CN112677828A - Method for calculating comprehensive capacitance of traction network in direct power supply mode with return line based on multi-conductor transmission line system loop method - Google Patents
Method for calculating comprehensive capacitance of traction network in direct power supply mode with return line based on multi-conductor transmission line system loop method Download PDFInfo
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- CN112677828A CN112677828A CN201910987468.7A CN201910987468A CN112677828A CN 112677828 A CN112677828 A CN 112677828A CN 201910987468 A CN201910987468 A CN 201910987468A CN 112677828 A CN112677828 A CN 112677828A
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Abstract
A traction network comprehensive capacitance calculation method based on a multi-conductor transmission line system loop method and adopting a direct power supply mode with a return line has clear and definite calculation process and conforms to the actual situation. The method comprises the following steps: (1) the conductors in the traction network with the return line in a direct power supply mode are classified according to the transmission and return functions, contact lines and carrier cables are transmission conductors, two parallel steel rails, return lines, a through ground wire and the ground are return conductors, then every two conductors participating in transmission and return form a loop, and the system is converted into a multi-transmission-conductor multi-return-conductor loop system; (2) deducing self potential coefficients in the loops and mutual potential coefficients among the loops to further construct a potential coefficient matrix, and solving an inverse matrix of the potential coefficient matrix to obtain a unit length capacitance matrix of each loop; (3) and finally obtaining the comprehensive capacitance in unit length of the traction network with the return line in the direct power supply mode according to the relationship between the capacitance matrix in unit length and the electric charges of each loop and the voltage of each loop generating the electric charges.
Description
Technical Field
The invention relates to a traction power supply system of an electrified railway, in particular to a traction network comprehensive capacitance calculation method based on a multi-conductor transmission line system loop method and adopting a return line direct power supply mode.
Background
With the development of the electrified railway and the implementation of the strategy of 'high-speed rail getting out' in China, the basic theory and the fine research requirements of the traction power supply system of the electrified railway are more and more urgent, and the comprehensive capacitance calculation of the traction network is the basis for realizing the accurate mathematical description of the traction network and further developing the researches of the resonance of the traction network, the overvoltage of the traction network, the electric arc of the traction network and the like. In the traction network of the electrified railway, the direct power supply mode with the return line is widely applied to field practice, the direct power supply mode comprises a plurality of conductors such as a contact line, a carrier cable, the return line and a steel rail, the physical structure and the electromagnetic field relationship are very complex, and the capacitance parameter calculation is very difficult. In a physical sense, the capacitance c per unit length is the ratio of the charge q per unit length to the voltage u between the conductors that induce the charge, so that the capacitance per unit length is only significant if the voltage value is well defined, whereas the voltage is the potential difference between the conductor potential and the reference conductor potential, leaving the single transmission conductor of the reference conductor, and it is not significant to directly discuss the capacitance parameters. 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, so that the development of electromagnetic space description research on the ground serving as a traction network of a complex multi-conductor transmission line system brings many limitations if the ground is taken as a reference conductor.
Disclosure of Invention
The invention aims to solve the problem of providing a traction network comprehensive capacitance calculation method based on a multi-conductor transmission line system loop method and adopting a direct power supply mode with a return line, so that the calculation process is clear and definite and conforms to the actual situation, and the problem that a traction network model which takes the ground as the reference in the prior art is easily misinterpreted as the ground which is a return channel of all conductors is solved.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the invention relates to a traction network comprehensive capacitance calculation method based on a multi-conductor transmission line system loop method and adopting a direct power supply mode with a return line, which comprises the following steps of:
(1) the conductors in the traction network with the return line in a direct power supply mode are classified according to the transmission and return functions, wherein contact lines and carrier cables are transmission conductors, two parallel steel rails, return lines, a through ground wire and the ground are return conductors, namely the system is a 7-conductor transmission line system consisting of 2 transmission conductors and 5 return conductors, then every two conductors participating in transmission and return form a loop, and the system is converted into a loop system with multiple transmission conductors and multiple return conductors;
(2) according to the constructed loop system, based on space electric field analysis, self-potential coefficients in the loops and mutual potential coefficients among the loops are deduced, so that a potential coefficient matrix is constructed, and an inverse matrix of the potential coefficient matrix is solved, so that a unit-length capacitance matrix of each loop can be obtained;
(3) and finally obtaining the comprehensive capacitance in unit length of the traction network with the return line in the direct power supply mode according to the relationship between the capacitance matrix in unit length and the electric charges of each loop and the voltage of each loop generating the electric charges.
