A method for constructing a state estimation model of a traction power supply system considering coupling of locomotive motion and electrical state

Abstract

This invention relates to a method for constructing a state estimation model for a traction power supply system that considers the coupling of locomotive motion and electrical state, belonging to the field of estimation model construction for rail transit power supply systems. The method first establishes a time-varying parameter model of the DC traction network dynamically updated with the locomotive position; secondly, it constructs a parallel filtering framework for locomotive motion and electrical state, using the electrical state prediction results to correct the locomotive position and achieve bidirectional information interaction; finally, it introduces an innovation saturation mechanism in the extended Kalman filter to limit abnormal disturbances, and constructs an adaptive factor based on the deviation between the theoretical and actual covariance of the innovation, adjusting the noise matrix weights online. Simulations show that, compared with traditional methods, this invention improves the voltage amplitude estimation accuracy by more than 60% and reduces the locomotive position estimation error to within 3 meters, effectively improving the dynamic sensing accuracy and robustness of the traction power supply AC / DC system under complex operating conditions, providing reliable data support for online monitoring and intelligent operation and maintenance.

Description

Technical Field

[0001] This invention belongs to the field of estimation model construction for rail transit power supply systems, and specifically relates to a method for constructing a state estimation model for traction power supply systems that considers the coupling between locomotive motion and electrical state. Background Technology

[0002] With the continuous expansion of urban rail transit operations and the increasing density of trains, the operating conditions of traction power supply systems exhibit strong time-varying, strong coupling, and high dynamic characteristics. As a crucial energy support system for urban rail transit, the accurate perception of the traction power supply system's operating status directly impacts train operation safety, traction power supply reliability, and the level of intelligent system operation and maintenance. Currently, urban rail transit traction power supply systems are equipped with data acquisition and monitoring systems, locomotive automatic monitoring systems, and traction substation monitoring systems, providing basic data conditions. However, in actual operation, measurement data is often affected by factors such as communication delays, sampling noise, abnormal data, and model errors, making it difficult to accurately reflect the true operating status of the system using raw measurement data. State estimation is a key technology in power system operating status perception and online analysis. Essentially, it utilizes system mathematical models, network topology parameters, and multi-source measurement data to optimally estimate the operating status of the system that cannot be directly and accurately obtained or is affected by noise, thus providing a reliable data foundation for real-time system monitoring, operation evaluation, fault diagnosis, and optimized control.

[0003] Compared to conventional power systems, urban rail transit traction power supply systems exhibit more pronounced mobile load characteristics. As a mobile load within the DC traction network, the locomotive's position changes continuously over time, causing real-time variations in traction network branch lengths, equivalent resistances, nodal admittance matrices, and measurement equations. Errors in locomotive position further complicate the DC network model, affecting the accuracy of state estimation. Therefore, it is necessary to propose a state estimation method suitable for AC / DC traction power supply systems, achieving high-precision and robust estimation of the system's operating state while considering the coupling relationship between locomotive motion and electrical states.

[0004] Current technology has the following shortcomings:

[0005] (1) Existing power system state estimation methods are mostly geared towards fixed topologies or quasi-steady-state operation scenarios, typically treating network structure and branch parameters as relatively stable. However, in urban rail transit traction power supply systems, locomotives, as mobile loads in the DC traction network, experience continuous changes in their position over time, causing real-time changes in traction network branch lengths, equivalent resistances, and nodal admittance matrices. When there is a deviation in locomotive position, inconsistencies will arise between the DC network model and the actual system, leading to measurement equation mismatch and consequently reducing the accuracy of electrical state estimation results.

[0006] (2) The bidirectional coupling relationship between locomotive motion state and electrical state has not been fully utilized. During the operation of the traction power supply system, the locomotive's operating state directly affects the structure of the DC traction network; at the same time, changes in the electrical state and branch parameters of the traction network can also reflect the network structure changes caused by locomotive position changes, providing auxiliary information for locomotive position correction. If an information interaction mechanism between locomotive motion state and electrical state is not established, it is difficult to use the electrical state to correct the locomotive position, and it is also difficult to use the corrected locomotive position to correct the electrical network model in real time.

