Design of Coupling Cancellation Control for a Double

IEEJ Journal of Industry ApplicationsVol.6 No.1 pp.29–35 DOI: 10.1541/ieejjia.6.29

Paper

Design of Coupling Cancellation Controlfor a Double-winding PMSM

Akira Satake∗a)Member, Yuriko Okamoto∗ Member

Satoru Kato∗∗ Non-member

(Manuscript received Feb. 8, 2016, revised June 13, 2016)

A double-winding permanent magnet synchronous motor (PMSM), which has two groups of three-phase windingson its one stator, has a coupling effect between the windings. This paper explains the deterioration of the currentcontrol performance of a double-winding PMSM by using a voltage equation of the motor. The proposed couplingcancellation control method improves as demonstrated by the results of simulations and experiments. A design methodfor the coupling cancelling control with a Bode diagram is also discussed.

Keywords: double-winding, permanent magnet synchronous motor, motor model, coupling, cancellation

1. Introduction

Recently, large-scale AC motor drive systems are requiredto modify machines to electric-powered for energy and main-tenance saving, and also improve their performance. Fordriving a large-scale motor, beside from a normal single in-verter drive for the motor, a method to utilize multi inverterto drive single motor, what is called multi inverter drive, iswell known.

The multi-inverter drive is categorized into two types; oneuses series reactors to integrate the output of the inverters (1),and the other uses a multi-winding motor to combine them.The latter method has advantages in the size and cost of theequipment because it needs no reactor. The multi-windingmotor has another advantages, such as reduced torque ripple,higher efficiency and system redundancy (2) (3).

Multi-winding motors can be used with open-loop controlsuch as simple V/f control, especially for induction motors.Although for applications with advanced performance, suchas steel mill or elevator, and for synchronous motors, espe-cially PMSM without damper windings, current control isrequired to output precise and stable torque from the mo-tor. For the current control, it is possible to use a sum ofcurrent of each phase of the inverters to calculate feedbackinformation, and with this method, the current of the motorcan be controlled with conventional single current controller.But with this method, it is obvious that only the sum of eachphase current is controlled and the individual current of eachwinding is not under control. If there are some difference in

a) Correspondence to: Akira Satake. E-mail: [email protected]∗ Advanced Technology R&D Center, Mitsubishi Electric Corpo-

ration8-1-1, Tsukaguchi-Honmachi, Amagasaki, Hyogo 661-8661,Japan

∗∗ Inazawa Works, Mitsubishi Electric Corporation1, Hishi-machi, Inazawa-City, Aichi 492-8682, Japan

impedance of each winding or inverter, there will be someunbalance in the current of each winding.

To balance load on the windings in the motor and the in-verters, balancing current of each winding is preferable. Forthe reason, individual current control for each winding isnecessary. Although on the multi-winding motor, windingsare magnetically coupled each other like transformer. It isknown that this coupling may bring interference between thewindings, and affects the control performance of the multi-winding motor (4).

For induction motors, a motor model for double-windingmotor was proposed, and decoupling method on the modelwas examined (5)–(8). For PMSMs, basic voltage equationfor double-winding motor was presented (9), and the equa-tion with phase shift between the windings (10), and also de-tailed motor model with spatial harmonics (11) (12) have beendiscussed.

About the control characteristic of double-winding PMSM,simulation results for the instability of current control waspresented (9), but theoretical investigation about the stabilitywas not discussed. Control algorithm for cancelling the ef-fect of coupling also proposed in some papers (9) (13)–(16), but theinvestigations are not enough to design the controller for thecoupling cancellation.

In this paper, theoretical and practical issues are discussed.Parameters in the voltage equation are related to practicalmethod to measure them, and examined in experiment witha trial motor. The instability from the coupling is illustratedwith general control method, and the effect of the proposedcoupling cancellation method is easy to estimate in the samemanner. Effect of the control algorithm is evaluated in exper-iments with a trial motor.

2. Modeling of Double-winding PMSM

2.1 Voltage Equation of Double-winding PMSMA structure of stator windings and their connections to the

drive circuits for this paper is shown in Fig. 1. There is no

c© 2017 The Institute of Electrical Engineers of Japan. 29

Coupling Cancellation Control for a Double-winding PMSM（Akira Satake et al.）

Fig. 1. Structure of Double-winding PMSM Drive

phase shift between 2 pairs of 3-phase stator windings, andeach 3-phase winding has different neutral point.

