When an impulse voltage wave strikes a transformer winding, the voltage does not distribute uniformly. The first few turns at the line end can experience a gradient approximately 10 times the average, driven by the spatial coefficient αl (typically 5–15). This article explains the capacitive initial distribution, the subsequent oscillatory transition, and why the neutral point of an ungrounded winding can reach up to 1.8 times the incoming wave amplitude—knowledge essential for evaluating whether a transformer’s internal insulation design is adequate, even when its nameplate BIL appears sufficient.
Engineering note: values and thresholds in this article are reference points for screening and discussion. Final acceptance should follow the project specification, applicable IEC/IEEE standards, local utility requirements and the approved factory test protocol.
At power frequency (50/60 Hz), the transformer winding behaves as an inductive divider: the voltage distributes roughly uniformly from line end to neutral. This is the final or steady-state distribution. But an impulse arrives in microseconds—far too fast for inductance to play any meaningful role. During the first fraction of a microsecond, the winding behaves as a purely capacitive network.
The winding can be modeled as a ladder of:
When the impulse wavefront arrives, current flows through the shunt capacitances Cg to ground at every point along the winding. This progressively drains charge, so each successive turn sees a lower voltage than the one before it. The result is an initial (capacitive) voltage distribution that is highly non-uniform: steep at the line end, flat near the neutral.
Over the subsequent tens of microseconds, the inductance of the winding “wakes up” and the voltage distribution transitions from the capacitive initial distribution toward the uniform inductive final distribution. This transition is oscillatory—during the oscillation, voltage at some points along the winding can temporarily exceed both the initial and final distributions. This is the mechanism that produces voltage overshoot at the neutral end.
The entry capacitance of the winding—the capacitance seen looking into the line terminal—is typically 500–5,000 pF for distribution transformers. This value determines how much of the incoming surge current enters the winding versus being diverted by the surge arrester.
The spatial coefficient α (alpha) captures the physics of how voltage decays along the winding during the initial capacitive distribution:
α = √(Cg / Cs)
Where Cg = capacitance to ground per unit length, Cs = series capacitance per unit length.
The dimensionless product αl (where l is the winding length in the same units as α) determines the shape of the voltage distribution:
What drives αl in practice:
The most severe consequence of non-uniform impulse distribution is the voltage gradient on the first few turns. For a typical distribution transformer with αl in the range of 5–15, the first-turn gradient is approximately 10 times the average gradient (full impulse voltage divided by total turns).
Consider a 15 kV-class transformer with 95 kV BIL and 500 turns on the high-voltage winding. The average gradient is 95 kV / 500 = 190 V/turn. But the first turn at the line end sees approximately 10 × 190 = 1,900 V across its insulation—and the first few turns may each see well above 1 kV.
This is why turn-to-turn insulation at the line end of a winding is critical. Even if the overall BIL test passes (because the major insulation from winding to ground holds), repeated impulse events can progressively erode the turn insulation at the line end through partial discharge until a turn-to-turn short circuit develops. A turn-to-turn fault at the line end is especially dangerous because it creates a shorted loop that draws heavy circulating current from the incoming line, rapidly escalating to a full winding failure.
The physical consequence for manufacturing: the first several turns at the line end typically receive reinforced turn insulation—additional paper layers, higher-grade conductor enamel, or interleaving that increases the effective series capacitance between those turns, reducing the local gradient.
If the neutral point of the winding is ungrounded (floating), a traveling wave arriving at the line terminal propagates through the winding and reaches the open neutral. Because the neutral is an open circuit, the wave reflects with a reflection coefficient of approximately +1, producing voltage doubling at the neutral point.
But voltage doubling is not the worst case. During the oscillatory transition from the capacitive initial distribution to the inductive final distribution, the voltage at the neutral point can overshoot beyond double the incoming wave—reaching approximately 1.8 times the incoming wave amplitude.
| Neutral Grounding Type | Reflection Coefficient | Maximum Neutral Voltage | Implication for Neutral Bushing BIL |
|---|---|---|---|
| Solidly grounded | −1 | ~0 (wave reflects inverted, no rise) | No special requirement; standard distribution-class bushing is adequate |
| Resistance-grounded | 0 to +0.8 (depends on R) | Up to ~1.3× incoming wave | May need one class higher BIL than line terminal if grounding resistance is high |
| Ungrounded (floating) | ~+1 | ~1.8× incoming wave | Neutral bushing BIL must be at least equal to line terminal BIL—often higher |
This phenomenon has a direct procurement implication: for an ungrounded-wye distribution transformer, specifying the neutral bushing at a lower BIL than the line bushing (a common cost-saving practice) creates a vulnerability. A surge arriving at any one line terminal can produce a neutral voltage that exceeds the neutral bushing BIL, causing a flashover internal to the tank.
In a standard disc winding, consecutive turns within a disc are at adjacent positions. In an interleaved disc winding, turns from different electrical positions are physically interleaved—for example, turn 1 is adjacent to turn 10, not turn 2. This dramatically increases the effective series capacitance Cs between turns, which reduces α and flattens the initial voltage distribution. Interleaving is the single most effective technique for reducing first-turn gradient but increases manufacturing complexity and cost.
A static ring is a conductive ring placed around the line-end turns of the winding, connected to the line terminal. It capacitively couples to the turns and “injects” charge into them, partially compensating for the charge drained by Cg. The effect is to grade the voltage at the line end, reducing the gradient on the first several turns. Static rings are simpler to manufacture than full interleaving and are common in layer-wound designs.
Layer-wound coils have inherently higher αl because the turn-to-ground capacitance Cg is larger (each layer has a large surface area facing the grounded core) while the series capacitance Cs between layers is lower (entire layers are separated by insulation). Disc-wound coils, especially when interleaved, achieve lower αl. For distribution transformers, layer winding is more economical; for power transformers, disc winding is standard.
A transformer that passes the standard BIL test (full-wave impulse applied line-to-ground) may still have a latent weakness in turn-to-turn insulation at the line end. The BIL test stresses the major insulation (winding-to-ground, phase-to-phase) but does not directly verify the integrity of turn insulation under the local gradient conditions produced by a real impulse.
For procurement engineers, this means: