**Single Machine Infinite Bus System:**

Figure 12.14 is the circuit model of a Single Machine Infinite Bus System through a line of reactance X_{e}. In this simple case

From Eq. (12.29b)

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

### Two Machine Infinite Bus System:

The case of two finite machines connected through a line (X_{e}) 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

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

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

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

The electrical power interchange is given by expression

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.