CN107239600A - A kind of offline Arc Modelling method for building up of dynamic bow net for considering the offline distance of bow net - Google Patents
A kind of offline Arc Modelling method for building up of dynamic bow net for considering the offline distance of bow net Download PDFInfo
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Abstract
The present invention discloses a kind of offline Arc Modelling method for building up of dynamic bow net for considering the offline distance of bow net, according to the relation of voltage gradient and electric arc dissipation power each with the offline distance of bow net, the offline distance of bow net is introduced into the electric arc equation of circuit breaker, the extendable of the offline Arc Modelling of bow net is realized；According to the actual conditions that bow net is offline, the dynamic trajectory of the offline distance of bow net is set up, and is introduced into Arc Modelling, the foundation of the offline Arc Modelling of dynamic bow net is realized；In the last dynamic offline integrated equivalent circuit of Arc Modelling insertion car net of bow net, set up its corresponding state equation and solve, obtain waveform when this dynamic arc occurs.The method of the present invention more meets the actual conditions that the offline distance of bow net is changed over time during bow net offline this, the offline Arc Modelling of dynamic bow net set up accordingly, the research of the influence caused for the offline electric arc of bow net to train system provides more favourable support.
Description
Technical field
The present invention relates to the offline arc technology field of bow net, specially a kind of dynamic bow net for considering the offline distance of bow net from
Line Arc Modelling method for building up.
Background technology
With the high speed and heavy loading of electric railway, by contact net irregularity, contact net fluctuation, pantograph vibration etc.
The offline problem of bow net that factor is caused is increasingly severe, and producing alternating current arc offline by bow net also turns into general in electric railway
All over phenomenon.The influence caused for the research offline electric arc of bow net to train system, sets up Arc Modelling as an important research
Work.Some scholars of early stage cast aside the complicated physical process of internal arctube, and electric arc is regarded as into one under based on certain hypothesis
Individual non-linear two-terminal element, circuit breaker is proposed by energy conservation equation, and this is also to apply most electric arcs at present
Model；Scholars many so far set up the offline Arc Modelling of bow net based on circuit breaker, will such as be dissipated in electric arc equation
The parameter of power and voltage gradient is expanded, introduce more such as train speeds and time constant influence because
Element, establishes the more accurate offline Arc Modelling of bow net.However, the circuit breaker set up so far is all by electric arc side
The offline distance (electric arc equivalent length) of bow net is set to a constant in journey, and under actual conditions the offline distance of bow net bow net from
Line is changed over time during this, that is to say, that the offline Arc Modelling of bow net set up so far does not account for bow
Net this dynamic process of offline distance change but substituted with static constant.In consideration of it, being necessary actual bow net is offline
The change of distance is introduced into Arc Modelling, sets up the offline Arc Modelling of dynamic bow net more tallied with the actual situation.
The content of the invention
In view of the above-mentioned problems, considering the offline distance of bow net it is an object of the invention to provide one kind, more meet actual bow
Net the offline Arc Modelling method for building up of dynamic bow net of offline Arc Modelling.Technical scheme is as follows：
A kind of offline Arc Modelling method for building up of dynamic bow net for considering the offline distance of bow net, comprises the following steps：
Step 1：According to the relation of voltage gradient and electric arc dissipation power each with the offline distance of bow net, by bow net from
Linear distance is introduced into the electric arc equation of circuit breaker, realizes the extendable of the offline Arc Modelling of bow net；
Step 2：According to the actual conditions that bow net is offline, the dynamic trajectory of the offline distance of bow net is set up, and is introduced into electricity
In arc model, the foundation of the offline Arc Modelling of dynamic bow net is realized.
Further, the circuit breaker in the step 1 is Habedank circuit breakers, and its electric arc is in train
Substituted in contact net system with conductance：
In formula：gmFor the electric arc conductance of Mayr parts；gcFor the electric arc conductance of Cassie parts；G is electric arc conductance；I is electricity
Arc current；τ1And τ2For time constant；P0For the dissipated power of electric arc；ucFor the voltage gradient of electric arc；
Because voltage gradient can change with the offline distance change of bow net, and it is direct ratio variation relation, ratio is normal
Number is about 15V/cm, therefore voltage gradient ucIt is expressed as：
uc=15Larc (4)
Wherein, LarcFor the offline distance of bow net；And electric arc dissipated power P0And LarcCorrelation, is expressed as：
Wherein, k1, β be dissipated power constant；N is electric arc constant undetermined.
Further, the method for building up of the dynamic trajectory of the offline distance of bow net is in the step 2：
According to the trend of the offline track of bow net, determine that bow net is offline apart from L in bow net off-line procedurearcWith time t pass
System：
Wherein, t1The time point departed from for bow net；t0For the bow net offline time point to ultimate range；t2For bow net again
The time point of contact, lmArrive the distance value of maximum offline for bow net.
