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Electrical Engineering in Japan, Vol. 113, No. 7, 1993
Translated from Denki Gakkai Ronbuwhi, Vol.
112-D,
o. 5
May
1993, pp.
483-489
Analysis of Brushless Three-Phase Synchronous Generator
Without Exciter
SAKUTARO NONAKA and
KATSUMI
KESAMARU
Kyushu University
KAZUO
HORITA
Tokyo Electric Power Co.
SUMMARY
Recently, a demand for small-capacity generators
has
k e n increasing
as
electric sources in small ships and
automobiles or
as
portable electric souxes driven by
engines.
It is desired that the structure of small-capacity
generatorsbe simple and robust, and that the generators
be highly reliable, easily maintained and controlled.
This paper describes an analysis of the original
brushless synchronous generator without exciter. The
output voltage can be adjusted in the wide range by
controlling the stator
dc
current. To analyze the
characteristicsof this generator, he finite element method
is applied. It is found that the results of theoretical
analysis agree well with the experimental results.
Key
words:
Brushless synchronous generatoq half-
wave rectifier, finite element method, magnetic field
analysis.
1. Introduction
Smallcapacity
ac
generators often
are
used in
bad
environments such
as
a very hot or very cold climate,
sand storms in the desert, violently vibrating vehicles and
ships, factories filled with corrosive gas, etc. It is also
demanded that they
be
operated without maintenance for
a long time.
AC
generators
used
for these purposes must
have simple structures, high reliability and easy
operability.
Permanent magnet-type and crow-ball-type
synchronous generators
are
brushless. However, the
permanent magnet-type generators
are
not favorable
because of their machining difficulty and impossibility of
field regulation. The crow-ball synchronous generators
also have disadvantages of complicated structure.
Brushless self-excited single-phase synchronous
generators developed by Nonaka [
1-31
produce constant
output voltages without using automatic voltage
regulators and are used widely as portable generators
inside and outside Japan.
The double frequency voltage induced in the field
winding by the negative phasesequence current which is
produced by the single-phase armatu~ eaction is
rectified to produce the field flux. Generators of this type
are
suited for constant-speed operation.
Earlier, we proposed single- and three-phase brush-
less synchronous generators with stator dc excitation
14-
61. These generators are suited for variable speed oper-
ation, and
are
equipped with two sets of stator windings
with a different number of poles. The field windings arc
equipped with diodes to rectify the induced ac currents.
They have very simple structure and
are
of brushless
type.
Experimental results obtained from a 3-kVA test
machine show good operating performances
[7-91.
Shibata proposed
a
brushless self-excited
ac
generator. In this machine, the stator winding is provided
with ac or dc exciting current and the rotor is equipped
with a main field winding and a three-phase exciting
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Fig. 1. Brushless three-phase synchronous
generator.
winding. Since the two rotor windings have a different
number
of
poles, the structure is complicated
[
10, 111.
To solve this difficulty, Shibata proposed a new
scheme in which a single-phase full-wave rectifier circuit
is connected between two midpoints of the two parallel
connected field windings [12, 131. In this scheme, the
four windings are connected so that they constitute a half-
wave rectifier circuit to provide a rectified current to the
field winding. It works in the same manner
as
a brushless
generator proposed earlier by the present autho rs [1-3. 7,
41.
In effect, Shibata s generator is based on the sam e
principle as the stator dc excited brushless generator
proposed earlier by the present authors [7].
We discussed the operating characteristics of a
brushless synchronous generator without exciter; the
stator of this machine is equipped with a two-pole dc
exciting winding and a four-pole three-phase main
winding. The excitation characteristics
are
analyzed
theoretically and the practicality has been confirmed
experimentally.
The flux distribution inside the machine has been
analyzed by the finite element method and it has been
confirmed that the rotor flux is kept constant despite the
presence of a large ripple componen t of field current. The
ig. 2.
Cross
section of generator.
study results have dem onstrated the effectiveness of the
half-wave rectifier circuit [7].
This paper aim s at ana lyzing the brushless four-pole
three-phase synchronou s generator without ex citer by
the
finite element method, taking into account the external
power source [9, 15, 161. The operating characteristics
are
analyzed taking into account the effects of c m
saturation and current interruption of rotor diodes. The
validity of the analysis is co nfirmed by c ompa rison with
experimen tal results. Th e effect of air-gap length on
the
operating characteristics also is analyzed to establish a
guideline for generator design.
