Analysis of PWM Voltage Detection Delay for
Current Source Type Electric Motor Emulator
Gensui Tanaka
Dept. of Technology of Science
Innovation
Nagaoka University of Technology
Nagaoka, Japans203164+tanaka@stn.nagaokaut.ac.jp

Hiroki Watanabe
dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japanhwatanabe@vos.nagaokaut.ac.jp

Abstract— This paper focuses on input voltage detection for
an electric motor emulator (EME), which imitates various
motor operations accurately. The EME has to detect the PWM
voltage of an inverter under test (IUT) as the input voltage of
the EME. The delay in the PWM voltage detection reduces theemulation accuracy. This paper reveals the relationship between
the cutoff frequency of a low-pass filter (LPF) for voltage
detection and the current control bandwidth of both the IUT
and the EME. The analysis result mentions that a low cutoff
frequency, such as 1 kHz, is acceptable under the current
control bandwidth of 100 Hz in the IUT. In addition, the cutoff
frequency of the LPF should be set to a frequency larger thaneight times the current control bandwidth of the IUT to keep thetransient response in any conditions. Furthermore, it is verified
that the phase lead compensation keeps the current responsewhen the cutoff frequency and the current control bandwidth of
the IUT are close.
Keywords—electric motor emulator, power hardware-in-theloop (PHIL), current control, low-pass filter (LPF)

I. INTRODUCTION
Recently, electrical motor emulator (EME) systems,
which imitate various motor behaviors by a power converter,
are attracted to the development of adjustable speed drive
systems, such as EVs [1-3]. The EME has significant
advantages, such as the easy test of an inverter without a large
motor bench, changing the motor parameters, and testing
conditions, including rotational speed and load torque.
Therefore, the EME reduces the cost and time to develop a
motor drive system, which contributes to the further spread ofEVs.
The accuracy of the EME is affected by the detection of
the output voltage of the inverter under test (IUT), which isthe same as the input voltage of the EME [4-7]. One of the
difficulties of the EME is that the EME has to detect thevoltage from the PWM waveform of the IUT output voltage,
which is a pulsed voltage generated by the PWM. Thus,
accurate and fast voltage detection methods are required for
the EME. In [4], the voltage command of the IUT is sent tothe controller of the EME instead of the voltage detection.
This method will reduce hardware and computational costs
and improve emulation accuracy. However, the output of the
IUT controller is needed to use the output voltage commandof the IUT. Ref. [5] uses a comparator-based circuit to directly
sample the PWM voltage at the logic level. This method has avery low delay due to the use of 200 MHz sampling by an
FPGA. However, this method requires a high-performance
controller in the EME.

XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE

Jun-ichi Itohdept. of Technology of Science
Innovation
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

The transient response and stability of the EME depend on
voltage detection delay. Thus, the EME uses fast voltage
detection methods [8-9]. A low-pass filter (LPF) is a simple
method for detecting the modulated voltage from the PWM
voltage. However, detection delay is an issue for the EME
because it reduces stability and limits the gain in the feedback
system. In contrast, the controller with a voltage detection
method that is too fast causes expenses. The detection speed
has one of the tread-off relations between performance andcost. However, past literature has not clarified the relationshipbetween voltage detection delay and EME performance. The
cost of implementation is reduced by using LPF to detect theoutput voltage of the IUT while maintaining the current
response of the EME.
This paper analyzes the effect of the voltage detection
delay on the performance of the EME. The new contributionof this paper is that the requirement for voltage detection in
the current source type EME is revealed in terms of stability
and keeping the current response of the EME. As a result, thecost of the EME will decrease because the too-fast voltage
detection is not needed. The relationship between the cutoff
frequency of the LPF for PWM voltage detection and thecurrent control bandwidth of the IUT is analyzed using Bodediagrams and pole plots. The limit of the cutoff frequency isrevealed in order to keep the accuracy of the current responseof the IUT. In addition, the desired current response isachieved by applying the phase lead compensation when thevoltage detection with the LPF does not keep the accuracy ofthe current response of the IUT.
This paper is organized as follows: First, the EME
configuration is introduced. Second, the acceptable cutoff
frequency is derived from the relationship between the LPF
and the current control bandwidth. Third, the phase leadcompensation improves the transient response. Finally, thesimulation and experimental results demonstrate the validityof the analysis results.
II. CURRENT SOURCE TYPE MOTOR EMULATOR
Fig. 1 shows an inverter test system configuration using acurrent source type EME. The EME is connected to the IUT
with only three-phase power lines and position or speed sensor
lines, as well as an actual motor. This paper selects an inductor
and a three-phase inverter as the coupling and power converter
for the EME. This configuration is the same as that of a PWM
rectifier. Thus, the controller of the EME has the same
configuration as the controller for the three-phase PWM
rectifiers. The detected output phase voltage of the IUT is sent
to the motor model implemented in the EME controller. The
motor current command of the EME is calculated by a motor

