analysis of grid connected dfig-based wind turbines during lvrt · 2018. 6. 17. · the...

Analysis of Grid Connected DFIG-BasedWind Turbines During LVRT

Dr.K.Suresh Kumar1 ,G.Angalaparameswari2 ,R.Geetha3, S.Waheeda Parveen4

1Associate Professor, 2Assistant Professor,3Assistant Professor, 4PG Scholar,

Velammal Engineering College* E-mail: wahee [email protected]

April 25, 2018

Abstract

Instability phenomenon of the grid-connected doubly fedinduction generator (DFIG) based wind energy conversionsystem (WECS) during low-voltage ride-through (LVRT) isnot highly concerned by researchers yet. The small-signaldynamics of DFIG WTs attached to weak ac grid with highimpedances is investigated in this paper, during the periodof LVRT. In order to carry out stability analysis, the in-fluence of the high-impedance grid is summarized as theinteraction between phase-locked loop (PLL) and rotor cur-rent controller (RCC). Eigen value and modal analysis resultshows that the problem of poorly damped poles are domi-nated by PLL, which may become unstable. To overcomethis problem a controller is designed which during deep volt-age sag, reduces the active rotor current which in turn isused to damp the oscillationsand the effect of various con-trol parameters on rotor current is also investigated. To vali-date the proposed control method, a time-domain computermodel is developed using SIMULINK/Sim Power System.

Key Words:Doubly fed induction generator (DFIG),LVRT, high-impedance grids, phase-locked loop (PLL), Ro-tor current controller(RCC), small-signal stability analysis.

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International Journal of Pure and Applied MathematicsVolume 118 No. 24 2018ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

1 INTRODUCTION

Due to the rapid growth of wind power penetration into modernpower system, wind turbines has to remain connected and injectreactive power to support stable operation of the system duringgrid faults as addressed in [1], [2]. Neglecting stress (transient overcurrent and voltage) and upholding stability are the requirement forsecure Low-voltage ride-though (LVRT) in wind energy conversion.

Among all types of WECSs, in this paper doubly fed induc-tion generator (DFIG) based wind turbines (WTs), which occupiesthe major portion of the market takes the center stage, that aredesigned in accordance with grid codes and technology progress.However, with continuously increasing penetration, large scale windplants located in remote areas connect AC grid via long transmis-sion lines with high impedance, which is seldom taken into accountby available LVRT technology of DFIG WTs and thus challengethe requirements of controllable stress and stability.

According to [3] and [4] wide research on LVRT of DFIG WTshas been concentrated on the substantial stress issues (includingover-current in rotor winding and over-voltage in DC bus), whichis induced by the coupling between the stator and rotor and alsodue to inadequate rotor-side converter (RSC) control voltage. How-ever, possible stability issues during faults are not well labelled yet.In this paper, as stated in [5] PLL-based vector control which is ex-tensively instigatedfor DFIG WECs during LVRT. subsequently thecontrol loops perform a vital part in dynamic performance, duringfault DFIG WTs are subjected to trip due to oscillatory instabil-ity owing to undesirable dynamics of control loops caused by theterminal voltage in high-impedance grid.

Further, transient instability issues are a concern during faultclearance if the oscillation are not controlled, which is extremelyinfluenced by initial states. Hence, it is necessary to prioritize asecure LVRT scheme for the high impedance gird connected WECsto overcome instability issues during faults. The problem of insta-bility during LVRT is gaining significant importance by both windpower industry and academia, since vast number of wind system areconnected with high impedance AC grid. In [6] stability problemof wind energy conversion system during fault due to the injectionof current to the high-impedance grid is addressed. The switching

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International Journal of Pure and Applied Mathematics Special Issue

PLLs frequency, to either zero or infinity with the change in refer-ence current is stated as a concern of stability in [7]. A prolongedvoltage sag due to the PLLs feedback due to the high impedancegrid is stated as the reason for the issue in [8]. On the other hand,to improve the PLL stability, progressive method is implemented in[9]. Neglecting the influence of rotor current papers [6][9] are focus-ing on the stability issues caused by PLL alone. The influence ofGSC stability issue on a type-4 WECs during the period of severevoltage sag is covered in [10].

In all the above papers, the effect of RSC which has a high in-fluence on instability issues during fault condition on DFIG basedWECs is not concentrated. On the other hand, in some papers,works related to the small-signal behavior of DFIG has been inves-tigated, as an extended scope of normal generation. Whereas in[11] [15], the stability challenge are studied omitting the dynamicsof current controller. Paper [16] covers stability analysis of currentloop for RSC, with practical compensating term of back electromo-tive force taken into account. However, it disregards dynamics ofPLL and AC grid impedance. Whereas the influences of both PLLand current controller are highlighted in publication [17] and [18],neglecting to state the effect of RSC parameters on stability issues.

