CN106815441A - A kind of computational methods of the Traction networks pressure of meter and the multiple offline arcing of EMUs bow net - Google Patents

Abstract

The present invention discloses a kind of computational methods of the Traction networks pressure of meter and the multiple offline arcing of EMUs bow net, initially set up including the n Traction networks distributed constant Equivalent Model of π types equivalent model series connection, the mathematical modulo of the offline electric arc of bow net is introduced into Traction networks distributed constant Equivalent Model and sets up Arc Modelling, the Traction networks loop state spatial model of meter and Nonlinear Dynamic arcing is set up based on state space theory；Recycle numerical analysis method carries out sliding-model control to above-mentioned Traction networks loop state spatial model；State-space Method is finally based on, net voltage fluctuation is drawn in the case of the multiple arcing of research bow net, blow-out.The State-space Method that the present invention is used can not only solve the Traction networks pressure Changeement in the case of multiple arcing, the analysis of the arcing of split-phase appearance was can be also used for, voltage during for power system other electric arcs generation and curent change analysis and other non-linear or time-varying model researchs can be promoted.

Description

A kind of computational methods of the Traction networks pressure of meter and the multiple offline arcing of EMUs bow net

Technical field

The present invention relates to electric arc influence in high-speed railway and protection technique field, specially a kind of meter and EMUs bow net are more The computational methods of the Traction networks pressure of secondary offline arcing.

Background technology

The vibration of high-speed railway Pantograph-OCS system, track or contact net irregularity and its too equal, repeatedly fire with bow net Arc, it produces amplitude overvoltage phenomenon to threaten Traction networks net pressure so that injection car body voltage waveform distortion, to traction main transformer pressure Device and in-car electrical equipment cause harm, and influence safe train operation.Due to the randomness of the offline electric arc of bow net, unstability and Non-linear, scene is difficult directly to survey.Therefore, very must for meter and the multiple arcing of bow net, the traction pressure fluction analysis of blow-out Will.

Because bow net arcing or electric spark phenomenon cause pantograph and contact line surface corrosion and scaling loss, at present, for bow The research of net electric arc is concentrated mainly on the analysis of internal arctube Wuli-Shili-Renli system approach, design is set about from material and weakens arcing device, Other theories are concentrated mainly on the researchs such as different arc mathematics models foundation, and existing Mathematical Modeling can be very good reaction The physical characteristic of electric arc, but it is rare for bow net electric arc essence to whole Traction networks produce impact analysis, it is difficult to determine bow net from During line arcing car body and Traction networks net pressure how fluctuating change.

The content of the invention

Regarding to the issue above, counted and the repeatedly traction of arcing offline of EMUs bow net it is an object of the invention to provide a kind of The computational methods of pressure are netted, the method is applicable not only to the impact analysis that EMU accidental conditions produce offline arcing, Can be also used for the influence research of the arcing of split-phase appearance.Technical method is as follows：

A kind of computational methods of the Traction networks pressure of meter and the multiple offline arcing of EMUs bow net, comprise the following steps：

Step 1：High-speed railway AT Traction networks are set up including the n Traction networks distributed constant of π types equivalent model series connection etc. Value model, the Mathematical Modeling of the offline electric arc of bow net is introduced into Traction networks distributed constant Equivalent Model and sets up Arc Modelling, is based on State space theory sets up the Traction networks loop state spatial model of meter and Nonlinear Dynamic arcing；

Step 2：Sliding-model control is carried out to above-mentioned Traction networks loop state spatial model using numerical analysis method；

Step 3：Traction networks loop state spatial model according to sliding-model control, first solves meter and bow net arcing Pantograph collector head voltage waveform, preserves this each state variable result of arcing solution, initial as secondary arcing state variable Value, is iterated solution, the Traction networks corrugating until trying to achieve meter and the multiple offline arcing of EMUs bow net.

Further, the Arc Modelling is by the equivalent electric arc models coupling Mayr Arc Modellings of Habedank, Cassie electricity Arc model is simultaneously subject to amendment and obtains, and its Mathematical Modeling representation is：

g_CWherein, g is the momentary arc conductance of Habedank equations；I is the momentary arc electric current of Habedank equations；g_c It is the instantaneous conductance of overall electric arc equation Cassie parts；g_MIt is the instantaneous conductance of overall electric arc equation Mayr parts；V is train Speed；τ₀It is initial time constant；α, γ, β are the dependent constant of influence electric arc dynamic characteristic.

Further, total (2n-1) individual state variable of Traction networks distributed constant Equivalent Model in the step 1, solves Sytem matrix A, the input matrix B of (2n-1) × (2n-1) rank state equations, obtain the state equation of system：

Wherein, x (t) is state variable, and u (t) is input vector；Choosing state variable x (t) is：

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

Input vector u (t) is：

U (t)=[u_S(t)]

In formula, u_ST () is traction substation busbar voltage,φ is initial phase angle.

Solving state equation：

Wherein, sytem matrix A is the triple diagonal matrix of (2n-1) × (2n-1) ranks, R_arcT () is electric arc Nonlinear Dynamic electricity Resistance；State variable i_j(t) (j=1,2 ..., n) it is Traction networks electric current apart from traction substation different distance；u_i(t) (i=1, 2 ..., n) it is supply conductor voltage apart from traction substation different distance, wherein u_nT () is also EMUs roof pantograph collector head Voltage；i_mT () is arc current, i.e. load current；Arc voltage is expressed as：

u_arc(t)=i_m(t)R_arc(t)

Position is occurred according to contact net line length and electric arc, suitable n is chosen, arc characteristic waveform and Traction networks are tried to achieve On voltage waveform everywhere.

Further, sliding-model control is carried out to Traction networks loop state spatial model to comprise the following steps that：

1) expression formula that Arc Modelling carries out after sliding-model control is：

Wherein, Δ t is step-length, t_k=k Δ t, represent t_kMoment；

2) Traction networks loop state spatial model discrete processes：

If 0≤t_k≤t_end, i.e. original state is 0 moment, a length of t during the reference of selection_end, step-length h=Δ t, then integrally Iterations is t_end/h；In t_k<t≤t_kIn+Δ t the times, sytem matrix A and input matrix B is continuous, and the moment all of shape State variable value x_k, it is known that then t_k+1The condition responsive at moment is expressed as：

Above formula abbreviation obtains following reduced form：

In formula,

Discrete state equations are obtained by t_k、t_k-1Moment parameter expression, substitutes into above-mentioned electric arc discrete model expression formula, obtains Traction networks loop discrete state model.

Further, the step 3 is concretely comprised the following steps：

1)t_kAt=0 moment, substituting into initial parameter solution electric arc equation carries out first time Solving Equation of State；

2) result was once tried to achieve in the past to time parameter t_k+1=t_k+ Δ t, state variable parameter x_kAnd arc parameters g_kEnter Row updates, per iteration once continuous update the system matrix A, until meeting iteration time limit t_k>t_endUntill, stop calculating, it is final real Existing nonlinear state equation solution；

3) for arcing situation again after blow-out, according to the n-th pantograph collector head voltage waveform parameters of output, amendment is led Draw net magnitude of voltage, again iteration, obtain (n+1)th bow net arcing rear haulage net corrugating change.

The beneficial effects of the invention are as follows：To there is the multiple blow-out of bow net, arcing phenomenon in EMUs running in the present invention Take into account, when adoption status spatial analytical method can not only solve to analyze different Arc Modellings using software emulation, need to repeat The Operating Complexity that module is brought is built, while the bow in the case of multiple arcing directly can also be solved using analysis result Transient voltage Changeement, is applicable not only to the impact analysis that EMU accidental conditions produce offline arcing, may be used also For crossing the influence research of the arcing that split-phase occurs, with certain universality.

