Weighted minimum absolute value-based online load flow calculation method for flexible traction power supply system

Abstract

The invention relates to a weighted minimum absolute value-based online load flow calculation method for a flexible traction power supply system, and belongs to the technical field of power system dispatching automation. The method comprises the following steps: firstly, establishing a tractive power supply system circuit model according to a real-time position relationship between all traction stations and a locomotive in the tractive power supply system; secondly, considering the problem of frequency asynchronization, selecting a state variable and measurement according to a system measurement condition, and establishing a measurement equation; then, considering the influence of bad measurement data, establishing a state estimation model of the flexible traction power supply system based on an estimation criterion of a weighted minimum absolute value, carrying out iterative solution by using a primal-dual interior point algorithm, and sensing the operation state of the system in real time; and finally, on-line load flow calculation of the flexible traction power supply system is carried out on the basis of a state estimation result. The method can be used for obtaining tide distribution and energy flow conditions in the flexible traction power supply system in real time, and safe and stable operation of the traction power supply system is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system dispatching automation, and particularly relates to an online power flow calculation method for a flexible traction power supply system based on weighted least absolute value. Background Technique

[0002] As the energy supply system for urban rail transit electric locomotives, ensuring the safe and stable operation of the traction power supply system is of utmost importance. Power flow calculation is a basic and important calculation task in the power network. According to given conditions such as the grid structure and parameters, it determines the steady-state operation state parameters of each part within the system, and then obtains the power flow distribution of the entire network in real time, which helps to promptly discover weak links and potential risks in the network, provides decision-making support for operation dispatching, and ensures the stable and efficient operation of the system. To improve the accuracy of the results, the data used for power flow calculation needs to conform to the real-time operation state of the system as much as possible. However, the operation environment of the traction power supply system is complex, and the measured data is easily interfered and generates noise. Therefore, state estimation needs to be carried out first to obtain high-precision data that is more in line with the true operation state of the system. Based on this, online power flow calculation can obtain a more accurate power flow distribution and energy flow situation. Summary of the Invention

[0003] The purpose of the present invention is to make up for the gaps and deficiencies in the prior art, and provide an online power flow calculation method for a flexible traction power supply system based on weighted least absolute value, so as to obtain the power flow distribution and energy flow situation of the entire network in real time, and then ensure the safe and stable operation of the system.

[0004] To achieve the above purpose, the technical solution of the present invention is: an online power flow calculation method for a flexible traction power supply system based on weighted least absolute value, including: establishing a circuit model of the traction power supply system according to the real-time position relationship between all traction substations and locomotives in the traction power supply system; selecting state variables and measured quantities and establishing a measurement equation; based on the estimation criterion of weighted least absolute value, establishing a state estimation model of the flexible traction power supply system, and iteratively solving it with the primal-dual interior point algorithm to perceive the operation state of the system in real time; based on the state estimation result, performing online power flow calculation for the flexible traction power supply system.

[0005] Further, the method includes the following steps:

[0006] Step S1: Establish a circuit topology model of the traction power supply system according to the quantity and position relationship between traction substations and locomotives in the traction power supply system;

[0007] Step S2: Considering the problem that the sampling frequency of the locomotive position is not synchronized with the online power flow calculation frequency, determine the state variables and measured quantities, and establish a measurement equation;

[0008] Step S3: Considering the bad measurement data, establish a state estimation model for the flexible traction power supply system based on the weighted least absolute value estimation criterion;

[0009] Step S4: Solve the state estimation model based on the primal-dual interior point algorithm to perceive the operating state of the system in real time;

[0010] Step S5: Based on the state estimation results, perform on-line power flow calculation for the flexible traction power supply system to obtain the power flow distribution and energy flow of the whole network.

[0011] Furthermore, Step S1 is specifically implemented as follows:

[0012] Step S11: Obtain the position information of all traction substations and locomotives in the traction power supply system; regard the position of the first traction substation in the up direction as the initial position (i.e., 0 km), and convert the positions of the remaining traction substations and locomotives into relative positions with respect to the initial traction substation;

[0013] Step S12: Split the up and down lines connected to the output port of the traction substation, and superimpose the position information of the down line on the total length of the up line, that is, the initial position of the down line is the relative position of the last traction substation;

[0014] Step S13: Based on the relative positions of each traction substation and locomotive at the initial moment of on-line power flow calculation, number the traction substations and locomotives respectively to obtain unique index identifiers, and sort the traction substations and locomotives according to the position size to establish a topological model;

[0015] Step S14: Regard the traction substation and the locomotive as power source nodes, and the adjacent nodes divide the catenary and the rail into several sections, and each section of the catenary and the rail is regarded as a resistor;

[0016] Step S15: Ignoring the influence of stray current and rail-to-ground conductance, combine the catenary resistance and the rail resistance to obtain the traction network circuit model.