Using virtual fixed coordinate in 2-phase, the interferencebetween each phase is eliminated, and the voltage equationof the first winding can be described as Eq. (1).[

vα1

vβ1

]=

[R + pL 0

0 R + pL

] [iα1

iβ1

]+

[pM 00 pM

] [iα2

iβ2

]+

[eα1

eβ1

]

· · · · · · · · · · · · · · · · · · · · (1)

In Eq. (1), the first right member indicates the voltage com-ponent from the self-impedance of the first winding, and thesecond member indicates the interference component by thecoupled flux from the second winding, and the third rightmember indicates the BEMF component of the flux from thepermanent magnet on the rotor. Note that R is the register andL is self-inductance, of the stator winding. M is the mutualinductance between 2 winding, and hereafter this inductanceis called ‘coupling inductance’. In Eq. (1) no saliency of themotor is considered, and the differences of motor parametersbetween the windings are not included.

Transforming Eq. (1) to the rotational coordinate thataligned to the magnet flux on the rotor derives Eq. (2). Notethatω is rotational speed in electric angle, and φ is the perma-nent magnet flux that interlinks the each windings. In Eq. (2),there is no difference in each flux linkage to the rotor magnetbetween the windings.[

vd1

vq1

]=

[R+pL − ωLωL R+pL

] [id1

iq1

]+

[pM − ωMωM pM

] [id2

iq2

]+

[0ωφ

]

· · · · · · · · · · · · · · · · · · · · (2)

Equation (2) shows that the additional BEMF and transientcomponents of voltages, from the fluxes that interlinks be-tween each windings, are included on the double-windingPMSM.

Combining Eq. (2) with the voltage equation for the sec-ond winding derives Eq. (3), with suffix 1 for the first wind-ing, and suffix 2 for the second one, that indicates the totalvoltage equation of the double-winding PMSM.⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣vd1

vq1

vd2

vq2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ =⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣R+pL − ωL pM − ωMωL R+pL ωM pMpM − ωM R+pL − ωLωM pM ωL R+pL

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣id1

iq1

id2

iq2

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ +⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

0ωφ0ωφ

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦· · · · · · · · · · · · · · · · · · · · (3)

Fig. 2. Configuration for Parameter Measurement

2.2 Parameter Identification of Double-windingPMSM Modeling of the double-winding PMSM withEq. (3) requires identification of the parameters in the equa-tion. The resistance R and the BEMF coefficient of PMSMφ can be measured with the same method for PMSM. Themeasuring method for the self-inductance L and the couplinginductance M should be investigated.

To make the method practical, measuring current wave-form on applying step voltage is examined. When the stepvoltage is applied to the first winding, there will be some dif-ference on the current waveform of the winding, while thesecond winding is open or close. Figure 2 shows the config-uration for the measurement.

Applying the step voltage Vtest on U-VW terminal of thefirst winding, the current on U-phase of the first winding Itest

and that on V and W phase Itest/2 are generated. Transform-ing these values into the fixed 2-phase coordinate, Eq. (4) arederived.

vα =

√23

vtest, iα =

√23

itest · · · · · · · · · · · · · · · · · · · (4)

From the current waveform on the measurement, the induc-tance of the first winding for alpha phase Ls can be calculatedfrom the interval time Δt and the rise of the U-phase currentΔi as follows.

Ls = vαΔtΔiα=

23

vtest · ΔtΔi

· · · · · · · · · · · · · · · · · · · · · · · · (5)

Assuming that the inductance of the double-windingPMSM is a summation of the coupling inductance M and anuncoupled ‘leakage’ inductance Ll, the inductance L, that ofthe first winding when the second winding is open as shownin Fig. 2, is described as follows.

L = Ll + M · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (6)

And the inductance Lc, that of the first winding while thesecond winding is closed, is as follows.

Lc = Ll +1

1M+

1Ll

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (7)

With these equations, Eq. (8) is derived.

Ll = L

⎛⎜⎜⎜⎜⎜⎝1 −√

1 − Lc

L

⎞⎟⎟⎟⎟⎟⎠ · · · · · · · · · · · · · · · · · · · · · · · · · · · (8)

These equations show that there will be some differencein Ls of the first winding, with difference conditions of open

30 IEEJ Journal IA, Vol.6, No.1, 2017


Fig. 3. Experimental Result of the Parameter Identifica-tion

or closed second winding. Utilizing this difference on exper-imental measurement enables identification of the couplinginductance M.

This method is applied to a trial model of double-windingPMSM. Voltage and current waveform of the experimentwith a trial motor #1 is shown in Fig. 3. To an applied stepvoltage on the first winding, a current on the first windingramps up, and there is a difference in its ramp rate, by theconnection of the second winding.

Parameters of the trial motor #1 is calculated from the ex-periment result. The self inductance L is 664 μH, and thecoupling inductance M is 251 μH. It means that 38% of in-ductance is coupled between the windings in the motor.

3. Current Control of Double-winding PMSM

3.1 Effect of Coupling between Windings For thecurrent control of the double-winding PMSM with 2 voltage-source inverters, following 2 methods are considered appro-priate.