Brief description of the drawings

Fig. 1 is Traction networks series equivalent model.

Fig. 2 is the calculation process of meter and Traction networks conditions at the arc equation.

Fig. 3-1 is load (R based on resistive_m=56.2 Ω, L_m≈ 0mH) when the offline electric arc electrical characteristic curve of bow net.

Fig. 3-2 is load (R based on perception_m≈ 0 Ω, L_m=91.6mH) when the offline electric arc electrical characteristic curve of bow net.

Fig. 3-3 is that load is resistance sense (R_m=56.2 Ω, L_m=91.6mH) when the offline electric arc electrical characteristic curve of bow net.

Fig. 4-1 is an arcing Traction networks corrugating.

Fig. 4-2 is secondary arcing Traction networks corrugating.

Specific embodiment

The present invention is described in further details with specific embodiment below in conjunction with the accompanying drawings.By state space theory and numerical value Analytic approach is combined, and not only considers once offline arcing situation, and Traction networks when can simultaneously consider that multiple arcing occurs Buckling, closer to the multiple arcing phenomenon of bow net is actually occurred, comprises the following steps that：

Step 1：Set up Traction networks loop and conditions at the arc spatial model

According to Fig. 1, the π type sections in series that traction pessimistic concurrency control is made up of n R, L, C is constituted, R_m、_LmFor load is equivalent Resistance and inductance, R_arcIt is the equivalent nonlinear resistance model of electric arc, R_S、L_SThe equivalent resistance of traction substation transformer is represented respectively It is anti-, u_ST () is traction substation busbar voltage, i_j(t) (j=1,2 ..., n) it is traction apart from traction substation different distance Net electric current, u_i(t) (i=1,2 ..., n) it is supply conductor voltage apart from traction substation different distance.

The Mathematical Modeling of the offline electric arc of bow net is introduced into Traction networks distributed constant Equivalent Model and sets up Arc Modelling, electric arc Model is by the equivalent electric arc models coupling Mayr Arc Modellings of Habedank, Cassie Arc Modellings and is subject to amendment and obtains, can be compared with Electric arc nonlinear characteristic is reacted well.

Determine that electric arc occurs position, it is assumed that Traction networks state-space model is by n π type dynamic impedance model series connection group Into then total (2n-1) the individual state variable of built Traction networks state-space model, solves (2n-1) × (2n-1) rank state equations Sytem matrix A, input matrix B, the state equation for obtaining system is as follows：

Wherein, x (t) is state variable, and u (t) is input vector；Choosing state variable x (t) is：

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

Input vector u (t) is：

U (t)=[u_S(t)]

In formula, u_ST () is traction substation busbar voltage,φ is initial phase angle；

Solving state equation：

The sytem matrix A of above formula state equation is the triple diagonal matrix of (2n-1) × (2n-1) ranks, R_arcT () is that electric arc is non- Linear dynamic resistance, and in A matrixes, only A ((2n-1), (2n-1)) element is time-varying, remaining element is permanent, input square Battle array B is permanent.

As shown in Figure 1, state variable i_mT () is arc current, namely load current, u_iT () (i=1...n) is distance The supply conductor voltage of traction substation different distance, arc voltage can be expressed as：

u_arc(t)=i_m(t)R_arc(t)

Position is occurred according to contact net line length and electric arc, suitable n is chosen, you can in the hope of arc characteristic waveform and Contact net any place voltage waveform.

Step 2：Sliding-model control is carried out to Traction networks loop state spatial model：

Because Arc Modelling is non-linear, therefore introducing electric arc rear haulage net state spatial model is the non-linear of time-varying State-space model, the sliding-model control equation below studied in the past：

G=e^At

State equation after discrete processes is expressed as：

For the method, because Traction networks modeling and electric arc generation position are relevant, i.e., state equation exponent number receives parameter n Influence.As n values increase, state equation variable increases, and in equation solution iterative process, is once needed to High Order Moment per iteration Battle array A, B calculate complicated, without operability again according to above formula sliding-model control.

