Maximal Power Point Tracking under

Speed-Mode Control for Wind Energy GenerationSystem with Doubly Fed Introduction Generator

Y. Zhao*, Zou*, Xu*, Kang*

*Huazhong University of Science and Technology / Electrical and Electronic College, Wuhan, China**Hubei University of Technology / School of Electrical and Electronic Engineering, Wuhan, China

Abstract The Doubly Fed Induction Generator (DFIG)with back-to-back four-quadrant converters between itsrotor winding and the grid can realize the maximal windenergy capture in variable-speed wind energy generationsystem. Based on the stator flux-oriented excitation vectorcontrol strategy, this paper presents that the systemdynamic characteristics under speed-mode control aresuperior to the dynamic characteristics under current-modecontrol in the process of Maximum Power Point Tracking(MPPT) and brings forward the explanation based on statespace theory. And it designs the gains of two typical PIcontrollers in the current inner loop and the speed outerloop under speed-mode control based on Internal ModelControl (IMC) theory and pole assignment method,respectively. At last, simulation results in MATLAB/SIMULINK are put forward to verify the good static anddynamic performance of the designed closed-loop controlsystem.

Keywords-Doubly Fed Induction Generator (DFIG);current-mode control; speed-mode control; PI controller;Internal Model Control (IMC); pole assignment

I. INTRODUCTION

The Doubly Fed Induction Generator (DFIG) producesconstant frequency power to the grid with variable rotorspeed in variable-speed wind energy generation system.It can realize the maximal wind energy capture with therotor speed varying from subsynchronous to super-synchronous speed when the wind speed is above thecut-in speed and under the rating speed; the generatedactive and reactive power can be controlledindependently; the four-quadrant ac-to-ac converterconnected between the rotor winding and the gridhandles only a fraction of the total power to achieve thefull control of the system. So with the rapid increase incapacity of single generator and wind farm, the researchand application of the DFIG progress at a rapid rate inwind power generating application. The frequencyconversion circuit between the rotor winding and the gridoften adopts the configuration of two back-to-backfour-quadrant voltage source converters, which is

popular at present, because of its powerful function. Therotor-side converter adopts stator flux-oriented vectorcontrol strategy to realize the decouple control of theactive and reactive power, and the grid-side converteradopts grid voltage-oriented vector control strategy tocontrol the dc-link voltage and the grid power factor.This paper discusses only the active power control of thesystem.

The excitation control strategy adopted in therotor-side converter based on the stator flux-orientedvector control enables Maximum Power Point Tracking(MPPT) to improve energy conversion efficiency bycontrolling the q -axis rotor current iqr, namely theactive component of rotor current. The basic theory ofMPPT is that the wind turbine can obtain the maximumwind energy when it rotates in a certain speed at a certainwind speed. Therefore, the Popt - cr characteristicshave been given out [1], where Popt is the maximumenergy that the power system obtains from wind energyand Or is the rotor speed. The MPPT control strategycan be divided into two hierarchical controls [2], i.e., thesetting of reference value and the tracing of referencevalue. Based on the MPPT principle, the reference valueis generally the active power Ps [3]- [5], theelectromagnetic torque Te [1],[6]-[7] or the rotor speedOr [1],[8]-[9]. The former two may be termed'current-mode control', and the last may be termed'speed-mode control'[ 1].

Based on a third-order model related to theelectromagnetic and mechanical aspects of DFIG,Section II presents a decoupled active and reactive powercontrol strategy. Comparing the current-mode controland the speed-mode control, Section III presents that thesystem dynamic characteristics under speed-modecontrol are superior to the dynamic characteristics undercurrent-mode control and brings forward the state spaceexplanation. Section IV designs the gains of two typicalPI controllers in the current inner loop and the speedouter loop under speed-mode control based on InternalModel Control (IMC) theory and pole assignment

1-4244-0449-5/06/$20.00 (C2006 IEEE IPEMC 2006

method, respectively. Simulation results inMATLAB/SIMULINK are brought forward to verify thegood static and dynamic performance of the designedclosed-loop control system in Section V.

II. MODELAND CONTROL STRATEGY OF DFIGThe DFIG equations depicted in a two axis d-q

reference frame rotating at synchronous speed arederived from Park's equations. The stator side of DFIGuses generator convention and the rotor side of DFIGuses motor convention.

