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Electrical Engineering in Japan, Vol. 1 17, No. 2, 1996 TrrnsllM fium Deaki G.wEai Ronbwhi, Vol. 115-B, No. 5, May 1995, pp. 524-532
Transmission Line Tower Models in Frequency Domain
SHOHEI KATO Toyo University
AZUMA MOCHIZUKI and EIICHI ZAIMA Tokyo Electric Power Co.
SUMMARY
"%is paper proposes a transmission line tower model in fresuency domain for back-flashover analysis, which has a uniform characteristic impedance and a uniform propagation constant. Most conventional tower models are constructed as a constant and uniform parameter transmission line that is independent of fiquency. However, the authors' models have the frequency dependency of the characteristic impedance and the propagation constant to express the fiquency characteristic of the transmission line tower.
Two models, a cylinder model and a f o u r - h e s model, were investigated to simulate the tower. Their surge responses were computed by numerical electro- magnetic field analysis based on the moment method. From the results, the two-port circuit constants were calculated in the fiequency domain, and the characteristic impedance and the propagation constant are derived from them. ?he complex artificial oscillations appeared in fkquency dependency of the parameters because the parameters were calculated numerically. The equations with analytical fonn were obtained by approximating with a smooth c w e to the oscillations. It is possible for the equations to represent the transmission line constants as a function of geometrical parameters such BS the tower height and the radius. Close agreement was found between the surge response computed by the numerical electromagnetic field analysis and the result calculated by inverse Laplace transformation of the analytical equations. To prove the model, the experimental results were com- pard with the computed ones of the cylinder model that has arms, and it was shown that the new model agrees
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closer with the experiment than conventional transmission line models.
Key words: Surge analysis; tower; tower model; fiequency characteristics; surge impedance; numerical electromagnetic field analysis.
1. Introduction
Transmission line theory is used widely because it has the advantage of easy treatment on a circuit simu- lator. However, in the surge analysis of transmission lines containing towers, an equivalent transmission line model is desirable which can accurately represent the surge phenomena. Accordingly, as an equivalent circuit of the tower, it is treated conventionally as a transmission line of constant characteristic impedance of about 100 R in many cases. However, various tower models, such as the 4-section model, have been proposed recently. Also, it has been pointed out that since the transmission line theory which is based on the TEM wave is applied to the Th4 wave, there is a problem in applying it to the propa- gation phenomena from voltage application to initial current [2].
On the other hand, in the analysis of the surge characteristics of the towers, it has been shown that the method of numerical electromagnetic field analysis in the hquency domain is useful as an analytical method because it can clarify the relation with the tower height or extension and the current paths [ 1, 21. Although the accuracy of this analytical method is high and it has the merit of simulating the surge phenomena well, the amount of calculation is enormous and there is a problem
1SSN0424-7760/96/OOO2-0029 0 1996 Scripta Technica, Inc.
r, 11 ' 17
(a) Multisection (b) Frequency (c) n-type model model model
Fig. 1 . Transmission line models.
Fig. 2. Two-port circuit model.
geometrical parameters such as tower height and distance between tower base can also be considered.
in that it lacks the connection with the EMTP model of other transmission lines. 2. Equivalent Circuit of Tower
As a method of analysis in the same frequency domain, Ametani et al. have proposed models for ana- lyzing the surge characteristics by measurement results of actual towers [3-6]. By this method, the simulation result which agrees well with the measured result after the 2.1 Equivalent circuit by transmission line wavefront can be obtained. However, the relation with the tower structure and the frequency dependency are not made clear.
Let us describe the equivalent circuit models of the tower in the fraequency domain and the method for deter- mining them.
models
It is known that the current flowing into the top of the tower is not a constant current but rather propagates in time and space variations. Three methods may be con- sidered for representing this phenomenon as a trans- mission line. As shown in Fig. I(a), the tower is divided into many sections and each section is expressed as a
In the method of numerical electromagnetic field analysis, the current and voltage in the frequency domain can be determined and the frequency characteristics of the impedance can be calculated. Thus this analytical method may be applied in the making of the frequency models.
