CN111709103A - Multi-conductor loop method-based traction network chain type parameter model with return line direct power supply mode - Google Patents

Multi-conductor loop method-based traction network chain type parameter model with return line direct power supply mode Download PDF

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CN111709103A
CN111709103A CN202010417076.XA CN202010417076A CN111709103A CN 111709103 A CN111709103 A CN 111709103A CN 202010417076 A CN202010417076 A CN 202010417076A CN 111709103 A CN111709103 A CN 111709103A
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邓云川
鲁小兵
李良威
袁勇
李剑
智慧
林忠良
陈勇
刘孟恺
吴萍
陈殷
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Abstract

A traction network chain type parameter model with a return line direct power supply mode based on a multi-conductor loop method is used for overcoming the problem that a traditional traction network model taking the ground as a reference is easily misunderstood as a return channel of all conductors of the ground. The method comprises the following steps: constructing a loop; calculating comprehensive impedance; calculating the comprehensive capacitance; deducing a multi-conductor transmission line equation; and deducing and solving a multi-conductor transmission line chain parameter equation matrix, regarding the multi-conductor transmission line system as a dual-port model, deducing the dual-port chain parameter equation matrix, substituting the multi-conductor transmission line equation obtained in the previous step into the chain parameter equation matrix and solving, and finally establishing a chain parameter model of the traction network with the return line in a direct power supply mode.

Description

Multi-conductor loop method-based traction network chain type parameter model with return line direct power supply mode
Technical Field
The invention relates to a traction power supply system of an electrified railway, in particular to a chain type parameter model based on a multi-conductor loop method, which is applied to a traction network of an electrified railway with a return line direct power supply mode.
Background
With the development of electrified railways in China and the implementation of a strategy of 'high-speed rail going out', the basic theory research of the electrified railway traction power supply system is more and more urgent, and the accurate traction network mathematical description and the electric parameter calculation are the basis of multiple researches, including a traction network chain type parameter model. In the traction network of the electrified railway, the direct power supply mode with the return line is widely applied to field practice, but the direct power supply mode consists of a plurality of conductors such as a contact line, a carrier cable, the return line, a steel rail and the like, and the physical structure and the electromagnetic field relation are very complex, so that the calculation and modeling of related parameters are very difficult. In the past mathematical models of the traction network based on the theory of multi-conductor transmission lines, the ground is generally regarded as a reference conductor and is easily misinterpreted as the ground being a return channel of all conductors. In fact, the steel rail, the return line, the through ground wire and the like can be used as a return channel, and therefore, considering the ground as a reference conductor brings many limitations to the description of the traction network as a complex multi-conductor transmission line system.
Disclosure of Invention
The invention aims to solve the technical problem of providing a traction network chain type parameter model based on a multi-conductor loop method and adopting a direct power supply mode with a return line, so as to overcome the problem that the traditional traction network model taking the ground as a reference is easily misunderstood as the return channel of all conductors, so that the model conforms to the actual situation and the calculation process is simpler and clearer.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention relates to a traction network chain type parameter model with a return line direct power supply mode based on a multi-conductor loop method, which comprises the following steps of:
(1) constructing a loop, and classifying conductors in a traction network in a direct power supply mode with a return line according to transmission conductors and return conductors, namely converting the system into a multi-transmission-conductor multi-return-conductor loop system consisting of 2 transmission conductors and 5 return conductors;
(2) calculating comprehensive impedance, deducing self-inductance coefficients in the loops and mutual inductance coefficients among the loops based on space magnetic field analysis according to the constructed loops, and constructing inductance coefficient matrixes of the loops; deducing a resistance matrix of unit length of each loop, and further constructing an impedance matrix of unit length of each loop; finally, on the basis of the impedance matrix of the traction network in unit length, obtaining the comprehensive equivalent impedance of the system in unit length;
(3) calculating the comprehensive capacitance, deducing an intra-loop self-potential coefficient and an inter-loop mutual potential coefficient according to the constructed loop, constructing a potential coefficient matrix to obtain a unit length capacitance matrix of each loop, and finally obtaining the unit length comprehensive capacitance of the traction network with the return line in the direct power supply mode by combining the relationship between the charge and the voltage of each loop;
(4) deducing a multi-conductor transmission line equation, according to the equivalent circuit of the multi-conductor transmission line system, combining a voltage equation and a current equation, deducing the multi-conductor transmission line equation, and solving a general solution of the equation by taking an excitation source as a single-frequency sinusoidal signal;
(5) and deducing and solving a multi-conductor transmission line chain parameter equation matrix, regarding the multi-conductor transmission line system as a dual-port model, deducing the dual-port chain parameter equation matrix, substituting the multi-conductor transmission line equation obtained in the previous step into the chain parameter equation matrix and solving, and finally establishing a chain parameter model of the traction network with the return line in a direct power supply mode.
