平成 27 年電気学会産業応用部門大会

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Online q-axis Inductance and Resistance Identification of IPM Synchronous
Motor Based on Relationship between Its Parameter Mismatch and Current
Xiang Ji*, Toshihiko Noguchi (Shizuoka University)
This paper proposes a new approach to achieve online identification of the q-axis inductance and the resistance of an interior
permanent magnet synchronous motor (IPMSM) based on the relationship between the q-axis inductance mismatch and thed-axis feedback current.

The value of the d-axis feedback current depends on the inductance mismatch, and the consecutive

samplings of the d-axis feedback current make it possible to calculate the true value of the inductance.

After the q-axis

inductance is identified, the resistance also can be identified by using the same identification system.

The proposed

identification technique is examined through some computer simulations and experiment tests.

The test results demonstrate thefast convergence of the identified value to the true one with a small error.
Keywords：interior permanent magnet synchronous motor, online, parameter, identification, P control, PI control

1. Introduction

MotorController

In recent years, interior permanent magnet (IPM) motors areid

widely used in a variety of industry, home appliance and+-automotive applications, owing to their high-efficiency andhigh-power-density features.

The IPM motor is usuallycontrolled by means of a field-orientation technique (vectorcontrol), and requires a current controller on the synchronous
rotating

referenceframe(dq-reference-frame)

instantaneous torque and the magnetic flux control.

for

*+

the+

PI-PI+-1sLd  R++

 L̂qLqL̂dLdPI-++-+-id

1sLq  Riq

The current
Fig. 1. Field-oriented control system of IPM motor.

control on the dq-reference-frame mainly consists of thecoordinate transformation, the PI regulation, and the decouplingidcompensation, which is based on the mathematical model of themotor.

+-Figure 1 shows the field-oriented control system of theIPM motor.

As can be seen in the figure, it is indispensable forthe controller not only to detect the magnetic-pole-position andthe motor currents, but also to know the motor parameters
accurately because the controller has an inverse model of themotor.

P*

Identification of the motor parameters is significantly++PI-+-1sLd  R++

 L̂qLqL̂dLdPI-+++--id

1sLq  Riq







important to control the motor properly in starting up of the(a) Proposed Lq identification system.

control as well as the running operation, and the on-line
parameter identification is particularly required during therunning condition.

This paper proposes a novel technique to+id

-Pachieve the on-line identification of the IPM motor parameters,
which requires only the d-axis feedback current information ofthe motor.

1R++

ωLˆqLqPI1sLq  RidThe proposed technique employs a P regulator

instead of the PI regulator in the d-axis current control loop.
Using this technique, the q-axis inductance Lq can be estimatedby checking the d-axis feedback currents twice when the motor is
working in the steady state. Some computer simulations andexperimental+-tests

havebeen

conductedtocheckthe*+PI-+-iq

(b) Simplified Lq identification system.

Fig. 2. Online Lq identification system.

1／4［ III - 239 ］Ⓒ 2015 IEE Japan平成 27 年電気学会産業応用部門大会

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identification performance of the proposed technique in theIdpaper.

Id1

P1
P2

Id2

2. Proposed Identification TechniqueFigure 2(a) shows the proposed Lq identification system.

In0the system, the PI regulator used in the d-axis current control loop

Lq1

Lq2

LqL̂qis replaced with a P regulator. Because the P regulator is unableto eliminate the steady-state error, the mismatch of Lq affects theFig. 3. Relationship between L̂q and Id.

d-axis feedback current. Figure 2(b) shows the simplified Lq
identification system. From Fig. 2(b), the rotation speed is equal
I d*

to its command, and the q-axis current is stable when the motor isoperated in the steady state because both of the controllers consistof the PI regulators.

Id

By setting the d-axis current command atzero, the d-axis feedback current can be expressed asId I qKd  R( Lq  Lˆ q ) .

Lq(1)

L̂ q

From (1), it is found that the mismatch of Lq has a linear
relationship with the d-axis feedback current Id when thecommand of the d-axis current is set at zero.

