전기 입구에서의 고조파 발생

소개

가변 주파수 드라이브 (VFD를) based on the 6-pulse rectifier topology are among the most widely deployed power conversion devices in industrial applications. Their inherent non-linear input characteristic makes them a significant source of harmonic distortion on electrical distribution systems. While the theoretical harmonic spectrum of a 6-pulse rectifier is well established and commonly described by the \(1/n\) amplitude model [1], practical measurements consistently reveal meaningful deviations from this ideal behaviour — deviations that carry real consequences for system design, filter sizing, and compliance with harmonic standards such as IEEE 519 [2] 및 IEC 61000-3-6 [3].

이 기사에서는 6펄스 VFD의 이론적이고 실제적인 고조파 스펙트럼을 비교 분석합니다., 고조파 차수 조사 3 ~을 통해 50 네 가지 부하 조건에 걸쳐 (25%, 50%, 75% 과 100% 정격 부하의). 고조파 크기, 위상각, 및 순서가 논의됩니다., 실제 시스템 동작을 고려하여 이상적인 전류 주입 모델의 한계를 조사합니다..

01 이론적 배경

6펄스 정류기는 기본 사이클당 6개의 전류 펄스를 생성하는 3상 전파 다이오드 또는 사이리스터 브리지로 구성됩니다.. 이상적인 조건에서 - 완벽하게 균형 잡힌 3상 공급, 완벽하게 부드러운 DC 전류를 생성하는 순수 유도성 DC 부하, 이상적인 스위칭 장치 - AC 라인 전류 파형은 푸리에 분해에 특정 고조파 차수만 포함된 준 구형파입니다. [1].

특성 고조파

These characteristic harmonics follow the relationship:

This yields harmonic orders 5, 7, 11, 13, 17, 19, 23, 25 등. The theoretical amplitude of each characteristic harmonic relative to the fundamental is given by:

어디에서 \(I_h\) is the RMS magnitude of the \(h\)-th harmonic current, \(I_1\) is the RMS magnitude of the fundamental current, 과 \(h\) is the harmonic order. This gives a 5th harmonic of 20% 기본의, a 7th of 14.3%, an 11th of 9.1%, 등 [1][4].

The total harmonic distortion under the ideal model is:

For a 6-pulse rectifier with purely inductive DC load this converges to approximately 28.6% [4].

Under this ideal model, all even harmonics and all triplen harmonics (3회, 9일, 15일, 21st…) are theoretically absent from the line currents. Triplen harmonics are zero-sequence — all three phases carry them with identical phase angles — and in a balanced three-phase system they cannot circulate in the line conductors. Even harmonics are suppressed by the half-wave symmetry of the rectifier waveform:

Harmonic sequence

The characteristic harmonics follow a defined sequence pattern with direct implications for rotating machinery and power system behaviour:

Negative-sequence harmonics rotate in opposition to the fundamental, producing reverse torque effects in induction motors and contributing to rotor heating. 포지티브 시퀀스 고조파는 기본과 동일한 방향으로 회전합니다. [4][5].

02 Practical Harmonic Spectra — Deviations from the Ideal Model

실제로, 이상형이 요구하는 조건 \(1/n\) 모델이 완전히 충족되지 않음. 최신 VFD의 이상적인 동작에서 가장 크게 벗어나는 것은 유도성 DC 부하 가정을 DC 버스의 대형 전해 커패시터로 대체한 것입니다.. 원활하게 연속적인 DC 전류를 끌어오는 것보다, 커패시터 공급 정류기는 순간 공급 전압이 DC 버스 전압을 초과하는 간격 동안에만 전류를 끌어옵니다., 좁은 생산, 고진폭 전류 펄스 [6].

그림 1 — 파형 비교

The Fourier decomposition of the peaked waveform reveals two systematic deviations from the \(1/n\) model. 에 lower harmonic orders (5th and 7th), practical magnitudes exceed or approach ideal values, driven by the narrow pulse shape concentrating energy in lower-frequency components. 에 higher harmonic orders (17th and above), the opposite dominates — AC-side inductance and finite pulse rise time attenuate these components more rapidly than \(1/n\) predicts. The crossover typically occurs between the 11th and 13th harmonic [4][6].

This behaviour is expressed by introducing a correction factor \(k_h\) to the ideal model:

어디에서 \(k_h > 1\) for lower-order harmonics, \(k_h < 1\) for higher-order harmonics, and \(k_h \approx 1\) near the 11th–13th. The value of \(k_h\) varies with load level, DC bus capacitance, and AC-side impedance [7].

