AT full parallel traction network locomotive position and Thevenin equivalent nonlinear identification method

Abstract

The invention discloses an AT full parallel traction network locomotive position and Thevenin equivalent nonlinear identification method. The method comprises the following steps: 1, obtaining a traction power supply system topological structure and related element parameters; 2, PMUs are arranged on the low-voltage side of each traction transformer, an AT station and a partition station; obtaining current and voltage measurement data of each phase at the PMU configuration position; 3, according to the topological structure and the element parameters in the step 1 and the measurement data in the step 2, considering the measurement uncertainty, and performing state estimation; and 4, according to the result of the step 3, identifying traction network Thevenin equivalent parameters seen from the locomotive port. According to the method, the position of the locomotive and the real-time power of the locomotive can be predicted after state estimation by using the current and voltage data measured by the AT, the method is rapid and accurate, and the method has good abnormal data resistance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of traction power grid monitoring, and particularly relates to an AT full-parallel traction grid locomotive position and Thevenin equivalent nonlinear identification method. BACKGROUND

[0002] The safe and stable operation of the electrified railway traction power supply system faces severe challenges, and the real-time position and power change of the locomotive as a dynamic load directly affect the voltage stability of the power grid. The traditional locomotive positioning mainly relies on the global satellite navigation system, but the positioning accuracy significantly decreases in satellite signal limited areas such as tunnels and mountainous areas, and cannot reflect the electrical coupling characteristics of the locomotive and the power grid. The existing satellite-based positioning method has the following two shortcomings: on the one hand, satellite signals are easily blocked in complex terrain, and the positioning update rate is usually only 1-10 Hz, which is difficult to meet the millisecond-level dynamic monitoring needs of high-speed locomotives; on the other hand, satellite positioning data and power grid electrical quantity measurement information are mutually isolated, which cannot support the coordinated analysis of the coupling stability of the vehicle and the grid, and it is even more difficult to be directly used for voltage stability evaluation.

[0003] There are two methods for calculating the equivalent system of a single power source using partial power grid area information: first, the direct line model, which generally cannot accurately handle the time-varying characteristics of actual loads and cannot track real-time changes in loads; second, the method based on Thevenin equivalence, which requires two or more system state voltage and current phasors, and estimates the single power transmission equivalent system parameters using parameter identification methods. Theoretically, the method based on Thevenin equivalence can accurately handle the time-varying characteristics of actual loads. However, under conditions that do not meet the continuous excitation condition, the identified single power transmission equivalent system may have a large error, which can easily lead to misjudgment. In the traction power supply system, the uncertainty of the locomotive position can affect the identification of the Thevenin equivalent parameters, and the uncertainty of the locomotive power can also affect the determination of the power margin, so the state estimation of the locomotive position and related current and voltage information is particularly important. SUMMARY

[0004] The purpose of the present application is to provide an AT full-parallel traction grid locomotive position and Thevenin equivalent nonlinear identification method, so that the locomotive positioning is no longer dependent on the satellite system, improving the accuracy of the locomotive positioning, and providing a new scheme for online monitoring of the voltage stability of the traction power supply system, and laying a good foundation for the basic work of the vehicle and grid coupling stability research.

[0005] To achieve the above purpose, the present application provides the following technical scheme: An AT full-parallel traction grid locomotive position and Thevenin equivalent nonlinear identification method, comprising the following steps: Step 1, obtaining the topology structure of the traction power supply system and the related element parameters; Step 2, at each traction transformer low-voltage side, AT (Autotransformer) and the PMU (Phasor Measurement Unit) of the partition are set; the measurement data of each phase current and voltage at the PMU configuration are obtained; Step 3, according to the topology and element parameters in step 1, and the measurement data in step 2, state estimation is performed considering the measurement uncertainty: S31, judging the section where the locomotive is located; S32, preliminarily estimating the position of the locomotive for single-vehicle and multi-vehicle cases respectively; S33, constructing a relevant pseudo-measurement vector for single-vehicle and multi-vehicle cases respectively; S34, obtaining the position and on-board power of the locomotive through state estimation; Step 4, according to the results of step 3, identifying the Thevenin equivalent parameters of the traction network seen from the port of the locomotive.

