Variable-speed drives are widely used to control motor speed, torque, process output and energy consumption — pumps, fans, compressors, conveyors, mills, crushers, rolling mills, mine winders and large synchronous motor drives. From a harmonic-study perspective they matter because they are power-electronic loads: they can inject harmonic currents into the network, interact with background harmonic voltage distortion, and modify the harmonic impedance seen from the point of connection.
The governing relationship is unchanged, and a drive can affect both sides of it — it injects harmonic current, and its input filters, rectifier, converter control and transformer also affect the harmonic impedance. A realistic drive model should therefore answer not only what harmonic current does the drive inject? but also what harmonic impedance does the drive present to the network?
Section 1
Why drive modelling matters — and is not universal
Variable-speed drives should not be modelled using one generic harmonic spectrum. A small diode rectifier drive, a large AFE drive, a PWM current-source drive, an LCI drive and a cycloconverter can have very different harmonic behaviour. The correct model depends on the front-end topology, switching method, motor operating point, filters, PFC capacitors, background distortion and manufacturer data.
The harmonic voltage at a bus is governed by the same relationship as for any component, and a drive acts on both the injection and the impedance:
\[ V_h=Z_h\,I_h \]
- \(V_h\)
- harmonic voltage at order \(h\)
- \(I_h\)
- harmonic current injected by the drive at order \(h\)
- \(Z_h\)
- network harmonic impedance at order \(h\)
Drives are not all the same. Their harmonic behaviour depends on the topology, semiconductor technology, converter pulse number, front-end arrangement, DC-link design, transformer winding configuration, passive filters, control strategy and operating point. A small LV pump drive with a six-pulse diode rectifier behaves very differently from a large medium-voltage active-front-end drive, a current-source inverter, a load-commutated inverter or a cycloconverter. So VFD harmonic behaviour is topology-dependent, and one generic model is not suitable for all VFD studies — the study engineer should first identify the drive type before selecting the harmonic model.
Section 2
Main drive types and responsibility
For harmonic studies, drives can be grouped into five broad categories — diode rectifier front-end drives, PWM active-front-end drives, PWM current-source inverter drives, load-commutated inverter drives and cycloconverter drives. Each has a different harmonic source mechanism and modelling requirement.
Table 1 — Drive types, harmonic behaviour and modelling approach.
| Drive Type | Main Harmonic Behaviour | Typical Modelling Approach |
|---|
| Diode front-end VSI drive | Characteristic rectifier current harmonics | Current source for screening; enhanced model for detail |
| PWM active-front-end drive | Lower low-order harmonics; control & switching sidebands | Norton or Thévenin equivalent |
| PWM current-source inverter drive | Harmonics from low switching frequency and control | Norton or Thévenin equivalent |
| Load-commutated inverter drive | Similar to line-commutated HVDC; large low-order harmonics | Norton/Thévenin equivalent with filters |
| Cycloconverter drive | Complex harmonic and interharmonic spectrum | Manufacturer-specific Norton/Thévenin equivalent |
The more complex and higher-power the drive, the more important it is to use manufacturer-provided harmonic data. For small and standard drives, a simplified current-source model may be acceptable for early screening; for large industrial, medium-voltage, active-front-end, current-source, LCI and cycloconverter drives, the model should normally be provided by the manufacturer — including the harmonic source spectrum, operational harmonic impedance, load and control-mode dependency, filter and power-factor-correction data, transformer data, frequency range of validity and model limitations. The manufacturer provides the converter-specific source and impedance data; the study engineer performs the network harmonic assessment using it.
Section 3
Classical diode rectifier front-end drives
A common LV drive uses a diode rectifier front end, a DC-link capacitor and a PWM voltage-source inverter feeding the motor. The grid-side part is normally an uncontrolled rectifier that draws non-sinusoidal current, because the DC-link capacitor charges only during parts of the AC waveform. For a six-pulse rectifier the characteristic harmonic orders are:
\[ h=6n\pm1\,,\quad n=1,2,3,\ldots \]
- \(h\)
- harmonic order
- \(n\)
- positive integer
For example, \(n=1\) gives the 5th and 7th harmonics, and \(n=2\) gives the 11th and 13th harmonics.
