Stator Flux Oriented Control

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Stator flux oriented control of a cascaded doubly-fedinduction machine

B.Hopfensperger, D.J.Atkinson and R.A.Lakin

Abstract: A cascaded doubly-fed induction machine (CDFM) is a connection of two wound rotorinduction machines. In comparison to a single doubly-fed induction machine (SDFM) brushes areobsolete. Due to recent developments in brushless doubly-fed machine design, there is a renewedinterest in associated control. Theoretical and experimental studies of a stator flux oriented controlmethod for a CDFM are presented. The use of vector control principles to control torque, speed,active and reactive power is investigated. It is found that the additional closed rotor circuit of theCDFM introduces a cross coupling between the d-axis and the q-axis. Nevertheless, the crosscoupling effect remains small in relation to the overall control concept so that the control of theCDFM resembles that of the SDFM.

List of symbolsAbbreviations:SDFM -CDFM -

SF-CDFM =

- single doubly-fed induction machinecascaded doubly-fed induction machinesingle frame cascaded doubly-fed induc-tion machinebrushless doubly-fed induction machinedoubly-fed reluctance machinemicrocontrollerpulse width modulation

Superscripts (for reference frames):abc

de* = demand valueOther:VI = side 1 of CDF M phase voltage in RMSvI , v2, v3, v4 = voltage space vector of respective

i , , 2, i,, i 4 = current space vector of respective

q 2 3 4 flux linkage space vector of respective

= side 1 of CDFM (stationary) reference frame= side 2 of CDFM reference frame= side 3 of CDFM reference frame= side 4 of CDFM reference frame= excitation reference frame for orientation

machme side

machine side

machine side

OIEE, 1999IEE Proceedings online no. 19990590DOL 10.1049/ipepa: 9990590Pape r fmt received 25thFebruary and in revised form 7th Ju ne1999B. Hopfensperger is withSiemensplc, Standard Drives,Varey Road, Congle-ton, Cheshire CW12 IPH ,UKD .J. A W o n s with the Departm entof Electrical and Electronic Engineering,Universityof Newcastle upon Tyne, MerzCourt, Newcastle upon Tyne, NE17RU, UKR.A. Lakrn is wth Microtech Ltd., Hawks Roa d Industrial Estate, Unit 13,Gatehead,NE8 3BL, UK

IEE Proc.-Electr. Power Appl., Vol. 146, No. 6 November 1999

rotor circuit loop flux linkage spacevectorelectromagnetic torque of machine A andB of CDFMtotal electromagnetic torque of C DFMside 1 active and reactive powerfrequency of side 1 and side 4mechanical rotor frequencymechanical angular frequency of rotor(side 2)mechanical angular frequency of side 4relative to side 1

angular frequency of the excitation refer-ence frame in elec. rads

rotor angle in mech. radrotor angle of machine A and B in elec.radangle between frame a and dangle between frame b and eangle between frame d and eangle between frame a and epole pair number of machme A andmachne Bresistance of respective machine sidecombined rotor resistanceself inductance of respective machine sidecombined rotor inductancemutual inductance of machine A and Bmechanical rotor speed, rpmconstants

1 Introduction

Recent developments by Wallace, Spee et ul. [l], in con-junction with Williamson [2] have resulted in improvementsin the design of the so-called brushless doubly-fed inductionmachine (BDFM). Their work has shed new light andinterest on the field of doubly-fed induction machines in

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general. Consequently, the importance of the control ofsuch machnes has increased.

Connecting the stator windings of a wound rotor induc-tion machne to a stiff voltage supply and the rotor wind-ings to a bi-directional power converter constitutes adoubly-fed machine arrangement. It is referred to as a sin-gle doubly-fed induction machine (SDFM) in this paper.The SDFM is the simplest type of doubly-fed machine 131.A field oriented control method for the SDFM was intro-duced by Leonhard [4] nearly 20 years ago. The rotor cur-

rent vector is oriented into a reference frame aligned withthe stator flux, enabling the torque and the stator activepower to be manipulated with the q-component of therotor current vector. Since the flux in the machine is mainlydetermined by the stiff stator voltage, this enables the statorreactive power to be controlied by the d-component of therotor current vector. Thls stator flux oriented control prin-ciple is now well established in research and industry. Dueto the decoupled active and reactive control possibilities,the main area of application for the SDFM is in variablespeed generating systems such as wind power [5] and hydropower [6].