model simultaneously with the motor speed and torque. The
EME imitates the motor behavior by controlling the motor
current due to the current control.
The state equation of an interior permanent magnet
synchronous motor (IPMSM) is implemented as the motor
model of the motor under test (MUT). The state equation of
an IPMSM based on the dq-axis is expressed as
Lq 
 Ra
 vd 
ωre 
 0 
 −
Ld  id   Ld  
id   LdP  =
i  +  v  +  − ωreψm  ..


i
L
R
q
q
q
   −ω q − a      
Lq 
re

Ld
Lq 

 Lq ..................................................................................... (1),where id and iq are the dq-axis current, vd and vq are the dq-axis
voltage, Ra is the armature resistance, Ld and Lq are the dq-axis
synchronous inductance, re is the electric angler frequency,m is the flux linkage of the permanent magnet, and P is thedifferential operator.
Here, the output torque Tout and the relationship between
the electric angular frequency and output torque on the dq-axis
are expressed as
Tout = p{ψmiq + ( Ld − Lq )idiq } .................................... (2),Pωre =

that the parameters in Table 1 and Table 2 are used in theanalysis.
Fig. 2 shows the analysis model based on the dq-axis. In
this paper, the field-oriented control is implemented in the
IUT controller. The q-axis current command is determinedfrom the torque command, and the d-axis current commandis set to zero. Thus, the IUT controller has no speed control,
and a constant speed is assumed. In this paper, the motor
speed is set to 3600 r/min. This configuration is the same as
the speed controlled by the load machine connected to the
IUT in the inverter test system, which uses a motor bench. In
addition, the IUT controller utilizes the decoupling control
for an IPMSM in order to cancel the cross-coupling terms
between the dq-axis. The input voltages of the motor model
Motor Drive Unit (MDU)
IUT

current
sensing

Table 2

A. Analysis by Bode diagram
This section analyzes the relationship between the cutoff
frequency of the LPF and the current control bandwidth ofboth the IUT and the EME based on the Bode diagram. Note

Lq

1
Ra+sLqJ

30×10-4 N・m

1
sLcoup

Lcoup
1
1+sTi

Kp(1+sTi)
sTi

×

LPF

s+LPF

0.0905 Wb

id

Lcoup

re
×

Fig. 2

Kp_cd(1+sTi_cd )sTi_cd

×

1
KT

Ym

re

re
×

T*

Lq

Kp(1+sTi)
sTi
Lcoup

SymbolValuePn
3.7 kW
7200 r/min
nTn
4.91 N・m
p
2
R
116 mW
Ld
2.59 mH
Lq
3.63 mH

×

m

×

Ld

×

Ld

re
iq

1
1+sTi

m

Parameter of an IPMSM.