The frequency characteristics in the surge analysis of the transmission lines so far have expressed the frequency characteristics of the earth and overhead lines. However, in the case where the TM wave travels along conductors such as towers, the characteristic impedance will change at locations even if the conductor is perfect [12] and the propagation characteristics will show the frequency characteristics. Accordingly, in this paper we will determine, in the numerical electromagnetic field analysis, the frequency characteristics of the propagation constants Z, and y expressing the distortion of the traveling wave propagating along the perfect conductor for the models of cylindrical tower with arms. Also, we will make a comparative study with the experimental results. Moreover, we will clarify from these results that the accuracy of the frequency models of the tower is higher than the conventional equivalent circuits and the
constant characteristic impedance line. ?he 4-section model [7] is equivalent to this method. One more method is the model, as shown in Fig. I@), in which both characteristic impedance and propagation constant are set as a constant transmission line but the respective constants are set as a function of frequency. 'The former method is simpler as a model. However, there are prob- lems such as the difference with the measured results is relatively large, and many element divisions are required to make the calculation accuracy better.
Moreover, an antenna analysis can be performed by constructing an equivalent circuit shown in Fig. I(c) in which Z, is considered as a parallel circuit of a constant characteristic impedance independent of frequency and an impedance element having frequency characteristics, and the impedance characteristics seen from the input termi- nals can be represented. In this method, the transmission line is considered mainly as a load of signal source. On the other hand, in the analysis such as in the surge
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Fig. 3. Layout of surge analysis for tower model.
characteristics of the tower where not only the impedance seen from the tower top but also the arm voltage are desirably determined as well as in the analysis consid- ering grounding impedance, there will be a problem in using the equivalent circuit of antenna as it is.
Accordingly, in this paper we will study the case where the conductor vertical to the earth such as tower or lightning arrester is expressed by a transmission line of uniform characteristic impedance. If this characteristic impedance is a constant value independent of fkqumcy as in a lossless transmission line, since it cannot represent the propagation of the TM wave, it will be considered as a function of frequency and the propagation constant also is considered as a function of frequency. In the antenna- related equivalent circuit of Fig. l(c), an impedance element is considered at the sending end and teceiving end, and the transmission line is considered as a lossless distortionless transmission line. By contrast, the proposed model becomes a simpler equivalent circuit as shown in Fig. l(b). However, there will be problems in the calcu- lation of its circuit constants and in the method of calculating the transmission line.
Ametani et al. have studied several frequency- dependent tower models [ 3 4 ] . But since their equivalent circuits are determined fiom the measured results or loop voltage method, problems arise, such as the analytical accuracy in short-time domain and the method of calcu- lating the equivalent circuit constants. Accordingly, we will study in this paper the transmission line model shown in Fig. l(b) in which the voltage changes at various parts of the tower can also be explained by a simpler equation and by the equations of characteristic impedance reflecting the tower structure.
0.00 SM IOM IS.00 20.00
Time (ns)
Fig. 4. Surge response of cylindrical model by numerical electromagnetic field
analysis.
2.2 Calculation method of equivalent circuit
To determine the equivalent circuit of the tower, if a two-port circuit parameter (F parameter) shown in Fig. 2 is considered, we have
If this F parameter is used, the characteristic impedance is
B C
Zo=-
Moreover, if the propagation constant is y and the tower height (line length) is h, we have
c o s h y h = m
where y = a +jp, a is the attenuation constant, and /3 is the phase constant.
In order to determine the F parameter, when the earth side is set as I2 = 0, i.e., opened, A is determined fiom the ratio of El to E2 and C fiom the ratio of I, to E2. Moreover, by letting the earth side be E2 = 0, i.e., short-circuited, D is determined from the ratio of I, to I, and B from the ratio of El to I,. In the ordinary ground- ing structure of the tower, the grounding resistance is not necessarily zero. However, since the earth is assumed to be a perfect conductor in the numerical electromagnetic field analysis, this condition holds.
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400.0
200.0
0.0
-200.0
T""." , I 1 I 1 - U 0.1 0.3 1 .o 3.0 10.0 30.0
f/f,
Fig. 5 . Frequency dependence of characteristic impedance in cylindrical model.