Fig. 1. LVRT scheme of DFIG-based wind turbines during gridfaults.

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2 Studied DFIG WT System and Mod-

eling

2.1 Description of studied DFIG system

The LVRT scheme of the studied DFIG-based WT along with high-impedance grid during symmetrical voltage sag is shown in Fig.1.Achopper controlled resistor is introduced in between the interme-diate DC circuit in order to dissipate the excessive energy dur-ing LVRT. In this paper, we consider that a severe symmetricalfault occurs on the grid at the point of common coupling alongthe transmission of weak grid. When grid fault endures, the faultpoint is demonstrated as equivalent residual voltage Ueqwith angu-lar frequency ω1. The impedance between the grid and the faultpoint, which plays an important role, consists impedance the of gridthat is of the long transmission lines and distribution impedance ofthe step-up transformers and the lines of wind farm. For differentfault condition, the value of grid impedance deviates from the pre-fault value. The impedance is designed in accordance withTheveninimpedance asZ1 = R1 + jω1L1.

Paper [1] addresses, general to most grid codes, during faultWECs are designed to inject reactive current in proportion to de-viation in voltage. Rotor side converter (RSC) is accountable forreactive current injection whereas the Grid-side converter (GSC)is accountable for upholding DC-bus voltage. Stator-voltage ori-ented vector-control based on phase-locked loop (PLL), withoutloss of generality, is utilized for the decoupled control between d-and q-axis currents. reference to alleviate. During LVRT, the DFIGconverter implemented in commercial WECs are generally viable ofslightly overloading.

2.2 System Modelling during LVRT in weak ACGrid

In order to synchronize DFIG with the grid, terminal voltage inPLL reference frame is utilized. The applied second order PI-basedPLL is represented as.

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ωd = (Kpp +Kip/S)(0 ∗ −θ) (1)θc = (ωδ + ω1)/S (2)

in which s represents Laplace operator, the feedback angle isgiven as θ and is selected as θ = ImU ct /Ut, where ω1 is angularfrequency. θc is the converter angle in the dq frame, during steadystate, ωg = ω1 and ωg is the grid converter angle in dq frame. Thephase difference is described as

δ =ωδ

S(3)

whereωδrepresent the angular speed difference between thesetwo frames. The transformation connection concerning vectors ingrid and converter dqframes is

F c = Fe−jδ (4)

in which F denotes standard space vector U,I and Ψ . The DFIGequations corresponding to the voltage and flux is represented as

Ut = RsIs + (jω1 + s)Ψs (5a)

Ur = RrIr + (jωs + s)Ψr (5b)

Ψs = LsIs + LmIr (5c)

Ψr = LrIr + LmIs (5d)

as shown in Fig.1,the design of PI-based RCC converter in dq frameis represented as

U (r ∗ c) = V cr + (Rr + jωcsσLr)Icr +LmLs

scslipαf

s+ αfU ct (6a)

V cr = (Kpi+Kiis/)(I∗cr − Icr) (6b)

in which f represents the cut-off frequency of first order low-passfilter. As the RCCs bandwidth is generally selected as much lesserthan switching frequency, U cr = U

(r ∗ c) is estimated.

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In the studied LVRT strategy, RSC is in charge of DFIG whileGSC only deals with slip power flowing through DC-bus which isdisturbed by RSCs dynamics. In this way, the dynamics of a givenGSC are actually conducted by RSC. Thus, RSC plays a fundamen-tal role in the dynamic behaviour of DFIG system. As discussingGSCs impacts is out of the scope of this paper, GSC is omittedin the following analysis. Based on this simplification, the currentinjected to the high impedance AC grid is

I1 = Cf (s+ jω1)Ut + Is (7)

where Cf is the shunt capacitor filter. In accordance with super-position theorem, the terminal voltage is the described as the sum-mation of the equivalent grid voltage and the voltage drop acrossthe impedance Z1.

Ut = Ueq − Vz1 = ueqejδ1 − (Z1 + sL1)I1 (8)in which the phase angle of equivalent grid voltage Ueq is denoted

as δ1 . Thus δ1 can be obtained, by solving (5) and (7) by neglectingCf and power dissipation on switching as well as the resistors ofDFIG. For steady state condition (8) is given as

Ut0 = K1ueqejδ1 +K2Ir0

K1 =1

[1 + Z1Zs

], K2 =

LmLs

[ 1Z1

+ 1Zs

]

(9)

Where Zs = Rs + jω1Ls.The value of δ1 can be obtained ,bysubstituting Utq0= 0 in (9) as

δ1 = a sin(Im{K2I∗r }(|K1|ueq)

)− 6 K1 (10)

which shows, in steady state the angle δ1 increases with lowerresidual grid voltage and large grid impedance.