The voltage equations can be written as

rlIds] F-Rs 0 0 0 ids FVds ]COiVfqs

Uqs O-Rs 00 iqs +p Vfqs + IV1s (1)Udr O Rr O idr /dr -C021/JqrUqr 0 0 0 Rr -iqr -Yqr 6021fdr

The stator and rotor flux linkages in (1) are

Vds --LsVqs = OVdr -LoLVqr O

0-Ls0

- Lo

Lo0

Lr0

idsLo iIqs0 idrLr J Liqrj

The motion equation is given by

J d + Boir = np (Tm -Te )dt (3)

The electromagnetic torque in (3) isTe = nfpLo(iqsidr - idsiqr) (4)

Equations (1) to (4) are set of differential equationsmaking up of a fifth-order model which describes thedynamic behavior of DFIG. The voltages, currents andflux linkages are expressed by the d -axis and q -axiscomponents in synchronous rotating reference frame.

It is assumed that (a). Neglecting the influence of thestator flux linkage's transient state and orienting thed-axis of the synchronous frame to the direction of thestator flux vector. This implies that the differential of thestator flux linkage is zero and its vector with constantmagnitude rotates in synchronous velocity. (b). OmittingRs because the voltage drop on it is small.From the assumption (a)

p s =O and Vds = VsVqs = O

The following voltage equations can be derived from(1) to (5) with the assumption (a) and (b).

Uds = 0

Uqs =Us

Udr = (Rr + Lrp)idr - (02 OLr iqr (6)

Uqr = (Rr + Lrp)iqr + 2 (JLr idr +Loims /Ls)

Where a represents the leakage coefficient,1 L2l/(Ls Lr); ims is the stator flux magnetizing

current, ims = Vs /Lo = Us /(col Lo).

02OLriqr U2I(QLs)Udr 1 ldr LoU

0.

Rr +OLrS L

(02 (oLr idr + L2jm SLS)Uqr I 'qr LPU

Tm-

Figure 1. Block diagram of the DFIG model

The excitation control strategy based on theassumption (a) and (b) is often termed stator flux-oriented vector control strategy. Then the stator voltagevector is oriented to the q -axis of the reference frame.Thus realizes the stator voltage vector orientation, andthe order of the DFIG model decreases from fifth to thirdwhich is beneficial to simplify the excitation controlsystem of DFIG. The rotor voltage equations in (6) and(3) make up of a new third-order model.As mentioned in section I, the reference value could

be active power Ps, electromagnetic torque Te or therotor speed Or in order to realize the MPPT. Therelationship between the reference values and the othervariables is

Te = npLo(iqsidr -idsiqr ) = LnQU5 lqrLs5

Ps = Uds ids + Uqs iqs = Us iqs = UsLoiqrLs

(7)

(8)

Eq. (3), (7), (8) and the rotor voltage equations in (6)compose the full DFIG model as shown in Fig. 1.

III. CURRENT-MODE CONTROLAND SPEED-MODECONTROL

Under current-mode control, active power P5 andelectromagnetic torque Te both have the proportionalrelationship with the q -axis rotor current iqr as (7) and(8) show. So, the reference value iqr for the currentinner loop can derived from Ps or Te directlyaccording to the certain proportion. Thus the activepower and electromagnetic torque adopt the open-loopcontrol as shown in Fig.2., where K1 = Ls /(Lo Us),K2 = Lscol/(LonpUs) . The cascaded control schemeunder speed-mode control is depicted in Fig.3., whereK3 = Lo np US /(Ls Co1) .The controller in the speedouter loop is a PI controller. The reference value of theactive power, electromagnetic torque and rotor speed inFig.2. and Fig.3. are determined by the MPPT theory.

The controllers in the current inner loop undercurrent-mode control or speed-mode control are bothtypical PI controllers. The cross-relation between thed-axis and q -axis rotor current components in (6) isfeed-forward compensated in both Fig.2. and Fig.3.

The active power, electromagnetic torque and rotorspeed have the definite relationship at a certain wind

~1XiiV jqr P1 1 iqrlZ t-Rr+cyLrs LonpUTTe

Figure 2. Block diagram of the controller in current-control mode

0) i¾ 1 iqr T n 0)rPi Rr +cyLrS - Js+B

Figure 3. Block diagram of the controller in speed-control mode

speed based on the MPPT theory, which implies that withanyone of them reaching its reference value the systemcan obtain the maximal wind energy in static state.

