CN110427703A - A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement - Google Patents
A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement Download PDFInfo
- Publication number
- CN110427703A CN110427703A CN201910714125.3A CN201910714125A CN110427703A CN 110427703 A CN110427703 A CN 110427703A CN 201910714125 A CN201910714125 A CN 201910714125A CN 110427703 A CN110427703 A CN 110427703A
- Authority
- CN
- China
- Prior art keywords
- current
- unit
- drainage net
- rail
- buried metal
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Landscapes
- Prevention Of Electric Corrosion (AREA)
Abstract
The invention discloses a kind of stray electrical current emulation modelling methods based under the conditions of multi-train movement, are related to stray electrical current simulation modeling field.The present invention is from stray electrical current distribution character, utilize " rail-drainage net-buried metal-the earth " the four layers of earth mat structural model for meeting practical subway line feature, all regard train and traction substation as DC source Injection Current over the ground jointly, the distributed model that single injection source acts on lower earth mat electrical quantity is released using imfinitesimal method based on this, again by each injection source exercising result be overlapped sliver road electrical quantity distribution situation, finally make the obtained all fronts stray electrical current of emulation and rail potential numerical value be more in line with actual value.The present invention solves traditional stray electrical current distributed model and is only driven by single train and the power supply of only one or two substation, there are model structure, simple and boundary condition and practical situation have the defects of larger difference, its simulation result and measured value is caused to there are problems that large error.
Description
Technical field
The present invention relates to stray electrical current simulation modeling field, specially a kind of stray electrical based under the conditions of multi-train movement
Flow emulation modelling method.
Background technique
With the rapid development of economy, China's urban population increases significantly and construction scale constantly expands, city is caused to be handed over
Logical pressure is more and more big.Urban track traffic with the advantages that its high speed, safety, big passenger capacity as solving traffic jam issue
Preferred option.At the same time, completely insulated due to that can not accomplish between rail and the earth during subway circulation, cause to exist
Partial DC electric current at the defective insulation between rail and the earth by flowing to greatly, then by greatly flowing back to traction substation or flowing to
At low potential, this part flows into the earth and irregular electric current is known as stray electrical current.Stray electrical current can be to buried along subway
Metal pipe line and reinforced concrete structure erode, and take measures that huge economic loss will be will cause not in time.Therefore, lead to
Founding mathematical models are crossed to carry out simulation analysis to the stray electrical current of sliver road, nationality takes corresponding protection to arrange by prediction result
Applying, which reduces stray electrical current, seems very urgent to the corrosion of buried metal.
In terms of influencing stray electrical current modeling factors, related scholar establishes traction current system using single side feeding mode
System, to study influence of the drainage net to rail potential and stray electrical current, but does not study the influence under polygon power supply mode.
The equivalent circuit model at resistance and transition resistance of by each layer web frame is established based on resistor network in relation to scholar, to study
Influence of the transition resistance to stray electrical current of rail ground, but " rail-drainage net-the earth " three layers of earth mat structural model are used only,
The distribution of web frame describes incomplete over the ground.
In terms of stray electrical current distributed model, related scholar by analysis return-flow system feature, establish with traction current,
Rail longitudinal electrical resistance and rail over the ground transition resistance be variable continuous backflow system model.Related scholar establishes on this basis
Consider the return-flow system continuous model that railway roadbed bar construction influences.Related scholar is based on electric field and establishes stray electrical current distributed mode
Type estimates the extent of corrosion of buried metal.Document above is all based under single vehicles operation and builds to stray electrical current
Mould, due to its simplify boundary condition and excessively Utopian assumed condition cause calculated result with measured value there are larger mistakes
Difference.Therefore, the multiple row vehicle stray electrical current distributed model met under practical subway operation conditions is established to be necessary.
Summary of the invention
The present invention is only driven by single train to solve traditional stray electrical current distributed model or only one or two of substation
Power supply, and boundary condition and practical situation simple there are model structure have the defects of larger difference, cause its simulation result and reality
There is large error in measured value, for prior art defect, provide a kind of based on spuious under the conditions of multi-train movement
Current simulations modeling method.
The present invention is achieved by the following technical solution: a kind of imitative based on the stray electrical current under the conditions of multi-train movement
True modeling method: all regarding train and traction substation as DC source, and web frame Injection Current, ground web frame use over the ground jointly
Four layers of earth mat structural model of " rail-drainage net-buried metal-the earth " release single injection source using imfinitesimal method and act on lower ground
Each injection source exercising result is then overlapped to obtain sliver road stray electrical current, rail by the distributed model of net electrical quantity
The distribution situation of road current potential, the specific steps are as follows:
1) single injection source model modeling:
The circulation path of stray electrical current is caused to be divided into four layers of ground web frame " rail-drainage net-buried metal-is big in subway
Ground "；Parameters are respectively as follows: R in modelGFor rail longitudinal electrical resistance, unit is Ω/km；RPFor drainage net longitudinal electrical resistance, unit
It is Ω/km；RMFor buried metal longitudinal electrical resistance, unit is Ω/km；RDFor the earth longitudinal electrical resistance, unit is Ω/km；IG(x) it is
Electric current of the rail at x, unit are A；IPIt (x) is electric current of the drainage net at x, unit is A；IMIt (x) is buried metal at x
Electric current, unit is A；ID(x) electric current for the earth at x, unit is A；UG(x) electricity between rail and the earth at x
Pressure, unit is V；UP(x) voltage between drainage net and the earth at x, unit are V；UMIt (x) is buried metal and the earth
Between voltage at x, unit is V；g1Transition conductance between rail and drainage net, unit are S/km；g2For drainage net with bury
