# How core balance current transformer works

FAQ | Feb 13,2023

Let Īa, Īb and Īc be the three line currents and Φa, Φb and Φc be corresponding components of magnetic flux in the core. Assuming that the CT is operating in the linear region (Read B-H Curve to get idea of linearity), magnetic flux because of individual phase current will be directly proportional to the phase current and hence we can write as below,
Φa = kIa
Φb = kIb
Φc = kIc
where k is constant of proportionality. Mind here that same constant of proportionality is used as all the three phase current are producing magnetic flux in the same core i.e. magnetic material.
Thus the resultant magnetic flux in the CBCT core,
Φr = k(Īa + Īb + Īc) …………………..(1)
But we know from theory of symmetrical components,
Īa + Īb + Īc = 3Ī0 = Īn
where, Io is zero sequence current and In is neutral current. Hence we can write as
Φr = kĪn …………………………(2)
Now let us consider two cases:
Case1: During normal condition
Īa + Īb + Īc = 0
Hence from equation (1),
Net resultant flux in the CBCT Core, Φr = 0 which means no secondary current and therefore the Earth Fault Relay won’t operate.
Case2: During earth fault, three phase current passing through the center of Core Balance Current Transformer will not be balanced rather a zero sequence current will flow. For example for single line ground fault,
If = 3Ia0 = In
Thus from equation (2),
Net magnetic flux in the CBCT core, Φr will have some finite value which in turn will induce current in the secondary circuit due to which earth fault relay will operate. Because of this reason, a Core Balance Current Transformer or CBCT is also called Zero Sequence Current Transformer.

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