A Linear Active Disturbance Rejection Control Applied For .
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.org391A Linear Active Disturbance Rejection Control applied for DFIGbased Wind Energy Conversion SystemAli Boukhriss1, Tamou Nasser2 and Ahmed Essadki 312Laboratoire de Génie électrique, ENSET, Université Mohamed 5Rabat, MoroccoEcole Nationale Suprieure d'Informatique et d'Analyse des Systemes, Université Mohamed 5Rabat, Morocco3Laboratoire de Génie électrique, ENSET, Université Mohamed 5Rabat, MoroccoAbstractThis paper proposes the control of a doubly fed inductiongenerator DFIG used in wind turbine energy conversion. Thecontrol strategy is based on the linear active disturbance rejectioncontrol ADRC to generate the control voltages of the rotor sideconverter RSC and the grid side converter GSC, due to thechanges in control inputs. The ADRC, based on the extendedstate observer ESO, estimate and compensate in real time all theinternal and external disturbance of the physical plant, such as,the parameter uncertainties due to the temperature variation, thecross-coupling terms and the load current variation into the dclink voltage. Simulations results are carried out with MATLAB/SIMULINK.Keywords: Doubly Fed Induction Generator, ActiveDisturbance Rejection Control, Extended State Observer, WindEnergy, Back To Back Converter.ADRC is used to control the rotor side converter RSC andthe grid side converter GSC.2. Dynamic ModelThe model system of converting wind power using DFIG isrepresented in Fig.1. The kinetic energy of wind isconverted by the turbine connected via a gear box to theaxis of the DFIG. The stator is connected to the networkthrough a back to back converter through the filter (Rf, Lf),while the stator is directly connected to the network.Vector control techniques are used for decoupling of activeand reactive power. Unity power factor is often set at GSCand reactive power is transited directly between thenetwork and the stator depending on the command of theRSC.1. IntroductionNow the global trend towards the use of renewableenergy is increasing, in this case, wind energy begins totake a large part in the global market. Variable speed windusing DFIG have a major advantage, seen mainly inreducing of the size and cost of power converters, in factthe power transiting through the back to back converter isabout 30–40% of its rated power [1], while allowing avariation of the rotor speed over a range of 0.7 to 1.3 of thesynchronous speed. The control of DFIG using PIcontroller is widely used [2][3], however it has a majordrawback when the internal DFIG parameters are subjectto variations due to the effects of temperature, whichconsequently affect the performance of regulators [4][5].ADRC method proposes a control law which is not basedon the accurate mathematical model of the system [6][7],therefore all internal and external disturbances areestimated and rejected in real time, hence the name of theactive disturbance rejection control ADRC. In this paper,Fig. 1 Schematic diagram of DFIG-based wind generation systems.In this paper three commands will be developed to ensurethe functioning of the wind turbine: Maximum power pointtracking control MPPT, control of rotor current at RSCand control of the DC link voltage and power factor atGSC.Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.org3923. Mathematical Model3.1 Turbine ModelThe power and the torque on the shaft of the turbine aregiven by the expression:1(1)Pt C p , Sv 321v3(2)Tt C p , S2 tWhere is the Tip speed ratio of the rotor blade tip speedto wind speed defined as: R(3) tv is the air density, S is the surface swept by the blades ofthe turbine, t is the turbine speed, v the wind speed, pitch angle and Cp represents the wind turbine powercoefficient given by the empirical expression:12.5 116 (4)C p , 0.22 0.4 5 e 0.0068 i 110.035 3 i 0.08 1(5)iFig.2 shows the Cp curve for 0.50.450.4Power Coefficient Cp0.350.3Fig. 3 Turbine model.3.2 DFIG ModelThe model of DFIG is established in the synchronousreference dq. Stator and rotor voltages are given by thefollowing expressions, where R, L, Lm, and and Irepresent respectively resistance of windings, inductance,mutual