Study of the Skin Effect Influence on Electric Railway System Supply Line Heating

Constantin-Florin OCOLEANU, Ioan POPA, Gheorghe MANOLEA

Electrical Apparatus and Technologies, Electromechanical University of Craiova, Faculty of Electrical Engineering, Faculty of Electromechanical, Industrial

Information, Environment Engineering Bd. Decebal, nr. 107, 200440 Craiova

ROMANIA

Abstract: - In this paper our purpose is to verify the influence of skin effect on Romanian Electric Railway System Supply Line Heating . The study of this influence has been made using the finite elements method and it has experimentally validated. We make this study on the copper wire used on the Romanian Electric Railway , heated in AC and DC current . The elaborate model is an electromagnetic and thermal field coupled problem. Key-Words: - skin effect, numerical modeling, coupled problem, finite elements method 1 Introduction

On the intensive traffic lines, the tension draw and also the heating limits of the contact line wire must be verified. The temperature limit is 85 °C and the critical areas are in electric substations proximity. The verification computations must take into account the line overloading and the time thermal constant. [6]

In catenary’s suspension type choosing for correct utilization, the next factors are most important:

trains speed ; technical - economical considerate ; meteorologist factors.

So, for trains speed up to 100 km/h is used a semi compensate catenary’s suspensions, which are able to assure a good collection of the current. For trains speed of 100-160km/h is used a complete compensate catenary’s suspensions, type Re 160, Re 200, Re250, and for high trains speed (250-300 km/h) is used compound catenary’s suspensions. Romanian electric Railway system supply contact line is a wire type TF-100, TF-85, TF-80.This wire are made in Romania, STAS 686-83.

On the main lines, in Romania are use catenary’s suspensions with a contact wire 100 mm2 section (TF-100) and suspension cable from OL-Zn 70 mm2

section or OL-Cu cable 70 mm2 section. Today, in many countries is extended the

utilization of contact line wire on copper with 0,1% Ag, for a 760 amperes current, substituting the contact line wire with cadmium, for working security and environment protection reasons. [8]

In some countries which has a development program to made high speed lines, 300-350 km/h, is extended the contact wire coil with 0,3-0,7% magnesium, 120mm2 section.

In figure 1 is presented geometrical form in transversal section of contact line wire, TF 100, STAS 686-71.[7]

Fig. 1. Line contact wire TF 100

ENVIRONMENTAL PROBLEMS and DEVELOPMENT

ISSN: 1790-5095 142 ISBN: 978-960-474-023-9

In alternative current the existence of skin effect leads on neuniformal repartition of current density Jon the transversal section of the wire. This is equivalent with a reduction of the effective section of wire and consequently the temperature increases compared to the consideration of a uniform density current repartition on wire transversal section. On the other hand, the electric rezistivity varies with temperature and it must taking into account in thermal model.

The contact line wire heat in alternative and direct current is made from copper, 100 mm2

section, with next characteristics : γ : 8900 kg/m3 ; α : 0,000017 1/°C ; ρ20 : 0,0179 Ωmm2/m ;

Numeric results will be compared with experimental results

2 Problem Formulation The used mathematical model has two

components, electromagnetic model and thermal model, both coupled through the source term (Joule specific loose).

( ) ( ) ( )yxJS ,2⋅θρ=θ (1)

2.1 Electromagnetic model

The electromagnetic model is governed by equation:

JAjyA

yxA

x−=⋅θσ⋅ω⋅−

∂∂⋅

µ∂∂+

∂∂⋅

µ∂∂ )(11

(2)

where :

σ - electric conductivity ; µ- magnetic permeability; A- magnetic potential vector; j- imaginary unity ; ω- pulsation ;

J - current density

2.2 Thermal model The temperature distribution in the analysis

domain is given by the thermal conduction equation in steady state :

0y

λyx

λx

=+

∂∂

∂∂+

∂∂

∂∂ Sθθ

(3)

where:

θ– temperature; λ – thermal conductivity ; S- source term;

2.3 Analysis domain and boundary conditions

For stabilized temperature determination in the contact line wire in alternative current, has used a coupled problem AC magnetic – steady state heat transfer in Quick Field Professional (version 5.4 ) . We determine the temperature in direct current using a no coupled problem-steady-state heat transfer.

The model of contact line wire is presented in figure 2.

The boundary condition for electromagnetic model is A =0 on Γ2 and for thermal model is of convection type (α, T0) on Γ1.

