Simple System

Simple System:

Simple System – Machine Connected to Infinite Bus

Figure 12.14 is the circuit model of a single machine connected to infinite bus through a line of reactance Xe. In this simple case

Simple System

From Eq. (12.29b)

Simple System

The dynamics of this system are described in Eq. (12.11) as

Simple System

Simple System

Two Machine System

The case of two finite machines connected through a line (Xe) is illustrated in Fig. 12.15 where one of the machines must be generating and the other must be motoring. Under steady condition, before the system goes into dynamics and

Simple System

the mechanical input/output of the two machines is assumed to remain constant at these values throughout the dynamics (governor action assumed slow). During steady state or in dynamic condition, the electrical power output of the generator must be absorbed by the motor (network being lossless). Thus at all time

Simple System

The swing equations for the two machines can now be written as

Simple System

Simple System

Subtracting  Eq. (12.39b) from Eq. (12.39a)

Simple System

Simple System

where
Simple System

The electrical power interchange is given by expression

Simple System

The swing equation Eq. (12.41) and the power angle equation Eq. (12.44) have the same form as for a single machine connected to infinite bus. Thus a two-machine system is equivalent to a single machine connected to infinite bus.

Leave a Reply

Your email address will not be published. Required fields are marked *