CN104361196A - Arc net off-line electric arc mathematical model for calculating train speed - Google Patents

Abstract

The invention relates to an arc net off-line electric arc mathematical model for calculating the train speed. According to the site operation measured data that a high speed railway arc net off-line electric arc changes along with the train speed and the maximum off-line distance, and in accordance with the Habedank electric arc model, the voltage gradient constant and the wasted power constant of the electric arc model are revised, the electric arc dynamic mathematical model which is simple, effective and applicable to an arc net system is established, and the influence of different model parameter values on the dynamic property of the arc net electric arc model is analyzed in details. The proposed arc net electric arc model is introduced into an off-line process, and when the arc net is subjected to middle off-line, the off-line overvoltage of the arc net at different train speeds is simulated and analyzed; in addition, when the arc net is subjected to small off-line, the simulation result and the measured result of an arc net electric arc testing system are compared so as to verify the correctness of the established arc net electric arc mathematical model. The invention provides an effective tool for simulation study of the electrified railway arc net off-line electric arc and the transient process of the electrified railway arc net off-line electric arc and the transient process.

Description

A kind of bow net off-line arc mathematics model taking into account train speed

Technical field

What the present invention relates to is Arc Modelling research field in contact Wire for High-Speed Electric Railway and pantograph collector head off-line procedure, comprises the foundation of bow net arc mathematics model, the determination of Arc Modelling parameter.

Background technology

High-speed railway tractive power supply system completes energy transferring by pantograph pan and contact line conducting wire sliding contact, train speed constantly promotes the fluctuation of aggravation contact net and train mechanical vibration, cause between pantograph pan and contact line conducting wire and frequently break-off occurs, be bow net off-line phenomenon.On-the-spot operation shows, when train speed rises to 350km/h and be above, in adjacent two overlap sections, bow net off-line may be increased to about 500 times, and the similar device for switching of the frequent off-line of bow net cut-offs, and period, complicated arc phenomenon occurred.Arc-plasma maintains bullet train by stream continuity, but its non-linear dynamic characteristic makes off-line Overvoltage Amplitude increase, and percent harmonic distortion increases, and serious threat Pantograph-OCS system is reliably flowed.Therefore, bow net off-line electric arc becomes domestic and international research emphasis.

At present two kinds are mainly contained to bow net off-line electric arc: experimental study and modeling effort.Wherein, experimental study is put to the test device-restrictive, and test condition and actual Pantograph-OCS system exist larger difference, carry out less.Tellini etc. utilize real osculatory and pantograph, in osculatory and pantograph without under longitudinal direction (current of traffic) motion conditions, [TELLINI B is studied to electric arc electromagnetic interference (EMI) in lifting bow process, MAEUECI M, GIANNETTI R.Conducted and Radiated Interference Measurements in the Line-Pantograph System [J] .Transportation Research Part C:Emerging Technologies October 2008,16 (5): 457-460.], Surajit etc. are by building off-line electric arc mechanism of production in bow net arc testing device analysis alternating current traction electric power system, utilize setting model different acquisition different tests data, analyze osculatory speed, supply voltage, system power, load characteristic and pantograph material are on impact [the SURAJIT M of arc voltage and electric current, DIERK B, RAJEEV T, et al.Pantograph Arcing in Electrified Railways-Mechanism and Influence of Various Parameters-Part II:With AC Traction Power Supply [J] .IEEE Transaction on Power Delivery, 2009, 29 (4): 1940-1950.], the deficiency that the external bow net arc testing device of domestic scholars analysis exists, make improvements, on improvement test unit basis, Wang Wangang [Wang Wangang, Wu Guangning, high Guoqiang, Deng. high-speed railway bow net arc testing system [J]. railway society, 2012, 34 (4): 22-27.], Yang Zhipeng [Yang Zhipeng, Li Huawei, Sun Zhongguo, Deng. the arc parameters based on bow net electric arc simulation test device is measured and is analyzed [J]. Beijing Jiaotong University's journal, 2012, 36 (2): 111-115.] etc. have studied bow net electric contact characteristic, bow net electric arc influence rule and dynamic perfromance thereof.Compare experimental study, model investigation is easy and practical, overcome the shortcomings such as experimental study condition restriction, existing literature research is more, generally utilize existing Arc Modelling research off-line electric arc and off-line surge characteristic [Huang Changping. bow net off-line is to the impact analysis [D] of bullet train. Chengdu: Southwest Jiaotong University, 2013:13-18.], and seldom relate to setting up the Arc Modelling being suitable for Pantograph-OCS system.Wang Jian etc. are based on the bow net arc energy conservation differential equation, Primary Study is carried out to bow net electric arc deterministic models, but how Parameters in Mathematical Model not to be obtained and how its value difference affects Arc Modelling dynamic perfromance and study [Wang Jian in great detail, Wang Wei, Qu Zhijian, Deng. based on the bow net electric arc Modeling Research [J] of energy conservation. electric railway, 2013,2 (5): 1-5.].Therefore, when carrying out modeling effort, foundation is suitable for the Arc Modelling of Pantograph-OCS system to research bow net off-line arc phenomenon, discloses bow net off-line superpotential transient state process most important.The present invention causes arc voltage and electric current form to change on result basis in the change of test unit gained train speed, in conjunction with circuit breaker, and according to the on-the-spot off-line electric arc that runs with train speed and maximum offline distance change tread measured data, set up the bow net arc mathematics model taking into account train speed.

