Evaluation Method of Energy Consumption for
Permanent Magnet Synchronous Motor Drive System
Daisuke Sato

Jun-ichi Itoh

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

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

Abstract— This paper discusses an evaluation method ofelectric energy consumption of a permanent magnet synchronous
motor (PMSM) drive system. The calculation method of the energy
consumption based on an efficiency map is proposed. First, it isconfirmed that the error ratio between the calculation result andthe measurement result is less than 5%. In addition, the energy
consumption of the PMSM drive system for actual hybrid electricvehicles is calculated by the proposed method. As a result, it isclarified that when the three-level inverter is employed, the energy
consumption decrease ratio compared with the two-level inverterin the light load region is higher than that in the heavy load region.

parameters or the optimization of the PMSM structure. However,
the energy consumption in the whole system included theinverter is not evaluated. Besides, the change of the energy
consumption by the inverter topology is not also evaluated.
Furthermore, the calculation method of the PMSM drive system
is not compiled systematically.

Keywords— Three-level inverter; Permanent magnet
synchronous motor; Electric energy consumption; Efficiency map;
Electric vehicle / Hybrid electric vehicle

I. INTRODUCTION
Recently, the drive systems applying the Permanent Magnet
Synchronous Motor (PMSM) have been researched actively inorder to improve the efficiency of the motor drive system. The
systems applying PMSM have higher efficiency and power
density than that applying the induction motor.
On the other hand, the multi-level inverter such as a threelevel inverter is an alternative converter of a typical two-level
inverter. The three-level inverter reduces both the harmonic lossof PMSM and the switching loss of the inverter. Therefore, inmotor drive systems, high efficiency is expected by
implementing the multi-level inverter.
In order to further improve the efficiency of the motor drive
system, the analysis of the inverter loss or the PMSM loss has
been individually reported in [1-4]. However, there is the tradeoff relationship between the inverter loss and the PMSM loss [5].
For example, by increasing carrier frequency, the PMSM loss isdecreased. On the other hand, the inverter loss is increased.
Therefore, the efficiency evaluation method of the total drive
system that includes the inverter and PMSM is necessary.
In general, the efficiency of the inverter or the PMSM isevaluated on constant speed and constant torque. Nevertheless,the speed and the torque changes continuously in a hybrid
electric vehicle (HEV), an electric vehicle (EV), a flywheel
energy storage system (FESS) and so on. Therefore, the drive
system should be evaluated by not only the instantaneous loss orefficiency but also the energy consumption according tooperation pattern. In [6-7], the reduction method of the energy
consumption in PMSM is proposed by the identification of the

In this paper, the calculation method of the energy
consumption in the PMSM drive system based on the efficiency
map is proposed. In addition, the energy consumption of the
PMSM drive system applying the two-level inverter and thethree-level inverter is evaluated. Thus, it clarifies the efficiency
improvement effect of the drive system applying the three-level
inverter when the PMSM is actually driven.
II. CHARACTERISTICS OF THREE-LEVEL INVERTER
Fig. 1 shows the circuit diagram three-level neutral-pointclamped inverter (T-type). The three-level inverter reduces the
harmonic component of the output voltage comparing to the
two-level inverter due to the possibility to output zero voltage
level. In other words, the reduction of the harmonic loss in the
PMSM is possible. In addition, the switching loss is reduced by
the three-level inverter because the varying voltage on theswitching is a half compared with the two-level inverter.
Furthermore, when the switches which are connected to theneutral point of the DC bus are constructed by RB-IGBTs, theconduction loss is same as the two-level inverter. Therefore, thetotal efficiency of the system applying the three-level inverter isimproved compared with the conventional system.
III. CALCULATION METHOD OF ENERGY CONSUMPTIONIn this section, the calculation method for the energy
consumption in the PMSM drive system based on the efficiency
map is proposed. In the proposed method, the total efficiency
map is made before calculation of the energy consumption. In
addition, the calculation requires the operation command of the
speed and the torque.
The efficiency of the drive system  which is a function of
the speed N [r/min] and the torque T is expressed by (1).

