JOURNAL OF SCIENCE & TECHNOLOGY • No 95 2013 OPTIMAL DESIGN OF A PERMANENT MAGNET SYNCHRONOUS GENERATOR FOR WIND TURBINE SYSTEM THIET KE TOI UU MAY P H A T DIEN D 6 N G B O NAM CHAM VfNH CUXJ CHO H S[.]
Trang 1OPTIMAL DESIGN OF A PERMANENT MAGNET SYNCHRONOUS GENERATOR
FOR WIND TURBINE SYSTEM
THIET KE TOI UU MAY P H A T DIEN D 6 N G B O NAM CHAM VfNH CUXJ
CHO H S T H 6 N G PHONG DIEN
Nguyen The Cong, Nguyen Thanh Khang Tran Due Hoan
Hanoi University of Science and Technology Institut National Polytechnique de Toulouse
Received February 25, 2013; accepted April 22, 2013
ABSTRACT
The exploitation of wind energy is developed in recent year because it has a source of clean, non-polluting and renewable energy Nevertheless, in the development of wind energy, the demand in research and development is always focus on the efficiency energy and minimized cost of wind turbine system
This paper descnbes the methodology to design, optimization and simulation of a 15kW at low wind speed (6m/s) the design will be focused to Permanent Magnet Synchronous Generator (PMSG) dedicated to wind turbine systems Firstly, the model of wind turbine system direct-dnve with wind speed, wind turbine will be presented Secondly, a coupled electromagnetic, thermal model used in design ofa PMSG will be demonstrated The developed genetic algorithm (GA) approach is presented
in three parts: the basic principles of the GAs the constrained optimization conversion and the multiobjective (power maximization and mass minimization) optimization method Finally, an analysis PMSG According to the obtained results, the optimal design of a PMSG by genetic algorithms to solve the efficiency wind energy is simulated and analysis
Keywords: Wind Energy, PMSG, Genetic Algorithm
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1 INTRODUCTION confrol strategies have made it possible to
Optimum wind energy exfraction is ' ^ ^ " ' ^ ^ ^ ^^^ ^°'*^g^ °^ *h^ P'^SG in many
achieved by running the Wind Turbine different ways
Generator (WTG) in variable speed because of Opportune wind turbine architecture is the higher energy gain and the reduced stresses designed using mathematical model of the Using the Permanent Magnet Synchronous system Once the model is made and tested Generator (PMSG) the design can be even more sufficiently, the controller for an optimal simplified by its high efficiency and advantages command sfrategy is developed so the wind
in start-up condition [1],[2] However, die turbine can perform always in die maximum
Trang 22 MODELING WIND TURBINE SYSTEM
The design composes the wind speed,
turbine and PMSG as Fig.l and its losses model
also estimate for the calculation of output
power
Fig I System design: Wind speed, wind turbine
and PMSG
2.1 Wind speed model
In order to robust modeling, the wind
speed have to variation in interval sufficient
large Thus, the stochastic model of wind speed
by decomposing a discrete Fourier
transformation with the mean value 6m/s is
used in this works [3] The wind speed so that
expressed as:
(1)
V^ (0 = 6 + 0,2 sin(0,1047/) + 2 sin(0,26650
+sin(l, 2930r) + 0.2 sin(3,6645/)
2.2 Wind turbine model
The conversion efficiency of the system
from wind power to electrical power is given by
the product of the power coefficient Cp [3],
alternator efficiency and power-electronic
converter efficiency Overall efficiency is
defined as the average conversion from energy
available in the wind to electrical energy
produced
- Static model: The mechanical power
developed by a wind turbine rotor varies
according to the equation:
P,=-pC^iA)7rR^V:
n„
(2)
(3)
where ,/?„,- blade radius [m]
p = air density [kg/m^],
r„, mechanical torque from wind blades p^^.m]
Fig 2 Power coefficient of wind turbine
The type of wind turbine in this work is
the three-bladed with the radius R,y=\Om (Fig.l) and the power coefficient Cp may be expressed
as a function of the tip speed ratio
A = R^Q.^/V^^ given by equation (e.g Fig.2):
Cp [A.) = -0.003002992/1' -0.001168U^ +0.1540t
- Dynamic model: The dynamic equation for
interaction between turbine-PMSG is written by equation of torque:
'^ - T,„ = ^ ^ ^ + / « " * (4)
dt where /"„,, T^m are respectively the wind turbine
and electromagnetic of PMSG torques, J„, and
f„ being the totai wind turbine inertia and
viscous friction coefficient (Typically in this
study, J„= 5.5N.m^ and/.=0.5)
2.3 Analytical sizing of permanent magnet motors
The most important in the design PMSG model is the variables chosen have to be independent Thus, the sizing model of PMSM
in this work has been developed in [4] This model depends on geometrical characteristics (number of pole pairp, number of slots per pole
and phase Nspp, radius/length ratioJ^ =rj//^ and slot depth/ bore radius ratio Rdr=d Ir)^
well as electromechanical features (current
density J^, yoke induction By, base speed Q^, corresponding power P^ at the base point and
nominal voltage F,)
The geometrical characteristics of PMSG are illustrated on Fig 3 With this topology, we have to define the 8 fundamentals dimensions that are calculated detail in reference [5],
Trang 3r
H
I,
d
w,
wr
d
dy
Bore radius
Air gap
Length active
Slot depth
Slot width
Tooth width
Rotor yolce thickness
Stator yoke thickness
Fig 3 PMSG topologies and nomenclature of
geometrical dimensions
In order to calculate the output power of
the generator, the inductance and resistance of
the armature winding must be known In the
calculation of the tooth tip leakage inductance
and magnetizing inductance, the permanent
magnets are assumed to have the same
permeability as air
The main inductance Lm can be calculated as:
(5) where V„ is the number of conductors per slot
The slot leakage inductance can be computed as
L,=2fi,lrPN,ppA^,Nl (6)
where A^, is the specific permeance of the slot
leakage For the proposed generator, with equal
current in the upper and lower conductor in the
slots, the average specific permeance of die slot
leakage for the one coil side in the slot can be
expressed as
Ih, Ih,
Xb,+b,) b^+bj 62 (7)
The corresponding stator inductance Z,,is
given by the following relation:
L^=^L„+L, (8)
A typical value of the stator per phase resistance at rate load and average ambient temperature is:
where CT^,, is the conductivity of copper and
/, = 7r(r, +0.5d,)/p is the end winding
The magnetic flux is approximated by
<S>,=2K,N^^B„rJ,N^ (10)
2.4 Losses model ofthe wind turbine system
In the losses model of wind turbine and PMSG, we have examined the mechanic losses
in turbine, copper loss and Iron loss in the PMSM
Mechanic losses in the turbine:
The copper losses of PMSG at a winding
can be calculated from the resistance R, and the
phase current /,:
P, =3R.I^ (12) The core losses have to be calculated for each part ofthe iron core They are divided into hysteresis losses and eddy current losses As the different values of induction for the yoke and the teeth of stator, so the core losses in yoke are calculated as follows [5]
Therefore, the core losses total in the PMSM is
Pf.r=pc-^p^^pi^''+p:i (13) Finally, the output power of system is calculated by:
P^.Jul=P.,na-P.ec-PM-Pj (14)
2.S Thermal model
The proposed thermal model of PMSG
in this paper is based on a lumped-parameter network of thermal resistances [5] The heat
Trang 4and convection modes The thermal horizontal
mode is neglected because of the relatively low
temperature difference between the generators
parts Finally, the temperatures in the all
regions of PMSG are found from differential
equations:
T = A7'+Bu (15)
3 OPTIMIZATION OF PMSG BY
GENETIC ALGORITHM
The optimization ofthe PMSG is carried
out using a multiobjective genetic algorithm
[6], Genetic algorithm base on the mechanics of
natural selection and natural genetics, and
implement in the most simplistic way, the
concept of survival of the fittest The detail
methodology is presented in [5]
Fig 4 Multiobjective optimization process
In this optimization, two objectives are
the maximized output power calculated by (14)
and minimized the weight of PMSG (reduced
material and maintenance cost) The
optimization also has to respect five constraints
to ensure the PMSG feasibility in relation to the
parametric variation of design variables in the
optimization process (Fig 4), these constraints
concerned the number of conductors in one slot,
the maximum temperature associated with the
copper windings in the PMSG, the
demagnetization limit of the magnets and the
minimum of slot width
4 RESULTS AND DISCUSSION
Fig 5 shows the global Pereto-optimal
front of output power and weight of PMSG
obtained by optimization process with 100
individuals and 200 generations In this figure,
we present an optimal solution whose
parameters are mentioned in Tab.l, its output power and weight are 15kW and 250kg, respectively
X
: lor;ri>ndiClon /
Fig.5 Optimization results Pareto-optimalfront
In order to validate the design of optimal solution exfracted from the Pareto-optimal front and obtained with the less accurate sizing, we take the simulation of wind turbine system, this simulation is taken by Matlab/simulink as Fig
6 with the wind speed is calculate by (1) during 30s (Fig 7) In this simulation, to respect the electrical circuit simulation, 3 phases of PMSG are connected directly with a diode bridge and debited on DC bus 600V This simulation topology enforces the methodology of this concept because it is fully "passive" (without the power electronic and confrol) and can be demonstrated the natural adaptation between wind turbine and optimized PMSG
Tab I Parameters of optimal PMSG
Geometric parameters
Bore radius r, [m]
Length active Ir [m]
Air gap stator-rotor g [m]
Magnet thickness /„ ]m\
Slot width w, [m]
Tooth width Wrfm]
Stator yoke thickness dy
rmi
Rotor yoke thickness d \m
0.382 0.77 0.011 0.044 0.014 0.014 0.012 0.012
Electromasnetic parameters
Resistance R, fl^l Inductance L, [HI
Flux [Wbl Nominal voltage F,[V]
Nominal torque fNml
Number of pole pairs p
12.3 0.52 12.0
300
3300
20
J
Trang 5Rotation speed of PMSG is shown on
Fig 8 naturally depends on the variation of
wind speed with the mean value 3.5 rad/s (33.4
rpm) and the maximal value of electromagnetic
torque of PMSG and wind turbine is 4.5 kNm
(Fig.9) we can confirm that the wind turbine
system in this study is low speed and high
torque
ilOOO
3000
2000
1000
0
Fig 8 Rotation speed of PMSG
!>»^VW^ f\/*^ •
1 PMSG [
Fig 9 Torque of wind turbine and PMSG
• • I r
Fig6 Wind turbine system simulation in
Matlab/simulink
Power production of wind turbine and
PMSG is shown on Fig 10 We note the output
power of PMSG is nearly the captured power of
wind turbine, particularly in the area of low
wind speeds, this result proves efficacy of this
concept in objective of exploiting wind system
at low wind speed In the area of high wind
speeds (>8m/s), the difference power of turbine
and PMSG can be explained by the losses in
system and the without of power electronic
control
Fig 7 Wind speed
'^ f^-J I 'A
V
Fig 10 Wind turbine and PMSG power
Three phases current of PMSG on 300
ms is zoom out on Fig 11, we observe that phase current in PMSG is sinusoidal and symmefric Note that the current of PMSG is proportion ofthe wind speed, i.e when the wind speed increases the current increased
Fig 11 PMSG current
5 CONCLUSIONS This paper tries to optimize and to maximize the power production of wind turbine system at low mean wind speed by optimal design of PMSG All results prove that the model developed Is effectiveness to adaptation between wind turbine and PMSG in systems of 15kW at low base wind speed and also excite a motivation to realize a prototype in the future
Trang 6REFERENCES
H Slootweg, E De Vries, "Inside wind turbines Fixed vs Variable speed" Renewable Energy Worid magazine, 2003
A Grauers, "Efficiency of three wind energy generator systems", Department of Elecfric Power Engineering, Chalmers University of Technology, Sweden
E Hau, "Wind turbines: Fundamentals, Technologies, Application, Economics, 2"'' edition Spring-Verlag, 2006
G Slemon, X Liu, "Modeling and desing optimization of permanent magnet synchronous motors", Elecfric Machines and Power systems, Vol 20, pp.71-92,1992
B Sareni, A Abdelli, X Roboam, D H Tran, "Model simpification and optimization of a passive wind turbine generator" Renewable Energy, Vol 34, N''12, pp 2640-2650, Dec 2009
K Deb, "Multiobjective optimization using evolutionary algorithms", John Wiley & Sons, Chichester, 2001
Author's address: Nguyen The Cong-Tel: 0903418713 -Email: cong nguyenthe@hust.edu vn
Department: Elecfric-Etectronic Equipments
School of Electrical Engineering
Hanoi University of Science and Technology
No 1, Dai Co Viet Str., Ha Noi, Viet Nam