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IEEE Transactions on Power Delivery, Vol. 12, No. 1, January 1997 483NUMERICAL ELECTROMAGNETIC FIELD ANALYSIS

OF TOWER SURGE RESPONSEMasaru Ishii, Senior Member, DEEE Yoshihiro Baba, Student Member, IEEE

University of TokyoTokyo, Japan

Abstract-Tower surge responses are compute d by the nu-merical electromagnetic code. The code used in thi s paper isnot th e one based on the circuit theory such as the Electro-Magne tic Ikansients Program (EMTP), but the one thatsolves the electric field equations directly by the momentmethod. The accuracy of this method is shown to be satis-fa ct 04 by comparison with experimental results that werecarried out on an actual UHV tower as well asreduced-scalemodels. And then by using this method, the influences oftower elements such as slant elements, horizontal elementsand crossarms on th e tower surge characteristics are investi-gated. In addition, the surge impedance of a full-sized towerhit directly by a lightning stroke is discussed.

Keywomb- Numerical electromagnetic analysis, Towersurge impedance, UH V tower

I. INTRODUCTIONTower surge response characteristics are important fac-

tors in analyzing lightning performance of transmissionlines. Especially for such tall structures as a doublecircuitUH V tower, the tower surge characteristics becomesmore important due to the longer surge propagation time.Agreement on this matter, however, has not been reachedyet.

Representative methods to investigate the tower surgecharacteristics include (i) measurement on real towers,(ii) measurement on reduced-scale models, (iii) analyticalstudy on simplified geometry, and (iv) numerical analysisbased on the electromagnetic theory.Measurements on full-sized towers by the so-called directmethod have been carried out mainly in Japan[l] 2] 3] toevaluate the tower surge characteristics. In this method,step current is injected into the tower top by a pulse gen-erator mounted on the tower top, and the voltage betweenthe tower top and a measuring wire, or across an insulatoris measured by a voltage divider. This method is straightrforward in evaluating the insulator voltage when the toweris struck by lightning, and the influence of the ground con-ductivity is automatically incorporated. But the measurement is not easily carried out, and it is impossible to know96SM436-6 WRD A paper recom mended and approved by the IEEETransmission and Distribution Committee of the IEEE PowerEngineering Society for presentation at the 1996 IEEWPES SummerMeeting, July 28 - August 1. 1996, Denver, Colorado. Manuscriptsubmitted December 29, 1995; made available for printing May 21,1996.

the characteristics of towers that have not been con-structed. In addition, it is quite difficult to set a verticalcurrent lead wire above the tower top to evaluate the cou-pling effect between a vertical lightning channel and theinsulator voltages.

Measurements on scale models[4] are more economicalthan on full-sized towers, and are flexible in investigatingvarious experimental arrangements. But it is not easy tomaintain the accuracy of the measurement, especially insimulating the direct method, since the geometrical size ofthe measuring devices is large relative to the whole system.

Theoretical studies based on the electromagnetic fieldtheory[5] SI 7] are useful in understanding the phenomenaqualitatively. But the analysis is limited to such simplegeometry as a cone or a cylinder, and even after such sim-plification, the latter still cannot be rigorously analyzedwithout a numerical procedure[8]. Although the derivedsimple formulas of the tower surge impedance are attrac-tive, there remains the problem of how to fit the shape of atransmission tower to a cylinder or a cone. The traveling-wave analysisof the tower surge characteristics by dividinga tower into a system of short transmission lines by usingone of the analytical formulas[9] might be included in thiscategory.

Numerical approach based on the dynamic electromag-netic field analysis has the possibility to overcome variousdifficulties in other methods. But the verification of theaccuracy of the computed results is essential before apply-ing this method to analyze the lightning performance oftransmission lines. The authors chose NEG2 (NumericalElectromagnetic Code[lO]) to analyze the tower surge r esponse. This computer code is written by FORTRAN ina self-consistent form. Ref.[lo] consists of three volumes,namely the theory, the source code and the users guide,and a copy is available from National Information Service,U.S. Department of Commerce. The users guide includesa description of sample data . It can cope with the scatter-ing of electromagnetic fields around a reasonably complexsystem of thin wires. NEG2 solves the electromagneticfield around thin wires in the frequency domain by the mo-ment method[ll]. To solve the timevarying electromag-netic fields, Fourier transform and inverse Fourier trans-form are used. The authors ran NEG2 on an IBM-PC forthe analysis in this paper.A transmission tower needs to be decomposed into thinwire elements, and the position, orientation and the ra-

0885-8977/97/$10.000 996 IEEE

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484dim of each element const itute th e input data , along withthe description of the source of excitation and the frequen-cies to be analyzed. There is restriction in the size andthe arrangement of individual elements in the analysis byNEG2. Therefore, although fairly complex tower struc-ture can be simulated, some simplification n the geometryis unavoidable to analyze the surge response of a transmis-sion tower. In this paper, the accuracy of the computedresults is verified through comparison with measurements,then this numerical method is applied to the analysis of thesurge response of a full-sized UHV tower. The systems un-der numerical analysisare postulated to be on the perfectlyconducting ground.

