Proceedings of 2016 4th International Conference on Control Engineering & Information Technology

(CEIT-2016) Tunisia, Hammamet- December, 16-18, 2016

Higher Order Sliding mode control For PMSG

In Wind power Conversion System
Bouzaini Karim#i, Ben Slama Sami*2, Cherif Adnane#3
Laboratory: Innovation of Communicant and Cooperative Mobiles (Innov-com,
(PO Box: 2083, Technology city, Km 3.5, Raoued ofAriana, Tunisia),
Faculty o{Sciences o{Tunis El Manar
PB 2092, Belvedere, Tunisia
Ibouzainikarim@gmail,com
3adnane.cher@fst.rnu.tn
*Information System Department, King Abdulaziz University, Jeddah, Saudi Arabia
2 benslama.sami@gmail.com, 2sabdullahl@kau.edu.sa

Abstract- Renewable Energy system (such as: Wind Turbine Ref. [3-4] the authors proposed an advanced control
(WT» provides a dispatching power and large-scale energy techniques and exploited an advanced tool a to design a high
recovery. This latter is a suitable technology in Grid power performance wind turbine controller. In contrast, in Ref. [5],
systems due to its high variability and high levels of renewable the authors presented three comparative Sensorless control
generation. A variable Speed WT is one essential objective of the
strategies applied for PMSG in WECS [5].
researches in this area. Hence, this paper proposed and discusses
an efficient design based on a Higher Order Sliding Mode Compared our work for the pervious related works, our
Control (HOSMC) applied to Permanent Magnet Synchronous contribution is specified by studying and developing a Novel
Generator (PMSG). The HOSMC can provide a feedback control method applied for PMSG.
linearization controller utilizes the torque estimate to ensure a The main idea is to evaluate the level of stability of power
torque reference. The HOSMC feedback provides the generators and the rate of penetration. After that, we will
relationship between the turbine speed and an additional input. apply a robust command against input parameters to regulate
To achieve a stable error dynamics and speed tracking, a linear the fluctuations (like: high order sliding mode control).
control theory is proposed. The applied speed reference is The paper is organized as follows. Description and
selected according to a classical MPPT algorithm. The reliability
mode ling of the WT are given in Section 2. Section 3
and the effectiveness of the proposed design is given by the
Matlab I Simulink environment, from which, the obtained results discusses the grid connection part. Section 4 presents the
have been treated and discussed in details. control strategies developed for the PMSG in WECS system.
The simulation results are discussed in Section 5, and finally,
Section 6 establishes the conclusions.
Keywords- wind turbine, sliding mode control, PMSG, AC/DC
converter, MPPT algorithm. 11. MODELING OF THE WIND CHIME
I. INTRODUCTION A. Modeling of aerodynamics (turbine, gearbox and shaft).
Nowadays, Wind System has become an efficient In this section, the aerodynamic power in the rotor of the
technology for several applications and it's considered as a turbine will be presented according to Eq.1 in order to define
kind of renewable fuels.Wind system is taking an important the aerodynamic torque [6].
role in effectively alleviating the worldwide energy crisis and

l
emission of greenhouse gas [1].
~n =~PJrR2V;Cp (1)
To increase the penetration of wind power systems in the C = Pm = _1_ JrR2v3C
electrical grid in seductive by consequence the cost of returns ne> 0 20 P p
t t

electric power industry. A lot of research and development Inserting the multiplier gain to the aerodynamic torque
work have been carried out on (WECS) and strategies of adaptation and the PMSG torque, the obtained system is as
system control for decades together and quite a good number follows:

:2'
of publications are available in the literature. Also recently a
considerable research work has been carried into areas related (5)
joc
m
=
to generator control and quite a number of papers are available
=_m
in the literature. tG
For example, the authors in Ref [2] used a look-up-table In our work, a multiplier is used to adapt the aerodynamic
(L.UT.) in low wind speeds to achieve maximum energy torque and the PMSG torque. The simplified model of this
capture, and a PI controller in high speeds to regulate the equation is defined as follows:
rotational speed and classical A W compensation. While, in

978-1-5090-1055-4 © 2016 IEEE

1
J dO m = Cm -C, (6) (15)
dt
Where Cr is the load torque given by:
C r = Ccm + f . Om (7)
The shaft which collects the multiplier and the generator I, = ~ [Uo,Jld + UO/ 1q 1 (16)
characterized by eq (8).
In order to improve the performance frequency signal a
J dO m = Cm -Ccm - f ·Om (8)
filter is required before the grid. The model of (RL) Filter
dt
selected is represented in elk (17).
B. Modeling ofPMSG
In this section we present the PMSG modelling.

I
The output voltage variation (vsd, vsq) is described by the
AC Grid
elk (9):

V'd = Ri,d + Ld :t i,d - pLqOmi,q (9)

Fig.1 Grid connection part
V,,, = Ri,,, + L" ~i,,, - pLdOmi,d + pOmrPm
dt The matrix writing is:
According to eq.9, the stator currents are given: d

j
VI) = RI[ + L-I[ + Vr ( 18)
di1d
Tt I (7' . )
= L ~ .I'd - RslSd + pOmL"lS'q
dt
(10) Such as:

+..
d

diSq _ 1 R·I "L . "

~02 : 'I[ = [ill]
= [VOl ~[2 'Vr = [Vd:
T7
--- r -
dt L (Sq .I' Sq P m d I .I'd -
P •• mrPm)
q Vo ~2
The relation between the electromagnetic torque (cem) and T03 IIJ vr3
the (isd, isq) currents are expressed as follows: According to the Park-transformation, the model of the filter
(11 ) in the landmark Park is defined as:

C. AC-DC converter module

(19)
The AC-DC converter is used to control PMSG of wind
chain system and to connect it to the grid chain [9].

I
The stator voltages generated in the landmark Park are
expressed by:

V,',T'd = U,d ~c (12) IV. SLIDING MODE CONTROL OF THE PMSG

V,'q =U,'q ~ A. PMSG control

2
The PMSG command is derived from a few parameters as
Where the generated wind turbine current is defined as: the quadratic and the direct stator current (isd, isq), the
im = ~(U,j'd + U,i,q) (13) referential mechanical speed (OmecJet) and the referential
stator current (IsdJet) [12]. Hence, the tow referential
voltages (VsdJef, Vs~ret) obtained from this command are
Ill. MODELING OF THE GRID CONNECTION
used as input parameters in the AC-DC converter control
In this section, we present and evaluate the grid connection block.
according to:
The capacitor B. Control method of sliding mode of order two
DC-AC converter This control strategy belongs to the variable structure
Filter controls. It consists of forcing the dynamic system to follow a
The capacitor voltage Uc according to im current is given specific surface from sliding defmed ones.
by the following system [7]:
The aim is to determine a command that leads to o-(t, x)

(:~i~.:~'i. (14)
and its first (r -I) derivatives to zero.
a = a(x,t) = ... = a(r-I) = 0
While, the DC-AC converter allows changing the output
capacitor signal to adapt the AC grid connection. This element
The trajectories under 0- are called "order r sliding mode
is represented by eq (15):
relatively to the sliding variable 0-
Then the command is defined as:

2
 (a 1, a2) are positive constants and

r = I: U = -asign(<7) (20)
(27)
{o-+ Io-I± Sign(o-)}
(21)
r=2:u=-a I

0"+ 10-1 2
(28)
C. Application o{this command to the PMSG in WECS
A control is synthesized by a high order sliding mode that
ensures a robust system performance to be against
parametric uncertainties and fluctuations.
any
Vsqre(=-
_.
JLq {PIPm
-
PIP" J Ld
(PIPm n n,
R . J f(PIPm. f
-~~+p~asd+-lsq +- -lsq--::'~
Ld J J J
n);:' . d
.
+::.~-a2s1g" fJ2
)}

The objectives of this command consist of forcing the (29)

machine speed to follow its reference trajectory (0) and
D. Ac IDc converter control
cancelling the direct current id'
The converter is controlled to impose the new reference
The sliding variable is defmed by the following system
voltages. This relationship is given in a reference to an
o-I = ~'.- ~nJecJc/ (22) imaginary mid-point of the capacitor voltage

j
{
CJ 2 -I"d
U,d _"I = ~c (30)
The first and second derivatives sliding mode variables are
given by Usq_rej" -- Vsq_rej. U2c

