Analysis method of electrical characteristics and transient overvoltage of pantograph-catenary arc considering time-varying parameters

Abstract

The application discloses a pantograph-catenary arc electrical characteristic and transient overvoltage analysis method considering the influence of time-varying parameters, in which, in the transient analysis of pantograph-catenary off-line arc, time-varying impedance and capacitive impedance parameters of a traction network are introduced into the pantograph-catenary arc electrical characteristic formation process for the first time, and an improved arc model considering the influence of train speed and a fine train-track grounding system model are combined to realize the unified analysis of the overvoltage of a train roof and a train body, avoid the overvoltage evaluation deviation caused by the static traction network parameters and the simplified grounding model, and improve the accuracy and engineering applicability of the pantograph-catenary off-line arc transient overvoltage analysis.

Description

Technical Field

[0001] This invention relates to the field of simulation modeling technology for traction power supply systems of electrified railways, and specifically to a method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters. Background Technology

[0002] The traction power supply system of an electrified railway consists of a traction substation, a traction catenary system, and the train, forming a closed electrical circuit. The train receives traction current from the overhead contact line via a pantograph, which is then supplied to the traction motor via the onboard high-voltage electrical system and the traction drive system to drive the vehicle. Simultaneously, the traction current returns to the rails, return conductor, and ground through the vehicle-rail grounding system, ultimately returning to the traction substation. As the sole entry point for energy into the train from the traction power supply system, the state of the pantograph-catenary system directly determines the quality of power reception and the safety of the power supply.

[0003] When the pantograph loses contact with the overhead contact line during train operation, the electric arc becomes a temporary energy transfer channel. The pantograph-catenary arc exhibits significant nonlinearity, strong dynamics in the zero-crossing region, and high-frequency components, easily triggering electromagnetic transient changes in traction network voltage, current, and electrical grounding status. This can lead to overvoltage issues on the roof of the overhead contact line and overvoltage between the train body and the rails, threatening the insulation and electromagnetic compatibility reliability of onboard equipment. Therefore, it is necessary to conduct an analysis of the electrical characteristics and transient overvoltages of the pantograph-catenary arc at the overall electrical circuit level of the "arc-traction network-train-grounding system".

[0004] Existing studies on pantograph-catenary arc transients mostly employ the "arc-vehicle-catenary" modeling and analysis method. The traction network often uses a π-type lumped-parameter two-port equivalent model or a chain circuit equivalent model based on multi-conductor transmission theory. The chain model can better preserve the self- and mutual impedance and self- and mutual capacitance coupling relationships between multiple conductors in the traction network while also considering computational efficiency. However, existing chain traction network models typically treat conductor self- and mutual resistance, self- and mutual inductance, as well as capacitance to ground and inter-conductor capacitance, as constant values. This makes it difficult to reflect the time-varying characteristics of traction network electrical parameters caused by changes in the distance between the train and the power supply point and the length of the equivalent power supply section as the train moves along the track. Especially during pantograph-catenary offline arc transients, although the arcing time is short, the voltage and current change rates are high, and the frequency components are high, making the inductive and capacitive reactance effects of the traction network more significant. If the traction network is still treated as static parameters, it is often difficult to accurately reflect the impact of real-time changes in traction network impedance and capacitive reactance on arc current, arc voltage, and transient overvoltage peak values, oscillations, and attenuation patterns, leading to biased analysis results.

[0005] Furthermore, transient overvoltages include not only overvoltages on the high-voltage side of the roof but also surge overvoltages from the car body to the track. Car body voltage is closely related to the return current and the car-rail grounding system. Taking the CRH3 EMU as an example, the high-voltage cable on the roof connects to the pantograph and supplies power to the onboard transformer. Under high-frequency transient conditions such as pantograph-catenary offline arcing, the voltage of the high-voltage cable core on the roof is transmitted to the car body through capacitive coupling with the shielding layer and the car body, which is one of the important sources of surge overvoltages in the car body. Simultaneously, factors such as the working grounding and the car body protective grounding methods, the car body impedance and the connection impedance between adjacent car bodies, and the grounding system impedance and track impedance can affect the return current distribution and the rise in car body voltage. If an oversimplified model is used for the car-rail grounding system, it is difficult to provide reliable analytical results for both roof overvoltages and car body overvoltages simultaneously.

[0006] Therefore, it is necessary to propose a method that focuses on the electrical characteristics of pantograph-catenary arcs and transient overvoltage analysis. Based on the construction of a unified coupled model of the arc, traction network, train high-voltage system, and vehicle-rail grounding system, this method takes into account the real-time changes in the impedance and capacitive reactance parameters of the traction network, and focuses on the key coupling factors of the vehicle-rail grounding system related to vehicle overvoltage. This will improve the accuracy and applicability of the analysis of roof overvoltage and vehicle overvoltage under transient conditions of pantograph-catenary offline arcs. Summary of the Invention

[0007] This invention provides a method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters. Under the transient condition of pantograph-catenary offline arc, the time-varying impedance and capacitive reactance parameters of the traction network are involved in the unified solution calculation of the arc electrical characteristics formation process. The method also focuses on the key coupling factors in the formation of overvoltage in the vehicle body, thereby improving the accuracy of transient overvoltage analysis.

[0008] This invention provides a method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arcs considering the influence of time-varying parameters. The method includes: A “traction network-train-grounding system” model is constructed, which includes a traction substation model, a multi-conductor traction network system model, a train high-voltage electrical system model, a vehicle-rail return grounding system model, and a pantograph-catenary arc model. The multi-conductor traction network system model adopts a chain circuit equivalent model that takes into account time-varying resistance and inductance parameters and time-varying capacitance parameters. The pantograph-catenary arc model adopts an improved Hadedank equation arc model that takes into account the influence of train running speed. Based on the established "arc-traction network-train-grounding system" model, under the transient working condition of pantograph-catenary offline arc, the time-varying impedance parameters and time-varying capacitive reactance parameters of the traction network conductor are involved in the unified solution calculation of pantograph-catenary arc current, arc voltage and transient overvoltage, so as to realize the influence analysis of the time-varying electrical parameters of the traction network on the electrical characteristics of pantograph-catenary arc, roof overvoltage and car body overvoltage response.

