1. 1 Slavko Vujević*, Petar Sarajčev* and Jakov Petrović** *University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, HR-21000 Split, Croatia TLM Model for the Lightning Transient Analysis of the GSM Base Station Workshop 'Impact of Communications Technology to EMC' **Zagrebinspekt d.o.o. HR 10000, Zagreb, Croatia Contact: slavko.vujevic@fesb.hr

2. 2 Transmission line model (TLM) for the GSM base station lightning transient analysis is presented. Introduction Workshop 'Impact of Communications Technology to EMC' TLM model is based on the use of the well-known ATP-EMTP software package. Direct lightning strike to the GSM base station tower is modelled with the Heidler's type of surge current source. The earthing grid and the GSM base station's tower structure are approximated by the circular cross section conductors. In numerical model, conductors are subdivided into segments (1D finite elements) and Clark's model with distributed parameters is used. Because of limitations of ATP-EMTP software package, the leakage resistance of buried segments is modelled as lumped parameter. Analytical expressions for distributed and lumped segment parameters are derived using the average potential method. Results obtained by the developed TLM model, are compared with the results obtained with more exact electromagnetic model (presented in [3]).

3. 3 Workshop 'Impact of Communications Technology to EMC' Transmission Line Model of the GSM base station tower (1) A Clark's model with distributed constant parameters is then applied on each tower segment. Input data for Clark's model are: a)Resistance per unit length b)Surge impedance c)Propagation velocity d)Segment length. GSM base station tower conductors are, by applying the finite element technique, subdivided into segments (1D finite elements).

4. 4 Ad b) Surge impedance of the GSM tower segment is defined by the following equation: Workshop 'Impact of Communications Technology to EMC' Ad a) Per unit resistance of the tower segment (1D finite element) can be computed as follows: where: ρ s – resistivity of the segment [Ωm], r o – equivalent radius of the tower segment conductor [m]. Transmission Line Model of the GSM base station tower (2)

5. 5 where: Q – electric charge uniformly distributed along the segment [C], ℓ - length of the segment [m], – average potential of the segment. Workshop 'Impact of Communications Technology to EMC' Per unit capacitance of the tower segment depends on the position of that segment, relative to the earth surface. It can be computed by means of average potential method, as follows: where: L – per unit inductance of the tower segment [H/m] C – per unit capacitance of the tower segment [F/m]. Transmission Line Model of the GSM base station tower (3)

6. 6 Per unit capacitance of the segment can be computed as follows, [4]: Workshop 'Impact of Communications Technology to EMC' Transmission Line Model of the GSM base station tower (4) The first integral in the expression for the per unit capacitance computation accounts for the self-capacitance, while the second integral accounts for the mutual capacitance between the tower segment and it’s image. where: ε 0 = 8.854∙10 -12 [As/Vm] – dielectric constant of the vacuum. I self, I mut - double integrals.

7. 7 Workshop 'Impact of Communications Technology to EMC' Transmission Line Model of the GSM base station tower (5) Once the capacitance is computed, one can easily obtain the needed value of the segment's per unit inductance from the following relationship: where μ 0 = 4π∙10 -7 [Vs/Am] is relative permeability of the vacuum. Value of the second integral (mutual per unit capacitance between segment and it’s image) depends on the position of the 1D finite element/segment relative to the earth surface, as will be explained later. All these integrals can be computed analytically. This fact contributes to the numerical stability of the derived method. Surge impedance of the GSM tower segment can be written as:

8. 8 Ad c) Modal propagation velocity of the surge current through the GSM tower segments is equal to the velocity of light, i.e.: Workshop 'Impact of Communications Technology to EMC' Ad d) Segment length (in meters) shouldn’t exceed maximum value which is defined by: where f max presents maximal frequency (in Hz) of interest, found in the lightning surge. c = 3  10 8 m/s Transmission Line Model of the GSM base station tower (6)

9. 9 Transmission Line Model of the earthing grid (1) Each conductor of the earthing grid, by applying the finite element technique, can be subdivided into segments (1D finite elements). Workshop 'Impact of Communications Technology to EMC' A Clark's model with distributed constant parameters is then applied on each segment. Input data for Clark's model are: a)Resistance per unit length b)Surge impedance c)Propagation velocity d)Segment length. Ad a) Per unit resistance of the earthing grid segment (1D finite element) can be computed as follows: Because of limitations of ATP-EMTP software package, the leakage resistance of buried segments is modelled as an additional lumped parameter.

