Study of Wind Turbine based Variable Reluctance Generator using Hybrid FEMM-MATLAB Modeling

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 7, No. 1, February 2017, pp. 1~11
ISSN: 2088-8708, DOI: 10.11591/ijece.v7i1.pp1-11  1
Journal homepage: http://iaesjournal.com/online/index.php/IJECE
Study of Wind Turbine based Variable Reluctance Generator
using Hybrid FEMM-MATLAB Modeling
Tariq Benamimour, Amar Bentounsi, Hind Djeghloud
LGEC, Lab. of Electrotechnique Dept., University of Mentouri Constantine, Algeria
Article Info ABSTRACT
Article history:
Received Jan 3, 2016
Revised Mar 21, 2016
Accepted Jun 13, 2016
Based on exhaustive review of the state of the art of the electric generators
fitted to Wind Energy Conversion System (WECS), this study is focused on
an innovative machine that is a Variable Reluctance Generator (VRG).
Indeed, its simple and rugged structure (low cost), its high torque at low
speed (gearless), its fault-tolerance (lowest maintenance), allow it to be a
potential candidate for a small wind power application at variable wind
speed. For better accuracy, a finite element model of a studied doubly salient
VRG is developed using open source software FEMM to identify the
electromagnetic characteristics such as linkage flux, torque or inductance
versus rotor position and stator excitation. The obtained data are then
transferred into look-up tables of MATLAB/Simulink to perform various
simulations. Performance of the proposed wind power system is analyzed for
several parameters and results are discussed.
Keyword:
Finite element analysis
Matlab/simulink
Modeling and simulation
Variable reluctance generator
Wind turbine
Copyright © 2017 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Tariq Benamimour,
LGEC, Lab. of Electrotechnique Dept.,
University of Mentouri Constantine,
Tel/Fax: +213 31819013, Algeria.
Email: tarekbenamimourelt@yahoo.fr
1. INTRODUCTION
Emerged recently in a context of energy crisis and rising pollution, the concept of sustainable
development has contributed to the development of renewable energies. Among the alternative resources,
wind power has seen the strongest growth. Various wind energy conversion systems (WECS) have been
proposed in association with different structures of electric generators where the major requirements are: high
power density, efficiency, high reliability, lowest maintenance, reduction of the system parts (gearless),
reasonable cost and other market criteria. The potential electrical generators candidates for WECS which
may satisfy the above criteria are standard self excited induction generator (SEIG), doubly-fed induction
generator (DFIG), permanent magnetic synchronous generator (PMSG) and, recently, a switched reluctance
machine (SRM) used either in high speed drive or low speed generator [1-4]. In a comparative study of
electrical generators fitted to wind turbine systems, the authors in [5] conclude that the PMSG seems to be
the most adapted candidate as illustrated in the Table 1 below taken from this reference, where the evaluation
is based in the main characteristics of the WECS, each them is graded from 1 to 5 points. Recently, due to
numerous advantages (simple structure, robustness, high performance, low cost), an innovative variable
reluctance generator (VRG) [6-14] has been recognized to have potential for wind power applications. This
explains our interest in the study of this type of generator.
The main contribution of this work is related to an original numerical-analytical approach carried
out under coupled FEMM-MATLAB user-friendly softwares used to model with better accuracy the studied
6/4 three-phase VRG fed with asymmetric half bridge converter [15].

 ISSN: 2088-8708
IJECE Vol. 7, No. 1, February 2017 : 1 – 11
2
The paper is organized as follows: Section 2 describes the main characteristics of wind turbine and
the finite element modeling of the studied VRG. In Section 3, the simulation process of WECS using
MATLAB/Simulink is presented and results are discussed. The paper concludes in Section 4.
Table 1. Wind Power Systems Evaluation [5]
2. MODELING OF WIND ENERGY CONVERSION SYSTEM
The wind energy conversion system (WECS) shown in Figure 1 is relatively standard. Usually, it
consists of four parts:
a. The wind turbine converts wind energy into kinetic energy.
b. The gearbox to adapt the speed of the turbine to that of the generator.
c. The generator that converts mechanical energy into electrical energy.
d. The static converter DC-AC which will not be examined in this study.
Figure 1. Wind Energy Conversion System
In order to perform simulations under MATLAB/SIMULINK environment, the mathematical model
of the WECS is represented by the synoptic diagram shown in Figure 2.
Generation
Systems
Characteristics
DFIG IG PMSG SRG
Power Density
Efficiency
Controllability
Reliability
Technological maturity
weight
Cost
4.5
4
5
4
5
3.5
4
3.5
3.5
4
3
5
3.5
4
5
5
5
4
4
5
3
3.5
3.5
4
5
4
2
5
 Total
30 26.5 31 26

