Harmonic Studies & Modelling

Converter-Based Generation and HVDC Harmonic Models

For converter-based generation and HVDC, the harmonic model is normally manufacturer-dependent. PV inverters, wind turbines, battery converters, STATCOMs and HVDC stations are controlled systems whose harmonic behaviour depends on topology, switching, filters, control loops, operating point and grid impedance — details that are proprietary and not available to a consultant in enough depth to rebuild reliably. This page is not about deriving converter models from first principles; it explains what data the manufacturer should provide, why a Norton or Thévenin equivalent (source plus impedance) is needed rather than an ideal current source, and how the study engineer should request, verify and apply that model to assess the network impact.

Reading time ≈ 14 min · Part Ten of the series

For converter-based generation and HVDC converter stations, the harmonic model is normally manufacturer-dependent. The purpose of this discussion is therefore not to imply that the study engineer should create detailed converter models from first principles — it is to explain what information is required, why it is required, and how it should be used in a harmonic study.

This applies especially to wind turbine generators, PV inverters, battery energy storage converters, STATCOMs, HVDC converters and other power-electronic converter-based equipment. These devices are controlled systems: their harmonic behaviour depends on the converter topology, switching strategy, filters, transformer, reactor, control loops, operating point, background distortion and grid impedance. Many of these details are proprietary and are not normally available to the consultant or system operator in sufficient detail to build a reliable model independently.

Key idea

Converter harmonic models are manufacturer-dependent — the engineer requests, verifies and applies them, not derives them.
A model must represent both emission and impedance — a Norton or Thévenin equivalent, not an ideal current source.
The same applies to PV inverters, wind turbines, BESS, STATCOMs and HVDC — all controlled, all grid-interactive.
If vendor data is missing, simplified assumptions are for screening only, and the limitation must be stated.

Key terms used on this page

01Converter-based generation (CBG)

Generation connected through power-electronic converters, such as PV, wind turbines and BESS.

02PV inverter

Converter that connects photovoltaic generation to the AC network.

03Wind turbine converter

Converter used in Type 3 or Type 4 wind turbine generator systems.

04BESS

Battery Energy Storage System — normally connected through a bidirectional converter.

05STATCOM

Voltage-source converter used mainly for reactive-power and voltage control.

06HVDC converter

Converter station used to connect AC and DC transmission systems.

07Norton equivalent

Harmonic current source in parallel with a harmonic admittance.

08Thévenin equivalent

Harmonic voltage source behind a harmonic impedance.

09Harmonic impedance

The impedance of a device or network at a specific harmonic order.

10Operating point

Converter active power, reactive power, voltage, control mode and grid condition being studied.

Section 1

Manufacturer-dependent models

Converter-based generation should not be represented by one universal harmonic model. The harmonic behaviour depends on converter topology, switching method, transformer and filter design, control system, operating point, background distortion and grid strength. Manufacturer data is therefore normally required for reliable harmonic studies.

Because converter behaviour is set by proprietary topology and control, the responsibility for the harmonic model sits with the equipment supplier, while the study engineer is responsible for using it correctly and assessing the network impact.

The responsibility split

Manufacturer / technology provider → provide the harmonic model and supporting data.
Study engineer → use the provided model correctly and assess the network impact.

Keeping this split clear avoids two common failure modes: a consultant inventing converter impedance from public information, and a manufacturer supplying only an emission spectrum with no impedance. Both leave the harmonic study unable to represent converter–grid interaction.

Section 2

What the manufacturer should provide

For wind turbine generators, PV inverters, BESS converters and similar converter-based generation, the manufacturer should provide a harmonic model that represents both harmonic emission and harmonic impedance. A simple ideal current source is usually not sufficient, because it cannot represent the interaction between the converter, its internal filters, its control system and the external grid impedance. The preferred representation is a Norton or Thévenin equivalent at the frequencies of interest:

Norton model = harmonic current source + harmonic admittance.
Thévenin model = harmonic voltage source + harmonic impedance.

