CN114861430B - Bow net off-line arc modeling simulation method with high-frequency characteristic - Google Patents
Bow net off-line arc modeling simulation method with high-frequency characteristic Download PDFInfo
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Abstract
The invention discloses a bow net off-line electric arc modeling simulation method with high-frequency characteristics, which fully considers the physical processes of high-frequency impedance change in different electric arc stages of arc starting, zero-rest arc quenching, zero-crossing re-ignition and the like when a bow net is off-line, simulates and calculates bow net discharge current with high-frequency oscillation and low-frequency zero-rest characteristics, a simulation result can more truly reflect the current characteristics of bow net off-line discharge, a simulation model has higher accuracy, and the defect of high-frequency current characteristics in the traditional bow net off-line discharge model is made up. By utilizing the model, effective data of the discharge current can be obtained in a simulation calculation mode, discharge experiments under high voltage and high current conditions are not required to be carried out, and a large amount of effective data of variable conditions can be provided for research of bow net off-line discharge electromagnetic interference by changing the conditions which are difficult to control in experiments such as bow net separation step signals, load impedance, line parameters and the like.
Description
Technical Field
The invention relates to the technical field of rail transit electromagnetic compatibility, in particular to a bow net offline arc modeling simulation method with high-frequency characteristics.
Background
In recent years, the traction power and the automation degree of the railway system in China are comprehensively improved, the scale and the number of the vehicle-mounted and trackside power electronic equipment reach unprecedented levels, and the problems of the electromagnetic environment safety and the adaptability of the railway system are increasingly prominent. A great deal of research indicates that mechanical separation of the pantograph and the contact line during train running can cause a discharge phenomenon between the carbon pantograph slider and the contact line, namely pantograph-catenary off-line arc. The arc discharge can generate pulse type transient electromagnetic disturbance with large energy and wide frequency band on sensitive equipment in a train control and communication system, and even influence the driving safety in serious cases. Therefore, research on the cause mechanism of the pantograph-catenary offline arc electromagnetic interference needs to be carried out, main characteristics and influencing factors of pantograph-catenary offline discharge electromagnetic interference are determined, and theoretical reference is provided for electromagnetic protection of pantograph-catenary offline discharge.
When a high-speed railway train runs in China, the effective value of 50Hz traction current can reach hundreds of amperes, transient current generated by bow net discharge rises to thousands of amperes within dozens of nanoseconds, and the frequency of bow net discharge current and radiation electromagnetic waves thereof can reach GHz. The transient current has a non-negligible influence on the railway electromagnetic environment, not only directly forms conducted interference on a traction power system, but also releases strong electromagnetic radiation in a space environment, and is coupled to train sensitive equipment such as a transponder transmission unit (BTM), a railway digital mobile communication system (GSM-R) and the like through a plurality of transmission paths to form pantograph-catenary discharge electromagnetic interference. For the problem, a large number of researches on bow net arc electromagnetic interference field test and experimental simulation are carried out at home and abroad, however, in the actual railway field, because the position of a current sensor is difficult to select, the acquisition difficulty of transient current waveforms generated by bow net discharge is high, and in a laboratory, because of the power limitation of a power supply and a load, a large-current and high-voltage discharge experiment under the condition of simulating the actual railway running power is difficult to carry out; meanwhile, the voltage of a contact network keeps alternating at 50Hz in the running process of the train, the influence of the instantaneous voltage of a pantograph-catenary gap on discharge is very critical, and the phase of a power supply at an off-line moment in an actual test environment is difficult to control; in addition, in actual testing, the broadband and large-amplitude current testing is always a technical problem which is difficult to break through at present, the railway electromagnetic environment is complex, and the measured current waveform is difficult to judge whether the current waveform is the current waveform of bow net discharge. In consideration of the factors, the difficulty of researching the bow net discharge problem by using an experimental or field actual measurement method is high, and the method for calculating the discharge current in the bow net discharge circuit is feasible by establishing the bow net discharge impedance change equation through a modeling method.
The traditional Mayr, cassie and improved models thereof enable the alternating current arc to be equivalent to a time-varying resistor, and although the current low-frequency zero-break phenomenon from stable arcing to arc extinguishing can be reasonably explained, the important characteristic of high-frequency oscillation of current during reignition is ignored. And according to the radiation field forming principle, the electromagnetic radiation interference of bow net discharge is due to high-frequency transient current in the line, wherein the current transient caused by gap impedance change of most possible bow net separation arcing and zero extinction and high-frequency oscillation current generated by high-voltage breakdown of a bow net gap after zero crossing. The reason for the high frequency characteristics of the current cannot be explained by these models, precisely because the existing ac arc models lack a physical description of the air breakdown. On the other hand, the existing alternating current arc model does not consider key factors of pantograph and catenary offline motion such as separation time, gap distance and the like, and does not calculate in an equivalent circuit of a railway traction power supply system, so that the research result cannot accurately describe the change of pantograph and catenary discharge current along with time, and the obtained model cannot be directly applied to simulation and calculation of the pantograph and catenary offline discharge current. The two factors compel researchers to consider establishing a pantograph-catenary discharge circuit model which gives consideration to the whole dynamic process of separation arcing, stable arcing, arc quenching and re-ignition breakdown, particularly pay attention to the impedance change mechanism of the re-ignition stage and the arc extinguishing stage after the current zero crossing, so that the transient change current in the pantograph-catenary discharge process is obtained through calculation.