The invention has the advantages that the traction network chain type parameter model based on the loop method of the multi-conductor transmission line system conforms to the actual situation, the problem that the traditional traction network model taking the ground as the reference is easily misunderstood as the return channel of all conductors is avoided, and the calculation process is simpler and clearer.
Drawings
The specification includes the following four figures:
fig. 1 is a schematic system structure diagram of a traction network with a return line and a direct power supply mode.
Fig. 2 is a schematic diagram of transmission and return conductors of a traction network with return lines for direct power.
Fig. 3 is a chain equivalent circuit diagram of a transmission conductor.
Fig. 4 is a schematic diagram of a two-port model of a transmission conductor.
Fig. 5 is an equivalent circuit diagram of a transmission line.
Detailed Description
The invention provides a novel traction network chain type parameter model with a return line direct power supply mode, which is based on a multi-conductor transmission system loop method. The derivation process of the chain type parameter model of the traction network is explained in detail by taking the traction network provided with the through ground wire and the return line direct power supply mode as an example in combination with the attached drawings.
Table 1 is a loop number table of the traction network with a return line direct power supply mode.
Table 2 shows typical parameters of the conductor of the traction network with the return line direct power supply mode.
Table 3 shows the inductance calculation results corresponding to the parameters in table 2.
Table 4 shows the capacitance calculation results corresponding to the parameters in table 2.
Table 5 shows the results of resistance calculations corresponding to the parameters of table 2.
Table 6 shows the calculation results of the basic parameters of the traction network in the examples.
Table 7 shows the calculation results of the electrical parameters of the traction network in the examples.
The invention relates to a traction network chain type parameter model with a return line direct power supply mode based on a multi-conductor loop method, which comprises the following steps:
firstly, a loop is constructed, and conductors in a traction network in a direct power supply mode with a return line are classified according to transmission conductors and return conductors, namely the system is converted into a multi-transmission-conductor multi-return-conductor loop system consisting of 2 transmission conductors and 5 return conductors.
The structure of the system provided with the through ground wire traction network with the return line direct power supply mode is shown in the attached figure 1, and the transmission return conductor is shown in the attached figure 2. The transmission conductor comprises a contact line and a catenary, and the return conductor comprises a steel rail 1, a steel rail 2, a return line, a through ground wire and the ground. The traction network system is thus a multi-loop transmission system with 2 transmission conductors 5 return conductors.
