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Machine Dynamic Equations

# Machine Dynamic Equations - Synchronous Machine Dynamic...

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Synchronous Machine Dynamic Equations March 30, 2011 DYNAMIC EQUATIONS Time constants from fundamental parameters T d 0 X ffd ω s R fd T d X d ω s R fd X ffd X d T q 0 X 11 q ω s R 1 q Classical machine model d dt ω ( t ) = π f s H ( P m P e P D )) d dt δ ( t ) = ω ( t ) ω s ( t ) P e ( t ) = Real { E t I t } + R a I 2 t P D ( t ) = K D ( ω ( t ) ω s ( t )) To include field flux variations also have (flux decay model) and have d dt Ψ fd = 0 (equation traditionally written in terms of voltage not flux). Applies to both model 1 and model 2. d dt E q ( t ) = 1 T d 0 E fd ( t ) E q ( t ) ( X d X d ) I d ( t ) To include q-axis damper winding (i.e., model 1) for cylindrical rotor also have d dt E d ( t ) = 1 T q 0 E d ( t ) + ( X q X q ) I q ( t ) Voltage transducer with simple thyristor exciter d dt V 1 ( t ) = 1 T R [ E t V 1 ( t )] E fd ( t ) = K A ( V ref V 1 ( t )) 1

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Or can model as a time constant in the exciter d dt E fd ( t ) = 1 T A [ E fd + K A ( V ref E t )] Single stage power system stabilizer with washout filter d dt V 2 ( t ) = K stab ω s d dt ω ( t ) 1 T w V 2 (
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