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lecture10 - FAMU-FSU College of Engineering Chapter 8:...

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Unformatted text preview: FAMU-FSU College of Engineering Chapter 8: Transient Analysis of Synchronous Machines (c) Feb 2004 Power Systems I 2 Synchronous Machines c Steady state modeling r rotor mmf and stator mmf are stationary with respect to each other r flux linkage with the rotor are invariant with time r no voltages are induced on the rotor circuits c Transient modeling r flux linkage changes with time r differential equations have time-varying coefficients r Parks transformation r dynamic behavior s sub-transient period, transient period, and steady-state period emf X S R A V T I G (c) Feb 2004 Power Systems I 3 Transient Analysis c Transient analysis will be applied in the dynamic study of generators c Generators experience dynamic behavior during r switching load r faults c Consider the transient behavior of an RL circuit with a switched voltage source R L t = 0 V(t) i(t) (c) Feb 2004 Power Systems I 4 ( 29 ( 29 ( 29 2 2 2 1 and , tan , , : where sin sin ) ( ) ( ) ( sin L R Z R L R L Z V I e I t I t i dt t i d L t i R t V m m t m m m + = = = =--- + =-- + =-- R L t = 0 V(t) i(t) Transient Analysis c The voltage source is sinusoidal: c The KVL equation are: ( 29 + = t V t v m sin ) ( (c) Feb 2004 Power Systems I 5 Example c Solve for the time-domain solution of the current r for a faulted generator having the following characteristics R = 0.125 L = 10 mH v ( t ) = 151 sin (377 t + ) r which will give (a) zero dc offset current, (b) maximum dc offset current (c) Feb 2004 Power Systems I 6 Example ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 08 . 08 . 08 . 40 377 cos 40 90 sin 40 90 377 sin 40 ) ( 9 . 1 90 1 . 88 Let (b) 377 sin 40 ) ( 1 . 88 Let (a) 1 . 88 sin 40 1 . 88 377 sin 40 ) ( s 08 . 125 . 01 . A 40 772 . 3 151 1 . 88 772 . 3 77 . 3 125 . 01 . 377 125 . t t t m e t e t t i t t i e t t i I j j Z--- +- = -- - = - = - = = = -- - + = = = = = = + = + = (c) Feb 2004 Power Systems I 7 0.05 0.1 0.15 0.2 0.25 0.3 0.35-40-20 20 40 t, sec i(t) 0.05 0.1 0.15 0.2 0.25 0.3 0.35-40-20 20 40 60 80 t, sec i(t) Example (a) zero dc offset current (b) maximum dc offset current (c) Feb 2004 Power Systems I 8 Transient Analysis c Synchronous Machines r Models and analysis were previously developed for steady state behaviors s rotor and stator magnetic fields are stationary with respect to each other s the flux linkage in the rotor circuit are constant in time s the per phase equivalent circuit becomes a constant generated emf in series with a simple impedance r Under transient conditions (time varying) the above assumptions are no longer valid s changing stator current are reflected in a dynamic flux linkage...
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This note was uploaded on 11/27/2011 for the course EEL 4213 taught by Professor Thomasbaldwin during the Spring '11 term at FSU.

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lecture10 - FAMU-FSU College of Engineering Chapter 8:...

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