Summary of the invention

The object of the present invention is to provide a kind of bow net off-line arc mathematics model research method based on improving Habedank Arc Modelling, the method runs measured data according to high-speed railway bow net off-line scene, consider the impact of train speed factor, establish simple effectively and be applicable to the arc mathematics model of Pantograph-OCS system, provide a kind of effective tool for during the electric arc modeling effort of bow net off-line.

The object of the invention is by following means realize:

A kind of bow net off-line arc mathematics model taking into account train speed, measured data is run with the scene of train speed and the change of maximum offline distance according to high-speed railway bow net off-line electric arc, based on Habedank Arc Modelling, set up simple effectively and be applicable to the arc mathematics model of Pantograph-OCS system, be specifically divided into following steps:

A, the scene operation measured data changed with train speed according to high-speed railway Pantograph-OCS system maximum offline distance, simulate maximum offline distance d _maxand the relational expression between train speed v is

d _max＝4.571×10 ^-6v ²+0.0238v-0.1411 (1)

B, take into account the voltage gradient u of train speed _c

u _C＝6.857×10 ^-5v ²+0.357v-2.117 (3)

Voltage gradient u _c

C, take into account the electric arc dissipated power P of train speed ₀

P ₀＝kg ^-β(4.571×10 ^-6v ²+0.0238v-0.1411) (5)

D, take into account the foundation of the bow net arc mathematics model of train speed:

Arc Modelling-bow net arc mathematics model is

$\left\{\begin{array}{c}\frac{{\mathrm{dg}}_C}{\mathrm{dt}}=\frac{1}{{\mathrm{\θ}}_C}[\frac{i^2}{{(6.857\×{10}^{-5}{v}^2+0.357v-2.117)}^2\·g_C}-g_C]\\ \frac{{\mathrm{dg}}_M}{\mathrm{dt}}=\frac{1}{{\mathrm{\θ}}_M}[\frac{i^2}{{\mathrm{kg}}^{-\mathrm{\β}}(4.571\×{10}^{-6}{v}^2+0.0238v-0.1411)}-g_M]\end{array}\right.---\left(7\right)$

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

Wherein, g _cand θ _cfor Cassie Arc Modelling conductance and time constant, g _mand θ _mfor Mayr Arc Modelling conductance and time constant, P ₀for electric arc dissipated power constant; Number k and β is model parameter, and its value value needs to determine according to actual tractive power supply system and on-the-spot operation Pantograph-OCS system electric arc measured data.

In model, k and β parameter value needs to determine according to actual tractive power supply system and on-the-spot operation Pantograph-OCS system electric arc measured data.

The determination of a, model parameter k

According to the simplification circuit model of actual tractive power supply system, the power factor of bow net off-line circuit is

Then arc resistance equivalence value R _arcfor

Flame current effective value I _rmsfor

Alternating current arc is had

$I_{\mathrm{rms}}^2{R}_{\mathrm{arc}}=k{R_{\mathrm{arc}}}^{\mathrm{\β}}{L}_{\mathrm{arc}}---\left(11\right)$

Simplify in bow net off-line circuit model, electric arc is as resistance element R _arcconsider, U _s, R _s, L _sfor traction substation and transformer equivalent circuit parameter, R ₁, L ₁, C ₁for the equivalent circuit parameter of contact net, R _c, L _cfor the equivalent circuit parameter of bullet train.

Derive k is according to above formula

Above formula gives k value and flame current effective value I _rms, electric arc equivalent resistance R _arc, equivalent arc length L _arcand the relational expression between arc parameters β, parameter k value occurrence can be similar in conjunction with the bow net arc testing system actual measurement arc voltage of Southwest Jiaotong University's high voltage laboratory development and current data and obtain.

The determination of b, model parameter β

Get the value of different values to parameter k by the known parameter beta of above-mentioned derivation to have a certain impact, and parameter beta is the index of electric arc conductance g.In order to improve accuracy and the validity of bow net arc mathematics model, go out the variation range of parameter beta below by the derivation of equation.

