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

Abstract

The application discloses a kind of flexible direct current transmission line fault transient electrical quantity determination methods, comprising: according to the circuit parameter of MMC converter station, construct MMC equivalent circuit when inter-pole short circuit;According to the transmission line parameter obtained, establish the equivalent model of two-port of direct current transmission line under complex frequency domain;According to the equivalent circuit of MMC when inter-pole short circuit and the equivalent model of two-port of direct current transmission line, obtain the expression of direct current fault transient under complex frequency domain;The expression of direct current fault transient under complex frequency domain is carried out Laplace transformation to obtain time domain response, the whole trend of transient process after fault can be given more accurately by the application.The calculation process is simple, avoids the complicated modeling simulation process in traditional simulation method.Meanwhile, it can well reflect the occurrence wave process when overhead line fails.The method can accurately express the overall development trend of the fault current flowing through the protection installation before the converter station is locked after the fault occurs, and has a positive significance for the fault current suppression and protection setting design of MMC-HVDC system.

Description

Technical Field

[0001] This invention belongs to the field of flexible DC transmission technology, and particularly relates to a method and system for determining transient electrical quantities during faults in flexible DC transmission lines. Background Technology

[0002] Currently, modular multi-level converters (MMCs) offer advantages such as convenient control, low switching frequency, low harmonics, and modular design, making them a commonly used topology in flexible DC transmission projects. Overhead lines are the primary method for transmitting high-power electricity in modular multilevel converter HVDC (MMC-HVDC) systems. However, due to the long transmission distances and direct exposure to the environment, the use of overhead lines increases the probability of straight-line faults, seriously threatening the safe and stable operation of the power system.

[0003] The switching of submodules in an MMC is nonlinear, and the electromagnetic transient process during a fault is complex. In engineering, simulation software (such as PSCAD / EMTDC) is usually used for simulation. However, simulation calculation has the following limitations: (1) DC engineering is highly complex and difficult to model; (2) The simulation system is limited in scale, and simulations are performed separately for different fault types and fault locations, resulting in long simulation times and low efficiency. Therefore, in order to accurately and efficiently analyze the transient process after a fault, the analytical calculation of fault current has become a key focus in the field of control and protection.

[0004] Current research on short-circuit fault current calculation in transmission lines typically employs a lumped parameter model, treating the transmission line as an equivalent RL series branch. This approach equates the DC system after a short-circuit fault to a linear circuit composed of resistors, inductors, capacitors, and a DC power source, and then solves the equations using circuit theory. However, this approach neglects the influence of distributed capacitance and fails to reflect the propagation delay and specific wave process of the line fault. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for determining transient electrical quantities during faults in flexible DC transmission lines, which can accurately determine the transient electrical quantities during faults in DC transmission lines.

[0006] The technical problem to be solved by the present invention is achieved through the following technical solution:

[0007] Firstly, a method for determining transient electrical quantities during faults in flexible DC transmission lines is provided, including:

[0008] Construct the MMC equivalent circuit under inter-pole short circuit based on the MMC converter station circuit parameters;

[0009] Based on the obtained transmission line parameters, establish an equivalent two-port model of a DC transmission line in the complex frequency domain;

[0010] Based on the MMC equivalent circuit and the two-port equivalent model of the DC transmission line during inter-electrode short circuit, the transient expression of DC fault in the complex frequency domain is obtained.

[0011] The time-domain response is obtained by performing a Laplace transform on the transient expression of a DC fault in the complex frequency domain.

[0012] In conjunction with the first aspect, further, the construction of the MMC equivalent circuit under inter-pole short circuit based on the MMC converter station circuit parameters includes:

[0013] Obtain MMC circuit parameters, including bridge arm resistance R. arm Bridge arm inductor L arm Smoothing reactor inductor L fw Submodule on-resistance R on and submodule capacitor C SM ;

[0014] Based on the obtained MMC converter station circuit parameters, an RCL series circuit is constructed and used as the MMC equivalent circuit under inter-electrode short circuit conditions, where the resistance is R. eq Inductance is L eq The capacitance is C eq ;

[0015]

[0016] Where N is the number of series sub-modules in the upper and lower arms of each phase of the MMC.