11. ACCURACY OF NUMERICAL ANALYSISA . Comparison of Experimental and Computed ResultsDue to the limitations of NEC-2 as mentioned above,

it is indispensable to inspect the validity of the computedresults when it is applied to t he analysis of tower surgeresponse characteristics. A series of well-documented mea-surements of surge characteristics on simple structures re-ported by Hara et ol.[12] 13] is chosen for comparison withthe numerical analysis.

In the experiments of Hara et al., surge responses of suchstructures of 3m in height as shown in Fig. 1were mea-sured. The vertical single conductor in Fig. l(a) had aradius of 2.5mm, and the vertical four conductors in Fig.l( b) had a radius of 16.5 and 404 apart. The exper-imentd setup on a metal plane is shown in Fig. 2[12][13].Step current having the risetime of 5ns was injected intothe horizontal current lead wire. The voltage between thetop of a structure and a horizontal voltage measuring wirewas observed together with the waveform of the current at

Y 404

(a) Single conductor. (b) Four parallel conductors.Fig. 1. Structures subject to analysis.

1

Voltage DividerVoltage MeasuringWire

Fig. 2. Setup of Hara et al.sexperknent[l2][13].

the top through electro-optical transducers, and the overarisetime of the measuring system was within 5ns[14]. Tangle between the voltage measuring wire and the currelead wire was 90 degrees.

In the numerical analysis by NEC-2, currents on eacwire segment is calculated. Therefore, lOkR resistanceinserted between the top of a structure and the end of thvoltage measuring wire, and the waveform of the curreflowing through the resistance is calculated to evaluate thvoltage between the top of the structure and the wire.

Figure 3 shows the measured and computed waveformof the voltage and the current a t the top of the single coductor. Figure 4shows those for the four parallel condutors. Not only the waveforms, bu t also the amplitudesthe measured and computed results are quite similar. Tsmall difference in the current waveforms between Fig. 4(

(a) Measured voltage. (b) Measured current.

(c) Computed voltage. (d) Computed current.Fig. 3. Mearured (a)(b)[12] and computed (c)(d)waveformsfor the single conductor of Fig. l(a).

(a) Measured voltage. (b) Measured current.[ d l50040030020010 00

-100-200-300

( c ) Computed voltage. (d) Computed current.Fig. 4. Measured (a)(b)(13] and computed (c)(d)waveformsfor the four parallel condudow of Fig. l(b).

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500400300zoo100

-100-200-300

-- - -- "- , I- e ' 0 @ Jg 40

1- 1- -

o , , / , ; , , , , ;Through the above comparison between the experimen-

tal and computed results, the numerical analysis usingNEC2 is proved to be practical enough to be applied tothe investigation of the tower surge response.

single conductorfour conductors

B . Influence of the Method of Current InjectionIf the surge current propagates along the tower at the

speed of light, the reflected wave from the ground shouldreturn to the tower top after twice of the tower travel time,which is 2Ons for the structures in Fig. 1. But in theboth computed and experimental raults of Figs. 3 and 4,the voltage waveforms reach their peaks at about 17-18nsafter the beginning, indicating tha t a negative voltage wavearrives at the top prior to the arrival of the reflected wave.This phenomenon occurs because the electromagneticwave in TEM mode illuminates the structure by themethod of current injection illustrated in Fig. 2. In thiscase, the electromagnetic wave of excitation arrives at thetower foot simultaneously with the arrival at the tower top,and a negative voltage wave is-induced at the tower footbefore the occurrence of the reflection of the voltage wavepropagating down from the tower top. This induced waveis observed in the current waveforms in Figs. 3 and 4 asthe gradual increase of the current before 2Ons.

Experiment Computationabout 3600 3790about 1200 1250

To verify the above explanation, an experiment em-ploying a different method of current injection is numer-ically simulated, where a current pulse generator havingthe impedance of 5kR s connected between the tower topand the current lead wire. The computed voltage and cur-rent waveforms at the tower top for the structure of Fig.l(b) are shown in Fig. 5. In this case, the electromagneticwave expands spherically from the tower top, and the in-fluence of the ground is observed only after twice of thetower travel time, that is 2Ons. The voltage waveform of

The tower surge impedance of the case of Fig. 5 is 139R,which is about 10% higher than 125R of the case of Fig. 3,computed for the same structure and employing a differ-ent method of current injection. This result implies thatwhen a lightning stroke hits a ground wire in mid-span, thedistribution of the electromagnetic field is different from ei-ther of the above two cases, and the tower surge impedancewill behave in between these two extreme cases.

