Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 50 (2014) 999 – 1007
The International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES14
Variable structure control of a doubly fed induction generator for wind energy conversion systems E. Bounadjaa,*, A. Djahbarb, Z. Boudjemac a
Electrical Engineering Department, University of Hassiba benbouali, Chlef, Algeria. Electrical Engineering Department, University of Hassiba benbouali, Chlef, Algeria. c Electrical Engineering Department, University of Djillali Liabes, sidi belabès, Algeria. b
Abstract This paper presents the powers control of a variable speed wind turbine (WT) device based on a doubly fed induction generator (DFIG). Indeed, to increase the efficiency of the WT system, a robust variable structure control has been applied. DFIG has been previously presented in several works with diverse control diagrams using generally conventional PI controllers. Nevertheless, this type of controllers does not sufficiently handle some of WT resource characteristics such as wind fluctuations effects. Indeed, these can reduce WT performances. Furthermore, DFIG parameter variations should be accounted for. In this context, this paper proposes a highorder sliding mode to control the WT DFIG. Simulation results show that the proposed approach presents attractive features such as chatteringfree behavior, good response to speed variations and robustness against machine parameter variations compared to the conventional first order sliding mode technique and even fuzzy sliding mode one. © 2014Elsevier The Authors. Published byaccess Elsevier Ltd. © 2014 Ltd. This is an open article under the CC BYNCND license Selection and peerreview under responsibility of the EuroMediterranean Institute for Sustainable Development (EUMISD). (http://creativecommons.org/licenses/byncnd/3.0/). Selection and peerreview under responsibility of the EuroMediterranean Institute for Sustainable Development (EUMISD) Keywords : Wind turbine (WT); Power control; Doubly Fed Induction Generator (DFIG); High order sliding mode; Fuzzy sliding mode.
1. Introduction Wind power has developed significantly during the past few years. However, its usage poses great challenges to operation and control of power systems. Doubly fed induction generator (DFIG) has gained increasing popularity in wind power generation recently due to its flexible controllability [1]. A DFIG comprises a wound rotor induction * E. Bounadja. Tel.: +213771531508. Email address:
[email protected]
18766102 © 2014 Elsevier Ltd. This is an open access article under the CC BYNCND license (http://creativecommons.org/licenses/byncnd/3.0/). Selection and peerreview under responsibility of the EuroMediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2014.06.119
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generator supplied on the stator side by the grid connection and on the rotor side by a power electronic converter [3]. So far, several research works have been presented with diverse control diagrams of DFIG. These control diagrams are usually based on vector control notion with conventional PI controllers [4,5]. With the improved technologies in materials, power electronics and blade design, classical controllers for wind energy conversion systems (WECSs) can be upgraded by developing more efficient strategies based on modern control techniques. Sliding mode control, based on the theory of variable structure systems (VSS), has attracted many research on control systems for the last two decades. It achieves robust control by adding a discontinuous control signal across the sliding surface, satisfying the sliding condition. Nevertheless, this type of control has an essential disadvantage, which is the chattering phenomenon caused by the discontinuous control action. To treat these difficulties, several modifications to the original sliding control law have been proposed [6]. In this context, two different methods have been applied in this paper; the first method is to combine a sliding mode controller with fuzzy logic to form a fuzzy sliding mode controller (FSMC). The other is by using a high order sliding mode controllers (HOSMC). Sliding mode control with their different improvements is recently used by several researchers like [4], [7], [8], [9], for the control of the DFIGbased WT. The principle idea brought by this paper is the comparison between a three different techniques of sliding mode control. These last are used to control the electrical power exchanged between the stator of the DFIG and the power network by controlling independently the active and reactive powers. For that purposes, sliding modes have been deeply investigated. This paper is devised in 5 sections as follows: in section 2 the system modeling is briefly reviewed. The control of active and reactive powers of the DFIG using three different nonlinear controllers; sliding mode, fuzzy sliding mode and high order sliding mode is presented in section 3. In section 4, the three controllers are compared in terms of power reference tracking, sensitivity to perturbations and robustness against machine parameter variations. Finally, in section 5 the main conclusions of the work are drawn. 2. Wind energy conversion system modeling: 2.1 System description: The simplified schematic diagram of the wind energy conversion system based on a DFIG, studied in this paper is shown in Figure 1. In this diagram, mechanical energy is produced by a WT and provided to a DFIG through a gear box. The stator winding of the DFIG is directly connected to the grid, whereas the rotor winding is fed by backtoback pulse width modulation (PWM) converter. The grid side converter (GSC) is connected to the grid via three chokes to improve the current harmonic distortion. The rotor side converter (RSC) controls the power flow from the DFIG to the grid by controlling the rotor currents of the DFIG.