[0017] In conjunction with the first aspect, further, establishing the two-port equivalent model of the DC transmission line in the complex frequency domain based on the acquired transmission line parameters includes:

[0018] Obtain transmission line parameters, including resistance R0 per unit length, inductance L0 per unit length, conductance G0 per unit length, capacitance C0 per unit length, and transmission line distance L.

[0019] Based on the transmission line parameters, the DC transmission line model in the complex frequency domain can be expressed using ordinary differential equations as follows:

[0020]

[0021] Solving equation (2) yields

[0022]

[0023] in, x is the position variable, s is the Labras operator, γ is the propagation coefficient, Z1 is the wave impedance, and U fU b These are the forward and reverse traveling waves of the transmission line voltage, respectively; I f I b These are the forward and reverse traveling waves of the transmission line current, respectively, and U and I represent the voltage and current of the DC transmission line in the complex frequency domain, respectively.

[0024] Taking x = 0 and x = L respectively, the DC transmission line is equivalent to a two-port equivalent model. The port characteristics of the two-port equivalent model are expressed as follows:

[0025]

[0026] Among them, U m U n I represents the voltage at each of the two nodes of the transmission line. m I n Let U represent the current at each of the nodes at both ends of the transmission line, and U be the node voltage vector.

[0027] The two-port equivalent model is represented by the current admittance matrix Y as follows:

[0028]

[0029] Combining the first aspect, further, the transient expression for DC faults in the complex frequency domain is obtained as follows:

[0030] The inductor voltage and capacitor current in the complex frequency domain are obtained by performing a Laplace transform on the inductor and capacitor in the MMC equivalent circuit when the electrodes are short-circuited, as shown in the following equation:

[0031] V L (s)=L eq sI L (s)-L eq i L (0 - (6)

[0032] I C (s)=C eq sV C (s)-C eq v C (0 - (7)

[0033] Among them, V L (s), I L (s) represent the voltage and current of the inductor in the complex frequency domain, respectively; V C (s), I C (s) represent the capacitor voltage and current in the complex frequency domain, respectively; L eq C eq These are the inductance and capacitance of the MMC equivalent circuit when there is a short circuit between the electrodes; i L(0-), v C (0-) represent steady-state DC current and voltage, respectively;

[0034] Construct an equivalent circuit for inter-electrode faults in transmission lines in the complex frequency domain;

[0035] Based on the single transmission line admittance matrix in the equivalent circuit of transmission line inter-electrode fault, a node admittance matrix is ​​established for the equivalent circuit of transmission line inter-electrode fault.

[0036] Based on the node admittance matrix established by the equivalent circuit of the inter-electrode fault of the transmission line and the two-port equivalent model of the DC transmission line in the complex frequency domain, the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain is obtained. Based on the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain, the actual circuit information and the termination of the transmission line, the equations for the relationship between the voltage at each node and the current in each branch are obtained.

[0037] Solving the equations relating the voltages at each node and the currents in the branches yields the transient expression F(s) for a DC fault in the complex frequency domain.

[0038] In conjunction with the first aspect, further, the step of performing a Laplace transform on the transient expression of a DC fault in the complex frequency domain to obtain the time-domain response includes:

[0039] The Laplace transform of the transient expression for DC faults in the complex frequency domain is performed using the following formula.

[0040]

[0041] Where f(t) is the transient expression of DC fault in the time domain; s = σ + jω is the Laplace operator; j is the imaginary number, ω is the frequency, σ is an arbitrary positive constant, z = st, and t is time;

[0042] Using rational function ξ β.α (z) for the function e z Perform a Pade approximation such that the first α+β+1 terms of their Taylor expansions are equal, ξ β.α The expression for (z) is as follows:

[0043]

[0044] Among them, P β (z), Q α (z) are polynomials of order β and α, respectively, where α-β > 2;

[0045] With ξ β.α (z) replace e z We obtain an approximate expression for f(t). As shown in the following formula:

[0046]

[0047] According to the residue theorem... By performing integral calculations, the time-domain response of the DC fault transient is obtained as shown in the following equation:

[0048]

[0049] Among them, z i For ξ β.α The poles of (z), k i is the residue corresponding to the pole.

[0050] Secondly, a system for determining transient electrical quantities during faults in flexible DC transmission lines is provided, comprising:

[0051] The MMC equivalent circuit construction module under inter-electrode short circuit is used to construct the MMC equivalent circuit under inter-electrode short circuit based on the MMC converter station circuit parameters.

