12. Harmonics Analysis

Principle

Harmonics in electrical systems are voltage or current wave components at multiples of the fundamental frequency (50 or 60 Hz). Non-linear loads such as rectifiers, VFDs, computers, and LED drivers draw non-sinusoidal currents which can be decomposed via Fourier analysis into harmonic frequencies (e.g., 3rd, 5th, 7th, etc.). Harmonic analysis calculates the level of distortion—typically quantified by Total Harmonic Distortion (THD)—and assesses their impact on system components (like overheating of neutrals, transformers, or resonance issues). The goal is to keep harmonic distortion within recommended limits (such as those in IEEE 519 or IEC 61000-3-6) to avoid equipment malfunction or excessive losses.

Key Metrics

  • Total Harmonic Distortion (THD): This is the ratio of the RMS of all harmonic components to the RMS of the fundamental. It is defined for both current (THDi) and voltage (THDv). For voltage, the formula is:
    THDV = √(V₂² + V₃² + ... + Vₙ²) / V₁
    For example, if a system exhibits a 5% 5th harmonic and a 3% 7th harmonic (with other harmonics negligible), then:
    THDV = √(0.05² + 0.03²) ≈ 0.058 (or 5.8%). Voltage THD is ideally kept below 5% for general systems.
  • Total Demand Distortion (TDD): Similar to THD, TDD normalizes the harmonic currents to the load current capacity rather than the instantaneous fundamental, preventing distortion figures from becoming exaggerated under light load conditions.
  • Harmonic Order and Phase Sequence: Triplen harmonics (3rd, 9th, etc.) in three-phase, 4-wire systems add in the neutral because they are zero-sequence. Other harmonics (like 5th and 11th) are negative sequence and can cause extra losses and torque oscillation in motors.

Calculations

For a given non-linear load, if the harmonic spectrum (expressed as a percentage of the fundamental) is known for each harmonic, you can:

  • Calculate the injection of each harmonic current.
  • Use the network impedance at each harmonic frequency to find the resulting harmonic voltages (Vₙ = Iₙ × Zₙ), noting that typically Zₙ ≈ n × X₁ (with resistance roughly constant or slightly increased due to skin effect).
  • Sum contributions vectorially (if phase angles are known) or conservatively by RMS to estimate overall distortion.

Example: A 6-pulse rectifier (typical VSD without filter) might have ~80% fundamental, 40% 5th, and 20% 7th harmonic contributions. With a 100 A RMS fundamental, the 5th harmonic is 40 A, and the 7th is 20 A. The current THD is then:

THDi = √(40² + 20² + …) / 100 ≈ 44%

If multiple such drives exist on a bus, their harmonic currents are combined (often assuming worst-case in-phase conditions for a conservative estimate).

Resonance Check

A key part of harmonic analysis is checking for resonance. A capacitor bank in combination with source inductance can form an LC circuit that resonates at a specific harmonic. The resonant order can be approximated as:

nres ≈ √(KVARcap / (system short-circuit MVAR))

If nres is near a major harmonic (e.g., 5th or 7th), engineers may add detuning reactors to shift the resonance away from that harmonic.

Effects and Correction

  • Neutral Current: In a 3-phase, 4-wire system with many single-phase SMPS loads, the 3rd harmonic currents add in the neutral since they are in phase. For instance, if each phase has a 50 A fundamental and 15 A of 3rd harmonic (30%), the neutral could see up to 45 A of 3rd harmonic current.
  • Transformer Derating: Harmonic loss factors, such as the extra eddy current loss factor FHL = Σ((Iₙ/I₁)² n²), can indicate when a standard transformer might overheat. K-rated transformers are designed to handle these additional losses.
  • Motor Heating: Harmonic currents cause torque ripple and increased losses in motors. Typically, if voltage THD is maintained below 5%, motors are unaffected; if not, additional filtering might be required.
  • Telephone Interference: Lower-order harmonics can interfere with communication lines, a concern addressed by older criteria such as the Telephone Interference Factor (TIF).

Industry Relevance

With the widespread use of VFDs, UPS systems, LEDs, and computers, harmonic issues are common. Excessive harmonics can lead to:

  • Nuisance overheating of transformers, neutrals, and capacitor failures.
  • Malfunction of sensitive equipment due to waveform distortion.
  • Utility interconnection challenges—many utilities enforce IEEE 519 limits (e.g., THDv < 5% at the point of common coupling) to ensure power quality.

In large installations, harmonic analysis is a routine part of design. For instance, a plant adding numerous VFDs might compute expected THD and then choose to install harmonic filters (such as tuned L-C or active filters) to mitigate distortion.

Standards

  • IEEE 519-2014: The de-facto standard for harmonic control in North America (and elsewhere), setting limits on harmonic currents (TDD) and voltage distortion at the point of common coupling.
  • IEC 61000-3-2 and 3-12: Standards that limit harmonics for equipment based on current rating, used for CE marking of appliances.
  • EN 50160: Defines utility supply quality in the EU, typically requiring supply voltage THD to be below 8%.
  • National Grid Codes: Often incorporate harmonic emission limits for connecting equipment.

Software Tools

  • Harmonic Analysis Software: Tools such as ETAP, SKM, and DIgSILENT have dedicated modules where nonlinear loads are modeled (either by specifying their harmonic spectrum or using typical models). These tools calculate bus harmonic voltages via superposition, identify resonance points, and compare THD against IEEE 519 limits.
  • Specialized Tools: MATLAB can be used for custom Fourier analysis, though most power system studies rely on the dedicated software above.
  • Power Quality Monitors: Instruments like the Fluke 435 can measure THD and individual harmonic percentages on-site, validating simulation results.
  • Filter Design Tools: Some software assists in designing passive filters (calculating L and C values) or evaluating active filter performance to mitigate harmonic distortion.
  • Spreadsheets for IEEE 519 Compliance: Some consultants use Excel models to quickly assess harmonic currents against system short-circuit ratios at the PCC.

Harmonic analysis has become an integral part of large electrical system design due to the prevalence of electronic loads. By using calculation tools and adhering to standards, engineers can mitigate harmonic issues to maintain power quality and ensure equipment longevity.