S2PC 2023, Kaohsiung, Taiwan

Current Control Bandwidth Required for Current Source Type Motor Emulator
Gensui Tanaka1, Hiroki Watanabe1, Jun-ichi Itoh1
1 Nagaoka University of Technology

This paper experimentally verifies the current control bandwidth, which is required for a current source type motor emulator (CSTME) toprevent control interference between the CSTME and the inverter under test (IUT). The preferred relationship of the current control bandwidth
between IUT and CSTME is verified in this paper. From the experimental results, the stability limit of the current control bandwidth is 2050
Hz when the current control bandwidth of the IUT is set to 500 Hz.
Keywords Motor emulator, Current control bandwidth, Stability analysis

expressed as

1. Introduction
In recent years, a motor emulator has been introduced for thedevelopment of a specific motor drive system. In particular, thecurrent source type motor emulator (CSTME) is suitable as theinverter test system without an actual motor because the CSTME
imitates accurate motor current compared with a voltage source
type motor emulator. However, the control instability occurs
because of the interference with the current control of the inverter
under test (IUT) and the one of the CSTME [1]. On the other hand,high performance is required for the power devices and thecontroller in order to achieve a sufficiently high current control
bandwidth of the CSTME and keep the system stable. This paper
experimentally verifies the current control bandwidth required for
the CSTME in order to prevent control interference between theCSTME and the IUT.

Tout = p{ miq + ( Ld − Lq )idiq } ............................................. (2),Pre =p(Tout − TL ) ....................................................... (3),J

where TL is the load torque, p is the pairs of poles, and J is the inertiaof the motor.
The current commands are obtained by solving the differential
equation (1), (2), and (3) for the using the backward Eular method
in a DSP.
Fig. 2 shows the block diagram of the system shown in Fig. 1.
The current control loop of the CSTME is inside the current control
loop of the IUT. Thus, the interference occurs between the currentIUTCurrent Source Type Motor Emulator
Lcoup.

2. Current Source Type Motor Emulator
Fig. 1 shows the system configuration of an inverter test systemusing the CSTME. The hardware configuration of the CSTME isthe same as a PWM rectifier. The CSTME imitates the motor
current according to the current command calculated by the motormodel. In this paper, the state equation of an interior permanent
magnet synchronous motor (IPMSM) as the motor model isimplemented. The state equation of an IPMSM based on the dq-axis
is expressed asR −id   LdP  =iq   − LdreLqLq  vd re    0 
Ld  id   Ld  ++ re m  ............... (1), R  iq   vq   −−Lq   Lq  Lq Nagaoka University of Technology
1603-1, Kamitomioka-machi, Nagaoka, Niigata, Japan, 940-2188

reTout*Current
Sensing
idq

idq *Eq.(1)Currentcontrol

PWM

Eq.(2)
Eq.(3)

reFig. 1. System Configuration of inverter test system using thecurrent source type motor emulator.
TLB
B

id*PIA

1R+sLdPI1sLcoup.

AreLcoup.

rereLcoup.
reLcoup.

Lqiq*PIA

1R+sLqid

reLcoup.

Ld×

Correspondence to: Jun-ichi Itoh, e-mail: itoh@vos.nagaokaut.ac.jp

DriveController

Voltage
Sensing
vdq×

where id and iq are the dq-axis current, vd and vq are the dq-axis
voltage, R is the armature resistance, Ld and Lq are the dq-axis
synchronous inductance, re is the electric angular frequency, m is
the flux linkage of the permanent magnet, and P is the differentialoperator.
Here, the output torque Tout and the relationship between theelectric angular frequency and the output torque on the dq-axis areCurrent
SensingPIABB

1sLcoup.

Fig. 2. Block diagram of the system shown in Fig. 1.

iq

S2PC 2023, Kaohsiung, Taiwan

Table 1. Experimental condition.

controls, and the system becomes unstable when the current control
bandwidth of both the CSTME and the IUT are close. The current
control bandwidth of the CSTME must be designed higher than theone of the IUT in terms of prevention for stability.