Transition conductance between ground metal, unit are S/km；g3Transition conductance between buried metal and the earth, unit are S/km；I
For train and traction substation Injection Current, unit is A；X is to the distance in injection source, and unit is km；
, as zero point, as x >=0, to be obtained according to the corresponding infinitesimal equivalent circuit of each layer of model at Injection Current:
According to Kirchhoff's second law (∑ U=0), by each layer infinitesimal equivalence voltage node Tu Ke get of model:
UG(x)-UP(x)+IP(x)RPDx=UG(x)+dUG(x)-UP(x)-dUP(x)+IG(x)RGdx (2)
UP(x)-UM(x)+IM(x)RMDx=UP(x)+dUP(x)-UM(x)-dUM(x)+IP(x)RPdx (3)
UM(x)+ID(x)RDDx=UM(x)+dUM(x)+IM(x)RMdx (4)
According to Kirchhoff's current law (KCL) (∑ I=0), can be obtained by each layer infinitesimal equal currents node diagram of model:
dIG(x)=g1dx×[UP(x)-UG(x)] (5)
dIP(x)=g2dx×[UM(x)-UP(x)] (6)
dIM(x)=- g3dx×UM(x) (7)
Arrangement formula (1)-(7) obtain the voltage U between rail and the earth at xG(x), between drainage net and the earth at x
Voltage UP(x), the voltage U between buried metal and the earth at xM(x), electric current I of the rail at xG(x), drainage net is at x
Electric current IP(x), electric current I of the buried metal at xM(x) differential equation value is respectively as follows:
Arrangement formula (8)-(13), matrix form are as follows:
It enables
Then have:
Formula (14) is a non-homogeneous differential equation group, general solution form are as follows:
In formula, f is a particular solution of non-homogeneous differential equation group；λ1~λ6For the characteristic value of matrix M；[b1i b2i b3i
b4i b5i b6i] T is respectively eigenvalue λiCorresponding feature vector；C1~C6For the constant coefficient determined by primary condition；It will be first
Beginning condition IG(0)=I/2,IP(0)=0, UP(0)=0, IM(0)=0, UM(0)=0 formula is substituted into
(15) constant coefficient C is acquired in1~C6With particular solution f, particular solution f are as follows:
Wherein: Z=RGRPRM+RGRPRD+RGRMRD+RPRMRD；
Rail potential, rail current, drainage net current potential equivalent according to symmetric relation, when proper x < 0 are as follows:
UG(- x)=UG(x) (17)
IG(- x)=- IG(x) (18)
UP(- x)=UP(x) (19)
IP(- x)=- IP(x) (20)
UM(- x)=UM(x) (21)
IM(- x)=- IM(x) (22)
It is just above the differential equation value of each layer earth mat structure voltage and current value under the effect of single injection source, it below will be each
Single injection source institute value is overlapped；
2) mostly injection source model modeling:
In more injection source equivalent models, it is assumed that d is the length of whole route, and unit is km, IS1~ISmRespectively route
The Injection Current of upper m traction substation, unit are A；IL1~ILnThe Injection Current of n train, unit are respectively on route
A；dS1~dSmThe distance between m traction substation and route originating point respectively on route, unit is km, dL1~dLnRespectively
For the distance between n train and route originating point on route, unit is km；
Assuming that the position of train originating point is x=0 on route, it is separation by whole route using the position in each injection source
Several sections are divided into, can be obtained by the track potential U of any position on route using principle of stackingG(x), track electricity
Flow IG(x), drainage net current potential UP(x), drainage net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x)
Numerical values recited；
In 0~dL1Section: i.e. in 0≤x < dL1In range, the single voltage and current numerical value of route any position is folded
Add much lower 0~d of injection source effectL1The track potential U of sectionG(x), track current IG(x), drainage net current potential UP(x), drainage
Net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
dL1~dS1Section: i.e. dL1≤ x < dS1Track potential U in rangeG(x), track current IG(x), drainage net current potential
UP(x), drainage net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
And so on: the track potential U on remaining sectionG(x), track current IG(x), drainage net current potential UP(x), drainage
Net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) the formula on numerical formula and above-mentioned section
Calculation is identical, last dLnCorresponding electric parameter formula is as follows on~d section:
dLn~D section (dLn≤ x≤d) track potential UG(x), track current IG(x), drainage net current potential UP(x), drainage
Net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
The stray electrical current numerical value of any position on route are as follows: ISC(x)=IG(x)|g1→0-IG(x)|g1；Wherein, IG(x)
|g1→0It indicates: track current when completely insulated between rail and drainage net；IG(x)|g1It indicates: the transition between rail and drainage net
Track current when conductance is actual value.
3) calculating of electric substation's injected value of current:
In practical subway operational process, not only there is train toward the earth injected value of current, there are also traction substations.Here
Train is equivalent to current source, flow valuve is taken to be obtained by operation simulation calculation.Traction substation is equivalent to ideal voltage source and electricity
The series connection of resistance, value are obtained according to the load setting of Rectification Power Factor by Rectification Power Factor external characteristic curve.
Electric current is positive with flowing out node, and inflow is negative, i.e., train Injection Current is positive value, and traction substation Injection Current
For negative value.The injected value of current of train node is obtained by traction computer sim- ulation.For traction substation node, electric substation can be turned
It is changed to DC source form in parallel with a resistor, so that it may obtain the injected value of current of electric substation's node.(since electric substation injects
The calculating of current value have been relatively mature with modeling, here without being described in detail).
It is compared with prior art the invention has the following advantages: provided by the present invention above-mentioned a kind of based on multiple row vehicle
Stray electrical current emulation modelling method under service condition, (1) are analyzed by the distribution character to stray electrical current, and the earth is thin
It is divided into four layers of ground web frame of " rail-drainage net-buried metal-the earth ", so that during subway circulation, stray electrical current
Circulating pathway is more in line with real case；(2) in singly injection source model, pass through general solution to non-homogeneous differential equation group and spy
Solution is solved respectively, so that calculated result value is more comprehensive；(3) in mostly injection source model, by the effect of single injection source
Under electric parameter amount be overlapped, obtain multiple row vehicle and stray electrical current numerical value under more electric substation's collective effects and rail electricity
Bit value, so that the generation path of stray electrical current is more in line with real case, more accurately.This method is detection, prevention and treatment subway
Power supply system causes stray electrical current to provide theoretical foundation.
Detailed description of the invention
Fig. 1 is metro traction power system structure chart involved in the present invention, and in figure: 1 is traction substation；2 be feed line；
3 be contact net；4 be train；5 be rail；6 be return wire；7 be electricity segmentation.
