Through traction power supply system load flow calculation method based on current balance equation

Abstract

The invention discloses a through traction power supply system load flow calculation method based on a current balance equation. The method comprises the steps that connection points between through traction power supply system devices are set as nodes; according to the current balance equation of the node i about all the nodes of the system, the current unbalance amount of the node i about all the nodes of the system is obtained; expanding the current unbalance amount into a Taylor series expression expressed by a voltage amplitude U and a phase angle delta of a node i, and ignoring secondary and above components to obtain a current unbalance equation; constructing a voltage correction equation of the system according to the current imbalance equations of all nodes of the system; and carrying out multiple iterations until convergence by using the voltage correction equation to obtain a system power flow characteristic result. According to the method, the problem that a traditional power flow algorithm is difficult to converge due to large voltage deviation and strong nonlinearity of a through traction power supply system is effectively solved, and high-precision evaluation on energy consumption, electric energy quality and power supply capacity of a system which is not put into operation is realized.

Description

Technical Field

[0001] This invention relates to the field of traction power supply system technology, and in particular to a power flow calculation method for a through traction power supply system based on the current balance equation. Background Technology

[0002] With the development of electric locomotives towards high speed and heavy load, the problems faced by traditional single-sided phase-differentiated traction power supply systems are becoming increasingly prominent. (1) The use of single-sided power supply results in insufficient power supply capacity at the end of the traction network power supply arm, significant fluctuations in network voltage, and difficulty in meeting the power supply requirements for supporting high-power traction loads. (2) New AC-DC-AC type electric locomotives mostly adopt regenerative braking, which generates a large amount of regenerative braking energy during braking. In traditional single-sided phase-differentiated traction power supply systems, there is an insulation separation between the traction network power supply, resulting in a shorter power supply arm length and limited utilization of regenerative braking energy. A large amount of regenerative braking energy is returned to the power system, which not only causes a certain degree of impact on the power system but also causes economic losses to the railway sector. (3) Electric locomotives / train sets coast through electrical phase separation, resulting in power / speed losses. Especially when electrified railways in western mountainous areas pass through phase separation, the probability of train sets stopping on slopes is extremely high due to the influence of long gradients and tunnels, and rescue is difficult. (4) Traditional traction power supply systems draw power from the power system, resulting in a weak power supply network, a single source of power, and poor system resilience.

[0003] To address this, both domestic and international experts have proposed a through-type traction power supply system. This system involves multiple traction substations working together in a group to form a grid-like power supply structure. Furthermore, some through-type traction power supply system topologies incorporate energy storage devices and negative sequence compensation devices. This eliminates the need for phase separation along the entire line, removes the risk of trains stopping on slopes, significantly enhances the power supply capacity at the end of the power supply arm, substantially improves the efficiency of regenerative braking energy utilization, and reduces coal consumption.

[0004] The through-type traction power supply system is currently still in the theoretical verification stage and has not yet been put into actual operation. It is difficult to accurately assess its energy consumption, power quality, and power supply capacity through field measurement methods. There is an urgent need to rely on high-precision power flow calculation methods to support its performance analysis and engineering applicability assessment. However, in special application scenarios such as mountainous areas in western China, through-type traction power supply systems are usually characterized by long distances, large loads, and weak grid support, resulting in significant voltage deviations at traction load nodes. Traditional power flow algorithms based on linearization assumptions (such as DC power flow and linear approximation methods) suffer from severely deteriorated convergence due to sensitivity to initial conditions and neglect of nonlinear coupling, and may even be unable to solve the problem. Summary of the Invention

[0005] The purpose of this invention is to provide a robust power flow calculation method for a through-type traction power supply system, so as to overcome the convergence difficulties of existing methods under strong nonlinearity and large voltage offset conditions, thereby providing a reliable tool for accurate evaluation of the electrical characteristics of this new power supply system.

[0006] The technical solution for achieving the objective of this invention is as follows:

[0007] A power flow calculation method for a through-type traction power supply system based on the current balance equation includes the following steps:

[0008] The connection points between devices in the through-type traction power supply system are designated as nodes;

[0009] Based on the current balance equation of node i with respect to all nodes in the system, the current imbalance ΔM of node i with respect to all nodes in the system is obtained. i and ΔN i ; where ΔM i ΔN i Let i be the real and imaginary parts of the current imbalance; where i = 1, 2, ..., z, and z is the total number of system nodes.

