This preview shows pages 1–9. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: FAMUFSU 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 timevarying coefficients r Parks transformation r dynamic behavior s subtransient period, transient period, and steadystate 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 timedomain 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 0.354020 20 40 t, sec i(t) 0.05 0.1 0.15 0.2 0.25 0.3 0.354020 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...
View
Full
Document
This note was uploaded on 11/27/2011 for the course EEL 4213 taught by Professor Thomasbaldwin during the Spring '11 term at FSU.
 Spring '11
 THOMASBALDWIN
 Flux, Volt

Click to edit the document details