The 2018 International Power Electronics Conference

Vector Control of Magnetically Modulated Motor
for Power Splitting of HEV Application
Toshihiko Noguchi1*, Sawanth Krishna Machavolu1, Masahiro Aoyama1 and Yuto Motohashi1
1 Graduate School of Integrated Science and Technology, Shizuoka University, Hamamatsu, Japan*E-mail: noguchi.toshihiko@shizuoka.ac.jp
the effective mechanical power. These extra harmoniccomponents of the magnetic flux cause additional power
losses, e.g., an eddy current loss in the PM and extra ironlosses in the rotor [3]. Therefore, optimization of the
motor geometry is significantly important to reduce thepower losses in the MMM, where an FEM based
electromagnetic analysis plays an important role for the
optimization [4]. However, technical discussion on thecontrol scheme of the MMM looks relatively inactivatedby researchers in the motor drive field, probably due toits electrical and mechanical complexity [5].
The voltage equation of the MMM have been
investigated because the mathematical motor model is thebasis of the vector control algorithm. The voltage
equation has been derived from a simplified magnetic
circuit of the MMM [6]. In this paper, this fundamental
investigation is described, and the operation principle isverified with a prototype of the MMM.

Abstract— This paper describes a vector control methodof a magnetically modulated motor. The motor has a quite
different structure from a standard permanent magnet
synchronous motor (PMSM) because of the two rotors withtwo different mechanical output shafts, i.e., an inner PM
rotor and an outer magnetic-flux modulator composed ofonly iron and air. Investigation on the vector control
method using a real machine is still unexplored, thus, thepaper discusses the vector control algorithm of the motor.
In addition, several experimental tests have been conducted
to examine the control performance of the mechanicaloutput power delivered by the two rotors, using a prototype
machine. It has been verified that the discussed algorithm
makes it possible to control the two rotor output power aswell as the stator input power like a conventional planetarygear-based HEV system, including the motoring andregenerating operations.
Keywords— Hybrid vehicle, magnetically modulated
motor, power split, vector control.

I.

INTRODUCTION

In order to enhance integration of a hybrid electricvehicle (HEV) power train with a power split mechanism,a magnetically modulated motor (MMM) is supposed to
be one of the solutions and has been studied intensively
in recent years. There are two rotors in the MMM, i.e.,
an inner rotor with permanent magnets (PMs) and anouter rotor which works as a magnetic flux modulator [1],[2]. The mechanical power is basically transferred to thedrive shaft by the outer rotor, and the mechanical engine
power is provided through the inner rotor in a standard
application. The electric power is supplied to the statorby the external power converter such as an inverter, andis converted to the mechanical power like a conventional
motor.
The MMM is possible to synthesize themechanical engine power and the electrical motor power
given by an inverter through the stator, and is capable todeliver the synthesized mechanical power to the drive
shaft through the modulator. In addition, it is possible toregenerate the surplus mechanical power from the engine
to the inverter if the drive shaft does not require higher
power than the engine output. The outer rotor modulates
the stator rotating magnetic flux, and the inner PM rotor
receives the modulated magnetic flux to generate theelectromagnetic torque.
Various high-frequency
components are generated through the magnetic flux
modulation process, which do not contribute to generate©2018 IEEJ

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Fig. 1. Simplified MMM model and magnetic circuit.

Fig. 2. Three-phase magnetic circuit of MMM.

The 2018 International Power Electronics Conference

II.

DERIVATION OF VOLTAGE EQUATION

It is assumed that the MMM discussed in the paper has
Ps : Ppm : Pmod = n : 2n : 3n (n is a positive integer)
relationship, where Ps is the pole pair number of thestator, Ppm is the pole pair number of the inner PM rotor,
and Pmod is the number of the modulator iron cores. Fig.
1 shows the most fundamental geometry and its magnetic
circuit of the MMM, where the least combination of Ps :Ppm : Pmod = 1 : 2 : 3 (n = 1) is assumed. Although the
MMM is a kind of synchronous machines, it has different
pole pair numbers between the stator and the rotor. In themagnetic circuit, the following reluctances are
considered; the stator back yoke reluctance Rs, the stator
tooth reluctance Rt, the air gap reluctance Rg, themodulator reluctance Rmod, the inner PM rotor core
reluctance Rr, and the reluctance corresponding to thetotal leakage flux Rleak. N is the number of the winding
turns for each phase.
The total reluctance of the three phases Ru, Rv, and Rw
are expressed by the following equation because thethree-phase reluctance variations caused by themodulator are in phase with each other:R u = R v = R w = R dc − R mod cos(Pmodθ mod ),(1)
R dc = R g + R t + R r + R s 3
where θmod is a position of the modulator. The total
number of flux linkage at the phase U coil is calculated as
 N2