To determine the F parameter by the layout shown in Fig. 3, the numerical electromagnetic field analysis will be carried out. The layout is considered in which a power source is put on the tower top and a return stroke is simulated. Then, 10 kR is inserted between the voltage-measurement grounding conductor (consisting of a horizontal conductor and a vertical conductor) and the tower top, and the voltage at both ends is considered as the tower top voltage. On the earth side, similarly, 10 kf2 also is inserted between tower base and the earth, and this terminal voltage is assumed to be the open voltage and the current at short-circuit is assumed to be the tower base current flowing into the earth from the tower. The length of the current application auxiliary conductor is three times the tower model height.
In this analysis, attention must be paid to the fact that all conductors including the earth are assumed to be perfect, and the calculated Z, and y are those including the effects of the current application auxiliary conductor and the earth. In the numerical analysis, since the voltage and current are determined under finite boundary condi- tions, the effect of the current application auxiliary conductor appears as a standing wave in the frequency characteristics of the characteristic impedance and propagation constant.
3. Derivation of Frequency Models
As the methods for simulating the towers, the cylin- drical model, four-frame model, etc., may be considered. However, here, we will study the cylindrical model and the four-frame model which simulates the frames of the tower.
3.1 Cylindrical model
The cylinder 1.8 mm in height and 6 mm in diame- ter used in our experiments and analyses so far will be considered as a tower model. The conductors, such as the current application auxiliary conductor, are also of the same diameter, i.e., 6 mm, and the horizontal length of the voltage measurement grounding conductor is 1.8 mm.
When the applied current in the layout of Fig. 3 is a unit step, the tower top voltage shown in Fig. 4 is obtained. The sampling time is 1/3 ns and is common in the following waveforms of this paper. In this waveform, the wave reflected from the earth reaches the tower top at about 12 ns and then weakens. However, the rise is steeper compared to a rectangular-wave response of a fmt-order lag system (RC circuit). Ihe crest value is about 365 R and agrees with the value of the equation for average characteristic impedance [ 121:
2h z = q h o hz(x)dx=60(ln- n - 1) (4)
where h is the height of the cylinder and u is the radius of the cylinder.
Figure 5 shows the frequency characteristics of the real part and imaginary part of Z,. However, the hori- zontal axis is normalized by the frequency
C fo=- 4h (5 1
where c is the velocity of light. l l i s implies that the
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00
C -0.5 t: 2 -1.0
- 1 5
-2.0
I I I I I 1 IJ 0.1 0.3 1 .o 3.0 10.0 30.0
r/r, Fig. 6. Frequency dependence of attenuation constant.
I 5 10 15 20 25
f/f,
c Qa - 3
f/f,
Fig. 7. Frequency dependence of tan ah.
quarter wavelength is equal to the tower height h. Both the real part and the imaginary part oscillate greatly. This may be due to the fact that the accuracy of the numerical analysis becomes worse at resonance and anti-resonance of the cylinder caused by the error resulting from the numerical calculation of Z, fiom Eq. (2), etc., in deter- mining the voltage and current. Since the imaginary part of Z, is negative, it is a capacitive impedance. The real part tends to become smaller as the fkquency becomes higher.
Figure 6 shows the frequency characteristics of the real part of yh, i.e., ah. However, the ordinate is a common logarithm of ah, and it shows a complicated oscillation as in the case of 2,. However, it is seen that overall, it tends to become larger at higher frequencies and the propagating wave attenuates.
Figure 7 shows the frequency characteristics of tan ph. According to transmission line theory, the resonant and anti-resonant points appear at every& in the case of short-circuit as terminals. The complicated oscillation also appears in the case of Fig. 7, however, large peaks appear
Fig. 8. Relation between phase constant and frequency.
periodically. When the relation between p and frequency is determined from these peaks, it becomes as shown in Fig. 8. From the slope of the straight line of Fig. 8 being about 0.5,
holds, and from it we have
and it is seen that the propagation velocity v is roughly equal to the velocity of light and may be considered constant independent of frequency.