[0006] In some embodiments, the method for judging the section where the locomotive is located is: In a full-parallel traction power network with m AT stations in each uplink and downlink, the section where the locomotive is located is judged according to the amplitude and phase of the T-phase and R-phase currents at the PMU configuration position; within the section, the current direction flowing to the catenary at the PMU configuration position is defined as positive, and when the T-phase current directions measured at the kth PMU configuration position and the k+1th PMU configuration position are both positive, the R-phase current directions are both negative and the amplitudes exceed a preset threshold, the vehicle is located between the kth PMU configuration position and the k+1th PMU configuration position.

[0007] In some embodiments, for single-vehicle cases, the voltage and current on the T, R, and F lines at the beginning and end of the AT section are obtained according to the section where the locomotive is located and the PMU measurement information, and the initial estimation value of the locomotive position is obtained. For multi-vehicle cases, according to the corresponding branch currents under the topology of different locomotive positions, the current loss is defined as the sum of the KCL equations of the nodes for which the currents cannot be measured and need to be constructed, and the best value of the initial position of the locomotive is determined when the current loss is the smallest, thereby determining the initial position of the locomotive.

[0008] In some embodiments, for single-vehicle cases, the relevant pseudo-measurement vector is constructed: when the locomotive cannot be installed with measurement devices, the locomotive voltage is constructed according to the initial estimation value of the locomotive position in S32. For multi-vehicle cases, the relevant pseudo-measurement vector is constructed: using the initial value of the locomotive position obtained in S32, the KCL equations of unknown currents, and the branch currents and node voltages to solve each unknown current vector.

[0009] In some embodiments, S34 includes the following steps: The Jacobi matrix of the system is established by the state estimation measurement equation and the branch current and node voltage relationship; The locomotive position in S32 is taken as an initial value, and the state estimation is performed by using the objective function and the iterative equation to obtain the locomotive position and the locomotive voltage and current.

[0010] In some embodiments, the branch current and node voltage relationship is: ; ; ; ; In the formula, is a coefficient matrix; is a branch current vector; is a voltage drop vector of adjacent nodes; is a T-phase self-impedance; is a T-phase mutual impedance with respect to R-phase; is a T-phase mutual impedance with respect to F-phase; is a R-phase mutual impedance with respect to F-phase; is a F-phase self-impedance; is a distance between ATs; is a distance between the locomotive and the front-end AT; is a R-phase self-impedance; is a contact net current at the front end of the AT section; is a rail current at the front end of the AT section; is a positive feeder line current at the front end of the AT section; is a contact net current at the end of the AT section; is a rail current at the end of the AT section; is a node voltage at the front end of the contact net; is a node voltage at the end of the rail; is a node voltage at the front end of the rail; is a node voltage at the end of the rail; is a node voltage at the contact between the locomotive and the contact net; is a node voltage at the contact between the locomotive and the rail; is a node voltage at the front end of the positive feeder line; is a node voltage at the end of the positive feeder line; represents a vector; The Jacobi matrix of the system is: ; In the formula, is a branch power of node 1 to node 5; is a branch power of node 2 to node 5; The objective function is: ; In the formula, is a state variable matrix; is a measurement matrix; is an observation matrix; is a weighting matrix; The iterative equation is: ; Wherein, ; In the formula, is an update matrix; is a transposed Jacobian matrix; is an x matrix of the lth iteration; is an update matrix of the lth iteration; is an x matrix of the (l+1)th iteration; is a Jacobian matrix; The locomotive voltage is: ; The current is: .

