XXIV Symposium
Electromagnetic Phenomena in Nonlinear Circuits
June 28 - July 1, 2016 Helsinki, FINLAND
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HARMONICS LOSSES IN HIGH-SPEED PM SYNCHRONOUS MACHINE
Irina Kruchinina, Member, IEEE, Yuvenaliy Khozikov, Alexandr Liubimtsev, Valentina Paltceva, Member, IEEE
Federal Agency for Scientific Organizations, Institute of Silicate Chemistry Russian Academy of Sciences
2, Makarova emb., 199034 St. Petersburg, Russia, e-mail: ikruch@isc.nw.ru, khozikov2010@yandex.ru, alex@tor.ru, valya_vp@bk.ru
Abstract - This paper presents the numerical method of the air gap
magnetic flux harmonics calculation in synchronous machine with
permanent magnet excitation. The method is based on the FEM
simulation. The model takes into account stator tooth zone design,
asymmetrical magnetic reluctance of salient pole rotor, steel parts
saturation. The harmonic analysis results are used as an input
data for the eddy losses calculation and heating evaluation. The
method is fast and highly automated, it does not require transient
with motion electromagnetic analysis, static and quasi-static (timeharmonics) problems are simulated instead.
I. INTRODUCTION
The overheating of permanent magnets (PM) is one of the
aspects that should be carefully examined in high-speed
synchronous machine in the design process [1]. The magnets
are heated due to eddy current losses, induced by high-order
magnetic flux harmonics. The source of these harmonics –
non-symmetrical stator winding construction, stator toothzone design, ferromagnetic materials saturation. Analytical
methods (for example, [2]) of magnetic flux harmonics
evaluation induced by 3-phase winding cannot deal with
saturation.
The method based on FEA [3] is proposed. In general, the
transient (with motion) nonlinear electromagnetic analysis is
required to calculate eddy currents in moving body. Some
assumptions (synchronous speed operation mode, constant
load, negligible eddy current shielding effect in permanent
magnets) allows to replace full transient electromagnetic
analysis with a series of static magnetic simulations. The air
gap magnetic flux harmonics are calculated with respect to
the actual geometry (different reluctance of rotor along d/q
axis, toothed stator, core saturation). Once the magnetic flux
harmonics are derived it is possible to run quasi-static (timeharmonics) simulation to calculate induced eddy currents in
rotor elements. The calculations are performed separately for
each harmonic. The total loss is then composed as a sum of
losses generated by each harmonic. The losses distribution is
used as an input data for heat transfer analysis.
The method was implemented as 2D, as many authors [4]
indicate that 2D analysis is sufficiently accurate for traditional
PM synchronous machine (ratio of rotor length to rotor
diameter is about 2, see datasheet Table I). The 3D simulation
is an option; it may be required in the case of skewed stator
slots, different length of stator and rotor lamination.
Fig.1. Geometry model of PM synchronous machine. Thick black circle
around the rotor represents the sleeve
II. HARMONIC ANALYSIS
A series of magnetostatic 2D problems is simulated. For
each problem the momentary values of stator winding
currents and the rotor position (angle of rotation) are assigned
(see Fig. 1). It is presumed that load angle and phase current
amplitude are time independent values (this corresponds to
the synchronous rotation speed mode with constant load).
Fourier transformation of the resulting air gap magnetic flux
distribution yields harmonics magnitude and phase. The
transformation is performed for each problem in the series
(i.e. for each moment of time).
This set of simulations reveal that for specific magnetic
flux harmonics their magnitude and phase changes in time. If
we consider the rotor as motionless and the stator as rotating,
that we can distinguish three types of magnetic flux
harmonics: motionless harmonics are placed stationary with
rotor, oscillating harmonics and rotating harmonics.
To reveal the nature of these harmonics four cases were
analysed. The case 1 – smooth stator without winding. As the
rotor is the only source of magnetic field, all magnetic flux
harmonics are of motionless type. The case 2 – smooth rotor
(made of steel). The 3-phase stator winding produces
magnetic flux harmonics of forward and backward rotation
[2]. The order of harmonics can be calculated as (6k±1).
Harmonics of (6k+1) order rotates in the same direction with
rotor; harmonics of (6k-1) order rotates in opposite direction.
On Fig. 2. the harmonics produced by rotor PM and by the
stator winding are placed on the same plot.