[0052] A module for constructing a two-port equivalent model of a DC transmission line in the complex frequency domain is used to establish a two-port equivalent model of a DC transmission line in the complex frequency domain based on the obtained transmission line parameters.

[0053] The module for obtaining transient expressions of DC faults in the complex frequency domain is used to obtain transient expressions of DC faults in the complex frequency domain based on the MMC equivalent circuit and the two-port equivalent model of the DC transmission line during inter-electrode short circuit.

[0054] The module for determining transient electrical quantities during line faults is used to perform a Laplace transform on the transient expression of a DC fault in the complex frequency domain to obtain the time-domain response.

[0055] In conjunction with the second aspect, further, the operations performed by the MMC equivalent circuit construction module during inter-electrode short circuit include:

[0056] Obtain MMC circuit parameters, including bridge arm resistance R. arm Bridge arm inductor L arm Smoothing reactor inductor L fw Submodule on-resistance R on and submodule capacitor C SM ;

[0057] Based on the obtained MMC converter station circuit parameters, an RCL series circuit is constructed and used as the MMC equivalent circuit under inter-electrode short circuit conditions, where the resistance is R. eq Inductance is L eq The capacitance is C eq ;

[0058]

[0059] Where N is the number of series sub-modules in the upper and lower arms of each phase of the MMC.

[0060] In conjunction with the second aspect, furthermore, the operations performed by the DC transmission line two-port equivalent model construction module in the complex frequency domain include:

[0061] Obtain transmission line parameters, including resistance R0 per unit length, inductance L0 per unit length, conductance G0 per unit length, capacitance C0 per unit length, and transmission line distance L.

[0062] Based on the transmission line parameters, the DC transmission line model in the complex frequency domain can be expressed using ordinary differential equations as follows:

[0063]

[0064] Solving equation (2) yields

[0065]

[0066] in, x is the position variable, s is the Labras operator, γ is the propagation coefficient, Z1 is the wave impedance, and U f U b These are the forward and reverse traveling waves of the transmission line voltage, respectively; I f I b These are the forward and reverse traveling waves of the transmission line current, respectively.

[0067] Taking x = 0 and x = L respectively, the DC transmission line is equivalent to a two-port equivalent model. The port characteristics of the two-port equivalent model are expressed as follows:

[0068]

[0069] Among them, U m U n I represents the voltage at each of the two nodes of the transmission line. m I n Let U represent the current at each of the nodes at both ends of the transmission line, and U be the node voltage vector.

[0070] The two-port equivalent model is represented by the current admittance matrix Y as follows:

[0071]

[0072] In conjunction with the second aspect, further, the operations performed by the DC fault transient expression acquisition module in the complex frequency domain include:

[0073] The inductor voltage and capacitor current in the complex frequency domain are obtained by performing a Laplace transform on the inductor and capacitor in the MMC equivalent circuit when the electrodes are short-circuited, as shown in the following equation:

[0074] V L (s)=L eq sI L (s)-Leq i L (0 - (6)

[0075] I C (s)=C eq sV C (s)-C eq v C (0 - (7)

[0076] Among them, V L (s), I L (s) represent the voltage and current of the inductor in the complex frequency domain, respectively; V C (s), I C (s) represent the capacitor voltage and current in the complex frequency domain, respectively; L eq C eq These are the inductance and capacitance of the MMC equivalent circuit when there is a short circuit between the electrodes; i L (0-), v C (0 - These represent steady-state DC current and voltage, respectively.

[0077] Construct an equivalent circuit for inter-electrode faults in transmission lines in the complex frequency domain;

[0078] Based on the single transmission line admittance matrix in the equivalent circuit of transmission line inter-electrode fault, a node admittance matrix is ​​established for the equivalent circuit of transmission line inter-electrode fault.

[0079] Based on the node admittance matrix established by the equivalent circuit of the inter-electrode fault of the transmission line and the two-port equivalent model of the DC transmission line in the complex frequency domain, the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain is obtained. Based on the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain, the actual circuit information and the termination of the transmission line, the equations for the relationship between the voltage at each node and the current in each branch are obtained.

