Transformer Energisation

When a transformer is switched on, voltage is suddenly applied to its winding. The transformer core then needs magnetic flux to operate.

The flux linkage is related to the time integral of the applied voltage:

This means that the flux in the core depends not only on the applied voltage, but also on the instant at which the transformer is energised.

After switching, the flux does not immediately settle to its normal steady-state value. It depends mainly on:

• the point on the voltage waveform at which the breaker closes
• the residual flux already present in the transformer core
• the nonlinear saturation characteristic of the core
• the impedance and damping of the connected network

If the resulting flux becomes too high, the transformer core enters magnetic saturation. Once the core is saturated, the transformer requires a very large magnetising current. This current is known as transformer inrush current.

Transformer inrush current

Inrush current is a large, temporary magnetising current drawn by a transformer during energisation.

For typical transformers, it may be several times the rated current. However, the actual magnitude is strongly dependent on the transformer design, residual flux, point-on-wave closing instant, and network strength.

Inrush current is usually:

• highly asymmetrical
• rich in low-order harmonics
• rich in DC offset
• gradually damped with time

The most severe energisation condition usually occurs when the breaker closes near a voltage zero. In this case, the prospective flux can reach a very high peak value, especially if residual flux is already present in the same direction.

When a transformer is de-energised, some magnetism can remain in the core. This remaining magnetism is called residual flux or remanent flux.

When the transformer is energised again, the newly produced flux may add to this residual flux:

If the residual flux and the prospective flux are in the same direction, the total flux can become very high. This can push the transformer deep into saturation and produce a severe inrush current.

This is why two energisations of the same transformer can produce very different results, even if the system configuration is unchanged.

The key point is:

Point-on-wave refers to the exact position on the voltage waveform at the instant the breaker closes.

The breaker may close:

• near a voltage zero
• near a voltage peak
• somewhere between zero and peak

For transformer energisation, closing near a voltage zero is usually the worst case because it can produce the highest flux offset.

Closing near the voltage peak is usually more favourable because it reduces the flux offset and therefore reduces the risk of deep saturation.

This is the basis of point-on-wave controlled switching.

In controlled switching, the breaker is commanded to close each phase at the most suitable instant on the waveform. The objective is to minimise the flux offset and therefore reduce the inrush current.

Controlled-switching strategies may be divided into two broad types:

• methods that consider measured or estimated residual flux
• simpler methods that do not consider residual flux

A method that includes residual flux information can target the optimum closing instant more accurately. Without residual flux information, inrush can still be reduced compared with the worst case, but it may not be fully minimised.

Transformer inrush current is not a clean sinusoidal current.

Because the transformer core saturates nonlinearly, the current waveform becomes distorted and contains harmonics.

The most important harmonic is usually the second harmonic.

The second harmonic is typically dominant during the early cycles of inrush. It has traditionally been used by transformer differential protection as an inrush-restraint quantity to help distinguish inrush from internal faults.

However, this should be understood as a teaching simplification. Modern numerical relays may also use waveform-based methods, gap detection, or other algorithms. In addition, some modern low-loss core steels may produce inrush currents with reduced second-harmonic content.

The harmonic content of inrush is not constant.

The magnitude and polarity of the harmonics change with time as the transformer core moves in and out of saturation.

This is important because these harmonic currents can interact with the frequency-dependent impedance of the network. If the network has a resonance near one of these harmonic frequencies, the voltage distortion can be amplified.

This is the key mechanism:

Transformer inrush produces harmonic currents. The power system contains inductance and capacitance. Therefore, the system has one or more natural resonance frequencies.

For transformer-energisation TOV, the critical case is usually a parallel resonance, because a parallel resonance presents a high impedance at the resonant frequency.

If one of the inrush harmonics is close to this high-impedance resonance, the harmonic voltage can be amplified.

For each harmonic order h, the relationship can be simplified as:

where:

• I(h) is the harmonic current produced by transformer inrush
• Z(h) is the network impedance at that harmonic frequency
• V(h) is the resulting harmonic voltage

If Z(h) is high at a particular harmonic frequency, even a moderate harmonic current can produce a large harmonic voltage.

This can result in a temporary overvoltage, or TOV.

A temporary overvoltage is an oscillatory overvoltage of relatively long duration at or near power frequency. It is different from slow-front, fast-front and very-fast-front impulse overvoltages.

