Path for Zero Sequence Currents in Transformers & Fault Calculations on a Power System Networks

Path for Zero Sequence Currents in Transformers:

In transformer positive sequence network and negative sequence impedances are equal. But zero sequence impedances of transformer depend on the connection of the primary and secondary windings and status of the neutral terminal in case of star connected windings.

The different connection type of transformer and its equivalent zero sequence circuits are shown in the figure below. The zero sequence currents path can be determined by using these equivalent zero sequence circuit.

Fault Calculations on a Power System Network:

Line to Ground Faults:

Let us consider a fault occurs between phase a and ground through impedance Zf at bus k of power system network as in fig below.

Conditions, derivation and equivalent sequence circuit is similar as of the single line to ground fault on the terminal of unloaded synchronous generator

Hence, the result is:

Where Zkk(0), Zkk(1) and Zkk(2) are diagonal element at k axis of corresponding bus impedance matrix and Vk(0) is prefault voltage at bus k

The fault current can be determined by using the matrix equation i.e.

Line to Line Faults:

Let us consider a fault occurs between phase a and b through an impedance Zf at bus k of power system network as in fig below.

Conditions, derivation, and equivalent sequence circuit are similar as of the line to line fault on the terminal of unloaded synchronous generator

Hence, the result is:

Where Zkk(0), Zkk(1) and Zkk(2) are diagonal element at k axis of corresponding bus impedance matrix and Vk(0) is pre fault voltage at bus k

The fault current can be determined by using the matrix equation i.e.

Double line to ground fault:

Let us consider a fault occurs between phase a and b through an impedance Zf to the ground at bus k of power system network as in fig below.

Conditions, derivation, and equivalent sequence circuit are similar as of the double line to ground fault on the terminal of unloaded synchronous generator

Hence, the results are:

Where Zkk(0), Zkk(1) and Zkk(2) are diagonal element at k axis of corresponding bus impedance matrix and Vk(0) is prefault voltage at bus k

The fault current can be determined by :