A Topology for Multiple Generation System With Doubly Fed Induction Machines and Indirect Matrix Converter

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009 4181

A Topology for Multiple Generation SystemWith Doubly Fed Induction Machines

and Indirect Matrix ConverterRubén Peña, Member, IEEE, Roberto Cárdenas, Senior Member, IEEE, Eduardo Reyes,

Jon Clare, Senior Member, IEEE, and Patrick Wheeler, Member, IEEE

Abstract—In this paper, a topology for a grid-connected gen-eration system, based on two doubly fed induction machines, ispresented. The proposed scheme is implemented using an indirectmatrix converter (IMC) consisting of an input stage, a three-to-twomatrix converter, and two output stages consisting of a pair ofvoltage source inverters. The input stage is connected to the gridand provides the required dc voltage for the output stages. Spacevector modulation (SVM) is used for the input stage producingthe maximum dc voltage, with unity power factor operation at theIMC grid-side input. Each of the output converters is connected tothe rotor of a DFIM. The rotor currents of each machine are vectorcontrolled for fast dynamic response and tight torque control.Moreover, the SVM algorithm used for the inverters is designed toprovide soft switching operation in the input converter. Simulationand experimental results obtained from a 2.5-kW experimentalprototype are presented. Steady-state and transient operation isdiscussed with the system running at below and above synchro-nous speed. The results demonstrate the feasibility of the proposedscheme for variable speed energy systems.

Index Terms—AC–AC conversion, induction generators, windpower generation.

I. INTRODUCTION

THE DOUBLY fed induction generator (DFIG) has longbeen considered a standard option for variable speed

generation systems involving limited speed range [1]–[4]. Apower electronics interface, connected between the stator andthe rotor circuit, provides bidirectional power flow for sub-and supersynchronous speed operation. If the speed range isrestricted, typically to ±30% of the synchronous speed, therequired power electronics can be rated to only a fraction ofthe machine nominal power.

Manuscript received October 23, 2008; revised July 17, 2009. First publishedAugust 4, 2009; current version published September 16, 2009. This work wassupported in part by Fondecyt Chile under Contract 1095062 and in part by theIndustrial Electronics and Mechatronics Millennium Nucleus.

R. Peña is with the Electrical Engineering Department, University ofConcepción, Concepción 4074580, Chile (e-mail: [email protected]).

R. Cárdenas is with the Electrical Engineering Department, University ofSantiago de Chile, Santiago 8320000, Chile (e-mail: [email protected]).

E. Reyes is with the Electrical Engineering Department, University ofMagallanes, Punta Arenas 621-0427, Chile (e-mail: [email protected]).

J. Clare and P. Wheeler are with the Power Electronics, Machines andControl Group, Faculty of Engineering, University of Nottingham, Nottingham,NG7 2RD, U.K. (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2009.2028353

Fig. 1. IMC.

The standard power electronic interfaces used with DFIGsare two back-to-back voltage source inverters (VSIs) with anintermediate dc link and capacitors. Based on this standardtopology, other schemes have been presented in the literatureaiming to extend the operating speed of the machine [5], [6], butthey require additional converters, and the rating of the powerelectronics interface increases.

In the last decade, an increasing interest in developingdirect frequency power converters has taken place, namely,matrix converters (MCs), indirect MCs (IMCs), and sparse MCs[7]–[11]. These topologies are all silicon solution for ac–acconversion with sinusoidal input and output currents withoutusing passive components in the dc link. On the contrary,generation systems based on back-to-back converters requirebulky dc capacitors increasing the size of the converter andreducing the reliability of the system. In the IMC topology,shown in Fig. 1, an input or rectifying stage is cascaded withan output stage. The input stage is a 3φ-to-2φ MC, whichprovides the dc voltage required by the output or invertingstage. As shown in Fig. 1, the output stage is implemented usinga standard VSI.

MCs have also been proposed to control the rotor current ofa DFIG. This is presented in [12] where only simulation resultsare discussed. The IMC topology can achieve similar perfor-mance, in terms of input/output characteristics, to that obtainedfrom MCs. Therefore, IMCs can also be used to control a DFIGoperating in a Scherbius scheme. For the application presentedin this paper, the main advantage of an IMC compared to astandard MC is that the former has a dc link available [9], [10],which allows the connection and control of several doubly fedmachines with only one input stage. Other advantages of theIMC topology are the possibility of soft switching commutationof the input stage [8], [9] and reduced switching losses of the

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4182 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 56, NO. 10, OCTOBER 2009

Fig. 2. Topology for two DFIGs and a two output IMC.

output stage by reducing the dc link voltage [13], [14], amongothers.