[0017] Furthermore, in Step S14, for the catenary resistance and the rail resistance, the resistance value calculation formulas are as follows:

[0018] r hi =r c l i (1)

[0019] r qi =r r l i (2)

[0020] In the formula, r hi and r qi are the resistance values of the i-th section of the catenary and the rail respectively; r c and rr are the unit resistance values of the catenary and the rail, respectively; l i is the length of the i-th section of the catenary and the rail, i.e., the distance between adjacent nodes.

[0021] Furthermore, step S2 is specifically implemented as follows:

[0022] Step S21: Construct the state quantity as:

[0023] x = [U tss , U train T (3)

[0024] In the formula, x is the state vector; U tss is the traction substation node voltage vector; U train is the locomotive node voltage vector; T is the transpose operator;

[0025] Step S22: Construct the measurement quantity as:

[0026] z = [U tss , U train , I tss , I train , P tss , P train T (4)

[0027] In the formula, z is the measurement vector; I tss and I train respectively represent the traction substation and locomotive node current vectors; P tss and P train respectively represent the traction substation and locomotive node active power vectors;

[0028] Step S23: The general form of the measurement equation is:

[0029] z = h(x) + e (5)

[0030] In the formula, h(·) is each measurement expression; e is the measurement error vector conforming to the normal distribution;

[0031] Step S24: Since the relative position of the locomotive changes continuously during its operation, the resistance values of the catenary and the rail will change in real time. Reflected in the measurement equation (5), it is manifested that the node admittance matrix is a function of the locomotive position. Considering the time-varying influence of the locomotive position, equation (5) is transformed into:

[0032] z = h(x, l) + e (6)

[0033] In the formula, l is the distance vector between adjacent nodes;

[0034] Step S25: The specific form of the measurement equation is:

[0035] I = Y(l)U (7)

[0036] P = Y(l)U 2 (8)

[0037] Wherein, Y is the nodal admittance matrix; U, I, and P are the nodal voltage, nodal current, and nodal power of each traction substation and locomotive node, respectively;

[0038] Step S26: The frequency of the online power flow calculation is in milliseconds. If the sampling period of the locomotive position and speed information is in seconds, it is necessary to give priority to synchronizing the update frequency of the locomotive position information with the online power flow calculation frequency; adopt a position extrapolation method based on the motion equation. The locomotive motion equation is:

[0039] m = m0 + v0Δt (9)

[0040] Wherein, m0 and v0 are the initial position and speed of the locomotive, respectively; m is the locomotive position after Δt time; Δt is the state estimation frequency;

[0041] Step S27: When performing state estimation, if the current locomotive position sampling value has not been updated, use the locomotive position information at the previous online power flow calculation moment and the locomotive speed information obtained from the previous sampling to calculate the locomotive position at the current calculation moment through Equation (9), so as to realize the synchronous update of the measurement equation.

[0042] Furthermore, Step S3 is specifically implemented as follows:

[0043] Step S31: The weighted least absolute value state estimation model is:

[0044]

[0045] Wherein, min represents taking the minimum value; w is the weight vector of the measurement z; ε is the residual vector;

[0046] Step S32: Introduce slack variables u, r:

[0047]

[0048] Step S33: Obtain the equivalent model of Equation (10) as:

[0049] min J(x) = w Τ (u + r)

[0050] s.t. 0 = z - h(x, l) + u - r (12).

