Transient Response

Calculated response to disturbances at t1 and t2:

Equations

Swing equation

(Describes the swings of the rotor angle (δ) during a disturbance)

dω/dt = ωs/(2 × H) × (Pm-Pe)

dω/dt = a × (Pm-Pe)

a = ωs/(2 × H)

Power transfer equation

(Active power transfer)

Is × X = v1 × sin(δ)

Is = v1 × sin(δ) / X

Pe = Is × v2

Pe = v1 × v2 × sin(δ)/X

Pe = Pmax × sin(δ)

Pmax = v1 × v2/X

(Reactive power transfer)

Q(var) = v1/X × (v1 - v2 × cos(δ))

dδ/dt = ω - ωs

v1 = Voltage induced in the stator winding by the rotor field (terminal voltage)

v2 = Voltage at receiving bus

Is = Stator winding current

X= impedance of the stator windings (neglecting resistance)

δ = rotor angle



  Pm               Is->      Pe 
  PM->G ---|------------------|
          v1∠δ     X         v2∠0

Power Transfer Calculator

System parameters:

{{inputGroup.title}}

{{field.unit}}

Variables

{{field.unit}}