Regarding the direct ac–ac power conversion topologies, ausual drawback is the voltage ratio limitation of these schemes;theoretically a maximum of about 86% of the input voltagecan be achieved at the output without introducing low orderharmonic distortion in the IMC input and output [7], [8], [10].However, this issue is not very significant in the proposedapplication because the required rotor voltage Vr depends onthe stator voltage Vs, the speed range (around ±30% of thesynchronous speed) and the stator to rotor turn ratio n, i.e., iflosses in the machine are neglected Vr = ±sVs/n with s is theper unit slip. Therefore, in the design of the system, the speedrange, the turns ratio, and the voltage ratio need to be taken intoaccount. This provides enough degrees of freedom to establisha design that allows operation of the power converter with avoltage ratio of less than 0.86 for the desired speed range. Theapplication of an IMC to control the rotor currents of a DFIG invariable speed generating system is reported in [15].

In this paper, a topology is proposed for a multigenerationsystem to take advantage of the multidrive capability of theIMC converter. The proposed scheme is shown in Fig. 2. Itconsists of two doubly fed induction machines (DFIMs) andan IMC with two outputs and a single input. A second-orderL–C filter is used at the input to improve the quality ofthe currents [16]–[19]. The filter capacitors also provide theessential decoupling to minimize the commutation inductancebetween phases. Usually, a resistor in parallel with the filterinductance improves the damping of the system [20].

Preliminary simulation results of this topology were pre-sented by the authors in [20] showing the feasibility of theproposed generation scheme. This topology is suitable forextended speed operation of the machine [5], multiple windenergy system [10], variable speed wind-diesel systems [21],and, in general, any multiple drive system operating in a re-stricted speed range. In the proposed topology, each pulsewidthmodulation (PWM) voltage source converter is used to regulatethe rotor current of a DFIG. For vector control of the DFIGrotor currents, two synchronous rotating axes orientated alongthe stator flux vectors are required. The input stage is controlledin order to provide the required dc voltage for the converteroutputs, with close to unity power factor operation at the IMCinput. The duty cycles for the output stages are arranged toachieve soft switching commutation in the input stage. The

operation of both machines at variable speed is presented anddiscussed in this paper. Simulation and experimental results areshown, including rotor current control performance, operationbelow and above synchronous speed for both machines androtor current tracking capability, using an experimental setupwith two 2.5-kW DFIGs. The power converter used has beenbuilt with the input stage, and the two output stages embeddedin a single power unit. Each generator is driven by commercialdrives.

The rest of this paper is organized as follows. In Section II,the vector control strategy for each of the DFIG is brieflyreviewed. Section III shows the control strategy for the inputmatrix and the two output stages of the IMC. Section IVdescribes the experimental setup used to validate the proposedtopology. Section V discusses simulation and experimental re-sults. Finally, an appraisal of the proposed strategy is presentedin the Conclusions.

II. VECTOR CONTROL OF DFIG

The machine equations for each DFIG in a d–q synchronousrotating frame are [1]

⎡⎢⎣

λds

λqs

λdr

λqr

⎤⎥⎦ =

⎡⎢⎣

Ls 0 Lm 00 Ls 0 Lm

Lm 0 Lr 00 Lm 0 Lr

⎤⎥⎦

⎡⎢⎣

ids

iqs

idr

iqr

⎤⎥⎦ (1)

[vds

vqs

]=

[Rs 00 Rs

] [ids

iqs

]+

d

dt

[λds

λqs

]

+[

0 −ωe

ωe 0

] [λds

λqs

](2)

[vdr

vqr

]=

[Rr 00 Rr

] [idr

iqr

]+

d

dt

[λdr

λqr

]

+[

0 −ωslip

ωslip 0

] [λdr

λqr

](3)

Te = 3p

2Lm(iqsidr − idsiqr) (4)

where λs = Lmims is the stator flux and λr is the rotor flux; Ls,Lm, and Lr are the stator, magnetizing, and rotor inductances,respectively; vs and is are the stator voltages and currents, re-spectively; vr and ir are the rotor voltages and currents,respectively; Rr and Rs are the rotor and stator resistances, re-spectively; ωe and ωr are the synchronous and rotating angularfrequencies, respectively, ωslip = ωe − ωr is the slip frequencyand ims is the magnetizing current; Te is the electrical torque;and p is the number of poles. In (1)–(4), the subscripts s and rdenote stator and rotor quantities, respectively. The subscriptsd and q denote direct and quadrature components referred tothe synchronous rotating frame. The factor three in (4) is due tothe scaling used in the transformations, so voltages and currentsin d–q frame represent phase rms values in steady state. Fieldorientation, for transforming the machine variables, uses theslip angle derived from

