XXIV Symposium
Electromagnetic Phenomena in Nonlinear Circuits
June 28 - July 1, 2016 Helsinki, FINLAND
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COMPARATIVE ANALYSIS OF THE THREE PHASE AND SIX PHASE
FRACTIONAL SLOT CONCENTRATED WINDING PERMANENT MAGNET
MACHINES
Cezary Jedryczka
Poznan University of Technology, Institute of Electrical Engineering and Electronics
Piotrowo 3a, 61-138 Poznań, Poland, e-mail: cezary.jedryczka@put.poznan.pl
Abstract - The paper deals with comparative analysis of the
permanent magnet synchronous motors with concentrated
windings. The classical 3 phase machines have been compared to
the multiphase, multi-star machines on a case study design. As
figures of merit the back electromotive force (emf) and
magnetomotive (mmf) force distortions as well as torque and
torque pulsation factor have been considered. The analyses have
been performed using own developed code for the synthesis and
analysis of the multiphase winding layouts, and professional FEM
package Maxwell for the torque, back emf and torque pulsations
studies. The nonlinearity of the magnetic circuit has been taken
into account.
phase character of considered drives such machines and their
supply systems can be called as multi-star [2]. Example of
using a multi-star supply system to power real 6 phase PMSM
machine has been illustrated schematically in Fig. 1.
b)
I. INTRODUCTION
Permanent magnet synchronous machines (PMSM) with
the fractional slot concentrated windings (FSCW) in relation
to the classical three phase machines with distributed
windings have lower cost of windings design, shorter end
turns, lower winding resistance, lower leakage and lower
mutual inductances, all contributing to the increase of
performance and efficiency [1, 3, 4]. The advantages of
PMSM machines with FSCW are especially apparent for low
speed applications such as direct drive torque motors, elevator
industry, marine propulsions systems as well as in wind
turbine generators [3, 4, 5, 6]. However, these machines
suffer from relatively high torque ripple and stray losses [3]
due to nonlinearity of the magnetomotive force (mmf) space
distribution. To mitigate these problems, the winding layouts
producing mmf space distribution with low content of sub and
super harmonics are searched for. As a one of the solutions
utilization of machines supplied from sources with a number
of phases greater than 3 is considered. Based on published
results and our own experience, these multiphase machines
offer many advantages, including: low distortion of mmf
waveform, low torque ripple, high winding factor and high
efficiency [1, 2, 5, 6]. On the other hand, powering and
controlling machines with 5, 7 or 10 phases, in spite of
continuous lowering costs of the semiconductor switches,
require development of customized inverters and novel
control strategies. To reduce inverter costs, the multiphase
machines discussed here contain the number of phases in
multiple of 3, facilitating the application of commonly used 3
phase intelligent power modules (IPM). In other words,
m phases machines described herein may be powered by a
given number k=m/3 of 3 phase drives/inverters. While these
drives must be synchronized with proper shift angle β
between the 3 phase stars of currents, the galvanic connection
between drives is not necessary. To indicate the multi three
Fig.1. Illustration of multi-star supply system for real 6 phase PMSM a);
phasor diagram b)
II. SYNTHESIS OF THE MULTI-STAR FSCW
For the synthesis of multi-star, multiphase FSCW windings
author developed own computer code. The winding layout is
searched for the desired number of phases and slots of the
machine basing on the mmf space distribution analysis using
mathematical programming methods. Winding patterns with
the highest winding factor and lowest total harmonic
distortion factor (THD) of mmf space distribution passing the
symmetry condition are determined after large number of
Monte Carlo procedure calls. To determine THD of mmf
space distribution and fundamental winding factor the Fast
Fourier transform (FFT) algorithm has been used. The
winding symmetry condition has been defined as follows:
∑∑ ( h
n−1
p
j =1 u =1
j
u
)
− huj +1 ≤ ε
(1)
where n is assumed number of time instants in single period of
supply system, hu is amplitude u-th harmonic of mmf, p is the
number of considered mmf harmonics, ε is setpoint accuracy.
In the time domain studied multi-star voltage systems can be
described by set of phasors defined as:
2


u i , j = U m sin ωt − ( j − 1) π − (i − 1) β
3


(2)
where i=1...k, j=1,2,3 and β = π/m.