More generally, for a \(p\)-pulse rectifier:
\[ h=kp\pm1\,,\quad k=1,2,3,\ldots \]
- \(p\)
- converter pulse number
- \(k\)
- positive integer
- \(h\)
- harmonic order
Under ideal conditions the magnitude may be approximated by:
\[ \frac{I_h}{I_1}\approx\frac{1}{h} \]
- \(I_h\)
- RMS harmonic current at order \(h\)
- \(I_1\)
- RMS fundamental-frequency current
- \(h\)
- harmonic order
This is only an ideal approximation — it should not be used as final manufacturer data, because real drive spectra depend on source impedance, transformer impedance, DC-link capacitance, loading, input reactor, control mode and filter design. Here \(I_1\) means fundamental-frequency current, not positive-sequence current; where sequence notation is used elsewhere, write \(I_{fund}\) for the fundamental to avoid confusion.
So six-pulse diode drives usually produce strong 5th and 7th harmonics, but the actual spectrum must not be assumed ideal without checking the drive design and supply impedance.
Section 4
Modelling diode rectifier drives
For many frequency-domain penetration studies, a diode rectifier drive may be represented as an ideal harmonic current source, \(I_h\angle\phi_h\) at each relevant order. This is simple and may be adequate when the drive is small compared with the system fault level or when the study is only for screening. Its limitation is that it does not capture the interaction between drive input current and the supply-point harmonic voltage, nor changes in conduction mode, background distortion or detailed rectifier operation. For more accurate studies, a harmonic matrix model, a Norton/Thévenin equivalent or a time-domain model may be required — in short, an ideal current source for screening, a Norton/Thévenin or detailed model for interaction.
\[ I_h=\big|I_h\big|\angle\phi_h \]
- \(I_h\)
- harmonic current phasor at order \(h\)
- \(\big|I_h\big|\)
- RMS magnitude of the harmonic current
- \(\phi_h\)
- phase angle of the harmonic current at order \(h\)
The phase angle is important because harmonic currents from several drives may add or cancel depending on their relative phase.
When is an ideal current source acceptable?
An ideal harmonic current source may be acceptable for early screening when the drive is small compared with the system fault level, the drive is a standard diode front-end type, and background distortion or supply-impedance interaction is not critical. It should not normally be used for final compliance studies, large drives, AFE drives, PWM CSI drives, LCI drives, cycloconverters, weak networks, or cases where a harmonic resonance is close to a characteristic harmonic.
Supply inductance and load level
The spectrum of a diode drive is strongly affected by the AC input inductance — from the upstream network, transformer leakage, line reactors, the drive input choke and cable impedance. Input inductance smooths the current waveform and changes the harmonic magnitudes. Load level also matters: at light load the rectifier may enter discontinuous conduction mode, giving a different spectrum from full load. So the maximum harmonic percentage may not occur at maximum load, while the maximum harmonic current in amperes often occurs near high load — the spectrum should be assessed over relevant loading levels.
Voltage unbalance and non-characteristic harmonics
Supply voltage unbalance can significantly affect diode-drive harmonics. Under balanced ideal conditions a six-pulse rectifier mainly produces the characteristic \(6n\pm1\) orders, but with an unbalanced supply non-characteristic harmonics — including triplen orders 3rd, 9th, 15th — can appear. Where the supply is unbalanced or triplen limits are important, a simple balanced current-source model may be insufficient.
Section 6
Active-front-end drives
An active-front-end (AFE) drive uses a controlled PWM rectifier (usually IGBT-based) instead of a diode rectifier, so it can control the input current waveform. The advantages include reduced low-order current harmonics, near-unity power factor, controlled DC-link voltage, bidirectional power flow and regenerative braking. Under ideal balanced conditions an AFE drive may draw nearly sinusoidal current, with current THD much lower than a diode drive — but it cannot be ignored in harmonic studies. It has a control system, a PWM carrier frequency, filters and converter impedance, and may interact with background harmonic voltage and grid impedance. So an AFE drive has lower low-order harmonics, but still requires impedance- and control-aware modelling for detailed studies.
An AFE drive uses a controlled grid-side converter. Its harmonic current is not determined only by a diode conduction pattern; it also depends on switching frequency, control loops, the PLL, the input reactor, filter design, operating point and background voltage distortion. A simple fixed harmonic current spectrum may therefore miss important interaction effects.
The PLL, or Phase-Locked Loop, is the control function that estimates the grid-voltage phase angle. If the grid voltage is distorted or weak, the PLL can influence the converter current response and harmonic impedance.
Modelling active-front-end drives
An ideal current source is usually not sufficient for AFE drives, because the input current depends on the converter control response and the background harmonic voltage at each frequency. The preferred frequency-domain representation is a Norton equivalent (harmonic current source + operational admittance) or a Thévenin equivalent (harmonic voltage source + operational impedance), including the converter control response, the input reactor, any passive filters, the PCC background-distortion interaction, and PWM carrier and sideband behaviour where relevant. The source and impedance should normally come from the manufacturer or from controlled measurements — an AFE drive is best represented by a manufacturer-provided Norton/Thévenin model.
