Electrical Power System & Lighting Design Reference

Vision Matrix Institute  |  Engineer's Toolkit  |  Formulas, Tables & Standards

Contents

  1. Power Distribution (AC/DC)
  2. Load Calculations
  3. Conductor & Cable Sizing
  4. Voltage Drop Calculations
  5. Short-Circuit Current Calculations
  6. Protective Device Coordination
  7. Grounding (Earthing)
  8. Lightning Protection
  9. Motor Starting & Protection
  10. Transformer Sizing & Impedance
  11. Harmonics & Power Quality
  12. Power Factor Correction
  13. Lighting Design (Illuminance)
  14. Energy Efficiency
  15. Thermal & Insulation Ratings
  16. Switchgear & Breaker Ratings
  17. Instrumentation & Measurement
  18. Standards Comparison & Worked Examples

1. Power Distribution (AC/DC)

Fundamentals

DC: P = V × I
Three-phase active power: P = √3 × VLL × I × cosφ (kW)
Three-phase reactive power: Q = √3 × VLL × I × sinφ
Three-phase line current: I = P / (√3 × VLL × cosφ)
Single-phase: P = V × I × cosφ
Apparent power: S = √(P² + Q²) = √3 × VLL × I Assumes balanced, sinusoidal waveforms. DC distribution uses the same power law without reactance or phase angle.
Generator
→
Transformer
(step-down)
→
Main Bus
→
CB1 → Load A
Figure 1: Generic single-line distribution — generator, transformer, main bus, and protected feeders (CB2 → Motor, CB3 → Panel follow the same bus).

2. Load Calculations

Aggregate loads by type (lighting, receptacles, HVAC, motors), then apply demand factors and diversity factors per the governing code (NEC 220, IEC 60364-6, or BS 7671 Appendix 4).

Motor full-load current (3-phase): IFL = Prated / (√3 × V × cosφ × η) η = motor efficiency. Typical unit loads: lighting 10–50 W/m², outlets 50–100 W/point.
Always verify total demand does not exceed supply capacity or breaker ratings after applying diversity.

3. Conductor & Cable Sizing

IEC 60364-5-52 NEC 310.15 BS 7671

Select conductor size so the design current Ib ≤ the cable's tabulated rating Iz, then derate for ambient temperature, grouping, and installation method.

Reference ampacity table — PVC/Cu, IEC 60364-5-52 Table B.52.2 (amps)

Size (mm²)A1A2B1B2CEF
1.514.514.017.516.519.52224
426253230364045
16615776698594101
50119110151133168180196
150240219300258344379406

A1–F = installation methods (insulated conduit in wall → spaced in free air). XLPE (90°C) insulation gives roughly 20–25% higher ampacity than PVC (70°C) at the same size.

Standard conductor sizes

Copper (mm²): 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240
Aluminium (mm²): 10, 16, 25, 35, 50, 70, 95, 120, 150, 185, 240, 300

Short-circuit withstand check: S² ≥ I²t × k² The conductor's I²t withstand must not be exceeded by the prospective fault energy let-through for the clearance time t (IEC 60364-4-43). See the Short-Circuit Calculator in the Engineer's Toolkit for the k-factor version of this check.

4. Voltage Drop Calculations

IEC 60364-5-52 Annex G Limits are typically 3% for lighting circuits and 5% total (feeder + branch).

Single-phase: ΔV = 2 × I × L × (R cosφ + X sinφ) / 1000
Three-phase: ΔV = √3 × I × L × (R cosφ + X sinφ) / 1000
DC: ΔV = 2 × I × L × R / 1000 R, X in Ω/km; L in metres (one-way route length). Valid for PF > 0.8; for lower PF, use full phasor summation.
Example: 16 mm² Cu, single-phase, 40 m, 32 A, PF 0.95 (R=1.15, X=0.10 Ω/km):
ΔV = 2 × 32 × 0.040 × (1.15 × 0.95 + 0.10 × 0.312) ≈ 2.9 V (≈ 1.25% of 230 V) — within limit.

