# Modeling and Optimal Design of an Eddy Current Coupling for Slip-Synchronous Permanent Magnet Wind Generators

- 2014

#### Abstract

—In this paper, the possibility of using an eddy current slip coupling to remove cogging torque and torque ripple in a slip-synchronous permanent magnet wind generator is investigated. Two different topologies are proposed. It is shown that two-dimensional (2-D) finite-element methods are inaccurate compared to three-dimensional (3-D) finite-element methods when solving eddy currents in eddy current couplings. The 3-D finite-element transient simulations are validated using a manufactured prototype 15-kW eddy current coupling. An analytical approximation is developed and used for the design optimization of two eddy current coupling topologies. Using the optimally designed eddy current coupling, it is shown that the analytical and 3-D finite-element solutions compare very well and that the proposed eddy current coupling topology has no torque ripple. The analytical approximation is well suited to the rapid design optimization of eddy current couplings that use a conductive material in the air gap. Arc length between the center and the side of the current loop (in meters). b Magnitude ratio between the flux density and its fundamental harmonic. B ag Analytically calculated air gap flux density (in tesla). B FE Air gap flux density determined by finite-element simulation (in tesla). B g Air gap flux density (in tesla). B g1 Peak of the fundamental air gap flux density (in tesla). B r Residual magnetic flux density (in tesla). B s Inner yoke flux density (in tesla). B y Outer yoke flux density (in tesla). C Vertical axis offset. dx Small element arc length (in meters). dy Small element length (in meters). dθ Small element angle (in radians). e elm Instantaneous induced element voltage (in volts). e i Induced loop voltage (in volts). F i Instantaneous force generated by loop current (in newtons). F pp Instantaneous force generated per pole (in newtons). H c Coercive magnetic field strength (in amperes per meter). h c Radial height of the conductive material (in meters). H g Air gap magnetic field strength (in amperes per meter). H m Permanent magnet (PM) magnetic field strength (in amperes per meter). h m Radial height of the PM (in meters). H s Inner yoke magnetic field strength (in amperes per meter). h s Radial height of the inner yoke (in meters). H y Outer yoke magnetic field strength (in amperes per meter). h y Radial height of the outer yoke (in meters). i Number of specific current loop. i i Induced current in the specific …

**DOI:**10.1109/TIE.2013.2282602