inductance, flux and current. The subscripts s, r, dand q respectively indicate stator, rotor, d-axis and q-axis.d ds . s qsdtd qs .Vqs Rs I qs s dsdt.d Vdr Rr I dr dr r qrdtd qr .Vqr Rr I qr r drdt ds Lm Lls I ds Lm I drVds Rs I ds qs Lm Lls I qs Lm I qr0.250.2 dr Lm Llr I dr Lm I ds0.15 qr Lm Llr I qr Lm I tic torque Te is written as:0246810Tip Speed Ratio121416Fig. 2 Turbine power coefficient.The turbine shaft is connected to that of the DFIG througha speed multiplier k. Fig.3 shows the mechanical modelwhere Jt and Jm represent respectively the coefficient ofinertia of the turbine and the generator and fv is theviscosity coefficient. Tt and Tm represent respectivelymechanical torque of turbine shaft and generator. m is therotational speed of the generator. Mechanical equation iswritten as: Jt d (6) 2 J m m f v m Tm Temk dtTe Lm3p( qs I dr ds I qr )2 Lm Lls(15)Active and reactive stator power is given in synchronousreference dq-axis by the expression:3(16)Ps (Vds I ds Vqs I qs )23(17)Qs (Vqs I ds Vds I qs )23.3 Back to Back PWM ModelingThe back to back allows bidirectional transit of powerbetween the rotor and the network [8]. Fig.4 represents therectifier and inverter connected by the dc link voltage.Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.org393The basic idea is the estimation and compensation of f. Eq.(24) can be written in an augmented state space form as: . x1 x2 b0 u .where x 2 h y x1 .h f(25)Or in the matrix form: .x Ax b0 Bu Eh y Cx(26)WhereFig. 4 back to back converter.tSmn indicates switching functions corresponding to theIGBT switches where (m denotes a, b and c arms and ndenotes inverter i or rectifier r). if , irec and iinv arerespectively the current in the filter, the output current ofthe rectifier and the input current of the inverter. iinv isconsidered as a load current for the rectifier converter. Indq-axis reference frame, relations between voltage andcurrent are given by:du dc irec iinvdt3irec S qr I qf S dr I df2dI dfLf R f I df L f s I qf Vds Vds1dtdI qfLf R f I qf L f s I df Vqs Vqs1dtVds1 Sdrudc(18)Vqs1 Sqrudc(23)C (19)(20)(21)(22)4. Active Disturbance Rejection ControlThe active disturbance rejection control was proposed byHan [9][10][11][12]. It is designed to deal with systemshaving a large amount of uncertainty in both the internaldynamics and external disturbances. The particularity ofthe ADRC design is that the total disturbance is defined asan extended state of the system; and estimated using a stateobserver, known as the extended state observer (ESO). Itwas also simplified to linear ADRC using the linear ESO,which makes it easy and convenient to implement [13][14].We consider the case of first order system for theillustration of the method.(24)y f y, w, t b0uWhere u and y are input and output variables. w is theexternal disturbance, and f(y,w,t) represents the combinedeffect of internal dynamics and external disturbance and b0parameter to estimate. 0 1 1 1 0 A ; B ; C ; E 0 0 0 0 1 A state observer of Eq. (25) will estimate the derivatives ofy and f since Eq. (25) is now a state in the extended statemodel.This observer denoted as a Linear Extended State ObserverLESO is constructed as: . z Az b0 Bu L y y whereL 1 y Cz 2 (27)L is the observer gain vector. To simplify the tuningprocess, the observer gains are parameterized as [15]: 2 L 20 0 Where, 0 is the bandwidth of the observer determined bythe pole placement technique [15]. The estimate is moreprecisely by increasing the bandwidth of the observer;however, a wide bandwidth increases the sensitivity tonoise. In practice, a compromise is made between thespeed at which the observer tracks the states and itssensitivity to sensor noise. With a properly designed ESO,z1 and z2 are tracking respectively y and f.The control law is given by:u z(28)u 0 2b0The original plant in Eq. (24) is reducing to a unit gainintegrator.y f z 2 u0 u0.(29)This can be controlled by a simple proportional controller.(30)u0 k p r z1 Where, r is the input signal reference to track.The controller tuning is chosen as kp c, where c is thedesired closed loop frequency [14].The combination of linear ESO and the controller is thelinear ADRC. Generally we choose 0 3 7 c, andconsequently, c is the only tuning parameter. Fig.5represents the implementation of the linear ADRC.Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.org394rotation speed sensor. Maximum power extracted can bewritten as:1R53(37)Pt max C p max t32 opt1R52Tm C p max 2 3 m2k optWhere, opt is the optimal tip speed ratio corresponding tomaximum power coefficient Cpmax.In a steady state and neglecting the effect of viscosity,Eq.(6) leads to Tm Tem. It follows that the electromagnetictorque reference is given by:ref2(39)Tem kopt mFig. 5 Architecture of the developed ADRC controller.5. Rotor Side ControlThe control strategy is based on the orientation of thestator flux on the d-axis. We recall that the voltage of astator phase in reference is given by:d s V Rs i dt(31) d s V R i s dtAngle s required to the Park transformation can becalculated as: s V Rs i dt s V Rs i dt s arctg s s (38)(32)(33)Neglecting the effect of the stator resistance Rs, it followsthat the voltage and the stator flux are rotating at the samespeed with a shift angle of 90 . It follows: Vds 0 (34) Vqs VsThe electromagnetic torque and the stator reactive powerare given by:3 L(35)Te p m ds I qr2 Ls L3 (36)Qs Vqs ds m I dr 2 Ls Ls Ls Lm Llswhere Lr Lm LlrThe electromagnetic torque Te and reactive power Qs arecontrolled respectively by the rotor currents Iqr and Idr.To get the electromagnetic torque reference Temref,Maximum Power Point Tracking (MPPT) strategy is usedto extract the maximum of power from the wind velocity.MPPT strategy applied in this paper only requires aWhere1R5(40)kopt C p max 2 32k optThe reference rotor currents are then deducted fromEqs.(35) and (36):1 2 Ls ref ref(41)I dr ds Qs Lm 3 Vqs 2 Lsrefref(42)I qr Tem3 p ds LmThe expressions of the rotor currents can be put into theform:dI dr VdrLmL d dsR(43) m r I r I qr rdt Lr Lr dr Lr Ls qs Lr Ls dtdI qr VqrLmL d qsR(44) r I qr r I dr r ds mdt Lr Lr Lr Ls Lr Ls dtThis, leads for the Idr current, and the same study is usedfor Iqr current, to:dI dr(45) f I dr , d , t b0u t dtWhere L d 1RrI dr r I qr m r qs ds b0 Vdr f L LLdt L rr s r u Vdr (46)f represents the generalized disturbance, Idr and u denoterespectively the output and the control input of the plant,b0 is the parameter gain to approximate. A linear activerejection control LADRC is easy to implement to controlthe rotor currents. Fig.6 shows a schematic block diagramfor the rotor side control.Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.org 2 12 3 f w iinv Vqs b0 I qfc c u Iqf 395(53)Where, f represents the generalized disturbance, w and Iqfare respectively the output and the control input of theplant. b0 the parameter to approximate.So the linear ADRC can be used in the voltage loop.6.2 Regulation of the Current LoopFig. 6 schematic block diagram for the rotor side control.6. Grid Side ControlThis converter has two roles: to maintain the DC busvoltage constant regardless of the magnitude and directionof the rotor power flow and maintain a unity power factorat the connection point with the grid. A voltage orientedcontrol VOC is used to control the grid side converterGSC.6.1 Regulation of the Voltage LoopIf we neglected losses in three phase PWM rectifier, theinput active power Pf is equal to the DC link power Pdc,that is:Pf PdcA phase locked loop PLL is used to orient the voltage onthe q-axis and so the voltage on the d-axis is equal to zero.The input active Pf and reactive power Qf is writing in dqaxis as:3(47)Pf Vqs I qf23(48)Q f Vqs I df23(49)Pdc u dcirec Vqs I qf2Thus let todu3(50)cu dc dc Vqs I qf u dciinvdt2Letting w udc2, then Eq. (50) can be expressed as:dw 32(51) Vqs I qf w1 2iinvdt ccEq. (51) can be written in the form:dw(52) f b0udtWhereEqs. (20) and (21) that represent the currents in the filtercan be written as:dI df1(54) Vds R f I df L f s I qf 1 Vds1 dtLfLfdI qf1(55) Vqs R f I qf L f s I df 1 Vqs1 dtLfLfThis led to put the current Idf, and the same studies can beused for Iqf, into the form:dI df(56) f I df , d , t b0u t dtWhere 1 Vds R f I df L f s I qf 1 b0 Vds1 f (57)Lf Lf u Vds1As above a linear ADRC can be applied.Fig. 7 schematic block diagram for the grid side control.7. Simulation