IJECE ISSN: 2088-8708 
Study of Wind Turbine based Variable Reluctance Generator Using Hybrid .... (Tariq Benamimour)
3
Figure 2. Synoptic Diagram of the WECS
2.1. Main Characteristics of Wind Turbine
The wind power converted into mechanical power by the turbine is given by (1):
3
),(
2
1
AvCP pm  (1)
where  is the air density (kg/m3
), A=R2
is the turbine swept area (m2
), R is the radius of rotor blade (m),
Cp (,) is the power coeficient function of the blade pitch angle  (deg) and the tip-speed ratio (TSR) given
by:
v
R t
 (2)
where t is the rotational speed of the turbine (rad/s)
Hence, the TSR (  ) can be controlled by the rotational speed of generator. The coefficient Cp can
be represented by the following relationship [16]:


0068.0].54.0
116
.[5176.0),(
21


i
eC
i
p (3)
with:
1
035.0
08.0
11
3




i
(4)
The characteristic of the generated power vs. rotational speed according to the wind speed is
represented in Figure 3. The power coefficient vs. tip speed ratio for different values of pitch angle is
depicted in Figure 4. The ideal curve of power vs. wind speed shown in Figure 5 illustrates one of the major
factors affecting the performance of the wind power through three distinct zones:
a. Zone I: below cut-in wind speed, the turbine does not produce power.
b. Zone II: at cut-in wind speed, the system begins to produce power (Pv3
) until nominal wind speed.
c. Zone III: the turbine produces constant power (pitch control).
d. Zone IV: at cut-off wind speed, the system stops.
To extract the maximum power from the wind turbine, it is necessary to adjust the rotor speed (  )
at optimum value of TSR (opt) with wind speed variation (v); this is achieved in zone II. Table 2 is shows
parameters of wind turbine

 ISSN: 2088-8708
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Figure 3. Mechanic Power Characteristic vs. Rotating
Speed of the Rotor for different Values of Wind
Speed
Figure 4. Power Coefficient vs. Tip Speed Ratio for
different Values of β
Figure 5. Typical Power Curve of a Wind Turbine
Table 2. Parameters of Wind Turbine
Parameter Value
Cut-in speed 4 m/s
Cut-out speed 30 m/s
Rated wind speed
Rated power
8 m/s
3 kW
Blade radius
Optimal power coef.
Optimal TSR
2 m
0.4131
7.5
2.2. Mathematical Model of the Generator
2.2.1. Operating Principle
The studied three-phase 6/4 Variable Reluctance Generator has six salient poles on the stator and
four salient poles on the rotor as depicted in Figure 6. The rotor has no windings or magnets while the stator
windings are distributed as three pairs connected in series and fed with asymmetric half bridge converter
where each phase is represented in Figure 7. There are two operating sequences: (i) excitation sequence by
switching Q1 and Q2; (ii) generation sequence to supply the load via the diodes D1 and D2.
2.2.2. Basic Equations
The generated voltage per stator k-phase is expressed by:






),(
).,()( kk
k
k
kkkkk
iL
i
dt
di
iLirV (5)
where rk is the phase resistance, ik is the phase current, Lk is the incremental inductance and  is the angular
speed (rad/s) of generator. The third term of equation (5) represents the induced EMF which depends
essentially on the rotational speed  (we assume that the current and inductance slope are constant).

IJECE ISSN: 2088-8708 
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The electromagnetic torque per k-phase is expressed by:





)(
2
1 2 k
kk
L
iT (6)
From (6) we can conclude that the instantaneous torque is positive for increasing inductance (motor) and
negative for decreasing inductance (generator) as shown in Figure 8.
2.2.3. Analytical Model of Inductance
The rotation of the rotor poles (free from windings and magnets) with respect to the excited stator
poles varies the inductance of the generator periodically from maximum at the aligned position, Lmax, to
minimum at the unaligned position, Lmin. Usually, the fundamental component of the non-linear inductance is
approximated by series Fourier expressed by:
)cos(.)( 10  rk NLLL  (7)
where L0=(Lmax+Lmin)/2 and L1=(Lmax-Lmin)/2
Usually, Lmin is considered as constant while Lmax is analytically expressed using polynomial series as [17]:
432
max 00035.00022.00056.00045.0136.0)( iiiiiL  (8)
From equations (6) and (7), one can deduce the following analytical expression of the electromagnetic
torque:
)sin(..
2
1
1
2
rrkk NLNiT  (9)
Equation (9) shows the effect of parameter L1 in calculating the torque, i.e. of the gap between the
inductances Lmax and Lmin which we shall examine below.
Figure 6. Diagram of the Studied 6/4 VRG
Figure 7. A Phase Circuit of VRG Fed by the Inverter Figure 8. Motor and Generator Modes of the
Variable Reluctance Machine

