IEEE PEDS 2017, Honolulu, USA
12 – 15 December 2017

Vector Control and Experimental Verification ofMagnetically Modulated Motor for
HEV Application
Toshihiko Noguchi, Sawanth Krishna Machavolu, Yuto Motohashi, and Masahiro Aoyama†
Shizuoka University and Suzuki Motor Corporation†
noguchi.toshihiko@shizuoka.ac.jp, sawanth.krishna.machavolu.16@shizuoka.ac.jp

Abstract-Vector control of a magnetically modulated motor(MMM) is described in this paper. The structure of the motor israther different from a standard permanent magnet
synchronous motor (PMSM) because it has two rotors with two
different mechanical output shafts, i.e., an outer magnetic-flux
modulator and an inner PM rotor. There have been several
studies on an electromagnetic field analysis and an optimum
design of the motor, but investigation on the vector control using
a real machine is still unexplored. Therefore, the paper
discusses the vector control algorithm of the MMM andexperimentally examines control performance of the mechanicaloutput power delivered by the two rotors, using a prototype
machine. Several experimental tests have been conducted undersome driving modes, assuming a hybrid electric vehicle (HEV)
application. It has been verified that the control algorithm
discussed in the paper makes it possible to control the two rotor
output power as well as the stator input power like a
conventional planetary-gear-based HEV, including the motoring
and regenerating modes.

due to its electrical and mechanical complexity. However,the detailed vector control (the field oriented control)
algorithm has not been explored yet [5].
The authors investigated the basic model of the MMM andits simplified magnetic circuit to derive the voltage equation,
which is the basis of the vector control [6]. In addition to that,a prototype has been produced for verification of theoperation principle, and some experimental tests have been
conducted to simulate the typical HEV driving modes. The
vector control is carried out on the basis of the derived
voltage equation, focusing on the followings:
1) relationship between the torque and the gear ratio;2) characteristic between the torque and the current;3) verification of the derived voltage equation with theexperimental results; and4) power flow of simulated HEV driving modes.
II.

I.

INTRODUCTION

In recent years, studies on a magnetically modulated motor(MMM) are intensively promoted for the purpose of
integrating a hybrid electric vehicle (HEV) system with apower split mechanism. The MMM has two rotors, i.e., anouter magnetic flux modulator and an inner permanent
magnet (PM) rotor [1], [2]. The former transfers themechanical power to the drive shaft, and the latter ismechanically coupled with the engine in a standard use. The
MMM can synthesize the engine power and the mechanicalmotor power converted from the input electric power supply,and deliver the synthesized mechanical power to the drive
shaft through the modulator. In addition, surplus mechanicalpower from the engine can be regenerated to the electric
power supply through the stator. The stator rotating magnetic
flux is modulated by the outer rotor, and the modulated
magnetic flux interlinks the inner PM rotor to generate thetorque; thus, additional power losses are caused by theinterlinking magnetic flux which includes various highfrequency components, e.g., eddy current loss in the PM andextra iron losses in the rotor [3]. Therefore, investigations on
the optimized configuration of the motor are still conductedusing FEM based electromagnetic analysis [4]. In addition,
an operation principle and a control algorithm are discussed

VOLTAGE EQUATION OF MAGNETICALLYMODULATED MOTOR

A. Simplified Magnetic Circuit of Basic Model
The MMM to derive the mathematical model has Ps : Ppm :Pmod = n : 2n : 3n (n is a natural number) relationship, where
Ps is a pole pair number of the stator, Ppm is the number of themodulator iron cores, and Pmod is a pole pair number of theinner PM rotor. The rotor is assumed to be a surface PM
structure. Fig. 1 shows a magnetic circuit of the MMM,
where Ps : Ppm : Pmod = 1 : 2 : 3 (n = 1). In the figure, Rs is
stator back yoke reluctance, Rt is stator tooth reluctance, Rg is
air gap reluctance, Rmod is modulator reluctance, Rr is inner
PM rotor core reluctance, and Rleak is reluctancecorresponding to the total leakage flux. The number of thewinding turns is N for each phase.
Fig. 2 is a three-phase magnetic circuit of the MMM.
Assuming that Ru, Rv, and Rw are the total reluctance of thethree phases, they can be expressed by the following equation
because the reluctance variations of the three phases causedby the modulator are in phase with each other:R u  R v  R w  R dc  R modcosPmod mod ,(1)
R dc  R g  R t  R r  R s 3
where mod is a modulator position. Solving the three-phasemagnetic circuit shown in Fig. 2, the total number of flux
linkage at the phase U coil can be obtained as587
978-1-5090-2364-6/17/$31.00 ©2017 IEEE

