CN113204888B - Contact line-steel rail equivalent method - Google Patents
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Abstract
The invention discloses a contact line-steel rail equivalent method, which relates to the field of traction power supply and comprises the steps of selecting contact lines and steel rail models, determining the self-impedance of a unit length contact line and a steel rail under power frequency, determining the mutual impedance between the contact lines and the steel rail, determining the capacitance to ground of the contact line and the steel rail, constructing a contact line-steel rail coupling circuit model, performing controlled source decoupling, writing KVL and KCL in a column to solve a port voltage-current relation, equivalently changing the unit length contact line-steel rail into a two-port model by using transmission parameters, and performing two-port cascade according to the line length. According to the invention, the decoupling of the contact line and the steel rail is realized through the controlled voltage source controlled by current, the coupling relation of the contact line and the steel rail can be accurately reflected, the two-port model is conveniently associated with other parts of a traction power supply system, and parameters obtained after cascading are used for load flow calculation, so that the number of nodes can be effectively reduced, the system scale is reduced, and the load flow can be solved.
Description
Technical Field
The invention belongs to the technical field of traction power supply of electrified railways, and particularly relates to a contact line-steel rail equivalent method.
Background
With the high-speed development of the electrified railway in China and the deep research of the country on the traction power supply system, the accurate establishment of the equivalent model of each part in the traction power supply system is beneficial to the analysis of the distribution characteristics of each electric quantity in the system. The contact line and the steel rail are indispensable links in a traction power supply system, and have the functions of transmitting electric energy and bearing the running of an electric locomotive. When traction current flows through the contact line and the steel rail, corresponding induced voltage is generated on the two lines, and the induced voltage has certain influence on the current distribution on the lines, so that accurate decoupling and equivalence of the contact line and the steel rail are very necessary.
At present, a lumped parameter equivalent or chain circuit model is generally adopted for a model or an equivalent method of a traction power supply system, and for the lumped parameter model: when the contact net is equivalent to the steel rail, the current of the contact line and the current of the steel rail in the same section are considered to be equal, the influence of the decoupling process on the induction voltage is not considered, and the distributed capacitance is not considered; for the chain circuit model, although the influence of mutual impedance and distributed capacitance is considered, the model is in a chain shape, and as the length of a line is increased, an admittance matrix is very large and is not beneficial to solving. Therefore, an equivalent model which accurately reflects the coupling relationship between the contact line and the steel rail and is beneficial to solving the power flow of each line in the traction power supply system is needed.
Disclosure of Invention
Aiming at the problems, the invention provides a contact line-steel rail equivalent method in order to accurately reflect the coupling relation between a contact line and a steel rail in a traction power supply system and facilitate the solution in load flow calculation.
The invention provides a two-port equivalent model aiming at accurately decoupling the coupling action of a contact line and a steel rail in a traction power supply system, considering distributed capacitance and solving the problems of large system scale and more nodes in load flow calculation.
