CN106815441B - A calculation method of traction network pressure considering multiple off-line arcing of EMU pantograph - Google Patents

Abstract

The invention discloses a method for calculating traction network voltage considering multiple off-line arcing of a pantograph-catenary of a motor train unit, which comprises the steps of firstly establishing a traction network distribution parameter equivalent model comprising n pi-shaped equivalent models connected in series, introducing a mathematical model of the pantograph-catenary off-line arc into the traction network distribution parameter equivalent model to establish an arc model, and establishing a traction network loop state space model considering nonlinear dynamic arcing based on a state space theory; carrying out discretization processing on the traction network loop state space model by using a numerical analysis method; and finally, researching the traction net pressure fluctuation under the conditions of multiple arc burning and arc extinguishing of the bow net based on a state space analysis method. The state space analysis method adopted by the invention not only can solve the problem of the change research of the traction network voltage under the condition of multiple arcing, but also can be used for the analysis of the arcing occurring in the over-phase, and can be popularized and used for the analysis of the voltage and the current change when other arcs of a power system occur and the research of other nonlinear or time-varying models.

Description

A calculation method of traction network pressure considering multiple off-line arcing of EMU pantograph

technical field

The invention relates to the technical field of arc influence and protection in high-speed railways, in particular to a method for calculating traction network pressure that takes into account multiple off-line arcing of a pantograph and catenary of an EMU.

Background technique

High-speed railway pantograph catenary system vibration, track or catenary irregularity, and excessively equalization, accompanied by multiple arcing of pantograph and catenary, it produces high-amplitude overvoltage phenomenon, which threatens the traction grid voltage, and distorts the voltage waveform injected into the car body. The main traction transformer and the electrical equipment in the vehicle cause harm and affect the safe operation of the train. Due to the randomness, instability and nonlinearity of the offline arc of the pantograph, it is difficult to directly survey the site. Therefore, it is necessary to analyze the traction pressure fluctuation considering the multiple arcing and arc extinguishing of the pantograph.

Due to the phenomenon of pantograph arc or electric spark, the surface of the pantograph and the contact line is corroded and burned. At present, the research on pantograph arc mainly focuses on the analysis of the physical and chemical characteristics inside the arc, and the arc weakening device is designed from the material. Other theories mainly focus on the establishment of different arc mathematical models, and the existing mathematical models can well reflect the physical characteristics of the arc. How the network pressure of the vehicle body and traction network fluctuates and changes during off-line arcing.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to provide a method for calculating the traction network pressure that takes into account the multiple offline arcing of the pantograph and catenary of the EMU. , can also be used to study the effect of arcing in the presence of excessive phases. The technical method is as follows:

A method for calculating traction network pressure considering multiple off-line arcing of a pantograph and catenary of an EMU, comprising the following steps:

Step 1: Establish an equivalent model of traction network distribution parameters for the high-speed railway AT traction network including n π-type equivalent models in series, and introduce the mathematical model of the offline arc of the pantograph into the equivalent model of the distribution parameters of the traction network to establish an arc model. The state space theory establishes the state space model of the traction network loop considering nonlinear dynamic arcing;

Step 2: using the numerical analysis method to discretize the state space model of the traction network loop;

Step 3: According to the state space model of the traction network loop processed by discretization, first solve the pantograph head voltage waveform that takes into account the primary arc of the pantograph, and save the results of each state variable solved for this arc as the secondary arc. The initial value of the state variable is solved iteratively until the traction grid pressure waveform that takes into account the multiple offline arcs of the pantograph and catenary of the EMU is obtained.

Further, the arc model is obtained by combining the Habedank equivalent arc model with the Mayr arc model and the Cassie arc model and modifying it, and its mathematical model representation is:

where g is the instantaneous arc conductance of the Habedank equation; i is the instantaneous arc current of the Habedank equation; g _c is the instantaneous conductance of the Cassie part of the overall arc equation; g _M is the instantaneous conductance of the Mayr part of the overall arc equation; v is the train speed; τ ₀ is the initial time constant; α, γ, and β are all related constants that affect the dynamic characteristics of the arc.

