Cable voltage drop and power loss
Voltage drop in a three-phase or single-phase cable line from the conductor resistance at the operating temperature and the reactance, the power loss in the cable and the sending-end voltage — including a long ESP submersible cable.
R = ρ_20 · (1 + α · (t − 20)) · L / S, X = x_0 · LΔU = k · I · (R · cos φ + X · sin φ), k = √3 (3~), 2 (1~)3~: ΔP = 3 · I² · R, 1~: ΔP = 2 · I² · RU_1 = U + ΔUThe in-phase component of the voltage drop per IEC 60364-5-52 (Annex G): a balanced load concentrated at the end of the line. IEC 60364-5-52 recommends at most 3 % for lighting and 5 % for other loads (6 and 8 % when supplied from the user's own substation). In a long ESP cable the drop is larger and is made up with the tap of the ESP transformer: U_1 ≈ U + ΔU. Calculate the smaller motor lead extension separately and add the drops. The size is also checked for current-carrying capacity and short-circuit withstand.
Source: IEC 60364-5-52:2009, Annex G; temperature coefficients of resistance of copper (0.00393) and aluminium (0.00403 1/°C) per IEC 60228
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Line-to-line voltage for three phases; for an ESP, the rated voltage of the submersible motor.
Induction motors at rated load 0.80–0.90, lightly loaded 0.3–0.6; heaters 1.
Cable route length; for an ESP, from the control panel or transformer to the motor.
At full load: PVC insulation 70 °C, XLPE 90 °C; 20 °C for no correction. Submersible cable: the average well temperature plus heating by the current.
Cables up to 1 kV about 0.08 Ω/km (IEC 60364-5-52), 6–10 kV 0.08–0.12, flat submersible cable about 0.1; overhead lines 0.3–0.4 Ω/km.
Unit converter for this formulaVoltage · Current · Length · Area · Temperature · Resistance · Power · Fraction and percent
- V1
- kV0.001
- ΔU/U — Voltage drop, % of U–
- U_1 — Sending-end voltage (for an ESP, the transformer tap)–
- R — Conductor resistance at the operating temperature–
- ΔP — Power loss in the cable–
- ΔP/P — Loss, % of the load power–
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Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.