Turbine
Grid Ps
GEAR BOX
BacktoBack Converter
DFIG g.Ps
Fig. 1. Schematic diagram of the wind energy conversion system.
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2.2 The DFIG model: The dynamic voltages and Àuxes equations of the DFIG in the synchronous dq reference frame are given by: °V ds ° °V ° qs ® °V ° dr ° °V qr ¯
d dt d + dt d + dt d + dt
= R s I ds + = R s I qs = R r I dr = R r I qr
ψ ψ
ds
qs
− ω sψ + ω sψ
qs
ds
ψ
dr
− ω rψ
qr
ψ
qr
− ω rψ
dr
ψ °ψ ° ® °ψ °ψ ¯
ds
= L s I ds + MI
dr
qs
= L s I qs + MI
qr
dr
= L r I dr + MI
ds
qr
= L r I qr + MI
qs
(1)
The powers at the stator side are expressed as follows [3]:
Ȧsȥ s M I qr ° Ps = − L s ° ® 2 °Q = − Ȧsȥ s M I + Ȧsȥ s dr ° s Ls Ls ¯
(2)
3. Control strategies of the DFIG: In this section, comparison of DFIG performances using different nonlinear controllers: sliding mode, fuzzy sliding mode and high order sliding mode, has been presented. 3.1 Sliding mode control: The main feature of this control is that it only needs to drive the error to a “switching surface”. In this study, the errors between the measured and references stator powers have been chosen as sliding mode surfaces, so the following expression can be written [11]:
°S d = PS − ref − PS ® °¯S q = QS − ref − QS
(3)
The first derivative of (3), gives:
°Sd = PS −ref − PS ® °¯S q = Q S −ref − Q S
(4)
Replacing the powers in (4) by their expressions given in (2), one obtains:
Ȧsȥs M °Sd = PS −ref + L I qr ° s ® 2 °S = Q + Ȧsȥs M I − Ȧsȥs S −ref dr °¯ q Ls Ls
(5)
Vdr and Vqr will be the two components of the control vector used to constraint the system to converge to Sdq=0. The control vector Vdqeq is obtained by imposing Sdq = 0 :
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Vqreq
Vqreq PSref
+

S(P)
K Sat
PSmes QSref (a)
+
S(Q)
K Sat
QSmes
Vqrn
+ +
PSref
Vqrref
Vdr
+ +

S(P)
K FL
PSmes
Vdreq n
+
QSref
Vdrref
(b)
+

S(Q)
K
QSmes
FL
Vqrn
+ +
Vqrref
Vdreq Vdr
n
+ +
Vdrref
Fig. 2. Bloc diagram of the power control of the DFIG by : (a) SMC;(b) FSMC.
Veqdq
ª º § § M2· M2· ¸¸ ¸¸ȥ s Ls ¨¨ Lr − « L s ¨¨ Lr − » 2 Ls ¹ Ls ¹ * § M · «− © ¸¸ gȦ s I qr » + Rr I dr − ¨¨ Lr − Qs + © « » ML r Ȧ sȥ s M Ls ¹ © » =« « § » M2· « Ls ¨¨ Lr − L ¸¸ » 2 § M · gȦ s ȥ s M s ¹ * «− © » ¸¸ gȦ s I dr + Ps + Rr I qr + ¨¨ Lr − «¬ »¼ Ȧsȥ s M L L s ¹ s ©
(6)
To obtain good performances, dynamic and commutations around the surfaces, the control vector is imposed as follows:
Vdq = Veqdq + K ⋅ sat (S dq )
(7)
The sliding mode will exist only if the following condition is verified:
S ⋅ S < 0
(8)
The block diagram of the active and reactive powers sliding mode control applied to the DFIG is shown in Figure 2.a. 3.2 Fuzzy sliding mode control of the DFIG: The disadvantage of sliding mode controllers is the chattering effect. In order to eliminate this phenomenon, a fuzzy sliding mode control method has been proposed. The fuzzy sliding mode controller (FSMC) is a modification of the sliding mode controller, where the switching controller term sat(S(x)), has been replaced by a fuzzy control input as given below [13].