TABLE 1
Name of conductor Rail 1R3 Rail 2R4 Return line R5 Ground through line R6 Ground R7
Contact line R1 1 2 3 4 5
Carrier cable R2 6 7 8 9 10
As shown in Table 1, loops 1 to 5 are formed between the transmission conductor contact line and the return conductors (rail 1, rail 2, return line, ground and earth), and the distances between the two conductors in the first four loops are d in sequence1～d4(ii) a Loops 6-10 are respectively formed between the carrier cable of the transmission conductor and the return conductors (the steel rail 1, the steel rail 2, the return line, the through ground wire and the ground), and the distances between two conductors in the first four loops are d in sequence6～d9. The contact line, the carrier cable, the steel rail 1, the steel rail 2, the return line and the through ground wire have the radius r1～r6. The distance between the carrier cable and the contact line, between the steel rail 1 and the steel rail 2, between the steel rail 1 and the return line, between the steel rail 1 and the through ground wire, between the steel rail 2 and the return line, between the steel rail 2 and the through ground wire, and between the return line and the through ground wire is l12、l34、l35、l36、l45、l46And l56。
Calculating comprehensive impedance, deducing self-inductance coefficients in the loops and mutual inductance coefficients among the loops based on space magnetic field analysis according to the constructed loops, and constructing inductance coefficient matrixes of the loops; deducing a resistance matrix of unit length of each loop, and further constructing an impedance matrix of unit length of each loop; and finally, obtaining the comprehensive equivalent impedance of the system in unit length on the basis of the impedance matrix of the traction network in unit length.
(1) Inductance calculation
First, the self-inductance l of loop i is calculatedii. The self-inductance of the non-ground return circuit is illustrated by taking the circuit 1 as an example, and the circuit current in the circuit 1 is assumed to be I1The current in the circuit is I1In the rail 1, the current is-I1The two components together form a basic space magnetic field unit between two conductorsThe formula of the magnetic linkage can obtain l11Comprises the following steps:
Figure BDA0002495393920000041
wherein m is a magnetic permeability. Similarly, the self-inductance l of the loop 2 to the loop 4 and the loop 6 to the loop 9 can be obtainedii(i＝1,2,3,4,6,7,8,9)
The self-impedance coefficient of the ground return circuit is illustrated by taking the circuit 5 as an example. Let the self-impedance coefficient l in the loop 555Comprises the following steps:
Figure BDA0002495393920000051
in the formula (I), the compound is shown in the specification,
Figure BDA0002495393920000052
ρ is the ground resistivity (Ω · m) and f is the frequency for the ground equivalent depth. Similarly, the self-impedance coefficient l in the loop 10 can be obtained1010。
Then, the mutual inductance l between the loop i and the loop j is calculatedij＝lji. The mutual inductance between the non-earth return circuits is illustrated by taking the circuit 1 and the circuit 7 as an example17. According to loop 1 current I1Flux linkage Y generated in the circuit 7 by contact lines1And the flux linkage Y generated in the circuit 7 by the rail 12The resultant flux linkage Y generated in the loop 7 by the loop 1 is obtained1+Y2The flux linkage can be compared with the current to further obtain l17Comprises the following steps:
Figure BDA0002495393920000053
in the same way, the mutual inductance l between the non-earth return circuit and the earth return circuit can be obtainedij。
(2) Inductance matrix of unit length of each loop
The unit length inductance matrix L (10 dimensions) of each loop of the traction network can be obtained from the previous step by the direct power supply mode of the through ground wire with the return line, wherein LiiIs the self-inductance of loop i, lijIs the mutual inductance between loop i and loop j, lij＝ljiThen, there are:
Figure BDA0002495393920000054
(3) resistance matrix of potential length of each loop
The resistance per unit length of the contact line, carrier cable, steel rail 1, steel rail 2, return line, through ground wire and earth is assumed to be R1、R2、…、R7The comprehensive resistance of the traction network is R, and the comprehensive resistance is considered in the following three conditions:
1) self-resistance in each loop: the self-resistance in each loop is the sum of the resistances of the transmission conductor and the return conductor which form the loop, namely, in the traction network comprehensive resistance matrix R, the value of the diagonal position is the sum of the resistances of the two conductors in the loop.
2) Mutual resistance between the loops of the common transmission conductor or the common return conductor: according to the relationship between the loop current and the voltage drop, the mutual resistance between the loops of the common transmission conductor or the common return conductor is equal to the resistance value of the common conductor.
3) Mutual resistance between two independent loops (i.e. not common transmission conductor and not common return conductor loops): the mutual resistance between the two independent loops is 0.
