Home / Technical Articles / The essential physics behind transformer differential protection (You MUST know)

Introduction to differential protection

Transformers are important system components available in many different constructions. The range of HV transformers reaches from small distribution transformers (from 100 kVA) up to large transformers having several hundred MVA.

The essential physics behind transformer differential protection you should know
The essential physics behind transformer differential protection you should know (photo credit: Kam Abbott via Flickr)

Apart from the large number of simple two and three-winding transformers, a range of complex constructions in the form of multi-winding and regulating trans- formers also exist.

Differential protection provides fast and selective short-circuit protection on its own, or as a supplement to Buchholz (gas pressure) protection.

It is usually applied on transformers above approx. 1 MVA. On larger units above approx. 5 MVA it is standard.

The transformer differential protection contains a number of supplementary functions (adaptation to transformation ratio and vector group, stabilisation against in-rush and over-excitation) and therefore requires some fundamental consideration for the configuration and setting calculation.

Essential physics

To better understand the protection response during short-circuits and switching operations, the physical principles of the transformer are initially covered in detail.

  1. Equivalent circuit of a transformer
  2. In-rush
  3. Sympathetic in-rush
  4. In-rush blocking
  5. Cross-blocking
  6. Transformer over-fluxing

1. Equivalent circuit of a transformer

The primary and secondary winding are linked via a magnetic core by means of the main flux Φ Figure 1. To obtain the flux, the magnetising current (excitation current) Im according to the magnetising curve is required.

Equivalent circuit of a transformer
Figure 1 – Equivalent circuit of a transformer

In the electrical equivalent circuit, this excitation requirement corresponds to the main reactance Xm. The leakage flux Φσ1 and Φσ2 are only linked to their respective own windings and make up the leakage reactances Xσ1 and Xσ2 .

R1 and R’2 are the respective winding resistances. All currents and impedances are referred to the primary side.

Xm = U/Im corresponds to the slope of the magnetising curve. During load and particularly in the event of short-circuits, the operating point is below the knee-point in the steep portion of the curve.

The magnetising current at nominal voltage only amounts to approx. 0.2% In, i.e. in the non-saturated segment of the curve Xm is approx. 500 times larger than the nominal impedance of the transformer and approx. 5000 times greater than the leakage reactances.

During load and short-circuit conditions, a simplified equivalent circuit may therefore be used for the calculations (Figure 2).

Simplified transformer equivalent circuit
Figure 2 – Simplified transformer equivalent circuit

The series reactance XT corresponds to the short-circuit voltage in %, relative to the nominal impedance of the transformer:

Transformer series reactance formulae

The series resistance corresponds to the ohmic short-circuit voltage in %, and is also based on the nominal impedance. For calculation of the short-circuit current, the resistance may be neglected, it must only be considered when calculating the DC time constant.

Table 1 lists typical transformer data.

Table 1 – Typical transformer data

Transformation ratio
voltage ux-t [%]
Open circuit current
[% IN]

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2. In-rush

When energizing a transformer, one-sided over-excitation results, due to remanance causing large magnetising current flow (in-rush current).

The flux does not return to zero when the transformer is switched off, but remains at the remanance point ΦRem, which may be above 80% of the nominal induction. When the transformer is re-energized, the flux increase starts at this point. Depending on the energizing instant on the sinusoidal voltage (point on wave), an off-set course of the flux can result.

For the large flux values in the saturation range, a very large magnetising current is required, and cyclic current peaks will result.

The curve form corresponds with the sinusoidal half-waves of a simple half-wave rectified AC current that decays with a very large time constant (Figure 3 below).

Origin of in-rush current
Figure 3 – Origin of in-rush current

The rush current is particularly large when cores of cold rolled steel with a nominal induction (1.6 to 1.8 Tesla) are operated close to the saturation induction (approx. 2 Tesla).

On a three-phase transformer, a three-phase rush current will result, which depends on the vector group and the method of star-point earthing on the transformer.

In general, two phases will saturate and draw large magnetising currents. On star delta transformers, these currents are coupled to the non-saturated phase via the delta winding.

This causes the typical rush currents as shown in Figure 5.

The rush currents in the three phases can be calculated from the required magnetisation (ImA and ImC) of the two saturated core-limbs A and C with the given equations. The current on phase B thereby corresponds to the current in the delta winding ID. The shown oscillogram of an in-rush occurrence confirms the calculated curves.

Amplitude and time constant depend on the transformer size (see figure 4).

Typical rush current of a star delta transformer
Figure 4 – Typical rush current of a star delta transformer

It must be noted that a similar rush current also arises when a close-in external short–circuit is switched off and the transformer is re-magnetised by the recovery of the voltage.

It however is substantially smaller than the in-rush following ener- gising of a switched-off transformer.

Typical in-rush current data
Figure 5 – Typical in-rush current data

Large rush currents can also occur when asynchronous systems are switched together via a transformer, as the large voltage difference can cause transient saturation of the core.

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3. Sympathetic in-rush

When transformers were connected in parallel, it was observed that the differential protection of the transformer that was in service issued a trip.

The reason for this is sympathetic in-rush current, which results from the rush current of the transformer that is being energized (Figure 6).

