Fault characteristic analysis method and system based on decoupling matrix of dc transmission line

Abstract

The application discloses a kind of based on decoupling matrix of DC transmission line fault characteristic analysis method, first equivalent DC transmission system is the circuit with unchangeable topological structure, using superposition principle will fault network equivalent pre-fault steady current and post-fault fault component network, deduce post-fault current wave analytical expression, based on the pole mode transformation of bipolar decoupling matrix, deduce the DC transmission line fault characteristic of the wave process scale of decoupled DC line in mode domain.The decoupling matrix and fault characteristic analysis method suitable for UHVDC transmission line proposed in the application, compared with traditional DC fault wave analysis method, considers the non-ideal transmission characteristics of wave at the boundary of converter, has higher analysis and calculation precision, has the advantages of simple and easy to operate, clear and so on, and has great popularization significance.

Description

Technical Field

[0001] This invention relates to the field of DC transmission line protection technology, specifically a fault characteristic analysis method and system based on the decoupling matrix of DC transmission lines. Background Technology

[0002] Due to factors such as lightning strikes, wildfires, smog, icing, and high temperatures, grounding faults frequently occur on UHV AC / DC transmission lines in nearby areas. These faults can easily lead to insensitive startup, main protection malfunctions, and other accidents, causing continuous commutation failures and seriously jeopardizing the safety of AC / DC hybrid power grids. Furthermore, high-resistance faults on UHV lines are often accompanied by arcing phenomena. The grounding impedance value of arcing high-resistance faults changes with the applied voltage, exhibiting significant nonlinear characteristics. The fault current shows obvious waveform distortion and contains a large number of harmonics, which can also cause commutation failures and compromise the stable operation of the system.

[0003] Traveling wave protection is the primary protection for ultra-high voltage direct current (UHVDC) lines, enabling rapid identification and isolation of faults on DC lines within the DC transmission system. In ±1100kV DC / 1000kV AC hybrid UHVDC power grids, the AC system comprises ultra-high voltage AC grids of different voltage levels. The ±1100kV DC transmission lines extend over 3300 kilometers, with significantly larger transmission capacities, leading to more severe electromagnetic induction and coupling phenomena between bipolar lines. To ensure the selectivity, speed, sensitivity, and reliability of traveling wave protection against electromagnetic induction and coupling between bipolar lines, it is necessary to study the solution matrix of bipolar decoupling for various types of faults that may occur on the DC line side of the DC transmission system, and to derive the fault characteristics of DC transmission lines at the wave process scale after decoupling.

[0004] For example, the method for processing traveling waves in flexible DC transmission lines disclosed in application number 201610996242.x obtains the transient traveling waves of pole-mode current and pole-mode voltage faults in the flexible DC transmission line; obtains the transient traveling waves of pole-mode reverse voltage faults; obtains the modulus maxima of the transient traveling waves of pole-mode reverse voltage faults, and obtains the equivalent pole-mode reverse voltage traveling wave of the transient traveling waves of pole-mode reverse voltage faults. The technical solution of this invention can effectively demonstrate the difference between fault traveling waves and high-frequency transient interference, making the overall characteristics of faults in flexible DC transmission lines more concise and intuitive; it can also eliminate the influence of DC and low-frequency signals in the transient traveling waves of pole-mode reverse voltage faults, highlighting the high-frequency characteristics of the traveling wave process, reducing the difficulty of analyzing the traveling wave process of flexible DC systems, and making the protection of ultra-high-speed flexible DC transmission lines possible. However, this method uses wavelet transform to analyze traveling waves and constructs protection based on traveling waves, but it does not consider the non-ideal transmission characteristics of traveling waves at the converter boundary, and the accuracy of fault analysis and calculation for ultra-high-voltage DC transmission lines cannot meet current needs. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide an analysis method that considers the irrational transmission characteristics of the converter in DC fault traveling wave analysis.

[0006] The present invention solves the above-mentioned technical problems through the following technical means:

[0007] The fault characteristic analysis method based on the decoupling matrix of DC transmission lines includes the following steps:

[0008] S1. Based on the switching function theory, construct a mathematical model of the high-voltage direct current system at both ends of a DC transmission line;

[0009] S2. Construct the DC equivalent circuit network after the fault using the superposition principle, which is divided into two parts: the normal component network before the fault and the fault component network describing the fault.

[0010] S3. Establish a transmission line model and solve for the general solution of the initial voltage and current traveling wave of the transmission line;

[0011] S4. Decouple the electrical coupling of the bipolar system by pole mode transformation and construct the DC line fault traveling wave equation in the mode domain;

[0012] S5. Determine whether it is a unipolar fault or a bipolar fault. If it is a unipolar fault, proceed to step S6; otherwise, proceed to step S7.

[0013] S6. Derive the initial traveling wave solution for a unipolar fault in a bipolar system;

[0014] S7. Derive the initial traveling wave solution for a bipolar fault in a bipolar system;

[0015] S8. Derive the traveling wave propagation characteristics after reflection at the transmission line boundary; specifically, the current reflection coefficient at the transmission line boundary is determined by the following formula:

[0016]

[0017] Among them, L dc L is the equivalent inductance on the DC side of the AC system and converter. r Z is the inductance of the smoothing reactor. lb Z is the impedance of the DC filter. c This is the wave impedance of the transmission line.

