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Vector Controlled Doubly Fed Induction Generator for
Wind Ap
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pscad 风力发电和直流输电部分、ETRAN 等
Vector Controlled Doubly Fed Induction Generator for
Wind Applications
Ani Gole, Dept. of Electrical and Computer Eng.,
This document discusses the theory of operation behind the doubly fed generator case
developed by Ani Gole (Univ. of Manitoba, Canada) and Om Nayak (Nayak Corporation,
Princeton, NJ). The controller concept is based on the paper by Pena et al [1].
13.8 kV, 500 HP
INDUCTION GENERATOR
Fig 1: Doubly Fed Induction Generator
The Doubly fed induction generator/motor allows power output/input into the stator
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winding as well as the rotor winding of an induction machine with a wound rotor winding.
Using such a generator it is possible to get a good power factor even when the machine
speed is quite different from synchronous speed. Such machines can therefore operate
without the need for excessive shunt compensation.
The
rotor
currents
(ira,irb,irc)
of
thttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlhe machine can be resolved
into the well known direct and quadrature components id and iq.
The component id
produces a flux in the air gap
which is aligned with the rotating flux vector linking the stator; whereas the
component iq
produces flux at right angles to this vector. The torque in the machine
is the vector cross product of these two vectors, and hence only the component iq
is contributes to the machine torque and hence to the power. The component id then
controls the reactive power entering the machine. If id and iq can be controlled
precisely, then so can the stator side real and reactive powers.
The procedure for ensuring that the correct values of id and iq
flow in the rotor
is achieved by generating the corresponding phase currents references ira_ref,
irb_ref and irc_ref, and then using a suitable voltage sourced converter (VSC) based
current
source
to
force
these
currents
into
the
rotorhttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.html. The latter action is
straightforward and can be achieved using current-reference pulse width modulation
(CRPWM) or other technique. The crucial step is to obtain the instantaneous position
of the rotating flux vector in space in order to obtain the rotating reference frame.
This can be achieved by realizing that on account of Lenz’s law of electromagnetism,
the stator voltage (after subtracting rotor resistive drop) is simply the derivative
of
the stator flux linkage ?a as in eqn. (1) which is written for phase a.
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va?iaRa?
d?a
…….(1) dt
The control structure shown in Fig. 2 can thus be used to determine the location (?s)
of the rotating flux vector.
Fig 2: Determination of rotating mag. Flux vector location
In Fig. 2, the three phase stator voltages (after removal of resistive voltage drop)
are converted into the Clarke (? and ?) components v? and v? , which are
orthttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlhogonal in the balanced
steady state. This transformation is given by:
?v???v??
?v?
?1?1/2?1/2??a??
v????2/3??0??b?……(2) 22????v??c?
Integrating v? and v??, we obtain ?? and ???, the Clarke components of stator flux.
Converting to polar form
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?1
|?|??s?tan(??/??)……(3)
The angle ?s gives the instantaneous location of the stator’s rotating magnetic field.
In practical control circuits, as in Fig. 2, some filtering is required in order to
rid the quantities ?? and ??? of any residual dc component introduced in the
integration process.
Now the rotor itself is rotating and is instantaneously located at angle ?r (labeled
“rotor angle” in the figure). Thus, with a reference frame attached to the rotor,
the stator’s magnetic field vector is at location ?s-??r , which we refer to the
“slip angle” ?slip.
The
instantaneous
values
for
thttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlhe desired rotor currents
can then be readily calculated using the inverse dq transformation, with respect to
the slip angle, as shown in Fig. 4. The
Fig. 4: Final step in generation of rotor phase reference currents
Once the reference currents are determined, they can be generated using a voltage
sourced converter operated with a technique such as current reference pulse width
modulation (CRPWM) as shown in Fig. 5. The Appendix gives a short introduction to
CRPWM.
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GA
GBGC
Fig. 5: CRPWM
Converter and Controller for rotor currents
:
As can be seen from Fig. 5, the rotor side VSC converter requires a dc power supply.
The dc voltage is usually generated using another voltage sourced converter connected
to the ac grid at the generator stator terminals. A dc capacitor is used in order
to
remove
ripple
and
keep
the
dc
bus
voltage
smhttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlooth.
This
relatively
grid
PWM
Converter is operated so as to keep the dc voltage on the capacitor at a constant
value. In effect, this means that the Grid side converter is supplying the real power
demands of the rotor side converter.
It is possible to operate this converter using a current reference approach used for
the rotor side converter. However, as mentioned earlier, CRPWM has the drawback that
the switching frequency and hence the losses are not predictable. Therefore, a
feedback controller is used in which the error between the desired and ordered
currents is passed through a proportional-integral controller which controls the
output voltage of a conventional Sinusoidal PWM Converter. The advantage of the SPWM
controller is that the number of switchings in a cycle is fixed, and so the losses
can be easily estimated a-priori.
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It is possible to control the d axis current by controlling the d-component of the
SPWM outphttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlut waveform and the
q axis current via the q component. However, this leads to a poor control system
response, because attempting to change id also causes iq to change transiently. Hence,
modifications have to be made to the basic P-I controller structure so that a decoupled
response is possible, and a request to change id changes id and not iq; and vice-versa.
If a voltage sourced converter with constant dc bus voltage is connected to an ac
grid through a (transformer) inductance L and resistance R, it can be shown that that:
RR---?---0––didLid1vd–edLx1---= =iqRiqL–eqRx2–?–---0–---LL
vd–ed
x1=----------------- ?id
Leq
x2=–-----–?iq
L
ed=–Lx1 vd ?Lid
eq=–Lx2–?Liq
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….(4)
Here v=vd is the voltage of the ac grid, and because this is chosen as the
vq
is
by
definition,
zero.