2.3 PLL-RCC Interaction

In Fig.2. based on (1), (3) and (4), PLL is denoted by the blue box.Accordingly, RCC along with DFIG is represented by the red box.The red arrowed line represents the PLL and RCC interaction.

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Fig. 2. PLL- RCC interaction due to high grid impedance

From (5) and (6) the consequence of RCC can be constructedas

(sσLr+Kp+Ki/s)Icr = (Kp+Kis)I

∗cr +s

cslipα/(s+αf )

LmLs

U ct−(s+jωcs)LmLs

Ψcs

(11)From (11) rotor current dynamics in converter dq frame is ob-

tained. The dynamic regulation of RCC by rotor current is obtaineddue to the changes in terminal voltage, rotor current reference andstator flux witnessed in converter dq frame, thus stating that dy-namics of RCC is influenced by PLL.

Is =Ut − Lm(s+ jω1)IrRs + Ls(s+ jω1)

(12)

according which demonstrates that stator current is directly in-fluenced by rotor current. From equations, (7), (8) and (12), it isclear that the rotor current dynamics can be transmitted to termi-nal voltage that decides PLLs dynamics with high grid impedance.Thus, dynamics of RCC also influence PLL.

As a result, a closed-loop, from PLLs output and back to PLLsinput, is enclosed by high-impedance grid as shown in Fig. 2. Ac-cording to (8), as grid impedance increases, voltage drop on theimpedance becomes more considerable, which indicates stronger in-teractions. Thus, due to the interaction of PLL and RCC duringLVRT DFIG WTs connected to a high-impedance grid are sub-jected to objectionable dynamic behaviour.

3 Small Signal Stability Analysis

First an analysis model has to be developed in order to investigatethe effect of control loop of RSC during LVRT for small signal anal-ysis of DFIG based WECs and complex torque coefficient approach

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[10]. Small-signal behaviour during faults can be studied for highorder DFIG system by varying the depth of voltage sag in the gridwith modal analysis method. As in paper [10] and [11] the lin-earized state-space representation of the small signal model of thestudied system is given as

∆x′ = A∆xFrom [10] and [11] it is studied that small signal model during

deep voltage sag is a twelve-order model that has six oscillationmodes. Varying the residual grid voltage Ueq, which is related tosteady state operating point during LVRT, the eigenvalues of matrixA can be obtained. It is found that a pair of unstable poles willresult in the failure of LVRT, which indicates oscillatory instabilitywith deficient damping.

Since the identified unstable poles are due to poor damping,the complex torque coefficient Approach (CTCA), that deals withproblem due to insufficient damping on synchronous generator (SG)at necessary frequency range is applied. In the CTCA method theanalysis of electrical subsystem and the mechanical subsystem areperformed separately.

4 Influence Factors of Small Signal Sta-

bility

According to [10] and [11], in small-signal stability performance ofthe DFIG system, PLL and RCC have a vital role. Operating pointswhich influence stability are highly related to the reference currentduring LVRT. Thus the trade of between PLL and RCC parame-ters are studied based on the proposed analysis model of CPCMof [11]. The bandwidth of PLL usually influence, fast tracking andfiltering characteristics. While bandwidth of RCC, usually respon-sible for the switching frequency of PWM converters. In [22], RCCsbandwidth lesser than one fifth of switching frequency is suggested.Besides various factor, the speed of the rotor during LVRT androtor current reference, have substantial role on stability analysis.Hence, it is essential to analyse the influences of these parameters.

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4.1 Effects of RSCs Control Parameters

Based on papers (20) and (21), parameters of PLL are influencedby both inherent and additional complex phase coefficients. Paper[11] addresses that there is increase in total restoring coefficientwith PLLs bandwidth with decrease in the total damping. [10]concludes that negative damping due to RCC intends to reducewith increasing in RCC bandwidth, thus a fast RCC will improvethe small signal stability during LVRT. Thus from above referencesit can be stated that, during LVRT the small signal stability ofDFIG WECS, the net damping can be increased with increase inthe RCC bandwidth.

4.2 Effects of Rotor Current Reference

According to [1] and [2] utmost of the grid codes does not state therequirement of active current injection during faults. For a severevoltage sag, where reactive current is highlighted, the active can bedesignated in a range within the capacity of RSC. It is stated thatwith the decrease in ir and with reduced 1 result in greater utd0which reduces the negative damping in [9] and [10]. [11] states thatstability of DFIG WTs during fault can be improved by limitingthe rotor current reference.