 N2


N 2 R mod N 2cosPmod mod iu2
R dc
R leak R dc

2
2


R N
1 N
(2)
 
 mod2 cosPmod mod iv .
2 R dc
R dc

1  N 2 R mod N 2 
cosPmod mod iw
2
2 R dc
R dc
The self inductance L of each phase and the mutual
inductance M can be derived from (2) as follows:L    Ldc  LaccosPmod mod 
1
1
.
(3)
M   Ldc  LaccosPmod mod 
2
2
R N2
N2
N2
 
, Ldc , Lac  mod2
R leak
R dc
R dc
B. Voltage Equation and Power Flow of Basic Model
The stator pole pair is different from the rotor pole pair in
the MMM, which is the most important different feature from
common PM motors. Therefore, it is necessary to discuss thevoltage equation of the MMM, taking the pole pair number
difference between the stator and the rotor into account. The
magnetomotive force of the PM for each phase Fu, Fv, Fw canbe expressed as
Fu  F cos Ppm pm
2Ppm  ,(4)
Fv  F cos Ppm pm 
3Ps 

4Ppm Fw  F cos Ppm pm 
3Ps 
where pm is an inner PM rotor position and F is the
maximum value of the PM magnetomotive force.
On the other hand, a three-phase voltage equation of the
MMM can be obtained on the stationary reference frame as vu   R 0 0   iu  d  L M M   iu  d  u 
 vv    0 R 0   iv    M L M   iv    v  , (5)v   0 0 R  i  dt  M M L  i  dt   w 
 w 
 w 
 w
where R is the stator winding resistance and u, v, w are thenumber of flux linkage for each phase after magnetic
modulation. There is a relationship u = LFu/N, for example.
By applying Clarke transformation and Park transformation
to (5), a two-axis voltage equation can be obtained on the -rotating reference frame as Ev   R  pL  L  i  



L
F
3
v   L R  pL i  ac
(6)
 E  .
    
 8 N  Pmodmod  Ppm pm

u  



Fig. 1. Basic model of MMM and magnetic circuit.

Through the above calculation process, the Park
transformation is carried out by the rotational coordinatetransformation using the rotational angle between thestationary reference frame and the rotating reference frame as  t  Pmodmodt  Ppm pmt   mod   pm ,(7)
where mod and pm are mechanical angular frequencies of themodulator and the inner PM rotor, respectively. As can be

Fig. 2. Three-phase magnetic circuit.

seen in (6), the voltage equation of the MMM is similar tothat of the common PM motor on the whole, but extra
electromotive forces caused by the asynchronous frequency
components are generated as follows:
3   Ldc FE  Ppm pm
sin Pmod mod 
2N
3 LacF Pmodmod  Ppm pm
sin 2 Pmod mod 
8 N
.
(8)
3   Ldc FE  Ppm pm
cosPmod mod 
2N
3 LacF Pmodmod  Ppm pm
cos2 Pmod mod 
8 N
On the other hand, the input electric power can becalculated as follows by using the voltage equation (6):3 LacFPi  v i  v i  R i2  i2  i
8 N
 R i2  i2  ωmod mod   pm pm .
(9)















3 LacF
3 LacFi , τ mod  Pmod
i
8 N
8 N
The following torque equation is obtained from (9) and therelationship of the synchronous frequency:PP(10) s  s  pm   s  mod .
Ppm
Pmod pm   Ppm

As is described, the MMM corresponds to a planetary gearwidely used as a mechanical power splitter, and is capable to
distribute the mechanical power among the electric power fed
by the inverter, the inner PM rotor, and the modulator.

588

TABLE I SPECIFICATIONS OF PROTOTYPE MMM.
Number of stator pole pairs Ps

Prototype MMM

4

Number of rotor pole pairs Ppm

8

Number of modulator cores Pmod

12

Stator outer diameter

120 mmRotor diameter

61.2 mmAxial length of core

49.5 mm

Air gap length

0.7 mmWinding connection

4 series-2 parallel

Maximum current

150 Arms

Armature winding resistance R

33.3 mInductance on rotating reference frame L

0.27 mH

Stator flux linkage a

3.8 mWb

Load 1Torque meter 1
Torque meter 2
Fig. 4. Experimental setup.

Load 2Invertor

Modulator

PM-rotor

Fig. 5. Block diagram of vector control system for MMM.
(PM-rotor side)(a) CrossResolver
section.

Resolver(Modulatorside)(b) HEVsystemapplication.

IV.

