Interharmonics — The Power Quality Disturbance That Doesn’t Show Up on Standard Harmonic Analysers
| 定义 | Frequency components that are NOT integer multiples of the fundamental — e.g. 75 赫兹, 130 赫兹, 267 Hz on a 50 Hz system |
| IEC definition | 符合IEC 61000-2-1: “Between the harmonics of the power frequency voltage and current, further frequencies can be observed which are not an integer of the fundamental” |
| 经典的来源 | Cycloconverters · Arc furnaces · AC/DC drives at variable speed · Induction furnaces · Pulsating loads not synchronised with the fundamental |
| New DER sources | PV inverters (MPPT algorithm ripple) · Wind turbines (slip frequency) · EV chargers (switching asymmetry) · HVDC converters (control loop interactions) |
| Most dangerous effect | Flicker — an interharmonic at frequency fIH produces voltage flicker at the beat frequency |fIH - 50| 赫兹. At 0–15 Hz beat frequency, the flicker falls in the range of peak human visual sensitivity |
| Field case | LV installation with PV panel + EV charger + microwave — simultaneous operation produces stochastic interharmonics causing light flicker and DC bus voltage fluctuations |
| Measurement problem | Standard FFT-based harmonic analysers (符合IEC 61000-4-7) assume integer multiples of fundamental — they misread interharmonics as spread noise rather than discrete tonal components |
| Regulatory status | 符合IEC 61000-3-6 provides planning levels for interharmonics at MV/HV — but emission limits for individual equipment at LV are not established |
01 What Are Interharmonics?
Classical harmonic analysis assumes that all non-sinusoidal content in the power system voltage and current waveforms consists of integer multiples of the fundamental frequency — 100 赫兹, 150 赫兹, 200 赫兹, 250 赫兹, and so on at 50 赫兹. This assumption holds for steady-state operation of most traditional non-linear loads: a 6-pulse rectifier connected to a stiff AC supply produces harmonic currents at the 5th, 7日, 11日, 13th orders, and their magnitude is relatively constant over time.
Interharmonics are frequency components that break this assumption. They occur at frequencies that are not integer multiples of the fundamental — 75 赫兹, 130 赫兹, 183 赫兹, 267 赫兹, or any other value between the harmonic orders. 符合IEC 61000-2-1 defines them precisely: “Between the harmonics of the power frequency voltage and current, further frequencies can be observed which are not an integer of the fundamental. They can appear as discrete frequencies or as a wideband spectrum.”
When an interharmonic component falls below the fundamental frequency — for example, 35 Hz或 20 Hz on a 50 Hz system — it is sometimes called a subharmonic. 符合IEC 61000-2-1 notes that “the term sub-harmonic does not have any official definition but is simply a special case of interharmonic for frequency components less than the power system frequency. Use of the term subsynchronous frequency component is preferred.” Subharmonics are particularly problematic because they can excite mechanical resonances in rotating machinery — turbine shaft torsional oscillations, for example — at frequencies below the fundamental, where standard vibration damping is not designed to operate.
02 Sources — Traditional and Emerging
Interharmonics arise whenever a power conversion device processes energy at a frequency that is not synchronised to the mains frequency. The output frequency of the conversion process modulates the mains frequency, producing sidebands — interharmonic components — at frequencies determined by the difference between the conversion frequency and the mains frequency and its harmonics.
