FACTS devices combine power electronics, reactors, capacitors, transformers, filters and control systems — so in harmonic studies they act in two ways at once: they can generate harmonic distortion, and they reshape the network harmonic impedance. This page separates thyristor devices (SVC, TCSC) from voltage-source converters (STATCOM, SSSC, UPFC, IPFC); shows when each is modelled as a current source, a voltage source or a controlled impedance; covers SVC filters and firing-angle dependency, STATCOM control interaction and weak-grid effects, active filtering, vendor data and the operating-range cases a credible FACTS harmonic study must run.
Reading time ≈ 32 min · Part Eight of the series
Flexible AC Transmission System (FACTS) devices control voltage, reactive power, power flow, dynamic stability and transmission capability. In harmonic studies they require careful modelling because they combine power electronics, reactors, capacitors, transformers, filters and control systems. They influence harmonic performance in two ways: they can generate harmonic distortion, and they can modify the harmonic impedance of the network.
The governing relationship is unchanged, and a FACTS device can affect both terms — injecting harmonic current or voltage, and changing the network harmonic impedance through its filters, reactors, capacitors, transformer and control system. The key message is that FACTS devices are not only harmonic sources; they are also frequency-dependent network impedance elements, which is why they must be represented carefully.
Key idea
Thyristor devices (SVC, TCSC) behave as harmonic sources; VSC devices (STATCOM, SSSC, UPFC, IPFC) as voltage sources behind a control-dependent impedance.
FACTS harmonic behaviour is operating-point dependent — a single fixed model and one operating point are not enough.
Always check both new emission and amplification of background distortion — low emission does not guarantee low impact.
In weak grids (\(SCR\leq 3\)), converter control and PLL interaction may exceed what standard frequency-domain models capture.
Key terms used on this page
01FACTS
Flexible AC Transmission Systems — power-electronic devices used to control voltage, reactive power, impedance or power flow.
02SVC
Static Var Compensator — normally made from thyristor-controlled and switched reactive components.
03TCR
Thyristor-Controlled Reactor — a shunt reactor controlled by thyristor firing angle.
04TSC
Thyristor-Switched Capacitor — a capacitor branch switched using thyristors.
05TCSC
Thyristor-Controlled Series Capacitor — series compensation using a capacitor and thyristor-controlled reactor.
06STATCOM
Static Synchronous Compensator — a shunt voltage-source converter for reactive-power and voltage control.
07SSSC
Static Synchronous Series Compensator — a series voltage-source converter.
08UPFC
Unified Power Flow Controller — a combination of shunt and series converters.
09IPFC
Interline Power Flow Controller — converters connected to more than one line, often through a shared DC link.
10PLL
Phase-Locked Loop — the converter control function that tracks grid-voltage angle.
11SCR
Short-Circuit Ratio — an indicator of grid strength.
Section 1
Why FACTS modelling matters
FACTS devices are not simple passive components. Some — such as SVCs and TCSCs — use thyristor switching and can generate characteristic harmonics. Others — such as STATCOMs, SSSCs and UPFCs — are voltage-source converters whose harmonic behaviour depends on converter topology, filters, control system and operating point. So a FACTS device may act as both a harmonic source and a frequency-dependent impedance.
The harmonic voltage at a bus is governed by the same relationship as for any component, and a FACTS device 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 injection at order \(h\)
\(Z_h\)
network harmonic impedance at order \(h\)
Symbols and notation used on this page
\(E_h\) — harmonic voltage source at order \(h\); \(I_h\) — harmonic current (or current source) at order \(h\); \(Z_h\) — harmonic impedance at order \(h\); \(Y_h\) — harmonic admittance at order \(h\), normally \(Y_h=1/Z_h\); \(\phi_h\) — phase angle at order \(h\). The symbol \(h\) is used only for harmonic order. Where sequence notation appears, the subscripts 0, 1 and 2 are the zero-, positive- and negative-sequence components.
A FACTS device may inject harmonic current or voltage and change \(Z_h\) through its filters, reactors, capacitors, transformer and control system. So it is both a harmonic source and a frequency-dependent network impedance element — and both roles must be represented in a harmonic study.