[0080] Solving the equations relating the voltages at each node and the currents in the branches yields the transient expression F(s) for a DC fault in the complex frequency domain.

[0081] In conjunction with the second aspect, the operations performed by the line fault transient electrical quantity determination module further include:

[0082] The Laplace transform of the transient expression for DC faults in the complex frequency domain is performed using the following formula.

[0083]

[0084] Where f(t) is the transient expression of DC fault in the time domain; s = σ + jω is the Laplace operator; j is the imaginary number, ω is the frequency, σ is an arbitrary positive constant, z = st, and t is time;

[0085] Using rational function ξ β.α (z) for the function e z Perform a Pade approximation such that the first α+β+1 terms of their Taylor expansions are equal, ξ β.α The expression for (z) is as follows:

[0086]

[0087] Among them, P β (z), Q α (z) are polynomials of order β and α, respectively, where α-β > 2;

[0088] With ξ β.α (z) replace e z We obtain an approximate expression for f(t). As shown in the following formula:

[0089]

[0090] According to the residue theorem... By performing integral calculations, the time-domain response of the DC fault transient is obtained as shown in the following equation:

[0091]

[0092] Among them, z i For ξ β.α The poles of (z), k i is the residue corresponding to the pole.

[0093] The beneficial effects of this invention are as follows: This invention can accurately provide the overall trend of the transient process after a fault. The calculation process is simple, avoiding the cumbersome and complex modeling and simulation process of traditional simulation methods. It can also well reflect the occurrence wave process during overhead line faults. The proposed method can accurately express the overall development trend of the fault current flowing through the protection installation point after a fault occurs and before the converter station is locked, which has positive significance for fault current suppression and protection setting design of MMC-HVDC systems. Attached Figure Description

[0094] Figure 1 This is a flowchart of the present invention;

[0095] Figure 2 This is a schematic diagram of the main circuit structure of the MMC-HVDC system to which this invention applies;

[0096] Figure 3 This is the equivalent circuit diagram of MMC when there is a short circuit between electrodes in this invention;

[0097] Figure 4 This is a schematic diagram of the equivalent model of a two-port DC transmission line in the complex frequency domain in this invention;

[0098] Figure 5 This is a schematic diagram of the equivalent circuit for inter-electrode faults in the MMC-HVDC system under the complex frequency domain in this invention. Detailed Implementation

[0099] To make the objectives, 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 with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0100] To better understand this invention, the relevant technologies in the technical solution of this invention are described below.

[0101] Example 1

[0102] like Figure 1-5 As shown, Figure 1 The diagram shows the main circuit structure of the MMC-HVDC system. It's important to note that the MMC-HVDC system comprises two AC systems, an MMC converter station, and a DC transmission line. The converter station's main equipment includes a converter transformer, AC filters, smoothing reactors, and a converter. The MMC-HVDC system rectifies three-phase AC power into DC power at the converter station, then transmits it via a DC transmission line to another converter station for inversion back into three-phase AC power. Each phase's upper and lower bridge arms in the MMC converter station consist of N half-bridge submodules connected in series with bridge arm reactors. Each half-bridge SM contains two IGBTs, a freewheeling diode group, and a storage capacitor. Smoothing reactors are connected at both ends of the DC line. During normal operation, the total number of SMs connected to each phase's upper and lower bridge arms in the MMC remains constant at any given time, always being N (half of all SMs in each phase), maintaining a stable DC voltage. Furthermore, the corresponding output AC voltage can be obtained by controlling the distribution of the N connected SMs between the upper and lower bridge arms.

[0103] Please see Figure 2 This invention provides a method for calculating transient electrical quantities during faults in flexible DC transmission lines based on numerical inverse Laplace transform, comprising:

[0104] Step S1: Based on the circuit parameters of the MMC converter station in the MMC-HVDC system, establish the equivalent circuit of the MMC under inter-pole short circuit and determine the equivalent circuit parameters. The specific process is as follows:

[0105] Step S1.1: Obtain MMC circuit parameters, including bridge arm resistance R. arm Bridge arm inductor L arm Smoothing reactor inductor L fw Submodule on-resistance Ron Submodule capacitor C SM Each phase of the MMC upper and lower bridge arm submodule group is obtained by connecting N submodules in series, where N is a positive integer greater than 1.