[0011] In some embodiments, step 4 specifically comprises the following steps: Establishing a Thevenin equivalent system equation; Using the U , I Data obtained by state estimation at multiple time points to form an overdetermined equation group; Solving the overdetermined equation group to obtain Thevenin equivalent parameters: equivalent potential and equivalent impedance .

[0012] Compared with the prior art, the present application has the following beneficial effects: The present application uses the current and voltage data measured by the AT to predict the position of the locomotive and the real-time power of the locomotive after state estimation, which is rapid and accurate and has good anti-exceptional data capability.

[0013] The present application considers the high resistance characteristics of the traction power grid when performing Thevenin equivalence, further improving the accuracy of Thevenin equivalence.

[0014] The present application can be applied to the study of vehicle-grid coupling stability and online monitoring of voltage stability, and has a wide range of applications. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 It is a schematic diagram of the topology structure of the traction power supply system of the present application; Figure 2 Schematic diagram of the line topology between two AT stations of the present invention; Figure 3 This is a schematic diagram of the Thevenin equivalent value of the present invention; Figure 4 This is a line topology diagram and node diagram between two AT stations of the present invention; Figure 5 This is a schematic diagram of the change of limit power with distance in Verification Example 1 of the present invention; Figure 6 This is a schematic diagram of the initial value results of the current loss locomotive position in Verification Example 3 of the present invention; Figure 7 This is a schematic diagram comparing the PV curve simulation of vehicle 1 in Verification Example 3 of the present invention with that of the present invention; Figure 8 This is a schematic diagram comparing the PV curve simulation of car 2 in Verification Example 3 of the present invention with that of the present invention; Figure 9 This is a schematic diagram comparing the simulation of the DC side voltage curve of the locomotive in Verification Example 4 of the present invention with the present invention. DETAILED DESCRIPTION

[0016] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0017] See also Figures 1-9 The present invention provides a nonlinear identification method for locomotive position and Thevenin equivalent in an AT fully parallel traction network. The method first obtains the original current and voltage data for each phase of the traction transformer's low-voltage side, the AT station, and the substation. The locomotive's current position is calculated using this data. State estimation is then used to iteratively correct the locomotive position and each phase's measurement data. The current and voltage on the locomotive are then calculated, and the locomotive's active and reactive power are then derived. The locomotive is treated as a constant-power load, and the main power grid and traction grid ahead of the locomotive are treated as black boxes. Thevenin equivalents are then applied to these grids to obtain equivalent voltages and equivalent impedances.

[0018] The specific steps are as follows: Step 1: Obtain the topology of the traction power supply system and related component parameters. The related component parameters include: the impedance matrix per unit length of the traction network line, and the distances between the traction station, AT station, and substation.

[0019] Step 2, obtaining PMU (Phasor Measurement Unit) measurement data: PMU is arranged at each traction transformer low-voltage side, AT (Autotransformer) and subarea; obtaining measurement data of each phase current and voltage at PMU configuration.

[0020] Step 3, according to the topological structure and element parameters in step 1 and the measurement data in step 2, due to the influence of instrument error, environmental factors and other factors, there is an indelible deviation or dispersion between the measured value and the true value, so the uncertainty of measurement needs to be considered, state estimation is carried out, and the position information of the locomotive and the voltage and current of the locomotive are estimated.

[0021] The state estimation includes the following steps: Step (1), judging the interval where the locomotive is located based on single vehicle condition.

[0022] In a full-parallel traction power grid with m AT stations in each uplink and downlink, the interval where the locomotive is located is judged according to the amplitude and phase of T-phase and R-phase current at PMU configuration position; in the interval, the current direction flowing to the catenary at PMU configuration position is defined as positive, when the T-phase current direction at the kth PMU configuration position and the k+1th PMU configuration position is positive, the R-phase current direction is negative and the amplitude exceeds a certain threshold, the vehicle is located between the kth PMU configuration position and the k+1th PMU configuration position.

