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Page 1: 167494/FULLTEXT01.pdf · Ño!"" #$ %#& '!"( ) %$$'%#'&'%# * + , + +**+- . %#& # ! ! " # "$ $%%&"'(")* * * + , - + . / 0+$%%&+ -** * ,1 , 2 , +3

ÑO

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Dedicated to…

Rafael, Rosa, Eloisa and Cristina, Wherever you are, you will be proud of this.

To a free young spirit, Christopher.

To Marianne, Because I am no one without you.

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List of Publications

This thesis consists of the summary of the following publications (either published or under review) that have resulted during the last five years doc-toral studies. Consequently, they will be referred in the text by appropriate roman numerals.

I. V. Cooray, R. Montaño and V Rakov, “A model to represent negative and positive lightning first return stroke with connecting leaders”. Journal of Electrostatics. Volume 60, Issues 2-4, March 2004, p. 97-109.

II. R. Montaño, N. Theethayi, V. Cooray, “On the Implementation of Agrawal et al. Model for Lightning Induced Voltage Calculations Using ATP-EMTP”, Paper in review at the IEEE Transaction on Power Deliv-ery.

III. R. Montaño, N. Theethayi, V. Cooray, “Lightning Induce Over voltage: Comparison of two analytical formulation”, Manuscript prepare for sub-mission to IEEE Transaction on Power Delivery.

IV. R. Montaño and V. Cooray “Penetration of lightning induced transient from high voltage to low voltage power system across distribution trans-formers”, Proceeding of the 27th International Conference on Lightning Protection, Avignon, France, September 2004.

V. R. Montaño, M. Edirisinghe, M. Fernando, V. Cooray, “Transient re-sponse of DC Converter station subjected to LIOV”, Proceeding of the VIII International Symposium on Lightning Protection. São Paulo, Brasil, November 2005.

VI. R. Montaño and V. Cooray, “Induced over voltage sensitivity analysis using STIDDA”. 26th International Conference on Lightning Protection, Crocow, Poland, pp.236-241, September 2002.

VII. N. Theethayi, Y. Liu, R. Thottappillil, T. Götschl, R. Montano, P. A. Lindeberg, U. Hellström, “Measurements of Lightning Transients Enter-ing a Swedish Railway Facility”, Proceeding of the 27th International Conference on Lightning Protection, Avignon, France, September 2004.

VIII. R. Montaño, V. Cooray, M. Becerra, M. Rahman, P. Liyanage, “Resis-tance Of Spark Channels”, Paper in review at the IEEE Transaction on Plasma Physic.

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IX. R. Montaño, M. Edirisinghe, V. Cooray and F. Roman, “Varistor mod-els- a comparison between theory and practice”, Proceeding of the 27th In-ternational Conference on Lightning Protection, Avignon, France, Sep-tember 2004.

X. R. Montaño, M. Edirisinghe, V. Cooray and F. Roman, “Response of Low Voltage Surge Protective Devices to Current Impulses with High Time Derivatives”, Paper in review at the IEEE Transaction on EMC.

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The papers below are other collaborated works that have resulted during the last five years of doctoral studies and they are not included in the thesis

[1.] Theethayi N. Liu Y., Montano R. and Thottappillil R., “Importance of the ground impedance in the study of parameters that influence crosstalk in multiconductor transmission line”. Paper in review at the Journal of Electric Power System Research.

[2.] M. Rahman, V. Cooray, R. Montaño, P. Liyanage, M. Becerra, “NOXporduction in spark discharges” Paper in review at the Journal of Electro-static.

[3.] Theethayi N., Liu Y., Montano R., Thottappillil R., Zitnik M., Cooray V. and Scuka V., “A theoretical study on the consequence of a direct light-ning strike to Electrified Railway System in Sweden”. Journal of Electric Power System Research, vol.74, no.2, pp.267-280, 2005.

[4.] P. Liyanage, R. Montaño and V. Cooray “Optical Signatures of Labora-tory Sparks with Currents Comparable to Return Strokes in Lightning Flashes” Proceeding of the 27th International Conference on Lightning Protection, Avignon, France, 13-16, September, 2004.

[5.] V. Cooray, V Rakov, C. A. Nucci, F. Rachidi and R. Montaño “On the constraints imposed by the close electric field signature on the equivalent corona current in lightning return stroke models” Proceeding of the 27th

International Conference on Lightning Protection, Avignon, France, 13-16, September, 2004.

[6.] M. Edirisinghe, R. Montaño and V. Cooray “Response of Surge Protec-tion Devices to Fast Current Impulses”, Proceeding of the 27th Interna-tional Conference on Lightning Protection, Avignon, France, 13-16, Sep-tember, 2004.

[7.] Liu Y, Theethavi N. Thottappillil R, Gonzalez R. M. and Zitnik M, “An improved ionization around grounding system and its application to strati-fied soil”, Journal of Electrostatics, vol. 60, Issues 2-4, pp. 206-209, March 2004.

[8.] Theethayi N. Liu Y., Montano R. and Thottappillil R., “On the influence of conductor heights and lossy ground in multiconductor transmission lines for lightning interaction studies in railway overhead traction sys-tems”. Journal of Electric Power Systems Research. vol. 71, 186-193, 2004.

[9.] D. Månsson, R. Montano, R. Thottappillil “Response of Surge Protective Devices to Very Fast Transient Conducted Pulses”, EUROEM 2004 Book of abstracts , Magdeburg, Germany, July 2004.

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[10.] Y. Liu, Theethayi N, Gonzalez R. M and Thottappillil R, “The residual resistivity in soil ionization region around grounding system for different experimental results”, IEEE international symposium on EMC, Boston, paper no. TH-PM-2-4, pp 794-799, Aug. 2003.

[11.] Theethayi N. Liu Y., Montano R. and Thottappillil R., “Crosstalk in mul-ticonductor lines in the presence of finitely conducting ground”, Confer-ence proceedings of 2003 IEEE International Symposium on EMC, Istan-bul Turkey, May 2003.

[12.] F. Roman, R. Montaño and V. Cooray, “Response of low voltage protec-tive devices under subsequent stroke-like impulse currents”. XIIIth Sym-posium on High Voltage Engineering, Netherlands 2003.

[13.] F. Roman, R. Montaño and V. Cooray, “Varistor response under subse-quent stroke-like impulse current”. XIIIth Symposium on High Voltage Engineering, Netherlands 2003.

[14.] Theethavi N. Thottappillil R., Liu Y. and Montano R., “Parameters that influence the crosstalk in multiconductor transmission line”, Conference Proceedings of the 2003 IEEE Bologna Powertech, Bologna, Italy, paper no. 68. (IEEE student paper award for high quality paper.)

[15.] Theethayi N., Liu Y., Montano R., Thottappillil R., Zitnik M., Cooray V. and Scuka V., “Modeling Direct Lightning Attachment to Electrified Railway System in Sweden”, Conference Proceedings of the 2003 IEEE Bologna Powertech, Bologna , Italy, paper no. 72.(IEEE student paper award for high quality paper).

[16.] Cooray V., Zitnik M., Strandberg G., Rahman M., Montaño R., Scuka V “A novel modification of the 'transmission line model' of lightning return strokes”, 26th International Conference on Lightning Protection, Cracow, Poland, pp.50-55, September, 2002.

[17.] Cooray V., Montaño R., Theethayi N., Zitnik M., Manyahi M., Scuka V “A channel base current model to represent both negative and positive first return stroke with connecting leaders.”, 26th International Conference on Lightning Protection, Cracow, Poland, pp.36-41, September, 2002.

[18.] Cooray V., Zitnik M., Manyahi M., Montaño R., Rahman M., Liu Y., “Physical model of surge-current characteristics of buried vertical rods in the presence of soil ionization” 26th International Conference on Light-ning Protection, Cracow, Poland, pp.357-362, September, 2002.

[19.] Y. Liu, M. Zitnik, R. M. Gonzalez and R. Thottappillil, “Time time-domain model of the grounding system including soil ionization and its application to stratified soil”, 26th International Conference on Lightning Protection, Cracow, Poland, pp.352-256, September, 2002.

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[20.] M. Aristizabal, R. Montaño, P. Chowdhuri and M. Martínez “Lightning induced overvoltages: sensitivity analysis on multiconductor overhead lines with ATP”. IEEE Winter Meeting, New York, EEUU, Jan 2002. Awarded for best student paper.

[21.] Martínez, M; R. Montaño; P. Chowdhuri and M. Aristizabal. “Used of ATP/EMTP for lightning Induced overvoltages calculations in overhead power lines considering the effect of neutral and ground wires.” EMTP/ATP Latin American Users News letter. Buenos Aires, Vol. 3, Ar-gentina, July. 2002.

[22.] Montaño, R.; Ackermann, T.; Söder, L.: “Impact of the Utgrunden Off-shore Wind Farm on Network Losses”, Proceeding of 2001 European Wind Energy Conference, 2-6 July 2001, Copenhagen, Denmark.

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Contents

List of Tables .............................................................................................. xiii

List of Figures ..............................................................................................xiv

List of important symbols and abbreviations............................................. xvii

1 Introduction ...........................................................................................1

2 Return Stroke Electromagnetic Fields ...................................................52.1 Cloud to ground lightning flash....................................................5

2.1.1 Cloud to ground lightning return stroke electromagnetic fields: theory and observations ..............................................................72.1.2 Return stroke models ...............................................................9

3 Lightning Induced Overvoltages On Overhead Power Lines ..............173.1 Rusk model.................................................................................183.2 Taylor et al. model .....................................................................193.3 Chowdhuri and Gross model ......................................................203.4 Agrawal et al. model ..................................................................213.5 Rachidi model.............................................................................223.6 Discussion ..................................................................................233.7 An overview of the methods used to evaluate lightning induced voltages 243.8 Monte Carlo simulations: Comparison of two analytical formulation [III] .......................................................................................28

3.8.1 Results....................................................................................313.8.2 Discussion..............................................................................33

3.9 Influence of ground losses on the lightning induced overvoltage calculations...............................................................................................34

4 Some Practical Applications Of Lightning Induced Overvoltages......394.1 Surge transfer from high voltage to low voltage side of distribution transformer in the event of nearby lightning strikes [IV] .....39

4.1.1 Case Studies - 1 .....................................................................404.1.2 Results and discussions..........................................................41

4.2 Transient response of DC converter station subjected to lightning induced overvoltages [V] .........................................................................46

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4.2.1 Case studies - 2 ......................................................................464.2.2 Results and discussions..........................................................47

4.3 Lossy ground effects on lightning induced voltages: A sensitivity analysis on different overhead power line configurations [VI]................49

4.3.1 Case studies - 3 ......................................................................504.3.2 Results and discussions..........................................................51

4.4 Measurements of lightning transients entering a Swedish railway facility [VII] .............................................................................................54

4.4.1 Measurement system..............................................................554.4.2 Discussion..............................................................................56

4.5 Breakdown mechanism in lightning induced effects: The role of arc resistance [VIII]..................................................................................57

4.5.1 Experimental setup ................................................................584.5.2 Discussion..............................................................................59

5 Response Of Surge Protective Devices To Lightning Type Transients ………………………………………………………………………..61

5.1 Varistor models ..........................................................................615.1.1 Simplified varistor model. .....................................................615.1.2 Durbak’s varistor model ........................................................62

5.2 Experimental setup .....................................................................635.2.1 Fast transient impulse current generator ................................635.2.2 Standard 8/20 s lightning impulse generator .......................65

5.3 Discussion ..................................................................................65

6 Conclusions and Scopes for Future Works..........................................716.1 Concluding remarks ...................................................................716.2 Scope for future work.................................................................74

7 Sammanfattning...................................................................................77

8 Acknowledgments ...............................................................................79

9 References ...........................................................................................83

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List of Tables

Table 3.1. Mean value of the voltage distribution for the two analytical formulations at both end of the power line. ..........................................................................31

Table 3.2. Mean value of the probability distribution of the ratio between the peaks values calculated with the two analytical formulations...................................33

Table 4.1. Lightning flash location for the different study cases. .............................40Table 4.2. Calculated peak over voltages .................................................................45Table 4.3. Measured currents and voltages at the technical house at Tierp.............57

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List of Figures

Figure 2.1. Coordinate system associate with the calculation of electromagnetic field from lightning flashes........................................................................................7

Figure 2.2. Typical electric field intensity and magnetic flux density for first and subsequent return stroke. Solid line: First return stroke. Dashed line: Subsequent return stroke. Adapted from Lin et al. [14]. ...................................9

Figure.2.3. The current waveform at different heights along the channel. (1) 0 m, (2) 10 m, (3) 20 m, (4) 30 m, (5) 40 m, (6) 50 m, (7) 100 m, and (8) 200 m. .......12

Figure 2.4. Electric (a) and magnetic (b) fields at (1) 100 km and (2) 50 m from the return stroke. Observe that the plot shows the magnetic field x c where c is the speed of light in free space. Curve c shows the electric field on a ten times faster time scale. ..............................................................................................12

Figure 2.5. Electric fields at (1) 100 km, (2) 100 m and (3) 50 m as predicted by the TCS and DU model. Curves a and b show the electric fields predicted by the TCS and DU models respectively when the channel base current is the same as that given in figure 2.3. Curves (c) and (d) show the respective waveforms when the models are modified to take into account the connecting leader......13

Figure 2.6. Current waveform to represent a 60 kA positive first return stroke. The waveform is also shown in a 10 times faster time scale (curve b)...................14

Figure 2.7. Electric (a) and magnetic (b) fields at (1) 100 km and (2) 100 m from a positive return stroke. Observe that the plot shows the magnetic field x 5c where c is the speed of light in free space. Curve c shows the electric field on a ten times faster time scale. ..............................................................................15

Figure 3.1. Geometry of the problem under consideration.......................................18Figure 3.2. Transmission line segment representing Rusck coupling model............19Figure 3.3. Transmission line coupling circuit associated with Taylor, Satterwhite

and Harrison model. ........................................................................................20Figure 3.4. Transmission line segment representing Chowdhuri - Gross coupling

model...............................................................................................................21Figure 3.5. Distributed circuit representation of Agrawal et al. model. ...................22Figure 3.6. Transmission line segment representing Rachidi coupling model. ........23Figure 3.7. Transmission line segment representation in ATP-EMTP. ....................25Figure 3.8. Agrawal et al. model simplification. ......................................................26Figure 3.9. Agrawal et al. equivalent model simplification using shunt current

source across the series line impedance ..........................................................27Figure 3.10. Input data histograms: (a) Lognormal distribution histogram for the

Peak current, (b) Continuous uniform distribution histogram for the x coordinate, (c) Continuous uniform distribution histogram for the y coordinate. .......................................................................................................30

Figure 3.11. Coordinate system of the line conductor and the lightning stoke.........31

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Figure 3.12. Voltage distribution Chowdhuri and Gross model: (a) Near end, (b). Far end.............................................................................................................32

Figure 3.13. Voltage distribution Agrawal et al. model: (a) Near end, (b) Far end..32Figure 3.14. Voltage peak ratio distribution: (a) Near end, (b) Far end. ..................33Figure 3.15. Probability distribution for the ratio between the peak values

calculated with the two analytical formulations: (a) Near end, (b) Far end.....33Figure 3.16. Overvoltage probability function values calculated with the two

analytical formulations and using the two transmission lines formulations. : (a) Near end, (b) Far end. ................................................................................34

Figure 3.17. Calculated voltages on a 1 km matched overhead power line induced by a typical subsequent return stroke ( g=0.001 S/m, r=10). Dashed line (“Ideal line”): induced voltage calculated taken into account the ground finite conductivity only when calculating the exciting fields, neglecting the ground impedance. Dotted line (“Ideal field”): result obtained when the finite ground conductivity is taken into account on the surge propagation along the line. Peak current 12 kA. Striking point: 50 m from the line center. Adapted from [53]. .................................................................................................................37

Figure 3.18. Calculated voltages on a 5 km matched overhead power line induced by a typical subsequent return stroke ( g=0.001 S/m, r=10). Dashed line (“Ideal line”): induced voltage calculated taken into account the ground finite conductivity only when calculating the exciting fields, neglecting the ground impedance. Dotted line (“Ideal field”): result obtained when the finite ground conductivity is taken into account on the surge propagation along the line. Peak current 12 kA. Striking point: 50 m from the line center. Adapted from [53]. .................................................................................................................37

Figure 4.1. Coordinate system for the study cases. ..................................................41Figure 4.2. Induced overvoltage at the high voltage side of the transformer, TM-1

[69]. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m...................................42Figure 4.3. Induced overvoltage at the high voltage side of the transformer, TM-2

[70]. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m...................................42Figure 4.4. Rise time comparison of the calculated induced overvoltage at the high

voltage side of the transformer. Red: 0 m model 1. Green: 0 m model 2........42Figure 4.5. Calculated induced voltages at the low voltage side of the transformer.

TM-1. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m. ...............................43Figure 4.6. Calculated induced voltages at the low voltage side of the transformer.

TM-2. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m. ...............................43Figure 4.7. Calculated induced voltages at the load terminal termination. TM-1.

Red: 0m. Green: 250m. Blue: 600m. Pink: 700m ...........................................44Figure 4.8. Calculated induced voltages at the load terminal termination. TM-2.

Red: 0m. Green: 250m. Blue: 600m. Pink: 700m. ..........................................44Figure 4.9. Considered power electronic circuit with harmonic filters. ...................46Figure 4.10. Lightning strike location for the HVDC study cases............................47Figure 4.11. Zoom of the transient voltage on the DC side of the conversion station.