Disclosure of Invention
The invention aims to solve the technical problem of providing a modeling simulation method which can truly reflect the current characteristic of pantograph-catenary offline discharge, has higher accuracy in a simulation model and can describe the high-frequency characteristic of pantograph-catenary discharge current.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a bow net off-line arc modeling simulation method with high-frequency characteristics comprises the following steps:
on the basis of analyzing a gap impedance change physical mechanism in the bow net off-line process, obtaining an expression of bow net gap impedance change along with time in the bow net separation arcing, current zero-break arc quenching and zero-passage arc reignition process;
establishing a bow net discharge circuit model considering high-frequency characteristics, wherein a bow net separation arc-drawing stage is described by changing contact resistance into arc-burning resistance and arc column inductance, a bow net arc extinguishing process is described by referring to a Mayr arc resistance model, and a re-burning at a bow net arc zero-crossing point is described by utilizing a Toosen discharge theory and a Toepler empirical formula;
fitting the relation between breakdown threshold voltage and pantograph-catenary gap distance by using experimental results, determining the time-varying rule of breakdown threshold voltage in the pantograph-catenary offline process by establishing an equation of time-varying gap distance, and determining the restrike breakdown time after zero-crossing arc extinction by comparing the breakdown threshold with the gap voltage;
in consideration of the high-frequency characteristics of the arc current in the extinguishing and re-burning processes, an arc inductor and a gap capacitor are added into an arc model, an arc network off-line arc impedance model is constructed, and the arc network discharge current with high-frequency oscillation and low-frequency zero-rest characteristics is simulated and calculated in a pi-type analog circuit.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the method, the physical process of high-frequency impedance change in different arc stages such as arc starting, zero-rest arc extinguishing, zero-cross reignition and the like during offline of the pantograph-catenary is fully considered, the pantograph-catenary discharge current with the characteristics of high-frequency oscillation and low-frequency zero-rest is simulated and calculated, the current characteristic of offline pantograph-catenary discharge can be truly reflected by a simulation result, and the simulation model has high accuracy and makes up for the defect of high-frequency current characteristics in the traditional pantograph-catenary offline discharge model. By utilizing the model, effective data of the discharge current can be obtained in a simulation calculation mode, a discharge experiment under the conditions of high voltage and large current is not required to be carried out, the condition which is difficult to control in the experiment can be realized by changing bow net separation step signals, load impedance, line parameters and the like, and a large amount of effective data of variable conditions is provided for the research of bow net off-line discharge electromagnetic interference.
Drawings
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of a method according to an embodiment of the invention;
FIG. 2 is an off-line arc equivalent of the pantograph-catenary configuration of the present invention;
FIG. 3 is a graph of breakdown threshold voltage as a function of bow net gap distance for an embodiment of the present invention;
fig. 4 is an equivalent circuit model diagram of offline pantograph-catenary discharge according to an embodiment of the present invention;
FIG. 5 is a Simulink simulation circuit diagram of an offline arc model of a pantograph according to an embodiment of the present invention;
FIG. 6 is a Simulink simulation model diagram of the breakdown determination module in an embodiment of the present invention;
FIG. 7 is a graph of arc resistance over time obtained by an off-line arc model of a pantograph in an embodiment of the present invention;
FIG. 8 is a graph of gap voltage variation in pantograph obtained from an offline arc model of a pantograph in an embodiment of the present invention;
FIG. 9 is a diagram of a loop current waveform obtained by simulation calculation according to an embodiment of the present invention;
FIG. 10 is a graph of a low frequency current waveform through a resistive-inductive branch in an embodiment of the present invention;
FIG. 11 is a waveform of a high frequency oscillating current at the time of extinction and re-ignition in an embodiment of the present invention;
FIG. 12 is a diagram of the frequency spectrum information of the current time domain waveform with high frequency characteristics after Fast Fourier Transform (FFT) in the embodiment of the invention;
wherein: 1. a contact line; 2. carbon slide plate of pantograph.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as specifically described herein, and it will be appreciated by those skilled in the art that the present invention may be practiced without departing from the spirit and scope of the present invention and that the present invention is not limited by the specific embodiments disclosed below.
As shown in figure 1, the embodiment of the invention discloses a bow net off-line arc modeling simulation method with high-frequency characteristics, which is based on the generation mechanism of the bow net off-line arc, the arc is equivalent to an RLC lumped parameter model as shown in figure 2, the whole bow net arc dynamic process is divided into different stages of bow net separation arcing, arc burning, current zero-rest extinguishing and re-burning after zero crossing, and impedance expressions in zero-rest extinguishing and re-burning after zero crossing are established to describe arc parameters (namely R) arc 、L arc 、C pc ) So as to calculate the current and voltage waveform of the bow net arc. In the bow net separation arcing stage, the arc resistance is expressed as contact resistance and becomes arc burning resistance, in the zero-crossing extinguishing stage, the arc resistance is expressed as an exponential function by referring to a Mayr classical arc model, and in the zero-crossing re-burning stage, the Toepler model for forming 'electron avalanche' by air breakdown is matched with gap capacitance for description. Meanwhile, a breakdown threshold value which dynamically changes along with the separation of the pantograph-catenary is used as the judgment of the re-ignition start, so that the modeling of the offline arc full-dynamic process of the pantograph-catenary considering the high-frequency characteristic is realized, and the discharge current with the high-frequency characteristic obtained by calculation can provide a reasonable explanation for the formation of the electromagnetic interference of the pantograph-catenary discharge.
