recitatin5 - Electric Energy Processing: Fundamentals and...

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1 Electric Energy Processing: Fundamentals and Applications 18-418: Recitation #5 Dr. Nermeen T. Mahmoud ( nermeentalaat@cmu.edu ) September 23,2009 Non- ideal transformer
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2 The Equivalent Circuit of Non-ideal Transformer The permeability is not infinite and the inductances are therefore finite. Not all the flux linking anyone of the windings links the others windings. Winding resistance is present. Losses occur in the iron core:- Magnetization losses. Eddy-current losses. [1]
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3 The Equivalent Circuit of Non-ideal Transformer Where : R p the copper resistance of the primary winding. R s the copper resistance of the secondary winding. X p the primary leakage inductance. X s the secondary leakage inductance. R c the core resistance (represents eddy-current losses) X m the magnetizing inductance. [2]
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4 The Equivalent Circuit of Non-ideal Transformer refer the secondary winding impedance to primary side, so the equivalent circuit is [2]
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5 The Equivalent Circuit of Non-ideal Transformer S S P Sp S P S Sp V N N V I N N I refer the secondary voltage and current to primary side, so the equivalent circuit is [2]
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6 The Approximate Equivalent Circuit of Non-ideal Transformer By neglect the core losses and magnetization losses, so the Approximate Equivalent circuit for the non-linear transformer is [2]
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7 The secondary winding of a transformer has a terminal voltage of v s ( t ) = 282.8 sin 377 t V. The turns ratio of the transformer is 50:200. If the secondary current of the transformer is i s ( t ) = 7.07 sin (377t 36.87°) A , what is the primary current of this transformer? What are its voltage regulation and efficiency? The impedances of the transformer shown in below referred to the primary side are R eq = 0.05 Ω , R C = 75 Ω , X eq = 0.225 Ω and X M = 20 Ω Example 5-1
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8 Example 5-1 A 8 . 36 20 50 200 * 8 . 36 5 * I I is side primary to reffered current secondary The V 0 50 200 50 * 0 200 * V V is side primary to reffered voltage secondary The A 8 . 36 5 8 . 36 2 07 . 7 I V 0 200 0 2 282 V are current and voltage secondary The 1 2 s sp 2 1 s sp s s N N N N
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9 Example 5-1 % 2 . 7 100 * 50 50 6 . 53 100 * V V V VR is load at this er transform the of regulation voltage The A 0 . 41 22.3 20 2 . 3 53.6 75 2 . 3 53.6 8 . 36 20 I I I I I is current
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recitatin5 - Electric Energy Processing: Fundamentals and...

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