5. Short-Circuit Current Calculations

IEC 60909 IEEE 142 Uses Thevenin equivalents and symmetrical components.

Peak current: Ip = κ × √2 × I''k,   κ = 1.02 + 0.98e-3(R/X) For faults far from generators, κ ≈ 1.53, giving Ip ≈ 2.1 × I''k.
Transformer-limited fault current: I''k ≈ Irated / (Z% / 100) E.g. a transformer with 5% impedance contributes 20 × its rated current at its terminals (before decay to steady-state Ik).
I''k
subtransient
→ decays →
Ik
steady-state
Figure 2: Fault current evolution — the subtransient current decays toward steady-state; peak Ip occurs on the first half-cycle.

6. Protective Device Coordination

IEC 60947-2 IEC 60269 IEEE C37.102

Selectivity is achieved when the downstream device clears a fault before the upstream device would operate, across the full range of prospective fault currents. Coordination studies compare manufacturer time-current characteristic (TCC) curves and I²t let-through energy — typically done with dedicated software (e.g. ETAP, SKM) rather than a single formula.

Fault
→
Fuse #1
(downstream, clears first)
|
Breaker #2
(upstream, backup)
Figure 3: Simplified coordination — the downstream device clears a fault before the upstream device needs to act.

7. Grounding (Earthing)

IEEE 80 IEC 60364-5-54

Vertical rod: R = ρ / (2πL) × ln(4L/d)
Horizontal strip/plate: R = ρ / (πL) × ln(2L² / (w·h))
Ring electrode: R = ρ / (2π²r) × ln(8r/d) ρ = soil resistivity (Ω·m), L = electrode length, d = diameter, w = strip width, h = burial depth, r = ring radius. A ground grid (mesh) uses the more complex IEEE 80 area-based formula.
Example: 3 m copper rod, 16 mm diameter, ρ = 100 Ω·m → R = 100/(2π×3) × ln(4×3/0.016) ≈ 35 Ω.
Multiple rods or deeper burial reduce resistance. Soil resistivity ranges from ~10 Ω·m (wet clay) to several thousand Ω·m (dry rock). Verify touch/step voltages against IEC 60479 / IEEE 80 limits.

8. Lightning Protection

IEC 62305 NFPA 780

Striking distance: D ≈ 10 × I0.65 (I in kA, D in m) Used with the rolling-sphere or protective-angle method to position air terminals. Surge arresters (SPDs) at transformers/switchgear should be coordinated per IEC 61643 and IEC 62305-4.

9. Motor Starting & Protection

IEC 60034 IEC 60947-4-1 NEMA MG1

Full-load current: IFL = Prated / (√3 × V × cosφ × η) Locked-rotor (starting) current is typically 5–8× IFL for direct-on-line starting. Star-delta starting reduces line starting current to roughly 1/3 of the DOL value.
Overload relays (thermal/magnetic) protect against sustained overcurrent; instantaneous elements handle short-circuit/locked-rotor conditions. See the Breaker Calculator in the Engineer's Toolkit for instantaneous trip range guidance by starting method.

10. Transformer Sizing & Impedance

IEC 60076

Rated current: S = √3 × VLL × Irated / 1000 (kVA)
Short-circuit current: Isc = Ifull / (Z% / 100) Typical transformer impedance is 5–12% (IEC 60076-5). Short-circuit withstand duration is usually 2 s per IEC, or limited by winding temperature rise per IEEE C57.12.
Example: 250 kVA, 11 kV/400 V, Z=5% → LV full-load current ≈ 360 A; maximum LV fault current ≈ 360/0.05 = 7200 A.

Common LV ratings (kVA): 15, 25, 45, 75, 112.5, 150, 225, 300… and up to MV sizes in 1 MVA+ increments.