In the fiquency characteristics of Z, and y in Figs. 5 to 8, the me characteristics are not clear because the complicated oscillations are superposed. Accordingly, we have considered the approximation of the frequency char- acteristics by a smoother curve if possible, and simpler analytical equations. Taking into account the fact that the function of 1 / 6 + s appears approximately in the rec- tangular-wave response of the transmission line of the TM wave [13], the following approximate equation is detennined as a Laplace h c t i o n of s:
Zd ( 1 +(ST&"]"
z,<4 =
33
E
b Y 5 D
.-
400.0
300.0
200.0
loo. 0
0.0
-100.0
0.1 0.3 1.0 3 .O 10.0 30.0
f/fo
Fig. 9. Frequency dependence of characteristic impedance in equivalent circuit of cylindrical model.
where To = 4Mc. rn = 1.2, n = 0.4
0.00 5.00 10.00 15.00 20 .oo Time (ns)
Fig. 10. Surge response of cylindrical model in equivalent circuit.
4h ZA=6O(ln- -1) - n (7)
Since 2, is related to the tower impedance at low Frequency fiom the relation 2, = cL, we have decided to use Eq. (7) by considering a mirror image of the cylinder close to the earth; Z,(s) of Eq. (6) denotes the frequency characteristics shown in Fig. 9. Moreover, the following equation is considered as an approximate equation of the attenuation constant ah:
(-2.5 +O.Sloglsl) ah=l0
The values of rn, n and a h are determined by many tests
so that the results of Figs. 5 to 8 can be approximated well, and the combinations of the other values may also be considered. Moreover, as a starting point of the approximate function, 1 m is used, but other func- tion forms may also be considered. However, we have decided to use the aforementioned values and functions in this paper.
When the tower top voltage due to the unit step current source of the transmission line using Eqs. (6) and (8) is determined by inverse Laplace transformation, the waveform shown in Fig. 10 can be obtained. By compar- ing the tower top voltage waveform of Fig. 4 obtained from the numerical electromagnetic field analysis and the result of Fig. 10, the two waveforms are seen to agree
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Fig. 11, Four-frame model. 0.1 0.3 1 .o 3.0 10.0
f/f,
Fig. 14. Frequency dependence of attenuation constant.
may be considered as a phenomenon in numerical calcu- lation and approximated even by the smooth curves shown in Fig. 9, which can represent the surge charac- teristics of the cylinder vertical to the earth.
ism m.oo
- r i i (d
Fig. 12. Surge response of four-frame model by
The conductor is assumed to be a perfect conductor whose resistance is zero. For this reason, the frequency characteristics of the propagation constant of Eqs. (6) and (8) express the phenomena caused by the changes of the
numerical electromagnetic field analysis. characteristic impedance (ratio of electric field to magnetic field) of the transmission line depending on the locations, but do not express the fiequency characteristics of the conventional conductor resistance.
u L I I I I I 1 0.1 0.3 1 .o 3.0 10.0
f/f,
Fig. 13. Frequency dependence of characteristic impedance in f o u r - h e model.
well. However, the rise of the wavefront portion up to 5 ns is slower than Fig. 4.
We have studied various combinations of m and n of Eq. (6) and the result of Fig. 10 is considered to be able to approximate Figs. 5 to 8. Therefore, it becomes clear that the complicated oscillations shown in Fig. 5
3.2 Four-frame model
Since the actual tower is a grid structure having arms and diagonal bracing and becomes a complicated conductor system, we decided to approximate the tower by four frames shown in Fig. 11 in addition to the cylinder. The respective h e conductors as well as the voltagemeasurement grounding conductor and the current application auxiliary conductor are 6 mm in diameter, the same as the cylindrical model, and the analysis is carried out with the layout of Fig. 3. However, the current at short-circuit is determined from the sum of the four tower-base currents.
Figure 12 shows the surge voltage waveform at the tower top. Compared to the cylindrical model of Fig. 4, the crest value itself becomes small as a matter of course, the rise is steep, and a flatness near the crest is seen. It is natural that the surge impedance drops because the num- ber of conductors has increased from one to four.
35
0 5 10 15 20
f / f ,
Fig. 15. Frequency dependence of tan Oh in four- frame model.