Further, the method comprises the following steps:
on the basis of analyzing a physical mechanism of gap impedance change in the bow net off-line process, an expression of bow net gap impedance change along with time in the processes of bow net separation arc discharge, current zero-break arc blowout, zero-crossing arc reignition and the like is obtained.
Establishing a bow net discharge circuit model considering high-frequency characteristics, wherein the bow net separation moment is described by changing contact resistance into arc resistance and arc column inductance, the bow net arc extinguishing process is described by referring to a Mayr arc resistance model, and the reignition at the bow net arc zero crossing point is described by using a Toepler discharge theory and a Toepler empirical formula.
The relationship between the breakdown threshold and the gap distance of the pantograph-catenary is fitted by using experimental results, the time change rule of the breakdown threshold in the offline process of the pantograph-catenary is determined by establishing an equation of the time change of the gap distance, and the restrike breakdown moment after zero-crossing arc extinguishing is determined by comparing the breakdown threshold with the gap voltage, so that the restrike breakdown is more truly and accurately described.
In consideration of the high-frequency characteristics of the arc current in the extinguishing and re-burning processes, the arc inductor and the gap capacitor are added into the arc model, a more accurate arc impedance model is constructed, and the bow net discharge current with the high-frequency oscillation and low-frequency zero-rest characteristics is simulated and calculated in the pi-type analog circuit.
The above steps are described in detail with reference to the specific contents
Bow net separation and arcing: in particular, the contact resistance R which can be regarded as constant exists when the bow net is in normal contact jc =0.2 omega, when the bow net is pulled out after mechanical vibration separation, the electric arc enters a stable combustion stage, and the arc arcing resistance value is changed into R 0 =2 omega, the arc column has larger inductance at the moment, and the value is L arc ＝1mH。
And (3) quenching the arc when the current passes zero: with the continuous change of the phase of the 50Hz alternating current, when the current passes through a zero point, the external circuit does not input energy for the electric arc any more, so that the electric arc is extinguished and changed into a high resistance in a short time, at the moment, the whole bow net electric arc is resistive, and the inductance of an arc column can be ignored. Referring to a calculation method of a Mayr arc resistance model, for a formed bow net arc, the conductance change of an arc extinguishing process at the zero crossing point of alternating current satisfies the equation:
where g is the conductance of the arc per unit length, P out For the arc dissipation power, τ is the model time constant, u h The recovery voltage gradient of the bow net gap.
Relating arc resistance to conductance
Substituting the formula into (1), and solving the equation to obtain the expression of the arc resistance in the arc quenching stage as follows:
considering the relatively short bow-web gap, u h Smaller relative to long gap arcs, the recovery voltage across the gap of the pantograph network after the current crosses zero (i.e. u h = 0), the expression can then be simplified to:
where τ =1ns, this formula indicates that during the current zero-crossing arc extinguishing phase, the arc resistance may vary from R to tens of nanoseconds 0 =2 Ω to several hundred megaohms, thereby generating a rapidly varying loop current, forming an electromagnetic disturbance source. Because of the high-frequency component of the current, the capacitance between the bow net electrodes is not negligible at this stage, and the value C is taken pc ＝0.1μF。
Breakdown threshold dynamic change: and in hundreds of microseconds after the arc high-resistance state is continued, the bow net gap is continuously increased until a breakdown threshold value is reached, and air breakdown discharge is formed. Because the pantograph carbon slide plate and the contact wire are not standard discharge electrodes such as a needle-needle, a needle-plate and the like, the empirical relation between the breakdown voltage and the electrode gap distance cannot be simply applied, but the relation is determined by fitting experimental data (shown in figure 3), and the breakdown voltage V is obtained by a high-voltage breakdown discharge experiment of the real pantograph carbon slide plate and the contact wire under different gaps in a laboratory jc The following fit relationship exists with the bow net gap length d:
wherein d has the unit of cm, V jc In kV.