Further, in the step 1, the equivalent model of the distribution parameters of the traction network has a total of (2n-1) state variables, and the system matrix A of the (2n-1)×(2n-1) order state equation is solved, and the input matrix B, Get the state equation of the system:

Among them, x(t) is the state variable, and u(t) is the input vector; the state variable x(t) is selected as:

x(t)=[i _s (t) u(t) i ₁ (t) u ₁ (t) i ₂ (t) u ₂ (t) … i _n (t) u _n (t) i _m (t )]

The input vector u(t) is:

u(t)=[ _uS (t)]

φ为初始相角。where u _S (t) is the bus voltage of the traction substation,

φ is the initial phase angle.

Solve the equation of state:

Among them, the system matrix A is a tridiagonal matrix of order (2n-1)×(2n-1), R _arc (t) is the arc nonlinear dynamic resistance; state variables i _j (t) (j=1,2, …,n) is the traction grid current at different distances from the traction substation; u _i (t) (i=1,2,…,n) is the traction grid voltage at different distances from the traction substation, where u _n ( t) is also the voltage of the pantograph on the roof of the EMU; im ( _t ) is the arc current, that is, the load current; the arc voltage is expressed as:

u _arc ( _t )=im (t)R _arc (t)

According to the length of the catenary line and the arc occurrence position, select the appropriate n to obtain the arc characteristic waveform and the voltage waveform everywhere on the traction network.

Further, the specific steps of discretizing the state space model of the traction network loop are as follows:

1) The expression after discretization of the arc model is:

Among them, Δt is the step size, and t _k = kΔt, which represents the time t _k ;

2) Discrete processing of the state space model of the traction network loop:

If 0≤t _k ≤t _end , that is, the initial state is time 0, the selected reference duration is t _end , and the step size h=Δt, then the overall number of iterations is t _end /h; when t _k <t≤t _k +Δt During the time, the system matrix A and the input matrix B are continuous, and all the state variable values x _k at this time are known, then the state response at time t _k+1 is expressed as:

The above formula can be simplified to the following simplified form:

In the formula,

The discrete state equation obtained is expressed by the parameters at time t _k and t _k-1 , and the discrete state model of the traction network loop is obtained by substituting the above discrete arc discrete model expression.

Further, the concrete steps of described step 3 are:

1) Starting from time t _k = 0, substitute the initial parameters to solve the arc equation to solve the first state equation;

2) Update the time parameter t _k+1 = t _k +Δt, the state variable parameter x _k and the arc parameter g _k with the result obtained in the previous time, and continuously correct the system matrix A every iteration until the iteration time limit t _k > t is satisfied _End , stop the calculation, and finally solve the nonlinear state equation;

3) For the situation of arcing again after arc extinguishing, according to the output voltage waveform parameters of the nth pantograph head, correct the voltage value of the traction network, and iterate again to obtain the traction network voltage waveform after the n+1th pantograph arcing. Variety.

The beneficial effects of the present invention are as follows: the present invention takes into account the phenomenon of multiple arc extinguishing and arcing of the pantograph and catenary during the operation of the EMU, and the state space analysis method can not only solve the problem of using software simulation to analyze different arc models, which requires repeated construction The operational complexity brought by the module can also directly use the analysis results to solve the transient voltage change research of the bow head under the condition of multiple arcing. It can also be used to study the influence of arcing with excessive phase occurrence, which has certain universality.

Description of drawings

Figure 1 is the equivalent model of the traction network in series.

Fig. 2 is the calculation flow taking into account the electric arc state equation of the traction grid.

Figure 3-1 is the electrical characteristic curve of pantograph offline arc when the load is mainly resistive (R _m =56.2Ω, L _m ≈0mH).

Figure 3-2 is the electrical characteristic curve of pantograph offline arc when the load is mainly inductive (R _m ≈ 0Ω, L _m =91.6mH).

Figure 3-3 is the electrical characteristic curve of the off-line arc of the pantograph when the load is inductive (R _m =56.2Ω, L _m =91.6mH).

