Harmonic study based on IEC standards | 国际电能质量论坛

This approach, fundamentally used in Europe, Asia, and many other regions, differs from the IEEE method in its normative structure, particularly concerning measurement techniques and spectral grouping .

1. IEC Normative Framework and Fundamental Principles

Unlike the IEEE approach, which focuses on limits at the point of connection, the IEC architecture is modular. It clearly distinguishes between measurement methods, equipment emission limits, and network analysis techniques.

1.1 The Structure of the IEC 61000 Series

For a comprehensive harmonic study, you must understand the interaction between several standards:

符合IEC 61000-4-7: This is the technical core of your study. It defines the measurement “toolbox”: how to instrument, sample, and process signals for harmonics and interharmonics up to 9 千赫 .
符合IEC 61000-4-30: This defines the performance classes of measurement instruments (Class A for advanced studies, guaranteeing the highest accuracy) .
符合IEC 61000-3-2 / -3-12: These set the harmonic current emission limits for individual equipment (≤16A and >16A的相, 分别) .
IEC TR 61000-3-6 / -3-7: Technical reports (non-normative but authoritative) providing principles for determining connection limits for distorting installations in MV, HV, and EHV networks.

1.2 Key Definitions according to IEC 61000-4-7

The IEC introduces specific concepts to handle the non-stationary nature of harmonics:

Spectral Component (Ci): The RMS value of the Discrete Fourier Transform (DFT) output for a given frequency (5 Hz resolution) .
Harmonic Sub-group (HG): To combat spectral leakage effects, the exact harmonic line is grouped with the two immediately adjacent spectral lines. This value is used for comparisons against limits .
Interharmonic Sub-group (IG): The grouping of spectral components located between consecutive harmonics .

Frequency axis — 5 Hz bins (10-cycle window, 50 Hz system)

HG h = 1 (50 赫兹) IG between h=1 and h=2 HG h = 2 (100 赫兹)

$$G_{sg,Ĥ} = \sqrt{\sum_{i=-1}^{+1} C^2_{n \cdot h + 我}}$$

Harmonic subgroup HG

$$G_{isg,Ĥ} = \sqrt{\sum_{i=2}^{N-1} C^2_{n \cdot h + 我}}$$

Interharmonic subgroup IG(N = 10, so i = 2..9, 8 bins)

$$G_{sg,h+1} = \sqrt{\sum_{i=-1}^{+1} C^2_{Ñ(h+1) + 我}}$$

Harmonic subgroup HG (h+1)

Harmonic subgroup (HG) — harmonic bin ± 1 neighbour Interharmonic subgroup (IG) - 8 bins between harmonics

图 1: Harmonic and Interharmonic Grouping according to IEC

Technical note: The harmonic sub-group of order n (HG_Ñ) is the square root of the sum of the squares of the harmonic line n and the two adjacent spectral lines. This method reduces uncertainty due to fundamental frequency fluctuations .

2. Data Acquisition and Modeling

The accuracy of an IEC-based study relies on strict adherence to measurement parameters and detailed source characterization.

2.1 Grid Data and Point of Connection

Grid Impedance: Unlike the American approach, which often uses the short-circuit ratio, the European approach (aligned with guides like the UK’s G5/4 or G5/5) often requires harmonic impedance. 理想的情况下, the network operator providesimpedance loci 作为频率的函数的 .
Background Distortion: On-site measurements according to符合IEC 61000-4-30 A级 (10-cycle window, precise synchronization) over a representative period (often one week) .

2.2 Non-Linear Load Data (Norton Model)

While IEC 61000-4-7 doesn’t prescribe a specific calculation model, industrial practice and newer standards (like IEC 61400-27-3 for renewables) require robust models :

Harmonic Current Source (Ih): The emission spectrum of the converter or load, measured in a laboratory according to IEC 61000-3-2.
Norton Impedance (Zh): The internal impedance seen from the load terminals. It is crucial for detecting resonance phenomena between the load and the network.

表 1: Measurement Parameters according to IEC 61000-4-30 Instrument Class

Parameter	A级 (Studies)	S级 (Surveys)
Measurement uncertainty (电压)	±0.1% (for U > 1% 您_nom)	±1.0%
Synchronization	Robust PLL with frequency tracking	May be less strict
Time aggregation	Very short (3小号) and short (10分钟) values	Identical

For a compliance study intended for a network operator, the use of Class A instruments is mandatory .