However, the current-mode control and the speed-mode control have great differences in dynamiccharacteristics. The responsive rate of the system is lowunder current-mode control and at worst the system cannot realize MPPT. On the contrary, the responsive rate ofthe system is fast under speed-mode control and canrealize MPPT. This can be explained as below. The statorof DFIG can acquire the expected active power andelectromagnetic torque rapidly because of the goodresponse performance of the current loop undercurrent-mode control. But this doesn't mean that thesystem reaches static state at the moment the rotorcurrent reaches its desired value. The error between themechanical power input and the active power the statorfed to the grid is divided into two parts: one part for rotorspeedup and the other part for the rotor-side converterfed to the grid. The part for acceleration decreases andthe other part increases with the rotor rotating velocityvarying until the system comes to equilibrium. Thistransient process is determined by the DFIG motioncharacteristics and out of control. So, with little influenceon the steady-state precision, the current-mode controldoesn't improve the system dynamic performancewhether the reference value is the active power orelectromagnetic torque, whether the control scheme isthe open-loop control in Fig.2. or the closed-loop control.The speed-mode control adds a speed outer loop to thecurrent inner loop to form a cascaded closed loop controlsystem, which including the motion part of the DFIGmodel as shown in Fig.3. That means the rotor speedvarying process, the balance of active power and thebalance of torque on the rotor shaft are in control.When analyzed with state-space theory, the q-axis

rotor voltage Uqr is regarded as input variables; theq -axis rotor current iqr and the rotor speed Or areregarded as state variables; the active power, electro-magnetic torque or rotor speed is regarded as outputvariable; the mechanical torque Tm is regarded as adisturbance. The control scheme of the current-modecontrol comprises only one state variable, the q -axiscurrent iqr, which is fed back to form a current closed

loop, hence some electromagnetic quantities such asiqr , Ps and Te can be controlled. But the schemedoesn't contain the other state viable or and the motioncharacteristics of DFIG, which reflect on theuncontrollable of the motion response. The controlscheme of the speed-mode control comprises both statevariables, the q -axis current iqr and the rotor speedC6r, which are fed back to form a current inner closedloop and a speed outer closed loop. Thus the closed-loopcontrol system holds the full system state informationand can control all the variables, not only theelectromagnetic ones but also the mechanic ones.Therefore, the dynamic characteristics under thespeed-mode control are superior to the ones undercurrent-mode control.

IV. CONTROLLERS

In order to achieve the excellent static and dynamicperformance, this paper adopts the excitation controlstrategy under speed-mode control with two typical PIcontrollers used in the current inner loop and the speedouter loop, respectively. The gains of the two PIcontrollers are designed based on IMC theory and poleassignment method, respectively.

A. PI Controller in Current Inner LoopThe controller in current closed loop can be easily

designed to get good dynamic performance of trackingintroduction and restraining disturbance by using theIMC method [9],[10]. For the first-order system, thecontroller becomes a simple PI controller.

The PI controller transfer function is

C(s) = Kpc + Kic I s (9)With the model of the object being 1/(Rr + ULrS) the

gains of the controller can obtained from below

Kpc =ULr TIKic = Rr IT

(10)

Thus the current inner loop equivalents an inertial linkwith filter parameter z . So, it is easy to design the gainsof the PI controller by adjusting zi to achieve nicedynamic performance and robust control of theinner-loop control system.

B. PI Controller in Speed Outer LoopThe controller in speed outer loop is a PI controller too.

The reference value for the current inner loop whichoffered by the outer loop controller represents below [3]

iqr = KPS(br -wr)+ Kis J(- )rt (1 1)

Where b is a parameter introduced to the typical PIcontroller.

The simplified block diagram of the control system isshown in Fig.4, where K4 = Lo nP US/(LS wo B),ri= J/B.

* +

(r Kis K4 Oil

Figure 4. Block diagram of the system under speed-mode control

From Fig.4., the system closed-loop transfer functionis derived as below

G(s)=- K4(bK,s s+Kis1)rfs13 + (r +rI)s2 + (KpsK4 + I)s + KisK4

The closed-loop characteristic equation is

D(s) = rris3 + (r +r1 )S2+ (KpsK4 + I)s + KisK4 (13)

Since the closed-loop control system is a third-ordersystem, the gains of the PI controller are designed basedon the pole assignment method to ensure good dynamiccharacteristics by assigning the closed-loop polescorrectly [11]. The dynamic characteristic of a high ordersystem are mainly determined by closed-loop dominantpoles. The dominant poles of the system is

S1,2 = -<rWr ±JrVI-2 (14)

And the non-dominant pole of the closed-loop controlsystem is

S3 =-nlrOr (15)Where n is a parameter which decides the third pole'slocation in complex plane. The bigger value it has, themore approximate the response characteristics of thethird-order system decided by S1,2,3 are to the responsecharacteristics of the two-order system decided by thedominant poles S1,2. Usually, n = 5-10.The characteristic equation of the third-order system

decided by Si 2,3 is

Dr (S) = (S2 + 2/rwrs + wr2 Xs + nSrwr ) (16)= s + (n + 2)4rWrS2 + wr7 (2nr2 +1)S+nfrWr

The gains of the controller are obtained by thecomparison of (13) and (16)

Kps = [7rr(2nr +1)-l n/K4Kis = n rrf1Or / K4

I.In the simulation, filter parameter z in the current

loop is 2ms, parameter n is 5 and b is 50 in speedcontroller. The damping ratio and the natural frequencythat the closed-loop control system expected is 1.2 and60Hz. Controllers parameters are designed asKp= 6.9,Kic = 408, Kps = 0.512, Kis = 11.88.