[0010] ΔM i and ΔN i Expanding this into a Taylor series expression in terms of the voltage magnitude U and phase angle δ at node i, and neglecting second-order and higher-order components, we obtain ΔM. i and ΔN i The current imbalance equation;

[0011] Based on the current imbalance equations of all nodes in the system, construct the voltage correction equations for the system.

[0012] Set the initial values ​​of voltage and current for all nodes in the system. Using the voltage correction equation, iterate multiple times until the voltage amplitude correction ΔU and phase angle correction Δδ for all nodes converge, and obtain the voltage amplitude U and phase angle δ for all nodes.

[0013] Furthermore, if the system is a direct power supply, then the common access point (PCC) of the three-phase transformer, the connection point between the three-phase transformer and the AC bus, the connection point between the primary winding of the traction transformer and the AC bus, the connection point between the secondary winding of the traction transformer and the T-line, the connection point between the secondary winding of the traction transformer and the rail, the connection point between the feeder and the T-line, the connection point between the feeder and the uplink traction network, the connection point between the feeder and the downlink traction network, the connection point between the locomotive and the traction network, and the connection point between the locomotive and the rail are designated as nodes; if the system is an AT power supply, then the common access point (PCC) of the three-phase transformer, the connection point between the three-phase transformer and the AC bus, the connection point between the primary winding of the traction transformer and the AC bus, the connection point between the secondary winding of the traction transformer and the T-line, the connection point between the feeder and the uplink traction network, the connection point between the feeder and the downlink traction network, the connection point between the locomotive and the traction network, and the connection point between the locomotive and the rail are designated as nodes. The connection points of the current bus, the primary and AC bus of the traction transformer, the secondary and T-line of the traction transformer, the secondary and F-line of the traction transformer, the positive feeder and T-line, the positive feeder and the upward traction network, the positive feeder and the downward traction network, the negative feeder and F-line, the negative feeder and the upward traction network, the negative feeder and the downward traction network, the AT transformer and the upward traction network, the AT transformer and the downward traction network, the locomotive and the traction network, and the locomotive and the rail are designated as nodes.

[0014] Preferably, the current balance equation of node i with respect to all nodes in the system is:

[0015] ;

[0016] In the formula, , For real parts and imaginary parts, Let J be the voltage magnitude at node j. Let be the phase angle of node j; Let i be the mutual conductance between nodes i and j. Let be the mutual susceptance of nodes i and j; Let be the equivalent current phasor injected by the locomotive into node i when node i is the connection point between the locomotive and the traction network or the connection point between the locomotive and the rail. , For real parts and imaginary parts;

[0017] The current imbalance ΔM of node i with respect to all nodes in the system i and ΔN i ,as follows:

[0018] ;

[0019] In the formula, express , express If node i is not the connection point between the locomotive and the traction network or the connection point between the locomotive and the rail, then let m i =0, n i =0; , Let i be the active and reactive power of node i. , , If node i is the connection point between the locomotive and the traction network, then , Let i be the voltage amplitude and phase angle at the connection point between the locomotive and the rail, i.e., node i+r; if node i is the connection point between the locomotive and the rail, then , The voltage amplitude and phase angle at the connection point between the locomotive and the traction network, i.e., node i+r;

[0020] The ΔM i and ΔN i The current imbalance equation is:

[0021] ;

[0022] In the formula, , For the voltage magnitude and phase angle correction at node j;

[0023] The current imbalance equations for all nodes in the system are as follows:

[0024] ,

[0025] Right now

[0026] ;

[0027] The voltage correction equation for the system is:

[0028] ;

[0029] In the formula, k is the number of iterations.

[0030] Preferably, the mutual conductance of nodes i and j mutual susceptance Based on the mutual admittance of nodes i and j To obtain, that is The mutual admittance Based on the equivalent nodal admittance matrix of the PCC point of the system traction transformer node admittance matrix and the admittance matrix of the traction network nodes get;

[0031] The admittance matrix of the traction network node

[0032] ;

[0033] In the formula, Z1 is the equivalent admittance matrix of traction network section 1, Z2 is the transmission line impedance matrix between traction network section 1 and section 2, and so on.

[0034] If the traction power supply system is direct, the traction network section is obtained by dividing it according to the connection point between the traction substation and the traction network, and the connection point between the locomotive and the traction network.

[0035] If the traction power supply system is AT power supply, then the traction network section is obtained by dividing it according to the connection point between the traction substation and the traction network, the connection point between the AT transformer and the traction network, and the connection point between the locomotive and the traction network.