Compared to a variable speed singly-fed machinearrangement with a cage induction machme, the SDFMhas the advantage of a reduced power converter rating,which is related to the desired speed range. As a drawback,the SDFM has slip-rings and brushes on the rotor side,which are subject to maintenance and additional cost.

(bi-directional)

Fig.1 CDFMnvrchinearrangement

A machine arrangement consisting of two wound rotorinduction machines, which avoids brushes, is shown inFig. 1. The stator of machine A (side 1) is connected to thestiff voltage mains supply and the rotor slip-rings ofmachne A (side 2) are then directly connected to the slip-rings of machine B (side 3). The stator of machme B (side4) is fed by a bi-directional power converter. Since the tworotors have a stiff mechanical coupling no brushes areneeded for the slip-ring connection. This brushless machinearrangement leads to a so-called cascaded doubly-fedinduction machine (CDFM). The idea of t h s machine con-nection has been known for more than a century [7, 81.

Several researchers investigated the stability and scalarcontrol schemes [9-111. In [l l] , it is pointed out that scalarcontrol methods lead to either poor steady state controlconditions or the control shows large dynamically unstableoperational areas. Field orientation control principles forthe CDFM were first applied by Bauer [I 13. In his methodthe rotor (side 2) current vector is oriented into an artificialflux reference frame based on measurements of the two sta-tor currents. A mathematical control extension allows thenon-accessible rotor current to be manipulated by the side4 current. Bauers scheme encounters stability problems athgher speeds and it is only applicable to a CDFM consist-ing of two identical machines. Krebs [12] continued thework of Bauer on a SF-CDFM and introduced anobserver for the non-measurable rotor currents to stabilise

the control method. Sathakumar and Koczara [13, 141investigated a stator (side 1) flux oriented control schemefor the CDFM by simulation. It is claimed that the q-axisside 4 current component in the side 1 flux reference framecontrols the active power flow in the CDFM and the d-axiscomponent the reactive power flow. In that case, theCDFM would behave exactly like a SDFM. To date, therehas been no comment on the influence of the closed rotorcircuit upon the control algorithm

This paper presents theoretical and experimental research

results on the stator flux oriented control method for theCDFM. The extent to whch the additional closed rotorcircuit loop affects the control scheme has been investio-ated.

Other machine types, which can generally be classified asa brushless doubly-fed machine, are the single-frame-CDFM (SF-CDFM), the brushless doubly-fed machine(BDFM) and the doubly-fed reluctance machine (DFRM).

The SF-CDFM is a more compact version of theCDFM. Both stator windings are fitted axially, alignednext to each other in a common frame. A cage rotor, withthe rotor bars cross-over between the two machine halves,goes over the whole machne length [15]. The analysis in[12], for example, is carried out on ths machine type.

Research into the BDFM is concentrated with Wallaceand Spec at the Oregon State University [l], together withmore recent work by Wihamson [2]. The BDFM machmepath was initiated by Hunt in 1907 [16]. He aimed to unitetwo machines into one. A special type of stator windingsets up two rotating fields, which interact with a specialtype of cage rotor. The latest control contribution to theBDFM is a rotor flux oriented control scheme [IA.

Having the same stator as a BDFM, but a reluctancetype rotor, leads to the doubly-fed reluctance machne(DFRM) [18]. The dynamic model of this machine type isidentical to the SDFM and therefore the same stator fluxoriented control method is applicable to the DFRM [19].

The analysis in this paper is applicable to the CDFM,the SF-CDFM, and is also relevant for the BDFM.

2 Experimental arrangements

The following investigation of the CDFM will be betterunderstood if the experimental equipment is first described.The complete laboratory arrangement is illustrated inFig. 2. The power circuit (thickened lines) consists of a bi-directional power converter and the CDFM. A 3.75kWDC machine (not shown in Fig. 2), acting as a primemover to the system, has a through-shaft so that onewound rotor induction machine of the CDFM is connectedon either side of the DC machine. Machme A of theCDFM is a 2.25kW, 4 pole pair and machme B a 2.25kW,2 pole pair wound rotor induction machme. The CDFM isdescribed in th s paper as a brushless machme arrangementwith directly interconnected rotor windings. However, dueto the machine configuration with one wound rotor induc-tion machine on either side of the DC machine, the slip-rings and brushes are still used in the laboratory set-up. Itis therefore possible to monitor the rotor quantities, whichassists in the understanding of the machine behaviour.Although set up in this way, the electrical behaviour of theCDFM remains unchanged.

The independently functioning front-end of the bi-direc-tional power converter creates a unity power factor inter-face at the grid connection point and controls the DC-linkvoltage to 650V. The gate drive circuits of the machine-sideinverter module are interfaced to the PWM signals comingfrom the external controller unit.

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-fft side nV

A

,6 il VI

v vinterface 4interface linterface 21 lintetface 3

1

c

4WC2

oscilloscope

0 0 0 00 0 0

+ * . fl_- .;.., ,. .. ....

. . . .., f2 f3

. ' . . .. ..' . . .P '.....

. I

100 200 300 400 5 0 O - W Q 700 8CO. . .

Fig. 2 Lu6orutury driveur rmgenlmt

The control hardware comprises two paralleled 16-bitfixed point 80C167 microcontrollers, denoted as yC1 andpC2 in Fig. 2. Microcontroller yCl performs most of thecontrol functions, which include current control with PWMgeneration, position and speed calculation. The microcon-troller's PWM unit generated interrupt request sets theswitching frequency of the machine-side inverter and alsodetermines the available processing time. A switching fre-quency of 2.5kHz was chosen, which gives 400p for soft-ware execution. Microcontroller pC2 performs theremaining functions such as angle calculation, power calcu-lation and power control. A high speed serial link providesthe communication link between both microcontrollers.The 10 bit A/D conversion for the measured quantities isshared between the microcontrollers depending on therespective control functions. The sensed quantities are theside 1 voltage and current, and the side 4 current.

Various interface circuits allow electrical isolationbetween power and control hardware. Incremental encodersignals are received at a timer-unit of pCl for position andspeed calculation. pCl produces control variables for datastorage and monitoring purposes on the PC and an oscillo-scope.

3

There are two possible ways to electrically connect the indi-vidual machines of the CDFM: either in positive phasesequence or in negative phase sequence. Positive phasesequence results by connecting the rotor windings (slip-rings) with same naming together. Owing to the back-to-back machine arrangement, the resulting rotor fields rotate

in opposite directions relative to the rotor. For negativephase sequence connection, with a phase-swap on side 3 ,the rotor fields have the same rotational direction. Thedeveloped torques of machine A and machine B are co-act-ing for positive phase sequence rotor connection and arecounter-acting for negative sequence connection [20].Therefore, only the positive phase sequence connection isof any real importance and it is the only connectionsequence considered in this paper.

Fig. 3 shows the frequency behaviour of the laboratoryCDFM with a 4/2 pole pair relationship. Side 1 is con-

Steady state operation of the laboratory CDFM

IEE Proc -Elect Powei A pp l Vol 146 N o 6, November 1999

nected to the 50Hz supply line. Side 2 and side 3 frequen-cies are identical due to the positive phase sequenceconnection. The CD FM reaches the synchronous point ofmachine A at 750 rpm v2 f = OHz). In the vicinity ofmachine A synchronous speed the individual machines losetheir electromagnetic coupling so that the CDFM can nolonger be regarded as one unit. It is not possible to drivethe CDFM through that crucial interval in motoring mode.A practical speed range for the laboratory CDFM is up to80% of machine A synchronous speed, which is up to 600rpm. The so-called cascaded synchronous point, related tothe sum of the individual pole pairs, is reached at 500 rpmwithf, = OHz.

