Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

236 
 

 

Modeling and Simulation of a Wind Turbine Driven 

Induction Generator Using Bond Graph 
A. Ramdane *, A. Lachouri *, M. Krikeb * 

*Team Leader in Automatic Laboratory, Electrical Engineering Department, Faculty of Technology,
 

University of 20 August 1955, Skikda. 21000, Algeria, ID, 83844-1133, USA.,
 

E-mail: Adlene_soft2005@yahoo.fr, alachouri@yahoo.fr,  krikeb@yahoo.fr     

 

Abstract - This paper deals with the modelling and 

simulation of wind turbine driven by induction 

generator. Usually in mechatronic systems, several 

types of energy are involved. By its nature of a power 

conserving description of a system, the Bond-Graph 

method is especially practical when several physical 

domains have to be modeled within a system 

simultaneously. This is certainly the case in wind 

turbine systems where mechanical and electrical 

systems in several combinations are present. This 

work presents an implementation of the wind turbine 

model in bond graph approach. Simulation results are 

carried out by means of simulation in 20-sim software 

environment. 

 

Keywords - wind turbine, modelling, bond graph, 

induction generator. 

 

I. INTRODUCTION 

 

    Energy consumption has increased considerably in 

recent years with the technology evolution. This has 

increased the demand for fossil fuels and has made 

firstly, electrical energy more expensive and 

secondly, the fossil fuels have a several disasters on 

the environment protection by the emissions of 

greenhouse gases and undesired particles into the 

atmosphere. Because of such reasons, it is 

necessary to focus on other forms of energy 

production to meet the growing needs of today's 

world. Furthermore, the wind energy, being one as an 

efficient source of alternative and cleanest sources of 

electricity, has emerged as one of the most preferred 

sources for electricity generation. 

 

The wind energy is the kinetic energy of the flowing 

air mass per unit time. Therefore, when performing 

wind power integrated network planning or analysis of 

the operation, the engineers have put a lot of effort in 

modelling the wind rather than focusing on the 

problem itself. Thus, a wind model compatible with 

the analytical tools of commercial power system is in 

imminent need.  

In Electromechanical Engineering, the global analysis 

of systems is difficult because of their heterogeneity 

and their multi-domains nature. Nevertheless, this 

system approach is essential because it underlines 

couplings between elements of different physical 

fields. To facilitate this analysis, the unified formalism 

Bond Graph is used. This modelling method 

illustrates the energetic transfers in the system. 

Moreover, this methodology offers interesting 

solutions in terms of system analysis.  

 

Much research has been done on the modelling and 

control of wind turbines [2], [4], [6] and [7]. Most of 

this research has been done using simple wind 

mechanical and aerodynamic models that overlook a 

number of important features. Research on wind 

turbines based on more sophisticated mechanical 

and aerodynamic models was made only with 

relatively simple models of electric generator, its 

controllers, and model of the power system. This is 

because most researchers who have studied the 

wind power, they are focusing on aspects either 

electrical or mechanical part, without paying attention 

to the operation of the complete electromechanical 

system. There are many types of WT models, ranging 

from single mass, one state model to multiple mass 

models. In a simulation point of view, it is desirable 

that the model is as simple as possible and can 

capture as much of the dynamics that appear in 

reality.  

 

In this context, our study is interested in the wind 

turbine system. This document is based on modelling 

and simulation method with Bond Graph (BG) applied 

to the wind turbine driven by generator induction. This 

method becomes a powerful tool when the complex 

interaction of subsystems of different types should be 

evaluated. The paper is organised as follows: The 

section 2 gives a brief introduction on bond graph 

methodology then, on finds in section 3 a modelling 

of different parts of wind turbine system and their 



Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

237 
 

bond graph in 20-sim software is presented. In 

section 4 is illustrated the simulation results and 

theirs discuss. A conclusion is given at the end of this 

paper. 

 

II. BOND GRAPH 

 

A. Bond Graph methodology 

The methodology of the bond graph modelling is 

based on the characterization of power exchange 

phenomena within a system. The idea of the bond 

graph modelling is the representation of dissipated 

power as the product flow and effort to bind the 

various junctions to reproduce the system. The bond 

graph is a powerful tool in modelling systems; 

especially in cases where subsystems of different 

physical character (mechanical, electrical, thermal, 

hydraulic …) are interact. The exchange of energy 

between the subsystems of a more complex system in 

bond graph modelling is of an essential significance. 