[0009] Furthermore, the multi-conductor traction network system model is constructed using a chain circuit equivalent model that considers time-varying resistive and inductive parameters and time-varying capacitance parameters, specifically including: Within the chain circuit equivalent modeling framework of a multi-conductor traction network, the traction network system is modeled based on time-varying resistance and inductance parameters and time-varying capacitance parameters. The time-varying resistance and inductance parameters include the self-resistance and self-inductance of each conductor in the traction network, as well as the mutual resistance and mutual inductance between conductors, which are dynamically updated according to the real-time position and operating status of the train. The time-varying capacitance parameters include the capacitance to ground of each conductor in the traction network and the mutual capacitance between conductors, which are dynamically updated according to the real-time position and operating status of the train.

[0010] Furthermore, the multi-conductor traction network system model is constructed using a chain circuit equivalent model that considers time-varying resistive and inductive parameters and time-varying capacitance parameters, specifically including: When modeling the traction network system based on time-varying resistance parameters, the time-varying resistance parameters, which are dynamically updated according to the real-time position and running status of the train, are introduced into the constructed functional mapping relationship model between conductor voltage and conductor current, thereby constructing a time-varying chain resistance model. The functional mapping relationship between conductor voltage and conductor current is shown in the following model: Establish a controlled voltage source U R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn The functional mapping relationship between them, where U R1 U R2 U Rn I represents the potential difference (i=1,2,...,n) across the i-th conductor, i.e., the conductor voltage. R1 I R2 、···、I Rn Let represent the current of the i-th conductor (i=1,2,...,n), and n be the number of conductors in the traction network system after equivalent merging and simplification. The specific formula is as follows: U = R*I + L*(dI / dx) Where U is the conductor voltage matrix; R is the conductor time-varying resistance matrix, including the time-varying conductor self-resistance and inter-conductor mutual resistance; L is the conductor time-varying inductance matrix, including the time-varying conductor self-inductance and inter-conductor mutual inductance; I is the conductor current matrix; dI / dx is the derivative of conductor current I with respect to time x. The time-varying self and mutual resistance / inductance involved in matrices R and L are all equal to the reference self and mutual resistance / inductance value per unit length multiplied by the time-varying resistance / inductance correction coefficient. The time-varying resistance / inductance correction coefficient is a function of time related to the real-time position and operating status of the train. The real-time position of the train is represented by the distance between the train and the power supply station side or the electrical distribution phase side.

[0011] Furthermore, the method specifically includes: Based on the Simulink platform, a controlled source module is constructed to establish a controlled voltage source U. R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn Functional mapping relationship between them; The controlled source module includes 2n input ports and n output ports, where the 2n input ports correspond to n conductor current quantities and their n differential components, and the n output ports correspond to n conductor voltage quantities. The mapping relationship between inputs and outputs is defined through the function m-file of S-Function.

[0012] Furthermore, the multi-conductor traction network system model is constructed using a chain circuit equivalent model that considers time-varying resistive and inductive parameters and time-varying capacitance parameters, specifically including: When modeling the traction network system based on time-varying capacitance parameters, the electrical behavior of the time-varying capacitor, which is dynamically updated according to the real-time position and running status of the train, is simulated using an equivalent controlled current source, thereby constructing a time-varying chain capacitor model. The functional relationship between the equivalent controlled current source and the time-varying capacitor is as follows: I = Y * (dU / dx) Where I is the output current matrix of the controlled current source; Y is the admittance matrix, which is determined by the time-varying capacitance matrix C of the conductor; U is the voltage matrix across the capacitor; dU / dx is the differential component of the voltage across the capacitor with respect to time x; The conductor time-varying capacitance matrix C includes the time-varying conductor-to-ground capacitance and the mutual capacitance between conductors. The time-varying capacitance involved in matrix C is equal to the reference capacitance value per unit length multiplied by the time-varying capacitance correction factor. The time-varying capacitance correction factor is a function that varies with time and is related to the real-time position and operating status of the train. The real-time position of the train is represented by the distance between the train and the power supply station side or the electrical distribution phase side.

[0013] Furthermore, the method specifically includes: Based on the Simulink platform, the fixed conductor capacitor element is replaced with a time-varying capacitor module. The time-varying capacitor module includes a controlled current source module, an Fcn module, a Derivative module, and a Clock module. The Fcn module is used to define the functional expression of the time-varying capacitor, and the output of the Fcn module serves as the control signal for the controlled current source module. The Derivative module is used to provide the differential component of the voltage across the capacitor. The voltage across the capacitor is fed back to the Derivative module through a voltage measurement module. The Clock module is used to provide the time quantity.

[0014] Furthermore, a pantograph-catenary arc model is constructed, specifically including: A pantograph-catenary arc model is constructed based on the Mayr and Cassie models in series. The arc length factor is constructed as a function of train speed to characterize the dynamic characteristics of the arc column as a function of speed. The overall arc conductance is expressed by the following equation:

[0015] In the formula, g is the total conductance of the electric arc, and i arc Let v be the arc current, v be the train speed, and g be the arc current. m With g c τ1 and τ2 are the conductances of the Mayr and Cassie parts, respectively, the time constants of the Mayr and Cassie parts, respectively, k is the power dissipation dielectric constant, and β is the power dissipation factor. The established pantograph-catenary arc model can simultaneously describe the small current characteristics in the zero-crossing region and the large current characteristics before and after the zero-crossing region, and takes into account the influence of train speed on the arc's electrical behavior.