60 I 1

40

N 2o

-20

-40 I Ispeed, rprn

Fig. 3rotor connection)

Frequencies j b r 1lrc 4 2 pole puir CDFM positive p h e sequence

The resulting frequency relationship of the CDFMbetween side 1 and side 4 follows as

f l = (P.4 + P S ) f r n + 4 (1)with p A and p B as the pole pair numbers and f, as the

mechanical rotor frequency. Negative frequencies in Fig. 3 symbolise reversed phase sequence in comparison to posi-tive frequency values.

It has to be mentioned that the laboratory machine setcould also be arranged in a 2/4 pole pair relationship. Thecascaded synchronous point would still be at 500 rpm, butthe machine A synchronous speed would result at 1500rpm. However, this machine arrangement is not favourablesince at the maximum practicable speed range of 80% ofmachine A synchronous speed, the majority of machinepower would flow via side 4. This counter affects the

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advantage of a doubly-fed machine system with reducedinverter power rating. The power flow in the machine isaffected by the machine pole pairs and it is preferable tochoose p A greater than p B [21].

4 Stator f lux oriented control of the CDFM

The expression 'stator' is ambiguous when used with theCDFM since there are two stators involved, but this termshall be used throughout this paper and it is solely related

to the machine A stator (side 1).4. I Dynamic model and reference framesThe individual machine side quantities expressed at theirrespective machine sides as space vectors are

d*gd t

vg = Rgi: + nd *; = Lgiz + LmBiz 4)

The corresponding reference frame system for the CDFMis shown in Fig. 4. Frame a is attached to the stationaryside 1. Frames b and c are identical and are attached to therotor of the CDFM. Frame d for side 4 moves with theangular velocity of mrAB= P A + pB)mmrelative to frame a.Although ths may not agree with the physical picture ofthe CDFM with both stators, side 1 and side 4, stationary,the reference frame of Fig. 4 is preferable for developingthe control of the CDFM. The machine can be regardedonly from one stationary reference frame and the viewthrough the CDFM goes from side 1 onto side 2 and side3. Side 4 is then seen relative to side 3. This view of theCDFM is adopted for all the following considerations.

ee t w e ~ d excitation reference frame e

>&AB d,z v d stator of machine B

(side 2 and side 3/,,.- - m _---,. __----f 7 %A)---

.d stator of machine A(side 1)

Fig. 4 Refrencefmmesand urglmjor the CDFM

Expressing the voltage equations of side 1 and side 4 inthe excitation reference frame e, which is attached to thestator flux, leads to

Since the rotor windings constitute a closed rotor circuitloop the voltage eqns. 3 and 4 can be combined with theconnection constraints for the positive phase sequence con-nection of

This creates the rotor loop voltage equation expressed inthe e frame as

with RR = R + R , as the combined rotor resistance and

\kk = @ - Pz = LmAiy + LEiz - LmBiz (10)as the rotor circuit loop flux linkage, which is an artificialquantity not physically existing in the CDFM. This is cre-ated by Kirchhoffs Law being applied to the flux linkagesin the rotor loop and is composed of the individual rotorflux linkages. LR = L2 + L3 is the combined rotor circuitinductance value. It is useful for further analysis to derivethe rotor loop flux linkage as a function of the stator flux.Resolving the side 1 flux eqn. 2, expressed in the e frame, interms of the side 1 current, and substituting it in eqn. 10yields

* l e - * e + y A - LmBi; 11)L1

112

In the same way, substituting the rotor current leads to

where k l and k2 are constants with the values

The voltage eqns. 6, 7 and 9, together with the flux linkageeqns. 2 and 5 expressed in the e frame, and eqn. 10 consti-tute the electrical model of the CDFM in the excitation ref-erence frame.

