IEEE Electrification Magazine - December 2017 - 55

we present a specific identification method of PMSMs. This
identification scheme has the advantage of evaluating the
magnetic saturation level according to the rotor position
and the stator current level in static behavior only. In a second step, we show how to build lookup tables for optimal
weakening control in both axis voltages by using optimization algorithms that give the maximum torque with the
minimum current level. These lookup tables are used not
only to expand speed range but also to compensate the
magnetic saliency created by the magnetic saturation.
Finally, an example with real data is presented to illustrate
the sequences and relevance of this method.

Let P = " A, B, C , , the index of the motor phases. The flux
equations are given by
dz P
= VPN - R P I P.
dt

(2)

Thus, the flux is given by
z P (t) = z 0 +

#

t

0

+Vcc
A

+Vcc
A IA = I0 3
2

IA = I0

An Identification Scheme of PMSM
The system PMSM with an inverter has an operating field
(torque versus speed) limited by the available power voltage, the maximum current level, and the magnetic saturation level. For optimal control of the system, it is
necessary to take into account this operating field (torque
versus speed, power voltage, and current level). For that
purpose, precise knowledge of the motor is required. With
this in mind, we propose a static method that, with zero
speed, identifies the magnetic flux and torque levels
according to the rotor position and the stator current level.

Electrical Installation
This identification procedure requires the following
measurements: angular position, torque motor, current,
and power-supply voltage. The electrical installation
can be given by two possible configurations, as illustrated in Figure 1. In this study, we chose the configuration
in Figure 1(a). Prior to applying any voltage, the electrical position of the motor at 0° must be identified to calibrate the position sensor. To do this, the motor is left
freewheeling, and a low voltage is applied, inducing a
positive current, I d. The motor naturally aligns with the
equilibrium position. Then, the position of the motor at
0° is noted, as shown in Figure 2. Once the motor shaft
is fixed by the bench, we then check the direction of the
positive torque.
The aim of this test is to excite the whole with several
levels of current I 0 (I 0 from 0 to I max A) for each electrical
position, varying from 0 to 360°. Notice that, for each rotor
position, the motor shaft must be fixed by the bench. The
voltage +Vcc is a staircase signal, which goes from 0 V to
the maximum voltage producing the maximum current
in phase A as I 0 = I max for a given rotor position, as seen in
Figure 3. The duration of the step must be enough to have
a constant current at the end of each step.

VAN
dc +
-
IC

N
IB

IC

IB
VBN

C

VBN

B

C

0V
(a)

B

0V
(b)

Figure 1. The electrical installation: (a) the configuration chosen for this
study and (b) an alternative possible configuration.

Torque
(N . m)

Id > 0
Iq = 0
0° position

Teta (°)

Figure 2. The process of finding the equilibrium position.

+Vcc (V)

I0(A)
- 100

- 40
- 30
- 20

We can easily identify the stator resistance, Rp, in the static regime for each stair indexed by i, based on the mean
square of the equations

- 10

(1)

VAN
dc +
-

N

Data Processing

3 ^ h ^
h
2 R p I A i = VAN - VBN i .

(3)

(VPN (u) - R P I P (u)) du.

Time (s)
Figure 3. The waveform of the voltage and current for a given
rotor position.

IEEE Elec trific ation Magazine / D EC EM BE R 2 0 1 7

55



Table of Contents for the Digital Edition of IEEE Electrification Magazine - December 2017

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