[0016] Furthermore, the method also includes: The constructed pantograph-catenary arc model is directly connected to the pantograph port of the multi-conductor traction network system model and the port of the train high-voltage electrical system model to form a unified solution nonlinear transient system, thereby obtaining the arc current, arc voltage and related transient response.

[0017] Furthermore, the model construction of the vehicle-rail return grounding system specifically includes: The vehicle-rail return current grounding system model adopts a refined model that takes into account the key coupling factors of vehicle body overvoltage. These key coupling factors include the grounding methods of the working grounding system and the vehicle body protective grounding system, the capacitive coupling between the high-voltage cable core and shielding layer on the roof and the vehicle body, the vehicle body impedance and the connection resistance of adjacent vehicle bodies, the grounding system impedance, and the track impedance. This allows the formation and distribution of vehicle body voltage and onboard return current during the pantograph-catenary offline arc transient process to be solved uniformly and used for vehicle body overvoltage analysis.

[0018] Furthermore, the method also includes: The constructed vehicle-rail return grounding system model is coupled with the multi-conductor traction network system model and the pantograph-catenary arc model at the corresponding ports, so as to obtain the transient response of the high-voltage side on the roof and the transient response of the vehicle body to the rail within a unified solution framework, providing a model basis for the analysis of vehicle body overvoltage.

[0019] This invention provides a method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arcs considering the influence of time-varying parameters. It offers the following advantages: For the first time, this invention integrates the time-varying impedance and capacitive reactance parameters of the traction network into the arc electrical characteristic formation process during offline pantograph-catenary arc transient analysis. Combined with an improved arc model that takes into account the influence of train speed and a refined vehicle-rail grounding system model, it achieves a unified analysis of overvoltages on the vehicle roof and body. This avoids overvoltage assessment deviations caused by static traction network parameters and simplified grounding models, thereby improving the accuracy and engineering applicability of offline pantograph-catenary arc transient overvoltage analysis. Attached Figure Description

[0020] Figure 1 This is an overall flowchart of one embodiment of the present invention; Figure 2 This is a schematic diagram of the MTL chain-type lumped π-type network model for the traction network; Figure 3 This is a schematic diagram of a 2n-port network for MTL. Figure 4 This is a schematic diagram of a lumped π-type structure; Figure 5 Schematic diagram of conductor composition for direct-supply traction power supply system (a) with return line and AT traction power supply system (b); Figure 6 A schematic diagram comparing the structure of a traditional chain-type resistive sensing module and the time-varying chain-type resistive sensing module of the present invention; Figure 7 This is a schematic diagram of a controlled source module for changing new controllable source modules when implementing resistive and inductive parameters according to an embodiment of the present invention; Figure 8 This is an equivalent schematic diagram of a time-varying self / mutual capacitance module according to an embodiment of the present invention (the functional relationship is taken as an example of a train traveling at a constant speed of 350km / h). Figure 9 This is a schematic diagram of the overall electrical structure of the CRH3 high-speed train. Figure 10 This is a schematic diagram of the train-rail return current and a schematic diagram of the components and coupling factors related to the car body voltage and the return current on the train. Figure 11 This is a schematic diagram of a vehicle-rail return grounding system model according to an embodiment of the present invention; Figure 12 The curves show the change in vehicle travel distance over time under both acceleration and deceleration conditions. Figure 13This is a comparative schematic diagram of simulation results of roof overvoltage caused by pantograph-catenary offline arc under acceleration conditions according to an embodiment of the present invention; Figure 14 This is a schematic diagram comparing simulation results of vehicle body overvoltage caused by pantograph-catenary offline arc under deceleration conditions according to an embodiment of the present invention. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to specific embodiments and accompanying drawings. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, certain operations related to the present invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0022] Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various embodiments. At the same time, the steps or actions in the method description can be rearranged or adjusted in a manner obvious to those skilled in the art. Therefore, the various orders in the specification and drawings are only for the clear description of a particular embodiment and do not imply a necessary order, unless otherwise stated that a particular order must be followed.

[0023] The first embodiment of this invention provides a method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters. This method is applicable to the electromagnetic transient analysis of electrified railway traction power supply systems under pantograph-catenary offline arc transient conditions. The traction power supply system consists of a traction substation, a traction network system, and the train, forming a closed loop. The traction network is a multi-conductor structure, and conductors may include contact wires, catenary wires, return wires, rails, grounding wires, and the ground, with a total number of conductors (n). The self-resistance, self-inductance, and mutual inductance between conductors constitute the system impedance network. Each conductor has a capacitance to ground (self-capacitance), and there is mutual capacitance between any two conductors. The arc transient process makes the high-frequency effects of the traction network impedance and capacitive reactance more significant. Therefore, the core of this invention's analysis method lies in realizing the time-varying characterization of the traction network system impedance network and capacitance network within a unified transient solution framework, and coupling it with the pantograph-catenary arc model and the train-rail grounding system model for unified solution. The following is a combination of... Figure 1 The method of the present invention will be described.

[0024] S100, construct an "arc-traction network-train-grounding system" model that includes a traction substation model, a multi-conductor traction network system model, a train high-voltage electrical system model, a vehicle-track return grounding system model, and a pantograph-catenary arc model. The multi-conductor traction network system model adopts a chain circuit equivalent model that takes into account time-varying resistance and inductance parameters and time-varying capacitance parameters. The pantograph-catenary arc model adopts an improved Hadedank equation arc model that takes into account the influence of train running speed.

[0025] In this embodiment, a closed electrical circuit model consisting of the traction substation, the traction network multi-conductor system, the train high-voltage system, and the vehicle-rail return grounding system is first established.