Bond graph is therefore a directed graph whose 

nodes represent subsystems and arrows - the transfer 

of energy between the subsystems. 

 

B. Bond Graph Elements 

In BG modelling, there are a total of nine different 

elements. We will first present the basic elements of 

BG and introduce the causality assignments. 

 

Source element: there are two type of 1-ports source: 

the effort source and the flow source. In each case, an 

effort or flow is assumed to be maintained constant 

independent of the power supplied; the constitutive 

relation and causality is showing in Fig.1. 

 

 
 

Fig .1. Sources elements 

 

Resistive element: is an element in which the effort 

and flow variables at the single port are related by a 

static function Fig2. 

 

Inertia element: the inertia port corresponds to the 

electrical inductors, the momentum p is related the 

flow f. There are two choices for the causality 

assignment for the I-element Fig2.  

 

Compliance element: is an element that relates effort 

e and displacement q. the power flows into the port 

and a sign convention similar to that used for the 

resistor is adopted Fig.2. 

 

 
 

Fig .2. Resistance, Inertia and compliance elements 

 

Transformer and gyrator: the transformer and gyrator 

can work in two ways; transformer transforms a flow 

to another flow or an effort to another effort. The 

gyrator transforms a flow into an effort or transforms 

the effort into a flow. 

 

 
 

Fig .3. Transformer and Gyrator elements 

 

Junctions: there are two different types of junctions 

that connect the different parts in BG, the 0-junction 

and 1-junction. Junctions are power conserving at 

each instant and the power transport of all bonds  add 

up to zero at all times. The junction elements 

represent the two types of connections, which, in 

electrical terms, are called the series, and parallel 

connections 
 

III. MODEL DESCRIPTION 
 

 
 

Fig .4. Wind turbine model description 

 

In this section, the dynamic simulation model is 

described for the proposed wind turbine energy 

conversion. The block diagram of the integrated 

overall system is shown in Fig.4. Afterwards, each 

sub-model of the wind turbine is presented and 



Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

238 
 

combined to obtain a complete model of the wind 

turbine. 

The all parts of system modelling in 20-sim software is 

showing in Fig.5. 

 

 
 

Fig .5. System Parts modelling in 20-sim software 

 

A. Aerodynamic Model  

Wind turbine electrical generation systems power 

comes from the kinetic energy of the wind. Thus, it 

can be expressed as the kinetic power available in the 

stream of air multiplied by a Cp factor called power 

coefficient or Betz’s factor. The Cp Mainly depends on 

the relation between the average speed of the air 

across the area covered by the wind wheel and its 

angular speed and geometric characteristics of the 

turbine. The power extracted by the wind turbine has 

the following expressions [2]:.  
 

𝑃𝑤 =
1

2
.𝜌.𝐴.𝐶𝑝.𝑉𝑊

3        (1) 

𝐴 = 𝜋.𝑅3           (2) 

Where  𝑃𝑤 is the air stream kinetic power, ρ the air 

density assumed to be constant, 𝐴 is the surface 

covered by the wind wheel and 𝑉𝑊 the average wind 
speed. The power that wind turbine can catch from 

wind is: 

𝑇𝑊 =
𝑃𝑤

Ω
        (3) 

There have been different approaches to model the 

power coefficient ranging from considering it to be 

constant for steady state and small signal response 

simulations to using lookup tables with measured 

data. Another common approach is to use an analytic 

expression [2]:  

𝐶𝑝 = 0.22(
116

𝜆′
− 0.4𝛽 − 5)𝑒

−12.5

𝜆′      (4) 

With:            

  
1

𝜆′
=

1

𝜆+0.08𝛽
−
0.035

𝛽3+1
            (5) 

Where λ is so called tip-speed ration and it is defined 

as λ =
ω𝑅

𝑉𝑤
            (6) 

and β is the pitch angle. 

 

Fig .6 Power Coefficient of wind turbine 
 

In general the 𝐶𝑝 coefficient is represented by the 

Graph which depends on the tip-speed ratio λ and the 

pitch angle β. 

The bond graph of aero-dynamical part of wind turbine 

model implemented in 20-sim software from [4] is 

show in Fig.4. 