N 2 R mod N 2
ψu = 
++cos(Pmodθ mod )iu
2
R dc
 R leak R dc

2
2


1 N
R N
.
(2)
− 
+ mod2 cos(Pmodθ mod )iv
2 R dc
R dc

1  N 2 R mod N 2− +cos(Pmodθ mod )iw
2
2 R dc
R dc
The self-inductance L of each phase and the mutualinductance M can be derived from (2) as follows:
L =  + Ldc + Lac cos(Pmodθ mod )
1
1
.
(3)
M = − Ldc − Lac cos(Pmodθ mod )
2
2
N2
N2
R N2
, Ldc =, Lac = mod2
 =R leak
R dc
R dc
One of the most significant different features of the
MMM from common PM motors is that the number ofthe stator pole pair is different from that of the rotor.
Therefore, the voltage equation of the MMM should bederived by taking the pole pair number difference into
account. The magnetomotive force of the rotor PM foreach phase Fu, Fv, Fw can be expressed as
Fu = F cos Ppmθ pm
2πPpm ,(4)Fv = F cos Ppmθ pm −3Ps 

4πPpm 
Fw = F cos Ppmθ pm −3Ps 
()

where θpm is a position of the inner PM rotor and F is the
maximum
amplitudeoftheequivalentPMmagnetomotive force.

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In general, a three-phase voltage equation of the PM
motor can be expressed as follows on the stationaryreference frame: vu   R 0 0   iu 
 L M M   iu ψ u 
 vv  =  0 R 0   iv  + d  M L M   iv  + d ψ v  ,v   0 0 R  i  dt  M M L  i  dt ψ 
 w 
 w 
 w 
 w
(5)where R is the stator winding resistance, and ψu, ψv, andψw are the number of flux linkages for each phase. In the
MMM case, it is necessary to consider the number of flux
linkage after modulation, which has a relationship such asψu = LFu/N.
The voltage equation on the γ-δ rotating reference
frame can be obtained by applying coordinatetransformations to (5) as− Eγvγ   R + pL − ωL  iγ  +=v   ωL R + pL  i  ω 3 LacF − E  . (6)


δ
δ
 
 
δ

 8 Nω = Pmod ωmod − Ppmω pm
It should be noted that the following rotational angle
between the stationary reference frame and the rotatingreference frame was used through the rotational
coordinate transformation:θ = ωt = Pmod ω mod t − Ppmω pm t = θ mod − θ pm ,(7)
where ωpm and ωmod are mechanical angular frequenciesof the inner PM rotor and the modulator, respectively.
As is shown in (6), the voltage equation of the MMM issimilar to that of the common PM motor whereas someextra electromotive forces are generated by the
asynchronous frequency components as follows:
3 ( + Ldc )F
sin (Pmodθ mod )Eγ = Ppmω pm
2N
3 LacFsin (2 Pmod θ mod )+ Pmod ω mod + Ppmω pm
8 N
. (8)
3 ( + Ldc )Fcos(Pmodθ mod )Eδ = Ppmω pm
2N
3 LacF+ Pmod ω mod + Ppmω pmcos(2 Pmodθ mod )8 N
The voltage equation has been discussed so far, and a
relationship of the electromagnetic torque between themodulator and the inner PM rotor is investigated asfollows:
3 LacFPi = vγ iγ + vδ iδ = R iγ2 + iδ2 + ω
iδ
8 N
2
2
(9)
= R iγ + iδ + ωmodτ mod + ω pmτ pm .

(

)

(

)

(
(

)
)

3 LacF
3 LacFiδ , τ mod = Pmod
iδ
8 N
8 N
The above equation is an input electric power, where
the first term represents a copper loss of the windings andthe second term corresponds to the mechanical output
power. Therefore, the following torque relationship canbe derived from the result of (9):PP
(10)
τ s = s τ pm = − s τ mod .
Ppm
Pmodτ pm = − Ppm

The 2018 International Power Electronics Conference

TABLE ISPECIFICATIONS OF PROTOTYPE MMM.
Number of stator pole pairs Ps

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 mΩInductance on rotating reference frame L

0.27 mH

Stator flux linkage ψa

3.8 mWb

Fig. 4. Block diagram of vector control system for MMM.
Prototype MMM

Load motor 1

Torque meter 1
Torque meter 2
Fig. 5. Experimental setup.

Load motor 2

TABLE II
EXPERIMENTAL TEST CONDITIONS.
(a) Radial cross section of MMM.
Resolver (PM-rotor side)

Resolver (Modulator side)

Stator
Coupling

80 V
10 kHzDead time

4 μs

Sampling interval of torque0.5 s

Coupling

PM-rotor

Fig. 4 is a block diagram of the vector control system
for the MMM. As can be seen in the figure, two of theresolvers are used to detect the rotational positions of theinner PM rotor and the modulator. The electric angle forrotational coordinate transformation is calculated by (7),and is used for the stator current control which is carried
For theout on the γ-δ stator reference frame.
convenience of the tests, the current commands are given
to the controller in a polar coordinate manner, i.e., acurrent amplitude Ia and a current phase angle βmeasured from δ-axis.
Fig. 5 shows the experimental setup, where the twoload machines are directly connected to the inner PM
rotor and the modulator, respectively. The two load
machines control their rotation speeds independently. On
the other hand, the prototype of the MMM does not havea speed control loop; thus the torque control is only
achieved by the controller indicated in Fig. 4. Two of themechanical output powers from both shafts are measured
with two torque meters. The input electric power is alsomeasured with a power meter to evaluate the total power
flow. A positive direction for both of the torque and the
speed is defined as a CCW rotation of the inner PM rotor.

Modulator(b) Axial cross section of MMM.
Fig. 3. Configuration of MMM.

The above equation shows that the MMM works like aplanetary gear used as a mechanical power splitter ofhybrid vehicles and that the mechanical power can be
distributed among the electric power fed by the inverter,
mechanical power of the inner PM rotor, and anothermechanical power of the modulator.
III.

Inverter DC-bus voltage
Inverter switching frequency

OUTLINE OF PROTOTYPE AND CONFIGURATION OF
EXPERIMENTAL SETUP

A small scale prototype of the MMM has beendeveloped to evaluate validity of the proposed vector
control technique. TABLE I shows major specificationsof a prototype MMM. N39UH (Nd-Fe-B, Br = 1.22 T,
Hcb = 965.7 kA/m@293 K) neodymium PM wasemployed in the inner rotor. A radial cross section andan axial cross section are shown in Fig. 3, where how thetwo rotating parts are installed in the prototype isillustrated. In general, the inner PM rotor is mechanicallyconnected to the combustion engine, while the magnetic
modulator is connected to the drive shaft in a typicalHEV application.
The electromagnetic torque isdelivered by the MMM according to (10) in either amotoring operation or a regenerating operation.

IV.

EXPERIMENTAL TEST RESULTS

A. Experimental Test Conditions
The experimental test conditions are indicated in
TABLE II. An inverter was used to operate the prototype
MMM, where the DC-bus voltage was 80 V, theswitching frequency was 10 kHz, and the dead time was

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18
14

2

Voltage (V)Theory_τpm
Theory_τmod
Engine asist mode_τpmEngine asist mode_τmod
EV mode_τpm
EV mode_τmodRegeneration mode_τpm
Regeneration mode_τmod

1
0

-1

12
10
8
6

-4
-8

-12

2
0
0

10

20

30

40

50

60

γ-axis current (A)

70

80

-16

90

0

10

20

30

40

50

60

70

80

90

60

70

80

90

δ-axis current (A)(a) Engine assist mode and EV mode.

0

10

20

30

40 50 60 70
δ-axis current (A)8090Theory_τpm
Theory_τmod4

Voltage (V)Fig. 6. Output torque and δ-axis current characteristic.
Measured_τpm
Measured_τmod2
Torque (Nm)Theory_vγ
Theory_vδ
Engine asist_vγ
Engine asist_vδ
EV mode_vγ
EV mode_vδ

0

4

-2
-3

4

16

4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
-18

12
10
8
6
4
2
0
-2

0

10

20

30

40

50

60

70

80

90

γ-axis current (A)0Theory_vγ
Theory_vδ
Regeneration mode_vγ
Regeneration mode_vδ

14
Theory_vγ
Theory_vδ
Regeneration mode_vγ
Regeneration mode_vδ

Voltage (V)Torque (Nm)38Theory_vγ
Theory_vδ
Engine asist_vγ
Engine asist_vδ
EV mode_vγ
EV mode_vδ

16Voltage (V)

4

0

10

20

30

40

50

δ-axis current (A)(b) Regeneration mode.
Fig. 8. Confirmation of voltage equation.

