The transformer is a static device where there is no mutual coupling between the sequence networks. The positive and the negative sequence impedance of the transformer is equal to its leakage reactance. For a transformer

Z1 = Z2 = Zleakage

Due to the possibility of a variety of connections in a 3-phase transformer the zero-sequence impedance of the transformer is complex. The zero sequence impedance and network of the transformer are different and complex than the zero sequence impedance and networks of other power system elements. The zero-sequence current can flow on either side of the transformer. The zero sequence impedance offered by the transformer is different from the positive and negative sequence impedance. But the difference in them is so small that the zero sequence impedance can be assumed to be equal to the positive and the negative sequence impedance.

Zero Sequence Impedance and Networks of Transformer

For a transformer winding with star connection and isolated neutral, no zero-sequence current can flow in that winding. For a delta-connected winding of the transformer, the zero-sequence current can flow if zero-sequence voltages are induced in the delta. Otherwise, for a delta-connected winding of the transformer, no zero-sequence current can flow through the winding as there is no return path available for the current.

Formation of Zero Sequence Networks of Transformer

The zero-sequence network of a transformer can be formed by using the following circuit. Here, Z0 is the zero-sequence impedance of the transformer, and 1, 2, 3, and 4 are the switches that are considered to be open by default. The position of the switch is changed for different connections of the transformer which will be discussed below.

Zero Sequence Impedance and Networks of Transformer

Figure: General Circuit for Determination of Zero Sequence Network of Transformer

For the given circuit for the general arrangement of the zero-sequence network of a transformer, there are two switches provided on either side of the transformer. A series and shunt switch is provided for each transformer side. Switches 1 and 2 are series switches. Switches 3 and 4 are shunt switches.

For series switch:

The series switch is closed for a particular side if that side is star connected and the neutral point is grounded. For transformer side with star connected and isolated neutral the series switch is kept open.

This means if the transformer’s primary side is star connected just operate on the series switch (1) and leave the shunt switch (3) as it is i.e. leave shunt switches open. Similarly operate on the series switch (2) and leave shunt switch (4) as it is if the secondary side is star connected.

For shunt switch:

The shunt switch is closed for a particular side if that side is delta connected.

This means if the transformer’s primary side is delta connected just operate on the shunt switch (3) and leave the series switch (1) as it is i.e. leave series switch -1 open. Similarly operate on the shunt switch (4) and leave series switch (2) as it is if the secondary side is delta connected.

For the final sequence network, the switches need not be shown. The switch is considered now for our simplicity to form the zero-sequence network.

Example for Forming Zero Sequence Network

This will be clearer if we see some possible connections of transformers.

Consider a Star-Star transformer with isolated neutral.

Figure: Star-Star Transformer

For primary side star and isolated neutral, we will be operating on switch -1 and leaving the shunt switch -3 as it is i.e. leave switch -3 open. As mentioned earlier, for star connection with isolated neutral keep the series switch -1 open.

And, for secondary side star and isolated neutral, we will be operating on series switch -2 and leaving the shunt switch -4 as it is i.e. leave switch -4 open. As mentioned earlier, for star connection with isolated neutral keep the series switch -1 open.

General Circuit for Zero Sequence Impedance and Networks of Transformer

Figure: General Circuit for Zero Sequence Networks of Star-Star Transformer

Zero Sequence Network with zero sequence impedance

Figure: Zero Sequence Equivalent Circuit for Star-Star Transformer


Let’s consider a Star-Delta transformer with grounded Y-Neutral (Star neutral point is grounded).

Figure: Star-Delta transformer with grounded Y-Neutral

Here the neutral of the star side is grounded so the zero-sequence current can flow in the star side of the transformer. We will make the series switch -1 closed and leave the shunt switch -3 open as it is.

No zero-sequence current can flow in the secondary side of the delta connection, so shunt switch -4 is kept closed and leaves the series switch -2 open as it is.

Figure: General Circuit for Zero Sequence Networks of Star-Delta Transformer with Grounded Y-Neutral

Zero Sequence Network with zero sequence impedance

Figure: Zero Sequence Equivalent Circuit for Star-Delta transformer with grounded Y-Neutral


For a transformer with Star-Delta Transformer with grounded Y-Neutral through reactor impedance Zn.

Figure: Star-Delta Transformer with Grounded Y-Neutral Through Reactor Impedance Zn

For the star side with grounded neutral, the series switch will be closed as it is in previous cases while the shunt switch is left as it is. If the star neutral is grounded through the reactor of impedance Zn, an impedance of 3Zn appears in series along with Z0 (zero sequence impedance) in the sequence network.

While for the secondary delta side, the shunt switch -4 is closed and leaves series switch -2 open as it is.

General Circuit for Zero Sequence Impedance and Networks of Transformer

Figure: General Circuit for Zero Sequence Networks of Star-Delta Transformer with Grounded Y-Neutral Through Reactor Impedance Zn

Zero Sequence Network with zero sequence impedance

Figure: Zero Sequence Equivalent Circuit for Star-Delta Transformer with Grounded Y-Neutral Through Reactor Impedance Zn

Zero Sequence Network for 3-phase Transformer with Possible Connections

Transformer Winding Arrangement Connection Diagram Zero Sequence Equivalent Circuit
1. Star-Star Transformer with isolated Neutral
2. Star-Star Transformer with Any One Neutral Grounded
3. Star-Star Transformer with both Neutral Grounded
4. Star-Delta Transformer with Grounded Y-Neutral
5. Star-Delta Transformer with Grounded Y-Neutral Through Reactor Impedance Zn
6. Star-Delta Transformer with Isolated Star
7. Delta-Delta Transformer
8. Star-Star Transformer with any One Neutral Grounded and Tertiary winding in Delta

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