Investigation of Optimal Operation Method for
Permanent Magnet Synchronous Motor Drive Systemwith 3-level Inverter
Jun-ichi Itoh

Daisuke Sato

Takaaki Tanaka

Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

Nagaoka University of Technology
Nagaoka, Japandsato@stn.nagaokaut.ac.jp

Nagaoka University of Technology
Nagaoka, Japantanaka_takaaki@stn.nagaokaut.ac.jp

Abstract— In this paper, an optimal converter drive method for
Permanent Magnet Synchronous Motor (PMSM) with a 3-level
inverter is discussed in terms of loss minimization. The 3-level
inverter can change an operation mode between two modulations
namely, PWM and 1’pulse modulation at a decided point. In thispaper, we discuss the interchange point for the two modulations
subject to the total loss of PMSM drive system in regards to themotor speed. First, the analysis on intersection point between
PWM and 1’pulse modulation is demonstrated, and then the
results show, that the motor drive system achieves the highest
efficiency with PWM before the intersection point. On one hand,
implementation of 1’pulse modulation can achieve the highest
efficiency.
Keywords-component; Permanent magnetic synchronous
motor, 3-level inverter, PWM drive, 1’pulse modulationI.

INTRODUCTION

Recently, electric vehicles (EV) are actively developed dueto the high demand of CO2 emission reduction fromautomobile industry. Demanding on the motor drive systems
for the EVs are to feature small size, lightweight and highefficiency. The typical motor that applied in EVs is known as
Permanent Magnet Synchronous Motor (PMSM) [1]. Then
inverter is applied to control the torque in a wide range ofvariable speed.
The inverter in an EV system is typically driven by two
modulations, that is, PWM at low speed region and 1-pulse
modulation (square wave modulation) at middle or high speed
region [2]. PWM can suppress the torque ripple because theharmonic component is relatively low. On the other hand,
implementation of 1-pulse modulation can reduce theswitching loss comparing to PWM and increases thefundamental amplitude of the output voltage. Hence, the 1pulse modulation is often applied to extend the operational
region of speed in the motor. In addition, pulse width of the 1pulse modulation can be varied in a 3-level inverter unlike a 2level inverter because the 3-level inverter can output zerovoltage level. Thus, it can arbitrarily decide the fundamental
amplitude of output voltage [3] and it is called as 1’pulse
modulation in order to distinguish from the standard 1-pulse
modulation that has constant voltage amplitude [4]. Therefore,
the interchange point from PWM to 1’pulse modulation can bedecided arbitrarily. However, the interchange point needs to beanalyzed in consider to achieve the highest efficiency in a drive
system.

Fig. 1. Circuit topology of neutral point clamped 3-level inverter.

The selection method of the interchange point may include
analyzing and comparing the losses for both the PWM and1’pulse modulation at a same motor speed. At each operation
region, the operation method of the smaller loss is selected,
which can achieve high efficiency. The study of loss analysisof the 3-level inverter loss or the PMSM loss has been
individually reported in Ref. [5-7]. However, the evaluation onlosses of the total drive system that is including the 3-level
inverter and PMSM has not been reported.
This paper discusses the selection method of theinterchange point in terms to achieve minimum loss, byanalyzing and comparing the losses for each operation. The
total losses of the drive system are subjected to the motor speed
and carrier frequency. The total losses are divided into theinverter loss and motor loss. Firstly, we express a quantitativeloss calculation method for the inverter. Secondary, abreakdown of losses for the inverter are showed by showing
the loss of each element. Thirdly, the loss analysis of PMSM isanalyzed by two-dimensional finite element method
electromagnetical field analysis (FEM). In addition, the total
loss analysis result will clearly demonstrate the relationshipbetween the operation method and total loss. At the end, theneutral-point-clamped 3-level inverter is demonstrated in order
to measure the loss of the motor drive system at different
carrier frequency for PWM.
II.

NEUTRAL-POINT-CLAMPED 3-LEVEL INVERTER

Fig.1 shows a circuit diagram of neutral-point-clamped 3level inverter. There are two topologies in the 3-level inverters:
neutral-point-clamped and T-type. In this paper, a neutral-

point-clamped type is selected as the interface converter for the
PMSM. However the loss analysis method that described inthis paper is applicable for the T-type as well.
A neutral-point-clamped 3-level inverter has a higher
conduction loss than 2-level inverter because the switching
devices are connected in series. On the other hand, theharmonic loss of the motor can be decreased without the needto increase carrier frequency because the output phase voltage
is 3 levels.
Fig. 2 shows a relationship between the motor speed andthe inverter output voltage. Operating area A is the PWM
region and the effect of decreasing of harmonic losses can beevaluated at the 3-level inverter. Area B is the PWM region in
2-level inverter. However, in 3-level inverter, it is the 1’pulse
modulation region and the effect of decreasing of the switchingloss can be evaluated.

Fig. 2. Comparison of operation method each inverter circuit
TABLE I.

At 1’pulse modulation, the voltage fundamental amplitudeis decided by zero-level phase α, and Fourier series expansionof U-phase voltage vu is expressed in (1). Furthermore, thefundamental amplitude can calculate form the first term of (1).
If α = 0, operation method becomes 1-pulse modulation asshown in area C.
∞⎡ 2 E dc⎤
Vu = ∑ ⎢cos{(2n − 1)α }sin{(2n − 1)ωt}⎥
π
(
)
2
n
−
1
n =1 ⎣⎦
2 E dc2 E dc=cos α sin ωt +cos(3α ) sin (3ωt )π
3π
2 E dc+cos(5α ) sin (5ωt ) + "
5π

III.

(1)

PMSM PARAMETERS.

Rating power Pr
Rating speed Nrd-axis inductance Ld
q-axis inductance Lq
Winding resistance Ra
Back-emf coefficient ΦArmature pairs of poles pRating Torque Tr

The switching loss is proportional to the current flows via
elements and the voltage applied to elements. Additionally, theapplied voltage to the elements is constant. Therefore, theaverage switching loss during output cycle is expressed in

Psw = E dc (eon + eoff ) f c

LOSS CALCULATION OF 3-LEVEL INVERTER

A. Loss Calculation of Inverter
In this section, we describe the loss calculation method forinverter [6-9]. The inverter loss Pinv is separated into follows:
the conduction loss of IGBT Pcon_IGBT, the conduction loss ofdiode Pcon_D, the switching loss of IGBT Psw and the recovery
loss of diode Prec, it is expressed in
Pinv = Pcon _ IGBT + Pcon _ D + Psw + Prec

1 θ2
von isw dθ
2π ∫θ1von = ron isw + v0

(3)
(4)

1 θ2
iout dθ2π ∫θ1(5),where, fc is the carrier frequency, Edc is the DC voltage and iout
is the output current. Furthermore, eon is the turn-on energy
when the current flowing along elements is 1A and the voltage
applied to elements is 1V. The same applies to the turn-off
energy eoff .
(6).

The recovery loss of the freewheeling diode is expressed in(2).

The conduction loss can be calculated by integrating the
product of current flowing along elements isw and the onvoltage von under the conduction time from θ1 to θ2. It is
expressed in (3). The on-state voltage von is proportional to thecurrent flowing along elements isw and calculated by linear
approximation of the on-resistance ron and the voltage drop by
PN junction v0. It is expressed in (4).

Pcon =

3.0 kW
12000 rpm
389 μH556 μH
0.0635 Ω
0.189 Vs/rad
6
4.0 NmPrec = E dc e rr f c

1 β
i out dθ
2π ∫α

(6),

where, err is the recovery loss energy.
B. Loss Calculation Results of 3-level Inverter
The loss of the 3-level inverter is calculated based onfollowing condition. The output power is decided from therated torque and the carrier frequency fc is 7, 12 and 16 kHz for
PWM, respectively. In addition, the modulation strategy for the
3-level converter is applied with unipolar modulation in Ref.
[10]. On the other hands, a vector control with id = 0 for PWM,
and V/f control adjoined stabilization control for 1’pulse
modulation [11] are applied for the motor. Furthermore,
switching devices are applied with IGBT (2MBI100VA-06050/Fuji electric). Table I shows the parameters of PMSM.

Fig. 3 shows the detail breakdown of the inverter losses.
The loss is standardized by the rated motor power. In PWM,
the loss at fc = 7 kHz is the smallest because the switching loss
increases in proportional to the carrier frequency. On the other
hand, the 1’pulse modulation is shown to have the smallest in
all speed range because the switching frequency is the same as
the output frequency, i.e. it is the lowest. Thus, the inverter loss
at 1’pulse modulation is smaller than that at PWM. In addition,
the conduction loss of IGBTs increases and the conduction lossof the diodes decreases with the increasing motor speed. This
reasons that the inverter selects the switching pattern which theoutput time of zero voltage is shortened, i.e. the conduction
time of IGBTs (Q1, Q4) increase and the conduction time ofclamp diodes decrease, when the output voltage becomes large
at high speed.
LOSS ANALYSIS OF PMSM

A. Development of PMSM Model
The motor loss can be classified: the copper loss by wiring
resistance, the iron loss occurring in the core or the magnet andthe mechanical loss. In this section, the mechanical loss isignored because the loss depends only on the motor speed. The
motor loss is analyzed by two-dimensional finite element
method electromagnetical field analysis (FEM). FEM analyzes
the magnetic field occurred in the motor, and then the losses
are calculated based on the results. At first, the twodimensional model of the motor is developed. Next, theanalysis is performed by inputting the current waveform which
is obtained from the simulation into motor phase.
Table II shows the analysis conditions. The time intervalper 1step is decided by considering the effect on the motor lossby the carrier frequency.
B. Loss Analysis Results of PMSM
Fig. 4 shows the breakdown of the motor loss, similar to
Fig. 3, the results are standardized by the rated motor power.
From the results, the copper loss and the iron loss at the stator
are dominant in the motor loss. The loss at 1’pulse modulationshows to be the largest because the harmonic components inthe output voltage and current are larger than that of PWM. As
the result, the eddy-current occurred in cores and the magnetics
becomes higher, and the eddy-current loss is also increase.
V.

Speed is 0.1 p.u. at PWM and 0.2 p.u. at 1’pulse modulation.

DISCUSSIONS TO MINIMIZE TOTAL LOSS

From the calculated inverter loss and the analysis of the
PMSM loss, the total loss of the drive system can bedemonstrated, and next will consider the optimal operation
method of 3-level inverter in terms of the minimalize loss.
The total loss of the motor drive system Ploss is expressed in
Ploss = Psw + Prec + Pcon + PCu + PFe + Pmec

(7),

where Pcon is the conduction loss, PCu is the copper loss, PFe is
the iron loss and Pmec is the mechanical loss. Here, 1’pulse
modulation can reduce the switching and recovery loss than
PWM drive.

(b)

Speed is 0.3 p.u..

Inverter loss [p.u.]

IV.

(a)

(c) Speed is 0.5 p.u..
Fig. 3. Inverter loss analysis results for each operation condition.
TABLE II.

PMSM PARAMETERS OF FEM.

Core (rotor, stator)
MagnetCoil turns per phase
Number of elements
Number of contact points
Time interval per 1step
Calculation time
Computer

35H300/Nippon SteelNMX-41SH/Hitachi Metals
11 Turns
48,953
26,6838.33e-6
8 hours
Xeon X5450 3.0GHz

In order to be higher efficiency than PWM drive comparedwith the 1’pulse modulation, the equation (8) should be
respected.
Psw _ PWM + Prec _ PWM > ΔPcon + ΔPCu + ΔPFe(8),

where, Psw_PWM and Prec_PWM are the switching loss and therecovery loss, respectively, ΔPcon, ΔPCu and ΔPFe are thedifference between PWM drive and 1’pulse modulation of the
conduction loss, the cupper loss and the iron loss, respectively.
The mechanical loss Pmec is ignored because the loss at PWM
drive equals to that at 1’pulse modulation in order to depend
only on a motor speed. In addition, the switching loss Psw andthe recovery loss Prec at 1’pulse modulation are ignored
because these are vanishingly lower than that at PWM drive.
Furthermore, it assumes that the current harmoniccomponent at PWM drive is vanishingly smaller than that at
1’pulse modulation. In addition, the difference between PWM

drive and 1’pulse modulation of the iron loss ΔPFe isformulated by the analysis result of the FEM. Under these
conditions, the equation (8) is expressed in (9).
Psw _ PWM + Prec _ PWM >InI out _ PWM

2Pcon _ PWM + 3R a I n + ae − bω (9),where, Iout_PWM is the RMS of the current at PWM, In is the
harmonic component of the current at 1’pulse modulation, aand b are constant value, ω is the electrical angular frequency.
In addition, In is expressed in (10) [12].