The technical scheme of the invention is as follows:
a contact line-rail equivalent method comprising the steps of:
s1, determining the self-impedance of the contact line and the steel rail in unit length according to the types of the contact line and the steel rail, specifically:
calculating the self-impedance Z of the unit length contact line under the power frequency according to the following formulaT：
Wherein r is1Effective resistance per unit length of contact line, DgFor equivalent depth of wire-ground loop, Rε1Is the contact line equivalent radius; similarly calculating self-impedance Z of unit length steel rail under power frequencyR；
S2, determining the mutual impedance Z between the contact line of unit length and the steel railM：
Wherein d is12The distance between the contact line and the steel rail;
s3, determining the contact line of unit length and the ground admittance of the steel rail, specifically:
calculating the contact line to ground admittance Y under power frequency according to the following formulaT：
YT＝j2πfCT
Wherein f is 50Hz power frequency, CTIs the contact line to ground capacitance; calculating the ground admittance of the contact line in unit length in the same way;
s4, constructing a unit length contact line-steel rail coupling circuit model, decoupling the circuit, and writing KVL and KCL equations in parallel:
wherein the content of the first and second substances,
the potential at the point A is shown as the potential at the point A,
the potential of the point B is shown as the potential of the point B,
is the potential of the point C, and the potential of the point C,
the potential of the point D is shown as the potential of the point D,
for the purpose of inputting a current to the contact line,
in order to output a current for the contact line,
for flowing through contact line self-impedance ZTThe current of (a) is measured,
for flow through self-impedance Z of railRThe port voltage-current relational expression is obtained after solving:
wherein the content of the first and second substances,
for the input port voltage to be the input port voltage,
is the output port voltage, Z11、Z12、Z21、Z21Is determined by the following formula:
wherein a ═ YT/2，b＝YR/2，c＝1/ZT，d＝1/ZRUsed for simplifying the formula and converting the formula into T parameter to obtain
And
transmission parameter equation of (2):
wherein A, B, C, D is a transmission parameter, and is determined by the following formula:
wherein det (Z) represents the determinant of the impedance parameter Z matrix;
s5, utilizing the T parameter to make the unit length contact line-steel rail equivalent to a two-port model;
s6, performing two-port cascade according to the line length, realizing equivalent contact line-steel rail distribution parameters by using the two-port cascade to achieve the purposes of reducing the number of nodes and reducing the system scale, establishing contact with a transformer and an electric locomotive in a traction power supply system during load flow calculation, and obtaining a transmission parameter matrix T after cascadeLDetermined by the following formula:
where L is the line length in km.
Further, in step S4, the decoupling method adopted when the contact line-rail coupling circuit model per unit length decouples the circuit is controlled source decoupling.
The invention has the beneficial effects that: the invention provides a two-port equivalent model after decoupling a contact line and a steel rail, which is a solution method for providing parameters of voltage, current and T of a two-port network port by realizing the decoupling of the contact line and the steel rail through a controlled voltage source controlled by current. The model is convenient to be connected with other parts of a traction power supply system, transmission parameters obtained after two port models are cascaded are used for load flow calculation, the number of nodes can be effectively reduced, the system scale is reduced, and the load flow calculation is facilitated.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a model diagram of a contact line-rail coupling circuit per unit length according to the present invention.
FIG. 3 is a model diagram of a unit length contact line-rail decoupling circuit according to the present invention.
FIG. 4 is an equivalent model diagram of a unit length contact line-rail two end openings according to the present invention.
Fig. 5 is a schematic view of a topology structure of a cable through power supply system in the traction power supply system according to the present invention.
Fig. 6 is an equivalent circuit model diagram of the cable through power supply system according to the present invention.
Detailed Description
The technical scheme of the invention is described in detail below with reference to the accompanying drawings and embodiments:
as shown in fig. 1, the present invention comprises the steps of:
the first step is as follows: selecting the contact line model and the steel rail model, and determining the self-impedance of the contact line in unit length and the self-impedance of the steel rail in unit length;
the method for determining the self-impedance of the contact line with unit length comprises the following steps:
establishing a Carson equivalent circuit by using the Carson theory, and calculating the self-impedance Z of the unit-length contact line under the power frequencyT：
In the formula, r1Effective resistance per unit length of contact line, DgFor equivalent depth of wire-ground loop, Rε1Is the contact line equivalent radius;
the method for determining the self-impedance of the steel rail in unit length comprises the following steps:
method for calculating self-impedance Z of unit-length steel rail under power frequency by using Carson theoryRThe method is the same as the method for determining the self-impedance of the contact line per unit length.
The second step is that: determining the mutual impedance between the contact line of unit length and the steel rail;
the method for determining the contact line-steel rail mutual impedance in unit length comprises the following steps:
calculating the mutual impedance Z between the contact net and the steel rail under power frequency by using the formula (2)M：
In the formula, DgFor equivalent depth of wire-ground loop, d12Is the distance between the contact line and the rail.