Section 2
Main types and why they are difficult
FACTS devices divide into two groups by switching technology. Line-commutated, thyristor-based devices include the Static Var Compensator (SVC) and the Thyristor-Controlled Series Compensator (TCSC). Self-commutated, voltage-source-converter (VSC) devices include the STATCOM, SSSC, UPFC and IPFC. Their harmonic behaviour differs: thyristor devices generate characteristic power-frequency harmonics through delayed firing, while VSC devices generate harmonics related to converter topology, modulation, switching frequency, controller behaviour and converter impedance. So thyristor-based FACTS → harmonic current source behaviour; VSC-based FACTS → harmonic voltage source and control-impedance behaviour — a distinction that is fundamental to selecting the model.
Two broad modelling families
Thyristor-based FACTS — such as SVCs and TCSCs — often produce harmonics through phase-controlled reactor current, and are usually represented as harmonic current sources. VSC-based FACTS — such as STATCOMs, SSSCs, UPFCs and IPFCs — normally behave as harmonic voltage sources behind converter and transformer impedance, with a control-dependent impedance.
Why FACTS harmonic modelling is difficult
FACTS harmonic behaviour depends on many interacting factors: operating point, control mode, switching technology, firing angle or modulation strategy, connected filters, transformer impedance, AC system strength, background voltage distortion and network harmonic impedance. An SVC at one firing angle may generate a different spectrum than at another; a STATCOM may have low emission yet still affect resonance or interact with background distortion. The message: FACTS harmonic behaviour is operating-point dependent, so a single fixed model may not be enough for all assessments.
Section 3
SVC harmonic modelling
An SVC usually combines thyristor-controlled reactors (TCR), thyristor-switched capacitors (TSC), thyristor-switched reactors (TSR), mechanically-switched capacitors and reactors, harmonic filters and the SVC transformer. The main harmonic source is normally the TCR, which controls reactive power by delaying the firing angle of antiparallel thyristors in series with a reactor. At \(\alpha=90^\circ\) the current is continuous and sinusoidal (ideal case); as the firing angle increases toward \(180^\circ\) the current becomes discontinuous and pulse-shaped, producing harmonics. In short, a larger firing delay → more waveform distortion → harmonic current generation.
TCR characteristic harmonics
In an ideal balanced TCR the current has half-wave symmetry, so even harmonics cancel. In a balanced three-phase arrangement the TCR is commonly delta-connected, trapping triplen harmonics inside the delta. The remaining characteristic orders are:
Orders \(6n+1\) are positive-sequence and orders \(6n-1\) are negative-sequence harmonics. TCR harmonic assessment must consider firing angle, because the maximum of each harmonic order does not necessarily occur at the same firing angle.
Non-characteristic harmonics
Real SVCs are not perfectly symmetrical, so non-characteristic harmonics can appear — from asymmetrical thyristor firing, unequal phase reactors, system voltage unbalance, control imbalance, equipment tolerances or negative-sequence background voltage. Even harmonics may appear if antiparallel firing is asymmetrical, and triplen harmonics (most importantly \(h=3\)) may escape the delta if the system or equipment is unbalanced. The ideal characteristic spectrum is suitable for screening, but non-characteristic harmonics should be considered for detailed assessment, especially where unbalance or tight compliance margins exist.
Section 4
TSC and TSR harmonic behaviour
Thyristor-switched capacitors and reactors operate differently from TCRs. A TSC is switched at a controlled instant so the capacitor voltage matches the system voltage, avoiding large transients and not creating continuous harmonic generation in normal operation; once switched in, it behaves mainly as a capacitor branch. So a TSC is normally not a continuous harmonic source, but it is an important harmonic impedance element — it may still interact with the network and other SVC components to create resonance. A TSR is also switched in steps and generally does not behave like a phase-controlled TCR. The message: the TCR produces continuous harmonic current, while TSC/TSR mainly affect harmonic impedance and switching states.
Section 5
SVC filters and connection arrangement
SVCs commonly require passive filters to absorb TCR-generated harmonic currents and keep voltage distortion within limits. They may be tuned to the 5th, 7th, 11th and 13th (or other) orders, with branch impedance:
\[ Z_F(h)=R+j\!\left(hX_{L1}-\frac{X_{C1}}{h}\right) \qquad\Rightarrow\qquad Z_F(h_n)\approx R \]
At the tuning frequency the filter provides low impedance. SVC filters must be represented explicitly because they affect harmonic current absorption, PCC voltage distortion, background harmonic amplification, filter component duty and the overall network impedance — they are part of the harmonic model, not an optional detail.