Stator

Coupling

Coupling

PM-rotor

Modulator(c) Mechanical configuration.
Fig. 3. Configuration of MMM and HEV application.

III.

PROTOTYPE AND EXPERIMENTAL SETUP

Specifications of the prototype MMM are listed in
TABLE I. The PM used in the prototype is N39UH (Nd-FeB, Br = 1.22 T, Hcb = 965.7 kA/m@293 K).
Fig. 3 shows a cross section of a motor and themechanical and electrical connection diagram for a HEV
application. The inner PM rotor and the modulator aremechanically connected to the engine and the drive shaft,respectively, and the motor can deliver the torque according
to (10) in a motoring mode or a regenerating mode.
Fig. 4 is a photograph of the experimental setup. The two
servo motors are connected to the modulator and the inner
PM rotor, respectively, and their rotation speeds arecontrolled independently with two servo amps. The MMM
is controlled by a single inverter, and only the torque control
is carried out with the vector control. By using two torquemeters, two of the mechanical output powers from both
shafts can be measured at the same time. The rotation
angles of the modulator mod and the inner PM rotor pm aredetected with resolvers mounted on the two shafts, which
are used for rotational coordinate transformation in thevector control. Fig. 5 shows a block diagram of the vector
control system.

HEV SIMULATED DRIVING MODES AND OVERVIEW
OF EXPERIMENTAL TESTS

A. HEV Simulated Driving Modes
Fig. 6 illustrates three driving modes that simulate HEV
operations, where collinear charts and simple power flow
diagrams are indicated. The following three driving modes
are examined through the experiments:
1) an engine assist mode;2) an EV mode; and3) a regeneration mode.
The first test is the engine assist mode, which superimposes
the motor output power onto the engine output power, anddelivers the synthesized mechanical power to the drive shaft.
The second test is conducted under the condition of zero
power from the engine, which is called an EV mode. In themode, the rotating speed of the inner PM rotor is fixed at 0
r/min. The last driving mode is the regeneration mode, where
the surplus mechanical power from the engine is regenerated
to the inverter through the stator while delivering themechanical power of the engine to the drive shaft.
B. Overview of Experimental Tests
The following four points are experimentally checked ineach driving mode:
1) relationship between the torque and the gear ratio;
2) the torque and current phase angle characteristic;3) consistency between the voltage equation and the test
results; and4) power flow.
The first point focuses on the relationship expressed by(10). As described previously, the two shafts of the MMM
are connected to the two load machines through the torquemeters, it is possible to measure the rotating speed and thetorque of the modulator and the inner PM rotor without589

Fig. 6. Driving modes assuming HEV system, collinear charts, and power flow of MMM.

3

which is drawn in the figure as solid lines. The measured modand pm agree with the theoretical values well.

Theory_τpm
Theory_τmod
Engine asist mode_τpmEngine asist mode_τmod
EV mode_τpm
EV mode_τmodRegeneration mode_τpm
Regeneration mode_τmod

1

-1
-2
-3

0

10

20

30

40

50

60

δ-axis current (A)

70

80

90

Fig. 7. Torque and -axis current characteristic.

EXPERIMENTAL TEST RESULTS

The experimental tests were conducted under the inverter
conditions of 80-V DC-bus voltage, 10-kHz switchingfrequency, 4-s dead time. The measurement of the torque
was performed every 0.5 s to calculate an average value for
15 s of the measured torque. In order to achieve the vector
control as accurately as possible, various compensation
techniques are implemented in the controller, i.e., dead timecompensation, discrete time error compensation, on-voltage
compensation of the main switching devices, and so forth [7].
The CCW rotation of the inner PM rotor shaft is defined as apositive direction for both of the torque and the speed.
A. Relationship between Torque and Gear Ratio
Fig. 7 shows the relationship between the torque and the axis current with keeping i = 0. i is varied every 20 A over
the range from 10 to 90 A. It is confirmed from the figurethat the torque of the modulator mod and the torque of theinner PM rotor pm are delivered in proportional to iregardless of the driving modes. As the theoretical equation(10) indicates, the relationship between mod and pm is pm   Ppm mod Pmod  2 mod 3 ,
(11)

2

0

Theory_τpm
Theory_τmod4

Measured_τpm
Measured_τmod2

Torque (Nm)V.

4

Torque (Nm)difficulty. On the other hand, the theoretical values of thetorque are available from (9), so comparable evaluation ispossible between the measured and the theoretical values.
The current phase angle  is changed by 15 deg. to check thesecond point. The third point examines the relationshipexpressed by (6). This test is carried out by giving the twoaxis current commands i* and i*, and comparing thetheoretical voltages calculated by (6) and the measured values
obtained from the controller.
Finally, power flow is
examined by measuring the input electric power, the output
mechanical power, the copper loss, and other losses.

