Harmonic Studies & Modelling

HVDC Converter Modelling for Harmonic Studies

An HVDC converter station is among the most complex elements in a harmonic study — converters, converter transformers, smoothing reactors, AC and DC filters, shunt compensation and control systems, all of it operating-point dependent. This page separates line-commutated converters (LCC), modelled as harmonic current sources behind essential AC filters, from voltage-source converters (VSC), modelled as harmonic voltage sources behind a control-dependent impedance; and covers characteristic harmonics and cross-modulation, filter detuning and anti-resonance, the emission-versus-amplification split, AC system impedance envelopes, vendor data and the operating range a credible HVDC harmonic study must cover.

Reading time ≈ 34 min · Part Nine of the series

HVDC converter stations are among the most complex network elements to represent in harmonic studies. They include power electronic converters, converter transformers, smoothing reactors, AC filters, DC filters, shunt compensation, control systems and operating-mode dependencies. The modelling approach depends strongly on the study objective: detailed HVDC design, filter rating and performance studies are normally carried out by the technology provider using specialist tools and detailed converter models, while wider network harmonic studies use simplified but technically meaningful equivalents that let utilities, consultants and system operators assess the interaction between the station and the surrounding AC network.

The practical question

Is the HVDC station being studied as a detailed converter system, or as part of a wider AC network harmonic study? The answer determines the required model complexity.

Key idea
  1. LCC HVDC → a harmonic current source plus essential AC filters; VSC HVDC → a harmonic voltage source behind a control-dependent converter impedance.
  2. An HVDC station is both a source and an impedance — and its filters and impedance change with operating point.
  3. Assess both new emission and amplification of background distortion; the worst case may not be at rated DC power.
  4. Vendor data is essential — LCC spectra and filter states, VSC harmonic voltages and converter impedance over frequency.
Key terms used on this page
01HVDC
High-Voltage Direct Current transmission.
02LCC
Line-Commutated Converter — normally thyristor-based and dependent on the AC system voltage for commutation.
03VSC
Voltage Source Converter — self-commutated converter using devices such as IGBTs.
04MMC
Modular Multilevel Converter — a common VSC HVDC topology.
05AC filter
A filter on the AC side that absorbs harmonic currents and provides reactive compensation.
06DC filter
A filter on the DC side that reduces DC-side harmonic or ripple components.
07Characteristic harmonics
Harmonic orders naturally produced by an ideal converter arrangement.
08Non-characteristic harmonics
Harmonics from unbalance, control effects, firing-angle asymmetry, background distortion or non-ideal conditions.
09Cross-modulation
Interaction where AC-side and DC-side quantities influence each other and create additional frequency components.
10Anti-resonance
A high-impedance condition that can amplify harmonic voltage.
11Operating point
The converter power transfer, reactive condition, filter status, pole configuration and control mode being studied.

Section 1

Why HVDC modelling matters

An HVDC converter station should not be treated as a fixed harmonic source. It can generate harmonics, absorb harmonics through filters, change the AC network impedance, amplify background distortion, and behave differently at different DC power levels. So the harmonic model must represent both emission and impedance — not only one of them.

HVDC converters divide into two main technologies: Line-Commutated Converter (LCC) HVDC and Voltage Source Converter (VSC) HVDC. Their harmonic behaviour is fundamentally different. An LCC converter uses thyristor valves commutated by the AC system voltage and behaves mainly as a harmonic current source on the AC side; a VSC converter uses self-commutated devices such as IGBTs and behaves more like a harmonic voltage source behind converter impedance. So LCC HVDC → harmonic current source plus filters; VSC HVDC → harmonic voltage source behind converter impedance — a distinction essential to building the model.

HVDC harmonic modelling is difficult because the station is not a simple passive component — it is both a harmonic source and a harmonic impedance. It can generate harmonic currents or voltages, absorb harmonic currents through filters, amplify background distortion, damp some frequencies, interact with AC and DC side impedances, change behaviour with operating point, and change filter configuration with power transfer. For an LCC station the connected filters and capacitor banks may change as DC power changes, so the impedance seen from the AC network is not fixed; for a VSC station the converter impedance may depend on the control system and operating point. The message: HVDC harmonic behaviour is operating-point dependent, and a single fixed equivalent may not represent all credible conditions.