Figure 13 shows the frequency characteristics of the real part and imaginary part of Z, determined in the numerical electromagnetic field analysis. However, the horizontal axis is normalized byfo = d4h. The oscillation period between the tower top and earth is determined by cylinder length rather than the frame height. However, since the surge propagation velocity of the tower is discussed with the height h as a reference in many cases, the respective characteristics are expressed by normalizing it withf,. In comparison to the characteristic impedance of the cylindrical model, the whole impedance becomes smaller and the peaks at resonance become slower. Besides, the imaginary part of the characteristic impedance at lower frequencies becomes positive.
Figure 14 shows the frequency characteristic of 01.
The characteristic that a also becomes larger when the frequency becomes higher is the same as in the case of the cylindrical model. However, as a whole, it becomes a smaller value than the case of the cylindrical model. This may be due to the fact that the current path becomes four times.
Figure 15 shows the frequency characteristics of tan ph. The oscillation is more complicated than the case of cylindrical model. However, the oscillations of large peaks occur at somewhat lower frequencies than the frequency of odd multiples o f f , . These peaks have occurred at the odd multiples of f, in the case of the cylindrical model. The difference is due to the fact that the frame length exceeds the height and that the propa- gation velocity drops due to the mutual interference of the respective current paths as a result of the 4-frame configuration. From Fig. 15, the resonant frequency is determined to be about 90 percent off,. Specifically, a value of about 90 percent of the velocity of light is
- Rcd part h
Y
c 250.0
8 200.0
.B 100.0
150.0
U -50.0
0.1 0.3 1.0 3.0 10.0 30.0 100.0
f / f ,
Fig. 16. Frequency dependence of characteristic impedance in equivalent circuit of four-
frame model.
obtained as the propagation velocity of the current wave of the four frames.
Based on Figs. 13 to 15, we have studied the trans- mission line model of the four-frame model expressed by simple analytical equations, similar to the cylindrical model. By referring also to the equivalent circuit of the cylindrical model, the following approximate equation for the circuit constants is determined:
Z d
(1 +(sTJ"}" (9) q s > =
where To = 4Wc, m = 6, n = 112.4 and p = 1.1 whlc.
Z, uses Eq. (7) in the case of cylindrical model. However, since the tower bases of many towers form a square, the interval between the feet of the tower is used as a, and since the propagation velocity of the current wave becomes about 90 percent of the velocity of light, p uses the coefficient of 1.1.
Moreover, the attenuation constant a h is approxi- mated by the following equation:
Similar to Eqs. (6) and (8), the values of m, n and ah are determined by many trials so that the results of Figs. 13, 14 and 15 can be approximated well.
The characteristic impedance by Eq. (9) becomes the frequency characteristics shown in Fig. 16. In comparison to Fig. 13, it is seen that the imaginary part becomes positive at low frequency in Fig. 13 but it
36
Time (ns)
Fig. 17. Surge response of four-6ame model in equivalent circuit.
becomes negative in Fig. 16. However, when the fre- quency approaches ZCTO, the imaginary part of Eq. (9) becomes zero, and since it also becomes close to the TEM wave at low fiequency physically, the imaginary part may be considered asymptotically approaching to zero.
Using the above circuit constants, when the tower top voltage waveform is detennined by applying a unit rectangular current to the tower top, the result of Fig. 17 is obtained. Compared to the waveform of the numerical electromagnetic field analysis shown in Fig. 12, it is seen that the portion of linear increase after rise becomes a slow increase in the equivalent circuit. However, good agreement is obtained for the crest value and the wave form as a whole. This shows that the surge characteristics of the f o u r - h e model can be expressed by the approxi- mation using Eqs. (9) and (10).
In the actual tower frames, the resistance and its tkquency characteristics also exist. If this aspect is to be considered by the proposed model, the superposition of the fiequency characteristics of the conductor resistance on the frequency characteristics of a may be considered. However, this will be a future subject.
