Electrical engineering

Active, reactive and apparent power, motor current, voltage drop and cable size (including long ESP cables), power factor correction, transformer sizing, energy use and cost, earth electrode resistance.

11 calculators

Power and current

Active, reactive and apparent power from current

Power of a three-phase or single-phase load from the voltage, current and power factor — for example, from clamp meter and panel voltmeter readings.

3~: S = √3 · U · I

Load and motor current from power

Operating current of a three-phase or single-phase load from its power; for a motor, from the shaft power and efficiency, with the starting current. Used to select the cable, circuit breaker and starter.

3~: I = P / (√3 · U · η · cos φ)

Cables

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 · L

Cable size for an allowable voltage drop

The smallest conductor size that keeps the voltage drop of a three-phase or single-phase line within the limit, and the next larger standard size — including long lines to well pads and submersible cables.

ΔU_a = δ · U / 100

Motors and transformers

Power factor correction: capacitor bank rating

Reactive power of a capacitor bank that raises the power factor from cos φ_1 to cos φ_2, and the resulting reduction of the supply current and line losses.

Q_c = P · (tg φ_1 − tg φ_2)

Power transformer rating

Design apparent power from the installed load, the demand factor and cos φ, and the transformer rating from the standard series for the allowed loading and the number of transformers in the substation.

S_p = K_d · P_inst / cos φ

Induction motor speed and slip

Synchronous speed from the supply frequency and the number of poles, slip from the rated speed, and the speed on a variable frequency drive — for example, of an ESP motor or a pumping unit drive.

n_s = 60 · f / p

Voltage dip at motor starting

Estimate of the voltage dip on the substation busbars during direct-on-line starting of an induction motor, and of its reduced starting torque — to check whether a large pump or compressor can be started from a given transformer.

S_st = √3 · U · K_i · I_n

Energy use

Electricity use and cost

Electricity used by equipment over a period from its power, load factor, efficiency and running time, and its cost at a tariff.

P_avg = P · K_l / η

Specific energy for lifting liquid

Electricity to lift 1 m³ and 1 t of liquid by a pumping system — ESP, rod pump, injection or transfer pump — against a given head with the overall efficiency, and the daily consumption.

e = ρ · g · H / (3.6 · 10⁶ · η)

Earthing

Resistance of vertical earth rods

Resistance to earth of a single vertical electrode — rod, pipe or angle — in uniform soil, of n rods in a row or in a ring with their mutual influence, and the number of rods for a required resistance.

R_1 = ρ / (2π · L) · (ln(8 · L / d) − 1)

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.