Connection arrangement
SVC winding and component connections strongly affect harmonic propagation. The TCR and TSC are often delta-connected to trap triplen harmonics; filters and fixed shunts may be in ungrounded wye to block zero-sequence and third-harmonic currents; and the SVC transformer may have a delta secondary to prevent zero-sequence harmonics entering the grid. The model should represent delta and wye connections, grounded or ungrounded neutral, the transformer vector group and the zero-sequence paths — especially for triplen and zero-sequence studies.
Section 6
SVC as a source and background amplification
For assessing new harmonic distortion caused by an SVC, the TCR is represented as a shunt harmonic current source because it injects non-sinusoidal current into the busbar. The harmonic spectrum depends on firing angle, reactor size, voltage level, operating point and filter status, and each order is a phasor:
RMS magnitude of the TCR harmonic current at order \(h\)
\(\phi_{TCR,h}\)
phase angle of the TCR harmonic current at order \(h\)
For each order, \(I_{TCR,h}\) is injected into the network model together with the SVC filters, transformer, TSC branches and external system impedance, so that:
\[ V_h=Z_{eq,h}\,I_{TCR,h} \]
\(Z_{eq,h}\)
equivalent impedance seen by the TCR harmonic current source
The harmonic source should be defined for all important orders, relevant firing angles, TSC in-service and out-of-service states, filter configurations and external network impedance scenarios. The rule: do not assess SVC harmonics for only one operating point — the maximum harmonic current for each order may occur at different firing angles.
Background harmonic amplification
An SVC may also amplify or damp pre-existing background distortion — a different assessment from new emission. Here the SVC is represented as a passive harmonic impedance network and the existing distortion as a harmonic voltage source, to answer: will the new SVC amplify existing background harmonic voltage? Conceptually the new PCC harmonic voltage is a function of \(V_{h,background}\), \(Z_{SVC,h}\) and \(Z_{system,h}\), and the assessment must include the TCR impedance as a function of firing angle, the TSC impedance, the filters, the transformer and the external system impedance envelope. This matters because FACTS devices can cause harmonic problems even when their own emission is low, by changing the impedance seen by background distortion.
System-wide SVC modelling
For a system-wide study the SVC should be represented by its main components — the TCR harmonic current source, the operating-point-dependent TCR impedance, the TSC branches, the filters, the SVC transformer and any mechanically switched shunts. A simplified equivalent may suffice for screening; for compliance, component duty or resonance, the model should include the actual topology and operating scenarios. Use manufacturer design data wherever available — for maximum and minimum component impedances, filter tolerances, TCR spectra, firing-angle dependency and the operating range.
Section 7
TCSC harmonic modelling
A Thyristor-Controlled Series Compensator is series-connected and controls the effective reactance of a line. It consists of a fixed series capacitor in parallel with a thyristor-controlled reactor, and can operate in bypassed-thyristor, blocked-thyristor, capacitive Vernier or inductive Vernier modes; in Vernier mode the firing angle controls the equivalent reactance. The harmonic behaviour comes mainly from the TCR part, but because the TCR is in parallel with the series capacitor, much of the harmonic current circulates locally through the capacitor branch rather than propagating into the system. So TCSC harmonic emission is usually less severe than a standalone TCR, but it still needs assessment.
Source representation and harmonic orders
TCSC harmonic generation can be represented as a series harmonic voltage source behind a low internal impedance — different from the SVC TCR, which is a shunt harmonic current source. So an SVC → shunt current-source injection; a TCSC → series voltage-source injection. Because the TCSC is in series with a line, both line terminals can be affected, and a correct model should represent the impedance at bus 1, the impedance at bus 2, the mutual impedance between them, and the line impedance and outage conditions — a simple single-bus Thevenin equivalent may not represent series-device propagation correctly. TCSCs may produce odd harmonics from TCR operation, with lower orders dominating in many installations (especially \(h=3,\ 5,\ 9\)); the exact spectrum depends on firing angle, operating mode, the capacitor-reactor arrangement, the number of series modules and line impedance. Model TCSC harmonics over the operating range, focusing especially on lower-order harmonics unless project data shows otherwise.
A TCSC is a series device, not a shunt source
A TCSC should not be represented as a single shunt current source at one bus. It is connected in series with the line, so its harmonic effect appears as a series voltage injection and can influence both terminals of the compensated line. The model should therefore include the line section, the series capacitor, the thyristor-controlled reactor, the bypass state, the operating mode and outage conditions.