[0106] Step S1.2: Establish the equivalent circuit of MMC under inter-electrode short circuit and determine the equivalent circuit parameters. The equivalent circuit model is an RLC series circuit, where the resistance is R. eq Inductance is L eq Capacitor C eq .

[0107] Understandably, in an MMC-HVDC system, after an inter-pole short circuit occurs in the transmission line, power transmission between the sending and receiving converter stations ceases. The SM capacitors, which are in operation, discharge to the fault point through the bridge arm, equivalent to a three-phase short circuit fault. For a period before the converter station is blocked, the number of SM capacitors in operation remains constant at N, and the control system has almost no impact on the short-circuit current. Therefore, the MMC can be considered equivalent to an RLC series circuit.

[0108] It should be noted that the equivalent resistance R in the equivalent circuit of the MMC converter station eq Equivalent inductance L eq Equivalent capacitance C eq The following formula can be obtained from the MMC circuit parameters:

[0109]

[0110] Step S2: Establish an equivalent two-port network model of the DC transmission line in the complex frequency domain. The specific process is as follows:

[0111] Step S2.1: Obtain the transmission line parameters, including resistance R0 per unit length, inductance L0 per unit length, conductance G0 per unit length, capacitance C0 per unit length, and transmission line distance L. m and n are the terminal node numbers at both ends (first and last ends) of the transmission line.

[0112] Step S2.2: In the complex frequency domain, establish a transmission line model and represent it using ordinary differential equations.

[0113] The transmission line is represented in the time domain by the following set of partial differential equations:

[0114]

[0115] Where u and i represent the voltage and current of the transmission line in the time domain, respectively.

[0116] By performing a Laplace transform on the partial differential equations in the time domain, the transmission line model in the complex frequency domain can be expressed using ordinary differential equations as follows:

[0117]

[0118] U and I represent the voltage and current of the transmission line in the complex frequency domain, respectively.

[0119] Step S2.3: Solve the ordinary differential equations of the transmission line model in the complex frequency domain to obtain its general solution as follows:

[0120]

[0121] In the formula, The propagation coefficient; U is the wave impedance. f U b These are the forward and reverse traveling waves of the transmission line voltage, respectively; I f I b These represent the forward and reverse traveling waves of the transmission line current, respectively; x is the position variable.

[0122] Step S2.4: Take x = 0 and x = L, which are the start and end 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 the admittance matrix.

[0123] 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:

[0124]

[0125] Concerning the electrical characteristics at both ends of the transmission line, in the complex frequency domain, the transmission line is considered as a one- or two-port network, and its port characteristics can be expressed in the form of a transmission parameter matrix as follows:

[0126]

[0127] Based on the above formula, when the transmission parameter matrix uses the admittance matrix, the port characteristics of a two-port network are expressed as follows:

[0128]

[0129] In the formula u m u n These represent the voltages at the beginning and end nodes m and n of the transmission line, respectively, and i m i n Let m and n be the currents at the first and last nodes of the transmission line, respectively. The equivalent model of the two ports of a DC transmission line is represented by the transmission line current admittance matrix Y as follows:

[0130]

[0131] Step S3: Calculate the DC fault transient in the complex frequency domain. The specific process is as follows:

[0132] Step S3.1: After establishing the equivalent MMC circuit for inter-electrode short circuit in step S1, the inductor in the equivalent circuit is L.eq Capacitor C eq The Laplace transform yields the following expressions in the complex frequency domain:

[0133] V L (s)=L eq sI L (s)-L eq i L (0 - (9)

[0134] I C (s)=C eq sV C (s)-C eq v C (0 - (10)

[0135] In the formula V L (s), I L (s) represent the transmission line inductance, voltage, and current in the complex frequency domain, respectively; V C (s), I C (s) represent the voltage and current of the transmission line capacitance in the complex frequency domain, respectively. L (0 - ), v C (0 - For steady-state DC current and voltage, they can be expressed as:

[0136]

[0137] In the formula U dc I dc These represent the DC voltage and current of the MMC in steady state, respectively.

[0138] In the complex frequency domain, inductors are represented using Norton's equivalent circuit; capacitors are represented using Thevenin's equivalent circuit.

