Lightning Protection Optimization for Large Wind Turbines with Method-of-Moments

Transcription

1 Lightning Protection Optimization for Large Win Turbines with Metho-of-Moments Florian Krug, Ralph Teichmann General Electric - Global Research Freisinger Lanstrasse 50, Munich, GERMAY Ulrich Jakobus, iels Berger EM Software & Systems GmbH Otto-Lilienthal-Str. 36, Böblingen, GERMAY Hans Steinbigler, Josef Kinersberger Laboratory for High Voltage Technology an Power Transmission, Technische Universität München Arcisstr. 21, München, GERMAY Abstract: - Electro-magnetic fiels ajacent to the lightning current path in win turbine generators are analyze. The metho of moments is use to analytically escribe the transient istribute electro-magnetic fiel cause by a lightning strike. A simulation tool using the metho of moments is presente. The electromagnetic fiel istribution uring a lightning strike in a win turbine hub is analyze in etail. The electromagnetic fiel analysis is extene by a statistical lightning risk evaluation for win turbine generators. Key-Wors: - Lightning protection, Metho-of-Moments, Win turbine, Power System, Risk Analysis, Electro-magnetic Fiel 1 Introuction Lightning strike effect on win turbine generators have recently become a major concern as the number an the height of win turbines continue to increase. The impact on win turbines range from isturbances on control electronics, amages to single components, such as blaes or electronic components, to fires resulting in a complete loss of the installation. Most of these effects result in unesirable owntimes with its financial implications for the win turbine operator. Further costs are ae if components nee to be replace. Lightning strike risk analyses for common structures are establishe proceures to ientify sensitive areas an etermine the probability an severity of amages cause by lightning strikes. Simple methos [3] an more sophisticate proceures [4] were introuce. Specific guielines an recommenations to assess an mitigate the risk of lightning amage for win turbine generators [1] [2] were presente by various international technical committees such as IEC or IEA. These recommenations focus on provision to safely conuct the lightning current thereby avoiing substantial amage. The electro-magnetic implications cause by the large transient lightning currents on control electronic components ajacent to the lightning current path have not yet been iscusse. This paper presents an analytical metho an a tool suitable for the analysis of irect lightning strike effects on sensitive electronic components in a win turbine generator. The simulation results for the electric an magnetic fiel istribution uring a lightning strike in a generic hub of a large win turbine are presente. 2 Risk Analysis An important initial step of a risk analysis is the estimation of the frequency of irect strikes to the win turbine. This frequency is mainly a function of the lightning activity at the installation site, the local geographical topology an the imensions of the turbine. The proceure of the estimation is escribe in [1] an [2]. It is base on investigations an experiences with common structures up to a height of 60 m. As an example a win turbine with three rotor blaes, a hub height of 100 m an blae length of 38.4 m is use. An offshore location with a istance of more than three times the total height of the turbine to the next turbine is assume.

2 The annual average number of irect lightning flashes to the win turbine can be assesse by the following formula: (1) 6 = g A C10 where g is the annual average groun flash ensity (1/(km 2 a)), A is the average collection area of irect lightning strikes (m 2 ) an C is the environment factor accoring to [1]. Data on the annual average groun flash ensity are given in stanars on lightning protection, e.g. in [5]. For example for a offshore installation site near the German orth Sea coast g is approximately 0.75 (1/(km 2 a)) [5]. The average collection area A for a win turbine place on a flat groun is calculate to be the area of a circle with a raius of three times the turbine height [1]. For the calculation of A reference [1] recommens the moeling of the turbine as a tall mast with a height equal to the hub height plus one rotor raius: h = = m (2) The average collection area of irect lightning strikes amounts to: ( 3h) π = ( ) = m A = π (3) The assumption that the win turbines are separate by a istance of more than three times the height of the turbines results in an environment factor C = 1. With the calculate values for g, A an C the annual average number of irect lightning flashes to the turbine is given by: = = 0.4 (4) a This means that the win turbine is hit by a lightning flash in average once within a perio of about two an a half year. A more etaile analysis shoul istinguish between upwar an ownwar lightning flashes. Win turbine generators with heights similar to this example are expose to both types of lightning ischarges. A tenency to experience a higher number of upwar flashes as the turbine height increases has been note. A nee for further ata of lightning flashes to win turbines, e.g. ata of lightning flashes to very high structures with moving parts, clearly exists. The estimation of the frequency of irect lightning flashes to the win turbine is a first step of a risk analysis. The next step is an investigation as to whether the lightning protection system being installe is sufficient. The consierations for this step of the risk analysis are base on the fact that not every lightning flash to the turbine causes amage, epening on the efficiency of the lightning protection system. In [1] a failure of the lightning protection system is calle a critical event. The permissible number of such critical events c per year can be calculate as follows: c ( E) 1 (5) with the efficiency E of the lightning protection system. This efficiency is correlate with the protection level efine in [1]. It can be calculate with the formula: c E 1 (6) For the permissible number of critical events the value c = /a is recommene in [1]. Using this value the efficiency of the example win turbine is: 3 10 E 1 = (6) 0.4 In [1] four levels for lightning protection systems are efine in accorance with [3]: level I through level IV. Accoring to [1] for the calculate efficiency E a protection level I is necessary with the following lightning current parameters: peak current 200 ka, average rate of current rise 200 ka/µs an total charge transfer 300 C. These ata are the basis for testing an simulation calculations for the lightning protection system of the win turbine generator being consiere. Further steps of the risk analysis must be carrie out for the ifferent areas of the system. Sensitive areas with a high risk of amage are for instance the rotor blaes an areas with control systems. Lightning amage statistics show that more than 50 % of amages occur in controls systems of the win turbine [6]. A highly sensitive component of the win power turbine is the pitch control system for the control of the blae angle. It is locate within the hub ajacent to the lightning current path. In orer to calculate the risk of amage for the components of this pitch control system it is necessary to etermine the electromagnetic fiel istribution insie the hub. This fiel istribution epens on the lightning current path from the point of impact to the groun an specifically on the lightning current istribution on an near the hub.

3 3 umerical Analysis There are few numerical methos to analyze the electro-magnetic impact of a lightning strike on a certain component within a complex mechanical structure. Each approach has its specific avantages. Time-omain approaches offer the opportunity to incorporate hysteresis effects an to calculate an impulse resonance irectly in time-omain. Frequency omain approaches can hanle frequency epenent material parameters an can exactly account for the infinite space. In this paper the metho of moments shall be introuce to perform these specific calculations to reuce the moel to conucting elements only. 3.1 The Metho of Moments The metho of moments (MoM) is a current-base numerical technique to first erive the current istribution on a meshe moel an to euce all other quantities (e.g. the nearfiel istribution) in a secon step. The MoM belongs to the integral equation methos base on the etermination an superposition of all fiel sources. Multiple istribute sources are exciting the set-up an inucing/influencing currents an charges on the metallic structure. The electro-magnetic effects of all sources are superimpose with the original fiel. Fig. 2: Wire segment basis functions an their weighting functions. For each connection between the iscrete elements (triangles for surfaces an segments for wires) a basis function has to be efine, which realizes the galvanic contact an escribes the current I e an charge at a given element (7) The triangular basis function g n (linear approximation of the current istribution) for the segment interconnections (noes) can be seen in Fig. 2. The segments an the expansion coefficients β n are unknown in (7) an have to be etermine. There are analogous basis functions an expansion coefficients for the connection between triangles (eges) an between segments with triangles (connection point) as shown in Fig. 3. The RWG (accoring to Rao-Wilton- Glisson [8]) basis functions are use in this case for the metallic eges.. Fig. 1: Scattering of waves with metallic an ielectric boies. Therefore only metallic structures carrying these sources (currents an charges) have to be consiere (see Fig. 1) an structure into iscrete elements. Wire structures are meshe into segments an soli structures are meshe into a triangular surface boy. 3.2 The Computer Coe FEKO The program flow of the computer coe FEKO [7] shall be use to escribe in etail the metho of moments. Fig. 3: Basis functions for triangular connections (eges) an connection points between segments an triangular patches. The electro-magnetic problem solver has to evaluate a set of unknowns (representing either the fiels or the sources) from a set of linear equations at a given excitation. In the metho of moments the set of linear equations is base on a number of bounary conitions (e.g. electric fiel is perpenicular to perfectly conucting structures, charges can be erive from the currents with the continuity equation) an a number of transformation equations (e.g. Greens function G ( r, r ) ),

4 which escribe the relation between a source element an the fiel strength or the coupling between two source elements. with the basic frequency f 0. The time-omain function or equivalent signal is given by (10), e.g. at the iscrete time sample t k = k T 0= k / ( f 0). u k = 1 1 ( ) V ( l) e l= 0 j2πklf0 / k (10) (8) These transformation equations (e.g. in (8) with the relation between the scattere electric fiel an all electric an magnetic line an surface currents) are integral equations. Therefore this metho belongs to the integral-equation methos. A harmonic approach is neee to replace the time-erivative by jω with the angular frequency ω. To enable a set-up an solution of these linear equations the linear equations have to be solve numerically. The resulting expansion coefficients irectly give the current an charge istribution on the iscrete elements of the structure. This calculation is a solution for a single frequency (time-harmonic continuous-wave (CW) signal) an can be repeate for a number of frequencies to etermine the frequency response of the system. This can be calle a filter. 3.3 Aitional Moules of FEKO The electro-magnetic coe FEKO has been selecte as the best choice to solve this problem because it combines the three main avantages, MoM base solver well fitte to this stuy with mainly conucting structures only Built-in Fourier-Transformation for time omain analysis Built-in optimizer for moel parameter optimization. In aition to metallic surfaces, also ielectric boies or non-perfect materials (e.g. finite conuctivity, skin effect etc.) can be consiere within the MoM framework. The Fourier-transform an the optimisation feature shall be escribe in etail below. The iscrete Fourier transform or spectrum V(l) for a time-omain signal u(k) is given in (9) e.g. at the iscrete frequency f l = l f 0 V ( l) = 1 k= 0 u( k) e. j2πklf0 / l (9) with the sampling perio T 0=1 / ( f 0) an is the number of samples. A system must be known in time-omain or in frequency omain with its impulse-response (shape, uration) or its filter characteristic (banwith an its resonance), respectively. A signal shall be known in timeomain or in frequency omain with its shape or with its spectrum, respectively. If the impulse response of a system has a finite uration T sys, a pulse signal with a pulse perio larger than T sys can be consiere. The system response can be escribe by the response of a single impulse or vice versa. FEKO uses this characteristic to solve timeomain problems using impulses by extening this to a pulse signal an by a iscrete sampling (relate to the pulse perio) of both spectrum an signal. For the time-omain analysis using impulse or pulse signals, mainly three ifferent cases can be specifie: a. All-pass behavior: The spectrum of the signal is very narrow compare to the banwith of the so-calle filter or system. This leas to a simple elay an attenuation of the impulse or pulse. b. Filter-behavior: Both the signal spectrum an the system banwith are in the same range. This leas to the necessity to combine the spectrum with the filter characteristic of the system an to apply an inverse Fourier transform to get the impulse or pulse response. c. Dirac-impuls behavior: The signal spectrum is very wieban an particularly constant in the pass ban of the system. The impulse s shape is simply the impulse response of the system scale with the signal energy of the single impulse. The yquist criterion has to be applie to sample the spectrum up to a maximum frequency f 0 > 2fmax of twice the signal banwith f max. It is also applie sample the spectrum with a pulse perio frequency f 0 corresponing to the uration T sys < T 0 of the system impulse response: (11)