Phase angle of harmonic currents also shifts with load, reflecting the changing commutation overlap angle \(\mu\) governed by:

어디에서 \(\omega\) is the angular frequency, \(L_s\) is the AC-side inductance per phase, \(I_d\) is the DC load current, 과 \(V_{LL}\) is the line-to-line supply voltage [5][8].

그림 2 — Harmonic spectrum: ideal vs practical at 100% 하중

표 1 — 고조파 크기 및 위상: 모든 부하 조건에서 h3 ~ h50

아래 표는 고조파 차수를 다루고 있습니다. 3 ~을 통해 50 4가지 부하 수준에서, 두 가지 크기를 모두 표시 (% 기본의) 및 위상각 (°) 각각에 대해. 특성 고조파가 강조 표시됩니다.. 값은 게시된 드라이브 측정값을 기반으로 한 실제 추정치입니다. 섹션을 참조하세요. 2 방법론에 대한.

표 2 — 이상적 vs 실용적 100% 하중: h3 ~ h50

이 표는 이상적인 모습을 비교한 것입니다. 1/N 실제 추정값에 대한 모델 진폭 100% 각 고조파 차수에 대한 부하, 시퀀스 분류 및 부호 있는 차이 포함. 실제 값이 이상적인 값을 초과하는 고조파는 ▲로 표시됩니다.; 이상보다 빨리 굴러가는 것들은 ▼로 표시되어 있습니다..

03 시스템 상호 작용 및 현재 소스 모델의 한계

전력 시스템의 고조파 분석은 전통적으로 전류 소스 주입 모델에 의존해 왔습니다., 각 비선형 부하는 공통 결합 지점에서 네트워크에 고정 고조파 전류를 주입하는 이상적인 전류원으로 표시됩니다. (PCC). 이 모델은 IEEE와 IEEE의 조화 평가 방법론을 뒷받침합니다. 519 [2] 및 IEC 61000-3-6 [3]. 그러나, the current source model is a significant simplification of the actual behaviour of a 6-pulse VFD.

그림 3 — Norton equivalent of a 6-pulse VFD on a distribution network

공급 임피던스 의존성

실제 전류원은 그것이 주입되는 네트워크의 임피던스와 무관합니다.. 6펄스 드라이브는 그렇지 않습니다.. A 3% 라인 리액터는 일반적으로 5차 고조파 전류를 대략적으로 감소시킵니다. 18% 에 12% 최대 부하 시 기본의 [6][7]. Norton의 동등한 공식은 이러한 종속성을 포착합니다.:

Resonance

커패시터 뱅크와 공급 인덕턴스 간의 병렬 공진은 특정 고조파 주파수에서 고임피던스 노드를 생성합니다.. 공진 주파수는:

어디에서 \(에스_{sc}\) 는 PCC의 단락 전력이고 \(Q_c\) is the reactive power of the capacitor bank [9].

Multiple drive interaction

Arithmetic addition of individual drive harmonic spectra consistently overestimates actual distortion at the PCC [2][3]. IEC 61000-3-6 addresses this through a summation law:

표 3 — IEC 61000-3-6 summation exponent α by harmonic order

In systems dominated by a single drive type, arithmetic summation (\(\alpha = 1\)) may be more representative than \(\alpha = 1.4\) for characteristic orders. Engineering judgement and where possible actual measurement remain essential [2][3].

04 Practical Implications and Mitigation

Transformer and cable sizing

Harmonic currents increase the RMS line current above the fundamental value:

Transformers supplying non-linear loads must be evaluated using the K-factor:

A typical 6-pulse drive installation without mitigation may present a K-factor of 4 에 8 depending on load level and system impedance [6][9].

Neutral conductor loading

Triplen harmonics are zero-sequence and circulate freely in the neutral conductor of four-wire systems. Installations combining VFDs with single-phase non-linear loads can produce significant neutral currents at the 3rd and 9th harmonic. The neutral conductor must be sized accordingly [9].

Motor and connected load considerations

Negative-sequence harmonics — the 5th, 11일, 17th and higher following the \(6k-1\) pattern — produce counter-rotating magnetic fields in the air gap, generating braking torque and elevated rotor temperature. Inverter-rated motors conforming to NEMA MG1 Part 31 or IEC 60034-25 incorporate design features that improve tolerance to harmonic content and are the recommended choice for all VFD applications. A detailed treatment of motor harmonic impedance, rotor loss mechanisms, and derating methodology is reserved for a subsequent article in this series.

Mitigation strategies

The tuning frequency of a passive filter is deliberately set below the target harmonic to avoid series resonance:

05 Measurement Considerations and Interpretation of Field Results

Instrument requirements

Harmonic measurement requires a power quality analyser capable of resolving individual harmonic components to at least the 50th order, implementing a synchronised DFT with a rectangular window of exactly 10 사이클 (200 ms at 50 Hz에서) as specified by IEC 61000-4-7 [10]. Rogowski coils are generally preferred for harmonic work above the 25th order due to their superior frequency response and absence of core saturation.