Section 2

LCC HVDC: basic harmonic behaviour

An LCC converter uses thyristor valves, normally arranged in a three-phase bridge. A twelve-pulse converter is obtained by connecting two six-pulse bridges through converter transformers with different phase shifts — typically one star-star and one star-delta arrangement — which reduces the lower-order characteristic harmonics. For an ideal twelve-pulse LCC converter, the characteristic AC-side harmonic orders are:

\[ h=12n\pm1\,,\quad n=1,2,3,\ldots \;\Rightarrow\; 11,\ 13,\ 23,\ 25,\ 35,\ 37,\ldots \]
\(h\)
harmonic order
\(n\)
positive integer
\(12n-1\)
negative-sequence characteristic harmonic order
\(12n+1\)
positive-sequence characteristic harmonic order
For example, \(n=1\) gives the 11th and 13th harmonics, and \(n=2\) gives the 23rd and 25th harmonics.

Orders \(12n-1\) are negative-sequence and orders \(12n+1\) are positive-sequence; under ideal conditions zero-sequence harmonics are not produced. In this context, positive-sequence harmonics have the same phase rotation as the fundamental positive-sequence system, while negative-sequence harmonics have the opposite phase rotation. A twelve-pulse LCC converter does not produce zero-sequence harmonics under ideal balanced conditions, but non-ideal conditions can introduce non-characteristic components. The message: LCC HVDC produces significant characteristic harmonic currents, which must normally be filtered before entering the AC network.

Notation: sequence index vs harmonic order

Do not confuse the sequence indices 0, 1 and 2 (zero-, positive- and negative-sequence) with the harmonic order \(h\). Where both are needed, use notation such as \(I_{1,h}\) for the positive-sequence current at harmonic order \(h\).

Section 3

Reactive power and filter switching

An LCC converter consumes reactive power because the converter current lags the AC voltage due to thyristor firing delay and commutation overlap; at rated operation the reactive demand may be a large fraction of active power. This is normally supplied locally by AC harmonic filters, capacitor banks, STATCOMs or synchronous condensers. In many LCC stations the AC filters also provide the required reactive compensation, so filters are switched in and out according to the operating point. The consequence: filter configuration changes with DC power transfer, and therefore station harmonic impedance changes with DC power transfer — one reason LCC harmonic assessment must consider several operating points, not only rated power.

Section 4

LCC as a harmonic current source

For initial or simplified studies, an LCC converter is represented as a harmonic current source injecting \(I_{LCC,h}\) at each relevant order, with the PCC harmonic voltage governed by:

\[ V_{h,new}=Z_{eq,h}\,I_{LCC,h} \]
\(V_{h,new}\)
new harmonic voltage contribution at order \(h\)
\(Z_{eq,h}\)
equivalent harmonic impedance seen from the converter connection point at order \(h\)
\(I_{LCC,h}\)
LCC harmonic current injection at order \(h\)
This equation explains why both the converter harmonic current spectrum and the AC network/filter impedance are required.

This is usually reasonable for the main characteristic harmonics, especially at higher orders, but can be less accurate for low-order and non-characteristic harmonics — particularly the 3rd — because of cross-modulation between AC and DC quantities. So the LCC current source is acceptable for many characteristic harmonic studies, but low-order non-characteristic harmonics may require more detailed modelling.

Characteristic and non-characteristic harmonics

The ideal LCC spectrum contains the characteristic \(12n\pm1\) harmonics, but real converters also produce non-characteristic harmonics — from AC voltage unbalance, negative-sequence voltage, transformer phase-reactance unbalance, valve firing-angle differences, DC current ripple, pre-existing background harmonics and control imperfections. The most significant is often the 3rd harmonic, arising from AC system unbalance and cross-modulation. Do not rely only on ideal characteristic harmonics for detailed LCC assessment, especially where low-order harmonics, unbalance or 3rd-harmonic filtering are important.