 

 
 

Fig .7 The bloc diagram Model of Aero-dynamical part of wind 
turbine model in 20-sim Software 

 

 

B. Mechanical Part 

The mechanical part of the wind turbine system 

includes all the mechanical elements of Systems 

(blades, lock rotor, shafts, Speed Multiplier (gear box) 



Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

239 
 

... etc.).This multiplier is modelled mathematically in 

[3] for the following equations: 

𝑪𝒓 =
𝑻𝒎

𝑮
         (7) 

𝛀𝒕𝒖𝒓𝒃𝒊𝒏𝒆 =
𝛀𝒎𝒆𝒄

𝑮
        (8) 

G: The speed multiplier gain 

𝑱 =
𝑱𝒕𝒖𝒓𝒃𝒊𝒏𝒆

𝑮𝟐
+ 𝑱𝒓           (9) 

 

The fundamental equation of dynamics used to 

determine the evolution of the mechanical speed from 

the total mechanical torque (𝑪𝒎𝒆𝒄) applied to the 
rotor: 

𝑱 
𝒅𝛀𝒎𝒆𝒄

𝒅𝒕
= 𝑪𝒎𝒆𝒄       (10) 

𝐽 The total inertia appears on the generator rotor. The 
mechanical torque depends on the electromagnetic 

torque (𝑪𝒆𝒎) produced by the generator, the torque of 

viscous friction (𝑪𝒗𝒊𝒔) and load torque (𝑪𝒓). 

𝑪𝒎𝒆𝒄 = 𝑪𝒓 − 𝑪𝒆𝒎 − 𝑪𝒗𝒊𝒔             (11) 

The viscous torque is modelled by. 

𝑪𝒗𝒊𝒔 = 𝒇.𝜴𝒎𝒆𝒄         (12) 

𝒇: Is the viscous friction coefficient. 

 

C. Three Masses Model  

The equivalent model of a wind turbine drive train is 

presented in Fig 6. The masses correspond to a large 

mass of the wind turbine rotor, masses for the 

gearbox wheels and a mass for generator 

respectively. 

 

Fig 6. Three-mass model of a wind turbine drive train. 
 

The inertia of the low-speed shaft also includes the 

inertia of the rotor, while the friction component 

includes bearing frictions. The dynamics of the low-

speed shaft is: 

𝑻𝒘𝒕 − 𝑻𝟏 − 𝑩𝒘𝒕𝛀𝒘𝒕 = 𝑱𝒘𝒕
𝒅𝛀𝒘𝒕

𝒅𝒕
     (13) 

Where: 

𝐵𝑤𝑡 Is the viscous friction of the low-speed shaft [Nm/(rad/s)], 

𝐽𝑤𝑡 Is the moment of inertia of the low-speed shaft [Kgm2],  

𝑇𝑤𝑡 Is the torque acting on the low-speed shaft [Nm], 

 𝜃𝑤𝑡 Is the angle of the low-speed shaft [rad], 

The inertia of the high-speed shaft also includes the 

inertia of the gearbox and the generator rotor. The 

friction coefficient covers bearing and gear frictions. 

The dynamics of the high-speed shaft is: 

𝑻𝒉 − 𝑻𝒈𝒆𝒏 − 𝑩𝒈𝒆𝒏𝜴𝒈𝒆𝒏 = 𝑱𝒈𝒆𝒏
𝒅𝜴𝒈𝒆𝒏

𝒅𝒕
     (14) 

Where: 

𝐵𝑔𝑒𝑛: The viscous friction of the high-speed shaft [Nm/(rad/s)]; 

𝐽𝑔𝑒𝑛  : The inertia moment of the high-speed shaft [Kgm
2]; 

𝑇𝑔𝑒𝑛 : The generator torque [Nm]; 

𝑇ℎ     : The torque acting on the high-speed shaft [Nm]; 

𝜃𝑔𝑒𝑛 : The angle of the high-speed shaft [rad]; 

The remaining part of the gearbox modeling is to 

apply a gear ratio, as defined below. 

𝑻𝒉 =
𝑻𝟏

𝑲𝒈𝒆𝒂𝒓
                                             (15) 

𝐾𝑔𝑒𝑎𝑟 is the drive train gear ratio. 