Thus, the traction network combined resistance R (symmetric matrix) can be expressed as:
Figure BDA0002495393920000061
in the formula, ones (5,5) represents a 5-dimensional matrix with elements of 1, and diag (×) represents a diagonal matrix.
(4) Impedance matrix per unit length of each loop
The impedance matrix per unit length of each loop obtained from equations (4) and (5) is:
Z＝R+jωL (6)
(5) the equivalent unit length comprehensive equivalent impedance Z corresponding to the unit length impedance matrix system of the traction network is
Suppose Δ U1、ΔU2、…、ΔU10The voltage drops of loop 1 to loop 10, respectively; i is1、I2、…、I10The currents through loop 1 to loop 10, respectively. Since 10 loops are in parallel, assume I0For the total current of all transmission conductors (or all return conductors), there is then Δ U1＝ΔU2＝…＝ΔU10＝ΔU，I1+I2+…+I10＝I0. Suppose k1、k2、…、k10The current distribution coefficient for 10 loops is I1＝k1I0、I2＝k2I0、…、I10＝k10I10. According to the relationship between the voltage drop of each loop and the flux linkage of the loop, the voltage drop of each loop can be obtained, and the relationship between the inductance and the current is as follows:
Figure BDA0002495393920000062
the comprehensive equivalent impedance Z of the equivalent unit length corresponding to the system can be obtained as follows:
Figure BDA0002495393920000063
and thirdly, calculating the comprehensive capacitance, deducing an intrinsic potential coefficient in the loop and a mutual potential coefficient between the loops according to the constructed loop, constructing a potential coefficient matrix to obtain a capacitance matrix of unit length of each loop, and finally obtaining the comprehensive capacitance of unit length of the traction network with the loop in a direct power supply mode by combining the relationship between the charge and the voltage of each loop.
(1) Calculation of potential coefficient of each loop
First, the potential coefficient of each circuit is calculated. The self-potential coefficient of the non-earth return circuit is illustrated by taking the circuit 1 as an example. Note PiiIs the self-potential coefficient in loop i. In loop 1, it is assumed that the contact line carries a charge of unit length q1c/m, then the electric charge carried by the steel rail 1 per unit length is-q1c/m, which together form a basic space electric field unit, and the electric potential between two conductors forming a loop is calculatedThe self-potential coefficient p in the loop 1 can be obtained11Comprises the following steps:
Figure BDA0002495393920000071
wherein e is the loop space dielectric constant. The self-potential coefficient p in the loop 2 to the loop 4 and the loop 6 to the loop 9 can be obtained in the same wayii(i ═ 1,2,3,4,6,7,8, 9). Further obtaining the self-potential coefficient p of the earth return circuitii(i＝5,10)。
Then, the mutual potential coefficient between each circuit is calculated. Note pijIs the mutual potential coefficient between loop i and loop j, pij＝pji. The mutual potential coefficient p between the non-ground return circuits is illustrated by taking the circuit 1 and the circuit 7 as an example17. According to the potential V generated by the contact line in the circuit 7c17And the potential V generated by the rail 1 in the circuit 7h17The potential V generated in the loop 7 by the loop 1 can be obtainedZ17Further find p17Comprises the following steps:
Figure BDA0002495393920000072
based on the above principle, the mutual potential coefficients between the common transmission conductor between the non-ground return circuits, the common return conductor between the non-ground return circuits and the ground return circuit, the common transmission circuit between the non-ground return circuits and the ground return circuit are calculated by referring to the mutual impedance coefficient and are continuously derived.