(a) Positive terminal. (b) Negative terminal. ...................................................47Figure 4.12. Zoom of the transient voltage on the AC side of the conversion station.

(a) Phase A. (b) Phase B and C. ......................................................................48Figure 4.13. Overhead lines configurations (all the distances are in meters). ..........50Figure 4.14. Geometry used for the induced overvoltage calculations.....................51

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Figure 4.15. Average Protective Ratio for the maximum positive peak achieved. Up: Horizontal configuration. Down: Vertical configuration. ...............................53

Figure 4.16. Average Protective Ratio for the minimum negative peak achieved. Up: Horizontal configuration. Down: Vertical configuration. ...............................54

Figure 4.17. Entrance of auxiliary power cable into the technical house. ................55Figure 4.18. Normalized measured voltage across a 12.8 cm gap. Doted line: Raw

voltage measurement. Solid line: Voltage corrected as in [99]. ......................59Figure 5.1. Simplified Varistor model......................................................................62Figure 5.2. Durbak’s Varistor model........................................................................62Figure 5.3. Calculated V-I characteristic used for Durbak’s varistor model according

to [103]. Continuous line A0, Dashed line: A1. ................................................63Figure 5.4. (a) Fast current impulse produced by Roman Generator (b) Normalized

frequency spectrum .........................................................................................64Figure 5.5. (a) Continuous line: input voltage impulse, Dash line: voltage

measurement setup response. (b) Initial portion of the impulse response. Continuous line: input voltage impulse. Dashed line: voltage measurement setup response. ................................................................................................64

Figure 5.6. Observed impulse duration for both tested varistors and GDTs. Triangles: Results associate with sample 1. Square: Results associate with sample 2. .........................................................................................................66

Figure 5.7. Comparison of the clamping vs. the maximum voltage achieved for a fast current impulse. ........................................................................................66

Figure 5.8. (a) Maximum clamping voltage vs. different varistor sizes from fast transient generator. (b) Maximum clamping voltage vs. different varistor sizes from Schaffner generator. Triangles: Results corresponding to sample 1. Square: Results corresponding to sample 2. ....................................................67

Figure 5.9. Resistance value of varistor S20K150 obtained when the voltage waveform is divided by the current waveform. An approximate resistance value for the varistor bulk resistance of 1 Ohm is obtained. ...........................69

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List of important symbols and abbreviations

c Speed of light in free space x x coordinate of the electromagnetic field evaluation point. y y coordinate of the electromagnetic field evaluation point.z z coordinate of the electromagnetic field evaluation point.r Radial distance from the coordinate system origin and the

evaluation point in the x-y plane. 22 yxr .h Dipole height. R1 Distance from the lower (image) dipole and the electromag-

netic field evaluation point. R2 Distance from the upper dipole and the electromagnetic field

evaluation point.Angle between the x axis and the radial distance (r).

i Incident scalar potential. Ez Vertical component of electric field. Er Horizontal component of electric field. H Horizontal component magnetic field.

o The charge density per unit length. u (x,t) Voltage induced in the line. u(x,t) Total line voltage. l Conductor length. R Resistance per unit length. L Inductance per unit length. C Capacitance per unit length. hl Conductor height.Ai

z Vertical component of the incident vector potential.d Minimum distance from the stroke location to the power

line.Ei

z Vertical component of the incident electric field.Ei

x Horizontal component of the incident electric field. Bi

y Horizontal/Transverse component of the incident magnetic field.

us Scattered line voltage. Imax Return stroke peak current.

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xs x coordinate of the lightning striking point ys y coordinate of the lightning striking point I0 See Imax.

c Critical frequency (Carson’s formulation). g Ground propagation constant. o Air permeability. o Air permittivity. g Relative permittivity of the ground. g Conductivity of the ground.

Ratio between the return stroke velocity and the speed of light in free space.

SPDs Surge Protective Devices. TCU Traveling Current Source. DU Diendorfer–Uman model.

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1 Introduction

Modern society, in this age of information technology, takes it for granted that the complex chain of electrical and electronic systems should have one hundred percent integrity. A failure (that disturbs the system integrity) is considered unacceptable from a customers’ (final user) perspective, and any implications/consequences due to failures have become very significant in all most all the aspects of modern life. Hence, in various engineering appli-cations that involve large distributed/scattered systems, e.g., telecommunica-tions, cable-TV and computer LAN or WAN networks, etc, the industries today are committed to seek and develop advanced technologies and prac-tices, which guarantee a better performance and efficiency for normal opera-tion of various interconnected electrical and electronic networks/systems. One of the major systems that feeds the above mentioned end user equip-ments is the power distribution network, which leads to a much more com-plex interconnected system. Transient phenomena in interconnected systems is common, which could be due to faults [1], switching [2-3] and lightning (direct or indirect) [2-3]. Depending on the magnitudes and frequencies of the various transients (over voltages/currents) the damage to the power dis-tribution network is inherent, but due to the interconnection, even the various low voltage electrical and electronic systems (sensitive systems) as men-tioned earlier are prone to those transients. Thus, there is increased demand to understand the characteristics and consequences of various transients oc-curring in different systems. With this objective in mind, this thesis has at-tempted to study the transients due to lightning, an unavoidable natural phe-nomenon.

Some examples on the consequences of the transient disturbances are pre-sented here. In 1987, a study [4] conducted in the United States, concluded that on an average nine out of ten enterprises were shut down because their computer systems failed to work for two weeks. The common reason of fail-ure was attributed to the fact that the computer’s electronic systems were exposed to transient electromagnetic interference that disturbed the data flow and data handling, which lead the system to crash [4].

Another example that strongly supports the need for transient studies is the series of blackouts experienced in the recent past in the power transmission systems. In the year 2003 [5], United States, Europe and Canada suffered a

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2

series of blackouts leaving more than 60 million people without electricity. In some cases the reasons for blackouts in power systems are unclear and it is believed that a lightning strike could be one of the causes for this anoma-lous situation.

Among the possible electromagnetic threats, lightning discharges are impor-tant as they, to a great extent, determine the protective measures that must be taken in the framework of lightning protection and Electromagnetic Com-patibility (EMC) [4]. It has been observed that the lightning induced volt-ages/currents have shorter rise times [6] than the standard impulses that are used for testing Surge Protective Devices (SPDs) in the laboratory. Given this, it is therefore of at most importance to evaluate the commercial SPDs under those impulse conditions that might not be included in the interna-tional standard test procedures. The non-standard voltage/current impulses may result in peak voltages in the electrical networks leading to severe power supply outages even though the SPDs on those networks have been selected based on the recommended practices stated in the international standards. This situation is undesirable as the risk of losing a sensitive sys-tem is high and must be avoided.

As mentioned earlier, a transient coming into the sensitive equipments will have many coupling paths, and the power supply is one of them. It has been a traditional practice in distribution systems to have power lines without the overhead ground wire. Although, the main purpose to have an overhead ground wire is to protect the phase wires from direct strikes, it is of interest to evaluate its effects on the voltages induced in the line due to nearby light-ning strikes.

For any given system to achieve an efficient and reliable lightning protection design, one has to resort to accurate mathematical models that are capable of reproducing the various aspects of lightning electromagnetic effects, namely, lighting discharge mechanisms, coupling mechanisms between lightning stroke and the system to be protected, propagation of lightning transients within the system and finally the behavior of various devices to incident lightning transients. The present thesis has to a certain extent focused on all the major topics listed above so as to advance our knowledge in subject of lightning protection and lightning electromagnetic interference.

This thesis has been organized in the following way.

In Chapter 2 the return stroke phase of lightning flash have been investi-gated. A new return stroke model is also proposed, that can predict the re-mote electromagnetic fields accurately when compared to experimental ob-servations.

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In Chapter 3 explains the phenomena of field to wire coupling mechanisms relevant to lightning electromagnetic field illumination to power lines. In this Chapter a comparison of various coupling models are also discussed. More importantly the influence of finitely conducting ground on lightning field to wire coupling mechanisms and the propagation of induced voltages over the power lines is also explained. A new methodology is proposed for the effi-cient implementation of a field to wire coupling model in ATP-EMTP like programs.

In Chapter 4 various case studies namely, effects of overhead ground wire on the lightning induced voltages in distribution systems, lightning induced voltages on a typical High Voltage Direct Current (HVDC) systems, light-ning surge transfer through distribution transformer and measurements of lightning transients in a typical railway technical house. As an additional investigation a discussion is also made on the role of arc resistance in light-ning protection studies. Some thoughts on arc characteristics and its relation to available arc models are also presented based on extensive experimental investigations.

In Chapter 5 the response of commercial SPDs -Varistors and Gas Discharge Tubes (GDTs) - when subjected to high derivative current impulses are dis-cussed based on experimental observations. The responses of the SPDs with fast current impulses were compared with a standard 8/20 s lightning im-pulses. These experimental results are compared with two available models for Varistor in the literature.

In Chapter 6, some important conclusions based on the various studies car-ried out in this thesis are outlined. A brief discussion the possible scope for future work is presented.

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2 Return Stroke Electromagnetic Fields

Lightning is one of the natural phenomena that have amazed mankind since the beginning of civilization. Historically, in almost all the societies, there are records depicting lightning as a punishment from a God. In the ancient times, certain important personalities tried to protect themselves from light-ning using techniques based on myths. For example, Julius Caesar used to wear a laurel crown and the Roman emperors used to wear a skin stripped from a cow under their robes during thunderstorms. But with time, people started questioning these techniques and also wondered whether this phe-nomenon arising from the sky was an act of god or a natural phenomenon?

It was in 1847, that Benjamin Franklin proposed his famous kite experiment to show that a lightning flash is an electrical phenomenon, i.e., caused due to the movement of electrical charges from cloud to ground. Since then, various researchers and engineers strived to understand the different physical mechanisms and the consequences associated with lightning flashes. Various physical processes associated with a lightning flash have been clearly identi-fied, extensively studied and reported in the literature. This chapter therefore is not intended to provide a thorough review of all those inherent events of a lightning flash. Instead, a brief description of the basics behind a cloud to ground lightning flash is provided for completeness. Special attention will be given to mathematical models developed to represent the remote return stroke electromagnetic fields and their comparison with experimentally ob-served return stroke electromagnetic fields [I].

2.1 Cloud to ground lightning flash To understand the mechanisms associated with a lightning flash, first one has to examine the source that produces this natural phenomenon, i.e., the charge structure of a thunder cloud. The first charge structure of a thunder cloud proposed in the literature is dates back to 1910s [7]. The model was a result of ground based measurements of the electrostatic field environment in the presence of a thunder cloud and the field changes associated with the effective neutralization of portions of those cloud charges due to lightning return strokes. In that model, only two charge centers were proposed, one positive located in the upper region of the cloud and the other negative that

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exists in the lower regions of the cloud [7]. It was not until 1937, that Simp-son and Scrase with an instrumented balloon confirmed the existence of these charges and more importantly, they identified the existence of a third charge center located at the cloud base [7-8]. Various theories explaining the mechanisms associated with the charging process of the cloud have been reported in the literature. Substantial observations seem to favor the fact that charging mechanisms are closely related to the presence of ice within the clouds [9]. In general, researchers consider (believe) a particular theory to explain the electrification process of the cloud [10]. Recent observations indicate that a thundercloud has a more complex charge structure than the theory presented by Simpson and Scrase. It appears that the charges are not located in well-defined regions but change from one polarity to another in a quasi-continuous mode [10].

Generally, a Cloud to Ground (CG) flash takes place either from the negative or the positive charge center to ground. The former leads to a negative ground flash while the later leads to a positive ground flash. Observations made from the electromagnetic field signatures of lightning flashes indicate that a CG is initiated by a set of electrical discharges taking place within the cloud [9-11]. This process, called preliminary break down, will result in the creation of a column of charges named stepped leader, which will progres-sively propagate in a stepped manner from the cloud towards the ground. In many cases both processes, the initial electrical break down and the stepped leader are termed as preliminary breakdown. In this Chapter, the initial elec-trical discharge that takes place inside the cloud will be termed preliminary breakdown and the stepping process (propagating towards the ground) will be referred to as the stepped leader. For negative stepped leaders (which is true in most of the cases), the length of each step is around 50 m with an average leader speed of 106 m/s [9-11].

When the stepped leader is traveling towards the ground, the magnitude of the induce charges of opposite polarity at the surface of the ground increases. As the stepped leader approaches the ground, the field at the ground and grounded objects increase. There will be field intensification at the tip of the ground structures due to the structure geometry that will lead to the initiation of upward electrical discharges from the structures’ tip. Such discharges are called upward connecting leaders. Several of these upward connecting lead-ers will be launched from different objects, but only one will succeed in in-tercepting the stepped leader. After the connection between the stepped leader and the ground/ground-object is made, a wave of zero potential will propagate along the stepped leader channel to neutralize the charges depos-ited along it [9, 11]. This will result in a luminous event that propagates from the ground to cloud with a speed close to the speed of light. This is called a Return Stroke. Once the channel is established between the cloud and ground

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several such strokes can take place along the same conductive channel. Typically, a negative ground flash may last for about 0.5 s with a mean number of strokes between four and five.

There is only limited information available on the mechanism of the positive flashes. However, available experimental results indicate that its mechanism is similar to the negative with some differences. For instance, observations reported in the literature show that the positive stepped leader propagates more or less continuously towards the ground [9]. Moreover, positive flashes may contain a single return stroke, while the negatives may contain several [12].

As it can be seen, all the processes associated with either positive or negative ground flashes involve the movement of electrical charges (leader phase) and currents (return strokes) between cloud to ground. As a result, this phe-nomenon emanates electromagnetic fields which propagate in air. With re-gard to this thesis, knowledge of those fields generated by lightning flashes are of prime importance as they interact with various electrical systems that are exposed to those fields; especially, the low voltage power networks as applicable to this thesis.

2.1.1 Cloud to ground lightning return stroke electromagnetic fields: theory and observations

Conventionally, the electromagnetic field generated form a lightning flash is expressed considering each current element I·dh along the lightning channel as a dipole antenna, wherein the lightning channel as such is assumed to be perpendicular to a perfectly conducting plane (figure 2.1).

r

z

h

Source

Image

dh

R2

R1

h

X

Y

Z

Figure 2.1. Coordinate system associate with the calculation of electromagnetic field from lightning flashes.

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Based on figure 2.1 and in cylindrical coordinates, the vertical component of electric field (Ez), horizontal component of electric field (Er) and horizontal component magnetic field (H ) at observation point (r, z, ) above the ground level from a dipole antenna in the time domain are given by [13]:

cR

dtdi

Rcr

cRi

Rczhr

dtc

RiR

rzhcR

dtdi

Rcr

cRi

Rczhrdt

cRi

RrzhdhtE

t

t

oz

232

2

22

42

220

252

221

31

2

2

141

22

0

151

22

)(2

)(2

)(2)(24

)(

(2.1)

cR

dtdi

Rcrzh

cRi

Rcrzh

dtc

RiR

rzhcR

dtdi

Rcrzh

cRi

Rcrzhdt

cRi

RrzhdhtE

t

t

or

232

22

42

0

251

131

2

1410

151

)()(3

)(3)(

)(3)(34

)(

(2.2)

cR

dtdi

Rcr

cRi

Rr

cR

dtdi

Rcr

cRi

RrdhtH

o

222

232

121

1314

)( (2.3)

The geometrical parameters h, z, R1 and R2 are defined in figure 2.1, while cis the speed of light in free space. Observe that the electric field -equations (2.1) and (2.2) - can be divided in three field components namely static (pro-portional to the current integral), induction (proportional to current) and radiation (proportional to current derivative). Similarly, for the magnetic field -equation (2.3)- only the induction and radiation component exists. This formulation was introduced to understand some features of the electromag-netic field data reported in the literature. Moreover, those set of equations are of important owing to the fact that the interaction of the electromagnetic fields from nearby lightning flashes with low voltage power network are highly sensitive to the shape and magnitude of illuminating fields.

The main features of the electromagnetic field signature from first and sub-sequent return strokes are presented in figure 2.2 [9, 14]. It has been reported in the literature that at close distances (<2km), after some tens of microsec-onds the electric field does not fall to zero even though the current flow has ceased [9, 11, 14]. This clearly indicates that close to the lightning channel,

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the electrostatic field component become dominant. The influence of the induction component on the electromagnetic field signature increases as the distance from the lightning channel increase. In this regards, observe that the magnetic field presents a “hump” corresponding to the induction component of the field. When the distance is larger than 40 km, the measured electric and magnetic field signatures have an identical wave shape which is due to the dominance of the radiation field component.

Figure 2.2. Typical electric field intensity and magnetic flux density for first and subsequent return stroke. Solid line: First return stroke. Dashed line: Subsequent return stroke. Adapted from Lin et al. [14].

Having seen the features of experimentally observed remote electromagnetic fields from lightning returns strokes, the next section is devoted to under-standing different return stroke models available in the literature and a new return stroke model. These models are utilized to reproduce the electromag-netic fields similar to those generated by lightning flashes. No detailed mathematics will be presented. The author requests the readers to refer to paper [I] for more details.