[0139] Step S3.2: Establish the equivalent circuit for inter-electrode faults in the transmission line of the MMC-HVDC system in the complex frequency domain. (See circuit diagram below.) Figure 4 The nodes in the circuit diagram are numbered (node-1 to node-6). The voltage at each node is denoted as U. n (s), where the subscript n is the node number; the current of each branch is denoted as I. nm (s), where n and m in the subscript are the node numbers at both ends of the branch connection, respectively.

[0140] Step 3.3: In the single transmission line admittance matrix Y nm Based on this, the nodal admittance matrix is ​​established for the equivalent circuit of inter-electrode faults in DC system transmission lines, as follows:

[0141]

[0142] Matrix Y Trans Middle Y nm,k That is, the transmission line admittance matrix Y nm The k-th element in.

[0143] Step S3.4: The equivalent two-port network model of the transmission line obtained in step S2 reflects the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain through the admittance matrix. Based on the actual circuit information and the termination of the transmission line, the equations representing the relationship between the voltage at each node and the branch current are obtained by using nodal analysis as follows:

[0144]

[0145] Step S3.5: Based on the MMC equivalent circuit obtained in Step S1 and the inductor and capacitor expressions in the complex frequency domain obtained in Step S3.1, the following boundary conditions are introduced:

[0146]

[0147] 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. R eq,L L eq,L C eq,L and R eq.R L eq,R C eq,R The equivalent resistance, inductance, and capacitance of the converter stations at the left and right ends are respectively. Step S3.6: Solve the equation (Equation (13)) that represents the relationship between the voltage of each node and the current of the branch to obtain the transient expression F(s) of DC fault in the complex frequency domain.

[0148] Step S4: After obtaining the transient expression of DC fault in the complex frequency domain, the frequency domain is converted to the time domain through the numerical inverse Laplace transform to obtain the corresponding time domain response. The specific process is as follows:

[0149] Step S4.1: After obtaining the transient expression F(s) of DC fault in the complex frequency domain from step S3, perform an inverse Laplace transform on F(s). The transform formula is as follows:

[0150]

[0151] In the formula, s = σ + jω, which is the Laplace operator; 1; z = st.

[0152] Step S4.2: Using the rational function ξβ.α (z) for the function e z Perform a Pade approximation such that the first α+β+1 terms of their Taylor expansions are equal, ξ β.α The expression for (z) is as follows:

[0153]

[0154] In the formula, P β (z), Q α (z) are polynomials of order β and α, respectively, where α-β>2.

[0155] Step S4.3: Use ξ β.α (z) Substitution e z An approximate expression for f(t) can be obtained. as follows:

[0156]

[0157] Step S4.4: Apply the residue theorem to... The time-domain response of the DC fault transient can be obtained by performing the integral calculation as follows.

[0158]

[0159] In the formula z i For ξ n.m The poles of (z), k i Let be the residues corresponding to the poles, and both can be complex numbers.

[0160] Example 2

[0161] A system for determining transient electrical quantities during faults in flexible DC transmission lines is provided, comprising:

[0162] The MMC equivalent circuit construction module under inter-electrode short circuit is used to construct the MMC equivalent circuit under inter-electrode short circuit based on the MMC converter station circuit parameters.

[0163] A module for constructing a two-port equivalent model of a DC transmission line in the complex frequency domain is used to establish a two-port equivalent model of a DC transmission line in the complex frequency domain based on the obtained transmission line parameters.

[0164] The module for obtaining transient expressions of DC faults in the complex frequency domain is used to obtain transient expressions of DC faults in the complex frequency domain based on the MMC equivalent circuit and the two-port equivalent model of the DC transmission line during inter-electrode short circuit.

[0165] The module for determining transient electrical quantities during line faults is used to perform a Laplace transform on the transient expression of a DC fault in the complex frequency domain to obtain the time-domain response.

[0166] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can 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.) containing computer-usable program code.

