# 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
```