Transformer short-circuit forces

The leakage field of the windings at the peak short-circuit current, the radial and axial forces on every winding, and the IEC 60076-5 checks: hoop stress, buckling, conductor tilting, spacer and end-ring pressure, temperature.

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INPUTone phase · mm · MPa

1 · Rating from the nameplate

Rated power [MVA] Frequency [Hz]

HV voltage [kV] line LV voltage [kV] line

HV connection LV connection

Short-circuit impedance [%] on the rated tap X/R of transformer and system together

System short-circuit power [MVA] IEC 60076-5 Table 2

2 · Core window one leg

Core leg diameter [mm] Window height [mm] yoke to yoke

3 · Windings core outwards

Heights from the lower yoke. A tapping gap carries no turns (the nominal tap with the tapping turns out). Windings stacked one above the other share both diameters.

4 · Fault IEC 60076-5

Duration [s] thermal, 2 s unless agreed Winding temperature before [°C] ambient + rise

Insulation

Example values, not a real unit. Results update as you type.

PEAK CURRENT î27.8 × I_r

GAP FLUX2.58 T

LEAKAGE FIELD · r–z, ONE LEG

AXIAL COMPRESSION ALONG THE HEIGHT

FORCE AGAINST TIME · FIRST 100 msF ∝ i²

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HOW IT'S CALCULATED · WITH YOUR NUMBERS

Step by step, with your numbers

01
Equilibrium████ ██ ███████ · ██████ = ██.██
02
Reactions████ ██ ███████ · ██████ = ██.██
03
Shear force████ ██ ███████ · ██████ = ██.██
04
Bending moment████ ██ ███████ · ██████ = ██.██
05
Deflection████ ██ ███████ · ██████ = ██.██
06
Stress████ ██ ███████ · ██████ = ██.██

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References: Rabins, AIEE Trans. 1956 — leakage field of concentric windings; IEC 60076-5:2006 — short-circuit current, Annex A withstand checks, temperature; Kulkarni & Khaparde, Transformer Engineering (2012) — buckling and a published FEM case.

ASSUMPTIONS & LIMITS

Core-type, concentric cylindrical windings on one leg. The field is axisymmetric: the outer legs, the tank, the leads and the clamping structure are not in it.
Core and yokes infinitely permeable; the windings' current uniformly spread over their cross-section (turn-by-turn detail and the conductor insulation are not modelled).
The tapping gap carries no turns (the nominal tap with the tapping turns cut out); other tap positions shift the ampere-turns and need their own run.
Peak forces at the first, fully offset current peak (k√2 from IEC 60076-5 Table 4). The axial force is carried by the end the winding is pushed towards; clamping prestress and the dynamic response of the pressboard are not included.
Mean hoop stress = radial force/(2π × conductor area). Bending between supports: a fixed-ended beam under the local force density J·B. Buckling: elastic ring theory with the elastic modulus of the conductor; work-hardened or pre-strained conductors buckle lower.

DISCLAIMER · For education and preliminary sizing only. Results must be reviewed by a qualified engineer before use in design.

BEYOND THE 2D WINDOW

Outer legs, leads, clamping structure and the dynamic response of the pressboard — we take the winding into a full 3D electromagnetic and structural study.

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