Section 5

LCC AC filters, detuning and anti-resonance

LCC converters generate harmonic currents too large to enter the AC network directly, so AC harmonic filters are essential components of most LCC stations. They provide low-impedance paths for converter harmonic currents and fundamental-frequency reactive compensation. Typical arrangements include single-tuned, double-tuned and triple-tuned filters and high-pass filters; for a twelve-pulse scheme, important filter frequencies commonly include the 11th, 13th, 23rd and 25th (and sometimes the 3rd and 5th, depending on non-characteristic harmonics). A simple tuned filter has branch impedance:

\[ Z_F(h)=R+j\!\left(hX_{L1}-\frac{X_{C1}}{h}\right) \]

At the tuning frequency the impedance becomes low and the filter absorbs that harmonic current — so LCC station harmonic performance is strongly dependent on AC filter design.

For LCC HVDC, AC filters are not optional details. They often provide both harmonic filtering and reactive-power support. Because filter branches may be switched in or out depending on DC power transfer and reactive-power balance, the harmonic impedance of the station can change significantly between operating points — which is exactly why one fixed filter condition is not enough.

Filter detuning

AC filters are sensitive to detuning from component tolerance, capacitor failure, temperature, network frequency variation and ageing. The tuning frequency is \(f_n=\tfrac{1}{2\pi\sqrt{LC}}\), and a small change in L and C shifts it:

\[ \frac{\Delta f_n}{f_n}\approx -\frac{1}{2}\!\left(\frac{\Delta L}{L}+\frac{\Delta C}{C}\right) \]

Detuning reduces filter effectiveness and shifts anti-resonance peaks: filter detuning → changed harmonic impedance → changed PCC distortion and component duty. Detailed LCC design studies include worst-case detuning; for wider network studies, nominal values may be adequate unless the study is close to the station or near a filter tuning frequency.

Anti-resonance between filters

Anti-resonance is a high-impedance condition created by interaction between filters, capacitors, transformers, cables and the external AC system. At anti-resonance, harmonic current injection can produce a high harmonic voltage. HVDC filters can therefore both reduce distortion at their tuning frequencies and create an amplification risk at other frequencies.

When several tuned filters are connected in parallel, each gives low impedance near its own tuning frequency, but between branches the combination may create anti-resonance — a high total impedance at an intermediate frequency. This matters because a high impedance peak can amplify harmonic voltage distortion if harmonic current or background voltage exists near that frequency. The complete filter-bank impedance must be checked over the full frequency range, not only at the tuned orders — filter design must consider the entire impedance profile.

Section 6

LCC cross-modulation

Cross-modulation means that AC-side distortion, DC-side ripple and converter controls interact so that one frequency component can create additional components at other frequencies. In an HVDC station this can occur through converter switching, control loops, DC voltage ripple, transformer saturation or unbalanced AC voltage — which is why HVDC cannot always be modelled as independent harmonic sources at each order.

In more detail, cross-modulation is the interaction between AC-side and DC-side harmonics through the converter switching process. The simplified current-source model assumes a perfectly smooth DC current; in reality the DC current contains ripple, and AC and DC side harmonics interact so the converter transfers disturbances from one side to the other. Conceptually: AC harmonic voltage → DC ripple → AC harmonic current (and DC harmonic → AC harmonic). It is especially important for low-order non-characteristic harmonics — for example, AC voltage unbalance can create a second harmonic on the DC side, which is modulated back to the AC side as a 3rd-harmonic current. So cross-modulation can make low-order harmonic assessment more complex, and 3rd-harmonic filtering may depend on a cross-modulation assessment.

