CN107239600B - A method for establishing dynamic pantograph-catenary offline arc model considering offline distance of pantograph-catenary - Google Patents

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

A method for establishing dynamic pantograph-catenary offline arc model considering offline distance of pantograph-catenary

technical field

The invention relates to the technical field of off-line pantograph-catenary arc technology, in particular to a method for establishing a dynamic pant-and-catenary off-line arc model considering the off-line distance of pantograph and catenary.

Background technique

With the high-speed and heavy-loading of electrified railways, the offline problem of pantograph and catenary caused by factors such as catenary irregularity, catenary fluctuation, pantograph vibration, etc. has become more and more serious. common phenomenon in. In order to study the effect of off-line pantograph arc on the train system, establishing an arc model has become an important research work. Some early scholars put aside the complex physical process inside the arc, regarded the arc as a nonlinear two-terminal element under certain assumptions, and proposed the black-box arc model through the energy conservation equation, which is also the most widely used arc model so far; So far, many scholars have established a pantograph-catenary off-line arc model based on the black-box arc model, expanded the parameters in the arc equation such as dissipation power and arc voltage gradient, and introduced more influencing factors such as train speed and time constant. Offline arc model for accurate pantograph. However, the black-box arc models established so far all set the offline distance of the pantograph (the arc equivalent length) in the arc equation as a constant, while in practice, the offline distance of the pantograph varies with time during the offline process of the pantograph. That is to say, the offline arc model of pantograph and catenary established so far does not take into account the dynamic process of the change of pantograph-catenary offline distance, but replaces it with a static constant. In view of this, it is necessary to introduce the change of the actual pantograph-catenary offline distance into the arc model, and establish a dynamic pantograph-catenary offline arc model that is more in line with the actual situation.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to provide a method for establishing a dynamic pantograph-catenary offline arc model which is more in line with the actual pantograph-catenary offline arc model considering the offline distance of the pantograph-catenary. The technical solution is as follows:

A method for establishing a dynamic pantograph-catenary offline arc model considering the offline distance of pantograph-catenary includes the following steps:

Step 1: According to the relationship between the arc voltage gradient and the arc dissipated power and the offline distance of the pantograph, the offline distance of the pantograph is introduced into the arc equation of the black box arc model, so as to realize the dynamic expansion of the offline arc model of the pantograph;

Step 2: According to the actual situation of the offline pantograph, establish the dynamic trajectory of the offline distance of the pantograph, and introduce it into the arc model to realize the establishment of the dynamic offline arc model of the pantograph.

Further, the black box arc model in the step 1 is the Habedank black box arc model, and its arc is replaced by conductance in the train catenary system:

where g _m is the arc conductance of the Mayr part; g _c is the arc conductance of the Cassie part; g is the arc conductance; i is the arc current; τ ₁ and τ ₂ are the time constants; P ₀ is the dissipation power of the arc; u _c is the voltage gradient of the arc;

Since the arc voltage gradient will change with the offline distance of the pantograph and catenary, and it is a proportional change relationship, the proportionality constant is about 15V/cm, so the arc voltage gradient _uc is expressed as:

u _c = 15L _arc (4)

Among them, L _arc is the offline distance of pantograph and catenary; and the arc dissipation power P ₀ is related to L _arc , which is expressed as:

Among them, k ₁ and β are the dissipation power constants; n is the undetermined arc constant.

Further, in described step 2, the establishment method of the dynamic trajectory of pantograph offline distance is:

According to the trend of the offline trajectory of the pantograph, determine the relationship between the offline distance L _arc of the pantograph and the time t during the offline process of the pantograph:

Among them, t ₁ is the time point when the pantograph and catenary is detached; _{t 0} is the time point when the pantograph and catenary is offline to the maximum distance; t ₂ is the time point when the pantograph and catenary is re-contacted, and lm is the distance value between the pantograph and catenary offline to the maximum distance.

Further, it also includes embedding the dynamic pantograph-catenary offline arc model into the vehicle-network integrated equivalent circuit, establishing its corresponding state equation and solving it, and obtaining the waveform when the dynamic arc occurs; the state equation is as follows:

Among them, i _s is the current of the traction substation, i ₁ is the current of the traction network, _ic is the arc current in the equivalent circuit, u ₁ is the voltage of the traction substation, u ₂ is the catenary voltage at the train end, The above five parameters are state variables; U _s is the equivalent power supply provided by the traction substation, R _s is the equivalent resistance provided by the traction substation, and L _s is the equivalent inductance provided by the traction substation; R ₁ is The equivalent resistance of the catenary to the ground, L ₁ is the equivalent inductance of the catenary to the ground, C ₁ is the equivalent capacitance of the catenary to the ground; L _c is the equivalent inductance of the locomotive, R _c is the equivalent resistance of the locomotive; R _a is the arc resistance;

The equation of state is solved by discretizing iterative calculation method:

Step a: Input known parameters and initial values of five state variables;

Step b: Calculate the offline distance L _arc (k+1) of pantograph and catenary by formula (6) and formula (7), and then calculate the arc conductance g _c (k+1) by formula (1), (2) (3) ;

Step c: The value of the state variable is updated through the iteration of the formula (8), and the arc current i _c (k+1) and the arc voltage u _a (k+1) are obtained by calculating the arc current and the arc conductance, and then obtain Waveforms of arc voltage u _a and arc current _ic .