Sympathetic inrush current
Figure 6 – Sympathetic inrush current

The voltage drop resulting from the initial rush current across the source resistance of the in-feed affects the second transformer in parallel and causes the sympathetic in-rush current (I2).

The current from the system (IT) decays rapidly. However a current still circulates between the two transformers due to the small damping (large time constant τ =  X/R of the windings).

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4. In-rush blocking

The in-rush current flows into the protected object from a single side and appears as an internal fault. The transformer differential protection must therefore be stabilized against this phenomenon.

The large amount of second harmonic in the rush current was already used with conventional protection for this purpose. The second harmonic is filtered out of the differential current (operating current) by means of a filter, and is then used as additional restraint current in the measuring bridge.

When it was above approximately 15% in relation to the 50(60) Hz fundamental, a very large additional restraint was introduced to prevent tripping.

Other manufacturers compared the 100(120) and 50(60) Hz components directly with a separate bridge circuit, which then directly blocked the protection, as it is now done in the software of numerical protection.

The 100(120) Hz component in the rush current depends on the base width of the sinusoidal caps (as shown in Figure 7).

It decreases as the base width B increases.

Investigations have shown that a base width greater than 240° hardly ever arises in practice, which implies a minimum second harmonic component of 17.5%. A setting of 15% therefore makes sense for in-rush blocking.

The 3rd harmonic may not be used for in-rush blocking, as it is strongly represented in the short-circuit current when CT saturation takes place.

Harmonic content of in-rush current
Figure 7 – Harmonic content of in-rush current

A more sensitive setting than 15% of the second harmonic should normally not be applied as the off-set short-circuit current will also have a second harmonic component in case of CT saturation.

In rare cases, for example with weak in-feed, a soft energization with a very small second harmonic component may occur. Under these conditions, a reduced setting of e.g. 12% may be considered. Preference should however be given to the cross-blocking function.

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5. Cross-blocking

This function, which was already applied in conventional relays, is now available in all numerical relays and may be activated, if desired.

It takes into account that the second harmonic component in the individual phases is different and may not be sufficient, in the phase with the smallest component, to activate the blocking.

The measuring system in all phases is therefore blocked when a single phase detects the rush blocking condition.

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6. Transformer over-fluxing

If the transformer is operated with excessively high voltage, then the required magnetization is also increased. The magnetizing current rises sharply when the operating point on the magnetizing curve is close to the point of saturation.

The wave form becomes more and more distorted with increasing odd harmonic content (as shown in Figure 8).

Magnetising current in the event of transformer over-fluxing
Figure 8 – Magnetising current in the event of transformer over-fluxing

The increased magnetising current appears as a tripping current in the differential protection with large overvoltage. This can cause tripping, depending on the con- figuration of the transformer.

Overvoltages can occur in the system, due to the distribution of reactive power flow in the event of tap changer problems, or following load shedding. This is particularly true for geographically large systems with long lines.

One critical case is the switching off of a power station under full load conditions which results in a severe overvoltage condition at the unit transformer as a result of the large excitation of the generator.

The transformer can tolerate the over-excitation, which causes heating, for a given time without sustaining damage. During this time the system regulation must ensure that the voltage returns to the permissible range.

Only if this does not occur, must the transformer be isolated by a special over-excitation protection having a U/f-dependent time delay. Tripping by the differential protection with a fast measurement due to these conditions must be avoided at all cost.

Modern numerical relays therefore provide an integrated blocking of the trip in the event of over-excitation (over-fluxing). It is based on the large 5th harmonic component in the tripping current which clearly indicates over-fluxing. Tripping is blocked when the ratio I150Hz/I50Hz exceeds a set value.

For this setting it must be noted that the 5th harmonic component again decreases if the over-voltage is very large (Figure 8). A typical setting is 30%.

If the over-voltage is very large, blocking is no longer sensible as the transformer is at risk. The blocking can therefore again be re-set when the 5th harmonic component is above a set ratio of the 50 Hz component, which increases as the over-voltage increases.

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Reference // Numerical Differential Protection by Gerhard Ziegler

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About Author


Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry fascilities. Professional in AutoCAD programming. Present on


  1. ahmed wi
    May 16, 2018

    i can’t save to pdf

  2. Bernard Pelei Petlane
    May 16, 2018

    Can this protection scheme be applied to Variable Frequency Transformers used on asynchronous networks

    May 15, 2018

    excellent information

  4. Dan Basescu
    May 15, 2018

    Very good article. Thank you.
    You said there like:
    …”It is usually applied on transformers above approx. 1 MVA. On larger units above approx. 5 MVA it is standard.”…
    For this could you provide standard reference , if any, by revert email.
    Thank you in advance and regards

  5. A.K.Bandopadhyay
    May 15, 2018

    very nice information regarding transformer.

  6. rodolfo m. maranan
    May 14, 2018

    i need to know some pointers of transformer

  7. vivek sharma
    May 14, 2018

    Thank you very much for above information.
    Can you please explain in detail about behavior of distribution lines (medium voltage) when any fault occurs on downstream side or during any transformer charging on downstream side having overhead or underground cables attached with the transformer.

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