[0018] This invention first treats the DC transmission system as an equivalent circuit with an invariant topology. Utilizing the superposition principle, it equates the fault network to the pre-fault steady-state current and the post-fault fault component network, deriving the analytical expression of the post-fault current traveling wave. Based on the polar mode transformation of the bipolar decoupling matrix, it derives the fault characteristics of the DC transmission line at the process scale of the decoupled DC line wave in the mode domain. The decoupling matrix and fault characteristic analysis method proposed in this invention, applicable to UHVDC transmission lines, considers the non-ideal transmission characteristics of the traveling wave at the converter boundary compared to traditional DC fault traveling wave analysis methods. It boasts higher analysis and calculation accuracy, and is simple, easy to implement, and clear, making its widespread application significant.

[0019] Furthermore, step S1 specifically involves: representing the AC system, converter transformer, and converter using an equivalent inductance, thus characterizing the DC system with this topology unchanged system; the equivalent impedance is determined by the following formula:

[0020] The equivalent impedance of the six-pulse converter station is:

[0021]

[0022] The equivalent impedance of the twelve-pulse converter station is:

[0023]

[0024] Where: μ is the commutation angle during the converter commutation process, L s For the equivalent inductance of the AC system, L t This is the equivalent inductance of the converter transformer referred to the converter side.

[0025] Furthermore, the general solution for the initial voltage and current traveling wave of the transmission line in step S3 is determined by the following formula:

[0026]

[0027]

[0028] Among them, u F and i F The initial voltage and current traveling waves of the fault are represented, t0 represents the time point when the fault occurs, and Z represents the initial voltage and current traveling waves of the fault. c U is the surge impedance of the transmission line. f This represents the initial voltage amplitude during the fault.

[0029] Furthermore, in step S4, the bipolar system line coupling characteristics are achieved through pole mode transformation, and the mode-domain downlink wave equation is determined by the following formula:

[0030]

[0031] Among them, L sC s These are the self-inductance and self-capacitance per unit length, respectively, L m C m These are the mutual inductance and mutual capacitance per unit length, respectively.

[0032] Furthermore, in step S6, when a bipolar system experiences a unipolar ground fault, the initial fault voltage and current traveling wave in the mode domain are determined by the following formula:

[0033]

[0034] Furthermore, in step S7, when a bipolar system experiences an inter-pole fault, the initial fault voltage and current traveling wave in the mode domain are determined by the following formula:

[0035]

[0036] Furthermore, in step S8, the reflection coefficient ρ at the fault point F , refractive index γ F They are determined by the following formulas respectively:

[0037]

[0038]

[0039] Corresponding to the above method, the present invention also provides a fault characteristic analysis system based on the decoupling matrix of DC transmission lines, comprising:

[0040] The model building module is used to construct a mathematical model of the high-voltage direct current system at both ends of a DC transmission line based on the switching function theory.

[0041] The equivalent circuit construction module is used to construct the DC equivalent circuit network after the fault using the superposition principle. It is divided into two parts: the normal component network before the fault and the fault component network describing the fault.

[0042] The transmission line model building module is used to build transmission line models and solve for the general solutions of initial voltage and current traveling waves of transmission lines.

[0043] A DC line fault traveling wave equation construction module is used to decouple the electrical coupling of the bipolar system through pole mode transformation and construct the DC line fault traveling wave equation in the mode domain.

[0044] The judgment module is used to determine whether it is a unipolar fault or a bipolar fault. If it is a unipolar fault, it enters the initial traveling wave solution derivation module for a unipolar fault; otherwise, it enters the initial traveling wave solution derivation module for a bipolar fault.

[0045] The module for deriving the initial traveling wave solution of a single-stage fault is used to derive the initial traveling wave solution of a bipolar system under a single-stage fault.

[0046] The module for deriving the initial traveling wave solution of a bipolar fault is used to derive the initial traveling wave solution of a bipolar system under bipolar fault conditions.

[0047] The traveling wave propagation characteristic derivation module is used to derive the traveling wave propagation characteristics after reflection at the transmission line boundary; specifically, at the transmission line boundary, the current reflection coefficient is determined by the following formula:

[0048]

[0049] Among them, L dc L is the equivalent inductance on the DC side of the AC system and converter. r Z is the inductance of the smoothing reactor. lb Z is the impedance of the DC filter. c This is the wave impedance of the transmission line.

[0050] Furthermore, the model building module specifically involves: representing the AC system, converter transformer, and converter with an equivalent inductance, thus characterizing the DC system using this system with an unchanged topology; the equivalent impedance is determined by the following formula:

[0051] The equivalent impedance of the six-pulse converter station is:

[0052]

[0053] The equivalent impedance of the twelve-pulse converter station is:

[0054]

[0055] Where: μ is the commutation angle during the converter commutation process, L s For the equivalent inductance of the AC system, L t This is the equivalent inductance of the converter transformer referred to the converter side.

[0056] Furthermore, the general solution for the initial voltage and current traveling waves of the transmission line in the transmission line model construction module is determined by the following formula:

[0057]

[0058]

[0059] Among them, u F and i F The initial voltage and current traveling waves of the fault are represented, i0 represents the time point when the fault occurs, and Z represents the initial voltage and current traveling waves of the fault. c U is the surge impedance of the transmission line. f This represents the initial voltage amplitude during the fault.

[0060] Furthermore, in the DC line fault traveling wave equation construction module, the bipolar system line coupling characteristics are realized through pole mode transformation, and the mode domain traveling wave equation is determined by the following formula:

[0061]

[0062] Among them, L s C s These are the self-inductance and self-capacitance per unit length, respectively, L m C m These are the mutual inductance and mutual capacitance per unit length, respectively.