Assuming that the longitudinal relative speed is 20cm/s, the pantograph contact pressure is 120N, and the mass of the pantograph head is 60kg when the pantograph is separated from the pantograph, if the pantograph is simplified into a spring oscillator, the change function of the pantograph gap length (cm) along with the time(s) within 200ms (namely 10 alternating current periods) can be calculated as follows:
d＝20t-100t 2 (5)
thus, the formula for the breakdown voltage over 200ms (i.e., 0 < t < 0.2 s) can then be written as:
after zero crossing, re-ignition: when the current zero crossing is extinguished, the arc resistance of the bow net keeps high resistance, the arc gap voltage is rapidly increased to the power supply voltage and then alternates sinusoidally, when the arc gap voltage is greater than the breakdown voltage, electrons are ionized and accelerated under the action of an external electric field, stronger impact ionization is caused on a motion path, the number of electrons is increased like avalanche, namely electron avalanche, and the air gap is broken down to cause discharge. According to Thomson's discharge theory and the Toepler arc model, if the electron density from the cathode x length is expressed as n e Then, there are: (dn) e /dx)＝αn e And alpha is the Thonsen first ionization coefficient, defined as the number of average ionizing collisions an electron travels along the electric field over a unit length. Using electron drift velocity v e ＝μ e E denotes the velocity of the charged particles in the direction of the electric field, where e Is the electron mobility, E is the applied electric field strength, and there are:
dn e ＝αn e dx＝αn e v e dt (7)
define conductivity as σ = en e μ e Assuming that the gap length of the bow net is d and the sectional area of the arc column is A arc Then the current density can be expressed as:
further arc resistance is calculated as:
measuring the rate of change of the electron density in (9) with time
The rewrite is:
after integration, there are:
substituting into equation (10) there is:
substituting the relation (5) of d changing along with time, and taking alpha mu e =0.5, the time-dependent relationship of the arc resistance during zero-crossing reignition is found to be:
the arc formed after complete breakdown burns sufficiently, the arc resistance is kept at the minimum value of 2 omega, and the arc resistance is increased again at the moment of extinction after about 10ms (namely half of alternating current period), then the process is continuously repeated until the bow net is lapped again, the gap impedance only keeps the contact resistance of the bow net, at the moment, the current is recovered to a stable 50Hz sine waveform, and low-frequency zero-break and high-frequency pulse oscillation do not occur any more.
Mathematical expression of the bow net off-line arc complete process:
through the analysis, the dynamic mathematical expression of the bow net off-line arc impedance considering the high-frequency characteristic is obtained as follows:
wherein, t 1 For the moment of bow net separation, the initial phase of arc discharge is determined by different separation moments under the control of bow net separation step signals, and the initial phase can be set as a simulation initial condition. t is t 1 Before the moment, the pantograph contact is good, and the pantograph gap impedance is only shown as pantograph contact resistance at the moment, and the inductance and the capacitance are negligible. t is t 1 ～t 2 For the continuous arc discharge stage, the arc impedance can be regarded as being kept unchanged, and the arc column has certain sensibility because the arc resistance is smaller in the stage. t is t 2 Current zero crossing at time, arc at delta t 2 The arc resistance rapidly increases in a short time, and the current changes instantaneously following the change rule of Mayr arc resistance, so that the gap capacitance is not negligible and is calculated as 1 muF. After the arc is extinguished, the gap voltage is changed into the power supply voltage in a short time, and then is continuously increased according to 50Hz sine alternation, and at t 3 The gap voltage is greater than the dynamic breakdown threshold voltage at the moment, the extinguished arc is reignited under the action of high-voltage air breakdown, and the arc resistance is 10 10 The omega becomes smaller instantly to be a stable arcing resistance, the breakdown reignition process follows the variation rule of the resistance value of the Toepler arc, and the gap capacitance in the transient process is not negligible and is marked as 1 muF. And then after the next 50Hz half period, zero-rest arc quenching is performed again, and the zero-crossing point is reignited.
An equivalent circuit model of bow net off-line discharge is established on the basis of the mathematical model and is shown in fig. 4. The arc impedance is equivalent to a two-port time-varying nonlinear resistor R arc Arc column inductor L arc And gap capacitance C pc A combination of (a) and (b).
The traction substation can be equivalent to a parameter U s 、R s And L s ，U s Is an AC high voltage with effective value of single-phase 27.5kV and 50Hz, R s And L s Equivalent resistance and inductance of power supply, whose values are R s ＝1mΩ、L s =0.01mH. The traction power supply network is equivalent to a pi-shaped structure R 1 ＝1mΩ、L 1 ＝0.01μH, contact line equivalent resistance and inductance, C 1 And C 2 Equivalent capacitance C for contact line to ground 1 ＝C 2 ＝0.01μF。R c And L c The equivalent resistance and inductance of the train body are respectively R c ＝133Ω、L c ＝0.01mH。
By means of a switch S 0 、S 1 、S 2 、S 3 To control the arc impedance state. Stable contact of bow with net, S 0 Closure, S 1 、S 2 、S 3 Opening, R jc Accessing a circuit; bow net begins off-line arc drawing, S 0 Breaking, S 1 、S 3 Breaking, S 2 Closure, R arc And L arc Accessing a circuit; short time of zero-crossing arc extinction, S 2 Breaking, S 1 、S 3 Closure, C pc And R arc Accessing a circuit; after zero crossing to before breakdown, S 1 、S 3 Breaking, S 2 Closure, R arc And L arc Accessing a circuit; short time of breakdown, S 2 Breaking, S 1 、S 3 Closure, C pc And R arc Accessing a circuit; stable arcing after breakdown, S 1 、S 3 Breaking, S 2 Closure, C pc And R arc And accessing the circuit.
