In practice, harmonic distortion cannot be captured by one number. It varies with load level, generation output, network configuration, the switching status of capacitor banks and filters, and the operating mode of nonlinear equipment. A defensible harmonic statement therefore needs three things: a measurement method, a statistical index, and an objective to compare against.
Key idea
- Assessment is a chain: measurement → statistical index → comparison with an objective.
- Report individual harmonics and THD — never one alone.
- Aggregate 10/12-cycle spectra into 3-second and 10-minute values, then weekly 95% statistics.
- Know the objective: planning level < voltage characteristic / compatibility level.
Section 1
The three-step method
Whatever the project, harmonic voltage is assessed in the same three steps:
\[ \text{measurement}\;\longrightarrow\;\text{statistical index}\;\longrightarrow\;\text{comparison with objective} \]
The measurement defines how the harmonic spectrum is obtained. The statistical index defines how the measured values are processed over time. The objective defines the value the result is compared against. The same recorded waveform can lead to different conclusions depending on whether the assessment uses 3-second values, 10-minute values, weekly 95% values, maximum values, planning levels, voltage characteristics or compatibility levels — which is exactly why all three steps must be stated.
Section 2
The harmonic spectrum as the starting point
Every assessment begins with the harmonic spectrum of voltage or current, obtained by Fourier analysis over a defined window. A distorted voltage is the sum of a fundamental and a series of harmonics:
\[ v(t)=V_1\sin(\omega t+\phi_1)+\sum_{h=2}^{\infty}V_h\sin(h\omega t+\phi_h) \]
- \(V_1,\phi_1\)
- fundamental voltage amplitude and phase
- \(V_h,\phi_h\)
- amplitude and phase of the \(h^{\text{th}}\) harmonic
- \(h\)
- harmonic order \((2,3,4,\ldots)\)
- \(\omega\)
- fundamental angular frequency, \(2\pi f_0\)
The harmonic frequency is simply an integer multiple of the fundamental:
\[ f_h = h\,f_0 \]
- \(f_h\)
- frequency of the \(h^{\text{th}}\) harmonic
- \(h\)
- harmonic order
- \(f_0\)
- fundamental frequency (50 or 60 Hz)
so in a 50 Hz system the 5th harmonic is 250 Hz, the 7th is 350 Hz and the 11th is 550 Hz. Each harmonic is normally expressed as a percentage of the fundamental, and the total distortion is the RMS of all harmonics referred to the fundamental:
\[ U_h\,(\%)=\frac{U_h}{U_1}\times 100 \qquad\qquad \text{THD}_V=\frac{\sqrt{\displaystyle\sum_{h=2}^{H}U_h^{2}}}{U_1}\times 100 \]
- \(U_h\)
- RMS voltage at harmonic order \(h\)
- \(U_1\)
- fundamental RMS voltage
- \(H\)
- highest harmonic order considered
THD is valuable because it reduces the whole spectrum to one number, but it does not reveal which order is responsible. For design and compliance, the individual harmonic values are often as important as the THD — so a harmonic study should always present both the spectrum and the THD.
Section 3
Measurement windows and time aggregation
Harmonic distortion is not constant; it follows load variation, switching operations, converter operating point and network changes. Values are therefore aggregated over defined intervals rather than read as instantaneous numbers. The standard measurement window is synchronised to the actual system frequency:
\[ 10\ \text{cycles at }50\ \text{Hz}=200\ \text{ms} \qquad\qquad 12\ \text{cycles at }60\ \text{Hz}=200\ \text{ms} \]
These 200 ms spectra are then combined into progressively longer intervals, giving a consistent path from the instantaneous waveform to a long-term power-quality figure:
\[ 200\ \text{ms spectrum}\;\rightarrow\;3\ \text{s value}\;\rightarrow\;10\ \text{min value}\;\rightarrow\;\text{daily / weekly statistics} \]
This aggregation, defined by the power-quality measurement standards (IEC 61000-4-7 for the harmonic calculation and grouping, IEC 61000-4-30 for the measurement and reporting), is what makes results comparable between instruments, sites and studies.
Section 4
Very short-time and short-time indices
Two aggregated indices are used throughout harmonic assessment. The very short-time value is the RMS of an individual harmonic over 3 seconds; the short-time value is the RMS over 10 minutes:
\[ U_{h,vs}\;\;(3\ \text{s}) \qquad\qquad U_{h,sh}\;\;(10\ \text{min}) \]
- \(U_{h,vs}\)
- very short-time harmonic value (3-second RMS)
- \(U_{h,sh}\)
- short-time harmonic value (10-minute RMS)
The 3-second value is more sensitive to short-duration changes; the 10-minute value better represents the sustained level and underpins most voltage characteristics. Weekly statistics are then derived from the 10-minute values.
