Multi-objective design optimization of a large-scale direct-drive permanent magnet generator for wind energy conversion systems

doi:10.1007/s11708-014-0320-z

Front. Energy

2014, Vol. 8

Issue (2) : 182-191 https://doi.org/10.1007/s11708-014-0320-z

RESEARCH ARTICLE

Multi-objective design optimization of a large-scale direct-drive permanent magnet generator for wind energy conversion systems

Arash Hasssanpour ISFAHANI¹(

), Amirhossein Haji-Seyed BOROUJERDI², Saeed HASANZADEH³

¹. Everette Energy, LLC, Dallas 75225, USA
². Faculty of Electrical and Engineering, Islamic Azad University, Islamshahr Branch, Tehran 33147-67653, Iran
³. Facuty of Electrical and Computer Engineering, Qom University of Technology, Qom 1519-37195, Inan

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Abstract

This paper presents a simultaneous multi-objective optimization of a direct-drive permanent magnet synchronous generator and a three-blade horizontal-axis wind turbine for a large scale wind energy conversion system. Analytical models of the generator and the turbine are used along with the cost model for optimization. Three important characteristics of the system i.e.,the total cost of the generator and blades, the annual energy output and the total mass of generator and blades are chosen as objective functions for a multi-objective optimization. Genetic algorithm (GA) is then employed to optimize the value of eight design parameters including seven generator parameters and a turbine parameter resulting in a set of Pareto optimal solutions. Four optimal solutions are then selected by applying some practical restrictions on the Pareto front. One of these optimal designs is chosen for finite element verification. A circuit-fed coupled time stepping finite element method is then performed to evaluate the no-load and the full load performance analysis of the system including the generator, a rectifier and a resistive load. The results obtained by the finite element analysis (FEA) verify the accuracy of the analytical model and the proposed method.

Keywords permanent magnet synchronous generator wind turbine direct-drive multi-objective optimization cost mass annual energy output finite element analysis (FEA)

Corresponding Author(s): Arash Hasssanpour ISFAHANI

Issue Date: 19 May 2014

Cite this article:

Arash Hasssanpour ISFAHANI,Amirhossein Haji-Seyed BOROUJERDI,Saeed HASANZADEH. Multi-objective design optimization of a large-scale direct-drive permanent magnet generator for wind energy conversion systems[J]. Front. Energy, 2014, 8(2): 182-191.

URL:

https://academic.hep.com.cn/fie/EN/10.1007/s11708-014-0320-z
https://academic.hep.com.cn/fie/EN/Y2014/V8/I2/182

Fig.1 Direct-drive wind energy conversion system

Turbine characteristics	Value
Cut-in speed/(m·s⁻¹)	3.5
Rated speed/(m·s⁻¹)	8−12
Cut-off speed/(m·s⁻¹)	20
$C ρ max ⁡$	0.39
$λ opt$	6.0
Average wind speed/(m·s⁻¹)	8

Tab.1 Turbine characteristics

Fig.2 Electrical equivalent circuit of a PMSG

Tab.2 Cost of different parts of system

Fig.3 Flowchart of design optimization algorithm

Tab.3 Design variables and their constraints

Fig.4 Pareto front in a three dimensional space

Fig.5 Pareto fronts in two dimensional spaces along with objective limitations

Tab.4 Pareto optimal solutions

Tab.5 Characteristics of selected generator

Fig.6 Flux lines due to permanent magnets

Fig.7 No-load voltage excitation of the generator and its harmonic contents

Fig.8 Electrical circuit coupled to the FE domain

Fig.9 Voltage experienced by the load

Fig.10 Cogging toque before (circles) and after (solid line) magnet skewing

$A z$	z-axis component of the magnetic potential vector
$B mg$	Air gap magnet flux density
$B$	Flux density
$C ρ$	Turbine power coefficient
$C gen$	Generator cost
$C tur$	Blade cost
$C PM$	Permanent magnet material cost
$C cu$	Copper material cost
$C lam$	Lamination cost
D	Air gap diameter
E	Back-emf rms value
F	Electrical frequency of the motor supply
f(U _i)	Probability density
$f B$	Frequency of the flux density distribution function
$J m$	Equivalent magnetizing current density of PMs
J	Current density
$K sf$	Stacking factor
$k h$	Hysteresis loss coefficient
$k e$	Eddy current loss coefficient
$k ex$	Extra loss coefficient
$k manu$	Manufacturing cost coefficient
$k w 1$	Fundamental harmonic winding factor
L	Generator stack length
$M$	Magnetization vector of the permanent magnet
$N ph$	Number of winding turns per phase
R	Blade radius
$T B$	Period of the flux density distribution function
$T rated$	Turbine rated torque
$T cut-in$	Turbine cut-in torque
$U a$	Average wind speed
U	Wind speed
$V cu$	Copper volume along each slot
$V end$	Copper volume along end winding
$V PM$	Volume of permanent magnet material
$V cu$	Volume of copper material
$V lam$	Volume of laminations
$w t$	Tooth width
$α$	Pole arc to pole pitch ratio
$β$	Current angle
$λ$	Tip speed ratio
$ω r$	Rotational speed of the wind turbine shaft
$ϕ P M$	Permanent magnet flux per pole
$σ c u$	Copper conduction resistivity
$ρ P M$	Mass density of permanent magnet
$ρ c u$	Mass density of copper
$ρ l a m$	Mass density of laminations
$τ$	Pole pitch
$τ s$	Slot pitch
$ρ a i r$	Air density
$ε$	Back-emf to terminal voltage ratio

Notation

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