[0063] Furthermore, in the single-stage fault initial traveling wave derivation module, when a bipolar system experiences a single-pole ground fault, the initial fault voltage and current traveling waves in the mode domain are determined by the following formulas:

[0064]

[0065] Furthermore, in the bipolar fault initial traveling wave derivation module, when a bipolar system experiences an inter-pole fault, the initial fault voltage and current traveling waves in the mode domain are determined by the following formulas:

[0066]

[0067] Furthermore, in the traveling wave propagation characteristic derivation module, the reflection coefficient ρ at the fault point... F , refractive index γ F They are determined by the following formulas respectively:

[0068]

[0069]

[0070] The advantages of this invention are:

[0071] This invention constructs a mathematical model of a two-terminal high-voltage direct current (HVDC) system, and based on this model, builds a DC equivalent circuit network, including a pre-fault normal component network and a fault component network. It derives an analytical expression for the current traveling wave after the fault, and based on the pole-mode transformation of the bipolar decoupling matrix, derives the fault characteristics of the DC transmission line at the process scale of the decoupled DC line wave in the mode domain. The decoupling matrix and fault characteristic analysis method proposed in this invention, applicable to UHVDC transmission lines, considers the non-ideal transmission characteristics of the traveling wave at the converter boundary compared to traditional DC fault traveling wave analysis methods, achieving higher analysis and calculation accuracy. It also boasts advantages such as simple and easy-to-implement steps and clear explanations, making its widespread application significant. Attached Figure Description

[0072] Figure 1This is a flowchart of a fault characteristic analysis method based on a decoupling matrix for DC transmission lines, as described in an embodiment of the present invention.

[0073] Figure 2 This is an equivalent (single-pole) schematic diagram of the DC transmission system used in the embodiments of the present invention;

[0074] Figure 3 This is a schematic diagram of the equivalent circuit of a DC line fault based on the superposition principle in an embodiment of the present invention;

[0075] Figure 4 This is a schematic diagram of the equivalent circuit of a single-pole grounding fault used in the analysis method of this invention embodiment;

[0076] Figure 5 This is a schematic diagram of the bipolar inter-electrode fault equivalent circuit used in the analysis method of this invention embodiment;

[0077] Figure 6 This is a schematic diagram of current traveling wave propagation used in the analysis method of this invention. Detailed Implementation

[0078] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. 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.

[0079] A fault characteristic analysis method based on the decoupling matrix of DC transmission lines, such as Figure 1 As shown, the main process of the equivalent method includes:

[0080] Step 1: Based on the switching function theory, construct a mathematical model of the two-terminal high-voltage DC system.

[0081] Based on the switching function theory, the AC system, converter transformer and converter are represented by an equivalent inductance, and the DC system is characterized by this system with an invariant topology.

[0082] The equivalent impedance of the six-pulse converter station is:

[0083]

[0084] The equivalent impedance of the twelve-pulse converter station is:

[0085]

[0086] Where: μ is the commutation angle during the converter commutation process, L s For the equivalent inductance of the AC system, Lt This is the equivalent inductance of the converter transformer referred to the converter side.

[0087] In deriving the equivalent impedance of the converter station using the switching function, the high-frequency components of the switching function are ignored, and only the fundamental frequency of the AC system is considered. The nonlinear power electronic devices are linearized, and the DC power supply part is represented by the no-load voltage and equivalent impedance of the DC converter according to Thevenin's theorem.

[0088] The no-load voltage on the rectifier side of the DC transmission system is:

[0089] U dcR =1.35N R U R cosα (3)

[0090] The no-load voltage on the inverter side of the DC transmission system is:

[0091] U dcI =1.35N I U I cosβ (4)

[0092] Where: N R and N I These represent the number of six-pulse bridges in the multi-bridge converters of the rectifier station and inverter station, respectively. R and U I α and β are the AC system line voltages on the rectifier side and inverter side, respectively, α is the trigger delay angle of the rectifier station trigger pulse, and β is the trigger lead angle of the inverter station trigger pulse.

[0093] Based on the above analysis, an equivalent circuit diagram of a typical DC transmission system can be obtained as follows: Figure 2 As shown.

[0094] Step 2: Construct the DC equivalent circuit network after the fault using the superposition principle. It is divided into two parts: the normal component network before the fault and the fault component network describing the fault.

[0095] When a fault occurs, due to the time delay of the DC control system, the DC power supply will maintain its pre-fault output value for a period of time. The faulty branch can be equivalently represented as the superposition of two voltage sources of equal magnitude but opposite direction. The network after the fault is shown in the attached diagram. Figure 3 The voltage source amplitude is the amplitude of the voltage at the fault point before the fault. According to the superposition theorem, the normal component network at the fault point before the fault (as shown in the attached diagram) Figure 3 (c) Superimposed fault component networks describing the faults (as shown in the appendix) Figure 3 (d) can represent the network after a fault. Fault-related additional power supply -u f The fault component network was subjected to a fault traveling wave.

[0096] Step 3: Establish a transmission line model and solve for the general solution of the initial voltage and current traveling wave of the transmission line.

[0097] The process by which a fault-dependent power source alternately establishes electric and magnetic fields on a transmission line can be expressed using the transmission equations for distributed parameter lines. On a lossless transmission line where line resistance and conductance are neglected, the transmission line equation is:

[0098]

[0099] In the formula, u and i are the voltage and current at any point on the transmission line, and L0 and C0 are the inductance and capacitance per unit length of the transmission line. The second-order partial differential form of the transmission line equation is the wave equation:

[0100]

[0101] The d'Alembert solution to the wave equation is

[0102]

[0103] In the formula, v is the wave velocity of the traveling wave propagating on the transmission line, and Z... c Let u1 be the wave impedance of the transmission line, u2 be the positive traveling wave propagating in the positive x-axis direction, and u3 be the negative traveling wave propagating in the opposite x-axis direction.

