CN107239600B - Dynamic pantograph-catenary offline arc model establishing method considering pantograph-catenary offline distance - Google Patents

Dynamic pantograph-catenary offline arc model establishing method considering pantograph-catenary offline distance Download PDF

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CN107239600B
CN107239600B CN201710356014.0A CN201710356014A CN107239600B CN 107239600 B CN107239600 B CN 107239600B CN 201710356014 A CN201710356014 A CN 201710356014A CN 107239600 B CN107239600 B CN 107239600B
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刘志刚
周虹屹
黄可
宋小翠
宋洋
成业
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Abstract

The invention discloses a dynamic pantograph-catenary offline arc model establishing method considering pantograph-catenary offline distance, which introduces the pantograph-catenary offline distance into an arc equation of a black box arc model according to the relation between arc voltage gradient and arc dissipation power and the pantograph-catenary offline distance respectively, so as to realize dynamic expansion of the pantograph-catenary offline arc model; according to the actual condition of the pantograph-catenary offline, establishing a dynamic track of the pantograph-catenary offline distance, and introducing the dynamic track into an arc model to realize the establishment of the dynamic pantograph-catenary offline arc model; and finally, embedding the dynamic bow net off-line arc model into a vehicle-net integrated equivalent circuit, establishing a corresponding state equation and solving to obtain the waveform when the dynamic arc occurs. The method of the invention is more suitable for the actual situation that the bow net off-line distance changes along with time in the process of the bow net off-line, and the established dynamic bow net off-line arc model provides more favorable support for the research of the influence of the bow net off-line arc on the train system.

