120 V vs 230 V: House Wiring, Copper, Losses and Voltage Drop

Branch currents are $I=P/(V\,\mathrm{PF})$: 120 V ordinary loads and 240 V large appliances for split phase; 230 V phase to neutral loads in both European alternatives. Three phase supply is 230√3 ≈ 400 V between phases. Circuits are assigned to legs or phases explicitly.

For every candidate conductor, the search checks both ampacity and voltage drop. US branch demand is multiplied by $1+0.25c$, then rounded up to a commercial breaker rating (minimum 15 A). IEC branch protection uses the next rating, minimum 16 A, with $I_B\le I_n\le I_z$. Services use the user’s design coincidence and a breaker candidate. Secondary sizing uses diversified current directly. NEC 2023 Table 310.16 is implemented through Southwire product allowable currents at 75 °C, 30 °C ambient and listed 75 °C terminations; 240.4(D) small-wire caps apply after the supplied ampacity correction. IEC 60364-5-52:2009 method B1 uses the Eland 70 °C PVC singles product ratings at 30 °C, with two loaded conductors for single phase branches and three for three phase circuits. Separate correction factors cover the actual ambient and grouping. The data are product candidates, not a reproduced standard table.

Copper resistance is corrected from 20 °C by $R_T=R_{20}[1+0.00393(T-20)]$. AWG area follows its geometric definition; its resistance uses 100% IACS conductivity. Metric resistance uses the manufacturer’s maximum DC values. Copper inventory is $m=\rho\sum A_kL_k$, with density 8960 kg/m³. Phase and neutral areas are equal. The PE ratio affects inventory only.

Steady-load drop is the first-order phasor projection of each phase impedance drop plus neutral displacement. Branches use $\Delta V=2IL(R'\cos\varphi+X'\sin\varphi)$. Shared secondaries have equally spaced house taps; every segment carries its actual downstream load. European houses rotate A–B–C. The end-of-feeder result is the maximum phase-to-neutral drop envelope.

The repeating daily on probabilities are $d_g=D_g[1+0.65\cos\theta_g+0.25\cos2\theta_g]$ and $d_h=D_h[1+0.8\cos\theta_h+0.15\cos2\theta_h]$, with evening peaks at 19 h and 20 h. Midpoint quadrature calculates first and second moments. Conditional independent switching gives $E[I^2]=E[I]^2+\mathrm{Var}(I)$; split phase 240 V branch currents are correlated between legs and cancel exactly in the neutral. Every live conductor and neutral contributes $R\,E[I^2]$.

Transformer winding loading is assessed separately from total kVA. The design current of the most-loaded 120 V section is compared with $I_r=S/(2V_{LN})$; European phase windings use $I_r=S/(3V_{LN})$. The 230 V and 400/230 V household alternatives are checked separately.

Split phase transformer load loss separates primary and secondary heating. For positive leg-current amplitudes $J_1,J_2$ at the common power factor,
$F_p=\frac{E[(J_1+J_2)^2]}{4I_r^2},\qquad F_s=\frac{E[J_1^2]+E[J_2^2]}{2I_r^2}.$
Rated balanced load loss $P_k$ is partitioned by the primary share $f_p$: $P_{load}=P_k[f_pF_p+(1-f_p)F_s]$. Primary variance includes the covariance of a 240 V load appearing in both legs; it is not the sum of independent secondary variances. EPRI's published winding data give the default partition $f_p=0.5$. European primary and secondary phase coils follow the same normalized phase-current heating factor under ideal transformer coupling, so the rated load loss scales with the sum of phase-current second moments. Constant no-load loss is added separately. Annual losses and shared inventories are allocated per house.

An independent power audit constructs every individual branch connection, sums currents upstream through the feeder taps, and reconstructs complex phase and neutral voltages down to each load terminal. It evaluates source power directly as $\mathrm{Re}\sum V_s I_s^*$ and receiving power as $\mathrm{Re}\sum V_l I_l^*$, with switching covariance included. Their difference is checked against the separately calculated branch, service and secondary heating. The input side does not contain any calculated loss term. Equations and stochastic aggregation are derived here; the references supply cable data, winding data and loss mechanisms.

All houses have the same connected powers, circuit lengths, power factor and daily duty shape in all alternatives. Switching is independent between circuits and houses conditional on time of day. The profiles are transparent illustrative schedules, not measured national demand data. Design coincidence is separate from operating duty and is supplied by the user.

Each branch has its own return conductor; no ring circuits or shared-neutral branch circuits. All large appliances remain single phase in the 400/230 V house. Optional US appliance neutrals add copper but carry no modeled 120 V appliance subload. Service includes a full neutral and PE; the utility secondary has a full neutral and no separate PE. PE area defaults to full phase area; actual permitted reductions are outside this inventory model.

The 50 kVA / four-house / 40 m US and 250 kVA / thirty-house / 200 m European networks are comparison scenarios, not national averages. Transformer no-load and rated load losses are illustrative editable assumptions, not claims about a particular product. Replace them with factory test losses for a real comparison. Each transformer supplies exactly the modeled feeder.

The US primary share of rated balanced load loss defaults to 0.5 from EPRI's example. It is an editable partition assumption, not measured data for the 50 kVA scenario transformer. Use winding resistance or loss-test data for a specific unit. The nameplate kVA is the total balanced rating; each 120 V section is allotted half of it. European phase-coil current ratios assume ideal magnetic coupling.

Rules and source data checked on 6 November 2026. US sizing follows the cited 2023 NEC ampacity basis, rather than claiming adoption of the 2026 edition in any jurisdiction. IEC sizing uses IEC 60364-5-52:2009 and the Eland / BS 7671 18th edition product basis; the IEC consolidated edition includes Amendment 1:2024. Check against the standard in force and the actual cable, termination, ambient and grouping conditions. The supplied correction factors must reflect those conditions. This is not an NEC Article 220 service-load calculation or a complete protective-device design.

Drop calculations use nominal-voltage currents and first-order impedance projections, suitable for the small-drop comparison budgets. They do not solve constant-power load feedback or transformer voltage regulation. The installation envelope uses only branch types whose circuit count is nonzero, and sums their peak drop with the maximum service phase drop conservatively; utility drop is shown separately at secondary coincidence. It is not a single coincident end-to-end power-flow snapshot.

Resistance is DC with temperature correction; skin/proximity effects, harmonics and triplen neutral currents are excluded. No motor starting, fault-loop impedance, disconnection time, short-circuit withstand, earthing design, cable thermal solution, transformer thermal aging or cooling auxiliaries. Candidate ranges are 14 AWG–4/0 AWG and 1.5–300 mm²; an unavailable design produces an input condition rather than extrapolation. A fixed copper temperature and reactance are screening assumptions.

Copper is conductor metal in branches, service and secondary only. Transformer windings, MV networks, transmission lines, sheaths, armour, insulation, switchgear and labour are excluded. Many utility secondaries use aluminium; this tool deliberately compares copper equivalents. No material price or installed-cost claim is implied. The daily integration resolution is exposed and tested at twice the default; no spatial interpolation is used.

The power audit is an auxiliary imposed-current network at nominal source voltage. Its receiving energy is a conservation diagnostic; the displayed useful load remains the nominal household energy target. The tool does not solve nonlinear constant-power voltage feedback. Transformer winding loading uses the supplied design coincidence, while annual heating uses operating first and second current moments. Factory winding ratings and thermal limits can impose additional restrictions.