间谐波 - 标准谐波分析仪上不会显示的电能质量干扰
| 定义 | 不是基波整数倍的频率分量 - 例如. 75 赫兹, 130 赫兹, 267 赫兹上 50 赫兹系统 |
| IEC定义 | 符合IEC 61000-2-1: “工频电压和电流的谐波之间, 可以观察到更多频率，这些频率不是基波的整数” |
| 经典的来源 | 循环变流器 · 电弧炉 · 变速 AC/DC 驱动器 · 感应炉 · 与基波不同步的脉动负载 |
| 新的 DER 来源 | 光伏逆变器 (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 |
| 测量问题 | 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 |
| 监管状况 | 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: “工频电压和电流的谐波之间, 可以观察到更多频率，这些频率不是基波的整数. 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 赫兹上 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 |
|---|---|---|---|
| 环路转换器 | 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 |
| 光伏逆变器 (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, 风力涡轮机, 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 赫兹系统, 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, 不间断电源系统, 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 赫兹系统, 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 测量挑战
间谐波提出了经典谐波不会出现的基本测量问题: 标准测量方法是针对整数倍频率分量而设计的，并且系统地无法正确表征非整数分量.
国际电工委员会 61000-4-7 局限性
符合IEC 61000-4-7 ——谐波分析仪的标准测量方法——规定了 200 毫秒测量窗口 (10 周期在 50 赫兹) 并应用 DFT 生成谐波子组 50 赫兹间隔. 精确的光谱分量 75 赫兹 (1 次和 2 次谐波之间的中间位置 50 赫兹和 100 赫兹) 生成的 DFT 输出分布在多个箱中，而不是集中在单个箱中 - 它表现为谐波阶次之间升高的噪声，而不是离散的噪声 75 Hz分量. 然后，该标准将此间能量分配给最近的谐波子组, 可能会夸大谐波幅度并完全掩盖间谐波.
频率分辨率问题
一 200 ms 测量窗口提供的频率分辨率为 1/0.2 = 5 赫兹. 这意味着间谐波分量比 5 无法解析 Hz 之外的频率 - 它们显示为单个加宽的光谱特征. 对于间谐波 52 赫兹和 54 Hz——在不同的 DER 设备中都是合理的——它们在一个问题中是无法解决的 200 窗口女士. 解决这些问题需要更长的测量窗口: 1 第二个为 1 赫兹分辨率, 10 秒为 0.1 赫兹分辨率. 但较长的窗口会增加测量过程中间谐波频率发生变化的可能性，这是 VFD 产生的间谐波的常见问题，其频率随电机速度连续变化.
| 测量方法 | 频率分辨率 | 间谐波检测 | 标准 |
|---|---|---|---|
| 符合IEC 61000-4-7 密度泛函理论 (200 毫秒) | 5 赫兹 | 差 - 间谐波分布在各个箱中, 错误识别为谐波含量 | 符合IEC 61000-4-7:2002+AMD1:2008 |
| 扩展窗口DFT (1 小号) | 1 赫兹 | 适用于平稳间谐波 - 不适用于时变 | 研究实践 |
| 插值快速傅里叶变换 / 无线快速傅里叶变换 | 亚赫兹分辨率 | 好——减少频谱泄漏, 更好的间谐波幅度估计 | IEEE P519.1 工作组 |
| 时频法 (小波, 短时傅里叶变换) | 多变的 | 最适合时变 — 捕获频率随时间的演变 | 研究——尚未标准化 |
| 概率模型 (PDF拟合) | 统计 | 最适合随机源 (光伏, 首页) - 特征分布不仅仅是均值 | MDPI 可持续发展 2025 |
06 电能质量视角
间谐波是介于所有标准框架之间的电能质量干扰. 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, 风力涡轮机, 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, 间谐波是标准分析最可能遗漏的解释.
从公用事业 PQ 工程角度来看, 当标准谐波分析无法解释观察到的问题时识别间谐波的实用协议 - 没有明显来源的闪烁, 不明原因的 VFD 跳闸, 谐波次数之间的噪声升高 — 是: 第一的, 扩展测量窗口 200 ms 提高频率分辨率; 第二, 查看谐波阶次之间的完整频谱，而不仅仅是谐波子组; 第三, 将间谐波频率与所连接设备的已知机械或开关频率相关联. 一台 VFD 运行电机 1,450 4 极电机上的转差频率为 |50 - 1450/60| = |50 - 24.17| = 25.83 Hz — 和间谐波 50 ± 25.83 = 24.17 赫兹和 75.83 赫兹. 寻找光谱分量 75.83 电源电压 Hz 确认 VFD 是高置信度的电源. 这种系统的方法改变了一个无法解释的问题 “测量噪声” 观察确诊, 可归因的 PQ 问题.
参考文献
- 莫约 RT 等人. “多个可持续电源和电动汽车并联运行产生的间谐波的时域聚合。” 可持续发展, 17(3), 1214, 二月 2025. DOI: 10.3390/苏17031214. 开放获取 CC BY 4.0.
- 符合IEC 61000-2-1:1990. 电磁兼容性 - 环境描述 - 公共供电系统中低频传导骚扰和信号的电磁环境. 符合IEC, 日内瓦. (间谐波的定义。)
- 符合IEC 61000-4-7:2002+AMD1:2008. 测试和测量技术 - 电源系统及其连接设备的谐波和间谐波测量和仪器的一般指南. 符合IEC, 日内瓦.
- 符合IEC 61000-3-6:2008. 限值 — 扭曲装置与中压连接的排放限值评估, 高压和超高压电力系统. 符合IEC, 日内瓦.
- IEEE 谐波建模与仿真工作组. “间谐波: 理论和建模。” IEEE电力输送交易, 飞行. 22, 不. 4, PP. 2335–2348, 2007.
- Yong J, 陈琳, 陈生. “背景谐波和间谐波的建模。” IEEE电力输送交易, 飞行. 26, 不. 2, PP. 900–909, 2011.
主要来源: 莫约 RT 等人. “多个可持续电源和电动汽车并联运行产生的间谐波的时域聚合。” 可持续发展, MDPI, 17(3), 1214, 二月 2025. DOI: 10.3390/苏17031214. 开放获取 CC BY 4.0. 支持参考文献: 符合IEC 61000-2-1 (定义), 符合IEC 61000-4-7 (测量), IEEE 谐波工作组 (2007).
SVG 图和 PQ 透视图 (部分 6) 是 Denis Ruest 的原创 IPQDF 编辑内容, 硕士. (应用), P.Eng. (ret。). IPQDF 不声称原始研究的作者.