When alternating current arc smooth combustion, when namely arc voltage is stablized, flame current I _arclarger, electric arc conductance g is larger; Electric arc dissipated power P simultaneously ₀also larger, namely when other preconditions are constant, electric arc conductance g is larger, the dissipated power P of electric arc ₀also larger.From formula (11), parameter beta should be negative value, i.e. β < 0.In order to the lower limit of calculating parameter β, electric arc is regarded as resistance element and considers have in a current cycle T

${\&Integral;}_0^T{i}^2{r}_{\mathrm{arc}}\mathrm{dt}={\mathrm{TI}}_{\mathrm{rms}}^2{R}_{\mathrm{arc}}---\left(13\right)$

I,r _arcfor momentary current and the resistance of alternating current arc.

The effective value of flame current can be expressed as again

$I_{\mathrm{rms}}=\sqrt{\frac{1}{T}{\&Integral;}_0^T{i}^2\mathrm{dt}}---\left(14\right)$

Push away electric arc equivalent resistance is

$R_{\mathrm{arc}}=\frac{{\&Integral;}_0^T{i}^2{r}_{\mathrm{arc}}\mathrm{dt}}{{\&Integral;}_0^T{i}^2\mathrm{dt}}=\frac{{\&Integral;}_0^T{i}^2{r}_{\mathrm{arc}}\mathrm{dt}}{I_{\mathrm{rms}}^{2}T}---\left(15\right)$

The average conductivity σ of electric arc is again

$\mathrm{\&sigma;}=A_0\sqrt{I_{\mathrm{rms}}}---\left(16\right)$

A ₀for constant, σ is corresponding I _rmselectric arc average conductivity.

Then electric arc equivalent resistance is

$R_{\mathrm{arc}}=\frac{L_{\mathrm{arc}}}{{\mathrm{\&pi;r}}^2\mathrm{\&sigma;}}---\left(17\right)$

Convolution (11), deriving relational expression between model parameter β and influence factor is

$I_{\mathrm{rms}}=A_1{L}_{\mathrm{arc}}^{\frac{2\mathrm{\&beta;}}{\mathrm{\&beta;}+3}}---\left(18\right)$

Above formula gives β value and flame current effective value I _rms, equivalent arc length L _arcbetween relational expression.Be approximated to inverse ratio by between flame current effective value and arc length, can derive to obtain β >-3.The comprehensive variation range obtaining parameter beta is-3 < β < 0.

Model parameter k is different from β value to be had a certain impact to arc voltage and electric current and volt-ampere characteristic thereof.

Compared with prior art, the present invention has following advantage:

1, the present invention runs measured data according to high-speed electric railway scene, improves, set up the arc mathematics model being suitable for Pantograph-OCS system to Habedank Arc Modelling, for the modeling effort of bow net off-line electric arc provides a kind of effective instrument.

2, train speed is counted bow net arc mathematics model by the present invention, can be used for bow net off-line transient state process etc. under modeling effort different lines vehicle speed.

Accompanying drawing explanation

Fig. 1 is that on-the-spot operation surveys Pantograph-OCS system maximum offline distance d _maxand graph of a relation between train speed v.

Fig. 2 be parameter k when getting different value to Arc Modelling dynamic perfromance impact effect figure (arc voltage curve when 2a parameter k gets different value, flame current curve when 2b parameter k gets different value, 2c flame current curve local detail, electric arc volt-ampere characteristic when 2d parameter k gets different value).

Fig. 3 be parameter beta when getting different value to Arc Modelling dynamic perfromance impact effect figure (arc voltage curve when 3a parameter beta gets different value, flame current curve when 3b parameter beta gets different value, 3c flame current curve local detail, electric arc volt-ampere characteristic when 3d parameter beta gets different value).

Fig. 4 Pantograph-OCS system off-line simplifies circuit model figure.

Bow net off-line over-voltage simulation figure (5a bow net off-line electric arc dynamic characteristic under Fig. 5 different lines vehicle speed, off-line place pantograph collector head superpotential during 5b 200km/h, off-line place pantograph collector head superpotential during 5c 250km/h, off-line place pantograph collector head superpotential during 5d 300km/h, off-line place pantograph collector head superpotential during 5e 350km/h, pantograph collector head superpotential peak curve under 5f different lines vehicle speed).

Fig. 6 bow net off-line simulation simulation result and pilot system measured result comparison diagram (under the little off-line form of 6a off-line over-voltage simulation curve, off-line superpotential measured curve under the little off-line form of 6b).

Embodiment

Below in conjunction with accompanying drawing, embodiment of the present invention is elaborated: this embodiment is implemented under premised on technical solution of the present invention, give detailed implementation process, but protection scope of the present invention is not limited to following embodiment.