θslip = θe − θr (5)

PEÑA et al.: TOPOLOGY FOR MULTIPLE GENERATION SYSTEM WITH DFIMs AND INDIRECT MATRIX 4183

Fig. 3. Control schematic of DFIG.

where θr is the rotor position. For the experimental results pre-sented in this paper, speed encoders have been used. However,sensorless operation is also feasible [22]–[24]. The referenceframe is orientated along the stator flux vector. The position ofthe stator flux vector (θe) is obtained from the stator flux α–βcomponents as

θe = tan−1

(λβs

λαs

). (6)

The α–β components of the stator flux can be calculated fromthe stator voltages and currents as

λαs =∫

(vαs − Rsiαs)dt

λβs =∫

(vβs − Rsiβs)dt. (7)

In the experimental implementation of (7), a band-pass filter(BPF) is used as a modified integrator to block the dc com-ponent of the measured voltages and currents. The BPF isdesigned with cutoff frequencies of 0.1 and 1 Hz. Therefore,because vs and is are 50-Hz signals, the performance deteriora-tion from integral action is negligible. The control schematic foreach DFIG is shown in Fig. 3, PI current controllers are used toregulate the reference rotor currents in the d–q frame. Compen-sation terms are added to the output of the current controllers tosimplify the design procedure. The outputs of the controllersgenerate the corresponding reference rotor voltage for eachmachine. A space vector modulation (SVM) algorithm is usedto impose the reference rotor voltages in the output stages. InFig. 3, E is the converter dc voltage, σ = 1 − L2

m/LsLr is thetotal leakage coefficient; the superscript “∗” denotes a demandcurrent and the superscripts α–β denote quantities referred tothe stationary stator frame. The blocks labeled e−jθslip andejθslip represent transformations from α–β to d–q coordinatesand vice versa, respectively. The magnitude and position of

the reference rotor vector voltage for each output converter isgiven by

|vr| =

√(v∗

αr)2 +

(v∗

βr

)2

θ = tan−1

(v∗

βr

v∗αr

). (8)

For stator flux orientation, the electrical torque is given by

Te = 3p

2L2

m

Lsimsiqr = ktiqr (9)

where kt = 1.5pL2mims/Ls is the torque constant.

III. CONTROL OF PROPOSED IMC TOPOLOGY

A. Control of Input Stage

The modulation strategy for the IMC input stage provides amaximum positive dc voltage commutating between the largestand second largest positive line input voltages [8], [9], [14].Each of the output stages generates the PWM voltage requiredby the rotor of the corresponding machine. For the SVMalgorithm controlling the input stage, a current reference vectoris used. Six sectors are considered, as shown in Fig. 4(a) and (b).The reference vector current is chosen with a zero phase shiftangle respect to the input phase voltage vector [see Fig. 4(a)].In this way, close-to-unity power factor operation is achieved atthe converter input. Fig. 4(b) also shows the current referencevector in the first sector with θin the angle of the current vectorreferred to the sector.

The interaction between the second-order power filter at theinput (see Fig. 2) and the IMC can lead to oscillations andeven instability when the output power is increased [25], [26].To increase the stability of the system, a synchronous rotatingfilter is used to eliminate the high-frequency components of theinput voltage. To implement the filter, the d–q components ofthe input voltage are calculated as

(vgd + jvgq) = (vαs + jvβs)e−jθef (10)

where the subindex g denotes grid voltage The angle θef isobtained from

θef =∫

(2π50)dt. (11)

From (10), the filtered voltages vgfd and vgfq are obtained as

vgfd =vgd

sτf + 1vgfq =

vgq

sτf + 1(12)

where τf is the filter time constant. Using (12), the angle of theinput voltage vector is calculated as

θin = tan−1(vfβs/vfαs)

(vfαs + vfβs) = (vgfd + jvgfq)ejθef . (13)

A synchronous rotating filter is used in this applicationbecause it produces a zero phase shift in the fundamental


Fig. 4. Sector definition for the input converter and current vectors.

component of the input voltage. The cutoff frequency of thefilter is obtained as fbw = 1/(2πτf ). Stability of IMCs and themethodology used in this paper to set the time constant τf of(12), are further discussed in the next section.