111. INFLUENCE OF TOWER ELEMENTSThe structure of actual towers is much more complex

compared with the simple structures in Fig. 1. It has slantelements, horizontal elements and crossarms in addition tothe four main poles of variable radius from the bottom tothe top. Influence of these elements of an actual trans&sion tower on the tower surge characteristics is investigatedby using the numerical method.

Figure 6(a) is the structure composed of four main poles,and Fig. 6(b) is the detail of the main pole having a vari-able radius. These structures subject to numerical elec-tromagnetic analysis are determined taking account of thestructure of an actual UHV tower[3] shown in Fig. 6(c).The numerical analysis simulates the measurement by thedirect method, and the arrangement of the measuring wiresis shown in Fig. 7 .The tower is directly connected to theconducting plane. A current pulse generator having theimpedance of 5kR is placed at the top of the tower, andconnected to the vertical current lead wire, which is meantto incorporate the influence of the induction from the ver-tical lightning channel hitting the tower. The tower topvoltage is evaluated through the current flowing the 1OkRresistor p l d etween the tower top and the horizontalvoltage measuring wire.

The waveform of the current having the risetime of 0 . 2 ~ ,used throughout in the numerical analysis of this part, isshown in Fig. 8(a). The tower top voltage of the funda-mental case for Model I is shown in Fig. 8(b). The tower

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486surge impedance, defined in the same way as the previoussection, evaluated from Fig. 8is 186R. The influence of theradius of the main poles is investigated for the structure ofModel I in Fig. 6(a), by replacing the poles to those havingconstant radii of O.lm or 0.3m. The voltage waveforms forthese cases are almost the same as in Fig. 8(b), and thetower surge impedance is 190R for 0 . h radius and 173Rfor 0.3m radius, respectively. It is known that the radiusof the main poles has some influence on the tower surgeimpedance, which might be difficult to take account of inusing an analytical formula for the evaluation of the towersurge impedance. c- 8m-1Omw

0 2m0 3m0.4m0 5m

0 6m0 m

(a)Model I. (b)Detail of (c) Actual UHV towerthe main pole.Fig. 6. Fundamental tower model for analysis(a)(b)and structure of modeled UHV tcwer(c).

, _ _ _ _ _ _ _ _ _ _ _ ;t- - - - - - - - - - -

Fig. 7. Arrangement of numerically analyzed setup.[* I [VI

-1.00

(a) Input current.Fig. 8. Computed waveforms of current and voltagefor the fundamental case.

(b) Tower top voltage of Model I.

Figure 9 shows various tower models introduced to eval-uate the influence of tower elements on the tower surgeresponse characteristics. The radii of the elements exceptthe main poles are O.lm in the upper part and 0.15m inthe lower part of a tower. Figure 10 shows the computedwaveforms of the tower top voltage for these structures.The waveform of Fig. 8(b) for the fundamental case is ex-

pressed in dotted lines in the figures in Fig. 10 excepFig. 10(d). The tower surge impedance for all of waveforms is summarized in Table 2.

Figure l0(a) shows that horizontal dements littlefluence the tower surge charaeteristics. The tower simpedance decreases only 3% by adding horizontalments to Model I. By contrast, slant elements considedecrease the tower surge impedance, indicating that influence on the electromagnetic field around the tcannot be disregarded. The change of the tower simpedance at Model 111 is about 20%. The waveforFig. 10(b) is smooth and similar to that of the tower wout slant elements.

15 5m10m t_i

(a)Model XI. (b)Model III. (c)Model IV. d) Model V.Fig. 9. Structures of numerically analyzed tcwer models.

[" I300250200150100500

-50-100-150

(a) Model U. (b)Model III.(with horizontal elements) (with slant elements)[" I

(c) Model IV. (d)Model V.(with crossarms) (with slant elements & crossarms)Fig. 10. Waveforms of computed tower top voltage.

Table 2. Calculated surge impedance of various model toweModel I 1 Model II I Model 111 I Model IV I Model V186R I 180R I 149a I Ism I 14W

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487it is much simpler than the actual tower. Horizontal el+ments can be omitted as they little affect the tower surgeresponse. But the restriction imposed by the numericalcode has made it difficult to adjust the angle of the slantelements and the width of the tower top of the numericalmodel to those of the actual tower. The narrower angle ofthe slant elements to the main poles and the wider widthof the tower top of the numerical model tend to lower thetower surge impedance, which must be the principd causeof the 9% difference between the measured and the com-puted surge impedance.