[0036] Compared with the prior art, the beneficial effect of the present invention is that it effectively solves the problem of the difficulty in convergence of traditional power flow algorithms caused by large voltage deviation and strong nonlinearity in through traction power supply systems, so as to achieve high-precision evaluation of energy consumption, power quality and power supply capacity of unoperated systems. Attached Figure Description

[0037] Figure 1 A schematic diagram of the overall structure of the traction power supply system.

[0038] Figure 2 A schematic diagram of the equivalent chain-like structure of the traction power supply system.

[0039] Figure 3 A schematic diagram for constructing the admittance matrix of the nodes in the traction power supply system.

[0040] Figure 4 This is a flowchart of the overall power flow calculation method. Detailed Implementation

[0041] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and specific examples.

[0042] like Figure 1 As shown, the overall structure of the traction power supply system includes an external power source, high-voltage transmission lines, a group of traction substations, and a traction network.

[0043] 1) External power source: The external power source is drawn from the power system and mainly consists of power plants, substations, transmission lines and other components, providing energy for the traction power supply system.

[0044] 2) High-voltage transmission line: The high-voltage transmission line is mainly composed of three-phase overhead transmission lines, which connect the external power supply to the PCC point of the traction power supply system and to each traction substation of the traction power supply system;

[0045] 3) Traction Substation Group: Define n (n≥2) traction substations as a traction substation group. Each traction substation in the group is supplied with power from the same two phases of the three-phase power system from the same substation (main substation). Each traction substation in the group uses a single-phase transformer or a secondary-side midpoint withdrawable single-phase transformer. Therefore, the corresponding traction network phases within the group are the same, eliminating the need for phase separation at substation outlets and section locations, thus achieving continuous power supply within the group.

[0046] 4) Traction network: The traction network consists of more than 10 conductors, including the up and down catenary, contact wire, return wire, ground wire, rail, and protection wire. It is connected to the secondary side of the traction transformer through feeder lines to provide direct power supply to locomotives whose positions are constantly changing.

[0047] Figure 2 The diagram shows the equivalent chain circuit of the traction network. For the traction network, locomotives, AT transformers, and substations are used as sections for segmentation. The π-type equivalent circuit of transmission lines is used to integrate these sections, achieving a mathematical modeling equivalent of the traction network. Wherein, I... k (k=1,2,…,n) represents the equivalent current source of the cross section k, Y k (k=1,2,…,n) denotes the equivalent admittance matrix of the k-section, Z k (k=1,2,…,n) represents the transmission line impedance matrix between section k and section k+1.

[0048] Figure 3 The diagram shows the construction of the overall system node admittance matrix. PCC represents the common access point of the traction power supply system to the external power grid, and its corresponding admittance matrix is ​​Y. GS ; TSSn (n=1,2,3) represents substation n, and the corresponding admittance matrix is ​​Y TS ;Y NET correspond Figure 2 The equivalent circuit of the traction network chain is represented by its node admittance matrix, where Mn (n=1,2,…) represents each cross section; HLn (n=1,2,3) represents the high-voltage transmission line between PCC point and TSSn; and Nn represents the connecting cable between the nth substation and the traction network.

[0049] Example:

[0050] The power flow calculation method for a through-type traction power supply system based on the current balance equation includes the following steps:

[0051] Step 1: Compile data on the power supply system and traction load of the traction substation group. Power supply system data includes external power source and transmission line parameters, traction substation group and feeder parameters, and traction network parameters; traction load data includes locomotive number, location, up / down direction, active power, and reactive power.

[0052] Step 2: Based on the traction network parameters and the locomotive position at the current moment, establish a dynamic mathematical model of the traction network and a dynamic mathematical model of the traction substation group's through power supply system, and respectively form the traction network node admittance matrix, the traction substation node admittance matrix, and the PCC point equivalent node admittance matrix.

[0053] Wherein, the PCC point equivalent nodal admittance matrix ,

[0054]

[0055] In the formula, y SA y SB y SC These are the three-phase equivalent admittances at the PCC point, respectively.

[0056] Traction transformer node admittance matrix ,

[0057]

[0058] The system topology in this invention considers bilateral power supply. No phase separation is implemented between adjacent substations or at the outlets of each traction substation to achieve continuous operation of the entire traction network. A chain circuit is used to model the entire traction network. The transverse connections in the traction network (such as locomotives, parallel lines, feeders, and connection points with the traction network) are considered as different cross-sections, while the longitudinal connections mainly consist of the traction network conductors between these cross-sections. The simplified overall network is as follows: Figure 2 As shown, the nodal admittance matrix is ​​as follows: As shown.