(2) Capacitance matrix calculation for unit length of each loop
Through the steps, a loop potential coefficient matrix P with n being 10 dimensions can be obtained, wherein P isiiIs the self-potential coefficient, p, of the loop iijIs the mutual potential coefficient between loop i and loop j, pij＝pji。
Further, the capacitance matrix C ═ P of unit length of each loop can be obtained-1Namely:
Figure BDA0002495393920000081
(3) traction network unit length integrated capacitance calculation
The relationship Q between each circuit unit length capacitance matrix C and each circuit charge and the voltage generating the charge is expanded as:
Figure BDA0002495393920000082
the total charge of each loop is q ═ q1+q2+…+qn. Meanwhile, because the circuits of the traction network are in parallel connection in a direct power supply mode with the return line, u is equal to u1＝u2＝…＝un. Therefore, the comprehensive capacitance C per unit length of the traction network provided with the through ground wire and adopting the direct power supply mode with the return line is as follows:
Figure BDA0002495393920000083
(4) and (3) deducing a multi-conductor transmission line equation, combining a voltage equation and a current equation according to the equivalent circuit of the multi-conductor transmission line system, and solving a general solution of the equation by taking the excitation source as a single-frequency sinusoidal signal.
For a multi-conductor transmission line system, a chain equation is usually used for description, and the chain equation is based on an equivalent circuit of the multi-conductor transmission line system, as shown in fig. 3. The transmission line equation 1 from the voltage equation is:
Figure BDA0002495393920000084
the transmission line equation 2 from the current equation is:
Figure BDA0002495393920000085
considering the excitation source as a single-frequency sinusoidal signal, then
Figure BDA0002495393920000091
Further obtaining:
Figure BDA0002495393920000092
Figure BDA0002495393920000093
differentiating and replacing the two sides of the above formula with respect to the position x to obtain:
Figure BDA0002495393920000094
Figure BDA0002495393920000095
the general solution to the above equation is:
V(x)＝V+re-αxe-jβx+V-re-αxejβx(20)
Figure BDA0002495393920000096
in the formula (I), the compound is shown in the specification,
Figure BDA0002495393920000097
the characteristic is a wave propagation coefficient, a is an attenuation coefficient of the wave in the transmission process along the conductor, and b represents the phase shift of the wave in the transmission process along the conductor;
Figure BDA0002495393920000098
is the wave propagation characteristic impedance.
And fifthly, deducing and solving a multi-conductor transmission line chain parameter equation matrix, regarding the multi-conductor transmission line system as a dual-port model, deducing the dual-port chain parameter equation matrix, substituting the multi-conductor transmission line equation obtained in the previous step into the chain parameter equation matrix and solving the chain parameter equation matrix, and finally establishing the chain parameter model of the traction network with the return line direct power supply mode.
Considering the multi-conductor transmission line system as a two-port model, as shown in fig. 4, the two-port chain parameter equation matrix is:
Figure BDA0002495393920000099
substituting the transmission line equation into the chain parameter equation matrix, and introducing V (0) and I (0) as boundary conditions to obtain:
Figure BDA0002495393920000101
in the formula (I), the compound is shown in the specification,
Figure BDA0002495393920000102
Figure BDA0002495393920000103
general solution according to voltage V (x) V+re-αxe-jβx+V-reαxejβx，V+e-αxe-jβxIs an incident voltage wave propagating forward in the direction of the line, and V-eαxejβxFor reflected voltage waves propagating in reverse along the line direction, the current is also composed of incident current waves and reflected current waves in the same way. As shown in fig. 5, the load impedance is ZLCharacteristic impedance of transmission line is ZcThen the reflection coefficient of the transmission line system at the load is:
Figure BDA0002495393920000104
the reflection coefficient at any point of the line is:
Figure BDA0002495393920000105
the input impedance at any position is:
Figure BDA0002495393920000106
the transmission line voltage and current expressions given by the reflection coefficient at the load are:
V(x)＝V+e-αxe-jβx[1+ξLe2α(x-L)ej2β(x-L)](27)
Figure BDA0002495393920000107
to solve the system of equations, a undetermined constant V needs to be calculated+For this reason, a boundary condition is introduced for the x ═ 0 position because:
Figure BDA0002495393920000108
from FIG. 5, it can be seen that:
Figure BDA0002495393920000111
substituting the transmission line voltage expression given by the reflection coefficient at the load can obtain:
Figure BDA0002495393920000112
example (b):
typical parameters of the conductor of the traction network with the return-line traction power supply system are shown in the following table 2, wherein the coordinate origin of the horizontal coordinate and the vertical coordinate is the center of the rail surface.