2.1.2 Return stroke models The electromagnetic field signatures associated with the return stroke current have been extensively reported in the literature [14-24]. Further, various theories and mathematical models have been developed seeking for explana-tions of the observed features in the measured electromagnetic fields [14-24]. Return stroke models can be broadly classified as:

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a. Gas dynamic or “physical” models, which are primarily concerned with the radial evolution of a short segment of the lightning channel and its associated shock wave.

b. Electromagnetic models that are usually based on a lossy, thin-wire antenna approximation to the lightning channel. These models in-volve a numerical solution of Maxwell’s equations to find the cur-rent distribution along the channel from which the remote electric and magnetic fields can be computed.

c. Distributed-circuit models, that can be viewed as an approximation to the electromagnetic models and they represent the lightning dis-charge as a transient process on a vertical transmission line charac-terized by per unit length resistance (R), inductance (L), and capaci-tance (C).

d. “Engineering” models in which the spatial and temporal distribution of the channel current (or the channel-charge density) is specified based on observed lightning return-stroke characteristics, namely, current at the channel base, the speed of the upward-propagating front, and the channel luminosity profile.

Models which belong to category (a) are primarily used to reproduce physi-cal parameters of the return stoke. Models in (b), (c) and (d) categories are mainly used to reproduce the electromagnetic fields from a return stroke; they further can be divided into two major types [18-19]:

Current propagation (CP) models (also termed transmission line type models), where the return stroke channel acts as a guiding structure for the current wave propagation, with the source located at the ground is feeding the line.

Current generation (CG) models (also referred to as traveling cur-rent source type models), where the release of the leader charge by the upward propagating return stroke front gives rise to the return stroke current.

Let us consider some details pertinent to the model presented in paper [I].

2.1.2.1 A model to represent negative and positive lightning first strokes with connecting leaders [I]

Traditionally, most of the models in the CP and CG categories use the cur-rent at the base of the channel as an input parameter. These models are gen-erally called models with specified channel base current or simply channel base current models. In the development of a mathematical model to de-scribe first return strokes it is necessary to take into account the attachment process that involves connecting leaders. Various models have been reported

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in the literature that considers the upward connecting leader process [25-28]. Gorin [26] presented a distributed circuit model to represent first-stroke, wherein the return stroke velocity initially increases to its maximum and thereafter decreases. The initial velocity increase is associated with the ‘final jump’ thought to be responsible for the formation of the initial rising portion of the return stroke current pulse. A new CG model in which the connecting leader is an integral part of the model is presented in [I]. This model allows one to overcome some limitations of previous CG models.

The following assumptions were made in the development of the model:

The channel base current is known. The charge density per unit length, o, deposited by the return stroke along the channel is assumed to be independent of the height (the model can accommodate any other charge profile too without diffi-culty). The slow front of the current waveform is assumed to be produced by the connecting leader as it moves through the streamer region of the stepped leader. On the basis of observations of laboratory sparks, it is assumed that the connecting leader moves upwards with an ex-ponentially increasing speed and that it merges into the return stroke proper when it encounters the hot region of the stepped leader chan-nel.The velocity profile of the return stroke proper is known. In the pre-sent simulations, it was assumed to decrease exponentially with height.The corona current injected into the channel at a given point decays exponentially with time. The source of current is the radial corona surrounding the descend-ing leader core above the contact point and the streamer zone be-tween the leader tip and the ground below the contact point The injected current propagates downward at the speed of light, and the current reflection at the ground level is equal to zero

2.1.2.1.1 First negative return stroke Since length of the connecting leader is a measure of the striking distance, the value of 70 m estimated for this parameter is not far from the striking distance estimated for a 30 kA peak current [29]. Figure 2.3 shows how the signature of the current waveform varies as a function of height. As apparent from this figure, the model predicts that the peak return stroke current de-creases while its rise time increases with height. This prediction is in agree-ment with the inferences made from optical observations.

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0 4 8 12 16 20Time, s

Cur

rent

, Arb

itrar

y un

its

1234

5

678

Figure.2.3. The current waveform at different heights along the channel. (1) 0 m, (2) 10 m, (3) 20 m, (4) 30 m, (5) 40 m, (6) 50 m, (7) 100 m, and (8) 200 m.

Figure 2.4 shows the electric and magnetic fields at two distances from the channel obtained with the model. These signatures compare well with the available experimental data [14]. The peak derivative of the electric field at 100 km generated by the model is 34 V/m/ s. This agrees with the typical values obtained from measurements [9, 11]. If a channel base current with a derivative of 24 kA/ s were used, the peak radiation derivative would have decreased to about 23 V/m/ s, somewhat smaller than the typical values obtained from measurements [30], thereby explaining our choice of deriva-tive of the current waveform, 37 kA/ s, which is slightly higher than the recommended value for negative first strokes but provide better agreement for distances around 100 km.

0 20 40 60 80 100Time, s

-2x100

0x100

2x100

4x100

6x100

V/m

1

ab

c

0 20 40 60 80 100Time, s

0x100

4x104

8x104

1x105

2x105

V/m

2

a

b

Figure 2.4. Electric (a) and magnetic (b) fields at (1) 100 km and (2) 50 m from the return stroke. Observe that the plot shows the magnetic field x c where c is the speed of light in free space. Curve c shows the electric field on a ten times faster time scale.

One of the key features of the developed model is that it predicts the slow front in the channel base current waveform which is the current signature generated by the connecting leader. This is mathematically incorporated into

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the model as a modification of the velocity profile of the discharge phase of the upward connecting leader.

Previously, Thottappillil and Uman [31] showed that a better agreement between the initial peak of the calculated and measured radiation fields of a subsequent return stroke for the case of a current waveform containing a slow front could be obtained if the return stroke velocity was assumed to increase exponentially from a small value to the experimentally measured value. However, in contrast to the present model, they did not attempt to connect the velocity profile to the duration of the slow front of the channel base current. Note that all the channel base current models of the CG type have the velocity profile and charge distribution, or the velocity profile and the discharge time constant profile as inputs.

Thus, in any other channel base current model of type CG, the only modifi-cation needed to introduce the connecting leader and hence to utilize a chan-nel base current with a slow front, is to change the velocity profile as given in paper [I] (the authors in [I] do not rule out the possibility of finding a bet-ter velocity profile for the connecting leader). For example, the electric fields generated by the Traveling Current Source (TCS) and Diendorfer–Uman (DU) models after this change is incorporated in them are also shown in figure 2.5. Note that the model predicted electromagnetic fields do not show the peculiar features that were present in them before this modification was made.

0 2 4 6 8 10Time, s

0

5

10

15

20

25

V/m

a

b

1

cd

0 20 40 60 80 100Time, s

-2x104

0x100

2x104

4x104

6x104

V/m

a

b

c

d

2

0 20 40 60 80 100Time, s

-4x104

0x100

4x104

8x104

1x105

V/m

a

b

c

d

3

Figure 2.5. Electric fields at (1) 100 km, (2) 100 m and (3) 50 m as predicted by the TCS and DU model. Curves a and b show the electric fields predicted by the TCS and DU models respectively when the channel base current is the same as that given in figure 2.3. Curves (c) and (d) show the respective waveforms when the models are modified to take into account the connecting leader.

2.1.2.1.2 Positive first strokes

Experimental observations based on both electric field and direct current measurements indicate that the main difference between the positive and

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negative return stroke currents is the presence of a long current tail in the former[9, 11]. The electric field measurements indicate that the first few tens of microseconds of the positive return stroke current is qualitatively similar to that of the negative first strokes. After this initial stage the negative cur-rent continues to decay, whereas the positive current starts to increase again, reaching a second peak within about 100 – 300 s and decay within a few milliseconds [32, 33]. Cooray [33] suggested that this second current en-hancement is produced when the positive return stroke front encounters a large source of positive charge, probably located on an extensive dendritic pattern of mainly horizontal branches in the cloud, as it reaches the cloud end of the leader channel. The current waveform shown in figure 2.6 has these features and can be used to represent a typical positive first return stroke current.

0 200 400 600 800 1000Time, s

-80

-60

-40

-20

0

kA

a

b

Figure 2.6. Current waveform to represent a 60 kA positive first return stroke. The waveform is also shown in a 10 times faster time scale (curve b).

The slow front duration, tf, of this current waveform is 21 s and the rise time of this current waveform is 22 s. This rise time is close to the corre-sponding median values of positive return stroke currents [30]. The peak value of the current waveform is 60 kA. This is larger than the median posi-tive current of 35 kA. This choice is based on the experimentally observed fact that, on average, the peak radiation fields of positives are two times larger than those of negative first strokes. Since the positive return stroke speeds do not differ significantly from those of negatives, the only plausible explanation for this experimental observation is the two times higher median current in positives than in the negatives. The derivative of the current wave-form is 30 kA/ s. This is also higher than the median value measured in positives but it will lead to electric field derivatives similar to those measured. The impulse charge associated with it is 28 C which is close to the experimentally measured value for a 60 kA positive current.

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The velocity profile used in calculating electromagnetic fields is similar to that used earlier for negative return strokes. Since the peak current is twice that of the negative the value o is assumed to be 0.002 C/m. This charge density leads to a connecting leader of length 130 m which is longer than the corresponding length obtained for negative strokes. The electromagnetic fields generated by the model at two distances are shown in figure 2.7. Note the long slow front and the slow tail of the radiation field. These signatures are similar to those observed in measured fields. The peak radiation field and the peak radiation field derivative at 100 km are about 12 V/m and 25V/m/ s respectively. These values also agree with the typical values ob-served for positive strokes [19].

0 40 80 120 160 200Time, s

-2x105

-1x105

-8x104

-4x104

0x100V

/m

a

b

2

0 40 80 120 160 200Time, s

-16

-12

-8

-4

0

V/m

ab

c1

Figure 2.7. Electric (a) and magnetic (b) fields at (1) 100 km and (2) 100 m from a positive return stroke. Observe that the plot shows the magnetic field x 5c where c is the speed of light in free space. Curve c shows the electric field on a ten times faster time scale.

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3 Lightning Induced Overvoltages On Overhead Power Lines

As explained in Chapter 2, every stroke in a given lightning flash produces electromagnetic fields that can illuminate the overhead and underground electrical networks. In order to represent this coupling phenomenon between the stroke and the wires experiencing the illumination, various models (field to wire coupling models) have been developed namely, Rusck [34], Taylor etal. [35], Chowdhuri and Gross [36], Rachidi [37], Agrawal et al. [38]. Con-sequently, various methodologies can be applied to determine the voltages and currents induced on the conducting systems due to an external field, considering any of the above mentioned models [34-38] that represent the general field to wire coupling mechanism under the limits of transmission line approximation [39-40]. Traditionally, the transmission line theory is used to calculate the induced voltages/currents, assuming that the response of the line satisfies a Transverse Electromagnetic (TEM) field structure, wherein the transverse dimension of the lines are smaller than the minimum significant wavelength [39-40]. Hence, the line can represented by a series of elementary segments connected in cascade and that each segment is progres-sively illuminated by the incident electromagnetic field, which can be used for solving the wave propagation along the line. Furthermore, although these models are well established and known, but the calculations involved in im-plementing those models for a practical problem is not trivial. This led to a restricted and limited use of commercial transient analysis software for the lightning interaction studies. Therefore, there is a need to have either a tool that will allow easier manipulation of the coupling models for the case of complex electrical networks or a methodology for easy and efficient imple-mentation of some of the coupling models in the available commercial tran-sient simulation packages (packages that can handle complex electrical net-works). In this Chapter, some comparisons among different field to wire coupling models available in the literature are presented. The models will be presented under the assumption that the conductors are located above a per-fectly conducting ground. Also, a brief description of solution techniques (time or frequency domain) used for the calculation of lightning induced overvoltages is presented. Finally, a discussion is made on the influence of the ground losses on the induced overvoltage calculations.

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3.1 Rusk model In 1958, Rusck [34] presented a field to wire coupling model derived in terms of the total distributed currents and voltages along the line. The pro-posed transmission lines equations associated with the model were derived relating the total electric field on the conductor surface to the scalar and vec-tor potentials.

Ez

Ey

Ex

Z

Y

X

Z2

Z1

x

x+ x

(l,0,hl) (0,0,0)

Figure 3.1. Geometry of the problem under consideration.

Considering the geometry presented in Figure 3.1 (Note: This line configu-ration and line terminations are used to explain all the coupling models in this chapter), the transmission line equations derived by Rusck are:

0),(),(t

txiLRix

txu (3.1)

tthx

Ct

txuCx

txi li ),,0,(),(),( (3.2)

In equations (3.1) and (3.2) u (x,t) is the voltage induced in the line due to the scalar potential ( i) of the incident field. R, L and C are the correspond-ing resistance, inductance and capacitance per unit length. The total voltage u(x,t) on the line is given by,

dzt

tzxAtxutxulh i

z

0

),,0,(),(),( (3.3)

In equation (3.3), hl is the height of the conductor and Aiz is the vertical com-

ponent of the incident vector potential. Therefore, the boundary conditions for the transmission corresponding to equations (3.1) and (3.2) are,

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dzt

tzAtiZtu

lh iz

01

),,0,0(),0(),0( (3.4)

dzt

)t,z,0,l(A)t,L(iZ)t,L(uh

0

iz

2 (3.5)

Observe that the forcing function appearing in the transmission line equa-tions associated with Rusck model are the incident scalar potential along the line and the vertical component of the incident vector potential at the line terminations. An important contribution of Rusk is that he proposed a sim-plified equation to estimate the peak induced overvoltage (equation 3.6) based on a given stroke location and stroke amplitude. A drawback of equa-tion (3.6) is that no information regarding the front and decay time can be obtained.

dhI

ZU lo

maxmax (3.6)

In (3.6) d is the distance of the stroke location from the line, Imax is the peak current of the corresponding return stroke, hl is the conductor height and Zois given by

304

1

o

ooZ (3.7)

Figure 3.2 depicts the transmission line representation of the Rusk model.

C x

L xR x L xR x

C x C x

u (x, t) u (x+2 x, t)u (x+ x, t)

tthxxC

i ),,0,(t

thxxCi ),,0,2(

tthxC

i ),,0,(

Figure 3.2. Transmission line segment representing Rusck coupling model.

3.2 Taylor et al. model In 1965, Taylor, Satterwhite and Harrison presented a model derived in terms of the distributed voltage and current sources [35]. Their proposed transmission line equations, in terms of total line voltage and line currents are,

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hiy dztzxB

tttxiLRi

xtxu

0

),,(),(),( (3.8)

hiz dztzxE

tC

ttxuC

xtxi

0

),,(),(),( (3.9)

Note that for the case of Taylor et al. model two forcing sources are used. Unlike the Rusk model, this formulation is based on the incident vertical electric field (Ei

z) and the incident horizontal (transverse) magnetic induction field (Bi

y). The corresponding transmission line representation associated with the Taylor et al. model is presented in figure 3.3

C x

- +

hiy dztzxxB

t0

),,(L xR x

- +

L xR xus(x, t) us

(x+ x, t)

C x C xh

iz dztzxxE

tC

0

),,(

us(x+2 x, t)

hiy dztzxxB

t 0

),,2(

hiz dztzxxE

tC

0

),,2(

Figure 3.3. Transmission line coupling circuit associated with Taylor, Satterwhite and Harrison model.

3.3 Chowdhuri and Gross model In 1967, Chowdhuri and Gross presented a new coupling model for the lightning induced voltage calculations for overhead lines [36]. Several changes have been introduced by Chowdhuri himself to improve his original formulation. The last modification was published by Chowdhuri in 1990 [41]. The corresponding transmission line equations based on the Chowdhuri coupling model are,

0),(),(t

txiLRix

txu (3.10) h

iz dztzxE

tC

ttxuC

xtxi

0

),,(),(),( (3.11)

Eiz is the vertical component of incident electric field. The boundary condi-

tions for the above set of equations are,

),0(),0( 1 tiZtu (3.12)

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),(),0( 1 tliZtu (3.13)

The equivalent transmission line representation based on Chowdhuri cou-pling model is shown in figure 3.4.

C x

L xR x L xR x

C x C x

u(x, t) u(x+2 x, t)u(x+ x, t)

hiz dztzxE

tC

0

),,(h

iz dztzxxE

tC

0

),,(h

iz dztzxxE

tC

0

),,2(

Figure 3.4. Transmission line segment representing Chowdhuri - Gross coupling model.

It should be mentioned here that the transmission line equations presented by Chowdhuri and Gross [36] are similar to those of Rusck [34], but they are expressed in terms of total line voltage and incident inducing voltages in-stead of total line voltage and incident scalar potentials [40].

3.4 Agrawal et al. model The simplest and accurate coupling model under the limits of transmission line approximation that is used for lightning induced voltage calculations was presented in 1980 by Agrawal, Price and Gurbaxani [38] wherein the transmission line equations were derived in terms of scattered line voltage (equations 3.14-3.15).

),,(),(),(

thxEt

txiLRi

xtxu i

x

s (3.14)

0),(),(

ttxu

Cx

txi s (3.15)

Hence, the propagating scattered voltage (us) along the line is due to the distributed voltage sources resulting from the horizontal component of inci-dent electric field (Ei

x) at the line height. Consequently, the total voltage on the line u(x,t) at any point and at any instant is given by,

hiz

s dztzxEtxutxu0

),,0,(),(),( (3.16)

The boundary conditions for the scattered voltages at the two line termina-tions are given by equations 3.17 and 3.18 respectively.

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hiz

s dztzEtiZtu0

1 ),,0,0(),0(),0( (3.17)

hiz

s dztzlEtLiZtLu0

2 ),,0,(),(),( (3.18)

The corresponding transmission line representation based on Agrawal et al.coupling model is shown in figure 3.5.