4.2 General features of the control

4.2. I Determination of the orientation angle E: Inorder to orientate the side 4 current vector into the statorflux reference frame the position of the stator flux relativeto the stationary reference frame has to be known. A com-mon way to achieve ths is by neglecting the stator resist-ance and measurement of the stator (side 1) voltage [22].With the neglect of the side 1 resistance the stator flux vec-tor lags 90 behind the stator voltage vector. Therefore,measuring the side 1 voltage in the a frame together with aCartesian to polar transformation .delivers he position angleal of the stator voltage vector. A subsequent subtraction ofd 2 gives the angle ,U.

-1

W

Fig. 5 Angle comtiuction methodfor the CDFM

The mechanical rotor position angle O,, is measured withan incremental encoder. Multiplying the angle 0 with thesum of the machine pole pairs P A + p B delivers OrAB,which is the angle between frames a and d. The angle Ebetween the e frame and the d frame can be thus calculatedas ,U - OrAB The angle construction method is displayed inFig . 5 All angles, apart from Om n Figs. 4 and 5 are inelectrical rad/s.

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4.2.2 Voltage and f lux constraints on side I: Byneglecting the resistance on side 1 the voltage eqn. 2reduces to

1..

From t h s it can be seen that a reference frame attached tothe stator flux has the same angular frequency as the statorvoltage with

n 200rpm normal resistance

(il. . - _._ _ ._. . - I _ - .

w e = w I * const .d tBy substituting q lu lW,'ldp in eqn. 14 and applying therules of diffrentiation, the magnitude of the stator fluxexpressed in the e frame is given by

and Q:l = 0 (16)

where V , is the stator phase voltage in RMS. The individ-ual components of the stator voltage space vector in theexcitation reference frame take the value

.us1 = W ~ P ?= V = const . (17)i l = 0 and

4.2.3 Influence of the closed rotor circuit: Theadditional closed rotor circuit on side 2 (= side 3 is the dis-tinct electrical difference between the CDFM and theSDFM. This rotor winding is not accessible and introducesanother set of voltage and flux equations to the machinemodel as covered above. The influence of this rotor circuitupon the control algorithm is investigated in the following.Consideration of the rotor loop voltage eqn. 9 in the eframe and splitting it into d-q-components, by regardingonly steady state, yields

wheremQ = we wrA= dQldt with Q = p 0 as the anglebetween the rotor reference frame b and the excitation ref-erence frame e.

From eqns. 18 and 19 it can be seen that the rotor circuitintroduces a cross coupling between the d-axis and the q-axis in the e frame. The degree of cross coupling dependson two parameters: the combined rotor resistance and therotor angular speed relative to the angular speed of theexcitation frame

The smaller the combined rotor resistance, the smaller isthe cross coupling effect. The second parameter w,, canvary between two extremes in the operational speed rangeof the CDFM. At standstill, mQ = 2 4 , , since the rotor isstationary and 'sees' the excitation reference frame rotatingwith synchronous speed. When the rotor reaches the syn-chronous speed of machine A, w, = 0. The closer the rotorspeed approaches the synchronous speed, the larger is theeffect of cross coupling in the above equations. At 80% ofthe subsynchronous speed of machine A, the influence ofthe cross coupling is five tinies that at standstill.

Simulation results showing the influence of the cross cou-pling on the rotor loop flux are presented in Fig. 6. Twodifferent cases of the rotor loop fl ux in the e frame are dis-played for step changes in the components of the side 4current.

IEE Proc -Electr Power A p p l , Vol 146, N o 6 , November1999

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-1.5 1

time, 400rns/div

Simulatedcross coupling influencein W eig.6step in id4e= 4 to 0 to 4A, step in fq4 = 0 to 4 to 0 1i) q component, (ii)d component

By ignoring the transient in the step response, the first setof simulations (middle graph), at a speed of 200 rpm,clearly shows the cross coupling effect in the q-componentof YRe denoted as flux R' in the graphs) caused by a stepin the d-component of i4e, and the effect in the d-compo-nent of Y R e aused by the q-component of i The secondset shows the case for 600 rpm (80%of speed range). Com-pared to the simulation results at 200 rpm, there is anincrease in the magnitude of the rotor loop flux linkage andits cross coupling. The value of the combined rotor resist-ance has a linear effect on the cross coupling. With half theresistance value, only half the cross coupling effect wouldoccur.