Fig. 2 is stray electrical current formation basic theory schematic diagram involved in the present invention, I in figure1And I2It is led for two adjacent with train
Draw DC current provided by power transformation；I3And I4For the DC current for returning to two neighboring traction substation by rail；I5And I6
For the stray electrical current for being leaked to the earth.
Fig. 3 is single injection source model equivalent circuit structure chart involved in the present invention.
Fig. 4 is the circuit infinitesimal equivalent circuit diagram between rail of the present invention and drainage net: a: voltage node figure；B: current node
Figure.
Fig. 5 is the circuit infinitesimal equivalent circuit diagram between drainage net and buried metal of the present invention: c: voltage node figure；D: electric current
Node diagram.
Fig. 6 is the circuit infinitesimal equivalent circuit diagram between buried metal and the earth of the present invention: e: voltage node figure；F: electric current section
Point diagram.
Fig. 7 is the source model equivalent circuit structure chart that injects involved in the present invention more: d is the length of whole route, and unit is
Km, IS1~ISmThe Injection Current of m traction substation, unit are A respectively on route；IL1~ILnN column respectively on route
The Injection Current of vehicle, unit are A；dS1~dSmThe distance between m traction substation and route originating point respectively on route,
Unit is km, dL1~dLnThe distance between n train and route originating point respectively on route, unit is km.
Fig. 8 is that electric substation's DC load involved in the present invention calculates equivalent circuit diagram: current source is underground engines, voltage source
In series with a resistor is traction substation.Electric substation's node is stationary nodes, such as node 1.Train node is mobile node, position
It changes with time, such as node 2.Assuming that contact net resistance per unit length is r, unit is Ω/km, then node 1 and section 2
Equivalent resistance between point is R12=rd12。
Fig. 9 is electric substation's equivalent transformation schematic diagram involved in the present invention.
Figure 10 is rail longitudinal electrical resistance R involved in the present inventionGStray electrical current scatter chart in all fronts when variation: RP=0.05
Ω/km, RM=0.01 Ω/km, RD=0.0001 Ω/km, g1=1/15S/km, g2=1/3S/km, g3=1/3S/km, g01=
1·10-9S/km.Rail longitudinal electrical resistance RGTake 0.005 Ω/km respectively, when 0.0137 Ω/km, 0.05 Ω/km, sliver road
Stray electrical current distribution curve it is as shown in the figure.
Figure 11 is rail longitudinal electrical resistance R involved in the present inventionGRail potential scatter chart in all fronts when variation: RP=0.05
Ω/km, RM=0.01 Ω/km, RD=0.0001 Ω/km, g1=1/15S/km, g2=1/3S/km, g3=1/3S/km, g01=
1·10-9S/km.Rail longitudinal electrical resistance RGTake 0.005 Ω/km respectively, when 0.0137 Ω/km, 0.05 Ω/km, sliver road
Rail potential distribution curve it is as shown in the figure.
Figure 12 is drainage net longitudinal electrical resistance R involved in the present inventionpStray electrical current scatter chart in all fronts when variation: RG=
0.0137Ω/km；RM=0.01 Ω/km；RD=0.001 Ω/km；g1=1/15S/km；g2=1/3S/km；g3=1/3S/km；
g01=110-9S/km.Drainage net longitudinal electrical resistance RPWhen taking 0.001 Ω/km, 0.003 Ω/km, 0.1 Ω/km respectively, sliver
The stray electrical current distribution curve of road is as shown in the figure.
Figure 13 is drainage net longitudinal electrical resistance R involved in the present inventionpRail potential scatter chart in all fronts when variation: RG=
0.0137Ω/km；RM=0.01 Ω/km；RD=0.001 Ω/km；g1=1/15S/km；g2=1/3S/km；g3=1/3S/km；
g01=110-9S/km.Drainage net longitudinal electrical resistance RPWhen taking 0.001 Ω/km, 0.003 Ω/km, 0.1 Ω/km respectively, sliver
The rail potential distribution curve of road is as shown in the figure.
Figure 14 is buried metal longitudinal electrical resistance R involved in the present inventionMStray electrical current scatter chart in all fronts when variation: RG=
0.0137 Ω/km, RP=0.05 Ω/km, RD=0.001 Ω/km, g1=1/15S/km, g2=1/3S/km, g3=1/3S/km；
g01=110-9S/km.Rail longitudinal electrical resistance RMTake 0.005 Ω/km respectively, when 0.02 Ω/km, 0.05 Ω/km, whole route
On stray electrical current distribution curve it is as shown in the figure.
Figure 15 is buried metal longitudinal electrical resistance R involved in the present inventionMRail potential scatter chart in all fronts when variation: RG=
0.0137 Ω/km, RP=0.05 Ω/km, RD=0.001 Ω/km, g1=1/15S/km, g2=1/3S/km, g3=1/3S/km；
g01=110-9S/km.Rail longitudinal electrical resistance RMTake 0.005 Ω/km respectively, when 0.02 Ω/km, 0.05 Ω/km, whole route
On rail potential distribution curve it is as shown in the figure.
Figure 16 is the earth longitudinal electrical resistance R involved in the present inventionDStray electrical current scatter chart in all fronts when variation: RG=
0.0137Ω/km；RP=0.05 Ω/km；RM=0.01 Ω/km；g1=1/15S/km, g2=1/3S/km, g3=1/3S/km；
g01=110-9S/km.The earth longitudinal electrical resistance RDIt is whole when taking 0.00001 Ω/km, 0.00005 Ω/km, 0.0001 Ω/km respectively
Stray electrical current distribution curve on route is as shown in the figure.
Figure 17 is the earth longitudinal electrical resistance R involved in the present inventionDRail potential scatter chart in all fronts when variation: RG=
0.0137Ω/km；RP=0.05 Ω/km；RM=0.01 Ω/km；g1=1/15S/km, g2=1/3S/km, g3=1/3S/km；
g01=110-9S/km.The earth longitudinal electrical resistance RDIt is whole when taking 0.00001 Ω/km, 0.00005 Ω/km, 0.0001 Ω/km respectively
Rail potential distribution curve on route is as shown in the figure.
