1264 IEEE Transactions on Power Delivery ,Vol. 6, No. 3, July 1991

AEOLIAN VIBRATIONS : WIND ENERGY INPUT EVALUATED FROM MEASUREMENTS ON AN ENERGIZED TRANSMISSION LINE

M. Kraus P. Hagedorn

Institut fur Mechanik, TH Darmstadt

6100 Darmstadt, W. Germany Hochschulstrasse 1

Abstract - Field tests carried out in Buren in a completely automated test station are described. From these measurements the wind power input in an actual transmission line is estimated. A comparison with re- sults from wind tunnel data is carried out. It corrobo- rates the method now being used for the calculation of aeolian vibrations in transmission lines, so that it can be used in the future with more confidence.

1. INTRODUCTION

Aeolian vibrations are caused by the shedding of vortices from a body exposed to laminar or turbulent flow [l]. In the case of overhead transmission lines, wind leads to vortex shedding and vibrations in the frequency range from 5 to 100 Hz with amplitudes some- times as large as the conductor diameter. These vibra- tions can cause severe damage or even breakdown of the conductor due to material fatigue. Dampers of different kinds are therefore being used to reduce the aeolian vibrations and to increase the conductors' life time. Both knowledge of the wind data and the corresponding wind power input and of the mechanical behavior of con- ductor and damper are required in estimating the vibra- tion levels. Calculations using an energy balance meth- od [ 2 ] are often done to predict the vibration amplitu- des and bending strains at different frequencies. These results are then used for damper design. Together with statistical meteorological data and appropriate models for damage accumulation they can possibly be used for life-time estimation in the future.

In this paper. computed vibration levels are com- pared to results obtained by vibration measurements on an energized transmission line. From these measurements the "wind forces" acting on an actual overhead conduc- tor are estimated and compared to the data obtained by wind tunnel experiments.

2. GENERAL REMARKS ON AEOLIAN VIBRATIONS

2.1 The Strouhal-Relation

For vortex-excited vibrations of taut wires Strouhal found the relation

f s = S X D

between the frequency fS of the vortex shedding and the wind velocity v perpendicular to the wire, D being the diameter of the wire and S the Strouhal number ( S = 0 . 2 ) .

2.2 The Energy Balance Method

Using a simplified model C2.31, the conductor vibration amplitudes can be approximately computed as a function of the wind speed perpendicular to the conduc- tor or of the frequency using the energy balance

Pw = PD + Pc. (2)

In (2) steady state vibrations are assumed, Pw is the power of the aerodynamic forces, P the power dissipa-

ted in the damper and Pc the power dissipated in the

conductor. In this balance the energy exchange between neighboring spans and towers is neglected. If no dam- pers are present, the term PD in (2) vanishes and the amplitude can then be calculated from Pw = Pc for given

wind speeds or vibration frequencies.

D

In these calculations it is assumed that the con- ductor is always vibrating in resonance, i.e. that each frequency is an eigenfrequency of the conductor. Due to this assumption the method does not give the actual vibration levels, but only the largest possible values (see [2,3]). This is in good agreement with the design philosophy of the safe borderline. The actual vibration levels depend on additional parameters changing in time (e.g. wind speed distribution, turbulence level, con- ductor length and tension).

2.2.1 Power Dissipated in the Conductor

The power dissipation in conductors ("self dam- ping") can be measured in laboratory spans as a func- tion of the frequency f and the amplitude A or the vi- bration angle p. It is usually approximated by formulas such as

P - K fnpmTEL c - 1 T t

or

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2.2.2 Wind Power Input

The power imparted to the conductor by the aero- dynamic forces is estimated on the basis of wind tunnel experiments, which are usually carried out with rigid cylinders rather than conductors. Not only do the re- sults differ considerably from author to author, but the test conditions are obviously much different from the ones at an overhead line [4,5.6,7,8].

With k = w/c the power spectrum of (7) is

Fig.l: Normalized wind power input, obtained by Farquharson Mc Hugh and Diana & Falco

Using laboratory results obtained in wind tunnels the "wind-power" can be written as

Pw = L f3 D4 F(A/D) (4)

over a wide range of Reynolds-numbers. In Fig.1 the experimentally determined wind power input F(.) is shown as a function of 2A/D (see [9] 1.