[0167] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0168] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0169] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

Claims

1. A method of determining a fault transient electrical quantity of a flexible DC power transmission line, characterized in that, include: Construct the MMC equivalent circuit under inter-pole short circuit based on the MMC converter station circuit parameters; Based on the obtained transmission line parameters, establish an equivalent two-port model of a DC transmission line in the complex frequency domain; Based on the MMC equivalent circuit and the two-port equivalent model of the DC transmission line during inter-electrode short circuit, the transient expression of DC fault in the complex frequency domain is obtained. The time-domain response is obtained by performing a Laplace transform on the transient expression of a DC fault in the complex frequency domain, including: The Laplace transform of the transient expression for DC faults in the complex frequency domain is performed using the following formula: （8） in, This is the transient expression for a DC fault in the time domain. , is the Laplace operator; For imaginary numbers, For frequency, Let be any positive constant. , For time; Using rational functions For functions Perform a Pade approximation, making the front of the Taylor expansion of both... The terms are equal. The expression is as follows: （9） in, , They are respectively , order polynomial, ; use Alternative get Approximate expression As shown in the following formula: （10）； According to the residue theorem... By performing integral calculations, the time-domain response of the DC fault transient is obtained as shown in the following equation: （11） in, for The extreme point, is the residue corresponding to the pole.

2. The method for determining transient electrical quantities during faults in a flexible DC transmission line according to claim 1, characterized in that, The construction of the MMC equivalent circuit under inter-electrode short circuit based on the MMC converter station circuit parameters includes: Obtain MMC circuit parameters, including bridge arm resistance. Bridge arm inductor Smoothing reactor inductor Submodule on-resistance and submodule capacitors ; Based on the obtained MMC converter station circuit parameters, an RCL series circuit is constructed and used as the MMC equivalent circuit under inter-electrode short circuit conditions, where the resistance is... Inductance is , capacitor is ; （1） in, This represents the number of series-connected submodules in the upper and lower arms of each phase of the MMC.

3. The method for determining transient electrical quantities during faults in a flexible DC transmission line according to claim 1, characterized in that, The step of establishing a two-port equivalent model of a DC transmission line in the complex frequency domain based on the obtained transmission line parameters includes: Obtain transmission line parameters, including the resistance per unit length of the transmission line. Inductance per unit length Conductivity per unit length Capacitance per unit length and transmission line distance ; Based on the transmission line parameters, the DC transmission line model in the complex frequency domain can be expressed using ordinary differential equations as follows: （2）； Solving equation (2) yields （3） in, , , For position variables, For the Labras operator, For the propagation coefficient, For wave impedance, , These are the forward and reverse traveling waves of the transmission line voltage, respectively. , These are the forward and reverse traveling waves of the transmission line current, respectively. Take 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: （4） in, , These represent the voltages at the nodes at both ends of the transmission line. , These represent the currents at the nodes at both ends of the transmission line. The node voltage vector; Two-port equivalent model using current admittance matrix Represented as: （5）。 4. The method for determining transient electrical quantities during faults in a flexible DC transmission line according to claim 2, characterized in that, The transient expression for DC faults in the complex frequency domain includes: The inductor voltage and capacitor current in the complex frequency domain are obtained by performing a Laplace transform on the inductor and capacitor in the MMC equivalent circuit when the electrodes are short-circuited, as shown in the following equation: （6） （7） in, , These represent the voltage and current of the inductor in the complex frequency domain, respectively. , These represent the capacitor voltage and current in the complex frequency domain, respectively. , These are the inductance and capacitance of the MMC equivalent circuit when there is a short circuit between the electrodes; , These are steady-state DC current and voltage, respectively. Construct an equivalent circuit for inter-electrode faults in transmission lines in the complex frequency domain; Based on the single transmission line admittance matrix in the equivalent circuit of transmission line inter-electrode fault, a node admittance matrix is ​​established for the equivalent circuit of transmission line inter-electrode fault. Based on the node admittance matrix established by the equivalent circuit of the inter-electrode fault of the transmission line and the two-port equivalent model of the DC transmission line in the complex frequency domain, the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain is obtained. Based on the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain, the actual circuit information and the termination of the transmission line, the equations for the relationship between the voltage at each node and the current in each branch are obtained. Solving the equations relating node voltages and branch currents yields the transient expression for DC faults in the complex frequency domain. .