Figure 18 is that stray electrical current distribution in all fronts is bent when transition conductance g1 changes between rail involved in the present invention and drainage net
Line chart: RG=0.0137 Ω/km, RP=0.05 Ω/km, RD=0.001 Ω/km, RM=0.01 Ω/km, g2=1/3S/km, g3
=1/3S/km；g01=110-9S/km.Rail longitudinal electrical resistance g1Take 1/15S/km respectively, when 1/3S/km, 1S/km, sliver
The stray electrical current distribution curve of road is as shown in the figure.
Figure 19 is that rail potential distribution in all fronts is bent when transition conductance g1 changes between rail involved in the present invention and drainage net
Line chart: RG=0.0137 Ω/km, RP=0.05 Ω/km, RD=0.001 Ω/km, RM=0.01 Ω/km, g2=1/3S/km, g3
=1/3S/km；g01=110-9S/km.Rail longitudinal electrical resistance g1Take 1/15S/km respectively, when 1/3S/km, 1S/km, sliver
The rail potential distribution curve of road is as shown in the figure.
Figure 20 is all fronts stray electrical flow point when transition conductance g2 changes between drainage net and buried metal involved in the present invention
Cloth curve graph: RG=0.0137 Ω/km；RP=0.05 Ω/km；RM=0.01 Ω/km；RD=0.001 Ω/km；g1=1/15S/
km；g3=1/3S/km；g01=110-9S/km.Drainage net and buried metal transition conductance g21/15S/km, 1/3S/ are taken respectively
When km, 1S/km, the stray electrical current distribution curve of sliver road is as shown in the figure.
Figure 21 is all fronts rail potential point when transition conductance g2 changes between drainage net and buried metal involved in the present invention
Cloth curve graph: RG=0.0137 Ω/km；RP=0.05 Ω/km；RM=0.01 Ω/km；RD=0.001 Ω/km；g1=1/15S/
km；g3=1/3S/km；g01=110-9S/km.Drainage net and buried metal transition conductance g21/15S/km, 1/3S/ are taken respectively
When km, 1S/km, the rail potential distribution curve of sliver road is as shown in the figure.
Figure 22 is that all fronts stray electrical current is distributed when transition conductance g3 changes between buried metal and the earth involved in the present invention
Curve graph: RG=0.0137 Ω/km, RP=0.05 Ω/km, RD=0.001 Ω/km, RM=0.01 Ω/km, g1=1/15S/km,
g2=1/3S/km, g01=110-9S/km.Rail longitudinal electrical resistance g3Take 1/15S/km respectively, it is whole when 1/3S/km, 1S/km
Stray electrical current distribution curve on route is as shown in the figure.
Figure 23 is that all fronts rail potential is distributed when transition conductance g3 changes between buried metal and the earth involved in the present invention
Curve graph: RG=0.0137 Ω/km, RP=0.05 Ω/km, RD=0.001 Ω/km, RM=0.01 Ω/km, g1=1/15S/km,
g2=1/3S/km, g01=110-9S/km.Rail longitudinal electrical resistance g3Take 1/15S/km respectively, it is whole when 1/3S/km, 1S/km
Rail potential distribution curve on route is as shown in the figure.
Specific embodiment
Below in conjunction with specific embodiment, the invention will be further described.
A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement: train and traction substation are all seen
Make DC source, web frame Injection Current, ground web frame use four layers of " rail-drainage net-buried metal-the earth " over the ground jointly
Earth mat structural model releases the distributed model that single injection source acts on lower earth mat electrical quantity using imfinitesimal method, then by each injection
Source exercising result is overlapped to obtain the distribution situation of sliver road stray electrical current, track potential, the specific steps are as follows:
1) single injection source model modeling:
In single injection source model modeling process, there is following hypothesis:
(1) all parameters are all equally distributed in tractive power supply system；
(2) impedance of feeder line is not considered；
(3) ignore the DC current revealed from contact net (rail).
The circulation path of stray electrical current is caused to be divided into four layers of ground web frame " rail-drainage net-buried metal-is big in subway
Ground "；Parameters are respectively as follows: R in modelGFor rail longitudinal electrical resistance, unit is Ω/km；RPFor drainage net longitudinal electrical resistance, unit
It is Ω/km；RMFor buried metal longitudinal electrical resistance, unit is Ω/km；RDFor the earth longitudinal electrical resistance, unit is Ω/km；IG(x) it is
Electric current of the rail at x, unit are A；IPIt (x) is electric current of the drainage net at x, unit is A；IMIt (x) is buried metal at x
Electric current, unit is A；ID(x) electric current for the earth at x, unit is A；UG(x) electricity between rail and the earth at x
Pressure, unit is V；UP(x) voltage between drainage net and the earth at x, unit are V；UMIt (x) is buried metal and the earth
Between voltage at x, unit is V；g1Transition conductance between rail and drainage net, unit are S/km；g2For drainage net with bury
Transition conductance between ground metal, unit are S/km；g3Transition conductance between buried metal and the earth, unit are S/km；I
For train and traction substation Injection Current, unit is A；X is to the distance in injection source, and unit is km；Based on " rail-drainage
Single injection source model equivalent circuit of net-buried metal-the earth " is as shown in Figure 3.