Ed
and
eq
are
reference,
the
d
anhttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmld q components of the
generated VSC voltage. Eqn. 4 clearly shows that attempting to change id using ed
will also cause a transient change in iq. If instead, we use the quantities Lx1 and
Lx2 to control the currents, the resulting equations are decoupled. Using feedback
PI control, we let the error in the id loop affect L x1 and in the iq loop, L x2
as
shown in Fig. 6.
In the selected circuit, the grid transformer rating is 4 kV (secondary) , 1 MVA with
10% leakage, giving an impedance ?L= 1.6 ?. Similarly a line-line voltage of 4 kV
gives a line to neutral voltage of 4/???kV, and as we are using peak quantities in
the dq conversion, vd = (4/???????kV?????????kV.
The detection of the ac grid voltage reference angle and the generation of d and q
components of current (as required in Fig 6) are done in a straightforward manner
using a d-q transformation block as in Fig. 7.
://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlar
The selection of idref for the grid side converter is through the control circuit
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shown in Fig 8, which attempts to keep the capacitor voltage at its rated value by
adjusting the amount of real power. The reactive power order is dialed in, but could
have been
generated by a similar controller whose objective would be to keep the ac voltage
at some set point.
If these reference voltages vdref1 and vqref1 (Fig. 6) are applied at the secondary
of the transformer, the desired currents idref and iqref will flow in the circuit.
The remaining parts of the controls are standard PWM controls. The control blocks
shown in Fig 9 convert the above references to phase and magnitude, taking care to
limit the magnitude
to the maximum rating of the grid side VSC converter. The reference for each of the
three
phase voltages is then generated by an inverse dq transformation.
Ea
Vhttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmla Vb Vc
r to pValfas
Transform X
beta Vbetas
3 to 2
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alfa Ed phi
Vsmag phivs
Fig 8: Voltage controller
Fig.10 shows a standard sinusoidal PWM controller, in which each of the phase voltages
is compared with a high frequency triangle wave to determine the firing pulse
patterns.
IGBT
PULSES
The following tests can be conducted to check the operation. Set the generator on
“speed Control”, i.e., the machine will run at the speed designated by the slider.
This is realistic because any externally connected wind turbine model would interface
to the machine module through the “speed signal”. Set the speed to 0.8 pu.
Set idref=0.5 pu and iqref =0 pu for the rotor side converter and vref = 10 kV and
iqref (Q order) for the grid side converter. Start the system. Observe that the powers
are indeed FIRING
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as expected. Increase idref (rotor converter) to 1 pu. The change should be effected
without any change in the reactive power. Similarly change iqref to 0.3 pu. And observe
that P does not change.
Change machine speed to 1.1 pu., with (rotor side) idref=0.5 pu and iqref =0. Notice
that the torque stays the same, but the power goes up with no change in reactive power.
This is because keeping idref constant maintains constant torque, and so P is
proportional to speed.
Monitor grid side converter currents. Observe that the dc capacitor voltage remains
fixed at its rated value and grid side currents are in phase with the ac voltage.
1) R. Pena, J.C. Clare and G.M. Asher, “Doubly fed induction generator using back
to back PWM converters and its application to variable speed wind energy generation”,
IEE Proc. Electrical Power Applications, Vol. 143., No.3., May 1996.
Current
Referenhttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlce
PWM
allows for the generation of any arbitrary current waveform in an R-L load. As shown
in Fig. A1, an upper and lower tolerance band is placed around the desired reference
waveform for the current as in the above figure. If the actual current is below the
lower threshold, the upper switch (T1/D1) is turned on which applies a positive
voltage (E/2) to the load. The current in the source thus rises in response to this
voltage. When the current rises above the upper threshold, the upper switch is turned
off and the lower switch (T2/D2) is turned on. This applies a negative voltage (-E/2)
to the load and causes the current to drop. Thus the difference between the desired
and actual currents is kept to within the tolerance band. By making the thresholds
smaller, the desired current can be approximated to any degree necessary. Note however,
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that there is a limit to which this can be done, because the smaller the threshold,
the smallehttp://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlr the switching
periods, i.e., the higher the switching frequency and losses.
Using this technique, any given current waveform can be synthesized. A method that
removes all harmonics can be constructed using the approach shown in Figure A1.
This approach suffers from the drawback that the switching frequency is not
predictable and can be very high making the circuit less attractive for larger ratings
such as ac side filters.
Fig A1: CRPWM Controller and Waveforms
? Clarke’s Transformation
A
alfa
B3 to 2 Transform
beta
C
alfa
2 to 3BTransformbeta
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C
A
???????????????????????????????
(
Forward (abc to ? ??????????????????????????????????????????
Reverse??????to abc)
0??a??a??1
1?1/2?1/2????????????b????1/2b
2????2/3????????0???2
2??????://doc.guandang.net/bd09eb32a265afe0eeb3efcb2.htmlpar
c????????c??????1/22?
(A1)??
? Park’s Transformation
thetaDStatorto Rotor
Qbeta
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thetaalfa
Rotorto StatorQbetaD
Forward (????to dq)
???????
Reverse (????to dq)
???????…….(A2)
?q???sin( )cos( )????????sin(
)cos( )??q?
?d?
?cos( )
sin( ????
???
?cos( )?sin( ??d?
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