상호고조파 — 표준 고조파 분석기에는 나타나지 않는 전력 품질 장애
| 정의 | Frequency components that are NOT integer multiples of the fundamental — e.g. 75 Hz에서, 130 Hz에서, 267 에 헤르츠 50 헤르츠 시스템 |
| IEC 정의 | 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” |
| 클래식 소스 | Cycloconverters · Arc furnaces · AC/DC drives at variable speed · Induction furnaces · Pulsating loads not synchronised with the fundamental |
| New DER sources | PV 인버터 (MPPT algorithm ripple) · Wind turbines (slip frequency) · 전기차 충전기 (switching asymmetry) · HVDC converters (control loop interactions) |
| Most dangerous effect | Flicker — an interharmonic at frequency fIH produces voltage flicker at the beat frequency |에프IH - 50| Hz에서. At 0–15 Hz beat frequency, the flicker falls in the range of peak human visual sensitivity |
| 현장사례 | LV installation with PV panel + EV 충전기 + microwave — simultaneous operation produces stochastic interharmonics causing light flicker and DC bus voltage fluctuations |
| 측정 문제 | Standard FFT-based harmonic analysers (IEC 61000-4-7) assume integer multiples of fundamental — they misread interharmonics as spread noise rather than discrete tonal components |
| 규제현황 | 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 Hz에서, 150 Hz에서, 200 Hz에서, 250 Hz에서, and so on at 50 Hz에서. 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, 7일, 11일, 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 Hz에서, 130 Hz에서, 183 Hz에서, 267 Hz에서, or any other value between the harmonic orders. 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 또는 20 에 헤르츠 50 Hz system — it is sometimes called a subharmonic. 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 f밖으로 — interharmonics at |nf손 ± mf밖으로| | 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 kHz에서 | 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 인버터 (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 (에프축차 ≠ f손) — interharmonics at nf손 ± fslip | Varies with wind speed — typically 45–55 Hz range (near fundamental) creating beats | Rapidly growing — offshore, onshore |
| EV 충전기 | 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, 상업 |
| 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, 풍력 터빈, 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 |에프IH – f기본적인|. On a 50 헤르츠 시스템, 상호고조파 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 시스템, and switch-mode power supplies. 이러한 DC 버스 전압 변동으로 인해 커패시터의 충전 및 방전이 고르지 않게 됩니다., 드라이브 제어 시스템이 관리해야 하는 DC 버스에 리플 생성. 높은 상호고조파 진폭에서, DC 버스 변동으로 인해 드라이브의 과전압 또는 저전압 보호가 작동되어 공급 품질 문제가 아닌 장비 결함으로 나타나는 예기치 않은 트립이 발생할 수 있습니다..
그리드 진동 및 비동기 공진
비동기 상호고조파 - 아래 구성 요소 50 Hz - 샤프트-발전기 시스템의 자연 기계적 공진 주파수와 일치하는 주파수에서 대형 터보 발전기 샤프트의 비틀림 공진을 일으킬 수 있습니다.. 이 비동기 공명 (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, HOME, and Microwave on the Same LV Circuit
A 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 동시에 헤르츠, the composite signal has a 1 Hz beat — a very slow amplitude modulation that, at sufficient amplitude, produces perceptible flicker at 1 Hz에서. 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. 에 대한 50 헤르츠 시스템, 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.
IEC 61000-4-7 limitation
IEC 61000-4-7 — the standard measurement method for harmonic analysers — specifies a 200 ms measurement window (10 cycles at 50 Hz에서) and applies a DFT to produce harmonic subgroups at 50 Hz intervals. A spectral component at exactly 75 Hz에서 (midway between the 1st and 2nd harmonic at 50 Hz and 100 Hz에서) 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
A 200 ms measurement window provides a frequency resolution of 1/0.2 = 5 Hz에서. 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 헤르츠 분해능, 10 seconds for 0.1 헤르츠 분해능. 그러나 창이 길수록 측정 중에 상호고조파 주파수가 변경될 확률이 높아집니다. 이는 주파수가 모터 속도에 따라 지속적으로 변하는 VFD 생성 상호고조파의 일반적인 문제입니다..