B . Influence of Arrangement at EzperimentThe arrangement of the current lead wire relative to the

voltage measuring wire influences the measured tower surgeimpedance, and the numerical analysisiscapableof disclosing small difference in the surge response characteristics.Taking advantage of this feature of the numerical method,this part of the paper is devoted to discuss the reasonablevalue of the surge impedance of the UHV tower of Fig.

The tower surge response is additionally computed fortwo arrangements, namely for the caseof a vertical currentlead wire, and for the case of a horizontal current lead wirewhich is perpendicular to the horizontal voltage measuringwire. The current pulse generator is placed at the top ofthe tower for all the cases. The computed waveforms ofthe tower top voltage of these cases are shown in Fig. 12.Table 3 summarizes he calculated tower surge impedancefor three arrangements of the current lead wire.

Due to the difference in the structure of the numericalmodel and the real UHV tower, the calculated tower surgeimpedance turned out t o be about 10% lower than themeasured value as seen in Fig. 11. According t o Table3, the value of the tower surge impedance is dependent onthe arrangement of the experimental setup, and the high-est value will be measured when the current lead wire isvertical and having high impedance. This condition CO-sponds to the situation when the tower is directly hit by alightning stroke, and the surge impedance of the actual

6(c).

136R I 12m

Crossarms cause oscillation in the rising part of the volt-age waveform when there are no slant elements as seen inFig. lO(c), but little influence the tower surge impedancenor the apparent tower travel time of the traveling wave.When there are slant elements, the oscillation caused bythe crossarms is smoothed. The decrease of the tower surgeimpedance by adding crossarms is only 5%, but the appar-ent travel time increases. Here the crossarms are actinglike capacitance.

The influence of the crossarms will increase a t a typicaltower design in the U.S., where the portion of the towerbelow the lower arm is less than the tower of Fig. 6(c).In addition, when a lightning stroke attaches a sky wiresupport, which is not modeled in the present analysis, theapparent travel time will increase further due to the in-creased path length.

IV. CHARACTERISTICS OF FULL-SCALEA. Comparisonwith f i l l -Scale Measurement

TOWER

The surge response of an independent full-sized UHVtower was measured by the direct method[3]. The structureof this tower is illustrated in Fig. 6(c). Both the voltagemeasuring wire and the current lead wire were horizon-tally stretched from the tower top, and the angle betweenthese wires was 130 degrees. A current pulse generator wasplaced on the tower top. Figure l l( a) shows the correctedstep response waveform of measured tower top voltage, andthe tower surge impedance for this arrangement was eval-uated as 126f2[3].

The tower surge response is numerically calculated forthe same arrangement by using the tower model V shownin Fig. 9(d). The difference in the numerical model fromthe previous section is that each tower foot is connected tothe perfectly conducting ground through 40R of resistanceto realize tower footing resistance of 10R. Fig. Il(b) showsthe computed tower top voltage waveform, and the towersurge impedance for this waveform is 115R. The measuredand the computed waveforms are in good agreement in-cluding the negative avershoot, and the difference in thetower surge impedance is 9%.

The tower model V of Fig. 9(d) is designed to numeri-cally simulate the full-sized UHV tower of Fig. 6 (c ) , though

115h2(a) Measured wavefom[3]. (b) Computed waveform.

Fig. 11. Measured and computed waveformsfor full-sizedUHV ower.

(V I........... .......... ............. ........... ....................... ....... . . . . .

0

-80.... d . Oi5 ....... . . . .

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488UHV tower at that time will be about 150s1. This valueis estimated based on the case of 1360 in Table 3 by com-pensating the about 10%difference between the numericaland the experimental values.

The analytical expression recommended by the IEEEWG[15] is based on the impedance of an inverted cone ex-cited by horizontal current injection[4]. The lowest valueof the surge impedance evaluated by this analytical expres-sion for the UHV tower in question was 1660 according tothe Discussion of ref.[3], by defining the radii of the towerby circles circumscribing around the square section. Thesurge impedance of this tower for the arrangement of hori-zontal current injection inferred from the numerical analy-sis is about 135R. This value is based on the case for 124Rin Table 3. In case the current pulse generator is not placedon the tower top, the tower surge impedance will decreasefurther for about lo%, according to the result of I1 of thisDaDer.

inverted cone yields higher value for the case of this UHVtower.