Symbols and notation used on this page

\(I_h\) — harmonic current at order \(h\); \(V_h\) — harmonic voltage at order \(h\); \(Z_h\) — harmonic impedance at order \(h\); \(Y_h\) — harmonic admittance at order \(h\), normally \(Y_h=1/Z_h\); \(E_h\) — converter-generated harmonic voltage source at order \(h\). The order satisfies \(f_h=hf_1\), where \(f_1\) is the fundamental frequency (normally 50 Hz in the UK and Ireland). The symbol \(h\) is used only for harmonic order; where sequence quantities appear, the subscripts 0, 1 and 2 are the zero-, positive- and negative-sequence components.

\[ I_h=I_{N,h}-Y_{N,h}\,V_h \]

\(I_h\): 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 \(h\)
\(V_h\): harmonic voltage at the converter terminal at order \(h\)

The Norton form is useful when the converter is represented as a harmonic current source with a parallel frequency-dependent admittance.

\[ V_h=E_{Th,h}-Z_{Th,h}\,I_h \]

\(V_h\): 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 AC network at order \(h\)

The Thévenin form is useful when the converter behaves as a harmonic voltage source behind a converter, transformer, filter and control-dependent impedance.

A Norton model is generally more natural when the converter harmonic behaviour is described as injected harmonic current; a Thévenin model is generally more natural when the converter behaves as a controlled harmonic voltage source behind an impedance. The two can be mathematically equivalent, but only if the source and impedance are defined for the same operating point, frequency range and control mode:

\[ I_{N,h}=\frac{E_{Th,h}}{Z_{Th,h}} \qquad\qquad Y_{N,h}=\frac{1}{Z_{Th,h}} \]

\(I_{N,h}\): Norton current source at order \(h\)
\(E_{Th,h}\): Thévenin voltage source at order \(h\)
\(Z_{Th,h}\): Thévenin impedance at order \(h\)
\(Y_{N,h}\): Norton admittance at order \(h\)

Do not convert between forms unless the impedance data is available and valid over the study frequency range.

The manufacturer should ideally provide the harmonic source spectrum; the harmonic impedance versus frequency; the operating-point dependency; the filter and reactor data; the transformer data; the control-mode assumptions; the frequency range of validity; phase-angle information where relevant; and the model limitations. This information allows the study engineer to include the converter correctly in the network model.

Table 1 — Converter-based generation harmonic-modelling considerations by technology.

Technology	Typical Harmonic Modelling Issue	Data Normally Required
PV inverter	Emission depends on inverter topology, filter and operating point	Harmonic current/voltage spectrum, impedance model, filter data
Type 3 wind turbine	Rotor-side/grid-side converter interaction and transformer/filter behaviour	Vendor harmonic model, turbine operating points, collector-network data
Type 4 wind turbine	Full-converter controls dominate the harmonic response	Vendor impedance or source model, control mode, grid-strength limits
BESS	Bidirectional converter behaviour changes between charge and discharge	Charge/discharge spectra, impedance model, control settings
STATCOM	Control-dependent shunt converter impedance	Harmonic voltage source and impedance versus frequency
HVDC VSC	Station behaviour depends on power transfer and controls	Vendor model over the operating range
HVDC LCC	Characteristic current harmonics and AC-filter states dominate	Harmonic current spectra and filter-switching states

For early screening, generic harmonic spectra may be used if no manufacturer data is available. However, for compliance assessment, filter design, grid-code submission or contractual studies, vendor-specific data should normally be requested. The report should clearly state whether the model is generic, preliminary, vendor-provided or validated by measurement.

The manufacturer should provide

converter type and topology;
rated power, voltage and current;
transformer impedance and vector group;
filter data, including L, C, R and damping;
harmonic current or voltage spectrum;
harmonic phase angles, where available;
harmonic impedance or admittance versus frequency;
positive-, negative- and zero-sequence behaviour, where relevant;
operating-point dependency;
active and reactive power control modes;
voltage-control or power-factor-control settings;
PLL and current-controller assumptions, where relevant;
grid-strength limitations;
frequency range of validity;
aggregation rules for multiple units;
model limitations.

