Reactive Power Dispatch Method in Wind Farms to Improve the Lifetime of Power Converter Considering Wake Effect

Transcription

1 Aalborg Univeritet Reactive Power Dipatch Method in Wind Farm to Improve the Lifetime of Power Converter Conidering Wake Effect Tian, Jie; Zhou, Dao; Su, Chi; Chen, Zhe; Blåbjerg, Frede Publihed in: IEEE Tranaction on Sutainable Energy DOI (link to publication from Publiher): /TSTE Publication date: 2017 Document Verion Accepted author manucript, peer reviewed verion Link to publication from Aalborg Univerity Citation for publihed verion (APA): Tian, J., Zhou, D., Su, C., Chen, Z., & Blaabjerg, F. (2017). Reactive Power Dipatch Method in Wind Farm to Improve the Lifetime of Power Converter Conidering Wake Effect. IEEE Tranaction on Sutainable Energy, 8(2), General right Copyright and moral right for the publication made acceible in the public portal are retained by the author and/or other copyright owner and it i a condition of acceing publication that uer recognie and abide by the legal requirement aociated with thee right.? Uer may download and print one copy of any publication from the public portal for the purpoe of private tudy or reearch.? You may not further ditribute the material or ue it for any profit-making activity or commercial gain? You may freely ditribute the URL identifying the publication in the public portal? Take down policy If you believe that thi document breache copyright pleae contact u at vbn@aub.aau.dk providing detail, and we will remove acce to the work immediately and invetigate your claim.

2 Reactive Power Dipatch Method in Wind Farm to Improve the Lifetime of Power Converter Conidering Wake Effect J. Tian, Student member IEEE, D. Zhou, Member, IEEE, C. Su, Member, IEEE, Z. Chen, Senior member, IEEE and F. Blaabjerg, Fellow, IEEE Abtract In Wind Farm (WF), the mot popular and commonly implemented active power control method i the Maximum Power Point Tracking (MPPT). Due to the wake effect, the uptream Wind Turbine (WT) in WF ha more active power generation than the downtream WT at the wind direction and wind peed that the WF ha wake lo. In the cae that WT upport the voltage control by reactive power, the uptream WT power converter may have horter lifetime even below the indutrial tandard. In thi paper, baed on the analyi of the wake effect, the reactive power capability of the Doubly Fed Induction Generator (DFIG) WT and the lifetime of DFIG WT power converter, a reactive power dipatch method i propoed in the WF with DFIG WT to improve the lifetime of the uptream WT power converter. The propoed reactive power dipatch method i analyzed and demontrated by the imulation on a WF with 80 DFIG WT. It can be concluded that, compared with the traditional reactive power dipatch method, the propoed method can increae the lifetime of the uptream WT power converter. Index Term lifetime, reactive power dipatch, voltage control, wake effect, wind farm. u v C t D k X A overlap A R P Q P r Q r P GSC I. NOMENCLATURE Ambient wind peed Downtream wind peed Thrut coefficient Pitch angle Tip-peed-ratio Blade diameter Decay contant Poition of the downtream wind turbine Overlap area Blade weep area Stator active power Stator reactive power Rotor active power Rotor reactive power Active power of the grid-ide converter Thi work wa upported in part by the Sino-Danih Centre for Education and Reearch, Aarhu, DK-8000, Denmark. J. Tian, D. Zhou, C. Su, Z. Chen and F. Blaabjerg are all with the Department of Energy Technology, Aalborg Univerity, Aalborg, 9220, Denmark ( jti@et.aau.dk, zda@et.aau.dk, cu@et.aau.dk, zch@et.aau.dk, fbl@et.aau.dk). Q GSC I T m p V φ P m m r R L l L m L k r σ R r L lr L r V r I r φ r U r P T P D V ce V f E on E off E rr V dc * V dc N f f e i a T T jm_t dt j_t T jm_d dt j_d R thjc Ractive power of the grid-ide converter rm tator current Stator frequency Mechanical torque Number of pole pair rm tator voltage Stator power factor angle Mechanical power Rotor mechanical angular peed Rotor electrical angular peed Stator winding reitance Stator leakage inductance Magnetizing inductance Stator inductance Slip Winding ratio between tator and rotor Leakage coefficient Rotor winding reitance Rotor leakage inductance Rotor inductance rm rotor voltage rm rotor current Rotor power factor angle Converter voltage IGBT lo Diode lo Voltage drop during IGBT on-tate Voltage drop during diode on-tate Turn-on energy of IGBT Turn-off energy of IGBT Revere-recovery energy of diode Dc-link voltage of power converter Reference dc voltage during tet Carrier ratio Switching frequency Fundamental frequency of current Current through each power component Switching period Mean junction temperature of IGBT Junction temperature fluctuation of IGBT Mean junction temperature of diode Junction temperature fluctuation of diode Thermal reitance from junction to cae

