Synchronous Generator : Concepts - 4

Synchronous Generator: Parallel-Generator Theorem:

Reference to Figure given above , where 2 generators are connected in parallel. Let the load be I amps at V volts such that V / I = Z.

Then , V = (I1+I2 )Z = [( E1-V)/Zs1+ ( E2-V)/Zs2 ]

= [ E1/Zs1 + E2/Zs2 ] Z – V[1/Zs1 + 2/Zs2]Z

i.e. V [1/Z +1/Zs1 + 1/Zs2]

= E1/Zs1 + E2/Zs2 i.e. V [1/Z0] = Isc

where Isc is the total short circuit current obtained by summing the terms E1/Zs1 and E2/Zs2where

1/Z0=1/Z +1/Zs1 + 1/Zs2

This theorem holds true for any number of generator.

The characteristics of a synchronous generator on infinite bus-bars are quite different from those when it operates on its own local load. In the latter case, a change in the excitation changes the terminal voltage, while the pf is determined by the load. When working on infinite bus-bars, on the other hand, no alternation of the excitation can change the terminal voltage which is fixed by the network, the point however, is affected. In both cases the power developed by a generator (or received by a motor) depends solely upon the mechanical power provided (or load applied to it).

Consider 2 alternators operating in parallel on infinite bus-bars, with identical initial operating conditions, i.e. the active and reactive powers are divided equally. Now suppose the excitation of alternator 1 is increased then as stated earlier, the kW loading of the 2 alternators remains unchanged as the mechanical input remains the same. The change is seen in the KVAR loading due to the changes in the individual load currents and points.

Similarly with change in steam supply of one of the alternator with excitation kept same, the change is observed in the kW loading of the 2 alternators. While the KVAR loading remains unaltered.

SYNCHRONIZING POWER (Ps):

Let for same cause the angle δ changes to δ I δ’.

The synchronous power, Ps = (E+ V) Zs sin (θ + δ) sinδ’

For large generator, Zx =Sx

i.e. θ = 900

Ps = ( E+ V ) Zs cos δ sinδ’

When an unloaded M/c is synchronized to a constant voltage bus bar

δ = 0,

Ps = (E+ V) Zs sin δ/ ph

when δ is small enough

Ps = (E+ V) Zs sin δ’/ ph

=V I_sc δ’ / ph where I_sc = E_f / Z_s

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