Direct Power Control of a PWM Rectifier Fed Autonomous Induction

Transcription

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ScienceDirect
Energy Procedia 36 (2013) 391 – 400
TERRAGREEN13 INTERNATIONAL CONFERENCE
Direct power control of a PWM rectifier fed autonomous
induction generator for wind energy applications
Z. Boudriesa, D. Rekioua Ziania, M. Sellamib
a
LTII Laboratory, Departement of Elctrical Engineering, University of Bejaia, Algeria
b
GE Laboratory, Departement of Elctrical Engineering, University of Bejaia, Algeria
Abstract
In this paper, a control strategy for a stand alone induction generator (IG) driven by a variable speed wind turbine for
use in remote area power supply is presented. The IG is excited simultaneously by a capacitor bank and a PWM
rectifier. During the voltage build up process, there is a variation in the flux linkage of the induction generator. The
variation of the magnetising inductance is taken into account due to saturation of the core. To achieve the main goal
of the control system, which consists to keeping the DC link voltage constant regardless of the magnitude of the load
power, a direct power control (DPC) technique is proposed. In DPC approach, the converter switching states are
selected directly by a switching table based on the instantaneous errors between the controlled and estimated values
of active and reactive power.
The simulation calculation was achieved using MATLAB®-SIMULINK® package and results are presented to
support the theoretical discussion.
©
Authors. Published
by Elsevier
Ltd.
© 2013
2010The
Published
by Elsevier
Ltd. Selection
and/or peer-review under responsibility of [name organizer]
Selection and/or peer-review under responsibility of the TerraGreen Academy
Keywords: Direct power control; PWM rectifier; induction generator; instantaneous active and reactive power;
magnetizing inductance
* Z. Boudries. Tel.: +213-34-215-006; fax: +213-34-051-005.
E-mail address: zboudries@yahoo.fr.
1876-6102 © 2013 The Authors. Published by Elsevier Ltd.
Selection and/or peer-review under responsibility of the TerraGreen Academy
doi:10.1016/j.egypro.2013.07.045
392
Z. Boudries et al. / Energy Procedia 36 (2013) 391 – 400
1. Introduction
The trend to reduce dependency of pollutant energetic sources, such as oil and coal, has been
increasing the attention given to renewable energy. The wind is a renewable energy which is clean
and abundant resource. Induction generators are widely used for wind powered electric generation.
For the stand-alone operating, the squirrel cage induction machine is preferred thanks to its
robustness, reduced cost and low maintenance. In addition, the induction generators do not need an
external power supplies to produce the excitation magnetic fields. The excitation can be provided
by means of PWM converter and a capacitor bank connected to the stator windings of the
induction generator. The device has to be controlled in order to maintain the DC voltage at a
constant value whatever the speed and the load values as long as the wind power is sufficient to
satisfy the electric needs.
Several works have already dealt with the study of the autonomous induction generator and different
solutions have been suggested to control the DC voltage. Field oriented control [1-9] and direct torque
control [10,11] were proposed to maintain the terminal voltage constant. These strategies are robust and
permits to obtain accurate control with excellent regulation of the DC voltage. With DTC, no speed-loop
is needed for the controller and a true sensorless controller is naturally obtained. It, consequently, appears
to be superior to vector control scheme.
In this paper, the conventional direct torque control scheme for induction motor drives is extended to
control directly the active power (DPC) delivered to an active load by a wind turbine driven squirrel cage
induction generator (SCIG). The SCIG is interfaced to the load through an AC-DC converter (PWM
rectifier). The goal of this proposed control system is to maintain the DC bus voltage at constant value
independently of the variations of the load.
The DPC for IG has been studied in some literatures [12, 13] and proved to have several advantages
over the conventional vector control. In this control strategy, the error in the reference power and the
actual power is utilized to generate the voltage control directly as in conventional DTC drives [14, 15].