A resonant TOV caused by transformer energisation can last for several cycles or longer. It is therefore a resonance-related phenomenon, not a fast switching impulse.

A weak system has higher source impedance.

Higher source impedance means:

• larger voltage drop during inrush
• greater voltage distortion
• higher chance of resonance near low-order harmonics
• lower damping
• higher risk of temporary overvoltage

A strong grid can absorb transformer inrush more easily. A weak grid reacts more strongly to the same energisation event.

For this reason, transformer energisation can be more problematic in:

• restoration after a blackout
• weak grids
• networks with long HV cables
• offshore renewable systems
• HVDC stations with AC harmonic filters
• lightly loaded systems

The practical point is:

When a transformer draws high inrush current, that current flows through the system impedance.

This produces a voltage drop:

As a result, the transformer terminal voltage and nearby bus voltage can dip.

This is known as an RMS voltage drop, voltage sag, or voltage dip.

The severity of the voltage dip depends mainly on:

• the magnitude of the inrush current
• the system impedance
• the transformer size
• the network strength
• the damping in the system

Inrush-related voltage dips may affect sensitive equipment such as:

• variable-speed drives
• industrial processes
• semiconductor and chip-manufacturing equipment
• protection and control systems

The key idea is simple:

Sympathetic inrush occurs when one transformer is energised and another nearby transformer, already in service, also begins to draw abnormal magnetising current.

This happens because the inrush current of the newly energised transformer distorts the voltage seen by the already energised transformer.

There are two main forms.

8.1 Parallel sympathetic interaction

In this case, two transformers share the same supply bus.

Transformer T₂ is energised. Its inrush current flows through the network impedance and causes voltage distortion at the common bus.

This distorted voltage is then applied to transformer T₁, which is already energised. The distorted voltage can disturb the flux in T₁ and push it into saturation. T₁ then starts drawing its own sympathetic magnetising current.

The mechanism can be remembered as:

8.2 Series sympathetic interaction

In this case, transformer T₂ is supplied through transformer T₁.

When T₂ is energised, its inrush current flows through T₁. T₁ sees this as a heavy transient load current.

This current can change the flux condition in T₁ and eventually cause saturation. As a result, T₁ begins to draw sympathetic current.

The mechanism can be remembered as:

Sympathetic inrush is important in wind farms and substations where several transformers may be energised in sequence. It can prolong the inrush period and increase harmonic distortion.

Pseudo-inrush is similar to transformer inrush, but the transformer is not actually switched off and re-energised.

It can occur after:

• a fault
• a voltage sag
• fault clearance
• delayed voltage recovery

During the disturbance, the transformer flux trajectory is disturbed. When the voltage recovers, the flux may not return smoothly to its normal steady-state trajectory.

If the recovered voltage and the transformer flux are not properly aligned, the core may enter saturation and draw a current similar to inrush.

Pseudo-inrush can cause:

• delayed voltage recovery
• harmonic distortion
• unwanted relay operation
• resonance and TOV in weak grids

The important point is:

Several methods can be used to reduce transformer inrush current.

10.1 Point-on-wave controlled switching

This is the most effective modern mitigation method.

The breaker is controlled to close at the optimum point on the voltage waveform.

It is most effective when it considers:

• residual flux
• breaker timing scatter
• mechanical closing delays
• phase-by-phase closing behaviour

Properly applied, point-on-wave controlled switching can substantially reduce transformer inrush current.

10.2 Pre-insertion resistors

A pre-insertion resistor is temporarily inserted in series during energisation.

The resistor reduces the voltage step applied to the transformer and limits the inrush current.

This method is effective, but it is relatively expensive and is less common today compared with controlled switching.

10.3 Tap changer adjustment

The transformer tap position can influence inrush.

Energising from a tap position that gives a larger number of energised turns reduces the volts-per-turn applied to the core. Lower volts-per-turn means lower flux density, which reduces the risk of saturation.

The same tap position can also increase the effective series impedance seen during energisation. This further helps to reduce the inrush current.

However, the tap position must be selected carefully. If the selected tap results in fewer effective turns, the volts-per-turn increases and the effective impedance decreases, which can make the inrush current worse.

10.4 Lowering system voltage before energisation

Reducing the system voltage before energisation reduces the prospective flux peak.