3 R thca P T a t on t e τ AD N f β 1 β 2 β 3 β 4 V m V I Thermal reitance from cae to ambient Power lo of each power emiconductor Ambient temperature On-tate time within a fundamental period Fundamental period of current Thermal time contant Annual damage Cycle-to-failure of power emiconductor Exponential coefficient of temperature wing Exponential coefficient of mean temperature Exponential coefficient of on-tate time Scaling factor of the lifetime model Magnetizing voltage (complex) Stator voltage (complex) Stator current (complex) I m Magnetizing current (complex) I r V r Rotor current (complex) Rotor voltage (complex) II. INTRODUCTION ENEWABLE energy i increaingly integrated into the Rmodern power ytem. E.g., in Denmark, the wind power generation got 42.2% of it national electricity demand by the end of 2015, while the wind power target i 50% of the electricity demand by 2020 [1]. Conequently, wind farm (WF) upporting the voltage control ha become an important iue. According to the grid code [2] and [3], a WF mut be equipped with the following three excluive control function: reactive power control, the power factor control and alo the voltage control. Moreover, in [4] and [5], the author propoed that WF can alo be employed to upport the econdary voltage control, where the voltage reference at the Point of Common Coupling (PCC) or the reactive power reference of the WF i generated and ent out by the Automatic Voltage Control (AVC) in the power ytem. Doubly fed induction generator (DFIG) baed wind turbine (WT) have ome amount of reactive power capabilitie both from the tator ide of the generator and from the Grid-Side Converter (GSC). Therefore, DFIG WT can be een a continuou reactive power ource. The reactive power capability of DFIG WT i analyzed in [6] and [7]. It depend on the active power generation of the WT, the voltage at the terminal of the WT and the current and voltage limit of the generator and the power converter. Other voltage control device in WF include witching capacitor bank, taperchanger tranformer, hunt reactor, tatic ynchronou compenator (STATCOM) and tatic var compenator (SVC) etc. In [8] and [9], the author propoed dipatch method among different voltage control device in WF in order to reduce the power lo on the connection cable and to reduce the operation cot of the dicrete device e.g. the witching capacitor bank and the tap-changer tranformer. Becaue of better economy and controllability, under the premie of providing ufficient voltage upport, the DFIG WT ha a higher priority to upport the voltage control compared to other voltage control device in the WF [8]. Recently, reliability iue in WT are becoming more and more of importance, epecially when the WF move from the onhore to the offhore. The harh environment force the WT ytem to operate up to 25 year due to the expenive offhore intallation and maintenance. According to a field urvey of WT ytem [10], the electrical part ha the highet failure rated compared to other part like the turbine, gearbox, generator and control. It can be inferred that the lifetime of the power converter i the hortet and determine the lifetime of WT ytem. Baed on the thermal tre analyi of power electronic converter in [10], the lifetime of WT power converter, defined a how many year it can continuouly operate at the current working condition, depend on the WT active power generation and reactive power generation, which are cloely related to the WT miion profile. Wake effect in the WF i an important iue, epecially in large-cale WF. The obviou effect of the wake i the power lo of the WT in a ingle wake or in multiple wake. Many work have focued on the development of wake model [11] and [12]. With the conideration of the wake effect, WF layout optimization method [13] and [14] and the active power control method [15] and [16] have been developed for the power lo reduction. Becaue of the wake effect, downtream WT available active power depend on the uptream WT active power control method. Beide, there i interaction between the WF output power and the network. In [17], the author preented the impact of the wake effect on the dynamic power ytem imulation. Furthermore, in [18], the author preented the influence of the wake effect on the inertial repone for the frequency control during the generation and load imbalance. In [19], the author preented a coordinated control method for the WF to upport the frequency control under the generation and load imbalance, conidering the influence of the wake effect on the inertial repone. The popular and commonly implemented active power control method in WF i the maximum power point tracking (MPPT) method for each WT to extract maximum active power from the wind. When the WT are employed to provide extra reactive power to upport the voltage control, the lifetime of WT power converter could be reduced due to it additional current tre in each power module, which i an important challenge for modern WF lifetime requirement [10]. With the implemented MPPT method, due to the wake effect, uptream WT ha more active power generation than downtream WT at the wind direction that the WF ha wake lo [15], which reult in horter lifetime of uptream WT. Conequently, by uing dipatching appropriate reactive power, (i.e. higher reactive power from the downtream WT, but lower reactive power from the uptream WT), the lifetime of each WT power converter can be compromied, and the lifetime of uptream WT power converter can be increaed. A reactive power dipatch method to balance the power

