A Maximum Power Control of Wmd Generator System Using a Permanent
Magnet Synchronous Generator and a Boost Chopper Circuit
Kenji Amei Yukichi 'Igkayasu Takahisa Ohji Masaaki Sakui
Faculty of Engineering, Toyama University, 3 190 Gofuku, Toyama
930-8555, Japan
Phone:+81-76445-6710
FAX: +81-76445-6710
E-mai1:amei @eng.toyama-u.ac.jp
Abstract
The wind generator system using a boost chopper for
generation control of permanent magnet synchronous
generator is proposed. And, the theoretical analysis of
characteristics of power generation is discussed. By
replacing main circuit composition of generator and
boost chopper with the equivalent circuit, characteristics
for generating power and DC output voltage were
expressed by the function of duty ratio of the boost
chopper and generator rotational frequency. Electric
power supplied from the generator is characterized by
the condition of the load with the peak point, Therefore,
the optimum duty ratio for obtaining the maximum
power was theoretically determined by differentiating the
characteristic equation of generating power with respect
to duty ratio of the boost chopper. It was verified
experimentally by the construction of the simulator of the
wind generator system, and the validity of derivation
technique f o r the maximum power point was c o n j h e d .
1 Introduction
Supply and consumption of the energy based on the
conventional fossil fuel are considered as a factor of
global warming and environmental deterioration. The
utilization of natural energy is noticed as a new energy
source which replaces conventional energy source. The
power generation by natural energy such as solar energy
and geothermal energy, wind force, wave force is
proposed.
For the real practical application, the
research of the performance to improvement and cost
reduction is actively promoted. Since the wind power
generation has been established on the basis of electric
motor technology which is already completed, it is
expected as natural energy power generating system of
which the practical application is most regarded
promising.
Wind generator system and the control method have
already been proposed in order to efficiently utilize the
wind energy which changes every moment [1][2]. The
0-7803-7156-9/02/$10.000 2002 IEEE
induction generator applied to conventional wind power
generation has the advantage which is solidly and
cheaply, maintenance-free. However, permanent magnet
synchronous generator is used for proposing wind
generator system because of power factor is low and an
excitation source of AC is necessary in induction
generator. Boost chopper circuit composed of one
switching device is used for the control of the generated
output in order to improve the efficiency [3].
The main circuit composition of generators and boost
chopper, etc. was replaced in the equivalent circuit in
order to theoretically analyze this wind generator system.
Characteristics such as generated output power and DC
output voltage were expressed in functions of duty ratio
of the boost chopper and the generator rotational speed.
The electric power generated from the generator has
characteristics by the condition of the load with the peak
point. Therefore, the optimum duty ratio for obtaining
the maximum power was theoretically deduced by
differentiating the equation of the generated output
power by duty ratio of the boost chopper. It was
verified experimentally by the production of the
simulator of the wind generator system. The validity of
derivation technique of proposing maximum power point
was confirmed. In proposing method, the value of each
part is calculated on the basis of the rotational speed
observed by the rotation sensor. The consideration on
characteristics of the windmill is unnecessary, because
the torque is controlled in proportion to the rotational
speed of the generator, and because characteristics of the
windmill are reflected in the change of the rotational
speed. Therefore, this method can be applied for all
windmills.
2 System Configuration
Fig.1 shows the system configuration of this
equipment. This equipment is constituted by a permanent
magnet synchronous generator, three-phase diode
rectifier circuits, boost chopper circuit and voltage
inverter circuit. Permanent magnet field excitation
three-phase synchronous generator is used in order to
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realize high efficiency and simplification of the power
conversion circuit. Generated AC power is rectified by
three-phase diode rectifier circuits in DC power.
Three-phase diode rectifier circuits have the
characteristics in which the phase of the largest
line-to-line voltage is conducted. The current phase
becomes always equal the phase voltage, and the power
factor of fundamental wave approximates to one.