Further, in addition to by the dynamic offline Arc Modelling of bow net it is embedded in the integrated equivalent circuit of car-net,
Set up its corresponding state equation and solve, obtain waveform when this dynamic arc occurs；State equation is as follows：
Wherein, isFor the electric current of traction substation, i1For the electric current of Traction networks, icFor the arc current in equivalent circuit, u1
For the voltage of traction substation, u2For the contact net voltage at train end, above-mentioned five parameters are state variable；UsFor traction power transformation
The equivalent source provided, RsThe equivalent resistance provided for traction substation, LsThe equivalent inductance provided for traction substation；R1
For contact net equivalent resistance, L over the ground1For contact net equivalent inductance, C over the ground1For contact net equivalent capacity over the ground；LcFor locomotive
Equivalent inductance, RcFor the equivalent resistance of locomotive；RaFor arc resistance；
The state equation is solved using discretization iterative calculation mode：
Step a：The initial value of the known parameter of input and five state variables；
Step b：By formula (6) and formula (7) calculate bow net it is offline apart from Larc(k+1) formula (1), (2) (3), are then passed through
Calculate electric arc conductance gc(k+1)；
Step c：The value of state variable is updated by the iteration of formula (8), while obtaining arc current ic(k+1) and pass through
Electric arc stream and electric arc conductance, which are calculated, obtains arc voltage ua(k+1) value, and then obtain arc voltage uaAnd arc current ic's
Waveform.
The beneficial effects of the invention are as follows：The method of name of the present invention more meets the offline distance of bow net in this offline process of bow net
In the actual conditions that change over time, the offline Arc Modelling of dynamic bow net set up accordingly is the offline electric arc of bow net to train system
The studying for influence caused of uniting provides more favourable support.
Brief description of the drawings
Fig. 1 is the offline track schematic diagram of simplification of the offline common trend of bow net.
Fig. 2 is the integrated equivalent model schematic diagram of car-net.
Fig. 3 is the calculation process schematic diagram of meter and bow net dynamic arc state equation.
Fig. 4 is arc voltage and Current calculation result schematic diagram based on bow net dynamic arc model.
Embodiment
The present invention is further elaborated with specific embodiment below in conjunction with the accompanying drawings.
According to investigation of the electric railway industry for exchange bow net arc current waveform, bow net electric arc can distort sine wave
Go out to produce the change of transient state at current zero-crossing point simultaneously.Found in the simulation work of bow net electric arc, Mayr black box electric arc moulds
Equation in type is the situation for being best suitable for this special current zero-crossing point；And Cassie circuit breakers are then adapted to actual feelings
The low-impedance situation of electric arc high current under condition.
Two kinds of situations of summary, Habedank circuit breakers combine Mayr circuit breakers and Cassie
Circuit breaker, its equation expression formula is made up of three parts：Mayr electric arc equations part, Cassie electric arc equation parts with
And electric arc conductance calculating section.This model proposes that electric arc can be replaced in train and contact net system with a conductance simultaneously
Generation.
In formula：gmAnd gcRespectively the electric arc conductance of Mayr parts and the electric arc conductance of Cassie parts；I is electric arc
Electric current；τ1And τ2All it is time constant；P0And ucThe respectively dissipated power of electric arc and the voltage gradient of electric arc.
Formula (1) (2) (3) is the algorithm of the circuit breaker used in the present embodiment, wherein electric arc dissipated power P0And
Voltage gradient ucThe two parameters are dynamic rather than constant in practical situations both, and its change has with the offline distance of bow net
Close.
For the voltage gradient u in formula (2)c, substantial amounts of experiment and theory analysis are shown, in electric arc generating process
Stabilization sub stage in be stable value on unit arc length.Arc waveform obtained by being tested according to existing electric arc shows
Show, the whole process that electric arc occurs can be divided into：It is unstable before starting the arc stage, unstable arc stage, stable arc stage, blow-out
Determine five stages of arc stage and blow-out stage.Wherein stablize arc stage occupy the 95% of whole electric arc generating process with
On, it is possible to it is considered as whole stabilization process by electric arc generating process is equivalent, its voltage gradient is on unit arc length
It is a stationary value, arc length here refers to equivalent arc length, that is, the offline distance of bow net.Electric arc can to sum up be obtained
Voltage gradient can change with the offline distance change of bow net, and be direct ratio variation relation, and its proportionality constant is shown according to experiment
About 15V/cm, so voltage gradient can be expressed as：
uc=15Larc (4)
In formula：LarcFor the offline distance of bow net.
For the electric arc dissipated power P in formula (1)0, the research of early stage show its change it is relevant with electric arc conductance and it
Between relation can be expressed with the form of exponential function, while P0Also and LarcCorrelation, can be expressed as：
In formula：G is electric arc conductance；k1, β be dissipated power constant；N is electric arc constant undetermined.