Using at Injection Current as zero point, as x >=0, according to each layer of model corresponding infinitesimal equivalent circuit such as Fig. 4, Fig. 5 and
Shown in Fig. 6, it can obtain:
According to Kirchhoff's second law (∑ U=0), by a, the c in each layer infinitesimal equivalence voltage node Fig. 4~6 of model,
E can be obtained:
UG(x)-UP(x)+IP(x)RPDx=UG(x)+dUG(x)-UP(x)-dUP(x)+IG(x)RGdx (2)
UP(x)-UM(x)+IM(x)RMDx=UP(x)+dUP(x)-UM(x)-dUM(x)+IP(x)RPdx (3)
UM(x)+ID(x)RDDx=UM(x)+dUM(x)+IM(x)RMdx (4)
According to Kirchhoff's current law (KCL) (∑ I=0), by the b in each layer infinitesimal equal currents node diagram Fig. 4~6 of model,
D, f can be obtained:
dIG(x)=g1dx×[UP(x)-UG(x)] (5)
dIP(x)=g2dx×[UM(x)-UP(x)] (6)
dIM(x)=- g3dx×UM(x) (7)
Arrangement formula (1)-(7) obtain the voltage U between rail and the earth at xG(x), between drainage net and the earth at x
Voltage UP(x), the voltage U between buried metal and the earth at xM(x), electric current I of the rail at xG(x), drainage net is at x
Electric current IP(x), electric current I of the buried metal at xM(x) differential equation value is respectively as follows:
Arrangement formula (8)-(13), matrix form are as follows:
It enables
Then have:
Formula (14) is a non-homogeneous differential equation group, general solution form are as follows:
In formula, f is a particular solution of non-homogeneous differential equation group；λ1~λ6For the characteristic value of matrix M；[b1i b2i b3i
b4i b5i b6i] T is respectively eigenvalue λiCorresponding feature vector；C1~C6For the constant coefficient determined by primary condition；It will be first
Beginning condition IG(0)=I/2,IP(0)=0, UP(0)=0, IM(0)=0, UM(0)=0 formula is substituted into
(15) constant coefficient C is acquired in1~C6With particular solution f, particular solution f are as follows:
Wherein: Z=RGRPRM+RGRPRD+RGRMRD+RPRMRD；
Rail potential, rail current, drainage net current potential equivalent according to symmetric relation and Fig. 3, when proper x < 0 are as follows:
UG(- x)=UG(x) (17)
IG(- x)=- IG(x) (18)
UP(- x)=UP(x) (19)
IP(- x)=- IP(x) (20)
UM(- x)=UM(x) (21)
IM(- x)=- IM(x) (22)
It is just above the differential equation value of each layer earth mat structure voltage and current value under the effect of single injection source, it below will be each
Single injection source institute value is overlapped；
2) mostly injection source model modeling:
More injection source equivalent models are as shown in Figure 7, it is assumed that: d is the length of whole route, and unit is km, IS1~ISmRespectively
For the Injection Current of m traction substation on route, unit is A；IL1~ILnThe Injection Current of n train respectively on route,
Unit is A；dS1~dSmThe distance between m traction substation and route originating point respectively on route, unit is km, dL1~
dLnThe distance between n train and route originating point respectively on route, unit is km；
Assuming that the position of train originating point is x=0 on route, it is separation by whole route using the position in each injection source
Several sections are divided into, can be obtained by the track potential U of any position on route using principle of stackingG(x), track electricity
Flow IG(x), drainage net current potential UP(x), drainage net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x)
Numerical values recited；
In 0~dL1Section: i.e. in 0≤x < dL1In range, the single voltage and current numerical value of route any position is folded
Add much lower 0~d of injection source effectL1The track potential U of sectionG(x), track current IG(x), drainage net current potential UP(x), drainage
Net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
dL1~dS1Section: i.e. dL1≤ x < dS1Track potential U in rangeG(x), track current IG(x), drainage net current potential
UP(x), drainage net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
And so on: the track potential U on remaining sectionG(x), track current IG(x), drainage net current potential UP(x), drainage
Net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) the formula on numerical formula and above-mentioned section
Calculation is identical, last dLnCorresponding electric parameter formula is as follows on~d section:
dLn~D section (dLn≤ x≤d) track potential UG(x), track current IG(x), drainage net current potential UP(x), drainage
Net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
The stray electrical current numerical value of any position on route are as follows: ISC(x)=IG(x)|g1→0-IG(x)|g1；Wherein, IG(x)
|g1→0It indicates: track current when completely insulated between rail and drainage net；IG(x)|g1It indicates: the transition between rail and drainage net
Track current when conductance is actual value.
3) calculating of electric substation's injected value of current:
In practical subway system, the traction current of train is provided jointly by whole electric substations of sliver road.
Therefore, all traction substations of sliver road should be thought of as one completely by the calculating of Rectification Power Factor DC side traction power supply
Electric power networks, and made the following assumptions in calculating process:
(1) train is equivalent to current source, flow valuve is taken to be obtained by operation simulation calculation；
(2) rectifier is equivalent to connecting for ideal voltage source and resistance, and value is according to the load setting of Rectification Power Factor, by whole
Stream unit external characteristic curve obtains；
(3) all parameters in tractive power supply system are all equally distributed.
Traction networks equivalent circuit is as shown in Fig. 8.In figure, current source is underground engines, and voltage source in series with a resistor is to lead
Draw electric substation.Electric substation's node is stationary nodes, such as node 1.Train node be mobile node, position change with time and
Variation, such as node 2.Assuming that contact net resistance per unit length is r, unit is Ω/km, then the equivalent electricity between 2 points of node 1 and section
Resistance is R12=rd12。
The Injection Current of train node is obtained by traction computer sim- ulation.For traction substation node, electric substation can be turned
It is changed to DC source form in parallel with a resistor, such as attached drawing 9, so that it may which the Injection Current for obtaining the node is Id=Ud/Req。
Electric current is positive with flowing out node, and inflow is negative, i.e., train Injection Current is positive value, and traction substation Injection Current
For negative value.Equivalent circuit is calculated by traction, according to the available corresponding equation YU=I of the nodal method of analysis.Equation is carried out
The voltage of available each node is solved, then by the node voltage of electric substation, 9 can find out each electric substation's direct current with reference to the accompanying drawings
Shown in the electric current of side such as formula (41).
It changes with time, train is run on the line, and following special circumstances will occur: train node is in traction substation
Near nodal, especially when the two is overlapped, the transadmittance between two nodes can be very big, at this moment should eliminate train node,
Retain traction substation node.The current value of train node is applied directly on electric substation's node.