The beneficial effects of the present invention are as follows: the method of the present invention is more in line with the actual situation that the offline distance of the pantograph and catenary changes with time in the process of the pantograph and catenary offline, and the dynamic pantograph-catenary offline arc model established accordingly is the offline arc of the pantograph and catenary. A study of the impact of the train system provides more favorable support.

Description of drawings

Figure 1 is a schematic diagram of a simplified offline trajectory of the common trend of pantograph offline.

Figure 2 is a schematic diagram of an equivalent model of vehicle-network integration.

Fig. 3 is a schematic diagram of the calculation flow taking into account the dynamic arc state equation of the pantograph.

FIG. 4 is a schematic diagram of the arc voltage and current calculation results based on the pantograph dynamic arc model.

Detailed ways

The present invention will be further elaborated below in conjunction with the accompanying drawings and specific embodiments.

According to the investigation of the current waveform of the AC pantograph arc in the electrified railway industry, the pantograph arc will distort the sine wave and produce transient changes at the zero-crossing point of the current. In the simulation work of pantograph arc, it is found that the equation in the Mayr black box arc model is the most suitable for this special current zero-crossing situation; while the Cassie black box arc model is suitable for the actual situation of high current and low impedance of the arc.

Combining the above two situations, the Habedank black box arc model integrates the Mayr black box arc model and the Cassie black box arc model. Its equation expression consists of three parts: the Mayr arc equation part, the Cassie arc equation part and the arc conductance calculation part. At the same time this model proposes that the arc can be replaced by a conductance in train and catenary systems.

In the formula: g _m and g _c are the arc conductance of the Mayr part and the arc conductance of the Cassie part, respectively; i is the arc current; τ ₁ and τ ₂ are both time constants; P ₀ and _uc are the dissipation power of the arc and The voltage gradient of the arc.

Equation (1) (2) (3) is the algorithm of the black box arc model used in this embodiment, wherein the two parameters of the arc dissipation power P ₀ and the arc voltage gradient u _c are dynamic rather than constant in actual situations , and its change is related to the offline distance of pantograph.

For the arc voltage gradient _uc in the formula (2), a large number of experiments and theoretical analysis show that the arc voltage gradient uc is a stable value per unit arc length in the stable stage of the arc generation process. According to the arc waveform obtained from the existing arc experiments, the whole process of the arc can be divided into five stages: arc starting stage, unstable arc stage, stable arc stage, unstable arc stage before arc extinguishing and arc extinguishing stage five a stage. The stable arcing stage occupies more than 95% of the entire arc generation process, so the arc generation process can be regarded as the entire stable process, and the arc voltage gradient is a stable value per unit arc length. The arc length here refers to The equivalent arc length, that is, the offline distance of the pantograph. In summary, the arc voltage gradient will change with the change of the pantograph-catenary offline distance, and it is proportional to the relationship. According to the experiment, the proportionality constant is about 15V/cm, so the arc voltage gradient can be expressed as:

u _c = 15L _arc (4)

In the formula: L _arc is the offline distance of pantograph.

For the arc dissipation power P ₀ in Eq. (1), early studies have shown that its change is related to the arc conductance and the relationship between them can be expressed in the form of an exponential function. At the same time, P ₀ is also related to L _arc , which can be expressed as for:

In the formula: g is the arc conductance; k ₁ , β are the dissipation power constants; n is the undetermined arc constant.

Through the above formulas (1)-(5), the relationship between the arc voltage gradient u _c and the arc dissipation power P ₀ and the pantograph-catenary offline distance L _arc can be obtained. In this way, the parameter of the pantograph-catenary offline distance is introduced into the arc equation, The change of the offline distance of pantograph will affect the entire pantograph offline arc. According to the fact that the pantograph is offline, the offline distance of the pantograph will change with time during the entire offline process. By adding the trajectory algorithm of the change of the pantograph offline distance into the arc equation through equations (1)-(5), the pantograph can be realized. A dynamic extension of the offline arc model.

The pantograph-catenary mechanics experiment (simulating the pantograph-catenary offline experiment by moving the vibrating beam) shows that the pantograph-catenary offline trajectories have the same trend, and they all experience three processes: pantograph-catenary detachment, offline to the maximum distance, and pantograph-catenary re-contact. Under this common trend, the specific off-line trajectory will be affected by various factors such as train speed, mechanical vibration of the train, airflow intensity, and unevenness of the contact line. Here is a simplified offline trajectory that satisfies the common trend of pantograph offline, as shown in Figure 1, where L _m is the maximum offline distance. The main reason for choosing such a trajectory is that the offline time of pantograph is short, and the train speed can be regarded as constant during the offline time. Therefore, the process of increasing and decreasing the offline distance is set to be the same.

