間高調波 — 標準的な高調波アナライザでは検出されない電力品質の乱れ
| 定義 | Frequency components that are NOT integer multiples of the fundamental — e.g. 75 ヘルツ, 130 ヘルツ, 267 Hz on a 50 Hz system |
| IECの定義 | 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” |
| 古典的なソース | Cycloconverters · Arc furnaces · AC/DC drives at variable speed · Induction furnaces · Pulsating loads not synchronised with the fundamental |
| New DER sources | 太陽光発電インバータ (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| ヘルツ. 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 |
| 測定の問題 | 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 |
| Regulatory status | 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 ヘルツ, 150 ヘルツ, 200 ヘルツ, 250 ヘルツ, and so on at 50 ヘルツ. 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番目の, 11番目の, 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 ヘルツ, 130 ヘルツ, 183 ヘルツ, 267 ヘルツ, 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.”
間高調波成分が基本周波数を下回る場合 — たとえば、, 35 Hzまたは 20 Hz on a 50 Hz システム — サブハーモニックと呼ばれることもあります. IEC 61000-2-1 とメモしています “分数高調波という用語には正式な定義はありませんが、電力システムの周波数よりも低い周波数成分に対する次高調波の特殊な場合にすぎません。. 準同期周波数成分という用語を使用することが好ましい。” 低調波は、回転機械の機械的共振、つまりタービン シャフトのねじり振動を引き起こす可能性があるため、特に問題になります。, たとえば、基本波よりも低い周波数で, 標準の振動減衰が機能するように設計されていない場合.
02 ソース — 伝統的なものと新しいもの
間高調波は、電力変換装置が主電源周波数に同期していない周波数でエネルギーを処理するたびに発生します。. 変換プロセスの出力周波数は主電源周波数を変調します。, 変換周波数と主電源周波数およびその高調波との差によって決定される周波数で、側波帯（高調波間成分）を生成します。.
| ソースの種類 | 生成メカニズム | 代表的な次数間高調波周波数 | 傾向 |
|---|---|---|---|
| Cycloconverters | Direct AC/AC frequency conversion produces output at arbitrary output frequency fアウト — interharmonics at |nf手 ± mfアウト| | 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 kHzの | 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 |
| 太陽光発電インバータ (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 |
| EVの充電器 | 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, コマーシャル |
| 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, 風力タービン, 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基本|. 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.
整流器負荷における DC バス電圧の変動
電源電圧の中間高調波成分により、ダイオード整流器 (可変周波数ドライブの DC バス コンデンサ) で見られるピーク電圧がサイクルごとに変動します。, UPSシステム, およびスイッチモード電源. これらの DC バス電圧の変動により、コンデンサの不均一な充電と放電が発生します。, DC バス上にリップルが発生し、ドライブの制御システムがこれを管理する必要がある. 高い間高調波振幅の場合, DC バスの変動により、ドライブの過電圧または不足電圧保護がトリガーされる可能性があり、供給品質の問題ではなく機器の故障として現れる予期せぬトリップが発生する可能性があります。.
グリッド振動と亜同期共振
準同期間高調波 — 以下のコンポーネント 50 Hz - シャフト発電機システムの自然な機械的共振周波数と一致する周波数で、大型タービン発電機シャフトのねじり共振を励起する可能性があります。. この亜同期共振 (SSR) このメカニズムは、直列補償送電線を介して接続された火力発電所で致命的なシャフト故障を引き起こしました. 最新の電力システムでは, HVDC コンバータの制御ループの相互作用により、相互接続された AC ネットワークを通じて伝播する同様の準同期発振が発生する可能性があります。HVDC 容量が拡大するにつれて懸念が増大しています。.
04 フィールドケース — PV, HOME, 同じ LV 回路上の電子レンジと
A 2025 MDPI Sustainability の論文は、特に現代の家庭用低電圧設備における次高調波発生の具体的な現場測定を提供します。, PVパネルを備えた回路, EV充電器, 電子レンジも同時稼働. この組み合わせは、DER の導入率が高い先進国における新たな標準的な住宅エネルギー環境を表しています。.