PWM carrier frequency and sidebands
PWM converters produce harmonic components related to the carrier frequency and its sidebands. If the switching frequency is high, the sidebands may lie above the range normally assessed; but in some lower-cost or higher-power drives the switching frequency is low enough that sidebands fall within the studied range — and if the carrier is close to a lower harmonic order, the sidebands may need to be included. So do not assume PWM harmonics are always outside the study range; choose the frequency range based on the drive technology and switching frequency.
Section 8
Load-commutated inverter drives
A load-commutated inverter (LCI) drive is a current-source drive using thyristor converters, typically for very large (multi-megawatt) motors. Its topology resembles a smaller line-commutated HVDC system: a thyristor rectifier, a large DC smoothing reactor, a load-commutated inverter, a large synchronous or induction motor, and harmonic filters and power-factor correction. LCI drives can produce significant low-order harmonic currents and may need substantial filtering and reactive compensation. So an LCI drive has similar harmonic behaviour to line-commutated converter systems.
In plain terms, an LCI drive is typically used for large synchronous motors, and its converter operation depends on motor speed, load angle, the commutation process, supply impedance and filtering. At low speed, during starting, or in weak-grid operation, the harmonic behaviour can differ from normal rated operation — so LCI drives should be assessed over the relevant operating states, not only at rated speed.
Modelling LCI drives
An LCI drive should normally be represented by a Norton or Thévenin equivalent at each harmonic frequency of interest. Because the front end is a controlled rectifier, the spectrum is similar to a line-commutated converter of the same pulse order. The model should include the harmonic current source, operational impedance, power-factor-correction capacitors, harmonic filters, transformer configuration, loading level and firing-angle dependency; the manufacturer should provide the harmonic injections and operational impedance over the operating range. If that is not possible, in-situ measurements at different loading levels — including with the drive out of service to identify background distortion — should be considered. Large LCI drives require manufacturer or measured harmonic data, because simplified assumptions may not be adequate for filter design or compliance.
Section 9
Cycloconverter drives
An interharmonic is a frequency component that is not an integer multiple of the fundamental frequency — for example, 175 Hz in a 50 Hz system. Cycloconverters and some controlled drives can produce interharmonics because their output frequency, switching pattern and control behaviour are not locked to integer multiples of the supply frequency.
A cycloconverter directly converts AC at one frequency to AC at a lower frequency without a DC link, and is used for very large low-speed drives such as mills, mine winders, rolling mills and pumped-storage applications. Its harmonic behaviour is more complex than other drive types because the input current spectrum includes both harmonics and interharmonics. The input current frequencies may be expressed conceptually as:
\[ (n p \pm 1)\,f_i \pm m\,f_o \]
- \(f_i,\ f_o\)
- input and output frequencies
- \(p\)
- pulse number
- \(m,\ n\)
- integers
Because the output frequency changes with motor speed, the spectrum changes with speed. So a cycloconverter is a complex harmonic and interharmonic source, and a manufacturer-specific model is normally essential.
Modelling cycloconverter drives
A cycloconverter should normally be represented by a Norton or Thévenin equivalent at the frequencies of interest, including the harmonic and interharmonic source spectrum, operational impedance, filter and PFC data, speed or output-frequency dependency, operating mode and loading level. Because the spectrum is complex and application-specific, it should normally be provided by the specialist manufacturer; if not, site measurements or detailed time-domain simulation may be needed. Cycloconverter harmonic assessment should not be based on generic six-pulse assumptions, because the spectrum can include significant high-order harmonics and interharmonics.
Important warning — cycloconverters
Do not use the six-pulse formula \(h=6n\pm1\) for cycloconverters unless it has been specifically justified. Cycloconverter spectra are application-specific and can include non-characteristic harmonics and interharmonics. Manufacturer data, measurement or time-domain simulation is normally required.
Section 10
Filters, PFC and background distortion
Many large drives include harmonic filters, power-factor-correction capacitors or input reactors, and these must be included in the harmonic model. They affect harmonic current absorption, network resonance, drive terminal distortion, background harmonic amplification and filter component duty. A drive harmonic source without its associated filters is usually incomplete, and filters modelled without the drive source may not represent the operating condition correctly — so the drive source and drive filters should be modelled together, unless the study objective explicitly requires them separated.
A filter connected to a drive does not operate in isolation. Its harmonic current, duty and effectiveness depend on the drive source spectrum and the network impedance. Likewise, the drive emission seen by the network depends on whether the input reactor, filter or PFC capacitor is in service. The study should therefore state exactly which drive-associated components are included in the model.