Description

Dynamic pantograph-catenary offline arc model establishing method considering pantograph-catenary offline distance
Technical Field
The invention relates to the technical field of pantograph-catenary offline electric arcs, in particular to a dynamic pantograph-catenary offline electric arc model establishing method considering pantograph-catenary offline distance.
Background
With the high speed and heavy load of the electric railway, the problem of pantograph-catenary offline caused by factors such as unsmooth contact network, fluctuation of contact network, and vibration of pantograph is more and more serious, and the generation of alternating current arc by pantograph-catenary offline is also a common phenomenon in the electric railway. In order to research the influence of the bow net off-line electric arc on a train system, establishing an electric arc model becomes an important research work. Some early scholars abandon the complex physical process inside the arc, regard the arc as a nonlinear two-terminal element on the basis of certain assumption, put forward the black box arc model through the energy conservation equation, this is the most used arc model at present; so far, many scholars establish a bow net off-line arc model based on a black box arc model, expand parameters such as dissipation power and arc voltage gradient in an arc equation, introduce more influence factors such as train speed and time constant, and establish a more accurate bow net off-line arc model. However, the black box arc model established so far sets the pantograph offline distance (arc equivalent length) in the arc equation to be a constant, and in practical cases, the pantograph offline distance changes with time in the pantograph offline process, that is, the pantograph offline arc model established so far does not consider the dynamic pantograph offline distance change process and replaces the static pantograph offline distance with a static constant. In view of this, it is necessary to introduce the change of the actual offline distance of the pantograph into the arc model to establish a dynamic offline pantograph arc model more suitable for the actual situation.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a dynamic bow net offline arc model building method that considers the bow net offline distance and better conforms to the actual bow net offline arc model. The technical scheme is as follows:
a dynamic pantograph catenary offline arc model building method considering pantograph offline distance comprises the following steps:
step 1: according to the relation between the arc voltage gradient and the arc dissipation power and the arc network off-line distance, introducing the arc network off-line distance into an arc equation of a black box arc model, and realizing dynamic expansion of the arc network off-line arc model;
step 2: and establishing a dynamic track of the pantograph-catenary offline distance according to the actual situation of the pantograph-catenary offline, introducing the dynamic track into the arc model, and realizing the establishment of the dynamic pantograph-catenary offline arc model.
Further, the black box arc model in the step 1 is a Habedank black box arc model, and an arc of the model is replaced by conductance in a train contact net system:
Figure BDA0001299118380000011
Figure BDA0001299118380000012
Figure BDA0001299118380000021
in the formula: gmArc conductance, which is the Mayr fraction; gcArc conductance which is the Cassie moiety; g is the arc conductance; i is the arc current; tau is1And τ2Is a time constant; p0Is the dissipated power of the arc; u. ofcIs the voltage gradient of the arc;
the arc voltage gradient u is changed along with the change of the offline distance of the pantograph-catenary and is in a proportional change relationship, and the proportionality constant is about 15V/cmcExpressed as:
uc＝15Larc(4)
wherein, LarcThe distance is the bow net off-line distance; while the arc dissipates the power P0And LarcRelated, expressed as:
Figure BDA0001299118380000022
wherein k is1β is the dissipation power constant, n is the pending arc constant.
Further, the method for establishing the dynamic trajectory of the pantograph-catenary offline distance in the step 2 comprises the following steps:
determining the offline distance L of the pantograph net in the offline process of the pantograph net according to the trend of the offline trajectory of the pantograph netarcRelationship to time t:
Figure BDA0001299118380000023
Figure BDA0001299118380000024
wherein, t1The time point of bow net detachment; t is t0The time point from the bow net offline to the maximum distance is taken; t is t2For the point in time of renewed contact of the bow net,/mThe distance value from the bow net off line to the maximum is shown.
Further, the dynamic bow net off-line arc model is embedded into a vehicle-net integrated equivalent circuit, a corresponding state equation is established and solved, and the waveform of the dynamic arc is obtained when the dynamic arc occurs; the equation of state is as follows:
Figure BDA0001299118380000025
wherein isFor drawing currents in substations i1To current of the traction network, icIs an arc current in an equivalent circuit, u1Voltage of traction substation, u2The five parameters are state variables, namely the voltage of a contact network at the train end; u shapesEquivalent power supply, R, for traction substationssEquivalent resistance provided for traction substations, LsEquivalent inductance is provided for a traction substation; r1For contact net equivalent resistance to earth, L1Is an equivalent inductance of a contact network to the ground, C1L being equivalent capacitance of contact net to groundcIs an equivalent inductance of the locomotive, RcIs the equivalent resistance of the locomotive; raIs an arc resistance;
solving the state equation by adopting a discretization iterative computation mode:
step a: inputting known parameters and initial values of five state variables;
step b, calculating the offline distance L of the pantograph by the formulas (6) and (7)arc(k +1), and then calculating the arc conductance g by the equations (1), (2) and (3)c(k+1)；
Step c: the value of the state variable is updated by iteration of equation (8) while the arc current i is obtainedc(k +1) andcalculating the over-current arc current and the arc conductance to obtain the arc voltage uaThe value of (k +1) and thus the arc voltage uaAnd arc current icThe waveform of (2).
The invention has the beneficial effects that: the method provided by the invention is more suitable for the actual situation that the bow net off-line distance changes along with time in the process of bow net off-line, and the established dynamic bow net off-line arc model provides more favorable support for the research on the influence of the bow net off-line arc on a train system.
Drawings
Fig. 1 is a simplified offline trace diagram of the bow net offline common trend.
Fig. 2 is a schematic view of a vehicle-grid integrated equivalent model.
Fig. 3 is a schematic diagram of a calculation flow that accounts for the pantograph dynamic arc state equations.
Fig. 4 is a diagram illustrating the calculation of arc voltage and current based on the dynamic arc model of the pantograph.
Detailed Description
The invention is further described in detail below with reference to the figures and the specific embodiments.
According to the investigation of the electrified railway industry for alternating current pantograph-catenary arc current waveforms, the pantograph-catenary arc can distort sine waves and generate transient changes at a current zero-crossing point. In the simulation work of the bow net arc, the equation in the Mayr black box arc model is the most suitable situation for the special current zero crossing point; and the Cassie black box arc model is suitable for the situation of high current and low impedance of the arc under the actual situation.
By combining the two situations, the Habedank black box arc model combines a Mayr black box arc model and a Cassie black box arc model, and the equation expression of the Habedank black box arc model comprises three parts: a Mayr arc equation section, a Cassie arc equation section, and an arc conductance calculation section. At the same time, the model suggests that the arc can be replaced by a conductance in the train and in the contact network system.