-2
80

-4

60

Iu
Iv
Iw

40

30 60 90 120 150 180 210 240 270 300 330 360
Current phase β(deg)Current (A)0Fig. 7. Output torque and current phase angle β characteristic.

set at 4 μs, respectively. The sampling period of torquemeasurement was 0.5 s, and the average torque for 15 s
was calculated. Many of the compensation control
techniques are employed to make the vector control as
precise as possible such as a dead time compensation, a
discrete time error compensation, an on-voltage
compensation of the IGBTs, and so on [7].

20
0
-20
-40
-60
-80
-0.010-0.0050.000
Time (s)

0.005

0.010

Current (A)90

B. Output Torque and Equivalent Gear Ratio
A relationship between the torque and the δ-axis
current iδ with the constant iγ = 0 is shown in Fig. 6,
where iδ is changed every 20 A over the range from 10 to
90 A. The output torque of the inner PM rotor τpm andthat of the modulator τmod are delivered in proportional toiδ regardless of the driving modes. The theoretical
relationship between τmod and τpm given by (10) is
indicated by the solid lines, and the test result agrees withthe theoretical relationship of τpm = -2τmod/3.

Iγ_refIγ
Iδ_ref
Iδ

60

30

0
-0.010-0.0050.000
Time (s)

0.005

0.010

(a) EV mode current waveforms.
30

Current (A)20

C. Output Torque and Current Phase Angle
Fig. 7 shows a torque characteristic where the current
phase angle β is varied every 15 deg from 0 to 360 deg(electric angle) with constant current vector amplitude of
90 A under the engine assist mode. As can be seen in the
figure, the torque characteristic similar to an SPMSM isconfirmed because of the surface PM structure of the
prototype rotor. However, τmod and τpm are in opposite
phase with each other and their ratio is kept at τpm = 2τmod/3.

Iu
Iv
Iw

10
0
-10
-20
-30
-0.010-0.0050.000
Time (s)

0.005

0.010

Current (A)30

D. Confirmation of Voltage Equation
Consistency was examined between the two-axis
voltages vγ and vδ calculated by (6) and their actualcommand values in the controller to confirm the validityof the voltage equation. Either iγ or iδ was varied in theIγ_refIγ
Iδ_ref
Iδ

20

10

0
-0.010-0.0050.000
Time (s)

0.005

0.010

(b) Regeneration mode current waveforms.
Fig. 9. Current waveforms in EV and regeneration modes.

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The 2018 International Power Electronics Conference

Fig. 10. Three driving modes, collinear charts, and power flow of MMM.

range from 10 to 90 A, and the rest one was kept constantat zero in the tests. The measured and the theoreticalresults of vγ and vδ are shown in Fig. 8, where all thethree driving modes are checked. Since the phasesequence and the inverter frequency are identical in theengine assist and the EV modes, both of thecharacteristics of vγ and vδ satisfy the same voltage
equation.
vγ = Riγ and vδ = ω (Liγ+ψa) from (6) when iδ = 0;
hence, both of the voltages are proportional to iγ. In asimilar way, if iγ = 0 is substituted into (6), vγ = − ωLiδand vδ = Riδ + ωψa are obtained, which means thevoltages are proportional to iδ. As shown in Fig. 8 (a),actual voltages vγ and vδ vary almost linearly, which
agrees with their theoretical values indicated by the solidlines. The driving modes, i.e., the engine assist and the
EV modes, hardly have influence on the relationships
between the voltages and the currents. However, Fig. 8(a) indicates a slight non linearity due to the magnetic
saturation because vγ or vδ includes inductance L. Fig. 8(b) shows vγ and vδ in the regenerative operation mode,
where either iδ = 0 or iγ = 0 condition is similarly given.
The actual values of the voltages agree with their
theoretical values for any conditions of the two-axis
currents.
Therefore, consistency between themathematical voltage equation of the MMM and the realmachine characteristics is appropriately confirmed.
The three-phase currents and the two-axis currents inthe EV and the regeneration modes are shown in Fig. 9.
The EV mode test condition was iγ = 0 and iδ = 90 A, andthe regeneration mode test condition was iγ = 0 and iδ =30 A. The balanced and sinusoidal three-phase current
waveforms are observed in Fig. 9 (a), and the two-axis
currents iγ and iδ are properly controlled to follow theircommand values with small deviations. On the other
hand, the current waveforms seem to have some ripples