2.3 The Vibration Amplitude

The energy balance (2) can be used to predict ap- proximately the maximum vibration amplitude or bending strain as a function of the vibration frequency. On the other hand, using data from the field tests the ampli- tude can be calculated directly from the measurement data [lo].

For monofrequent planar free vibrations of a taut string with fixed ends, the displacement can be written as

w.(x.t) = Ai sin(kix) sin (wit) (5)

with the frequency w = i s/L and the wave number

k . = is/L. i

In the field measurements, the cable vibrations can be approximated as a superposition of the different modes, so that w(x,t) is of the form

w(x,t) = 1 Ai sin (kix) sin(wit) i

The cable acceleration is measured at locations x = x0,

so that the measurement signal is

m(t) = - 1 Ai "4 sin(kixo) sin(wit). ( 7 )

i

i

Equation (8) is valid for w > 0 and Gm(.) is an even

function.

In the energy balance method the calculations are carried out with monofrequent vibrations and we there- fore wish to substitute ( 6 ) by a monofrequent vibration with the same mechanical energy and with a certain am- plitude A and a nominal, dominating circular frequency

(9) w(x, t) = A sin(- Od x) sin(wdt).

Equating the total mechanical energies of (6) and (9) leads to

w . 2 A2=1[-$] AT

i d

If we multiply G .(U) by the correction fac tor mm

1 C(0) := w2 0; sin2(% C O

we obtain

G ( w ) := G ( U ) C(O) = AA mm

and according to (10) A is given by

(11)

(12)

In the experiments, the time functions are not monofrequent but correspond to narrow band signals, S O

that the power spectra are no longer singular. The dominating circular frequency wd can then be defined by the centroid of the spectrum

as shown in Fig.3. This gives better results than defining wd by the maximum of GAA(w). due to the

roughness of the spectra. Of course all the calculations are carried out with FFT. i.e. a discretized version of the Fourier transform [ll].

3. DESCRIPTION OF THE TEST FACILITY

A fully automated test facility was built for the measurement of the vortex-induced vibrations in Biiren (Westfalen). Germany, by a consortium formed by the po- wer utilities Vereinigte Elektrizitatswerke Westfalen (VEW) Dortmund, PreussenElektra and Bayernwerke and by Richard Bergner GmbH and the Institut fur Mechanik of the Darmstadt Technical University. In this test sta- tion, data are collected on the conductor vibrations and on meteorological conditions in an actual transmis-

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sion line.

The earth wire (conductor 240140 (similar to HAWK conductor, diameter 21.9 mm, weight 0.987 kg/m, T-= 86400 N, T = 14000 N, 26 x 3.45 mm aluminium. 7 x 2.86 mm steel) of the 220 kV transmission line Lippborg-Bu- ren is used for the measurements between the towers 113 and 114; Fig.2 shows location and elevation of the test site. It is situated in a hilly terrain steadily ascen- ding from northwest to southeast up to 300 m above

/Paderborn

I N Test- site BUREN

114 113

Fig.2: Location and elevation of the test site

sea level over the town of Biiren with only some low in- dustrial buildings in the neighborhood of the site. The following variables are measured:

- air temperature on top of one tower, - wind speed perpendicular and parallel to

- tension in the conductor, - vertical acceleration at four discrete

the transmission line on top of one tower,

points of the conductor (distance from the clamps approx. 2-4m).

The wind speed is measured by means of an ultra- sonic anemometer on tower 114. the tension in the con- ductor is registered with a force transducer at the clamp on tower 113 and the vertical acceleration is de- termined by means of accelerometers. The analog signals obtained by these transducers are amplified and trans- mitted to a cabin, where they are filtered and digiti- zed. These data are then evaluated on a HP 9000/310 computer system with programs written in HP BASIC 4.0.

After a set-up procedure concerning the choice, description and calibration of the data channels. FFT parameters, A/D converter adjustments, trigger parame- ters, etc., the variables described above are sampled with prespecified time intervals (5-10 minutes) between two measurements. With the chosen parameters (number of channels (8). FFT block size (512). sampling frequency (250 Hz), number of required averages (10)) the recor- ding of the data frames takes about 20 seconds. These data are then further processed in a second phase ta- king approx. 300 seconds. The mean value, minimal and maximal values are computed from the recorded time his- tory together with the standard deviation for each channel. averaged over the chosen number of frames. Since the measured vibrations are not exactly mono-

requent, a nominal "dominating" frequency is calcula- ted using the centroid of the acceleration spectrum (see Fig.3) for all four acceleration channels. This gives more reliable results than the frequency with the maximum amplitude because of outliers. The data re- sulting from these computations are then stored on a disk - the real time data are not stored - and later analyzed and evaluated in the Institut fur Mechanik in Darms tad t .

Fig.3: Computation of the "dominating" frequency

4. RESULTS OF FIELD MEASUREMENTS

4.1 Wind Conditions

Fig.4:

Wind speed tdsl

The Strouhal-Relation (mean value and standard deviation)

The first measurement series, taken in October and November 1987. was used mainly for checking the test facility. After that a total of 51 measurement se- ries was registered during 1988 between May and Decem- ber with more than 30 000 single measurements. Some of the results are given below.

To check the Strouhal relation, the measured "do- minant frequency" was plotted versus the wind speed in Fig.4 and a linear regression was performed using these data.

E Wind speed Wsl 18

Statistical distribution of wind speed and "dominating" frequency

Fig.5:

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Fig.6: Statistical distribution for the Strouhal number

I 885 t I -I

Fig.7: The Strouhal number as a function of the wind speed (Mean value mS and standard deviation)

The correlation coefficient r = 0.93 shows that there is indeed a strong linear dependence between the frequency and the wind speed in the examined range of wind speeds between 1 and 10 m/s . Fig.5 shows the two- dimensional statistical distribution with relation to the wind speed and the "dominant frequency". Fig.6 gives the one-dimensional statistical distribution for the Strouhal number and Fig. 7 shows the relation between the Strouhal number and the wind speed perpendicular to the conductor.The turbulence level of the wind flow

S t = L

V (15)

is depicted in Fig.8. s being the standard deviation

and mv the mean value of the wind velocity (both taken

for the time of the individual measurement of about 20 seconds). This is an important result since it contains information about the laminarity of the wind flow. Du- ring our measurements the turbulence level was of the order of 5 1 5 % (Fig.8). a value much larger than in most wind tunnel experiments (1-2%), but realistic f o r real transmission lines.

I

Fig.8:

e 16

Mean value and standard deviation of the turbulence level

No correlation was found between the wind speed and time of the day (Fig.9).

The statistical density of the total wind speed is shown in Fig.10 (the maximum wind speed is about 20 d s ) together with the distribution of the wind velo- city component perpendicular to the conductor. It can be noted that the overall wind speed follows a Rayleigh distribution but this is not the case for the perpendi- cular component.

Fig.9: Time dependence of the wind speed (Mean value and standard deviation)

A

ze

Fig.10: Statistical distribution for the overall wind speed and the wind speed perpendicular to the conductor

4.2 Vibration Amplitudes

Because of the exposed situation of the test site, vibrations with significant amplitudes did not occur very often; approximately. 500 measurements with amplitudes larger than 0.01 Am could be registered. Additional measurements using optical devices showed similar results

Fig.lla: Comparison between amplitudes computed from measurements and from the energy balance

Using only those data, the vibration amplitude was calculated from the field measurements as described in 2.3. These amplitudes obtained from the field tests are shown in Fig.lla together with the results of the energy balance using the RIBE 11 wind power model. This

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wind power model corresponds with the coefficients gi- ven in [2,p.264]. which were obtained by averaging the results of [5] for standing harmonic waves. The cable's self-damping was measured in the lab and the coeffi- cients in (3a) were found as K1 = 6*10 E-7, n = 2.91. m = 2.47, t = 1.56. For all frequencies the amplitudes in the field are always smaller than the ones computed with this wind power model.

In the further computations we used the maximum amplitudes in 1 or 2 Hz intervals as an envelope (Fig.llb) for the amplitude. At a given wind speed per- pendicular to the conductor the vibration level may reach this envelope but remains far below it in many cases.

Fig.llb: Envelope of computed amplitudes

The existence o r non-existence of high vibration amplitudes is obviously affected by additional factors. During the evaluation of the data it was observed, that the high level vibrations did not occur at random in time, but they would typically persist for time inter- vals from some minutes up to several hours and vanish then again. To explain this phenomenon a comparison between filtered data with Am > 0.01 and the complete data set was carried out. In Fig.12 the registered vi- bration amplitude was plotted as a function of the wind speed component longitudinal to the cable and the tur- bulence level. It was found that measurements with lar- ge amplitudes were associated to low turbulence levels and small wind velocity components in the direction longitudinal to the cable. In the bar chart of Fig.13 the mean values and standard deviations of the longitu- dinal wind speed component and the turbulence level of the complete data set and of the measurements with A/D > 0.01 are compared. It can be seen, that there is a significant difference between the corresponding va- lues of the two data sets.

U Wind speed arallel t o cable in ds

Fig.12: Vibration amplitude versus longitudial wind velocity and turbulence level

B All measurements

1 Measurements with A/D > 0 .01

66.0

mean value std.dev mean value std.dev. Wind speed (component Turbulence level parallel t o cable1

Fig.13: Influence of the longitudinal wind velocity and the turbulence level

The probability of a given wind speed perpendicular to the cable leading or not leading to high vibration am- plitudes does therefore strongly depend on the two fac- tors mentioned above. This explains at least to some extent the "cloudiness" of the data in Fig.lla.

The envelope does however represent the worst case ob- served in the experiments and can therefore be compared to curves calculated using the safe borderline concept. Statistical correlations with different meteorological data may possibly give more insight.

4.3 Wind Power input

Using the envelope of the amplitude described in the previous section and the energy balance method, the normalized wind power shown in Fig.14 was calculated from the field tests.

_ _

I Fig.14: Function F(A/D)

Fig.15: Comparison between wind power input calculated from the measurements and laboratory results

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In Fig.15 the normalized wind power inputs previously obtained and based on wind tunnel experiments are com- pared with the measurement results. Although the test conditions in both cases are quite different and also the turbulence levels are of a different order. the re- sults are quite similar.

The field tests therefore showed that the methods presently being used for the estimation of vibration levels in conductors of overhead transmission lines are in good overall agreement with practical observations.

5. CONCLUSION

In this paper. first a short review is given of the energy balance method used in the computation of the amplitudes of aeolian vibrations in conductors of overhead transmission lines. It is pointed out, that the wind power input obtained from wind tunnel experi- ments should be verified for an actual line.

Field tests carried out in Buren in a completely automated test station are described. From these measu- rements the wind power input in an actual transmission line is estimated. A comparison with results from wind tunnel data is carried out. This corroborates the method now being used for the calculation of aeolian vibrations in transmission lines, so that it can be used in the future with more confidence. In addition the field tests showed that the wind power input strongly depends on the turbulence level and the compo- nent of the wind velocity parallel to the cable.

The authors thank the Deutsche Forschungsgemeinschaft for their support of this work.

c11

121

c31

c41

c51

C6l

c71

CSl

6. REFERENCES

EPRI; Transmission line reference handbook, wind induced conductor motion, Electric Power Research Institute, Palo Alto, California, 1979

HAGEDORN. P.; On the Computation of Damped Wind- Excited Vibrations of Overhead Transmission Lines, Journal of Sound and Vibration 83 (19821, 265-27 1

HAGEDORN, P.: KRAUS. M.; Vibrations of Overhead Transmission Lines: Computations and Experiments, Proceedings of the European Conference on Mathe- matics in Industry (ECMI), Glasgow, 1988

FARQUHARSON. F. B.; Mc HUGH, R. E.; Wind Tunnel Investigation on Conductor Vibration Using Rigid Models, IEEE Transaction Paper October 1956. 87 1-877

DIANA. G.: FALO3. M.: On the Forces Transmitted to a Vibrating Cylinder by a Blowing Fluid, Meccanica Vol.VI, No.1. 1971

RAWLINS. C. B.; Recent Developments in Conductor Vibration Research. Electric Products Division, Alcoa Laboratories, Massena, N.Y., 1958

RAWLINS. C. B.; Power Imparted by Wind to a Model of a Vibrating Conductor, Electric Products Division, Alcoa Laboratories. Massena. N.Y..Report No. 93-82-1. 1982

RAWLINS. C. B.; Model of Power Imparted by Turbu- lent Wind to Vibrating Conductor, Electric Pro- ducts Division, Alcoa Laboratories. Massena, N.Y., Report No. 93-83-3, 1983

ERVIK. M.: Estimating Aeolian Vibration Level Ea- sed on the Energy Balance Principle, CIGRE. Study Committee 22, WG1. 1975

KRAUS. M.; Messung der Windeingangsleistung bei wirbelerregten Schwingungen elektrischer Freilei- tungen. Diplomarbeit. Institut fur Mechanik 11, TH Darmstadt. 1987

PAF’OULIS. A.: Signal Analysis, McGraw-Hi11 Book Company, 1984

7. USED SYMBOLS

Amplitude signal Correction factors

Conductor diameter F(WD) Normalized wind power G, Autospectrum of the acceleration

K1.K2 Self-damping coefficients

L Span length Pw Power of aerodynamic forces

P,, Power dissipated in dampers

Pc Power dissipated in conductors

S Strouhal number T.T-Conductor tension

aeff Effective value of acceleration

a(t) Acceleration signal f Vibration frequency fd Dominating frequency

fS Strouhal frequency

ki Wave number

m Mean value m,n,t Exponents S

t V

xO W 17 w w .

S t&dard deviation Turbulence level Wind velocity Location of accelerometer

Displacement of conductor Vibration angle Mass densitiy Eigenfrequency

8. BIOGRAPHY

Professor Peter Hagedorn, born in Berlin, April 1941 received a doctor’s degree in mechanical engineering at the Escola Politecnica da Universidade da Sa0 Pau- Io, Brazil. He taught in Karlsruhe and Rio de Janei- ro, and as a visiting pro- fessor at other univer- sities. Since 1975 he is professor of mechanics at the TH hrmstadt. W. Ger- -Y.

Dip1.-Ing. Michal Kraus, born in Prague, May 1961 received a degree in engineering at the TH Darm- stadt. Presently he is wor- king as a doctoral student in the Institut fur Mecha- nik at the TH hrmstadt.

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Discussion

C. B. Rawlins (Alcoa, Massena, NY): I’d like to congratulate the authors for their report on a careful and innovative program. The question, whether the power balance method is well enough advanced to permit accurate prediction of aeolian vibration levels in the field, is fundamental. We like to assume that it is, but previous efforts to prove it have yielded mixed results. Reports by Tompkins et al. [l], and Diana et al. [2] are worth noting.

Part of the difficulty in validating the power balance method is that its predictions rely on two data bases, that on power from the wind and that on conductor self damping. There is a variety of sources on each of these, and there is considerable dispersion among the various sources. By a careful selection of source data on wind power and on self damping, it is possible to obtain quite a variety of predictions of the severity of vibration.

The authors have dealt with the dispersion among sources on wind power by comparing their field data with several, four, of these sources. However, they appear to have used only one source of data on self damping. It isn’t quite clear what the relationship is between the sample of conductor used to measure self damping in the laboratory, and the conductor actually in the line. Were the cables from the same factory? How long had the field conductor been in service, and was the laboratory sample vibrated for an extended period to simulate the effect of aging upon self damping? Would the authors please expand on this point?

References

[l] J. S. Tompkins, L. L. Merrill and B. L. Jones, “Quantitative

Relationships in Conductor Vibration Damping”, Trans. AIEE Power Apparatus & Systems, Vol. 1 5 , Pt. 111, 1956, pp. 819-94. G. Diana, M. Gasparetto, F. Tavano and U. Cosmai, “Field Mea- surement and Field Data Processing on Conductor Vibration (Com- parison between experimental and analytical results)”, CIGRE, Proc. ofthe29th Session, Paper No. 22-11, Sept. 1982.

Manuscript received July 25, 1990

M. Kraus, P. Hagedorn (Institut fuer Mechanik 11, Technical University Darmstadt): It is known, not only to the authors, that there exists not only differences between wind power inputs, but also between the measure- ments of self-damping. In order to minimize the possible error in the measurement of self-damping the sample of conductor used for the mea- surement was cut from the transmission line not far from the location where the measurements of wind power input were taken. Therefore the conductor and the sample are identical. The field conductor is in use for about 13 years in the 220 kV transmission line Lippborg-Buren as an earth cable. Because of the identity of field conductor and sample no artificial aging was necessary.

The measurement of the self-damping of the conductor were carried out twice, with different samples from the cable in the vibration laboratory of Richard Bergner GmbH, Schwabach. The two measurements showed only minor differences in the measured self-damping.

Manuscript received October 19, 1990.