Sharing of load when two alternators are in parallel

Load Sharing

 When several alternators are required to run in parallel, it probably happens that their rated outputs differ. In such cases it is usual to divide the total load between them in such a way that each alternator takes the load in the same proportion of its rated load in total rated outputs. The total load is not divided equally. Alternatively, it may be desired to run one large alternator permanently on full load, the fluctuations in load being borne by one or more of the others. If the alternators are sharing the load equally the power triangles are as shown in Fig

Sharing of load when two alternators are in parallel

 Consider two alternators with identical speed load characteristics connected in parallel as shown in Fig:

Let E1, E2 be the induced emf per phase,

Z1, Z2 be the impedances per phase,

I1, I2 be the current supplied by each machine per phase

Z be the load impedance per phase,

V be the terminal voltage per phase

From the circuit we have V = E1 - I1Z1 = E2 - I2Z2 and hence, I1 = E1 - V/Z1 and I2 = E2 - V/Z2

and also V = (I1 + I2 ) Z = IZ solving above equations

I1 = [(E1- E2) Z + E1 Z2]/ [ Z( Z1 + Z2) + Z1Z2]

I2 = [(E2- E1) Z + E2 Z1]/ [ Z( Z1 + Z2) + Z1Z2]

The total current I = I1 + I2 = [E1Z2 + E2Z1] / [ Z( Z1 + Z2) + Z1Z2]

And the circulating current or synchronizing current I_s = (E1 - E2) / (Z1 + Z2)