From (13), the duty cycles, dγdδ , for the active vectors ineach sector, with unity modulation index, are given by [8], [9]

dγ = sin(π/3 − θin) dδ = sin(θin). (14)

In the modulation of the input stage, zero vectors are notconsidered (only active vectors are used). This results in anonconstant average dc voltage, which is a factor to considerwhen calculating the duty cycles for the output stages, byadjusting the output modulation indexes. Hence, the modifiedduty cycles for the input stage dR

γ and dRδ are given by [9]

dRγ =

dγ

dγ + dδdR

δ =dδ

dγ + dδ(15)

and the average dc voltage in a commutation period is [9]

E = dRγ · Vline−γ + dR

δ · Vline−δ

E =√

32

V̂in

(dγ + dδ)(16)

where Vline−γ and Vline−δ are the line input voltages for each ofthe corresponding sectors (see Fig. 4) and V̂in is the amplitudeof the line input voltage.

B. Stability of Proposed Control System

The stability of an IMC has not been analyzed before, anda brief discussion is presented in this section. To analyze thestability of the proposed system, it is assumed that the IMC isconnected to a strong grid and operating with unity power factorat the input. Constant power operation of the system, during avoltage perturbation, is also assumed.

Fig. 5 shows the phasor diagram corresponding to the casewhen the IMC is supplying energy to the grid. The currentsand voltages are referred to a d–q synchronous rotating frameoriented along the grid voltage vector. The phase angle betweenthe input voltage vector Vi and the input current Ii is 180◦. Ifa voltage perturbation Δvid + jΔviq is produced in the IMC

Fig. 5. Phasor diagram considering for an input voltage perturbation.

input voltage, then the power supplied to the grid remainsconstant. This can be written as

Pm0 =(Vi0+Δvid+jΔviq) ◦ (Iid0+Δiid + jΔiiq)=Vi0Iid0

(17)

where the symbol “◦” denotes dot product, Pmo is the powersupplied to the grid, and Vio, Iid0 are the input voltage andcurrent at the quiescent point. Neglecting the second-orderterms (e.g., ΔviqΔiiq ≈ 0) in (17) yields

ΔvidIid0 = −ΔiidVi0 ⇒ Δiid = −Pm0Δvid

V 2i0

. (18)

In (18), the converter losses have been neglected.Using the phasor diagram of Fig. 5, and considering unity

power factor operation at the input stage in steady state beforeand after the voltage perturbation, the q-axis incremental cur-rent can be calculated as

tan(θ) ≈ Δviq

Vi0=

ΔiiqIid0

⇒ Δiiq = Pm0Δviq

V 2i0

. (19)

From (18) and (19) it is concluded that the IMC can berepresented by incremental resistances in the d–q axis. If theIMC is supplying energy to the grid (Pm0 < 0), then Reqd =Δvid/Δiid = −V 2

i0/Pm0 is positive and Reqq = Δviq/Δiiq =V 2

i0/Pm0 is negative. On the other hand, if the MC is supplyingenergy from the grid to the rotors (Pm0 > 0), then Δvid/Δiidis negative and Δviq/Δiiq is positive.

The effects produced by a negative incremental resistancein the stability of a power converter system have alreadybeen investigated (see [16] and [17]). The negative incrementalresistance, representing the IMC input impedance, is in parallelwith the capacitor of the second-order power filter connectedbetween the input stage and the grid (see Fig. 2). As discussedin [16], a negative value of incremental resistance reduces the


damping coefficient of the eigenvalues associated to the inputstage and may produce oscillation and even instability. More-over, as shown in (18) and (19), the value of the incrementalresistances Reqd, Reqq are dependent on the magnitude of thepower Pm0. Therefore, the effects of the negative resistance aremore noticeable when the input stage is operating at full power.

There are several methods proposed in the literature toincrease the stability of direct MCs [18], [19], [27]. Filteringof the input voltage signals [18], the use of PLLs to track theposition of the input voltage vector [19], active damping [27],etc. To investigate the application of all these techniques to theproposed IMC-based generation system is considered outsidethe scope of this paper.

As mentioned in Section III-A, in this paper, oscillationsand instability due to interaction between the second-orderpower filter and the IMC, is reduced by filtering the inputvoltage signal before being used by the modulation algorithm.Using (12) in (18) and (19), i.e., with vid ≈ vgd and viq ≈ vgq,the incremental d–q components of the input current are ob-tained as

Δiid = − Pm0

V 2io

Δvgd

sτf + 1

Δiiq = − Pm0

V 2io

Δvgq

sτf + 1. (20)

The stabilizing effects of (20) can be explained assumingthat a very narrow low-pass filter is used. If τf → ∞ it canbe shown from (20) that Δiid = Δiiq = 0 for any voltageperturbation (Δvgd + jΔvgq). Therefore, in this case, Zeqd →∞, Zeqq → ∞ and the damping coefficients of the input stageare similar to the damping of the filter (ζfilter) at any operatingpoint. However, a very large value of τf cannot be used inthe modulation algorithm because, in this case, the voltageperturbations are completely neglected. Therefore, a tradeoffbetween stability and control performance is used to set τf .In this paper, the time constant τf has been adjusted usingexperimental work, considering full power operation of theIMC (which corresponds to the worst case operating point).