The MATLAB/Simulink software is used for realizing the building of a bow net off-line arc model with high-frequency characteristics, a Simulink simulation circuit is shown in figure 5, and the model comprises a variable resistor R arc Arc column inductor L arc Bow net gap capacitor C pc And switch S 0 、S 1 、S 2 、S 3 The arc dynamic impedance module, the breakdown judgment module, the bow net separation step signal, the resistance calculation module, the alternating current power supply and the power supply side equivalent resistance R s Power supply side equivalent inductance L s Vehicle body load equivalent resistance R c Vehicle body load equivalent inductance L c Equivalent resistance R of contact network 1 Inductor L 1 Capacitor to ground C 1 And C 2 And current and voltage probes.
The bow net separation step signal is connected with the switch S after passing through logical negation 0 Connected to each other before separation S 0 Closed, separated S 0 And (5) disconnecting. As shown in fig. 6, a Simulink simulation model of the breakdown determination module is that threshold is a breakdown threshold calculated by a fitting function written into the interpolated MATLAB Fcn, whether breakdown occurs is determined by comparing the threshold with a power supply voltage absolute value | u |, if breakdown occurs, a calculation result is 1, if breakdown does not occur, the calculation result is 0, and a breakdown determination signal torf is output by the module. When torf value is 1, the gap capacitance C of bow net pc Connected switch S 1 And arc column inductance L arc Connected switch S 2 Closed, when torf is 0, switch S 3 And (5) closing. The resistance calculation module realizes the calculation of formula (15), and the inputs of the module are breakdown judgment signal torf and bow net separation step signal t 3 The sum loop current I outputs a calculation result R of the change of the arc resistance value along with the time arc (t) the module is directly connected to a variable resistor which takes the R of its output arc The value is obtained. The oscilloscope 1 collects loop current, low-frequency current flowing through the resistance inductor, high-frequency current flowing through the capacitor, and pantograph-catenary gap voltage in four channels. The oscilloscope 2 collects the time-dependent change of the arc resistance of the pantograph-catenary, the arc column inductance and the gap capacitance of the pantograph-catenary and breakdown judgment signals through four channels. Because Variable resistors (Variable resistors) in MATLAB belong to Simscape class, the Variable resistors need to be built under a physical signal loop, and oscilloscopes, breakdown judgment modules and the like are Simulink class, signal conversion needs to be set between signals in different modes, such as signal conversion 1-6 in the figure.
The simulation time length is 0.2s, the sampling interval time is 5e-10s, namely the sampling frequency is 2GHz, and the number of simulation sampling points is 400M. The pantograph-catenary separation time is set to be 0.015s, namely, the current is in a stable 50Hz sine state before 0.015s, the safety of stable power supply and an electromagnetic environment of a train can be guaranteed, the current waveform presents the characteristics of low-frequency zero-rest and high-frequency oscillation after 0.015s of pantograph-catenary off-line electric arc occurs, the characteristics of the low-frequency zero-rest are mainly influenced by the dynamic change of an arc resistor, and the current of the high-frequency oscillation is just a disturbance source of pantograph-catenary discharge electromagnetic radiation and is mainly influenced by a ground capacitor, a pantograph-catenary gap capacitor and a loop inductor of a contact wire.
The following are the simulation results and the calculation conclusions of the model:
the change of the arc resistance with time obtained by applying the pantograph-catenary offline arc model with the high-frequency characteristic is shown in fig. 7, the arc resistance is rapidly increased in a short time of a zero-crossing arc quenching stage, and the change rule follows equation (3). The bow net gap resistance is in a high resistance state and lasts for hundreds of microseconds, after the bow net gap voltage reaches a breakdown threshold value, the bow net off-line arc is reignited again, an air breakdown discharge loop is conducted, the arc resistance is rapidly reduced in a short time, the change rule follows an equation (14), the arc is continuously drawn after reignition, and when the next alternating current half period comes, the change is repeated. With the increase of the bow net gap (the maximum gap appears at 0.05 s), the larger the breakdown voltage is, the longer the arc high-resistance state duration is, and therefore, the time occupied by the high resistance is changed from increasing to decreasing.
The change situation of the gap voltage of the pantograph and catenary obtained by model calculation is shown in fig. 8, when 0.015s occurs pantograph and catenary disconnection, the gap voltage of the pantograph and catenary quickly reaches a peak value above 40kV, and after stable arc discharge, the gap voltage of the pantograph and catenary quickly drops to the partial voltage of an arc resistor in a circuit, which is about ten volts. After each zero crossing point, the bow net gap is opened instantly, and the gap voltage can rise to the power supply voltage within hundreds of microseconds. When the voltage of the pantograph-catenary gap reaches a breakdown threshold value (the breakdown threshold value dynamically changes along with the vertical movement of the pantograph-catenary according to a formula (4-6)), air breakdown occurs, insulating air in the pantograph-catenary gap is conducted to form a discharge loop, and the voltage of the pantograph-catenary gap is reduced to the reduction level of the arc resistance voltage division again. Along with the movement of the spring vibrator of the pantograph, the pantograph-catenary gap distance is increased and then decreased, the breakdown voltage and the pantograph-catenary gap distance are in positive correlation, and the breakdown voltage is in a variation trend of being increased and then decreased.