[0051] u ≥ 0

[0052] r ≥ 0

[0053] Further, step S4 is specifically implemented as follows:

[0054] Step S41: Construct the Lagrangian function of formula (12):

[0055] L = w Τ (u + r) - λ Τ (z - h(x, l) + u - r) - α Τ u - β Τ r (13)

[0056] where λ, α, and β are Lagrange multipliers;

[0057] Step S42: Obtain the optimal value according to the KKT conditions, and get:

[0058]

[0059] L λ = z - h(x, l) + u - r = 0 (15)

[0060] L u = w - λ - α = 0 (16)

[0061] L r = w + λ - β = 0 (17)

[0062] L α = AUe = 0 (18)

[0063] L β = BRe = 0 (19)

[0064] where A = diag(α); B = diag(β); U = diag(u); R = diag(r); e = [1, 1,..., 1] T ;

[0065] Step S43: Introduce a perturbation parameter μ to relax formulas (18) and (19), and get:

[0066]

[0067] Step S44: Use Newton's method to solve formulas (14) to (17) and formula (20), and the following can be obtained:

[0068]

[0069] -dλ - dα = -L u (23)

[0070] dλ - dβ = -L r (24)

[0071]

[0072] It can be obtained from Equations (23) and (24) that:

[0073] dα = L u -dλ (27)

[0074] dβ = L r +dλ (28)

[0075] Step S45: Substitute Equations (27) and (28) into Equations (25) and (26), and it can be obtained that:

[0076]

[0077] Step S46: Substitute Equations (29) and (30) into Equation (22), and it can be obtained that:

[0078]

[0079] It can be obtained from Equations (21) and (31) that:

[0080]

[0081] Step S47: First, solve for dx and dλ from Equation (32), and then solve for dα, dβ, du, and dr respectively through Equations (27), (28), (29), and (30). After one iteration, correct the values of each variable, and repeat the iteration process until the convergence condition is satisfied;

[0082] Step S48: Save the node voltage estimation value U se .

[0083] Furthermore, in Step S47, the convergence condition is: α Τ u + β Τ r < 0.001.

[0084] Furthermore, the specific implementation of Step S5 is as follows:

[0085] Step S51: Substitute U se into Equations (7) and (8) to calculate the node current and node power respectively;

[0086] Step S52: Calculate the active power loss:

[0087]

[0088] where n is the number of nodes and G is the branch admittance matrix;

[0089] Step S53: Save and output the on-line power flow calculation results.

[0090] The present invention also provides a computer-readable storage medium, on which computer program instructions capable of being run by a processor are stored. When the processor runs the computer program instructions, the method steps described in any of the above can be implemented.

[0091] Compared with the prior art, the present invention has the following beneficial effects: The online power flow calculation method of the flexible traction power supply system based on weighted least absolute value proposed by the present invention can obtain the power flow distribution and energy flow situation of the traction power supply system in real time, and the principle is simple and easy to implement, suitable for engineering practice, and has broad application prospects. Description of the Drawings

[0092] Figure 1 It is a schematic diagram of the overall process of the embodiment of the present invention;

[0093] Figure 2 It is a circuit model diagram of the traction power supply system adopted in the embodiment of the present invention;

[0094] Figure 3 It is a simplified circuit diagram of the traction power supply system of Beijing Subway Line 13A adopted in the embodiment of the present invention, with a total of 23 traction substations and 46 locomotives.

[0095] Figure 4 It is a schematic diagram of the voltage estimation results of each traction substation and locomotive node in the embodiment of the present invention. Detailed Embodiments

[0096] The technical solution of the present invention will be specifically described below in conjunction with the drawings.

[0097] The present invention provides an online power flow calculation method for a flexible traction power supply system based on weighted least absolute value, including: establishing a circuit model of the traction power supply system according to the real-time position relationship between all traction substations and locomotives in the traction power supply system; selecting state variables and measurements and establishing a measurement equation; based on the estimation criterion of weighted least absolute value, establishing a state estimation model of the flexible traction power supply system, and iteratively solving it with the primal-dual interior point algorithm to perceive the system operation state in real time; based on the state estimation result, performing online power flow calculation of the flexible traction power supply system.

[0098] The following is the specific implementation process of the present invention.

[0099] As Figure 1 shown, an online power flow calculation method for a flexible traction power supply system based on weighted least absolute value proposed in the embodiment of the present invention includes the following steps:

[0100] Step 1: Establish a circuit topology model of the traction power supply system according to the quantity and position relationship between traction substations and locomotives in the traction power supply system;

[0101] Step 2: Considering the problem of asynchronous sampling frequencies of locomotive positions and online power flow calculation frequencies, determine the state variables and measured quantities, and establish a measurement equation;

[0102] Step 3: Considering the bad measurement data, establish a state estimation model for the flexible traction power supply system based on the weighted least absolute value estimation criterion;

[0103] Step 4: Solve the state estimation model based on the primal-dual interior point algorithm to perceive the operating state of the system in real time.