As shown in FIG. 10 and 11, under the premise of other conditions are constant, the stray electrical current numerical value of 0-8km be expert at track longitudinal direction
Resistance RGReach maximum value when taking 0.0137 Ω/km, the stray electrical current numerical value of 8-46.2km is with driving rail longitudinal electrical resistance RGIncreasing
Increase greatly；With rail longitudinal electrical resistance RGContinuous increase, all fronts stray electrical current in addition to other than route beginning is reduced,
Whole afterwards is all in increase tendency, and rail potential is reduced also in route beginning, whole thereafter to greatly improve.Therefore, steel
Rail longitudinal electrical resistance RGInfluence of the variation to all fronts earth mat electrical quantity it is very big, should give attention.
As shown in Figures 12 and 13, under the premise of other conditions are constant, the stray electrical current numerical value of 0-15km is with drainage steel
Muscle structure longitudinal electrical resistance RpIncrease and increase, the stray electrical current numerical value of 15-46.2km is with drainage bar construction longitudinal electrical resistance Rp
Increase it is unchanged, with drainage net longitudinal electrical resistance RpContinuous increase, all fronts stray electrical current at route beginning in addition to having slightly
Variation is outer, and whole thereafter almost unchanged, the numerical value of all fronts rail potential is also almost unchanged.Therefore, drainage net longitudinal electrical resistance Rp's
Change the influence very little to all fronts earth mat electrical quantity, can be ignored.
As shown in FIG. 14 and 15, under the premise of other conditions are constant, the stray electrical current numerical value of 0-15km is with metal mesh
Longitudinal electrical resistance RMIncrease and increase, the stray electrical current numerical value of 15-46.2km is with metal mesh longitudinal electrical resistance RMIncrease without change
Change, with buried metal longitudinal electrical resistance RMContinuous increase, all fronts stray electrical current in addition to route beginning have slightly variation other than,
Whole almost unchanged afterwards, the numerical value of all fronts rail potential is also without significant change.Therefore, buried metal longitudinal electrical resistance RMVariation pair
The influence very little of all fronts earth mat electrical quantity, can be ignored.
As shown in FIG. 16 and 17, under the premise of other conditions are constant, the stray electrical current numerical value of sliver road is with big
Ground soil longitudinal electrical resistance RDIncrease there is no variation.With the earth longitudinal electrical resistance RDContinuous increase, all fronts stray electrical current and steel
Rail potential value only has very small variation.Therefore, the earth longitudinal electrical resistance RDInfluence of the variation to all fronts earth mat electrical quantity very
It is small, it can be ignored.
As shown in Figures 18 and 19, under the premise of other conditions are constant, the stray electrical current numerical value within the scope of 0-5km is with row
Transition conductance g between track and drainage bar construction1Increase and gradually become equal from increase tendency, it is miscellaneous within the scope of 5-10km
Current values are dissipated with transition conductance g between driving rail and drainage bar construction1Increase and gradually become equal from reduction trend,
The stray electrical current numerical value of 10-46.2km is with transition conductance g between driving rail and drainage bar construction1Increase and increase；With
Transition conductance g between rail and drainage net1Continuous increase, subway all fronts stray electrical current at route beginning in addition to being reduced
Outside, whole thereafter is in increase tendency, and rail potential is integrally in reduction trend.Therefore, transition conductance g between rail and drainage net1
Influence of the variation to all fronts earth mat electrical quantity it is very big, should give attention.
As shown in figs 20 and 21, under the premise of other conditions are constant, 0-15km stray electrical current numerical value is with drainage reinforcing bar
Transition conductance g between structure and metal mesh2Increase and increase, the stray electrical current numerical value of 15-46.2km is with drainage bar construction
The transition conductance g between metal mesh2Increase it is unchanged；With transition conductance g between drainage net and buried metal2Continuous increase,
All fronts stray electrical current only has large change at route beginning, thereafter the whole variation for there was only very little, and all fronts rail potential is almost
Do not change.Therefore, the transition conductance g between drainage net and buried metal2Influence of the variation to all fronts earth mat electrical quantity very
It is small, it can be ignored.
As depicted in figures 22 and 23, under the premise of other conditions are constant, the stray electrical current numerical value of 0-15km is with metal mesh
The transition conductance g between the earth soil3Increase and increase, the stray electrical current numerical value of 15-46.2km is with metal mesh and the earth soil
Transition conductance g between earth3Increase it is unchanged；With transition conductance g between buried metal and the earth3Continuous increase, completely it is spuious
Electric current only has large change at route beginning, and whole thereafter almost unchanged, all fronts rail potential is also without variation.Therefore, it buries
Transition conductance g between ground metal and the earth3Variation to the influence very little of all fronts earth mat electrical quantity, can be ignored.
The scope of protection of present invention is not limited to the above specific embodiment, and for those skilled in the art and
Speech, the present invention can there are many deformation and change, it is all within design and principle of the invention it is made it is any modification, improve and
Equivalent replacement should be all included within protection scope of the present invention.
