No. E-13-AAA-0000 Sliding Mode Control of DFIG Under

No. E-13-AAA-0000

Sliding Mode Control of DFIG Under Unbalancedand Harmonic Distorted Grid Voltage with Balanced

Stator Voltage

Amir Elahi, Golam Reza ArabDept. of Electrical Engineering

Shahrekord UniversityShahrekord, Iran

[email protected]

Jafar SoltaniDept. of Electrical Engineering

Isfahan University of technologyIsfahan, Iran

[email protected]

Abstract—This paper suggested an enhanced control strategyfor Doubly Fed Induction Generator (DFIG) based on windgeneration with Series Grid Side Converter (SGSC) underunbalanced and harmonic distorted grid voltage conditions. Inorder to balancing stator voltage and subsequently stator androtor currents, a seriesvoltage is generated by SGSC and injectedto the grid. Furthermore the fluctuations of stator active andreactive power and electromagnetic torque have been removed. Anovel control method based on Sliding Mode Control (SMC) andwithout sequential decomposition of measured variables, ispresented for control of SGSC. Also a new enhanced controlmethod for dc link voltage is suggested using Parallel Grid SideConverter (PGSC). The controller is capable of removingoscillation in dc voltage link.Finally the proposed control methodfor DFIG system with SGSC has been validated by simulationresults for a 2MW DFIG in both unbalanced and harmonicdistorted grid voltage conditions.

Keywords—DFIG; Sliding Mode Control; Unbalanced GridVoltage; Sequential Decomposition

I. INTRODUCTION

Nowadays, due to the increased concern aboutenvironmental pollutions, the increase of greenhouse gasemissions, and decrease of fossil fuels, the use of renewableenergies attracted the attentions more than ever. Among theseenergies, the wind energy has been developed more than othertypes of energies, due to its profitability and low maintenancecosts. Among the used machines in wind turbines, DFIG hasthe most usage in electrical energy conversion [1]. Based onEN50160 standard [2] the network may has a certainpercentage of voltage unbalance and harmonic distortions.This distorted voltage can cause many problems in theperformance of DFIG like as existence of 2ωs oscillations onactive and reactive power, generating unequal heat in rotorand stator windings, and torque ripple generation on machineshaft.

Control methods of the wind turbines that are equippedwith grid connected DFIGs can be classified into two generalcategories: vector control and Direct Power Control (DPC)methods. In vector control methods by regulating rotor andstator currents in separate loops by using PI controllers, statoractive and reactive power control can be achieved.

In [3] two separate PI controllers were used; one forcontrol the positive sequence component of rotor current, andthe other for controlofnegative sequence.This method needsprecise regulation of PI controllers; in addition it is not robustto parameter variations. For instance, if the stator or rotorresistance changes due to heat increase, the PI coefficientshould be retuned. Proportional Integral Resonant (PI-R)controllers are used in [4] and it had a better dynamicresponse, but it is still need to regulate the controllerparameters precisely, and it is not robust to parametervariations. Also in this reference, the parameters aretransferred to synchronous reference frame and it needs morecalculations. In [5] a control method based on DPC+ ispresented which provides the direct control of active andreactive power of DFIG in unbalanced grid voltage condition.In thispaper, only one of the twocontrol targetscan becompletely obtained, 1)sinusoidal and symmetrical statorcurrent, or 2) regulated active and reactive generated power. In[6] a control method based on sliding mode control has beensuggested. In this method the active and reactive powercompensation component are calculated via a simple methodand proposed three control targets, can be achieved, but ineach time only one of the control targets can be realized. In [7]the sliding mode control method without decomposition isused for controlof active and reactive power under unbalancedand harmonic distortedgrid voltage, but stator voltages andcurrents, rotor currents are still unbalanced and dc link voltageis not controlled properly.

In all investigated references, the rotor and stator currentsand stator voltages are unbalanced or harmonically due to thedirect connection of stator to unbalanced or harmonically gridvoltages. In order to overcome above problems, [8] issuggestedto use three converter structures consist of RotorSide Converter (RSC), PGSC and SGSC with common dcvoltage linkthat is shown in Fig. 1.In this paper three controltargets are identified to PGSCand a conventional vectorcontrol with PI-R controller is applied to RSC,such thatseparation of negative and positive sequences is mandatory,but it is not possible to achieve all control targetssimultaneously. Furthermore this method is not robust toparameter variation.