[0026] The traction network employs a chain-like equivalent model that considers the real-time changes in impedance and capacitive reactance parameters. This model dynamically updates the conductor's self-resistance, self-inductance, mutual inductance, and ground capacitance and mutual capacitance parameters according to the train's real-time position and operating status. This allows for accurate characterization of the impact of changes in the traction network's equivalent impedance and capacitive reactance on the arc response under high-frequency transient conditions. Specifically: 1. Modeling of Multi-Conductor Traction Network System In this embodiment, the equivalent power source and power supply circuit of the traction substation are first established, and the basis for multi-conductor parameter calculation and equivalent chain modeling of the traction network is established. Based on multi-conductor parameter calculation methods (Carson formula, etc.), the self- and mutual impedance and self- and mutual admittance parameters of the traction network conductors are established. The conductors can be equivalently merged according to engineering needs to reduce the model size, but the principle of current conservation and consistency of equivalent electrical characteristics after merging must be met.

[0027] 1) Calculation of electrical parameters of each conductor in the traction network In this embodiment, the self and mutual impedance and self and mutual admittance parameters of the traction network conductor are established based on multi-conductor parameter calculation methods (such as Carson formula, etc.). The conductors can be equivalently merged according to engineering needs to reduce the model size, but the principle of current conservation and consistency of equivalent electrical characteristics after merging must be met.

[0028] MTL chain parameter modeling of traction network, such as Figure 2 As shown: For any given n+1 conductors forming a traction network multi-conductor transmission line, one of them is selected as the reference conductor. Based on the theory of multi-conductor transmission lines (MTL), a frequency domain equation representing the MTL matrix form is established as follows: (1) In the formula, V and I are both n×1 column vectors, representing the voltage and current on the n transmission lines respectively; Z and Y are both n×n matrices, representing the impedance and admittance per unit length of the n transmission conductors respectively, and both are symmetric matrices; z is the axial variable of the transmission line. For frequency.

[0029] The first-order coupled phasor MTL equation (1) is transformed into a decoupled second-order ordinary differential equation. Based on the port circuit relationship of the distributed transmission line, a second-order differential equation for the position z of the transmission line is established: (2) Equation (2) can be viewed as a network with 2n ports, representing the constraint characteristics between the network's endpoints and origin. Here, n ports are at the left origin and n ports are at the right endpoint, as shown below. Figure 3 As shown.

[0030] According to the beginning of the transmission line Terminal By addressing the constraints and decoupling the equations through similarity transformations, we can obtain the phasors of n voltages V(0) and n currents I(0) on the left side of the transmission line, and the phasors of n voltages... n currents Phasor relationships: (3) In the formula, Let be the chain parameter matrix of MTL. The calculation results of each submatrix of the above matrix are as follows: (4) In the formula, , These are the characteristic impedance matrix and characteristic admittance matrix of the chain parameter matrix, respectively.

[0031] Based on the calculation results of the 2n-port network above, the generalized Thevenin equivalence theorem is used to convert the 2n-port network into a lumped π-type structure, such as... Figure 4 As shown. Based on the circuit topology corresponding to the lumped π-type structure port, assuming that the transmission line is an electrically short line at the frequency under study, the parameter matrix of the traction network per unit length in the lumped π-type structure circuit is derived as follows: (5) Substituting into equation (4), the equivalent chain parameter matrix of the lumped π-type structure of a unit-length 2n-port network can be derived as follows: (6) In the formula, , These are the eigenvectors and eigenvalues ​​of matrix YZ, respectively.

[0032] Equation (5) is the lumped π-type MTL chain parameter model per unit length of the traction network. The chain parameter model of the entire traction network transmission line can be formed by connecting N lumped chain parameter parts per unit length in series: (7) Therefore, by calculating the impedance and admittance matrix per unit length of each line in the traction network and substituting them into the above formula, the MTL chain lumped π-type network model of the entire traction network can be obtained.

[0033] For overhead conductors that are not good conductors above ground, the soil conductivity will have a certain impact on their loop magnetic field. In order to accurately establish a traction network model over a wide frequency range, the Dubanton complex image method can be used to calculate the electrical parameters of each overhead conductor in the traction network.

[0034] The formulas for calculating the self-impedance and mutual impedance of two overhead conductors are as follows: (8) In the formula, p is the skin depth, and ; The soil electrical conductivity is taken as 0.01 S / m.

[0035] Based on the relationship between admittance and impedance: (9) In the formula, is the vacuum permittivity.

[0036] Based on the installation parameters of the traction network line, Equation (8) and Equation (9), calculate the impedance matrix and admittance matrix per unit length of the traction network line. Substitute these into Equation (5) and Equation (6) to obtain the chain parameter matrix of the MTL of the traction network per unit length. Based on the relationship of the traction network length, establish a chain parameter model that characterizes the electrical connection between conductors of different unit lengths in the traction network.

[0037] 2) Simplification of the multi-conductor transmission line model of the traction network my country's traction power supply system mainly includes direct-supply traction power supply systems with return lines and automatic-charge (AT) traction power supply systems. Regardless of whether it's a direct-supply traction power supply system with return lines or an AT power supply system, the number of transmission lines is relatively large. When establishing a chain-parameter circuit, the direct-supply traction power supply system with return lines requires establishing the self-impedance, mutual impedance, and mutual admittance of 10 conductors, while the AT traction power supply system requires establishing the self-impedance, mutual impedance, and mutual admittance of 12 conductors. To simplify the model structure and reduce the computational load, it is necessary to perform equivalent merging and simplification of the multi-conductor circuit.