2. Circuit Configuration and Machine S tructure
2.1
Circuit
configuration
The circuit configuration of a brushless three-phase
four-pole synchronou s generator is shown in Fig.
1.
The
stator is equipped with four-po le three-phase m ain wind-
ing
W
nd two-pole dc exciting winding W,. he rotor
shown in Fig. 1 is of salient-pole type but the nonsalient-
pole-type rotor can be used in practice
as
well. Four field
windings W,-, to
WM
f the rotor are equipped with diodes
Dfl to Df4 to constitute a half-wave rectifier circuit. The
two-pole static field produced by the stator dc exciting
winding is compensated almost completely by the
ac
component of the field current. Accordingly, the
ac
voltage induced in the exciting winding is very small and
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Table
1.
Specificationof generator winding
I
Items
w1
Number of phases
Number
of
poles
Number
of
slots
Number of coils per phase
Number of coil
turns
Number of turns in series
Per
Phase
4
36
6
20
120
Type of winding Concentric
the constant voltage characteristicsare realized easily by
the stator dc current.
2.2 Machine structure
The cross section of a 3-kVA test machine is
shown in Fig.
2.
The stator core has an outer diametex of
216
mm,
an
inner diameter of
145 mm
and an air-gap
length of 0.5 mm. The laminated core is
120
mm thick.
The winding specificationsof this machine is shown in
Table 1.
3. Analysis by Finite Element Method
3.1 Assumptions
To apply the finite element method, the following
assumptions
are made.
i) The electromagnetic field is two-dimensional
extending in the axial direction.
ii) The eddy current and hysteresis are neglectad.
iii) The skin effect of winding current is neglected
and the current Rows uniformly over the whole cross
section.
iv) The rotor rotates at a constant speed or at a,,,.
v) Leakage fluxes at the coil ends
of
four-pole
main
winding and field winding
are
negligible in corn-
parison with the leakage flux of two-pole exciting
winding.
ing
Field wdg.
w e
1
2
24
12
34
408
Concentric
400
Concentrated
3.2 Fundamental equations
Generally speaking, the two-dimensional electro-
magnetic field in the rectangular coordinate
system
X-Y)
without taking into account the eddy current is expressed
by
where A, is the Z-component of vector potential
A; v
is
the magnetic reluctivity; and J , is the forced current
density representing load current density, field current
density, and exciting current density).
If the load consists of a wye-connected pure
resistance, the voltage equation of the generator is
represented
by
where
R
is the load resistance
of
each phase including the
main winding resistance;
ya,
y,,,
y,
are the flux inter-
linkagesof phase-a, phase-b and phase-c main windings.
The voltage equation
of
exciting winding is given
bY
3)
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etting
of initial values
Calculation of current
variation
61 and
vector
potential variation 64
NO
Fig.
3.
Flow chart for analysis.
where
\y,
is the flux interlinkage of exciting winding;
L,
is the coil end leakage inductance;
Re
is the winding
resistance;
E, is
the
dc
exciting voltage.
respective field windings; and
R
is the rtsiatances of
respective field windings.
Equations 2) to
4)
are approximated by backward
The voltage equation
of
field winding is given
by
difference equations
as
shown below.
For instance, Eq.
3)
is approximatedby
where
v,,, yfl,
Y typo
is the
f lux
interlinkages of
where
A4 a .
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Fig. 4. Finite element subdivision.
The electromagnetic field under discussion is
analyzed by the finite element method taking into account
the external power source using the aforementioned
fundamental equations. The matrix to
be
solved in this
analysis is given in
[15]
and [16].
3.3 Method of analysis
The analysis is conducted following the flowchart
shown in Fig. 3. The motion of the rotor is simulated by
moving the stator coil by one slot at a time in the
opposite direction. The effect of slot harmonics is
neglected, and the effect of core saturation is taken into
account by using the Newton-Raphson method. The
B-H
curve
of
the core is approximated by the following
equations:
For 0
I
B-0.2)2
S 4,
v
=2.873[86+ 14
B - .2))))
~ - 2 0 1 . 1 1 0 ~ ~ - 0 . 2 ) ~ ) 4 1 - 0 . 2 / ~ ~
B2
For B-0.2)2> 4,
~=2, 873 7,92O{ B
.2))
7,2581
3 =17,Y20
X
2,873
1 .2/B
B
To simulate the current interruption, it is assumed
that the rotor diode
turns
on when the winding-induced
voltage exceeds the forward voltage drop
of
diode (0.7
V) and turns
off
when the current vanishes.
ap length nm)
Fig.