C x

- +

Ex xL xR x- +

Ex xL xR x

C x C xus(x, t) us

(x+2 x, t)us(x+ x, t)

Figure 3.5. Distributed circuit representation of Agrawal et al. model.

3.5 Rachidi model In 1993, Rachidi presented a field to wire coupling model [37] in terms of incident horizontal magnetic field forcing source and scattered line currents. The corresponding transmission line equations based on Rachidi coupling model are,

0),(),(

ttxi

LRix

txu s (3.19)

h ix

sdz

ytzxB

LttxuC

xtxi

0

),,(1),(),( (3.20)

It is interesting to note that Rachidi coupling model in terms of scattered line currents is a dual of Agrawal et al. coupling model, which is in terms of scattered line voltages. Consequently, the total current in the line at any point and at any time is related with the total scattered current by,

hiy

s dztzxBL

txitxi0

),,0,(1),(),( (3.21)

The boundary conditions at the line terminations are,

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hiy

s dztzBLZ

tuti01

),,0,0(1),0(),0( (3.22)

hiy

s dztzlBLZ

tlutLu02

),,0,(1),(),( (3.23)

Figure 3.6 shows the transmission line representation of Rachidi model.

C x

L xR x L xR x

C x C x

u(x, t) u(x+2 x, t)u(x+ x, t)

h ix dz

ytzxB

L0

),,(1 h ix dz

ytzxxB

L0

),,(1 h ix dz

ytzxxB

L0

),,2(1

Figure 3.6. Transmission line segment representing Rachidi coupling model.

3.6 Discussion It has been shown that there isn’t a unique formulation to represent the light-ning induced voltage for overhead power lines. The variety of models as discussed in the previous section has led considerable discussion and contro-versies within the power community, concerning validities and accuracies for the engineering applications. Although, the basis for all the formulations are from Maxwell equations, the dilemma arises due to the fact that in each coupling model different forcing sources are adopted and expressed in terms of different components of illuminating electromagnetic fields. For instance the coupling model of Rusk are in terms of the scalar potential ( i) of the incident field, Chowdhuri in terms of the incident vertical component elec-tric field (Ei

z), Agrawal et al. in terms of horizontal component of incident electric field (Ei

x) and Rachidi in terms of the transverse component of the incident magnetic field (Bi

x). An important observation is that, if the trans-mission line equations corresponding each of the coupling models based on Taylor et al. or Agrawal et al. or Rachidi are solved independently for the total line voltages for any case of stroke location, one can arrive at the same total line voltages even though each coupling model is unique. This has been demonstrated by Nucci et al. in [40].

Comparisons either analytically or numerically among various models namely Chowdhuri, Rusck, Taylor et al. and Agrawal et al. coupling models have been reported in the literature [40, 42, 43]. In [42] it was concluded that Chowdhuri model does not consider a source term namely the contribution

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of the incident magnetic field component. In 1994 Cooray [43] showed that the coupling model of Rusk is identical to that of Agrawal et al. provided that the lightning channel is vertical. Indeed most of the calculations of in-duction in power lines due to lightning are performed by assuming a vertical lightning channel.

Although various comparisons among the available coupling models have been presented in the literature [40, 42, 43], the reported results consider just few particular numerical cases [40, 42] or comparisons are made from a theoretical point of view where no numerical results are presented [43]. Moreover, since Agrawal et al., Rusck, Taylor et al. and Rachidi model can be considered as equivalents, it will be worth making detailed comparisons of Chowdhuri coupling model with any of those previously mentioned mod-els based on statistical approach (with large number of cases) and not just with few or specific cases as in the literature [40, 42]. Consequently, the proposed comparison is made with Agrawal et al. model which seems to have received high credibility among the power community. However, be-fore presenting the comparisons of the two coupling models, let’s first dis-cuss the possible ways of solving the transmission line equations and the difficulties in the implementation of the Agrawal et al. coupling model in transient analysis programs namely ATP-EMTP.

3.7 An overview of the methods used to evaluate lightning induced voltages

Various approaches can be applied to solve the transmission line equations, i.e., Finite-Difference Time-Domain (FDTD), Method of Moments (MoM), Finite Element Method (FEM), etc. Note that if the transmission line equa-tions are solved entirely in frequency domain an Inverse Fast Fourier Trans-form (IFFT) can be performed on frequency response to obtain the corre-sponding results in time domain. Traditionally, a direct time domain (FDTD) or frequency domain (FD-IFFT) methodology has been adopted to solve the field to wire coupling problems involving transmission line equations [44-45]. By calculating lightning induced voltages in frequency domain, the problem is considerably simplified because all the time integrals or time derivatives are transformed to corresponding proportional or inversely pro-portional frequency terms. However, the frequency domain approach does not provide an easy way to implement power equipment models that involve a non linear characteristic [44].

Time domain approach has been widely used for the calculation of transients in power systems. In this regard, various transient analysis programs are

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available since late seventies. The inherent advantage of adopting a time domain approach is the freedom available to the user in incorporating their own models for non-linear elements like SPDs, circuit breakers, switches, power electronics, etc. which are more realistic problems and has been at-tempted in this thesis.

It is to be mentioned here that owing to the advantages of time domain simu-lations as mentioned above, the author favors using time domain simulations rather than a frequency domain approach. However, in this thesis both meth-odologies have been used in several study cases as discussed in papers [II-VI]. On one hand, the frequency domain approach was implemented to ana-lyze two distribution type line arrangements, where only the induce voltages and the influence of a finitely conducting ground were evaluated and that no power system components were simulated. On the other, a modification of Agrawal et al. formulation is proposed for its easy and efficient implementa-tion in transient analysis program, i.e., ATP-EMTP. One of the important advantages using this program is that it has inbuilt power line models namely Semlyen [46], Marti [47] and Noda [48] setups, that can handle any multi-conductor overhead power line configuration. Moreover, those setups are capable of including the frequency dependant skin effect and ground losses, line transpositions, conductor bundling, etc. Let’s discus the possible drawbacks associated with the direct implementation of Agrawal et al.model in ATP-EMTP. In ATP-EMTP a transmission line segment is repre-sented as shown in figure 3.7, which effectively is a two-port network con-nected in cascade.

C x2

L xR x L xR x

V(x, t) V(x+2 x, t)

Transmission line model segment ( x)

C x2

C x2

C x2

Transmission line model segment ( x)

Figure 3.7. Transmission line segment representation in ATP-EMTP.

Observe that each segment no matter whichever line model/setup is used, the moment one defines the line geometry and material mediums the impedance and admittance parameters (line constants as described in ATP-EMTP [46, 49]) are fixed. Hence, one cannot insert a source term in series with the line impedance of figure 3.7, as the impedance and admittance parameter of the line is embedded within an inaccessible two-port network. Therefore, it is

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inherent that the Agrawal et al. model cannot be directly implemented in the ATP-EMTP with the available line models/setups, which indeed is a draw-back. Various studies have been reported in the literature where the model has been inefficiently implemented. In [50], the coupling phenomena associ-ated with the lightning fields due to indirect strikes were programmed using the models language available in the ATP-EMTP [49].

On the other hand Borghetti et al.[51] has used a separate Lightning Induced Over Voltage (LIOV) code written in a high level programming language for modeling the coupling phenomena, wherein the calculated output volt-ages/currents where linked to the ATP-EMTP externally. Note, though [50] and [51] have used the Agrawal et al. model for the induced voltage calcula-tions, neither of them used the available built in line models/setups within the ATP-EMTP as discussed earlier.

As mentioned earlier, Agrawal et al. model cannot be implemented in a user-friendly way in combination with the available built in line models/setups. To make it convenient and efficient for the ATP-EMTP users for lightning induced voltage calculations with indirect strikes, a methodology is proposed that will allow the user to implement both the Agrawal et al. model and the available built in line models/setups, thereby all the computational capabili-ties and features of ATP-EMTP software can be effectively used. The de-tailed derivation of the proposed methodology is presented in paper [II] and the modified transmission line segment that is still equivalent to Agrawal etal. coupling model is presented in figure 3.8

C x2

- +

Ex xL xR x

us(x, t)

us(x+ x, t)C x

22

i(x,t)

1u1

i(x+ x,t)

isC x2

Figure 3.8. Agrawal et al. model simplification.

Note that it was decided to add the sources with the shunt elements, i.e., with the capacitance because of the following reasons. For typical overhead wires the ground losses and conductor losses do not affect the admittance of the line. It has been shown in [52] that the frequency dependent skin effect losses, affects only the internal series impedance of the line. Also it was explained in [53] that the ground losses specifically ground admittance has negligible influence on the line capacitance and overall line admittance and that the ground impedance largely modifies the series external impedance of the line. This is the reason why in ATP-EMTP line models [49] the fre-quency dependent losses are included in the series impedance of the line.

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One can also put a current source in parallel with the series impedance branch as shown in figure 3.9, thereby removing the voltage source that was in series with the series impedance of the line as in figure 3.5. The time do-main shunt current source in figure 3.9 will be a convolution of the horizon-tal component of electric field and the inverse of the frequency dependant line series impedance, which is difficult to compute a priory. Therefore, such an approach is considered not suitable for efficient implementation in ATP-EMTP. On the other hand the approach presented in figure 3.8 is simple and easier to implement with ATP-EMTP in conjunction with any line mod-els/setup.

C x

L xR x

Ex x Zl

L xR x

C x C xus(x, t) us

(x+2 x, t)us(x+ x, t)

Ex x Zl

Figure 3.9. Agrawal et al. equivalent model simplification using shunt current source across the series line impedance

In general a complete equivalent circuit of a transmission line has also con-ductance element connected in parallel to the capacitance of the line. This element represents the conduction current between the conductor and the surrounding medium. In the case of overhead power lines, this conductance is negligible and is usually neglected. Therefore in the analysis presented in paper [II], the line conductance terms had not been included. This analysis can be also extended to the case with shunt conductance too. Consequently, an additional current source directly proportional to the admittance value of the conductance will appear in parallel to the source term shown in figure 3.8.

As mentioned earlier, the line constants (impedance and admittance parame-ters) are fixed for a given line configuration and material medium. Thus, the impedance and admittance parameter of the line are embedded within an inaccessible two-port network. It is interesting to note from figure 3.8, that with the new circuit formulation, the forcing source associated with Agrawal et al. model is not in the series with the series impedance branch of the line section but effectively between the two transmission line segments, i.e., con-nected between the accessible port of two adjacent line segments. Hence, with this new methodology there isn’t any limitation for the direct imple-

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mentation of the Agrawal et al. model in the ATP-EMTP with the available frequency dependant line models/setups.

3.8 Monte Carlo simulations: Comparison of two analytical formulation [III]

Nucci et al. has shown that Chowdhuri – Gross model is not complete as it neglects the contribution from the horizontal component of electric field [42]. However, the simulation results comparing Agrawal et al. and Chowd-huri – Gross models presented in [42] show that the consequence of missing the horizontal component of electric field term in the final total induced voltage is significant only for very particular cases that are decided mainly by the stroke location and its orientation along the line. In all the simulations and the discussions to follow the lightning channel vertical and not tortuous.

It is to be noted that the occurrences of those particular cases as mentioned above are highly probabilistic, therefore comparisons and judgment of cou-pling models based on particular cases alone is not appropriate and com-plete. Consequently, in paper [III] an attempt to compare the two coupling models on a statistical basis is made. For this, the Monte Carlo methods have been adopted and from these simulations, it will be shown that even though the two coupling models predict different induced voltage levels for a given particular case, the cumulative probability density distribution of the induced voltages show only nominal difference whether one uses Agrawal et al.model or Chowdhuri – Gross model. This is the message the author likes to provide with for the power system protection engineers.

Moreover, various methods have been proposed to evaluate lightning per-formance of distribution lines [54-57]. The Institute of Electrical and Elec-tronic Engineers (IEEE) in the standard 1410-2004 [54] has presented a pro-cedure to calculate the probability of the occurrence of an induced voltage larger than the critical impulse flashover voltage (CFO) based on Rusck formulation. Borghetti et al. has shown in [55] that a similar result as those obtained in [54] can be achieved by using Monte Carlo method in combina-tion with a program to calculate the lightning induced voltages based on Agrawal et al. model. Since the IEEE method and Monte Carlo method are found to be equivalent, the author would like to make statistical comparisons based on Monte Carlo method but by using either the Agrawal et al. model or the Chowdhuri – Gross model as discussed in [III]. Therefore the study will be more focused on the comparisons among the two coupling models based on a valid statistical analysis associated with the evaluation of the performance of power distribution lines [54-55].

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In the present analysis we have not included any case of direct strikes so as to focus only on indirect strikes as applicable to the present work and ground losses and corona effects are not considered as the aim of the work is to mainly focus on the comparison between the two coupling models prediction of induced voltages. For calculations of the return stroke electromagnetic fields, a simple Transmission Line (TL) type return stroke model is adopted where the stroke is propagating with a constant velocity equal to one thirds the speed of light.

In the study, 10000 events were considered. Each event was defined by a peak current and the coordinates of the striking point of the lightning flash (xs,ys). For the peak current a lognormal distribution with mean value of 33kA and a standard deviation of 0.6 was used [58]. For the location of the lightning stroke a continuous uniform distribution was used. These are pre-sented in figure 3.10.

Observe that the ys coordinate in the histogram have least events for dis-tances between 0-100 m. This is due to the fact that, for a given return stroke current there will be a minimum distance to be fulfilled in order to ensure that the stroke will result in a nearby strike and not a direct one. Hence, the electro-geometric model was used to identify whether there was a direct strike or not for this the striking distance was calculated using equation (3.24) based on [58].

65.08 oId (3.24)

In equation (3.24) I0 is the peak value of the return stroke in kilo amperes and d is the striking distance. The simulations were carried out with the two coupling models using ATP – EMTP [49]. For all the cases a conductor was located at a height 10 m over a perfectly conducting ground. The line was terminated by a resistance that has a value equal to the surge impedance of the line. The length of the conductor is 1km and the midpoint of the line is at the origin of the assumed coordinate system (0,0,h). Thus, due to the sym-metry of the problem, the position of the stroke was kept within the first quadrant. Observe that the near end is located in the positive x-axis and the far end is on the negative one as illustrated in figure 3.11.

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0 50 100 150 200 250 300 3500

100

200

300

400

500

600

700

800

Current [kA]

No.

of

even

ts

(a)

0 100 200 300 400 500 6000

200

400

600

800

1000

1200

Xs distribution [m]

No.

of

even

ts

(b)

0 100 200 300 400 500 6000

200

400

600

800

1000

1200

Ys distribution [m]

No.

of

even

ts

(c)

Figure 3.10. Input data histograms: (a) Lognormal distribution histogram for the Peak current, (b) Continuous uniform distribution histogram for the x coordinate, (c) Continuous uniform distribution histogram for the y coordinate.

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Y

X

1000 m

Striking point (x,y)

Z

Near end

Far end

Figure 3.11. Coordinate system of the line conductor and the lightning stoke.

3.8.1 Results

In total 10000 cases were simulated. For both the models, the calculated induced voltage peak values at the near and far ends for each event were recorded. Moreover, regardless the coupling model used for the calculation of the induced voltages, there were negligible number of cases where the peak values are grater than 300 kV. However, for the comparison between the two analytical formulations, all the events are taken into account. In figures 3.12-3.13 the peak induced overvoltage distributions are shown. Ob-serve that the obtained results resemble a log normal distribution, irrespec-tive of the adopted field to wire coupling model. Their corresponding mean values are presented in table 3.1.

Table 3.1. Mean value of the voltage distribution for the two analytical formulations at both end of the power line.

ModelMean value near end [kV]

Standard Devia-tion near end [kV]

Mean value far end [kV]

Standard Devia-tion far end [kV]

Chowdhuri - Gross model 31.62 40.03 37.86 45.76

Agrawal et al.model 43.49 48.78 42.50 49.48

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0 50 100 150 200 250 3000

100

200

300

400

500

600

700

800Voltage Distribution Near End Chowdhuri Model

Voltage[kV]

Nro

of

even

ts

(a)

0 50 100 150 200 250 3000

200

400

600

800

1000

1200Voltage Distribution Far End Chowdhuri Model

Voltage[kV]

Nro

of

even

ts

(b)

Figure 3.12. Voltage distribution Chowdhuri and Gross model: (a) Near end, (b). Far end.

0 50 100 150 200 250 3000

100

200

300

400

500

600Voltage Distribution Near End Agrawal Model

Voltage[kV]

Nro

of

even

ts

(a)

0 50 100 150 200 250 3000

100

200

300

400

500

600Voltage Distribution Far End Agrawal Model

Voltage[kV]

Nro

of

even

ts

(b)

Figure 3.13. Voltage distribution Agrawal et al. model: (a) Near end, (b) Far end.

From table 3.1 it is observed that for Chowdhuri - Gross formulation mean values are smaller than the ones obtained with the Agrawal et al. formula-tion. These differences between the mean values of two coupling models are 27.3% and 10.9% for the near and far ends respectively with Agrawal et al.formulation as the base. Also notice that there aren’t any significant differ-ences between the voltage distributions as can be seen in figures 3.12 – 3.13.

To quantify the deviation in the calculated induced voltages between the two coupling models, for each given case/event, the peak voltage ratio between the Chowdhuri – Gross model and the Agrawal et al. model were estimated. Consequently, the distribution and a probability function of these ratios were computed and shown in figure 3.14 -3.15. Their corresponding mean values and standard deviation are shown in table 3.2.

