1. The Physics of Harmonic Generation & Fourier Decomposition
In linear circuits containing only resistors, inductors, and capacitors, current is directly proportional to voltage, yielding a smooth 50 Hz sinusoidal waveform. However, modern commercial and industrial loads are dominated by non-linear power electronics: variable speed drives (VSDs/VFDs), uninterruptible power supplies (UPS), switched-mode power supplies (SMPS) in server racks, LED drivers, and electric vehicle (EV) charging rectifiers.
These devices do not draw current continuously. Instead, bridge rectifiers conduct only during brief peaks of the voltage cycle to charge internal DC-bus smoothing capacitors. According to Fourier theorem, any periodic non-sinusoidal waveform f(t) with fundamental angular frequency ω can be decomposed into an infinite series of sinusoidal components:
Where $I_1$ is the 50 Hz fundamental current, $h$ is the harmonic integer order (2, 3, 4...), $I_h$ is the RMS current of harmonic $h$, and $\theta_h$ is its phase angle.
Total Harmonic Distortion ($THD_I$)
The global index measuring harmonic distortion relative to fundamental current is the Current Total Harmonic Distortion:
The True RMS current heating conductors and switchgear is related to $THD_I$ by:
A 6-pulse drive with $THD_I = 40\%$ draws $1.077 \times I_1$ in true RMS thermal current.
Transformer K-Factor & Eddy Current Derating
Harmonics cause severe overheating in distribution transformers due to high-frequency eddy currents in windings ($P_{ec} \propto h^2$) and stray losses in structural tanks:
Standard UK distribution transformers are rated for linear loads ($K = 1$). Supplying IT server rooms or VFD banks with $K = 4$ to $K = 13$ without a dedicated K-rated transformer requires derating the unit nameplate capacity by 20% to 45% under BS EN 60076.
2. Triplen Harmonics & The Neutral Overload Phenomenon (BS 7671 Table 4Aa)
In a balanced 3-phase 4-wire linear system, fundamental currents in Phases L1, L2, and L3 are displaced by 120° electrical. Their vector sum at the neutral star point equals zero ($I_N = I_{L1} + I_{L2} + I_{L3} = 0$), allowing standard installations to use a neutral conductor identical to or half the size of the line conductors.
⚠️ The Triplen Inversion: Why Neutral Currents Sum Arithmetically
Triplen harmonics are odd multiples of the 3rd harmonic order ($h = 3, 9, 15, 21...$). Calculating their electrical phase shift between line conductors:
Because $360^\circ$ is co-phasal, triplen currents in all three phases are completely in phase with each other. Instead of cancelling at the neutral star point, triplen currents sum algebraically (arithmetically) in the neutral conductor:
If each phase carries 100 A fundamental and 40% 3rd harmonic ($I_3 = 40\text{ A}$), the neutral conductor carries:
| 3rd Harmonic Content of Line Current | Rating Factor (Line Size Basis) | Rating Factor (Neutral Size Basis) | Design Sizing & Protection Rule |
|---|---|---|---|
| 0% – 15% | 1.00 | — | Standard cable sizing on line current. Standard line-sized neutral conductor. |
| 15% – 33% | 0.86 | — | Cable derated to 86% of continuous current capacity ($I_z$). Neutral conductor equal to phase conductor. |
| 33% – 45% | — | 0.86 | Cable sized strictly on neutral current ($I_N$). Neutral conductor must be equal to or greater than phase conductor. |
| > 45% | — | 1.00 | Neutral Current ($I_N$) dictates sizing. Regulation 431.2.3 requires dedicated overcurrent detection and switching in the neutral. |
3. The Parallel Resonance Disaster (hr = √{Ssc/Qc}) & 7% Detuned Reactors
Power Factor Correction (PFC) capacitor banks are routinely installed to eliminate DNO reactive power charges. However, capacitors introduce a dangerous capacitive reactance ($X_C = 1 / (2\pi f C)$) that forms a parallel resonant circuit with the upstream supply transformer inductance ($X_L = 2\pi f L_{tx}$).
Parallel Resonant Frequency
The harmonic order at which parallel resonance occurs between the supply transformer short-circuit capacity ($S_{sc}$) and the capacitor bank reactive power ($Q_c$) is given by:
For example, a typical 1000 kVA transformer ($z_{sc} = 5\% \rightarrow S_{sc} = 20\text{ MVA}$) fitted with a 200 kVAR raw capacitor bank resonates at:
If a plant outage drops the fault level to 5 MVA, $h_r$ drops directly onto the 5th harmonic ($h_r = 5.0$). At resonance, the parallel impedance skyrockets, causing massive harmonic current amplification, severe voltage ringing, capacitor dielectric breakdown, and switchgear fires.
The 7% Detuned Anti-Resonance Reactor Solution
To prevent parallel resonance, iron-cored inductive reactors are connected in series with each capacitor step under BS EN 60076-6. The detuning factor $p$ is defined as the ratio of reactor reactance to capacitor reactance at fundamental frequency:
The series resonant frequency of the LC branch is shifted far below any operating harmonic:
The Electrical Effect: Below 189 Hz, the branch is capacitive (providing 50 Hz reactive power). Above 189 Hz (specifically at 250 Hz 5th harmonic and 350 Hz 7th harmonic), the branch becomes purely inductive, completely eliminating parallel resonance with the grid.
4. ENA EREC G5/5 Issue 1 (2020) Connection Governance
The Energy Networks Association (ENA) Engineering Recommendation **G5/5** governs the connection of non-linear equipment to UK transmission and distribution networks.
⚡ The Contractor Trap: Stage 1 vs Stage 2 Assessment
Contractors often rely on individual manufacturer CE / UKCA certificates claiming "IEC 61000-3-12 compliance" and assume their installation automatically passes G5/5 Stage 1.
- Stage 1 is an AGGREGATE Screen: G5/5 Stage 1 current limits apply to the summed total emission of all distorting loads at the Point of Common Coupling (PCC), scaled against the minimum three-phase short-circuit power (Ssc,min), not the maximum transformer nameplate rating.
- Stage 2 Voltage Impact: If total non-linear load exceeds Stage 1 current allowances, a Stage 2 assessment is mandatory. Stage 2 evaluates the incremental harmonic voltage distortion ($THD_V$) superimposed on background network distortion, ensuring the total remains within the 5.0% THD planning level at 400V.