and ResultsSimulation of the DFIG wind turbine and the appliedcontrol strategies have been carried out with theMatlab/Simulink. The parameters of the DFIG coupled tothe turbine are given in Appendix. Simulations are made inthree tests:Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.org3.1 Test A3961000Idr & Idr-ref & Iqr & Iqr-ref (A)5000-500-1000-1500-20000.40.60.811.2time (s)1.41.61.82Fig. 8 rotor current Idr & Iqr and their reference Idr ref & Iqr ref.413x 10f-Idrz2-Idr1211f-Idr & z2-IdrA constant wind speed v 12m/s is applied to the turbine,which leads to a torque electromagnetic referenceTemref 7911mN and a machine rotor speed equal ton 1740rpm. A stator reactive power reference is set at0 MVAR, which will be changed to 1MVAR at t 1s andthen to 0 Mvar at t 1.5s. Rotor currents Idr and Iqr andtheir references Idr ref and Iqr ref are plotted in Fig. 8. It isclear that the rotor currents follow well their referencesdepending on response time imposed by the desired closedloop frequency cb 60rd/s which correspond to tr 50ms.Fig. 9 and Fig. 10 show the general disturbance f Idr andf Iqr with their estimates by a linear ESO Z2Idr and Z2Iqr;we can see that the ESO estimates in real time the totaldisturbances which will then be rejected by the linearADRC. Rotor currents Idr and Iqr and their estimates Z1Idrand Z1Iqr are illustrated in Fig. 11; here also the ADRCputs again in evidence its performances. The decouplingeffect between the direct and quadratic stator flux isillustrated in Fig. 12. Reactive stator power and theirreference are shown in Fig. 13. The stator voltage vs andthe stator current is are in phase before t 1s and they areno longer in phase after t 1s, indeed, the reactive poweris a step change from 0 to 1MVAR as shown in Fig. 14.Fig. 15 illustrates the regulation of DC bus voltage Udc,which follows its reference after a transitional regime.IdrIdr-refIqrIqr-ref1098760.43.2 Test B0.60.811.2time (s)1.41.61.82Fig. 9 general disturbance f Idr and their estimate z2Idr.53x 10f-Iqrz2-Iqr2.82.6f-Iqr & z2-IqrA second test is performed linearly varying wind speedfrom 10 m/s at t 1s to 10.7m/s at t 1.5s. Thecorresponding rotor speed varies between n 1450rpm(hypo synchronous mode) to n 1550rpm (hypersynchronous mode) as shown in Fig. 16. Rotor power Prtransiting through the back to back converter is negative inhypo synchronous mode and positive in hyper synchronousmode indeed the slip changes the sign as illustrated inFig. 17.2.42.223.3 Test C1.8A third test is performed under the conditions of the firsttrial to reveal the robustness of the controller. Rotorresistance was varied by taking the values of 0.5Rr, Rr andfinally 1.4Rr to highlight the possible variations in therotor resistance which can be due to a temperature rise.Fig. 18 demonstrates robust control based on linear activedisturbance rejection control. The global uncertainties areestimated and compensated in real time.0.511.5time (s)Fig. 10 general disturbance f Iqr and their estimate z2Iqr.Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.2
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): s2000stator current Is (A)& voltage Vs (V)Idr & Z1-Idr & Iqr & Z1-Iqr 00-25000.90.511.50.920.940.960.9821time (s)1.021.041.061.081.1time (s)Fig. 14 stator voltage Vs and stator current Is.Fig. 11 rotor current Idr & Iqr and their estimate z1Idr & z1Iqr.20004UdcUdc-ref1800phid-sphiq-s16003Udc & Udc-ref (V)1400dq-flux (Wb)21120010008006000400200-10-200.20.40.60.81time (s)1.21.41.61.800.20.40.60.81time (s)1.21.41.61.822Fig. 15 DC link voltage Udc and Udc ref.Fig. 12 direct and quadratic stator flux ds & qs .15605x 10Qs-refQs141540121520rotor speed (rpm)Qs & Qs-ref (VAR)1086415001480201460-2-40.40.60.811.2time (s)1.41.61.8Fig. 13 stator reactive power Qs and their reference Qs ref.214400.40.60.811.2time (s)Fig. 16 rotor speed.Copyright (c) 2013 International Journal of Computer Science Issues. All Rights Reserved.1.41.61.82
