Engineering CalculatorsParallel Path Circulating CurrentWork in progressPremium
Circulating current between electrically-parallel winding strands (or hairpin sub-conductors) that sit at different depths within the same slot — the AC loss mechanism the Motor Winding calculator explicitly doesn't model. Solves a coupled network using the classical slot-leakage loop inductance between strand positions, and shows what transposition buys you.
Work in progress: this uses a newly-derived, cross-checked-but-not-FEA-validated model. Treat results as order-of-magnitude / relative comparisons (e.g. transposed vs untransposed), not precise absolute predictions — see the assumptions note below for what it does and doesn't capture.
New to Slot-Leakage Loop Inductance (Classical Machine Design)? Read the guide: Parallel Path Circulating Current: Why Untransposed Strands Fight Each Other — a plain-language explainer of the standard behind this calculator.
Circulating current arises when electrically-parallel strands sit at different depths within a slot: the slot-leakage field builds up with depth, so each strand links a different amount of flux, and because the strands are joined at both ends the resulting EMF difference drives current around the loop between them — on top of, not instead of, the useful bundle current. This calculator solves the N strands as a coupled network (every strand at the same terminal voltage, currents summing to the bundle current) using the classical slot-leakage loop inductance between two strand positions, Lloop = (μ₀·lactive/bslot)·|yj−yk| — a thin-strand approximation cross-verified this session against the modern hairpin-winding literature, classical transformer leakage theory, and an independent first-principles energy derivation. The thin-strand approximation over-predicts (conservatively) circulating current for strands whose height is comparable to their separation — a finite-conductor-height correction is not applied. The model assumes the strands shown are the slot's full conductor content (other, non-parallel turns sharing the same slot are not separately modelled); 2-D/3-D field fringing, iron saturation, and end-region leakage are also not modelled. Transposition is modelled as each strand's length-averaged position — a simplification of the true continuous effect. No external absolute-watt worked example exists in the literature for this exact configuration, so validation here is structural (zero circulating current for identical positions or ideal transposition, current-deviation conservation, loss never decreasing) plus a self-consistent hand-derived numeric case. Verify against FEA before relying on absolute magnitudes for a final design.
Validated: a closed-form 2-strand solution hand-derived from this same model, Iδ = [jω·Lloop·Ibundle/2] / [2R+jω·Lloop], reproduces this calculator's output to 4 significant figures. Strands at the same position, or under ideal transposition, give exactly zero circulating current; swapping two strands' positions leaves total loss unchanged; current deviations from the ideal share always sum to zero; total loss never falls below the ideal equal-sharing loss.