In [9] by using the previous structure and controlalgorithm, among three introduced objective functions, each

Sliding Mode Control of DFIG under Unbalanced and Harmonic Distorted Grid Voltage with Balanced Stator Voltage28th Power System Conference - 2013 Tehran, Iran

2

time it is only possible, to access one of thesetargets.[10]applyingseries converter with separate dc voltagelink by using control method based on phasor analysis. Thisstructure and method have increased system costs, and also itis not robust to uncertainties.

In this paper, using sliding mode controllers and withoutdecomposition of variables, control of stator active andreactive powers, dc link voltage (Vdc), electromagnetic torque(Te) and total power of network can be achieved,simultaneously. Also currents and voltages of stator andcurrents of rotor have been balanced. By using this structureand suggested control methods, in addition to reducing torqueripple and removing stator unbalance heat windings, thecontrol system will be robust to parameter uncertainties.

This paper organized as follows; first in section II themathematical model of DFIG in stationary reference frame ispresented. In sections III,IV and V after descriptionmathematical model of DFIG converters and their objectivefunctions, designing of these controllers based on slidingmode control are given.Simulation results are given in sectionVI that demonstrates the effectiveness of the proposedsolution.

Fig. 1. Configuration of DFIG system with SGSC

II. MATHEMATICAL MODEL OF DFIG

DFIG electrical equivalent circuit, based on space vectorsand by considering motor condition in stationary referenceframe, is shown in Fig. 2. Voltage equations of DFIG instationary reference frame can be expressed as:

(1) = + = + − Where

(2) = + = +

In above equations Rs and Rr are stator and rotorresistance. Also Ls and Lrare stator and rotorinductance, andLm is magnetization inductance. Instituting (2) into (1) gives:

(3) = + +

− ( + )

Fig. 2. Equivalent circuit of DFIG in stationary reference frame

In this equation, = − / . By using above equations,space phasor of rotor currents in stationary reference frame isderived as:

(4)

= − − +( + )Many researches have investigated Ps and Qs control by

RSC. But since torque ripple can reduce lifetime of machineshaft, in this paper electromagnetic torque control wasperformed instead of Ps. The torque and stator reactive powerequations based on stationary reference frame variables, areexpressed as:

(5)= 32 ( − )= 32 ( − )

III. RSC

A. Modeling

A schematic of RSC is shown in Fig. 3. In thisfigureUraN,UrbN andUrcN represent the voltages between of eachconverter leg and common point of dc link (N point).

Fig. 3. Schematic of RSC

(6)= ( − ) , = 1 −= ( − ) , = 1 −= ( − ) , = 1 −Where u0 = Vdc /2, and by solving the above equations,

switch conditions will be obtained as:


3

(7)= 0.5 (1 + / )= 0.5 (1 + / )= 0.5 (1 + / )

The relationship between rotor voltages in stationaryreference frame and the voltage between each converter legand N point can be obtained as:

(8)

=

= 13 2 −1 −1−1 2 −1−1 −1 2 ,= 23 ⎣⎢⎢⎡1 −12 −120 √32 − √32 ⎦⎥⎥

⎤ , = −where M1 is the transformation matrix between Vr and

phase voltages of DFIG windings, M2 is Clarke’stransformation matrix, and M3 is transition matrix from rotorreference frame to stationary one. In the above matrix, θr isrotor angle.

B. SMC of the RSC

Regarding to the importance of Te ripple reduction andstator reactive power control, Te and Qs have been selected forcontrol targets of RSC. Therefore, the following slidingsurfaces have been suggested:

(9)= + ∫ , = ∗ -= + ∫ , = ∗ -

Where λTe and λQs are positive constants and set to 1. Thederivation of sliding surfaces respect to timeexpressed as:

(10) = ∗ - + ( ∗ − ) = ∗ - + ( ∗ − )T andQ will be obtained based on (5) as follow:

(11) = 32 + і − − і = 32 ( + і − − і )

By separating (4) to real and imaginary parts andsubstituting in (11), then (10) can be rewrittenas:

(12) = − 32 − −

Where and are functions of the state variables, thereference inputs and their time derivatives, but they do notdepend on the control signals and .By substituting (8)into (12), yields:

(13) = − 32Since matrix is time-varying. The controls defined

in Ur cannot perform their switching depending on .Inthis case a transformed vector of new switching functions isrequired to achieve a time-invariant control matrix [12].Design the transformation as:

(14)∗ = 23Where ∗ = [ ∗ ∗ ∗] is the transformed switching

function, is the pseudoinverse matrix of given as:

(15)= ( ) = 32 ( )Finally the control input can be expressed as:

(16)= u sgn(S∗)sgn(S∗) = [sgn(s∗) sgn(s∗) sgn(s∗)]It can be proved that for a sufficiently large dc link

voltage, system (12) with a control input of (16) and referencesliding surface (14), the output error will converge to zero infinite time. ([7,12] )

IV. PGSC

A. Modeling

A schematic of PGSC is shown in Fig. 4. Electricalequations of PGSC in stationary reference frame can bewritten as:

(17)= −Where:

(18-a)= 32 ( + )(18-b)= 32 ( − )(18-c) = + +

Where and are grid-side converter output active andreactive powers respectively. . is the space vector of gridvoltage.Ugn=[U U U ]T is space vector represents thevoltage between each inverter leg and N point.The relationshipbetween abc and dq axis voltagescanbe written as:

(19)=


4

Fig. 4. Scheme of PGSC

B. SMC of the PGSC

The control objectives in PGSC are dc link voltageregulation and reactive power control. In this paper,incontradiction of the previous researches, an enhanced controlmethod based on sliding mode is suggestedto regulate dc linkvoltage, such that the error of Vdc controlis used to designsliding surfaces.Superiority of this control method comparingto other works are no need to PI controller coefficient tuningand robustness to parameter variations. Furthermore inproposed control method,Vdc ripple significantly decreased.Itcan be proved that, in this state, the total active power of thesystem can be controlled without fluctuation. Since the secondobjective function in PGSC is reactive power of grid side, thefollowing sliding surfaces can be selected:

(20)

= + + ∫ , =∗ -= + ∫ , = ∗ -

By derivative from sliding surfaces:

(21)

= − − + ( ∗ − ) = ∗ - + ( ∗ − ), and are positive constants and set to 1. It should

be mentioned that for reducing PGSC converter powerrating,Qg

* is taken equal to zero.By derivation of active and reactivepower of PGSC from (18), and substituting (17) and(18-c) into(21):

(22)

= − 32 −− −Where and are functions of the state variables, the

reference inputs and their time derivatives, but they do notdepend on the controls and .By substituting (19) in(22), yield:

(23) = −Similarly to RSC control design, Finally the required

voltage for PGSC can be derived as:

(24)= ⎣⎢⎢⎡ (− − )( ( − √3 ) + ( + √3 ) )( ( + √3 ) + ( − √3 ) )⎦⎥⎥

⎤

By using these voltages, the on or off states of the inverterswitches can be obtained similarto (7). The designed controlleris robust to uncertainties, and the proof of its stability easilycan be shown and are discarded because of paper Numberlimit.

V. SGSC

A. Modeling

A schematic of SGSC is shown in Fig. 5. Main purpose ofSGSC is for balancing stator voltages and currents andalsorotor currents in unbalanced and harmonic distorted gridvoltage conditions. In this condition,series converter usedtobalance stator voltages, and subsequently stator and rotorcurrents by injecting an unbalanced series voltage to gridvoltage. As well as, ifthe network voltage is fluctuated withharmonic, SGSC makes statorvoltages and currents free ofharmonic distortion.From Fig. 5, output voltage of SGSC canbe calculated as:

(25)= −= −

The relationshipbetween abc and dq axis voltages of SGSCcan be written as:

(26)=

Fig. 5. Scheme of SGSC

B. SMC of the SGSC

As was mentioned in the previous section, the objective ofSGSC control is stator voltage balancing. In the other words,SGSC should generate the fluctuated term of grid voltage innegative sign and deal as a series active filter.So, the referencevoltages of SGCS can be expressed as:

(27)∗ = − ∗∗ = − ∗Where ∗ , ∗ are stator reference voltages, and ∗ ,∗ are SGSC reference voltages.Therefore, the following

sliding surfaces are defined as:

(28)= , = ∗ −= , = ∗ −and are positive constants and set to 1. Using the

Differentiating (28), yields:


5

(29) = − 0 0

Where and are functions of the reference inputs, butthey do not depend on the control signals ,

.Substituting (26) in (29), concludes:

(30) = −Similarly to previous sections, the required voltage for

SGSC can be obtained as follows:

(31)= ⎣⎢⎢⎢⎢⎡ ( )(− 12 + √32 )(− 12 − √32 )⎦⎥⎥

⎥⎥⎤By using these voltages, the on or off states of the inverter

switches can be obtained similar to(7). The stabilityproofeasily can be shown and are discarded because of paperNumber limit.