SymbolParameter
DC link voltage of IUT
Vdc _IUT
DC link voltage of MEVdc _ME
Coupling inductor
Lcoup.
Current control bandwidth of IUT fc_IUT
Switching frequency of IUT
fsw_IUT
Switching frequency of ME
fsw_ME

3. Experimental Results
Table 1 shows the experimental condition. The switchingfrequency and the DC link voltage of the CSTME should be higher
than that of the IUT.
The PI current control and the feed-forward compensation inorder to cancel the interference between the inductor on the dq-axis
are implemented in the controller of the CSTME. In this paper, notethat the voltage command, which is output from the controller of
the IUT using a D/A converter, is received by the A/D converter of
the CSTME instead of the PWM voltage detection. In contrast,
torque control is implemented in the controller of the IUT. In thiscase, the d-axis current command is set to zero, and the q-axis
current command is determined from the torque command.
Fig. 3 shows the waveform when the torque step applies to theIUT. The current control bandwidth of the IUT is set to 500 Hz. As
shown in Fig. 3, torque and current oscillations are smaller when
the current control bandwidth of the CSTME is higher. In addition,
torque and current oscillations are occurring in Fig. 3 (b) and Fig. 3(c). However, the oscillation is decreasing only in Fig. 3 (c). Thus,
the stability limit of the current control bandwidth of the CSTME isbetween 2000 Hz and 2050 Hz. Therefore, the CSTME requires thecurrent control bandwidth that is approximately four times thecurrent control bandwidth of the IUT.

0Value
280 V
320 V
1.73mH
500 Hz
10 kHz40 kHz5000 r/min/div

Rotational speed

2 N・m/div

0Output torque0q-axis current

5 A/div0Three-phase current

10 A/div
4 msec/div(a) fc_ME is set to 3000 Hz0Rotational speed

5000 r/min/div
2 N・m/div0

Output torque0
5 A/div

q-axis current

4. Comparison with simulation results
In this section, the required bandwidth is obtained by simulation
containing the delay factors. The simulation model is implemented
by a continuous system, and the delay factors are implemented as
the first-order delay. Adding delay factors are as follows:
1) output of PI (caused by voltage command update) (A in Fig. 2)2) current feedback (caused by sampling delay) (B in Fig. 2)
In this simulation, the different sampling delay is added to theCSTME and the IUT because the switching frequency of theCSTME is different from that of the IUT.
Table 2 shows the error rate between the stability limit obtainedby simulation and one of the experiments. In this case, the stability
limit of the CSTME obtained by experiments is 2050 Hz. The
stability limit without the delay factor is 991 Hz with an error rateof 51.6% compared to the experimental result. In the case of adding
the delay factor of 1), the stability limit is 1501 Hz with an error
rate of 26.8%. Furthermore, adding the delay factor of 2), an error
rate decreases to 16.4%. In this case, the stability limit is 2386 Hz,
which is higher than the experimental limit because theexperimentally limit is lower due to the damping factor, which islosses of the circuit. From these results, the stability limit of theCSTME is estimated with high accuracy by containing the delay
factors 1) and 2).

0
Three-phase current

10 A/div
4 msec/div(b) fc_ME is set to 2050 Hz0Rotational speed

5000 r/min/div
2 N・m/div0

Output torque

0q-axis current

5 A/div

0
Three-phase current

10 A/div
4 msec/div(c) fc_ME is set to 2000 Hz
Fig. 3. Waveforms of torque step response when fc_IUT isset to 500 Hz.
Table 2. Relationship between stability limit and delay factor.

References

Stability limit Error
condition
51.6%
Without delay factor
993 HzWith delay factor of A in Fig. 21501 Hz
26.8%
With delay factor of A and B in Fig. 22386 Hz16.4 %[1] K. S. Amitkumar, R. Sudharshan Kaarhik, and Pragasen Pillay, "A Versatile
Power-Hardware-in-the-Loop Based Emulator for Rapid Testing of Transportation

Electric Drives," in IEEE Transaction on Transportation Electrification, vol. 4, no.
4, December 2018.