[0104] Wave velocity and wave impedance depend on the parameters of the transmission line, and are expressed as follows:

[0105]

[0106]

[0107] In fault component networks, u F and i F Let the initial voltage and current traveling waves of the fault be represented, with the fault point as the starting point of the x-axis and the direction of the x-axis along the transmission line. Before reflection and refraction occur, only positive traveling waves exist on the transmission line. The relationship between the initial voltage and current traveling waves is as follows:

[0108] u F =Z c i f (10)

[0109] According to Kirchhoff's laws, the boundary conditions at the fault point can be obtained as follows:

[0110]

[0111] Combining equations (8) and (9), the initial voltage and current traveling waves of the transmission line can be obtained as follows:

[0112]

[0113] The voltage of the fault-addition power supply is the voltage at the fault point before the fault. For a DC system, this can be considered a constant DC voltage with an amplitude of U. f .

[0114] The fault-addition network is superimposed on the normal network after the fault. Assuming the fault occurs at time t0, there is no traveling wave on the transmission line before time t0. Therefore, considering the entire time range before and after the fault, the initial voltage and current traveling waves can be expressed as:

[0115]

[0116]

[0117] As can be seen from the above formula, the initial voltage and current traveling waves are both negative polarity step waves, and the amplitude of the wavefront is related to the line wave impedance, transition resistance, and the voltage at the fault point before the fault.

[0118] Step 4: Decouple the electrical coupling of the bipolar system by pole mode transformation and construct the DC line fault traveling wave equation in the mode domain.

[0119] In a bipolar system, there is electromagnetic coupling between the positive and negative electrical quantities. When abstracted into a mathematical model, this is represented by mutual impedance between the positive and negative lines. The transmission line equation for a bipolar system is:

[0120]

[0121]

[0122] Among them, u p u n These are the positive and negative voltages, i p i n These are the positive and negative currents, L. s C s These are the self-inductance and self-capacitance per unit length, respectively, L m C m These are the mutual inductance and mutual capacitance per unit length, respectively.

[0123] The polar voltage and current are represented in matrix form:

[0124]

[0125]

[0126] Because there is coupling between the electrical quantities of different poles, it is necessary to perform coordinate transformation on the pole electrical quantities in order to decouple them. The transformed electrical quantities are called moduli, and the matrix used for the transformation is called the pole-mode transformation matrix.

[0127]

[0128]

[0129] Substituting equations (19) and (20) into the transmission line equation and transforming them, we can obtain the wave equation in terms of modulus:

[0130]

[0131] Let the coefficient matrix of the wave equation be a diagonal matrix, then the polar mode transformation matrix can be obtained as follows:

[0132]

[0133] The transformed wave equation is

[0134]

[0135] The zero-mode and line-mode components only have self-impedance, and their inductance and capacitance can be expressed as:

[0136]

[0137] The wave impedances of the zero mode and the line mode are

[0138]

[0139] Determine whether it is a unipolar or bipolar fault. If it is a unipolar fault, proceed to step five; if it is a bipolar fault, proceed to step six.

[0140] Step 5: Derive the initial traveling wave solution for a unipolar fault in a bipolar system.

[0141] Taking a positive-pole grounding fault as an example, the expression for the initial traveling wave of a unipolar grounding fault in a bipolar system is derived to obtain the fault characteristics. (Appendix) Figure 4 This is a schematic diagram of a positive grounding fault.

[0142] When a positive ground fault occurs, the boundary conditions at the fault point are:

[0143]

[0144] Performing a polar mode transformation on the above equation, we obtain

[0145]

[0146] The fault initial voltage and current traveling waves of the modulus satisfy

[0147]

[0148] Combining equations (27) and (28), the fault initial voltage and current traveling waves of the modulus are obtained as follows:

[0149]

[0150] Considering the entire time range before and after the fault, the fault initial voltage and current traveling wave of the modulus can also be written in the form of a step wave. The amplitude of the wavefront is related to the line mode and zero mode wave impedance, transition resistance and the voltage at the fault point before the fault.

[0151] When there is a negative ground fault, the initial voltage and current traveling wave amplitude of the modulus fault are the same as those when there is a positive ground fault. The polarity of the initial voltage and current traveling wave of the line modulus fault is the same as that when there is a positive ground fault. The polarity of the initial voltage and current traveling wave of the zero modulus fault is opposite to that when there is a positive ground fault.

[0152] Step 6: Derive the initial traveling wave solution for a bipolar fault in a bipolar system.

[0153] In the case of a bipolar fault, the voltage value of the additional power supply is the voltage difference between the two fault points before the fault, as shown in the attached figure. Figure 5 As shown, assuming the voltage amplitudes at the positive and negative fault points are equal, denoted as U. f The voltage amplitude of the fault-addition power supply is 2U. f .

[0154] For bipolar inter-pole faults, the boundary conditions at the fault point are:

[0155]

[0156] During bipolar inter-electrode faults, the initial voltage and current traveling waves still satisfy equation (29). After performing a polar mode transformation on the boundary conditions, combining equation (30), we can obtain:

[0157]

[0158] After a bipolar inter-pole fault, there is no zero-mode component on the line. The amplitude of the initial voltage and current traveling wave front of the line-mode fault is related to the line-mode wave impedance, the transition resistance, and the voltage difference between the two fault points before the fault.