A. model parameter k value is different from the impact analysis of electric arc dynamic perfromance: introduced by the bow net arc mathematics model set up herein and simplify in bow net off-line circuit model, parameter k gets k=1000W Ω cm respectively ^-1, k=2000W Ω cm ^-1with k=3000W Ω cm ^-1under circuit parameter and other arc mathematics model parameter constant situations, obtain arc voltage change curve as Fig. 2 a, flame current change curve is as Fig. 2 b, flame current Changing Pattern is seen in order to clearer, flame current local detail is carried out amplification as Fig. 2 c, obtain electric arc volt-ampere characteristic as Fig. 2 d by arc voltage and electric current.

B. model parameter β value is different from the impact analysis of electric arc dynamic perfromance: in like manner, parameter beta gets β=-0.5 respectively, β=-1.5 and β=-2.5, under circuit parameter and other arc mathematics model parameter constant situations, obtain arc voltage change curve as Fig. 3 a, flame current change curve, as Fig. 3 b, sees flame current Changing Pattern in order to clearer, flame current local detail is carried out amplification as Fig. 3 c, obtain electric arc volt-ampere characteristic as Fig. 3 d by arc voltage and electric current.

C. bow net off-line over-voltage simulation is analyzed: carry out simplification equivalence with resistance, inductance and electric capacity electrical equipment to high-speed electric railway bow net off-line circuit, MATLAB/Simulink is utilized to build off-line circuit model as Fig. 4, ARC is set up bow net Arc dynamic mathematical model, cut-offs simulate Pantograph-OCS system off-line procedure with arc switch.To generation in off-line form (10ms < t < 100ms) time, under different lines vehicle speed, bow net off-line superpotential emulates, Fig. 5 a is bow net off-line electric arc dynamic characteristic, off-line place pantograph collector head superpotential when Fig. 5 b is 200km/h, off-line place pantograph collector head superpotential when Fig. 5 c is 250km/h, off-line place pantograph collector head superpotential when Fig. 5 d is 300km/h, off-line place pantograph collector head superpotential when Fig. 5 e is 350km/h, Fig. 5 f is pantograph collector head superpotential peak curve under different lines vehicle speed.

D. simulation analysis result and pilot system measured result contrast verification: Southwest Jiaotong University high voltage laboratory is by developing high-speed railway bow net arc testing system, test actual measurement is carried out to bow net off-line electric arc electrical specification and off-line superpotential, the optimum configurations of adjustment bow net arc mathematics model, off-line superpotential under little off-line (t < 10ms) form is emulated, Fig. 6 a is off-line over-voltage simulation curve under little off-line form, and Fig. 6 b is off-line superpotential measured curve under little off-line form.

Claims (2)

1. take into account the bow net off-line arc mathematics model of train speed for one kind, measured data is run with the scene of train speed and the change of maximum offline distance according to high-speed railway bow net off-line electric arc, based on Habedank Arc Modelling, set up simple effectively and be applicable to the arc mathematics model of Pantograph-OCS system, be specifically divided into following steps:

A, the scene operation measured data changed with train speed according to high-speed railway Pantograph-OCS system maximum offline distance, simulate maximum offline distance d _maxand the relational expression between train speed v is

d _max＝4.571×10 ^-6v ²+0.0238v-0.1411 (1)

B, take into account the voltage gradient u of train speed _c

u _C＝6.857×10 ^-5v ²+0.357v-2.117 (3)

Voltage gradient u _c

C, take into account the electric arc dissipated power P of train speed ₀

P ₀＝kg ^-β(4.571×10 ^-6v ²+0.0238v-0.1411) (5)

D, take into account the foundation of the bow net arc mathematics model of train speed:

Arc Modelling-bow net arc mathematics model is

Wherein, g _cand θ _cfor Cassie Arc Modelling conductance and time constant, g _mand θ _mfor Mayr Arc Modelling conductance and time constant, P ₀for electric arc dissipated power constant; Number k and β is model parameter, and its value value needs to determine according to actual tractive power supply system and on-the-spot operation Pantograph-OCS system electric arc measured data.

2. take into account the bow net off-line arc mathematics model of train speed according to claim 1, it is characterized in that, the method that the employing of bow net arc mathematics model parameter k and β is following is determined:

The determination of a, model parameter k

Above formula gives k value and flame current effective value I _rms, electric arc equivalent resistance R _arc, equivalent arc length L _arcand the relational expression between arc parameters β;

The determination of b, model parameter β

Between model parameter β and influence factor, relational expression is

Above formula gives β value and flame current effective value I _rms, equivalent arc length L _arcbetween relational expression; The variation range of β is-3 < β < 0.