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IEEE TRANSACTIONS ON ENERGY CONVERSION 1
Parameter Identification of Multiphase Induction
Machines With Distributed Windings—Part 1:
Sinusoidal Excitation Methods
Alejandro G. Yepes, Member, IEEE, Jose A. Riveros, Jes´ us Doval-Gandoy, Member, IEEE,
Federico Barrero, Senior Member, IEEE,
´
Oscar L ´ opez, Member, IEEE, Blas Bogado, Student Member, IEEE,
Martin Jones, and Emil Levi, Fellow, IEEE
Abstract—Multiphase induction machines (IMs) are gaining in-
creasing interest in industry due to their numerous advantages over
the conventional three-phase ones. A lot of different parameter es-
timation methods have been developed for three-phase IMs, but the
existing literature regarding specific identification techniques for
multiphase IMs is almost nonexistent at this point. This paper pro-
poses simple offline methods to estimate the stator resistance and
stator leakage inductance of multiphase IMs with distributed wind-
ings, under different conditions, utilizing the machine’s degrees
of freedom associated with the nonflux/torque producing current
components. Once these parameters are identified, the rotor ones
can be easily calculated by combination with the total values ob-
tained from locked-rotor tests. The procedure enables segregation
of the stator and rotor parameters in a simple manner, something
that is very difficult to achieve in three-phase IMs where, usually,
equality of leakage inductances and a constant stator resistance
are assumed. In this manner, the magnetizing inductance can be
then also more accurately assessed from no-load tests, because the
error in its estimation that would be caused by assuming both leak-
age inductances to be equal is avoided. The proposed methods are
experimentally tested on two different five-phase IMs.
Index Terms—Experimental testing, multiphase induction ma-
chines (IMs), parameter estimation.
NOMENCLATURE
Variables
h Harmonic order. The sign of its
value indicates positive- or negative-
sequence.
i
r
Rotor current.
Manuscript received May 16, 2012; revised August 17, 2012; accepted
September 14, 2012. This work was supported by the Spanish Ministry of
Science and Innovation and by the European Commission, European
Regional Development Fund (ERDF) under Project DPI2009-07004 and Project
DPI2012-31283. Paper no. TEC-00171-2012.
A. G. Yepes, J. Doval-Gandoy, and
´
O. L´ opez are with the Department
of Electronics Technology, University of Vigo, Vigo 36310, Spain (e-mail:
agyepes@uvigo.es; jdoval@uvigo.es; olopez@uvigo.es).
J. A. Riveros and F. Barrero are with the Department of Electronic Engineer-
ing, University of Seville, Seville 41004, Spain (e-mail: jariveros@esi.us.es;
fbarrero@us.es).
B. Bogado is with the Department of Systems and Automatics, University of
Seville, Seville 41004, Spain (e-mail: bbogado@esi.us.es).
M. Jones and E. Levi are with the School of Engineering, Technology and
Maritime Operations, Liverpool John Moores University, Liverpool, L3 3AF,
U.K. (e-mail: m.jones2@ljmu.ac.uk; e.levi@ljmu.ac.uk).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEC.2012.2220967
i
s
Stator current.
k ∈ [1,ρ] Identifier of x–y plane.
L
lr
Rotor leakage inductance.
L
ls
Stator leakage inductance.
L
m
Mutual inductance.
L
r
= L
lr
+ L
m
Rotor self-inductance.
L
s
= L
ls
+ L
m
Stator self-inductance.
n Total number of phases.
n
ω
=(ω
s
− ω
r
) /ω
s
Slip (normalized).
p ∈ [0,n − 1] Phase identifier. Takes a value
0, 1, 2, ... to denote phases
a, b, c,..., respectively.
R
r
Rotor resistance.
R
s
Stator resistance.
ρ = ⌈n/2⌉− 2 Total number of x–y planes.
s Generic signal that may be replaced
by i
r
, i
s
or v
s
.
v
s
Stator voltage.
ω
k
≥ 0 Frequency in the kth x–y plane. A
sign is added in front to indicate
positive- or negative-sequence.
ω
r
Rotor angular speed (electrical).
ω
s
Synchronous frequency (electrical).
Other symbols
x Estimated value of x.
x Complex conjugate of x.
⌈x⌉ Maps x to the smallest following in-
teger (ceiling function).
⌊x⌋ Maps x to the largest previous inte-
ger (floor function).
|x| Absolute value of x.
|x| Module of x.
∠x Phase of x.
[X]
−1
Inverse of [X].
[X]
T
Nonconjugated transpose of [X].
[X
m
] mth row of [X], with m ≥ 1.
j =
√
−1 Imaginary unit.
Bold symbols denote complex values and nonbold symbols
denote real values. Capital letters inside brackets denote arrays.
I. INTRODUCTION
M
ULTIPHASE induction machines (IMs) offer several
advantages over their three-phase counterparts [1], [2].
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