1、 Abstract Large-scale centralized development and utilization of wind energy are widely adopted in China.Therefore,the output current of wind farm is generally very large during faults.The current characteristics play an important role in the setting calculation and reliable operation of the relay p
2、rotection.In the period of faults,the output current is related to the operating status of DFIGs,low voltage ride-through(LVRT)and control strategies.The current frequency characteristics of DFIG-based wind turbines are discussed in this paper.When the crowbar works with the voltage severely dropped
3、,the interharmonic component appears in the output current.The initial amplitude of the interharmonic component is related to the voltage drop,the crowbar resistance,the slip and the initial active power and the decay speed is rapid.When the converter works with the voltage slightly dropped,the seco
4、nd harmonic appears.The initial amplitude is related to the initial value of the fundamental frequency component and the PI controller coefficient.The decay speed is slower than the interharmonic component.In the case of an asymmetric fault,the negative sequence component makes the third harmonic ap
5、pear.The third harmonic component always exists until the fault cleared.The main non-fundamental frequency components in the output current are studied by the quantitative calculation method of DFIG models in order to be made full use of,which helps the relay protection to improve the protection cri
6、teria.As a consequence,we can improve the performance and applicability of relay protection effectively,which has important guiding significance for the development of new relay protection principles.Index Terms Frequency characteristics,DFIG,relay protection,low voltage ride through Manuscript rece
7、ived July 15,2018.This work was supported in part by the National Natural Science Foundation of China(51677026,51377022).W.J.is with School of Electrical Engineering of Southeast University,Nanjing,210096 China(Tel;+86-13407534203,E-mail:).Y.L.is with School of Electrical Engineering of Southeast Un
8、iversity,Nanjing,210096 China(E-mail:).T.H.is with R&D Department,NR Electric CO.,LTD.,Nanjing,211102 China(e-mail:).I.INTRODUCTION N the case of a growing shortage of fossil fuels,the clean and renewable energy is the imperative choice for humans to achieve sustainable development.Compared with oth
9、er energy,the wind energy development in large-scale commercialization is more mature.Especially,the governments in the world are also formulating policies to encourage the development and utilization of wind energy.In recent years,the installed capacity of wind turbines has experienced explosive gr
10、owth.However,the current research on the impact of wind power connected to the power system is still insufficient.Therefore,it is necessary to conduct in-depth research 1-5.In China,large-scale centralized development of wind energy is very common,and the scale of wind farms is generally very large.
11、After a fault in wind farm,the control strategy of the wind turbine changes,which makes wind generators different from the traditional synchronous generators.Obviously,since the DFIG-based wind turbines have varieties of low voltage ride-through modes during faults,it is non-linear in the equivalent
12、 sequence networks of DFIGs.During the fault,the output voltage and current of DFIG will contain harmonic components 6-11.In this paper,the generation mechanism of intermediate harmonic and harmonic components in the output current and voltage of DFIG after the fault is studied.The output current of
13、 DFIG wind turbines contains harmonics,interharmonics,etc.Different frequency component has different influence on the relay protection.Some may cause the incorrect operation of relay protection,while some may play a positive role in relay protection.Therefore,it is of great significance to study th
14、e frequency characteristics of the output current of DFIG wind turbines after faults.It is also of great significance for the development of new relay protection principles.Study on Non-fundamental Frequency Components in the Output Current of DFIG-based wind turbines during faults Wei Jin,Yuping Lu
15、,Senior Member,IEEE,and Tao Huang I 2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201805280000024 Page1/7 1638 II.FREQUENCY COMPONENTS CORRESPONDENCE IN DIFFERENT COORDINATE SYSTEMS To maintain frequency stability of the stator,the converter
16、 of DFIG should change the AC excitation according to the change of the rotor speed.The frequency coupling relationship among the stator and rotor windings is shown in Fig.1.Where the angular frequencies of the electrical quantities in the stator and rotor windings are respectively 1 and 2,the rotor
17、 speed r.Suppose the dq coordinate system rotates counterclockwise at a synchronous angular velocitys.1dq and2dq are the the angular frequency of the stator and rotor in the synchronous rotating dq coordinate system corresponding to the ABC/abc coordinate system.According to the relationship between
18、 the different coordinate systems,The following equations should be satisfied.121122rdq sr dq s(1)ABCcbadqr s121dq2dq Fig.1 Schematic diagram of the relationship between stator and rotor frequency of DFIG Taking 2 as the reference and substituting s r ss into equation(1),we can obtain the frequency
19、relationship between the rotor and stator in different coordinate systems.As is shown in TABLE I.TABLE I FREQUENCY RELATIONSHIP BETWEEN THE STATOR AND ROTOR ABC/abc Coordinate System dq Synchronous Rotating Coordinate System stator 2(1)ss 2 ss rotor 2 2 ss When the DFIG-based wind turbine is in norm
20、al operation,2 ss and s are the current frequency in the rotor and stator weddings.They are both DC in dq coordinate system by coordinate transformation.When a symmetrical or asymmetrical fault occurs in the system,some AC frequency components appear in the rotor circuit and the converter circuit(in
21、 dq coordinate system).Therefore,corresponding harmonic components are generated on the stator side considering the coupling relationship.III.INTERHARMONIC COMPONENTS IN OUTPUT CURRENT DURING CROWBAR PROTECTION A.Transient Process Analysis of Putting Crowbar Protection If a three-phase short-circuit
22、 fault occurs in the stator winding,according to the principle of flux conservation,the DC component and the fundamental AC component will be induced in the stator winding,and the rotor winding will induce(1)ss andss frequency current components.In the case of an asymmetrical fault,a(2)ss frequency
23、current component in the rotor winding is induced by the s frequency negative sequence current component in the stator winding.When the rotor winding is suddenly short-circuited by the crowbar resistance cbR,in the rotor winding,the DC current is also induced to maintain the flux linkage and is cont
24、inuously attenuated.At the same time,the stator winding induces the(1)ss frequency current component.As a result,when the crowbar is put into the grid after a fault,the correspondence between different frequency current components is shown in TABLE II.TABLE II CORRESPONDING RELATIONSHIP BETWEEN DIFF
25、ERENT CURRENT FREQUENCY COMPONENTS WHEN CROWBAR WORKS Fault Type Stator Current Frequency Rtator Current Frequency Symmetrical Fault DC(1)ss s ss(1)ss DC Asymmetric Fault DC(1)ss s ss s(2)ss(1)ss DC As is described in TABLE II,different from the transient characteristics of the conventional synchron
26、ous machine and the asynchronous machine,(1)ss frequency component appears in the stator current in addition to the DC component and the fundamental frequency component.(1)ss ranges in(0.7 1.3)s for the reason of the slip within 0.3 0.3.There is no doubt that this harmonic current makes it difficult
27、 to extract fault component and influences relay protections.2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201805280000024 Page2/7 1639 B.Interharmonics Analysis in Output Current of DFIG Suppose a fault occurs at the time 0 t,and the voltag
28、e amplitude drops to the k times.If the crowbar resistance is cbR,the rotor resistance is rR(r r cbR R R)after putting into crowbar.We have the following equations.|0|0|/()()()0()()()()()()()()()P P Ps s s s s sP P Pr r r r s rP P Ps s s m rP P Pr m s r rk p R p p p j pR p p p js pp L p L pp L p L p
29、 I I II II(2)Where()p I and()p are the image functions of current and flux space vector,|0|s and|0|r the initial value of the stator and rotor flux linkage,p the Laplace operator.From(2),we have 0 0 0 0/()s s s rs s|s s|s|r|m j t t T js t tT Psa b a b ss r ssj k j k L kke e e eZ Z Z Z L L L i(3).Whe
30、re ssL and rrL are the stator and rotor transient inductance,sT and rTthe stator and rotor transient time constant.In addition,there are 2mss srLLLL,2mrr rsLLLL,ssssLTR,rrrrLTR,()s s r s rrar s rj L R js LZR js L,and(1)(1)s s r s rrbr s rj L R j s LZR j s L.In the steady state operation,we have foll
31、owing equations.|0|0|0|0|0|sssr ss rr s ss m mjLL Lj L Lu ui(4)According to(3)and(4),the stator positive sequence current expression can be obtained./|0|11()s s s rj t t T js t tT Pssa b a bk k k ke e P e eZ Z Z Z i(5)In(5),thess frequency component in the stator fault current space vector is the in
32、terharmonic component.If expressed as(1)()msti,We have/(1)|0|1()|rtTm s sabkkI t P eZZ(6)In(6),the value of(1)()msIt is related to the voltage drop value k,the crowbar resistancecbR,the operating state|0|sP ands before the fault.It decays with time.The initial amplitude of the(1)ss frequency compone
33、nt at 0 t is(1)|0|1(0)|m s sabkkIPZZ(7).Therefore,the amplitude of the steady-state positive-sequence fundamental frequency current component in the stator is 1|makIZ(8).In fact,(1)(0)msI is much larger than 1 mI.Fig.2 shows the schematic diagrams of the relationship between(1)(0)msIand 1 mI with th