( 1 ) Single current control for total current, same volt-age reference to the 2 inverters

( 2 ) Individual current control for each winding, differ-ent voltage reference for each inverter

Method 1 works just as 1 large inverter for the motor,because double-winding PMSM is normally designed fromsingle-winding motor by dividing windings connected in par-allel or serial in the motor. There is no problem for the con-trol in this method, but there are no advantages of ‘doublewinding’ in this method either.

In method 2, each current is controlled individually, nor-mally with the same current reference. With method 1, theremay be some current unbalance between the windings, be-cause of unbalance on impedance of each windings, or onoutput voltage from each inverter. With method 2, these prob-lems are eliminated.

To the contrary, the coupling between winding discussedin chapter 2 may bring interference to each current control.Equation (3) shows that the current in one winding generatesvoltage to another winding, which works as disturbance forthe current control. Counter action of the current control ofone winding invokes another disturbance to the current con-trol of another winding, so the interference runs between the

Table 1. Parameters of trial motor #2

Fig. 4. Trial Motor #2

Fig. 5. Conventional Current Control Block Diagram

windings, and may deteriorate control performance.The effect of the interference is investigated with simula-

tions. Parameters of the motor (trial motor #2) are listed inTable 1. The coupling inductance of the trial motor #2 has70% portion of the self inductance, and that means the twowindings in the trial motor #2 are quite coupled. The pictureof the trial motor #2 is shown in Fig. 4.

On the simulations, current of each winding is controlledindividually on each d-q coordinate, as the control block di-agram in Fig. 5. To make the investigation simple, the motordoes not rotate in the simulation, and current step referenceis input on q-axis of both windings, while reference on d-axisof both windings stay 0. The current feedback controller con-sists only with a proportional component. From the controlsampling rate, the sampling delay in Fig. 5 is 166.7 μs.

Figure 6 shows the simulation result. Current control re-sponse ωcc is set to 1250 rad/s, and the proportional gain ofthe current control Kp = ωcc L. In Fig. 6 the response is oscil-latory and close to unstable condition. There is also vibrationcurrent on 2nd winding, caused by the interference from the



Fig. 6. Step response simulation, with coupling

Fig. 7. Step response simulation, without coupling

Fig. 8. Bode diagram of Open-loop Response of theControl

1st. On the contrary, Fig. 7 shows a result with no couplinginductance, or M = 0. The response is stable and likely admitmore improved response. The difference between Figs. 6 & 7suggests the effect of the coupling for the control response.3.2 Design Method for Coupling Cancellation To

illustrate the transfer characteristics of the system, investi-gating frequency response of the loop is effective. For thecurrent control loop, stability of the control can be estimatedby the frequency response from the input to the controller tothe output of detected current, which is indicated in Fig. 5.

Figure 8 shows Bode diagrams of the open loop frequencyresponse of the current loop for the q-axis on 2nd winding.The grey line indicates the characteristics of the original sys-tem with coupling that corresponds to the step response inFig. 6. And the black line indicates the one without coupling,

Fig. 9. Block diagram of Double-winding PMSM

Fig. 10. Block diagram of Coupling Cancellation

where the coupling inductance is set to 0, and it correspondsto the response in Fig. 7.

In Fig. 8, the no-coupling characteristic represents a natu-ral 1st order lag with some delay time from sampling, but thewith-coupling characteristic shows divergence from the no-coupling one from 1000 rad/s to higher, with larger gain andsmaller phase lag. With this investigation, it is clear that thisdivergence comes from the coupling of the windings. Check-ing the gain margin, the no-coupling characteristic has themargin of 13 dB, where the with-coupling one has that ofonly 3 dB, which indicates that the stability of the control inwith-coupling condition is not sufficient. It seems that thisinsufficiency brings the oscillation on step response in Fig. 6.

This degradation of the stability restricts the performanceof the current control, and a countermeasure is required. Tomake the point clear, illustrating block diagram of the double-winding PMSM from the voltage equation in Eq. (3) will beeffective. Figure 9 shows the block diagram, from the 1stand 3rd line of Eq. (3), which represents the double-windingPMSM in d-axis, while ω sets to 0 for simplification. In thediagram, s is Laplace operator that means derivation.

From Fig. 9, it is understandable that the disturbance volt-age from one winding to another is cancelled by feed-forwarding counter voltage. In the calculation of the countervoltage, the effect of R is negligible because it affects onlyin lower frequency that is far from the current control band-width.

Figure 10 indicates the idea of coupling cancellation withthe block diagram. The disturbance voltage from one wind-ing to another has transfer function from point A to point Bin Fig. 9. In this transfer function, effect of R is negligiblebecause it affects only in lower frequency that is far fromthe current control bandwidth. With this approximation, thetransfer function results M/L.