4 load among WT i eentially to dipatch the reactive power requirement of each WT in the WF in proportion to it reactive power capability [20]. However, even with thi method implemented, the lifetime of uptream WT power converter could even be horter than the indutrial tandard, while the downtream WT could have very long lifetime. In thi paper, an reactive power dipatch method i propoed to improve the lifetime of uptream WT power converter, by trading-off the lifetime of each WT power converter. Baed on the reference of each WT active power, the calculation of the lifetime of the each WT power converter and the reactive power capability of each WT, the appropriate reactive power for each WT can be generated. Thi paper i organized a follow. DFIG model and reactive power capability of DFIG WT are analyzed in Section III. The method to evaluate the lifetime of WT power converter i introduced in Section IV. The propoed reactive power dipatch method to improve the lifetime of uptream WT power converter i dicued in Section V. Simulation cae tudie on a WF with 80 NREL 5 MW DFIG WT to analyze and demontrate the propoed method i carried out in Section VI. Finally, ome concluding remark are drawn in Section VII. III. DFIG MODEL AND REACTIVE POWER CAPABILITY The typical configuration of DFIG WT i hown in Fig. 1. The reactive power from the tator ide of the generator and the reactive power from the GSC can be generated by the DFIG WT and integrated into the power ytem. Fig. 1. Configuration of the DFIG WT. A. DFIG Model The teady-tate equivalent circuit of a DFIG i hown in Fig. 2, where Z eq / i the equivalent impedance of the power converter. When the WT operate with a leading or lagging power factor, the tator current can be calculated by [21] Tm / p I (1) 3V co where the mechanical torque can be calculated by, Pm Pm T m / p (2) m The voltage acro the magnetizing branch can be calculated by r V V I ( R j L ) (3) m l The magnetizing current can be calculated by, The rotor current can be calculated by, I V m m j L (4) m Ir I Im (5) The rotor voltage can be calculated by, V V I ( R j L ) (6) r m r r lr The lip can be calculated by, r (7) I R jx l V m V jx m V r / I m jx lr P ag Rr I r / Fig. 2. Steady-tate equivalent circuit of DFIG. RSC Re q / jxeq B. Reactive Power Capability of DFIG WT Depending on the active power of the WT, the reactive power capability of DFIG WT which i limited by the tator current, the rotor current and the rotor voltage i analyzed in [6]. The reactive power from the tator ide of the generator can be calculated by / Q 3V I in (8) The maximum reactive power from the tator ide of the generator limited by the tator current can be calculated by combining (1) and (8) at the maximum tator current. The maximum reactive power from the tator ide of the generator limited by the rotor current can be calculated by combining (1)-(5) and (8) at the maximum rotor current. The maximum reactive power from the tator ide of the generator limited by the rotor voltage can be calculated by combining (1)-(6) and (8) at the maximum rotor voltage. The reactive power capability of the GSC, which depend on the active power from the rotor-ide of the generator and the capability of the converter, can be calculated by Q S P (9) 2 2 GSC GSC r where the active power from the rotor-ide of the generator can be calculated by P V I co (10) r r r r

5 IV. LIFETIME OF POWER CONVERTER The method to etimate the lifetime of the power electronic component in the WT ytem tart with miion profile input the generated active power and required reactive power. With the help of the DFIG model and the lo model of the power electronic component, the lo diipation of each IGBT and the diode can be calculated, both of which conit of conduction loe and witching loe. Baed on a thermal model of the power module, the thermal profile of the power emiconductor can be calculated in term of the mean junction temperature and the junction temperature fluctuation at the given active power and reactive power. They are cloely related to the thermal reitance and thermal capacitance of the power module a well a it applied cooling olution. Afterward, the B 10 lifetime data can be obtained from the manufacturer at fixed thermal tre, and it can be further extended to the mean junction temperature and the junction temperature fluctuation at any freedom by uing Coffin-Manon equation. Finally, the annual damage, which i defined a the annual cycle over the cycle-to-failure, can be calculated. If the miion profile i annually repeated, the lifetime expectancy of the power converter reciprocal of the annual damage can be etimated. By uing thi approach, the lifetime of the GSC and Rotor- Side Converter (RSC) can be etimated. Although the lifetime expectancy of the power converter i heavily dependent on it deign criteria and it working environment (e.g. the power device election, annual local wind peed and wind condition), a lifetime comparion between the GSC and RSC of a typical 2 MW DFIG i performed in [10], it i evident that the lifetime of the RSC i much lower compared to the GSC, which indicate that the lifetime of back-to-back power converter can imply be determined by the RSC. Fig. 3. Flowchart to etimate the lifetime of rotor-ide converter at fixed active power and reactive power. The detailed flowchart to etimate the lifetime of the RSC i hown in Fig. 3. Baed on the requirement of the active power P and the reactive power Q, the procedure tart with the loading tranlation to calculate the rotor-ide current Ir and voltage Vr of the DFIG [22], L P V L Q I r kr[ j( )] L 3V L L 3V (11) m 1 m m 1 L L L Q L L P V r [( V ) j ( )] k L L V L V (12) r r r r m 1 m 3 1 m 3 where V denote the tator voltage and ω denote the tator frequency; L m denote the magnetizing inductance; L denote the tator inductance the um of the tator leakage inductance L l and the magnetizing inductance, while L r denote the rotor tator inductance the um of the rotor leakage inductance L lr and the magnetizing inductance; σ denote leakage coefficient of the DFIG, defined a (L L r - L m 2 )/L L r ; denote the lip value; and k r denote the winding ratio between the tator and the rotor. Baed on the complex term of the rotor current and voltage, the diplacement angle φ r can be obtained. The lo diipation of the IGBT and the diode can be calculated according to the lo model of the power device, both of which conit of the conduction lo and the witching lo [23]. The lo diipation of the IGBT P T can be expreed a, N P f V ( i ( n)) i ( n) d( n) T T e ce a a n1 V dc [( E ( ( )) ( ( ))] * on ia n Eoff ia n Vdc (13) where the firt term i the conduction lo, and the econd term i the witching lo. V ce i the voltage drop of the IGBT during it on-tate period, E on and E off are the turn-on and the turn-off energy diipated by the IGBT at a certain dc-link voltage V dc *, which are proportional to the actual dc-link voltage V dc. All the information can be found in the manufacturer dataheet. Beide, d i the duty cycle for each witching pattern, which can be calculated by uing the rotor voltage a well a it diplacement angle in the cae of the Space Vector Modulation (SVM) with a ymmetrical modulation equence method of the no-zero vector and zerovector. N i the carrier ratio between the witching frequency f and the fundamental frequency f e. i a i the current through each power component, T i the witching period, and the ubcript n i the n th witching pattern. Similarly, the lo diipation of the diode P D can be expreed a, N P f V ( i ( n)) i ( n) [1 d( n)] T D e f a a n1 V E ( i ( n)) dc * rr a Vdc (14) The firt term i the conduction lo, and the econd term i the witching lo. V f i the voltage drop during it on-tate period, E rr i the revere-recovery energy diipated by the diode, which i normally given by the manufacturer at a certain dc-link voltage. It can be een that the IGBT and the diode conduct complementarily within a witching period. Moreover, the IGBT and the diode lo in (13) and (14) are aimed for the entire bridge. For each power emiconductor (the IGBT or the diode), the lo will only be a half.

6 Since the mean junction temperature T jm and the junction temperature fluctuation dt j are regarded a the two mot important reliability indicator, they can be calculated a [23], 4 3 (15) T P R P R T jm _ T / D thjc _ T / D ( i ) thca _( j ) a i1 j1 [1 exp( t )] 2 4 on thjc _ T / D( i) 2 j _ T/ D thjc_ T/ D( i) i1 1 exp( te thjc_ T/ D( i) ) (16) dt P R In (15), R thjc i the thermal reitance from the junction to cae of the power module, R thca i the thermal reitance of the cooling ytem, in which ubcript i and j denote four-layer and three-layer Foter tructure for the power module and the cooling, repectively. P i the power lo of each power emiconductor, and T a i the ambient temperature. In (16), t on denote the on-tate time within each fundamental period of the current at the teady-tate operation, t e denote the fundamental period of the current, τ denote the thermal time contant of each Foter layer. Baed on the B 10 lifetime model of the power emiconductor [23], [24], the cycle-to-failure of the IGBT and the diode N f can be calculated, N f 4 dtj exp( ) t (17) on Tjm 273 where β 1, β 2, and β 3 are exponential coefficient related to the temperature fluctuation, the mean temperature and the on-tate time, repectively. β 4 denote the caling factor of the lifetime model. The annual damage AD can be defined a ratio between the total thermal cycle per year and it related cycle-to-failure, fe AD (18) N f It i noted that the contant wind peed all over the year i aumed, and there i no downtime during the operational year. Beide, the wind direction i not taken into account a well. In the cae of a real wind profile, the wind peed ditribution can be conidered by uing Miner rule [25], where the variou thermal tree have the ame effect on wear-out degradation. A a reult, the actual annual damage can be calculated conidering the weighting factor of the individual wind peed. Meanwhile, due to the wake effect, although WT in the WF cannot trictly follow the MPPT algorithm at the ambient wind peed, each of them eentially obey the MPPT at it equivalent wind peed a aforementioned. A a reult, the wind direction only affect the equivalent wind peed for each WT, and thi factor can be conidered a well. Moreover, in the cae of the reactive power compenation required from the DFIG ytem, ince the injection from the tator ide of the generator upported by the RSC i more effective and efficient compared to the GSC compenation [26], the reactive power injection from the tator ide of the generator will only be focued on in the following. V. PROPOSED REACTIVE POWER DISPATCH METHOD Conidering the active power difference among the WT in the WF becaue of the wake effect, the propoed reactive power dipatch method aim to increae the lifetime of the uptream WT power converter which i overly hort, and moreover to maximize the total lifetime of the overall WT power converter. The propoed reactive power dipatch method can be formulated by the objective function, the contraint and the control variable a decribed below. The objective function: n Max( WT LWT ( PWT, Q )) i i i WT (19) i i1 where n i the number of WT in the WF. The lifetime of the the i th WT power converter L WTi, which depend on the i th WT active power P WTi and reactive power Q WTi, can be obtained in lifetime look-up-table a dicued in Section IV. WTi i the weight coefficient. When the lifetime of the WT power converter i overly hort, the weight coefficient i et to be a large value, and when the lifetime of the WT power converter i overly long, the weight coefficient i et to be a mall value, to make ure the lifetime of the WT power converter, which i overly hort, can be increaed. Following contraint are exiting: 0 QWTi QWTi _ cap (20) n QWTi Qlo QWF (21) i1 V V V (22) WT _min WTi WT _max where over-excited reactive power injection i aumed and the reactive power of the i th WT Q WTi i limited by the reactive power capability of the i th WT Q WTi_cap. Q WTi_cap depend on the active power of each WT and the voltage at the terminal of the i th WT a preented in Section III. The total reactive power of all the WT plu the reactive power lo on the WF connection cable Q lo hould be equal to the reactive power reference of the WF Q WF. V WTi i the voltage at the terminal of WT i. V WT_min and V WT_max are the down and up voltage limit at the terminal of the WT. The reactive power of each WT are the control variable. In thi work, the reactive power of each WT are generated with the Particle Swarm Optimization (PSO) baed optimization algorithm [15]. The flow chart of the optimization algorithm i hown in Fig. 4. In the iteration of the optimization algorithm, the firt tep i to limit the reactive power of each WT by the contraint (20)-(22). In contraint (20), the reactive power capability of each WT depend on the active power of each WT and the voltage at the terminal of each WT. The voltage at the terminal of each WT and the power lo on the connection cable can be obtained by the WF power flow calculation, with the active power of each WT, the voltage at PCC and the reactive power of each WT. Finally, the reactive power of each WT can be obtained by the lifetime

7 calculation and comparion of the objective function (19). Initialization Calculate reactive power of each WT: QWTi, by the PSO interative mechanim By WF power flow calculation, calculate the voltage at the terminal of each wind turbine: VWTi and the reactive power lo on the connection cable: Qlo, with the active power of each WT: PWTi and the voltage at PCC: VPCC Calculate the reactive power capability of each wind turbine:qwti_av, with the active power of each WT: PWTi and the the voltage at the terminal of each wind turbine: VWTi Contraint (20) - (22) atified? Ye No Obtain the lifetime of each WT power converter from the lifetime look-up-table, with the active power of each WT: PWTi and the reactive power of each WT limited by contraint (20) - (22): QWTi Calculate the objective function (19), update the warm poition and obtain the globle bet poition for the PSO iterative program End condition atified? Ye Obtain the optimal reactive power of each WT : QWTi_OPT Fig. 4. Flow chart to obtain the reactive power for each WT, with the PSO baed optimization algorithm. VI. CASE STUDY AND DISCUSSION In thi ection, the propoed reactive power dipatch method i analyzed and demontrated in a WF with 80 NREL 5 MW DFIG WT. The layout of the WF, which i the ame with the offhore WF of Horn Rev 1 in Denmark, i hown in Fig. 5. The ditance between two adjacent WT in the ame row or in the ame column i 819 m, which i 6.5 time of the blade diameter. The parameter of the NREL 5MW WT are encloed in the appendix Table I. A. Active Power Generation To etimate the active power generation of each WT in the WF, the active power curve a hown in Fig. 6 [27] i aumed to be implemented in the WT control ytem. The active power curve incorporate 5 control region, where the MPPT i implemented in region 3. The active power of each WT i etimated by the Katic model [28] and [15]. The WF i aumed to be an offhore WF and the decay contant k=0.04 i adopted [29]. The highet power loe of the WF, becaue of the wake effect, appear at the wind direction that are aligned to the ymmetry axe of the WF [11]. In thi cae tudy, the high power lo appear at the wind direction of around 41, 90, No Y (km) Wind direction α North u Column No. n of WT m_n α= WT m_n α=352 X (km) α=311 Fig. 5. Layout of the WF with 80 NREL 5 MW WT. Active power (pu) Fig. 6. Active power curve of the NREL 5 MW WT. Active power (pu) Column No. n of WT m_n Row No. m of WTm_n 3m/ 4m/ 5m/ 6m/ 7m/ 8m/ 9m/ 10m/ 11m/ 12m/ 13m/ 14m/ 15m/ Fig. 7. Active power of the WT in each column at 270 wind direction and at the wind peed from 3 m/ to 15 m/ with the reolution of 1 m/. 131, 172, 221, 270, 311 and 352. At thee wind direction the WT have the mot different active power generation. In order to illutrate the difference of each WT active power generation, the active power generation of each WT at 270 wind direction and at the wind peed in the range of 3 m/ to 15 m/ are calculated and hown in Fig. 7. At thi wind direction, WT in the ame row will not caue the wind peed deficit for WT in other row. Thu, the WT in the ame column (a hown in Fig. 5, WT m_n i marked with it row No. m and column No. n) have the ame active power generation.

8 B. Reactive Power Capability A analyzed in [6], the over-excited reactive power capability of the DFIG WT i limited by the maximum rotor current. At tator voltage of 0.9 pu, 1.0 pu and 1.1 pu, the maximum reactive power from the tator ide of the generator in term of active power generation are hown in Fig. 8. To make ure that the WT i able to generate the rated active power at the tator voltage in the range of 0.9 pu to 1.1 pu, the maximum rotor current i elected to be 1.11 pu. It hould be noticed that, in thi cae tudy, the rated power and the rated tator phae voltage have been ued a the bae value for the normalization. Reactive power capability (pu) Fig. 8. Over-excited reactive power capabilitie from the tator ide of the generator in term of the WT active power, at tator voltage of 0.9 pu, 1.0 pu and 1.1 pu. At 270 wind direction, according to each WT active power a hown in Fig. 7 and the WT over-excited reactive power capability from the tator ide of the generator a hown in Fig. 8, each WT over-excited reactive power capabilitie from the tator ide of the generator at the ambient wind peed in the range of 3 m/ to 15 m/ are hown in Fig. 9, where the tator voltage i aumed to be 1.0 pu. Reactive power capability(pu) Column No. n of WT m_n 3m/ 4m/ 5m/ 6m/ 7m/ 8m/ 9m/ 10m/ 11m/ 12m/ 13m/ 14m/ 15m/ Fig. 9. Reactive power capability of the WT in each column, at 270 wind direction and at the wind peed from 3 m/ to 15 m/ with the reolution of 1 m/. C. Lifetime of the Power Converter In the DFIG ytem, although the active power flowing through the RSC i exactly the ame a the GSC, the thermal loading of the RSC i much higher than the GSC [10]. Not only the RSC i normally required to excite the rotor-ide of the generator in order to guarantee the unity power factor operation at the tator ide of the generator, but alo the rotor voltage i much lower than the grid voltage, which reult in the higher current tre of the RSC. Beide, the operation frequency of the RSC i alo much lower than the GSC, which caue high thermal cycling. A tated in Section IV, the lifetime of the power converter i typically decided by the RSC. Moreover, the reactive power compenation from the RSC further affect it reliability. A the under-excited reactive power relieve the tre of the RSC, while the overexcited reactive power impoe it thermal tre [25], only the over-excited reactive power i concerned. Lifetime (year) Lifetime (year) Under load area Reactive power capability limit Over load area Active power (pu) Reactive power (pu) Active power (pu) (a) Reactive power (pu) (b) Fig. 10. Lifetime of the DFIG WT power converter in term of active power and reactive power. (a) Active power from 0 pu to 1 pu and the reactive power from 0 pu to 1 pu. (b) Active power from 0.8 pu to 1 pu and the reactive power from 0 pu to 0.2 pu. According to the parameter of the DFIG lited in Table I

9 a well a the reliability data of power device lited in Table II, the lifetime of the power converter i hown in Fig. 10 in term of variou amount of active power and reactive power. It i noted that, if the reactive power keep contant, the lifetime i decreaing with higher active power except for the area around the active power of 0.4 pu. It i becaue the DFIG operate at the ynchronou operation, and the low operation frequency reult in relatively high thermal tre in pite of the low generated active power. Moreover, in the condition of the ame amount active power, the higher reactive power caue a lower lifetime due to it higher thermal tre induced by the additional reactive power. Furthermore, the huge difference of lifetime can be found between the light load (with no active power and reactive power injection) and the heavy load (with 1.0 pu active power and reactive power injection). Auming that no reactive power i required and 1.0 pu active power i provided all the year around, the lifetime of the RSC i 11.4 year. D. Reactive Power Dipatch Compared with the reactive power control method that dipatche the reactive power requirement of each WT in the WF in proportion to it reactive power capability, the optimization reult obtained by the optimization algorithm are hown in Fig. 11, at the 270 wind direction, at the 12 m/ wind peed, at the 1.0 pu voltage at PCC and at the 0.44 pu, 0.50 pu and 0.63 pu reactive power of the WF. The weight coefficient in the objective function (19) i et to be (11.4/L WTi ) 3, where 11.4 i the lifetime of the WT power converter when the WT i working at the rated power and no reactive power output. The optimized reactive power for each WT i hown in Fig. 11 (a). The lifetime of each WT power converter with the optimized reactive power for each WT i hown in Fig. 11 (b). In Fig. 11 (b), it can be een that the lifetime of the WT power converter in column 1 i increaed from 8.1 year, 7.6 year and 6.5 year to 11.3 year repectively, at the 0.44 pu, 0.50 pu and 0.63 pu reactive power of the WF. And the total lifetime of all the 80 WT power converter i increaed from year, year and year to year, year and year repectively, at the 0.44 pu, 0.50 pu and 0.63 pu reactive power of the