Voltage gradient u can be drawn by above-mentioned formula (1)-(5)cWith electric arc dissipated power P0With bow net it is offline away from
From LarcRelation, thus introduces bow net in electric arc equation apart from this parameter offline, and the change of the offline distance of bow net can shadow
Ring the whole offline electric arc of bow net.According to the reality that bow net is offline, the offline distance of bow net can be in whole off-line procedure over time
Change, the Trajectory Arithmetic of the offline distance change of bow net is added in electric arc equation by formula (1)-(5), it is possible to realize bow net
The extendable of offline Arc Modelling.
Bow net Experiments of Machanics (bow net test experiment is simulated by mobile walking beam) show that the offline track of bow net has
Identical trend, can all undergo three processes：Bow net departs from, offline contact again to ultimate range, bow net.Become jointly this
Under gesture, specific offline track can be more by such as mechanical oscillation of train speed, train, current rate, contact line irregularity etc.
The influence of the factor of kind.Here a kind of offline track of simplification for meeting the offline common trend of bow net is provided, as shown in figure 1, L in figurem
It is offline ultimate range.The such track of selection mainly considers that bow net Offtime is shorter, the train speed in Offtime
Degree can be considered constant, therefore the increase process and reduction process of offline distance be set to the same.
Track according to Fig. 1, if bow net depart from time point be set to t1, bow net is offline to the time point of ultimate range
It is set to t0, time point for contacting again of bow net be set to t2, bow net arrive offline maximum distance value be set to lm, then bow net off-line procedure
Middle LarcRelation with time t is：
Arc Modelling can be introduced by the dynamic process of the offline distance change of bow net by bringing formula (6) (7) into formula (1)-(5).
To obtain the waveform of the offline electric arc of bow net on train, it is necessary to set up car-net one comprising Pantograph-OCS system electrical contact
Body equivalent model, provides a kind of integrated equivalent model of car-net of simplification, as shown in Figure 2 here.Electric arc is with one two in figure
The form incorporation model of terminal type non-linear resistance, uses RarcExpression.Traction substation U in models、RsAnd LsIt is equivalent, wherein
UsThe equivalent source provided for traction substation, RsAnd LsFor its equivalent resistance and inductance.Contact net circuit is equivalent to a π types
Equivalent circuit, wherein R1、L1And C1For contact net equivalent resistance, inductance and electric capacity over the ground.In addition, the equivalent load of locomotive is (equivalent
Inductance and resistance) it is expressed as RcAnd Lc.For the dynamic parameter in Fig. 2, u1And isIt is the voltage and electricity of traction substation
Stream, i1It is the electric current of Traction networks, u2It is the contact net voltage at train end, ic、uaAnd ucBe respectively arc current, arc voltage and by
Pantograph bow voltage.
Set up by above-mentioned model, bow net electric arc is embedded in the way of electric arc conductance in the integrated equivalent model of car-net,
So when the offline electric arc of bow net occurs, solving electric arc and namely calculating its electric arc conductance.Next built according to Fig. 2 institutes representation model
State equation when vertical electric arc occurs.By five parameter i shown in Fig. 2s、i1、ic、u1、u2As state variable to set up state side
Journey：
In formula：RaFor arc resistance.
Consider arc resistance RaIt is continually changing, the state equation shown in formula (8) is nonlinear.According to state equation
Non-linear nature, below using discretization iterate to calculate mode solving state equation.
It is arrange parameter first, for the integrated equivalent model parameter of the car shown in Fig. 2-net：Using conventional 20.5km,
50Hz, 2 × 27.5kV exchange high ferro supply line, its us=27.5kV, Rs=0.177 Ω, Ls=31.8mH, R1=2.95
Ω, L1=23.5mH, C1=0.081 μ F, Rc=56.19 Ω and Lc=91.6mH.To cause electric arc result of calculation to be tied with experiment
It is really close, the parameter n=1 in formula (5), β=0.5 and k1=2500000.To the offline track of bow net shown in Fig. 1, it is considered to one
The situation of individual low speed, its maximum offline is apart from Lm=0.01m.
Followed by iterate to calculate, its calculation procedure is：
(1) initial value of known parameter and five state variables is inputted.
(2) calculated by formula (6) (7) bow net it is offline apart from Larc(k+1), then calculated by formula (1) (2) (3)
Electric arc conductance gc(k+1), wherein k is iterations.
(3) value of state variable is updated by the iteration of formula (8), while obtaining arc current ic(k+1) and electricity is passed through
Arc stream and electric arc conductance, which are calculated, obtains arc voltage ua(k+1) value.
Specific calculating process is as shown in Figure 3.