[0059]

[0060] Taking the first cross-section under AT power supply mode as an example, the explanations of Y1 and Z1 are given.

[0061]

[0062] In the formula, the subscripts T, R, and F represent the positive feeder, rail, and negative feeder, respectively, and u and d represent the up and down directions, respectively. 12 This indicates the length of the line between sections 1 and 2. (V,W=Tu, Fu, R, Td, Fd, V≠W) represents the mutual impedance per unit length between lines V and W. (V=Tu, Fu, R, Td, Fd) represents the line's self-impedance per unit length.

[0063]

[0064] In the formula, the subscript indicates the expression. Similarly, but the corresponding y represents the self-impedance and mutual impedance of the corresponding node at that node.

[0065] Step 3: Set the initial values ​​of voltage and current at each node of the system.

[0066] If the traction network adopts a direct power supply method, then the external power supply, traction transformer, and initial voltage matrix of the traction network section are respectively...

[0067]

[0068] If the traction network adopts AT power supply, the initial voltage of the external power supply is the same as that of the direct power supply, and the initial voltages of the traction transformer and each section of the traction network are the same. and They are respectively

[0069]

[0070] If the traction network has n cross sections, then the initial node voltage matrix of the system is represented as follows:

[0071]

[0072] The initial system current matrix is ​​as follows

[0073]

[0074] In the formula, Let m be the current matrix injected into the system by the h-th locomotive, and m be the number of locomotives at the current moment.

[0075] The locomotive's injected current matrix differs depending on its direction of travel and the power supply method of the traction network. Specifically:

[0076]

[0077] Step 4: Initialize the number of iterations to k=0.

[0078] Step 5: Write the current balance equation.

[0079] According to Kirchhoff's Law (the algebraic sum of currents flowing into or out of a node is zero), the current balance equations for all nodes in the through-type traction system are as follows:

[0080]

[0081] In the formula, z represents the number of system nodes; i and j are node numbers; Let J be the node voltage at node j; Let i be the mutual admittance of nodes i and j; Inject current into node i to the traction load (i.e., the locomotive). If there is no traction load at node i, Then it is 0.

[0082] Record 'r' is the difference between the rail node number (the connection point between the locomotive and the rail) and the contact wire node number (the connection point between the locomotive and the traction network) at the cross-section formed by the locomotive segmentation. The equivalent current phasor injected by the locomotive at node i is...

[0083]

[0084] make , , Substitution The locomotive current injected at node i is obtained as follows:

[0085]

[0086] In the formula: , , .

[0087] Step 6: Construct the voltage correction equation.

[0088] Joint Japanese style ,make , , Thus, the current balance equations for any node with respect to the real and imaginary parts can be obtained as follows:

[0089]

[0090] Mode In the middle, the node voltage amplitude U j and phase δ j All are unknowns, not true solutions, M i and N i The value is not zero, therefore it will generate current imbalance ΔM with respect to the real and imaginary parts respectively. i and ΔN i If the node is a locomotive node, then it is...

[0091]

[0092] If the node is not a locomotive node, then its current imbalance ΔM i and ΔN i In the formula Based on this, let m i =0, n i =0 is sufficient.

[0093] The current imbalance ΔM i and ΔN i Expanding this into a Taylor series expression in terms of magnitude U and phase angle δ, and neglecting second-order and higher-order components, we have:

[0094]

[0095] For nodes i = 1, 2, ..., z, the following formulas can be written: The current imbalance equation shown can be written in matrix form as follows:

[0096]

[0097] Abbreviated as

[0098]

[0099] In the formula, k is the number of iterations; , , , , , , and Together they form the Jacobian matrix ; It is the voltage correction matrix to be determined; For formula The current imbalance matrix is ​​calculated based on the voltage obtained from the k-th iteration.

[0100] For any i and j, I ij O ij L ij and K ij It can be represented as

[0101]

[0102] Finally, the Jacobian matrix required for the k-th iteration is formed. and current imbalance and .

[0103] Step 7: Iteratively update node voltages.

[0104] Utilization The node voltage correction amount is obtained from the voltage correction equation shown. The node voltage can then be iteratively updated. The node voltage update calculation formula is as follows:

[0105]

[0106] when and When the iteration reaches convergence, it is considered to have reached convergence, and the convergence index ε is generally taken as 10. -3 ~10 -5 Through form After iterating until the node voltages converge, the power of each node and branch can be calculated to obtain the system power flow characteristics.

