TuCB.1
Proceedings of the 3rd International Conference on Systems and Control, Algiers, Algeria, October 29-31, 2013
Sliding mode control of a Brushless doubly fed induction generator M Abdelbasset. MAHBOUB and S. DRID Abstract- This paper presents a sliding mode control (SMC) associated to the field oriented control (FOC) of a Brushless doubly fed induction generator (BDFIG) based wind energy conversion
systems
(WECSs).
The
stator
of this
machine
incorporates two sets of three phase windings with din'erent number of poles. The study of operation of the wind turbine leads us to two essential cases: optimization of the power for wind speeds lower than the nominal speed of the turbine and limitation
of
the
power
for
higher
speeds.
Conventional
electrical grid connected WECS present interesting control
special cage [3]. To gain some insight into this process, and thereby to understand the need for special rotor designs [3].The power rating of the converter depends on the adjustable speed range, which is limited in variable speed wind turbines. Therefore, the converter rating is a small percentage of the machine rating [4]. In BDFIG the active and the reactive power of the power winding can be controlled through controlling the magnitude.
demands, due to the intrinsic nonlinear characteristic of wind
Powe r winding
mills and electric generators. The SMC is a robust nonlinear algorithm which uses discontinuous control to force the system
GRID
states trajectories to join some specified sliding surface, it has been
widely
used
for
its
robustness
to
model
parameter
uncertainties and external disturbances, is studied. In order to verify the validity of the proposed method, a dynamic model of the proposed system has been simulated, to demonstrate its performance.
I.
INTRODUCTION
Brushless doubly fed induction generators (BDFIGs) promise significant advantages for wind-power generation [1], as they offer high reliability and low-maintenance requirements by virtue of the absence of a brush gear. This is particularly important as more and more installations are being constructed offshore and in difficult-to-reach places. Moreover, the cost of manufacturing a BDFIG is likely to be less than that of an equivalent doubly fed induction generator (DFIG) due to the absence of the slip-ring system and to the simpler structure of the rotor winding [1]. Efforts have been directed towards eliminating the slip rings and brushes while maintaining the benefits of DFIG. Brushless doubly fed induction generator (BDFG) was patented by Hunt. Figure (1) depicts the BDFG construction feature [2]. The stator of this machine incorporates two sets of three phase windings with different number of poles. One of them is connected directly to the grid, and is called the power winding (PW), since it handle most of machine power. The other one is connected via a bi-directional converter to the grid; it handles a small percentage of machine power and is called the control winding. The rotor of the BDFM carries a cage of special design, the operation of the machine relies on the interaction of the two stator windings through the intermediate action of this M Abdelbasset. MAHBOUB is with LSPIE Research Laboratory, Electrical Engineering Department, University of Batna, Rue M.E.H., Boukhlof ,ALGERIA (e-mail: mahboub_19@ yahoo.fr; *corresponding author). S. DRID is with LSPIE Research Laboratory, Electrical Engineering Department, University of Batna, Rue M.E.H., Boukhlof ,ALGERIA (e-mail:
[email protected] @ yahoo.fr;
Figure 1.
Brushless doubly fed Induction generator (BDFG) [2].
A number of scalar control algorithms have been developed for BDFIGs, such as open-loop control, closed loop frequency control, and phase-angle control, and they speed were shown to stabilize the machine over a wide range. However, vector-control (VC) methods, also known as field-oriented control, are known to give better dynamic performance. This can be implemented by using a vector control scheme in which a conventional proportional plus integral (PI) controller is used [5]. This paper a new variable structure controller using a dynamic model with a unified reference frame based on the power winding flux oriented controlled is proposed, the sliding mode control (SMC) is conception for the power loop of the outer loop associated to power flux oriented vector control scheme. II.
THEORY OF OPERATION
The operation of BDFIG relies on the interaction between the two stator winding's magnetic fields through the rotor. This condition can be achieved if the rotor field induced by the power winding (PW) couples and synchronizes with the control winding (CW) stator field and vice versa. This can occur if the frequency and distribution of the current induced in the rotor by the PW field matches that induced by the CW field. This is achieved when the following two relations are satisfied [3].
978-1-4799-0275-0/13/$31.00 ©2013 IEEE
(1)
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Proceedings of the 3rd International Conference on
(2) Where:
stator flux by angular speed of COs (The d- axis is assumed p to be aligned with the PW flux space vector) [7] are: ct d\jfs ct ·ct q p R Vs s 1s + -\jfspCOsp pp p dt
COs and cosc are the angular frequency of PW and CW p
--
respectively, and cor is the rotor angular speed.