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Table 3.2. Mean value of the probability distribution of the ratio between the peaks values calculated with the two analytical formulations

Near end Far end

Mean value Lossless line [%] 67.26 88.21 Standard deviation Lossless line [%] 9.78 22.03

40 50 60 70 80 90 100 1100

200

400

600

800

1000

1200Ratio distribution between peak values: Near end

Ratio [%]

Nro

of

even

ts

Chowdhuri/Agrawal

(a)

60 80 100 120 140 160 180 200 220 2400

500

1000

1500

2000

2500

3000

3500

4000Ratio distribution between peak values: Far end

Ratio [%]

Nro

of

even

ts

Chowdhuri/Agrawal

(b)

Figure 3.14. Voltage peak ratio distribution: (a) Near end, (b) Far end.

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1-0.2

0

0.2

0.4

0.6

0.8

1Probability Function: Near end

Ratio [%]

Pro

babi

lity

[%]

Chowdhuri/Agrawal

(a)

0.6 0.8 1 1.2 1.4 1.6 1.8 210

-3

10-2

10-1

100

Probability Function: Far end

Ratio [%]

Nro

of

even

ts [

%]

Chowdhuri/Agrawal

(b)

Figure 3.15. Probability distribution for the ratio between the peak values calcu-lated with the two analytical formulations: (a) Near end, (b) Far end.

3.8.2 DiscussionAs mentioned earlier, the aim of the comparison between the two formula-tion as discussed in the previous section for lightning induced over voltage calculations is to evaluate the models in broader perspective and not based on just few particular case studies as in [40, 42]. The exhaustive calculations in the previous section have shown that there is a strong correlation between the voltage distribution and the return stroke current distribution. As it can be seen from figures 3.12-3.13, the obtained voltage distribution is log-

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normal type. However, when the two models are compared based on indi-vidual peak values there are differences.

According to [42], Chowdhuri and Gross formulation should yield to larger induced overvoltages than Agrawal et al. model. This is based on the fact that this model does not consider the horizontal component of the electric field [40, 42]. However, it can be observed from the simulation results that in most of the cases Agrawal et al. formulation achieved lager peak induced over voltages, whereas only for few particular cases this situation is oppo-site. When a large number of cases were analyzed, these differences on the calculated peak values between two coupling models were around 60% to 80%. Also, observe from figure 3.14 that for the near end induced voltages, this ratio gives almost a normal distribution, while at the far end it resembles a log normal distribution. Consequently, the probability of occurrence of an induced voltage (Vi) larger than a given voltage (vo), i.e., P(Vi vo) is larger for the case of Agrawal et al. model than the Chowdhuri - Gross model. This is clearly seen in figure 3.16. Observe that the probabilistic distribution of the calculated induced voltage presents lower deviations for the case of the far end than for the case of the near end, i.e., 3.42% and 5.78% respectively.

0 50 100 150 200 250 30010

-3

10-2

10-1

100

Probability Function: Near end

Overvoltage [kV]

Pro

babi

lity

[%]

Chowdhuri

Agrawal

(a)

0 50 100 150 200 250 30010

-3

10-2

10-1

100

Probability Function: Far end

Overvoltage [kV]

Pro

babi

lity

[%]

Chowdhuri

Agrawal

(b)

Figure 3.16. Overvoltage probability function values calculated with the two ana-lytical formulations and using the two transmission lines formulations. : (a) Near end, (b) Far end.

3.9 Influence of ground losses on the lightning induced overvoltage calculations

Until now the analyses presented in the thesis have been based on the case of lightning electromagnetic fields propagating over a perfectly conducting ground. Though this assumption yields to a considerable simplification of the problem studied and that it is not a realistic scenario. It is known that a soil with finite conductivity will not entirely reflect the electromagnetic

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fields incident to it and there will be fields penetrating into the soil. This phenomenon will seriously affect the line impedance parameter particularly the external impedance and also the signatures of the propagating lightning electromagnetic pulses incident on the overhead line. Indeed, these two situations has been studied separately by different researchers, i.e., either treating only the influence of the lossy ground on the waves propagating along the lines [59-61] or the influence of a finitely conducting ground on the lightning electromagnetic fields incident on the line [62-64]. Rachidi etal. have shown the influence of ground losses on both the incident lightning electromagnetic fields and also propagating waves along the conductors [53].

The problem of wave propagation in wires above a lossy ground was first treated by Carson [59] in 1926. According to him the total external imped-ance of the wires is a sum of wires’ external impedance calculated under perfect ground conditions and a frequency dependant ground impedance term due to the penetration of magnetic fields into the ground. In his deriva-tions of the ground impedance, he neglected the displacement currents in the soil and used a low frequency approximation of the ground propagation con-stant. The low frequency limit depends on the ground conductivity and ground permittivity, therefore, Carson’s formulation is only valid if the maximum frequency of the propagating signal is below one tenth of the critical frequency given by equation 3.25. In 1949, Sunde, extended Car-son’s ground impedance expressions as given by equations (3.26 and 3.27) for self and mutual ground impedances respectively, for wide range of fre-quencies [60] by taking into account complete ground propagation constant as given by (3.28).

g

gc (3.25)

022

2

2du

uu

ejZg

uhoSunde

gkk

k

(3.26)

022

cos2

duuduu

ejZ klg

uhhoSunde

gkl

lk

(3.27)

)( oggog jj (3.28)

The set of equations proposed by Sunde cover the frequency range associ-ated with lightning transients. It is to be noticed that other researchers [52-53, 65-66] have developed a similar formulations related with the problem adopting a more accurate approach than Carson. The author feels that those

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formulations even if included in the present calculations will not lead to sig-nificant deviations compared to Sunde formulation.

As mentioned earlier, a finitely conducting ground will considerably affect the wave shape of the propagating lightning electromagnetic pulse. Various theories have been described in the literature that describes this phenome-non. The presence of finitely conducting ground affects the horizontal com-ponent of the incident electric field at a given line height. Equation (3.29) expresses the ratio of the Fourier transform of the horizontal electric field to that of the vertical electric field. This equation is known as the WavetiltFormula [53, 62].

o

gg

z

r

j

jEjEjW 1

)()()( (3.29)

Wavetilt formula is applicable to strokes located at distances beyond 5km [53]. It has been shown by Rachidi et al. [53] that for stroke located close distances (in the range of 200m or so), Wavetilt formula is in considerable error. A more appropriate formulation known as Cooray-Rubinstein formula-tion given by equation (3.30), that overcomes the drawbacks of Wavetilt formula have been reported in the literature [52-53, 63-64]. It should be re-membered that the presence of finitely conducting ground is incorporated as a correction term in the total incident horizontal electric field, i.e., the total horizontal electric field at a given line height is the sum horizontal electric field calculated at the line height under perfect ground conditions and the electric field at the ground level (calculated as the product of magnetic field at the ground level with prefect ground condition and the ground surface impedance).

o

gg

oprpr

j

cjrHjzrEjzrE ),0,(),,(),,( (3.30)

To demonstrate the influence of a finite conducting ground on the lightning induced voltages two results are shown in figures 3.17-3.18. Observe that for a line of 1 km length the calculated induced voltage is considerably affected by the ground impedance (figure 3.17). However when the line length in-creases the surge attenuation along the line is no longer negligible and the induced voltage is affected by the ground loses both in the incident lightning electromagnetic pulse and the propagating surges along the line [53].

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Figure 3.17. Calculated voltages on a 1 km matched overhead power line induced by a typical subsequent return stroke ( g=0.001 S/m, r=10). Dashed line (“Ideal line”): induced voltage calculated taken into account the ground finite conductivity only when calculating the exciting fields, neglecting the ground impedance. Dotted line (“Ideal field”): result obtained when the finite ground conductivity is taken into account on the surge propagation along the line. Peak current 12 kA. Striking point: 50 m from the line center. Adapted from [53].

Figure 3.18. Calculated voltages on a 5 km matched overhead power line induced by a typical subsequent return stroke ( g=0.001 S/m, r=10). Dashed line (“Ideal line”): induced voltage calculated taken into account the ground finite conductivity only when calculating the exciting fields, neglecting the ground impedance. Dotted line (“Ideal field”): result obtained when the finite ground conductivity is taken into account on the surge propagation along the line. Peak current 12 kA. Striking point: 50 m from the line center. Adapted from [53].

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4 Some Practical Applications Of Lightning Induced Overvoltages

Engineers in charge for the operation and maintenance of complex distrib-uted systems, e.g., power systems, telecommunications systems, cable TV systems, electrified railway systems, etc., has a difficult task in identifying the reasons for failure of their equipments and apparatus in the event of tran-sients i.e., due to the lightning strikes with reference to the present work. A service provider has the responsibility to account for the reliability of their systems as a large number of customers depend on the interrupted operation of those systems. Thereby customers’ expectations are duly met with. Con-sequently, from a service providers’ perspective there is need to understand the causes of system outages and how those outage could be avoided. Light-ning is one of the major sources for electrical overstresses that can cause failure, permanent degradation, or temporary malfunction of electrical and electronic devices and systems. For example, insurance claims resulting from lightning damage in Colorado, Utah, and Wyoming during the period from 1987 to 1993 resulted in over $7 million a year [67]. Thus, it is also necessary to investigate the possible coupling paths through which the light-ning transients sneak into the systems, so that by providing suitable/adequate protections, those sneaking transients could be either diverted or suppressed. To address the above issues as a first step, in this chapter various study cases are treated that correspond to lightning interaction with practical distribution type systems, electrified railway systems and HVDC systems. For all the induced voltage calculations presented in this chapter Agrawal et al. field to wire coupling model [38] was adopted.

4.1 Surge transfer from high voltage to low voltage side of distribution transformer in the event of nearby lightning strikes [IV]

In electrical power systems, the low voltage networks are more sensitive to incoming transients, as they usually have lower insulation level. The charac-teristics of those transients depend on various associated coupling mecha-nisms within the distribution system itself. It could be either via direct light-

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ning strike (externally generated) or switching operations/faults (internally generated) or indirect lightning strikes (externally generated). As applicable to present work, indirect lightning strikes is not of significant importance for high voltage power system, but it is really harmful for low voltage networks. Therefore, it is essential to understand the possible coupling path that these transients can make through to the final consumer in the low voltage side. Traditionally, a distribution system is primarily radial with a step down transformer located near the load centers [68]. Consequently, it is important to evaluate different existing circuit models of the distribution transformers, since they play an important role in affecting the shapes and magnitudes of the transients before it reaches the final customer service point. For this, two distribution transformer circuit models taken from [69] known as TM-1 and from [70] known as TM-2, will be used for analysis in this thesis. These models will be analyzed with different low voltage configurations and the simulations are carried out using the computer program of ATP-EMTP. The differences among the two circuit models of TM-1 and TM-2 are such that in TM-1 [69] the high and low voltage terminals’ stray capacitances, the ca-pacitance between the high voltage and low voltage bushings as well as the magnetization branch of the transformer are considered, while TM-2 was derived based on laboratory measurements by Piantini et al. [70]. The circuit model details of TM-1 and TM-2, implemented for the present simulations can be found in paper [IV].

4.1.1 Case Studies - 1 In total six different cases were analyzed. The length of the overhead wire was equal to 500 m on the high voltage side and 200 m on the low voltage side as shown in figure 4.1. The induced overvoltages were calculated for different stroke locations. These are presented in table 4.1 and the corre-sponding reference system with the different stroke location is shown in figure 4.1.

Table 4.1. Lightning flash location for the different study cases. Study case Number X coordinate [m] Y coordinate [m]

1 100 0 2 100 250 3 100 600 4 100 700

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0m 250m 600m 700m

Transformer Terminal

Load Terminal

13.8/0.22 kV y

x

100m

High Voltage terminal

Figure 4.1. Coordinate system for the study cases.

The high and low voltage power line height was 10m. The return stroke peak current was 15 kA. The ratio ( ) between the return stroke velocity and the speed of light in free space was assumed to be 0.1. A simple transmission line type model was used for representing the return stroke. As shown in table 4.1, the position along the x axis of the lightning stroke was kept con-stant at 100m from the power line for all the cases. The termination resis-tance at the high voltage terminal of the power network and the load terminal had a value equal to the surge impedance of the line.

4.1.2 Results and discussions As mentioned earlier, the lines at both the ends were terminated in its surge impedance, this was done to avoid any ambiguities associated with reflec-tions at the line terminations and more importantly if at all there is any re-flection in the system under study, it would be solely due to the transformer, so that any comparisons we make will be more focused to the transformers alone. More over, the aim was to investigate, how the induced transients are transferred from the high voltage side of the transformer to the low voltage network. Thus no results will be reported for voltage at the high voltage ter-minal of the line namely y=0m. Only the voltages at the high voltage side of the transformer, at the low voltage side of the transformer and at the load terminal will be presented. The simulation results on the high voltage side of the transformer model TM-1 and TM-2 are presented in figure 4.2 and 4.3 respectively.

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Figure 4.2. Induced overvoltage at the high voltage side of the transformer, TM-1 [69]. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m.

Figure 4.3. Induced overvoltage at the high voltage side of the transformer, TM-2 [70]. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m

Comparing figures 4.2 and 4.3 it is seen that isn’t any considerable differ-ence between the calculated voltages whether one uses TM-1 or TM-2. However, on careful observation of the rising portion of the calculated in-duced voltages as shown in figure 4.4, it is seen that the rise time for volt-ages with TM-2 is approximately 0.5 sec smaller than that of TM-1.

Figure 4.4. Rise time comparison of the calculated induced overvoltage at the high voltage side of the transformer. Red: 0 m model 1. Green: 0 m model 2.

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Now let’s consider the induced voltages at the low voltage side of the trans-former TM-1 and TM-2 as shown in figures 4.5 and 4.6. The influences of transformer are more considerable at the low voltage side rather than the high voltage side. The induced voltages at the low voltage side of the trans-former show smaller rise times and are oscillatory. It is observed that in the case of TM-1 the voltage oscillations persist until 10 s while for TM-2 it lasts for only 5 s. This was not observed at the high voltage terminal of the transformer. Therefore, it can be concluded that the transformer TM-2 has higher damping factor than TM-1. Comparing the magnitudes voltages at the low voltage side of the transformer, it is observed that peak voltage of TM-2 is 10% lower than TM-1. It is important to note that the peak induced volt-age in the low voltage side of the transformer (no matter which transformer model is adopted), considerably exceeds the basic insulation level of low voltage networks, i.e., it is highly probable this might result in an insulation breakdown.

Figure 4.5. Calculated induced voltages at the low voltage side of the transformer. TM-1. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m.

Figure 4.6. Calculated induced voltages at the low voltage side of the transformer. TM-2. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m.

Next we consider the induced voltages at the load terminal to figure out as to what would be the levels of induced voltages that will propagate along the line for a given distance. Note that the load terminal was terminated in line

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characteristic impedance. However, this might not represent a real situation for the low voltage termination because the responses at the load will depend on the characteristic of the connected load, which might be way different from the line characteristic impedance. The simulation results for this case are presented in figure 4.7 and 4.8. It can be seen that the signature of the induced voltage at the load is similar with both transformer models. A reason why the induced voltages suffer distortions at the load, which is different from the low voltage side of the transformer, is due to the fact that the in-jected transformer secondary voltage on to the line interacts with the distrib-uted sources due to the horizontal component of electric field on the line and the riser source at the load due to the vertical component of electric field. Table 4.2 summarizes the peak values of the induced voltages at the high voltage side, low voltage side of transformers and load terminal for both the transformer models.

Figure 4.7. Calculated induced voltages at the load terminal termination. TM-1. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m

Figure 4.8. Calculated induced voltages at the load terminal termination. TM-2. Red: 0m. Green: 250m. Blue: 600m. Pink: 700m.

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Table 4.2. Calculated peak over voltages Over voltage TM-1[kV] Over voltage TM-2 [kV] Distance

[m] HV LV Load HV LV Load 0 28.8 3.8 3.9 30.65 3.4 5.1 250 77.8 8.0 7.8 78.9 6.0 9.2 600 31.4 29.57 39.6 30.63 21.41 39.6 700 19.82 13.29 30.2 20.19 15.91 30.1

The presence of transformer considerably affects the resulting over voltage at various points of the distribution system due to nearby lightning strikes. When the peak induced voltage on the line is calculated separately without a transformer and with a transformer, it was seen that (for the case treated here) just because of the presence of the transformer the peak induced volt-age at the high voltage side of the transformer is twice compared to case in the absence of the transformer. The main reason for this is the input imped-ance of the transformer, which is larger than the surge impedance of the line under study. Note that the parameters of the lines will depend on the geome-try of the system and not on the operating voltage of the network. Also note that the line parameters at both sides of the transformer are the same.

Some changes were observed in the wave shape of calculated overvoltage with the different transformer models. However, no conclusions related to the model can be drawn from this study presented here because the trans-formers used in [69] and [70] are of different sizes. It is believed that their associated transfer functions are different. Also, it has been reported in the literature that the transformer response is governed by several parameters associated with its design/construction namely rated power, insulation type, voltage level, transformation ratio, winding, connection, etc [71-73]. A large variety of transformers types with different rated characteristics can be found connected in power networks of the same rated voltage. Although the net-work characteristics are similar for different cases (line arrangement, con-ductor height/size, insulators, etc), their corresponding induced voltages might differ since the system response is highly dependant on the character-istics of the transformer as seen from the simulations presented here. The author like to mention here that this study was to mainly demonstrate that how the presence of a transformer connected to a typical overhead line con-figuration can significantly affect the surge transfer characteristics from the high voltage to low voltage side of the transformer in the event of nearby lightning strikes. Moreover while designing the appropriate lightning protec-tion simulations has to be made with the interconnected system too so that more realistic insulation coordination can be achieved.