[;~1[;:J 9[::::J
(23)
= + With V\d ret and V,q _ret the control variables are
calculated from the command of the PMSG
Where:
The overall structure of the controlled conversion chain is
represented in the fig (3) based on a maximum power
extraction algorithm (MPPT). This latter is applied to the most
interesting operating area, which presents the second area (A2)
(24) of wind turbine operation whose orientation angle blade value
0 is equal to zero (see fig (2))[9-11].
IP- [
IP12
Puwer
The control laws applied to the PMSG is

[ V'd_".l
Vsq_ref
l = 9-1[_[XI
X
J+[uIJl
2 U2
(25)
.:AJ ,:
I

I
I
1

,
1

Pn~~--7-------------~I--'~------~
Where rp-I invertible matrix, and (uI, u2) are present, the
"new" command variables.
Compared to the classical sliding mode strategies, these
new orders quasi-continuous controls are computed [8].
According to (Levant, 2005a) as follows [4]:

l r- UIJ =
U2 a1
f':~;:::("'»)1
I' 1 <71 +1<7,1:;:
1
(26)

Fig.2 Wind Turbine Characteristics

W"md

n iSd
im .el
~ l~
~
~
v
I" ~
PMSC
Turbll1t!: " ult/pIlQl" shqf/ ACIDC

f3 le.. ' I'm Convene.'

r--- r-r---+ C ....
V. d
Uc
r--:-:- v. ~
C ap-ac.itor
+
ACIDC Convelt:er

V·"TTU'f +
Filter
+

-
I......t HiRhlqrdtr Grid
Ildlng .A :0
Lo·, ,! up ~-_"f mlld~ OJ" ,,!rt.tr Vc
MI'PT f-+ robl" Cflnrrol V.d _',i f onlTOl
i HI '"
---=--- V:9J</

Fig. 3 Wind Turbine System Control 3

 V. RESULTS AND DISCUSSION
In order to study and to evaluate the performances of the
WECS, several simulation testes have been made under
Matlab/Simulink environment. The used model parameter
input is described in table I

TABLE 1 PARAMETER OF WIND TURBINE AND PMSG

Parameter Signification

R 1.3 wind radius (m)

p 1.22 density of air at atmospheric pressure at 15°C
(Kg/m')
G 1.5 speed multiplier gain
PI 3 Number of pole pair of PMSG
J1 0.0014 total inertia (turbine+shaft +PMSG) (Kg.m')
f 0.001 Coefficient of viscous friction ofthe PMSG (A). isd current component
R, 0.94 stator Resistance ([2) ·3,---------,---------,-------.-----------;,---------,--------,
Ld, Lq 0.012 d,q stator inductance (H)
<Dm 0.404 Magnetic flux of the rotor (Weber) .,
The input wind profile is illustrated in FigA. ·5

,
____ 0 ______ 0 _____ •• _____ 0 ______ 0 ______ 0 ______ • ____ 0 ______ 0 ______ 0 _

·7
8.5

·8
:[ 8
E
:0
•
~ 7.5 --or ---- o----------- ,r------- o--------- ,r---------------
·g O!-----~-------:::-------6:O:
0 -------:O:---------::::::---------:-!,20

•
time(s)

(b). isq current component

'"
~ -- ·f ---- · -----------f------- ·--------- f---------- · ---- of----
Fig.6 direct and quadratic component of the current
L _____ • __ _
6.5
____ 0 ___________ , _______ 0 _________ , _________ _ 0 _____

, ,

6L-____ ~ ______ ~ ______ _ L_ _ _ _ _ _- L_ _ _ _ _ _~_ _ _ _~

o 20 40 60 80 100 120
Time(s)
Fig. 4 input wind profile

The mechanical speed, resulting from the MPPT algorithm is

given bay (fig. 5)
The basic parameters used for the PMSG command area:
- The direct and quadratic stator current (fig.6)
- The direct and quadratic control voltage (fig.7)

(c).vsd-refvoltage component

(D).vsq-refvoltage component
time{s)
Fig. 5 the mechanical speed ofthe PMSG Fig.7 direct and quadratic component of the voltage control
4
The simulation results show that the application of HOSMC is This work can be ameliorated by adding a pitch control
performed. In fact, this later generates a less fluctuating power system to limit the aerodynamic power to the nominal value of
compared to the classical sliding mode (SM) control (fig.8). thePMSG.
It should be noted that reached a negative power value caused
the generative mode machine functioning. ABBREVIATION LIST
Cl' aerodynamic efficiency ofthe turbine and the speed

U,d,U,q Represent the converter control signals.

