VOLTAGE SAG INFLUENCE ON FATIGUE LIFE OF THE DRIVETRAIN OF FIXED SPEED WIND TURBINES

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1 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. VOLAGE SAG INFLUENCE ON FAIGUE LIFE OF HE DRIVERAIN OF FIXED SPEED WIND URBINES Barinath V. 1, D. Santo-Martin an H. M. Jenen 1 1 Aarhu School of Engineering, Aarhu Univerity, Dalga Avenue, Aarhu C, Denmark Department of Electrical Engineering, Univerity Carlo III Mari, Spain vb@age.k ABSRAC Occurrence of voltage ag ue to electrical gri fault an other network iturbance generate tranient of the generator electromagnetic torque which reult in ignificant high tree an noticeable vibration for the win turbine mechanical ytem an may alo have a etrimental effect on the fatigue life of important rivetrain component. he high penetration of win energy in the electrical gri eman new requirement for the operation of win energy converion ytem. Although fixe pee win turbine technology i nowaay replace by variable pee win turbine. In ome countrie (Spain an Germany) with high win energy penetration it i manatory or uner bonu to retrofit thee fixe pee win turbine an provie rie through capability. An electro-mechanical moel i built to imulate the gri iturbance that eaily excite the aynchronou generator poorly ampe by the tator flux ocillation which caue high tranient of the generator electromagnetic torque. hi paper focue in etimating the reulting ignificant tree tranient ue to the electromagnetic torque tranient, which tranmit to the win turbine mechanical ytem that may have a etrimental effect on the fatigue life of rivetrain component. he capability to imulate thee phenomena i a novel apect in the preent effort. Keywor: moel, voltage ag, win turbine, rivetrain, fatigue life, aynchronou generator, win energy converion ytem. INRODUCION Due to increaing environmental concioune, renewable energy ha regaine interet. Among the everal renewable energy ource being explore, win energy i one of the promiing ource. he win inutry, in particular, ha een an unquenchable eman a a reult, an the nee for reliable an afforable win turbine now i all the more apparent. Unfortunately, recurrent rivetrain failure have characterize the inutry an have prevente turbine in achieving their intene - year eign life. he component mot reponible for owntime i the gearbox [1]. Gearbox replacement an lubrication account for 38% of the part cot for the entire turbine ytem []. hi ituation call for the implementation of new an avance imulation technique to be integrate into the gearbox-eign proce o that thi component can meet it intene eign life. In many countrie like Germany, Spain, etc., new gri coe have been etablihe [3, 4, 5] emaning new win farm to behave a conventional power plant. One of the main requirement etablihe in thee new gri coe i the o-calle win turbine low voltage rie through (LVR) capability. hi pecification aim to improve tranient tability in a power ytem with a high penetration of win energy by guarantying that the win turbine remain connecte when voltage iturbance appear while atifying certain reactive power requirement. hi LVR requirement i well etablihe for the new variable pee win turbine equippe with power electronic converter but recently ue to the high win energy penetration in ome countrie i being applie to oler fixe pee win turbine (FSW) a hown in Figure-1 like in Spain or Germany what implie to retrofit them to provie the LVR capability. Mot of the tuie concerning LVR have been focue on the electrical or control ytem while neglecting or implifying the mechanical component. Unfortunately gri iturbance eaily excite the aynchronou generator poorly ampe tator flux ocillation which evelop the tranient in electromagnetic torque that affect the whole rive train component. Figure-1. Simulation tructure of the fixe pee win turbine ytem with active tall. Conierable reearch ha been one on riethrough capability of win turbine. Mot of thi reearch, however, ha been one uing relatively imple mechanical an aeroynamic moel of win turbine that neglect a number of ignificant characteritic from mechanical point of view. It i very important to tuy both the electrical an mechanical apect of win turbine imultaneouly, ince an electrical network iturbance uch a voltage ag can affect mechanical performance by the torque tranient which may have a etrimental effect on the fatigue life. 16

2 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. Since the aim of the tuy i to imulate the impact of the voltage ag impact on the etrimental effect on the fatigue life of rivetrain component uner variou operating conition. A computational moel wa built in MALAB/Simulink [6] environment which contain the etaile electrical an mechanical ytem of a win turbine. hi computation moel i expecte to provie the overall accuracy neee uring the eign, evelopment, teting, an eployment by coniering the interaction apect of the Win turbine ytem in repone to the voltage ag uring the gri iturbance. WIND URBINE MODEL DESCRIPION Generator moeling Applying the tanar moeling aumption of linearity to the magnetic circuit an inuoial itribute tator wining, the general complex vector moel of an inuction machine (IM) in the ynchronou reference frame can be expree a: φ u = Ri+ + jωφ t φr = Ri r r+ + jωφr t φ = Li + L i m r φ = Li+ Li r m r r where u i the tator voltage; i an rotor current; linkage; L r L L, i r (1) are the tator an ϕ an ϕr are the tator an rotor flux L r are the tator an rotor an inuctance;, are the tator an rotor leakage inuctance; r R are the tator an rotor reitance, repectively; the gri pulation an the lip parameter. R, ω i Figure-. Inuction Machine equivalent circuit of the ynamic moel in aynchronou reference frame (-q). hi moel can be written in the following matrix form: φ R i 1 φ u = jω t φ R + r r i r φr 1 i L Lm φ = i L r m L r φ r A each complex equation tan for two real one, thi vector form can be expane eaily. hee algebraic-ifferential equation () can be expree a a tate variable moel of fluxe (3) with U a an exogenou or perturbation variable: Ψ = Aφ () t Ψ+ U (3) t he homogeneou time varying linear ytem aociate to (5) i: Ψ = Aφ () t Ψ (4) t he time-variant an complex coefficient matrix A ϕ can be approximate by: RL r RL m R jω jω σll r σll r L Aφ = (5) RL r m RL r Rr jω σll r σll r L Where L () i the average value of tator an rotor leakage inuctance? When ubtituting the tator an rotor reitance by an average value R the matrix A ϕ can be again approximate by: A φ R R jω L L R R jω L L he aynchronou generator ynamic can be characterize by the time-varying linear moel (5) in the homogeneou form or by (3) when coniering iturbance. hi moel can be linearize at the equilibrium pointψ, an being coniere, locally, a a timeinvariant ytem (7). Ψ = ( Aφ) Ψ = A t Ψ φ Ψ (7) (6) 17

3 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. Dynamic analyi he olution to equation (7) can be evelope in term of the known tate-tranmiion matrix that in thi cae take the form of the matrix exponential function in the time omain an when uing the Laplace tranform yiel in: Aφ t () t e () Ψ = Ψ 1 aj( I Aφ ) Ψ () = ( I Aφ ) Ψ () = Ψ() I A φ he root of the characteritic equation I A ϕ, calle alo Eigen value of the homogeneou ytem or pole of the tranfer function within the frequency-omain, characterize locally the ynamic behavior of (7). From (6, 7) calculating the root of λi A ϕ it can be prove that the eigen value of the ytem can be approximate by the iagonal term of the matrix: R λ1 L R λ L jω jω Figure-3. Example of pole location of the linearize inuction machine moel while changing the lip parameter. he tator of the IM i irectly couple to the gri an unfortunately any gri iturbance eaily excite the poorly ampe tator flux pole (Figure-3). he electromagnetic torque of the generator i a calar value [7] which ynamic epen only on the tator an rotor flux, being given by (9) an hown by Figure-3 that the former are poorly ampe: e (8) (9) 3 L 3 * m Lm elec = Pp φr φs = Pp Im( φr φs ) (1) σll σll S R S R Where P the number of the generator pole i pair; Im i p the imaginary part of the calar prouct of the two vector an leakage coefficient iσ = 1 -L (L L ). m r Drive train moeling In the current invetigation the ource of iturbance i the generator torque ue to the gri iturbance that caue the voltage ag an ince the application of more ophiticate aeroelatic moel are not ue an the emphai ha been given more towar the tuy of etrimental effect on the life of gear box ue to the network iturbance that caue the electromagnetic torque tranient. he aeroynamic torque on the rivetrain of a Win urbine (W) varie continuouly over the time ue to the proper unteay an non-linear characteritic of the complex aeroynamic; thi aeroynamic torque i mae contant in the preent tuy. he electrical generator run in a relatively high pee compare to the aeroynamic rotor. In the rivetrain a low pee haft (LSS) in the rotor ie are connecte to a high pee haft (HSS) in the electrical generator ie by uing a gearbox. Real intallation are continua with infinitely egree of freeom, but a etaile invetigation with a reuce number of DOF i, a a rule, entirely ufficient for analyzing ynamic behavior. Conequently, it i enible to look at a mathematical moel that reflect the relevant feature of the real technical ytem a accurately a poible. Any retriction on movement (linkage) between the boie are realize with joint with pecific propertie. Such mechanical ytem are ecribe mathematically by couple orinary ifferential an algebraic equation. Mathematical moeling of the rivetrain ytem he repreentation of the rivetrain containing the gear box an an ieal rotor moel i hown in Figure-4. In thi moel the next conieration were mae: rotor, gear an LSS are rigi boie an HSS i flexible. he tangential velocity vector at the contact point for the firt gear expree in the bae of the fixe reference frame i: N { ( ) ˆ } { ˆ } () v1 = ω1 r1 = q& 1 t n3 r1n1 = q& 1 t r1ˆn (11) q& r 1 1 Where an are the angular velocity an the raiu of the firt gear. he tangential velocity at the contact point for the econ gear i expree in the bae N : { ( ) ˆ } { ˆ } ( ) v = ω r = q& t n3 rn1 = q& t rˆn (1) q& r Where an are the angular velocity an the raiu of the econ gear. 18

4 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. Figure-4. Dynamic repreentation of W rivetrain. At the contact point the tangential velocity mut to be equal for both gear ( v1 = v ), an the contraint relation i: q& () t r + q& () t r = q& ( t) = n q& ( t) (13) 1 1 g where ng = r1 r i the gear ratio. he kinetic energy for the ytem can be expree a: = I q () t I q () t I q () t ( L) q () t I ( ) q ( t) ( ) q ( t) & ψ + η + ψ η & & & & & η (14) haft 3 L Where q& 3 i the angular velocity panne by the hape function ψ over all the haft length? I 1, I an I 3 are the rotational inertia for the rotor an gearbox, an the generator, repectively. An I haft i the haft rotational inertia itribution per unit length. he potential energy for the ytem can be expree a: L 1 = haft 3 ( ) ( ) ( ) (15) U GJ η ψ η q t η Where GJ haft i the haft torional tiffne itribution per unit length? By uing Lagrange equation, virtual work principle for external an amping loa, the contraint relation an auming ψ ( η) = η L compatible with the haft bounary conition relative to the rigi boy movement an contant haft ection an propertie, the equation of motion for the ytem [8,9] are: [ M ]{ q } + M & + D { q } + [ K ]{ q } = { F } && & (16) Where { q } i the configuration vector which contain the generalize coorinate,[ ] M i the ma matrix, M & i the firt time erivative of the ma matrix, [ ] D i the 19

5 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. amping matrix, [ K ] i the tiffne matrix, an { } F i the vector of generalize force. he intervening vector an matrice in the equation of motion (16) are expree in etail a below: { } = { q q } 1 3 q (17) [ M] ( ) ( ) ( 3 ) 3 I1+ ng I + I3 + IhaftL ng I3 + IhaftL = (18) ng I + IhaftL I + IhaftL I& 1 I& 1 M & + D = + = D (19) haft Dhaft [ K] { } = GJ haft L = aero g gen gen n elec () F (1) Where D i the HSS amping,, an are aero aeroynamical, generator an electromagnetic torque, repectively. An I & 1 i the firt time erivative of I 1 which varie a the pitching angle of the blae change. gen elec ORQE RANSIENS IN HE DRIVERAIN DURING HE HREE PHASE BALANCED VOLAGE SAG he voltage ag i characterize by the intantaneou rop in the magnitue of the generator torque ue to an electrical gri failure, hort circuit, overloa or tarting of large motor an tranformer energizing [1]. A a conequence, the pretenion of the rive train i lot an large ynamic ocillation occur. hee iturbance are uually name a low-frequency tranient. he voltage ag event are choen uring the rate operating conition in orer to emontrate the nonlinear character of the torque tranient' amplification within the rivetrain. SUDY CASE he application coniere inclue fault. he emphai i place on the evelope torque tranient an their propagation up-tream of the rivetrain to tuy the impact of the over-current or over-voltage conition that may arie for hort uration of operation thoe are le harmful for quirrel-cage inuction machine. he wortcae cenario (fault electrically cloet to the W, minimum fault impeance, W operating at rate power), are tuie in orer to ae the maximum tree evelope. For thi reaon, any protection of the W (over-/uner-voltage, over-/uner-frequency, over-pee, over-current, phae unbalance) are alo ignore, coniering the W fulfill the low voltage rie through capability. hi i in accorance with [11], where loa cae of imultaneou electrical an W protection ytem fault are inclue. Figure-5 preent the rivetrain torque for a choen voltage ag event with a everity of.45 pu for a win pee of 1m/ (rate power) hown in Figure-5(a). Figure-5(b) how the normalize electromagnetic torque exhibit high tranient uring the voltage ag event. During the event a utaine torque ocillation are oberve, ue to the interaction of the air-gap magnetomotive force (MMF), iminihing graually. With current generator parameter ue in the tuy (Appenix 1) how maximum amplitue of 4.5 time the rate torque [1]. he propagation of the torque tranient in the rivetrain i etermine by it torional characteritic. Due to conieration of the flexible haft between the gearbox an the generator with a conierable amping the torque tranient are not impacte a uch in the up-tream. hi tranient i completely filtere out by the elaticity of the high-pee ie before reaching the high-pee ie of the rivetrain. Figure-5(c) how the tranient that are tranmitte to the rivetrain uptream are till have a conierable impact. he rivetrain experience a torque pike, approximately ouble the rate torque a hown in Figure-5(c), ying out in le than 1 m., it i intereting to note, that the larget torque tranient o occur uring the voltage ag event that tranmit from the flexible haft to the rivetrain ytem. From Figure-5(b) an (c), it i the flexible haft which i coniere in the current imulation illutrate the reuction in the ocillation of the rivetrain ignificantly an mitigate fatigue amage to certain extent to the rivetrain. Still ome of the ocillation tranmit to the rivetrain ytem hown in Figure-5(). hee torque tranient that are etecte numerically will provie a brief view on the etrimental effect of the fatigue life of the rivetrain ue to voltage ag that arie uring the network iturbance of the W ytem uring normal operation. 11

6 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. Figure-5. Network iturbance at win pee 1 m/ with lowet phae voltage of.45 pu. (a) Voltage Sag event. (b) orque on High-pee haft. (c) Electromagnetic torque fluctuation. () orque on Low-pee haft. FAIGUE EVALUAIONS In wiely ue eign practice of gearboxe, fatigue evaluation are bae eentially on the time hitory of the Low-pee haft torque on the rotor ie. hi practice of eign i of only limite preciion which may lea to the over-eign or uner-eign of the component in the rivetrain ytem of the W. It i very evient from the torque tranient in the Figure 5 an 6. From the preent tuy a better loa pectra for the overall rivetrain ytem can be obtaine, that can be later ue in tuying the etrimental effect of the fatigue life uner unexpecte ervice loaing conition viz. voltage ag. However, a novel approach i aopte in the preent tuy that only etimate the correct loa amplitue een by rivetrain a ytem, but not the aociate loa frequencie. hi methoology can be implemente to etimate the component wie (Stage wie of the rivetrain ytem) loaing hitory to have an accurate etimation of the etrimental effect on the life of the rivetrain ytem which i not in the interet of the preent tuy. Voltage ag occurrence Accoring to [13] the voltage ag frequency can be emontrate by the number of event a a function of ag voltage in percent of nominal a hown in Figure-6, which ecribe the expecte number of unafe an troubling hutown a a function of voltage enitivity. 111

7 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. Figure-6. Number of event a a function of voltage ag magnitue. In the preent tuy it i coniere a location with 1 event per year at 8 % of nominal voltage. hi cenario i alo coniere in [13] an match with the contribution from each voltage ytem (345 kv, 3 kv, 138 kv, 69 kv) an for each of the form ag magnitue range (phae-to-groun, phae-to-groun, phae-tophae an 3 phae). Etimating the etrimental effect on rivetrain fatigue life he loaing pectrum on the low-pee ie (rotor ie) of the rivetrain i obtaine by extracting Rain Flow Counting (RFC) of the overall loaing hitory uring the voltage ag event. ypical proceure ue for fatigue life aement uner obtaine ranom loaing on the rivetrain uring the voltage ag event are implemente to perform thi tak. he etimate tre hitory from the ranom loaing hitory a hown in Figure-7 i ubjecte to the rainflow cycle-counting metho, which allow in etermining the amplitue an meaning value of counte cycle, their occurrence moment an time of uration a hown in Figure-8. Influence of the tre mean value wa taken into conieration with the Marrow tre-life characteritic [14]. 11

VOL. 6, NO. 3, MARCH 11 ISSN 1819-668 6-11 Aian Reearch Publihing Network (ARPN). All right reerve. Figure-7.

8 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. Figure-7. Stre hitory that are encountere uring the voltage ag event. Figure-8. Etimate Rainflow matrix of the tree regitere uring the voltage ag event. 113

9 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. On the aumption of the linear Palmgren-Miner hypothei of amage accumulation an the tre-life fatigue characteritic of the material, the amage-time function wa etermine. he loa egment, where the influence on the material fatigue wa ignificant, were etermine on the bai of the fixe amage-intenity level. he mean an the amplitue of the tre hitory ( σ an σ ) are etimate in orer to calculate the ai amage D i mi caue by the torque tranient uring the voltage event by the following equation. ni Di = () N ( σ, σ ) Where n i fi ai mi i equal to 1 for a cycle an.5 for a half cycle, N fi( σ ai, σ mi) i the function returning a number of cycle to failure accoring to the amplitue σ ai an the mean value σ mi that form the etermine tre cycle an the fatigue characteritic of the material which can etimate by well known Marrow tre-life characteritic. ' ( )( b σ = σ σ N ) (3) a f m f N fi Where 1 σ ai = ' σ f σ mi 1/ b (4) ' σ f the fatigue trength coefficient an b i the fatigue trength exponent. o itinguih the amplitue an the mean value of the ranom hitory the cycle count i performe at the time of voltage ag event which i fixe time interval. Computation of the fatigue amage caue by the coniere loaing interval i uually realize with the aumption of hypothei of the linear fatigue amage accumulation. he wiely ue Palmgren Miner hypothei aume that the total amage occurre per voltage ag event can be expree a the um of particular amage caue by itinguihe cycle a hown in Figure-9. k i (5) i= 1 D= D k Where i the number of cycle that are calculate from the ranom loaing hitory? Coniering the event per year of normal operating conition of the W the etimate accumulate amage for a pan of year of ervice life i given by Figure-9. Damage value for the particular cycle. D N N* D = (6) In the current invetigation the number of event of the voltage ag per year i coniere to 1. he expecte life time coniering the voltage ag that are 114