[0038] For a direct traction power supply system with a return line, the conductor composition is as follows: Figure 5 As shown in Figure a, the upstream catenary CW1 and contact wire JW1 of the same line are merged into contact network T1, and the upstream rails R1 and R2 are merged into rail R01. The downstream catenary CW2 and contact wire JW2 are merged into contact network T2, and the downstream rails R3 and R4 are merged into rail R02. Similarly, for the AT traction power supply system, the conductor composition is as follows: Figure 5As shown in Figure b, CW1 and JW1 on the same line are merged into T1, CW2 and JW2 are merged into T2, R1 and R2 are merged into R01, and R3 and R4 are merged into R02. Therefore, the number of conductors involved in the modeling of the direct power supply traction network system with return line is merged into 6, and the number of conductors involved in the modeling of the AT power supply traction network system is merged into 8. The corresponding impedance / admittance parameter merging process is as follows: Assume that the voltages to ground of contact wires T1 and T2 are u T1 u T2 The currents are i T1 i T2 The ground voltages of the catenary cables CW1 and CW2 are u, respectively. C1 u C2 The currents are i C1 i C2 The voltages to ground of contact wires JW1 and JW2 are respectively u J1 u J2 The currents are i J1 i J2 The ground voltages of rails R01, R02, R1, R2, R3, and R4 are respectively u R01 u R02 u R1 u R2 u R3 u R4 The voltages to ground of return lines NW1 and NW2 are u, respectively. N1 u N2 The current is i N1 i N2 The voltage to ground of positive feeders FW1 and FW2 is u. F1 u F2 The current is i F1 i F2 .

[0039] The combined contact wire current is equal to the sum of the catenary wire and contact wire currents, and the combined rail current is equal to the sum of the currents of the two parallel rails. The voltage drop per unit length between the merged contact network, catenary wire, and contact wire, as well as between the merged rails and the two parallel rails before the merger, is equal. For a direct-supply traction network system with a return line, the series impedance matrix after conductor merging is derived as follows: (10) Similarly, for the AT power supply traction network system, the series impedance matrix after conductor merging is derived as follows: (11) The combined charge of the overhead contact line is equal to the sum of the charges of the catenary wire and the contact wire; the combined charge of the rails is equal to the sum of the charges of the two parallel rails. The voltage to ground between the merged overhead contact system, catenary wire, and contact wire, as well as between the merged rails and the two parallel rails before the merger, are equal. For a direct-supply traction network system with a return line, the capacitance matrix after conductor merging is derived as follows: (12) For the AT traction network system, the capacitance matrix after conductor merging is derived as follows: (13) 3) Time-varying modeling of traction network electrical parameters Subsequently, time-varying characterization of traction network electrical parameters was introduced into the offline arc transient analysis of the pantograph-catenary system. This included two parts: time-varying modeling of system resistance and inductance parameters and time-varying modeling of self and mutual capacitance parameters. These were then solved in a unified manner with the arc model, the train high-voltage system, and the vehicle-track grounding system.

[0040] a. Time-varying modeling of resistance and inductance parameters In this embodiment, when modeling the traction network system based on time-varying resistance parameters, the time-varying resistance parameters, which are dynamically updated according to the real-time position and operating status of the train, are introduced into the constructed functional mapping relationship model between conductor voltage and conductor current, thereby constructing a time-varying chain resistance model.

[0041] Specifically, establish a controlled voltage source U R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn The functional mapping relationship between them, where U R1 U R2 U Rn I represents the potential difference (i=1,2,...,n) across the i-th conductor, i.e., the conductor voltage. R1 I R2 、···、I Rn Let represent the current of the i-th conductor (i=1,2,...,n), and n be the number of conductors in the traction network system after equivalent merging and simplification. The specific formula is as follows: U=R*I+L*(dI / dx)(14) Where U is the conductor voltage matrix; R is the conductor time-varying resistance matrix, including the time-varying conductor self-resistance and inter-conductor mutual resistance; L is the conductor time-varying inductance matrix, including the time-varying conductor self-inductance and inter-conductor mutual inductance; I is the conductor current matrix; dI / dx is the derivative of conductor current I with respect to time x. The time-varying self and mutual resistance / inductance involved in matrices R and L are all equal to the reference self and mutual resistance / inductance value per unit length multiplied by the time-varying resistance / inductance correction coefficient. The time-varying resistance / inductance correction coefficient is a function of time related to the real-time position and operating status of the train. The real-time position of the train is represented by the distance between the train and the power supply station side or the electrical distribution phase side.

[0042] Modeling details: In this embodiment, a controlled source module is built based on the Simulink platform to establish a controlled voltage source U. R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn The function mapping relationship between the inputs and outputs is defined by the function m-file of S-Function. The controlled source module includes 2n input ports and n output ports, where the 2n input ports correspond to n conductor current quantities and their n conductor current differential components, and the n output ports correspond to n conductor voltage quantities.

[0043] In the traditional chain model, the system's resistance-inductance module includes inputs and outputs of n conductors. To characterize the self-resistance, inductance, mutual resistance, and inductance of each conductor, this embodiment extends it to a novel module with 2n inputs and 2n outputs, such as... Figure 6 As shown. Compared to the traditional chain-type resistive-inductor module, this new model module adds n pairs of controlled source ports to the original n pairs of conductor ports, used to introduce controlled voltage sources U. R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn The defined coupling relationships. The relationship between these controlled voltage sources and current sources is defined in the controlled source module. Figure 2 It is established in the controlled source module.

[0044] like Figure 7 As shown, the controlled source module has 2n inputs and n outputs, where the 2n inputs include n currents and n current derivatives, and the outputs are n controlled voltages. The relationship between the inputs and outputs is defined through a function m-file ( Figure 7 The function is implemented using the S-Function, where n controlled voltages control the voltage output of the traction network mutual inductance module. This function in the m-file considers the dynamic changes in the distance between the train and the substation during train operation, reflects the impact of speed changes, and adapts to the effects of train operating states (traction, coasting, braking) and their switching.

[0045] b. Time-varying modeling of self and mutual capacitance parameters In this embodiment, when modeling the traction network system based on time-varying capacitance parameters, the electrical behavior of the time-varying capacitor, which is dynamically updated according to the real-time position and running status of the train, is simulated using an equivalent controlled current source, thereby constructing a time-varying chain capacitor model.