Filter / PFC checklist
For each large drive, state whether the model includes:
- input line reactor;
- DC-link reactor;
- converter transformer;
- harmonic filter branches;
- PFC capacitor bank;
- EMC/RFI filter, if relevant to the frequency range;
- motor-side filter, if relevant;
- drive bypass mode;
- filter outage cases;
- capacitor/reactor tolerances;
- filter thermal duty.
Background harmonic distortion
Background distortion can affect drive harmonic emission, especially for controlled converters — AFE drives, PWM CSI drives, cycloconverters and large thyristor drives — which may respond to background harmonic voltages through their control system or commutation process. The simplified interaction is background voltage distortion → drive response → drive current, so the drive current spectrum may change when the supply waveform is distorted. The message: drive harmonic emission is not always independent of the network, and a constant current-source model cannot capture this interaction.
In practice, for controlled drives the harmonic current spectrum may change when the supply voltage is distorted. So if background distortion is high or close to compliance limits, the study should not rely only on a fixed current-source spectrum unless the manufacturer confirms that this is valid.
Section 11
Norton and Thévenin equivalents
For detailed VFD studies, Norton or Thévenin equivalents are generally preferred. The Norton equivalent is a harmonic current source plus a harmonic admittance; the Thévenin equivalent is a harmonic voltage source plus a harmonic impedance. The two are interchangeable if defined consistently.
\[ I_h=I_{N,h}-Y_{N,h}\,V_h \]
- \(I_h\)
- harmonic current exchanged with the network at order \(h\)
- \(I_{N,h}\)
- Norton harmonic current source at order \(h\)
- \(Y_{N,h}\)
- Norton harmonic admittance at order \(h\)
- \(V_h\)
- terminal harmonic voltage at order \(h\)
\[ V_h=E_{Th,h}-Z_{Th,h}\,I_h \]
- \(V_h\)
- terminal harmonic voltage at order \(h\)
- \(E_{Th,h}\)
- Thévenin harmonic voltage source at order \(h\)
- \(Z_{Th,h}\)
- Thévenin harmonic impedance at order \(h\)
- \(I_h\)
- harmonic current exchanged with the network at order \(h\)
These models are better than a fixed current source because they represent both emission and network interaction, whereas a constant current source represents only emission and not converter impedance.
Table 2 — What each drive model represents.
| Model | Represents Emission | Represents Impedance Interaction | Typical Use |
|---|
| Ideal current source | Yes | No | Screening for simple rectifiers |
| Current source with filters | Partly | Partly | Improved but still incomplete |
| Norton / Thévenin equivalent | Yes | Yes | Preferred for detailed studies |
| Time-domain model | Yes | Yes | Detailed design and validation |
Use Norton/Thévenin models where converter–grid interaction matters.
Table 3 — Recommended VFD harmonic model by drive type.
| Drive Type | Typical Preliminary Model | Preferred Detailed Model |
|---|
| Small six-pulse diode drive | Harmonic current source | Norton equivalent or measured spectrum if significant |
| Large diode rectifier drive | Harmonic current source with reactor/filter data | Norton equivalent including input impedance |
| AFE drive | Not recommended as a fixed current source only | Thévenin/Norton model with control-dependent impedance |
| PWM CSI drive | Manufacturer spectrum | Norton/Thévenin model with filter and impedance |
| LCI drive | Manufacturer harmonic source model | Detailed vendor model or time-domain model |
| Cycloconverter | Not suitable for generic six-pulse assumptions | Vendor model, measurement or time-domain simulation |
Operating-point dependency
Drive harmonic behaviour changes with operating point — motor load, speed, torque, rectifier firing angle, PWM modulation index, switching frequency, DC-link voltage, control mode and supply voltage unbalance. The worst case may be different for different orders: the highest 5th-harmonic current may occur at one load level and the highest 11th at another. So one operating point may not represent the drive harmonic envelope, and for large drives the manufacturer should provide a harmonic envelope or operating-point-dependent look-up tables.
Section 12
Measurement, time-domain models and aggregation
Where manufacturer models are not available, measurements may support model development — voltage harmonics, current harmonics, load level, drive speed, operating mode, filter status and background distortion. For meaningful source separation, measurements should ideally be taken with the drive both in service and out of service, which helps estimate the natural background distortion and the additional drive contribution. The limitation: measured current includes both drive behaviour and network influence, so measurement-based models must be interpreted carefully.
