perform inverse Laplace transform on F(s), and the transformation formula is expressed as:

In the formula, s=σ+jω is the Laplacian operator; 1; z=st.

Step S4.2: Use the rational function ξ _β.α (z) to perform Pade approximation on the function e ^z , so that the first α+β+1 items of the two Taylor expansions are equal, and the expression of ξ _β.α (z) is as follows :

In the formula, P _β (z) and Q _α (z) are polynomials of order β and α respectively, and α-β>2.

如下：Step S4.3: Use ξ _β.α (z) instead of e ^z to get the approximate expression of f(t)

as follows:

进行积分计算如下，即可获得直流故障暂态的时域响应。Step S4.4: Use the residue theorem to

The integral calculation is performed as follows, and the time-domain response of the DC fault transient can be obtained.

In the formula, z _i is the pole of ξ _nm (z), and _ki is the residue corresponding to the pole, both of which may be complex numbers.

Example 2

Provided is a flexible direct current transmission line fault transient electrical quantity determination system, including:

The MMC equivalent circuit building block for short circuit between poles is used to construct the equivalent circuit of MMC for short circuit between poles according to the circuit parameters of the MMC converter station;

The two-port equivalent model building block of the DC transmission line in the complex frequency domain is used to establish the two-port equivalent model of the DC transmission line in the complex frequency domain according to the obtained transmission line parameters;

The DC fault transient expression acquisition module in the complex frequency domain is used to obtain the DC fault transient expression in the complex frequency domain according to the MMC equivalent circuit and the DC transmission line two-port equivalent model when the poles are short-circuited;

The line fault transient electrical quantity determination module is used to perform Laplace transform on the DC fault transient expression in the complex frequency domain to obtain the time domain response.

Those skilled in the art should understand that the embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present application is described with reference to flowcharts and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

Claims (10)

1. A method for determining fault transient electric quantity of a flexible direct current transmission line is characterized by comprising the following steps:

constructing an MMC equivalent circuit during interelectrode short circuit according to the MMC converter station circuit parameters;

establishing an equivalent model of two ports of the direct current transmission line in a complex frequency domain according to the acquired transmission line parameters;

obtaining a direct-current fault transient expression under a complex frequency domain according to an MMC equivalent circuit and two-port equivalent models of a direct-current transmission line during interelectrode short circuit;

and performing Laplace transform on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.

2. The method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 1, wherein the step of constructing the inter-pole short-circuit-time MMC equivalent circuit according to the MMC converter station circuit parameters comprises the following steps:

obtaining MMC circuit parameters including bridge arm resistance R _arm Bridge arm inductance L _arm Smoothing reactor inductance L _fw Submodule on-resistance R _on And a sub-module capacitor C _SM ；

An RCL series circuit is constructed according to the obtained MMC converter station circuit parameters and is used as an MMC equivalent circuit during interelectrode short circuit, wherein the resistance is R _eq Inductance is L _eq A capacitor of C _eq ；

And N is the number of the MMC each-phase upper and lower bridge arm series sub-modules.

3. The method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 1, wherein the establishing of the two-port equivalent model of the direct current transmission line in the complex frequency domain according to the acquired transmission line parameters comprises:

obtaining transmission line parameters including transmission line unit length resistance R ₀ Inductance L per unit length ₀ Conductivity per unit length G ₀ Capacitance per unit length C ₀ And a transmission line distance L;

according to the transmission line parameters, the direct current transmission line model in the complex frequency domain is expressed by using a common differential equation as follows:

solving the formula (2) to obtain

Wherein,

x is the position variable, s is the Laplacian operator, gamma is the propagation coefficient, Z ₁ Is wave impedance, U _f 、U _b Respectively a transmission line voltage forward traveling wave and a transmission line voltage backward traveling wave; i is _f 、I _b The forward traveling wave and the backward traveling wave of the transmission line current are respectively;

taking x =0 and x = l, respectively, and equating the dc transmission line to a two-port equivalent model, where the port characteristics of the two-port equivalent model are as follows:

wherein, U _m 、U _n Respectively representing the voltages at the nodes at the two ends of the transmission line, I _m 、I _n Respectively representing transmissionsThe current of nodes at two ends of the line, U is a node voltage vector;

the two-port equivalent model is represented by a current admittance matrix Y as:

4. the method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 2, wherein the obtaining of the direct current fault transient expression in the complex frequency domain comprises:

when the interelectrode short circuit occurs, the inductance and the capacitance in the MMC equivalent circuit are subjected to Laplacian transformation to obtain the inductance voltage and the capacitance current under a complex frequency domain, as shown in the following formula:

V _L (s)＝L _eq sI _L (s)-L _eq i _L (0 _- ) (6)

I _C (s)＝C _eq sV _C (s)-C _eq v _C (0 _- ) (7)

wherein, V _L (s)、I _L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; v _C (s)、I _C (s) are respectively capacitance voltage and current in complex frequency domain; l is _eq 、C _eq Respectively an inductor and a capacitor of the MMC equivalent circuit during interelectrode short circuit; i.e. i _L (0 _- )、v _C (0 _- ) Respectively, steady-state direct current and voltage;

constructing an inter-electrode fault equivalent circuit of the transmission line in a complex frequency domain;

establishing a node admittance matrix for the inter-transmission line fault equivalent circuit on the basis of a single transmission line admittance matrix in the inter-transmission line fault equivalent circuit;

obtaining a relation between current and voltage at two ends of the transmission line in a complex frequency domain according to a node admittance matrix established by the transmission line interpolar fault equivalent circuit and a direct current transmission line two-port equivalent model in the complex frequency domain, and obtaining an equation of the relation between voltage of each node and branch current according to the relation between the current and voltage at two ends of the transmission line in the complex frequency domain, actual circuit information and the termination condition of the transmission line;

and solving an equation of the relation between the voltage of each node and the current of the branch circuit to obtain a direct-current fault transient expression F(s) in a complex frequency domain.

5. The method for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 1, wherein the step of performing laplace transform on the direct current fault transient expression in the complex frequency domain to obtain a time domain response comprises the steps of:

laplace transformation is carried out on a direct current fault transient expression under a complex frequency domain by adopting the following formula

Wherein f (t) is a transient expression of the direct current fault in the time domain; s = σ + j ω, which is laplacian; j is an imaginary number, ω is a frequency, σ is any normal number, z = st, t is time;

using rational functions xi _n.m (z) to function e ^z Carrying out Pade approximation to ensure that the first alpha + beta +1 terms of the Taylor expansion of the two are equal to each other, and xi _n.m The expression of (z) is as follows:

wherein, P _β (z)、Q _α (z) are respectively beta, alpha order polynomials, alpha-beta > 2;

using xi _β.α (z) alternative e ^z Obtaining an approximate expression of f (t)

As shown in the following formula:

according to the leave theorem pair

And (3) performing integral calculation to obtain the time domain response of the direct current fault transient as shown in the following formula:

wherein z is _i Is xi _β.α Pole of (z), k _i The residue corresponding to the pole.

6. The utility model provides a flexible direct current transmission line trouble transient state electrical quantity confirms system which characterized in that includes:

the MMC equivalent circuit construction module is used for constructing an MMC equivalent circuit during the interelectrode short circuit according to the circuit parameters of the MMC converter station;

the direct current transmission line two-port equivalent model building module in the complex frequency domain is used for building a direct current transmission line two-port equivalent model in the complex frequency domain according to the acquired transmission line parameters;

the direct current fault transient expression acquisition module under the complex frequency domain is used for acquiring a direct current fault transient expression under the complex frequency domain according to the MMC equivalent circuit and the two-port equivalent model of the direct current transmission line during the interelectrode short circuit;

and the line fault transient electrical quantity determining module is used for performing Laplace transformation on the direct current fault transient expression in the complex frequency domain to obtain a time domain response.

7. The system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the operations executed by the MMC equivalent circuit building module during the short circuit between the electrodes comprise:

obtaining MMC circuit parameters including bridge arm resistance R _arm Bridge arm inductance L _arm Smoothing reactor inductance L _fw Submodule on-resistance R _on And a sub-module capacitor C _SM ；

According to the obtained MMC converter station circuit parametersEstablishing RCL series circuit as MMC equivalent circuit in interelectrode short circuit, wherein the resistance is R _eq Inductance is L _eq A capacitor is C _eq ；

And N is the number of the upper bridge arm series submodule and the lower bridge arm series submodule of each phase of the MMC.