Section 7

LCC impedance, compliance and operating cases

An LCC station also presents a harmonic impedance to pre-existing AC harmonics. It depends on the converter transformer reactance, valve behaviour, smoothing reactor, DC line or cable impedance, DC filters, the ground-return or leakage path, the operating point and control action — but at most orders it is often dominated by the AC filters. So the AC filters are the dominant station impedance at many orders, while the converter internal impedance may be important at low orders; the converter detail required depends on the study objective and frequency range.

Compliance: emission and amplification

For a new LCC connection, compliance has two parts that can be analysed separately by superposition. The new-emission assessment treats the converter as a harmonic source, \(V_{h,new}=Z_{eq,h}I_{LCC,h}\). The background-amplification assessment treats the station as a harmonic impedance interacting with background voltage distortion — the total being a function of \(V_{h,background}\), \(Z_{LCC,h}\) and \(Z_{system,h}\). The rule: HVDC compliance is not only about converter emission; it must also consider background distortion amplification.

Modelling for new distortion and background amplification

For new distortion, the simplified model includes the LCC harmonic current source, the AC filter impedance and the external AC system impedance, with the source representing harmonic order, magnitude, phase angle (if available), operating point, monopolar or bipolar operation and filter configuration; the external impedance is usually a harmonic impedance envelope. The study should find the combination of operating point, filter status and network impedance that gives the highest PCC distortion — and maximum distortion may not occur at rated DC power: at low DC power the harmonic content can be proportionally higher while fewer filters are connected for reactive balance. For background distortion, the station is represented mainly as a passive harmonic impedance (AC filters, converter transformer, converter impedance, external AC system); the converter and transformer impedance may be neglected if the filters dominate, but this may be inaccurate for low-order harmonics. So a filter-only model may suffice for general studies, but include converter impedance when low-order accuracy is required. For system-wide studies the LCC model should include the harmonic current source, AC filters, converter transformer, converter impedance if required, shunt compensation and the operating point and filter status — matched to the selected DC transfer level, across minimum, intermediate and maximum DC power, monopolar and bipolar operation and credible switching states. Model the LCC operating range, not only the nameplate condition.

Section 8

VSC HVDC: basic behaviour and representation

An MMC, or Modular Multilevel Converter, is a VSC topology made from many converter submodules. It produces an AC voltage waveform with many voltage levels, which normally reduces low-order harmonic emission compared with older two-level converters.

A VSC HVDC converter uses self-commutated devices such as IGBTs, commonly with modular multilevel converter (MMC) topology. It produces an AC voltage by controlling many cells or modules, giving a close approximation to a sinusoid with harmonic content set by design and control. Compared with LCC, VSC HVDC typically has lower harmonic emission, smaller or no AC filters, higher-frequency harmonic components, possible interharmonics and a control-dependent harmonic impedance. So VSC harmonic studies are often more about converter impedance than large harmonic current emission.

VSC as a harmonic voltage source

A VSC converter is normally represented as a harmonic voltage source behind converter impedance, conceptually \(U_{VSC,h}\) behind \(Z_{VSC,h}\):

\[ V_h=U_{VSC,h}-Z_{VSC,h}\,I_h \]
\(V_h\)
harmonic voltage at the AC connection point
\(U_{VSC,h}\)
VSC converter-generated harmonic voltage at order \(h\)
\(Z_{VSC,h}\)
VSC equivalent harmonic impedance at order \(h\)
\(I_h\)
harmonic current exchanged with the AC network at order \(h\)
This is a conceptual Thevenin representation. The actual equivalent may include the converter arm impedance, phase reactor, transformer, filters and control-system impedance.

Here \(U_{VSC,h}\) is the converter-generated harmonic voltage and \(Z_{VSC,h}\) the converter internal impedance; the model also includes the converter reactor, converter transformer, AC filters (if present) and external AC system impedance. So LCC → current source; VSC → voltage source behind impedance — one of the most important modelling differences between the two technologies.