5.
No-load characteristics.
4.
Results of
Analysis
Taking into account the asymmetrical flux
distribution, the domain under discussion is divided into
1960
elements
and 1028
nodes.
The generator constants are
as
follows:
Re=7 . 0n ,
LezO.01 H, R/=3.0tl
The effect
of
air-gap length on the no-load voltage
is shown in Fig.
5.
The terminal voltage
E ,
de reeses
in
inverse proportion to the air-gap length if the exciting
current I is less than about 2 A.However, the terminal
voltage decreases monotonically due
to
the core satura-
tion if the exciting current I, is larger than 2
A .
The
flux
distributions in no-load conditions for e,,, = 0,
40
are
shown in Fig.
6.
The field current varies
greatly
because
it flows through the half-wave rectifier circuit but the
field flux is kept almost constant.
Waveforms
of
rotor
flux,
stator flux and terminal
voltage in no-load conditions
are
given in Fig.
7.
As
shown in Fig.
6,
he rotor field flux yt -yp is kept almost
constant while it decays slightly due to the presence of
field resistance.
The current waveforms
in
the no-load conditions
of
3 kW
are
shown in Fig.
8.
The waveform
of
field current
indicates that one diode is in the off-state impectively
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1
6 m =
o
Fig. 6
Flux
distributions with rotor angles at no-load.
Mechanical angle
of rotor n
deg)
Fig. 7. Waveforms of f lux linkages
and
voltage
at
no-load.
E I I O
l*O a d * 11
Mechanical angle
of rotor Om
deg)
: Gaplength
- 0 z m m
Gap
length
- 0 5 m m
:
Gaplength
-
Omrn
_ _
Fig. 8. Waveforms of currents
with
some values
of gap length at
full load.
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I
I
I
39
0 Meas.
voltage
P
-0 .0
0,5
1.0
1.5 1 0
1 5
1.0
3J
Li-.
~ x ~ i t i n gurrent
IS A )
Fig. 9. No-load saturation curves.
of the air-gap length during the 90 deg-period of 6 .
However, the
flux
interlinking with the field winding
in
the off-state is kept constant by the action of thr field
windings in the on-state.
5. Comparisonwith Experimental Results
The no-load saturation curves are shown in Fig.
9.
The
dc
average of field current
or =
< s
proportional to exciting current
I
and the theoretical
value agrees well with the experimental value.
h
5
h
The load characteristics for I
= 2.1
A are shown in
Fig.
10.
The field current is kept constant irrespectively
of load current and air-gap length. The operating charac-
teristics
of
terminal voltage
Ed
becomes more remarkable
as the air-gap length decreases.
The load characteristics forE ,
= 220 V
are shown
in Fig. 11.
In
the case of large air gap, the exciting
current does not vary
so
much but its absolute value is
rather large. This means that the armature reaction can be
reduced by increasing the air-gap length but the required
field current and exciting current
are
increased. For
instance, the excitation
loss,
which is about
130
W
for
the air-gap length of
0.2 mm,
is increased to about
240
W if the air-gap length is as large as 1.0 mm. Therefore,
it is necessary to make the air-gap length as small as
possible in designing the machine.
The m e a d current waveforms in the on-load
condition of 3 kW are shown in Fig.
12.
The effect of
slot ripple
is
observable due
to the
absence of skew slots.
Except for the slot ripple, the measured waveforms agree
well with the theoretical waveforms.
6. Conclusions
The operating characteristics
of
a brushless four-
pole three-phase synchronous generator without exciter
are analyzed by the fink element method. Special
attention is paid to the effect of air-gap length on the
operating characteristics and it has been found that it is
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2
2
4
Load
current I
( A )
Fig. 11. h a d characteristics Ed = 220 V constant .