Section 3

PV inverters

PV inverters should not normally be modelled only as ideal constant current sources for detailed harmonic studies. That simplification may be useful for early screening, but it cannot capture the interaction between the inverter output filter, converter control, background voltage distortion and grid impedance. For a realistic assessment, the manufacturer should provide a Norton or Thévenin equivalent that includes both the inverter harmonic source and the inverter harmonic impedance — in short, a PV inverter model = harmonic source + frequency-dependent impedance, not a simple fixed harmonic current source.

The study engineer should then use this model to assess harmonic emission, resonance interaction, background distortion amplification and compliance at the PCC.

Aggregating many converters

When many converters are connected in parallel — as in a PV plant, wind farm or large BESS — the harmonic current magnitudes should not always be added arithmetically. Phase diversity, transformer phase shifts, collector-network impedance and manufacturer aggregation guidance can all affect the combined spectrum. The report should state whether converter emissions have been added arithmetically, by phasor summation, by statistical summation, or using manufacturer-provided aggregation factors:

\[ I_{h,total}=\sum_{k=1}^{N} I_{h,k} \]

\(I_{h,total}\): total harmonic current at order \(h\)
\(I_{h,k}\): harmonic current contribution from converter \(k\) at order \(h\)
\(N\): number of converters or converter groups

This is a phasor sum. If phase angles are not available, the adopted summation method should be clearly stated.

Section 4

Wind turbine generators

For type 3 and type 4 wind turbine generators the same principle applies: harmonic behaviour depends strongly on the converter design, filters, control system and operating point. For type 3 turbines, the rotor-side converter, grid-side converter, machine and filters can all influence harmonic behaviour. For type 4 turbines, the full converter decouples the generator from the grid, but the grid-side converter, smoothing reactor, filters, transformer and control system still determine the harmonic emission and impedance.

The wind turbine manufacturer should therefore provide a suitable harmonic model. It should not only state the harmonic current emission — it should also represent the converter impedance and any filters that can influence network resonance. The study engineer should not be expected to derive detailed WTG converter impedance from public information or simplified assumptions.

Section 5

HVDC converter stations

HVDC converter stations are even more manufacturer-specific. Detailed HVDC harmonic design is normally carried out by the supplier using specialist tools and detailed converter, control and filter models; for wider network studies, the supplier should provide an appropriate simplified equivalent for use by the system operator or consultant.

For LCC HVDC this may include the harmonic current source spectra, the AC filter configurations, the filter impedances and detuning assumptions, the converter transformer impedance, the station impedance where required, and the operating-point and pole-configuration dependency. For VSC HVDC this may include the harmonic voltage source spectra, the converter internal harmonic impedance, the phase reactor impedance, the converter transformer impedance, AC filter data where applicable, the control-mode assumptions and the frequency range of validity.

So the HVDC harmonic model must be supplied or validated by the HVDC technology provider. The consultant can explain the required modelling philosophy, perform network studies using the provided data, test sensitivity cases and assess compliance — but the converter-specific harmonic source and impedance data should come from the supplier.

Section 6

Role of the study engineer

Operating-point dependency

Converter harmonic behaviour may change with active power output, reactive power output, voltage-control mode, charge/discharge mode, converter temperature, switching pattern and grid strength. A model at rated output may not represent low-output or standby operation. Studies should therefore include the credible operating points that produce the highest emission or the lowest damping.

Recommended operating cases

maximum active power export;
minimum active power export;
zero active power with reactive-power control, where applicable;
maximum reactive power export;
maximum reactive power import;
BESS charging mode;
BESS discharging mode;
STATCOM-only operation;
weak-grid condition;
strong-grid condition;
converter transformer tap extremes, where relevant;
filter branch in service and out of service.

Background distortion and converter response

Background harmonic voltage distortion can influence converter current, because the converter does not operate against an ideal sinusoidal voltage. Depending on its control system and impedance, the converter may absorb, amplify or partially compensate the existing distortion. The study should therefore state whether background distortion is ignored, represented as a voltage source, or included in a combined harmonic assessment.