The phasors in the considered system are described by
numbers from 1 to 2m - see the example phasor diagram of
the real 6 phase system shown in Fig.1. It can be noted that
the shift angle β between the 3 phase stars defines also the
phasors’ angular offset for whole 6 phase system.
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II. CASE STUDY PROBLEM
As a case study problem the comparative analysis between
3 phase and 6 phase PMSM machines has been performed.
For both 3 and 6 phase machines the single layer (SL) and
double layer (DL) winding designs have been tested. To
eliminate influence of the magnetic circuit geometry the 3
phase and 6 phase machines differs only in the winding
design. Studied machines have 48 slots in the stator and 44
poles in the rotor. The machines of 3 different rotor structures
have been examined. The structures of the rotors and major
dimensions of the magnetic circuit have been shown in Fig. 2.
Fig.2. Stator and the considered rotor structures of studied PMSM machine,
a) SIPM; b) SPM and c) IPM
Fig.4. Comparison of: a) average electromagnetic torque Tav; b) torque
pulsation factor εT
III. RESULTS
IV. CONCLUSIONS
In the first step the analysis of mmf space distribution has
been performed for studied 3 phase and 6 phase single and
double layer winding layouts. The values of fundamental
winding factor (kwf), percentage value of the highest subharmonic of mmf (Smax) and order of the highest sub-harmonic
of mmf (Smax order) have been summarized in Table I.
Analyzing presented selected results it can be concluded
that considered six phase windings layouts are characterized
by lower content of sub-harmonics in the mmf waveform as
compared with the studied 3 phase FSCW machines. Also all
studied multiphase machines exhibited higher average value
of the electromagnetic torque as compared to the reference 3
phase machines. Moreover, the investigated multiphase
PMSM machines with FSCW are characterized by
significantly lower torque pulsations.
In summary, multiphase machines offer improved
functionality and mitigate known issues associated with
classical 3 phase FSCW machines.
More detailed description of performed studies and
comprehensive report of results will be presented during the
Conference and will be included in the extended version of
the paper.
TABLE I
SUMMARY OF MAGNETOMOTIVE FORSE ANALYSIS
Winding
winding factor kwf
Smax [%]
Smax order
0.958
21.44
14
3ph_SL
0.949
17.15
14
3ph_DL
0.991
13.17
2
6ph_SL
0.983
1.73
2
6ph_DL
Due to nonlinearity of the magnetic circuit in order to
analyze and compare of the performance of the machines
characterized by the abovementioned winding layouts a finite
element method (FEM) has been applied next. Twelve
different field models have been elaborated in the Ansys
Maxwell environment for each winding layout and rotor
structure. Results of performed FEA have been presented in
Fig. 3 and 4 for back emf distortion and electromagnetic
torque waveform analyses, respectively.
ke [%]
Fig.3. Percentage harmonic content ke of the line to line back emf
waveforms for machines with IPM rotor structure
REFERENCES
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Permanent Magnet Machines: Opportunities and Challenges, IEEE TRANS.
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Verification of a Short-Circuit Proof Six-Phase Permanent Magnet Machine for
Safety Critical Applications," Magnetics, IEEE Transactions on , vol.50, no.11,
pp.1,4, Nov. 2014,
[3] Magnussen F, Heinz Lendenmann, Member, Parasitic Effects in PM Machines
With Concentrated Windings, IEEE TRANSACTIONS ON INDUSTRY
APPLICATIONS, VOL. 43, NO. 5, 2007,
[4] Meier F., Permanent-magnet synchronous machines with non-overlapping
concentrated windings for low-speed direct-drive applications, Ph.D.
dissertation, Royal Inst. Technol.,Stockholm, Sweden, 2008.
[5] Piech J., Permanent Magnet Machines for Elevators in Super High-Rise
Buildings, Council on Tall Buildings and Urban Habitat CTBUH 2014, pp. 823,
[6] Scuiller F., Charpentier J., Semail E., Multi-star multi-phase winding for a high
power naval propulsion machine with low ripple torques and high fault tolerant
ability, Vehicle Power and Propulsion Conference (VPPC), 2010 IEEE.
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Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND