Electrical Power

Electrical power is how factories, workshops and buildings get their energy: a high-voltage supply stepped down by a transformer, carried as three-phase alternating current through cables and protective devices to motors, lights and electronics, and increasingly topped up by solar panels and batteries. This guide covers AC power and power factor, three-phase systems, transformers, induction motors and drives, cable sizing and voltage drop, protection and earthing, harmonics and energy, solar and backup power, and electrical safety and testing. One 11 kW, 400 V motor, the one that drives the hydraulic press, runs through every page, from its 14.2 kVA of apparent power to its 1.5 kA fault current, and every number is computed. The low-voltage electronics side is in Electronics Fundamentals and Power Electronics.

Start here: what do you need?

I need to…	Go to
understand kW, kVA, kvar and power factor	AC Power Basics
work with line and phase voltage, star and delta	Three-Phase Systems
size a transformer or find a fault level	Transformers and Distribution
choose, start, protect or run a motor on a drive	Induction Motors and Drives
size a cable and check voltage drop	Cable Sizing and Voltage Drop
pick breakers, fuses and RCDs, check the earth loop	Protection, Earthing and RCDs
correct power factor, cope with harmonics, read the bill	Power Factor, Harmonics and Energy
size a solar array, battery, UPS or generator	Solar PV, Batteries and Backup Power
work safely, test an installation or find a fault	Electrical Safety, Testing and Troubleshooting

A suggested order

Start with AC Power Basics and Three-Phase Systems. Then follow the power from the source: Transformers and Distribution, Cable Sizing and Voltage Drop, Protection, Earthing and RCDs and the load in Induction Motors and Drives. Power Factor, Harmonics and Energy and Solar PV, Batteries and Backup Power deal with energy, and Electrical Safety, Testing and Troubleshooting is for everyone.

1. AC Power Basics: RMS values, phasors, real, reactive and apparent power, power factor and the power triangle.
2. Three-Phase Systems: Line and phase quantities, star and delta, balanced loads, power and current and why industry uses three phases.
3. Transformers and Distribution: Turns ratio, losses and efficiency, regulation, kVA sizing, inrush, short-circuit current and distribution layout.
4. Induction Motors and Drives: Slip, torque, the nameplate, efficiency classes, starting methods and variable-speed drives.
5. Cable Sizing and Voltage Drop: Current rating and derating, voltage drop, short-circuit withstand and a worked three-phase feeder.
6. Protection, Earthing and RCDs: Fuses and breakers, trip curves, fault levels, earth-fault loop impedance, RCDs and selectivity.
7. Power Factor, Harmonics and Energy: Power factor correction, capacitor sizing, harmonics and THD, demand and the energy bill.
8. Solar PV, Batteries and Backup Power: Array and string sizing, yield, inverters, battery capacity, UPS and generators, with worked examples.
9. Electrical Safety, Testing and Troubleshooting: Shock and arc-flash hazards, lockout, insulation and earth tests, motor and cable faults and a troubleshooting table.

One motor, from the transformer to the fault

Quick reference: the equations

What you need	Equation
Power triangle	S² = P² + Q², cos φ = P ÷ S
Three-phase power	P = √3 VL IL cos φ
Line current	I = P ÷ (√3 V cos φ)
Synchronous speed	ns = 120 f ÷ p
Slip and torque	s = (ns − n) ÷ ns, T = P ÷ ω
Transformer	V₁ ÷ V₂ = N₁ ÷ N₂ = I₂ ÷ I₁, Isc = In ÷ Zpu
Voltage drop	ΔV = √3 I L (R cos φ + X sin φ)
Cable fault withstand	I² t ≤ k² S²
Power factor correction	Qc = P (tan φ₁ − tan φ₂)
PV energy	E = kWp × peak sun hours × PR

Related guides and tools

• Three-Phase Power and Power Factor Calculator and Wire Ampacity and Voltage Drop Calculator.
• Ohm’s Law and Power Calculator and Reactance and Resonance Calculator.
• Motion Control and Actuators for drives, and System Integration for panels, supplies and grounding.
• Hydraulics and Pneumatics, whose press this guide’s motor drives.
• The Power and Energy converters, and the Downloads library (wire gauges and an electrical formula sheet).

Safety first

• Electric shock kills at currents far below what a fuse notices. Isolate, lock out and prove dead before touching anything.
• Arc flash can burn and blind at a distance: use fast protection, correct PPE and work dead whenever possible.
• Mains wiring must be done and inspected by competent people and to the code that applies (IEC 60364, BS 7671, NEC).
• Stored energy: capacitors, drives, solar arrays and batteries stay live after the supply is off.
• The numbers here are for study and preliminary design. Real installations need the code tables, a design by a competent engineer and inspection and testing.

FAQ

Where do I start?

Read AC Power Basics then Three-Phase Systems.

Can I do my own electrical wiring?

Where the law and your skills allow it, but wiring to the mains is regulated nearly everywhere: it needs a qualified person or an inspection. See Electrical Safety, Testing and Troubleshooting.

Which standard applies to me?

It depends on the country: IEC 60364 and national versions (BS 7671 in the UK, VDE in Germany, NEC / NFPA 70 in the United States and Canada’s CEC). Always use the edition in force locally.

Where are controls and materials?

They are the next guides in this series.

References

• Wildi, T., Electrical Machines, Drives and Power Systems, Pearson; Glover, J. D., et al., Power System Analysis and Design, Cengage; Fitzgerald, A. E., et al., Electric Machinery, McGraw-Hill.
• IEC 60364 (low-voltage electrical installations), IEC 60034 (rotating machines), IEC 60076 (power transformers), IEC 60947 (low-voltage switchgear), IEC 62548 (PV arrays).
• BS 7671, NFPA 70 (NEC) and NFPA 70E; IEEE Standards 519, 1584 and 399; US DOE sourcebooks on motors and compressed air.

Last reviewed: November 2026. Values are typical; check the standard, the manufacturer’s data and the code that applies to your installation.