[0159] Step 7: Derive the propagation characteristics of traveling waves after reflection at the transmission line boundary.

[0160] When the initial traveling wave of a fault propagates along the line, it will be reflected at points of impedance discontinuity. For DC fault traveling waves, the line boundary and the fault point are the points of impedance discontinuity encountered during propagation. Due to the poor transmission characteristics of voltage transformers, current traveling wave detection devices all use current traveling waves for detection. Therefore, this invention presents the reflection characteristics of current traveling waves at the transmission line boundary. In the following text, "traveling wave" refers to current traveling waves. Figure 6The propagation process of traveling waves and the symbols for each traveling wave are given. Here, R and I represent the rectifier side and inverter side, respectively; ρ R ρ I ρ F These are the reflection coefficients of the rectifier side boundary, the inverter side boundary, and the fault point, respectively; γ F It is the refractive index of the fault point.

[0161] For ease of description below, the appendix will be... Figure 6 The names of the traveling waves in the code are as follows: i F It is the initial traveling wave of the fault being analyzed; ρ R i F ρ I i F The initial traveling wave of the fault on the rectifier side and inverter side is reflected at the line boundary. Therefore, the first wavefront detected by the current transformer is the initial traveling wave of the fault and its reflected wave at the line boundary; ρ F ρ R i F ρ F ρ I i F This is called the reflected wave from the fault point on the rectifier side and inverter side, ρ F ρ 2 R i F ρ F ρ 2 I i F The secondary reflection wave at the line boundary of the fault point reflected wave on the rectifier side and inverter side, γ F ρ R iF, γ F ρ I i F This is called the refracted wave at the fault point on the rectifier side and inverter side, γ F ρ R ρ I i F γ F ρ R ρ I i F The second wavefront detected by the current transformer is either the fault-point reflected wave and its secondary reflection wave at the line boundary, or the fault-point refracted wave and its reflection wave at the line boundary, depending on the distance of the fault.

[0162] The initial traveling wave of the fault is reflected once at the line boundary. The secondary reflection of the fault point reflected wave at the line boundary and the reflection of the fault point refracted wave at the line boundary are both reflected twice at the line boundary. The reflection coefficients of the two reflections are the same or similar. Therefore, the reflection characteristics of the line boundary are analyzed using the first reflection as an example.

[0163] Taking a unipolar system as an example, at the boundary of the transmission line, the current reflection coefficient can be expressed as:

[0164]

[0165] Among them, L dc L is the equivalent inductance on the DC side of the AC system and converter. r Z is the inductance of the smoothing reactor. lb The impedance of the DC filter;

[0166] When the transition resistance is a fixed value, the refraction and reflection coefficients at the fault point are constant. Therefore, after reflection and refraction at the fault point, the waveform of the traveling wave will not change, but the amplitude will change. The refraction and reflection coefficients at the fault point are shown in the following formula.

[0167]

[0168]

[0169] Example 2

[0170] Corresponding to the method in Example 1, this example discloses a fault characteristic analysis system based on the decoupling matrix of DC transmission lines, such as... Figure 1 As shown, the equivalent method mainly includes the following modules:

[0171] The model building module is used to construct a mathematical model of a two-terminal high-voltage direct current system based on the switching function theory.

[0172] Based on the switching function theory, the AC system, converter transformer and converter are represented by an equivalent inductance, and the DC system is characterized by this system with an invariant topology.

[0173] The equivalent impedance of the six-pulse converter station is:

[0174]

[0175] The equivalent impedance of the twelve-pulse converter station is:

[0176]

[0177] Where: μ is the commutation angle during the converter commutation process, L s For the equivalent inductance of the AC system, L t This is the equivalent inductance of the converter transformer referred to the converter side.

[0178] In deriving the equivalent impedance of the converter station using the switching function, the high-frequency components of the switching function are ignored, and only the fundamental frequency of the AC system is considered. The nonlinear power electronic devices are linearized, and the DC power supply part is represented by the no-load voltage and equivalent impedance of the DC converter according to Thevenin's theorem.

[0179] The no-load voltage on the rectifier side of the DC transmission system is:

[0180] U dcR =1.35N R U R cosα (3)

[0181] The no-load voltage on the inverter side of the DC transmission system is:

[0182] U dcI =1.35N I U I cosβ (4)

[0183] Where: N R and N I These represent the number of six-pulse bridges in the multi-bridge converters of the rectifier station and inverter station, respectively. R and U I α and β are the AC system line voltages on the rectifier side and inverter side, respectively, α is the trigger delay angle of the rectifier station trigger pulse, and β is the trigger lead angle of the inverter station trigger pulse.

[0184] Based on the above analysis, an equivalent circuit diagram of a typical DC transmission system can be obtained as follows: Figure 2 As shown.

[0185] The equivalent circuit construction module is used to construct the DC equivalent circuit network after a fault using the superposition principle. It consists of two parts: the normal component network before the fault and the fault component network describing the fault.

[0186] When a fault occurs, due to the time delay of the DC control system, the DC power supply will maintain its pre-fault output value for a period of time. The faulty branch can be equivalently represented as the superposition of two voltage sources of equal magnitude but opposite direction. The network after the fault is shown in the attached diagram. Figure 3 The voltage source amplitude is the amplitude of the voltage at the fault point before the fault. According to the superposition theorem, the normal component network at the fault point before the fault (as shown in the attached diagram) Figure 3 (c) Superimposed fault component networks describing the faults (as shown in the appendix) Figure 3 (d) can represent the network after a fault. Fault-related additional power supply -u f The fault component network was subjected to a fault traveling wave.