The interaction of the second-order input filter with the IMCis affected mainly by the operating power of the IMC inputstage. Machine parameter variations have negligible effects onthe stability of the IMC. Nevertheless, parameter variations,such as rotor resistance and inductances in the machine, mayaffect the performance of the system, for instance, introducingsome detuning in the current control loops of the vector controlsystem. However, this problem is also present when the DFIGsare fed by voltage source PWM inverters. The effect of thestator resistance variation, which may affect the stator fluxposition calculation, is negligible, because the stator resistancevoltage drop is small compared with the stator voltage.

C. Control of Output Stages

For each output stage, an SVM is used to impose thecorresponding reference rotor voltage, v∗

r,i = |V ∗r,i|∠θi in the

machine, where i = 1, 2 corresponds to the output stages oneand two, respectively. Fig. 6 shows the standard space vectors

Fig. 6. Voltage space vector and reference output voltage vector.

Fig. 7. Switching sequence for soft switching of the input stage.

used in VSI and the reference output vector. For each outputstage, the duty cycles, dα,i and dβ,i, are

dα,i = ki · sin(π/3 − θi) dβ,i = ki · sin(θi) (21)

where ki = V̂r,i/E = 2V̂r,i(dγ + dδ)/√

3V̂in is the modulationindex and V̂r,i is the fundamental maximum line output voltage[see (8)] for the corresponding output stage. Considering themodulation of the input stage, the duty cycles for the activevectors at the output stage are given by [8], [9]

dαγ,i = dγ · dα,i dβγ,i = dγ · dβ,i

dαδ,i = dδ · dα,i dβδ,i = dδ · dβ,i. (22)

The duty cycle for the zero vectors of each VSI, d0,i, and itscorresponding values, d0γ,id0δ,i, within each commutation ofthe input stage is [9]

d0,i = 1 − (dγ + dδ) · (dα,i + dβ,i)

d0γ,i =dγ

(dγ + dδ)d0,i d0δ,i =

dδ

(dγ + dδ)d0,i. (23)

The switching patterns of the output stages are arrangedin order to minimize the commutation losses [8], [9]. Softswitching operation of the input converter is achieved by com-mutating this stage when the zero vectors are applied to thecorresponding output stages, i.e., the commutation of the inputstage is carried out with zero current in the dc bus. The sequenceis shown in Fig. 7, with ts and tcom as the switching period andcommutation time of the input stage, respectively.


Fig. 8. Performance of rotor currents to step changes in reference demands.(a) Step changes in d–q rotor current reference demands for DFIG1. (b) Phaserotor current of DFIG1 and DFIG2.

IV. SIMULATION AND EXPERIMENTAL RESULTS

A. Simulation Results

The entire scheme, including the model described by (1)–(4)for each generator, the vector control of both generators and theSVM for the input and the two outputs of the IMC, has beensimulated using Matlab and Simulink. Two six-pole DFIMs areused (see parameters in the Appendix). Each machine is rated at2.5 kW, 1300 r/min with a stator voltage of 110 V.

Fig. 8 shows the rotor current control performance for theDFIG1. The speeds of both generators are 750 r/min, andinitially the rotor currents in both machines are regulated to zero[see Fig. 8(a) and (b)]. The q-axis rotor current is increased to7 A at t = 0.25 s and reduced to zero again at t = 1.25 s,whereas the d-axis rotor current is stepped up to 5 A at t =0.75 s and reduced to zero again at t = 1.75 s [see Fig. 8(a)].The rotor current dynamics are very good with a small couplingbetween the d–q axis currents during the transient. A similarperformance is observed when step changes in rotor currentsare applied to DFIG2 while the rotor currents in DFIG1 areregulated to zero.

Fig. 9 shows the performance of the current controller withthe two machines operating at variable speed. The speed ofDFIG1 is increased from 750 to 1250 r/min whereas the speedof DFIG2 is reduced from 1250 to 750 r/min [see Fig. 9(c)].Fig. 9(a) shows the rotor current performance for DFIG1 whena 5 A step change in q-axis rotor current demand is appliedwith the d-axis rotor current regulated to zero. The phaserotor currents are also shown. Fig. 9(b) shows the results forthe transients conditions corresponding to DFIG2. Again gooddynamic is observed for the d–q rotor current controller forboth machines with small coupling between the d–q currentcontrollers.