4.2.4 Side I to side 4 relationships: For the statorflux oriented control of a SDFM, the rotor current d-q-components are directly linked to the respective stator cur-rent d-q-component in the e frame. It is the case that thestator active power is directly linked to the rotor current q-component and the stator reactive power to the rotor cur-rent d-component. In the following, it is investigatedwhether such a direct relationship between side 4 and side 1also exists for the stator flux oriented CDFM.

Relating the side 4 currents to the side 1 currents in the eframe for the CDFM with the help of eqn. 12, and split-ting it into d-q-components with Yq I e 0, gives

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From eqn. 20 it can be seen that the side 1 current d-com-ponent is manipulated by the side 4 current d-component,but there is also the rotor loop flux d-component present,which is subject to cross coupling. The stator flux compo-nent in eqn. 20 is constant as derived above. A similar rela-tionship exists for the q-axis components in eqn. 21, wherethe q-component of the rotor loop flux is subject to crosscoupling. It shows that the side 1 current components aremanipulated by the respective side 4 current component,but not in a totally decoupled manner as it is the case for

the SDFM.Employing eqns. 20 and 21, together with the side 1voltage constraints of eqn. 17, and substituting it in the side1 active and reactive power eqns. 29 and 30, creates thestator active and reactive power equations of the CDFM inthe e frame as

The side 1 active power expressed in the e frame is depend-ent on the side 4 q-axis current component, but also on theq-axis component of the rotor loop flux, which is subject tocross coupling. The side reactive power is influenced bythe side 4 d-axis current component and also contains thed-component of the rotor loop flux. Compared to aSDFM, the CDFM does not yield a totally independentdecoupled relationship between the side 4 current compo-nents and the side 1 power components.

4.3 Inner current control loopThe use of a voltaoe source inverter as a control unitrequires the implementation of a fast current control loopon side 4. This current control loop ensures that the currentvalues demanded by the outer control loops (power orspeed) actually appear on side 4 of the CDFM. The effectof the current loop is analysed in the following.

Resolving eqn. 11 in terms of the rotor current and sub-

stituting it in the side 4 flux linkage equation in the e framegives

(24)?n B ,p; + LnLAL?nB py + k3i;,pi ~k l k l L1

Fig.7

602

with the constant

Replacing eqn. 24 in the side 4 voltage eqn. 7 and consid-ering only the steady state yields

It is enough to consider only the steady state since all thecontrol quantities are DC values in the excitation referenceframe. The second terms of eqns. 25 and 26 constituteslight cross coupling effects in the voltage equations, andthe third term of eqn. 26 is a slip proportional back EM Fterm related to the stator flux. The cross coupling terms ineqns. 25 and 26 are an order of magnitude smaller thanthe back EMF term. Their minor influence upon the con-trol is compensated by the PI-controllers in each axis.However, the third term of eqn. 26 acts as a disturbance tothe output of the PI-controller of the q-axis. It is possible tocompensate the influence of this back EMF term by choos-ing high PI-controller gains, but a steady state trackingerror will persist [23]. The tracking error can be eliminatedby adding a feed forward term to the output of the q-axiscontroller with the value

(27)L m A L m B f iv lf e e d fo rward = w 1 W, A B )

klL1 w1

This also results in easier tuning. The complete current con-trol structure for the CDFM in stator flux orientation isshown in Fig. 7. For clarity the CDFM is symbolised as asingle machine.

It should be noted that the cross coupling withn the cur-rent control loop is not to be confused with the cross cou-pling within the machine control structure, as covered inSection 4.2. The cross coupling within the current controlloop is compensated by the PI-controllers in each axis, butthe cross coupling due to the rotor circuit flux remains.

grid- I7 T

calculationof t 1

ff-term I 1I

Siuior lux conirol structure ojihe CDFM - inner current control loop

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I

-1 J I

2000,

&&&%3j+y,

_ _ - . I _ . _

+$$&+#+*1500 ~ ; - rQ;i.; - . c ~

_ - . _ _, . I I . .I , : j .