VSC harmonic generation

VSC harmonic generation depends on the converter topology, number of levels, switching frequency, modulation strategy, dead time, sampling frequency, control system and operating point. In two-level VSCs the switching harmonics relate to the switching frequency and its sidebands; in MMCs the effective switching behaviour depends on the number of levels and the modulation method. Unlike LCC, VSC spectra are not easily computed from simple universal characteristic-harmonic equations — they are proprietary and vendor-specific. Use vendor-provided VSC harmonic voltage spectra rather than idealised equations.

Section 9

VSC frequency range, impedance and compliance

An interharmonic is a frequency component that is not an integer multiple of the fundamental frequency. For example, in a 50 Hz system, 175 Hz is an interharmonic because it is not \(h\times 50\) Hz for any integer \(h\).

VSCs can produce harmonic and interharmonic components above the range normally considered for LCC. LCC studies often focus up to \(h=50\); VSC studies may require frequencies above the 50th harmonic where switching-related components, supraharmonics or high-frequency resonances are relevant. So the AC network harmonic impedance may be required above the 50th harmonic, and at these frequencies transformer stray capacitances, cable frequency-dependent effects and filter parasitics become more important.

VSC converter harmonic impedance

The total VSC station impedance includes the converter internal active impedance, the phase reactor, the converter transformer and AC filters (if present). The converter internal impedance is control dependent — it may appear inductive, capacitive, or even exhibit negative resistance at some frequencies, which can reduce damping and contribute to harmonic instability. So the VSC converter impedance is not simply a physical reactor; it includes control-system behaviour and must be supplied by the vendor or represented with a suitable converter model.

Background amplification and compliance

A VSC station may amplify or damp background distortion depending on its equivalent impedance: if the VSC input impedance and network impedance create a resonance, background distortion can be amplified. So low VSC emission does not automatically mean no harmonic risk — the converter impedance and control interaction must also be checked. Compliance has two parts: new distortion, a function of \(U_{VSC,h}\), \(Z_{VSC,h}\) and \(Z_{system,h}\); and background distortion, a function of \(V_{h,background}\), \(Z_{VSC,h}\) and \(Z_{system,h}\). The VSC harmonic voltage should be obtained from the supplier, often as a conservative non-consistent maximum set (the maximum of each harmonic over the full operating range). VSC emission data is vendor-specific and should not be replaced by generic characteristic-harmonic assumptions. For system-wide studies the VSC model should include the harmonic voltage source, converter internal impedance, converter reactor, converter transformer, AC filters (if present) and external AC system impedance; a simplified model may suffice for general screening if converter control interaction is not the objective, while detailed studies need vendor data for the harmonic voltage spectrum, converter impedance over frequency, operating-point dependency, control-mode assumptions and frequency range of validity. Use vendor impedance data for VSC harmonic interaction studies.

Section 10

LCC vs VSC comparison

Table 1 — LCC and VSC HVDC harmonic modelling compared.
AspectLCC HVDCVSC HVDC
Switching deviceThyristorIGBT or similar self-commutated device
Main source typeHarmonic current sourceHarmonic voltage source
Characteristic harmonics\(12n\pm1\) for twelve-pulseVendor-specific, topology/modulation dependent
Emission magnitudeUsually highUsually lower
AC filtersNormally essentialOften small or not required
Reactive power compensationMajor requirementConverter can control reactive power
Filter switchingImportant, operating-point dependentUsually less important
Cross-modulationImportant, especially low-orderPresent but generally less dominant
Converter impedanceMay matter at low orders; filters often dominateVery important and control dependent
Simplified modelCurrent source plus filtersVoltage source behind impedance

So an LCC study focuses on current harmonics, filters, reactive compensation and cross-modulation; a VSC study focuses on voltage harmonics, converter impedance and control interaction.

Section 11

Connection assessment and AC system impedance

For both LCC and VSC, a new connection assessment should consider two separate effects: new harmonic emission (what the converter adds to the network) and amplification of background harmonic distortion (how the station changes the existing environment). The general superposition concept is:

\[ V_{h,total}=V_{h,background}+V_{h,new} \]
\(V_{h,total}\)
total harmonic voltage at order \(h\)
\(V_{h,background}\)
pre-existing harmonic voltage at order \(h\)
\(V_{h,new}\)
harmonic voltage contribution caused by the HVDC station
This should be treated as a phasor relationship where phase-angle information is available. If phase angles are not available, the report should state the adopted summation method.