According to the trajectory shown in Fig. 1, set the time point when the pantograph and catenary is separated as t ₁ , the time point when the pantograph and catenary is offline to the maximum distance is set as t ₀ , the time point when the pantograph and catenary re-contact is set as t ₂ , and the time point when the pantograph and catenary is offline to the maximum distance is set as t 2 . The maximum distance value is set to l _m , then the relationship between L _arc and time t in the offline process of pantograph and catenary is:

Putting equations (6) and (7) into equations (1)-(5), the dynamic process of the change of pantograph-catenary off-line distance can be introduced into the arc model.

In order to obtain the waveform of the offline arc of the pantograph on the train, it is necessary to establish an equivalent model of the vehicle-network integration including the electrical contact of the pantograph system. Here, a simplified equivalent model of the vehicle-network integration is given, as shown in Figure 2 . The arc in the figure is embedded in the model in the form of a two-terminal nonlinear resistor, expressed by R _arc . The U _s , R _s and L _s used in the traction substation in the model are equivalent, where U _s is the equivalent power supply provided by the traction substation, and R _s and L _s are their equivalent resistance and inductance. The catenary line is equivalent to a π-type equivalent circuit, wherein R ₁ , L ₁ and C ₁ are the equivalent resistance, inductance and capacitance of the catenary to ground. In addition, the equivalent loads (equivalent inductance and resistance) of the locomotive are represented as R _c and L _c , respectively. For the dynamic parameters in Fig. 2, u ₁ and is are the voltage and current of the traction substation, _{i 1} is the current of the traction grid, u ₂ is the catenary voltage at the train end, _ic , u _a and _uc are respectively Arc current, arc voltage and pantograph tip voltage.

Through the establishment of the above model, the pantograph arc is embedded in the vehicle-network equivalent model in the form of arc conductance. Therefore, when the pantograph offline arc occurs, the solution of the arc is to calculate its arc conductance. Next, according to the model shown in Figure 2, the state equation when the arc occurs is established. The five parameters i _s , i ₁ , _ic , u ₁ , u ₂ shown in Fig. 2 are used as state variables to establish the state equation:

In the formula: R _a is the arc resistance.

Considering that the arc resistance R _a is constantly changing, the state equation shown in equation (8) is nonlinear. According to the nonlinear nature of the state equation, the discrete iterative calculation method is used to solve the state equation below.

The first is to set the parameters. For the equivalent model parameters of the vehicle-network integration shown in Figure 2: using a conventional 20.5km, 50Hz, 2×27.5kV AC high-speed rail power supply line, its u _s =27.5kV, R _s =0.177 Ω, L _s =31.8 mH, R ₁ =2.95 Ω, L ₁ =23.5 mH, C ₁ =0.081 μF, R _c =56.19 Ω and L _c =91.6 mH. In order to make the arc calculation results close to the experimental results, the parameters in formula (5) are n=1, β=0.5 and k ₁ =2500000. For the offline trajectory of pantograph and catenary shown in Figure 1, consider a low-speed situation, and its maximum offline distance L _m =0.01m.

Then there is the iterative calculation, and the calculation steps are:

(1) Input known parameters and initial values of five state variables.

(2) Calculate the offline distance L _arc (k+1) of pantograph and catenary by formula (6) (7), and then calculate the arc conductance g _c (k+1) by formula (1) (2) (3), where k is the number of iterations.

(3) The value of the state variable is updated through the iteration of equation (8), and the arc current i _c (k+1) and the arc voltage u _a (k+1) are obtained by calculating the arc current and arc conductance.

The specific calculation process is shown in Figure 3.

The waveforms of arc voltage u _a and arc current ic are obtained as shown in _FIG . 4 . The trend of the waveform shown in Fig. 4 is consistent with the trend of the waveform shown in the experimental results of the OHLICE team [S. Midya, D. Bormann, T. Schutte, and 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 (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:

in the formula: g_mArc conductance, which is the Mayr fraction; g_cArc 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. of_cIs 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/cm_cExpressed as:

u_c＝15L_arc(4)

wherein, L_arcThe distance is the bow net off-line distance; while the arc dissipates the power P₀And L_arcRelated, expressed as:

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 net_arcRelationship to time t:

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:

wherein i_sFor drawing currents in substations i₁To current of the traction network, i_cIs 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 shape_sEquivalent power supply, R, for traction substations_sEquivalent resistance provided for traction substations, L_sEquivalent 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 ground_cIs an equivalent inductance of the locomotive, R_cIs the equivalent resistance of the locomotive; r_aIs 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 obtained_c(k +1) and calculating the arc voltage u by the arc current and the arc conductance_aThe value of (k +1) and thus the arc voltage u_aAnd arc current i_cThe waveform of (2).

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