[0007] (3) In the traction power supply system, the locomotive frequently switches between traction, coasting and braking conditions, and the DC side voltage, current and power are prone to rapid fluctuations. At the same time, abnormal measurements and ill-conditioned changes in local branch parameters may lead to abnormal amplification of the filtering information. Traditional extended Kalman filtering or general adaptive filtering methods usually directly use the information for state updates. When the information contains abnormal disturbances, it is easy to cause over-correction of the state, decrease in estimation accuracy or even filter instability, which makes it difficult to meet the high-precision and robust state estimation requirements of the traction power supply AC / DC system under complex operating conditions. Summary of the Invention

[0008] The purpose of this invention is to address the problem that existing methods are difficult to adapt to the time-varying network topology and measurement anomalies caused by locomotive movement, and to provide a method for constructing a traction power supply system state estimation model that considers the coupling between locomotive movement and electrical state.

[0009] To achieve the above objectives, the technical solution of the present invention is: a method for constructing a state estimation model for a traction power supply system considering the coupling of locomotive motion and electrical state, comprising:

[0010] A time-varying parameter model of the DC traction network is established, and the traction substation and locomotive are equivalent to DC network nodes. The length of adjacent branches and equivalent resistance are determined according to the real-time position of the locomotive, and the DC node admittance matrix that changes dynamically with the locomotive position is obtained.

[0011] A filtering framework is constructed to allow the locomotive motion state estimation model and the traction power supply system electrical state estimation model to operate in parallel. The DC traction network branch parameters and electrical measurement model are updated based on the locomotive position estimation results, and the locomotive position is corrected by feedback based on the electrical state prediction results.

[0012] An innovation processing module and an adaptive adjustment module are integrated into the extended Kalman filter architecture. The innovation processing module is used to limit and suppress anomalous innovations, and the adaptive adjustment module is used to adjust the noise covariance matrix online according to the statistical characteristics of the innovation.

[0013] Furthermore, in the time-varying parameter model of the DC traction network, for the section unit between adjacent traction substations, based on the longitudinal resistance and transition resistance parameters of the contact network, rails, and drainage network, the distributed parameter resistance network of the return section is subjected to centralized equivalent processing and star-delta transformation to calculate multiple equivalent resistance parameters of the section unit. Specifically,

[0014] In the time-varying parameter model of the DC traction network, for a section unit between adjacent traction substations, the distances from the locomotive to the first and last traction substations of the section are l1 and l2, respectively; the voltages of the first and last traction substations are U1 and U2, respectively; and the longitudinal resistances of the contact wire, rail, and drainage network are r, respectively. c r t and r d The transition resistances are r td and r g After performing centralized equivalent processing and star-delta transformation on the distributed parameter resistive network of the return section, the equivalent resistance of the segment element is calculated as follows:

[0015] R1 = r d r g l1 / (r d l1 2 + 2r g ) + r td / l1

[0016] R2 = r g 2 / (r d l1 2 + 2r g )

[0017] R3 = r t l1(R1 2 + 2R1R2) / (R1 2 + 2R1R2 + R2r t l1)

[0018] R4 = R1 + 2R2.

[0019] Furthermore, in the electrical state estimation model, the electrical state variables include three types of parameters: AC system node voltage amplitude, AC system node voltage phase angle, and DC system node voltage. Specifically,

[0020] In the electrical state estimation model, the electrical state variables Represented as:

[0021]

[0022] In the formula, U ac,kLet θ be the voltage magnitude vector of the AC system at time k. k Let U be the phase vector of the AC system at time k. dc,k Let be the voltage vector of the DC system at time k.

[0023] Furthermore, in the electrical state estimation model, the system measurement vector includes AC system measurement data, DC system measurement data, and pseudo-measurement data of the AC / DC converter interface. Specifically,

[0024] In the electrical state estimation model, the system measurement vector Represented as:

[0025]

[0026] In the formula, z ac,k For the measurement vector of the AC system, z dc,k z is the measurement vector for the DC system. vsc,k This is a pseudo-measurement vector for the converter model.

[0027] Furthermore, a time-varying parameter exponential smoothing model is used for state prediction. This model includes horizontal and vertical components, where the smoothing parameter is adaptively and dynamically assigned based on the locomotive's real-time operating conditions to track sudden changes in the system state. Specifically,

[0028] State prediction is performed using a time-varying parameter exponential smoothing model, and the prediction formula is as follows:

[0029]

[0030] In the formula, For state prediction function, This is the predicted state value at time k+1. This is the predicted state value at time k. Let a be the state estimate at time k. k and b k Let α be the horizontal component and the vertical component at time k, respectively. k and β k These are time-varying parameters that are dynamically assigned adaptively based on the real-time operating conditions of the locomotive. With β k Unit quantities of the same dimension.

[0031] Furthermore, in the DC system measurement model, the DC network node admittance matrix is ​​associated with the locomotive position, and the DC node current and power measurements are determined through the correlation between the DC node voltage and this time-varying admittance matrix. Specifically,

[0032] In the measurement equations of a DC system, the admittance matrix of the DC network nodes at time k is... Indicates locomotive position Functions:

[0033]

[0034] In the formula, m k Let k be the locomotive's position vector at time k;

[0035] The equation for DC system current measurement is:

[0036]

[0037] The equation for power measurement in a DC system is:

[0038]

[0039] In the formula, U dc,i I dc,i and P dc,i Let N represent the voltage, current, and power at node i in the DC system; dc G represents the number of nodes in a DC system. dc,ij For the corresponding element in the node admittance matrix of the DC system. and These are current measurement noise and power measurement noise, respectively.

[0040] Furthermore, in the locomotive position state estimation model, the motion state variables include the locomotive's position parameters and velocity parameters, and the measurements include the locomotive's position measurements and velocity measurements. Specifically,

[0041] In the locomotive position state estimation model, the motion state variables Measurement Represented as:

[0042]

[0043] In the formula, m and v are the position and velocity vectors of the locomotive, respectively; z m,mea and z v,mea These are the locomotive's position and speed measurement vectors, respectively.

[0044] Furthermore, the state transition process for locomotive position estimation is based on kinematic recursion, combined with time intervals, locomotive acceleration measurements, and process noise, to calculate the locomotive position and velocity state at the next moment. Specifically,

[0045] The state transition equation for locomotive position estimation is:

[0046]

[0047] In the formula, Let I be the locomotive motion state variable at time k, and let I and 0 be the identity matrix and the zero matrix, respectively. denoted as the time interval; E is an appropriate dimension matrix matching the acceleration dimension (usually an all-one or identity matrix). The acceleration measurement vector of the locomotive at time k-1; w loc,k This refers to the noise in the location estimation process.

[0048] Furthermore, the information processing module performs the following operations: It presets a reasonable range for information fluctuations; when the information amplitude is within this range, it retains the original information; when the information amplitude exceeds this range, it performs amplitude limiting. The boundary of the reasonable range is dynamically adjusted based on the recursive statistics of the information. Under normal operating conditions, it maintains a wide boundary to utilize effective measurements; under abnormal operating conditions, it tightens the boundary to suppress the impact of abnormal information. Specifically,

[0049] In the aforementioned innovation saturation mechanism, the i-th component of the innovation vector... The saturation treatment formula is:

[0050]

[0051] In the formula, and These are the ith component of the saturated feed and the original feed at time k, respectively. The saturation threshold is sgn(·); sgn(·) is the sign function, updated through the following recursive relationship:

[0052]

[0053]

[0054] in, Let be the recursive statistic of the i-th innovation component at time k; and These are the forgetting factor of the i-th information component and the forgetting factor of the recursive statistic, respectively. and These are the positive adjustment gain of the i-th innovation component and the positive adjustment gain of the recursive statistic, respectively.

[0055] Furthermore, the adaptive adjustment module adjusts the noise covariance matrix in the following way: it calculates the ratio of the trace of the innovation theory covariance matrix to the actual covariance matrix; when this ratio is greater than 1, it reduces the process noise covariance matrix and increases the measurement noise covariance matrix to dynamically adjust the weight distribution of prediction and measurement information. Specifically,

[0056] The formula for constructing the adaptive factor is:

[0057]

[0058] In the formula, tr(⋅) represents the matrix trace operation. The covariance matrix of the innovation theory is... The actual covariance matrix of the new information; , N is the length of the sliding window. The information vector is the information vector from past time points; based on an adaptive adjustment factor. For the process noise covariance matrix Q k And the measurement noise covariance matrix R k Perform online corrections:

[0059]

[0060]

[0061] in, Let be the prediction error covariance matrix at time k. Let be the state transition Jacobian matrix at time k-1. Let be the estimation error covariance matrix at time k-1. Let be the process noise covariance matrix at time k-1. Let K be the Kalman gain matrix at time k. Let be the measurement Jacobian matrix at time k. Let be the measurement noise covariance matrix at time k.