Rectified DC power is boosted by the chopper circuit,
and it is regenerated to the electric power system through
the inverter with a high power factor. Since the validity
of theoretical analysis method and the derivation
technique of a maximum power point of wind generator
system is mainly discussed in this paper, the inverter
controlled with the high power factor is replaced a load
resistance connected with DC link.
3 Derivation of the equivalent circuit
3.1 Boost chopper circuit[4]
The AC power output from the generator is converted
into DC power through diode rectifier circuits, and it is
boosted by the boost chopper circuit. In this chapter,
the operation of the boost chopper circuit is theoretically
analyzed. Generator and rectifier circuits which supplied
the boost chopper circuit with electric power were
replaced in a DC voltage source in order to facilitate the
analysis. And, the inverter circuit connected with an
output of the boost chopper circuit was simulated as load
resistance connected with DC link, since it is controlled
in the operation at the high power factor as a current
source. The circuit configuration of the boost chopper is
shown in fig.2. When it is assumed that the inductance
and the capacitance of the equivalent circuit are
sufficiently large, the current of the switching device is
smoothed by the inductance, and DC output voltage is
smoothed by the capacitance. The energy is stored in
L d c , when SW was turned on in the period of t o n .
And, the energy is transferred to C , , when SW was
turned off in the period of teff. Following equation is
obtained.
'dcl'on
= Vdc2to,7
I
Fig.2 Boost chopper circuit
It is expressed by a duty ratio.
VdC,=
bdcl
tOff
1
-- 1 - a 'del
Where a is as follows.
a=-
to"
(3)
ton + t o 8
It is possible that boost chopper circuit and load
resistance R , are considered a kind of variable
resistance changed by duty ratio from the viewpoint of
the DC voltage source. This variable resistance R,,
is defined as:
I del =-Vdd
Rdd
(4)
The output current I,, is expressed by output voltage
Vdcz and load resistance R, .
Idc 2
=LL
(5)
4
Following equations are obtained, because input power
and output power of the boost chopper is equal.
vdc,'dc,
= 'dc2Idc2
(6)
By substituting (2) in (6), Vdc,and V,,, are eliminated.
I d , , = (l- a ) f d c l
(7)
By dividing of both sides of (2) in I,, , (7) is substituted.
In addition, (4) and (5) are substituted to (8).
R,, = (1 --a)'
R,
(9)
From equation (9), it was confirmed that the boost
chopper from the viewpoint of the DC voltage source
could be expressed in the function of the duty ratio.
(1)
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3.2 Permanent Magnet Synchmnous Generator
Since the power for excitation source is not required
for the permanent magnet synchronous generator, high
efficiency is expected. And, since the electromotive
force in proportion to rotational speed is generated, it is
possible to take out the generated output in the easiness.
The equivalent circuit for one phase is shown in fig. 3.
The constant of the generator is defined as K, and a field
magnetic flux by the permanent magnet is defined as 4 ,
and the mechanical angular velocity is defined as w, .
Induced electromotive force E of permanent magnet
synchronous generator is shown like the following,
E = K&og
(10)
Fig.4 Connection diode rectifier circuits to the generator
From this, the relationship between V,,, and line to line
voltage Vu and phase voltage V, is shown as
following.
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343
v,, = -v
Terminal voltage V, of the generator is shown like the
following, when line current of the generator is defied
as I, .
. .
V8 = E - RJ8 - J X J ,
(1 1)
Where, R, is the winding resistance, and X s is the
synchronous reactance.
R
LL
= -V*
3&
From (12)"and (14), the equation of I,,
concisely expressed is obtained.
and I,
3.3 Diode rectifier circuits
3.4 The calculation of the electric power in AC side
The generator is connected with rectifier circuits like fig.
4. It is assumed that the AC power generated from the
generator is converted into DC power through diode
bridge rectifier circuits.
= vdc,'dcl
3v8'8
(12)
Where, Vdcl, I,, are DC side voltage and DC side
current, respectively.
Three-phase diode rectifier
circuits have the characteristics in which the phase of the
largest line to line voltage is conducted. The resistance
value per one phase of rectifier circuits from the
viewpoint of A.C. side is defined as R , , and the
maximum value of line-to-line voltage is defied as
Vwd.