⎛ 2 E dc⎞cos{(2n + 1)α } ⎟⎜(2n + 1)π⎟I n = ∑ ⎜⎜
⎟
2
2
n =1
ω Ld + L q
⎜⎜
⎟⎟
⎝
⎠

(a)

Speed is 0.1 p.u. at PWM and 0.2 p.u. at 1’pulse modulation.

(10)

If the equation (9) is respected, the total loss at 1’pulse
modulation is lower than that at PWM drive. Therefore, in thiscase, the use of 3-level inverter can achieve higher efficiency
drive than the use of 2-level inverter. In other words, if theequation (9) is not respected, the total loss at 1’pulse
modulation is higher than that at PWM drive. The use of a 3level inverter is not benefit and a 2-level inverter has a costadvantage with that kind of system.

VI.

EVALUATION BY EXPERIMENTATION

The drive system of PMSM was implemented to compare
the total loss with the implementation of spoken operation
method. In this section, the total loss that measured by thesystem is showed.
Fig. 6 shows a configuration of the developed drive system.
The power consumption of the inverter is measured by thepower meter (WT1800/YOKOGAWA). The measured power
points for the inverter are between the DC bus capacitor andthe output of inverter. In addition, the torque meter is put
between the test motor and the load motor. The operation
conditions are output torque T = 2.0 Nm and carrier frequency
fc = 10, 12 and 16 kHz for PWM. The motor control method
uses a vector control with id = 0 and applied a balance control
because voltage of two DC capacitors should be equalized [13].
Furthermore, switching devices are selected with IGBT
(2MBI50P-140/Fuji electric) in order to confirm that thevalidity of (9). Besides, the tested motor is the same as table II.
The loss of the motor is separated as follows. Firstly, themotor loss is the difference between the output power of theinverter and the shaft power of the motor. The copper loss is

Speed is 0.3 p.u..

(c) Speed is 0.5 p.u..
Fig. 4. Motor loss analysis results for each operation condition.
7kHz
12kHz
16kHz
1'pulse0.1
T otal loss [p.u.]

Fig. 5 shows relationship between the motor speed and thetotal loss, and the optimal interchange point of the operation
method. For the speed region under 0.3 p.u., the PWM drive (fc= 7 kHz) shows to achieve the smallest loss. On the other hand,at the speed region over 0.3 p.u., 1’pulse modulation shows toachieve the smallest loss because the rate of the inverter loss intotal loss is higher. In this region, the equation (9) is respected.
Thus, the high efficiency can be achieved by interchange theoperation method at 0.3 p.u. speed in this case.

(b)

0.09
0.08
0.07
0.06

0.1

0.2

0.3
0.4
Speed [p.u.]

0.5

0.6

Fig. 5. The total loss of a PMSM drive system and switching point ofoperation method.

