Transformer Energization Study — EMTP/ATP Simulation, Closing Resistors & Point-on-Wave Controlled Switching

Introduction

Energizing a power transformer is not a routine breaker closure — it is an electromagnetic event that generates inrush currents of 6–10× rated current, voltage dips of 5–15% on the supply bus, and harmonic currents (predominantly 2nd harmonic) that challenge the stability of differential protection relays. A poorly planned energization can cause false differential trips, nuisance tripping of upstream overcurrent relays, harmonic resonance with capacitor banks, and mechanical stress on the transformer windings from the peak inrush force. This article covers the complete energization study methodology using EMTP/ATP, along with the design of closing resistors and point-on-wave controlled switching to mitigate inrush.

1. The Physics of Transformer Inrush

1.1 Why Inrush Occurs

When a transformer is de-energized, the core steel retains residual flux (remanence) — typically 50–80% of the rated peak flux density. When re-energized, the applied voltage forces the flux to follow the integral of the voltage waveform:

φ(t) = φ_remanent + (1/N) × ∫ v(t) × dt

If energization occurs at a voltage zero crossing, the flux must integrate from remanence to 2× the rated peak — deep into saturation. At this flux level, the magnetizing impedance collapses from tens of thousands of ohms to near the air-core impedance (a few hundred ohms), and the inrush current becomes limited only by the winding DC resistance and system impedance:

i_inrush_peak ≈ (√2 × V) / √( (R_system + R_winding)² + (X_system_air-core)² )

1.2 Key Inrush Parameters

Parameter	Typical Value	Influencing Factors
Peak inrush (× I_rated)	6–10×	Residual flux, switching angle, core material
Duration (seconds)	0.1–10 s	Transformer size (larger → longer decay)
2nd harmonic content	20–65% of fundamental	Core saturation depth
DC offset decay time constant	0.1–1.0 s (small TX) to 5–30 s (large TX)	L/R ratio of the energization path
Mechanical force (× rated)	36–100× (∝ I²)	Peak current squared

1.3 Worst-Case Conditions

Factor	Worst-Case Value
Switching angle	0° (voltage zero crossing — maximum flux offset)
Residual flux polarity	Same polarity as the natural flux at switching instant
Residual flux magnitude	80% of rated peak (worst-case for grain-oriented steel)
Source impedance	Minimum (strong grid → highest inrush)
Transformer core	Grain-oriented silicon steel (square loop → highest remanence)

2. EMTP/ATP Simulation

2.1 Model Requirements

An accurate energization study requires:

Component	Model Type	Critical Parameters
Transformer	Saturable reactor with hysteresis (ATP Type-96, BCTRAN + HYSDAT)	Saturation curve (flux-current pairs), hysteresis loop, winding resistance
Source	Three-phase Thevenin equivalent	Short-circuit MVA, X/R ratio
Circuit breaker	Time-controlled switch per pole	Pole closing spread times
Pre-insertion resistor	Time-controlled resistor in parallel with main contacts	R value, insertion time
Connected cable/line	PI-section or distributed parameter	Surge impedance, capacitance

2.2 Step-by-Step Simulation Procedure

Step 1: Build the circuit model in ATPDraw
Step 2: Set the transformer initial conditions (residual flux per phase)
Step 3: Define the breaker closing sequence (instant, pole spread)
Step 4: Run a baseline case at worst-case switching angle
Step 5: Sweep switching angle from 0° to 360° in 10° steps (36 runs)
Step 6: Sweep residual flux from 0% to 80% in 20% steps with each angle
Step 7: Extract: peak inrush, 2nd harmonic content, decay time constant, peak voltage dip
Step 8: Generate cumulative probability distribution of peak inrush

2.3 Statistically Worst-Case

Since residual flux is random (determined by the last de-energization point-on-wave), the worst-case inrush is not a deterministic value — it is the 95th or 99th percentile of a statistical distribution:

Percentile	Typical Inrush Multiple
50th (median)	3–5×
90th	6–8×
95th	7–9×
99th	8–11×

2.4 Simulation Outputs to Extract

Output	Use
Peak phase current × time	Set overcurrent pickup above inrush; verify mechanical withstand
2nd harmonic × time	Verify differential relay 2nd harmonic restraint margin
RMS current decay	Verify that upstream protection resets before transformer thermal limit
Neutral current	Size neutral CT; verify ground fault detection
Voltage dip at source bus	Verify no other connected equipment undervoltage trip
Voltage harmonic spectrum	Verify no resonance with existing capacitor banks

3. Closing Resistors (Pre-Insertion Resistors)

3.1 Principle

A pre-insertion resistor is connected in series with the transformer for 8–12 ms before the main circuit breaker contacts close. The resistor:

Limits the initial inrush current during the first half-cycle (the worst peak)
Dampens the DC offset by dissipating energy
Reduces the voltage dip on the source bus

After the insertion time, the main contacts close, shorting out the resistor.

3.2 Resistor Sizing

R_pre_insertion ≈ (0.5 to 1.0) × ω × L_air-core

Where L_air-core is the transformer's air-core inductance (approximately 0.2–0.5 × X% in p.u.).

For a 110 kV, 60 MVA transformer with X% = 12%, X_base = 110²/60 = 201.7 Ω → X = 24.2 Ω:

L_air-core ≈ 0.35 × 24.2 / 377 = 0.0225 H  (at 60 Hz)
R ≈ 1.0 × 377 × 0.0225 = 8.5 Ω → Select 8–10 Ω

3.3 Effect on Inrush

Configuration	Peak Inrush (× I_rated)	Reduction
No closing resistor	8.0×	—
R = 5 Ω, t = 10 ms	4.5×	44%
R = 10 Ω, t = 10 ms	3.8×	53%
R = 20 Ω, t = 10 ms	3.2×	60%

Higher R values provide more reduction but increase the energy dissipated in the resistor (I²Rt). The resistor must be rated for the short-time thermal duty.

4. Point-on-Wave Controlled Switching

4.1 Principle

A controlled switching device (CSD) closes each pole at the optimal point on the voltage wave to minimize inrush:

For a single-phase transformer or a three-phase transformer with a grounded-wye primary: close at the voltage peak (90° or 270°) — the flux starts at zero and follows the cosine, never exceeding the rated peak
For a delta-connected primary: close the first pole at the phase-to-phase voltage peak, then close the remaining two poles 90° (5 ms at 50 Hz) later

4.2 Controlled Switching Performance

Parameter	Random Switching	Controlled Switching
Peak inrush	6–10×	1.5–3.0×
2nd harmonic	40–65%	10–25%
Voltage dip	5–15%	1–3%
Mechanical stress	36–100× rated	2–9× rated

4.3 Accuracy Requirements

The CSD must close each pole within ±1 ms of the target electrical angle. At 50 Hz, 1 ms = 18° — a significant fraction of a quarter-cycle (5 ms). A closing error of +2 ms at a voltage peak targeting 90° means closing at 126° — still acceptable but with degraded performance.

4.4 Compensating for Remanence

Even with perfect point-on-wave switching, residual flux in the core can cause significant inrush. Advanced CSDs measure the residual flux during de-energization (via a flux integration algorithm) and adjust the closing angle to compensate:

φ_target = -φ_remanent  (cancel the residual flux)

This requires a voltage measurement on the transformer side of the open breaker — possible with busbar VTs if the transformer is directly connected, or with capacitive voltage taps on the transformer bushings.

5. Impact on Protection Systems

5.1 Differential Relay (87T)

The 2nd harmonic restraint must be set to avoid tripping on inrush while still tripping on internal faults with CT saturation:

Setting Recommendation	Value
2nd harmonic restraint pickup	15–20% (lower for controlled switching; higher for random)
Cross-blocking mode	"Any phase blocks all phases" or "Phase-segregated"
5th harmonic restraint (overexcitation)	30–35%

5.2 Overcurrent Relays (50/51)

Time-overcurrent (51) must coordinate so the inrush current does not cause pickup at time settings above 0.1 s. Instantaneous overcurrent (50) must be set above the maximum inrush peak to avoid nuisance tripping.