WF. E. Annual Lifetime Conumption The effectivene of the propoed reactive power dipatch method depend on the wind direction and wind peed ditribution at the WF location area and the WF layout. The reaon are a follow. Only at the wind direction that the WF ha wake lo, WT have different active power generation and the propoed method can improve the lifetime of the uptream WT power converter. A hown in Fig. 10, at low active power and low reactive power, the WT power converter ha very long lifetime, and therefore the power converter lifetime conumption can be neglected. Optimal reactive power of each WT(pu) Lifetime of the power converter (year) (a) (b) Fig. 11. Comparion between the propoed reactive power dipatch method and the method that dipatche the total reactive power for all WT to each WT in proportion to the reactive power capability of each WT. (a) Reactive power of the WT in each column; (b) Lifetime of the WT power converter of the WT in each column. The lifetime of the uptream WT power converter i increaed by acrificing the lifetime of downtream WT power converter. At oppoite wind direction, uptream WT and downtream WT will be tranferred to be the downtream WT and uptream WT. Thu, the effect of the propoed method will be weakened. The lifetime of the power converter a hown in Fig. 10 i obtained by the aumption of the contant active and reactive power injection all the year around. Taking into account the factor of wind peed and wind direction ditribution, the annual lifetime conumption defined a the percentage of lifetime conumed in one year i ued in thi paper to demontrate the propoed reactive power dipatch method. The annual wind direction and wind peed data a hown in Fig. 12 are adopted to calculate the annual lifetime conumption of each WT power converter. The wind direction ditribution and the wind peed ditribution a

10 hown in Fig. 13 are generated by the WAP climate analyi tool with the data a hown in Fig. 12. The wind roe i eparated into 36 ector each with 10. Wind direction (degree) (a) Annual lifetime conumption (%) Q WF_PRO = 0.8Q WF_Capability Q WF_OPT = 0.8Q WF_Capability Q WF_PRO = 0.5Q WF_Capability Q WF_OPT = 0.5Q WF_Capability Q WF = 0 Wind peed (m/) WT (m-1)*10+n Fig. 14. Comparion of the annual lifetime conumption of each WT power converter between the propoed reactive power dipatch method and the method that dipatche the reactive power reference for the WF to each WT in proportion to each WT reactive power capability. (b) Fig. 12. (a) Annual wind direction time erie; (b) Annual wind peed time erie. With the active power curve a hown in Fig. 6 implemented and compared between the propoed reactive power dipatch method and the method that dipatche the total reactive power for all WT to each WT in proportion to each WT reactive power capability, the annual lifetime conumption of each WT power converter i hown in Fig. 14, where WT m_n a hown in Fig. 5 are repreented by WT (m- 1)ₓ 10+n. It can be een that, the annual lifetime conumption of the WT in column 1 can be reduced by the propoed method. When the WT provide the total reactive power injection of 0.5 and 0.8 time the total reactive power capability of all the WT, the annual lifetime conumption of the WT 1_1 power converter i reduced by 5.01% and 7.15%, repectively. Frequency of occurrence (%/(m/)) Fig. 13. Wind direction ditribution in each wind roe ector and wind peed ditribution in all the wind roe ector. VII. CONCLUSIONS The lifetime of the WT power converter depend on the WT active power and reactive power miion profile. Conidering the wake effect, the WT in a WF have different active power generation. By dipatching the reactive power among WT, the lifetime of uptream WT power converter, which ha horter lifetime even than the indutrial tandard, can be increaed by acrificing the lifetime of downtream WT power converter which ha much longer lifetime. In thi paper, an reactive power dipatch method among DFIG WT in a WF i propoed to increae the lifetime of uptream WT power converter which i overly hort and to increae the total lifetime of all the WT power converter. The propoed method generate the reactive power for each WT by the PSO baed optimization algorithm baed on the difference of each WT active power generation becaue of wake effect and the reactive power for each WT i limited by each WT reactive power capability. At the wind direction where there i no wake lo in the WF and at high wind peed that each WT are operating at the rated power, the active power generation of each WT are all the ame. On the other ide, at the lower wind peed and lower reactive power requirement for the WF, the lifetime conumption of the WT power converter can be neglected. Additionally, the trade-off for the lifetime between the uptream WT power converter and downtream WT power converter will be weakened at oppoite wind direction. Thu, the effectivene of the propoed method depend on the wind direction and wind peed ditribution and the layout of the WF. It can be concluded that, compared with the traditional reactive power dipatch method, the propoed method can increae the lifetime of the uptream WT power converter and the total lifetime of all the WT power converter. Moreover, the propoed method can be ued for any WF

