Synchronous machines in rigid network operation can be driven in any of the 4 quadrants.
The according mode of operation is characterized by the corresponding phase angle of the stator current, if terminal voltage is assumed to be placed on the real axis.
-active power output (generator)
-active power input (motor)
-reactive power output (over excited), machine acts like capacitor
-Reactive power input (under excited), machine works like reactance coil
Reactive power is independent from load but solely depending on excitation; as a consequence reactive power output derives from over excitation whereas reactive power input arises from under excitation.
When a single generator operated alone, the real and reactive powers supplied by the generators are fixed, constrained to be equal to the power demanded by the load, and the frequency and terminal voltage were varied by the governor set points and the field current.
When a generator is operating in parallel with an infinite bus, the frequency and terminal voltage were constrained to be constant by the infinite bus, and the real and reactive powers were varied by the governor set points and the field current.
However when a generator is operating in parallel with another same size generator as shown here:
The basic constraint is that the sum of the real and reactive powers supplied by the two generators must equal the P and Q demanded by the load. The system frequency is not constrained to be constant, and neither is the power of a given generator constrained to be constant.
The power-frequency diagram for such a system immediately after G2 has been paralleled to the line is shown below:
The total power Ptot (which is equal to Pload) and reactive power respectively are given by:
Ptot = Pload = PG1 + PG2
Qtot = Qload = QG1 + QG2
When the governor set points of G2 are increased, as a result, the power-frequency curve of G2 shifts upward as shown here:
The total power supplied to the load must not change. At the original frequency f1, the power supplied by G1 and G2 will now be larger than the load demand, so the system cannot continue to operate at the same frequency as before. In fact, there is only one frequency at which the sum of the powers out of the two generators is equal to P load. That frequency f2 is higher than the original system operating frequency. At that frequency, G2 supplies more power than before, and G1 supplies less power than before.
Thus, when 2 generators are operating together, an increase in governor set points on one of them
1. increases the system frequency.
2. increases the power supplied by that generator, while reducing the power supplied by the other one.
When the field current of G2 is increased, the resulting behavior is analogous to the real-power situation as shown below:
When 2 generators are operating together and the field current of G2 is increased,
1. The system terminal voltage is increased.
2. The reactive power Q supplied by that generator is increased, while the reactive power supplied by the other generator is decreased.
If the slopes and no-load frequencies of the generator’s speed droop (frequency-power) curves are known, then the powers supplied by each generator and the resulting system frequency can be determined quantitatively.