How do Zig-Zag Earthing Transformers work?

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Earthing of power systems is an important consideration for both safe step-and-touch and maximum fault level considerations.  There are however specifically "isolated networks" where the system is "non-effectively earthed" based on a Petersen Coil principle which is somewhat based on a Neutral Grounding Reactor approach, but that is not the focus of this page.

Star windings are easily earthed as typically done in the following four options at the neutral star point of the three windings.

However delta connected systems do not have any "neutral" point as the star point of the three phases.  Hence a different earthing method is required as either a star/delta earthing transformer or a special "cross connected" transformer known as a Zig Zag Earthing Transformer. 

The first is reasonably straight forward as the delta winding forces the condition that only zero sequence currents can flow.

The Zig-Zag also only allows zero sequence currents to flow but at first is not quite so obvious as to how.

Zig Zag Earthing Transformer Operation

At the outset allow me to state clearly:

For Zero Sequence currents, the Zig-Zag windings are effectively zero impedance - fault current is limited purely by the main transformer impedance, the line impedance to the fault, the impedance of the fault, the return ground impedance and any earthing impedance in the earth leg from the zig-zag to earth.

For Positive or Negative Phase Sequence, the Zig-Zag windings are effectively infinite impedance.

Some explanations of Zig-Zag Earthing Transformers (ZZET) jump straight in to sequence component diagrams and calculations of Positive, Negative and Zero Sequence impedances.

A useful reference paper on ZZET was written by Anna Guldbrand of Lund University in 2006: "Central or Local Compensation of Earth-Fault Currents in Non-Effectively Earthed Distribution Systems"

I prefer to explain ZZET by simply considering where current can flow using the "age-old" and very simple "follow the arrow" technique (smile)

These types of transformers look complicated, but in reality are just applying the law of Ampere.Turns balance across two windings on the same limb, i.e. if current is flowing in one winding, current must be flowing in the other.

The trick is in the means of connecting the principal six windings (some ZZET have 12 windings in total - refer section on Combined ZZET and Auxiliary TF). 

The non-polarity end of the A-phase top winding is connected to the non-polarity end of the B phase bottom winding.  
The non-polarity end of the B-phase top winding is connected to the non-polarity end of the C phase bottom winding.  
The non-polarity end of the C-phase top winding is connected to the non-polarity end of the A phase bottom winding.  

The cross connection of the windings on different limbs creates current flow dependencies which only apply if the currents in all windings are in phase ... i.e. the currents are Zero Sequence currents and hence are the physical reality of a earth fault.

Current flowing up from the neutral (purple) to the polarity end of A phase bottom winding will therefore flow up and through the top winding of C-phase and onto the grid (Figure 1).

Figure 1 (Click to enlarge)

Figure 1

As C-phase top has current flow, there must be corresponding current flow in C-phase bottom (orange) (Figure 2)

Figure 2 (Click to enlarge) 

Figure 2

Therefore there must be current flow (orange) in from the earth and out on B phase to the grid (Figure 3):

Figure 3 (Click to enlarge)

Figure 3

As B-phase top has current flow, there must be corresponding current flow in B-phase bottom (green) (Figure 4)

Figure 4 (Click to enlarge)

Figure 4

Therefore there must be current flow (green) in from the earth and out on A phase to the grid (Figure 5):

Figure 5 (Click to enlarge)

Figure 5

It is to note that all currents in each set of top or bottom windings as well as the earth connection are IN-PHASE.  They must therefore be real ZERO SEQUENCE currents Ia-0, Ib-0, Ic-0, the sum of which is the total earth fault current Ia-0 + Ib-0 + Ic-0 = If.

Note that Positive Sequence and Negative Sequence 3-phase currents cannot flow through the ZZET because the currents are not in phase.  Hence the ZZET presents itself as an open circuit for

  • a balanced system (e.g. no fault)
  • an unbalanced system with no fault
  • a system with a phase-phase fault

It is also to note that as shown in Figure 6, if any one phase is not connected to the grid, e.g. a single fuse blows (unlikely) or a connection has not been made, the earthing transformer winding dependencies cannot work and there is no earth fault current able to flow.  The open circuit of one phase (Figure 6 C-phase grid connection is not connected) means there cannot be corresponding current flow in its bottom winding, and the corresponding flow on to the windings on the other cores.

Figure 6 (Click to enlarge)

Figure 6

It is therefore critical that Earthing Transformers are solidly connected to the earth and to the grid.  It is therefore somewhat inconsistent to provide mechanical switching of Earthing Transformers In/Out of service via switchgear.

Earth Fault Detection with Earthing Transformers

There are three earth fault scenarios for each consideration of where the ZZET is located with respect to the line CTs:

  • ZZET to left of main CTS
    • EF between TF and Earthing Transformer
    • EF beyond the Restricted Earth fault line CTs
    • EF between the Earthing Transformer the Restricted Earth fault line CTs
  • ZZET to right of main CTs
    • EF between ZZET and line CTs
    • EF between line CTs and main transformer
    • EF to the right of ZZET
Figure 7

Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Combined Earthing Transformer and Auxiliary Transformer

The Earthing Transformer is essentially a voltage transformer with special connections.

There is also a requirement to provide a station auxiliary supply which usually requires an Auxiliary Transformer associated with the Power transformer.

The substation footprint size therefore must cater for the Power Transformer, the Earthing Transformer and the Auxiliary Transformer

However in addition to the zig-zag windings, the same limbs can be used to provide a third winding as the station low voltage 400 V 3-phase, 240 V 1-phase supply. 

This eliminates the need for a separate auxiliary transformer, saving substation land cost (equipment footprint) and equipment cost. (tick)(thumbs up)(big grin)(star)

However this extra winding #3 must be balanced with a fourth winding to ensure ampere.turns balance on each limb is achieved.

Figure 13

This can be seen considering a phase load connected to one station auxiliary phase. 
In order to present the scenario, all windings on the limb are considered as 1:1:1:1

If the load creates 3 units of current flowing OUT of the polarity terminal of the Auxiliary wining #3, there must be ampere turns balance along the core.

There must be a total of 3 units of current flowing INTO the polarity terminals of other windings .. and also respecting Kirchhoff's Law!

The first balancing current to consider is on Winding #2, noting direction of current must respect polarity rules.  The single "up" red arrow in Winding #2 crosses over to become the blue arrow in the right-side limb.
This current flows on the grid to the grid transformer(s) delta winding where it passes through the blue phase winding and back out on the red phase terminal.

The red arrow flowing out of the Main Power Transformer now becomes the red unfilled arrow flowing "down", which also respects polarity rules.
We now have two unfilled arrows only partially balancing the three solid arrows in Winding #3, hence ampere.turns balance has not yet been achieved. 
We will come back to that.

The red unfilled arrow in Winding #1 crosses over to become the yellow arrow in the centre phase.  This limb now requires that current to be balanced as well.
We will come back to that.

Returning to the red "up" arrow on Winding #2, it crosses over to the blue phase.  That unfilled blue current must also have a balancing current somewhere.

We now have a requirement for three balancing which are in-phase.
This can be achieved in Winding #4 connected in delta.

Hence the three solid red arrows in Winding #3, is balanced by:

  • one unfilled arrow on Winding #1 (note polarity markings)
  • one unfilled arrow on Winding #2 (note polarity markings)
  • one unfilled arrow on Winding #4 (note polarity markings)

The one yellow arrow on Winding #2 is balanced by one yellow arrow on Winding #4

The one blue arrow on Winding #1 is balanced by one blue arrow on Winding #4

All currents are balanced on each limb.


Figure 14

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