The torsion of the drive train is modelled using a 

torsion spring and a friction coefficient model, 

described according to: 

𝑻𝟏 = 𝑲𝒘𝒕𝜽∆ + 𝑫𝒘𝒕�̇�∆      (16) 

𝜽∆ = 𝜽𝒓 −
𝜽𝒈𝒆𝒏

𝑲𝒈𝒆𝒂𝒓
     (17) 

Where: 

𝐷𝑤𝑡 is the viscous friction of the low-speed shaft [Nm/(rad/s)] 

𝐾𝑤𝑡 is the torsion stiffness of the drive train [Nm/rad] 

𝜃∆is the torsion angle of the drive train [rad] 

 

𝑻𝟏(𝒕) = 𝑲𝒘𝒕 (𝜽𝒓 −
𝜽𝒈𝒆𝒏

𝑲𝒈𝒆𝒂𝒓
) + 𝑫𝒘𝒕 (𝜴𝒘𝒕 −

𝜴𝒈𝒆𝒏

𝑲𝒈𝒆𝒂𝒓
)  (18) 

After simplification and substituting equations obtains 



Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

240 
 

{
 
 
 
 

 
 
 
 𝑱𝒘𝒕

𝒅𝛀𝒘𝒕

𝒅𝒕
= 𝑻𝒘𝒕 − 𝑲𝒘𝒕 (𝜽𝒓 −

𝜽𝒈𝒆𝒏

𝑲𝒈𝒆𝒂𝒓
) − (𝑫𝒘𝒕 + 𝑩𝒘𝒕)𝛀𝒘𝒕

                                                               + 
𝑫𝒘𝒕

𝑲𝒈𝒆𝒂𝒓
𝛀𝒈𝒆𝒏[𝑵𝒎]

          

𝑱𝒈𝒆𝒏
𝒅𝛀𝒈𝒆𝒏

𝒅𝒕
=

𝑲𝒘𝒕

𝑲𝒈𝒆𝒂𝒓
(𝜽𝒓 −

𝜽𝒈𝒆𝒏

𝑲𝒈𝒆𝒂𝒓
) +

𝑫𝒘𝒕

𝑲𝒈𝒆𝒂𝒓
𝛀𝒘𝒕                        

                                − (
𝑫𝒘𝒕

𝑲𝒈𝒆𝒂𝒓
+ 𝑩𝒈𝒆𝒏)𝛀𝒈𝒆𝒏 − 𝑻𝒈𝒆𝒏[𝑵𝒎]           

�̇�∆ = �̇�𝒘𝒕 −
�̇�𝒈𝒆𝒏

𝑲𝒈𝒆𝒂𝒓
[𝒓𝒂𝒅 𝒔⁄ ] 

        (19) 

Three first order differential equations have been 

derived in this section in order to describe the 

behavior of the drive train. In the next section, the 

effect on the tower from the aerodynamic thrust is 

considered. 

Bond graph bloc diagram model of three masses 

system is showing in Fig.8. 

 

 

Fig 8. Multi masses system model 
 

D. Electrical Part 

The generator used for the wind system is an 

asynchronous squirrel-cage generator whose 

parameters are quoted in table1. The model of the 

asynchronous machine is deduced from the two-

phase machine by supposing that the variables are 

expressed in a reference frame x-y turning at the 

speed of the electric field. The results obtained by 

simulation illustrate the behaviour of this generator 

and give the par values of operation. 

The induction machine equations are [2]: 

 

{
  
 

  
 

𝑈𝑠𝑥 = 𝑅𝑠𝐼𝑠𝑥 + 𝑆Ψ𝑆𝑋 − 𝜔𝑆. Ψ𝑆𝑌

𝑈𝑠𝑦 = 𝑅𝑠𝐼𝑠𝑦 + 𝑆Ψ𝑆𝑦 − 𝜔𝑆. Ψ𝑆𝑥

0 = 𝑅𝑟𝐼𝑟𝑥 + 𝑆Ψ𝑟𝑥 − (𝜔𝑆 − 𝜔𝑟)Ψ𝑟𝑦

0 = 𝑅𝑟𝐼𝑟𝑦 + 𝑆Ψ𝑟𝑦 − (𝜔𝑆 − 𝜔𝑟)Ψ𝑟𝑥

    𝐶𝑒   =  𝑃. 𝐿𝑠𝑟(𝐼𝑠𝑦. 𝐼𝑟𝑥 − 𝐼𝑠𝑥. 𝐼𝑟𝑦)
ΨS = Ls. Is + Lsr. Ir                          

Ψr = Lr. Ir + Lsr. Is                         

                 (20)      

 

This system can be presented as follows: 

{
 
 
 
 

 
 
 
 

𝑆Ψ𝑠𝑥  = 𝑈𝑠𝑥 − 𝑅𝑠. 𝐼𝑠𝑥 + 𝜔𝑠. Ψ𝑠𝑦

𝑆Ψ𝑠𝑦 = 𝑈𝑠𝑦 − 𝑅𝑠. 𝐼𝑠𝑦 + 𝜔𝑠. Ψ𝑠𝑥

𝑆Ψ𝑟𝑥  = 𝑅𝑟. 𝐼𝑟𝑥 + (𝜔𝑆 − 𝜔𝑟)Ψ𝑟𝑦

𝑆Ψ𝑟𝑦  = 𝑅𝑟. 𝐼𝑟𝑦 + (𝜔𝑆 − 𝜔𝑟)Ψ𝑟𝑥

    𝐶𝑒   =  𝑃. 𝐿𝑠𝑟(𝐼𝑠𝑦. 𝐼𝑟𝑥 − 𝐼𝑠𝑥. 𝐼𝑟𝑦)

𝐼𝑠       =
Lr.Ψs+Lsr.Ψr

Ls.Lr−Lsr
2
                          

𝐼𝑟      =
Ls.Ψr+Lsr.Ψs

Ls.Lr−Lsr
2
                         

                 (21)      

     
𝑈𝑆𝑋 ,𝑈𝑠𝑦 : The stator voltage Components expressed in x-y 
reference. 

𝐼𝑆𝑋 , 𝐼𝑠𝑦 : The stator current Components expressed in x-y 
reference. 
𝑅𝑆  : Stator resistance; 

𝑅𝑟 : Rotor resistance; 

𝐿𝑆  : Stator Inductance; 

𝐿𝑟  : Rotor Induction; 

𝐿𝑆𝑟 : Mutual inductance; 

𝑃   : Number of pole pairs; 

𝐶𝑒  : Electromechanical torque; 

𝜔𝑆  : Speed of the electric field; 

𝜔𝑟  : Electric rotor speed; 

 

The bond graph of induction machine in 20-sim 
software using library developed in [5] is showing in 
Fig.9. 
 

 

Fig 9. Induction Generator bond graph model 
 

IV. SIMULATION RESULTS 

Simulation step is done on a specific bond graph 

software 20-sim, which is an object oriented 

hierarchical modelling software. It allows users to 

create models using bond graph, block-diagram and 

equation models. A list of numerical values of wind 

turbine system parameters used in this simulation is 

presented in Table-1. 

 

 

Ce

Omega2

Omega1

Omega3

Constant1

1

0.00875 s

LinearSystem2

1

0.004375 s

LinearSystem1Constant2

Constant3

20

s

LinearSystem3

K

Gain

1

0.004375 s

LinearSystem4

20

s

LinearSystem5

K

Gain1



Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

241 
 

Table 1. Model Parameters 
 

Nominal Power Pn=180KW 

Rotor Diameter D=23.2m 

Rotor Speed Ω=42tr/min 

Multiplier Coefficient 23.75 

Number of Blades 3 

Air Density ρ=1Kg/m3 

Turbine  Moment Inertia JT=102,8Kgm
2 

Generator Moment Inertia JG=4,5Kgm
2 

Rigidity Coefficient K12=2700Nm/rad 

Damping Coefficient B12=0.1Nms/rad 

Number of Pairs P=3 

Stator Resistance Rs=0.0092Ω 

Rotor Resistance Rr=0.0061Ω 

Stator  Mutual Inductance Lls=186μH (Ls= Lls+ Lm) 

Rotor  Mutual Inductance Llr=427μH (Lr= Llr+ Lm) 

Magnetizing Inductance Lm=6.7mH (Lsr= Lm) 

 

The Fig.5 shows all parts of system modelling 

implemented in 20-sim software. The Fig.6 presents 

the Power Coefficient 𝐶𝑝 evolution function of tip-

speed ration (λ). Through this figure, we can easily 

see that the evolution of the 𝐶𝑝 retrieve its maximum 

at the 𝜆𝑜𝑝 = 3. The Fig.7 illustrated a bond graph bloc 

diagram Model of Aero-dynamical part of wind turbine 

and Fig.8 presents a Bond graph of Multi mass model 

under 20-sim software. The Fig.9 depicts Induction 

Generator bond graph model. The Fig.10 and Fig.11 

show the mechanical power and torque curves 

respectively of the wind turbine. They occur the 

maximum point at the  𝜆𝑜𝑝 = 3 . The Fig.12 shows the 

power coefficient with blade pitch 𝛽 and its maximum 

value at 𝜆𝑜𝑝 = 3. With regard to the instantaneous 

torque (Fig.13), we can indicate the presence of 

oscillations in magnitude for a very short time at start 

up, and then these oscillations are cleared. Figures 

(Fig.14-16) show the curves velocities of multi-mass 

model. They have strong oscillations during the 

transient regime during 0.02s, and converse to its 

nominal speed at 157rad /s. 

