🎓 Lesson 4
D3
Understanding THDv, THDi, and Interharmonics in Industrial Environments
THDv, THDi, and interharmonics are unwanted extra electrical 'ripples' in voltage and current waveforms that can overheat equipment, trip protections, or disrupt sensitive blasting control systems.
🎯 Learning Objectives
- ✓ Calculate THDv and THDi from measured voltage/current spectral data using IEEE Std 519–2022 definitions
- ✓ Analyze harmonic spectra to identify dominant harmonic orders and their likely sources (e.g., 5th/7th from 6-pulse VFDs powering ventilation fans)
- ✓ Explain how interharmonics below 2 kHz disrupt time-synchronized electronic detonator networks (e.g., NONEL® or digital initiators)
- ✓ Apply IEEE Std 519–2022 planning limits to design harmonic mitigation for a 3.3 kV underground substation feeding a blast-hole drill rig VFD
📖 Why This Matters
In mining operations, harmonic distortion isn’t just an academic concern—it directly impacts safety and reliability. A recent incident at a South African platinum mine saw repeated misfires during precision delay blasting due to interharmonic noise (182 Hz) from a nearby DC drive rectifier corrupting digital initiator timing signals. Voltage THDv > 8% caused thermal tripping of soft-starters on primary crushers, delaying production by 14 hours. Understanding THDv, THDi, and interharmonics is essential to protect blast control integrity, prevent equipment failure, and comply with grid interconnection standards.
📘 Core Principles
Harmonics arise from nonlinear loads—common in mining: VFDs (for pumps, conveyors, drills), arc furnaces (in on-site smelting), and SCR-based motor controllers. THDv measures waveform purity of supply voltage; high THDv indicates source impedance issues or upstream distortion. THDi reflects load behavior—high THDi from a VFD may stress transformers and cables but not necessarily distort voltage if system short-circuit capacity is high. Interharmonics (e.g., 125 Hz, 378 Hz) occur between integer harmonics and stem from amplitude modulation (e.g., PWM carrier frequency sidebands) or slip-frequency interactions in wound-rotor drives—critical because many electronic detonators sample at ~1 kHz and alias interharmonics into timing-critical bands.
📐 Key Calculation
THD is defined as the square root of the sum of squares of harmonic magnitudes (up to the 50th order), normalized to the fundamental component. IEEE Std 519–2022 specifies calculation methodology and measurement windows (e.g., 10-cycle RMS for steady-state assessment).
💡 Worked Example
Problem: A power quality logger records voltage harmonics at a surface substation feeding a blast-holes drilling rig: V₁ = 400 V (fundamental), V₅ = 12.8 V, V₇ = 8.4 V, V₁₁ = 3.1 V, V₁₃ = 2.2 V; all other harmonics < 1.0 V. Calculate THDv.
1.
Step 1: Sum squares of harmonic voltages (orders 2–50): (12.8)² + (8.4)² + (3.1)² + (2.2)² = 163.84 + 70.56 + 9.61 + 4.84 = 248.85 V²
2.
Step 2: Take square root: √248.85 ≈ 15.78 V
3.
Step 3: Divide by fundamental: 15.78 / 400 = 0.03945 → THDv = 3.95%
Answer:
The result is 3.95%, which falls within the IEEE 519–2022 recommended limit of ≤5% for 400 V LV systems.
🏗️ Real-World Application
At Chile’s Escondida copper mine, a new fleet of battery-electric LHDs introduced wideband interharmonics (1.2–2.3 kHz) via regenerative braking inverters. These frequencies overlapped with the 2.048 MHz carrier signal used by the site’s wireless blast initiation network (Wi-Blast™), causing intermittent sync loss and aborting two scheduled blasts. Root-cause analysis confirmed interharmonic energy coupling through shared grounding conductors. Mitigation included installing isolated grounding grids for blast control cabinets and adding 2nd-order passive filters tuned to 1.8 kHz—reducing interharmonic RMS by 92% and restoring 100% initiation reliability.