0

-2

-4
0

30 60 90 120 150 180 210 240 270 300 330 360
Current phase β(deg)Fig. 8. Torque and current phase angle  characteristic.

B. Torque and Current Phase Angle Characteristic
The torque and the current phase angle characteristic isshown in Fig. 8, which is measured under the condition of theengine assist mode. The reference phase angle  = 0 isdefined at the -axis position, and the current phase angle  isvaried every 15 deg. from 0 to 360 deg. The current vector
norm is also kept constant at 90 A in the test. Since theprototype has the surface PM structure of the rotor, thesimilar characteristic to the SPMSM is obtained. As is seenin the figure, the relationship (11) can be confirmed at every
measured point, which conforms with the theoretical values.

590

8

18

Voltage (V)

14
12
10

i = 0v

4Voltage (V)Theory_vγ
Theory_vδ
Engine asist_vγ
Engine asist_vδ
EV mode_vγ
EV mode_vδ

16

8
6

v
i = 00-4Theory_vγ
Theory_vδ
Engine asist_vγ
Engine asist_vδ
EV mode_vγ
EV mode_vδ

-8

4
2

-12

v

v

0

-16
0

10

20

30

40 50 60 70
γ-axis current (A)

80

90

0

10

20

30

40 50 60 70
δ-axis current (A)

80

90

16

Theory_vγ
Theory_vδ
Regeneration mode_vγ
Regeneration mode_vδ

i = 0

Theory_vγ
Theory_vδ
Regeneration mode_vγ
Regeneration mode_vδ

14

v

12
10

Voltage (V)Voltage (V)(a) Engine assist mode and EV mode.
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18

i = 0
v

8
6
4
2
0

v
0

10

20

30

40 50 60 70
γ-axis current (A)

v

-2
80

90

0

10

20

30

40 50 60 70
δ-axis current (A)8090(b) Regeneration mode.
Fig. 9. Two-axis voltages and currents characteristics.
80
90

60

Current (A)20

Current (A)

Iu
Iv
Iw

40

0
-20

Iγ_refIγ
Iδ_ref
Iδ

60

30

-40
-60

0

-80
-0.010-0.0050.000
Time (s)

0.005

0.010

-0.010-0.0050.000
Time (s)

0.005

0.010

(a) Current waveforms in EV mode.
30
30

20

Iu
Iv
Iw

10

Current (A)Current (A)C. Consistency between Voltage Equation and Test Results
In order to confirm the validity of the voltage equation (6),consistency is examined between the two-axis voltages
calculated by (6) and their commands in the controller in thefollowing cases:
1) i is varied under i = 0 condition; and2) i is varied under i = 0 condition.
Fig. 9 shows the measured and the theoretically calculated
results of the two-axis voltages in the three driving modes.
The engine assist mode and the EV mode satisfy the same
voltage equation because their phase sequence and theirinverter operating frequency are identical.
When i = 0, v = Ri and v =  (Li+a) from the voltage
equation (6), which means that both of the two-axis voltages
are proportional to i. On the other hand, substituting i = 0
into (6), the voltage equations v = Li and v = Ri + aare obtained, which also means the two-axis voltages areproportional to i. As can be seen in Fig. 9 (a), the two-axis
voltages vary almost linearly with the two-axis currents in theboth conditions of i = 0 and i = 0, and the relationships
between the voltages and the currents are independent of thedriving modes, i.e., the engine assist mode or the EV mode.
However, the voltage v in the i = 0 condition and thevoltage v in the i = 0 condition include the inductance L as
proportional coefficients. Fig. 9 (a) indicates that L isdecreased as the currents goes up due to the magnetic
saturation phenomenon, which is confirmed by the significant
deviations from the theoretically calculated voltages in higher
current ranges. Fig. 9 (b) shows the two-axis voltages in thecondition of i = 0 or i = 0, making the driving mode
regenerative operation. The measured results also agree withthe theoretical values for any conditions of the two-axis
currents even in the regeneration mode; hence, consistency
between the voltage equation and the real machine can be
confirmed.
Fig. 10 shows the three-phase currents and the two-axis
currents in the EV mode and the regeneration mode. The test
condition of the EV mode was i = 0 and i = 90 A, while theregeneration mode was performed under the condition of i =0 and i = 30 A. I can be seen in Fig. 9 (a) that the threephase currents are balanced and sinusoidal waveforms andthat the two-axis currents are following their commands withsmall deviations. On the other hand, similar waveforms ofthe currents are observed in the regeneration mode shown in
Fig. 9 (b). The current waveforms seem to have some ripples,but it should be noted that the vertical axis scale of the graphs
is 1/3 of Fig. 9(a); thus, the current control on the rotating -reference frame is carried out properly. The phase sequenceof the three-phase currents is changed to a negative one asshown in Fig. 9 (b) because of the regenerating operation.
D. Power Flow
Fig. 11 shows power flow diagrams in three driving modes
assuming the HEV system. The engine assist mode and the
EV mode were operated at i = 0 and i = 90 A, while theregeneration mode was examined at i = 0 and i = 30 A
similar to the case shown in Fig. 10. The test results shown