U com = U eq + U F
(9)
The proposed fuzzy sliding mode control, which is designed to control the active and reactive powers of the DFIG is shown in Figure 2.b. 3.3 High order sliding mode control of the DFIG: Sliding mode control (SMC) is one of the most interesting nonlinear control approaches. Nevertheless, a few drawbacks arise in its practical implementation, such as chattering phenomenon and undesirable mechanical effort. In order to reduce the effects of these problems, high order sliding mode seems to be a very attractive solution. This method generalizes the essential sliding mode idea by acting on the higher order time derivatives of the
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sliding manifold, instead of influencing the first time derivative as it is the case in SMC, therefore reducing chattering and avoiding strong mechanical efforts while preserving SMC advantages [9]. In order to ensure the stator active and reactive powers convergence to their references, a robust highorder sliding mode strategy is used. Considering the sliding mode surfaces given by (5), the following expression can be written:
And
Ȧ sȥ s M I qr ° S d = PS − ref + L s ® ° S = Ȋ (t,x ) + ȁ (t,x )V ¯ d 1 1 dr Ȧ sȥ s M Ȧȥ I dr − s s ° S q = Q S − ref + Ls Ls ® ° S = Ȋ (t,x ) + ȁ (t,x )V dr 2 2 ¯ q
(10)
2
(11)
Basing on the super twisting algorithm introduced by Levant in [14], the proposed high order sliding mode controller contains two parts:
Vdr = v1 + v2
(12)
With
v1 = − k 1 sign ( S d ) Ȗ
v 2 = − l1 S 1 sign ( S d ) Vdr = w1 + w2
(13)
w 1 = − k 2 sign(S q )
(14)
With Ȗ
w2 = −l2 S 2 sign(S q ) In order to ensure the convergence of the sliding manifolds to zero in finite time, the gains can be chosen as follows [14,15,16]. λi °ki > K mi ° 4λ i K Mi (ki + λ i ) ° 2 ; i = 1, 2 ® li ≥ K 2m i K m i ( k i − λ i ) ° ° 0 < γ ≤ 0 .5 ° ¯
(15)
4. Simulation results In this section, simulations are realized with a 1.5 MW generator coupled to a 398V/50Hz grid. Parameters of the machine are given in appendix A. In the aim to evaluate the performances of the three controllers: SMC, FSMC and HOSMC, three categories of tests have been realized: pursuit test, sensitivity to the speed variation and robustness against machine parameter variations. 4.1 Pursuit test The objective of this test is the study of the behavior of the three controllers in reference tracking, while the machine’s speed is considered constant and equal to its nominal value. The simulation results are presented in Figures 3 and 4. As it’s shown by Figure 3, for the three controllers, the active and reactive generated powers tracks almost perfectly their references and ensures a perfect decoupling between the two axes. Therefore it can be
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considered that the three types of controllers have a very good performance for this test. On the other hand, Figure 4 shows the harmonic spectrum of one phase stator current of the DFIG obtained using Fast Fourier Transform (FFT) technique for the three controllers. It can be clear observed that the total harmonic distortion (THD) is reduced for HOSMC (THD = 2.91%) when compared to FSMC (THD = 2.94%) and SMC (THD = 3.07%). Therefore it can be concluded that the proposed controller (HOSMC) is the most effective in eliminating chattering phenomenon. 4.2 Sensitivity to the speed variation The aim of this test is to analyze the influence of a speed variation of the DFIG on active and reactive powers for the three controllers. For this objective and at time = 0.015s, the speed was varied from 150 rad/s to 75 rad/s. The simulation results are shown in Figure 5. This figure express that the speed variation produced a slight effect on the powers curves of the system with SMC and FSMC controllers, while the effect is almost negligible for the system with HOSMC one. It can be noticed that this last has a nearly perfect speed disturbance rejection, indeed; only very small power variations can be observed (fewer than 2%). This result is attractive for wind energy applications to ensure stability and quality of the generated power when the speed is varying. 4.3 Robustness In order to test the robustness of the used controllers, machine parameters have been modified: the values of the stator and the rotor resistances Rs and Rr are doubled and the values of inductances Ls, Lr and M are divided by 2. The machine is running at its nominal speed. The results presented in figure 6 show that parameters variations of the DFIG increase the timeresponse only of the FSMC controller. On the other hand this results show that parameter variations of the DFIG presents a clear effect on the powers curves (especially in their errors curves) and that the effect appears more significant for FSMC and SMC controllers than that with HOSMC one. Thus it can be concluded that this last is the most robust among the proposed controllers studied in this work.