Obtain arc voltage uaAnd arc current icWaveform it is as shown in Figure 4.The trend and OHL of waveform shown in Fig. 4
Waveform trend identical [S.Midya, D.Bormann, T.Schutte, and shown in the experimental result of ICE team
R.Thottappillil,“Pantograph arcing in electrified railways-mechanism and
influence of various parameters-part II:with AC traction power supply,”IEEE
Trans.on Power Del,vol.24,pp.1940-1950,October.2009.]。
Claims (4)
1. a kind of offline Arc Modelling method for building up of dynamic bow net for considering the offline distance of bow net, it is characterised in that including following
Step：
Step 1：According to the relation of voltage gradient and electric arc dissipation power each with the offline distance of bow net, by bow net it is offline away from
From being introduced into the electric arc equation of circuit breaker, the extendable of the offline Arc Modelling of bow net is realized；
Step 2：According to the actual conditions that bow net is offline, the dynamic trajectory of the offline distance of bow net is set up, and is introduced into electric arc mould
In type, the foundation of the offline Arc Modelling of dynamic bow net is realized.
2. the dynamic bow net offline Arc Modelling method for building up according to claim 1 for considering the offline distance of bow net, it is special
Levy and be, the circuit breaker in the step 1 is Habedank circuit breakers, and its electric arc is in train contact network system
It is middle to be substituted with conductance：
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In formula：gmFor the electric arc conductance of Mayr parts；gcFor the electric arc conductance of Cassie parts；G is electric arc conductance；I is electric arc electricity
Stream；τ1And τ2For time constant；P0For the dissipated power of electric arc；ucFor the voltage gradient of electric arc；
Because voltage gradient can change with the offline distance change of bow net, and it is direct ratio variation relation, proportionality constant is about
For 15V/cm, therefore voltage gradient ucIt is expressed as：
uc=15Larc (4)
Wherein, LarcFor the offline distance of bow net；And electric arc dissipated power P0And LarcCorrelation, is expressed as：
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Wherein, k1, β be dissipated power constant；N is electric arc constant undetermined.
3. the dynamic bow net offline Arc Modelling method for building up according to claim 2 for considering the offline distance of bow net, it is special
Levy and be, the method for building up of the dynamic trajectory of the offline distance of bow net is in the step 2：
According to the trend of the offline track of bow net, determine that bow net is offline apart from L in bow net off-line procedurearcWith time t relation：
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Wherein, t1The time point departed from for bow net；t0For the bow net offline time point to ultimate range；t2Contacted again for bow net
Time point, lmArrive the distance value of maximum offline for bow net.
4. the dynamic bow net offline Arc Modelling method for building up according to claim 3 for considering the offline distance of bow net, it is special
Levy and be, in addition to the dynamic offline Arc Modelling of bow net is embedded in the integrated equivalent circuit of car-net, set up its corresponding
State equation is simultaneously solved, and obtains waveform when this dynamic arc occurs；State equation is as follows：
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Wherein, isFor the electric current of traction substation, i1For the electric current of Traction networks, icFor the arc current in equivalent circuit, u1To lead
Draw the voltage of electric substation, u2For the contact net voltage at train end, above-mentioned five parameters are state variable；UsCarried for traction substation
The equivalent source of confession, RsThe equivalent resistance provided for traction substation, LsThe equivalent inductance provided for traction substation；R1To connect
Touch net equivalent resistance, L over the ground1For contact net equivalent inductance, C over the ground1For contact net equivalent capacity over the ground；LcFor the equivalent of locomotive
Inductance, RcFor the equivalent resistance of locomotive；RaFor arc resistance；
The state equation is solved using discretization iterative calculation mode：
Step a：The initial value of the known parameter of input and five state variables；
Step b：By formula (6) and formula (7) calculate bow net it is offline apart from Larc(k+1), then calculated by formula (1), (2) (3)
Electric arc conductance gc(k+1), wherein k is iterations；
Step c：The value of state variable is updated by the iteration of formula (8), while obtaining arc current ic(k+1) and electric arc is passed through
Stream and electric arc conductance, which are calculated, obtains arc voltage ua(k+1) value, and then obtain arc voltage uaAnd arc current icRipple
Shape.
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| CN112528565B (en) * | 2020-12-18 | 2024-03-15 | 辽宁工程技术大学 | Arc net arc modeling method and simulation loop considering arc random characteristics |
| CN114499722A (en) * | 2022-01-10 | 2022-05-13 | 北京全路通信信号研究设计院集团有限公司 | Double-system magnetic suspension train ground communication electromagnetic interference simulation system |
| CN114499722B (en) * | 2022-01-10 | 2024-03-22 | 北京全路通信信号研究设计院集团有限公司 | Dual-system magnetic levitation train-ground communication electromagnetic interference simulation system |
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