[0062] Compared with existing technologies, this invention has the following advantages: By introducing a time-varying parameter model of the DC traction network that changes in real time with the locomotive's position, this invention can effectively avoid measurement model mismatch problems caused by fixed topology assumptions or position deviations, thus improving the accuracy of electrical state estimation. By constructing a parallel coupled estimation framework for locomotive motion state and electrical state, the DC network parameters can be corrected in real time using the locomotive position estimation results, and the locomotive position can be corrected using electrical state prediction information, achieving coordinated optimization of locomotive position and electrical state. By introducing an innovation saturation mechanism and an adaptive covariance adjustment strategy, the invention can suppress the amplification of innovation caused by abnormal measurements, sudden changes in operating conditions, and ill-conditioned changes in local branch parameters, avoiding over-correction of filtering and improving the robustness and numerical stability of the algorithm under complex operating conditions. Therefore, this invention can effectively improve the accuracy, robustness, and real-time adaptability of dynamic state estimation of traction power supply AC / DC systems, providing reliable data support for online monitoring, operation evaluation, fault diagnosis, and intelligent operation and maintenance of urban rail transit traction power supply systems. Attached Figure Description

[0063] Figure 1 This is an equivalent model for a DC network.

[0064] Figure 2 This is a flowchart of the state estimation process for a traction power supply system based on parallel adaptive extended Kalman filtering.

[0065] Figure 3 The voltage amplitude state is estimated for locomotive node No. 4.

[0066] Figure 4 A comparison of RMSE metrics for different state estimation algorithms.

[0067] Figure 5 A comparison of RMSE indices for different locomotive position estimation methods. Detailed Implementation

[0068] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0069] This invention provides a method for constructing a state estimation model for a traction power supply system that considers the coupling between locomotive motion and electrical state, comprising:

[0070] A time-varying parameter model of the DC traction network is established, and the traction substation and locomotive are equivalent to DC network nodes. The length of adjacent branches and equivalent resistance are determined according to the real-time position of the locomotive, and the DC node admittance matrix that changes dynamically with the locomotive position is obtained.

[0071] A filtering framework is constructed to allow the locomotive motion state estimation model and the traction power supply system electrical state estimation model to operate in parallel. The DC traction network branch parameters and electrical measurement model are updated based on the locomotive position estimation results, and the locomotive position is corrected by feedback based on the electrical state prediction results.

[0072] An innovation processing module and an adaptive adjustment module are integrated into the extended Kalman filter architecture. The innovation processing module is used to limit and suppress anomalous innovations, and the adaptive adjustment module is used to adjust the noise covariance matrix online according to the statistical characteristics of the innovation.

[0073] The following is a detailed implementation process of the present invention.

[0074] 1. Modeling of the AC / DC traction power supply system for subways

[0075] This invention addresses dynamic state estimation for AC / DC traction power supply systems in subways. Since locomotives act as moving loads in the DC traction network, their operating positions change continuously over time, causing variations in the DC system network structure. First, a rapid calculation model of the DC network considering the locomotive's moving load characteristics is established, enabling real-time updates of the DC network parameters based on the locomotive's position.

[0076] The DC traction network consists of an overhead contact line, rails, a drainage network, and transition resistors. For a section unit located between adjacent traction substations, let the distances from the locomotive to the first and last traction substations of the section be l1 and l2, respectively; let the voltages of the first and last traction substations be U1 and U2, respectively; and let the longitudinal resistances of the overhead contact line, rails, and drainage network be r, respectively. c r t and r d The transition resistances are r td and r g Based on the above parameters, a segment unit distributed parameter circuit model can be used to describe the electrical connection relationship between the contact wire, rail return circuit, and drainage network, such as... Figure 1 As shown in (a).

[0077] The distributed parameter resistivity network of the return current section is subjected to centralized equivalent processing, and then transformed into an equivalent resistivity network through a star-delta transformation, such as... Figure 1 As shown in (b), after equivalence, the main equivalent resistance in the segment element can be expressed as: R1 = r d r g l1 / (r d l1 2 + 2r g ) + r td / l1, R2 = r g 2 / (r d l1 2 + 2r g ), R3 = r t l1(R1 2 + 2R1R2) / (R1 2 + 2R1R2 + R2r t l1), R4 = R1 + 2R2. Furthermore, compared to the locomotive traction current, the stray current is very small, and the longitudinal resistance of the rail is much smaller than the transition resistance. Therefore, when analyzing the traction substation and locomotive operating conditions, the grounding portion can be ignored, and the track branch resistance and the contact wire branch resistance can be combined. Thus, the section unit can be further simplified into a rapid calculation model, such as... Figure 1 As shown in (c).