The loop current waveform obtained by simulation calculation is shown in fig. 9, and it can be seen that high-amplitude and fast-changing pulses appear at intervals of 10 milliseconds in about 0.018 to 0.09 seconds, high-frequency oscillation of the current generates three physical processes of bow net separation, zero current rest and breakdown reignition, and the maximum pulse amplitude is about 5000A. Because the pulse amplitude is much larger than the 50Hz sine wave amplitude, the waveform diagram is longitudinally compressed, and the zero-rest characteristic of the current is not obvious. In the low-frequency current waveform through the resistance-inductance branch circuit shown in fig. 10, a significant low-frequency zero-break can be seen, and the obtained waveform is similar to the research result of the related alternating-current arc. And the zero-rest time changes along with the dynamic change of the breakdown threshold, namely when the pantograph-catenary gap is larger, the breakdown threshold is larger, and the zero-rest time is longer, which is more similar to the actual physical mechanism.
With the alternating current periodically passing through zero, the arc extinction and reignition occurs at a frequency of 100Hz, the high frequency oscillating current waveform at the extinction and reignition point is shown in fig. 11, with a pulse amplitude of about 5000A, a duration of about 150 mus, and an oscillation period of about 50ns. The frequency spectrum information of the current time domain waveform with high-frequency characteristics after Fast Fourier Transform (FFT) is shown as a curve (2) in fig. 12, compared with a noise signal curve (1), the bow net discharge current signals are all distributed with energy in a frequency range of 1GHz, the high-frequency oscillation current can generate radiation disturbance, and the interference on vehicle-mounted sensitive equipment is easily formed. The embodiment can explain the generation mechanism of electromagnetic interference of pantograph-catenary offline discharge, the transient change of impedance causes high-frequency oscillation of loop current when the pantograph-catenary is offline, high di/dt causes electromagnetic radiation, and when electromagnetic waves are transmitted to the vehicle-mounted sensitive equipment in space, interference voltage is formed by coupling at a port, errors such as noise, error codes and missing codes are formed, and the normal work of the vehicle-mounted sensitive equipment is influenced.
According to the method, by describing impedance changes of different arc stages of arc discharge, zero-rest arc blowout and zero-cross reignition when the pantograph-catenary is offline, the pantograph-catenary discharge current with high-frequency oscillation and low-frequency zero-rest characteristics is simulated and calculated, the current characteristics of the pantograph-catenary offline discharge can be reflected more truly by a simulation result, and the simulation model has higher accuracy and makes up for the defect of high-frequency current characteristics in the traditional pantograph-catenary offline discharge model. By utilizing the model, effective data of the discharge current can be obtained in a simulation calculation mode, a discharge experiment under the conditions of high voltage and large current is not required to be carried out, the condition which is difficult to control in the experiment can be realized by changing bow net separation step signals, load impedance, line parameters and the like, and a large amount of effective data of variable conditions is provided for the research of bow net off-line discharge electromagnetic interference.
Claims (8)
1. A bow net off-line arc modeling simulation method with high-frequency characteristics is characterized by comprising the following steps:
on the basis of analyzing a gap impedance change physical mechanism in the bow net off-line process, obtaining an expression of bow net gap impedance change along with time in the bow net separation arcing, current zero-break arc quenching and zero-passage arc reignition process;
establishing a bow net discharge circuit model considering high-frequency characteristics, wherein the bow net separation moment is described by changing contact resistance into arc resistance and arc column inductance, the bow net arc extinguishing process is described by referring to a Mayr arc resistance model, and the reignition at the bow net arc zero crossing point is described by using a Toepler discharge theory and a Toepler empirical formula;
fitting the relation between the breakdown threshold and the gap distance of the pantograph-catenary by using an experimental result, determining the time variation rule of the breakdown threshold in the offline process of the pantograph-catenary by establishing an equation of the time variation of the gap distance, and determining the restrike breakdown time after zero passage arc extinction by comparing the breakdown threshold with the gap voltage;
in consideration of the high-frequency characteristics of arc current in the extinguishing and re-burning processes, arc inductance and gap capacitance are added into an arc model, an arc network off-line arc impedance model is constructed, and arc network discharge current with high-frequency oscillation and low-frequency zero-rest characteristics is simulated and calculated in a pi-type analog circuit;
the method for establishing the bow net off-line discharge equivalent circuit model comprises the following steps:
AC high voltage U s One end of (1) is connected to an equivalent resistor R of a power supply s And equivalent inductance L s The first path is divided into two paths, the first path passes through a resistor R 1 Rear and inductance L 1 Is connected with the first end of the capacitor, and the second path is connected with an alternating current high voltage U through a capacitor C1 s Is connected to the other end of the inductor L 1 The other end of the first path is divided into two paths, the first path passes through a capacitor C 2 With said alternating current high voltage U s The other end of the first path is connected with the second path in sequence through a switch S 1 Capacitor C pc Resistance R c And an inductance L c Rear and said U s Connecting; switch S 0 And a resistor R jc A terminal is connected with an inductor L after being connected in series 1 And switch S 1 Node of, switch S 0 And a resistor R jc The other end of the capacitor C is connected in series pc And a resistor R c A node of (a); variable resistor R arc One end of the switch is connected with an inductor L1 and a switch S 1 Node of (2), variable resistor R arc The other end of the first switch is divided into two paths, the first path is through a switch S 3 Rear connection capacitor C pc And a resistor R c The second path of the node (S) passes through the switch (S) in turn 2 And an inductance L arc Rear connection capacitor C pc And a resistor R c A node of (a);