[0187] The transmission line model building module is used to build transmission line models and solve the general solutions for the initial voltage and current traveling waves of transmission lines.

[0188] The process by which a fault-dependent power source alternately establishes electric and magnetic fields on a transmission line can be expressed using the transmission equations for distributed parameter lines. On a lossless transmission line where line resistance and conductance are neglected, the transmission line equation is:

[0189]

[0190] In the formula, u and i are the voltage and current at any point on the transmission line, and L0 and C0 are the inductance and capacitance per unit length of the transmission line. The second-order partial differential form of the transmission line equation is the wave equation:

[0191]

[0192] The d'Alembert solution to the wave equation is

[0193]

[0194] In the formula, v is the wave velocity of the traveling wave propagating on the transmission line, and Z... c Let u1 be the wave impedance of the transmission line, u2 be the positive traveling wave propagating in the positive x-axis direction, and u3 be the negative traveling wave propagating in the opposite x-axis direction.

[0195] Wave velocity and wave impedance depend on the parameters of the transmission line, and are expressed as follows:

[0196]

[0197]

[0198] In fault component networks, u F and i F Let the initial voltage and current traveling waves of the fault be represented, with the fault point as the starting point of the x-axis and the direction of the x-axis along the transmission line. Before reflection and refraction occur, only positive traveling waves exist on the transmission line. The relationship between the initial voltage and current traveling waves is as follows:

[0199] u F =Z c i F (10)

[0200] According to Kirchhoff's laws, the boundary conditions at the fault point can be obtained as follows:

[0201]

[0202] Combining equations (8) and (9), the initial voltage and current traveling waves of the transmission line can be obtained as follows:

[0203]

[0204] The voltage of the fault-addition power supply is the voltage at the fault point before the fault. For a DC system, this can be considered a constant DC voltage with an amplitude of U. f .

[0205] The fault-addition network is superimposed on the normal network after the fault. Assuming the fault occurs at time t0, there is no traveling wave on the transmission line before time t0. Therefore, considering the entire time range before and after the fault, the initial voltage and current traveling waves can be expressed as:

[0206]

[0207]

[0208] As can be seen from the above formula, the initial voltage and current traveling waves are both negative polarity step waves, and the amplitude of the wavefront is related to the line wave impedance, transition resistance, and the voltage at the fault point before the fault.

[0209] The DC line fault traveling wave equation construction module is used to decouple the electrical coupling of the bipolar system through pole mode transformation and construct the DC line fault traveling wave equation in the mode domain.

[0210] In a bipolar system, there is electromagnetic coupling between the positive and negative electrical quantities. When abstracted into a mathematical model, this is represented by mutual impedance between the positive and negative lines. The transmission line equation for a bipolar system is:

[0211]

[0212]

[0213] Among them, u p u n These are the positive and negative voltages, i p i n These are the positive and negative currents, L. s C s These are the self-inductance and self-capacitance per unit length, respectively, L m C m These are the mutual inductance and mutual capacitance per unit length, respectively.

[0214] The polar voltage and current are represented in matrix form:

[0215]

[0216]

[0217] Because there is coupling between the electrical quantities of different poles, it is necessary to perform coordinate transformation on the pole electrical quantities in order to decouple them. The transformed electrical quantities are called moduli, and the matrix used for the transformation is called the pole-mode transformation matrix.

[0218]

[0219]

[0220] Substituting equations (19) and (20) into the transmission line equation and transforming them, we can obtain the wave equation in terms of modulus:

[0221]

[0222] Let the coefficient matrix of the wave equation be a diagonal matrix, then the polar mode transformation matrix can be obtained as follows:

[0223]

[0224] The transformed wave equation is

[0225]

[0226] The zero-mode and line-mode components only have self-impedance, and their inductance and capacitance can be expressed as:

[0227]

[0228] The wave impedances of the zero mode and the line mode are

[0229]

[0230] The judgment module is used to determine whether it is a unipolar fault or a bipolar fault. If it is a unipolar fault, the judgment module is used; if it is a bipolar fault, the initial traveling wave solution derivation module for the unipolar fault is used.

[0231] The module for deriving the initial traveling wave solution of a single-stage fault is used to derive the initial traveling wave solution of a single-stage fault in a bipolar system.

[0232] Taking a positive-pole grounding fault as an example, the expression for the initial traveling wave of a unipolar grounding fault in a bipolar system is derived to obtain the fault characteristics. (Appendix) Figure 4 This is a schematic diagram of a positive grounding fault.

[0233] When a positive ground fault occurs, the boundary conditions at the fault point are:

[0234]

[0235] Performing a polar mode transformation on the above equation, we obtain

[0236]

[0237] The fault initial voltage and current traveling waves of the modulus satisfy

[0238]

[0239] Combining equations (27) and (28), the fault initial voltage and current traveling waves of the modulus are obtained as follows:

[0240]

[0241] Considering the entire time range before and after the fault, the fault initial voltage and current traveling wave of the modulus can also be written in the form of a step wave. The amplitude of the wavefront is related to the line mode and zero mode wave impedance, transition resistance and the voltage at the fault point before the fault.

[0242] When there is a negative ground fault, the initial voltage and current traveling wave amplitude of the modulus fault are the same as those when there is a positive ground fault. The polarity of the initial voltage and current traveling wave of the line modulus fault is the same as that when there is a positive ground fault. The polarity of the initial voltage and current traveling wave of the zero modulus fault is opposite to that when there is a positive ground fault.

[0243] The module for deriving the initial traveling wave solution of a bipolar fault is used to derive the initial traveling wave solution of a bipolar system under bipolar fault conditions.

[0244] In the case of a bipolar fault, the voltage value of the additional power supply is the voltage difference between the two fault points before the fault, as shown in the attached figure. Figure 5 As shown, assuming the voltage amplitudes at the positive and negative fault points are equal, denoted as U. f The voltage amplitude of the fault-addition power supply is 2U. f .

[0245] For bipolar inter-pole faults, the boundary conditions at the fault point are:

[0246]

[0247] During bipolar inter-electrode faults, the initial voltage and current traveling waves still satisfy equation (29). After performing a polar mode transformation on the boundary conditions, combining equation (30), we can obtain:

[0248]

[0249] After a bipolar inter-pole fault, there is no zero-mode component on the line. The amplitude of the initial voltage and current traveling wave front of the line-mode fault is related to the line-mode wave impedance, the transition resistance, and the voltage difference between the two fault points before the fault.

[0250] The traveling wave propagation characteristic derivation module is used to derive the traveling wave propagation characteristics after reflection at the transmission line boundary.

[0251] When the initial traveling wave of a fault propagates along the line, it will be reflected at points of impedance discontinuity. For DC fault traveling waves, the line boundary and the fault point are the points of impedance discontinuity encountered during propagation. Due to the poor transmission characteristics of voltage transformers, current traveling wave detection devices all use current traveling waves for detection. Therefore, this invention presents the reflection characteristics of current traveling waves at the transmission line boundary. In the following text, "traveling wave" refers to current traveling waves. Figure 6 The propagation process of traveling waves and the symbols for each traveling wave are given. Here, R and I represent the rectifier side and inverter side, respectively; ρ R ρ I ρ F These are the reflection coefficients of the rectifier side boundary, the inverter side boundary, and the fault point, respectively; γ F It is the refractive index of the fault point.

[0252] For ease of description below, the appendix will be... Figure 6 The names of the traveling waves in the code are as follows: i F It is the initial traveling wave of the fault being analyzed; ρ R i F ρ I i F The initial traveling wave of the fault on the rectifier side and inverter side is reflected at the line boundary. Therefore, the first wavefront detected by the current transformer is the initial traveling wave of the fault and its reflected wave at the line boundary; ρ F ρ R i F ρ F ρ I i F This is called the reflected wave from the fault point on the rectifier side and inverter side, ρ F ρ 2 R i F ρ F ρ 2 I i F The secondary reflection wave at the line boundary of the fault point reflected wave on the rectifier side and inverter side, γ F ρ R iF, γ F ρ I i F This is called the refracted wave at the fault point on the rectifier side and inverter side, γ F ρ R ρ I i F γ F ρ R ρ I i FThe second wavefront detected by the current transformer is either the fault-point reflected wave and its secondary reflection wave at the line boundary, or the fault-point refracted wave and its reflection wave at the line boundary, depending on the distance of the fault.

[0253] The initial traveling wave of the fault is reflected once at the line boundary. The secondary reflection of the fault point reflected wave at the line boundary and the reflection of the fault point refracted wave at the line boundary are both reflected twice at the line boundary. The reflection coefficients of the two reflections are the same or similar. Therefore, the reflection characteristics of the line boundary are analyzed using the first reflection as an example.

[0254] Taking a unipolar system as an example, at the boundary of the transmission line, the current reflection coefficient can be expressed as:

[0255]

[0256] Among them, L dc L is the equivalent inductance on the DC side of the AC system and converter. r Z is the inductance of the smoothing reactor. lb The impedance of the DC filter;

[0257] When the transition resistance is a fixed value, the refraction and reflection coefficients at the fault point are constant. Therefore, after reflection and refraction at the fault point, the waveform of the traveling wave will not change, but the amplitude will change. The refraction and reflection coefficients at the fault point are shown in the following formula.

[0258]

[0259]

[0260] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fault characteristic analysis method based on the decoupling matrix of DC transmission lines, characterized in that, Includes the following steps: S1. Based on the switching function theory, construct a mathematical model of the high-voltage direct current system at both ends of a DC transmission line; S2. Construct the DC equivalent circuit network after the fault using the superposition principle, which is divided into two parts: the normal component network before the fault and the fault component network describing the fault. S3. Establish a transmission line model and solve for the general solution of the initial voltage and current traveling wave of the transmission line; S4. Decouple the electrical coupling of the bipolar system by pole mode transformation and construct the DC line fault traveling wave equation in the mode domain; S5. Determine whether it is a unipolar fault or a bipolar fault. If it is a unipolar fault, proceed to step S6; otherwise, proceed to step S7. S6. Derive the initial traveling wave solution for a unipolar fault in a bipolar system; S7. Derive the initial traveling wave solution for a bipolar fault in a bipolar system; S8. Derive the traveling wave propagation characteristics after reflection at the transmission line boundary; specifically, the current reflection coefficient at the transmission line boundary is determined by the following formula: Among them, L dc L is the equivalent inductance on the DC side of the AC system and converter. r Z is the inductance of the smoothing reactor. lb Z is the impedance of the DC filter. c This is the wave impedance of the transmission line.

2. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 1, characterized in that, Step S1 specifically involves: representing the AC system, converter transformer, and converter with an equivalent inductance, and characterizing the DC system using this system with an unchanged topology; the equivalent impedance is determined by the following formula: The equivalent impedance of the six-pulse converter station is: The equivalent impedance of the twelve-pulse converter station is: Where: μ is the commutation angle during the converter commutation process, L s For the equivalent inductance of the AC system, L t This is the equivalent inductance of the converter transformer referred to the converter side.

3. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 2, characterized in that, The general solution for the initial voltage and current traveling wave of the transmission line in step S3 is determined by the following formula: Among them, u F and i F The initial voltage and current traveling waves of the fault are represented, t0 represents the time point when the fault occurs, and Z represents the initial voltage and current traveling waves of the fault. c U is the surge impedance of the transmission line. f This represents the initial voltage amplitude during the fault.

4. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 3, characterized in that, In step S4, the bipolar system line coupling characteristics are achieved through pole mode transformation, and the mode domain downwave equation is determined by the following formula: Among them, L s C s These are the self-inductance and self-capacitance per unit length, respectively, L m C m These are the mutual inductance and mutual capacitance per unit length, respectively.

5. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 4, characterized in that, In step S6, when a bipolar system experiences a unipolar ground fault, the initial fault voltage and current traveling wave in the mode domain are determined by the following formulas:

6. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 5, characterized in that, In step S7, when a bipolar system experiences an inter-pole fault, the initial fault voltage and current traveling wave in the mode domain are determined by the following formulas:

7. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 6, characterized in that, In step S8, the reflection coefficient ρ of the fault point F , refractive index γ F They are determined by the following formulas respectively:

8. A fault characteristic analysis system based on the decoupling matrix of DC transmission lines, characterized in that, include: The model building module is used to construct a mathematical model of the high-voltage direct current system at both ends of a DC transmission line based on the switching function theory. The equivalent circuit construction module is used to construct the DC equivalent circuit network after the fault using the superposition principle. It is divided into two parts: the normal component network before the fault and the fault component network describing the fault. The transmission line model building module is used to build transmission line models and solve for the general solutions of initial voltage and current traveling waves of transmission lines. A DC line fault traveling wave equation construction module is used to decouple the electrical coupling of the bipolar system through pole mode transformation and construct the DC line fault traveling wave equation in the mode domain. The judgment module is used to determine whether it is a unipolar fault or a bipolar fault. If it is a unipolar fault, it enters the initial traveling wave solution derivation module for a unipolar fault; otherwise, it enters the initial traveling wave solution derivation module for a bipolar fault. The module for deriving the initial traveling wave solution of a single-stage fault is used to derive the initial traveling wave solution of a bipolar system under a single-stage fault. The module for deriving the initial traveling wave solution of a bipolar fault is used to derive the initial traveling wave solution of a bipolar system under bipolar fault conditions. The traveling wave propagation characteristic derivation module is used to derive the traveling wave propagation characteristics after reflection at the transmission line boundary; specifically, at the transmission line boundary, the current reflection coefficient is determined by the following formula: Among them, L dc L is the equivalent inductance on the DC side of the AC system and converter. r Z is the inductance of the smoothing reactor. lb Z is the impedance of the DC filter. c This is the wave impedance of the transmission line.

9. A fault characteristic analysis system based on a decoupling matrix for DC transmission lines according to claim 8, characterized in that, The model building module specifically involves representing the AC system, converter transformer, and converter using an equivalent inductance, thereby characterizing the DC system with this topology-unchanged system; the equivalent impedance is determined by the following formula: The equivalent impedance of the six-pulse converter station is: The equivalent impedance of the twelve-pulse converter station is: Where: μ is the commutation angle during the converter commutation process, L s For the equivalent inductance of the AC system, L t This is the equivalent inductance of the converter transformer referred to the converter side.

10. A fault characteristic analysis system based on a decoupling matrix for DC transmission lines according to claim 9, characterized in that, The initial voltage and current traveling wave general solution of the transmission line in the transmission line model construction module is determined by the following formula: Among them, u F and i F The initial voltage and current traveling waves of the fault are represented, t0 represents the time point when the fault occurs, and Z represents the initial voltage and current traveling waves of the fault. c U is the surge impedance of the transmission line. f This represents the initial voltage amplitude during the fault.

11. The fault characteristic analysis method based on the decoupling matrix of a DC transmission line according to claim 10, characterized in that, In the DC line fault traveling wave equation construction module, the bipolar system line coupling characteristics are realized through pole mode transformation, and the mode domain traveling wave equation is determined by the following formula: Among them, L s C s These are the self-inductance and self-capacitance per unit length, respectively, L m C m These are the mutual inductance and mutual capacitance per unit length, respectively.

12. The fault characteristic analysis system based on the decoupling matrix of a DC transmission line according to claim 11, characterized in that, In the single-stage fault initial traveling wave derivation module, when a bipolar system experiences a single-pole ground fault, the initial fault voltage and current traveling waves in the mode domain are determined by the following formulas:

13. The fault characteristic analysis system based on the decoupling matrix of a DC transmission line according to claim 12, characterized in that, In the bipolar fault initial traveling wave derivation module, when a bipolar system experiences an inter-pole fault, the initial voltage and current traveling waves in the mode domain are determined by the following formulas:

14. The fault characteristic analysis system based on the decoupling matrix of a DC transmission line according to claim 13, characterized in that, In the traveling wave propagation characteristic derivation module, the reflection coefficient ρ at the fault point F , refractive index γ F They are determined by the following formulas respectively:

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