[0078] 2. State estimation of traction power supply system based on parallel adaptive extended Kalman filter

[0079] 2.1 Electrical State Estimation Model

[0080] This invention comprehensively considers the operating states of the AC medium-voltage ring network, AC / DC converter interfaces, and DC traction network to construct a unified electrical state variable. The electrical state variable includes the AC system node voltage amplitude, AC system node voltage phase angle, and DC system node voltage, which can be expressed as:

[0081]

[0082] In the formula, U ac,k and θ k These are the voltage magnitude vector and phase angle vector of the AC system at time k, respectively; U dc,k Let be the voltage vector of the DC system at time k.

[0083] The system measurement vectors, including AC system measurements, DC system measurements, and converter pseudo-measurements, can be represented as:

[0084]

[0085] In the formula, z ac,k z is the measurement vector for the AC system. dc,k z is the measurement vector for the DC system. vsc,k This is a pseudo-measurement for the converter model.

[0086] Traction power supply AC / DC systems exhibit strong nonlinear and time-varying characteristics. In particular, the DC system is affected by changes in locomotive traction, coasting, and braking operating conditions, causing node voltages to fluctuate rapidly with changes in traction load. Traditional two-parameter exponential smoothing models typically use fixed smoothing coefficients, which often fail to meet the model's ability to quickly track different locomotive operating conditions, easily leading to prediction lag. Therefore, to improve the model's ability to quickly track sudden changes in system states, a time-varying parameter exponential smoothing model is adopted:

[0087]

[0088] In the formula, This is the predicted state value; This is the state estimate; a k and b k These are the horizontal and vertical components, respectively; α k and β k These are time-varying parameters, which are dynamically and adaptively assigned values ​​based on the locomotive's current real-time operating conditions.

[0089] For an AC system, the relationship between measurements and state variables can be expressed as:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] In the formula, N ac U represents the number of nodes in the communication system. ac,i and θ i These represent the voltage magnitude and phase angle at node i of the AC system, respectively; P ac,i and Q ac,i These represent the active and reactive power injected into node i of the AC system, respectively; P bran,ij and Q bran,ij These represent the active and reactive power of branch ij in the AC system, respectively; G ac,ij and B ij These represent the conductance and susceptance of branch ij in the AC system, respectively; B gi Let θ be the susceptance to ground of node i in the AC system; ij = θ i - θ j This represents the phase angle difference between the nodes at both ends of a branch in an AC system.

[0097] For DC systems, based on a fast calculation model, traction substations and locomotives are considered as nodes. System measurements include voltage, current, and power at each node. Unlike conventional fixed topology networks, locomotives in DC systems exhibit mobile load characteristics, with their location m... k The lengths and equivalent resistances of adjacent branches change in real time, thus altering the nodal admittance matrix. Therefore, the nodal admittance matrix of the DC network at time k can be expressed as a function of the locomotive position.

[0098]

[0099] In the formula, m k Let be the locomotive's position vector at time k.

[0100] Based on the nodal admittance relationship, the relationship between various measurements and state variables of a DC system can be expressed as follows:

[0101]

[0102]

[0103]

[0104] In the formula, U dc,i I dc,i and P dc,i Let N represent the voltage, current, and power at node i in the DC system; dc G represents the number of nodes in a DC system. dc,ij This represents the corresponding element in the node admittance matrix of the DC system.

[0105] For AC / DC converter interfaces, pseudo-measurement equations for power balance and control modes are established:

[0106]

[0107]

[0108] In the formula, and Let k be the voltage and voltage control quantity of the i-th DC-side node of the converter, respectively; droop This is the droop coefficient; and P represents the active power of the AC and DC side nodes of the i-th converter, respectively. loss,i The power loss of the i-th converter can be obtained by the following formula.

[0109]

[0110] In the formula, Let be the current at the i-th DC-side node of the converter; a, b, and c are the converter loss coefficients.

[0111] 2.2 Locomotive Position State Estimation Model

[0112] To account for the impact of locomotive motion on the dynamic state estimation of the traction power supply system, locomotive position and speed are used as motion state variables and quantities:

[0113]

[0114] In the formula, m and v are the position and velocity vectors of the locomotive, respectively; z m,mea and z v,mea These are the locomotive's position and speed measurement vectors, respectively.

[0115] Within an extremely short timescale, the locomotive's operation can be approximated as a linear process following the equations of motion. When the locomotive's basic states, such as position, velocity, and acceleration, are known, the state transition equation for position estimation can be described as...

[0116]

[0117] In the formula, I and 0 are the identity matrix and the zero matrix, respectively; _a_ is the time interval; _a_ is the acceleration measurement vector of all locomotives; _w_ is the acceleration measurement vector of all locomotives. loc,k This refers to the noise in the location estimation process.