5
2
Active power (W )
5
x 10
0
Psref Psmes (FSMC) Psmes (SMC)
4
Psmes (HOSMC)
6 8
Qsref Qsmes (FSMC)
1
Qsmes (SMC)
1.5
Qsmes (HOSMC)
2 2.5 3 3.5 4
10 0
x 10
0.5
Reactive pow er (Var)
0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Time (s)
0
Fig. 3. References tracking.
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Time (s)
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Fundamental (50Hz) = 2106 , THD= 2.94%
Fundamental (50Hz) = 2109 , THD= 3.07% 2000
1500
1500
M ag
M ag
2000
1000
1000
500
500 0
0
(a)
200
400
600
800
1000
Frequency (Hz)
0 (b)
0
200
400 600 Frequency (Hz)
800
1000
Fundamental (50Hz) = 2104 , THD= 2.91% 2000
M ag
1500 1000 500 0
0
100
200
300
(c)
400
500
600
700
800
900
1000
Frequency (Hz)
Fig. 4. Spectrum harmonic of one phase stator current for (a) SMC; (b) FSMC, (c) HOSMC. 5
5
x 10
2
Psmes (FSMC)
4
Psmes (HOSMC)
Psmes (SMC)
6 8
x 10
Qsref
0.5
Qsmes (FSMC)
1
Qsmes (SMC)
1.5
Qsmes (HOSMC)
2 2.5 3 3.5 4
10 0
0
Psref
Reactiv e pow er (Var)
A ctive pow er (W )
0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Time (s)
0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Fig. 5. Sensitivity to the speed variation.
Time (s)
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5
x 10
Psref Psmes (SMC) Psmes (HOSMC)
4 6 8
Qsmes (SMC) Qsmes (HOSMC)
2 2.5 3 3.5 4
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Time (s)
0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Time (s)
40
FSMC SMC HOSMC
10 20
FSMC SMC HOSMC
30 40
Reactive power error (% )
30
0
Active power error (% )
Qsmes (FSMC)
1.5
10
50 0
Qsref
1
10 0
x 10
0.5
Psmes (FSMC)
2
A ctiv e p o w er (W )
0
R eactiv e p o w er (V ar)
0
20 10 0 10 20 30 40
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Time (s)
50 0
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Time (s)
Fig. 6. Sensitivity to the machine’s parameters variation on the DFIG control.
5. Conclusion This paper dealt with nonlinear and robust control techniques of a DFIGbased wind turbine. These variable speed systems have several advantages over the traditional WT operating methods, such as the reduction of the mechanical stress and an increase in the energy capture. To fully exploit this latest advantage, many control schemes have been developed for maximum power point tracking (MPPT) control schemes. In this context, this paper proposes a high order sliding mode to control the WT DFIG according to references given by an MPPT. Its main features are a chatteringfree behavior, a finite reaching time, and robustness with respect to external disturbances (grid) and unmodeled dynamics (DFIG and WT). The proposed control strategy has been tested using the MATLAB Simulation on a 1.5MW threeblade DFIGbased WT. The obtained results clearly show the HOSMC approach effectiveness in terms of power reference tracking, sensitivity to perturbations and robustness against machine parameters variations compared to more techniques as SMC and FSMC and even compared with results presented in other recent works such as [2] and [4].
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Appendix A. Machine parameters. Parameters
Rated Value
Nominal power Stator voltage Stator frequency Number of pole pairs Nominal speed Stator resistance Rotor resistance Stator inductance Rotor inductance Mutual inductance
1.5 MW 398 V 50 Hz 2 150 rad/s 0.012 ȍ 0.021 ȍ 0.0137 H 0.0136 H 0.0135 H
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