lect8 - Lecture 8 EE743 Direct Current(DC Machines Part II...

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Lecture 8 - EE743 Lecture 8 - EE743 Direct Current (DC) Machines - Part II Professor: Ali Keyhani Professor: Ali Keyhani
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2 Shunt-connected DC Machine DC Machines
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3 DC Machines The dynamic equations (assuming r fext =0) are: f af r a a la a a a a f ff f f f i L e dt di L i r e V dt di L i r V ϖ = + + = + = Where L ff = field self-inductance L la = armature leakage inductance L af = mutual inductance between the field and rotating armature coils e a = induced voltage in the armature coils (also called counter counter or back emf back emf )
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4 DC Machines ) ( ) 1 ( : ) 1 ( : r p m L e a a a a a a aa a f af r a a la a a a a f f f f f ff f f ff f f f J B T T e i r V r L i L e dt di L i r e V winding armature the For i r V dt d p r L dt di L i r V winding field the For ϖ τ τ ϖ τ τ + = - + + = = = + + = + = = = + =
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5 DC Machines - Shunt DC Machine Shunt DC Machine Time-domain block diagram The machine equations are solved for: 1 1 1 G V p r i f f f f = + = τ ( 29 2 1 1 G i L V p r i f af r a a a f = - + = ϖ τ ( 29 f a af e L e m r i i L T G T T B p J = = - + = 3 1 ϖ
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6 Time domain block diagram DC Machines - Shunt DC Machine Shunt DC Machine G 1 G 3 G 2 L af X X r ϖ i a i f i f i a + - + - V a V f V f
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7 State-space equations DC Machines - Shunt DC Machine Shunt DC Machine Let [ ] r a f t i i X ϖ , , = + = t r r r dt t 0 ) 0 ( ) ( θ ϖ θ Re-writing the dynamic equations, ; L a f af r m r a aa r f aa af a aa a a f
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