Fig. 10 shows the dc voltage, Fig. 10(a), and the operationof the IMC with bidirectional power flow [Fig. 10(b) and (c)].The input current and the equivalent phase voltage for power

Fig. 9. Performance of rotor current controllers for both machines at variablespeed. (a) Step change in q-axis current demand in DFIG1. (b) Step change inq-axis current demand in DFIG2. (c) Speeds of DFIG1 and DFIG2.

Fig. 10. DC bus voltage and IMC input phase current and voltage. (a) DCvoltage. (b) Phase current and voltage for power flow from the grid into the dcbus. (c) Phase current and voltage for power flow from the dc bus to the grid.

flowing from the grid into the dc bus is shown in Fig. 10(b)whereas operation with net power flow from the dc bus to thegrid is shown in Fig. 10(c). In both cases, near unity powerfactor operation is observed.

B. Experimental Results

The proposed topology has been experimentally tested usingthe set up shown in Fig. 11. One of the DFIGs is driven bya dc machine, fed by a commercial dc drive, whereas thesecond DFIG is driven by a squirrel-cage induction machine(IM). Different machines are used due to the facilities available


Fig. 11. Experimental setup.

in the laboratory. A DSP board, based on the TMS320C6713processor, is used as the control platform. Tasks implemented inthe DSP include vector control strategy for each DFIG, controlof the dc and ac drives and the calculation of the switching timesfor the input and output converter stages. Voltage transducersand current sensors are used to measure the stator voltages andstator and rotor currents. The rotor position in each machine ismeasured with a 10 000 ppr encoder. An interface board, basedon an FPGA, is used to implement the SVM for each stageand data acquisition. Communication between the DSP and aPC is carried out using a DSK6713HPI (Host Port Interface)daughtercard. The input stage uses six SK 60GM123 modulesand each output stage uses an SK35GD126 module. Both theinput stage and the two output stages are set in a single powerboard. The switching frequency for the input and outputs stagesis 10 kHz. The sampling time of voltages, currents and positionsignals is 100 μs.

Fig. 12 shows the modulation index, proportional to the mag-nitude of the rotor voltage, versus speed for each DFIG whenthe speed of both machines is varied from 750 to 1250 r/min(from sub- to supersynchronous speed), with idr = iqr = 0. AV-shape waveform is obtained because in DFIGs the machineback EMF is proportional to the slip velocity. With load, thecurves are shifted slightly to the right because of the rotorlosses.

Fig. 13 shows the performance of the rotor current controllersfor DFIG1 with a test similar to the one carried out in the sim-ulation (see Fig. 8), i.e., the speeds of both machines regulatedto 750 r/min and rotor currents initially set to zero. In DFIG1, a7 A step-up demand of q-axis rotor current is applied at t =0.25 s and then reduced to zero at t = 1.25 s. Additionally, inthe same machine, a 5 A step demand of d-axis rotor currentis also applied at t = 0.75 s and reduced to zero at t = 1.75 s.The rotor current controller dynamic response is very good withslight coupling between the d–q rotor currents components.Moreover, despite the lack of dc capacitors in the dc link, theDFIG2 rotor currents are not affected very much by the stepchanges in the rotor currents of DFIG1. A slightly higher rippleis present in the rotor current of DFIG2 when the load impact is

Fig. 12. Speed and modulation index versus speed for each DFIG.

applied because of the ripple increase in the voltage at the inputof the converter. The results are very much equivalent to thoseobtained in the simulations.

A similar performance is observed when step changes in theDFIG2 rotor current are applied. This is shown in Fig. 14. Thespeeds of both machines are regulated at 750 r/min and initiallythe rotor currents, in each machine, are set to zero. For theDFIG2, a 7 A step demand in the q-axis rotor current is appliedat t = 0.25 s. The step demand is reduce to zero at t = 1.25 s.Additionally, a step demand of 5 A in the d-axis rotor current ofthe same machine is applied at t = 0.75 s and reduced to zero att = 1.75 s. Again, the response of the current control system isvery good with a slight coupling between the d–q axes. Similarto the situation shown in Fig. 13, the rotor current regulation, inDFIG1, is not affected by the rotor current transients in DFIG2and a minor increase in current ripple is observed.

Figs. 13 and 14 show that the current control systems ofboth machines are effectively decoupled, even when no dc linkcapacitors are used in the proposed generation scheme. Asidefrom the small increase in the current ripple, no other couplingeffect between the two machines is noticed. A similar currentcontrol performance is observed at super synchronous speed.The dip and rise observed in the speeds are caused by the speedregulation of the ac and dc drives.