Weak-grid modelling warning

In weak grids, converter harmonic impedance and control interaction may become important. A simple fixed harmonic current-source model may not capture PLL dynamics, current-control interaction, negative damping, harmonic instability or cross-frequency coupling. In such cases, vendor impedance models, EMT simulation or impedance-based stability analysis may be required.

The PLL, or Phase-Locked Loop, is the converter control function that estimates the grid-voltage phase angle. Harmonic distortion or voltage unbalance can influence the PLL and therefore affect the converter current response — one reason weak-grid behaviour can matter.

What the study engineer should confirm

The study engineer’s role is to define the modelling requirements, request the correct data, build the network model, apply the manufacturer model correctly and interpret the results. In doing so, the engineer should confirm:

whether the model is Norton, Thévenin, impedance-only or current-source-only;
whether the model includes converter transformer and filter impedance;
whether the model is valid for the selected operating point;
whether multiple converter units are aggregated correctly;
whether background harmonic distortion is included;
whether weak-grid behaviour is important;
whether control-dependent impedance is represented;
whether both minimum and maximum generation cases are studied;
whether outage or reduced-availability cases are required;
whether the model supports the required frequency range.

If vendor data is not available, simplified assumptions may be used only for preliminary screening, and the limitation should be clearly stated.

Suitable report statement

“The converter-based generation and HVDC harmonic models should be provided by the relevant equipment manufacturer or technology provider. The modelling descriptions in this section are intended to clarify the required model structure and the technical information that should be requested. They are not intended to replace manufacturer-specific harmonic models.”

Section 7

Practical engineering message

For converter-based equipment, the most important point is that harmonic emission and harmonic impedance are both required. The minimum concept is that the converter harmonic impact = harmonic source + frequency-dependent impedance + network interaction. A constant current source may be adequate only for very early screening or a conservative approximation; it is not normally sufficient for detailed assessment of resonance, background distortion amplification, filter design or compliance where converter–grid interaction is important.

The correct workflow

Request the manufacturer harmonic model → verify its scope and validity → include it in the network harmonic model → study operating points and impedance envelopes → assess emission, amplification and compliance.

Common modelling mistakes

Using a generic converter spectrum for a final compliance study.
Treating PV, wind, BESS, STATCOM and HVDC converters as identical.
Ignoring converter transformer and filter impedance.
Ignoring operating-point dependency.
Ignoring harmonic phase angles.
Adding many converter spectra arithmetically without justification.
Ignoring background distortion.
Ignoring weak-grid control interaction.
Using a vendor model outside its stated frequency range.
Not stating whether the model is Norton, Thévenin, impedance-only or current-source-only.
Not checking whether the model represents positive-, negative- and zero-sequence behaviour.

In short: converter-based generation harmonic models are highly technology- and manufacturer-dependent. A robust study should not rely on a generic converter source unless the study is clearly preliminary, and the model should state whether the converter is represented as a Norton equivalent, Thévenin equivalent, impedance-only model or harmonic source spectrum. For PV, wind, BESS, STATCOM and HVDC projects, the report should then state:

the operating points studied;
the vendor data used;
the aggregation method;
the background-distortion treatment;
the control assumptions;
the frequency range;
the model limitations.

Where grid strength is low or control interaction is important, standard frequency-domain harmonic studies may need support from vendor impedance models, EMT studies or specialised impedance-based analysis.

Key message

This approach keeps the responsibility clear: the manufacturer provides the converter-specific model, and the study engineer uses it to assess the impact on the network. Request a model that gives both source and frequency-dependent impedance over the relevant range and operating points; verify it before use; and state any simplification as a limitation — the tenth instalment of this series on harmonic studies in power systems.

Part Ten Reading now

Converter-Based Generation and HVDC Harmonic Models

Why converter harmonic models are manufacturer-dependent; the data to request; Norton/Thévenin equivalents; PV inverters, wind turbines and HVDC; and the role of the study engineer.

Series progress 10 of 11

Part Eleven

Variable-Speed Drive Modelling

Diode, active-front-end, current-source, load-commutated and cycloconverter drives; characteristic harmonics and interharmonics; Norton/Thévenin models; filters and aggregation.