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In regards to use of SPDs to divert/control the voltage level at the low volt-age side of the transformer, the simulation results indicate that it is not suffi-cient by just connecting an SPD only at the low voltage terminal of the trans-former and ignoring the load terminal. This is because the total voltage on the line is decided by a) lightning fields interacting the overhead line in the low voltage side, b) load at the service terminals (which is again connected to the overhead line) and c) reflections produced by the transformer (that propagate along the line). All these have to be considered together in decid-ing the suitable surge protection scheme.

4.2 Transient response of DC converter station subjected to lightning induced overvoltages [V]

The progress in semiconductor technology has resulted in the development of a variety of cost effective devices that today are used in high voltage DC power systems. It is foreseen that such a technology will have a wider appli-cations in the future DC power links. Therefore, it is of interest to understand the response of DC power stations when they are subjected to lightning in-duced over voltages. In addition to this it is also necessary to identifying the coupling mechanisms and surge transfer characteristics from DC to AC sys-tems and vice versa. The study presented in this section is conducted utiliz-ing the network components in ATP-EMTP and adopting the field to wire coupling model of Agrawal et al. [38].

4.2.1 Case studies - 2

U

POS001POS001

U

U

POS001Filter

Figure 4.9. Considered power electronic circuit with harmonic filters.

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Three circuit configurations were considered, they are, a six pulse power converter similar to Nelles et al. [74] without harmonic filter connected at the AC side, the same power converter of Nelles et al. [74] but with har-monic filters corresponding to 5th and 7th harmonic connected at the AC side. The values of the filter components are similar to those used by Khatri et al. in [75]. The general schematic of the six pulse power converter with the filter is shown in figure 4.9. In all the three cases the transient response of the system were analyzed for a 10 kA return stroke with the stroke located at 500 m from the high voltage DC converter station and 100 m from the HVDC power line as shown in figure 4.10.

100m

500m Striking point

Figure 4.10. Lightning strike location for the HVDC study cases.

4.2.2 Results and discussions The transient responses of a line commutated circuit with a diode bridge rectifier are presented in this section. Due to the short time duration (micro second scale) of the lightning induced overvoltage, the transient signal ap-pearing at the terminals of the converter (on the DC side), is a sharp voltage pulse superimposed on the DC signal at around 13.5ms, which can be seen in the zoomed view of figure 4.11.

Figure 4.11. Zoom of the transient voltage on the DC side of the conversion station. (a) Positive terminal. (b) Negative terminal.

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It should be remembered that the voltage appearing across the terminals DC terminals is the difference between voltages appearing on the positive and the negative pole/line, i.e. the differential voltage. Looking at the induced voltages from figure 4.11 it is seen that the differential transient voltage is negligible since their shapes and magnitudes are identical. In order to inves-tigate the possible coupling path and surge transfer characteristics between DC and AC side, the voltage signal appearing on the AC side of the con-verter station was calculated, which is shown in figure 4.12.

13.40 13.40 13.40 13.40 13.41 13.41 13.41[ms]-300

-200

-100

0

100

200

300

400

[kV] (a)

(b)

Figure 4.12. Zoom of the transient voltage on the AC side of the conversion station. (a) Phase A. (b) Phase B and C.

With regard to the cases where the harmonic filters were connected, no dif-ferences were observed on the calculated transient voltage wave shapes at the AC side. The reason for this could be the following. The frequency con-tent of the lightning voltage transients lay much above the central frequency of the harmonic filters (originally designed for low frequency applications). Therefore, the transients pass through the filters without any distortion. Note also that the harmonic filter does not provide any overvoltage protection to the system against these types of transients. Thus, further protection meas-ures have to be provided if lightning induced over voltages are to be diverted from the system. It was observed that the transient response of the converter station at the AC terminals was the same with and without the harmonic filters.

The results indicate that lightning induced voltage transients do not represent a critical threat for a high voltage DC converter station whereas the common mode induced voltage could have larger peak values. It should be mentioned here that we did not include logic or control systems in the present study. Moreover, we did not study the failure modes of the diodes or spark over at the terminals. There could be situations where the lightning induced transient can change the conduction mode of the diodes. This may result in an errone-ous status in the control system, leading to partial or total loss of the power. Moreover, the control units of the station are powered by an auxiliary power transformer connected to the AC side of the converter station which could be

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a possible coupling path for lightning transients as discussed in the previous sections. More importantly, the simulation showed that the transient voltages propagate to the AC system through the diodes. These voltages are affected neither by the load connected on the DC side of the converter station nor by the harmonic filters connected on the AC side. Thus, the full voltage tran-sient may sneak into the control system through the auxiliary transformer, causing unwanted system upsets and damage, since the control system has a low insulation level, making it vulnerable to the transient voltages caused by lightning strikes in the vicinity.

4.3 Lossy ground effects on lightning induced voltages: A sensitivity analysis on different overhead power line configurations [VI]

The cases previously analyzed were calculated under the assumption that the overhead lines were located above a perfectly conducting ground. Also, the lightning induced voltages previously calculated were based on the imple-mentation of the new circuital approach as described in paper [II] in ATP-EMTP, i.e., all the calculations were made in the time domain. To implement the effects of lossy ground on the electromagnetic fields incident on the overhead line in ATP-EMTP like programs is not an easy task. In [50], the field to wire coupling phenomena with ground losses associated with the lightning fields due to indirect strikes were programmed using the models language [49] available in the ATP-EMTP. However, this approach adopted in [50] is an inefficient way to compute the lightning induced voltages as there are other programming languages that are faster and more versatile than the model language of ATP-EMTP. Therefore, there is a need for a computer program that will allow easier implementation of the coupling models for complex electrical networks over a lossy ground. Several of such computer programs are available today, STIDDA is one of them.

STIDDA (Sobre Tensiones Inducidas Debido a Descargas Atmosféricas) is the Spanish abbreviation for induced over voltages due to lightning flashes. The program was developed in the High Voltage Laboratory at the Simón Bolívar University, Caracas-Venezuela. It was designed to calculate the in-duced over voltages on an overhead power line due to a cloud to ground lightning flash in its vicinity. The program uses the Agrawal et al. coupling model to represent the field to wire coupling mechanism and solves the transmission line equations in frequency domain.

This section is aimed at investigating, how the induced voltages are affected by the presence of a finitely conducting ground. In STIDDA, the influence

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of a lossy ground on the waves propagating on transmission lines (line im-pedance parameters) were considered based on Sunde’s formulation [60] as discussed in the previous Chapter. On the other hand the effect of a finitely conducting ground on the lightning electromagnetic fields incident on the power lines were based on Cooray-Rubinstein approach [53, 63-64]. Also the effect of overhead ground wires on the magnitudes of the voltages in-duced in the phase wires is studied. Moreover, a sensitivity analysis is also carried out. The parameters that were considered for this are return stroke velocity, current rise times and stroke location.

4.3.1 Case studies - 3 In the present study two standard overhead distribution type power lines namely horizontal and vertical configuration were considered as shown in figure 4.13. In both horizontal and vertical configurations the study was made with and without ground wires leading to four separate study cases.

10 1.64 0.6

1.12

10

0.6

1.12

0.60.6

Figure 4.13. Overhead lines configurations (all the distances are in meters).

In total, three observations point were selected along the line located at 500, 1500 and 2000 m from the line centre. The ground conductivities were either perfectly conducting or 0.01S/m or 0.001S/m or 0.0001S/m and the ground relative permittivity was kept constant 10 for all the cases [53, 76]. In order to ensure that all the events treated will result in a close by flash and not a direct strike to ensure this the electro-geometric model was used [58], which has been already explained in Chapter 3 (equation 3.24). The cases simulated can be classified into three major categories with the stroke current kept constant at 50kA, namely:

Category-1: Stroke velocity was constant at 1.1x108m/s, current rise time was constant at 1.2 s and the distance of the stroke from the line centre was varied from 150m to 1500m.

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Category-2: Stroke velocity was constant at 1.1x108m/s, distance of the stroke from the line centre was 150m and current rise time was varied from 0.5 s to 10 s.

Category-3: Distance of the stroke from the line centre was 150m, current rise time was constant at 1.2 s and the stroke velocity was varied from 1.1x108m/s to 2.0x108m/s.

In all the categories, 10 values were chosen for each variable. Note that the strike point of the lightning is equidistant to both ends of the power line as shown in figure 4.14.

Yo

Y

X

Y

Z

Strike Point

r

r

Figure 4.14. Geometry used for the induced overvoltage calculations.

4.3.2 Results and discussions In total, 1440 cases were performed. The simulation results presented in the figures 3 to 15 of paper [VI] are discussed here. Let’s consider the case in which the point of strike is the variable. It is seen that when the ground was perfectly conducting and the point of strike is at 150 m, the positive peak voltages were in the range of 100 kV for all the observations points. When the striking point was moved far away from the power line the peak values were reduced. This is because as can be seen from equations (2.1 to 2.3) [13], the electric and magnetic fields are inversely proportional to the dis-tance terms.

It was observed that when the rise time of the current at the base of the channel is increased, the calculated overvoltage peak value become smaller. This is because as can be seen from equations (2.1 to 2.3), the lightning elec-tromagnetic fields have a component, which is proportional to the stroke current derivative. Since the peak current is kept constant, the maximum derivative of the current decreases with increasing the rise time.

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Consider now the return stroke velocity as the variable. In general, when the ground conductivity is high and the distance to the point of strike is small the induced voltage is mainly governed by the static field component. If the current is kept constant, the charge per unit length will decrease with in-creasing return stroke velocity. Therefore, the amplitude of the induced volt-age decreases with increasing velocity when the ground conductivity is high. However, when the conductivity is low, the horizontal component of electric field dominates. This field is proportional to the speed of propagation of the current in the channel. Therefore, as the ground conductivity is decreased, the induced voltage increases with increasing return stroke speed. This be-havior is shown in the figures no. 3 and 7 of paper [VI].

It is important to mention that when the losses in the ground are taken into account the induced over voltage will present a bipolar wave shape. The negative peak of this voltage increases with decreasing ground conductivity. Moreover, the negative values obtained in all the cases are larger than the positive ones. Consequently, for low ground conductivity soils, the impor-tant voltage magnitude to be considered is the negative one.

It has been reported in the literature that, the larger the conductor heights, larger will be the induced voltage due to the capacitive coupling [77]. Therefore, since the conductor of lowest height in the vertical configuration is at the same height as the horizontal line configuration and the two upper conductors in the vertical arrangement that are at 0.6 and 1.2 meters respec-tively from the lower conductor location, the induced voltages appearing on the vertical array are expected to be larger than those calculated for the hori-zontal line configuration. It is important to mention here that the author is not making a comparison on the performances between a vertical conductor arrangement and the horizontal conductor arrangement of phase wires. In-stead, a comparison is being made between two arrangements in terms of presence and absence of ground conductors on the levels of induced voltages on the phase wires. Author feels this information would be more valuable for the power industry as in any case whether it is horizontal or vertical configu-ration the presence of a ground wire is necessary to protect the phase wires from direct strikes too.

It has been reported in the literature [76-79] that the magnitude of induced voltages obtained is reduced when an overhead ground conductor is placed in system. To compare these results in a systematic manner the protective ratio concept is used. This is defined as the ratio between the peak value of the induced voltage obtained with a ground wire and the peak induced volt-age calculated without ground wire for a given case. These results are sum-marized in figures 4.15-4.16 for positive and negative peak voltages respec-tively, wherein the corresponding average protective ratio is shown for all

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the cases discussed above. In average the calculated protective ratio for the positive peaks was in the order of 70%, which is in good agreement with the results presented in the literature [76-79]. Also, this value changed when the ground losses were accounted. Observe that, for the lower ground conduc-tivities, the ground wires do not help in reducing the positive peak voltage appearing on the line, while the negative peak voltages are considerably reduced. More importantly, for cases of lower ground conductivities the negative voltage magnitudes are larger than their positive counterparts. It was observed that in some cases when the ground conductivity is high, the protective ratio for the negative peak is larger than unity. However, it can be noticed that when the ground conductivity is high the negative peak voltages are negligible in comparison with corresponding positive ones. Therefore, the concept of the protective ratio to determine the effectiveness of the ground wire on the reduction of the induce voltages should also account for the ground conductivity, which is an important message the author would like to convey.

0

0.2

0.4

0.6

0.8

1

1.2

Prot

ectiv

e R

atio

tf Vo Yo tf Vo Yo tf Vo Yo

500 m 1500 m 2000 mVariables-Observation Point

Protective Ratio-Positive peaks Horizontal Configuration

Inf 0.01 0.001 0.0001

0

0.2

0.4

0.6

0.8

1

1.2

Prot

ectiv

e R

atio

tf Vo Yo tf Vo Yo tf Vo Yo

500 m 1500 m 2000 mVariables-Observation points

Protective Ratio Vertical Configuration

Inf 0.01 0.001 0.0001

Figure 4.15. Average Protective Ratio for the maximum positive peak achieved. Up: Horizontal configuration. Down: Vertical configuration.

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Pr

otec

tive

Rat

io

tf Vo Yo tf Vo Yo tf Vo Yo

500 m 1500 m 2000 mVariables-Observation point

Negative Protective Ratio-Horizontal Configuration

Inf 0.01 0.001 0.0001

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Prot

ectiv

e R

atio

tf Vo Yo tf Vo Yo tf Vo Yo

500 m 1500 m 2000 mVariable-Observation Points

Negative Protective Ratio-Vertical Configuration

Inf 0.01 0.001 0.0001

Figure 4.16. Average Protective Ratio for the minimum negative peak achieved. Up: Horizontal configuration. Down: Vertical configuration.

4.4 Measurements of lightning transients entering a Swedish railway facility [VII]

Until now, all the results analyzed in the thesis are based on exhaustive nu-merical calculations and not based on experimental investigations. Therefore one could question the validity of models and simulations discussed in this thesis. To validate one needs to have experimental results for a later com-

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parison with the theory. Special attention should be given to large distributed networks where the system components are exposed to direct or indirect lightning strikes. In this regard, various experimental results have been re-ported with distribution power system based on natural lightning flashes [80-84] or from triggered lightning [6, 85-88]. However, not much field data is available related to transients coupling with electrified railway systems a system much different from the conventional power distribution system. In the summer 2003, Uppsala University in association with the Swedish Rail-way Administration (Banverket) decided to investigate how lightning tran-sient enter into the railway systems. The chosen place for the measurement was a technical house at Tierp station, approximately 60 km from Uppsala.

4.4.1 Measurement system The measurement station was located at 17.51 degrees longitude and 60.3467 latitude. The cable entering into the technical house is shown in figure 4.17. The auxiliary power supply cable enters first into the switchgear unit and then to a three-phase step down transformer and through the fuse unit reaches the Banverket local supply unit. Measurements were made at this point using a data acquisition system (DAQ) as shown in the figure 4.17.

Figure 4.17. Entrance of auxiliary power cable into the technical house.

A four channel programmable Data Acquisition (DAQ) system NIPCI6115, controlled through a desktop computer was connected to four sensors meas-uring electric field near the track, phase voltage, phase current, and earth current, respectively. Detailed information related to the measurement setup is given in paper [VII].

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4.4.2 DiscussionThe measurement system was installed in Tierp on May 22, 2003 and oper-ated until September 03, 2003. Although it was aimed to record the tran-sients caused by lightning, it was found that the system has several transients apparently not caused by lightning, but probably caused by switching opera-tions, arcing at pantograph etc. We do not consider those events and concen-trate only on the transients that were caused due to lightning. Since the elec-tric field antenna was placed to correlate a given event with a lightning flash, we considered only the case where the trigger settings were kept on electric field (channel – 0). By comparing the data from lightning location system, it was found that in the year 2003 within a radius of 50km around the meas-urement station 7757 strokes were recorded. The largest lightning activity took place on 30th of July and about 1500 strokes were recorded by the lightning location system. In the paper [VII] we show measured transient records for two flashes corresponding to the 30th of July. Records corre-sponding to two flashes, 15.40.35.625 (flash 1) and 16.01.01.905 (flash 2). The flash name indicates the time stamp of the data acquisition computer. The overall electric field record, phase to neutral voltage and the earth cur-rent flowing out of the equipotential bar are presented in paper [VII]. The phase current was not shown because no appreciable current above the noise level was registered. For flash 1, there are two return strokes at about 7 ms and 20 ms. For flash 2 there are about four return strokes at about 16 ms, 42 ms, 80 ms and 110 ms. The bipolar pulses corresponding to the preliminary breakdown activity in the cloud also can be seen at around 0 ms, before the first return strokes in both the flashes. The vertical scale of the electric field record has to be multiplied by some unknown constant, because it is not calibrated. The maximum recorded over voltage is about 4 kV. It is to be noticed that the phase to neutral voltage signature resembles the derivative of the electric field, while the earth current wave shape is more like the electric field. It should be mentioned that the transformer transfer function has a large influence on the transferred surge from primary to secondary [89].

It is important to be mentioned that it was not possible to identify the light-ning flashes that caused the records corresponding to flash 1 and flash 2 due to timing problem as described below. The time recorded by the DAQ sys-tem upon a field trigger was corresponding to the computer time whereas the lightning location system was recording the strokes based on the GMT time. In addition to that the computer time was not corrected with every hour or day as the measurement station was not accessible at such a convenience. For example, on July 29, the computer time was adjusted to GMT within one second accuracy. On August 5, it was found that the computer time has drifted ahead of GMT time by 37 seconds. This result in about 5.3 seconds drift per day assuming a linear relation which it might not be the real case.