This method reduces the number of PI controllers used when compared to the vector control based
variable speed wind turbine generator systems. The DPC like DTC is a stator flux based control technique
having the advantages of robustness and fast controls [16]. DPC has following advantages: Simpler
voltage and power estimation algorithm, Easy implementation of the unbalanced and distorted line voltage
compensation to obtain sinusoidal currents (low THD), excellent dynamics and no coordinate
transformation is required [17]
The whole control system thus obtained is simulated using MATLAB-SIMULINK software.
Simulations results for a 5.5 kW induction generator are presented and discussed to verify the
effectiveness of the developed control strategy.
2. System description
The studied overall system is represented in Fig.1. It comprises a wind turbine, an induction
generator, a PWM rectifier and an active load.
The goal of the device is to keep the DC bus voltage Vdc at a constant value whatever the load
variations.
393
3. Induction machine model
The model of the induction generator in the stationary reference frame Į-ȕ is established in
assumption of saturation of the core. The electrical equations are then written as follows [18]:
ªVsDº
«V »
« sE»
«0»
« »
¬0¼
ª
« ls
«
0
0
0 ºªisD º «
« » «0
Rs
0
0 »«isE » «
». Rr
Z.lr
Z.(.lr Lm)»«imD» «
»« » «lr
Rr ¼«¬imE»¼ «
Rr Z.(lr Lm)
«
«0
«¬
ª Rs
«0
«
«Rr
«
¬Z.lr
2
' mD
m
m
º
i
' i .i
Lm L .
Lm. mD mE »ªdisD º
i
im »« »
dt
2
»« di
»
' imD.imE
' imE
ls
Lm.
Lm Lm.
»« sE »
im
im »« dt »
(1)
.
2
»«dimD»
' imD
' imD.imE
0 lr Lm Lm.
Lm.
»« »
im
im »« dt »
2 » dimE
« »
' imD.imE
' imE
Lm.
lr Lm Lm. »«¬ dt »¼
lr
im
im »¼
0
Where Rs, Rr, ls and lr are the stator and the rotor phase resistances and leakage inductances
respectively, Lm is the magnetising inductance and Z n pp .: (ȍ is the rotor speed in rd/s, npp the
machine poles pairs number).
Besides VsĮ, isĮ, Vsȕ and isȕ are the Į-ȕ stator voltages and currents respectively. imĮ and imȕ are the
magnetizing currents, along the Į and ȕ axis, defined by:
i mD
®i
¯ mE
i s D i rD
i s E i rE
(2)
Where irĮ and irȕ are the Į-ȕ rotor currents.
im
2
i mD i mE
2
(3)
Thus the saturation effect is taken into account by the expression of the magnetizing inductance Lm
with respects to the magnetizing current im defined as:
To express Lm in function of im we use a polynomial approximation of degree 12 [18].

° Lm
°
®
°L m '
°¯
n
¦ a .i
f ( im )
j
j
m
j 0
dL m
d im
n
¦ j.a . i
j
j1
m
j 0
This model takes account of both saturation and cross magnetizing effects.
(4)
394
4. Model of three-phase PWM converter
The converter can be expressed, in a-b-c reference frame with following equations [19]:
ªVsa º
«V »
« sb »
«¬ Vsc »¼
ªi a º
ªi a º ª Va º
d
R ««i b »» L ««i b »» «« Vb »»
dt
«¬i c »¼
«¬i c »¼ «¬ Vc »¼
(5)
Where L and R are the line inductance and resistance, respectively. ia, ib and ic are the AC side
rectifier currents.
The AC rectifiers voltages Va, Vb and Vc are defined as:
Va
Vb
Vc
Vdc
2S a S b Sc 3
Vdc
Sa 2S b S c 3
Vdc
S a S b 2Sc 3
(6)
Sa, Sb and Sc are the switching states of the rectifier
The relationship between the AC side rectifier currents ia, ib and ic and the DC bus voltage Vdc can
be written as:
C dc
dVdc
dt
Sa i a Sb i b Sc i c i L
(7)
Where Cdc is the dc link capacitance, iL the load current.