START
Edc
2

Edc
2

U

Create efficiency maps of drive system (N, T)

V

Input operation command functions N(t), T(t),operation time To and sampling time Ts
Initialize (t = 0)Wnot < ToFig. 1. Circuit diagram three-level neutral-point-clamped inverter(T-type). The total efficiency of the PMSM drive system applying
the three-level inverter is improved compared with the conventional
system.



2N / 60T N ,T  2N / 60T  Pinv N ,T   Pmot N ,T 

yesCalculate consumption power P by Eq. (3)
W=W+P



t = t + Ts

where, Pinv and Pmot are the losses of the inverter and PMSM,
respectively and these are also the functions of the speed N andthe torque T. The speed N and the torque T are the functions oftime t because these are given by the operation command.
Therefore, the energy consumption of the drive system W isexpressed by (2).
W 

2N t  / 60T t 1  N t , T t  dt N t , T t  3600



However, the mathematization of the actual efficiency or thecomplex operation command of the speed or the torque isimpossible to derive. Thus, the look-up table is applied.
Therefore, (2) is discretized and replaced by (3).
2N n / 60T n1  N n, T nT s N n , T n  3600
n0

To / T s

W 



where, To is the operation time and Ts is the sampling time of theoperation commands.
Fig. 2 shows the calculation flowchart of the energy
consumption using the efficiency map. As the input, theefficiency map (N, T), the operation command of the speed N(t)and the torque T(t), the operation time To and sampling time Ts
are given. Then, the energy consumption is calculated by (3).
IV. COMPARISON BETWEEN CALCULATION RESULT AND
MEASUREMENT RESULT OF ENERGY CONSUMPTIONIn this section, the proposed calculation method of theenergy consumption is evaluated. Therefore, the measured
energy consumption by the actual drive system is compared withthe calculated one.
A. Configuration of actual PMSM drive system
Fig. 3 shows the configuration of the PMSM drive system
for the energy consumption measurement. The inverter for thetest motor is the three-level inverter. This inverter controls the
speed of PMSM. In addition, if the inverter is driven as the two-

Output electric energy
consumption W
END

Fig. 2 Calculation flowchart of energy consumption in the PMSM
drive system using efficiency map.

level inverter, the switches which are connected to the neutral
point of the DC bus always turn off. The IGBTs (2MBI150U2A060, 600V, 150A, Fuji electric) are applied to the switches.
APL-II (Myway) is applied as the DC power supply. The DC
link voltage is 180 V. On the other hand, the inverter for the load
motor controls the load torque based on the current control. The
power consumption is measured by the power meter (WT1800,
YOKOGAWA).
Table 1 shows the parameters of the prototype PMSM. The
prototype PMSM is designed as the mini model of the EV/HEV.
The winding type is the concentrated winding. Therefore, thecoil end of the concentrated winding is shorter than that of the
distributed winding. However, the distributed winding makes
the current waveform become distorted.
B. Energy consumption in EV system
Fig. 4 shows the operation command of the vehicle velocity
called JC08 mode. JC08 mode is defined by Ministry of Land,
Infrastructure, Transport and Tourism of Japan. It is 20 minutesof the operation command assumed the driving in urban area andhighway.
In addition, the running resistance of the vehicle is definedby the air resistance, the rolling resistance, the gradientresistance and the acceleration resistance. The air resistance is
proportional to the square of the velocity. The rolling resistanceand the gradient resistance do not depend on the velocity. The
acceleration resistance is proportional to the acceleration. The
velocity is time function because it given by the operationcommand. Therefore, running resistance is expressed by (4)FL t   K 2 V t   K1
2

dV t 
 K0 
dt



DC
supply(APL-II/Myway)

Edc

180 V

Threelevel
T-typeNPC
inverter

V is the velocity,  is the density of air, Cd is the air resistancecoefficient, A is the projected area of the vehicle,  is the rolling
resistance coefficient, M is the mass of the vehicle, Mi is theequivalent inertia weight of the rotating part in the drive
mechanism, g is the gravitational acceleration and  is thegradient angle.

Test
motor

TorquePower Meter
Detector(WT1800/(TH-2105/
YOKOGAWA)ONO
SOKKI)

Iin

When the calculation of the energy efficiency is applied, therunning resistance FL is converted to the load torque of PMSM
TL. The velocity V is also converted to the speed of PMSM N.
The running resistance and the velocity are expressed by (8), (9).

