Elektrotehniški vestnik 85(4): 142-148, 2018 Original scientific paper
A comparative study between a simplified fuzzy PI and classic PI input-output linearizing controller for the wind-turbine doubly fed induction generator
Fatima Zohra Belaimeche, Abderrahim Bentaallah, Sarra Massoum, Patrice Wira
ICEPS Laboratory, Electrical Engineering Faculty, Sidi Bel-Abbes University, Algeria E-mail: lalem_sarra@yahoo.fr
Abstract. The paper presents a comparative study of a linearizing control with classic PI and fuzzy PI controllers of the active and reactive stator power of a doubly fed induction generator (DFIG) applied to a wind-energy conversion systems (WECS).
The paper discusses the operating principles of the power-generation scheme. Simulation results show that the preented input-output linearizing control provides a decoupled control, perfect tracking of the generated active and reactive power and robustness the active- and reactive-power variations.
Keywords: Doubly-Fed Induction Generator (DFIG), Input-Output linearization, Fuzzy Logic Controller (FLC).
Primerjalna študija poenostavljenega mehkega PI in klasičnega regulatorja pri dvojno napajanem asinhronskem generatorju v vetrnih elektrarnah
V prispevku smo predstavili primerjalno študijo uporabe klasičnega in mehkega regulatorja PI za linearizirano krmiljenje delovne in jalove moči pri dvojno napajanem asinhronskem generatorju v vetrnih elektrarnah. Predstavili smo principe delovanja obeh regulatorjev. Rezultati simulacije potrjujejo, da predlagano krmiljenje ponuja nadzor odklopa, beleženje proizvedene delovne in jalove moči in stabilnost pri odstopanju proizvedene moči.
1 Introduction
Wind energy is one of the most important and promising sources of the renewable energy all over the world, mainly because it is considered to be non-polluting and economically viable. At the same time, there has been a rapid development of the related wind-energy conversion technology [1].
In terms of the wind-power generation technology, because of the numerous technical benefits (higher energy yield, reduced power loses and improved supply), the modern MW-size wind turbines always use a variable-speed operation which is achieved by the converter system [2].
The used converters are typically associated with individual generators and they contribute significantly sto the costs of wind turbines. Among the variable-speed wind-turbine generators, doubly-fed induction generators (DFIGs) and permanentmagnet synchronous generators (PMSGs) with primary converters are emerging as the preferred technologies [2].
DFIG is widely used for the variable-speed generation, and it is one of the most important generators for the wind-energy conversion systems.
Both the grid-connected and stand-alone operation are feasible through an AC/DC/AC frequency converter [1, 3]. The major DFIG advantage is that the power electronic equipment has to handle a fraction (20-30%) of the total system power in order to guarantee the stability in acceptable conditions [1, 4].
In order to improve control of the active and reactive power generated by DFIG [1], the paper proposes a robust simplified input-output linearizing Fuzzy-PI controller. The controller exhibits excellent dynamics and steady-state performances.
The paper presents a comparative analysis of a simplified input-output linearizing control with a proportional integral (PI) controller and a fuzzy-PI controller for the doubly-fed induction wind-energy conversion system (WECS). Theoretical analysis, modeling and simulation results are provided. A control strategy is developed to control the active and reactive power in order to maximize the wind energy production.
Fig.1 shows the DFIG wind-energy conversion system structure
Control System
Figure 1. Wind-energy conversion-system-based DFIG.
Received 18 February 2018 Accepted 18 June 2018
A COMPARATIVE STUDY BETWEEN A SIMPLIFIED FUZZY PI AND CLASSIC PI INPUT-OUTPUT LINEARIZING.
143
2 Turbine model
Wind turbines convert the wind kinetic energy into mechanical energy by producing a torque. Since the wind-energy is in the form of the kinetic energy, its magnitude depends on the air density and the wind speed.The wind power developed by the turbine is given by equation (1) [15, 16]:
Pt = 1 Cp {X)pn R2 F:
(1)
where p is the air density, R is the radius of the wind turbine, V is the speed of the wind, Cp (X,ß) is the power coefficient, ß is the blade pitch angle, and X is the tip speed ratio of the rotor blade tip speed to the wind speed and is defined by [1]:
V
The expression of the turbine torque:
Ct = 1 Cm (Aß)pn R3 V2
(2)
(3)
In the model, the Cp (A ,P) value of the turbine rotor is approximated using a non-linear function according to [1].

