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International Journal of Applied Electromagnetics and Mechanics 26 (2007) 175–182 IOS Press

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Optimization of a small passive wind turbine generator with multiobjective genetic algorithms
A. Abdelli, B. Sareni∗ and X. Roboam
LEEI, UMR INPT-ENSEEIHT/CNRS No. 5828, 2 rue Camichel, BP 7122, 31071 Toulouse Cedex 7, France

Abstract. In this paper Multiobjective Genetic Algorithms (MOGAs)are used for the design of a small wind turbine generator (WTG) coupled to a DC bus through a diode bridge. The originality of the considered system resides in the suppression of the Maximum Power Point Tracker (MPPT). The poor efficiency of the corresponding passive structure is considerably improved by optimizing the generator characteristics associated with the wind turbine in relation to thewind cycle. The optimized configurations are capable of matching very closely the behavior of active wind turbine systems which operate at optimal wind powers by using a MPPT control device. Keywords: Multiobjective optimization, genetic algorithms, wind energy, vertical axis wind turbine

1. Introduction The optimization of wind energy transfer is generally achieved by controlling the speed of aWind Turbine Generator (WTG). In particular, the rotor speed should vary in accordance with the wind speed by maintaining the tip speed ratio to the value that maximizes aerodynamic efficiency. For that purpose, many different Maximum Power Point Tracking (MPPT) control strategies have been developed, allowing to regulate the Permanent Magnet Synchronous Generator (PMSG) voltage [1,2]. The highefficiency of these generators is counterbalanced with higher costs and greater complexity of the electronic devices. On the other hand, simpler system structures consist in only using a passive rectifier directly connected to the DC bus (see Fig. 1). Such system is characterized by very low cost but usually offers poor efficiency relatively to the wind power. However, thanks to a suitable choice of thesystem design variables associated with the wind turbine generator sizing (especially electrical and geometrical parameters) it is possible to improve significantly the global system efficiency. In this paper, we propose an original approach based on Multiobjective Genetic Algorithms for sizing a small passive WTG. The whole system mass and the extracted output power are considered as optimizationcriteria. The obtained power efficiency is finally close to the one offered by active WTGs coupled with MPPT control devices.
∗

Corresponding author. E-mail: sareni@leei.enseeiht.fr.

1383-5416/07/$17.00  2007 – IOS Press and the authors. All rights reserved

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A. Abdelli et al. / Optimization of a small passive wind turbine generator with multiobjective genetic algorithms
Wind CycleBlade Generator Rectifier DC-bus

~
PMSG

+

Udc
=

Fig. 1. Synoptic of the passive wind turbine generator (without MPPT control system).

2. The sizing and simulation models of the wind turbine generator Two classes of models have been developed for sizing and simulating the WTG. On the one hand, fine accurate models based on the use of empirical equations, finite elements and a completecircuit representation of the WTG have been used for the system analysis and validation. On the other hand, surrogate models which approximate the system behavior have been employed in the optimization process in order to reduce computing times. 2.1. The wind Cycle The wind Cycle is represented by a typical wind speed sample V W (t) which is approximated with the empirical relation
VW (t) = 10 +0.2 sin(0.105t) + 2 sin(0.367t) + sin(1.293t) + 0.2 sin(3.665t).

(1)

2.2. The wind turbine characteristics A Savonius Vertical Axis Wind Turbine of radius R = 0.5 m and height H = 2 m is considered as case study. Its power coefficient C p is defined by the following empirical interpolation:
Cp = −0.1299λ3 − 0.1168λ2 + 0.4540λ,

(2)

where λ denotes the tip speed ratio, depending on...