4.3 Power Factor Correction, Harmonics, and Power Quality

4.3 Power Factor Correction, Harmonics, and Power Quality

Quick Summary: Induction motors, transformers, and discharge lighting draw lagging reactive power, depressing the power factor and inflating current throughout an installation. Shunt capacitor banks restore power factor towards unity, while harmonics from modern non-linear loads (VFDs, UPS units, switch-mode power supplies, LED drivers) distort waveforms, overheat neutral conductors, and resonate with capacitors. Both topics are written-test favourites because they connect theory directly to cable sizing and protective-device behaviour.

---

1. Why Power Factor Matters

For the same real power $P$, line current is inversely proportional to power factor:

$$I_L = \frac{P}{\sqrt{3} \, V_L \cos\phi}$$

Example: a 30 kW 400 V 3-phase load draws $30{,}000/(\sqrt{3} \times 400 \times 0.95) = 45.6\text{ A}$ at 0.95 PF, but $30{,}000/(\sqrt{3} \times 400 \times 0.70) = 61.9\text{ A}$ at 0.70 PF — a 36% current increase with zero extra useful output.

Consequences of Low Power Factor

1. Higher I²R losses in cables and transformer windings (losses grow with the square of current).
2. Larger voltage drop ($V = I \times Z$), pushing utilization voltage towards the 4% limit.
3. Reduced usable capacity of the intake, transformer, and switchgear (a 45 kVA ceiling is reached with less real kW delivered).
4. Utility reactive-energy charges for larger consumers whose meters register kVArh; within the Electrician's ≤45 kVA scope the dominant penalties are thermal and voltage-drop effects.
5. Diagnostic value: chronic low PF usually means under-loaded or oversized motors.

2. Shunt Capacitor Bank Correction

Capacitors draw leading reactive current that cancels the motor's lagging reactive current. The required correction is:

$$Q_c = P \times (\tan\phi_1 - \tan\phi_2)$$

Worked Example

Correct a $P = 30\text{ kW}$ load from $\cos\phi_1 = 0.75$ to $\cos\phi_2 = 0.95$:

• $\tan\phi_1 = \tan(\arccos 0.75) = 0.882$; $\tan\phi_2 = \tan(\arccos 0.95) = 0.329$.
• $Q_c = 30 \times (0.882 - 0.329) = 30 \times 0.553 = 16.6\text{ kVAr}$ → select a standard 17–20 kVAr 3-phase capacitor bank.
• Line current falls from $30{,}000/(\sqrt{3} \times 400 \times 0.75) = 57.7\text{ A}$ to $45.6\text{ A}$.

Practical Installation Rules

• Connect capacitor banks at the main switchboard (bulk correction) or at large motor terminals (individual correction); never over-correct an individual motor beyond its no-load magnetising kVAr (self-excitation risk when the supply is removed).
• Capacitors must discharge to a safe voltage within the manufacturer-stated time before re-energisation or maintenance.
• Provide short-circuit protection (HRC fuses or an MCCB) and an inrush-limiting contactor or series reactor.

3. Harmonics from Non-Linear Loads

Linear loads draw sinusoidal current; non-linear loads draw pulsed current and inject harmonics — integer multiples of the 50 Hz fundamental: VFDs, UPS rectifiers, computers and SMPS, LED drivers, battery chargers, and arc welders.

• Triplen harmonics (3rd = 150 Hz, 9th, 15th): zero-sequence — they are in phase across L1/L2/L3 and add arithmetically in the neutral (Chapter 3.4), producing neutral currents that can exceed phase current. Design response: full-size or double neutral, and the 0.86 cable derating when triplen content is 15–33%.
• Other effects: transformer and capacitor overheating, nuisance MCB tripping, RCD blinding (choose Type F or B where appropriate, Chapter 5.4), and distorted voltage (THD) that mal-times sensitive controls.
• Mitigation: segregate dirty loads on dedicated DBs (Chapter 3.4), detuned (series-reactor) capacitor banks, passive or active harmonic filters, and K-rated transformers for heavy non-linear concentrations.

4. Power Quality at Commissioning

• Voltage sag from motor starting: DOL starting of large motors (6–8 × FLC) depresses voltage for adjacent consumers — the reason reduced-voltage starters (star-delta, soft starter) are required for larger motors (Chapter 3.2).
• Verification: post-turn-on checks include voltage measurement at the intake and at circuit extremities (400 V / 230 V within the declared variations), phase rotation, and observation of flicker under load cycling (Chapters 7 and 8).

5. Harmonic Orders, Sequence, and Neutral Behaviour

Examiners expect candidates to classify harmonics by their phase sequence, because sequence decides where the current goes:

Only the triplen (zero-sequence) orders accumulate in the neutral conductor — which is why a modern office full of computers and LED drivers can overheat a neutral that is perfectly balanced at 50 Hz.

6. Power Factor Correction in the ≤45 kVA Context

Within the Electrician licence scope (small factories, workshops, eating houses), correction is usually applied as a fixed or automatically switched capacitor bank at the main intake, sized from the maximum-demand calculation rather than per-motor. The design sequence is: (1) compute installation kW and existing PF from meter readings or nameplates; (2) choose a target PF (typically 0.95); (3) size $Q_c = P(\tan\phi_1 - \tan\phi_2)$; (4) verify the capacitor's cable, breaker, and discharge device; and (5) record the bank on the SLD with its kVAr rating and protection. Becausecapacitors raise the fault level slightly and can resonate with supply inductance when harmonics are present, detuning reactors are added whenever non-linear load exceeds roughly 15–20% of the installation.