[0046] The functional relationship between the equivalent controlled current source and the time-varying capacitor is as follows: I=Y*(dU / dx)(15) Where I is the output current matrix of the controlled current source; Y is the admittance matrix, which is determined by the time-varying capacitance matrix C of the conductor; U is the voltage matrix across the capacitor; dU / dx is the differential component of the voltage across the capacitor with respect to time x; The conductor time-varying capacitance matrix C includes the time-varying conductor-to-ground capacitance and the mutual capacitance between conductors. The time-varying capacitance involved in matrix C is equal to the reference capacitance value per unit length multiplied by the time-varying capacitance correction factor. The time-varying capacitance correction factor is a function that varies with time and is related to the real-time position and operating status of the train. The real-time position of the train is represented by the distance between the train and the power supply station side or the electrical distribution phase side.

[0047] Modeling details: In this embodiment, based on the Simulink platform, the fixed conductor capacitor element is replaced with a time-varying capacitor module. The time-varying capacitor module includes a controlled current source module, an Fcn module, a Derivative module, and a Clock module. The Fcn module is used to define the functional expression of the time-varying capacitor, and the output of the Fcn module serves as the control signal for the controlled current source module. The Derivative module is used to provide the differential component of the voltage across the capacitor. The voltage across the capacitor is fed back to the Derivative module through a voltage measurement module. The Clock module is used to provide the time quantity.

[0048] In the traditional π-type chain modeling method, the conductor's self-capacitance is equivalent to the capacitance to ground at the conductor's input and output terminals, while the mutual capacitance between the two conductors is equivalent to the coupling capacitance at the input and output terminals. The time-varying modeling method proposed in this invention retains this topology, meaning the connection between self-capacitance, mutual capacitance, conductors, and grounding points remains unchanged. However, it replaces static capacitors with time-varying capacitor modules to characterize the dynamic influence of train position and operating conditions on capacitor characteristics.

[0049] like Figure 8As shown, the equivalent core of the time-varying capacitor module is to represent the capacitor's behavior as a controlled current source. Its output current is determined by the voltage across the capacitor and its rate of change over time, reflecting the time-varying characteristics of the dynamic capacitor. In the specific implementation, a combination of a controlled current source and a function module (Fcn) is used for modeling. The Fcn module defines the functional expression of the time-varying capacitor. Its inputs include two parts: a time variable (obtained through the Clock module) and the differential signal of the voltage across the capacitor (obtained through the Derivative module). The output of the Fcn module serves as the control signal for the controlled current source, driving the current source connected to a conductor or ground. To ensure closed-loop logic, the voltage across the capacitor (i.e., the controlled current source) is fed back to the Derivative module through a voltage measurement module, thus forming a dynamic coupling of voltage and current, intuitively demonstrating the capacitor's time-varying characteristics.

[0050] Figure 8 In the Fcn module, the function expression for the time-varying capacitor is: C24a*(1+0.0972*u(1))*u(2)(16) Where C24a represents the mutual capacitance between the second and fourth conductors per unit length, u(1) represents time; (1+0.0972*u(1)) represents the distance between the train and the substation, which is the functional relationship between the distance between the train and the substation and time when the train is traveling at a constant speed of 350 km / h; u(2) represents the differential of the voltage across the capacitor (the capacitor can be a self-capacitance or a mutual capacitance). Figure 8 The output of the Fcn module is: the mutual capacitance C24a per unit length multiplied by the distance (1+0.0972u(1)) to obtain the mutual capacitance between the 2nd and 4th conductors corresponding to the total distance from the train to the substation. The mutual capacitance multiplied by the differential of the voltage across the mutual capacitance equals the current flowing through the mutual capacitance. The current of the mutual capacitance is the input of the controlled current source.

[0051] 2. Establishment of pantograph-catenary arc model and coupling method In terms of pantograph-catenary arc modeling, this invention employs an improved Hadedank equation arc model that takes into account the influence of train speed. Based on a series structure of the Mayr and Cassie models, this model constructs the arc length factor as a function of train speed to characterize the dynamic characteristics of the arc column as a function of speed. The overall arc conductance is expressed by the following equation: (17) In the formula, g is the total conductance of the electric arc, and i arc Let v be the arc current, v be the train speed, and g be the arc current. m With g cLet τ1 and τ2 be the conductances of the Mayr and Cassie portions, respectively, and let k be the power dissipation dielectric constant and β be the power dissipation factor. This model can simultaneously describe the small current characteristics in the zero-crossing region and the large current characteristics before and after the zero-crossing, and takes into account the influence of train speed on the electrical behavior of the arc.

[0052] The constructed pantograph-catenary arc model is directly connected to the pantograph port and the train high-voltage system port of the time-varying chain model of the traction network to form a unified solution nonlinear transient system, thereby obtaining the arc current, arc voltage and related transient response.

[0053] (4) Modeling of train-rail grounding system and consideration of key factors of overvoltage in car body To achieve overvoltage analysis of the train body, this invention focuses on key coupling factors related to the voltage rise of the train body and the return current to the track in the modeling of the train's vehicle-rail return grounding system. Taking the CRH3 EMU as an example, its overall electrical structure is as follows: Figure 9 As shown: The EMU consists of two traction units with identical electrical structures. The pantographs are located on car bodies 2 and 7 respectively, and are connected by a high-voltage cable on the roof, supplying power to the onboard transformer. During train operation, only one pantograph contacts the overhead contact line to obtain traction current. The current is transmitted through the high-voltage lead on the roof and the high-voltage cable to the onboard transformer and converter, supplying the traction motor. Simultaneously, the traction current flows into the rails through the working grounding system and returns to the traction network and traction substation.