This is simplified — in practice both terms depend on the harmonic impedance of the station and the network. A harmonic connection study must not assess only the new source; it must also check whether the station impedance changes the response of the existing network.

External AC system impedance

The external AC system is normally represented by a harmonic impedance envelope — a range of possible \(Z_{AC,h}\) values at the connection point, considering different operating conditions and outages. This matters because distortion depends on system impedance: a weak grid, outage or resonance may give a much higher harmonic voltage than the base case. HVDC harmonic studies require AC system impedance envelopes — for LCC, especially to determine how much converter harmonic current enters the network; for VSC, to check interaction between converter impedance and network impedance.

Background harmonic distortion

Background distortion should be included where required — it may come from existing converters, industrial loads, wind and solar plants, distribution networks or resonance already present, and may be represented as \(U_{fn}\) or \(V_{h,background}\). The station impedance may either amplify or damp it. Background harmonics are part of the connection environment and should not be ignored where significant.

Section 12

Vendor data, planning uncertainty and measurement

HVDC harmonic modelling normally requires vendor data. For LCC: harmonic current spectra over the operating range, filter bank configurations, filter impedance values, filter detuning ranges, converter transformer impedance and tap range, converter impedance where required, and monopolar and bipolar operating conditions. For VSC: harmonic voltage spectra over the operating range, converter internal impedance, phase reactor impedance, converter transformer impedance and tap range, AC filter impedance (if installed), control mode and frequency range of validity, and high-frequency emission data if relevant. HVDC harmonic models should be vendor-supported wherever possible; where vendor data is unavailable, simplified assumptions should be used only for screening, with limitations stated clearly.

Modelling warning — one fixed equivalent is not enough

Do not use one fixed HVDC harmonic equivalent for all studies unless its validity has been confirmed. The converter source spectrum, station impedance, filter status, control mode and background-distortion response may all change with operating point. A model valid at rated bipolar power may not be valid at low power, monopolar operation, reduced filter availability or a weak-grid condition.

The HVDC supplier should provide
  • converter type: LCC or VSC/MMC;
  • rated DC voltage and power;
  • converter transformer impedance and vector group;
  • smoothing reactor data;
  • AC filter branch data;
  • DC filter branch data, where relevant;
  • shunt capacitor/reactor status logic;
  • harmonic source spectrum for each operating point;
  • harmonic source phase angles, where available;
  • station harmonic impedance versus frequency;
  • control-mode assumptions;
  • pole configuration: monopolar, bipolar, metallic return or earth return;
  • frequency range of validity;
  • background-distortion response assumptions;
  • component duty limits;
  • model limitations.

Planning-stage uncertainty

HVDC projects are often studied before the final converter and filter design exists. At feasibility, detailed modelling may not be possible and only high-level estimates can be made; at the design stage the technology provider should carry out detailed studies using the selected design, filters, controls and layout. For planning-stage network studies the engineer may need typical harmonic spectra, generic filter assumptions, impedance envelopes, sensitivity cases and conservative source values. HVDC harmonic conclusions at planning stage should be treated as provisional until vendor-specific data is available.

Operating conditions and measurement

Studies should cover a range of conditions. For LCC: minimum, maximum and intermediate DC power, monopolar and bipolar operation, filter bank switching states, reactive-power control states and the AC network impedance envelope. For VSC: different active power levels, different reactive-power or voltage control modes, converter operating points, weak-grid conditions, AC filter in-service state (if applicable) and high-frequency impedance scenarios. HVDC harmonic performance must be checked over the operating range, not only at rated power. For an existing station, measurements over a sufficiently long period can capture different power levels, filter states, network conditions, seasonal variation and background levels — but measurements alone may not separate the HVDC contribution from background distortion unless both voltage and current are measured and the network impedance is understood. Measurement data is valuable, but responsibility and source separation require analysis.

Operating points to consider
  • minimum DC power transfer;
  • intermediate DC power transfer;
  • maximum DC power transfer;
  • monopolar operation;
  • bipolar operation;
  • reverse power transfer, if applicable;
  • filter minimum configuration;
  • filter maximum configuration;
  • one filter branch out of service;
  • low short-circuit level;
  • high short-circuit level;
  • reactive-power or voltage-control mode changes;
  • weak-grid condition for VSC schemes.

Section 13

AC/DC interaction and detailed studies

For detailed HVDC harmonic analysis, both AC and DC sides may need to be represented — especially for LCC converters, where AC and DC harmonics are linked through cross-modulation. The model may include the AC network impedance, converter transformer, valve group, DC smoothing reactor, DC filters, DC line or cable, control system and return path. For VSC converters the converter energy storage can partially decouple AC and DC harmonics, but interaction still exists. Detailed AC/DC interaction studies require specialised models — standard frequency-domain harmonic penetration models may not be enough.

When time-domain or harmonic-domain studies are required

Simplified frequency-domain models are useful for many network studies, but may not be adequate when cross-modulation is important, low-order non-characteristic harmonics are critical, converter control interaction is significant, interharmonics matter, weak-grid converter stability is a concern, vendor-specific switching behaviour must be represented, or AC and DC side interaction must be solved accurately. In those cases, time-domain, harmonic-domain or specialised converter models may be needed. The rule: use simplified frequency-domain models for planning and network screening, but use detailed converter models for design, rating and control-interaction studies.

Component duty

An HVDC harmonic study should not only check voltage distortion — it should also check station equipment duty. AC filters, DC filters, converter transformers, smoothing reactors, capacitor banks and reactors may experience increased RMS current, harmonic current, voltage stress and thermal loading. A solution that reduces PCC distortion is not acceptable if it overloads filter branches or converter-station components.

Section 14

Workflow and sensitivity

A practical HVDC harmonic modelling workflow is as follows:

  1. Identify the technology — LCC or VSC.
  2. Define the study objective — planning screening, connection compliance, filter design, background amplification, component rating or AC/DC interaction.
  3. Select the source representation — a harmonic current source for LCC, a harmonic voltage source for VSC.
  4. Include the station impedance — AC filters, compensation, transformer and converter impedance (LCC); converter impedance, phase reactor, transformer and filters (VSC).
  5. Include the external AC system impedance envelope.
  6. Include background harmonic distortion where required.
  7. Assess multiple operating points.
  8. Perform new-emission and background-amplification assessments separately.
  9. Use detailed vendor models if simplified models are not adequate.
Table 2 — Relative sensitivity of HVDC harmonic results to modelling choices.
ParameterTypical ImpactComment
Converter technologyVery highLCC and VSC need different source models
AC filter configurationVery high for LCCChanges impedance and reactive balance
Filter detuningHighAffects LCC harmonic performance
DC power transfer levelHighChanges emission and filter status
Monopolar / bipolar operationHighChanges source and compensation
AC system impedance envelopeVery highControls PCC distortion
Background distortionHighMay be amplified or damped
Converter transformer impedanceMedium to highAffects commutation and transfer
VSC converter impedanceVery highControl-dependent and vendor-specific
Low-order harmonic interactionHighMay require detailed modelling
High-frequency rangeHigh for VSCMay extend beyond the 50th harmonic

HVDC harmonic studies are dominated by the source model, the station impedance and the operating condition.

The study engineer should confirm
  • whether the HVDC model includes both source and impedance;
  • whether the model is for LCC or VSC;
  • whether AC and DC filters are represented explicitly or inside an equivalent;
  • whether the model is valid for the selected operating point;
  • whether filter switching is represented;
  • whether background distortion is included;
  • whether AC system impedance envelopes are applied;
  • whether monopolar/bipolar operation is covered;
  • whether component duty is assessed;
  • whether EMT or vendor impedance-based analysis is needed for control-sensitive cases.