TABLE I.CHARACTERISTICS OF DFIG

Machine Characteristic Value

rating active power (kW) 4

mutual inductance (H) 0.28

stator inductance (H) 0.287

rotor inductance (H) 0.287

stator resistance (Q) 0.5

rotor resistance (Q) 0.816

number of pole pair 3

Inertia(kgm2g ) 0.05

Fig.5. shows the simulation results under current-mode control. The mechanical torque fed into the rotorshaft is constant power torque, Pm = 4 kW. The activepower as the reference value for the control systemchanges from 5kW to 3.33kW at i.1s. The stator-sideactive power Ps in Fig.5 (a) and the q -axis rotorcurrent iqr in Fig.5(b) have fast response within 5msbecause of the good dynamic performance of the currentinner loop. While at the same time, the rotor-side activepowerPrin Fig.5 (a) and the rotor mechanical rotatingspeed Wr in Fig.5 (c) reach their static value at 1.5s. Thetransient process lasts at least 0.4s and it will last longerwith bigger rotor inertia. Fig.5 (d) shows the rotorcurrent in rotor-side reference frame.

6000 20 , , 1

5000 _

(17)

Where n, zr,(Or, r and zi have the relationshipbelow

(n + 2)4rWOr = (rZ + 'Zl )/(frri) (18)Simulation results indicate that there exists overshoot

even if Sr is larger than 1 because of the influence ofthe zero point which the PI controller introduced into theclosed-loop control system. The parameter b in (12)allows placing independently the unique zero.

V. SIMULATION RESULTS

The characteristics of the rounded induction machinethat have been used in the simulations are shown in Table

(a) (b)

(c) (d)

Fig. 5. Simulation results under current-mode control

(a) (b)

(c) (d)

Fig.6 Simulation results under speed-mode control

Fig.6. shows the simulation results under speed-modecontrol. The PI controller is designed based on poleassignment method in Section IV. The mechanical torquefed into the rotor shaft is a constant powertorque, Pm = 4 kW. The rotor speed as the referencevalue for the control system changes from 800rpm to1OOOrpm at 1 .3s. The stator-side active power Ps and therotor-side active power Pr in Fig.6(a), the q -axis rotorcurrent iqr in Fig.6(b) and the rotor mechanical rotatingspeed in Fig.6(c) reach their static value at 1.4s. Fig.6 (d)shows the rotor current in rotor-side reference frame. Thetransient process lasts only 0.is. There is a dip in thestator-side active power curve and the q -axis rotorcurrent curve as shown in Fig.6(a) and (b). This impliesthat, at the beginning of the transient process, the errorbetween the mechanical power input and the activepower the stator fed to the grid is larger than the errorunder current-mode control, and the part of the error forrotor speedup is larger than that under current-modecontrol too. The rotor accelerates rapidly with theappropriate change of theiqr. So, the transient processwith all the electrical and mechanical variables varyingdoes not last long.

REFERENCE

[1] R. Pena, J. C. Clare, and G. M. Asher, "Doubly fed inductiongenerator using back-to-back PWM converters and its applicationto variable-speed wind-energy generation," Proc. Int. Elec. Eng.,Electr. Power Appl., vol. 143, no. 3, pp.231-241, May 1996.

[2] L. Jing, F. Yong, S. Jiahua, and W. Weisheng, "Research onsubsection and layer control strategy of doubly-fed variable speedwind turbine," Proc. Power System Technology, Vol. 29, No.9,pp.15-21, May 2005.

[3] A. Tapia, G. Tapia, J. X. Ostolaza, and J. R. Sanenz, "Modelingand control of a wind turbine driven doubly fed inductiongenerator," IEEE Trans. Energy Convers., vol. 18, no. 2,pp.194-204, June 2003.

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1495, June 2004.

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VI. CONCLUSIONS

This contribution presents that the speed-mode controlis superior to the current-mode control because of thecontrollable of all the state variables under thespeed-mode control. To get good static and dynamicperformance, two typical PI controllers are designedbased on the IMC and pole assignment method underspeed-mode control, respectively. The simulation resultsshow the good performance of the control system.