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2.2.4. Numerical Model of Inductance by FEA
Due to the high saturation of the magnetic circuit of the generator, it is very difficult to model
analytically the different characteristics. Thus, a 2-D non-linear finite element model using FEMM software
is performed. The schemes of magnetic flux density at the two extreme postions of rotor are depicted in
Figure 9. The finite element analysis (FEA) of the studied generator, with parameters given in Table 3,
allowed us to represent, as a function of the position and the current, the characteristics of linkage flux in
Figure 10 and inductance in Figure 11. In addition, the data given by the FEA are stored in a matrix in order
to build the look-up tables for 46 rotor positions, from 45° to 90°, correspondind to the decreasing inductance
(generator mode) and 6 different current values, from 0 to 10 A. Using MATLAB Look-up Table bloc, one
could plot the 3-D curves shown in Figure 12 and Figure 13.
Figure 9. Plot of Magneticflux at Aligned and Unaligned Postions of Rotor
Figure 10. Linkage Flux vs. Current at different Rotor
Positions
Figure 11. Inductance vs. Rotor Position at
different Currents
Figure 12. Flux/Position/Current Characteristic Figure 13. Current /Position/Torque Characteristic

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Table 3. Parameters of VRG
Parameter Value
Number of stator poles 6
Number of rotor poles 4
Outer diameter
Rotor bore diameter
Air-gap length
228.4 mm
114.2 mm
0.25 mm
Shaft diameter
Stator pole angle
Rotor pole angle
40 mm
30 deg
30 deg
3. SIMULATION RESULTS OF WECS UNDER MATLAB/SIMULINK
3.1. Simulation of the Turbine and Gearbox
Based on equations (1) to (4) representing the mathematic model of the turbine, we conctructed the
Simulink diagram shown in Figure 14. The coupling turbine-gearbox with a gear ratio K is depicted in
Figure 15.
Figure 14. Model of the Turbine under Simulink
Figure 15. Bloc Diagram of the Wind Turbine and Gear Box
3.2. Simulation of the Generator
The simulink diagram model for the studied generator is shown in Figure 16. For simplifying the
simulation process, we took the same parameters in all phases, we neglect the mutual inductance, eddy effect
and hysteresis phenomena, and we assume that all switches of the inverter are ideal. As depicted in
Figure 17, the ultimate model of the generator contains several modules such as the three phases of the VRG,
the power inverter and its controllers. As mentioned previously, each phase contains the same parameters
while the stator windings are detailed in Figure 18 with an angular shift of 120° between them.
For starting the simulation process, we compute the position (the mechanical angle of the rotor)
from an integration of the speed, taking in account the original angle of the rotor when the simulation starts
as shown in Figure 19. The modeled torque equation using simulink is represented in Figure 20. The power
inverter contains three blocks, an exciting source and a load as depicted in Figure 21. Each block of the
inverter is represented in Figure 22.

 ISSN: 2088-8708
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Figure 16. Simulink Diagram of the Studied VRG
Figure 17. Blocs of One Phase of the Machine
Figure 18. Bloc Diagram of Calculating the Inductance of Phase Winding

IJECE ISSN: 2088-8708 
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Figure 19. Bloc Diagram of the Position Sensor
Figure 20. Bloc Diagram of Calculating the Electromagnetic Torque
Figure 21. Bloc Diagram of the Inverter
Figure 22. Bloc Diagram of an Inverter arm

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3.3. Discussion of Results
For getting high performances of the machine, the control bloc must work respectively to a specified
turn-on angle (Θon=40°) and turn-off angle (Θoff =60°). To validate our model, we have used the same
conditions of simulation and same parameters as in [17]. The dynamic waveforms of currents and voltages in
the three phases of the generator are depicted in Figure 23 and Figure 24 respectively. The converted energy
by the proposed system can be estimated using the flux-current curve as represented in Figure 25. The
dynamic waveforms of the currents at different values of the turn-off angle Θoff are shown in Figure 26. All
these results confirm the validity of our model compared to the work of S. Song and W. Liu [17] and allow
us to consider other development prospects.
Figure 23. Dynamic Currents in the Three Phases Figure 24. Dynamic Voltages in the Three Phases
Figure 25. Flux vs. Current Diagram Figure 26. Dynamic Current for different θoff Values
4. CONCLUSION
This work allowed us to model and simulates a variable speed wind turbine associated conveniently
with gearless variable reluctance generator. This objective has been achieved using a user-friendly program
coupling the open source software FEMM with MATLAB/SIMULINK widely used by the academic
community. Another contribution of this work lies in the calculation by the finite element method of
inductances at aligned and unaligned position. This allowed us to carry out a detailed analysis of system
performances. It gave good results in dynamic non-linear generator operation. Currently, there are a little
research results in this field; a continuation to the work would be followed to optimize the system
performance by developing efficient control strategies.
REFERENCES
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International Journal of Electrical and Computer Engineering, vol/issue: 2(3), pp. 353-370, 2012.
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Technique,” International Journal of Electrical and Computer Engineering, vol/issue: 5(5), pp. 929-938, 2015.

IJECE ISSN: 2088-8708 
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[3] T. Z. Khaing and L. Z. Kyin, “Control Analysis of Stand-Alone Wind Power Supply System with Three Phase
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