[0054] Combination Figure 10 The diagram showing the train-rail return current illustrates how the grounding methods of the working grounding system and the protective grounding system, as well as the distribution of grounding wheel axle positions, play a decisive role in the car body voltage and the return current to the upper vehicle. The high-voltage cable on the roof consists of a cable core, insulation layer, shielding layer, and protective layer. The shielding layer is connected to the car body for grounding. The cable core voltage can be transmitted to the car body through capacitive coupling between the cable core and the shielding layer / car body. This capacitive coupling has a significant impact on the surge overvoltage of the car body, especially under high-frequency transient conditions such as pantograph-catenary offline arcing. Furthermore, the car body impedance parameters (including the car body impedance and the resistance of adjacent car body connections), the grounding system impedance, and the track impedance jointly affect the distribution of return current between the "rail return current" and the "car body return current." When the track impedance is relatively large, the return current to the upper vehicle is more likely to increase, leading to a rise in car body voltage.

[0055] Based on the above key coupling factors, a model of the train-track grounding system is established as follows: Figure 11 As shown, it is coupled with the time-varying chain model of the traction network and the arc model at the corresponding ports, so as to obtain the transient response of the high voltage side of the roof and the transient response of the car body to the rail simultaneously within a unified solution framework, providing a model basis for the overvoltage analysis of the car body.

[0056] S200, based on the established "arc-traction network-train-grounding system" model, enables the time-varying impedance parameters and time-varying capacitive reactance parameters of the traction network conductors to participate in the unified calculation of pantograph-net arc current, arc voltage and transient overvoltage under the transient working condition of pantograph-net offline arc. This realizes the influence analysis of the time-varying electrical parameters of the traction network on the electrical characteristics of the pantograph-net arc, roof overvoltage and car body overvoltage response.

[0057] Model validation: To demonstrate the technical solution of this invention, which focuses on "analysis method of pantograph-catenary arc characteristics and transient overvoltage," and to verify the parameter update mechanism of the time-varying chain equivalent module of the traction network in this invention and its ability to describe the time-varying law of the supply voltage, this embodiment selects acceleration and deceleration operating conditions to compare and verify the time-varying chain module of the traction network (based on a traction network system with direct return line power supply). It should be noted that this verification step aims to examine whether the voltage response law of the network side caused by the real-time update of the traction network impedance and capacitive reactance parameters is reasonable, thereby providing a reliable traction network foundation for subsequent pantograph-catenary offline arc transient analysis; therefore, arc triggering events are not introduced separately in the verification conditions to avoid interference from the superposition of multiple factors in the interpretation of the parameter update effect.

[0058] The specific settings are as follows: Based on the output torque and speed target commands set by the traction drive system module, the train operation conditions and their time processes are simulated, and the acceleration and deceleration sequences are ensured to be applied synchronously in the traction network time-varying chain module and the train traction drive system module. Condition 1 is the acceleration condition, in which the train speed accelerates uniformly from 50 km / h to 300 km / h within 20 s; Condition 2 is the deceleration condition, in which the train speed decelerates uniformly from 300 km / h to 50 km / h within 20 s. For Condition 1 and Condition 2, the relationship between the distances L1 and L2 between the train and the traction substation and time t is determined by equation (2), and the corresponding running distance variation curves with time are shown in the figure. Figure 12 : (18) Under the above operating conditions, a traditional fixed-parameter traction network model and a time-varying optimization model combining resistance, inductance, and capacitance were established for comparative simulation. The comparison results of the roof power supply voltage are shown in [reference needed]. Figure 13 and Figure 14 Simulation results show that under acceleration conditions, the train's running distance increases faster, the equivalent impedance of the traction network increases faster, and the supply voltage decreases faster; under deceleration conditions, the running distance increases more slowly, the time-varying impedance effect weakens, and the supply voltage decreases more slowly. These trends are consistent with reality, thus verifying the ability of the time-varying chain module to characterize the real-time changes in traction network impedance and capacitive reactance, and the rationality of the calculation results.

[0059] The above examples illustrate the present invention only to aid in understanding it and are not intended to limit the scope of the invention. Those skilled in the art can make various simple deductions, modifications, or substitutions based on the principles of this invention.

Claims

1. A method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters, the method comprising: A "traction network-train-grounding system" model is constructed, which includes a traction substation model, a multi-conductor traction network system model, a train high-voltage electrical system model, a vehicle-rail return grounding system model, and a pantograph-catenary arc model. The multi-conductor traction network system model adopts a chain circuit equivalent model that takes into account time-varying resistance and inductance parameters and time-varying capacitance parameters. The pantograph-catenary arc model adopts an improved Hadedank equation arc model that takes into account the influence of train running speed. Based on the established "arc-traction network-train-grounding system" model, under the transient working condition of pantograph-catenary offline arc, the time-varying impedance parameters and time-varying capacitive reactance parameters of the traction network conductor are involved in the unified solution calculation of pantograph-catenary arc current, arc voltage and transient overvoltage, so as to realize the influence analysis of the time-varying electrical parameters of the traction network on the electrical characteristics of pantograph-catenary arc, roof overvoltage and car body overvoltage response.

2. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 1, characterized in that, The multi-conductor traction network system model is constructed using a chain circuit equivalent model that considers time-varying resistive and inductive parameters and time-varying capacitance parameters, specifically including: Within the chain circuit equivalent modeling framework of a multi-conductor traction network, the traction network system is modeled based on time-varying resistance and inductance parameters and time-varying capacitance parameters. The time-varying resistance and inductance parameters include the self-resistance and self-inductance of each conductor in the traction network, as well as the mutual resistance and mutual inductance between conductors, which are dynamically updated according to the real-time position and operating status of the train. The time-varying capacitance parameters include the capacitance to ground of each conductor in the traction network and the mutual capacitance between conductors, which are dynamically updated according to the real-time position and operating status of the train.

3. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 2, characterized in that, The multi-conductor traction network system model is constructed using a chain circuit equivalent model that considers time-varying resistive and inductive parameters and time-varying capacitance parameters, specifically including: When modeling the traction network system based on time-varying resistance parameters, the time-varying resistance parameters, which are dynamically updated according to the real-time position and running status of the train, are introduced into the constructed functional mapping relationship model between conductor voltage and conductor current, thereby constructing a time-varying chain resistance model. The functional mapping relationship between conductor voltage and conductor current is shown in the following model: Establish a controlled voltage source U R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn The functional mapping relationship between them, where U R1 U R2 U Rn I represents the potential difference (i=1,2,...,n) across the i-th conductor, i.e., the conductor voltage. R1 I R2 、···、I Rn Let represent the current of the i-th conductor (i=1,2,...,n), and n be the number of conductors in the traction network system after equivalent merging and simplification. The specific formula is as follows: U = R*I + L*(dI / dx) Where U is the conductor voltage matrix; R is the conductor time-varying resistance matrix, including the time-varying conductor self-resistance and inter-conductor mutual resistance; L is the conductor time-varying inductance matrix, including the time-varying conductor self-inductance and inter-conductor mutual inductance; I is the conductor current matrix; dI / dx is the derivative of conductor current I with respect to time x. The time-varying self and mutual resistance / inductance involved in matrices R and L are all equal to the reference self and mutual resistance / inductance value per unit length multiplied by the time-varying resistance / inductance correction coefficient. The time-varying resistance / inductance correction coefficient is a function of time related to the real-time position and operating status of the train. The real-time position of the train is represented by the distance between the train and the power supply station side or the electrical distribution phase side.

4. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 3, characterized in that, The method specifically includes: Based on the Simulink platform, a controlled source module is constructed to establish a controlled voltage source U. R1 U R2 U Rn and controlled current source I R1 I R2 、···、I Rn Functional mapping relationship between them; The controlled source module includes 2n input ports and n output ports, where the 2n input ports correspond to n conductor current quantities and their n differential components, and the n output ports correspond to n conductor voltage quantities. The mapping relationship between inputs and outputs is defined through the function m-file of S-Function.

5. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 2, characterized in that, The multi-conductor traction network system model is constructed using a chain circuit equivalent model that considers time-varying resistive and inductive parameters and time-varying capacitance parameters, specifically including: When modeling the traction network system based on time-varying capacitance parameters, the electrical behavior of the time-varying capacitor, which is dynamically updated according to the real-time position and running status of the train, is simulated using an equivalent controlled current source, thereby constructing a time-varying chain capacitor model. The functional relationship between the equivalent controlled current source and the time-varying capacitor is as follows: I = Y * (dU / dx) Where I is the output current matrix of the controlled current source; Y is the admittance matrix, which is determined by the time-varying capacitance matrix C of the conductor; U is the voltage matrix across the capacitor; dU / dx is the differential component of the voltage across the capacitor with respect to time x; The conductor time-varying capacitance matrix C includes the time-varying conductor-to-ground capacitance and the mutual capacitance between conductors. The time-varying capacitance involved in matrix C is equal to the reference capacitance value per unit length multiplied by the time-varying capacitance correction factor. The time-varying capacitance correction factor is a function that varies with time and is related to the real-time position and operating status of the train. The real-time position of the train is represented by the distance between the train and the power supply station side or the electrical distribution phase side.

6. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 5, characterized in that, The method specifically includes: Based on the Simulink platform, the fixed conductor capacitor element is replaced with a time-varying capacitor module. The time-varying capacitor module includes a controlled current source module, an Fcn module, a Derivative module, and a Clock module. The Fcn module is used to define the functional expression of the time-varying capacitor, and the output of the Fcn module serves as the control signal for the controlled current source module. The Derivative module is used to provide the differential component of the voltage across the capacitor. The voltage across the capacitor is fed back to the Derivative module through a voltage measurement module. The Clock module is used to provide the time quantity.

7. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 1, characterized in that, Constructing a pantograph-catenary arc model specifically includes: A pantograph-catenary arc model is constructed based on the Mayr and Cassie models in series. The arc length factor is constructed as a function of train speed to characterize the dynamic characteristics of the arc column as a function of speed. The overall arc conductance is expressed by the following equation: In the formula, g is the total conductance of the electric arc, g m With g c The conductances of the Mayr and Cassie portions are respectively, i arc Let τ be the arc current, v be the train speed, τ1 and τ2 be the time constants of the Mayr and Cassie parts, respectively, k be the power dissipation dielectric constant, and β be the power dissipation factor. The established pantograph-catenary arc model can simultaneously describe the small current characteristics in the zero-crossing region and the large current characteristics before and after the zero-crossing region, and takes into account the influence of train speed on the arc's electrical behavior.

8. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 7, characterized in that, The method further includes: The constructed pantograph-catenary arc model is directly connected to the pantograph port of the multi-conductor traction network system model and the port of the train high-voltage electrical system model to form a unified solution nonlinear transient system, thereby obtaining the arc current, arc voltage and related transient response.

9. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 1, characterized in that, The model construction of the vehicle-rail return grounding system includes: The vehicle-rail return current grounding system model adopts a refined model that takes into account the key coupling factors of vehicle body overvoltage. These key coupling factors include the grounding methods of the working grounding system and the vehicle body protective grounding system, the capacitive coupling between the high-voltage cable core and shielding layer on the roof and the vehicle body, the vehicle body impedance and the connection resistance of adjacent vehicle bodies, the grounding system impedance, and the track impedance. This allows the formation and distribution of vehicle body voltage and onboard return current during the pantograph-catenary offline arc transient process to be solved uniformly and used for vehicle body overvoltage analysis.

10. The method for analyzing the electrical characteristics and transient overvoltage of pantograph-catenary arc considering the influence of time-varying parameters as described in claim 9, characterized in that, The method further includes: The constructed vehicle-rail return grounding system model is coupled with the multi-conductor traction network system model and the pantograph-catenary arc model at the corresponding ports, so as to obtain the transient response of the high-voltage side on the roof and the transient response of the vehicle body to the rail within a unified solution framework, providing a model basis for the analysis of vehicle body overvoltage.

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