10. 10 Workshop 'Impact of Communications Technology to EMC' Ad b) Surge impedance of the earthing grid segment is defined by the following equation: Transmission Line Model of the earthing grid (2) where: L – per unit inductance of the earthing grid segment [H/m] C – per unit capacitance of the earthing grid segment [F/m]. ε r – relative dielectric constant of the earth, ε 0 = 8.854∙10 -12 [As/Vm] – dielectric constant of the vacuum, μ 0 = 4π∙10 -7 [Vs/Am] is permeability of the vacuum, μ r = 1 is relative permeability of the earth.

11. 11 Again, per unit capacitance of the buried conductor segment depends on the position of the segment respective to the earth surface. Following figure shows a buried segment in arbitrary position, relative to the earth surface. Per unit capacitance of the segment can be computed by means of average potential method. Workshop 'Impact of Communications Technology to EMC' Transmission Line Model of the earthing grid (3)

12. 12 Similarly to the aforementioned analysis employed for the GSM tower model, per unit capacitance of the segment can be computed as follows, [4], [5]: Workshop 'Impact of Communications Technology to EMC' Ad c) Propagation velocity of the lightning surge in the earth can be estimated by the following relation: where c represents velocity of the light in the air and ε r presents the relative dielectric constant of the earth. Transmission Line Model of the earthing grid (4)

13. 13 Workshop 'Impact of Communications Technology to EMC' Ad d) Each of the earthing grid segments should satisfy the following relation for the maximum length (in meters): where: ρ – resistivity of the earth [Ωm], f max - maximal frequency of interest found in the lightning surge [Hz]. Transmission Line Model of the earthing grid (5)

14. 14 Workshop 'Impact of Communications Technology to EMC' Leakage resistance of the buried conductor segments Leakage conductance of the buried segment is represented in EMTP with the concentrated resistance on each side of that segment. Double value of the resistance on each side of the segment is chosen (2  R L ) in order to obtain value of R L after the parallel connection. - self resistance of the segment in homogeneous and unbounded medium (earth), where: - mutual resistance between segment and its image in relation to earth surface, Value of the earthing grid conductor's segment resistance (R L ) is composed of two terms: ρ – resistivity of the earth [Ωm].

15. 15 Workshop 'Impact of Communications Technology to EMC' Analytical solution of double integral I self The double integration is performed along the segment axis (curve  ’ in the Figure below) and along the curve on segment surface, which is parallel to the segment axis (curve Γ in the Figure below). Expressions for distributed and lumped segment parameters include two double integrals. The first of them is integral:

16. 16 Workshop 'Impact of Communications Technology to EMC' Analytical solution of double integral I mut (1) The second double integral is: Analytical solution of integral I mut depends on the position of the segment relative to the earth surface. Three different segment arrangements will be examined: Segment is parallel to the earth surface Segment is perpendicular to the earth surface Segment is in aslope position to the earth surface If segment is buried at depth h parallel to the earth surface, integral solution is (r o  2  h  I self  I mut ):

17. 17 Workshop 'Impact of Communications Technology to EMC' Analytical solution of double integral I mut (2) If segment is perpendicular to the earth surface, the first integration is carried out along the axis of segment image (curve Γ s in the Figure), while the second integration is carried out along the curve on segment surface, which is parallel to the segment axis (curve Γ in the Figure).

18. 18 Workshop 'Impact of Communications Technology to EMC' Analytical solution of double integral I mut (3) If segment is perpendicular to the earth surface, the integral solution is: where:

19. 19 Workshop 'Impact of Communications Technology to EMC' Analytical solution of double integral I mut (4) If segment is in aslope position to the earth surface, parameters signed in the Figure can be computed as follows: where d represents orthogonal projection of the segment onto the earth surface.