5.3 Harmonic Resonance Check

The 2nd harmonic content of the inrush current can excite a parallel resonance between the transformer's magnetizing inductance and shunt capacitor banks. Calculate:

f_resonance = 1 / (2π × √(L_m × C_shunt))

If f_resonance × 2 ≈ power frequency (i.e., the 2nd harmonic excites a resonance near 100/120 Hz), install a detuning reactor (typically 7% or 14%) in series with the capacitor bank.

FAQ

Q: Why does a larger transformer have a longer inrush decay time?

The inrush current decay time constant is L_sat / R, where L_sat is the saturated winding inductance and R includes the winding resistance and the system resistance. Larger transformers have proportionally higher L/R ratios (inductance scales with physical size; resistance scales more slowly). A 500 MVA transformer can have an inrush decay time of 15–30 seconds, during which the differential relay's 2nd harmonic restraint must remain active.

Q: Can I eliminate inrush entirely with controlled switching?

No — controlled switching can reduce inrush to 1.5–3.0× rated current, but zero inrush is impossible because (1) residual flux is never perfectly cancelled (measurement uncertainty, core material variability), (2) the three phases cannot all be closed simultaneously, and (3) the breaker closing time has a statistical scatter of ±0.5 ms even with modern drives. A 90% reduction from uncontrolled levels is excellent; zero is not a realistic target.

Q: What happens if a pre-insertion resistor fails in service (open circuit)?

If the resistor opens before the main contacts close, the energization reverts to the uncontrolled case — maximum inrush. If the resistor fails shorted permanently, the main contacts short an already-closed path, which is harmless. If the resistor fails during insertion (fuses open), the transformer sees a brief energization through the resistor followed by an interruption and re-energization through the main contacts — this double-transient can actually produce higher inrush than a single uncontrolled closure. Pre-insertion resistors should be tested annually.

Q: Should I perform an energization study for every new transformer?

Yes, for any transformer ≥10 MVA or any transformer protected by a differential relay. The study is relatively inexpensive (1–3 days of engineering time), and the cost of an incorrect protection setting is a false trip that takes a healthy transformer out of service — potentially during peak demand when energization is attempted at the worst possible time.

Q: How does series compensation on the transmission line affect transformer energization?

Series capacitors on the transmission line introduce a subsynchronous resonance risk. The inrush current contains low-frequency components (sub-harmonics) that can interact with the series capacitor compensation network at frequencies below the power frequency. If the transformer is energized through a series-compensated line, a detailed subsynchronous resonance (SSR) study is required in addition to the standard energization study.

Q: What is the effect of GIC (geomagnetically induced currents) on energization?

GIC produces quasi-DC magnetizing current that partially saturates the transformer core, reducing the residual flux margin for energization. If a transformer is energized during a geomagnetic disturbance (solar storm), the combined GIC + energization inrush can be 20–50% higher than the standard worst-case. For transformers in high-latitude regions (>50° geomagnetic latitude), this scenario should be included in the energization study.

References & Standards

Document	Title	Relevance
IEC 60076-7	Loading guide — Transformer energization and inrush	Inrush limits and temperature effects
IEEE C57.12.00	Standard for liquid-immersed transformers	Mechanical withstand of inrush
CIGRE TB 568	Controlled switching for transformer energization	CSD application guide
ATP Rule Book	Alternative Transients Program	EMTP/ATP modeling of transformers
IEEE C37.230	Guide for protective relay applications	Inrush restraint settings
CIGRE TB 262	Switching overvoltages — mitigation	Pre-insertion resistor design

*Du Fu, ZY POWER Production Engineer — Every transformer energization is a transient. Make sure yours is a controlled one.*