The third step: determining a contact line of unit length and the ground admittance of the steel rail;
the method for determining the ground admittance of the contact line with unit length comprises the following steps:
calculation of contact line to ground admittance Y at Power frequency Using equation (3)T：
YT＝j2πfCT (3)
Wherein f is power frequency, 50Hz, CTIs the contact line to ground capacitance;
the determined unit length of steel rail is admittance to ground YRThe method of (3) is the same as determining the contact line to ground admittance per unit length.
The fourth step: constructing a contact line-steel rail coupling circuit model with unit length, decoupling the circuit and writing KVL and KCL equations in parallel as shown in figure 2, and solving a port voltage and current relational expression;
(1) column write KVL, KCL equation:
in the formula (I), the compound is shown in the specification,
the potential at the point A is shown as the potential at the point A,
the potential of the point B is shown as the potential of the point B,
is the potential of the point C, and the potential of the point C,
is the potential of point D; for writing convenience and simplifying the formula, let: a ═ YT/2，b＝YR/2，c＝1/ZT，d＝1/ZR；
(2) Solving the formula (4) to obtain a port voltage and current relational expression:
in the formula (I), the compound is shown in the specification,
for the input port voltage to be the input port voltage,
in order to output the port voltage,
for the purpose of inputting a current to the contact line,
outputting current for the contact line; z11、Z12、Z21、Z21Is determined by the following formula:
(3) converting formula (6) to the T parameter to obtain
And
transmission parameter equation of (2):
where A, B, C, D is a transmission parameter, determined by:
wherein det (Z) represents a determinant of a matrix of impedance parameters Z;
the fifth step: the unit length contact line-rail equivalent is a two-port model using the T parameter, as shown in fig. 4.
And a sixth step: two-port cascade is carried out according to the line length, the two-port cascade is used for realizing the equivalence of contact line-steel rail distribution parameters, the purposes of reducing the number of nodes and reducing the system scale are achieved, the two-port cascade is used for establishing contact with a transformer and an electric locomotive in a traction power supply system during load flow calculation, and a transmission parameter matrix T is obtained after cascadeLDetermined by the following formula:
where L is the line length in km.
In the method, the decoupling method is controlled source decoupling when the single-length contact line-steel rail coupling circuit model is decoupled in the fourth step, as shown in fig. 3.
Example (b):
as shown in fig. 5, the figure is a schematic diagram of a topological structure of a cable through power supply system comprising two short loops, an external power supply of the system is provided by a 220kV public power grid, the external power supply is reduced to 110kV by a central substation and is connected to a cable traction network, three traction transformers, cables, a contact network and steel rails form two short loops, and the transformation ratios of the transformers are all 110/27.5; the 110kV single-phase voltage is reduced to 27.5kV by a traction transformer and then sent into a contact net, the lengths of a left short loop and a right short loop are respectively 25km and 30km, a left short loop train is located at a position 10km away from a No. 1 traction transformer, a right short loop train is located at a position 15km away from a No. 2 transformer, two locomotives simulate the condition of constant power, P is 20MW, and the power factor is 0.98.
FIG. 6 is a schematic diagram of an equivalent circuit model of a cable feed-through power supply system, in which an external power source and a central substation are equivalent to a voltage source series system impedance and a power source voltage USIs 110 & lt 0 degree kV, and the system impedance ZS0.1598+ j5.6344 Ω; cable andthe traction transformer is two-port equivalent, after the contact line-steel rail is converted into unit length two-port by using the above-mentioned equivalent method, they are cascaded according to specific length, Ic1、Ic2Respectively taking flows from two locomotives.