4. Analysis of Tower Surges Using Frequency Models
We have proposed two kinds of tower models, i.e., cylindrical model and a four-frame model. The applica- tion of the respective models to the actual towers depends on the tower structure. For example, the cylindrical model can be used in the pole type and the f o u r - h e
1
0 ' 0 40 80 120 160 200
Tirnc(ns)
(a) Applied c m n t
O J o 40 80 120 160 200
lirne(ns)
@) Tower-top voltage
Fig. 18. Surge response of cylindrical tower model with arms: experimental results by Hara et
al. [8].
model can be used in the tower if the arm is smaller compared to the diameter of the tower itself.
The distributed-constant line analysis has also been carried out [%lo]. Accordingly, we have studied the experimental results reported so far to see if the proposed models can be applied to the surge analysis.
Hara et al. have used a vertical cylinder provided with a horizontal conductor in cross shape as the tower model, measured the surge characteristics, and obtained the results shown in Fig. 18 [8]. Moreover, they have compared this model with the analysis using the conven- tional transmission line theory. However, it cannot be said that the measured result and analytical result do not necessarily agree. Accordingly, we have attempted to apply the proposed frequency models to this and carried out surge analysis by using the equivalent circuit shown in Fig. 19. The current application conductor is a transmission line of constant characteristic impedance 500 n, and Eqs. (7) and (8) of the cylindrical fiequency model are applied to the parts from tower top to arm root, arm root to the earth, and arm root to its tip.
From the fact that the current is applied fiom above the earth and that the current flowing into the tower top is orthogonal to the tower model, since Z, from tower
37
ZC. aC 5 0 m
i i zL,t’
Fig. 19. Equivalent circuit of cylindrical tower model with arms.
top to arm root will decrease by 20 R, respectively, then the case where the tower and current path become a straight line [ I ]
is used. Similarly, the one between arm root and earth uses Z, = 336 R. Since the arm may be considered part of the horizontal line if it is approximated by a horizontal line, Z, of Eq. (7) is a characteristic impedance at low frequency. Thus, by applying the characteristic impedance of the conventional horizontal line to the arm portion,
2h Z,=60h(-) a
will be used. Specifically, for the arm portion, it is approximated by a horizontal wire 9 m in height and 25 mm in radius following Hara et al., and Z, = 394 R is used. The attenuation constant a uses Eq. ( 5 ) for both the tower itself and the arm portion, and the grounding resistance is assumed to be 25 R again following Hara et al. Besides, the transformation from the s domain to time domain is performed by numerical Laplace transforma- tion.
Figure 20 shows the analytical results for com- parison with the results of the transmission line model by Hara et al. [83. In comparison to Fig. 18, it is seen that the tower-top voltage agrees well with the measured results, and the waveforms are closer to the measured results than the analysis by the distributed-constant line so far. Thus the usefulness of the frequency models are
2.2, , h I I
0.5
Frequency model Conventional tnn~- - - -
- (a) Applied current
mission line model
SO0
400
300 I 200
>” 100
0 0 so loo 150 200
Tlmc(nr)
- Frequency model - - - Conventional trahs.
Fig. 20. Surge response of cylindrical tower model with arms by equivalent circuit analysis.
(b) Tower-top voltage mission line model
shown. When they are applied to UHV towers, the ana- lytical results [ 1 l ] which agree well with the measured values also are obtained.
‘The frequency models taking into m u n t the fre- quency characteristics of the cylinder vertical to the earth have been proposed by Ametani et a]. [3-51. Compared to those models, the special feature of the models in this research is that the time variation of the tower-top voltage from the initial part can be explained naturally in addition to the surge impedance, although they are experimental equations determined by numerical simu- lations.
5. Conclusions
For performing surge analysis of transmission lines containing towers simply and with good accuracy, by using the numerical electromagnetic field analysis, we have determined the characteristic impedance expressing the phenomenon of the distortion of the TM wave propa- gating along the tower and the frequency characteristics of the propagation constant, which are different from the frequency characteristics of conventional conductor
38
resistance. From these results, we have proposed models in which the tower is expressed by a uniform trans- mission line of uniform characteristic impedance and propagation constant. We have determined the charac- teristic impedances and propagation constants for two kinds of tower models, i.e., a cylindrical model and a four-frame model. They are expressed by simple analyti- cal equations. Since the characteristic impedances are expressed as a h c t i o n of the tower height and the distance between the tower feet in these models, the changes of the surge characteristics due to the tower structure can be explained.
