21 Energy and co-energy

# 21 Energy and co-energy - Lecture 19 Energy and co-energy...

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Unformatted text preview: Lecture 19 Energy and co-energy Consider a ferromagnetic, electromagnetic device without moving parts or stationary moving parts (device with movable parts but that are kept fixed), either linear λ = Li or nonlinear λ = f(i). By Faraday’s law we know d e dt λ = . The instantaneous power consumed by the device is ( ) ( ) ( ) ( ) ( ) d t p t e t i t i t dt λ = = Therefore in the time interval dt, the device absorbs ( ) dW p t dt id φ λ = = joules Since this device does not produce heat, nor does it produce mechanical energy, then dW φ must be stored in the device as a magnetic field. If we consider a device operating at a current i then ( ) W d W p t d t i d λ φ φ λ = = = ∫ ∫ ∫ Figure 1 - Nonlinear characteristic curve of a device The co-energy stored at ( λ , i ) is defined as ' i W d i φ λ = ∫ And corresponds to the area under the curve λ (i). One identity relating W φ and W φ ’ is ' 0 0 W W i φ φ λ + = This means the sum of the areas on both sides of the curve is equal to the total area of the...
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21 Energy and co-energy - Lecture 19 Energy and co-energy...

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