10 VOL. 6, NO. 3, MARCH 11 ISSN Aian Reearch Publihing Network (ARPN). All right reerve. etimate from the accumulate amage D that caue by the itinguihe cycle in time interval of i given by. D = (7) From the ummary of invetigation an the calculation there i expecte impact on the current fatigue life coniering the gri iturbance how a conierable reuction, aroun 1%, of the fatigue life i expecte. CONCLUSIONS In thi paper, the torque tranient that evelope in the rivetrain of a W ue to electrical iturbance have been analyze, for a gri connecte, contant pee W. he quantitative reult of thi current invetigation are not necearily repreentative of other W [15, 16], ince they epen critically on the rive train torional characteritic, a well a on the generator parameter. However, the imulation reult preente provie a clear inication of the effect of variou abnormal operating conition an a comparative evaluation of their everity. From the current invetigation on the etrimental effect of fatigue life ue to electrical iturbance a methoology i propoe for etermining the fragment of ervice loaing that trongly influencing the material fatigue i a goo tool for preparation of fatigue tet on the W ytem at the early eigning tage. hi approach can be extene to tuy the effect of electrical iturbance on rivetrain ytem in component wie by etimating loaing hitory an their regitere ervice hitorie which help to have a better eign an tet etup conieration or while preliminary preparation for further proceing. A hortene ervice hitory ha the ame frequency characteritic a the ervice hitory, an it i an important avantage of the metho. Appenix-1 1. Drivetrain Specification ue in Simulation Ratio 1:84.3 Mechanical power 18 kw. Generator Specification ue in Simulation Rate power Slip at rate power Voltage U N 165 kw SN x 6 V he coniere generator parameter in p.u. are.48, L =.148, REFERENCES R r =.44, L r =.1791 R = [1] Win urbine Data Summary able Win Stat Newletter (1-4). 7. (1). [] C. Walfor. 6. O an M Cot Moel Quantifying the Influence of Reliability, Win urbine Reliability Workhop. Global Energy Concept Seattle, WA. cwalfor@globalenergyconcept.com. [3] C. Jauch, J. Matevoyan,. Ackerman, S. Bolik. 5. International comparion of requirement for connection of win turbine to power ytem. Win Energy. 8(3). [4] 7. Spanih Royal Decree RD 661/7. BOE. [5] 7. German ranmiion Coe, Vn. [6] H. Klee, Simulation of Dynamic Sytem with MALAB an Simulink. CRC Pre. [7] D. W. Novotny,. A. Lipo Vector Control an Dynamic of AC Drive. Oxfor: Clarenon Pre. [8] J. F. Manwell, J.G. Mc Gowan, A.L. Roger.. Win Energy Explaine: heory, Deign an Application. Chicheter, NY: Wiley. [9] H. Baruh Analytical ynamic. McGraw Hill. [1] R. A. enenbaum. 4. Funamental of applie ynamic. Springer-Verlag. [11] H. J. Bollen Math.. Unertaning Power Quality Problem: Voltage Sag an Interruption. New York: IEEE Pre/Wiley-Intercience. [1] IEC 614-1, Win urbine Generator Sytem- Part 1: Safety Requirement, n Eition. [13] 7. Stanar IEEE (Chapter 7). [14] ASM E , 1997, Stanar practice for cycle counting in fatigue analyi. Annual Book of ASM Stanar. 3(1): Philaelphia. [15] R. Faaeineja, G. Mochopoulo. 8. Invetigation of Voltage Sag Impact on Win urbine ower Vibration. Win Energy. 11(4). [16] J. Martinez-García, J.A. Dominguez-Navarro. 8. Behaviour Improvement uring Fault of Fixe Spee Stall Control Inuction Generator Win urbine. Win Energy. 1(6). 115

Compensation of backlash effects in an Electrical Actuator

Compensation of backlash effects in an Electrical Actuator 1 Compenation of backlah effect in an Electrical Actuator R. Merzouki, J. C. Caiou an N. M Siri LaboratoireeRobotiqueeVeraille 10-12, avenue e l Europe 78140 Vélizy e-mail: merzouki@robot.uvq.fr Abtract