Claims (1)
1. a kind of stray electrical current emulation modelling method based under the conditions of multi-train movement, it is characterised in that: by train and traction
Electric substation all regards DC source as, and web frame Injection Current, ground web frame use " rail-drainage net-buried metal-over the ground jointly
Four layers of earth mat structural model greatly " release the distributed model that single injection source acts on lower earth mat electrical quantity using imfinitesimal method, then
Each injection source exercising result is overlapped to obtain the distribution situation of sliver road stray electrical current, track potential, it is specific to walk
It is rapid as follows:
1) single injection source model modeling:
The circulation path of stray electrical current is caused to be divided into four layers of ground web frame " rail-drainage net-buried metal-the earth " in subway；
Parameters are respectively as follows: R in modelGFor rail longitudinal electrical resistance, unit is Ω/km；RPFor drainage net longitudinal electrical resistance, unit be Ω/
km；RMFor buried metal longitudinal electrical resistance, unit is Ω/km；RDFor the earth longitudinal electrical resistance, unit is Ω/km；IG(x) exist for rail
Electric current at x, unit are A；IPIt (x) is electric current of the drainage net at x, unit is A；IMIt (x) is electric current of the buried metal at x,
Unit is A；ID(x) electric current for the earth at x, unit is A；UG(x) voltage between rail and the earth at x, unit are
V；UP(x) voltage between drainage net and the earth at x, unit are V；UM(x) between buried metal and the earth at x
Voltage, unit are V；g1Transition conductance between rail and drainage net, unit are S/km；g2For drainage net and buried metal it
Between transition conductance, unit is S/km；g3Transition conductance between buried metal and the earth, unit are S/km；I be train and
Traction substation Injection Current, unit are A；X is to the distance in injection source, and unit is km；
, as zero point, as x >=0, to be obtained according to the corresponding infinitesimal equivalent circuit of each layer of model at Injection Current:
According to Kirchhoff's second law (∑ U=0), by each layer infinitesimal equivalence voltage node Tu Ke get of model:
UG(x)-UP(x)+IP(x)RPDx=UG(x)+dUG(x)-UP(x)-dUP(x)+IG(x)RGdx (2)
UP(x)-UM(x)+IM(x)RMDx=UP(x)+dUP(x)-UM(x)-dUM(x)+IP(x)RPdx (3)
UM(x)+ID(x)RDDx=UM(x)+dUM(x)+IM(x)RMdx (4)
According to Kirchhoff's current law (KCL) (∑ I=0), can be obtained by each layer infinitesimal equal currents node diagram of model:
dIG(x)=g1dx×[UP(x)-UG(x)] (5)
dIP(x)=g2dx×[UM(x)-UP(x)] (6)
dIM(x)=- g3dx×UM(x) (7)
Arrangement formula (1)-(7) obtain the voltage U between rail and the earth at xG(x), the voltage between drainage net and the earth at x
UP(x), the voltage U between buried metal and the earth at xM(x), electric current I of the rail at xG(x), electricity of the drainage net at x
Flow IP(x), electric current I of the buried metal at xM(x) differential equation value is respectively as follows:
Arrangement formula (8)-(13), matrix form are as follows:
It enables
Then have:
Formula (14) is a non-homogeneous differential equation group, general solution form are as follows:
In formula, f is a particular solution of non-homogeneous differential equation group；λ1~λ6For the characteristic value of matrix M；[b1ib2ib3ib4ib5ib6i]T
Respectively eigenvalue λiCorresponding feature vector；C1~C6For the constant coefficient determined by primary condition；By primary condition IG(0)
=I/2,IP(0)=0, UP(0)=0, IM(0)=0, UM(0)=0 it substitutes into formula (15) and acquires often
Coefficient C1~C6With particular solution f, particular solution f are as follows:
Wherein: Z=RGRPRM+RGRPRD+RGRMRD+RPRMRD；
Rail potential, rail current, drainage net current potential equivalent according to symmetric relation, when proper x < 0 are as follows:
UG(- x)=UG(x) (17)
IG(- x)=- IG(x) (18)
UP(- x)=UP(x) (19)
IP(- x)=- IP(x) (20)
UM(- x)=UM(x) (21)
IM(- x)=- IM(x) (22)
Just it is above the differential equation value of each layer earth mat structure voltage and current value under the effect of single injection source, below infuses each list
Enter source institute value to be overlapped；
2) mostly injection source model modeling:
In more injection source equivalent models, it is assumed that d is the length of whole route, and unit is km, IS1~ISmM respectively on route
The Injection Current of traction substation, unit are A；IL1~ILnThe Injection Current of n train, unit are A respectively on route；dS1
~dSmThe distance between m traction substation and route originating point respectively on route, unit is km, dL1~dLnRespectively line
The distance between the train of road n and route originating point, unit are km；
Assuming that the position of train originating point is x=0 on route, it is separation by sliver k-path partition using the position in each injection source
At several sections, the track potential U of any position on route can be obtained by using principle of stackingG(x), track current IG
(x), drainage net current potential UP(x), drainage net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) number
It is worth size；
In 0~dL1Section: i.e. in 0≤x < dL1In range, much by the single voltage and current numerical value superposition of route any position
Injection source acts on lower 0~dL1The track potential U of sectionG(x), track current IG(x), drainage net current potential UP(x), drainage net electric current
IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
dL1~dS1Section: i.e. dL1≤ x < dS1Track potential U in rangeG(x), track current IG(x), drainage net current potential UP
(x), drainage net electric current IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
And so on: the track potential U on remaining sectionG(x), track current IG(x), drainage net current potential UP(x), drainage net electricity
Flow IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) the formula on numerical formula and above-mentioned section calculates
Mode is identical, last dLnCorresponding electric parameter formula is as follows on~d section:
dLn~D section (dLn≤ x≤d) track potential UG(x), track current IG(x), drainage net current potential UP(x), drainage net electric current
IP(x), buried metal current potential UM(x) and buried metal electric current IM(x) numerical value is respectively as follows:
The stray electrical current numerical value of any position on route are as follows: ISC(x)=IG(x)|g1→0-IG(x)|g1；Wherein, IG(x)|g1→0Table
Show: track current when completely insulated between rail and drainage net；IG(x)|g1Indicate: the transition conductance between rail and drainage net is
Track current when actual value.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910714125.3A CN110427703A (en) | 2019-08-03 | 2019-08-03 | A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910714125.3A CN110427703A (en) | 2019-08-03 | 2019-08-03 | A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN110427703A true CN110427703A (en) | 2019-11-08 |
Family
ID=68412438