TABLE 2
Figure BDA0002495393920000113
The calculation results of the integrated inductance, the integrated capacitance, and the integrated resistance are shown in tables 3,4, and 5 below, respectively.
TABLE 3 (Unit: 10)-8H/km)
Figure BDA0002495393920000114
TABLE 4 (Unit: 10)-9s/km)
Figure BDA0002495393920000121
TABLE 5 (Unit: omega/km)
Figure BDA0002495393920000122
The obtained wave propagation coefficient is 0.0002+0.0011j, the wave propagation characteristic impedance is 332.49-5.947j, and the obtained chain parameter model is as follows:
Figure BDA0002495393920000123
in the application aspect of the chain type parameter model, a 220kV incoming line power supply is adopted for the traction network in a direct power supply mode with a return line, the system short-circuit capacity is 2000MVA, the traction transformer is in a Vv wiring mode, the installation capacity is 25+25MVA, the short-circuit impedance is 10.5%, relevant parameters are shown in the following table 6, the length of a power supply arm is 20 kilometers, the rated power of a terminal load is 11000kW, and the power factor is close to 1. The chain parameter model is used to calculate the relevant electrical parameters such as reflection coefficient, input impedance, voltage, current, etc., and the calculation results are shown in table 7 below.
TABLE 6
Load impedance (omega) Impedance of system and transformer (omega) Reflection coefficient at load Power side input impedance (omega)
56.8182 3.9325 -0.7068+0.0735i 59.3873+6.6678i
TABLE 7
Figure BDA0002495393920000131
The foregoing is a further description of the invention with reference to examples to facilitate understanding of the invention by those skilled in the art. In addition, further modifications in combination with actual operating conditions may be effected by persons skilled in the art without departing from the spirit and scope of the invention.

Claims (1)

1. A traction network chain type parameter model with a return line direct power supply mode based on a multi-conductor loop method comprises the following steps:
(1) constructing a loop, and classifying conductors in a traction network in a direct power supply mode with a return line according to transmission conductors and return conductors, namely converting the system into a multi-transmission-conductor multi-return-conductor loop system consisting of 2 transmission conductors and 5 return conductors;
(2) calculating comprehensive impedance, deducing self-inductance coefficients in the loops and mutual inductance coefficients among the loops based on space magnetic field analysis according to the constructed loops, and constructing inductance coefficient matrixes of the loops; deducing a resistance matrix of unit length of each loop, and further constructing an impedance matrix of unit length of each loop; finally, on the basis of the impedance matrix of the traction network in unit length, obtaining the comprehensive equivalent impedance of the system in unit length;
(3) calculating the comprehensive capacitance, deducing an intra-loop self-potential coefficient and an inter-loop mutual potential coefficient according to the constructed loop, constructing a potential coefficient matrix to obtain a unit length capacitance matrix of each loop, and finally obtaining the unit length comprehensive capacitance of the traction network with the return line in the direct power supply mode by combining the relationship between the charge and the voltage of each loop;
(4) deducing a multi-conductor transmission line equation, according to the equivalent circuit of the multi-conductor transmission line system, combining a voltage equation and a current equation, deducing the multi-conductor transmission line equation, considering that an excitation source is a single-frequency sinusoidal signal, and solving the general solution of the single-frequency sinusoidal signal;
(5) and deducing and solving a multi-conductor transmission line chain parameter equation matrix, regarding the multi-conductor transmission line system as a dual-port model, deducing the dual-port chain parameter equation matrix, substituting the multi-conductor transmission line equation obtained in the previous step into the chain parameter equation matrix and solving, and finally establishing a chain parameter model of the traction network with the return line in a direct power supply mode.
CN202010417076.XA 2020-05-18 2020-05-18 Multi-conductor loop method-based traction network chain type parameter model with return line direct power supply mode Pending CN111709103A (en)

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Application publication date: 20200925