TABLE I
SYNCHRONOUS MACHINE DATASHEET
Rotor diameter 53 mm
Stator lamination length 104 mm
Frequency 800 Hz (48000 rpm)
Phase current 400 A per slot (RMS value)
Angle between rotor and stator magnetic flux is 157°
Fig. 2. Rotor magnetic flux harmonics spectrum (case 1), stator magnetic flux
harmonics spectrum (case 2), negative values means backward rotation
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The result of rotor and stator magnetic flux interaction is
studied in case 3a – the full-featured geometry of salient-pole
rotor and stator tooth-zone with respect to predefined load
angle and steel parts saturation. Fundamental harmonic of
magnetic flux stay motionless with rotor and could be
calculated as the vector sum of stator and rotor fundamental
harmonics. Higher harmonics interaction is more complex
and produces oscillating harmonics (such as 5, 7, 11, 13),
which are the sum of motionless and rotating harmonics of
the same order. Stator winding magnetic flux harmonics that
does not have matching rotor harmonics are purely rotating
harmonics (such as 23, 25). Fig. 3 shows the resulting
magnetic field harmonics spectrum.
III. PERMAMENT MAGNETS HEATING
The only heat sink available is the rotor surface. The
thermal flux through shaft and bearing is negligible.
Convection coefficient from the rotor surface is estimated to
be 80 W/(m2·K) [5]. Permanent magnets are in close contact
with rotor elements (core and sleeve) so eventually all
elements heated up to the same temperature. Thermal analysis
yields the overheating of the magnets to be of 145 °C. It is
well below the Curie temperature for NdFeB magnets
(310 °C) [6].
rotating
Fig.4. Total rotor losses produced by high-order rotating magnetic field
harmonics. Numbers denote the harmonic order with respect to the
fundamental harmonic (800 Hz)
IV. CONCLUSIONS
oscillating
rotating
Fig. 3. Magnetic flux harmonics magnitude and phase fluctuation during
rotor rotation (case 3a) as seen from rotor.
The case 3b is the same as case 3a but with rotor static
eccentricity of 10% of the air gap length. Rotor eccentricity
breaks the magnetic circuit symmetry, and adds odd
harmonics to magnetic flux spectrum. The described above
analysis was performed. It reveals that total odd harmonics
distortion coefficient is about 4%. Such a small distortion
(despite the large change of 10% in the air gap length) is
related to the fact that PM permeability is close to unity. The
effective non-magnetic gap is much longer than the geometric
air gap.
Steady state magnetic analysis can be successfully applied
for air gap magnetic flux harmonics evaluation for traditional
synchronous machines. The key is to solve series of
problems, thus revealing the harmonic dynamics. The
superposition of losses produced by each harmonic gives the
total Joule losses. These losses are primary located inside the
sleeve and on sleeve surface. The sleeve-to-magnet thermal
resistance is a small value so all rotor elements features the
same temperature. Losses heating cause significant, but not
severe temperature rise. The analysis was performed for the
case of stator winding fed with smooth sinusoidal wave. In
case the stator winding powered from inverter, the heating
might increase. The proposed method could handle that case
too.
II. PERMANENT MAGNETS EDDY CURRENTS
ACKNOWLEDGEMENTS
High order rotating magnetic flux harmonics induce eddy
currents in the rotor elements. Oscillating harmonic can be
presented as a sum of the rotating and motionless parts.
Motionless (stationary placed with rotor) magnetic harmonic
does not induce eddy currents in rotor elements. To calculate
the eddy current the rotating magnetic field of proper
amplitude, frequency and pole-number is injected in the air
gap by means of artificial boundary condition.
The result of time-harmonic (AC) analysis is the eddy
currents and Joule losses distribution in the conducting
elements of the rotor. FEM simulation allows to calculate
losses separately for each part (core, PM, sleeve). The losses
are distributed mainly in the sleeve, only 9% of volume losses
are generated in PM.
As it is shown on Fig. 4, the 5th, 7th, and tooth order 23th
and 25th magnetic flux harmonics are main contributors to the
rotor eddy losses. Total losses value is used as an input for
thermal analysis.
This work was supported in part by the RFBR under Grant
14-08-00817.
REFERENCES
[1] Adrian Mlot, Marian Lukaniszyn, “Magnet eddy-current loss reduciton
in a high-speed permanent magnet machine with concentrated windings”,
Maszyny Elektryczne – Zeszyty Problemowe Nr 3/2015 (107), pp. 31-37.
[2] Slobodan N. Vukosavic, “Electrical Machines”, Springer Science &
Business Media, pp. 650, 2012.
[3] ELCUT - finite element analysis system. Version 6.0. User's guide,
2013. Tor Ltd. , Saint Petersburg, Russia, 295.
[4] Rafal Marek Wojciechowski, Cezary Jedryczka, Andrzej Demenko, Jan
K. Sykulski, “Strategies for two-dimensional and threedimensional field
computation in the design of permanent magnet motors”, IET Sci. Meas.
Technol., pp. 1–10, 2015.
[5] David A. Howey, Peter R. N. Childs, Andrew S. Holmes, “Air-Gap
Convection in Rotating Electrical Machines”, IEEE transactions on
industrial electronics, vol. 59, No. 3, pp. 1367–1375, 2012.
[6] https://en.wikipedia.org/wiki/Neodymium_magnet.
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Proceedings of EPNC 2016, June 28 - July 1, 2016 Helsinki, FINLAND