Ai specific value

~)d' VOq
Modulated voltage by the inverter in the landmark Park

U Od ' U Oq current lines generated by the filter in the coordinate

system Park
i, The modulated current grid side.
V Oi Single voltage modulated by the inverter for phase i
Vri Single voltage for the (i) grid phase.
iJi current generated by the filter for phase i.

Time(s)
Fig.8 Wind turbine power variation vs. Time REFERENCES

The reactive power is given by (fig.9). [I] GUAN WeiLU Yan. Status and development trend of wind power
generation at home and abroad [J]. Jilin Electric Power,2008,l:47-50
It is shown that the reactive power incurs several fluctuations [2] F. D. Bianchi, H. De Battista, and R. 1. Mantz, Wind Turbine Control
noticed in some time intervals. This fluctuation can be Systems: Principles, Modelling and Gain Scheduling Design,
reduced by applying the HOSM control to the DCIAC (Advances in Industrial Control Series). London, U.K.: Springer-Verlag,
converter. 2006.
[3] T. Senjyu, R. Sakamoto, N. Urasaki, T. Funabashi, H. Fujita, and H.
Sekine, "Output power leveling of wind turbine generator for all
operating regionsby pitch angle control,"IEEE Trans. Energy Convers.,
voI. 21, no. 2,pp. 467-475, Jun. 2006.
[4] C. Evangelista, F. Valenciaga, and P. Puleston, "Active and reactive
power control for wind turbine based on a MIMO 2-sliding mode
algorithm with variable gains,"IEEE Trans. Energy Convers., voI. 28,
1.5
no.3,pp.682-689,Sep.2013.
[5] Jemaa Brahmi, Lotfi Krichen and Abderrazak Ouali "A comparative
0.5
study-between-three-sensorless control strategies for PMSG in wind
energy conversion system" Applied Energy 86 (2009) 1565-1573.
~o ~----~------~------------ __ ~~ ____ doi: 10. 1016Zi.apenergy.2008. 11.010
f
~.o.5 [6] R.J. Wai, C.Y.Lin and Y.R.Chang. "Novel maximum-power-extraction
algorithm-for-PMSG-wind-generation
system".IETElectLPoweLAppI.2007,5:275-283.
-1.5 [7] ALevant. "Quasi-continuous high-order sliding-mode controllers".
IEEE Transactions on Automatic Control, 50(11), 1812-1816,2005.
[8] A Levant. "Homogeneity approach to high-order sliding mode
design", Automatic, VoI.41, pp. 823-830,2005.
time(s)
[9] Md. Enamul Haque, Michael Negnevitsky and Kashem M. Muttaqi,"A
Fig.8 reactive power Novel Control Strategy for a Variable-Speed Wind Turbine With a
Permanent-Magnet Synchronous Generator," IEEE Transactions On
VI. CONCLUSIONS Industry Applications,Yol. 46, No. I, pp. 331-339, January/February
This paper presents model developments of wind energy 2010/.
conversion chain and higher order sliding mode control [10] D. Zhi, L. Xu, and B. W. Williams, "Improved direct power control of
grid-connected DC/AC converters," IEEE Transactions on Power
strategy ofPMSG used in WECS. Electronics, vol. 24, no. 5, pp. 1280-1292, May 2009.
From the obtained results, it can be concluded that this non- [11] A BouscayroI, Ph. Delarue, X. Guillaud, "Power strategies for
linear control method has worked satisfactorily. In terms of maximum control structure of a wind energy conversion system with a
robustness against parameters variation, a comparative study synchronous machine", Renewable Energy 30 (2005)2273-2288,
www.eIsevier.com/locate/renene.
has been presented between this command and classical [12] W. Qiao, X. Yang, and X. Gong,"Wind speed and rotor position
sliding mode control to prove the durability of HOSMC. sensorless control for direct-drive PMG wind turbines," IEEE Trans.
In addition, the MPPT algorithm based on the characteristic Ind. AppI., voI. 48, no. I, pp. 3-11, Jan/Feb. 2012.
curve ofthe WT was ensured.
Moreover, from the results it can also be concluded that
with the control mode proposed, the power fluctuation coming
from a wind generator is effectively compensated.