0Iγ_refIγ
Iδ_ref
Iδ

20

10

-10
-20
-30
-0.0100-0.0050.000
Time (s)

0.005

0.010

-0.010-0.0050.000
Time (s)

0.005

0.010

(b) Current waveforms in regeneration mode.
Fig. 10. Current waveforms on stationary and rotating reference frames.

in Fig. 7 indicate that pm < 0 and mod > 0 when i = 0 and i =90 A in the engine assist mode or the EV mode. The
collinear chart depicted in Fig. 6 also indicates that the MMM
is operated under the pm > 0 and mod > 0 condition.
Therefore, the mechanical power of the inner PM rotor is
negative pm pm < 0, i.e., the rotor receives the mechanicalpower from the load machine regarded as the engine, while
the mechanical power of the outer modulator is positivemodmod > 0, i.e., the modulator delivers its mechanicalpower to the load machine. In the case, supplemental electric
power is provided by the inverter, which is converted to theassist mechanical power for the engine in the MMM.
The rotation speed of the inner PM rotor is zero in the EV
mode, which simulates the stopped engine. It is found from
Figs. 6 and 7 that pm = 0 and mod > 0, and that mod > 0
when i = 0 and i = 90 A in this mode. Therefore, themechanical power of the inner PM rotor is zero, while that of591

Fig. 11. Power flow of MMM in three driving modes assuming HEV system.

the modulator is positive, which means that the MMM gives
the mechanical power to the load machine through themodulator. In the case, the inverter feeds positive electric
power to the MMM; hence, it is found that the MMM simply
converts the electric power received from the inverter to themechanical power.
The regeneration mode makes it possible to regenerate thesurplus mechanical power of the inner PM rotor to theinverter through the stator windings, transferring themechanical power to the drive shaft through the modulator at
the same time. Negative input electric power from theinverter to the MMM vi + vi < 0 is a requirement of theregeneration. As described previously, vi < 0 is thecondition of the regeneration mode because of i = 0. Fig. 12shows the result of the input electric power to the MMM byusing the measured v. As seen in the figure, the input
electric power is negative in the range of the -axis current i
from 10 to 50 A, which allows the regenerative operation. In
fact, the regeneration mode has been achieved when i = 0
and i = 30 A because the electric power of the inverter ismeasured negative.
Other losses indicated in Fig. 11 are a residue calculated by
the difference between the measured value and the theoreticalvalue. Iron loss and mechanical loss are not included in thevoltage equation of (6), so more than 15 % of the total input
power seems to be the iron loss and the mechanical loss
indicated as other losses.

Fig. 12. Input electric power in regeneration mode.

three driving modes are operated properly. It has been found,however, that iron loss of the motor is relatively dominant in
the power flow due to the harmonics of the magnetic flux
modulated by the outer modulator, which is a future work to
improve the motor performance.
The authors intend to analyze the harmonic components
caused by the magnetic flux modulation, and to investigate
the optimum design of the outer modulator and the inner PM
rotor to reduce the motor power losses.
REFERENCES
[1]

[2]

VI.

CONCLUSION

This paper discussed a voltage equation and a torqueequation of the magnetically modulated motor. The vector
control algorithm has been derived from the voltage equation,
and a prototype of the motor has been developed. An
experimental system has been set up, and various
experimental tests have been conducted with the prototype,assuming three HEV driving modes. Feasibility of thederived voltage equation has been confirmed through the tests,
comparing the theoretical values calculated from the equation
with the measured two-axis voltages. In addition, it has been
confirmed that the torque equation of the motor satisfies a
relationship of the gear ratio corresponding to a planetary
gear, which can be applied to the power splitter of the HEV
system. Furthermore, the power flow has been investigatedthrough the tests based on the three driving modes, and all the

[3]

[4]

[5]

[6]

[7]

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