VI. SIMULATION RESULTS

To verify the proposed controlalgorithm,simulationsareperformed by usingMATLAB/SIMULINK software. DFIG parameters are listedin Table 1.Simulation is performed in three tests.

TestA: DFIG is connected to network, with 20%unbalanced voltages in phase’sb and c.

Test B: DFIG is connected to a network with voltageharmonic distortions about: V5= 6%and V7=5%.

In test A and B, simulations are performed, one time forDFIG with RSC and PGSC, and the other time for DFIG withRSC, PGSC and SGSC.

Test C: the robustness of proposed control algorithmagainst parameter variations for DFIG with SGSC is verified.

TEST AThe results of simulation, in a state that it is connected to

unbalanced voltage network are shown in Fig. 6. Thesimulation results show that in a state that SGSC isconnectedto DFIG structure, in addition to supplying control objectives,Ps andTeripple is decreased significantly. Te ripple Reductioncan increase the useful lifetime of machine shaft, bearings, andfewer needs for periodical repairs and services. In addition, incontrol scheme with RSC and PGSC based on Fig. 6.A.d, the2ωs fluctuation is seen in stator active power, but it has beenremoved in DFIG with SGSC based on Fig. 6.B.d.removingactive power fluctuation can be improved network stability. Itcan be observed that rotor currents, stator currents andvoltages in 3 converter scheme with proposed algorithm havebeen balanced, While in control method with 2 converter, therotor and stator currents are unbalanced and this causedcreating unbalance heat in stator and rotor windings and it willalso affected on power quality generated by DFIG.

TEST BIn this test, DFIG simulation is presented in a state that it is

fed by a network with voltage harmonic distortions. It isassumed that the network voltage, in addition to fundamentalharmonic, has fifth and seventh order of harmonics with THDpercent equal to 8. The simulation results are shown in Fig.7.Since the resultant of rotating magnetic field of fifth orderharmonic is in opposite direction of rotating field caused byfundamental harmonic, existence of this harmonic order indouble converter structure, create breaking torque on machineshaft which will reduce shaft lifetime and increase Te ripple.

TABLE I. DFIGPARAMETERS

parameter Rs Rr Lls Llr Lm Vdc* Rg C Lg

Stator voltage(rms)

RatedPower

P (polepairs)

value 2.6m

2.9m

77.306 83.369 2.5mH

1200V

0 16mF

0.25mH

690V

2 MW 2


6

(A)

(B)Fig. 6. Simulation results under unbalanced grid voltage for DFIG with (A) RSC and PGSC. (B) RSC, PGSC and SGSC.(a) Zoom of the Stator voltage. (b)Statorcurrents. (c)Rotor currents. (d)Stator active power. (e)Grid side reactive power. (f)Stator reactive power. (g)Electromagnetic torque. (h)DC link voltage.

Fig. 7.B.g shows that by adding SGSC and suggestedcontrol method, the problem of breaking torque and torqueripple are resolved by removing fifth and seventh order

harmonics. Also it shows, THD of stator voltages have beendecreased greatly in comparison to double converter structure.

(A)


6

(A)




(A)


6

(A)




(A)

No. E-13-AAA-0000

(B)Fig. 7. Simulation results under harmonic distorted grid voltage for DFIG with (A) RSC and PGSC. (B) RSC, PGSC and SGSC.(a) Zoom of the Stator voltage.(b)Stator currents. (c)Rotor currents. (d)Stator active power. (e)Grid side reactive power. (f)Stator reactive power. (g)Electromagnetic torque. (h)DC link voltage.(A) two converter struccture. (B) three converter structure

TEST CSince the machine parameters change while working due

to windings heat and network voltage conditions, the controlmethod should be robust against parameter variations and itshould be able to meet the control objectives even in thisconditions. Among machine parameters, stator and rotorresistance have the most uncertainty. Therefore, stator androtor resistance have been increased 40% their nominal values,while grid line inductance(Lg) has been decreased their respectvalues with the same percentage. The grid voltage like test a,

is considered to be unbalanced in two phases. The simulationresults for DFIG with series converter and the suggestedcontrol algorithm is shown in Fig. 8.

Changes in Rs and Rr caused error estimation in stator androtor fluxes. Since sliding mode control of PGSC and SGSCdon’t need information about machine parameters, PGSC’sreactive power control and SGSC’s voltage control is notunder the effect of parameter variations in no way.

Fig. 8. Simulation results under parameter variations for DFIG with RSC, PGSC and SGSC.(a)Stator voltage. (b)Stator active power. (c)Grid side reactivepower. (d)Stator reactive power. (e)Electromagnetic torque. (f)DC link voltage.

CONCLUSION

In this paper, sliding mode techniqueis used to controlofDFIG with SGSC in unbalanced and harmonic distorted gridvoltage condition.Also a novel method for dc linkvoltagecontrol is presented based on sliding mode control. Thesuggested control method is capable to reduce dc link voltageripples. As well as, harmful electromagnetic torque ripples onMachine shaft are reduced intensely and generated activepower fluctuationsare removed perfectly. Furthermore theproposed control algorithm is able to free the stator currentsand voltages and rotor currents from harmonic and balancethem. The simulation results in addition to confirming theabove statements show the simultaneous achievement of allcontrol objectives with better precision and robustness againstparameter variations in comparison to the previous controlmethods.

REFERENCES

[1] J. Hu, and Y. He, “DFIG wind generation systems operating with limitedconverter rating considered under unbalanced network conditions-analysis and control design,” Renew. Energy, vol. 36, no. 2, pp. 829-847,Feb. 2011.

[2] Voltage Characteristics of Electricity Supplied by PublicDistribution System, European Standard EN50160, CENELEC,Brussels, Belgium, 2007.

[3] Y. S. Lai, and J.H. Chen, “A new approach to direct torquecontrol of induction motor drives for constant inverter switching

frequency and torque ripple reduction,”Energy Conversion,IEEE Transactions on, vol.16, no.3, pp. 220-227, Sep 2001.

[4] J. I. Jang, and Y. S. Kim; and D. C. Lee, “Active and Reactive PowerControl of DFIG for Wind Energy Conversion under Unbalanced GridVoltage,”Power Electronics and Motion Control Conference,2006.IPEMC 2006. CES/IEEE 5th International, vol. 3, no. 1, pp.14-16,Aug. 2006.

[5] D. S. Martin,J. L. R. Amenedo, and S. Arnalte, “Direct PowerControl Applied to Doubly Fed Induction Generator UnderUnbalanced Grid Voltage Conditions,”Power Electronics, IEEETransactions on, vol.23, no.5, pp. 2328-2336, Sept. 2008.

[6] L. Shang, and J. Hu, “Sliding-Mode-Based Direct PowerControl of Grid-Connected Wind-Turbine-Driven Doubly FedInduction Generators Under Unbalanced Grid VoltageConditions,”Energy Conversion, IEEE Transactions on, vol.27,no.2, pp. 362-373, June 2012.

[7] M. I. Martinez, G. Tapia, A. Susperregui, and H. Camblong,“Sliding-Mode Control for DFIG Rotor and Grid-Side Converters UnderUnbalanced and Harmonically Distorted Grid Voltage,”EnergyConversion, IEEE Transactions on, vol.27, no.2, pp. 328-339, June2012.

[8] Y. Liao, H. Li, J. Yao, and K. Zhuang, “Operation and control of a gridconnected DFIG-based wind turbine with series grid-side converterduring network unbalance,” Electr. Power Syst. Res., vol. 81, no. 1, pp.228–236,2011.

[9] J. Yao, H. Li, Z. Chen, X. Xia, X. Chen, Q. Li, and Y. Liao,“Enhanced Control of a DFIG-Based Wind-Power GenerationSystem With Series Grid-Side Converter Under UnbalancedGrid Voltage Conditions,”Power Electronics, IEEETransactions on, vol.28, no.7, pp. 3167-3181, July 2013.


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[10] S. Zhang, K. Tseng, S. S. Choi, T. D. Nguyen, and D. Yao,“Advanced control of series voltage compensation to enhancewind turbine ride through,” IEEE Trans. Power Electron., vol.27, no. 2, pp. 763–772, Feb. 2012.

[11] L. Xu, “Coordinated control of DFIG’s rotor and grid sideconverters during network unbalance,” IEEE Trans. PowerElectron., vol. 23, no. 3, pp. 1041–1049, May 2008.

[12] V. Utkin, “Sliding mode control design principles andapplication to electric drives,” IEEE Trans. Ind. Electron, vol.40, no. 1, pp. 23-36, Feb. 1993.

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No. E-13-AAA-0000 Sliding Mode Control of DFIG Under