Measurement point selection

For compliance assessment against IEEE 519 [2] or IEC 61000-3-6 [3], measurement must be performed at the PCC as defined in those standards. Recording simultaneously at the drive input and the PCC provides direct information about the harmonic impedance of the intervening network — valuable for resonance risk assessment.

Operating condition during measurement

IEC 61000-3-6 recommends that harmonic assessment be based on the 95th percentile of measured values over a representative observation period — typically one week [3]. Where continuous monitoring is not practical, measurements should be taken at a minimum of three load points spanning the expected operating range.

상호 고조파

Modern VFDs may generate interharmonic currents — components at non-integer multiples of the fundamental — particularly during speed ramps and transient operating conditions. IEC 61000-4-7 defines the measurement methodology using sub-group analysis with a 200 ms window [10]. Their presence should be noted as they can contribute to flicker, ripple control interference, and sub-synchronous torque oscillations.

Emission studies and compliance with utility limits

Most utilities will not accept field measurements alone as the basis for a connection approval or compliance demonstration. A formal harmonic impact study, conducted in accordance with the utility’s accepted methodology and submitted prior to commissioning, is the standard requirement in the majority of jurisdictions [2][3]. The utility’s need to assess cumulative impact on all customers connected to the same network is fundamental to the IEC 61000-3-6 framework, which allocates emission limits based on the agreed power of the installation relative to the short-circuit capacity of the network [3].

결론

The ideal \(1/n\) amplitude model systematically misrepresents the harmonic spectrum of a modern capacitor-fed 6-pulse drive. Lower-order characteristic harmonics are more load-sensitive than the model predicts; higher-order harmonics roll off faster. The crossover occurs near the 11th–13th harmonic. THD varies from approximately 22% at full load to 45% or more at 25% load — a range that spans the boundary between compliant and non-compliant for many utility connection agreements.

The representation of a 6-pulse drive as an ideal harmonic current source breaks down in the presence of supply impedance variation, background voltage distortion, network resonance, and multi-drive interaction. The Norton equivalent provides a more faithful description, and the frequency dependence of both \(Z_h(H)\) 과 \(Z_\text{체계}(H)\) must be accounted for in any rigorous analysis.

For compliance studies submitted to electrical utilities, field measurement alone is unlikely to be accepted. A formal harmonic impact study is the standard requirement. High-fidelity simulation tools produce spectra significantly closer to measured field values, reducing the risk of unnecessary mitigation measures and over-designed filter solutions. The three-stage approach — theoretical screening, high-fidelity simulation, and post-commissioning measurement — provides a proportionate and technically defensible framework across the full project lifecycle.

참조

1. Mohan, N., Undeland, T.M., Robbins, W.P., 전력 전자: 컨버터, Applications and Design, 3rd ed., 존 와일리 & 자제, 2003.
2. IEEE 표준 519-2022, IEEE Standard for Harmonic Control in Electric Power Systems, IEEE, 2022.
3. IEC 61000-3-6:2008, Electromagnetic Compatibility — Limits — Assessment of Emission Limits for the Connection of Distorting Installations to MV, HV and EHV Power Systems, IEC, 2008.
4. Arrillaga, J., 왓슨, N.R., 전원 시스템 고조파, 2nd ed., 존 와일리 & 자제, 2003.
5. Boldea, I., Nasar, S.A., The Induction Machine Handbook, CRC 보도, 2002.
6. Skibinski, G., Kerkman, R., Schlegel, D., “EMI emissions of modern PWM AC drives,” IEEE Industry Applications Magazine, 비행. 5, 아니. 6, PP. 47–81, 1999.
7. Rockwell Automation, Harmonics and IEEE 519, Application Guide DRIVES-AP001A, 2013.
8. 모레이라, J.C., Lipo, T.A., “Modeling of saturated AC machines including air-gap flux harmonic components,” 산업 응용 프로그램에 IEEE 거래, 비행. 28, 아니. 2, PP. 343–349, 1992.
9. Dugan, R.C., McGranaghan, M.F., Santoso, S., Beaty, H.W., 전력 시스템 품질, 3rd ed., McGraw 언덕, 2012.
10. IEC 61000-4-7:2002+A1:2008, Electromagnetic Compatibility — Testing and Measurement Techniques — General Guide on Harmonics and Interharmonics Measurements and Instrumentation, IEC, 2008.
11. IEC 61000-4-30:2015, Electromagnetic Compatibility — Testing and Measurement Techniques — Power Quality Measurement Methods, IEC, 2015.