Figure BDA0001299118380000031
Figure BDA0001299118380000041
Figure BDA0001299118380000042
In the formula: gmAnd gcArc conductance of the Mayr part and arc conductance of the Cassie part, respectively; i is the arc current; tau is1And τ2Are all time constants; p0And ucRespectively the dissipated power of the arc and the voltage gradient of the arc.
The equations (1), (2) and (3) are the algorithm of the black box arc model used in this example, in which the arc dissipation power P0And arc voltage gradient ucThese two parameters are dynamic rather than constant in practical situations and their variation is related to the bow net offline distance.
For the arc voltage gradient u in equation (2)cExtensive experimental and theoretical analysis has shown that the arc generation process is a stable value per arc length in the stable phase. According to the arc waveform obtained by the existing arc experiment, the whole process of arc generation can be divided into: the method comprises five stages, namely an arc striking stage, an unstable arc stage, a stable arc stage, an unstable arc stage before arc quenching and an arc quenching stage. The stable arcing stage occupies more than 95% of the whole arc generation process, so the arc generation process can be equivalently regarded as the whole stable process, the arc voltage gradient of the stable arcing stage is a stable value in unit arc length, and the arc length refers to the equivalent arc length, namely the offline distance of the pantograph-catenary. In summary, the available arc voltage gradient changes with the change of the offline distance of the pantograph-catenary and is a proportional change relationship, and experiments show that the proportionality constant is about 15V/cm, so the arc voltage gradient can be expressed as:
uc＝15Larc(4)
in the formula LarcIs the bow net offline distance.
For the arc in equation (1)Dissipated power P0Early studies showed that its changes are related to arc conductance and that the relationship between them can be expressed in the form of an exponential function, while P0Also LarcCorrelation, can be expressed as:
Figure BDA0001299118380000043
in the formula: g is the arc conductance; k is a radical of1β is the dissipation power constant, n is the pending arc constant.
The arc voltage gradient u can be obtained by the above formulas (1) - (5)cAnd arc dissipated power P0Distance L from bow netarcTherefore, the parameter of the offline distance of the pantograph is introduced into an arc equation, and the change of the offline distance of the pantograph can influence the whole offline arc of the pantograph. According to the actual offline of the pantograph-catenary, the distance of the pantograph-catenary from the line can change along with time in the whole offline process, and a track algorithm of the change of the pantograph-catenary from the off-line distance is added into an arc equation through the formula (1) -the formula (5), so that the dynamic expansion of the pantograph-catenary off-line arc model can be realized.
Bow net mechanics experiments (simulating bow net off-line experiments by moving vibrating beams) show that the bow net off-line tracks all have the same trend and all go through three processes of bow net separation, off-line to maximum distance and bow net re-contact, under the common trend, the specific off-line track can be influenced by various factors such as train speed, mechanical vibration of the train, air flow strength, contact line irregularity and the like, a simplified off-line track satisfying the bow net off-line common trend is provided, as shown in figure 1, L in the figuremIs the offline maximum distance. Such a trajectory is selected mainly in view of the fact that the bow net off-line time is short, during which the train speed can be considered constant, and therefore the course of increasing and decreasing the off-line distance is set to be the same.
According to the trace shown in FIG. 1, let the time point of the bow net detachment be t1The time point from the bow net off line to the maximum distance is set as t0The time point of the pantograph to be contacted again is set as t2Distance value from bow net off-line to maximumIs set to lmL in the bow net off-line processarcThe relationship with time t is:
Figure BDA0001299118380000051
Figure BDA0001299118380000052
the dynamic process of the bow net off-line distance change can be introduced into the arc model by bringing the formulas (6) and (7) into the formulas (1) to (5).
In order to obtain the waveform of the pantograph-catenary offline arc on the train, a vehicle-catenary integrated equivalent model containing pantograph-catenary system electrical contact needs to be established, and a simplified vehicle-catenary integrated equivalent model is provided as shown in fig. 2. The arc is modeled as a two-terminal nonlinear resistor with RarcAnd (4) expressing. U for traction power transformation in models、RsAnd LsEquivalent of, wherein UsEquivalent power supply, R, for traction substationssAnd LsIs its equivalent resistance and inductance. The equivalent of the contact network line is a pi-shaped equivalent circuit, wherein R1、L1And C1The equivalent resistance, inductance and capacitance of the contact network to the ground. Further, the equivalent loads (equivalent inductance and resistance) of the locomotive are respectively represented as RcAnd Lc. For the dynamic parameters in FIG. 2, u1And isIs the voltage and current of the traction substation, i1Is the current of the traction network, u2Is the contact network voltage at the train end, ic、uaAnd ucRespectively arc current, arc voltage and pantograph head voltage.
Through the model establishment, the bow net electric arc is embedded into the vehicle-net integrated equivalent model in an electric arc conductance mode, so that when the bow net off-line electric arc occurs, the electric arc is solved, namely the electric arc conductance of the electric arc is calculated. The equation of state at the time of arc occurrence is next established according to the model shown in fig. 2. Five parameters i shown in FIG. 2s、i1、ic、u1、u2As state variablesTo establish the equation of state:
Figure BDA0001299118380000053
in the formula: raIs an arc resistance.
Taking into account the arc resistance RaIs constantly changing, the equation of state shown in equation (8) is nonlinear. According to the nonlinear property of the state equation, the state equation is solved by adopting a discretization iterative computation mode.
Firstly, setting parameters, for the vehicle-network integrated equivalent model parameters shown in figure 2, adopting the conventional 20.5km, 50Hz, 2 × 27.5.5 kV alternating current high-speed rail power supply line us＝27.5kV，Rs＝0.177Ω，Ls＝31.8mH，R1＝2.95Ω，L1＝23.5mH，C1＝0.081μF，Rc56.19 Ω and Lc91.6 mH., where n is 1, β is 0.5 and k is k in equation (5) to approximate the arc calculation result to the experimental result1Consider the low speed case for the pantograph offline trajectory of fig. 1, with the maximum offline distance L being 2500000m＝0.01m。
Then, iterative computation is carried out, and the computation steps are as follows:
(1) the known parameters are input as well as the initial values of the five state variables.
(2) The offline distance L of the pantograph is calculated by the equations (6) and (7)arc(k +1), and then calculating the arc conductance g by the equations (1), (2) and (3)c(k +1), where k is the number of iterations.
(3) The value of the state variable is updated by iteration of equation (8) while the arc current i is obtainedc(k +1) and calculating the arc voltage u by the arc current and the arc conductanceaThe value of (k + 1).
The specific calculation process is shown in fig. 3.
To obtain an arc voltage uaAnd arc current icThe trend of the waveform shown in fig. 4 is consistent with the trend of the waveform shown in the experimental results of OH L ICE group s.midya, d.bormann, t.schutte, and r.thottappill,“Pantograph arcing in electrified railways-mechanism andinfluence of various parameters-part II:with AC traction power supply,”IEEETrans.on Power Del,vol.24,pp.1940-1950,October.2009.]。