この研究の重要な発見は、これら 3 つのデバイスを同時に動作させると、確率的な影響が生じるということです。, 確率的な次高調波放射 — 決定論的なものではない, 古典的な非線形負荷の予測可能な調和パターン. 間高調波の周波数と振幅はサイクルごとにランダムに変化します, によって駆動される:
- 太陽光発電インバータ MPPT アルゴリズム — 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 ヘルツ. 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. のために 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 測定への挑戦
間高調波は、古典高調波では発生しない基本的な測定上の問題を引き起こします。: 標準測定法は整数倍の周波数成分を対象に設計されており、非整数成分を正しく特性評価することが体系的にできていません。.
IEC 61000-4-7 制限
IEC 61000-4-7 — 高調波アナライザの標準測定法 — は、 200 ms測定ウィンドウ (10 でのサイクル 50 ヘルツ) そして DFT を適用して次の高調波サブグループを生成します。 50 Hz間隔. 正確にスペクトル成分 75 ヘルツ (第 1 高調波と第 2 高調波の中間 50 Hzと 100 ヘルツ) 単一のビンに集中するのではなく、複数のビンに分散した DFT 出力を生成します。これは、離散的なノイズとしてではなく、高調波次数間の上昇したノイズとして現れます。 75 Hz成分. 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 ヘルツ. 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と 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.
| 測定方法 | 周波数分解能 | 間高調波検出 | 標準 |
|---|---|---|---|
| IEC 61000-4-7 DFT (200 MS) | 5 ヘルツ | 悪い — ビン全体に相互高調波が広がります, 高調波成分として誤認される | IEC 61000-4-7:2002+AMD1:2008 |
| 拡張ウィンドウDFT (1 の) | 1 ヘルツ | 定常的な次数間高調波には適していますが、時間とともに変化する高調波には適していません | 研究実践 |
| 補間FFT / ウィフト | サブヘルツ解像度 | 良好 — スペクトル漏れを低減します, より良い次間高調波振幅推定 | IEEE P519.1ワーキンググループ |
| 時間周波数法 (ウェーブレット, STFT) | 変数 | 時間変化に最適 — 時間の経過に伴う周波数の変化を捕捉します | 研究 – まだ標準化されていない |
| 確率モデル (PDF フィッティング) | 統計的 | 確率的ソースに最適 (PV, HOME) — 平均値だけでなく分布を特徴づける | MDPI Sustainability 2025 |
06 電力品質の観点
間高調波は、すべての標準フレームワークの間にある電力品質の乱れです。. 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 kHzの. 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, 風力タービン, EVの充電器, 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.
ユーティリティ PQ エンジニアリングの観点から, 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: 初め, extend the measurement window beyond 200 ms to improve frequency resolution; 第2, 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と 75.83 ヘルツ. 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.
参照
- Moyo RT et al. “Time-Domain Aggregation of Interharmonics from Parallel Operation of Multiple Sustainable Sources and Electric Vehicles.” Sustainability, 17(3), 1214, 2月 2025. DOI: 10.3390/su17031214. Open access CC BY 4.0.
- 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. IEC, ジュネーブ. (Definition of interharmonics.)
- 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. IEC, ジュネーブ.
- IEC 61000-3-6:2008. Limits — Assessment of emission limits for the connection of distorting installations to MV, HVおよびEHV電源システム. IEC, ジュネーブ.
- IEEE Task Force on Harmonics Modeling and Simulation. “次数間高調波: Theory and Modeling.” 電力供給上のIEEEトランザクション, フライト. 22, しない. 4, PP. 2335–2348, 2007.
- Yong J, Chen L, Chen S. “Modeling of background harmonics and interharmonics.” 電力供給上のIEEEトランザクション, フライト. 26, しない. 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, 2月 2025. DOI: 10.3390/su17031214. Open access CC BY 4.0. Supporting references: IEC 61000-2-1 (定義), IEC 61000-4-7 (測定), IEEE Task Force on Harmonics (2007).
SVG 図と PQ パースペクティブ (セクション 6) Denis Ruest によるオリジナルの IPQDF 編集コンテンツです, 修士号. (適用済み), P.Eng. (レット。). IPQDF は元の研究の著者であることを主張していません.