Journal of Materials Processing Technology 161 (2005) 363–367 Geometry optimization of solid rotor eddy current brake by using sensitivity analysis and 3D finite elements Konstantinos V. Tatis ∗ , Antonios G. Kladas 1 , John A. Tegopoulos 2 Faculty of Electrical and Computer Engineering, National Technical University of Athens, 9 Iroon Polytechneiou Street, 15780 Athens, Greece Abstract The paper presents an optimization procedure for eddy current brakes, considering both copper and solid iron rotors. The rotor geometry optimization has been performed based on analytical solutions and 3D finite elements combined to sensitivity analysis technique. Optimum dimensions of copper parts and solid iron slots have been investigated. © 2004 Elsevier B.V. All rights reserved. Keywords: Eddy currents; Finite element methods; Optimization methods; Rotating machines 1. Introduction Eddy current brakes can be attractive rivals of mechanic brakes used for over-speed protection of wind turbines in cases of disturbances. They provide important advantages such as good reliability, low cost and involve no mainte- nance requirements. Especially for wind turbines equipped with permanent magnet generators, they can provide reliable braking operation in cases of loss of the grid connection due to faults. In such situations the decelerating torque provided by the generator connected to dump loads, can be substantially increased by the parallel connection of an eddy current brak- ing machine connected on the same shaft. The configuration of a wind turbine system operating under such disturbance conditions is shown in Fig. 1. This work is related to a project concerning the design and construction of a 25 kW grid connected, stall regulated, vari- able speed wind turbine, equipped with a permanent magnet (PM) generator. The PM generator has already been opti- mized and tested through a prototype [1]. ∗ Corresponding author. Tel.: +3 10 7723588. E-mail addresses: ktatis@central.ntua.gr (K.V. Tatis), kladasel@central.ntua.gr (A.G. Kladas), tegopoul@power.ece.ntua.gr (J.A. Tegopoulos). 1 Member, IEEE; Tel.: +3 10 7723765. 2 Life fellow, IEEE; Tel.: +3 10 7723766. In order to enable braking operation the number of poles of the induction machine brake must be greater than the one of the PM generator. Moreover, in order to obtain a simple structure only solid rotor machine configurations have been considered. The design of the brake as well as the evaluation of the equivalent circuit parameters can be obtained by using fi- nite element techniques [2,3]. However, the optimization of the rotor geometry may require laborious and expensive nu- merical schemes especially when 3D configuration should be considered [4,5]. Although both stochastic [6] and determin- istic optimization algorithms can be implemented [7–9], the sensitivity analysis technique combined with finite element methods enables robust and fast convergence [1]. 2. Methodology The geometry optimization of the eddy current brake is based on solid rotor configuration for construction simplicity purposes. The analysis problem has been solved either by using existing solutions of closed form (case of rotating field around non-salient rotor) or by 3D finite elements (slotted stator and rotor case). A particular reduced scalar potential formulation necessitating no source field calculation has been adopted to develop the 3D finite element model [11]. The analysis methods as well as the optimization procedure are developed hereafter. 0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.07.052