5.2.1 Representation of Generators

In Fig. 5.1, , , , which are the three-phase voltages at the generator terminal bus, are expressed in phasors in rectangular coordinates. Similarly, the voltages at the generator internal bus may be given by , , . In fact the voltages at the generator internal bus are balanced, that is:

(5.45)

(5.46)

In the three-phase power flow equations of the generator, and can be considered as independent state variables of the internal generator bus while and , and and are dependent state variables and can be represented by and . We have:

(5.47)

(5.48)

(5.49)

(5.50)

5.2.2 Power and Voltage Mismatch Equations in Polar Coordinates

5.2.2.1 Power Mismatch Equations at Network Buses

The network buses include all buses of the network except the internal buses of generators. The power mismatch equation of phase p at the network bus i are given by:

(5.51)

(5.52)

where p = a, b, c. and are the active and reactive loads of phase p at bus i.

5.2.2.2 Power and Voltage Mismatch Equations of Synchronous Machines

PQ Machines. For a PQ machine, the total three-phase active and reactive powers at the terminal bus of the machine are specified:

(5.53)

(5.54)

where and are the specified active and reactive powers of the generator at bus I, which are in the direction of into...