[0023] The judgment method of multi-vehicle operation condition is the same as that of single-vehicle condition.

[0024] Step (2), preliminarily estimating the position of the locomotive.

[0025] For single vehicle condition: As shown in the figure, according to the interval where the locomotive is located and the PMU measurement information, the current values on the T, R and F lines at the beginning and end of the AT section are obtained, the distance between the two AT stations is L, and it is assumed that the vehicle is at a distance d from the beginning of the AT section, the voltage and current equations in the AT section are: Figure 2 ; ; ; ; In the formula, is the voltage of the locomotive; is the voltage loss from the beginning of the AT section to the locomotive; is the voltage between the catenary and the rail at the beginning of the AT section; is the voltage loss from the end of the AT section to the locomotive;​ is the voltage between the catenary and the rail at the end of the AT segment; is the current of the rail at the head end of the AT section; is the self-impedance on phase R; is the current of the contact network at the first end of the AT segment; is the mutual impedance between phase T and phase R; is the current of the positive feeder at the beginning of the AT segment; is the mutual impedance between phase R and phase F; is the self-impedance on phase T; is the mutual impedance between phase T and phase F; is the current of the end rail of the AT section; is the current of the contact network at the end of the AT segment; is the current of the positive feeder at the end of the AT segment.

[0026] In the above formula, 、 、 is an unknown parameter, and the rest are component parameters and quantity measurements. Therefore, the initial estimate of the locomotive position can be obtained by solving : .

[0027] For the multi-car situation, since the relevant current vector cannot be directly obtained, the current loss method is needed to determine the initial position of the locomotive: Assume that locomotive 1 is located at x kilometers in the AT segment, and locomotive 2 is located at y kilometers in the AT segment. , Substitute into the branch current and node voltage equations: ; ; ; ; ; Where, is the T-phase self-impedance; is the mutual impedance of T relative to R; is the mutual impedance of T relative to F; is the mutual impedance of R relative to F; is the self-impedance of phase F; The distance between AT stations; The distance between the locomotive and the front AT; is the R phase self-impedance; is the contact network current at the first end of the AT segment; is the rail current at the head end of the AT section; is the positive feeder line current at the beginning of the AT section; is the catenary current at the end of the AT section; is the rail current at the end of the AT section; is the catenary voltage at the beginning of the AT section; is the rail voltage at the end of the AT section; is the rail voltage at the beginning of the AT section; is the rail voltage at the end of the AT section; is the voltage at the node where the locomotive contacts the catenary; is the voltage at the node where the locomotive contacts the rail; is the positive feeder line voltage at the beginning of the AT section; is the positive feeder line voltage at the end of the AT section; represents a vector.

[0028] The above calculation expressions are used to solve the corresponding branch currents of the locomotive at different positions in the topology. The current loss is defined as the sum of the KCL equations of the nodes related to the current, which cannot be measured and need to be constructed. When the current loss is the smallest, the initial value of the locomotive position is the best.

[0029] Step (3), construct the related pseudo-measurement vector.

[0030] For single vehicle case: The locomotive cannot be installed with measurement devices, and the locomotive voltage needs to be constructed according to the initial value of the locomotive position in step (2): ; ; For multiple vehicle cases, the initial value of the locomotive position obtained in step (2) and the KCL equation of the unknown current are used to solve the unknown current vector.

[0031] Step (4), obtain the locomotive position, locomotive voltage, and current through state estimation, which are used to monitor the position of the locomotive and the related state parameters of the locomotive.