200 V / 50 Hz
Twolevelinverter

Rectifier

Load
mtor

4 Nm
7200 r/min

Maximum speed

12000 r/min

Rated current

16.9 Arms

Armature pairs of poles

6d-axis inductance

0.389 mH

q-axis inductance

0.556 mH

Winding resistance

0.0635 

Back-EMF coefficient

0.0182 Vs/radV  N 



2

N n   N n  1 1
2
K 2 N n   K1
 K0 


Ts




As the condition of the energy consumption measurement,
JC08 mode is applied to the speed command. JC08 is defined by
the velocity of the vehicle. Hence, it is converted to the speed of
PMSM. In this case, the speed is assumed to 12000 r/min at 160
km/h. The load torque command is obtained by (10). However,the prototype PMSM is smaller than the actual PMSM for
EV/HEV. Thus, the torque command is decided by the actual
vehicle parameters which are scaled down based on theparameters of the prototype PMSM. Note that the acceleration
resistance is ignored because the equivalent inertia weight of therotating part in the actual drive mechanism is not clear. In
addition, it assumes that the effect of the load torque by theacceleration resistance is negligibly small. Furthermore, JC08 is
assumed as the driving in urban area and highway. Therefore,
the load torque is decided to be approximately 15% of the
maximum torque at 0 r/min and half of the maximum torque atthe maximum speed. The load torque command is expressed by
(11).

80
Velocity [km/h]TL n  

Table 1. Parameters of IPMSM.
Maximum power
3 kW
Base speed

FL  TL 

where,  and  are the proportional constant. Therefore, the load
torque applied in (3) is expressed by (10).

Fig. 3
Configuration of PMSM drive system for energy
consumption measurement. The IGBTs (2MBI150U2A-060, 600V,
150A, Fuji electric) are applied to the switches of the three-level
inverter. The DC link voltage is 180 V.

Maximum torque



60
40
20



TL n  8.544  10 9  N n  0.58 
2



0

500
1000
Time [s]Fig. 4 Operation command of speed (JC08 mode). It is 20 minutesof the operation command assumed the driving in urban area andhighway

where,
K2 

1
Cd A 
2





K1  M  M i 





K0  Mg  cos   sin  Fig. 5 shows the measurement result of energy consumptionof the PMSM drive system for the EV system by each inverter
topology. When the energy consumption is measured, thesystem is warmed up in order to avoid the variation in themechanical loss or the copper loss which is dependent on thetemperature. It is confirmed that the winding temperature ismaintained nearly constant. In addition, the carrier frequency is
4 kHz. From Fig. 5, the average energy consumption by the twolevel inverter and by the three-level inverter are 70.8 Wh and68.2 Wh, respectively. Therefore, the energy consumption
decreases by 3.67% when the three-level inverter is applied. Thisis caused by the reduction of the switching loss and the harmonicloss. However, the switch which is connected to the neutral pointof the DC bus consists of two IGBTs connected anti-serially.
Thus, the conduction loss of the three-level inverter is larger than

Energy consumption [Wh]75

Two-level

Average: 70.8 Wh

Three-level

Average: 68.2 Wh

70
65
60
55

2

4
6
Cycle number

8

Fig. 5 Energy consumption of PMSM drive system for EV systemby each inverter topology. The energy consumption decreases by
3.67% when the three-level inverter is applied.

that of the two-level inverter because the number of switches
through which the current flows is three per one phase. When
the RB-IGBT applies to the switch which is connected to theneutral point of the DC bus, the energy consumption by threelevel is expected to further decrease.

(a)With two-level inverter. The maximum efficiency is 83.7%(5400 r/min, 1.09 Nm)

Table 2 shows the calculation result based on Fig. 2 of theenergy consumption. The error ratio between the calculation
results and the measurement results is less than 5% in the systemapplied the both inverter topologies.

(b)With three-level inverter. The maximum efficiency is 87.5%(5400 r/min, 1.08 Nm).
Fig. 6 Efficiency map of PMSM drive system.

C. Energy consumption in flywheel energy storage system
The flywheel energy storage system (FESS) is applied to thepower leveling system because it is long life time due to no
chemical structure.

Table 2 Calculation result of energy consumption of the PMSM
drive system for the HEV system by each inverter topology.
Inverter topology
Calc.
Meas.
Error ratio

Next, the calculation results of the energy consumption arecompared with the measurement results because the proposed
calculation method is evaluated. Note that the efficiency map of
the prototype drive system is necessary. Therefore, theefficiency map is made by the measuring efficiency of the
prototype drive system.
Fig. 6 shows the efficiency map of the prototype system
when each inverter drives the prototype PMSM. The maximum
efficiency is 83.7% (5400 r/min, 1.09 Nm) with the two-level
inverter and 87.5% (5400 r/min, 1.08 Nm) with the three-level
inverter.

Fig. 7 shows the operation command of the FESS for powerfluctuation compensation control [8]. In the FESS, when PMSM
is operated as a generator during deceleration, kinetic energy isconverted into the electrical energy. On the other hand, during
acceleration, the electrical energy is stored as kinetic energy,
which is working as a motor.
In addition, the output torque of the PMSM is decided by theinertia of the flywheel and the acceleration. Therefore, the load
torque command is expressed by (12).
TL n  J f  J m 

N n  N n  1Ts

where, Jf is the inertia of the flywheel and Jm is the inertia of the
PMSM.

Two-level

68.4 Wh70.8 Wh

3.39%

Three-level65.2 Wh68.2 Wh

4.40%

Fig. 8 shows the measurement result of energy consumptionof the PMSM drive system for the FESS by each inverter
topology. The average energy consumption by the two-level
inverter and by the three-level inverter are 67.4 Wh and 57.8 Wh,
respectively. Therefore, the energy consumption decreases by
14.3% when the three-level inverter is applied.
Table 3 shows the calculation result of energy consumptionof the PMSM drive system for the FESS by each inverter
topology. The error ratio between the calculation results and themeasurement results is less than 5% in the system applied theboth inverter topologies. Therefore, the validity of the proposed
calculation method is confirmed.

The efficiency map of PMSM driven by the two-level
inverter (carrier frequency: 5 kHz) is drawn. In this section, theefficiency map of PMSM driven by the three-level inverter isalso necessary. Therefore, it is obtained by the scaling efficiency
map of the PMSM driven by the two-level inverter.

7000

Speed [r/min]

6000
5000
4000
3000

0

200

400

Energy consumption [Wh]

600
800
1000
1200
Time [s]Fig. 7 Operation command of FESS for power fluctuationcompensation control.
80
75
70
65
60
55
50
45
40
35
30

2-levelAverage: 67.4 Wh

3-levelAverage: 57.8 Wh

1

2
3
4
Cycle number
Fig. 8 Energy consumption of the PMSM drive system for the FESS
by each inverter topology. The energy consumption decreases by
14.3% when the three-level inverter is applied.
Table 3 Calculation result of energy consumption of the PMSM
drive system for the FESS by each inverter topology.
Inverter topology
Calc.
Meas.
Error ratio
Two-level

66.0 Wh67.4 Wh

2.16%

Three-level

59.6 Wh57.8 Wh

3.06%

V. EVALUATION OF THREE-LEVEL INVERTER IN ACTUAL HEV
In this section, the energy consumption of the actual HEV
drive system is evaluated. In particular, the energy consumptionof the system with the three-level inverter is compared with thatwith the two-level inverter. In addition, the operation condition
when the three-level inverter reduces the energy consumption
more effectively is considered. However, the detailed
specifications of the actual HEV drive system are not clear.
Therefore, the specifications are inferred by literatures.
From [9], the parameters of the inverter assume that the input
voltage is 650 V and the maximum output current is 141 A.
From these parameters, the IGBT (6MBI300V-120-50，1200 V，
300 A, Fuji electric) is applied to the switching device. In
addition, two IGBTs connected anti-serially is applied to theswitch which is connected to the neutral point of the DC bus in
the three-level inverter. Moreover, the carrier frequency is 5 kHz
in the both inverters. Then, the inverter efficiency map isobtained by the circuit simulator (PLECS Blockset, Plexim)
based on the above conditions. Note that the trend of the loss
analysis results in the circuit simulator almost agrees with thatof the measurement results in [10].