Upon comparing the measured results of the surge characteristics of the tower models provided with cross- shaped arms in the cylinder and the analytical results of the proposed tower models in time domain, it is shown that they agree well and that the technique can analyze with good accuracy the surge characteristics of a conductor vertical to the earth.
We will report on another occasion the applications to the surge analysis of complicated tower models and transmission lines for the case where the overhead ground wires are attached or the case where the voltage across arcing horns is analyzed.
Acknowledgment
Part of this research was carried out with a grant from the Subsidy-General Research (C) of the Scientific Research Expenditures of the Ministry of Education.
REFERENCES
I . Kato, Okabe, Yamiida, Sawada and Zaima. Electro- magnetic field analysis of surge Characteristics of towers. Documents of the High-Voltage Study Group of the I.E.E., Japan, HV-92-28, 1992.
2. Kato, Okabe and Zaima. Analysis of the mea-
3.
4.
5 .
9.
10.
11.
12.
13.
surement method of surge characteristics of towers by reflection method. Ibid., HV-92-33, 1992. Motoyama, Nagaoka and Ametani. A study on tower and corona models in lightning surge analysis. Ibid., HV-87-13, 1983. Nagaoka and Ametani. Frequency characteristics of tower impedance. 1991 Joint National Conference of Electrical and Information-Related Institutions, s7-5. Ametani, Kasai and Ishihara. Frequency-dependent tower impedance at imperfect conductor earth. Documents of the Power Engineering Study Group ofthe I.E.E., Japan, PE-91-167, 1991. Nagaoka A study of frequency-dependent tower model. Trans. I.E.E., Japan, Vol. 1 1 1-B, p. 51, January 1991. Technical Report of the I.E.E., Japan. A new technique for lightning surge analysis in power systems. Part 11, No. 244, 1987. Hara, Yamamoto, Kitai, Hiramatsu, Hayashi, Nagai and Matsumura. Transmission line model of tower arms. Documents of the High-Voltage Study Group of the I.E.E., Japan, HV-90-70, 1990. Hara, Hiramatsu, Kitai and Yamamoto. Equivalent distributed constant line model for a vertical conductor. Trans. I.E.E., Japan, Vol. 1 12-B, p. 107, January 1992. Hara, Yamamoto, Hayashi and Nagai. Tower mod- els for lightning surge analysis. Trans. I.E.E., Japan, Vol. 114-B, p. 595, June 1994. Kato, Mochizuki, Yamada, Sawada and Zaima. Fre- quency characteristics of towers. Documents of the High-Voltage Study Group of the I.E.E., Japan,
S. A. Scheikunoff. Electromagnetic Waves. D. Van Nostrand, 1943. Takeuchi and Kato. Surge impedances of transmis- sion line towers. Documents of the High-Voltage Study Group of the I.E.E., Japan, HV-87-12, 1987.
HV-92-96, 1992.
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AUTHORS (from left to right)
Shohei Kato graduated in 1971 from the Depamnent of Electrical Engineering, Yokohama National University. He received his Dr. of Eng. degree from the University of Tokyo in 1976. He became a Professor on the Faculty of Engineering, Toyo University in 1993. He is engaged mainly in research on high-voltage measurement methods, numerical electromagnetic field analysis, discharge phenomena and surge analysis.
Azuma Mochizuki received his Master’s degree in 1984 in Electrical Engineering at the Science and Engineering Research Division of the Graduate School, Science University of Tokyo. He joined Tokyo Electric Power Co. in 1984. He is engaged mainly in research on substation technology and insulation coordination of UHV, etc. He is currently a Senior Researcher in the Electric Power Research Section of Power Technology Research Laboratory.
Eiichi Zaima graduated in 1974 from the Department of Electrical Engineering, University of Tokyo. In 1990, he received his Master’s degree from the Massachusetts Institute of Technology. He joined Tokyo Electric Power Co. in 1974. He is engaged mainly in study and research on substation technology and insulation coordination of UHV, etc. He is currently a Deputy Head of the Electric Power Research Section, Power Technology Research Laboratory. He received a Paper Award from the I.E.E., Japan in 1993.
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