In order to simplify calculation procedure, iteration difficulty is reduced, the present embodiment is dynamic to traction net state side and equivalent electric arc first State Resistance model for prediction is operated by following discrete processes method：

Arc Modelling selected by the present embodiment is Habedank models, and its Mathematical Modeling representation is as follows：

Wherein, g is the momentary arc conductance of Habedank equations；I is the momentary arc electric current of Habedank equations；g_cFor The instantaneous conductance of overall electric arc equation Cassie parts；g_MIt is the instantaneous conductance of overall electric arc equation Mayr parts；V is train speed Degree；τ₀It is initial time constant；α, γ, β are the dependent constant of influence electric arc dynamic characteristic.

Electric arc is obtained after carrying out sliding-model control：

Wherein, Δ t is step-length, t_k=k Δ t, represent t_kMoment.

Consider 0≤t_k≤t_end, wherein t_k=k Δ t, represent t_kAt the moment, step-length h=Δ t are taken, then Global Iterative Schemes number of times is t_end/h.Assuming that in t_k<t≤t_kIn+Δ t the times, sytem matrix A and input matrix B is continuous, and the moment all of state variable Value x_k, it is known that then t_k+1The condition responsive at moment is represented by：

Above formula abbreviation can obtain following reduced form：

In formula,

The nonhomogeneous property system of linear equations of each step can be equivalent to solve to nonlinear time-varying state equation iterative.

Traction networks state model is processed according to above-mentioned three formula of formula, obtains discrete state equations by t_k、t_k-1Moment parameter list Reach, substitute into electric arc discrete model expression formula, you can obtain Traction networks loop discrete state model.

Step 3：The Traction networks pressure of meter and the multiple arcing of EMUs bow net is calculated

It is as follows multiple arcing electro-magnetic transient iterative step to be carried out using numerical analysis method：

(1)t_kAt=0 moment, substitute into initial parameter and solve electric arc equation and then carry out first time Solving Equation of State.

(2) result was once tried to achieve in the past to time parameter t_k+1=t_k+ Δ t, state variable parameter x_kAnd arc parameters g_k It is updated, continuous update the system matrix A is once then needed per iteration, until meeting iteration time limit t_k>t_endUntill, stop meter Calculate, finally realize nonlinear state equation solution.

(3) arcing situation again after blow-out is considered, according to the n-th pantograph collector head voltage waveform parameters of output, amendment Supply conductor voltage value, again iteration, you can obtain (n+1)th bow net arcing rear haulage net corrugating change, specific algorithm flow See Fig. 2.

Wherein, the original state variate-value of algorithm can influence iterations, it is therefore desirable to the initializaing variable of state equation Suitable assignment is carried out, parameter setting is as follows：

(1) can substantially think that magnitude of voltage is equal everywhere for Traction networks when train normally runs, even electric substation's initial voltage phase Parallactic angleIt is 90 ° (primary power voltage is zero) that then voltage considers tax zero with electric current initial value on contact net circuit；

(2) to simplify calculating, electric arc dynamic electric resistor uses equivalent distribution principle, because arc resistance is smaller and Mayr electric arcs Model and Cassie Arc Modellings use series equivalent approach, and arc resistance divides acquisition equally to portions of resistance by their entirety.

According to above analysis method, arc characteristic waveform when can obtain three kinds of loads is as shown in Fig. 3-1,3-2,3-3.

Uninterrupted phenomenon of restriking carries out multiple arcing analysis after extinguishing for an arcing, by taking arcing twice as an example, according to Above flow, preserves each state variable result of arcing, is substituted into as the initial value of secondary arcing, and i.e. available two are solved again Two arcing Traction networks pressure results of secondary arcing Traction networks corrugating, such as arcing of Fig. 4-1 and Fig. 4-2.Comparison diagram 4-1 and Fig. 4- 2 analyses a, arcing is produced and can cause that Traction networks press distortion, but it is unobvious to distort；If electric arc resume combustion again, Traction networks pressure distortion Increase, Traction networks will inject more multiple-harmonic current, and vehicle body equipment and whole Traction networks are caused harm.Consider successively, Multiple blow-out, arcing will cause that supply conductor voltage distortion is more serious.