| 측정 방법 | 주파수 분해능 | 상호고조파 감지 | 기준 |
|---|---|---|---|
| IEC 61000-4-7 DFT (200 MS) | 5 Hz에서 | 나쁨 — 빈 전체에 상호고조파를 확산시킵니다., 고조파 성분으로 잘못 식별함 | IEC 61000-4-7:2002+AMD1:2008 |
| 확장된 창 DFT (1 에스) | 1 Hz에서 | 고정 상호고조파에 적합 - 시변에서는 실패 | 연구실습 |
| 보간된 FFT / 위프트 | 서브헤르츠 분해능 | 양호 — 스펙트럼 누출을 줄입니다., 더 나은 상호고조파 진폭 추정 | IEEE P519.1 작업 그룹 |
| 시간-주파수 방법 (잔물결, STFT) | 변하기 쉬운 | 시간 변화에 가장 적합 - 시간에 따른 주파수 변화를 포착합니다. | 연구 — 아직 표준화되지 않음 |
| 확률 모델 (PDF 피팅) | 통계 | 확률론적 소스에 가장 적합 (PV, HOME) — characterises distribution not just mean | MDPI Sustainability 2025 |
06 전력 품질 관점
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 kHz에서. 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, 풍력 터빈, EV 충전기, 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.
유틸리티 PQ 엔지니어링 관점에서, 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: 첫 번째, extend the measurement window beyond 200 ms to improve frequency resolution; 초, 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 4극 기계의 rpm은 다음과 같은 슬립 주파수를 생성합니다. |50 - 1450/60| = |50 - 24.17| = 25.83 Hz — 및 상호고조파 50 ± 25.83 = 24.17 Hz and 75.83 Hz에서. 스펙트럼 성분 찾기 75.83 공급 전압의 Hz는 VFD가 높은 신뢰도를 갖는 소스임을 확인합니다.. 이러한 체계적인 접근 방식은 설명할 수 없는 상황을 변화시킵니다. “측정 소음” 진단된 관찰, 원인 있는 PQ 문제.
참조
- Moyo RT 등. “여러 지속 가능한 소스와 전기 자동차의 병렬 작동으로 인한 상호 고조파의 시간 영역 집계.” 지속 가능성, 17(3), 1214, 2월 2025. DOI: 10.3390/su17031214. 오픈 액세스 CC BY 4.0.
- IEC 61000-2-1:1990. 전자기 호환성 - 환경 설명 - 공공 전원 공급 시스템의 저주파 전도성 방해 및 신호에 대한 전자기 환경. IEC, 제네바. (상호고조파의 정의.)
- IEC 61000-4-7:2002+AMD1:2008. 테스트 및 측정 기술 - 전원 공급 시스템 및 이에 연결된 장비에 대한 고조파 및 상호 고조파 측정 및 계측에 대한 일반 가이드. IEC, 제네바.
- IEC 61000-3-6:2008. 한계 - 왜곡된 설비를 MV에 연결하기 위한 방출 한계 평가, HV 및 EHV 전력 시스템. IEC, 제네바.
- 고조파 모델링 및 시뮬레이션에 관한 IEEE 태스크 포스. “상호 고조파: 이론 및 모델링.” 전력 공급에 IEEE 거래, 비행. 22, 아니. 4, PP. 2335-2348, 2007.
- J용, 첸 패, 첸 S. “배경 고조파 및 상호 고조파 모델링.” 전력 공급에 IEEE 거래, 비행. 26, 아니. 2, PP. 900-909, 2011.
기본 소스: Moyo RT 등. “여러 지속 가능한 소스와 전기 자동차의 병렬 작동으로 인한 상호 고조파의 시간 영역 집계.” 지속 가능성, MDPI, 17(3), 1214, 2월 2025. DOI: 10.3390/su17031214. 오픈 액세스 CC BY 4.0. 지원 참고자료: IEC 61000-2-1 (정의), IEC 61000-4-7 (측량), 고조파에 관한 IEEE 태스크 포스 (2007).
SVG 다이어그램 및 PQ 관점 (섹션 6) Denis Ruest의 원본 IPQDF 편집 콘텐츠입니다., 석사. (적용된), 물리 공학과. (퇴사.). IPQDF는 원본 연구의 저자임을 주장하지 않습니다..