 

 
Fig 10. Mechanical Power  in 20-sim software 

 
Fig 11. Mechanical Torque In 20-sim Software 

 

 
Fig 12. Power Coefficient                                                    

 

 
Fig 13. Torque characteristic 

 

 
Fig 14. First mass Speed 

 
 

Fig 15. Second mass Speed 

0 2 4 6 8 10 12 14

Lamda

0

50000

100000

150000

200000 Pm(W)

0 0.5 1 1.5 2 2.5 3
time {s}

-10

0

10

20

30

Ce (N.m)

0 0.5 1 1.5 2 2.5 3
time {s}

0

50

100

150

200

Omega3(rad/s)

0 0.5 1 1.5 2 2.5 3
time {s}

0

50

100

150

200

Omega1(rad/s)



Journal of Renewable Energy and Sustainable Development (RESD)      Volume 1, Issue 2, December 2015 - ISSN 2356-8569 

242 
 

 
Fig 16. Third mass Speed 

 

 

V. CONCLUSION  

 

In this paper, a power conversion system was 

studied with a “system viewpoint methodology” 

by using a Bond Graph technique. However, the 

different fields of energy conversion, the 

nonlinearity and the different dynamics of the 

system involve the use of a global unified 

formalism for studying the global system. The 

software ‘‘20-sim’’ permit to implemented the 

bond graph system model’s. The simulation 

results from this approach confirm one of the 

benefits of BG as a generally usable approach to 

modelling mechatronic systems and offers 

interesting solutions in terms of system 

diagnosis and analysis. 

 

REFERENCES 

 
[1] A.Djeziri, R. Merzouki, B. Ould Bouamama, G. 

Dauphin-Tanguy. ‘Bond Graph Model Based For 

Robust Fault Diagnosis’ IEEE, 2007, 1-4244-

0989-6/07. 

 

[2] Sanae Rechka, GillesRoy, Sébastien Dennetiere 

et Jean Mahseredian,’Modélisation de systèmes 

électromécanique multi-masses à base de 

machines asynchrones, à l’aide des outils 

MATLAB et EMTP,avec Application aux éoliennes 

,juillet 2004. 

 

[3] F. Kendouli, K. Nabti, K. Abed et H. Benalla,’ 

Modélisation, simulation et contrôle d’une turbine 

éolienne à vitesse variable basée sur la 

génératrice asynchrone à double alimentation ‘ 

Revue des Energies Renouvelables Vol. 14 N°1 

(2011) 109 – 120. 

 

[4] J.G. Slootweg, S.W.H.H Polinder and W.L. king, 

‘General Model for representing variable speed 

wind turbines in power systems dynamics 

simulations’, IEEE Transaction on power system, 

Vol 18, No. 1, February 2003, pp. 144-151. 

 

[5] Sergio Junco, Gonzalo Dieguez, Facundo 

Ramirez, ‘ une librairie 20-sin pour la simulation 

basée bond graphs de système de commande 

des machines électrique ‘cifa_2008_T18-I-07-

0338. 

 

[6] Lucian Mihet-Popa, Frede Blaabjerg, Ion Boldea,’ 

Wind Turbine Generator Modeling and Simulation 

Where Rotational Speed is the Controlled 

Variable’,IEEE Transactions On Industry 

Applications, Vol. 40, No. 1,  January/February 

2004. 

 

[7] B. ChittiBabu , K.B. Mohanty,’ Doubly-Fed 

Induction Generator for Variable Speed Wind 

Energy Conversion Systems- Modeling & 

Simulation', International Journal of Computer and 

Electrical Engineering, Vol. 2, No. 1, February, 

2010 ,1793-8163. 

 

[8] Tore Bakka and Hamid Reza Karimi,’ Wind 

Turbine Modeling Using The Bond Graph’, 2011 

IEEE International Symposium on Computer-

Aided Control System Design (CACSD),Part of 

2011 IEEE Multi-Conference on Systems and 

Control Denver, CO, USA. September 28-30, 

2011. 

 

 

 

 

 

 

 

 

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