Claims (5)

1. it is a kind of count and the multiple Traction networks pressure of offline arcing of EMUs bow net computational methods, it is characterised in that including following Step：

Step 1：High-speed railway AT Traction networks are set up includes the Traction networks distributed constant equivalence mould of n π types equivalent model series connection Type, the Mathematical Modeling of the offline electric arc of bow net is introduced into Traction networks distributed constant Equivalent Model and sets up Arc Modelling, based on state Space Theory sets up the Traction networks loop state spatial model of meter and Nonlinear Dynamic arcing；

Step 2：Sliding-model control is carried out to above-mentioned Traction networks loop state spatial model using numerical analysis method；

Step 3：Traction networks loop state spatial model according to sliding-model control, first solve meter and arcing of bow net by electricity Bow bow voltage waveform, preserves this each state variable result of arcing solution, as secondary arcing state variable initial value, enters Row iteration is solved, the Traction networks corrugating until trying to achieve meter and the multiple offline arcing of EMUs bow net.

2. computational methods of the multiple Traction networks pressure of offline arcing of meter according to claim 1 and EMUs bow net, it is special Levy and be, the Arc Modelling is by the equivalent electric arc models coupling Mayr Arc Modellings of Habedank, Cassie Arc Modellings and adds Obtained with correcting, its Mathematical Modeling representation is：

$\frac{{\mathrm{dg}}_C}{dt}=\frac{1}{{\mathrm{\&tau;}}_0{g}^{\mathrm{\&alpha;}}}(\frac{i^2}{{(6.857\&times;{10}^{-5}{v}^2+0.357v-2.117)}^2\&CenterDot;g_C}-g_C)$

$\frac{{\mathrm{dg}}_M}{dt}=\frac{1}{{\mathrm{\&tau;}}_0{g}^{\mathrm{\&alpha;}}}(\frac{i^2}{{\mathrm{\&gamma;g}}^{\mathrm{\&beta;}}(4.571\&times;{10}^{-6}{v}^2+0.238v-0.141)}-g_M)$

$\frac{1}{g}=\frac{1}{g_C}+\frac{1}{g_M}$

Wherein, g is the momentary arc conductance of Habedank equations；I is the momentary arc electric current of Habedank equations；g_CIt is entirety The instantaneous conductance of electric arc equation Cassie parts；g_MIt is the instantaneous conductance of overall electric arc equation Mayr parts；V is train speed；τ₀ It is initial time constant；α, γ, β are the dependent constant of influence electric arc dynamic characteristic.

3. computational methods of the multiple Traction networks pressure of offline arcing of meter according to claim 2 and EMUs bow net, it is special Levy and be, total (2n-1) the individual state variable of Traction networks distributed constant Equivalent Model, solves (2n-1) × (2n- in the step 1 1) the sytem matrix A of rank state equation, input matrix B, obtain the state equation of system：

$\stackrel{\&CenterDot;}{x\left(t\right)}=Ax\left(t\right)+Bu\left(t\right)$

Wherein, x (t) is state variable, and u (t) is input vector；Choosing state variable x (t) is：

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

Input vector u (t) is：

U (t)=[u_S(t)]

In formula, u_ST () is traction substation busbar voltage,φ is initial phase angle；

Solving state equation：

Wherein, sytem matrix A is the triple diagonal matrix of (2n-1) × (2n-1) ranks, R_arcT () is electric arc Nonlinear Dynamic resistance； State variable i_j(t) (j=1,2 ..., n) it is Traction networks electric current apart from traction substation different distance；u_i(t) (i=1, 2 ..., n) it is supply conductor voltage apart from traction substation different distance, wherein u_nT () is also EMUs roof pantograph collector head Voltage；i_mT () is arc current, i.e. load current；Arc voltage is expressed as：

u_arc(t)=i_m(t)R_arc(t)

Position is occurred according to contact net line length and electric arc, suitable n is chosen, tried to achieve each on arc characteristic waveform and Traction networks Place's voltage waveform.