Here \(h\) means harmonic order. For a 50 Hz system, \(h=3\) means 150 Hz, \(h=5\) means 250 Hz, and \(h=9\) means 450 Hz.
Section 8
STATCOM harmonic modelling
A STATCOM is a self-commutated VSC device, commonly using modular multilevel converter (MMC) technology. Unlike an SVC it does not use thyristor phase-controlled reactors; it generates an AC voltage with a converter and controls reactive current through the difference between converter voltage and system voltage. Its harmonic behaviour depends on converter topology, the number of voltage levels, switching frequency, modulation strategy, dead time, sampling cycle, the PLL, the inner current control, the outer voltage or reactive-power control, and the operating point. STATCOM emissions are often lower than an SVC and may not need large passive filters — but the STATCOM cannot be ignored: it may affect harmonic impedance, background distortion, control interaction, harmonic damping and resonance stability.
STATCOM as a harmonic voltage source
A STATCOM is normally represented as a harmonic voltage source behind an internal harmonic impedance, conceptually \(E_h\) behind \(Z_{STATCOM,h}\):
\[ V_h=E_h-Z_{STATCOM,h}\,I_h \]
\(V_h\)
harmonic voltage at the STATCOM connection point
\(E_h\)
converter-generated harmonic voltage at order \(h\)
\(Z_{STATCOM,h}\)
equivalent STATCOM harmonic impedance at order \(h\)
\(I_h\)
harmonic current exchanged with the AC network at order \(h\)
This is a conceptual Thevenin-type representation. The impedance may include the converter, reactor, transformer, filters and the control-system effect.
So an SVC TCR → harmonic current source; a STATCOM → harmonic voltage source behind impedance. For emission studies the vendor may provide maximum harmonic voltages over the operating range; a non-consistent set of maxima (the maximum for each order, even though those maxima may not all occur at the same operating point) may be used conservatively for distortion assessment.
STATCOM model = harmonic voltage source + control-dependent impedance
The harmonic voltage source represents converter-generated distortion; the impedance represents the converter internal impedance, phase reactor, step-up transformer, filters and control response. At low harmonic orders the control behaviour may be important; at higher harmonic orders the passive components may dominate.
STATCOM harmonic impedance
The STATCOM harmonic impedance is not only the passive components — it may include the effect of converter control. The equivalent impedance may include the converter internal impedance, the phase reactor, the step-up transformer, the harmonic filters, controller transfer functions, PLL influence and current-controller influence. At low frequencies (up to roughly the 5th harmonic) the impedance may depend on operating point and controller behaviour; at medium and high frequencies passive components such as reactors and transformers may dominate. So low-frequency STATCOM impedance → control dependent; higher-frequency impedance → passive-component dominated. The vendor should provide impedance data for relevant operating points where detailed assessment is required.
Section 9
Control interaction and weak grids
The PLL, or Phase-Locked Loop, is the control block that estimates the grid-voltage phase angle. If the measured voltage is distorted, the PLL may pass part of that distortion into the converter control reference — which is why it matters for harmonics.
STATCOM control systems can shape harmonic impedance. The phase-locked loop (PLL) measures the grid voltage and determines the phase angle used by the control; the current controller regulates converter current; the outer loop regulates DC voltage, AC voltage or reactive power. If the background grid voltage contains harmonic distortion, that distortion can enter the control through the PLL and measurement chain, so the converter output voltage reference may then contain harmonic components. The practical sequence is: background voltage distortion → PLL and control response → converter voltage-reference distortion → STATCOM harmonic voltage. This is why STATCOM modelling may require control-system information, especially in weak grids.
STATCOMs in weak networks
In weak networks, converter impedance and control interaction become more important. A useful screening indicator of grid strength is the short-circuit ratio \(SCR\):
\[ SCR=\frac{S_{sc}}{S_{conv}} \]
\(SCR\)
short-circuit ratio at the converter connection point
\(S_{sc}\)
short-circuit power at the converter connection point
\(S_{conv}\)
converter rating
A low \(SCR\) means the converter is electrically connected to a weak grid, so its controls and harmonic impedance can interact more strongly with the AC network.
When the ratio is low the converter interacts more strongly with the AC system. If \(SCR\leq 3\), the STATCOM impedance model may need to include PLL impedance shaping and cross-coupling effects — cross-sequence coupling, cross-frequency coupling, subsynchronous interaction and harmonic-range instability.