Decoupling control Coupling inductor×

id

Motor model Controller of the EME

1
Ra+sLdParameter of the circuit.

Parameter
Output power
Maximum speed
Output torque
Pole pairs
Winding resistanced-axis inductanceq-axis inductanceflux linkage ofpermanent magnet
Moment of inertia

III. CLARIFICATION OF ACCEPTABLE VOLTAGE DETECTION
DELAY TIME

LPF

controller of the EM E

Symbol Value
Parameter
DC link voltage of IUT Vdc _IUT 280 V
DC link voltage of ME
Vdc _ME 320 V
Coupling inductor
Lcoup 1.73mH
Switching frequency of IUT fsw_IUT 10 kHz
Switching frequency of ME fsw_ME 40 kHz

Table 1 shows the circuit parameter, and Table 2 shows
the MUT parameter. The EME circuit requires a power ratingand DC link voltage higher than one of the IUT. The
calculation period and the deletion of the switching devices
determine the switching frequency of the EME.

s+LPF

current
control

Configuration of an inverter test system using an EME.
Table 1

The current commands are obtained by solving thedifferential equations (1), (2), and (3) using the backward
Euler method in a DSP.

Kp_cd(1+sTi_cd )sTi_cdmotor modelof the MUT

position or s peed sensor lines

Fig. 1

where TL is the load torque, p is the pares of poles, and J is theinertia of the motor.

id*voltage & current
coupling
sensing

drive
controllerp(Tout − TL ) .................................................. (3),J

Controller of the IUT

Current Source Type Electric Motor Emulator (EME)

Lcoup

1
sLcoupAnalysis model for the relationship between the cutoff frequency of the LPF and the responses of the current control for the IUT.

iqare the output voltages of the IUT detected by the LPF. Thus,
the LPFs are inserted in front of the motor model in Fig. 2.
Fig. 3 shows the simplified model shown in Fig. 2. It is
assumed that the interference between the dq-axis of the
IPMSM and the coupling inductor are eliminated throughdecoupling control for simplification of the model. The gainof the IUT current control is designed to obtain a first-orderdelay response with the integration time as the electrical time
constant of the motor. The gain of the EME current control isdecided by comparison with the secondary standard form,
with the coupling inductor serving as the control target.
Consequently, the open-loop transfer function is a seriesconnection of the integral element of the IUT current control
system, the LPF, and the second-order standard form.

Fig. 5 shows the closed loop Bode diagram for cutoff
frequency variation. The IUT current control bandwidth is set
to 500 Hz, and the EME current control bandwidth is set to2000 Hz, respectively. A gain peak occurs when the LPF
cutoff frequency is 3 kHz or lower, which may worsen thecurrent response. In contrast, a gain peak dose does not appear,
and there is little effect on the current response when the LPF
cutoff frequency is 4 kHz or higher. Consequently, the voltage
detection delay should be acceptable when the LPF cutoff
frequency is set to eight times or more than the IUT current
control bandwidth.

0
-60
-120
-180
-240
-300
-360

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz
1

10

100
Frequency [Hz]1000

Simplified model.

Gain [dB]-40

decreasing by-20dB/dec

-80

IUT

-120
-160 110

LPF

s2+2zLPFs+LPF2s

LPF
s+LPF

open loop trasferfunction
2103(= fLPF) 104(= fEME)
105
Frequency [Hz](a) fIUT = 100 Hz，fLPF = 1000 Hz，fEME = 10000 Hz.
10 (= fIUT )20
2000(= fEM E)

0-20

not decreasingby -20dB/dec

-40

IUT

-60
-80 2
10

s

LPF

s+LPF

500(= fIUT )LPF
s +2zLPFs+LPF2
2

open loop trasferfunction

103(= fLPF)
104
Frequency [Hz](b) fIUT = 500 Hz，fLPF = 1000 Hz，fEME = 2000 Hz.
Fig. 4 Open-loop Bode diagram of the model shown in Fig. 3.

bandwidth suppresses the gain peak. In particular, the gain
peak does not occur when the IUT current control bandwidthis 100 Hz. This is because the cutoff frequency of the LPF andthe IUT current control bandwidth are sufficiently disparate,
as explained in Fig. 4. Therefore, applying an LPF with a low
cutoff frequency is acceptable while keeping the current
response when the current control bandwidth of the IUT is low.
Fig. 7 shows the closed-loop Bode diagram for EME
current control bandwidth variation. Note that the IUT current
control bandwidth is 500 Hz, and the cutoff frequency of the
LPF is 1 kHz. Increasing the EME current control bandwidth
suppressed the gain peak. However, the reduction in effect isless significant than when the IUT current control bandwidthis lowered. This is because the gain crossing angularfrequency remains unaffected mainly when the EME current
control bandwidth is designed to be sufficiently high relative
to the EME current control bandwidth, as shown in Fig. 4(b).

5000

4
2
0
-2
-4
-6
-8
-10
100

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz
1000

2000

1000

2000

Frequency [Hz]
0

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

1

10

iq

0

Gain [dB]

10
0
-10
-20
-30
-40
-50
-60

EME2

s2+2zEMEs+EME2

40

Phase [deg.]

Phase [deg.]

Gain [dB]Fig. 6 shows the closed-loop Bode diagram for IUT
current control bandwidth variation. Note that the cutoff
frequency of the LPF is 1 kHz, and the EME current control
bandwidth is 2000 Hz. Decreasing the IUT current control

s+LPFs

Fig. 3Gain [dB]Fig. 4 shows the open loop Bode diagram of thesimplified model as shown in Fig. 3. As shown in Fig. 4(a),the gain decreases at -20 dB/dec at a frequency up to fIUT andby -40 dB/dec above fIUT when the cutoff frequency of the
LPF is higher than the current control bandwidth of the IUT.
As a result, the gain crossover angular frequency of the open
loop transfer function is fLPF, intersecting 0 dB at -20 dB/dec.
In contrast, as shown in Fig. 4(b), the slope is steeper than 20 dB/dec and crosses 0 dB at a maximum of -40 dB/dec
when the fLPF is close to or lower than the fIUT. In the open
loop Bode diagram, it is recommended that the cutoff
frequency of the LPF be set at a higher than the current
control bandwidth of the IUT in order to achieve a slower
gain gradient near the gain crossover angular frequency.

LPF

IUT

iq*

-60
-120

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

-180
100
1000
5000
100
Frequency [Hz]Frequency [Hz](a) Overview.
(b) Enlarged view.
Fig. 5 Closed-loop Bode diagram for cutoff frequency variation.

Gain [dB]

1
10
100
100
1000
5000
Frequency [Hz]Frequency [Hz](a) 300 Hz.
(b) 100 Hz.
Fig. 6 Closed-loop Bode diagram for IUT current control bandwidth variation.

1000

5000

100
Frequency [Hz]

1000

5000

1
10
100
100
1000
5000
Frequency [Hz]Frequency [Hz](a) 3000 Hz.
(b) 4000 Hz.
Fig. 7 Closed-loop Bode diagram for EME current control bandwidth variation.

1000

5000

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz
1

10

100
Frequency [Hz]

1000

5000

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

1

10

10

5000

5000

Phase [deg.]
10

1

1000

1000

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

1

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz
100
Frequency [Hz]100
Frequency [Hz]B. Analysis by pole plot
This section analyzes the cause of the gain peak on the
Bode diagram when using an LPF with a low cutoff frequency,such as 1 kHz, based on the root locus. The gain peak issuppressed by decreasing the current control bandwidth of the
IUT.
Fig. 8 shows the pole plot for cutoff frequency variation.
The dominant pole is the real pole when the LPF is not used.
In contrast, the dominant poles are complex conjugate poles
when the LPF is used. The poles are close to the pole whenthe LPF is not used, according to an increase in the cutoff
frequency of the LPF. This result is the same as in Fig. 5. The
poles caused by inserting the LPF are the real poles when the
cutoff frequency is set to 4 kHz or 5 kHz. In contrast, thesepoles are the complex conjugate poles when the cutoff
frequency of the LPF is set to 3 kHz or less. As a result, anovershoot occurs in the closed-loop Bode diagram, as shownin Fig. 5.
IV. IMPROVEMENT OF TRANSIENT RESPONSE WITH PHASE
LEAD COMPENSATION
Chapter III clarified the acceptable voltage detection delay.
However, the cutoff frequency of the LPF also has to be high

0
-60
-120
-180
-240
-300
-360

10
0
-10
-20
-30
-40
-50
-60

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz
1

10

0
-60
-120
-180
-240
-300
-360

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

1.0
Imaginary [s ]

0
-60
-120
-180
-240
-300
-360

10

Gain [dB]

10
0
-10
-20
-30
-40
-50
-60

1

Phase [deg.]

0
-60
-120
-180
-240
-300
-360

1 kHz
2 kHz
3 kHz
4 kHz
5 kHz

10
0
-10
-20
-30
-40
-50
-60

-1

Gain [dB]
Phase [deg.]
Gain [dB]
Phase [deg.]

10
0
-10
-20
-30
-40
-50
-60

×104

0.5

0
× w/o
-0.5 × 2 kHz
× 4 kHz-1-3.5 -3.0
Fig. 8× 1 kHz× 3 kHz× 5 kHz-2.5-2.0 -1.5
Real [s-1]

-1.0

-0.5

0
×104

Pole plot for cutoff frequency of LPF variation.

in order to accept the voltage detection delay when the current
control bandwidth of the IUT is high. In this case, there isconcern that the voltage detection accuracy will deteriorate
due to the remaining harmonic components, making it
impossible to calculate the motor current accurately. In
contrast, the motor current is calculated accurately when the
cutoff frequency of the LPF is low enough relative to theswitching frequency of the IUT. Although, the voltage
detection delay is not accepted, and the current responsedeteriorates. Therefore, the current response is able to be
improved by implementing phase lead compensation whenusing an LPF with a low cutoff frequency.

20Log(K/)Fig. 9 shows the Bode diagram of phase leadcompensation. The transfer function with the frequency
characteristic shown in Fig. 6 is expressed as....................................................... (4),Fig. 10 shows the closed loop Bode diagram with thephase lead compensation. Note that K is set to 1, Tcomp is set to1/(2fLPF), and  is set to 0.01. Gain peak and phase delays
occur in cases without compensation. In contrast, the samecharacteristics as those without LPF insertion are obtained byapplying compensation. Therefore, the desired current
response is maintained even when using an LPF with a low
cutoff frequency. This is achieved by compensating for theunacceptable voltage detection delay with phase leadcompensation.
Fig. 11 shows the pole plot when applying the phase leadcompensation. The dominant pole is the complex conjugate
pole without the phase lead compensation. In contrast, thedominant pole becomes the real pole when the phase leadcompensation is applied. In addition, the poles with phase leadcompensation are located in the same place as those without
the LPF, as shown in Fig. 8. Therefore, applying the phaselead compensation removes the influence of utilizing the LPF.
These results agree with the analysis using the Bode diagram
shown in Fig. 9.
V. EXPERIMENTAL RESULT
Fig. 12 shows the difference in the current response withand without an LPF, with an acceptable detection delay. Notethat the LPF is not utilized in Fig. 8(a) to verify its influence.
Instead, the voltage command is directly inputted from the
IUT controller to the EME controller, providing a clear viewof the absence of the LPF. An overshoot is not observed in the
q-axis current response when an LPF is not utilized. Similarly,
an overshoot does not occur when the IUT output voltage is
detected by an LPF with a cutoff frequency of 4 kHz.
Consequently, the current response is equivalent when an LPF
has an acceptable voltage detection delay time.
Fig. 13 shows the current response using an LPF with anunacceptable voltage detection delay. Note that the cutoff
frequency of the LPF is 1 kHz. Each gain of the phase leadcompensation is set to K = 1, Tcomp = 1/(2fLPF), and  = 0.2.
It is possible to fully compensate the LPF on the transfer
function by using a small  value, as shown in Fig. 7.
However, the EME controller becomes unstable due to (4)being a pseudo-differential form. The determination of the

10
0
-10
-20
-30
-40
-50
-60
0
-60
-120
-180
-240
-300
-360

Fig. 10



1/T
1/T
Open loop Bode diagram of phase lead compensation.