I q*

Based on thisIq

linear characteristic, it is possible to estimate the true value of Lq.
As shown in Fig. 3, the basic mathematic knowledge tells that if*

two points on the straight line is given, the whole equation of theline is known.
By setting two different arbitrary values of Lq to the controller,
which may have the parameter mismatch, two corresponding

Fig. 4. Confirmation of relationship between L̂q and currents.

d-axis feedback current values are recorded in the memory.
Assuming that the following consecutive sampling actions areperformed:
Id = Id1 when Lˆq  Lq1 , and
Id = Id2 when Lˆ q  Lq 2 ,the true value of Lq can be calculated by the following equation:
Lq I d 1 Lq 2  I d 2 Lq1
I d1  I d 2.

L̂q(2)

Equation (2) implies that the true value of Lq can be calculated
regardless of any parameters and any variables used in (1).
Therefore, the proposed identification technique requires only thed-axis feedback current information to estimate Lq.

3. Computer Simulation Results

Fig. 5. Simulation result of Lq identification.
Table 1. Parameters of test IPMSM.
Number of poles
4
Winding resistance
4.3 ΩGain of d-axis P regulator
1 V/A
q-axis inductance
67 mH
d-axis inductance
27 mH
Setup d-axis inductance
1.0 mH
Field flux linkage
0.544 Wb
Setup field flux linkage
1.0 WbRotation speed
6000 r/min

Some computer simulations have been conducted to verify theidentification performance of the proposed technique.

Table 1shows the test motor parameters which are used in thesimulations.
Figure 4 shows at here helps to confirmed the linear
characteristic which mentioned in Equation (2).
the L̂q linear in the controller, the d-axis
decreased linear.

After increase

feedback current

Based on this simulation result, the two-point
speculate method is possible to adapt the online identification.

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Table 2. Physical constants of test setup.
SymbolDescriptionValue

0.08

L q (H)

0.06

Winding resistance

0.48 Ω

Ldd-axis inductance

13.0 mH

Lq_id

Lqq-axis inductance

24.5 mH



Magnetic flux linkage

0.0674 Wb

Kdd-axis P regulator gain

5.0 V/A

^

0.04

R

Lq_d

0.02
0.00
050

100t (ms)150200(a) L̂ q and its identified value.

p

Number of poles

6ζDamping coefficient

0.0002 Ns/r

Po

Rated output power

1.5 kW0.05

0.0

Id-0.20.04
L q (H)

0.03^

Id (A)

Idav-0.4

Lq_d0.02

Lq_id0.01-0.6050

100t (ms)

150

0.00
-400

200t (ms)0200(a) q-axis inductance.

(b) d-axis current.

3.6

3.0

Iq

2.7

Iqav

1.8

I (A)

2.0
Iq (A)

-200

1.0

Iq_av
Iq_comd
Id_comd
Id_av

0.9
0.0

0.0
050

100t (ms)

150

-0.9
-400

200

-200

0200t (ms)(b) Current waveforms.

(c) q-axis current.

Fig. 7.

Experimental result of Lq identification.

5.0
 (rad/s)

rad_comd
radvalue is 66.48 mH, where the true value is 67 mH.

4.0

Theidentification error is 0.78 %, and the convergence time for theidentification is only 0.08 s.

3.0
2.00

4. Experiment Result of Lq Identification
Experimental tests have been conducted to confirm the current

50

100t (ms)

150

200

and the Lq identification characteristics.

The experimental setup

parameters are listed in Table 2.
Figure 6 shows theexperimental results when L̂q is intentionally changed as(d) rotation speed.

Fig. 6. Experimental result to confirm relationship betweenL̂ q and currents.

indicated by the dotted line in Fig. 6(a).

While L̂q is changed,

the d-axis current and the q-axis current vary as shown in Fig.
Then another simulation result is shown in Fig. 5 which uses
the proposed identification theory.

The rotation speed and theq-axis current are controlled to be equal to their commands.

AsL̂q of the controller changes from Lq1 to Lq2 and so on, the d-axis

feedback current also changes accordingly.

The final identified

6(b) and Fig. 6(c). From the results, the d-axis current decreases
linearly with L̂q , while the q-axis current is kept stable as
described in the theoretical consideration.

The identified value

is around the true value and the error is within 15 %.

As thed-axis current decreases, the identification result exhibits

3／4［ III - 241 ］Ⓒ 2015 IEE Japan平成 27 年電気学会産業応用部門大会

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speculate method can be effectively used to identify Lq.

0.045

If Kd ischanged to another value, it is possible to adjust the identificationtime.

Lq (H)

0.030

One of the most important advantages of the proposed

0.015

Lq_didentification method is no sensitivity to the winding resistance.

Lq_id

Figure 8 shows the identification result with the extra resistanceadded to the motor windings.

0.000-100-500t (ms)

50

100

9.8 %.

(a) q-axis inductance.

I (A)5. Winding Resistance Identification

Iq_comd
Iq_av
Id_comd
Id_av

2.0

The same system can be used for the winding resistanceidentification. After Lq is identified as described in the previous

1.0

section, the system is changed to the configuration shown in Fig.

0.0

9.

-1.0-100-500t (ms)

50

100

following equation:

R.

*R

Experimental result of Lq identification with extra

+id

+-+

PI-

By giving a certain value of the d-axis current command,e.g., i d*  1 , the winding resistance R can be calculated by the(b) Current waveforms.

Fig. 8.

By setting Kd = 5, the identification time can beshortened to 80 ms.

4.0
3.0

After consecutive sampling of thecurrents, the final result is obtained as 26.9 mH and the error is

K d (id*  id ).
id(3)Figure 10 shows the experimental result. The identification result
is 0.493 Ω and the true value is 0.48 Ω, where the identification

P1RidPI1sLq  Riq-error is within 2.7 %.

6. Conclusion
An online parameter identification technique of the IPM motor

has been proposed in this paper. The most unique features of theFig. 9.

Simplified R identification system.

technique are capability to identify Lq and R by using only the1.5

motor d-axis feedback current information, and robustness to theRidenR ()1.2

winding resistance variation as well as the control variables.

RrealAccording to the simulation and the experiment results, theRave

proposed technique can estimate Lq and R within the identification

0.9

error of 9.8 % and 2.7 %, respectively. The identification takes

0.60.3

100 ms. In the future, the identification of the other motor
parameters will be presented on the basis of the same algorithm.
0204060t (ms)Fig. 10.

References

Experimental result of R identification.
(1)

tendency of the decrease due to the magnetic saturation.

Basedon Fig. 6(d) in the identification, the speed is kept stable even it
go over the command signal the PI regulator can recovery it.
But based on Fig. 6(b) when the L̂q far beyond true value the(2)current fluctuation be came larger.
Fig. 7 gives an experiment result by employing the two-point
speculate method.

(3)

For checking the current, Kd is changed to a

low value such as 1.0.

Because of that the identification also

caused more time.

The result is 27.3 mH, where theidentification error is 11.3 %.

This result shows two-point(4)

Xiang Ji and Toshihiko Noguchi, “Off-line Parameter Identification ofInterior Permanent Magnet Motor by Searching Minimum Point of Current
Norm Characteristics,” International Symposium on Power Electronics,Electrical Drivers, Automation and Motion pp. 282-287(2014)
Toshihiko Noguchi, Shigenori Togashi, and Ryo Nakamoto,“Short-Current Pulse-Based Maximum-Power-Point Tracking Method forMultiple Photovoltaic-and-Converter Module System,” IEEE Trans. on
Ind. Elec. Vol.49, pp.217-223 (2002)
J.K. Seok, K.T. Kim, and D.C. Lee., “Automatic mode switching of P/PI
speed control for industry servo drives using online spectrum analysis oftorque command,” IEEE Transactions on Industrial Electronics, Vol. 54,pp. 2642-2647 (2007)
B.K. Bose, “A High-Performance Inverter-Fed Drive System of an Interior
Permanent Magnet Synchronous Machine,” IEEE Trans. on Ind. Appl.,
vol. 24, pp. 987-997, Sep./Oct. 1988.

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