5. A system for determining transient electrical quantities during faults in flexible DC transmission lines, characterized in that, include: The MMC equivalent circuit construction module under inter-electrode short circuit is used to construct the MMC equivalent circuit under inter-electrode short circuit based on the MMC converter station circuit parameters. A module for constructing a two-port equivalent model of a DC transmission line in the complex frequency domain is used to establish a two-port equivalent model of a DC transmission line in the complex frequency domain based on the obtained transmission line parameters. The module for obtaining transient expressions of DC faults in the complex frequency domain is used to obtain transient expressions of DC faults in the complex frequency domain based on the MMC equivalent circuit and the two-port equivalent model of the DC transmission line during inter-electrode short circuit. The module for determining transient electrical quantities during line faults is used to perform a Laplace transform on the transient expression of a DC fault in the complex frequency domain to obtain the time-domain response, including: The Laplace transform of the transient expression for DC faults in the complex frequency domain is performed using the following formula: （8） in, This is the transient expression for a DC fault in the time domain. , is the Laplace operator; For imaginary numbers, For frequency, Let be any positive constant. , For time; Using rational functions For functions Perform a Pade approximation, making the front of the Taylor expansion of both... The terms are equal. The expression is as follows: （9） in, , They are respectively , order polynomial, ; use Alternative get Approximate expression As shown in the following formula: （10）； According to the residue theorem... By performing integral calculations, the time-domain response of the DC fault transient is obtained as shown in the following equation: （11） in, for The extreme point, is the residue corresponding to the pole.

6. The system for determining transient electrical quantities during faults in a flexible DC transmission line according to claim 5, characterized in that, The operations performed by the MMC equivalent circuit construction module during inter-electrode short circuit include: Obtain MMC circuit parameters, including bridge arm resistance. Bridge arm inductor Smoothing reactor inductor Submodule on-resistance and submodule capacitors ; Based on the obtained MMC converter station circuit parameters, an RCL series circuit is constructed and used as the MMC equivalent circuit under inter-electrode short circuit conditions, where the resistance is... Inductance is , capacitor is ; （1） in, This represents the number of series-connected submodules in the upper and lower arms of each phase of the MMC.

7. The system for determining transient electrical quantities during faults in a flexible DC transmission line according to claim 5, characterized in that, The operations performed by the DC transmission line two-port equivalent model construction module in the complex frequency domain include: Obtain transmission line parameters, including the resistance per unit length of the transmission line. Inductance per unit length Conductivity per unit length Capacitance per unit length and transmission line distance ; Based on the transmission line parameters, the DC transmission line model in the complex frequency domain can be expressed using ordinary differential equations as follows: （2）； Solving equation (2) yields （3） in, , , For position variables, For the Labras operator, For the propagation coefficient, For wave impedance, , These are the forward and reverse traveling waves of the transmission line voltage, respectively. , These are the forward and reverse traveling waves of the transmission line current, respectively. , These represent the voltage and current of a DC transmission line in the complex frequency domain, respectively. Take 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: （4） in, , These represent the voltages at the nodes at both ends of the transmission line. , These represent the currents at the nodes at both ends of the transmission line. The node voltage vector; Two-port equivalent model using current admittance matrix Represented as: （5）。 8. The system for determining transient electrical quantities during faults in a flexible DC transmission line according to claim 5, characterized in that, The operations performed by the DC fault transient expression acquisition module in the complex frequency domain include: The inductor voltage and capacitor current in the complex frequency domain are obtained by performing a Laplace transform on the inductor and capacitor in the MMC equivalent circuit when the electrodes are short-circuited, as shown in the following equation: （6） （7） in, , These represent the voltage and current of the inductor in the complex frequency domain, respectively. , These represent the capacitor voltage and current in the complex frequency domain, respectively. , These are the inductance and capacitance of the MMC equivalent circuit when there is a short circuit between the electrodes; , These are steady-state DC current and voltage, respectively. Construct an equivalent circuit for inter-electrode faults in transmission lines in the complex frequency domain; Based on the single transmission line admittance matrix in the equivalent circuit of transmission line inter-electrode fault, a node admittance matrix is ​​established for the equivalent circuit of transmission line inter-electrode fault. Based on the node admittance matrix established by the equivalent circuit of the inter-electrode fault of the transmission line and the two-port equivalent model of the DC transmission line in the complex frequency domain, the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain is obtained. Based on the relationship between the current and voltage at both ends of the transmission line in the complex frequency domain, the actual circuit information and the termination of the transmission line, the equations for the relationship between the voltage at each node and the current in each branch are obtained. Solving the equations relating node voltages and branch currents yields the transient expression for DC faults in the complex frequency domain. .

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