Fig. 9Gain [dB]

The detected voltage using the LPF is compensated byinserting (4) before the motor model in the EME controller. A
linear approximation of the gain characteristics of the LPF
shows that the gain is 0 dB up to the cutoff frequency, and thenit decays at -20 dB/dec. Therefore, in order to cancel the gain
characteristics of the LPF, K should be set to 1, Tcomp should
be set to 1/(2fLPF), and  should be set to the frequency range
to be compensated.

0

Phase [deg.]

where K is the compensation gain coefficient, Tcomp is thereciprocal of the break angler frequency comp, and  is thecoefficient that determines the gain compensation range.

1

1

W/ LPF, W/O compensation
W/ LPF, W/ compensation
W/O LPF
10100
Frequency [Hz]W/ LPF, W/O compensation
W/ LPF, W/ compensation
W/O LPF
10100
Frequency [Hz]

1000

5000

1000

5000

Closed loop Bode diagram with phase lead compensation.

1.0

Imaginary [s-1]Tcomp s + 1
αTcomp s + 1



0

×104

0.5
Enlarged in (b)

0
-0.5
-1

-7

1.0

Imaginary [s-1]K ( s) = K

20logK

-6

-5

-4

-3
-2
Real [s-1](a) Overview.

-1

0

1
×105

×104

0.5

W/ comp.
W/O comp.

0
-0.5
-1
-2.0

Dominant pole when W/ com p.
(same pole with W/ LPF)

-1.0
-0.5
0
0.5
×104
Real [s-1](b) Enlarged view.
Fig. 11 Pole plot when applying phase lead compensation.
-1.5

optimal alpha value represents a topic for future research. As
shown in Fig. 8(a), the utilization of an LPF with a 1 kHz
cutoff frequency results in an overshoot of the q-axis current
and distortion of the phase current.

(a) W/O LPF.
Fig. 12

Tout [2N・m/div]

Tout [2N・m/div]

iq [5A/div]

iq [5A/div]i3f [10A/div]i3f [10A/div]

4[msec/div]

4[msec/div](b) W/ LPF (fLPF = 4 kHz).
Step response with LPF having an acceptable detection delay.

Tout [2N・m/div]

Tout [2N・m/div]

iq [5A/div]

iq [5A/div]i3f [10A/div]i3f [10A/div]

4[msec/div]

4[msec/div]

overshootdistortion(a) W/O compensation.
(b) W/ compensation.
Fig. 13 Step response with LPF having an unacceptable detection delay with phase lead compensation.

VI. CONCLUSION
This paper clarified the delay time required to maintain thecurrent response of the IUT. The LPF with a low cutoff
frequency, such as 1/10 of the carrier frequency, causes thegain peak in the closed-loop Bode diagram of the current
control of the IUT. In contrast, the LPF with a cutoff
frequency of 4 kHz does not cause the gain peak in the closedloop Bode diagram of the current control of the IUT. Thus, thedesired current response is maintained by designing the LPF
cutoff frequency to be more than eight times the IUT current
control bandwidth. This indicates that not only is the current
response maintained, but the LPF is also utilized for PWM
voltage detection by selecting the cutoff frequency
appropriately. On the other hand, the phase lead compensation
is applied in order to achieve the desired current responsewhen utilizing an LPF with an unacceptable voltage detection
delay. Analysis and experimental results show that the desired
current response can be achieved by applying for phaseadvance compensation when the desired delay time cannot be
met using an LPF.

[3]

[4]

[5]

[6]

[7]

[8]

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