20. 20 Workshop 'Impact of Communications Technology to EMC' Analytical solution of double integral I mut (5) If segment is in aslope position to the earth surface, the integral solution can be written as: where for r o << ℓ:

21. 21 Workshop 'Impact of Communications Technology to EMC' Lightning surge model Lightning surge model used for the simulation is based on the Heidler's model of current source, which can be described with the following expression: where: I o, η – peak value of the lightning current and it’s correction factor, respectively n – factor influencing the rate of rise of the function – the strike duration; interval between t = 0 and the point on the tail where the function amplitude has fallen to 50 % of its peak value – duration of the lightning surge front.

22. 22 Verification of the model (1) 60x60 m earthing grid with 10x10 meter square meshes, constructed of copper conductors with diameter 1.4 cm, buried at 0.5 m depth, is considered for the numerical examples. Concerning the injection of the lightning surge current, two scenarios are considered: - injection of the current in the corner point of the grid (point 1) - injection of the current in the middle point (point 25). Workshop 'Impact of Communications Technology to EMC' Soil is homogenous with resistivity 100 Ωm and relative permittivity 36, according to [3]. Lightning surge current parameters are: 1.0167 kA amplitude and 1/20 μs shape.

23. 23 In ATP ‑ EMTP simulation all parameters of the earthing grid conductor segments are computed according to the presented mathematical relations, by means of a computer program (preprocessor) developed for that purpose. Compress -> Extract (grouping feature of the EMTP) has been employed. Workshop 'Impact of Communications Technology to EMC' Verification of the model (2)

24. 24 Temporal transient voltage response in nodes 1, 9 and 17. Scenario 1 - results Spacial transient voltage distribution (3D graphical form). Workshop 'Impact of Communications Technology to EMC' Verification of the model (3)

25. 25 Scenario 2 - results Temporal transient voltage response in nodes 25, 33 and 49. Spacial transient voltage distribution (3D graphical form). Workshop 'Impact of Communications Technology to EMC' Verification of the model (4)

26. 26 GSM base station numerical example (1) Workshop 'Impact of Communications Technology to EMC'

27. 27 Following figures present temporal transient overvoltages: a) In the GSM tower foot (junction between tower and earthing grid), b) In the middle (point 25) of the earthing grid. Direct lightning strike into the top of the GSM tower is considered. Following lightning current parameters are selected: 80 kA amplitude and 1/20 μs shape. Resistivity of the soil is 100 Ωm, and relative permittivity 9. Simulation results a) b) Workshop 'Impact of Communications Technology to EMC' GSM base station numerical example (2)

28. 28 Conclusion Workshop 'Impact of Communications Technology to EMC' Due to the limitations of the transmission line model approach and the application of the ATP-EMTP software package, the electromagnetic coupling between segments could not be taken into account. By comparing the presented results with those obtained by more exact electromagnetic model (presented in [3]), good agreement has been obtained, both in the computed amplitude of the overvoltage, as well as in the temporal and spatial overvoltage distributions. The earth model is limited to the heterogeneous earth. The soil ionization effect can be included.

29. 29 References Workshop 'Impact of Communications Technology to EMC' [1] Kizilcay, M.; Høidalen, H. K.: "ATP ‑ EMTP Beginner’s Guide for EEUG Members", European EMTP ‑ ATP Users Group e. V., 2000. [2] Prikler, L.; Høidalen, H. K.: "ATPDRAW Version 3.5 for Windows 9x/NT/2000/XP – Users’ Manual", European EMTP ‑ ATP Users Group e. V., 2002. [3] Grcev, D. L.: "Computer Analysis of Transient Voltages in Large Grounding Systems", EEE Transactions on Power Delivery, Vol. 11, No. 2, pp. 815-823, 1996. [4] Petrović, J.: "Using the ATP-EMTP Software Package in the LPS Analysis", B. Sc. Thesis, University of Split, FESB Split, Split, 2004, (in Croatian). [5] Vujević, S., Sarajčev, P. and Sarajčev, I., "EMTP Modelling of Direct Lightning Strikes to the GSM Base Station Tower", SoftCOM 2005, Split, Marina Frapa, 2005.

30. 30 THANK YOU ! Workshop 'Impact of Communications Technology to EMC'