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Consequently all the stroke locations 37 seconds earlier than flash 1 and flash 2 are included as possible lightning strokes corresponding to this two measured events. The recorded current and voltages are summarized in table 4.3 for flash 1 and flash 2.

Table 4.3. Measured currents and voltages at the technical house at Tierp

Event ID Line to neutral Voltage [kV] Earth Current [A]

Flash 1 4.1 kV 0.28 Flash 2 3.6 kV 0.55

The corresponding electric field measured for flash 1 and 2 had a difference about 1 unit for first return strokes. An important remark from the data col-lected is that the supply voltage waveforms were not found in all the records that were created between the times 15.37.49 to 15.41.08 on July 30. The reason for this could be that the 22 kV auxiliary power conductors were not carrying power during this period possibly due to a switching operation re-lated to lightning. By comparing the recorded electric field for the above mentioned events, it can be seen that the polarity are similar. But if we ob-serve the corresponding voltages we see that the initial polarities of the two are opposite. Similar behavior for the polarity is seen if we compare the cor-responding earth currents. At present we don’t know the reason for this dif-ference in polarity.

4.5 Breakdown mechanism in lightning induced effects: The role of arc resistance [VIII]

Various electrical breakdown process are in association with the different physical stages of a Lightning flash namely preliminary breakdown, return stroke, dart leader, among others. Indeed, lightning is considered the larger electrical discharge taking place in nature. Also, on the lightning induced overvoltage context, the electromagnetic field impinging an overhead power line can give rise to a flash over either within two conductors, along the insu-lator or over the surge protective devices. Therefore, it is essential to under-stand how this electrical breakdown process could be adequately model for a better understanding of its physical mechanism as well as for engineering applications. Several physical parameters/properties have been modeled in the literature and the resistance of the spark channel is one of them. More importantly, an understanding of the way in which the resistance of the spark channel varies as a function of time is important, not only for the compre-hension of the gas discharge physics but also in various industrial applica-tions where electric sparks are used as ultra fast switches. However, the ex-perimental data reported in the literature on the temporal variation of the

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resistance of spark channels is scanty [90]-[95] and it is inherent more ex-perimental data on the subject.

Recently, Engel et al. [96] compared the experimental results associated with the resistance of a spark channel as reported in [97] with the predictions of several theoretical models. It was showed in [96] that some theories agree better with the experimental data than others. However, the current wave-form used in [97] had a very short decay time, i.e., about 3 s. Moreover, the majority of the current wave form reported in regards to the arc resistance channel has time durations shorter than 10 s. More importantly, Norinder and Karsten [98] presented in 1948 a pioneer work whereas the resistance of the spark channel for various gap lengths was measured. The maximum peak current obtained by Norinder and Karsten was between 23-100kA [98]. However, their generated current was ring type with a decay time of 60 s. It is to be noticed that no data have been reported in the literature for lightning current impulse with a long decay time. Therefore, it is of interest to investi-gate how various theories fare with experimental data of this kind. In this section the results of two experiments conducted to measure the time varying resistance of spark channels are discussed. In the first experiment a 1cm gap spark channel was created by using current impulses generator with peak values between 35kA and 48kA. The second experiment is the results of a 12.8cm gap channel with peak currents amplitudes ranging from 200A to 2200A. The results are presented in paper [VIII].

4.5.1 Experimental setup For the first experiment, a high energy discharge with a 10/350 µs current impulse was created between two spherical electrodes kept approximately 1cm apart. This current impulse was produced with a Haefely impulse cur-rent generator. Several data sets were collected for two different peak current values of 38kA and 48kA. For the current measurement, a Rogowski coil (Pearson Current monitor 1080, 200 kA, 1.5MHz, 250 ns) connected to a PC via a data acquisition card (Dias 733 from Haefely) was used. The voltage was measured using a high voltage probe of type North Star PVM-5 con-nected to a Leccroy LC574, 1GHz, 4Gsa/s transient recorder. The computer with the data acquisition card was placed in a separate screened room while the transient recorder was placed closer to the experimental setup, in the high voltage hall, in a screened box and isolated from the main power supply by means of UPS.

In second experiment (where the spark was created by the Marx generator), it was observe that it over shoots the zero line becoming negative for a short period of time. This negative overshoot in the voltage is created partly by the inductance in the circuit and partly due to the response of the voltage di-

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vider. These effects can be corrected by using the procedure outlined in [99]. The corrected waveform is shown in figure 4.18 by the solid line. Observe that the overshoot disappear almost completely after the application of the correction

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time [us]

Vol

tage

[p.

u.]

Figure 4.18. Normalized measured voltage across a 12.8 cm gap. Doted line: Raw voltage measurement. Solid line: Voltage corrected as in [99].

4.5.2 DiscussionIn total six different models were evaluated and compared with the experi-mental results namely Barannik et al.[90], Demenik et al. [91], Kushner etal. [92], Rompe and Weizel [93], Toepler [94] and Vlastos [95]. The com-parison indicates that the resistance models need to be improved due to the large disagreement with the obtained data. It is important to be noticed that the models reported by Demenik et al. [91], Kushner et al. [92] and Vlastos [95] are function of the radius of the arc resistance. Consequently, the dy-namic model of the arc resistance radius presented by Braginskii was used. This radius formulation is not function of the gap length. Therefore, it will lead to same channel radius irrespectively of the length of the spark. Fur-thermore, for small distances, the electrode effects play an important role on the dynamic behavior of the arc channel. Therefore, further investigation leading to more accurate resistance formulation is needed.

It was observed that the majority of the models present larger differences especially with the experimental results obtained with the high energetic current impulse (current generator). However, this is not the case for Kushner et al. model. Hence, to have better match with the recent experi-ments, a new set of constants for the model has to be establish. The experi-

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mental results indicate that these constants can not be a fix value. It has to be connected to the energy dissipated in the spark.

Also, the result shows the importance on various corrections that we have made in the present study. If the anode and cathode voltage drop would have not been considered for the case of small gaps, larger discrepancy between theory and practice were expected. However, as can be observed from the results in paper [VIII], the simulation and experimental results are over-lapped. On the other hand, if the obtained voltage with the Marx generator experiment would have not been corrected, negative resistance values will be obtained. Therefore, it is important to quantify the unwanted distortion on the measured voltage that could lead to erroneous results.

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5 Response Of Surge Protective Devices To Lightning Type Transients

Up to now, the lightning electromagnetic environment and its interaction with distributed systems were investigated. No details about the components designed to divert the transients have been made. In this chapter experimen-tal results of the transient response of Surge Protective Devices (SPDs) against fast impulses will be discussed. The time derivatives of the currents used during the experiments were corresponding to the subsequent return strokes [12]. Those experiential results were compared with SPDs response to standard 8/20 µs lightning current impulses. Also, to investigate how various theories agree with experimental data, two varistor models available in the literature were compared against the experimental data. Finally, a brief account on the response of SPDs against fast voltage impulses is given. This chapter will cover the results presented in papers [IX] and [X].

5.1 Varistor models Various mathematical models to represent the transient behavior of Metal Oxide Varistor (MOV) have been developed based on standard lightning impulse tests. These models are routinely used in ATP-EMTP type programs for the analysis of the various electronic circuits under transient conditions. In this section two of these models namely Simplified Varistor model [100] and Durbak’s model [101] will be presented.

5.1.1 Simplified varistor model. The simplest varistor model consists of a combination of resistance, induc-tance and capacitance. The first two represent the characteristics of the leads of the component while the last one represents the properties of the material and packaging. All these three components will be connected with a variable resistor, which represent the non-linear characteristic of the varistor.

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R L

C

Figure 5.1. Simplified Varistor model

The V-I characteristic for the non-linear branch is given in [102] and is mathematically represented as,

)log(4

)log(321 )log()log( ii ebebibbu (5.1)

In equation (5.1) i is the varistor current and b1, b2, b3, b4 are constant values defined in [102] for a given varistor type.

5.1.2 Durbak’s varistor model The IEEE working group [100] strongly recommends the use of Durbak’s model [101] for transient analysis with varistors. The characteristic of the variable resistor associated with this model is represented by two non-linear branches, A0 and A1, separated by an R, L parallel combination that will play an important role for fast front signals. The equivalent circuit diagram for this varistor model is presented in figure 5.2.

L0

R0

L1

R1

C A0 A1

Figure 5.2. Durbak’s Varistor model

Observe that if the circuit component values are properly selected for high frequency signals, the inductance L1 will limit the current flow through the non-linear branch A1 while for low frequencies; these two non-linear branches will be in parallel. By combining these two branches, it is expected that the model could have a better performance at different frequency ranges. Therefore, the assumed values of the two nonlinear components will consid-erably affect the model’s response at different frequencies. According to [103], the V-I characteristic of the two non-linear components is obtained by

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the ratio currents flowing in A0 and A1 branches. Consequently, in [103] a current ratio equal 0.02 is recommended. Based on this assumption, the V-I characteristics (A0, A1) were determined. These are shown in figure 5.3.

100

101

102

103

104

2.6

2.65

2.7

2.75

2.8

2.85

2.9

2.95

3

Current [A]

Vol

tage

[V

]A0A1

Figure 5.3. Calculated V-I characteristic used for Durbak’s varistor model according to [103]. Continuous line A0, Dashed line: A1.

5.2 Experimental setup

5.2.1 Fast transient impulse current generatorThe “Fast Transient Generator” or “Roman Generator”, developed at Upp-sala University by Roman [104-105] was used as a “High Current Derivative Impulse Generator”. The generator produced peak currents up to 1500A with 10 ns rise time and its rate-of-rise is in the order of 1011 A/s. The cur-rent impulse is ring wave type as shown in figure 5.4. The Voltage and cur-rent waveforms were recorded with LeCroy 9350L oscilloscope with sam-pling rate of 500 Ms/s. The voltage drop across the test sample was meas-ured with 3 Tektronix resistive voltage attenuators, which gives total at-tenuation of 1000 times. The step response of the voltage measurement system is presented in figure 5.5.

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106

107

108

109

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1

Am

plitu

de

log(f)

0 100 200 300 400 500 600 700 800 900 1000-1

-0.5

0

0.5

1

Cur

rent

[A

]

time [nsec]

(a)

(b)

Figure 5.4. (a) Fast current impulse produced by Roman Generator (b) Normalized frequency spectrum

0

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0 2 4 6 8 10Time [ns]

Volta

ge [V

]

(a)

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0 0.5 1 1.5 2Time [ns]

Volta

ge [V

]

(b)

Figure 5.5. (a) Continuous line: input voltage impulse, Dash line: voltage measure-ment setup response. (b) Initial portion of the impulse response. Continuous line: input voltage impulse. Dashed line: voltage measurement setup response.

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The voltage measurement setup was a coaxial assembly which was neces-sary to observe the sub-microsecond pulse without any test connections arti-facts [106-108]. The Current was measured with a Rogowoski coil (EATON Current Probe, 10 kA, 520 A/V) terminated with a 50 resistor at channel entrance to the oscilloscope. For all the measurements a pre-trigger of 100 ns was used to have the complete picture of the full transient behavior of the SPD.

5.2.2 Standard 8/20 s lightning impulse generator To inject a standard 8/20 µs lightning current impulse to the test sample, a NSG650 Schaffner generator was used. The voltage and current signatures were recorded with a LeCroy 9350L oscilloscope with sampling rate of 250Ms/s. A Tektronix P6015A high voltage probe with inner impedance of 100 M , bandwidth of 75MHz and a 1000 times attenuation factor was used for voltage measurements. The current was measured with a 5kA Rogowoski coil which gives 20 A/V (Pulse current transformer model 411) terminated with a 50 resistor and 10 times attenuation was added at the channel input of the oscilloscope.

5.3 Discussion It was observed from the experimental results that the SPDs had a fast re-sponse time when they were subjected to fast transient impulse currents. In most of the cases, the current amplitude was reduced to less than 50% of the peak value within the first two cycles. Also, the total duration of the applied current impulse, as seen from figure 5.4, was reduced to around 600 ns for the gas discharge tubes. On the other hand for the varistors, the peak current amplitude was reduced to less than 20% within the first two cycles with total pulse duration of 200ns. With regard to the time reduction observed experi-mentally for the fast current impulse, numerical simulations with either of the varistor models indicated that it could be due to the attenuation associ-ated with the bulk resistance of the varistor (paper IX) itself, i.e., an increase in the circuit resistance will result in a shorter time duration compared to generator current under short circuit conditions. Moreover, when the diame-ter of those disk type varistors decrease, the current impulse time duration also decrease as shown in figure 5.6. The reason for this is the fact that the varistor bulk resistance is inversely proportional to the disk area, which is further proportional to square of the radius. Therefore, a decrease in the disk diameter will result in a larger current attenuation due to the increase of the resistance.

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0

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300

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S20K

95

S20K

150

S20K

230

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230

EC90

EC15

0

EC23

0

Surge Protector Type

Curr

ent I

mpu

lse

Tim

e D

urat

ion

[ns]

Figure 5.6. Observed impulse duration for both tested varistors and GDTs. Trian-gles: Results associate with sample 1. Square: Results associate with sample 2.

Now consider the voltage signatures. It was observed that the gas discharge tube presents a narrow spike whose peak was 6 to 7 times larger than their nominal rated values for each of the components. A similar observation can be found in the voltage drop across the varistor’s terminal, i.e., it was almost 7 times higher than their corresponding clamping voltage specified in the manufacturer data sheet (figure 5.7). Therefore, when a fast current transient are impressed on the varistors or GDTs, neither the varistors nor the GDTs will provide the protection level as given by the manufacturer, i.e., it will not protect the downstream connected loads against such current impulses.

0

200

400

600

800

1000

1200

Volta

ge [V

]

S07K20 S14K17 S20K20 S20K150Varistor Type

Clamping Voltage [V] Measured voltage [V]

Figure 5.7. Comparison of the clamping vs. the maximum voltage achieved for a fast current impulse.

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If the voltage measured across the SPDs terminals for the two current pulses previously presented (Fast transient and Standard 8/20 s lightning impulse currents) are compared, it was seen that the clamping voltages due to fast transients for the tested components are considerably greater than those ob-served with standard 8/20 µs lightning current impulses.

800

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]

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Max

imum

Cla

mpi

ng V

olta

ge[V

]

(b)

Figure 5.8. (a) Maximum clamping voltage vs. different varistor sizes from fast transient generator. (b) Maximum clamping voltage vs. different varistor sizes from Schaffner generator. Triangles: Results corresponding to sample 1. Square: Results corresponding to sample 2.

It is observed from figure 5.8b that decreasing the disk diameter of the varis-tor result in higher clamping voltage. However, no clear conclusion can be made for fast current impulse test results. The reason for this could be the following: for the standard 8/20 s current impulse, the inductive impedance of the leads is much smaller than the bulk resistance of the varistor, i.e., the transient response of the varistor will be controlled mainly by the varistor

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resistance. However, when the varistor is subjected to high current derivative impulses, its response are governed by the inductance of the leads, i.e., the influence of the non linear resistance of the varistor becomes less dominant. Also, it was observed that when the injected peak current values are in-creased, the current impulse time duration also increased. This can be ex-plained by considering only the envelope function of the analytical expres-sion for the ring wave form given by equation (5.2),

11

tMax eII (5.2)

In equation (5.2) is indirectly connected to the resistance, inductance and capacitance of the experimental setup, i.e., generator and the test object.

11 ln1

II

t Max (5.3)

Equation (5.3) clearly shows that the time of appearance of a given current value is proportional to the peak current of that given signal.

Another important observation was that when the series combination of a varistor and a GDT was investigated, significant differences in the time du-ration of the currents impulses were obtained. When the varistor is con-nected to the line the pulse duration is around 400 ns while for the case when the GDT was connected to the line the pulse decay in around 250 ns. This observation was not expected since if it is considered that the transient re-sponse of both surge protectors is polarity independent [108]. Moreover, if the current signatures are different for the two cases analyzed (varsitor con-nected to the line or GDT connected to the line), then one could expect some difference also on the voltage signature. However, the voltages recorded for the two study cases are almost identical. The author expresses his difficulty to explain this unexpected result and proposes that further investigation has to be made in order to have a better understanding of this phenomenon.

With regard to the compassion between varistor models and experimental results, it was observed that for all the cases with slow front current input signal, the models are capable of reproducing the behavior of the varistor with a good accuracy. However, a closer look at the initial portion of the measured voltage signals and simulated voltages, it was seen that there are differences. On the other hand, when the comparison are made between the experimental results and Durbak’s model, for the varistors with fast transient current impulses, a better agreement was found than the simple varistor model. However, the peak values obtained by using these two models did not differ considerably.

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Also, it is important to mention that the results obtained by using the Roman Generator show that the resistance of the varistor during the conduction stage can also depend on the fast current signatures. The results indicate that even the bulk resistance may vary as a function of time. These dependencies are probably due to the skin depth of the varistor material. An experimental data corresponding to this situation is shown in figure 5.9.

-4.5

-3.5

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

4.5

0.00 20.00 40.00 60.00 80.00 100.00 120.00 140.00

time (ns)

Res

ista

nce

(Ohm

s)

Figure 5.9. Resistance value of varistor S20K150 obtained when the voltage wave-form is divided by the current waveform. An approximate resistance value for the varistor bulk resistance of 1 Ohm is obtained.