calculated by the winding resistance and the RMS of the motor
current. The mechanical loss is calculated by the torque at noload running. Finally, the iron loss is the value which thecopper loss and the mechanical loss are excepted in the motorloss.
Fig. 7 shows U-V line-to-line voltage and U phase current
waveforms of the 3-level inverter at carrier frequency fc = 16
kHz. From Fig. 7, it is noted that the current waveform isdistorted because the PMSM is a concentrated windings andback electromotive force of the motor contains harmoniccomponent. In addition, the reason includes that the inductanceof the motor is smaller than typically PMSMs.
Fig. 8 shows measurement results of the drive system loss.
The rate of the mechanical loss and the iron loss increases with
the increasing motor speed, because a mechanical loss and aniron loss are proportional to motor frequency, i.e. the speed andmotor voltage, respectively. Therefore, when a PMSM isturned at high speed, it is effective to use a magnetic material
which an iron loss decreases due to decrease the total loss.
Fig. 9 shows analysis results of the inverter loss using
simulation. From Fig. 8 and Fig. 9, the measurement result isbasically consistent with analysis results. The inverter loss isdominated by the conduction loss. This reason is that theoutput current is larger than that of a 2-level inverter. In
addition, the conduction loss is not depends on the carrier
frequency because the harmonic components in the current are
decreased by the 3-level inverter. Furthermore, the loss at fc =10 kHz is the smallest, because the switching frequency is thelowest.
Fig. 10 shows the analysis results of the motor loss using
FEM and compare between the analysis results and themeasurement results. As the result, the eddy-current loss ofstator dominates more than half of the motor loss at 0.5 p.u.
speed because the eddy-current loss increases in proportional tothe motor frequency. In addition, the loss of fc = 12 kHz is thesmallest at 0.3 p.u. speed. The reason is that the copper loss by
the harmonic components of the current is smaller than that offc = 10 kHz. Furthermore, the amplitude of magnetic flux
density is decreased by carrier frequency but the frequency ofthat increases, therefore, the motor loss is the smaller than thatof fc = 16 kHz.
Fig. 11 shows the total loss of developed PMSM drive
system based on measurement results. The loss at 10 kHz is thesmallest because the rate of the inverter loss is larger than thatof the motor loss. The rate of the motor loss in the total loss is
low because the harmonic components of the voltage and thecurrent decrease as the 3-level inverter. Therefore, it isdesirable that carrier frequency is lowered as much as possible
with that kind of system. However, if the carrier frequency has
a profound effect on the motor loss, it is contemplated that the
optimal carrier frequency is changed by motor speed.
VII. CONCLUSION
In this paper, the loss minimized operation method of a 3level inverter was considered in order to achieve a highefficiency motor drive system. As the result, it can be obtainedthat the total loss decreases when the operation method isinterchanged at the point where the curve of PWM loss
intersects with 1’pulse modulation. In addition, if the rate of
the inverter loss is lower, the use of a 3-level inverter is notbenefit and a 2-level inverter has a cost advantage with thatkind of system. Furthermore, the motor drive system by aneutral-point-clamped 3-level inverter was tested and the lossesof the system were measured and compared with analysis
results at each carrier frequency. As the result, when a rate of a
motor loss in total loss is lower, it is high efficiency that a

Fig. 6. Configuration of the developed drive system.

Fig. 7. U-V line-to-line voltage and U phase current waveform of using the 3level inverter at carrier frequency fc = 16 kHz.
0.07
0.06
0.05

Iron loss
Copper loss
Mechanical loss
Inverter loss

0.04
0.03
0.02
0.01
0

0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0

10kHz

12kHz
16kHz
Carrier frequency(a) Speed is 0.1 p.u..

Iron loss
Copper loss
Mechanical loss
Inverter loss
10kHz

12kHz
16kHz
Carrier frequency(b) Speed is 0.3 p.u..

0.12
0.1
0.08

Iron loss
Copper loss
Mechanical loss
Inverter loss

0.06
0.04
0.02
0

10kHz

12kHz
16kHz
Carrier frequency(c) Speed is 0.5 p.u..
Fig. 8. Loss measurement results of developed PMSM drive system.

carrier frequency is lower. In the future work, the 3-level
inverter will be operated with 1’pulse modulation and the loss
will be compared at PWM and 1’pulse modulation.
Furthermore, calculation of a motor loss will be simplified.

eddy-current (stator)

0.02

hysteresis (stator)
eddy-current (rotor)

0.01

hysteresis (rotor)
eddy-current (magnet)

0
Speed is 0.1 p.u..

(b)

Speed is 0.3 p.u..

12kHz
16kHz
Carrier frequency(a) Speed is 0.1 p.u..

copperMotor loss [p.u.]

(a)

10kHz

Speed is 0.3 p.u..

Motor loss [p.u.](b)(c) Speed is 0.5 p.u..
Fig. 10. Analysis result of the motor loss using FEM.
T otal loss of drive system [p.u.](c) Speed is 0.5 p.u..
Fig. 9. Analysis result of the inverter loss using simulation.

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0.1
0.09
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12kHz
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