2 J l O O O - - - - - - _ . _ _ . . . . . . .. : ,. .\&4*&~.+&4 . - I_ -0 500-- ~I I I . * I

2-

a-.- 0

-5. I

-10time, 250ms/dN

Fig.8 E x - r h e n t dCDFM dynamics - current control loopiae = 0 to 5 to OA, idc = 2A, nm - 400rpm

a.-

12, . . . : . . . . . . ,

600

Experimental results obtained from the inner currentcontrol loop are presented in Figs. 8 and 9. Fig. 8 showsdynamics for a step change in the d-component of i4efromOA to 5A and back to OA. The q-component is kept at 2Aand the speed is approximately 400 rpm. It can be seen thatthe influence of the cross coupling caused by the rotor loopflux has only a marginal effect on the results. The side 4

IEE Proc.-Electr. Power Appl , Vol. 146, No. 6 ovember 1999

-1000 J

1

-1

I

time, 250ms/div

Fig. 10Q, = 1.7 to 0.5 to 1.7kVAr, PI = 4 . 5 k W

Experimentnl C D F P dynamics -power control loop

4.4 Power control loopWhen the SDFM is used as a variable speed generator, theinner current control loop is extended with an outer powercontrol loop in a cascaded manner. The d-axis is extendedwith a reactive power loop and the q-axis with a activepower loop. Taking the same approach with the CDFMleads to a control structure where the side 4 d-axis currentdemand is the output of the reactive power PI-controller,and the side 4 q-axis demand value is the output of theactive power PI-controller. Active and reactive power com-ponents are calculated in the stationary frame a by measur-

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ing side 1 current and voltage (see the power equations inthe Appendix). The DC machine acts as a prime mover tothe system.

Fig. 10 shows experimental dynamics for a step in theside 1 reactive power demand value from 1.7kVAr to0.5kVAr and back to 1.7kVAr. It can be seen that with anouter power control loop side 1 active and reactive powercan be controlled totally independently of each other. Atthe same time, the side 4 current component id4e of theinner loop, shown in Fig. 10, changes accordingly to

eqn. 23 and iq4eremains almost unaffected from the stepchange, confirming the minor influence of the cross cou-pling effect in this case. Regarding the reactive power flowin the CDFM, the reduced magnetising reactive power onside 1 during the step is compensated by an increased mag-netising reactive power supplied via side 4, expressed by theincreased magnitude in id4@.

Fig. 1 1 displays the experimental results for a step in theside 1 active power demand value from -1kW to 4 S k Wand back to -1kW (the generating, DC machine acts asprime mover). Again, active and reactive power show nosign of cross coupling. Now performs a step change tojustify eqn. 22. As seen already in Fig. 9, the cross cou-pling effect due to the rotor circuit is more pronounced inthe d-axis of the e frame. The d-component of i4e shows aslight change at the step in Fig. 11.

1500 1 . 1

1000 , r*UY~* ?&&f +i- Y**+ {+?qP p&?&.

. . . . . . . . . . . . . . . . . . .500, . , . . I . # .

6 . . . . . . .3 , , , I . ,

, P1 . I . ,-500 - ., . - ,- ~ , - , -

. . . . . . . . . . .1000 . . . . . . . .

. . . . . . . . .

time, 100ms/div

Fig. 11Q , = IkVAr,P, '=-l t o 4 5 t o - 1 k W

ExperimeniulCDFM dynmnlcs-powe r controlloop

With the implementation of an outer active and reactivepower control loop, the side 1 active and reactive powercan be controlled independently of each other. The currentcomponents of the inner loop are nearly proportional tothe power components, with only a slight cross couplinginfluence compensated by the outer power control loop.