This can reduce:

• inrush current
• voltage dip
• saturation severity

However, this method may not be sufficient for severe resonance cases. The reduced voltage must also remain within the permitted operating range.

10.5 De-fluxing

De-fluxing means actively reducing the residual flux before energisation.

This can help reduce inrush, but it is generally not practical for routine power system operation. It is more suitable for controlled or special situations.

Temporary overvoltage caused by transformer energisation is mainly a resonance problem.

Therefore, mitigation should focus on both:

• reducing the harmonic source, meaning the inrush current
• reducing the network resonance risk

11.1 Detune the network

The resonance frequency can be shifted away from dangerous low-order harmonics.

This can be done by changing:

• cable configuration
• shunt capacitor switching state, meaning in or out of service
• reactor switching state, meaning in or out of service
• network topology

The aim is to avoid resonance near important inrush harmonics, especially the 2nd to 5th harmonics.

11.2 Add load before energisation

Load provides damping.

More damping means lower voltage amplification during resonance.

This is especially useful during restoration, when the system may be lightly loaded and weakly damped.

11.3 Energise through a low-impedance path

A stronger source reduces system impedance.

Lower system impedance reduces voltage distortion and voltage amplification.

This may be achieved by energising after more generation is online or by using a stronger network connection.

11.4 Surge arresters

Surge arresters provide protection against high overvoltages, but they should not be treated as the primary mitigation method for resonant TOV.

This is because:

• arresters clamp only above certain voltage levels
• prolonged TOV can overheat the arrester
• thermal runaway may occur if the energy duty is exceeded

Therefore, surge arresters should be considered as protective equipment, not as the main solution for resonance. Their energy duty must be verified in the EMT study.

Transformer energisation is nonlinear and sensitive to initial conditions. Therefore, electromagnetic transient simulation is required.

The EMT model should include:

• transformer leakage impedance
• winding resistance
• nonlinear saturation curve
• core losses
• residual flux
• air-core inductance
• magnetic coupling
• breaker closing time and pole scatter
• frequency-dependent cable and line models
• capacitor banks and reactors
• equivalent source/network representation
• load and damping representation

For this type of study, the frequency range of interest is typically from DC to about 1 kHz. This upper limit is set by the highest resonance of practical interest for the energisation study. Therefore, the cable and line models should be valid over the frequency band in which resonance and harmonic amplification are being assessed.

The EMT study should check:

• peak inrush current
• RMS voltage dip
• TOV magnitude
• TOV duration
• surge arrester energy
• transformer terminal voltage stress
• insulation coordination margin

The purpose of the study is not only to calculate the worst voltage or current. It is also to understand why the problem occurs and which mitigation measure is effective.

A single deterministic energisation simulation is usually not enough.

Transformer energisation depends strongly on uncertain parameters such as:

• residual flux magnitude
• residual flux polarity
• breaker closing instant
• initial voltage level
• saturation curve
• tap position
• system topology

A Monte Carlo study runs many simulations with different combinations of these uncertain inputs.

For example:

• 100 simulations
• 500 simulations
• 1000 simulations

The results can then be used to assess:

• typical inrush current
• worst-case inrush current
• probability of unacceptable voltage dip
• probability of excessive TOV
• sensitivity to residual flux
• sensitivity to breaker closing angle

This gives a more reliable engineering conclusion than a single worst-case or manually selected switching case.

The complete transformer energisation mechanism can be remembered as:

At the same time, the large inrush current flows through the system impedance and causes a voltage dip:

So transformer energisation can create both:

• RMS voltage sag
• temporary overvoltage

This is why transformer energisation studies are important in modern power systems.

Transformer energisation should not be treated as a simple switching operation.

It is a nonlinear transient event involving:

• magnetic saturation
• residual flux
• point-on-wave closing
• harmonic current generation
• parallel network resonance
• RMS voltage dip
• temporary overvoltage
• surge arrester energy duty

In modern power systems, the risk is increased by weak networks, long HV cables, offshore renewable systems, HVDC stations, harmonic filters, and low damping.

The recommended engineering approach is:

The most effective practical mitigation for high inrush is usually:

However, if the dominant issue is resonance and temporary overvoltage, the network itself may also need to be modified, detuned, or damped.

Finally, insulation coordination and surge arrester energy duty should always be checked against the relevant project requirements and applicable standards.