The method has the advantages that the physical significance of the method for calculating the comprehensive capacitance of the traction network based on the loop method of the multi-conductor transmission line system is clear and accords with the actual situation, the problem that the traditional traction network model taking the ground as the reference is easily misunderstood that the ground is a backflow channel of all conductors is solved, and the calculation process is simpler and clearer.
Drawings
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 non-earth return conductors of a traction network with a return line for direct power.
Detailed Description
The invention provides a novel method for calculating comprehensive capacitance of a traction network, which is based on a loop method of a multi-conductor transmission system. The calculation process of the comprehensive capacitance of the traction network is explained in detail by taking the traction network which is provided with a through ground wire and adopts a direct power supply mode with a return line as an example in combination with the attached drawing.
The invention relates to a traction network comprehensive capacitance calculation method based on a multi-conductor transmission line system loop method and adopting a direct power supply mode with a return line, which comprises the following steps of:
1. the conductors in the traction network with the return line in a direct power supply mode are classified according to the transmission and return functions, wherein contact lines and carrier cables are transmission conductors, two parallel steel rails, return lines, a through ground wire and the ground are return conductors, namely the system is a 7-conductor transmission line system consisting of 2 transmission conductors and 5 return conductors, then every two conductors participating in transmission and return form a loop, and the system is converted into a loop system with multiple transmission conductors and multiple return conductors.
The structure of the system provided with the through ground wire and adopting the direct power supply mode with the return line to draw the net is shown in the attached figure 1, and the schematic diagram of the transmission and return conductors is shown in the attached figure 2. The contact line and the carrier cable are transmission conductors, and the steel rail 1, the steel rail 2, the return line, the through ground wire and the ground are return conductors. The traction network system is thus a multi-loop transmission system with 2 transmission conductors 5 return conductors. As shown in the attached 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 line 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. Carrier cableThe distance between the contact line, the steel rail 1 and the steel rail 2, the steel rail 1 and the return line, the steel rail 1 and the through ground wire, the steel rail 2 and the return line, the steel rail 2 and the through ground wire and the return line and the through ground wire is l12、l34、l35、l36、l45、l46And l56。
2. According to the constructed loop system, the self-potential coefficient in the loop and the mutual potential coefficient between the loops are deduced based on space electric field analysis, so that a potential coefficient matrix is constructed, and the inverse matrix of the potential coefficient matrix is solved, so that the capacitance matrix of each loop in unit length can be obtained.
Note piiIs the self-potential coefficient in loop i.
(1) The self-potential coefficient of the non-ground return circuit is described by taking the circuit 1 as an example.
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 self-potential coefficient p in the loop 1 can be obtained according to the calculation formula of the potential between the two conductors forming the loop11Comprises the following steps:
wherein ε represents a dielectric constant in circuit space.
Therefore, the self-potential coefficient p in the circuits 1 to 4 can be obtained by combining the circuit numbers and the conductor numbers shown in Table 1 and FIG. 2ii(i ═ 1,2,3,4) is:
self-potential coefficient p in circuit 6 to circuit 9ii(i ═ 6,7,8,9) is:
(2) the self-potential coefficient of the ground return circuit is described by taking the circuit 5 as an example.
Self-potential coefficient p in circuit 5 (i.e. earth return circuit formed by contact line and earth)55Comprises the following steps:
in the formula, DgAt the same depth as ground.
Similarly, the self-potential coefficient p in the loop 10 can be obtained1010Comprises the following steps:
3. and finally obtaining the comprehensive capacitance in unit length of the traction network with the return line in the direct power supply mode according to the relationship between the capacitance matrix in unit length and the electric charges of each loop and the voltage of each loop generating the electric charges.
Note pijIs the mutual potential coefficient between loop i and loop j, pij＝pji。
(1) And the mutual potential coefficient between the frame non-earth return circuits is illustrated by taking the circuit 1 and the circuit 7 as an example.
In loop 1 (i.e. the loop formed by the contact line and the rail 1), it is assumed that the contact line carries a charge per unit length of q1c/m, then the electric charge carried by the steel rail 1 per unit length is-q1c/m, the potential V generated by the contact line in the loop 7 (i.e. the loop formed by the carrier cable and the steel rail 2)c17Comprises the following steps:
potential V generated by rail 1 in circuit 7h17Comprises the following steps:
the potential V generated by the loop 1 in the loop 7Z17Comprises the following steps:
thus, the mutual potential coefficient p per unit length of the circuit 1 between the circuits 7 can be obtained17Comprises the following steps:
(2) deriving the result p from the mutual potential coefficients of the circuit 1 and the circuit 212The mutual potential coefficient when the transmission conductor is shared between the non-earth return circuits is illustrated as an example.
(3) Deriving the result p from the mutual potential coefficients of the circuit 1 and the circuit 616The mutual potential coefficient when the non-earth return circuit shares the return conductor is illustrated as an example.
(4) Deriving the result p from the mutual potential coefficients of the circuit 1 and the circuit 100110The mutual potential coefficient between the non-earth return circuit and the earth return circuit is illustrated as an example.
(5) Deriving the result p from the mutual potential coefficients of the circuit 1 and the circuit 515The mutual potential coefficient when the loop is transmitted between the non-ground return loop and the ground return loop is illustrated as an example.
(6) Mutual potential coefficient derivation results p of the circuits 5 and 100510The mutual potential coefficient between the ground return circuits is illustrated by way of example.
Calculating a capacitance matrix of each loop unit length:
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:
step five: 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:
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:
example (b):
typical parameters of the conductor of the traction network with the return-current traction power supply system are shown in a table 2, wherein the coordinate origin of a horizontal coordinate and a vertical coordinate is the center of a rail surface. Table 1 is a loop number table of the traction network with a return line direct power supply mode. The calculation results are shown in table 3, the first row and the first column in the table are loop numbers, the contents in the table are loop self-potential coefficients and mutual potential coefficients obtained through calculation in the second step and the third step, and the last row in the table is a traction network unit length comprehensive capacitor obtained through the fourth step based on the loop self-potential coefficients and the mutual potential coefficients.
TABLE 1
| Name of conductor | Rail 1 | |
Return line | Through ground wire | Ground (earth) |
| Contact wire | 1 | 2 | 3 | 4 | 5 |
| Carrier cable | 6 | 7 | 8 | 9 | 10 |
TABLE 2
TABLE 3 (Unit: 10)-12s/km)
Claims (1)
1. A traction network comprehensive capacitance calculation method based on a multi-conductor transmission line system loop method and adopting a return line direct power supply mode comprises the following steps:
(1) the conductors in the traction network with the return line in a direct power supply mode are classified according to the transmission and return functions, wherein contact lines and carrier cables are transmission conductors, two parallel steel rails, return lines, a through ground wire and the ground are return conductors, namely the system is a 7-conductor transmission line system consisting of 2 transmission conductors and 5 return conductors, then every two conductors participating in transmission and return form a loop, and the system is converted into a loop system with multiple transmission conductors and multiple return conductors;
(2) according to the constructed loop system, based on space electric field analysis, self-potential coefficients in the loops and mutual potential coefficients among the loops are deduced, so that a potential coefficient matrix is constructed, and an inverse matrix of the potential coefficient matrix is solved, so that a unit-length capacitance matrix of each loop can be obtained;
(3) and finally obtaining the comprehensive capacitance in unit length of the traction network with the return line in the direct power supply mode according to the relationship between the capacitance matrix in unit length and the electric charges of each loop and the voltage of each loop generating the electric charges.
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Citations (5)
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| CN105653818A (en) * | 2016-01-21 | 2016-06-08 | 中铁二院工程集团有限责任公司 | Electrified railway traction net impedance calculation method |
| CN106080269A (en) * | 2016-06-21 | 2016-11-09 | 西南交通大学 | Band return wire direct feeding system tunnel impedance of traction electric network computational methods |
| CN106427670A (en) * | 2016-07-09 | 2017-02-22 | 中铁二院工程集团有限责任公司 | Calculation method of comprehensive current carrying capacity of traction electric network in direct feed manner with return cable for electrified railway |
| KR20170046494A (en) * | 2015-10-21 | 2017-05-02 | 한국철도기술연구원 | Design Apparatus and Method of Wireless Power Transmission System for Catenary Status Monitoring System |
| CN107391785A (en) * | 2017-06-06 | 2017-11-24 | 中铁二院工程集团有限责任公司 | A kind of multi-conductor transmission lines system space electric field describes method |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20170046494A (en) * | 2015-10-21 | 2017-05-02 | 한국철도기술연구원 | Design Apparatus and Method of Wireless Power Transmission System for Catenary Status Monitoring System |
| CN105653818A (en) * | 2016-01-21 | 2016-06-08 | 中铁二院工程集团有限责任公司 | Electrified railway traction net impedance calculation method |
| CN106080269A (en) * | 2016-06-21 | 2016-11-09 | 西南交通大学 | Band return wire direct feeding system tunnel impedance of traction electric network computational methods |
| CN106427670A (en) * | 2016-07-09 | 2017-02-22 | 中铁二院工程集团有限责任公司 | Calculation method of comprehensive current carrying capacity of traction electric network in direct feed manner with return cable for electrified railway |
| CN107391785A (en) * | 2017-06-06 | 2017-11-24 | 中铁二院工程集团有限责任公司 | A kind of multi-conductor transmission lines system space electric field describes method |
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