The mean value of DC voltage is shown like
the following.
v,,
3 6
=-
The whole aspect of wind generator system of fig. 1 is
shown in detail in fig. 5. Resistance value R, per one
phase of rectifier circuits from the viewpoint of A.C. side
is shown like the following by generator terminal voltage
V, and line current I , .
From (14) and (15), the following equation is obtained.
The following equation is obtained, when (4), (9) and
(16) are substituted in (17).
V,,cosBdB
n z
3
= -V-,t
7r
Fig.3 Equivalent circuit per one phase of synchronous
generator
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Fig.5 Whole aspect of wind generator system
is defined like the following in order to facilitate the
calculation.
7r2
R, =-R
18
dc'
It2
7r2
x = -(1 - a)"RL
=-(1-a)2RL
18
18
The line current of the generator is shown like (19) from
(1 l ) , and the amplitude is expressed as (20).
I
*
E
=
m
The follbwing equation is obtained, when (24) is
differentiated in a .
Generated output P is shown like the following, when
it is expressed in the function of x .
From ( l o ) , (18) and (20), generated output power P is
calculated.
I
P = 31VgllZg COS p
= 3R, 11,12
The following equation is obtained, when both sides is
differentiated in a .
dP dP dx
-=-d a a!~ d a
- ?r2(K~w,)2RL(1-a)
3
{:;
-(1
[{y;-(I
The DC voltage V,, is obtained from (14).
-a)2 RL}' -(Raz + X s 2 )
-a)'R,
+ Ra}' + X S 2 ] '
(27)
It has the extreme value, when (27) becomes the zero.
Duty ratio ama,
in the maximum power point is shown
in (28), because a is within 0 I a < 1 .
(22)
And, output voltage Vdc2 of the boost chopper circuit is
calculated like (23) by multiplying the duty ratio in Vdc,.
v
dc2
=- a
1 -a
3.6 DC voltage in maximum power point
'del
By substimting amax
deduced in (28) in (22) and (23),
output voltage V,,, of rectifier circuits and output
voltage V,,, of the boost chopper circuit are calculated
like the following equation.
3.5 The derivation of the maximum power point
The generated output power is shown by a function of
duty ratio a and angular velocity w , , as it is shown
in equation (21), and it has characteristics with the peak
point. The rotational speed of the generator always
changes by wind velocity. Duty ratio a of the boost
chopper must be controlled in order to effectively take
out the electric power, while the maximum power point
is pursued. Based on (21),duty ratio amax
in which the
electric power becomes maximum value is deduced. It
By solving (30) on R,, it is shown as a function of
O g and ' d c 2 .
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By substituting instant rotational speed w , and output
DC voltage reference Vdcz* in equation (31), the value
of the load resistance R , for fixedly maintaining DC
voltage is calculated. The parameter necessary for the
theoretical analysis is shown at table 1.
4. The experimental verification
Fig.6 Simulation system for the wind power generation
Simulation system shown in fig. 6 was produced, and
the maximum power control of wind generator system
was verified experimentally by using it. Ratings and
parameters of the simulator system are shown in tables 2.
The windmill is simulated by controlling the speed in the
induction motor driven by the inverter with feedback
control. In actual wind generator system, rotational
speed shows the characteristics which change with the
change of load torque. However, in produced windmill
simulation system, the consideration for the load torque
is yet insufficient, and it is simulated only by the speed
control. Then, the rotational speed of the generator was
tested under the always-fixed condition, and it was
examined on three rotational speeds of 1200rpm ,
15OOrpm, 18OOrpm , as an example. Load resistance
R , for three kinds of rotational speed is calculated by
substituting fixed DC voltage reference Vdcz' and three
kinds of rotational speed in (31), respectively. In these
conditions, DC output voltage and generated output
power were observed, when duty ratio a of the boost
chopper circuit was changed from 0 to about 0.9. The
analysis method was evaluated in comparison with
experimental result and calculated value from theoretical
equations.