[0032] Take the locomotive position in step (2) as the initial value, and iteratively perform state estimation to obtain the locomotive position and state variables such as locomotive voltage and current; The measurement equation for state estimation is: ; ; ; ; As Figure 4As shown, nodes 1-8 represent the first end of the catenary, the last end of the catenary, the first end of the rail, the last end of the rail, the connection between the locomotive and the catenary, the connection between the locomotive and the rail, the first end of the positive feeder, and the last end of the positive feeder, respectively; wherein, is the measurement; is the observation matrix; is the state vector; is the error vector; is the branch active power from node i to node j; is the branch reactive power from node i to node j; In the traction power supply system, the branch current and the node voltage equation are arranged into the form of ; wherein, ; ; ; wherein, is the coefficient matrix; is the branch current vector; is the adjacent node voltage drop vector; The relationship between the branch current and the node voltage is obtained, i.e. The expression of the node injection power is obtained by using the current expression, and the expression is only composed of the node voltage amplitude and phase, impedance, and locomotive position. Further, the system Jacobian matrix H is obtained: ; The state estimation minimizes the following objective function: ; wherein, is the state variable matrix; is the measurement matrix; is the observation matrix; is the weighting matrix; The iterative equation is: ; wherein, ; wherein, is the update matrix; is the transposed Jacobian matrix; is the x matrix of the lth iteration; is the update matrix of the lth iteration; is the x matrix of the (l+1)th iteration; is the Jacobian matrix; Rinitial is constructed by residual and updated in iteration process: ; ; ; wherein, is dynamic weight coefficient; is attenuation factor, low noise environment: = 0.95~0.99, high noise / abrupt scene: = 0.9~0.95; is; is intermediate update of covariance matrix; is weighting matrix of the lth iteration; is measurement; is state estimation; is extraction of diagonal element.

[0033] After iteration convergence, the voltage at both ends of the car is: ; The current flowing through the car is: .

[0034] Step 4, according to the locomotive position and the voltage and current of the locomotive in step 3, the traction net Thevenin equivalent circuit seen from the locomotive port is identified, including equivalent potential E , equivalent reactance X and equivalent resistance R .

[0035] The specific method of Thevenin equivalence is: As shown in Figure 3 , the Thevenin equivalent system equation is: ; The potential E , I , U in the above formula is decomposed into real and imaginary parts to obtain two equations:

[0036]

[0037] wherein, is real part of locomotive voltage; is real part of equivalent potential; is real part of locomotive current; is imaginary part of locomotive current; is imaginary part of locomotive voltage; is imaginary part of equivalent potential.

[0038] The U and I data estimated by using multiple time point states (time window measurement information is multiple time point discrete data, 1s, 1000Hz data is used to represent 1000 time point data in a time window) constitute an over-determined equation group; the over-determined equation group is solved by using a least square method, and the parameter estimation analytical solution is: ; Wherein, ; ; ; In the formula, is a coefficient matrix, is a transpose matrix of .

[0039] Final Thevenin equivalent parameters: ; ; In the formula, is an equivalent potential; is an equivalent impedance; is the i-th element of the x vector.

[0040] In a specific embodiment, the experimental data is collected by using an AT traction station built by MATLAB / SIMULINK to perform experiments, and the AT traction station topological structure is as shown in Figure 1 . Among them, the short circuit capacity of the 220KV side power grid is 1000MVA, the unit length impedance matrix of the traction network line, the parameters of the autotransformer and other parameters are obtained by field experiments, the voltage stability locomotive model is a continuously increasing power load, the vehicle network coupled locomotive model is a complete dynamic characteristic, PMUs are arranged at each low voltage side of the traction transformer, the AT and the partition, and the measurement data of the current and voltage of each phase at the PMU configuration are obtained, the power reference in the following verification example is 100MW, and the voltage reference is 27.5kv. The PMU resolution is 1000Hz, and the time window is 1s.

[0041] Verification example 1 As shown in Figure 4 , in order to verify the accuracy of the equivalent and the effect of the power margin calculation, the TR two-phase load is continuously increased every 1km on the attached Figure 1 , and the voltage stability limit power is calculated, and the PMU measurement data is stored for the method of the application. The limit power obtained by simulation and the voltage stability limit power obtained by the method of the application are compared as shown in Table 1, and the comparison graph is as shown in the attached Figure 5 .

[0042] Table 1 Limit power comparison table

[0043] Verification Example 2 like Figure 6 As shown in Table 2, in order to verify the state estimation iterative correction of the locomotive position proposed in the present invention, the comparison between the locomotive position before and after state estimation and the actual position is calculated in Verification Example 2.

[0044] Table 2 Comparison of locomotive position before and after state estimation and actual position

[0045] As can be seen from Table 2, the average error between the locomotive position estimated by the state and the true locomotive position is 0.02 km, and the maximum error is 0.128 km.

[0046] Verification Example 3 like Figure 5 As shown, in order to verify the effectiveness of the current loss method proposed in the present invention under the condition of multiple vehicles and the accuracy of multi-vehicle position identification and power margin accuracy, Figure 1 The locomotive load is added at 2.6 km and 18.3 km between the two phases of the uplink TR, and the data measured by the PMU is stored for this embodiment. The initial values ​​of the current loss locomotive position are 3 km and 18 km respectively, as shown in the attached figure. Figure 6 As shown in the figure, the locomotive positions after state estimation are 2.89 km and 18.22 km respectively. The limit power simulation results of locomotive 1 are 0.2749 and 0.2630 for locomotive 2. The limit power results of the present invention are 0.2740 for locomotive 1 and 0.2627 for locomotive 2. The corresponding PV curves are compared. Figure 7 and Figure 8 .

[0047] Verification Example 4 In order to verify the applicability of the present invention in the study of vehicle-grid coupling stability, the attached Figure 1 A locomotive load is added at 4.4 km between the two phases of the uplink TR, and the data measured by the PMU is stored and used in the method of the present invention to obtain the locomotive position of 4.37 km. The DC side voltage of the locomotive obtained by simulation is compared with the DC side voltage of the locomotive obtained by the Thevenin equivalent parameter, as shown in FIG. Figure 9 As shown in the figure, the two have the same characteristics and can accurately judge the stability of vehicle-grid coupling.

[0048] The present invention can determine the position of the locomotive based on the measurement data. The judgment process is rapid and accurate, and the anti-interference ability is strong. The Thevenin equivalent value of the locomotive port takes into account the high-resistance characteristics of the traction power supply system, and the identification result is accurate. The present invention has a wide range of applications and can be applied to research directions such as online monitoring of voltage stability of the traction power supply system and stability of vehicle-grid coupling.

Claims

1. A nonlinear identification method for locomotive position and Thevenin equivalent in an AT full parallel traction network, characterized in that: The following steps are involved: Step 1: Obtain the traction power supply system topology and related component parameters; Step 2: Install a PMU at the AT station and the substation on the low-voltage side of each traction transformer; obtain the current and voltage measurement data of each phase at the PMU location; Step 3: Based on the topology and component parameters described in step 1 and the measurement data described in step 2, taking into account measurement uncertainty, perform state estimation: S31, determining the section where the locomotive is located; S32, preliminarily estimating the position of each locomotive for the single-vehicle and multiple-vehicle situations; S33, constructing relevant pseudo-measurement vectors for single-vehicle and multi-vehicle situations respectively; S34, obtaining the position of the locomotive and the onboard power through state estimation; Step 4: Based on the results of step 3, identify the Thevenin equivalent parameters of the traction network viewed from the locomotive port.

2. The method for identifying locomotive positions and Thevenin equivalent nonlinearity of an AT full parallel traction network according to claim 1, characterized in that: The method for determining the section where the locomotive is located is: In a fully parallel traction grid with m AT stations in both the upstream and downstream directions, the locomotive section is determined based on the amplitude and phase of the T-phase and R-phase currents at the PMU configuration location. Within this interval, the direction of the current flowing to the contact network at the PMU configuration is defined as positive. When the directions of the contact network T-phase currents measured at the k-th PMU configuration and the k+1-th PMU configuration are both positive, and the directions of the R-phase currents are both negative, and the amplitudes exceed the preset threshold, the vehicle is located between the k-th PMU configuration and the k+1-th PMU configuration.