Figure 4-1 is the waveform of primary arc traction network pressure.

Figure 4-2 shows the waveform of the secondary arc traction network pressure.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Combining state space theory and numerical analysis method, not only one off-line arcing situation is considered, but also the traction network pressure change when multiple arcing occurs, which is closer to the actual occurrence of multiple arcing of pantograph and catenary. The specific steps are as follows:

Step 1: Establish traction network loop and arc state space model

As shown in Figure 1, the traction network model is composed of n π-shaped parts composed of R, L, and C in series. _Rm and _Lm are the equivalent resistance and inductance of the load, R _arc is the non-linear resistance model of the arc equivalent value, and R _S and L _S represent the equivalent impedance of the traction substation transformer respectively, u _S (t) is the bus voltage of the traction substation, i _j (t) (j=1,2,…,n) is the distance from the traction substation Traction grid current at different distances, u _i (t) (i=1,2,...,n) is the traction grid voltage at different distances from the traction substation.

The arc model is established by introducing the mathematical model of the offline arc of the pantograph into the distribution parameter equivalent model of the traction network. The arc model is obtained by combining the Habedank equivalent arc model with the Mayr arc model and the Cassie arc model and modifying it, which can better reflect the nonlinear characteristics of the arc. .

Determine the location of the arc, assuming that the traction network state space model is composed of n π-type equivalent lumped parameter models in series, then the built traction network state space model has a total of (2n-1) state variables, and solve (2n-1) × The system matrix A of the (2n-1) order state equation, input the matrix B, and the state equation of the system is obtained as follows:

Among them, x(t) is the state variable, and u(t) is the input vector; the state variable x(t) is selected as:

x(t)=[i _s (t) u(t) i ₁ (t) u ₁ (t) i ₂ (t) u ₂ (t) … i _n (t) u _n (t) i _m (t )]

The input vector u(t) is:

u(t)=[ _uS (t)]

φ为初始相角；where u _S (t) is the bus voltage of the traction substation,

φ is the initial phase angle;

Solve the equation of state:

The system matrix A of the above equation of state is a tridiagonal matrix of order (2n-1)×(2n-1), R _arc (t) is the nonlinear dynamic resistance of the arc, and in the A matrix, only A((2n -1), (2n-1)) elements are time-varying, other elements are constant, and the input matrix B is constant.

It can be seen from Figure 1 that the state variable im (t) is the arc current, that is, the load current, u _i ( _t ) (i=1...n) is the traction network voltage at different distances from the traction substation, and the arc The voltage can be expressed as:

u _arc ( _t )=im (t)R _arc (t)

According to the line length of the catenary and the location of the arc, selecting the appropriate n, the arc characteristic waveform and the voltage waveform at any point of the catenary can be obtained.

Step 2: Discretize the state space model of the traction network loop:

Since the arc model is nonlinear, the state space model of the traction network after the introduction of the arc is a time-varying nonlinear state space model. The discretization processing in previous studies is as follows:

G=e ^At

The state equation after discretization is expressed as:

For this method, since the modeling of the traction network is related to the location of the arc, that is, the order of the state equation is affected by the parameter n. As the value of n increases, the variables of the state equation increase. In the iterative process of solving the equation, the high-order matrices A and B need to be discretized again according to the above formula for each iteration, which is complicated to calculate and has no operability.

In order to simplify the calculation steps and reduce the difficulty of iteration, in this embodiment, the state square of the traction network and the equivalent arc dynamic resistance model are first operated according to the following discrete processing methods:

The arc model selected in this embodiment is the Habedank model, and its mathematical model is represented as follows:

where g is the instantaneous arc conductance of the Habedank equation; i is the instantaneous arc current of the Habedank equation; g _c is the instantaneous conductance of the Cassie part of the overall arc equation; g _M is the instantaneous conductance of the Mayr part of the overall arc equation; v is the train speed; τ ₀ is the initial time constant; α, γ, and β are all related constants that affect the dynamic characteristics of the arc.

After the arc is discretized, we get:

Among them, Δt is the step size, and t _k =kΔt, which represents the time t _k .

