Energy_Conversion_For_ECE321 - lecture 3

Energy_Conversion_For_ECE321 - lecture 3 - Energy...

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Energy Conversion S.D. Sudhoff Spring 2008
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Spring 2008 ECE321 2 Reading Electromechanical Motion Devices ¾ Sections 2.1-2.8 Techniques for Analysis of Electromechanical Systems ¾ Section 5.1.1-5.1.9 ¾ See course web page
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Spring 2008 ECE321 3 Overall Goal • We know how to ¾ (1) flux linkage in terms of current and position ¾ (2) current in terms of flux linkage and position • Using either (1) or (2), we can find an expression for force or torque for an electromechanical device ! No other information needed.
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Spring 2008 ECE321 4 5.1.1 Magnetic System Descriptions • For single winding systems, we may describe our magnetics (ignoring hysteresis) with one of the following ¾ Form 1: (5.1-1) ¾ Form 2: (5.1-3) ) x , ( f i λ = ) x , i ( f i =
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Spring 2008 ECE321 5 5.1.1 Magnetic System Descriptions • For multi-winding systems, we may describe our magnetics (ignoring hysteresis) with one of the following ¾ Form 1: (5.1-2) ¾ Form 2: (5.1-4) • Form 2 is most common for both single and multi-winding systems ) x , ( λ f i λ = ) x , ( i i f λ =
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Spring 2008 ECE321 6 5.1.2 Field Energy • Physical definition of the coupling field… • Energy into the coupling field ¾ (5.1-5) m e f W W W + =
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Spring 2008 ECE321 7 5.1.2 Field Energy • We will assume a lossless field ¾ This implies ¾ Concerns
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Spring 2008 ECE321 8 5.1.2 Field Energy • Calculation of field energy ¾ Energy entering through j’th winding: (5.1-7) ¾ By Faraday’s law (5.1-6) ¾ Thus (5.1-8) ¾ Or (5.1-10) = f t t j j j , e dt i e W 0 dt d e j j λ = = f t t j j j , e dt dt d i W 0 = = J j j j e f , j , j d i W 1 0
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Spring 2008 ECE321 9 5.1.2 Field Energy • In a system with K inputs ¾ (5.1-10) • Mechanical Energy ¾ (5.1-11) • Combining these results ¾ (5.1-12) = = J j j j e f , j , j d i W 1 0 λ = f x x e m dx f W 0 = = f f , j , j x x e J j j j f dx f d i W 0 0 1
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Spring 2008 ECE321 10 5.1.3 Calculation of Field Energy • A mathematical experiment ….
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Energy_Conversion_For_ECE321 - lecture 3 - Energy...

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