Claims (2)

1. a dynamic pantograph catenary offline arc model building method considering pantograph offline distance is characterized by comprising the following steps:
step 1: according to the relation between the arc voltage gradient and the arc dissipation power and the arc network off-line distance, introducing the arc network off-line distance into an arc equation of a black box arc model, and realizing dynamic expansion of the arc network off-line arc model;
step 2: according to the actual condition of the pantograph-catenary offline, establishing a dynamic track of the pantograph-catenary offline distance, and introducing the dynamic track into an arc model to realize the establishment of the dynamic pantograph-catenary offline arc model;
the black box arc model in the step 1 is a Habedank black box arc model, and the electric arc of the model is replaced by conductance in a train contact network system:
Figure FDA0002418648390000011
Figure FDA0002418648390000012
Figure FDA0002418648390000013
in the formula: gmArc conductance, which is the Mayr fraction; gcArc conductance which is the Cassie moiety; g is the arc conductance; i is the arc current; tau is1And τ2Is a time constant; p0Is the dissipated power of the arc; u. ofcIs the voltage gradient of the arc;
the arc voltage gradient u is changed along with the change of the offline distance of the pantograph-catenary and is in a proportional change relationship, and the proportionality constant is about 15V/cmcExpressed as:
uc＝15Larc(4)
wherein, LarcThe distance is the bow net off-line distance; while the arc dissipates the power P0And LarcRelated, expressed as:
Figure FDA0002418648390000014
wherein k is1β is the dissipation power constant, n is the undetermined arc constant;
the method for establishing the dynamic trajectory of the bow net offline distance in the step 2 comprises the following steps:
determining the offline distance L of the pantograph net in the offline process of the pantograph net according to the trend of the offline trajectory of the pantograph netarcRelationship to time t:
Figure FDA0002418648390000015
Figure FDA0002418648390000016
wherein, t1The time point of bow net detachment; t is t0The time point from the bow net offline to the maximum distance is taken; t is t2For the point in time of renewed contact of the bow net,/mThe distance value from the bow net off line to the maximum is shown.
2. The method for establishing the dynamic pantograph net offline electric arc model considering the pantograph net offline distance according to claim 1, further comprising the steps of embedding the dynamic pantograph net offline electric arc model into a vehicle-network integrated equivalent circuit, establishing a corresponding state equation and solving the state equation to obtain a waveform when the dynamic electric arc occurs; the equation of state is as follows:
Figure FDA0002418648390000021
wherein isFor drawing currents in substations i1To current of the traction network, icIs an arc current in an equivalent circuit, u1Voltage of traction substation, u2The five parameters are state variables, namely the voltage of a contact network at the train end; u shapesEquivalent power supply, R, for traction substationssEquivalent resistance provided for traction substations, LsEquivalent inductance is provided for a traction substation; r1For contact net equivalent resistance to earth, L1Is an equivalent inductance of a contact network to the ground, C1L being equivalent capacitance of contact net to groundcIs an equivalent inductance of the locomotive, RcIs the equivalent resistance of the locomotive; raIs an arc resistance;
solving the state equation by adopting a discretization iterative computation mode:
step a: inputting known parameters and initial values of five state variables;
step b, calculating the offline distance L of the pantograph by the formulas (6) and (7)arc(k +1), and then calculating the arc conductance g by the equations (1), (2) and (3)c(k +1), where k is the number of iterations;
step c: the value of the state variable is updated by iteration of equation (8) while the arc current i is obtainedc(k +1) and calculating the arc voltage u by the arc current and the arc conductanceaThe value of (k +1) and thus the arc voltage uaAnd arc current icThe waveform of (2).
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