Cp=fß,ß)=c
c
C2 - cß-c
^ (-C ^ exp
+CA
i
0.035
With
___
A + 0.08ß ß3 + i
and
C = 0.5176 ; C = 116 ; C = 0.4 ; C = 5
C = 21 ; C = 0.0068 .
(4)
(5)
0.5 r 0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 -0 ^
								beta=0			
											
			/	\					beta= 10		
			1/								
					\				-beta= 20		
		/									
		/	/		\	■■■					
		/ /		X	\						
						\					
				\	\	\					
				\							
			\	\	\	\\			\		
Figure 2. Power coefficient as a function of the speed ratio (X) and the angle (P).
3 Mathematical model of the Turbine DFIG model
The most significant feature of the wound-rotor machine, which is widely used for the wind-power generation, is that it has to be fed from both the stator and the rotor side. Normally, the stator is directly connected to the grid and the rotor is interfaced through a variable-frequency back-to-back AC- DC- AC power converter to provide a bidirectional rotor power flow [5].
The DFIG operating principle can be analyzed using the classical theory of rotating fields and the well known d-q model, as well as both the three-to-two and the two-to-three axes transformation. In order to deal with the machine dynamic behavior in the most realistic possible way, both the stator and rotor variables are referred to their corresponding natural reference frames in the developed model. In other words, the stator-side current and voltage components are referred to a stationary reference frame, while the rotor-side current and voltage components are referred to a reference frame rotating at the rotor electrical speed [5,6].
The stator and rotor voltage components are:
Vsd = RsIsd + é -aA9
d^sa
V,„ = R..I.„ +-asésd
sq	s sq
dt
Vrd = RrIrd + é - (as )érq
d^ra
V = R I	- (a -a )i
rq	r rq	s	r rd
(6)
where:
Vsd ,Vsq > Vrd ,Vrq > Isd ,Vsq ,Vrd > Vrq represent the direct and quadrature voltage and current for the stator and rotor respectively.
The magnetic equations are:
ésd = LJsd + LmIrd
$sq = LsI sq + LmIrq
é ¿ = LI, + L I ,
rrd	r rd	m sd
é =LI,+LI
rq	r rd	m sq
(7)
The expression of the electromagnetic torque based on the dq stator fluxes and dq rotor currents is:
Q ="P^iUq -Wd)	(8)
The DFIG active and reactive power of the stator and rotor of the are:
2
4
6
8
2
4
6
8
20
144
BELAIMECHE, BENTAALLAH, MASSOUM, WIRA
}Ps (Vsd Isd + Vsq Isq )
}q = (V I - VI )
I ^ s V sq sd	sd sq /
(9)
sq sd	sd sq
4 General concept of the input-output
linearizing contol
In order to linearize the system, the MIMO system is considered [8]:
\x = f (x) + g.u 1 y = h(x)
(10)
where x is the state vector; u is the output; f and g are smooth vector fields; h is a smooth scalar function. In order to obtain the input-output linearization of the multi-input multi-output system, output y of the system is differentiated until the inputs appear:
y = Lfh( x) + Lgh( x)u
(11)
y = Lr~lfh(x) + Lh( x)u
(12)
£
Linearization Controller Nonlinear System
u |-1 |-1
u = -E (x)A(x) + E (x)v |-^-x = f(x) + g ■ u | | ►Ij = h(x) |
Figure 3. Schematic diagram of the input-output linearizing control.
where r is the relative rank of y. Performing the above procedure for each input yi, we get a total of m equations in the above form written as [8].
' y(r)1'		u
	= A( x) + E( x)	
V('m ) _y * .		u . m _
(13)
where the m*m matrix E(x) is defined as [8-9]:
LgiV-lh ...... vA
E (x) = ............
L L rm -1h L L m-1h Lg1Lf hm ...... LgmLf hm
A(x) = [Ef\ ...... Lr'fhm f
(14)
(15)
Matrix E(x) is the decoupling matrix for the system. If E(x) is nonsingular, then original input u is controlled by the coordinate transformation [7]:
u = ET\ x) A( x) + E~\x)v where
V = [V1 ...... Vm Y
(16)
(17)
Substituting (15) into (13) provides a linear differential relation between the output y and new input v:
y(r )1
■,,(rm )
y m

(18)
where Lf and Lg represent the Lie derivative of h(x) with respect to f(x) and g(x) respectively. If Lgihj(x)=0 for all i, then the inputs do not appear and we have to differentiate again [8]:
The procedure of the input-output linearizing control is shown in Fig. 1.
5 A Simplified input-output linearizing
control with a pi classic controller
In the stator flux-field-oriented frame
Ad =0s and 0sa = 0
V = Vs I Vq = 0
Substituting (19) into (7) yields:
j =0^_LmLT
sd L L rd
ss
I =-i
sq	j rq
L
(19)
(20)
(21)
According to (21) the direct and quadrature components of the stator and rotor currents are linear and so the state vectors are [7]:
x =[x1 x2 J =[ird Kq f
(22)
By substituting (7), (19), and (21) into (6), we get the following aquations hold:
vrd=Rld +
Vrq=RrIrq +
L 2 ^ m	d
Ls	dt
L 2) m	d
Ls	dt
f L ^ J Lm
r - T, L 2 ^ J Lm
r - T,
I,
(23)
I + g LmVs
Ird + gs t
Arranging (23) as in (10):
v
v
v
rq o s
A COMPARATIVE STUDY BETWEEN A SIMPLIFIED FUZZY PI AND CLASSIC PI INPUT-OUTPUT LINEARIZING.
145
dj± = -R i +
dt aLr rd
V Lr J
d/ ^
dt rq L, rq L
d'rq R ■	T T "rq
— = — 'rq - ®Md + ^rLrIrd
dt o	o
Defining the input of the DFIG system:
u = [" u2 ]T =[urd urq f
(24)
(25)
Ji		Ps		usd'sd + usqlsq
_ J 2,				u i + u ,i sq sq sd sq
J =
From (21) and (26) it follows:
(26)
0s	Lm
Ji =Y"sd -~T d'd + "sq'rq)
0-u - Lm.
L sq L
S	s
J2 =~T"sq	("sq'rd + usd'rq )
Differentiating (27) until the input appears
-Lm'rd ) -
Ji =
L,
'm'rd) j U sq'rq , (usdfi + Usqf2) Ls	Ls
LmUsd	LmUsq
m -u.---u„,
(28)
oLL
s r
ur.
Ji =-rL (0
Ls
oL,
Lm*rd) j ' L
-(usqfi u sdf 2 )
Lmusq	Lmusd
--~urd - urq
oL L rd oL rq
Rewriting (28) in the form of (13):
Ji J2 where:
= A( x) + E(x)
(29)
A( x) =
T1 (0 -LmXi)-Lmu s-X2 - Lm (uf + usf2)
L sq 2 Ls
Ls
u	L	L
Y (0s -LmXi)-jmusdX2 - Lm (usqfi + u sdf2 )
(30)
E (x) =
L u , m sd	Lmusq
oLsLr	oL
Lmusq	Lu m sd
oLL	oL„
(31)
Since E(x) is nonsingular, the control scheme is given from (16) as:
urd	= E-'(X)	- A(x) +	Vi 1
u _ rq _			_V2 i_
(32)
To track the control and to obtain a robust control of the parameter variations, the input system is[8]:
v		* Ji	- kpiei	- kii jeidt	(33)
	=	*		f	
V2 _		J2	- kp2e2	- ka 1 e2dt	
Since the rotor-side controller decouples the active and reactive power, the stator active and reactive powers are selected as the output [7-9]:
where e1 is the error between the demanded and the achieved active power, and e2 is related to the reactive power [6-7],
(27)
Figure 4. DFIG control diagram using a simplified input-output linearizing control
6 Simplified input-output linearizing
control with a fuzzy-pi controller
This type of control system is based on the fuzzy logic that makes use of the tolerance, uncertainty, imprecision and fuzziness in the human decision-making process, offers a very satisfactory performance with no need of a detailed mathematical model of the system.
R;f-
Fuzzy Logic Controller
Base of knoniedae
d

		Block of		Interface of		
fiizziftcatiotL	>	Inference	>	defuzsification		Process
Output
Figure 5. Structure of the proposed fuzzy logic controller.
As shown in Fig. 5, our focus is on the fuzzy logic control based on mamdani system. This system has three main parts. First, by using the input membership functions, the inputs are fuzzified, then based on the rule base and inference system, outputs are produced and finally the fuzzy outputs are defuzzified and applied to the main control system. At any time interval,the error and the error change rate are chosen as inputs. Fig. 4 shows a block diagram where the fuzzy controllers are integrated into the rotor side converter to control the DFIG. The main objective of this part is to control the active and the reactive power.
<
L
L

u
u
2
s r
s
146
BELAIMECHE, BENTAALLAH, MASSOUM, WIRA
7 Flc design
The inputs of the fuzzy controller are the error (e) and the error change rate (Ae) and its output is (Au). The universe of (e), (Ae), and (Au) are partitioned into three fuzzy sets, i.e. N (negative), Z (zero) and P (positive). Each fuzzy set is represented by either a triangular or a trapezoidal membership function. The FLC rule base contains nine rules based on IF-THEN [4].
8 Simulation results and discussion
Some illustrations will be introduced now in order to show the dynamic performances of the proposed control system. The controllers are tested at reference tracking and robustness to parameter variations. Our simulations are made on a 1.5 MW generator connected to a 398 V/50 Hz grid.
The DFIG parameters are: Rs = 0.012 Q, Ls = 0.0137 H, Rr =0.021 Q, Lr = 0.0136 H, Lm = 0.0135 H, F = 0.0024 Nm/s, J = 0.0031 kg. m2 and R = 35.25 m.
8.1	Pursuit test
The aim of test is to the study the behaviour of the two controllers at reference tracking with the machine speed constant at its nominal value. As seen from the simulation results shown in Fig.6, the active and reactive powers of the two controllers track almost perfectly their references, contrary to the FLC controller where the coupling effect between the two axes is very clear.
8.2	Sensitivity to the speed variations
The aim of this test is to analyze the impact of speed variations on the DFIG active and reactive powers.
Power curves at variation show important oscillations of the PI controller system with, while they are almost negligible for the fuzzy PI system. Here, there are any variations and the power variations are very small. This result is attractive for the wind-energy applications for ensuring stability and quality of the generated power at speed variations.
Ps Ps-refL
0.4 . , .0.5 Time(s)
Figure 6. Active and reactive powers for PI classic controller
										Irq
				1						
										
										
										
										UJMMMMi
										
										
										
0.4 r ,,0.5
Time(s)
Figure 7. Rotor currents at reference tracking for the PI classic controller
Ps
—Ps-ref —
,.,0.5 0.6
,'k 1													Qs —Qs-ref
1													
k							y						
				I									
„ /				1									
y													
JM	0.445		0.45 0.		5 0.45			J					
													
													
													
													
0.5 Tlme(s)
0.4 0.5 Tlme(s)
Figure 8. Active and reactive power for the PI fuzzy controller
l 10
3000
2500
1000
500
0.1
3.2
3.3
0.9
4 5
1 0f
-1.5
l 10
03
0 1
3 4 5
-10
0.1
A COMPARATIVE STUDY BETWEEN A SIMPLIFIED FUZZY PI AND CLASSIC PI INPUT-OUTPUT LINEARIZING.
147
2000
<
E 1000 -------------------
S
D
U
ii 0|-----------
0 n
-1000 ----------
-2000 ----------
0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time(s)
Figure 9. Rotor currents at reference tracking for the Pi-fuzzy controller
		t					1 0	" [		1 f			1		
														—Ps-ref Ps-PI —Ps-PI film	
	/														
M													/		
	0	0.002 0.004			00f 0.001		.010.795		0.1		0.10				
H															
															
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time(s)
		I 10'														
																
		-	r													
														Qs-ref —Qs-PI		
		0	i 0452		0.454											
	105													—	s-P Ifjzzy	
	5															
																
																
	0		0.0	5	00		1									
			luiiiuuija		itiülUJiM											
																
Time(s)
Figure 10. Active and reactive power at speed variations for PI classic and Pi-fuzzy controller
9 Conclusion
A simplified input-output linearizing fuzzy control applied to a turbine DFIG is propose. A simulation study is made to use it on DFIG of a wind-energy conversion system. The performance of classic PI controller and fuzzy controller used in a wind-power generation are compared. While the design parameters of the PI classic controller have to be tested and adjusted, the fuzzy controller shows strong robustness to parameter of the control system. Comparing the simulation results shows that the fuzzy controller outperforms the PI classic controller. The results are highly consistent with the theoretical calculations and validate correctness of the presented simulation system.
References
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[2]	H.Bekka, S.Taraft, D.Rekioua, S.Bacha: "Power control of a wind generator connected to the grid in front of strong winds", Journal of Electrical Systems (2013), No.9, Vol.3, p. 267- 278
[3]	D.Rekioua, "Wind power electric systems: Modeling, simulation and control, Green energy and technology", Springer, 2014.
[4]	Md.Arifujjaman, "Vector control of a DFIG based wind turbine", Journal of Electrical & Electronics Engineering (2009), No.9, Vol.2, p.1057-1065, Istanbul.
[5]	I.Meny, "Modélisation et réalisation d'une chaîne de conversion éolienne petite puissance", Laboratoire d'électrotechnique de Montpellier (LEM).
[6]	B.Multon, "Etat de l'art des aérogénérateurs électriques", Rapport ECRIN, May 2002.
[7]	JM.Carrasco and al, "Power-electronic systems for the grid integration of renewable energy sources", IEEE Trans. Industrial Electronics (2006), N.53, Vol.4, pp. 1002-1016.
[8]	A.Boyette, P.Poure, S.Saadate," Direct and indirect control of a Doubly Fed Induction Generator wind turbine including a storage unit", In:32th edition of Industrial Electronics Conference IECON2006, IEEE, Paris, France November 6-10, 2006, p. 2517-2522.
[9]	F.Poitiers, B.Toufik, A.Machmoum, "Advanced control of a doubly-fed induction generator for wind energy conversion", Electric Power Systems Research, No.79, 2009, p. 1085-1096.
[10]MJ.Hany,	"Design and Implementation of Neuron-Fuzzy Vector control for Wind-Driven Doubly-Fed Induction generator", IEEE transactions on sustainable energy conversion, No.4, Vol.2, October 2011.
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[12]A.Chaiba,	R.Abdessemed, ML.Bendaas, A.Dendouga, "Performances of Torque TrackingControl for Doubly Fed Asynchronous Motor using PI and Fuzzy Logic Controllers", Journal of Electrical Engineering, No.2, Vol.5, 2005, p. 25-30, Romania.
[13]A.Kerboua,	M.Abid, " hybrid fuzzy sliding mode control of a doubly-fed induction generator in wind turbines", Rev. Roum. Sci. Techn. - Électrotechn. Et Énerg., No.57, Vol.4, 2012, p. 412-421, Bucharest.
[14]M.Bezza,	B.EL.Moussaoui, A.Fakka," Sensorless MPPT fuzzy controller for DFIG wind turbine", Energy Procedia, 2012, Vol.18, p. 339-348.
[15]L.Krichen,	B.Francois, A.Ouali, "A fuzzy logic supervisor for active and reactive power control of a fixed speed wind energy conversion system", Electric Power Systems Research, No.78, 2008, p. 418-424.
[16]Z.Boudjema,	A.Meroufel, A.Bounadja," Nonlinear control of a doubly fed induction generator supplied by a matrix converter for wind energy conversion systems", In: journal of electrical engineering, No.4, Vol.13, December 2013, p. 269-277, Romania.
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Fatima Zohra Belaimeche received the license and the Master degrees in Automatic from the University of Sidi Bel-Abbes (Algeria). Currently, she is a PHD student at the same university. She is a member of the ICEPS (Intelligent Control Electrical Power System) laboratory and her areas of interest are Nonlinear controls of DFIG driven WT.
Abderrahim Bentaallah received his BS, MSc and PhD degrees in Electrical engineering from the Sidi Bel-Abbes University, Algeria, in 1991, 2005 and 2009, respectively. He is currently Professor of electrical engineering at this University. He is member of ICEPS. His research interest is in robust control of electric machines.
Sarra Massoum received the license and the Master degree in Automatic from the University of Sidi Bel-Abbes (Algeria). Currently, she is a PHD student at the same university. She is member of the ICEPS (Intelligent Control Electrical Power System) laboratory and her areas of research are electrical machine control.
Patrice Wira is with the MIPS laboratory (Modelisation, Intelligence, Processus et Systemes) of the University of Haute Alsace where he is an associate professor since 2002. He received the M.Sc. degree and the Ph.D. in electrical engineering, all from University of Haute Alsace. His current research interests are artificial neural networks, adaptive control systems and neuro-control applied to robotics and to visual servoing. His research works also include artificial neural networks applied to harmonic compensation and active power filters