Characteristics of DC output voltage at three kinds of
rotational speeds are respectively shown in fig. 7(a),7(b)
0
0.2
0.8
1
Duty Ratio a
Fig.7(a) Characteristics of DC output voltage( 1200rpm)
x
'I
Experimentall
0
0
0.2
0.6
0.4
0.8
1
Duty Ratio a
Table 1 Parameters for analysis
Generator Constant
Field flux
'Svnchronous meed
lPole
0.6
0.4
K 25.OV.slradlwb
I
cp
N
P
Fig.7(b) Characteristics of DC output voltage( 1500rpm)
00156wb
1SMh"
16
I
i
2?
300
Table 2 Ratings and parameters
0
INV 2.2kW. ZOOV
Inverter
Induction Motor LM 2.2kW. 200V. 9.OA. 4Poles. 60Hz
SG 1.5kW. 165V. 6.6A. 6Poles. 90Hz
PM Generator
m
ninde hridue
U
)iode
IGBT
Inductor
Capacitor
P
200
-
.3 100
S O W . SOA
600V.50A
SW 600V.SOA
Ldc 1.4mH
Cdc 450V. 3300uF
DB
Q
D
o
I-
1
I-l
L
1
0
0.2
L-
0.4
.-L
0.6
0.8
1
Duty Ratioa
Fig.7(c) Characteristics of DC output voltage(l8OOrpm)
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and 7(c). DC output voltage of experimental value is
slightly lower than that of theoretical value at all
rotational speeds. However, experimental value and
theoretical value showed the almost similar tendency,
and it was confirmed that the technique of the theoretical
calculation simulated the wind generator system.
Characteristics of the generated output power are shown
in fig. 8. Though the experimental value is slightly
lower than theoretical value as well as characteristics of
DC voltage, duty ratio in the maximum power point is
almost equal. From this fact, it was confirmed that the
maximum power point could be always pursued by
controlling the boost chopper circuit using duty ratio
theoretically calculated. In the theoretical analysis, it
was assumed that voltage and current of the generator
were sine wave. But, in the experiment, the distortion
was generated in the effect of the overlap angle in the
voltage of the generator. The effective fundamental
wave component was dropped by this, and the DC
voltage drop was generated. ON-state voltage drop of
the switching device and effect by the armature reaction
of synchronous generator are considered as a cause of
the others.
for electric power regeneration will be examined, while
the factor of the error which arises between theoretical
value and experimental value is further examined.
References
[l] T.Tanaka, T.Toumiya, T.Suzuki: “A study for adapted
control interval of wind power system with resistance
load controlled by hill-climbing method”, 1998 National
convention record 1.E.E.Japan p.7-332
[2] K.Aoki, T.Nakano: ”Neural network based maximum
power control wind generator system”, 2000 National
convention record 1.E.E.Japan p.7-176
[3] N.Yamamura, M.Ishida, T.Hori: “A Simple Wind
Power Generating System with Permanent Magnet Type
Synchronous Generator”, IEEE PEDS’99, pp.849-854,
1999
[4] Eduard.Muljadi, Stephen.Drouilhet, fichard.Holz,
Vahan Gevorgian: “Analysis of Permanent Magnet
Generator for Wind Power Battery Charging”, IEEE Ind.
Appl. Conf. 1996, Vol.1 pp.541-548, 1996
5. Conclusion
In this paper, characteristics of power generation on
wind generator system, which used the boost chopper
circuit for generation control of permanent magnet
synchronous generator, were theoretically analyzed.
The generated output power was shown as a function of
rotational speed of the generator and duty ratio of boost
chopper. The control method which pursued the
maximum power point on the basis of the derivative was
proposed. And, it was verified that duty ratio generated
in the maximum power had theoretically been deduced
by the experiment in three kinds of rotational speed areas.
In the future, the optimum control method of the inverter
1200
E lo00
t
3
800
0.
3
600
?t
400
u
200
Fig.8 Characteristics of generating power
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