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910714125.3A Pending CN110427703A (en) | 2019-08-03 | 2019-08-03 | A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110427703A (en) |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111324966A (en) * | 2020-03-04 | 2020-06-23 | 西南交通大学 | CDEGS-based urban rail transit stray current simulation calculation method |
| CN111338233A (en) * | 2020-03-03 | 2020-06-26 | 西南交通大学 | Simulation modeling method for subway stray current distribution in urban power grid |
| CN112364476A (en) * | 2020-09-29 | 2021-02-12 | 北京交通大学 | Method for analyzing stray current and track potential characteristics of steel rail backflow |
| CN112836364A (en) * | 2021-01-27 | 2021-05-25 | 西南交通大学 | Unified calculation method for urban rail transit stray current |
| CN112883597A (en) * | 2020-12-31 | 2021-06-01 | 国网上海市电力公司 | Method for calculating transformer direct-current magnetic bias ground potential caused by stray current of subway |
| CN113076575A (en) * | 2021-03-18 | 2021-07-06 | 中铁第四勘察设计院集团有限公司 | High-speed rail bridge section simulation detection method based on direct-current path model |
| CN113361049A (en) * | 2021-04-16 | 2021-09-07 | 国网上海市电力公司 | Transformer bias current calculation method based on subway near-zone earth and power grid model |
| CN116047363A (en) * | 2023-04-03 | 2023-05-02 | 华东交通大学 | Method and system for monitoring stray current of rail train |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109256771A (en) * | 2018-10-16 | 2019-01-22 | 国网湖南省电力有限公司 | Metro stray current and its caused transformer neutral point DC current calculation method |
| CN109374998A (en) * | 2018-09-14 | 2019-02-22 | 北京交通大学 | DC traction system track potential and stray electrical current dynamic analog device |
-
2019
- 2019-08-03 CN CN201910714125.3A patent/CN110427703A/en active Pending
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109374998A (en) * | 2018-09-14 | 2019-02-22 | 北京交通大学 | DC traction system track potential and stray electrical current dynamic analog device |
| CN109256771A (en) * | 2018-10-16 | 2019-01-22 | 国网湖南省电力有限公司 | Metro stray current and its caused transformer neutral point DC current calculation method |
Non-Patent Citations (2)
| Title |
|---|
| 汪佳: "多列车运行下地铁杂散电流分布研究", 《中国优秀博硕士学位论文全文数据库(硕士)信息科技辑》 * |
| 田涌: "多区间多列车动态杂散电流建模分析", 《城市轨道交通研究》 * |
Cited By (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111338233A (en) * | 2020-03-03 | 2020-06-26 | 西南交通大学 | Simulation modeling method for subway stray current distribution in urban power grid |
| CN111324966A (en) * | 2020-03-04 | 2020-06-23 | 西南交通大学 | CDEGS-based urban rail transit stray current simulation calculation method |
| CN111324966B (en) * | 2020-03-04 | 2021-03-16 | 西南交通大学 | CDEGS-based urban rail transit stray current simulation calculation method |
| CN112364476A (en) * | 2020-09-29 | 2021-02-12 | 北京交通大学 | Method for analyzing stray current and track potential characteristics of steel rail backflow |
| CN112364476B (en) * | 2020-09-29 | 2023-09-26 | 北京交通大学 | Method for analyzing stray current and track potential characteristics of steel rail backflow |
| CN112883597A (en) * | 2020-12-31 | 2021-06-01 | 国网上海市电力公司 | Method for calculating transformer direct-current magnetic bias ground potential caused by stray current of subway |
| CN112836364A (en) * | 2021-01-27 | 2021-05-25 | 西南交通大学 | Unified calculation method for urban rail transit stray current |
| CN112836364B (en) * | 2021-01-27 | 2022-08-19 | 西南交通大学 | Unified calculation method for stray current of urban rail transit |
| CN113076575A (en) * | 2021-03-18 | 2021-07-06 | 中铁第四勘察设计院集团有限公司 | High-speed rail bridge section simulation detection method based on direct-current path model |
| CN113361049A (en) * | 2021-04-16 | 2021-09-07 | 国网上海市电力公司 | Transformer bias current calculation method based on subway near-zone earth and power grid model |
| CN116047363A (en) * | 2023-04-03 | 2023-05-02 | 华东交通大学 | Method and system for monitoring stray current of rail train |
| CN116047363B (en) * | 2023-04-03 | 2023-08-18 | 华东交通大学 | Method and system for monitoring stray current of rail train |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110427703A (en) | A kind of stray electrical current emulation modelling method based under the conditions of multi-train movement | |
| CN109256771B (en) | Subway stray current and method for calculating transformer neutral point direct current caused by same | |
| CN104217086A (en) | Urban public transport network optimization method | |
| CN108868712B (en) | A kind of oil reservoir development production optimization method and system based on connectivity method | |
| CN107301482A (en) | A kind of power distribution network medium-voltage line paths planning method based on city integrated piping lane | |
| CN107609208B (en) | Traction network modeling method considering tunnel section comprehensive grounding system structure | |
| CN111324966B (en) | CDEGS-based urban rail transit stray current simulation calculation method | |
| CN105372559B (en) | A kind of limited continuation method of chain type transmission line of electricity one-end fault ranging | |
| CN106055852A (en) | Subway train operation and traction power supply system coupled simulation modeling method | |
| CN114202316B (en) | Urban rail transit train schedule optimization method based on deep reinforcement learning | |
| CN109670240B (en) | Urban multi-mode public transport network initial line generation method | |
| CN113361049B (en) | Transformer bias current calculation method based on subway near-zone earth and power grid model | |
| CN105303021A (en) | Adaptive real-time dynamic mathematic modeling method for direct-current traction power supply system in urban railway traffic | |
| CN106405326A (en) | Time-domain fault range finding method for co-tower double-loop DC power transmission line based on single-loop electrical quantity | |
| CN112364476A (en) | Method for analyzing stray current and track potential characteristics of steel rail backflow | |
| CN106019077B (en) | A kind of current mode traveling wave ranging device Optimizing method | |
| Zhou et al. | A uniform model for stray current of long-line DC metro systems | |
| CN114117832B (en) | Analysis method for dynamic stray current distribution of rail transit | |
| CN110244810A (en) | Method for acquiring stray current value in traction power supply system | |
| CN105403812A (en) | Triangular ring network line single-end fault distance measuring method based on fault traveling wave line decomposition and distance calibration | |
| CN114722714A (en) | Electric power-traffic coupling network expansion planning method considering traffic balance | |
| CN109975596A (en) | Earth current is distributed research method under a kind of monopole the earth method of operation | |
| CN103258236B (en) | A kind of heavy passenger flow of urban rail transit network distribution method based on scene | |
| CN112836364A (en) | Unified calculation method for urban rail transit stray current | |
| CN115422691A (en) | Rail transit stray current model obtaining method considering train traction characteristics |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20191108 |