Important modelling limitation
A standard harmonic penetration study assumes linear behaviour at each harmonic frequency. It may not capture converter-control interactions, cross-frequency coupling, limiters, PLL dynamics, subsynchronous interaction or harmonic instability. Where the grid is weak or the control response is important, vendor impedance models, EMT simulation or specialised impedance-based stability analysis may be required.
Section 10
SVC vs STATCOM harmonic behaviour
Both provide dynamic reactive compensation, but their harmonic behaviour differs.
Table 1 — SVC and STATCOM harmonic behaviour compared.
Aspect
SVC
STATCOM
Main technology
Thyristor-controlled reactor/capacitor
Voltage-source converter
Main harmonic source type
Current source from TCR
Voltage source from converter
Harmonic dependency
Firing angle and operating point
Modulation, control and operating point
Characteristic harmonics
Significant low-order \(6n\pm1\)
Usually lower, often switching-related
Filters
Usually required
Often smaller or not required
Background distortion effect
May amplify through passive impedance
May interact through converter impedance/control
Control influence
Mainly susceptance variation
Impedance shaping and active damping
Weak-grid behaviour
Can have sub-fundamental interaction
PLL/control interaction can be important
So an SVC harmonic study → emission from the TCR and passive resonance; a STATCOM harmonic study → converter voltage emission and impedance interaction.
Section 11
SSSC, UPFC and IPFC
A Solid State Series Compensator (SSSC) is a series-connected VSC that injects a controllable voltage in series with the line through a transformer. Its behaviour is similar to other VSC devices, but the injection point is in series, so it is represented as a series harmonic voltage source behind the converter and transformer harmonic impedance. SSSC harmonics appear as series voltage injection, not a simple shunt current source, and the network model must represent both sides of the series connection and the line impedance accurately.
A Unified Power Flow Controller (UPFC) combines a shunt converter and a series converter, so harmonic generation may come from the shunt converter (behaving like a STATCOM), the series converter (behaving like an SSSC), or both. A complete model should include both converters, their transformers, coupling reactors, filters and the common DC-link interaction where relevant; for simplified studies the combined effect may be represented by equivalent voltage or current sources depending on the objective. UPFC modelling must consider both shunt and series converter paths.
An Interline Power Flow Controller (IPFC) uses converters connected in series with different lines, often sharing a common DC link, and may include a shunt converter. Each series converter may need to be represented as a harmonic voltage source in series with its line, with the model including a harmonic voltage source for each line, the converter internal impedance, the series transformer, the line impedance and the common DC-link interaction where relevant. IPFC modelling is multi-terminal and line-specific — a single equivalent source may not suffice if harmonic propagation in individual lines matters.
Both converter paths and DC-link interaction may matter
IPFC
Multiple series voltage sources, possibly with a common DC link
Multi-line propagation may need explicit representation
Section 12
Active harmonic filtering by FACTS devices
Active filtering means the converter is deliberately controlled to reduce harmonic distortion, not only to regulate voltage or reactive power. It may do this by injecting a compensating harmonic current or voltage, or by shaping its apparent impedance so it behaves like a damping element at selected frequencies.
Modern VSC-based FACTS devices can sometimes provide active harmonic filtering — the control is designed not only to regulate voltage or reactive power but also to reduce harmonic distortion. This may be achieved by harmonic current compensation, harmonic voltage compensation, virtual impedance shaping, virtual resistance or active damping of resonance. The converter improves performance in two ways: it can inject a compensating harmonic current or voltage to reduce distortion, and it can shape its equivalent impedance so it behaves like a damping element at selected frequencies. So harmonic compensation → controlled source action; active damping → controlled impedance action — both may be implemented in the converter control.
Modelling active filtering
A FACTS device with active filtering can be represented by a Thevenin equivalent (a harmonic voltage source plus an equivalent impedance) or a Norton equivalent (a harmonic current source plus an equivalent admittance). The two forms convert as:
The two forms are equivalent only if the source and impedance are defined consistently for the same operating point and frequency range.