4. computational methods of the multiple Traction networks pressure of offline arcing of meter according to claim 3 and EMUs bow net, it is special Levy and be, carrying out sliding-model control to Traction networks loop state spatial model comprises the following steps that：

1) expression formula that Arc Modelling carries out after sliding-model control is：

$g_C\left(t_k\right)=g_C\left(t_{k-1}\right)+\frac{\mathrm{\&Delta;}t}{{\mathrm{\&tau;}}_0{g}^{\mathrm{\&alpha;}}}\left(\frac{i^2}{{\left(6.857\&times;{10}^{-5}{v}^2+0.357v-2.117\right)}^2\&CenterDot;g_C}-g_C\right)$

$g_M\left(t_k\right)=g_M\left(t_{k-1}\right)+\frac{\mathrm{\&Delta;}t}{{\mathrm{\&tau;}}_0{g}^{\mathrm{\&alpha;}}}(\frac{i^2}{{\mathrm{\&gamma;g}}^{\mathrm{\&beta;}}(4.571\&times;{10}^{-6}{v}^2+0.238v-0.141)}-g_M)$

$R_{arc}\left(t_k\right)=\frac{1}{g\left(t_k\right)}=\frac{1}{g_C\left(t_k\right)}+\frac{1}{g_M\left(t_k\right)}$

Wherein, △ t are step-length, t_k=k △ t, represent t_kMoment；

2) Traction networks loop state spatial model discrete processes：

If 0≤t_k≤t_end, i.e. original state is 0 moment, a length of t during the reference of selection_end, step-length h=△ t, then Global Iterative Schemes are secondary Number is t_end/h；In t_k<t≤t_kIn+△ t the times, sytem matrix A and input matrix B is continuous, and the moment all of state variable Value x_k, it is known that then t_k+1The condition responsive at moment is expressed as：

$x_{k+1}=x_k+\frac{h}{2}\&lsqb;(A_k{x}_k+B_k{u}_k)+(A_k{x}_{k+1}+B_k{u}_{k+1})\&rsqb;$

Above formula abbreviation obtains following reduced form：

${\stackrel{\&OverBar;}{A}}_k{x}_{k+1}={\stackrel{\&OverBar;}{B}}_k$

In formula,

${\stackrel{\&OverBar;}{A}}_k=I-\frac{h}{2}{A}_k$

${\stackrel{\&OverBar;}{B}}_k=(I+\frac{h}{2}{A}_k)x_k+\frac{h}{2}{B}_k(u_k+u_{k+1})$

Discrete state equations are obtained by t_k、t_k-1Moment parameter expression, substitutes into above-mentioned electric arc discrete model expression formula, obtains Traction networks Loop discrete state model.

5. computational methods of the multiple Traction networks pressure of offline arcing of meter according to claim 4 and EMUs bow net, it is special Levy and be, the step 3 is concretely comprised the following steps：

1)t_kAt=0 moment, substituting into initial parameter solution electric arc equation carries out first time Solving Equation of State；

2) result was once tried to achieve in the past to time parameter t_k+1=t_k+ △ t, state variable parameter x_kAnd arc parameters g_kCarry out more Newly, per iteration once continuous update the system matrix A, until meeting iteration time limit t_k>t_endUntill, stop calculating, finally realize non- Linear state equations are solved；

3) for arcing situation again after blow-out, according to the n-th pantograph collector head voltage waveform parameters of output, Traction networks are corrected Magnitude of voltage, iteration, obtains (n+1)th bow net arcing rear haulage net corrugating change again.