4.5 Speed control loopThis Section considers the behaviour of a speed controlloop for the CDFM. To obtain the developed torque of theCDFM for stator flux orientation, the torque equation hasto be developed as a function of the stator flux linkage andthe side 4 current vector. Resolving eqn. 11 in terms of therotor current and substituting it in eqn. 33 yields

Carrying out the cross product and considering the con-straint of Yql = 0 results in the following torque equation

(28)This equation looks rather complicated and does not give astraightforward relationship between iq4'? and the torque atfirst sight. Both side 4 current components appear ineqn. 28, whch indicates that the torque may be affected byeither a change in id/ or iqde.However, if id4 is kept at aconstant value, then the term

remains constant. No cross coupling is involved since Yq R rwould only be affected by a change in id4e.

7

, . . . .. . . . . . . . . . . ., , . . ., , . . . ,. . . . . . . . . . . . . .

a . . . , .. : . . . . :i*.,:. . . . . . . . . . . . . . .

400, . . . . .. . . .. . . . . . . . .00>. 200p 100d , oz 1009 200

.-

. . . .. . . . . . .-300 . . . .-400 ' I

time 500rnsldiv

ExpeiunentulCDFM dynumics- speed control loop ut no-loudig. 12nm = 250 to 630 to 250 rpm, i = 3A

The remaining term in eqn. 28 is governed by butthe d-component of the rotor loop flux is present, which issubject to cross coupling caused by iq4e. This cross couplinghas no influence in ths case because iq4ewould take a cer-tain value to give a set torque, despite the effect in Y d R e .

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Consequently, for a fixed value of the torque devel-oped by the CDFM in the stator flux reference frame ismanipulated by the q-component of despite cross cou-pling caused by the rotor circuit. As long as saturation isavoided, the larger the set value for id , the more reactivepower is supplied by terminal 4 and the less via side 1.Additionally, the larger the magnitude of id4e,the less mag-nitude of iq4e s necessary to develop a certain torque value.However, this effect is only minor.

Extending the q-axis of the inner current control loop

with an outer speed loop, so that the output of the PI-speed-controller gives the side 4 q-axis current demandvalue, and setting the side 4 d-axis current demand value toa constant value allows the CDFM to be applied to speedcontrol applications. The speed is obtained from positionmeasurements with an incremental encoder.

Experimental results of a speed control loop at no-loadare shown in Fig. 12. It can be seen that the q-componentof i varies, depending on the torque demand value set bythe outer speed loop controller to follow the desired speedramp. The d-component remains unaffected.

The last graph in Fig. 12 displays the rotor voltage andshows clearly the change in frequency and magnitude ofthe rotor voltage for varying speed. The closer the speedapproaches machine A synchronous speed, the more therotor voltage magnitude and frequency reduces.

5 Conclusions

This paper presents theoretical and experimental results ofa stator flux oriented control scheme. Ths scheme has notpreviously been applied to the CDFM. In particular, theinfluence of the closed rotor circuit loop on the controlstructure has been investigated. It is found that the presenceof the closed rotor circuit loop introduces a cross couplingbetween the d-axis and the q-axis in the stator flux refer-ence frame. However, the cross coupling has only a minoreffect on the overall control concept. It is therefore possibleto achieve decoupled control of active and reactive powerin the CDFM in a manner similar to that established forthe SDFM. In comparison to a previous field oriented con-trol method for the CDFM, the scheme in this paper isindependent of the CDFM machine combination.

6 Acknowledgments

The authors wish to thank Microtech Ltd., Gateshead, andRobert Bosch GmbH, Erbach, for help and hardware sup-port. B. Hopfensperger wishes to thank the Department ofElectrical Engineering, University of Newcastle for finan-cial support.

References

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Appendix

Stator side 1 active and reactive powers are calculated interms of space vector components (non-power invarianttransformation) from the side 1 voltage and current as

CI

The torque of machine A expressed in the e frame, involv-ing the stator flux linkage, can be written in space vectorform as

(31)3 LmAT e ~ p ~ x i;

L1and the torque for machine B as

Combining both torque equations gives for the CDFMtorque

Te A B T e A + T e B

IEE Proc.-Elecrr. Power Appl. , Vol. 146. No. 6 , November 1999 605

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Stator Flux Oriented Control