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0 1 1 0 3 I 4 0 7 2 0
Mechanical
angle
of rotor
8,
degrees)
Fig. 12. Measured waveforms at full load.
desired greatly to reduce the air-gap length as much as
possible.
The generator discussed in this paper is particularly
suited for variable speed operation and maintenance-free
operation.
REFERENCES
1.
Harada and Nonaka. Self-excited single-phase syn-
chronous generator. Patent No. 244444 Sho 33-
2367).
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Nonaka. Jour. I.E.E.,
Japan,
Vol.
82,
p. 627, Apr.
1962.
Nonaka and Muta. Ibid., Vol. 91, p. 1291, July
1971.
Nonaka and Kesamaru. 1981 National Conv.
IEEJ,
No. 701.
Nonaka, Kesamaru and Fujii. Papex of Technical
Meeting on Rotating Machine, I.E.E., Japan,
RM-
S.
Nonaka and
K.
Kesamaru. Brushless Separately-
Excited Three-Phase Synchronous Generator
without Exciter. International Conference on
Electrical Machines, Budapest, p. 446,1982.
Nonaka and Kesamaru. Trans. I.E.E.. Japan, Vol.
S. Nonaka and K.Kesamaru. Analysis of Voltage-
adjustable Brushless Synchronous Generator
without Exciter. I
Trans.
ndustr. Applic., Vol.
S.
Nonaka and K. Kesamaru. Magnetic Field
Analysis
of Brushless
4-pole Single-phase
Synchronous Generator without Exciter.
International Conference on Electrical Machines,
Cambridge, p. 1177. 1990.
F. Shibata ad T.
Fulrami.
A Brushless, Self-Excited
Poly-phase Synchronous Generator. IEEE Trans.
Power Apparatus Syst., Vol. PAS-102, No. 8,2413,
1983.
Shibata andNaoe.Trans. .E.E., Japan, Vol. 109-D,
p. 251, Apr. 1989.
Shibata and Fukami. Ibid., Vol. 109-D, p. 865,
Nov. 1989.
Shibata and Naoe. bid., Vol. 110-D, p. 1005, Sept.
1990.
Nonaka. Self-excited three-phase synchronous
generator. Patent
No.
272321 Sho 35-1 1263).
Nakata, Takahashi and Fujiwara. Paper of Joint
Technical Meeting on Rotating Machine and Static
1981.
T. Nakata and N. Takahashi. Direct Finite Element
Analysis of Flux and Current Distributions under
Specified Conditions. IEEE
Trans.
Magnetics, Vol.
82-5, 1982.
105-B, p. 851, Oct. 1985.
IA-25, NO . 126, 1989.
Apparatus, I.E.E.,
Japan
RM-81-40, SA-81-30,
MAG-18, 235, 1982.
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AUTHORS from left to right)
Sakutaro Nonaka graduated in 1952fromKyushu University and was ap pointed a Lecturer
there
in 1954. He also has
a Dr. f Eng. degree. He
was
promoted to a n Assistant Professor at Kyushu U niversity in 1955 and to Full Professor at
Kyushu Institute of Technology in 1965. He was appointed a Full Professor at Kyushu University in 1967 and Ch air of
Electrical Apparatus Div. He serve d as a Director of Supercon ducting Magnet Research Ce nter from April 1989 to March
1991. He has been nvolved in research on brushless single-phase synchrono us generator, sinusoidal input/output-type
PWh4
current source converter-inverter system, superconducting motor, linear induction motor for new railway system,
magnetically levitated railway system, etc. He was awarded a 1971-outstanding paper prize from EEJ and 1985-IEEElIAS
outstanding paper prize. He served
as
a 1983-chairman of Kyushu Branch of IEEJ. He has been serving as a member of
operation committee of ICEM since 1980 and electrical machinery committee of IEEE/IAS since 1986. He is a member
of the pow er electronics study group.
Katsumi Kesam aru graduated from Sag a University in 1972 and obtained a Ph.D. from Kyushu University in March
1977.He was appointed anAssistant at Kyushu University in A pril 19 77 and promo ted to Associate Professor in July 1989.
He s interested in the brushless gen erator and magn etic field analysis.
Kazuo H orita graduated from Kagoshima University in March 1991 and obtained a Masters
degne
from Kyushu
University the same year. He joined Tokyo Electric Power Co. in April 1991.
144
