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Topic 3

# Topic 3 - ECE341 Energy Conversion(Spring 2011 Topic 3...

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1 J. Wang 4/18/2011 1 square4 Ideal transformer and Dot convention (68-72, 84) square4 Impedance transfer (72) square4 Real transformer and equivalent circuit (86-89) square4 Transformer testing (90-91) square4 Per unit system (94-100) square4 Auto transformer and three phase transformers (109-125) It would be very helpful to read numerical examples in the text book. Topic 3: Transformer and Per-unit System ECE341 Energy Conversion (Spring 2011) J. Wang 4/18/2011 2 From generator to load: ECE 341 Topics Synchronous Generator in the concentrating solar power plant Step-up Transformer Three Phase 765 kV High Voltage Lines Step-down Transformer Three Phase 22 kV Distribution Lines Induction machines and power electronics in home appliance and Electrical Vehicles

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2 Transformer J. Wang 4/18/2011 3 Isn’t this looking like an alien robot? Principle of a Transformer J. Wang 4/18/2011 4 Lp M p φ φ φ + = Ls M s φ φ φ + = dt d N dt d N t v Lp p M p p φ φ + = ) ( dt d N dt d N t v Ls s M s s φ φ + = ) ( ) ( ) ( t e t e Lp p = ) ( ) ( t e t e Ls s = s p s p N N t e t e / ) ( / ) ( =
3 Ideal Transformer J. Wang 4/18/2011 5 a N N t v t v S p s p = = ) ( ) ( out s s s p p p in P I V I V P = = = θ θ cos cos s p θ θ = out s s p p in S I V I V S = = = Ignore the leakage flux: Power conservation: a N N t i t i P s s p 1 ) ( ) ( = = Relationship between currents: Impedance Transformation (Ideal Transformer) J. Wang 4/18/2011 6 s s L L L I V I V Z = = a I I N N V V p s S p s p = = = 2 ' 2 / / a Z a I V Z L p p L = =

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4 Dot Convention J. Wang 4/18/2011 7 First, for the primary winding, set the dot on the terminal with current flowing into it.
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