Lecture1

# Lecture1 - Lecture 1 Magnetic Coupling of Multiple Coils In...

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Lecture 1 Magnetic Coupling of Multiple Coils In this lecture, we shall develop the space dependent NxN inductance matrix [L( θ m )] which embeds the magnetic coupling of N coils in an electric machine. The magnetic energy W m ( θ m ) is computed and since the system is assumed to be linear, it is the same value as the co-energy W m 1 ( θ m ). With the co-energy, it is possible to obtain the torque T e acting on the rotor. In order to keep the presentation simple, the development begins with order N=2. Consider two windings, whose axes make an angle θ m . The flux linkage vector and the current vector are related by the 2x2 inductance matrix [L( θ m )]. 11 12 11 21 22 22 () mm LLi θθ λ ⎡⎤ ⎤⎡ = ⎢⎥ ⎥⎢ ⎦⎣ ⎣⎦ Applying Faraday’s Law of Electromagnetic Induction. 11 12 11 12 1 1 21 22 2 2 21 22 m LL vi i d dd i dt dt dt θ ∂∂ == + Question : What is the magnetic energy ' WW = of the two coils carrying current 1 ˆ i , 2 ˆ i at the position ˆ m ? Since the system is conservative, the end-point can be reached by any path.

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## This note was uploaded on 02/23/2010 for the course ECSE 462 taught by Professor Bon-tekooi during the Spring '09 term at McGill.

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Lecture1 - Lecture 1 Magnetic Coupling of Multiple Coils In...

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