| Source type | Generation mechanism | Typical interharmonic frequencies | Trend |
|---|---|---|---|
| Cycloconverters | Direct AC/AC frequency conversion produces output at arbitrary output frequency f出 — interharmonics at |nf手 ± mf出| | Continuous spectrum — depends on output speed | Legacy — rolling mills, large drives |
| Arc and induction furnaces | Chaotic arc current creates random non-periodic waveform — all frequencies present simultaneously | Wideband — continuous spectrum below 2 千赫 | Stable — still widely used |
| VFDs at variable speed | At non-integer speed ratios, VFD output frequency and harmonics beat against mains frequency — interharmonics appear at beat frequencies | Varies with motor speed — sweeps continuously during acceleration | Growing — dominant in industry |
| PV inverters (MPPT) | Maximum Power Point Tracking algorithm perturbs operating point periodically — ripple on DC bus creates interharmonic injection at the perturbation frequency and its harmonics | Typically 5–100 Hz sidebands around harmonics | Rapidly growing — dominant new source |
| Wind turbines | Variable rotor speed creates slip frequency (frotor ≠ f手) — interharmonics at nf手 ± fslip | Varies with wind speed — typically 45–55 Hz range (near fundamental) creating beats | Rapidly growing — offshore, onshore |
| 电动车充电器 | Switching frequency asymmetry and DC bus ripple create intermodulation products — exacerbated when grid voltage is itself distorted | 2–10 Hz sidebands around fundamental and harmonics | Rapidly growing — residential, 广告 |
| HVDC converters | Control loop interactions between AC and DC sides produce subsynchronous oscillations — interharmonics at control loop frequencies | Subsynchronous (5–45 Hz) — potentially dangerous for grid stability | Growing — major concern for TSOs |
Traditional interharmonic sources — cycloconverters, arc furnaces — were large, identifiable, and typically located at industrial facilities where their PQ impact could be assessed and managed at the connection point. The new DER-based interharmonic sources — PV inverters, wind turbines, EV chargers — are small, numerous, geographically distributed, and installed without individual PQ impact assessment. Each device produces interharmonic emissions that are below any individual equipment limit. But thousands of devices operating simultaneously on the same LV feeder, each with stochastic interharmonic emission at slightly different frequencies, create a composite interharmonic environment that was not anticipated in the design of existing LV infrastructure and is not characterised by current monitoring equipment.
03 Effects — Flicker, Equipment Malfunction, and Grid Oscillations
Flicker — the most sensitive effect
The most important and best-documented effect of interharmonics is voltage flicker. An interharmonic component at frequency fIH modulates the fundamental voltage, producing amplitude variations at the beat frequency |fIH – f根本|. On a 50 Hz system, an interharmonic at 55 Hz produces flicker at 5 Hz — squarely in the 1–15 Hz range of peak human visual sensitivity as characterised by the IEC flickermeter. An interharmonic at 62 Hz produces 12 Hz flicker. The flicker intensity is proportional to the interharmonic amplitude: even an interharmonic of only 5% amplitude can produce visible flicker that would fail the IEC 61000-4-15 flickermeter assessment.
DC bus voltage fluctuations in rectifier loads
Interharmonic components in the supply voltage cause cycle-by-cycle variations in the peak voltage seen by diode rectifiers — the DC bus capacitors of variable frequency drives, UPS systems, and switch-mode power supplies. These DC bus voltage fluctuations cause uneven charging and discharging of the capacitors, producing ripple on the DC bus that the drive’s control system must manage. At high interharmonic amplitudes, the DC bus fluctuation can trigger overvoltage or undervoltage protection in the drive — causing unexpected trips that appear as equipment faults rather than supply quality problems.
Grid oscillations and subsynchronous resonance
Subsynchronous interharmonics — components below 50 Hz — can excite torsional resonances in large turbogenerator shafts at frequencies that coincide with the natural mechanical resonance frequency of the shaft-generator system. This subsynchronous resonance (SSR) mechanism has caused catastrophic shaft failures in thermal power stations connected via series-compensated transmission lines. In modern power systems, HVDC converter control loop interactions can produce similar subsynchronous oscillations that propagate through the interconnected AC network — a growing concern as HVDC capacity expands.
04 Field Case — PV, 首页, and Microwave on the Same LV Circuit
一 2025 paper in MDPI Sustainability provides a concrete field measurement of interharmonic generation in a modern domestic low-voltage installation — specifically, a circuit with a PV panel, an EV charger, and a microwave oven operating simultaneously. This combination represents the emerging standard residential energy environment in developed countries with high DER adoption.
The study’s key finding is that the simultaneous operation of these three devices produces stochastic, probabilistic interharmonic emissions — not the deterministic, predictable harmonic patterns of classical non-linear loads. The interharmonic frequencies and amplitudes vary randomly from cycle to cycle, driven by:
- PV inverter MPPT algorithm — the perturb-and-observe algorithm varies the operating point at a rate that is not synchronised to the mains, injecting interharmonics at the perturbation frequency and its sidebands with the mains harmonics
- EV charger switching — the charger’s switching frequency varies slightly with battery state of charge, producing interharmonic emissions that sweep across a frequency range rather than sitting at a fixed value
- Microwave magnetron — the magnetron oscillation frequency is not precisely mains-synchronised, producing broadband interharmonic content in the 50–3000 Hz range
The study demonstrates that when multiple interharmonic sources operate simultaneously, the total interharmonic content can be significantly higher than the sum of individual contributions — a superadditive aggregation effect. This occurs when two sources produce interharmonics at close but not identical frequencies, creating a beat pattern that amplifies the composite amplitude at the beat frequency. For a PV inverter producing an interharmonic at 53 Hz and an EV charger producing one at 54 Hz simultaneously, the composite signal has a 1 Hz beat — a very slow amplitude modulation that, at sufficient amplitude, produces perceptible flicker at 1 赫兹. No individual device would produce this flicker alone.
The paper’s methodological contribution is a probabilistic model of interharmonic generation — characterising not just the mean interharmonic amplitude but its statistical distribution using probability density functions fitted to real-time measurements. This probabilistic approach is more accurate than deterministic worst-case models and more useful than simple statistical summaries: it allows the prediction of how often a given interharmonic amplitude will be exceeded, which is the information needed to assess compliance with planning levels expressed as 95th-percentile values. 对于一个 50 Hz system, the IEC 61000-3-6 planning level for interharmonics at LV is 0.2% — the probabilistic model allows engineers to determine whether the 95th percentile of the interharmonic distribution at a given installation exceeds this level.
05 The Measurement Challenge
Interharmonics present a fundamental measurement problem that does not arise for classical harmonics: standard measurement methods are designed for integer-multiple frequency components and systematically fail to correctly characterise non-integer components.
The IEC 61000-4-7 limitation
符合IEC 61000-4-7 — the standard measurement method for harmonic analysers — specifies a 200 ms measurement window (10 cycles at 50 赫兹) and applies a DFT to produce harmonic subgroups at 50 Hz intervals. A spectral component at exactly 75 赫兹 (midway between the 1st and 2nd harmonic at 50 Hz and 100 赫兹) produces DFT output that is spread across multiple bins rather than concentrated in a single bin — it appears as elevated noise between the harmonic orders rather than as a discrete 75 Hz component. The standard then assigns this interbin energy to the nearest harmonic subgroup, potentially inflating the harmonic amplitude and obscuring the interharmonic entirely.
The frequency resolution problem
一 200 ms measurement window provides a frequency resolution of 1/0.2 = 5 赫兹. This means interharmonic components closer than 5 Hz apart cannot be resolved — they appear as a single broadened spectral feature. For interharmonics at 52 Hz and 54 Hz — both plausible from different DER devices — they are irresolvable in a 200 ms window. Resolving them requires longer measurement windows: 1 second for 1 Hz resolution, 10 seconds for 0.1 Hz resolution. But longer windows increase the probability that the interharmonic frequency has changed during the measurement — a common problem with VFD-generated interharmonics whose frequency varies continuously with motor speed.
| Measurement method | Frequency resolution | Interharmonic detection | 标准 |
|---|---|---|---|
| 符合IEC 61000-4-7 DFT (200 毫秒) | 5 赫兹 | Poor — spreads interharmonics across bins, misidentifies as harmonic content | 符合IEC 61000-4-7:2002+AMD1:2008 |
| Extended window DFT (1 小号) | 1 赫兹 | Good for stationary interharmonics — fails for time-varying | Research practice |
| Interpolated FFT / WIFFT | Sub-Hz resolution | Good — reduces spectral leakage, better interharmonic amplitude estimation | IEEE P519.1 working group |
| Time-frequency methods (wavelet, STFT) | Variable | Best for time-varying — captures frequency evolution over time | Research — not yet standardised |
| Probabilistic model (PDF fitting) | Statistical | Best for stochastic sources (光伏, 首页) — characterises distribution not just mean | MDPI Sustainability 2025 |
06 电能质量视角
Interharmonics are the power quality disturbance that falls between all the standard frameworks. They are too high in frequency for the classical mechanical resonance analysis used in power system stability studies. They are too low in frequency for EMC analysis, which begins at 150 千赫. They are not addressed by the harmonic emission limits in IEC 61000-3-2 (which applies to integer harmonics up to the 40th order). And they are not correctly characterised by the standard measurement method in IEC 61000-4-7.
The result is a disturbance class that is growing in significance as DER penetration increases — driven by PV inverters, wind turbines, 电动车充电器, and HVDC links — but is systematically invisible to the measurement infrastructure most utilities and industrial engineers have deployed. When a PQ analyser running IEC 61000-4-7 shows clean harmonic compliance at a site that is generating visible flicker, interharmonics are the most likely explanation that the standard analysis will miss.
From a utility PQ engineering perspective, the practical protocol for identifying interharmonics when standard harmonic analysis fails to explain an observed problem — flicker without an obvious source, unexplained VFD trips, elevated noise between harmonic orders — is: first, extend the measurement window beyond 200 ms to improve frequency resolution; 第二, look at the full spectrum between harmonic orders rather than only at the harmonic subgroups; third, correlate the interharmonic frequency with the known mechanical or switching frequencies of connected equipment. A VFD running a motor at 1,450 rpm on a 4-pole machine produces a slip frequency of |50 - 1450/60| = |50 - 24.17| = 25.83 Hz — and interharmonics at 50 ± 25.83 = 24.17 Hz and 75.83 赫兹. Finding a spectral component at 75.83 Hz on the supply voltage confirms the VFD as the source with high confidence. This systematic approach transforms an unexplained “measurement noise” observation into a diagnosed, attributable PQ problem.
参考文献
- Moyo RT et al. “Time-Domain Aggregation of Interharmonics from Parallel Operation of Multiple Sustainable Sources and Electric Vehicles.” Sustainability, 17(3), 1214, 二月 2025. DOI: 10.3390/su17031214. Open access CC BY 4.0.
- 符合IEC 61000-2-1:1990. Electromagnetic compatibility — Description of the environment — Electromagnetic environment for low-frequency conducted disturbances and signalling in public power supply systems. 符合IEC, 日内瓦. (Definition of interharmonics.)
- 符合IEC 61000-4-7:2002+AMD1:2008. Testing and measurement techniques — General guide on harmonics and interharmonics measurements and instrumentation for power supply systems and equipment connected thereto. 符合IEC, 日内瓦.
- 符合IEC 61000-3-6:2008. Limits — Assessment of emission limits for the connection of distorting installations to MV, 高压和超高压电力系统. 符合IEC, 日内瓦.
- IEEE Task Force on Harmonics Modeling and Simulation. “间谐波: Theory and Modeling.” IEEE电力输送交易, 飞行. 22, 不. 4, PP. 2335–2348, 2007.
- Yong J, Chen L, Chen S. “Modeling of background harmonics and interharmonics.” IEEE电力输送交易, 飞行. 26, 不. 2, PP. 900–909, 2011.
Primary source: Moyo RT et al. “Time-Domain Aggregation of Interharmonics from Parallel Operation of Multiple Sustainable Sources and Electric Vehicles.” Sustainability, MDPI, 17(3), 1214, 二月 2025. DOI: 10.3390/su17031214. Open access CC BY 4.0. Supporting references: 符合IEC 61000-2-1 (定义), 符合IEC 61000-4-7 (measurement), IEEE Task Force on Harmonics (2007).
SVG diagrams and PQ Perspective (部分 6) are original IPQDF editorial content by Denis Ruest, M.Sc. (Applied), P.Eng. (ret.). IPQDF does not claim authorship of the original research.