The operation during simultaneous transition trough syn-chronous speed for both generators is shown in Fig. 15. A rampup speed from 750 to 1250 r/min is applied to DFIG1 whereasthe speed of DFIG2 is ramped down from 1250 to 750 r/min.In both machines, the d-axis rotor current demand is set to zero(i.e., the machines are fully magnetized from the grid) whereasthe q-axis reference rotor current is set to 7.5 A. The dc voltageis also shown. In both machines, the rotor currents are wellregulated, even when variations in the dc voltage due to supplyvoltage regulation are observed.


Fig. 13. Rotor step current control performance for DFIG1 and regulation of current in DFIG2.

Fig. 14. Rotor step current control performance for DFIG2 and regulation ofcurrent in DFIG1.

Fig. 16 shows the power flow in both machines for the testconditions shown in Fig. 15. Regarding the active power flowin the machine, motor convention is used. Positive power is de-

fined to produce a motoring (accelerating) torque. In Fig. 16(a),the stator (Ps1 and Ps2) and rotor (Pr1 and Pr2) generatedpowers are shown, as well as the total rotor power, injected intothe grid by the IMC input stage. Power transference betweenthe rotors is noticed because, at a certain time, one of themachines is operating below synchronous speed while the otheris operating at super synchronous speed. Fig. 16(b) shows thepower generated by each generator (stator and rotor) and thetotal power generated by the two machines.

Fig. 17 shows the performance of the current controllerfor the machines during step changes in reference currentsat variable speed. A 5 A q-axis rotor current step demandis applied to each machine while the corresponding d-axiscurrents are regulated at zero [see Fig. 17(a) and (d)]. DFIG1speed increases from 750 to 1250 r/min [see Fig. 17(c)] whereasthe speed of the DFIG2 is decreased from 1250 to 750 r/min[see Fig. 17(f)]. The results show good dynamic performanceand good regulation of the rotor currents below and abovesynchronous speed. Again, the average dc voltage exhibits achange in magnitude [see Fig. 17(g)], because of the regulationof the IMC input voltage. The IMC input voltage regulationis mainly produced by the voltage drop in the input filter andthe leakage inductance of the variac (see Fig. 11), due to thechange in power flow direction However, the control strategycompensates the variation in dc voltage in each sampling time.

Finally, Fig. 20 shows the dc voltage, the input converterphase voltage, and the IMC input current for bidirectionalpower flow. Fig. 20(a) shows the dc voltage, Fig. 20(b) and(c) shows the input converter current and phase to neutral


Fig. 15. Rotor current regulation for both machines during transitions through synchronous speed.

Fig. 16. Power flow in both machines for the test condition of Fig. 15.

voltage for operation below and super synchronous speed,respectively.

The next results emulate the operation of the system in a windenergy variable speed generation system. In a variable speedsystem, usually the electrical torque is regulated as

Te = koptω2r (24)

where kopt is a constant which depends on the wind turbinecharacteristic. Equation (24) ensures that, in steady state, thewind turbine captures maximum energy from the wind [28].Using (9) and (24), the reference q-axis rotor current, for eachmachine, is set as

i∗qr =Te

kt=

koptω2r

kt. (25)


Fig. 17. Current controller performance for both machines at variable speed.

Fig. 18. DFIG1 performance in a variable speed wind energy system.


Fig. 19. DFIG2 performance in a variable speed wind energy system.

Fig. 20. (a) DC voltage. (b) Input phase current and voltage for subsynchronous speed. (c) Input phase current and voltage for super synchronous speed.

For this test, the d-axis rotor demand current is set to zero.The reference speeds for the machines driving each of theDFIGs can be set using an emulation of a corresponding windturbines according to the strategy described in [29]–[31]. In thispaper, the wind turbines emulated have negligible inertia. Thisis rather unrealistic but it is the most drastic test in terms ofvariable speed operation for wind energy generation. Figs. 18and 19 show the q-axis rotor current, the rotational speed andthe generated power of DFIG1 and DFIG2, respectively. Theq-axis rotor current error in each generator is shown inFigs. 18(a) and 19(a), respectively, showing the good regulation

of the rotor current tracking. From Fig. 18(b) and (c) [and alsoFig. 19(b) and (c)], it is concluded that the rotational speedcan be used to determine the rotor power flow direction ineach machine. This information may be used to implement amodulation strategy for the IMC aiming to reduce the ripplein the dc current, hence the ripple in the IMC input current.This fact has been considered by the authors in [20], where onlysimulation results are presented. The experimental verificationof that modulation strategy is the subject of future work.

As shown in Fig. 20, for steady-state operation, the phaseangle between the input voltage and current is almost zero.


These results are also in agreement with the simulations resultsshown in Fig. 10. A small reactive current is present in the inputproduced by the second-order input power filter (see Fig. 2).

