Flexible AC Transmission Systems: Modelling and Control

Modeling of power system components such as transmission lines, loads, etc. have been discussed in [23][6]. In the following, the formulation of three-phase Newton power flow in rectangular coordinates will be presented where the modeling of synchronous generator is discussed in detail.
In three-phase power flow calculations, all buses may be classified into the following categories:
Slack bus. Similar to that in single-phase positive-sequence power flow calculations, a slack bus, which is usually one of the generator terminal buses, should be selected for three-phase power flow calculations. At the slack bus, the positive-sequence voltage angle and magnitude are specified while the active and reactive power injections at the generator terminal are unknown. The voltage angle of the slack bus is taken as the reference for the angles of all other buses. Usually there is only one slack bus in a system. However, in some production grade programs, it may be possible to include more than one bus as distributed slack buses.
PV Buses. PV buses in three-phase power flow calculations are usually generator terminal buses. For these buses, the total active power injections and positive-sequence voltage magnitudes are specified.
PQ Buses. PQ buses are usually load buses in the network. For these buses, the active and reactive power injections of their three-phases are specified.
A synchronous machine may be represented by a set of three-phase balanced voltage sources in...