the traction substation can be equivalent to a parameter U s 、R s And L s ，U s Is an alternating-current high voltage with the effective value of single phase 27.5kV and 50Hz, R s And L s Equivalent resistance and inductance of power supply, whose values are R s ＝1mΩ、L s =0.01mH; the traction power supply network is equivalent to a pi-shaped structure, R 1 ＝1mΩ、L 1 =0.01 muH, contact line equivalent resistance and inductance, C 1 And C 2 Equivalent capacitance C for contact line to ground 1 ＝C 2 ＝0.01μF；R c And L c The equivalent resistance and inductance of the train body are respectively R c ＝133Ω、L c ＝0.01mH；R arc Is a variable resistor; l is arc Is arc column inductor, C pc Is a bow net gap capacitance;
by means of a switch S 0 、S 1 、S 2 、S 3 To control the arc impedance state; stable contact of bow with net, S 0 Closure, S 1 、S 2 、S 3 Opening, R jc Accessing a circuit; the bow net begins off-line arcing, S 0 Breaking, S 1 、S 3 Breaking, S 2 Closure, R arc And L arc Accessing a circuit; short time of zero-crossing arc extinction, S 2 Breaking, S 1 、S 3 Closure, C pc And R arc Accessing a circuit; after zero crossing to before breakdown, S 1 、S 3 Breaking, S 2 Closure, R arc And L arc Accessing a circuit; in a brief time of breakdown, S 2 Breaking, S 1 、S 3 Closure, C pc And R arc Accessing a circuit; stable arcing after breakdown, S 1 、S 3 Breaking, S 2 Closure, C pc And R arc And accessing the circuit.
2. The bow net offline arc modeling simulation method with high frequency characteristics according to claim 1, wherein the expression of bow net separation arcing is as follows:
contact resistance R regarded as constant exists when bow net is in normal contact jc =0.2 Ω, when the bow net is arcing after mechanical vibration separation, the arc enters a stable combustion stage, and the arc arcing resistance value becomes R 0 =2 Ω, the arc column inductance is greater at this time, and value L is taken arc ＝1mH。
3. The bow net offline arc modeling simulation method with high frequency characteristics as set forth in claim 1, wherein the current zero-rest arc quenching expression is:
with the continuous change of the phase of the 50Hz alternating current, when the current passes through a zero point, the external circuit does not input energy for the electric arc any more, so that the electric arc is extinguished and changed into a high resistance in a short time, and because the electric arc is resistive during the extinguishing, the inductance of an arc column is ignored; referring to a calculation method of a Mayr arc resistance model, for a formed pantograph-catenary arc, the conductance change of an arc extinguishing process at the zero crossing point of alternating current satisfies the equation:
where g is the conductance of the arc per unit length, P out For the arc dissipation power, τ is the model time constant, u h A recovery voltage gradient for the bow net gap;
relating arc resistance to conductance
Substituting the formula into (1), and solving the equation to obtain the expression of the arc resistance in the arc quenching stage as follows:
neglecting the recovery voltage across the gap of the pantograph network after a zero crossing of the current, i.e. u h =0, the expression is then simplified to:
where τ =1ns, this formula indicates that during the current zero-crossing arc extinguishing phase, the arc resistance may vary from R to tens of nanoseconds 0 The frequency of the current is changed from 2 omega to hundreds of megaohms, so that a rapidly-changed loop current is generated to form an electromagnetic disturbance source, and the capacitance between the pantograph-grid electrodes at the stage cannot be ignored due to the existence of a high-frequency component of the current, and the value C is taken pc ＝0.1μF。
4. The bow net offline arc modeling simulation method with high-frequency characteristics according to claim 3, wherein a rule of a breakdown threshold value changing with time in a bow net offline process is as follows:
in hundreds of microseconds after the arc high-resistance state is continued, the bow net gap is continuously increased until the breakdown threshold value is reached, and air breakdown discharge is formed; through a high-voltage breakdown discharge experiment of a real pantograph carbon slide plate and a contact wire under different gaps in a laboratory, the breakdown voltage V jc The following fit relationship exists with the bow net gap length d:
wherein d is represented by cm, V jc The unit of (b) is kV;
assuming that the longitudinal relative speed is 20cm/s, the pantograph contact pressure is 120N and the pantograph head mass is 60kg when the pantograph is separated, if the pantograph is simplified to be a spring oscillator, the change function of the pantograph gap length along with time within 200ms is calculated as follows:
d＝20t-100t 2 (5)
thus, the formula for the breakdown voltage in 200ms is then written as:
5. the pantograph offline arc modeling simulation method of claim 4, having high frequency characteristics, wherein zero-crossing arc restrike is expressed as:
when the current zero crossing is extinguished, the arc resistance of the bow net keeps high resistance, the arc gap voltage is rapidly increased to the power supply voltage and is subjected to sine alternation, when the arc gap voltage is greater than the breakdown voltage, electrons are ionized and accelerated to move under the action of an external electric field, stronger impact ionization is caused on a moving path, the number of the electrons is increased like avalanche, namely electron avalanche, and the air gap is broken down to cause discharge; according to Thomson's discharge theory and the Toepler arc model, if the electron density from the cathode x length is expressed as n e Then, there are: (dn) e /dx)＝αn e α is the Thomson first ionization coefficient, defined as the number of average ionizing collisions for an electron traveling along the electric field over a unit length; using electron drift velocity v e ＝μ e E denotes the velocity of the charged particles in the direction of the electric field, where μ e Is the electron mobility, E is the applied electric field strength, and there are:
dn e ＝αn e dx＝αn e v e dt (7)
define conductivity as σ = en e μ e Assuming that the gap length of the bow net is d and the sectional area of the arc column is A arc Then the current density is expressed as:
further arc resistance is calculated as:
measuring the rate of change of the electron density in (9) with time
The rewrite is:
after integration, there are:
substituting equation (10) with:
substituting the relation (5) of d changing along with time, and taking alpha mu e =0.5, yielding the time-varying relationship of the arc resistance during zero-crossing restrike as:
the arc formed after complete breakdown is fully combusted, the arc resistance is kept at the minimum value of 2 omega, the arc resistance is extinguished after half an alternating current period and is increased again at the moment, then the process is continuously repeated until the pantograph and catenary are lapped again, the gap impedance only keeps the contact resistance of the pantograph and catenary, the current is recovered to be a stable 50Hz sinusoidal waveform, and low-frequency zero-break and high-frequency pulse oscillation do not occur any more.
