Transformer Design & Calculation Workbench

Quantities are derived from the calculated design (incl. ~5 % core cutting allowance). Unit prices are indicative supply-only USD values — edit them to your actual quotes; edited prices are kept when the design recalculates. The Excel file contains live formulas (Amount = Qty × Price, auto-summing total) plus a second sheet with the full design data. The BOM is issued in Excel only — not in the PDF report.

Plate values are populated straight from this design — enter your own manufacturer name, serial number and year of manufacture before fitting to a real unit. Tapping voltages shown for the maximum HV tap; a full design includes every tap. Once the unit is built and tested, log the results in the test report generator to produce a matching test report.

α is set by winding geometry and insulation design (ground vs series capacitance) — this tool does not compute it from first principles. Typical published ranges: ≈4–7 for smaller/MV windings or units with static-ring stress control, ≈10–20 for larger EHV windings without special mitigation. Enter your own value if you have it from a detailed capacitance calculation; otherwise use this to explore how sensitive line-end stress is to α. C_g does not change the §13 shape (which depends on α alone) but it does set the time scale of the §13b transient — on estimate from geometry it is taken as the HV→LV coaxial capacitance of this design, 2πε₀ε_rh / ln(r₃/r₂), which ignores the HV-to-tank and winding-to-yoke paths and so is a lower bound.

Method — §13: classical uniform-RLC-ladder model. Initial distribution e(x)/V₀ = sinh(α(1−x/L))/sinh(α) (x = 0 at line end); final (steady-state, grounded neutral) distribution is linear. Line-end gradient concentration factor = α·coth(α) versus a uniform winding.
Method — §13b: the same ladder solved in the time domain instead of at t = 0⁺ only. The winding is discretised into n sections, each with series inductance L/n (air-core solenoid inductance — core flux cannot follow a fast front), series capacitance C_s·n, ground capacitance C_g/n and a series resistance set by the damping factor ζ. Node equations M·v̇ = i_j − i_j+1 (M tridiagonal, symmetric, positive-definite — solved by the Thomas algorithm) and L·i̇ = v_j−1 − v_j − R·i are integrated with 4th-order Runge–Kutta under a standard 1.2/50 µs double-exponential wave and the same wave chopped on the tail. The envelope traces are max|v| over the whole simulation at each point of the winding — this is the oscillatory overshoot between the initial and final distributions that the §13 static curves cannot show, and it is what actually sets peak turn-to-turn stress.
Still an estimate. A uniform ladder with lumped C_g/C_s ignores mutual inductance between sections, the real (non-uniform) capacitance of interleaved or shielded discs, static-ring effects, tap-lead capacitance and frequency-dependent losses. It will tell you whether your design is in comfortable or marginal territory and how sensitive it is to α — it is not a substitute for FEM-extracted capacitance matrices plus a full transient solve before finalising insulation and static-ring design. Where analytical methods break down →

k = 1.8 is the IEC 60076-5 default for power transformers (assumes a high X/R ratio, i.e. worst-case DC offset). Use a higher value only if you have calculated the actual system X/R ratio and it justifies it.

Method: peak asymmetrical current I_peak = k√2 × I_sc (I_sc from this design's %Z). Radial force from the classical leakage-flux model: F_r = B_avg·(N·I_peak)·π·D_m with B_avg = μ₀·N·I_peak/(2·h_w) — the triangular/trapezoidal ampere-turn profile plotted above, averaged across each winding's radial build. Ampere-turn balance means HV and LV carry equal and opposite totals; the per-winding figures differ only through their own mean diameters. The outer winding goes into tension (bursting), the inner into compression (buckling risk) — both are evaluated in §14b.

ε is the fraction of ampere-turns not axially balanced between HV and LV. Even a nominally balanced pair carries a few percent from tap-zone gaps, winding-height tolerances and end-turn effects — 2–5 % is a realistic first-cut band. Use 8–15 % for a winding with a mid-height tap gap, and check the extreme tap position, which is usually the worst case. n_s = 1 layer treats the inner winding radial build as one bonded ring (optimistic — right for epoxy-bonded CTC or a fully keyed disc winding); raise it to the number of layers that can buckle independently for a conservative bound on a plain layer winding.