[0104] Step 5: Based on the state estimation results, perform online power flow calculation for the flexible traction power supply system to obtain the power flow distribution and energy flow situation of the whole network.

[0105] For the above online power flow calculation method of the flexible traction power supply system based on the weighted least absolute value, the implementation of Step 1 includes the following steps:

[0106] 1) Obtain the position information of all traction substations and locomotives in operation within the traction power supply system. Consider the position of the first traction substation in the up direction as the initial position (i.e., 0 km), and convert the positions of the remaining traction substations and locomotives into relative positions with respect to this initial traction substation.

[0107] 2) Split the up and down lines connected to the output port of the traction substation, and superimpose the position information of the down line on the total length of the up line, that is, the initial position of the down line is the relative position of the last traction substation.

[0108] 3) Based on the relative positions of each traction substation and locomotive at the initial moment of the online power flow calculation, number the traction substations and locomotives respectively to obtain unique index identifiers, and sort the traction substations and locomotives according to the position size to establish a topological model.

[0109] 4) Consider both the traction substation and the locomotive as power source nodes. Adjacent nodes divide the catenary and the rail into several sections, and each section of the catenary and the rail is regarded as a resistor with a resistance value of:

[0110] r hi =r c l i (1)

[0111] r qi =r r l i (2)

[0112] In the formula, r hi and r qi are the resistance values of the i-th section of the catenary and the rail respectively; r c and r r are the unit resistance values of the catenary and the rail respectively; l iis the length of the \(i\)-th section of the catenary and the rail, i.e., the distance between adjacent nodes.

[0113] 5) Ignoring the influence of stray current and rail-to-ground conductance, the resistance of the catenary and the rail are combined to obtain the traction network circuit model, as Figure 2 shown.

[0114] For the above-mentioned online power flow calculation method of the flexible traction power supply system based on weighted least absolute value, the implementation of step 2 includes the following steps:

[0115] 1) Construct the state variables as:

[0116] x = [U tss , U train T (3)

[0117] where \(x\) is the state vector; U tss is the node voltage vector of the traction substation; U train is the node voltage vector of the locomotive; \(T\) is the transpose operator.

[0118] 2) Construct the measurements as:

[0119] z = [U tss , U train , I tss , I train , P tss , P train T (4)

[0120] where \(z\) is the measurement vector; I tss and I train represent the node current vectors of the traction substation and the locomotive respectively; P tss and P train represent the active power vectors of the traction substation and the locomotive respectively.

[0121] 3) The general form of the measurement equation is:

[0122] z = h(x) + e (5)

[0123] where \(h(·)\) is each measurement expression; \(e\) is the measurement error vector that conforms to the normal distribution.

[0124] 4) Since the relative position of the locomotive changes continuously during its operation, according to Eqs. (1) and (2), it can be seen that the resistance values of the catenary and the rail will change in real time. Reflected in the measurement equation (5), it shows that the nodal admittance matrix is a function of the locomotive position. Considering the time-varying influence of the locomotive position, Eq. (5) is transformed into:

[0125] z = h(x, l) + e (6) ​​

[0126] In the formula, l is the distance vector between adjacent nodes.

[0127] 5) The specific form of the measurement equation is as follows:

[0128] I = Y(l)U (7)

[0129] P = Y(l)U 2 (8)

[0130] In the formula, Y is the nodal admittance matrix; U, I, and P are the nodal voltage, nodal current, and nodal power of each traction substation and locomotive node, respectively.

[0131] 6) The frequency of online power flow calculation is in the millisecond level. If the sampling period of the locomotive position and speed information is in the second level, it is necessary to prioritize the synchronization of the locomotive position information update frequency and the online power flow calculation frequency. Using the position extrapolation method based on the motion equation, the locomotive motion equation is:

[0132] m = m0 + v0Δt (9)

[0133] In the formula, m0 and v0 are the initial position and speed of the locomotive, respectively; m is the locomotive position after Δt time; Δt is the state estimation frequency.

[0134] 7) When performing state estimation, if the current locomotive position sampling value has not been updated, the locomotive position at the current calculation moment is calculated by using the locomotive position information at the previous online power flow calculation moment and the locomotive speed information obtained from the previous sampling through formula (9), and then the synchronous update of the measurement equation is realized.

[0135] For the above online power flow calculation method of the flexible traction power supply system based on weighted least absolute value, the implementation of step 3 includes the following steps:

[0136] 1) The weighted least absolute value state estimation model is:

[0137]

[0138] In the formula, min represents taking the minimum value; w is the weight vector of the measurement z; ε is the residual vector.

[0139] 2) Introduce slack variables u, r:

[0140]

[0141] 3) Obtain the equivalent model of formula (10) as:

[0142]

[0143] For the above-mentioned online power flow calculation method of the flexible traction power supply system based on weighted least absolute value, the implementation of step 4 includes the following steps:

[0144] 1) Construct the Lagrangian function of formula (12):

[0145] L = w Τ (u + r) - λ Τ (z - h(x, l) + u - r) - α Τ u - β Τ r (13)

[0146] Where λ, α, and β are Lagrange multipliers.

[0147] 2) Take the optimal value according to the KKT conditions to obtain:

[0148]

[0149] L λ = z - h(x, l) + u - r = 0 (15)

[0150] L u = w - λ - α = 0 (16)

[0151] L r = w + λ - β = 0 (17)

[0152] L α = AUe = 0 (18)

[0153] L β = BRe = 0 (19)

[0154] Where A = diag(α); B = diag(β); U = diag(u); R = diag(r); e = [1, 1, …, 1] T .

[0155] 3) Introduce the perturbation parameter μ to relax formulas (18) and (19) to obtain:

[0156]

[0157] 4) Use the Newton method to solve formulas (14) to (17) and formula (20) to obtain:

[0158]

[0159] -dλ - dα = -L u (23)

[0160] dλ - dβ = -L r (24)

[0161]

[0162] From equations (23) and (24), we can obtain:

[0163] dα = L u -dλ (27)

[0164] dβ = L r +dλ (28)

[0165] 5) Substituting equations (27) and (28) into equations (25) and (26), we can obtain:

[0166]

[0167] 6) Substituting equations (29) and (30) into equation (22), we can obtain:

[0168]

[0169] S = A -1 U + B -1 R (31)

[0170]

[0171] From equations (21) and (31), we can obtain:

[0172]

[0173] 7) First, solve for dx and dλ from equation (32), and then solve for dα, dβ, du, and dr respectively through equations (27), (28), (29), and (30). After one iteration, correct the values of each variable, and then repeat the above steps until the convergence condition is met: α Τ u + β Τ r < 0.001.

[0174] 8) Save the estimated value of the node voltage U se .

[0175] For the above online power flow calculation method of the flexible traction power supply system based on weighted least absolute value, the implementation of step 5 includes the following steps:

[0176] 1) Substitute U se into equations (7) and (8) to calculate the node current and node power respectively.

[0177] 2) Calculate the active power loss:

[0178]

[0179] where n is the number of nodes and G is the branch admittance matrix.

[0180] 3) Save and output the online power flow calculation results.

[0181] Based on the above model and process design, this example conducts a test case simulation in the MATLAB environment. The modeling and solution process is shown in Figure 1 as follows.

[0182] According to an embodiment of the present invention, in order to further verify the effectiveness of the above online power flow calculation method for a flexible traction power supply system based on weighted least absolute value, the operation data of a certain subway line 13A (such as Figure 3 ) are used for simulation verification. The measurement errors and estimation errors of all node voltages are compared, and the results are shown in Table 1. The estimated results of the node voltages at traction substations and locomotives are shown in Figure 4 as follows. The root mean square error results of the power flow calculation are shown in Table 2.

[0183] Table 1 Results of measurement errors and estimation errors of node voltages

[0184]

[0185]

[0186] Analyzing the simulation results obtained from Table 1, Table 2 and Figure 4 it can be seen that: the online power flow calculation method for a flexible traction power supply system based on weighted least absolute value can obtain calculation results closer to the actual operating state of the system, and is applicable to engineering practice, verifying the effectiveness and practicality of the method of the present invention.

[0187] The main processes implemented by the method of the present invention include the establishment of a flexible traction power supply system, a state estimation and an online power flow mathematical model and its solution method.

[0188] The present invention establishes a traction power supply system circuit model based on the real-time positions of traction substations and locomotives, establishes a state estimation model based on the weighted least absolute value criterion, iteratively solves the model based on the primal-dual interior point algorithm to obtain the estimation results, and further conducts online power flow calculation to effectively obtain the real-time power flow distribution and energy flow situation of the traction power supply system.

[0189] The present invention also provides a computer-readable storage medium, on which computer program instructions that can be run by a processor are stored. When the processor runs the computer program instructions, the method steps as described in any of the above can be implemented.

[0190] This patent is not limited to the above-mentioned best implementation mode. Anyone inspired by this patent can come up with various other forms of online power flow calculation methods for flexible traction power supply systems based on weighted least absolute values. All equal changes and modifications made within the scope of the patent application according to this invention shall fall within the scope covered by this patent.

Claims

1. An online power flow calculation method for a flexible traction power supply system based on weighted least absolute value, characterized in that Including: Establish a circuit model of the traction power supply system according to the real-time position relationship between all traction substations and locomotives in the traction power supply system; Select state variables and measured variables and establish a measurement equation; Based on the estimation criterion of weighted least absolute value, establish a state estimation model for the flexible traction power supply system, and use the primal-dual interior point algorithm to iterate and solve to perceive the operating state of the system in real time; Based on the state estimation results, conduct on-line power flow calculation for the flexible traction power supply system.

2. The online power flow calculation method of a flexible traction power supply system based on weighted least absolute value according to claim 1, characterized in that, The method includes the following steps: Step S1: Establish a circuit topology model of the traction power supply system according to the quantity and position relationship between traction substations and locomotives in the traction power supply system; Step S2: Considering the problem that the locomotive position sampling frequency is not synchronized with the on-line power flow calculation frequency, determine the state variables and measured variables, and establish a measurement equation; Step S3: Considering the bad measurement data, establish a state estimation model for the flexible traction power supply system based on the estimation criterion of weighted least absolute value; Step S4: Solve the state estimation model based on the primal-dual interior point algorithm to perceive the operating state of the system in real time; Step S5: Based on the state estimation results, conduct on-line power flow calculation for the flexible traction power supply system to obtain the power flow distribution and energy flow situation of the whole network.

3. A method for online power flow calculation of a flexible traction power supply system based on weighted least absolute value according to claim 2, characterized in that The specific implementation of step S1 is as follows: Step S11: Obtain the position information of all traction substations and locomotives in the operating state in the traction power supply system; regard the position where the first traction substation in the up line is located as the initial position, and convert the positions of the remaining traction substations and locomotives into the relative positions with respect to the initial traction substation; Step S12: Split the up line and down line connected to the output port of the traction substation, and superimpose the position information of the down line on the total length of the up line, that is, the initial position of the down line is the relative position of the last traction substation; Step S13: Based on the relative positions of each traction substation and locomotive at the initial moment of on-line power flow calculation, number the traction substations and locomotives respectively to obtain unique index identifiers, and sort the traction substations and locomotives according to the position size to establish a topology model; Step S14: Regard the traction substation and the locomotive as power source nodes, and adjacent nodes divide the catenary and the rail into several sections, and each section of the catenary and the rail is regarded as a resistor; Step S15: Ignoring the influence of stray current and rail-to-ground conductance, combine the catenary resistance and the rail resistance to obtain the traction network circuit model.

4. A method for online power flow calculation of a flexible traction power supply system based on weighted least absolute value, characterized in that In step S14, for the catenary resistance and the rail resistance, the resistance value calculation formula is as follows: r hi ＝r c l i (1) r qi ＝r r l i (2) Wherein, r hi and r qi are respectively the resistance values of the i-th section of the catenary and the rail; r c and r r are respectively the unit resistance values of the catenary and the rail; l i is the length of the i-th section of the catenary and the rail, that is, the distance between adjacent nodes.