IJCSI International Journal of Computer Science Issues, Vol. 10, Issue 2, No 2, March 2013ISSN (Print): 1694-0814 ISSN (Online): 1694-0784www.IJCSI.orgthe ADRC based on linear ESO is easy to implement. Itdoes not require exact knowledge of the internal dynamicsof physical plant, which is the main reason that makes itrobust against changes in internal parameters that affect thetime constants of the DFIG current loops as in thetraditional PI controller.44x 1032rotor power Pr (W)39810-1-2-3-40.511.5Appendix2time (s)Doubly fed induction generator parameters:Fig. 17 rotor power Pr in hypo and hyper synchronous mode.Rated power 1.5MWGrid voltage line to line rms U 690V f 50HzStator and rotor resistance Rs 10.3m Rr 8.28 m Stator and rotor inductance Lls 280. Llr 117.7 Mutual inductance Lm 26.96mHNumber of pole pairs p 21500rotor current Ir-abc (A)1000500Turbine parameters0-500-1000-15000.511.52time (s)Rotor diameter D 60mTotal moment of inertia Jt 303.96kgm2Optimal tip speed ratio opt 6.5Maximal power coefficient Cpmax 0.48DC link parametersFig. 18 instantaneous rotor current ir .DC link voltage Udc 1400VFilter Lf 0.25mH Rf 0.785m DClink capacitor C 50 mF1000Idr-refIdr 0.5RrIdr RrIdr 1.4RrRotor current controller parameters500Desired closed loop frequency cr 60rd/sObserver bandwidth r0 5 cr 300rd/s0Idr (A)Parameter gain br0 2432-500Filter current controller parameters-1000-15000.5Desired closed loop frequency cf 300rd/sObserver bandwidth f0 5 cf 1500rd/s11.52time (s)Parameter gain bf0 -4000Voltage loop parametersFig. 19 rotor
4. Active Disturbance Rejection Control . The active disturbance rejection control was proposed by Han [9][10][11][12]. It is designed to deal with systems having a large amount of uncertainty in both the internal dynamics and external disturbances. The particularity of the ADRC design is that the total disturbance is defined as
ON ACTIVE DISTURBANCE REJECTION CONTROL: STABILITY ANALYSIS AND APPLICATIONS IN DISTURBANCE DECOUPLING CONTROL QING ZHENG ABSTRACT One main contribution of this dissertation is to analyze the stability char-acteristics of extended state observer (ESO) and active disturbance rejection control (ADRC).
ing control technology, known as active disturbance rejection con-trol to this day. Three cornerstones toward building the founda-tion of active disturbance rejection control, namely, the track-ing di erentiator, the extended state observer, and the extended state observer based feedback are expounded separately. The paper
practical control strategy that is Active Disturbance Rejection Control (ADRC) [10-14] to the EPAS system. The controller treats the discrepancy between the real EPAS system and its mathematical model as the generalized disturbance and actively estimates and rejects in real time, the disturbance
shift. The active disturbance rejection concept, introduced in section III, could very well serve as the basis of the new paradigm, which is characterized in section IV. Also included in section III is the demonstration of the broad range applications of the active disturbance concept. Finally, the paper is concluded with a few remarks in .
The Active Disturbance Rejection Controller (ADRC), invented by Han Jing-Qing who serves in Chinese Academy of Science, is a new type of nonlinear controller which is based on active disturbance rejection control technology. It does not depend on system model andcan estimate and compensate the influences of all the
e recently developed active disturbance rejection con-trol (ADRC) is an e cient nonlinear digital control strategy which regards the unmodeled part and external disturbance as overall disturbance of the controlled system [ ] . e ADRC mainly consists of a tracking di erentiator (TD), an extended state observer (ESO), and a nonlinear state error
Payroll Rejection Resolution Guide 12/23/2019 Page 1 . Payroll Rejection Resolution Guide. Overview . This is a list of common warning and rejection codes you may encounter and how to resolve them. If you encounter a rejection code that . The system reserves 5% of the participant balance to account for potential market fluctuations
continue to meet with strategy groups and conduct shared reading and guided reading groups with a focus on print strategies and fluency based on students [ needs. **Although the unit details 22 sessions, this unit could easily utilize 6 weeks of instruction within the reading workshop.