Method. Hoop stress σ = F_r/(2π·N·a) — ring tension F_r/2π carried by the winding's total conductor section. Compared against the widely used industry ceiling of 0.9 × Rp0.2 for the outer (tensile) winding; IEC 60076-5 itself sets no numeric stress limit, it requires demonstrated withstand. Buckling uses the classical thin-ring result under uniform external pressure with n_s equally spaced radial supports: σ_cr = (n_s²−1)·E·t²/(12·R²), E = 110 GPa for copper, t = inner-winding radial build (divided by the independent-layer count), R = its mean radius. n_s = 2 degenerates to the free-buckling case σ_cr = E·t²/(4R²), as it should. Axial force uses the residual ampere-turn method: F_ax = μ₀·π·D_m·(ε·N·I_peak)²/(2·h_w) — the radial leakage flux created by the unbalanced ampere-turns acting on the axial current. Spacer pressure = F_ax divided by the true bearing area of the radial spacer columns, checked against ≈35 MPa, a common design ceiling for precompressed transformerboard under short-circuit (ultimate crushing is well above this; the design limit protects clamping stability and prevents permanent set). Limits of this check. Uniform, monolithic rings; no allowance for winding ovality, conductor tilting, joint and lead forces, cumulative axial forces through the clamping structure, or the dynamic amplification when the fault frequency is near a mechanical natural frequency. A genuine withstand demonstration is either a certified short-circuit test or FEM electrodynamic force mapping per IEC 60076-5 — treat everything here as a sizing sanity-check, not a certificate of conformance or product certification. When you need FEM → · Simulation software directory →

t = 2 s is the IEC 60076-5 standard design duration; use your protection's actual clearing time if it's faster (this lowers the temperature rise, since heating scales with t). θᵢ defaults to a typical pre-fault hot winding temperature — use the actual value if you have it (this calculator does not compute a hot-spot temperature itself).

Method: adiabatic (no heat loss during the fault) temperature rise for copper conductors, Δθ ≈ 0.0062·J²·t — i.e. Δθ = J²·ρ·t/(c·γ) (J in A/mm² at fault current, t in seconds; ρ ≈ 0.0211 Ω·mm²/m at the reference temperature, c = 385 J/(kg·K), γ = 8 890 kg/m³) — the standard short-form of the IEC 60076-5 thermal withstand check. Current density at fault J = (rated current density) × (SC current multiple), i.e. this design's own conductor sizing carried through to fault conditions. Compared against 250 °C, the commonly cited maximum for normal Kraft-paper-insulated copper windings (check your actual insulation class — thermally upgraded paper permits higher). Adiabatic means no cooling during the fault — correct for the short IEC-standard duration, but this is still a first-cut check: it doesn't account for uneven current distribution, contact/joint hot-spots, or aluminium conductors.

Sections 6 and 14 use closed-form formulas: reactance from the ampere-turn/duct expression with a Rogowski correction for end fringing, and a single total radial force. This section solves the leakage field itself on a mesh, which needs no fringing factor and produces the axial force distribution along the winding — the quantity closed-form methods handle worst and the one that governs winding collapse when ampere-turns are not balanced.

Method & validity. Axisymmetric magnetostatics solved for the flux function u = r·A on a mesh fitted to the winding geometry, with the core leg and yokes treated as infinitely permeable (flux normal, tangential B zero) and a remote flux-parallel outer boundary. Forces come from J×B, scaled to the asymmetric peak short-circuit current from section 14.

Verified: operator symmetry to 4×10⁻¹⁴; leakage inductance converging to the classical value as the winding is made tall (ratio 0.9994 at h/build = 139) and tracking the Rogowski factor at every height between; gap field within 0.06 % of hand calculation; two independent energy formulations agreeing to 0.8 %; insensitivity to the outer boundary position; net axial force 6×10⁻¹⁷ N and antisymmetry 0.000 % for a symmetric winding pair.

Not verified against an independent solver or a measured works impedance. Treat it as a physically-grounded estimate, not as certification evidence. 2D axisymmetric also means it cannot represent three-limb asymmetry, leads, or anything genuinely 3D, and it models the windings as smeared current regions — no individual conductors, no eddy or proximity effects, no core saturation.

Formula: $\text{TOC} = \text{CAPEX} + (A \times P_0) + (B \times P_k)$. A factor capitalises continuous no-load losses across the operational lifetime (8,760 h/year); B factor capitalises load-dependent copper losses based on expected load profile and loss factor.

Standards reference: IEC 60076-14 governs liquid-immersed transformers using high-temperature insulation materials and ester fluids. Natural and synthetic esters provide K-class fire safety (>300 °C fire point per IEC 61099/62770) allowing reduced substation clearances under NFPA 850 / IEC 61936-1.

Method: Core magnetostriction sound power $L_{WA} \approx 45 + 10\log_{10}(W_{\text{core}}) + 20\log_{10}(B_m/1.7) + \Delta L_{\text{fans}}$. Sound pressure $L_p$ is calculated over the measurement surface contour at 1 m/2 m distance per IEC 60076-10.

Method: Harmonic currents from solar inverters, wind converters and data center UPS rectifiers increase winding eddy-current losses ($P_{\text{EC}} \propto h^2$). Harmonic Loss Factor $F_{\text{HL}}$ evaluates maximum permissible continuous loading to prevent premature insulation thermal degradation.