3. Step-by-Step Analysis Methodology according to IEC

3.1 Frequency Scan Analysis

Before calculating distortions, identify the resonance frequencies of the combined system (格 + 电缆 + transformers of the installation).

方法: Inject a current of 1 A at a variable frequency and calculate the resulting impedance.
目标: Identify parallel impedance peaks.
Specific IEC Risk: Interharmonic sub-groups (IG) can excite these resonances, even if integer harmonics are filtered.

Impedance |在| (Ž) Inductive ωL Capacitive 1/ωC Resonance (250 赫兹)

f_res = 250 赫兹 — 5th harmonic order 在_高峰 ≈ 38 Ž — parallel resonance Q ≈ 8 — quality factor

图 2: Frequency Scan and Resonance Risk

An impedance peak at 250 Hz would amplify the 5th harmonic. If the peak is at 275 赫兹, the interharmonic components around that frequency will be the problem.

3.2 Calculation of the Installation's Contribution (Incremental)

The IEC approach, adopted by guides like G5/5, distinguishes between your site'sincremental contribution 和total distortion.

Formula: Using the Norton model. $在_{Ĥ, inc} = \frac{在_{格} (Ĥ) \times 在_{load} (Ĥ)}{在_{格} (Ĥ) + 在_{load} (Ĥ)} \times 我_{Ĥ, 源}$ In practice, 软件 (PowerFactory, ETAP, EMTP) solves the system for each frequency.
Verification: This incremental voltage must not exceed a certain percentage of the background voltage (often 1% 至 2% depending on national guides).

3.3 Calculation of Harmonic Sub-groups

This is the most characteristic step of the IEC approach. You do not present the exact 250 Hz line, but the HG5 sub-group.

Perform the DFT on a10-cycle window (200 ms for 50 赫兹, ~166.6 ms for 60 赫兹) .
Obtain the spectral components C_i with a 5 Hz step.
Calculate the sub-group for harmonic order *n*:

$Ĥ ĝ_{Ñ} = \sqrt{\sum_{我 = - 1}^{+ 1} Ç_{我}^{2}}$

哪里 $Ç_{0}$ is the exact harmonic line, 和 $Ç_{- 1}$ and $Ç_{+ 1}$ are the adjacent lines .

3.4 Time Aggregation and Statistical Evaluation

符合IEC 61000-4-30 requires aggregation to smooth out variations :

Very short values (3 秒): Aggregation of the 15 windows of 200 毫秒.
Short values (10 分钟): Aggregation of the 200 values of 3s.
Comparison: Compliance is generally verified on the short values (10 分钟), ensuring that 95% of the values (或 99% depending on the contract) are below the planned limits.

4. Compliance and Study Report

4.1 Comparison with Compatibility and Planning Levels

IEC TR 61000-3-6 defines three distinct levels :

Emission Level: What your installation injects (the calculated HGs and IGs).
Planning Level: An internal limit for the network operator, stricter than the compatibility level, to maintain a safety margin.
Compatibility Level: The reference disturbance level (例如, THDv = 8%) at which 95% of equipment is expected to function correctly .

Your report must demonstrate that the sum of your contribution and the background distortion is below the planning level at the Point of Common Coupling (PCC).

4.2 Mitigation and Filtering

If limits are exceeded, the study must propose solutions:

Passive Filters: Tuned for the problematic harmonic sub-groups (HG).
有源滤波器: Inject currents to cancel harmonics in real-time.
Detuning: Modifying the impedance (例如, adding line reactors) to shift a resonance peak away from critical frequencies.

4.3 Content of the Final Report

An IEC-compliant report must include:

Single-line diagram of the installation and the upstream network.
Input data: Grid impedance, load current spectra (with proof of measurements or certifications according to IEC 61000-3-2).
Simulation results: Tables of HGs and IGs for normal and contingency operating conditions.
Statistical analysis: Cumulative probability curves of the calculated levels compared to the limits .

结论: Explicit statement of compliance or a plan for corrective actions.