[0118] The measurement equation for locomotive position estimation can be described as follows:

[0119]

[0120] In the formula, v loc,k Measurement noise for position estimation; H loc,k The measurement matrix for position estimation is a sparse matrix. Only when the measured quantity is the same locomotive state information as the state quantity description, the corresponding element in the matrix is ​​1, and the rest of the elements are 0.

[0121] 2.3 Parallel Adaptive Extended Kalman Filter Algorithm

[0122] The extended Kalman filter is used for recursive estimation, which mainly consists of prediction and update:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128] In the formula, and These are the prediction error covariance matrix and the estimation error covariance matrix, respectively; K k H is the Kalman gain matrix; k F is the Jacobian matrix of the measurement equation; k Q is the state transition matrix; k With R k These are the covariance matrices of process noise and measurement noise, respectively.

[0129] The information reflects the degree of matching between the state prediction model and the measurement information, and is defined as the deviation between the actual and predicted measurement values:

[0130]

[0131] From equations (12) and (13), we can see that the locomotive position m k The DC network node admittance matrix affects the current and power measurement equations. Since branch admittance is inversely proportional to the electrical distance between adjacent nodes, when the distance between the locomotive and the traction substation or other locomotives is small, the corresponding branch admittance will increase significantly, widening the numerical differences between elements in the node admittance matrix. In this case, the current and power measurement equations become more sensitive to voltage prediction errors, and even small state prediction deviations can yield large innovations. Directly using this innovation for state updates can easily lead to over-correction of the filter, affecting estimation accuracy. To suppress the impact of abnormal innovations on state updates, an innovation saturation mechanism is introduced. The basic idea is to retain the original information when the innovation is within a reasonable fluctuation range, allowing the measurement to participate normally in state correction; when the innovation amplitude exceeds a set boundary, it is limited to the boundary range to weaken over-correction caused by poor measurement or ill-conditioned parameters. For the i-th component in the innovation vector, its saturation processing form is:

[0132]

[0133] In the formula, and These are the ith component of the saturated feed and the original feed at time k, respectively. is the saturation threshold; sgn(·) is the sign function.

[0134] The saturation boundary is dynamically adjusted based on real-time changes in the new information as follows:

[0135]

[0136]

[0137] In the formula, For the recursive statistics of new information; and Forgetting factor; and The adjustment gain is positive. The above equations constitute a two-layer adjustment strategy based on real-time feedback of innovation. Under normal conditions, Generally, the values ​​remain within a relatively small range; however, when the measurement is subjected to abnormal perturbations, or when the innovation is pathologically amplified due to differences in model structure, This increases accordingly, providing feedback information for adjusting the saturation boundary. Based on this, the boundary parameters... By including nonlinear terms The recurrence relation is updated. When When the value is small, the nonlinear term maintains a large value, making Maintain a relatively loose boundary range to make full use of effective measurement information; while when As it increases, this term will decrease rapidly, thereby tightening the saturation boundary to suppress the adverse effects of anomalous innovations.

[0138] The theoretical covariance matrix of the new information and the actual covariance matrix They are respectively:

[0139]

[0140]

[0141] In the formula, N is the length of the sliding window.

[0142] Constructing adaptive adjustment factors for:

[0143]

[0144] In the formula, tr(·) is the trace of the matrix.

[0145] By introducing an adaptive adjustment factor, Q can be adjusted. k With R k Perform online corrections. The adaptive adjustment method is as follows:

[0146]

[0147]

[0148] To achieve bidirectional information exchange between the locomotive's motion state and the electrical state of the traction power supply system, this invention introduces a locomotive position feedback correction method based on the electrical state prediction results during the parallel filtering process. Specifically, at time k, the predicted locomotive position is first obtained based on the locomotive motion state model, and simultaneously, the predicted electrical state of the traction power supply system is obtained based on the electrical state prediction model. Since changes in locomotive position alter the branch length, equivalent resistance, and node admittance matrix of the DC traction network, and the DC node voltage, current, and power distribution are closely related to the branch parameters, the electrical state prediction results can be used to estimate the DC traction network branch parameters and further deduce the locomotive position correction value.