REFERENCES[l ][2]

M. Kawai, Studies of the Surge Response on a TransmissionTower, IEEE %S. PAS-83, No.1, pp.30-34 (1964)M. Ishii et al., Multi story lkansmission Tower Model for Lightning Surge Analysis, IEEE %S. PWJXD-6, No.3, pp.13271335 (1991)T. Yamada et al., Experimental Evaluation of a UHV ToweModel for Lightning Surge A~ l y s i s ,EEE %S. PWRD-10No.1, pp.393-402 (1995)W. A. Chisholm et al., Trav el Time of Transmission TowersC. F. Wagner and A. R. Hileman, A New Approach t o theCalculation of the Lightning Performance of Transmission LineI11 - A SimpM ed Method: Stoke t o Tower, AIEE 7tnw. 79pp.589-603 (1960)M. A. Sargent and M. Darveniza, Tower Surge ImpedanceW A. Chisholm et al., Lightning Surge Response of Transmission Towers, IEEE 1pans. PAS-102, No.9, pp.3232-324(1983)

[3][4][5]

IEEE PAS-104, N0.10, pp.2922-2928 (1985)

[6][7]

IEEE PUS . AS-88, NO5, pp.680-687 (1969)

I /from the above results, the surge impdance of the UHVtower of Fig. 6(c) is concluded to be about 1500 in thecase of vertical current injection, and about 1350 in thecase of horizontal current injection. The analytical expres-sion recommended by the IEEE WG yields at least 10 to

[S] A. raunstein, T he Induced Overvoltages Across th e InsulatoStrings of Power Transmission Systems due t o Direct LightninStrokes, IE EE PES Summer Meeting, Paper C72 559-3 (1972[9] W. A. Chisholm, discussion t o [2][lo] G. J. Burke et aZ., Numerical Electromagnetic Code(NEC),,,TechnicalDocument 116, Naval Ocean systems CenterSan Diego (1980)20% higher value. This might come from different current

distribution in an actual transmission tower from that fora cone.

V. CONCLUSIONSThe numerical electromagnetic analysis by using N E G 2

is applied to the investigationof the tower surge response.The usefulness of this method is verified from the goodagreement between the experimental and computed resultsin the measurement of tower surge response characteristics.Although there is restriction in the s tructure which can beproperly analyzed by N E C 2 , it is much more flexible thanthe classical modeling of the tower by a cylinder or a cone.

By using the numerical method, the influence of towerelements on the tower surge response characteristics is in-vestigated. Horizontal elements little influence the towersurge characteristic, whereas slant elements lower the towersurge impedance for more than 10%. Crossarms distort thewaveform of tower top voltage, but if slant elements exist,the oscillation in the waveform is smoothed. This charac-teristic agrees with the experience of experiments on realtowers.

The surge impedance of an independent full-sized UHVtower is investigated by using the numerical method andthe experimental result. It turns out that the arrangementof the measuring wires affect the tower surge impedance,and the highest surge impedance for the UBV tower isestimated to be about 15052. This value corresponds tothe case when a vertical lightning stroke directly hits thetower top. The analytical expression of the tower surgeimpedance recommended by the IEEE WG based on the

[ll] R. F. Ha r& to n, Field Computation by Moment MethodsTh e Macmillan Company, New York (1968)

[12] T. Hara et al., E mpiric al Formulas of Surge Impedance for Single and Multiple Vertical Cylinder, IE E Japan %TL~., 110-BNo.2, pp.129-137 (1990) (tn apanue)[13] T. Hara et al., Transmission Tower Model for Surge AnalysisConference of IEE J apa n for Power & Energy Society, FukuokaNo.270 (1991) ( in Japanese)[14] T. Hara et al., Emp irica l Formulas of Surge Impedance foTransmission Tower, 20th ht.Conf. on Lightning ProtectionInterlaken, Paper 3.7P (1990)[15] IEEE Working Group Report, Estimating Lightning Performance of Tkansmission Lines I1- Updates t o Analytical ModelsIEEE %S. PWRD-8, No.3, pp.12541267 (1993)

Masaru Ishii (SM87) was born in TokyoJapan, on March 11, 1949. He received B.SM.S. and Dr.Eng. de ee es in electrical engneering all from the University of Tokyo i1971, 1973 and 1976, respectively. He joineInstitute of Industrial Science, the Universitof Tokyo in 1976, and has been a Professosince 1992. His specialty is high voltage engneering. He is a member of the IEE of Japan

Yoshihiro Baba S95) was born in Waka yma, Japan, on February 24, 1971. He receiveB.S. degree in electrical engineering from thUniversity of Tokyo in 1994. He has beenpaduate student of the University of Tokysince 1994.