11. Harmonics & Power Quality

IEEE 519 IEC 61000

THDI = √(I2² + I3² + …) / I1 × 100% In = RMS amplitude of harmonic order n; I1 = fundamental RMS. IEEE 519 typically limits THD to 5–8% at the point of common coupling.
Nonlinear loads (VFDs, rectifiers, IT equipment) inject harmonics. Third-harmonic currents are zero-sequence and add arithmetically in neutrals — oversize neutrals or use delta transformers where high triplen-harmonic loads are expected.

12. Power Factor Correction

IEEE 141

Required reactive compensation: Qkvar = P × (tanφ1 − tanφ2) φ = arccos(PF). Capacitor current (3-phase): Ic = Qkvar × 1000 / (√3 × V).
Example: 100 kW load, PF 0.8 → 0.95: tanφ1=0.75, tanφ2=0.33 → Q = 100 × (0.75−0.33) = 42 kVAR.

See the Power Factor Correction Calculator in the Engineer's Toolkit to compute this directly for your load.

13. Lighting Design (Illuminance)

EN 12464-1 IESNA RP-20

Point source: E = I × cosθ / d²
Lumen method (room lighting): N = (E × A) / (F × UF × MF) E = target illuminance (lux), A = room area (m²), F = lumens per luminaire, UF = utilization factor, MF = maintenance factor, N = number of luminaires needed.
SpaceTypical illuminance (lux)
Offices300–500
Classrooms~300
Warehouses~200
Roads5–50

See the Lighting Calculator in the Engineer's Toolkit to size luminaires for a room directly.

14. Energy Efficiency

IEC 60034-30 IEC 60076-20

Efficiency η = Pout / Pin. Motor efficiency classes IE1–IE5 per IEC 60034-30; transformer losses per IEC 60076-20. LED lighting typically exceeds 100 lm/W versus 50–80 lm/W for fluorescent.

15. Thermal & Insulation Ratings

IEC 60071 IEC 60664

Insulation thermal classes: B (130°C), F (155°C), H (180°C). Basic Insulation Level (BIL) and clearance/creepage distances are set per IEC 60071 and IEC 60664 based on system voltage and pollution degree (approx. 0.8 mm/kV clearance in air, 1.5–2 mm/kV creepage under pollution).

16. Switchgear & Circuit-Breaker Ratings

IEC 62271 IEC 60947 UL 489

Key ratings: nominal voltage Un, rated current In, breaking capacity Icu, short-time withstand Icw (1 s), and service breaking capacity Ics (typically 75% of Icu). Rule of thumb: fuses sized 125–135% of continuous current; motor protection relays set to 110–125% of motor FLA.

17. Instrumentation & Measurement

IEC 61869

Current Transformer: Is = Ip × (Np / Ns)
Voltage Transformer: Vs = Vp × (Ns / Np) E.g. a 100/5 A CT gives Is = Ip/20. Never open-circuit a CT secondary under load.

18. Standards Comparison & Worked Examples

Code/StandardBranch max dropTotal max drop
NEC (informational)3%5%
IEC 60364/BS 7671 (lighting)3%–
IEC 60364/BS 7671 (other)5%–
AS/NZS 30005%5%

Worked examples

1. Conductor sizing: 50 kW, PF 0.9, 400 V, 60 m, 3% drop limit → I ≈ 80.1 A → 25 mm² Cu (119 A) satisfies both ampacity and ΔV ≈ 1.55%.
2. Short-circuit: 50 kVA, 400 V, Z=5% → Ifull=72.2 A → Isc ≈ 1.44 kA rms, Ip ≈ 3.0 kA peak.
3. Ground rod: 3 m rod, 16 mm dia., ρ=100 Ω·m → R ≈ 35 Ω.
4. Motor starting: 37.3 kW, 480 V, η=90%, PF=0.85 → FLA ≈ 63 A, DOL locked-rotor ≈ 380 A.
5. Transformer selection: 200 kW, PF 0.9, +50% future growth → required ≈ 333 kVA → select standard 400 kVA.