[0149] Suppose the locomotive is located between adjacent traction depots s and s+1, and the coordinates of the traction depots at both ends of the section are m and m respectively. s and m s+1 The equivalent resistance per unit length of the traction network is r. eq If the branch resistance between the locomotive and the first or last traction substation of the section is estimated from the electrical condition prediction results, then... and Then, the locomotive position correction value based on the first or last traction depot can be obtained:

[0150]

[0151]

[0152] Subsequently, the predicted position of the locomotive motion model and the position correction value obtained from the electrical state feedback are weighted and fused to form the corrected predicted locomotive position value:

[0153]

[0154] In the formula, This represents the predicted locomotive position after incorporating electrical condition feedback information; This represents the locomotive position predicted by the locomotive motion state model; This represents the fusion weight between the motion model's predicted position and the electrical feedback position correction value.

[0155] Through the aforementioned feedback correction steps, the electrical state prediction results can correct the locomotive position prediction value before filtering and updating. Subsequently, the corrected locomotive position prediction value is filtered and updated to obtain an estimated value, which is used to correct the DC traction network branch parameters and node admittance matrix, thereby achieving coordinated estimation between the locomotive motion state and the electrical state.

[0156] This invention constructs a parallel adaptive extended Kalman filter based on innovation saturation (IS-PAEKF) algorithm. This algorithm uses locomotive position estimation results to update the DC traction network branch parameters and nodal admittance matrices in real time, and uses electrical state prediction information to perform feedback correction on the locomotive position, thereby realizing information interaction between the locomotive's motion state and electrical state. The overall flowchart is as follows: Figure 2 As shown.

[0157] 3. Simulation Cases

[0158] 3.1 Case Setup

[0159] To verify the feasibility and accuracy of the proposed method, a simulation experiment was conducted based on the design of a planned subway line, using MATLAB 2022b as the simulation software. The line includes 23 traction substations and 38 locomotives, with locomotive operating status obtained through traction calculations. For the AC system, a centralized power supply AC model for the 23 traction substations was established, and the AC system network topology and node electrical parameters were obtained using the Matpower 7.1 toolkit. The actual electrical quantities of the AC and DC networks were obtained through precise power flow calculations. To simulate measurement errors in the actual system, zero-mean Gaussian noise was superimposed on the actual values ​​to construct the measurement data. Specifically, the standard deviation of the AC voltage phase angle measurement was set to 0.5°, and the standard deviation of all other electrical measurements was taken as 1% of the corresponding actual value.

[0160] To measure the accuracy of the estimation results, root mean square error (RMSE), mean absolute error (MAE), and mean vector error (MVE) are introduced as metrics to evaluate the estimation accuracy of the algorithm. The definitions of these metrics are as follows:

[0161]

[0162]

[0163]

[0164] In the formula, x i x i,mea and , respectively, are the true value, measured value, and estimated value of the i-th state variable; n is the dimension of the state variable.

[0165] 3.2 Comparative Analysis of Results

[0166] To evaluate the effectiveness and accuracy of the algorithm of this invention in dynamic state estimation of traction power supply AC / DC systems, weighted least squares method and adaptive extended Kalman filter method were used for comparative verification. The state estimation results of the algorithm are as follows: Figure 3 and Figure 4 As shown.

[0167] Because the power of a locomotive changes drastically during transitions between different operating conditions, the corresponding node voltage typically fluctuates significantly, exhibiting more pronounced dynamic characteristics compared to other nodes in the system. Therefore, to verify the proposed method's ability to track dynamic state changes in the system, the locomotive node voltage is selected as a typical example for analysis. Figure 3 It can be seen that the node voltage fluctuates significantly during locomotive operation, especially during power changes where voltage abruptly changes. Comparing the estimation results of different algorithms shows that the proposed method can better track the trend of locomotive node voltage changes and can still quickly approximate the true value during voltage abrupt changes. Further analysis reveals… Figure 4 The RMSE curves show that the proposed method achieves smaller estimation errors, indicating that the method has higher estimation accuracy and stability in the dynamic state estimation of traction power supply AC / DC systems.

[0168] To quantify the estimation accuracy of the algorithm, the estimation error values ​​of each method after 100 seconds of filtering were compared with the evaluation metrics of different estimation algorithms. Table 1 shows these values.

[0169] Table 1 Comparison of Evaluation Metrics for Different State Estimation Algorithms

[0170]

[0171] As shown in Table 1, although all three state estimation algorithms can achieve effective estimation of the system state, the method of this invention has smaller estimation errors in both voltage amplitude and phase angle compared to AEKF and WLS. Specifically, compared with WLS, the estimation accuracy of the method of this invention is improved by more than 60%; compared with AEKF, the estimation accuracy is improved by more than 40%, indicating that the proposed method can achieve better state estimation performance overall.

[0172] To verify the performance of the proposed method in locomotive position estimation, a segment-velocity extrapolation algorithm and an adaptive Kalman filter algorithm were used for comparison. The extrapolation method specifically combines the initial coordinates of the segment from the segment positioning and the locomotive velocity, and uses the equations of motion to calculate the locomotive position in real time, following the same state transition process as the locomotive position estimation method. The results of the three position estimation methods are shown below. Figure 5 As shown in Table 2.

[0173] Table 2 Comparison of Evaluation Indicators for Different Locomotive Position State Estimation Methods

[0174]

[0175] Depend on Figure 5 As shown in Table 2, the position estimation error of the method proposed in this invention is significantly smaller than that of the extrapolation method and the AEKF method, and the error can be quickly converged in the early stage of filtering. This is because by estimating the locomotive position and electrical state in parallel, the electrical state can be used to dynamically correct the DC traction network parameters, and the network model can be fed back to the locomotive position estimation process. Thus, the locomotive position deviation is continuously and effectively corrected throughout the filtering process, further reducing the locomotive position estimation error.

[0176] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for constructing a state estimation model for a traction power supply system considering the coupling of locomotive motion and electrical state, characterized in that, include: A time-varying parameter model of the DC traction network is established, and the traction substation and locomotive are equivalent to DC network nodes. The length of adjacent branches and equivalent resistance are determined according to the real-time position of the locomotive, and the DC node admittance matrix that changes dynamically with the locomotive position is obtained. A filtering framework is constructed to allow the locomotive motion state estimation model and the traction power supply system electrical state estimation model to operate in parallel. The DC traction network branch parameters and electrical measurement model are updated based on the locomotive position estimation results, and the locomotive position is corrected by feedback based on the electrical state prediction results. An innovation processing module and an adaptive adjustment module are integrated into the extended Kalman filter architecture. The innovation processing module is used to limit and suppress anomalous innovations, and the adaptive adjustment module is used to adjust the noise covariance matrix online according to the statistical characteristics of the innovation.

2. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 1, characterized in that, In the time-varying parameter model of the DC traction network, for the section unit between adjacent traction stations, based on the longitudinal resistance and transition resistance parameters of the contact network, rail, and drainage network, the distributed parameter resistance network of the return flow part is centrally equivalently processed and transformed by star-delta transformation to calculate multiple equivalent resistance parameters of the section unit.

3. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 1, characterized in that, In the electrical state estimation model, the electrical state variables include three types of parameters: AC system node voltage amplitude, AC system node voltage phase angle, and DC system node voltage.

4. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 3, characterized in that, In the electrical state estimation model, the system measurement vector includes AC system measurement data, DC system measurement data, and pseudo measurement data of the AC / DC converter interface.

5. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 3, characterized in that, A time-varying parameter exponential smoothing model is used for state prediction. The time-varying parameter exponential smoothing model includes horizontal and vertical components, wherein the smoothing parameter is dynamically assigned adaptively according to the real-time operating conditions of the locomotive to track the sudden change in system state.

6. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 3, characterized in that, In the DC system measurement model, the DC network node admittance matrix is ​​associated with the locomotive position, and the DC node current and power measurements are determined by the correlation between the DC node voltage and this time-varying admittance matrix.

7. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 1, characterized in that, In the locomotive position state estimation model, the motion state variables include the locomotive's position parameters and velocity parameters, and the measurements include the locomotive's position measurements and velocity measurements.

8. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 7, characterized in that, The state transition process for locomotive position estimation is based on kinematic recursion. By combining time intervals, locomotive acceleration measurements, and process noise, the locomotive position and velocity state at the next moment can be calculated.

9. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 1, characterized in that, The information processing module performs the following operations: presets a range for information fluctuations; retains the original information when the information amplitude is within this range; and performs amplitude limiting when the information amplitude exceeds this range. The boundary of the range is dynamically adjusted according to the recursive statistics of the information. Under normal operating conditions, the boundary is kept wide, and under abnormal operating conditions, the boundary is tightened to suppress the impact of abnormal information.

10. The method for constructing a traction power supply system state estimation model considering the coupling of locomotive motion and electrical state according to claim 1, characterized in that, The adaptive adjustment module adjusts the noise covariance matrix in the following way: it calculates the ratio of the trace of the innovation theory covariance matrix to the actual covariance matrix. When the ratio is greater than 1, it reduces the process noise covariance matrix and increases the measurement noise covariance matrix to dynamically adjust the weight distribution of prediction information and measurement information.

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