Fig. 2. Contact line wire model

3 Problem Solution We have determinate the stabilized temperature

value in alternative and direct current , and the obtained values where experimentally validated. 3.1 Numerical results

We have solved an electromagnetic and thermal field coupled problem for determination the stabilized temperature value for alternative current. For a direct current we have solved a steady state heat transfer problem. One determined the temperature values by neglecting the resistivity variation with temperature ( )θρ ).

ENVIRONMENTAL PROBLEMS and DEVELOPMENT

ISSN: 1790-5095 143 ISBN: 978-960-474-023-9

The current density distributions in contact line wire for 201 A, and 301 A are shown in figure 3 and figure 4 .

Fig. 3. The current density distributions – AC current, i=201 A

Fig. 4. The current density distributions – AC current, i=301 A

In figure 5 and figure 6 are shown temperatures values for 201 A , 301 A, AC current and in figure 7 and figure 8 for 201 A, 301 A DC current.

Fig. 5. Temperature in contact wire –AC current , i=201A, θ0=22.7 °C

Fig. 6. Temperature in contact wire –AC current , i=301A, θ0=23.5 °C

ENVIRONMENTAL PROBLEMS and DEVELOPMENT

ISSN: 1790-5095 144 ISBN: 978-960-474-023-9

Fig. 7. Temperature in contact wire –DC current , i=201A, θ0=22.7 °C

Fig. 8. Temperature in contact wire –DC current , i=301A, θ0=23.5 °C

3.2 Experimental validation Experimentally we obtained contact wire

temperature in AC current for 201 A, 301 A and 201 A, 301 A DC current.

The results obtained for ∆θ (θmax-θ0) AC current

201 A, 301 A and DC current are shown in figure 9 and figure 10.

Fig. 9. Evolution of ∆θ for 201 A, AC, DC current

Fig. 10. Evolution of ∆θ for 301 A, AC, DC current

4 Conclusion The experimental results and also the numerical

results, show skin effect influence on Electric Railway System Supply contact line wire heating.

For 201 A current value at stabilized regime, we remark a difference between ∆θ obtained experimentally in AC current and DC current about 5°C, and for 301 A value a difference about 7 °C.

In future, the numerical model must take into account the resisivity variation with temperature and skin effect influence on electric railway system supply line heating will be evaluate.

ENVIRONMENTAL PROBLEMS and DEVELOPMENT

ISSN: 1790-5095 145 ISBN: 978-960-474-023-9

References: [1] Popa I., Cauţil I., Floricău D., Ocoleanu F.,

Modeling of high currents dismountable contacts, 8th International Workshop Computational of Electrical Engineering, September 14 – 16 September 2007, Wilkasy, Poland, Book of Abstracts, pp. 44-47 .

[2] Popa I., Cauţil I., Influence of Skin Effect on the Temperature Distribution in a Cylindrical Current Leads, International Symposium on Electrical Apparatus and Technologies (SIELA 2005), Plovdiv 2 – 3 June 2005, Bulgaria, pp. 119 – 124.

[3] Popa I,., Modélisation numérique du transfert thermique. Méthode des volumes finis. Edition Universitaria, Craiova, 2002.

[4] Oberrrtl K., Influence of skin effect on mutual inductance of double-cage induction motors, Electrical Engineering, vol.87, 2005, pp. 103–111.

[5] Wang Yaw-Juen, Analysis of the Skin Effect for Calculating Frequency-Dependent Impedance of the TRTS Power Rail, Proc. Natl. Sci. Counc. ROC(A), Vol. 23, No. 3, 1999, pp. 419-428.

[6] Nicola Doru, Cismaru Daniel, Tracţiune electrică,fenomene, modele, soluţii ,in romanian, Vol.1, Sitech, Craiova, Romania, 2006.

[7] Drăghici A., Calceanu I., Cartea mecanicului de locomotive electrice, in romanian, 1980.

[8] Onea Romulus, Construcţia, exploatarea şiîntreţinerea instalaţiilor fixe de tracţiune electrică feroviară, in romanian, ASAB, Bucureşti, 2004.

[9] Mihăilescu D., Locomotive şi trenuri electrice cu motoare de tracţiune asincrone, in romanian, EDP, Bucureşti, Romania.

[10]Condacse N., Locomotive şi trenuri electrice, in romanian, EDP, Bucureşti, Romania, 1980.

ENVIRONMENTAL PROBLEMS and DEVELOPMENT

ISSN: 1790-5095 146 ISBN: 978-960-474-023-9