5. A method for online power flow calculation of a flexible traction power supply system based on weighted least absolute value according to claim 3, characterized in that The specific implementation of step S2 is as follows: Step S21: Construct the state quantity as: x = [U tss , U train T (3)​ where x is the state vector; U tss is the traction substation node voltage vector; U train is the locomotive node voltage vector; T is the transpose operator; Step S22: Construct the measured quantity as: z = [U tss , U train , I tss , I train , P tss , P train T (4)​ where z is the measurement vector; I tss and I train represent the traction substation and locomotive node current vectors respectively; P tss and P train represent the traction substation and locomotive node active power vectors respectively; The general form of the measurement equation is: z = h(x) + e (5) In the formula, h(·) is each measurement expression; e is a measurement error vector conforming to the normal distribution; Step S24: Since the relative position of the locomotive changes continuously during its operation, the resistance values of the catenary and the rail will change in real time. Reflected in the measurement equation (5), it is manifested that the nodal admittance matrix is a function of the locomotive position. Considering the time-varying influence of the locomotive position, equation (5) is transformed into: z = h(x, l) + e (6) In the formula, l is the distance vector between adjacent nodes; The specific form of the measurement equation is: I = Y(l)U (7) P = Y(l)U 2 (8) Wherein, Y is the nodal admittance matrix; U, I, and P are respectively the nodal voltage, nodal current, and nodal power of each traction substation and locomotive node; Step S26: The frequency of the online power flow calculation is in milliseconds. If the sampling period of the locomotive position and speed information is in seconds, it is necessary to prioritize synchronizing the update frequency of the locomotive position information with the online power flow calculation frequency; Using the position extrapolation method based on the motion equation, the locomotive motion equation is: m = m0 + v0Δt (9) Wherein, m0 and v0 are respectively the initial position and speed of the locomotive; m is the locomotive position after Δt time; Δt is the state estimation frequency; Step S27: When performing state estimation, if the current locomotive position sampling value has not been updated, then use the locomotive position information at the previous online power flow calculation moment and the locomotive speed information obtained from the previous sampling to calculate the locomotive position at the current calculation moment through Equation (9), thereby realizing the synchronous update of the measurement equation.

6. A method for on-line power flow calculation of a flexible traction power supply system based on weighted least absolute value, characterized in that, The specific implementation of Step S3 is as follows: Step S31: The weighted least absolute value state estimation model is: Wherein, min represents taking the minimum value; w is the weight vector of the measurement z; ε is the residual vector; Step S32: Introduce slack variables u, r: Step S33: Obtain the equivalent model of Equation (10) as:

7. A method for on-line power flow calculation of a flexible traction power supply system based on weighted least absolute value, characterized in that The specific implementation of Step S4 is as follows: Step S41: Construct the Lagrangian function of Equation (12): L = w Τ (u + r) - λ Τ (z - h(x, l) + u - r) - α Τ u - β Τ r (13) Wherein, λ, α, β are Lagrange multipliers; Step S42: Take the optimal value according to the KKT condition to obtain: L λ = z - h(x, l) + u - r = 0 (15) L u = w - λ - α = 0 (16) L r = w + λ - β = 0 (17) L α = AUe = 0 (18) L β = BRe = 0 (19) where \(A = \text{diag}(\alpha)\); \(B=\text{diag}(\beta)\); \(U = \text{diag}(u)\); \(R=\text{diag}(r)\); \(e = [1, 1, \ldots, 1]\) T ; Step S43: Introduce the perturbation parameter μ to relax Equations (18) and (19) to obtain: Step S44: Use the Newton method to solve Equations (14) to (17) and Equation (20) to obtain: -dλ - dα = -L u (23) dλ - dβ = -L r (24) From Equations (23) and (24), it can be obtained that: dα = L u -dλ (27) dβ = L r + dλ (28) Step S45: Substitute Equations (27) and (28) into Equations (25) and (26) to obtain: Step S46: Substitute Equations (29) and (30) into Equation (22) to obtain: From Equations (21) and (31), it can be obtained that: Step S47: First, solve dx and dλ from Equation (32), and then solve dα, dβ, du, and dr through Equations (27), (28), (29), and (30) respectively. After one iteration, correct the values of each variable, and repeat the iteration process until the convergence condition is met; Step S48, save the node voltage estimation value U se .

8. A method for online power flow calculation of a flexible traction power supply system based on weighted least absolute value, characterized in that In step S47, the convergence condition is: α Τ u + β Τ r < 0.

001.

9. A method for online power flow calculation of a flexible traction power supply system based on weighted least absolute value, characterized in that, The specific implementation of Step S5 is as follows: Step S51: Substitute U se into equations (7) and (8) to calculate the node current and node power respectively; Step S52: Calculate the active power loss: Wherein, n is the number of nodes, and G is the branch admittance matrix; Step S53: Save and output the online power flow calculation results.

10. A computer-readable storage medium, on which computer program instructions that can be run by a processor are stored. When the processor runs the computer program instructions, the method steps described in any one of Claims 1-9 can be implemented.

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