34、e change of k and cbR in the three cases of 0.2 s,0 s,0.2 s./cb rRRkI(pu)I(pu)I(pu)k k/cb rRR/cb rRR(1)(0)msI1 mI1 mI1 mI(1)(0)msI(1)(0)msI0.2 s 0 s 0.2 s Fig.2 the comparison between(1)ss frequency component and fundamental frequency component As is shown in fig.1,(1)(0)msI decreases while 1 mI inc
35、reases with k increasing.That is to say,the percentage of the(1)ss frequency component in the stator current gradually decreases as k increases.When the crowbar protection is applied,the voltage generally sags severely.The(1)ss frequency component is the main component of the stator current.The(1)ss
36、 frequency current decays quickly and is with a short duration.IV.HARMONIC COMPONENTS IN OUTPUT CURRENT UNDER CONVERTER CONTROL A.Converter control process analysis When under converter control,the LVRT control strategy is“disconnecting the outer loop of power control and directly setting the curren
37、t command value”.Furthermore,the current command value changes according to the output state.The control block diagram is shown in Fig.3.When a symmetrical or asymmetrical fault occurs,an AC component appears in part of the control quantities,which affects the output harmonic frequency characteristi
38、cs of DFIG-based wind turbines.2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201805280000024 Page3/7 1640*rdi/m s ssL u L riIriPkkp*rdu*rqi riIriPkkp*rqus rrsL s rrsL dq/abc PWM*rau*rbu*rcurdirqi*gdisugiIgiPkkp*gdu*gqi giIgiPkkp*gqusgL sgL P
39、WM*gAu*gBu*gCugdigqi*dcuguIguPkkpdq/ABCdcuRSCGSC Fig.3 Converter control process during fault B.Transient response of control quantity at fault After a fault,the stator voltage may consist of the fundamental frequency positive and negative sequence components under converter control,while the stator
40、 current may consist of the fundamental frequency positive and negative sequence components,along with attenuation DC component.Therefore,the stator active power can be expressed as:/(1)|0|/0 1 1 2 21()|Re()cos()cos(2)rstTm s s s s sabtTs s s s s s skkI t P e PZZP P e t P t ui(9)In(10),the fundament
41、al frequency and the second fundamental frequency components appear in the stator active power.The relationship among the stator active power|0|sP,the rotor active power|0|rP,and the input mechanical power mP at the initial time is as follows according to fig.4.|0|0|0|(1)m s r sP P P s P(10)Suppose
42、that the rotor speed and the input mechanical power keep to be constant after the fault in short time,we have|0|(1)dc rdc s su i s P P(11)RotorStatormPsPrPrdcigdcidcugPFig.4 the power relationship in DFIG-based wind turbine Assume that the PI controller has a low latency.gdi and gqi can quickly foll
43、ow the change of*gdi and*gqi.We have*()()g gd gq guP dc dc guI dc dc gqi ji k u u k u u dt ji i(12).Furthermore,the active power output of the grid-side converter is Re()g s gP=ui(13).The DC-bus output power is equal togP(dc gdc gu i P).From(9)(13),we have|0|(1)g ssdcrdc gdcdc dcP s P PduC i idt u u
44、(14).Where C is the DC bus capacitor.All insP,gP and dcu contain the attenuated fundamental frequency component and the second fundamental frequency component.The following equation can be used to representdcu./_ 1 122cos()cos(2)stTdc ac dc s dcdc s dcu U e tUt(15)Where 1 dcU and 2 dcU the DC voltag
45、e amplitude of attenuated fundamental frequency component and second fundamental component,1 dc and 2 dc the initial phase angle。Fig.5 shows the simulation waveform of the stator output active power and DC-bus voltage of DFIG-based wind turbine during the phase-phase short circuit,single-phase groun
46、ding fault and three-phase short circuit.In the early stage of the fault,both sP and dcu contain fundamental frequency component with a large amplitude,and the fundamental frequency component is continuously attenuated.Furthermore,the second fundamental frequency component appears at asymmetric faul
47、ts.In steady state,there are no AC components in the waveforms at symmetric faults.However,the second fundamental frequency component is the main component in the waveforms in the case of asymmetrical faults.t(s)P s(pu)u dc(V)Phase-phaseSingle-phaseThree-phasePhase-phaseSingle-phaseThree-phase Fig.5
48、 Simulation waveform of the stator output active power and DC-bus voltage of DFIG-based wind turbine C.Second Harmonic Component Analysis The following two conditions should be satisfied when an 2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.
49、201805280000024 Page4/7 1641 AC component does not generate other frequency components through the control loop:a)The d-axis and q-axis amplitudes of the AC component are equal.b)The d-axis and q-axis parameters of the control loop are equivalent to the AC component.At the beginning of the fault,the
50、 DC voltage dcu contains the fundamental frequency component,and only circulates in the d-axis control loop.The d-axis and q-axis control parameters are asymmetrical for dcu,which results in new frequency components.For the attenuation of the fundamental frequency component in the DC voltage,the d-a