Considering 0≤t _k ≤t _end , where t _k =kΔt, representing the time t _k , and taking the step size h=Δt, the overall number of iterations is t _end /h. Assuming that the system matrix A and the input matrix B are continuous in the time t _k <t≤t _k +Δt, and all the state variable values x _k at this time are known, the state response at time t _k+1 can be expressed as:

The above formula can be simplified to the following simplified form:

In the formula,

Iteratively solving the nonlinear time-varying equation of state can be equivalent to solving a non-homogeneous linear system of equations at each step.

The traction network state model is processed according to the above three equations, and the discrete state equation is expressed by parameters at time t _k and t _k-1 , and the discrete state model of the traction network loop can be obtained by substituting into the arc discrete model expression.

Step 3: Calculation of traction network pressure taking into account the multiple arcing of the pantograph and catenary of the EMU

The steps for iterative solution of multiple arc electromagnetic transients by numerical analysis method are as follows:

(1) Starting at time t _k =0, the arc equation is solved by substituting the initial parameters, and then the first state equation is solved.

(2) Update the time parameter t _k+1 = t _k +Δt, the state variable parameter x _k and the arc parameter g _k with the result obtained in the previous time, and the system matrix A needs to be continuously revised for each iteration until the iteration time limit t is satisfied _{When k} >t _end , the calculation is stopped, and the nonlinear state equation is finally solved.

(3) Considering the situation of arcing again after arc extinguishing, according to the output voltage waveform parameters of the nth pantograph head, correct the voltage value of the traction network, and iterate again to obtain the n+1th pantograph post-arcing traction The network voltage waveform changes, and the specific algorithm flow is shown in Figure 2.

Among them, the initial state variable value of the algorithm will affect the number of iterations, so it is necessary to appropriately assign the initial variable of the state equation, and the parameters are set as follows:

为90°(初始电源电压为零)，则接触网线路上电压与电流初始值均考虑赋零；(1) When the train is running normally, it can be basically considered that the voltage values of all parts of the traction network are equal, that is, if the initial voltage phase angle of the substation

is 90° (the initial power supply voltage is zero), then the initial values of the voltage and current on the catenary line are considered to be zero;

(2) In order to simplify the calculation, the arc dynamic resistance adopts the principle of equivalent distribution. Since the arc resistance is small and the Mayr arc model and the Cassie arc model are equivalent in series, the resistances of the two parts are obtained by the equal division of the overall arc resistance.

According to the above analysis method, the arc characteristic waveforms under three loads can be obtained as shown in Figures 3-1, 3-2, and 3-3.

Carry out multiple arc analysis for the phenomenon of uninterrupted re-ignition after the first arc is extinguished. Taking the two arcs as an example, according to the above process, save the results of each state variable of the first arc, and substitute it as the initial value of the second arc. After solving, the waveform of traction grid pressure for secondary arcing can be obtained, as shown in Figure 4-1 for primary arcing and Figure 4-2 for traction grid pressure results for secondary arcing. Comparing the analysis of Fig. 4-1 and Fig. 4-2, the primary arc will distort the traction grid voltage, but the distortion is not obvious; if the arc reignites again, the traction grid voltage distortion will increase, and more harmonic currents will be injected into the traction grid. , causing damage to the internal equipment of the car body and the entire traction network. Considering in turn, multiple arc extinguishing and arcing will make the voltage distortion of the traction network more serious.

Claims (2)

1. A method for calculating traction network pressure for calculating multiple off-line arcing of a pantograph-catenary of a motor train unit is characterized by comprising the following steps of:

step 1: establishing a traction network distribution parameter equivalent model comprising n series-connected pi-type equivalent models for the high-speed railway AT traction network, introducing a mathematical model of bow net off-line electric arc into the traction network distribution parameter equivalent model to establish an electric arc model, and establishing a traction network loop state space model considering nonlinear dynamic arcing based on a state space theory;

step 2: carrying out discretization processing on the traction network loop state space model by using a numerical analysis method;