V. CONCLUSION

A topology for a multiple machine variable speed energysystem has been proposed. The scheme uses two double fedIMs and an IMC. The possibility of having multiple outputs inthis converter topology is exploited. Therefore, an IMC withtwo outputs is used in order to supply the rotors of the cor-responding machines. The rotor currents of both machines arevector controlled using a reference frame aligned with the statorflux. Experimental results have shown excellent performance ofthe current control strategy for step changes in reference, bothat fixed and variable speed and for sub- and supersynchronousspeed operation. The tracking of the rotor currents of bothgenerators has also been experimentally verified, showing goodoperation of the control scheme. The system has been testedin variable speed energy wind energy systems, emulating theoperation of two wind turbines, regulating the q-axis rotorcurrent in order to maximize the energy captured. Both transientand steady-state results show the feasibility of the proposedtopology.

APPENDIX

Machine parameters: Rs = 0.45 Ω, Rr = 0.54 Ω, Ls =0.0854 H, Lm = 0.0818 H, Lr = 0.0860, six poles, turnsratio = 1.38. Stator delta connected, rotor star connected.

IMC input filter parameters: L = 2 mH, C = 2 μF (deltaconnected), R = 100 Ω in parallel with the inductance. Cur-rent controllers: ≈350 rad/s with 0.8 damping factor. Cut-offfrequency of synchronous rotating filter: 25 Hz.

ACKNOWLEDGMENT

The authors would like to thank Dr. L. Empringham andDr. L. de Lillo of the Power Electronics Machines and ControlGroup, University of Nottingham, U.K., for all their technicaladvice during the implementation of the experimental rig usedin this paper.

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Rubén Peña (S’95–M’97) was born in Coronel,Chile. He received the Electrical Engineering degreefrom the University of Concepcion, Concepcion,Chile, in 1984 and the M.Sc. and Ph.D. degrees fromthe University of Nottingham, Nottingham, U.K., in1992 and 1996, respectively.

From 1985 to 2008, he was a Lecturer with theUniversity of Magallanes, Punta Arenas, Chile. Heis currently with the Electrical Engineering Depart-ment, University of Concepción, Chile. His main in-terests are in control of power electronics converters,

ac drives, and renewable energy systems.

Roberto Cárdenas (S’95–M’97–SM’07) was bornin Punta Arenas, Chile. He received the B.S. degreefrom the University of Magallanes, Punta Arenas, in1988 and the Msc. and Ph.D. degrees from the Uni-versity of Nottingham, Nottingham, U.K., in 1992and 1996, respectively.

From 1989 to 1991 and 1996 to 2008, he was aLecturer with the University of Magallanes. From1991 to 1996, he was with the Power ElectronicsMachines and Control Group, University ofNottingham. He is currently with the Electrical

Engineering Department, University of Santiago de Chile, Santiago, Chile. Hismain interests are in control of electrical machines, variable speed drives, andrenewable energy systems.

Eduardo Reyes was born in Valparaiso, Chile.He received the Electrical Engineering degree fromthe University of Magallanes, Punta Arenas, Chile,in 2007, where he is currently working towardthe M.Sc. degree in the Electrical EngineeringDepartment.

His main interests are control of power electronicsconverters and ac drives.

Jon Clare (M’90–SM’04) was born in Bristol, U.K.He received the B.Sc. and Ph.D. degrees in electricalengineering from the University of Bristol, Bristol.

From 1984 to 1990, he was a Research Assis-tant and a Lecturer with the University of Bristol,involved in teaching and research in power elec-tronic systems. Since 1990, he has been with thePower Electronics, Machines and Control Group,University of Nottingham, Nottingham, U.K., and iscurrently a Professor in power electronics. His re-search interests include power electronic converters

and modulation strategies, variable speed drive systems, and electromagneticcompatibility.

Dr. Clare is a member of the Institution of Engineering Technology.

Patrick Wheeler (M’00) received the B.Eng. (Hons)degree and the Ph.D. degree in electrical engineeringfor his work on matrix converters from the Uni-versity of Bristol, Bristol, U.K., in 1990 and 1994,respectively.

In 1993, he moved to the University ofNottingham, Nottingham, U.K., and worked as aResearch Assistant with the Department of Elec-trical and Electronic Engineering. In 1996, he wasappointed Lecturer (subsequently Senior Lecturer in2002 and Professor in power electronic systems in

2007) with the Power Electronics, Machines and Control Group, Universityof Nottingham. His research interests are in variable speed ac motor drives,particularly different circuit topologies, power converters for power systems,and semiconductor switch use.

Dr. Wheeler is a member of the Institution of Engineering Technology.

A Topology for Multiple Generation System With Doubly Fed Induction Machines and Indirect Matrix Converter

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