in the regeneration mode shown in Fig. 9 (b), but thevertical axis scale of the graphs is 1/3 of Fig. 9(a).
Therefore, the current control in the regeneration mode isproperly achieved.
As described previously, theregenerating operation makes a phase sequence of thethree-phase currents negative.
E. Collinear Chart and Power Flow
Fig. 10 shows collinear charts of the three driving
modes that simulate HEV system, i.e., the engine assist
mode, the EV mode, and the regeneration mode. The
engine assist mode and the EV mode were operated at iγ= 0 and iδ = 90 A, while the regeneration mode was
examined at iγ = 0 and iδ = 30 A. The modulator (thedrive shaft) speed can be adjustable by changing theinverter frequency and/or the inner PM rotor (the engine)
speed in the engine assist mode. On the other hand, theEV mode is achieved by fixing the inner PM rotor (theengine) speed at zero, and the modulator (the drive shaft)speed can be changed by controlling only the inverter
frequency. The regeneration mode is achieved by anegative frequency of the inverter.
The test results shown in Fig. 6 indicate that τpm < 0and τmod > 0 when iγ = 0 and iδ = 90 A in the engine assist
or the EV mode. The collinear chart depicted in Fig. 10
also indicates that the MMM is operated under the ωpm >0 and ωmod > 0 condition. Therefore, the mechanicalpower of the inner PM rotor is negative τpm ωpm < 0, i.e.,
the rotor receives the mechanical power from the load
machine (the engine), while the mechanical power of theouter modulator is positive τmod ωmod > 0, i.e., themodulator delivers its mechanical power to the load
machine (the drive shaft). The supplemental electric
power is provided by the inverter, which is converted tothe assist mechanical power for the engine in the MMM.
It is found from Fig. 6 that ωpm = 0 and ωmod > 0, and

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The 2018 International Power Electronics Conference

REFERENCES

that τmod > 0 when iγ = 0 and iδ = 90 A in the EV mode.
Therefore, the mechanical power of the inner PM rotor iszero, whereas that of the modulator is positive. This
operating condition means that the MMM gives themechanical power to the load machine through themodulator with standstill inner PM rotor (engine). The
inverter provides the MMM with positive electric powerin the case; hence, the MMM simply converts thereceived electric power to the mechanical power.
The surplus mechanical power of the inner PM rotor
can be regenerated to the inverter through the stator
windings with transferring the requested mechanicalpower to the modulator (the drive shaft) at the same time.
Negative electric power of the inverter vγiγ + vδiδ < 0 is arequirement of the regeneration. As described previouslyin (9), vδiδ < 0 is the condition of the regeneration mode
because of iγ = 0. This condition is satisfied in the rangeof iδ from 10 to 50 A. In the actual experimental test, theregeneration mode has been achieved when iγ = 0 and iδ =30 A because the electric power of the inverter ismeasured negative.
The voltage equation (6) does not include any ironlosses and mechanical loss; thus, these losses are residual
quantities calculated by the difference between themeasured value and the theoretical value. The total of theiron losses and the mechanical loss represented as otherlosses seems to be more than 15 % of the total input
power.
V.

[1]
[2]
[3]
[4]
[5]
[6]
[7]

CONCLUSIONS

The voltage equation and the torque equation of themagnetically modulated motor have been investigated in
the paper. On the basis of the mathematical model, thevector control algorithm has been derived from thevoltage equation. In order to confirm the feasibility ofthe derived vector control algorithm, a prototype wasdeveloped and an experimental system was set up.
Assuming the three HEV driving modes, i.e., the engine
assist, EV, and regeneration modes, various experimental
tests were conducted with the prototype motor.
As a result, feasibility of the derived voltage equation
was confirmed by comparing the theoretical values
calculated from the equation with the measured voltages.
The torque equation of the motor is also feasible because
it satisfies a relationship of the equivalent gear ratio
between the inner PM rotor and the outer magnetic
modulator. This characteristic can be represented bycollinear charts, which corresponds to a planetary gear
actually used as a power splitter of the HEV system.
The power flow of the motor was also investigatedthrough the three driving mode tests. Proper operation
was confirmed in every driving mode. However, because
the iron loss was dominant in the miniature prototype,high efficiency was not achieved. This iron loss was
likely caused by the harmonics of the magnetic flux
modulated by the outer modulator, which is a future work
to improve the motor efficiency.

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