6. The bow net offline arc modeling simulation method with high-frequency characteristics according to claim 5, wherein a bow net offline arc impedance dynamic mathematical expression considering high-frequency characteristics is constructed as follows:
wherein, t 1 For the bow net separation time, the bow net separation step signal control is adopted, and different separation times determine the initial phase of arc starting, and the initial phase is set as a simulation initial condition; t is t 1 Before the moment, the bow net contact is good, and at the moment, the bow net gap impedance is only expressed as bow net contact resistance, and the inductance and the capacitance are ignored; t is t 1 ～t 2 In the continuous arc discharge stage, the arc impedance is regarded as being kept unchanged; t is t 2 Current zero crossing at time, arc at delta t 2 The arc resistance is rapidly increased within a short time, and the current is instantaneously changed according to the change rule of the Mayr arc resistance, so that the gap capacitance cannot be ignored and is calculated to be 1 muF; after the arc is extinguished, the gap voltage is changed into the power supply voltage in a short time, and then is continuously increased according to 50Hz sine alternation, and at t 3 The gap voltage is greater than the dynamic breakdown threshold voltage at the moment, the extinguished arc is reignited under the action of high-voltage air breakdown, and the arc resistance is 10 10 The omega is instantaneously reduced to be stable arcing resistance, the breakdown reignition process follows the variation rule of the resistance value of the Toepler arc, and the gap capacitance in the transient process is not negligible and is marked as 1 mu F; and then after the next 50Hz half period, zero-rest arc quenching is performed again, and the zero-crossing point is re-ignited.
7. The bow net offline arc modeling simulation method with high frequency characteristics as set forth in claim 5, wherein:
the arc resistance obtained by applying the pantograph-catenary offline discharge equivalent circuit model with the high-frequency characteristic changes along with time, the arc resistance is rapidly increased within a short time of a zero-crossing arc extinguishing stage, and the change rule follows a formula (3); the bow net gap resistance is in a high resistance state and lasts for hundreds of microseconds, after the bow net gap voltage reaches a breakdown threshold value, the bow net off-line arc is reignited again, an air breakdown discharge loop is conducted, the arc resistance is rapidly reduced in a short time, the change rule follows an equation (14), the arc is continuously ignited after reignition, and when the next alternating current half period comes, the change is repeated; the breakdown voltage is larger along with the increase of the bow net gap, the duration of the arc high-resistance state is longer, and therefore, the time occupied by the high resistance is increased and then reduced.
8. The pantograph offline arc modeling simulation method with high frequency characteristics of claim 5, wherein: the bow net gap voltage change condition calculated by the bow net off-line discharge equivalent circuit model is subjected to bow net off-line in 0.015s, the bow net gap voltage quickly reaches the peak value above 40kV, and the bow net gap voltage quickly drops to the partial voltage of an arc resistor in a circuit after stable arcing, wherein the partial voltage is about ten volts; after each arc extinguishing at the zero crossing point, the bow net gap is opened instantly, and the gap voltage can rise to the power supply voltage within hundreds of microseconds; when the voltage of the pantograph-catenary gap reaches a breakdown threshold value, the breakdown threshold value dynamically changes along with the vertical motion of the pantograph-catenary according to a formula (4) -a formula (6), air breakdown occurs, insulating air of the pantograph-catenary gap is conducted to form a discharge loop, and the voltage of the pantograph-catenary gap is reduced to the reduction level of the arc resistance voltage division again; along with the movement of the spring vibrator of the pantograph, the pantograph-catenary gap distance is increased and then decreased, the breakdown voltage and the pantograph-catenary gap distance are in positive correlation, and the breakdown voltage is in a variation trend of being increased and then decreased.
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