5 To approximate the shape of a lightning stroke (on bottom of Fig. 4) a number of preefine pulse shapes can be chosen as excitation in FEKO, e.g. a ramp function or a ouble logarithmic shape (as given in equation (11) an the lower part of Fig. 4). Fig. 4: Double exponential impulse shape (top) for time omain analysis of a lightning stroke (bottom) For a rise time of T 1 = 10 µs an a fall time of T 2 = 350 µs the time constants can be set to τ 1 = µs an τ 2 = 5.45 µs. In FEKO the impulse shape an its spectrum can be combine with the filter characteristic of the system sample by FEKO in frequency omain. The program coe FEKO has a built-in inverse Fourier transformation allowing the calculation of the resulting impulse (or pulse) response of the quantity being specifie. This approach is neee for the cases b. an c. where the entire frequency response of the system must be calculate. In the case being consiere the geometry is very small relative to the wavelength of the highest frequency in the signal spectrum. Hence case a. is vali. It is sufficient to run only one calculation at one specific frequency e.g. at the center of the banwith of the all-pass to etermine the attenuation an elay. 3.4 Parameter Optimization Another avantage of the software package FEKO is the possibility to efine nearly all-geometrical an electro-magnetic parameters as a variable. The value of such a variable usually has to be fixe for one calculation. The values of istinct variables an the settings of subsequent calculations can be embee into an optimization proceure, such that the value (or a set of values) of one ore more quantities from the output-file from FEKO can be extracte to calculate an aim-function. This can be use in conjunction with a stanar optimizer (e.g. conjugate graient or simplex algorithm) to etermine a next value for the istinct variables. FEKO has a built-in-moule for such optimizations for a number of preefine aim-functions among which are gain, pattern, impeance matching or fiel-strength shaping. FEKO also allows the user to embe it into a user-efine optimization algorithm (e.g. written in MATLAB/Simulink) to perform specific moel optimizations. 3.5 Limitations FEKO is a frequency omain solver an cannot take into account a hysteretic behavior of the ferrite boy. This problem can be aresse by some worst-case stuies in the frequency omain, however, a goo knowlege of the materials an their influence on the current istribution is require. The frequency omain approach will also not allow an analysis of the influence of specific circumstances such as a shorting of the lighting strike by a burne insulation on the shape of the impulse response. However, it is possible to etermine the maximum fiel strength at arbitrary positions enabling a etermination of the probability an the position of such an event. 3.6 Time Domain Analysis The transition from a harmonic CW-signal to a pulse or impulse signal can be performe in both the frequency omain (using a spectrum or spectral ensity) an the time omain (using the signal shape). The main requirement for such an approach is the linearity of the system. The Fourier transformation is commonly use to switch between these two omains. 4 Electromagnetic Simulation Results The moel in this stuy was irectly transferre from a CAD-file. In a first step the moel has been reuce to the relevant parts (e.g. without etails as are screws or aitional holers). In a secon step the reuce moel was meshe into triangular surfaces an wire segments. The cables an their en loas were entere in FEKO to set some material parameters. The etaile waveforms of the lightning currents an the corresponing magnetic fiels are of interest. With efficient measurement methos like the timeomain measurement principle [9] a eeper unerstaning of the lightning current influence on the electrical energy systems is possible.

6 4.1 Lightning Strike Current Density In Fig. 6 the current istribution for a harmonic stimulus (f = 500 khz) is shown. Material Parameter: E-GJS400-18U-LT Input: Lightning Current Fig. 5: Current istribution at 500 khz 4.2 Magnetic Fiel The result of the numeric electro-magnetic fiel simulation is shown in Fig. 7. Fig. 6: Magnetic fiel istribution 5 Conclusion The effects of lightning strikes on large win turbine generators are iscusse. Special attention is given to the transient electro-magnetic fiel istribution in areas close to the lightning current path. The metho of moments is presente as one approach to solve transient electro-magnetic fiel problems. Basic requirements are geometrical, material ata an excitation source waveform. A commercially available simulation tool was evaluate. The tool was use to specifically analyze the electro-magnetic fiel istribution in the hub of a large win turbine uring a typical lightning strike. Initial results using this approach are encouraging; the valiation of the simulation results using measurements will be iscusse in a future publication. A statistical risk evaluation metho of amages to large win turbine generators is also presente. A etaile electro-magnetic fiel analysis conucte for critical areas in the win turbine in conjunction with a statistical evaluation of the lightning strike risks serve as a founation to minimize harware amage in win turbine installations. References: [1] IEC TR , 2002/07, Win turbine generator systems, Part 24: Lightning protection. [2] IEA: Recommene practices for win turbine testing an evaluation, 9. Lightning Protection for Win Turbine Installations. [3] IEC , 1993/09, Protection of structures against lightning, Selection of protection levels for lightning protection systems. [4] IEC TR 61662, 1995/04, Assessment of the risk of amage ue to lightning. [5] VDE V , 2000/11, Blitzschutz, Risikomanagement; Abschätzung es Schaensrisikos für bauliche Anlagen. [6] Cotton, I., et al., Lightning protection for win turbines. 25th ICLP Int. Conf. on Lightning Protection, Rhoes, Greece, September [7] FEKO, software prouct of EM Software & Systems, see [8] S.M. Rao, et al., Electromagnetic Scattering by Surfaces of Arbitrary Shape, IEEE Trans. Antennas an Propagation, Vol. 30, o. 3, 1982, pp [9] F. Krug, P. Russer, The Time-Domain Electromagnetic Interference Measurement System, IEEE Trans. on Electromagnetic Compatibility, Vol. 45, o. 2, 2003, pp