3. The method for identifying locomotive positions and Thevenin equivalent nonlinearity in an AT full parallel traction network according to claim 1, characterized in that: For a single vehicle, the voltage and current on the T, R, and F lines at the beginning and end of the AT segment are calculated based on the locomotive's location and PMU measurement information, giving an initial estimate of the locomotive's position. For the multi-car situation, based on the corresponding branch currents under different locomotive position topologies, the current loss is defined as the sum of all unmeasurable KCL equations for current-related nodes. When the current loss is minimized, it is the optimal initial value of the locomotive position, thus determining the initial locomotive position.

4. The method for identifying locomotive positions and Thevenin equivalent nonlinearity of an AT full parallel traction network according to claim 3, characterized in that: In the case of a single vehicle, the relevant pseudo-measurement vector is constructed: when the locomotive cannot be equipped with a measurement device, the locomotive voltage is constructed based on the initial estimate of the locomotive position described in S32; In the case of multiple vehicles, the relevant pseudo-measurement vectors are constructed: the initial value of the locomotive position obtained by S32 is used, and the KCL equation at the unknown current and the branch current and node voltage are solved to obtain each unknown current vector.

5. The method for identifying locomotive positions and Thevenin equivalent nonlinearity in an AT full parallel traction network according to claim 1, characterized in that: S34 includes the following steps: The Jacobian matrix of the system is established through the state estimation measurement equation and the relationship between branch current and node voltage; The locomotive position described in S32 is used as the initial value, and the state estimation is performed using the objective function and iterative equation to obtain the locomotive position and the locomotive voltage and current.

6. The method for identifying locomotive positions and Thevenin equivalent nonlinearity in an AT full parallel traction network according to claim 1, characterized in that: The relationship between the branch current and the node voltage is: ； ； ； ； Where, is the coefficient matrix; is the current vector of each branch; is the voltage drop vector of the adjacent nodes; is the T-phase self-impedance; is the mutual impedance of T relative to R; is the mutual impedance of T relative to F; is the mutual impedance of R relative to F; is the self-impedance of phase F; The distance between AT stations; The distance between the locomotive and the front AT; is the R phase self-impedance; is the contact network current at the first end of the AT segment; is the rail current at the head end of the AT section; is the positive feeder current at the beginning of the AT segment; is the contact network current at the end of AT segment; is the rail current at the end of the AT section; is the voltage of the contact network head end node; is the rail end node voltage; is the node voltage at the rail head end; is the rail end node voltage; is the node voltage at the contact point between the locomotive and the catenary; is the node voltage at the contact point between the locomotive and the rail; is the voltage of the node at the head end of the positive feeder; is the voltage at the end node of the positive feeder; represents a vector; The Jacobian matrix of the system is: ； Where, is the active power of the branch from node 1 to node 5; is the active power of the branch from node 2 to node 5; The objective function is: ； Where, is the state variable matrix; is the measurement matrix; is the observation matrix; is the weighting matrix; The iterative equation is: ； in, ； Where, is the update matrix; is the transposed Jacobian matrix; is the x matrix of the lth iteration; is the update matrix of the lth iteration; is the x matrix of the l+1th iteration; is the Jacobian matrix; The locomotive voltage is: ； The current is: 。 7. The method for identifying locomotive position and Thevenin equivalent nonlinearity of an AT full parallel traction network according to claim 1, characterized in that: Step 4 specifically includes the following steps: Establish the Thevenin equivalent system equations; The state estimation at multiple time points is obtained U 、 I The data constitute an overdetermined system of equations; Solving the overdetermined system of equations yields the Thevenin equivalent parameter: the equivalent potential and equivalent impedance .

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