11 layout and at any wind direction and wind peed ditribution at the WF area. VIII. APPENDIX TABLE I Parameter of the 5 MW DFIG WT WT Rated Mechanical Power 5 MW Rotor Diameter 126 m Hub Height 90 m Cut-In, Rated, Cut-Out Wind Speed 3 m/, 11.4 m/, 25 m/ Cut-In, Rated Rotor Speed 6.9 rpm, 12.1 rpm Gearbox ratio 97 DFIG Rated Mechanical Power 5.0 MW 1.0 pu Rated Stator Phae Voltage 548 V (rm) 1.0 pu Rated Rotor Phae Voltage 381 V (rm) pu Rated Stator Current 2578 A (rm) pu Rated Rotor Current 3188 A (rm) pu Rated Stator Frequency 50 Hz 1.0 pu Number of Pole Pair 3 Stator Winding Reitance mω pu Rotor Winding Reitance mω pu Stator Leakage Inductance mh pu Rotor Leakage Inductance mh pu Magnetizing Inductance mh pu Power converter DC-link voltage 1600 V 1.684pu Switching frequency 2 khz TABLE II Parameter ued in lo model and thermal model of power emiconductor Lo model Thermal model IGBT Diode V 1 ka, T j=150 ºC (V) 2.45 / V 1 ka, T j =150 ºC (V) / 1.95 E 1 ka, T j=150 ºC (mj) 430 / E 1 ka, T j =150 ºC (mj) 330 / E 1 ka, T j=150 ºC (mj) / Fourth order thermal reitance (ºC/kW) Four order thermal time contant () IX. 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12 [27] J. Jonkman, S. Butterfield, W. Muial, and G. Scott, "Definition of a 5- MW Reference Wind Turbine for Offhore Sytem Development," Golden, CO: National Renewable Energy Laboratory, Tech. Rep. NREL/TP , Feb [28] I. Katic, D. Højtrup, and N. O. Jenen, "A ample model for cluter efficiency," in Proc European Wind Energy Aociation Conf., pp [29] N. G. Mortenen, D. N. Heathfield, L. Myllerup, L. Landberg and O. Rathmann, Wind Atla Analyi and Application Program: WAP 8 Help Facility. Riø National Laboratory, Rokilde, DK. 335 topic. ISBN , Jie Tian (S 2013) received the B.Eng. and M.Sc. degree from Yanhan Univerity, China, in 2005 and 2011 repectively. He i now a Ph.D. Student with the Department of Energy Technology, Aalborg Univerity, Aalborg, Denmark. He i working on the advanced coordinative control of the wind power converion ytem. Frede Blaabjerg (S 86 M 88 SM 97 F 03) wa with ABB-Scandia, Rander, Denmark, from 1987 to From 1988 to 1992, he wa a Ph.D. Student with Aalborg Univerity, Aalborg, Denmark. He became an Aitant Profeor in 1992, Aociate Profeor in 1996, and Full Profeor of power electronic and drive in Hi current reearch interet include power electronic and it application uch a in wind turbine, PV ytem, reliability, harmonic and adjutable peed drive. He ha received 17 IEEE Prize Paper Award, the IEEE PELS Ditinguihed Service Award in 2009, the EPE-PEMC Council Award in 2010, the IEEE William E. Newell Power Electronic Award 2014 and the Villum Kann Ramuen Reearch Award He wa an Editor-in-Chief of the IEEE TRANSACTIONS ON POWER ELECTRONICS from 2006 to He i nominated in 2014 and 2015 by Thomon Reuter to be between the mot 250 cited reearcher in Engineering in the world. Dao Zhou (S 12, M 15) received the B.S. in electrical engineering from Beijing Jiaotong Univerity, Beijing, China, in 2007, the M.S. in power electronic from Zhejiang Univerity, Hangzhou, China, in 2010, and the Ph.D. from Aalborg Univerity, Aalborg, Denmark, in He i currently a Potdoctoral Reearcher in Aalborg Univerity. Hi reearch interet include power electronic and reliability in renewable energy application. Dr. Zhou received the Renewable and Sutainable Energy Converion Sytem of the IEEE Indutry Application Society Firt Prize Paper Award in 2015, and Bet Seion Paper at Annual Conference of the IEEE Indutrial Electronic Society (IECON) in Autria in He erve a a Seion Chair for variou technical conference. Chi Su (S 11 M 13) received the B.Eng. and M.Sc. degree from Huazhong Univerity of Science and Technology (HUST), China, in 2003 and 2007 repectively, and Ph.D. degree from Aalborg Univerity, Denmark, in He i now working at the Department of Energy Technology, Aalborg Univerity a an Aitant Profeor. Hi reearch interet include power ytem ocillation and it wide-area control, wind power integration, protection and communication in ditribution ytem, and application of artificial intelligence in power ytem. Zhe Chen (M 95 SM 98) received the B.Eng. and M.Sc. degree from Northeat China Intitute of Electric Power Engineering, Jilin, China, and the Ph.D. degree from the Univerity of Durham, Durham, U.K. He i currently a Full Profeor with the Department of Energy Technology, Aalborg Univerity, Aalborg, Denmark, where he i the Leader of the Wind Power Sytem Reearch Program. He i the Danih Principal Invetigator for Wind Energy of the Sino-Danih Centre for Education and Reearch. He ha authored or coauthored more than 320 publication in hi technical field. Hi current reearch interet include power ytem, power electronic, electric machine, wind energy, and modern power ytem. Dr. Chen i a Fellow of the Intitution of Engineering and Technology, U.K., and a Chartered Engineer in the U.K. He i an Aociate Editor (Renewable Energy) of the IEEE TRANSACTIONS ON POWER ELECTRONICS.