Example contact line-rail parameters were set as follows:
self-impedance per unit length of contact line ZT＝0.117+j0.581Ω；
Self-impedance per unit length of rail ZR＝0.091+j0.465Ω；
Mutual impedance Z between contact net and steel railM＝0.05+j0.339Ω；
Contact line to ground admittance YT＝j3.59×10-6s；
Rail ground admittance YR＝j5.09×10-6s；
The T parameters of the contact net-steel rail two ports in unit length are as follows:
two-port transmission parameter matrix T after cascade connection of contact lines and steel rails according to line length from left to right in FIG. 6LRespectively as follows:
after the power flow calculation, the effective values of the voltages of the input ends of the traction transformers are 109.72kV, 110.07kV and 109.82kV respectively, the effective value of the output current of the traction transformer No. 1 is 477.90A, the effective value of the output current of the traction transformer No. 2 is 673.34A, the output current of the traction transformer No. 3 is 412.32A, the voltages of the two locomotive ends are 26.21kV and 25.99kV respectively, the current taking values are 778.55A and 785.25A respectively, and the obtained data accurately reflect the power flow of each line of the system.
Claims (2)
1. A contact line-rail equivalent method, comprising the steps of:
s1, determining the self-impedance of the contact line and the steel rail in unit length according to the types of the contact line and the steel rail, specifically:
calculating the self-impedance Z of the unit length contact line under the power frequency according to the following formulaT：
Wherein r is1Effective resistance per unit length of contact line, DgFor equivalent depth of wire-ground loop, Rε1Is the contact line equivalent radius; similarly calculating self-impedance Z of unit length steel rail under power frequencyR；
S2, determining the mutual impedance Z between the contact line of unit length and the steel railM：
Wherein d is12The distance between the contact line and the steel rail;
s3, determining the contact line of unit length and the ground admittance of the steel rail, specifically:
calculating the contact line to ground admittance Y under power frequency according to the following formulaT：
YT＝j2πfCT
Wherein f is 50Hz power frequency, CTIs the contact line to ground capacitance; in the same wayCalculating the ground admittance Y of the unit length railR；
S4, constructing a unit length contact line-steel rail coupling circuit model, decoupling the circuit, and writing KVL and KCL equations in parallel:
wherein the content of the first and second substances,
the potential at the point A is shown as the potential at the point A,
the potential of the point B is shown as the potential of the point B,
is the potential of the point C, and the potential of the point C,
the potential of the point D is shown as the potential of the point D,
for the purpose of inputting a current to the contact line,
in order to output a current for the contact line,
for flowing through contact line self-impedance ZTThe current of (a) is measured,
for flow through self-impedance Z of railRThe port voltage-current relational expression is obtained after solving:
wherein the content of the first and second substances,
for the input port voltage to be the input port voltage,
is the output port voltage, Z11、Z12、Z21、Z21Is determined by the following formula:
wherein a ═ YT/2，b＝YR/2，c＝1/ZT，d＝1/ZRUsed for simplifying the formula and converting the formula into T parameter to obtain
And
transmission parameter equation of (2):
wherein A, B, C, D is a transmission parameter, and is determined by the following formula:
wherein det (Z) represents the determinant of the impedance parameter Z matrix;
s5, utilizing the T parameter to make the unit length contact line-steel rail equivalent to a two-port model;
s6, performing two-port cascade according to the line length, and realizing the contact line-steel rail by using the two-port cascadeEquivalence of distribution parameters is used for establishing connection with a transformer and an electric locomotive in a traction power supply system during load flow calculation, and a transmission parameter matrix T is obtained after cascadingLDetermined by the following formula:
where L is the line length in km.
2. The contact line-rail equivalent method as claimed in claim 1, wherein the decoupling method adopted when the contact line-rail coupling circuit model per unit length decouples the circuit in step S4 is controlled source decoupling.
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| CN114824846B (en) * | 2022-05-19 | 2022-12-02 | 湖南经研电力设计有限公司 | Short conductor-based power transmission pole tower grounding method |
| CN116388186B (en) * | 2023-06-06 | 2023-08-25 | 清华大学 | Tidal current calculation method, device, equipment and medium of alternating current traction power supply system |
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