8. The system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the operations executed by the direct current transmission line two-port equivalent model building module in the complex frequency domain comprise:

obtaining transmission line parameters including transmission line unit length resistance R ₀ Inductance L per unit length ₀ Conductivity per unit length G ₀ Capacitance per unit length C ₀ And a transmission line distance L;

according to the transmission line parameters, the direct current transmission line model in the complex frequency domain is expressed by using a common differential equation as follows:

solving the formula (2) to obtain

Wherein,

x is the position variable, s is the Laplacian operator, gamma is the propagation coefficient, Z ₁ Is wave impedance, U _f 、U _b Respectively a transmission line voltage forward traveling wave and a transmission line voltage backward traveling wave; i is _f 、I _b The forward traveling wave and the backward traveling wave of the transmission line current are respectively, U, I respectively represent the direct current transmission under the complex frequency domainVoltage current of the transmission line;

taking x =0 and x = l, respectively, and equating the dc transmission line to a two-port equivalent model, where the port characteristics of the two-port equivalent model are as follows:

wherein, U _m 、U _n Respectively representing the voltages at the nodes at the two ends of the transmission line, I _m 、I _n Respectively representing the current of nodes at two ends of a transmission line, and U is a node voltage vector;

the two-port equivalent model is represented by a current admittance matrix Y as:

9. the system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the operation performed by the direct current fault transient expression obtaining module in the complex frequency domain comprises:

when the interelectrode short circuit occurs, the inductance and the capacitance in the MMC equivalent circuit are subjected to Laplacian transformation to obtain the inductance voltage and the capacitance current under a complex frequency domain, as shown in the following formula:

V _L (s)＝L _eq sI _L (s)-L _eq i _L (0 _- ) (6)

I _C (s)＝C _eq sV _C (s)-C _eq v _C (0 _- ) (7)

wherein, V _L (s)、I _L (s) are the voltage and current of the inductor in the complex frequency domain, respectively; v _C (s)、I _C (s) are respectively capacitance voltage and current in complex frequency domain; l is _eq 、C _eq Respectively an inductor and a capacitor of the MMC equivalent circuit during interelectrode short circuit; i.e. i _L (0 _- )、v _C (0 _- ) Respectively, steady-state direct current and voltage;

constructing an inter-electrode fault equivalent circuit of the transmission line in a complex frequency domain;

establishing a node admittance matrix for the inter-transmission line fault equivalent circuit on the basis of a single transmission line admittance matrix in the inter-transmission line fault equivalent circuit;

obtaining a relation between current and voltage at two ends of the transmission line in a complex frequency domain according to a node admittance matrix established by the transmission line interpolar fault equivalent circuit and a direct current transmission line two-port equivalent model in the complex frequency domain, and obtaining an equation of the relation between voltage of each node and branch current according to the relation between the current and voltage at two ends of the transmission line in the complex frequency domain, actual circuit information and the termination condition of the transmission line;

and solving an equation of the relation between the voltage of each node and the current of the branch circuit to obtain a direct-current fault transient expression F(s) in a complex frequency domain.

10. The system for determining the fault transient electrical quantity of the flexible direct current transmission line according to claim 6, wherein the line fault transient electrical quantity determination module performs operations including:

laplace transformation is carried out on a direct current fault transient expression under a complex frequency domain by adopting the following formula

Wherein f (t) is a transient expression of the direct current fault in the time domain; s = σ + j ω, which is laplacian; j is an imaginary number, ω is a frequency, σ is any normal number, z = st, t is time;

using rational functions xi _β.α (z) to function e ^z Carrying out Pade approximation to make the first alpha + beta +1 terms of the Taylor expansion equations equal and xi _β.α The expression of (z) is as follows:

wherein, P _β (z)、Q _α (z) is respectively beta, alpha-order multiThe formula, alpha-beta is more than 2;

using xi _β.α (z) alternative e ^z Obtaining an approximate expression of f (t)

As shown in the following formula:

according to the leave theorem pair

And (3) performing integral calculation to obtain the time domain response of the direct current fault transient as shown in the following formula:

wherein z is _i Is xi _β.α Pole of (z), k _i The residue corresponding to the pole.

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