(3)
P and P e are the number of pole pairs of PW and CW p
respectively, in our case P 3 and Pc 1, and Nr is the p number of rotor bars. The ± sign accounts for the case which the CW is excited in positive or negative phase sequence. =
=
(4)
(5)
Figure 2.
(6) Different reference frame in BDFIG
If the conditions stated in equations (1) and (2) are satisfied, then a cross coupling between the two stator fields will occurs via the rotor, and hence a nonzero average torque will be produced. This mode of operation the BDFM is called "Synchronous Mode".
(7)
(8)
To avoid the direct mutual coupling between the two stator field windings their number of poles should be different [4]. III.
DYNAMIC MODELING
In order to derive the model of assumptions are made [6]. •
•
BDFM,
the following
Assume linear magnetic circuit, and neglect saturation. Sinusoidal distributed stator winding
No direct mutual coupling between the power and control •
In BDFM there are three different initial reference frames with different pole pair type distribution as shown in Fig (2). The fIrst one is the PW reference frame (ds ' qsP ) p
related to a P pole pair type distribution, the second is the p
CW reference frame (dsc ,qsc) related to a Pc pole pair type distribution and located at mechanical angular position Be from (ds ,qs ) and the third is the rotor reference frame p p
( dr ,qr)related to a ppand pcpole pair type distribution
(1) Where: , Vsc and Vr are the PW, CW and rotor winding p voltage vector respectively. vs
Rs ,Rsc and Rr are p resistances.
the
PW,
CW
and
Ls ,Lsc and Lr are the self inductances of the PW, p CW and rotor winding respectively. Lm
rotor.
p
is the mutual inductance between the PW and the
Lmc is the mutual inductance between the CW and the
rotor.
\jf sp , \jfse and \jf r are the PW, CW and rotor flux space vector respectively.
and located at B r from ( ds ,qsP ). p
The BDFM equations are obtained in the d-q reference frame which rotates synchronously with the power winding
rotor
The powers winding active and reactive power are expressed as:
978-1-4799-0275-0/13/$31.00 ©2013 IEEE
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Proceedings of the 3rd International Conference on
(9)
Substituting (13)-(14) into (l2),yields (15)
(10)
(16) IV. VECTOR CONTROL OF BDFG Where:
The target of the vector control is to achieve independent control of the active and reactive power of the PW. This can be fulfilled using the vector control technique described in the following section. A.
PW power control
The model of the BDFG is derived in the PW synchronously rotating d-q reference frame with the d-axis
1 I.
aligned with the PW flux. Accordingly \jI�p = \jIsp
But
there is no component in the q-axis
B.
(11)
1 I
Since the PW is connected directly to the grid, \jI sp
l I
and v,p
Control of CW currents
From equation (3) to (10), the dynamic relation between
the CW current and the voltage in the d-axis (V�p and i�p ) and q-axis (V�p and i�p ) can be obtained as follows:
are constant. Consequently, equations (9) and (10)
can be simplified as follows:
(17)
(12) (18) It can be seen from equation (12) that the active and reactive power can be regulated by the q-component and dcomponent of the PW current respectively. From (6) and (11) the equations linking the rotor currents to the power winding currents are deduced as below: Isp -'q
M
p Ir -Ls
'q
V. SLIDING MODE CONTROL One considers the system described by the following state space equation: [x ]=[A][X ]+[B][U]
p
(13)
(19)
with, [X ] ERn is the state vector [U] ER m is the control input vector; [A] and [B] are system parameter matrices. The first phase of the control design consists of choosing
1.d
r
d M 'd M'ds \jIr - pi sp el e ----'-...!. --... = Lr
(14)
the number of the switching surfaces
s
(x ) .Generally this
number is equal the dimension of the control vector [U]. In order to ensure to convergence of the state variable reference valueX switching surface:
ref
to its
, [8] proposes a general function of the
978-1-4799-0275-0/13/$31.00 ©2013 IEEE
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Proceedings of the 3rd International Conference on
s (x ) Where A
=
(�t + r (x )
is a strictly positive constant; r is the smallest
ds dt
positive integer such that e
(x )
=
(20)
e
A
X ref
-
-::f::.
0 : ensure controllability;
X is the error variable. The second phase
consists to find the control law which meets the sufficiency conditions for the existence and reachability of a sliding mode such as [9]
s(x)s(x)