Table 1 — Harmonic indices and what each one captures.
| Index | Typical Interval | Practical Meaning |
|---|
| \(U_{h,vs}\) | 3 seconds | Captures short-term harmonic variation |
| \(U_{h,sh}\) | 10 minutes | Represents the sustained harmonic level |
| Weekly 95% value | One week | Used for long-term assessment and compliance |
| Maximum value | One week or agreed period | Worst case — but may include transient events |
Maximum values must be treated with care: a single maximum can be produced by a transient such as transformer energisation or capacitor switching, which is not representative of sustained performance.
Section 5
Why 95% values are used
Because distortion varies over time, a single maximum rarely represents normal operation. A 95% value is the level not exceeded for 95% of the assessment period. If the weekly 95% value of the 5th harmonic is 4%, then 95% of the relevant 10-minute values during that week were at or below 4%. This avoids over-reacting to a handful of unusual readings while still describing the sustained performance of the system. The core compliance check is therefore:
\[ U_{h,95\%}\;\le\;U_{h,\text{objective}} \]
- \(U_{h,95\%}\)
- statistical (95th-percentile) harmonic index
- \(U_{h,\text{objective}}\)
- applicable harmonic objective or limit
Section 6
Compatibility levels, voltage characteristics and planning levels
These three terms are routinely confused, yet they mean very different things. Getting them right is the single most important step in interpreting a harmonic objective.
Compatibility levels
Compatibility level = the disturbance level equipment should generally be able to tolerate.
Compatibility levels coordinate equipment emission against equipment immunity, mainly for LV and MV systems. They are system-coordination values for electromagnetic compatibility — not site-specific contractual limits applied at each customer measurement point.
Voltage characteristics
Voltage characteristic = the level normally expected at the customer’s supply terminals.
Voltage characteristics describe the quality of supply that a user can expect under normal conditions on public LV and MV networks. They describe the supply, but they do not represent the typical value at every site — the actual distortion at a given location may be much lower than the characteristic value.
Planning levels
Planning level = the operator’s internal target for managing total distortion.
Planning levels are internal objectives used by the system operator when connecting nonlinear or disturbing installations, and they matter most at MV, HV and EHV. They let the operator allocate harmonic emission between users so the combined effect of many installations stays acceptable. Because they carry a planning margin, they sit below the other two:
Planning level < compatibility level or voltage characteristic — the gap covers future connections, uncertainty, background distortion and the aggregation of many users.
Table 2 — The three reference levels at a glance.
| Reference Level | Mainly Used at | Purpose |
|---|
| Compatibility level | LV, MV | Coordinate equipment emission and immunity (EMC) |
| Voltage characteristic | LV, MV (public networks) | Describe the supply quality the user can expect |
| Planning level | MV, HV, EHV | Allocate emission and manage system-wide distortion |
Section 7
Why HV and EHV objectives are different
At LV and MV, harmonic objectives are largely about the immunity of end-use equipment connected directly to the network. At HV and EHV, end-use equipment is normally not connected directly, so the objectives are about coordination rather than immediate immunity. Transmission-level objectives are set to control:
Table 3 — What HV and EHV harmonic objectives are designed to control.
| Objective Controls | Why It Matters at HV / EHV |
|---|
| Disturbance transfer between voltage levels | Distortion propagates through transformers into large areas |
| Overall distortion on the transmission system | Many users share one network |
| Harmonic allocation between large users | No single connection should consume the whole margin |
| Future connection margin | Headroom must remain for later schemes |
This is why HV and EHV planning levels can be far lower than the levels that would cause immediate equipment malfunction. The purpose is not only to prevent immediate damage, but to maintain long-term harmonic coordination across the network.
Section 8
The assessment period
A minimum measurement period of one week is standard for harmonic voltage assessment, because it captures weekday and weekend variation, different operating patterns, load changes and switching conditions. Shorter periods miss important operating cases.
Table 4 — Assessment period and its limitation.
| Assessment Period | Limitation |
|---|
| A few minutes | May capture only one operating point |
| One day | May miss weekly operating variation |
| One week | Captures normal weekly variation — the practical minimum |
| Longer period | For contractual, seasonal or special studies |
For complex sites, seasonal operation, industrial cycles or variable renewable generation, longer periods may be required.
Section 9
Harmonic current, harmonic voltage and the frequency scan
Most objectives are written as voltage distortion, yet most harmonic sources inject current. The two are linked by the network impedance:
\[ V_h = Z_h\,I_h \]
- \(V_h\)
- harmonic voltage at order \(h\)
- \(I_h\)
- injected harmonic current at order \(h\)
- \(Z_h\)
- system harmonic impedance at order \(h\)
So voltage distortion depends on both the user’s emission and the network’s frequency response. A weak system, or one that resonates near a characteristic harmonic, can produce high voltage distortion from only moderate current injection. Connection studies must therefore check the network impedance against frequency — a frequency scan — not just the current magnitude. The driving-point impedance is:
\[ Z(h)=\frac{V_h}{I_h} \]
- \(Z(h)\)
- driving-point (system) harmonic impedance at order \(h\)
- \(V_h,I_h\)
- harmonic voltage and current at order \(h\)
If \(Z(h)\) peaks near a harmonic source frequency, the voltage distortion at that order is amplified. The elements that shape this response are:
Table 5 — Network elements and their harmonic relevance.
| Network Element | Harmonic Relevance |
|---|
| Capacitor banks | Can create parallel resonance |
| Cables | Add capacitance and shift resonance |
| Transformers | Add inductance and damping |
| Filters | Create tuned impedance paths |
| Generators | Often present a higher source impedance |
| Power-electronic converters | Inject characteristic harmonic currents |
A complete assessment therefore combines an emission calculation with the network frequency response — the two halves of \(V_h = Z_h I_h\).
Section 10
Treatment of maximum values
Maximum harmonic values can be useful, but they must be interpreted carefully because they may include switching transients, measurement artefacts or unusual short-duration conditions. Transformer energisation, for instance, can produce a short burst of distortion that is not representative of sustained performance. For this reason, planning and compliance work usually prefers 95% or 99% values over the absolute maximum.
Maximum values show the worst case; percentile values show the normal, sustained performance — the two answer different questions.
Section 11
Using harmonic objectives in design
The same objective is used for different purposes depending on the project stage — checking an existing site, defining the maximum emission for a new connection, setting the target residual distortion for a filter, or specifying the environment a piece of equipment must operate in.
Table 6 — How a harmonic objective is applied.
| Application | Purpose |
|---|
| Power-quality monitoring | Check actual harmonic voltage levels |
| Connection studies | Allocate harmonic emission limits |
| Filter design | Define the mitigation target |
| Equipment duty assessment | Check capacitor, transformer and cable stress |
| Compliance assessment | Compare measured or calculated values with limits |
| Planning studies | Maintain system-wide harmonic coordination |
Whatever the application, a harmonic statement should pin down four things:
- What is being assessed — voltage distortion, current emission or equipment duty.
- Where — the PCC, customer bus, an internal switchboard, or transformer / equipment terminals.
- Which index — \(U_{h,vs}\), \(U_{h,sh}\), 95%, 99%, maximum or THD.
- Which objective — a planning level, voltage characteristic, compatibility level or contractual limit.
The practical process runs straight down the chain of indices to the comparison:
\[ U_h(t)\;\rightarrow\;U_{h,vs}\;\rightarrow\;U_{h,sh}\;\rightarrow\;U_{h,95\%}\;\rightarrow\;\text{comparison with objective} \]
This is why a bare statement such as \(\text{THD}_V = 5\%\) is incomplete: it means little until it is clear whether the figure is a 10-minute value, a weekly 95% value, a maximum, a simulation result, or a measurement at one operating point.
Section 12
Key message
Harmonic indices turn time-varying measurements into values that can be compared against an objective: measure the spectrum over 10/12-cycle windows, aggregate into 3-second and 10-minute values, then evaluate weekly 95% (or maximum) statistics. The crucial distinction is between compatibility levels (EMC coordination), voltage characteristics (the supply quality a user can expect) and planning levels (the operator’s internal allocation target).
A complete harmonic statement = measurement method + assessment interval + statistical index + comparison objective + assessment location.
Key message
The physics never changes: \(V_h = Z_h I_h\). The harmonic source sets the injected current, the network impedance sets the resulting voltage, the chosen index decides how that voltage is represented statistically, and the chosen objective decides whether it is acceptable. State the measurement method, the assessment interval, the statistical index, the comparison objective and the assessment location — only then can two harmonic figures be compared fairly and technically.