The copper loss of PMSM does not depend on the inverter
topologies because it is dominated by the fundamental
component [5]. In addition, the difference of the harmonic ironloss in the magnetic steel sheet by the inverter topology is slightbecause the magnetic steel sheet is the structure which isdifficult for the eddy current to flow. Therefore, the different
component of the loss by the inverter topology is the eddy
current loss in the permanent magnet. The eddy current loss inthe permanent magnet is relatively small when PMSM is driven
by the sinusoidal voltage. Thus, this loss can be considered to be
independent from the fundamental frequency. In other words,
the eddy current loss in the permanent magnet is dominated by
the harmonic component. Although the characteristic ofharmonic component at each modulation index is different
between the two-level inverter and the three-level inverter, thechange of the eddy current loss in the permanent magnet by the
inverter current phase or the inverter current amplitude is small
in the distributed winding PMSM [2][11]. Hence, the eddy
current loss in the permanent magnet does not depend on themodulation index of the inverter. For these reasons, this loss is
independent of the speed or torque of the PMSM. Therefore, the
PMSM loss decreases by constant when the PMSM is driven thethree-level inverter. From the loss analysis results of PMSM by
the finite element method, the average eddy current losses byapplying the two-level inverter and by applying the three-level
inverter are 299 W and 144 W, respectively [5]. In this time, the
PMSM loss applying the three-level inverter is smaller 155 W
than applying the two-level inverter.
Fig. 9 shows the efficiency map of the HEV drive systemapplying each inverter. When the three-level inverter is applied,the high efficiency region around 95% enlarges.
Then, the energy consumption is calculated when the PMSM
is operated based on JC08 mode. The two patterns of the load
torque command are given because the change of the energy
consumption is also evaluated by the load torque. Therefore the
0% gradient and 10% gradient are assumed. The load torquecommands are obtained in the same way as (11). These at the
0% gradient and 10% gradient are expressed by (13) and (14),respectively.
T0 n  1.389  10 7  N n  10 





T10 n  1.389  10 7  N n  40 



2

2

Fig. 10 shows the calculation results of the energy
consumption when the HEV drive systems are driven based on
JC08 mode. The energy consumption is normalized by theenergy consumption using the two-level inverter. In 0% gradient,
the energy consumption applying the three-level inverter issmaller 2.2% than applying the two-level inverter. On the other
hand, in 10% gradient, the decreasing ratio of the energy
consumption is 1.0% by applying the three-level inverter.

current. Consequently, the ratio of the conduction loss increases
as the current becomes large. The conduction loss of the threelevel inverter is same as that of two-level inverter in principle.
In addition, the copper loss is proportional to the square of thecurrent. Thus, the ratio of the copper loss also increases as thecurrent becomes large. Hence, the effect of the decreasingenergy consumption by the three-level inverter grows weak as
the load torque becomes large.
VI. CONCLUSION(a)

In this paper, the calculation method of the energy
consumption based on the efficiency map is proposed. It is
confirmed that the error ratio between the calculation result andthe measurement result of the energy consumption is less than
5%. In addition, the energy consumption of the PMSM drive
system for HEV is calculated by the proposed method. As aresult, it is clarified that when the three-level inverter is
employed, the energy consumption decrease ratio comparedwith the two-level inverter in the light load region is higher thanthat in the heavy load region.

With two-level inverter.

REFERENCES[1](b) With three-level inverter.
Fig. 9 Efficiency map of PMSM drive system with each inverter
topology for HEV.

Energy consumption [p.u.]1
0.98

877.3 Wh

-2.2%(-19.6 Wh)

2912 Wh -1.0% (-27.3 Wh)
2885 Wh857.7 Wh

0.96
0.94
0.92
0.9

Two-level Three-level
0% gradientTwo-level Three-level
10% gradientFig. 10 Energy consumption of PMSM drive system for HEV by
JC08 mode.

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employed, the decreasing ratio of the energy consumption
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