The author would like to emphasize that, the over voltage protection schemes cannot be decided based on the conventional data provided by the manufacturer of the SPD’s. The results based on such data may not be valid for very fast incoming transients. Such fast transients could produce high voltage stresses resulting in a serious damage to the devices that are to be protected. Therefore a new concept of overvoltage protection has to be de-veloped to cover the different shapes of transients (fast and slow), that could be generated in electrical networks due to lightning flashes.

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6 Conclusions and Scopes for Future Works

6.1 Concluding remarks In this thesis investigations on various key issues associated with the light-ning interaction phenomena with overhead distribution power lines have been carried out. The following are the list important conclu-sions/contributions that can be derived from the thesis:

a) Return stroke phenomena: - Return stroke modeling was carried out to reproduce the experimentally observed remote lightning electro-magnetic fields, so as to have a proper source representation. This is because the lightning induced voltages on any given system depend mainly on the incident lightning electromagnetic fields. The return stroke model developed belongs to the current generation type and was applicable to both negative and positive first return strokes. The key feature of the model is in its capability to reproduce the slow front of the channel base current waveform for first return strokes due to the connecting leaders. In the model, this feature is mathe-matically represented as a modification in the velocity profile of upward connecting leader. It is also shown that the channel base cur-rent models belonging to the current generation type available in the literature may produce electromagnetic fields with characteristics that are different from the experimental observations when the chan-nel base current contains a slow front.

b) Implementing Agrawal et al. field to wire coupling models in ATP-EMTP: - In this thesis, it has been shown that there are difficulties in implementing the Agrawal et al. field to wire coupling models in user friendly transient analysis packages. Therefore a new and com-putationally efficient technique based on circuit theory is proposed for an easier implementation of Agrawal et al. field to wire coupling models in ATP-EMTP a like ATP-EMTP (a package widely used by power engineers). This was necessary so that the built in line models of ATP-EMTP can be easily included in conjunction with Agrawalet al. model.

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c) Judging the validity of coupling models: - An important question is how to judge the validity of a given model. In this thesis it is shown that judging the validity of coupling models by just simulating spe-cific/special cases alone is incomplete and it is claimed/shown that a more appropriate statistical comparisons have to be for a judicious judgment. Two field to wire coupling models namely Chowdhuri – Gross model [36] and Agrawal et al. model [38] were compared, it was demonstrated that the differences among the two models exists only for very particular cases of stroke location and its orientation to the line. Moreover, it was also shown that the above said differences do not have significant influences, when a statistical type of analysis (Monte Carlo method) for outage calculations and insulation coordi-nation practices are carried out.

d) Surge transfer through distribution transformers: - A detailed study has been carried out to investigate the transients sneaking through a distribution type transformer from high voltage side to low voltage side. The simulation shows a dramatic change in the voltage signa-tures when the comparisons are made between the high voltage and low voltage sides of the transformer. The transferred surge at the low voltage side propagates along the overhead line and combines with the fictitious sources existing along the line due to the field to wire coupling mechanisms. Hence at the load terminal a modified transformer secondary induced voltages appear which has to be con-sidered for appropriate insulation coordination. Also, the protection level achieved by connecting a surge protector on the low voltage side of the transformer alone is not sufficient. The main reason is that, there is a major contribution on the load side due to the light-ning electromagnetic fields coupling to the distribution line.

e) Transients sneaking into a typical HVDC converter station: - A study was made to see the response of a typical HVDC converter station when lightning flashes occur in the vicinity of high voltage DC transmission line systems. The simulation shows that the magni-tudes of induced voltages are not harmful for the selected system configuration (6 pulse diode bridge converter with and without har-monic filter). Also, the transients were entering into the converter station from the DC to AC side without any attenuation/distortion in the wave shape no matter whether harmonic filters exist or not.

f) Parameters that influence lightning induced voltages in distribution systems: - For the sensitivity analysis two different distribution power line configurations were chosen (vertical phase wire ar-

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rangement and horizontal phase wire arrangement). Several cases were studied with the variables as ground conductivity, return stroke velocity, position of the stroke from the line centre, stroke current rise time, presence and absence of overhead ground wire and posi-tion of the voltage induced along the line. The results indicate that the ground conductivity has a large influence on the wave shape and the amplitude of the induced voltages. A bipolar nature in the in-duced voltage wave forms were obtained when the finitely conduct-ing ground was included and this feature dominates with decreasing ground conductivity. This phenomenon also influences the induced voltages on the phase wires when two different distribution power line configurations were analyzed with and without ground wires. Therefore, the amplitude of both polarities of lightning induced volt-ages has to be considered for appropriate insulation coordination practices.

g) Lightning transients entering typical Swedish railway facility: -For the first time lightning transients entering the local power supply of a typical Swedish railway facility located at Tierp in Sweden were measured. This was necessary for validating the models and simula-tions presented in the thesis as a future study. At this facility, cloud to ground lightning at a distance of 5 – 10 km caused peak over voltage of 3 – 5 kV in the low voltage auxiliary power supply net-work.

h) Role of arc resistance in lightning interaction studies: -In regards with the study undertaken to measure the resistance of spark chan-nels in air with two different current waveforms, the results show that the resistance of spark channels initially decreases, reaches a minimum value and then recover as the current in the spark gap de-creases. The minimum resistance of spark channel decreases with increasing peak current. The results were compared with various theories that attempt to predict the temporal variation of the resis-tance of spark channels. This comparison shows that further devel-opments in the existing theoretical models are needed in order to re-produce with better accuracy the dynamic behavior of the channel resistance.

i) Response of SPDs to lightning transients: - How reliable are the ex-isting commercial SPDs to lighting type transients? To answer this questions investigations have been carried out to study the behavior of SPDs when subjected to fast (representative of typical subsequent strokes) and slow (representative of typical first strokes) lightning type transients. When SPDs are subjected with high current deriva-

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tive impulses, the results clearly reveal that the clamping voltage due to these fast transients was considerably larger than the one observed with standard 8/20 s current impulses. Study was also made to evaluate the applicability of existing varistor models developed for transient analysis. By comparing two available models of varistor, it was shown that for a slow front impulse, those two models had a good agreement with the experimental data. However, for current impulses into the sub-nanosecond range, further modifications on the existing models are required.

6.2 Scope for future work The author is aware of the fact that there are several aspects of lightning interaction with power distribution systems that needs further deeper investi-gation so as to advance our knowledge in lightning protection and EMC. Some of the issues that came into the author’s notice during the making of this thesis and based on his experiences with the subject under study could be the following:

Although a methodology was presented for the efficient imple-mentation of Agrawal et al. model in ATP-EMTP, it would be also advantageous to have a simple model that could consider the ground loses effects on the propagating lightning electro-magnetic fields.

Underground power distribution system has considerably in-creased in the last decade, especially in urban areas. However, no calculation/methodology has been reported in the literature to evaluate the lightning electromagnetic field interaction with un-derground power distribution systems. Therefore there is a scope to extend the models and analysis presented in the thesis to such systems too.

Different models to predict the behavior of the surge protection devices can be found in the literature. However, the majority of these models have been developed based on standard lightning voltage/current impulses. Such standard impulses do not cover the complete lightning frequency spectrum, i.e., sub-microsecond components are ignored. It was shown in this thesis that, existing models for varistors are incapable of reproducing the experimentally observed varistor responses under fast tran-sients. Therefore, further developments are necessary for devel-

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oping better varistor models that are applicable to faster tran-sients as well.

The results of the comparison of various arc resistances model were previously presented in the thesis whereas considerably differences were found between the theoretical models and the experimental results.

Finally, there are still many open questions with regard to the subject of this thesis or missed a mention in the thesis. The author strongly believes that even though the problems previously presented are efficiently solved, there will be always new observations or phenomena or problems from Mother Nature. All these will keep us wondering and keep us alive as a researcher.

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7 Sammanfattning

Det moderna informationssamhällets har idag ett stort förtroende till kom-plexa elektriska och elektroniska system. Från kundens sida anses ett avbrott vara helt oacceptabelt och implikationerna/konsekvenserna av dessa avbrott har blivigt väldigt djupgående. Därför, i de ämnesområden som involverar stora distribuerade system såsom telekommunikation, kabel-tv, LAN- och WAN nätverk etc. är industrin idag hängiven att hitta och utveckla avance-rad teknologi och metoder för att garantera normal drift av olika samman-kopplade elektriska och elektroniska nätverk/system. Ett av de största system som förser slutanvändaren är el-kraftnätet, som är sammankopplat och leder till fler mindre komplexa system. Det är vanligt med transient fenomen i dessa system och kan uppstå genom ett brott på en ledning, en brytning av en ström eller ett blixtnedslag (direkt eller indirekt). Beroende på magnitud och frekvens utseende hos de olika transienterna (över-spänningarna/strömmar-na) kommer skada på el-kraftnätet att vara ofrånkomlig, men p.g.a. samman-koppling till komplex känsliga nätverk kommer även dessa att vara utsatta för transienterna. På grund av detta finns det ett ökat krav på att förstå karak-teristiken hos och konsekvenserna av de olika typer av transienter som in-träffar i olika system. Med detta i åtanke är denna avhandling ett försök att studera transienterna från åska (blixtnedslag), som är ett ofrånkomligt natur-fenomen. För att korrekt återge interaktionen mellan blixtens elektromagne-tiska fält och de elektriska nätverken, är det väsentligt att ha en modell för den s.k. ”återledaren” som är kapabel att reproducera den elektromagnetiska karakteristiken av en blixt. Flera modeller har utvecklats för att studera kopplingen mellan det elektromagnetiska fältet och tråd/ledarstrukturer. Den populäraste, enklaste och mest noggranna bland de tillgängliga modellerna är Agrawal et. al. I denna är kopplingsmekanismen representerad av flera distribuerade källor/generatorer längst ledarstrukturen, varav varenda distri-buerad källa är relaterad till den horisontella komponenten av det infallande elektromagnetiska fältet vid just den punkten av ledaren. Å andra sidan, ATP-EMTP är ett välkänt transientsimulationsprogram, vidaspritt bland elkraftsingenjörer. I detta programpaket finns inbyggda modeller av Seml-yen, Marti eller Noda uppställningar. Det finns ett problem med att applicera Agrawal et. al. modellen med de inbygga elkraftsledarmodellerna i ATP-ETMP, vilket är att spänningskällan från den horisontella komponenten av det elektriska fältet i Agrawal et. al. är i serie med impedansen i ledarstruktu-ren och inte mellan två transmissionsledarsegment. Utöver detta propagerar

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det elektromagnetiska fältet som kopplar med elkraftsledarna över ett ändligt ledande jordplan. Därför kommer jordmånen att selektivt absorbera högfre-kventa komponenter hos det elektromagnetiska fältet, vilket leder till en förändring av vågformen. En ändligt ledande jord kommer också att produ-cera komponenter på marknivå av fältet som är horisontella. Flera approxi-mationer finns tillgängliga i litteraturen för att beräkna det horisontella elekt-riska fältet, däribland ”the wave-tilt”, ytimpedans och Cooray-Rubenstein approximationen. Därför är det viktigt att studera förändringen av den indu-cerade spänningen när elkraftsledaren befinner sig över ett ändligt ledande plan. Däröver, för att skydda från transienter inducerade från blixtnedslag (direkt eller indirekt) är det nödvändigt att använda överslagsskydd (eng. ”surge protective devices”, SPD) kapabla att avleda inkommande transienter för att undkomma skada i känsliga system. Emellertid tar standard procedu-rer för att testa SPD’er inte i åtanke existerande submikrosekunds fenomen hos transinterna. Därför, för att kunna skydda känslig utrustning på lågspän-nings sidan av nätet är det av yttersta nödvändighet att förstå responsen hos SPD’er när utsatta för transienter med hög strömderivata.

Denna avhandling är riktad mot att undersöka problemen som beskrivs ovan. Speciellt studeras en ny modell för återledaren, en ansats med en enkel kretsmodell för att på ett effektivt sätt applicera Agrawal et. al. modellen i ATP-EMTP, effekten av jordmåns konduktiviteten på karakteristiken av den inducerade spänningen samt responsen hos SPD’er när de utsätts för transi-enter med extremt hög strömderivata.

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8 Acknowledgments

It has been an honor and great pleasure to pursue my Ph.D. studies at the Division for Electricity and Lightning Research at Uppsala University, a world class institution with more than 70 years of experience in the field. During these last five years in Uppsala, I had the opportunity to cooperate with a large number of people that have made this moment possible to hap-pen. Therefore, I would like to express my gratitude to:

Prof. Vernon Cooray, a brilliant scientist, a person with a great imagination and excellent communication skills. Someone who takes a complex subject and reformulates it in a way that anyone can understand every single detail. I am grateful to him and I would like to express my sincere thanks for giving me the opportunity to learn and do research under his extraordinary guid-ance.

Prof. Rajeev Thottappillil, for sharing with me his knowledge and practical expertise in the field of Electromagnetic Compatibility and Lightning. His advices always came at the right moment, which helped me to keep going during hard times. His excellent guidance, continuous support and encourag-ing attitude make me feel confident to face upcoming challenges in my fu-ture research career.

Prof. Viktor Scuka, who always was available when his help was required. I have immense gratitude to Prof. Francisco Roman for introducing me to the field of surge protection devices and for sharing with me all his experimental expertise, no matter in which part of the globe he was.

Dr. Nelson Theethayi, for the support and continuous encouragement during these 5 years of research. For his interesting and fruitful technical discus-sions. A person that will never let aside a good idea, keeping on developing it until finally it becomes an excellent scientific contribution. But more im-portantly, many thanks for his invaluable friendship.

Mr. Ulf Ring, a genius with excellent skills to create whatever experimental setup was needed. For his help and assistance in anything that was neces-sary. For the greats moments we shared together in the High Voltage Lab.

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Ms. Gunnel Ivarsson and Mr.Thomas Götschl for being always there to help me whenever it was required.

Mr. Marley Becerra, for the great moments spent either discussing technical problems, or philosophizing on what should be our task and duties as scien-tists, or simply while having fun during a drink on a Friday night.

Mr. Daniel Månsson, for his assistance and help on several high voltages activities, good technical discussions and for always bringing crazy com-ments that made us all laugh and relax on the most stressing moments. Also, for his help during the writing of the thesis sammanfattning.

Dr. Yaqing Liu and Dr. Mighanda Manyahi, for the interesting technical discussions, for their friendship and the fun times while sharing the room. Also, I would like to thank Dr. Mihael Zitnik for his guidance during the high voltage training.

Mr. Surajit Midya, a new young student that joined recently Uppsala Univer-sity and who brought a fresh attitude with good scientific skills to our group.

Prof. Miguel Martinez, Prof. P. Chowdhuri and Mr. Mauricio Aristizabal for believing in a thesis proposal that later was awarded with the best student paper/thesis at the IEEE winter meeting 2002.

Jakke Makela, for all the interesting scientific discussions with practical purposes, held during the last year and also for letting me get close to his beautiful family. Also, I would like to express my gratitude to the members of his working group, Mr. Joni Jantunen, Mr. Ari Hamalainen, Mr. Tom Ahola and Mr. Niko Porjo. They showed me that a good team attitude can make a great difference while doing research.

In April 2005, I had the great opportunity to meet an extraordinary team at Colombo University, Sri Lanka. Thus, I have a great appreciation to Prof. Mahendra Fernando, Prof. Chandima Gomez and Prof. Upul Sonnadara, for their help, assistance and for providing a great environment to do research. Also, the measurement campaign would have not been possible without the assistance of Mr. Velupillei Jeyanthiran, Mr. S. R. Sharma, Mr. J. A. P. Bo-dhika, Mr. Chandana Perera, Mr. Suranga Edirisinghe and Mr. Nishshanka Jayawantha. This great research team made me feel like at home. Special thanks to Mr. Karunarathna who was always taking good care of us during this measurement campaign.

I also had the opportunity to meet and cooperate with two great young re-searchers from the University of Colombo, Sri Lanka, excellent colleagues

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and with whom I am proud to be co-author in several publications. There-fore, I am thankful to Mr. Prasanna Liyanage and Mr. Mahesh Edirisinghe for the good time spent during several experiments and technical discus-sions.

I had also the opportunity to meet good friends in Sweden who always made me feel at home, they taught me many things that are not possible to find in books and shared great moments based on their life experiences. These spe-cial thanks go to Mr. Carlos Rios, Mrs. Elvia Serrano, Mr. Francisco Vale-ska, Mrs. Claudia Loaiza, Mr. Carlos Geywitz, Maria Fernanda Gomez, Timo Marquez and Alexander Kessar. Thanks for all the great moments and good philosophical discussions that we had.

I would have never been able to reach this moment if during the summer 1992 I would not had the opportunity to improve my English skills and shared good moments with my relatives in Trinidad and Tobago. I am grate-ful to all of them for being supportive to my initiatives.

To all the staff and colleagues at the Division for Electricity and Lightning Research which in different ways have provided me assistance during my Ph. D. studies.

Last but not least, I would like to express my sincere gratitude to my wife, Marianne; my mother, Raiza; my sisters, Lisbeth A, Lisbeth; my brothers, Rafael, and Juan C.; my grandparents, Cruz R. and Brigida; my uncle Fran-cisco; my aunties, Gloria, Gladys, Beatriz, Elena and Emma; my two neph-ews, Daniel and Ralph and my good friends Cesar A. and Gustavo, thanks for continuing supporting and encouraging me to take new challenges in life.

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