Section 15

Reporting and summary

A harmonic study report should clearly state how the HVDC station was represented.

Examples of a clear modelling statement

“The LCC HVDC station was represented as a harmonic current source with operating-point-dependent harmonic spectra, together with AC filter banks, shunt compensation, converter transformer impedance and relevant station impedance; filter configurations were matched to the selected DC power transfer levels.”

“The VSC HVDC station was represented as a harmonic voltage source behind converter internal impedance, including the phase reactor, converter transformer and AC filters where applicable, using vendor-provided converter impedance and harmonic voltage spectra.”

“The HVDC station impedance was assessed against background harmonic voltage distortion and AC system impedance envelopes to identify possible amplification or damping; where vendor-specific data was unavailable, simplified frequency-domain models were used for screening only.”

Common modelling mistakes
  • Treating LCC and VSC HVDC as the same harmonic model.
  • Representing LCC HVDC as a current source without AC filters.
  • Representing VSC HVDC as an ideal voltage source without converter impedance.
  • Using only rated-power operation and ignoring low-power operation.
  • Ignoring filter switching and outage states.
  • Ignoring background distortion amplification.
  • Ignoring AC system impedance envelopes.
  • Ignoring control-dependent impedance for VSC schemes.
  • Ignoring DC-side filters and smoothing reactor where they influence the result.
  • Not checking filter and converter-station component duty.
  • Using vendor data outside its stated frequency range or operating range.

To summarise: HVDC stations act both as harmonic sources and as harmonic impedance elements. For LCC the converter is usually a harmonic current source with ideal twelve-pulse characteristic orders \(h=12n\pm1\); the AC filters and shunt compensation are critical because they absorb most converter harmonic current and determine the station impedance, and studies must consider operating power level, filter switching, reactive compensation, monopolar/bipolar operation, filter detuning and AC system impedance. For VSC the converter is usually a harmonic voltage source behind converter internal impedance, \(U_{VSC,h}\) behind \(Z_{VSC,h}\); emissions are normally lower than LCC, but the converter impedance is highly important because it can amplify or damp background harmonics, and VSC behaviour is vendor-specific. Both assessments should include new harmonic emission and background distortion amplification.

In short: HVDC converter stations are active, operating-point-dependent harmonic elements. LCC HVDC should normally be represented as a harmonic current source together with AC filters, converter transformer, smoothing reactor, DC-side elements and filter-switching states. VSC HVDC should normally be represented as a harmonic voltage source behind converter, reactor, transformer, filter and control-dependent impedance. A robust study should assess both new emission and amplification of background distortion, and should state:

  • the vendor data used and its frequency range of validity;
  • the converter technology and source representation;
  • the station impedance and filter configuration;
  • the DC power range and pole configurations covered;
  • the AC system impedance envelopes;
  • the background-distortion treatment;
  • the component-duty checks;
  • the model limitations.
Key message

LCC modelling focuses on current harmonics, filters and operating configurations; VSC modelling focuses on voltage harmonics, converter impedance and control interaction. A robust HVDC harmonic study should state the converter technology, source representation, station impedance, filter configuration, operating points, AC system impedance envelope, background distortion, vendor-data assumptions and model limitations. Only then can the harmonic impact of an HVDC converter station be assessed correctly — the ninth instalment of this series on harmonic studies in power systems.

Multi-Part Technical Series

Harmonic Studies in Power Systems

A practical series on how harmonic studies are set up and solved — from choosing the modelling domain, through frequency scan, harmonic penetration and balanced versus unbalanced modelling, to time, hybrid and harmonic-domain methods.

Part Nine Reading now

HVDC Converter Modelling for Harmonic Studies

LCC as a harmonic current source with essential AC filters and VSC as a harmonic voltage source behind a control-dependent impedance; characteristic harmonics, cross-modulation, detuning, anti-resonance and operating-range assessment.

Series progress 9 of 11