Claims

1. A method for power flow calculation of a through-train power supply system based on current balance equations, characterized in that, The method comprises the steps of: Setting the connection points between the through traction power supply system equipment as nodes; According to the current balance equation of node i about all nodes of the system, the current imbalance amount ΔM of node i about all nodes of the system is obtained i and ΔN i ; wherein, ΔM i , ΔN i are the real part and the imaginary part of the current imbalance amount; wherein, i = 1, 2, … z, z is the total number of system nodes; The ΔM i and ΔN i are expanded into Taylor series expressions represented by the voltage amplitude U and phase angle δ of node i, and the second and higher order components are ignored, to obtain the current imbalance equations of ΔM i and ΔN i ; Building a voltage correction equation of the system according to current imbalance equations of all nodes of the system; Setting initial values of voltage and current of all nodes of the system, and using the voltage correction equation to iterate until the voltage amplitude correction amount ΔU and the phase angle correction amount Δδ of all nodes converge, so as to obtain the voltage amplitude U and the phase angle δ of all nodes.

2. The power flow calculation method according to claim 1, wherein: If the system is direct supply, the public access point PCC of the three-phase transformer, the connection point between the three-phase transformer and the AC bus, the connection point between the primary of the traction transformer and the AC bus, the connection point between the secondary of the traction transformer and the T line, the connection point between the secondary of the traction transformer and the rail, the connection point between the feeder and the T line, the connection point between the feeder and the uplink traction network, the connection point between the feeder and the downlink traction network, the connection point between the locomotive and the traction network, and the connection point between the locomotive and the rail are set as nodes; If the system is AT power supply, the public access point PCC of the three-phase transformer, the connection point between the three-phase transformer and the AC bus, the connection point between the primary of the traction transformer and the AC bus, the connection point between the secondary of the traction transformer and the T line, the connection point between the secondary of the traction transformer and the F line, the connection point between the positive feeder and the T line, the connection point between the positive feeder and the uplink traction network, the connection point between the positive feeder and the downlink traction network, the connection point between the negative feeder and the F line, the connection point between the negative feeder and the uplink traction network, the connection point between the negative feeder and the downlink traction network, the connection point between the AT transformer and the uplink traction network, the connection point between the AT transformer and the downlink traction network, the connection point between the locomotive and the traction network, and the connection point between the locomotive and the rail are set as nodes.

3. The method of claim 2, wherein, The current balance equation of the node i with respect to all nodes of the system is: ； wherein , are real and imaginary parts, is the voltage magnitude of node j, is the phase angle of node j; is the mutual conductance of nodes i and j, is the mutual susceptance of nodes i and j; is the equivalent current phasor injected by the locomotive into node i when node i is the connection point of the locomotive and the traction network or the connection point of the locomotive and the steel rail, , are real and imaginary parts; the current imbalance amount AM of the node i with respect to all nodes of the system i and ΔN i as follows: ； wherein represents , represents , if node i is not a connection point of the locomotive to the traction network or a connection point of the locomotive to the steel rail, then let m i = 0, n i = 0; , is the active and reactive power of node i; , , ; if node i is a connection point of the locomotive to the traction network, then , is the voltage amplitude and phase angle of the connection point of the locomotive to the steel rail, i.e. node i+r; if node i is a connection point of the locomotive to the steel rail, then , is the voltage amplitude and phase angle of the connection point of the locomotive to the traction network, i.e. node i+r; The ΔM i and ΔN i The current imbalance equation is: ； wherein , is the voltage amplitude, phase angle correction for node j; The current imbalance equation of all nodes of the system is: ， That is, ； The voltage correction equation of the system is: ； In the formula, k is the iteration number.

4. The method of claim 3, wherein, The mutual conductance of the nodes i and j The mutual susceptance The mutual admittance of the nodes i and j , that is The mutual admittance The equivalent node admittance matrix of the system PCC point The traction transformer node admittance matrix And the traction network node admittance matrix ​ The traction network node admittance matrix ； wherein Z1is the transmission line impedance matrix between the cut 1 and the cut 2, and so on. If the traction power supply system is direct supply, the traction network section is obtained according to the connection point between the traction substation and the traction network and the connection point between the locomotive and the traction network; If the traction power supply system is AT power supply, the traction network section is obtained according to the connection point between the traction substation and the traction network, the connection point between the AT transformer and the traction network, and the connection point between the locomotive and the traction network.

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