4.3 Effect of Rotor Speed During Fault

The speed of the rotor during fault have greater influence on stabil-ity. The lower speed exerted by the rotor has the highly damagingimpact. Paper [11] addresses, small signal stability of DFIG systemis at higher threat for the grid fault happen at a lower wind speed,contrasting the case of transient stress problems like over voltageand over current.

5 Simulation Validation

In this section, the full order model of DFIG is used for a case study,proposed stability analysis of the typical 10 KW DFIG-WECS usingSim Power Systems toolbox in Mat lab/ Simulink. Obtained results

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of response rotor currents in grid for various values of PLL and RCCbandwidths, rotor speeds, and residual grid voltages are as follows.

5.1 Voltage stability analysis

5.1.1 Stator and Grid Voltage during fault duration

In this paper, three phase symmetrical fault is considered at thePCC,the duration of the fault period is taken as 1 sec for whichthe system is short circuited. Fig.3. shows the stator voltage andcurrent during the fault duration.

Fig.3.Stator voltage and current during fault

Fig.4 represents the grid voltage and current during the threePhase symmetrical fault duration

Fig.4.Grid voltage and current during fault duration

5.1.2 Stator and Grid Voltage during fault ride through

The obtained simulation results of stator voltage and current duringthe period of LVRT is shown in Fig.5.It can be seen from the resultsthat by implementing the proposed controller design the system ismade to stay in connected with the grid during the period of LVRT.

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Fig.5.Stator voltage and current during fault duration

Fig.6.shows the grid voltage and current during LVRT,for whichthe short circuit condition as explained in Fig.4. is rectified usingthe proposed controller design.

Fig.6.Grid voltage and current during fault duration

Fig. 7 shows the responses of rotor current indq frame to differentamplitude (a)CASE 1 (0.8 pu) (b) CASE 2 (1 pu) (c) CASE 3(1.2pu) of grid voltage during fault (ueq = 0.29 p.u., ωr = 0.8 p.u., αPLL = 15.5 Hz).As predicted ,lower residual grid voltage results inhigher risk of DFIG system during LVRT.

Fig.7 Rotor current response in dq frame to different amplitude(ueq = 0.29 p.u., ωr = 0.8 p.u.,αPLL = 15.5 Hz). (a) CASE 1 (0.8

pu)(b) CASE 2 (1 pu)(c) CASE 3(1.2 pu)

In Fig.8 the responses of rotor current at different rotor Speeds(a) CASE 1 (1550 rpm) (b) CASE 2 (1500rpm) (c) CASE (1600rpm).Itis seen, with lower rotor speed operation of DFIG the oscillationsare predominantly high.

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Fig.8 Rotor current response in dq frame to different Speed (ueq= 0.29 p.u., ωr = 0.8 p.u.,αPLL = 15.5 Hz). (a ) CASE 1 (1550

rpm)(b) CASE 2 (1500 rpm)(c) CASE 3 (1600 rpm)

In the same way, Fig 9 compares the influence of PLLs band-width on dq frame for three different bandwidth (a)CASE 1 (15.5Hz) (b) CASE 2(13.5Hz) (c) CASE 3 (14.18Hz).As stated with in-crease in PLLs bandwidth ,the FIG system behaves negative damp-ing.

Fig.9 Responses of rotor current in dq frame to different PLLbandwidth (ueq = 0.29 p.u.,ωr= 0.8 p.u., αPLL = 15.5 Hz). (a)

CASE 1 (15.5 Hz)(b) CASE 2(13.5Hz)(c) CASE 3 (14.18Hz)

Finally in Fig.10 the response of RCCs bandwidth on the d-and q-axis rotor currents are compared in three case (a) CASE 1(15.5 Hz) (b) CASE 2(13.5) (c) CASE 3 (14.2).As analysed before,the results shows that with decrease in RCC bandwidth, there isan increase in oscillations with increasing amplitude.

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Fig.10 Responses of rotor current in dq frame to different RCCbandwidth (ueq = 0.29 p.u., ωr = 0.8 p.u., αPLL = 15.5 Hz). (a)

CASE 1 (15.5 Hz)(b) CASE 2(13.5)(c) CASE 3 (14.2)

TABLE-I

6 Conclusion

In this paper, small signal behaviour of DFIG based wind turbinesconnected to weak AC grid during deep voltage sag is investigated.According to the simulation results, optimizing the parameters ofPLL and RCC can improve the small signal stability during LVRT.During deep voltage sag, the proposed controllerreduces the activerotor current which in turn is used to damp the oscillations. Fromthe obtained simulation results it is evident that, during LVRT,thesmall signal stability of system becomes worse at lower speed ofrotor.

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analysis of grid connected dfig-based wind turbines during lvrt · 2018. 6. 17. · the...

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