The source represents the active-filtering contribution; the impedance or admittance represents the converter control response and passive components — an active filter is a controlled source plus a control-dependent impedance. Conceptually, the compensating current reduces what reaches the grid:
\[ I_{grid,h}=I_{source,h}-I_{comp,h} \]
\(I_{grid,h}\)
remaining harmonic current flowing into the grid at order \(h\)
\(I_{source,h}\)
harmonic current produced by the network or load source
\(I_{comp,h}\)
compensating harmonic current injected by the FACTS device
This is a simplified conceptual equation. Actual performance depends on measurement, control delay, current limits, frequency range and stability margins.
For standard propagation studies a linearised frequency-domain model may be sufficient, but if the active-filtering control includes nonlinear elements such as limiters, instability detection, auto-tuning or switching logic, the frequency-domain model may not be adequate, and time-domain or real-time simulation may be required.
Section 13
Vendor data, study cases and the two assessments
FACTS harmonic modelling often requires vendor information, because many important parameters are proprietary or depend on detailed control implementation.
Table 3 — Vendor data required for FACTS harmonic modelling.
Data
Purpose
Harmonic current spectrum
SVC/TCR emission assessment
Harmonic voltage spectrum
STATCOM/VSC emission assessment
Operating-point dependency
Check the full range of operation
Converter impedance
Assess resonance and background amplification
Controller bandwidth
Identify low-frequency interaction
PLL behaviour
Assess weak-grid interaction
Filter data
Represent harmonic mitigation
Transformer impedance
Represent transfer and damping
TSC/TCR impedance range
Assess SVC resonance
Component tolerances
Worst-case tuning and impedance
Max/min branch impedances
Impedance-envelope assessment
Active damping transfer function
Represent control-based damping
FACTS harmonic models should be vendor-supported where possible; for third-party studies, simplified models may be used but their limitations should be clearly stated.
The FACTS vendor should provide
device type and topology;
rated voltage and MVAr range;
transformer and reactor data;
filter branch data;
harmonic source spectrum;
harmonic impedance or admittance versus frequency;
operating-point dependency;
control mode: voltage, reactive-power, power-flow, damping or active-filtering;
PLL and current-controller assumptions where relevant;
frequency range of validity;
positive-, negative- and zero-sequence behaviour, where relevant;
weak-grid limitations;
outage or bypass modes;
model limitations and recommended use.
The study engineer should confirm
whether the device is shunt, series or combined shunt-series;
whether the source is current-source or voltage-source type;
whether the impedance is passive or control-dependent;
whether background distortion affects the device response;
whether the model includes filters and transformer impedance;
whether all operating modes are covered;
whether weak-grid behaviour requires EMT or impedance-based analysis;
whether active filtering is enabled or disabled;
whether the model suits compliance, resonance, component-duty or stability assessment.
Study cases
A FACTS harmonic study should include multiple operating conditions. For an SVC: different TCR firing angles, TSC in and out of service, credible filter outages, the maximum capacitive and inductive range, the system impedance minimum and maximum, and background distortion. For a STATCOM: maximum capacitive output, maximum inductive output, zero reactive output, the weak-grid condition, different controller modes, background distortion and the manufacturer impedance envelopes. The message: FACTS harmonic performance cannot be proven with one operating point.
Emission and impedance must both be checked
Two assessments are normally required. The harmonic emission assessment checks the new distortion caused by the device, \(V_{h,new}=Z_{eq,h}I_{h,device}\) (or, for VSC devices, a function of \(E_{h,device}\) and \(Z_{eq,h}\)). The background distortion amplification assessment checks whether the device changes the network impedance so as to amplify existing distortion — the total being a function of \(V_{h,background}\), \(Z_{device,h}\) and \(Z_{system,h}\). The two can be separated by superposition. The rule: low device emission does not guarantee low harmonic impact, because background distortion may still be amplified.
Section 14
Workflow and sensitivity
A practical FACTS harmonic modelling workflow is as follows:
Identify the FACTS technology — SVC, TCSC, STATCOM, SSSC, UPFC or IPFC.
Define whether the device is shunt-connected, series-connected, or combined shunt and series.
Identify the harmonic source type — current source, voltage source, or controlled impedance.
Include all passive components — reactors, capacitors, filters, transformers, damping resistors.
Define operating cases and switching states.
Include vendor harmonic emission data or conservative maximum spectra.
Include converter or device harmonic impedance data.
Check new harmonic emission.
Check amplification or damping of background distortion.
Perform sensitivity studies for network impedance, component tolerances and control modes.
Table 4 — Relative sensitivity of FACTS harmonic results to modelling choices.
Parameter
Typical Impact
Comment
Operating point
Very high
Emission and impedance may change
Firing angle
Very high for SVC/TCSC
Controls TCR harmonic generation
Converter control
Very high for STATCOM/VSC
Shapes impedance and emission
Filter configuration
Very high
Controls absorption and resonance
TSC/MSC switching state
High
Changes impedance and resonance
External system impedance
High
Determines distortion amplification
Background distortion
High
May be amplified or damped
Component tolerances
High
Shift tuning and impedance
SCR
High for VSC devices
Weak-grid interaction
Transformer / vector group
Medium to high
Affects propagation and zero sequence
Neutral grounding
High for triplen harmonics
Determines zero-sequence paths
FACTS harmonic studies require operating-range and impedance-sensitivity assessment, not only nameplate data.
Section 15
Reporting and summary
A harmonic study report should clearly state how the FACTS device was represented. A weak statement — “the SVC was included in the harmonic model” — tells the reader nothing.
Examples of a clear modelling statement
“The SVC was represented using a TCR harmonic current source, operating-point-dependent TCR impedance, TSC branches, harmonic filters and SVC transformer impedance; TCR harmonic spectra were assessed over the relevant firing-angle range.”
“The STATCOM was represented as a harmonic voltage source behind a vendor-provided harmonic impedance, including converter reactor, step-up transformer, passive filters and operating-point-dependent converter impedance.”
“The converter active-filtering function was represented as a controlled harmonic source with an associated control-dependent impedance over the specified frequency range.”
Common modelling mistakes
Treating a STATCOM as a simple passive shunt capacitor or reactor.
Treating an SVC TCR and a STATCOM as the same type of harmonic source.
Ignoring TCR firing-angle dependency.
Ignoring filter and transformer impedance.
Modelling a TCSC as a shunt current source instead of a series voltage source.
Ignoring both terminals of a series-connected device.
Ignoring control-dependent impedance in VSC-based FACTS devices.
Ignoring PLL interaction in weak grids.
Using a single operating point for a device with a wide MVAr range.
Assuming active filtering is available without confirming the control function and limits.
To summarise: FACTS devices both generate harmonics and modify the network harmonic impedance. Thyristor-based devices (SVC, TCSC) generate harmonics through thyristor firing; the main SVC source is the TCR, with characteristic orders \(h=6n\pm1\) under ideal balanced conditions. The TCR is represented as a harmonic current source for emission studies, while the TCR, TSC, filters and transformer are also represented as impedance elements for background-amplification studies. VSC-based devices (STATCOM, SSSC, UPFC, IPFC) are represented as harmonic voltage sources behind a converter internal impedance, with behaviour depending on topology, modulation, switching frequency, controller design, PLL behaviour, operating point and system strength.
For weak grids, especially \(SCR\leq 3\), control interaction, impedance shaping and cross-frequency coupling may become important — needing vendor models, EMT studies or specialised impedance-based analysis. Active-filtering functions may be represented as controlled harmonic sources or control-dependent impedances, reducing distortion by direct compensation or active damping.
In short: FACTS devices should be modelled according to their technology and connection point. Thyristor-based devices (SVC, TCSC) are strongly influenced by firing angle, filters and operating mode; VSC-based devices (STATCOM, SSSC, UPFC, IPFC) should normally be represented as harmonic voltage sources behind converter, transformer and control-dependent impedance. For weak-grid or control-sensitive cases, standard frequency-domain studies may need to be supported by vendor impedance models, EMT simulation or specialised impedance-based analysis. A clear harmonic study should then state:
the device topology;
the source representation;
the impedance representation;
the filter and transformer data;
the control mode and operating range;
the weak-grid assumptions;
the active-filtering status;
the model limitations.
Key message
FACTS devices must be assessed for both emission and impedance interaction. A robust study should state the FACTS technology, source representation, impedance representation, operating range, filter configuration, transformer model, control influence, background-distortion treatment, network impedance scenarios and vendor-data limitations. Only then can the harmonic impact of SVCs, STATCOMs and other FACTS devices be assessed correctly — the eighth 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.
08
08Part EightReading now
FACTS Device Modelling for Harmonic Studies
SVC, TCSC, STATCOM, SSSC, UPFC and IPFC as harmonic sources and control-dependent impedances; firing-angle and converter-control dependency; weak grids; active filtering; operating-range assessment.