Time-domain modelling
Time-domain simulation gives a more detailed representation — rectifier switching, PWM control, DC-link dynamics, the motor model, background distortion, voltage unbalance and filter dynamics. But it needs many parameters and can be computationally expensive, so it is normally reserved for detailed manufacturer studies, special industrial drive assessments, model validation, harmonic-instability investigation and filter-design verification. For routine network penetration studies, a validated Norton or Thévenin equivalent is usually more practical.
Aggregation of multiple drives
When many drives are connected in parallel, the harmonic currents should not automatically be added arithmetically. Diversity of loading, phase angles, transformer phase shifts, input reactors and different drive types may reduce or change the combined spectrum. The report should state whether drive aggregation uses arithmetic summation, phasor summation, statistical summation or manufacturer diversity factors. For the same order the total is, in principle, a phasor sum:
\[ I_{h,total}=\sum_{m=1}^{M} I_{h,m} \]
- \(I_{h,total}\)
- total harmonic current at order \(h\)
- \(I_{h,m}\)
- harmonic current contribution from drive \(m\) at order \(h\)
- \(M\)
- number of drives or drive groups
If phase angles are unknown, conservative assumptions may be used, but direct arithmetic summation of all drives can be overly conservative — especially with many small drives at random operating conditions. Aggregation should consider drive type, operating diversity, harmonic phase angles, load-level diversity, background distortion and common filters or transformers. For large drives, each unit should normally be represented individually or by a validated aggregate model.
Section 14
Reporting and summary
A harmonic study report should clearly state how variable-speed drives were represented. A weak statement — “VFDs were included as harmonic sources” — gives the impression that all drives were treated with one simplified model.
Examples of a clear modelling statement
“Six-pulse diode front-end drives were represented as harmonic current sources for screening, with associated line reactors, filters and power-factor-correction capacitors represented separately.”
“Active-front-end and current-source drives were represented using manufacturer-provided Norton or Thévenin equivalents, including harmonic source spectra and operational impedance over the relevant frequency range.”
“Large thyristor-based LCI and cycloconverter drives were represented using manufacturer-provided harmonic source and impedance data, including operating-point dependency, filter configuration and background-distortion assumptions.”
Common modelling mistakes
- Using one generic VFD harmonic spectrum for all drive types.
- Applying six-pulse harmonic assumptions to AFE drives, LCI drives or cycloconverters.
- Using \(I_h/I_1\approx 1/h\) as final data instead of for screening only.
- Ignoring phase angles.
- Ignoring input reactors, drive transformers, filters and PFC capacitors.
- Modelling drive filters without the drive source.
- Ignoring background-distortion interaction.
- Ignoring low-load or low-speed operating cases.
- Adding many drive spectra arithmetically without justification.
- Using a fixed current-source model where Norton/Thévenin interaction is required.
To summarise: variable-speed drives are important harmonic sources whose behaviour depends on topology, semiconductor technology, front-end type, transformer configuration, filters, control strategy, loading and background distortion. For a simple six-pulse diode drive the characteristic harmonics are \(h=6n\pm1\), and for a general \(p\)-pulse drive \(h=kp\pm1\). A simple ideal current source may be acceptable for preliminary screening of standard diode front-end drives, but not for controlled converter drives or where network interaction matters. For AFE, PWM CSI, LCI and cycloconverter drives, the preferred model is a Norton or Thévenin equivalent — a harmonic source plus a harmonic impedance — which represents both emission and interaction with grid impedance and background distortion. Associated line reactors, converter transformers, harmonic filters and PFC capacitors must be included explicitly or in the equivalent.
In short: variable-speed drive harmonic modelling should be based on drive topology. Small diode rectifier drives may be screened using harmonic current-source spectra, but large drives, controlled front ends, PWM CSI drives, LCI drives and cycloconverters normally require manufacturer-supported Norton or Thévenin models, measured spectra or detailed simulation. A clear study should then state:
- the drive type and pulse number;
- the source representation and harmonic impedance;
- the input reactor, transformer, filter and PFC data;
- the operating points studied;
- the background-distortion treatment;
- the aggregation method;
- the model limitations.
Without these details, the calculated harmonic emission and resonance interaction may not be reliable.
Key message
Simple rectifier drives may be screened with harmonic current sources, but large or controlled drives require manufacturer-supported harmonic source and impedance models. A robust VFD harmonic study should state the drive type, front-end topology, source representation, harmonic impedance, filter/PFC representation, operating points, background distortion, manufacturer-data assumptions and model limitations — only then can the harmonic impact of variable-speed drives be assessed correctly. This is the eleventh and final instalment of the series on harmonic studies in power systems — which has now travelled from the choice of study domain, through the modelling of every major network component and source, to the converter-based and drive equipment that increasingly shapes harmonic performance.