For the coupling cancellation, feed-forward components ofvd are added to the voltage references, with the coupling coef-ficient M/L. With this components, the interference voltagesfrom the coupling in the motor are eliminated.

Figure 11 shows the block diagram of the improved currentcontrol with the coupling cancellation. The cancelling feed-forward with the cancelling gain Kc are applied between the



Fig. 11. Improved Current Control Block Diagram

Fig. 12. Bode diagram with Coupling Cancellation

Fig. 13. Step response with Coupling Cancellation,1250 rad/s

output of each current controller, which eliminates the inter-ference and make the characteristic of the windings as if nocoupling exists.

Effect of the coupling cancellation is expressed in the Bodediagram in Fig. 12. The diagram shows that the cancellationreduces the boost of gain around 4000 rad/s, and improvesthe gain margin from 3 dB to 10 dB.

From the Bode diagram in Fig. 12, the stability of currentcontrol is quite improved with the coupling cancellation. Fig-ure 13 shows step response of the current control on similarcondition to Fig. 6, with coupling cancellation. There are novibrations in the response in Fig. 13, and the current control

Fig. 14. Step response with Coupling Cancellation,2500 rad/s

Fig. 15. Experimental setup of the current control

Fig. 16. Experimental result without the cancellation

is stable.Moreover, the Bode diagram in Fig. 12 suggests extra im-

provement of the current control bandwidth. Figure 14shows higher control response, from 1250 rad/s to 2500 rad/s.The step response have a little overshoot, but the controlstill keeps stability. Comparison between Fig. 6 and Fig. 14makes the advantage of the coupling cancellation methodclear.3.3 Experimental Result Current control with and

without the coupling cancellation are applied to an experi-mental controller, and current control performance with thetrial motor #2 is actually investigated.

Figure 15 shows the outline of experimental setup of thecurrent control. The coupling cancellation gain is set to 0 incase of no cancellation, or M/L in case of cancellation. De-tailed structure of the control is equal to Fig. 11.

Performance of the current control is investigated with stepresponse. Figure 16 shows the response of q-axis currentwithout the coupling cancellation, and Fig. 17, with the can-cellation. In the experiment, motor parameters and control



Fig. 17. Experimental result with the cancellation

Fig. 18. Simulations result with error in Kc

conditions are equal to the simulation, and Fig. 6 correspondsto Fig. 16, Fig. 7 to Fig. 17. The oscillatory manner in the stepresponse in Fig. 16 is quite resemble to Fig. 6, with mutualinteraction in the current oscillation, although the oscillatingfrequency is slightly different.

With coupling cancellation, the oscillatory manner is mod-erated and the current control response is improved to the de-signed 1250 rad/s. There is a small oscillation and mutual in-teraction in the current waveform in Fig. 17. Figure 18 showsa simulation result, where the gain Kc is set to half of its orig-inal value. The response in Fig. 18 has similar characteristicswith the experimental result in Fig. 17, which suggests someerror in the coupling cancellation gain Kc in the experiment.

4. Conclusion

This paper presented a design method for cancelling thecoupling effect in the double-winding PMSM.

For the precise modeling of the motor, a measuring methodfor the coupling parameter was proposed and examined in ex-periment. Using a motor model with the parameters, an eval-uation of the stability of the current control became possiblewith the simulation using Bode diagrams.

Cancelling algorithm for the coupling effect was also pre-sented, and the effect of the method was also possible to eval-uate with Bode diagrams, which enabled the design of thecancelling parameter with general control theory. The advan-tage of the coupling cancellation was examined with simula-tions and actual experiments with a trial motor.

With the proposed method, a deterioration of current con-trol performance of the double-winding permanent magnet

synchronous motor will be reduced, and higher driving per-formance in large-scale motor is expected.

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Akira Satake (Member) was born on December 29, 1961, in Nara,Japan. He received the B.E. degree from Tokyo Uni-versity, Japan, in 1985. He joined Industrial Sys-tem Laboratory of Mitsubishi Electric Corporation in1985. His research focused on motor drive technolo-gies, including controls for mechatronics componentsand power-electronic circuits. He received R&D100awards with sensor-less servo drive system in 2014.He is currently a group manager for research of motordrive in Advanced Technology R&D Center of Mit-

subishi Electric Corp., Amagasaki, Japan.



Yuriko Okamoto (Member) received master’s degree in mechanicalengineering from Osaka University in 2011. Shejoined Advanced Technology R&D Center of Mit-subishi Electric Corporation and has been engaged indrive system of motor control.

Satoru Kato (Non-member) received master’s degree in electrical en-gineering from Gifu University in 1992. He joined In-azawa Works of Mitsubishi Electric Corporation andhas been engaged in the development of the controlsystem of the elevator.


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Design of Coupling Cancellation Control for a Double