and step 3: according to a traction network loop state space model subjected to discretization processing, solving pantograph bow voltage waveforms for accounting for primary arcing of the pantograph nets, saving each state variable result solved by the arcing, taking each state variable result as a secondary arcing state variable initial value, and carrying out iterative solution until traction network voltage waveforms for accounting for multiple offline arcing of the pantograph nets of the motor train unit are obtained;

the arc model is obtained by combining a Habedankl equivalent arc model with a Mayr arc model and a Cassie arc model and modifying, and the mathematical model expression mode is as follows:

wherein g is the instantaneous arc conductance of the Habedank equation; i is the instantaneous arc current of the Habedank equation; g_CTransient conductance which is part of the entire arc equation Cassie; g_MInstantaneous conductance, which is part of the overall arc equation Mayr; v is train speed; tau is₀Is an initial time constant; alpha, gamma and beta are all relevant constants influencing the dynamic characteristic of the electric arc;

in the step 1, the traction network distribution parameter equivalent model has 2n-1 state variables, a system matrix A of a (2n-1) x (2n-1) order state equation is solved, and a matrix B is input to obtain a state equation of the system:

wherein x (t) is a state variable, u (t) is an input vector; selecting the state variable x (t) as:

x(t)＝[i_s(t) u(t) i₁(t) u₁(t) i₂(t) u₂(t) … i_n(t) u_n(t) i_m(t)]

the input vector u (t) is:

u(t)＝[u_S(t)]

in the formula u_S(t) is the bus voltage of the traction substation,phi is an initial phase angle;

solving a state equation:

wherein R is_m、L_mLoad equivalent resistance and inductance; r_S、L_SRespectively representing equivalent impedance of a transformer of the traction substation; the system matrix A is a (2n-1) × (2n-1) order tri-diagonal matrix, R_arc(t) is an arc nonlinear dynamic resistance; state variable i_j(t), j ═ 1,2, …, n, traction network currents at different distances from the traction substation; u. of_i(t), i ═ 1,2, …, n, traction network voltages at different distances from the traction substation, where u is_n(t) is also the voltage of the pantograph head of the motor train unit roof; i.e. i_m(t) is the arc current, i.e. the load current; the arc voltage is expressed as:

u_arc(t)＝i_m(t)R_arc(t)

selecting proper n according to the length of the contact network line and the arc generation position to obtain the characteristic waveform of the arc and the voltage waveforms of all positions on the traction network;

the method specifically comprises the following steps of carrying out discretization processing on the traction network loop state space model:

1) the expression of the arc model after discretization is as follows:

where △ t is the step size, t_kK △ t, representing t_kTime of day;

2) discrete processing of a traction network loop state space model:

if t is not less than 0_k≤t_endThat is, when the initial state is 0, the selected reference time is t_endWhen the step h is △ t, the overall iteration number is t_endH; at t_k<t≤t_k+ △ t, the system matrix A and the input matrix B are continuous, and all the state variable values x at that moment_kAre all known, then t_k+1The state response at the time is expressed as:

the above formula is simplified to the following simplified form:

in the formula (I), the compound is shown in the specification,

obtaining a discrete state equation from t_k、t_k-1And (5) time parameter expression is substituted into the arc discrete model expression to obtain a traction network loop discrete state model.

2. The method for calculating the traction network voltage considering multiple off-line arcing of the pantograph-catenary of the motor train unit according to claim 1, wherein the specific steps in the step 3 are as follows:

1)t_kstarting at the moment of 0, substituting the initial parameters to solve an arc equation to solve a first state equation;

2) the result of the previous calculation versus the time parameter t_k+1＝t_k+ △ t, state variable parameter x_kAnd arc parameter g_kUpdating, and continuously correcting the system matrix A once per iteration until an iteration time limit t is met_k>t_endStopping calculation until the calculation is finished, and finally realizing the solution of the nonlinear state equation;

3) and for the re-arcing condition after the arc is extinguished, correcting the voltage value of the traction network according to the output nth pantograph bow voltage waveform parameter, and iterating again to obtain the voltage waveform change of the traction network after the n +1 th pantograph bow-type arc is ignited.

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