5. Direct Power Control (DPC) system
Based on the principles of DTC strategy, direct power control (DPC) is developed in this paper to
control the DC voltage delivered by a PWM rectifier fed induction generator. In this strategy, there are
no internal current control loops and no PWM modulator block. The converter switching states are
selected by a switching table based on the instantaneous errors between the controlled and estimated
values of active and reactive power and the angular flux position. Therefore, the key point of the DPC
implementation is a correct and fast estimation of the reactive and active line power.
A. Flux estimator
Based on the measured DC link voltage Vdc and converter switching states Sa, Sb, Sc , the flux
components are calculated in (Į-ȕ) coordinates system as follows [20] :
395
\D
\E
B.
³
³
2
1
Vdc (S a (S b S c ) L.i D
3
2
1
Vdc (S b S c ) L.i E
2
(8)
Active and reactive power estimator
The measured line currents ia, ib DQG WKH HVWLPDWRU IOX[ FRPSRQHQWV ȥĮ, ȥȕ are used to the power
estimation [19, 20].
p
Z e .(\ D i E \ E i D )
q
Z e .(\ D i D \ E i E )
(9)
Ze is the flux electric pulsation defined by:
Ze
dJ \
dt
,
J\
arctg
\E
(10)
\D
C. Block scheme of the DPC system
Fig.1 shows the configuration of the proposed control system based on DPC method. The controller
features relay control of the active and reactive power by using hysteresis comparators and a
switching table. In this configuration, the DC bus voltage is regulated by adjusting the active power
transmitted to the load.
As shown in Fig.1, the active power control, p*, is provided from the outer PI dc voltage controller
block. The reactive power control, q*, is directly given from the outside of the controller. Errors
between the controlled and the estimated feedback power are input to the hysteresis comparators and
digitized to the signals d p and dq defined as:
dp
1 if p * p t h p , d p
0 if p * p d h p
dq
1 if q * q t h q , d q
0 if q * q d h q
Where hp and hq are the hysteresis band.
(11)
396
Wind
turbine
Gear box
Self excited
Induction
generator
LOAD
L, R
Cdc
PWM Rectifier
C

Current mesurement
Instantaneous power &
flux estimator
Sa
Sb
Sc
Sector
selection
Sa Sb Sc
Vdc
Switching
Table
dq
dp
Vdc *
PI
-
p
-
q
p*
*
q
Fig. 1. Block scheme of DPC
Also, the phasH RI WKH IOX[ YHFWRU LV FRQYHUWHG WR WKH GLJLWL]HG VLJQDO șn. For this purpose, the
stationary coordinates are divided into twelve (12) sectors, as shown in Fig.2, and the sectors can be
numerically expressed as:
(n 2)
S
S
d T n d (n 1)
6
6
n 1,2,...,12
Į
Ĭ6
Ĭ5 Ĭ4
Ĭ3
Ĭ7
Ĭ2
Ĭ8
Ĭ1
Ĭ9
Ĭ10 Ĭ11
ȕ
Ĭ12
Fig. 2. Į-ȕ plane divided into twelve sectors to detect the phase of the voltage vector
(12)
397
The digitized variables d p, dq DQGWKHIOX[YHFWRUSRVLWLRQȖȥ DUFWJȥȕȥĮ) form a digital word,
which by accessing the address of the lookup table selects the appropriate voltage vector according to
the switching table I.
Table 1. Switching table for direct instantaneous power control
dp
dq
Ĭ1
Ĭ2
Ĭ3
Ĭ4
Ĭ5
Ĭ6
Ĭ7
Ĭ8
Ĭ9
Ĭ10
Ĭ11
Ĭ12
0
1
101
111
100
000
110
111
010
000
011
111
001
000
0
0
111
111
000
000
111
111
000
000
111
111
000
000
1
1
101
100
100
110
110
010
010
011
011
001
001
101
1
0
100
110
110
010
010
011
011
001
001
101
101
100
6. Simulation results
To study the performances of the DPC system, the PWM rectifier with the whole control scheme
has been simulated using the MATLAB SIMULINK software. The main electrical parameters of the
power circuit and control data are given in table II.
Table 2. Machine and power circuit parameters [18]
Machine Parameters
Power circuit parameters
Parameter
Value
Parameter
Value
Rs
1.07131ȍ
R
0.2 ȍ
Rr
1.29511 ȍ
L
10mH
ls
0.0089382 ȍ
Cdc
1mF
lr
0.0048613 ȍ
RL
100 ȍ
npp
4
The graph presented in Fig.3 illustrates the phase voltage built up. The phase voltage value is fixed
to 220V by an appropriate choice of the capacitance in the bank connected to stator winding of the
induction generator (C=200P F).
In Fig.4 is presented the response to step change of the controlled DC voltage (from 465V to 550V)
for a value of load fixed to 100 $V FDQEHREVHUYHG WKH '& YROWDJHLV YHU\FORVH WRLWVUHIHUHQFH
value that it tracks with a good accuracy and stability.
Fig.5 depicts the active power waveform, in ac side, when the DC voltage step change is applied.
We can note that active power changes from about 2000 W (for Vdc = 465V) to 3000 W (for Vdc = 550
V). These values correspond to the load power demand in the DC side, witch is expressed by:
p
Vdc2
RL
398
Fig.6 shows the line current evolution, when the step change to Vdc is applied. The current variation
follows the power demand and there is a good agreement between the observed values and those
calculated from the relation expressing the power assessment between the AC and DC side of the
converter, that is given by:
Vdc2
RL
p
3
Vm I m
2
(13)
The effect of DC load variation (Fig.7) on the operation of the system is illustrated in Fig.8,9 and
10. It can be seen that changes in load don’t affect DC link voltage which remains almost. This is due
to the fact that the system acts as a voltage generator, adjusting the power demand as a function of
load variations, by regulating current values according to equation (13).
150
600
550
500
465
100
400
250
Vdc(V)
Vsa (V)
200
50
0
-50
300
200
-100
-150
100
-200
-250
0
0
0.2
0.4
0.6
0.8
1
0
1.2
0.2
0.4
time(s)
0.8
1
1.2
1.1
1.2
time(s)
Fig. 3. A phase voltage built up
2
0.6
Fig. 4. DC voltage
x 10 4
60
40
1.5
isa(A)
p(W)
20
1
10
0
-10
-20
0.5
0.3
0.2
0
-40
0.6
0.7
0.8
0.9
1
time(s)
Fig. 5. Active power
1.1
1.2
-60
0.6
0.7
0.8
0.9
1
time(s)
Fig. 6. Current of phase a
399
500
110
465
400
90
350
80
75
70
300
Vdc(V)
RL(
100
60
250
200
150
100
50
40
0
0.2
0.4
0.6
0.8
1
1.2
50
0
0
0.2
0.4
time(s)
0.6
0.8
1
1.2
1
1.2
time(s)
Fig.7. The load variation
Fig. 8. DC voltage
5000
15
4500
10
4000
isa(A)
p(W)
5
3000
2000
0
-5
1000
-10
0
-15
0
0.2
0.4
0.6
0.8
time(s)
Fig. 9. Active power
1
1.2
0
0.2
0.4
0.6
0.8
time(s)
Fig. 10. Current of phase a
7. Conclusion
A Direct Power Control (DPC) scheme is presented that directly controls the active power
delivered by an induction generator to an active load. An AC-DC (PWM rectifier) is used as the power
electronic interface between the load and the induction generator. To control the converter, a
switching table based on the errors in instantaneous values of controlled and estimated active and
reactive power is used. The simulation results agree with theoretical previsions illustrated by the by
the power assessment between the Ac and DC sides of the converter, and clearly, show that the
system acts as a voltage generator adjusting the power delivered by the generator to the load demand
with an aim to keeping the DC bus voltage as constant value. Since constant DC voltage is achieved a
DC load can use it directly, or, if required it is a matter of having an inverter to produce a constant
voltage and frequency AC output.
400
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