Renewable Modelling · Small-Signal Stability & Islanding

Modelling IBGs for Small-Signal Stability and Unintentional Islanding

Two studies, almost opposite modelling needs. Small-signal stability asks whether tiny disturbances grow or decay — you linearise the system and read the eigenvalues, and inverter-based generation (IBG) matters only through how it reshapes the machines that remain. Unintentional islanding asks whether a disconnected pocket of grid can keep running undetected — and here it is the protections that carry the study. This guide covers both: eigenvalues, damping and mode shapes; how IBG changes electromechanical damping without adding modes of its own; the non-detection zone and the reactive-power balance that gives an island away; passive and active anti-islanding; and the IBG functions to model for each. It continues the modelling series that runs from frequency stability through the large- and long-term-voltage guides.

Reading time ≈ 34 min · Small-signal & islanding, step by step

Earlier pages introduced how the inverter-based generator (IBG) differs from a synchronous machine, the inverter and its controls, the RMS / phasor and EMT models, and the frequency- and voltage-stability studies. This page applies the same modelling logic to two special studies: small-signal stability, where only very small disturbances are examined, and unintentional islanding, where the question is whether the IBG can tell it has been cut off from the main grid. They share a page for a reason that is itself the lesson: their modelling requirements are almost opposite.

Why these two topics sit together

Small-signal stability normally ignores protection trips, current limiters and large-disturbance nonlinear behaviour, because the disturbance is tiny. Islanding studies do the reverse: they lean heavily on protection, detection logic and trip / reconnection behaviour. That contrast is the whole point — it shows, more sharply than any single study could, that the IBG model you need depends on the phenomenon, not on the plant technology name.

The two studies at a glance

Part A — Small-signal stability: small disturbances; a linearised model; eigenvalues and damping; the controls and capabilities matter; protection usually ignored.

Part B — Unintentional islanding: a network section becomes separated; local generation may keep it energised; detection / protection is central; active and passive anti-islanding functions matter; RMS or EMT depending on the detection method.

Abbreviations used on this page

IBGInverter-based generation (or generator)

RMSRoot-mean-square (phasor) simulation

EMTElectromagnetic transient (time domain)

EMTP®Electromagnetic Transients Program (an EMT tool)

PVPhotovoltaic

WTGWind-turbine generator

DFIGDoubly-fed induction generator

PLLPhase-locked loop

MPPTMaximum power point tracking

ROCOFRate of change of frequency

LOMLoss of mains

NDZNon-detection zone

FRTFault ride-through

LVRT / HVRTLow- / high-voltage ride-through

PODPower oscillation damping

PSSPower system stabiliser

STATCOMStatic synchronous compensator

P(f)Active power as a function of frequency

P(V)Active power as a function of voltage

Q(V)Reactive power as a function of voltage

PCCPoint of common coupling

POIPoint of interconnection

Key idea

Small-signal stability is judged by linearising the system and reading the eigenvalues of the state matrix: a complex pair \(\lambda = \sigma \pm j\omega\) is a stable mode only if \(\sigma \lt 0\), with damping ratio \(\zeta = -\sigma/\sqrt{\sigma^2+\omega^2}\); a mode below \(\approx\)3–5% damping is treated as critical.
IBGs have no internal rotor angle, so they create no classical electromechanical mode of their own — but by displacing machines, shifting dispatch and power flows, and lowering inertia they reshape the damping and mode shapes of the machines that remain (and their own fast controls can add PLL / control modes in weak grids).
An unintentional island survives only inside the non-detection zone — where the IBG output nearly matches the local load in both active and reactive power at the instant of disconnection; a mismatch in either moves frequency or voltage and helps the protection detect the island.
The two studies need near-opposite model content: small-signal needs the controls and capabilities but not the protections / limiters (it works with tiny increments), whereas islanding needs almost everything — because it is the protections that must detect and disconnect.

Key terms used on this page

01Small-signal stability

Whether the system returns smoothly to its operating point after a very small disturbance — whether tiny oscillations decay or grow.

02Linearisation

Replacing the nonlinear model with a small-disturbance approximation around one operating point; valid only near that point.

03State matrix

The matrix \(A\) describing how small changes in the system states evolve with time; its eigenvalues decide stability.

04Eigenvalue

A mode of the linearised system, \(\lambda = \sigma \pm j\omega\); the real part sets decay or growth, the imaginary part sets the oscillation frequency.

05Damping ratio

\(\zeta = -\sigma/\sqrt{\sigma^2+\omega^2}\); how quickly a mode decays. Below about 3–5% is treated as poorly damped.

06Mode shape

Which machines, controllers or states take part in a mode, and whether they move together or against each other.

07Participation factor

A measure of which state variables are most involved in a mode — generator, exciter, governor, plant controller or PLL state.

08Synchronising / damping torque

Synchronising torque pulls the rotor back after an angle disturbance; damping torque shrinks the oscillation over time.

09Unintentional islanding

A network section separates from the main grid but stays energised by local generation, undetected — a safety and power-quality hazard.

10Loss of mains (LOM)

Loss of connection to the main utility grid; anti-islanding / LOM protection detects it and disconnects the generator.

11Non-detection zone (NDZ)

The range of active / reactive mismatch where the island’s voltage and frequency stay near normal, so passive protection may not detect it.

12Anti-islanding (passive / active)

Passive watches voltage, frequency, ROCOF or vector jump; active injects a small perturbation and watches the response.

Symbols used on this page

\(\lambda = \sigma \pm j\omega\) — an eigenvalue (mode); \(\sigma\) its real part (damping / growth), \(\omega\) its imaginary part (oscillation, in rad/s), \(j\) the imaginary unit.
\(\zeta\) — damping ratio; \(f = \omega/2\pi\) — the oscillation frequency in Hz.
\(\Delta P,\ \Delta Q\) — the active- and reactive-power mismatch between local generation and local load at the instant of islanding.

Part A · Section 1

What small-signal stability is

Start with the plain idea. Small-signal stability asks whether the power system returns smoothly to its operating point after a very small disturbance — a small load change or a small control movement. It is not about large faults or protection trips; it is about whether tiny oscillations decay or grow.

The method is linearisation: replace the nonlinear power-system model with a small-disturbance approximation around one operating point. The result is valid only near that point. If the disturbance is large enough to activate protection, current limits, LVRT / HVRT or a controller mode switch, it is no longer a pure small-signal study. What are the “states” that get linearised? The things with memory: generator rotor angles and speeds, controller integrator states, PLL states, and plant-controller states. Around the operating point, the way small changes in these states evolve can be written as a compact state-space form:

\[ \Delta\dot{x} = A\,\Delta x + B\,\Delta u, \qquad \Delta y = C\,\Delta x + D\,\Delta u \]

\(\Delta x,\ \Delta y,\ \Delta u\): small deviations of the state, output and input vectors
\(A\): state matrix — its eigenvalues decide stability
\(B,\ C\): input and output matrices
\(D\): the part of the input that appears directly in the output

The state matrix \(A\) is the heart of it: it describes how the small changes evolve with time, and its eigenvalues are read directly for stability.

An eigenvalue tells whether one oscillation mode decays, stays constant, or grows. For power systems, eigenvalues often appear as complex pairs, because many modes oscillate:

\[ \lambda = \sigma \pm j\omega \]

\(\lambda\): the eigenvalue (mode)
\(\sigma\): the real part — it controls damping or growth
\(\omega\): the imaginary part — it controls the oscillation frequency (rad/s)
\(j\): the imaginary unit

If \(\sigma \lt 0\), the oscillation decays (stable). If \(\sigma = 0\), it neither decays nor grows (marginal). If \(\sigma \gt 0\), it grows — unstable. The oscillation frequency is \(f = \omega/2\pi\) (with \(\omega\) in rad/s and \(f\) in Hz).

The damping ratio turns those two numbers into a single, percentage-like measure of how quickly the mode decays:

\[ \zeta = \frac{-\sigma}{\sqrt{\sigma^2 + \omega^2}} \]

A larger positive \(\zeta\) means faster decay; a small \(\zeta\) means the oscillation lingers; a negative \(\zeta\) means instability. The commonly quoted 3–5% warning range is a practical screening criterion, not a universal law. Figure 1 shows where these modes sit.

Figure 1 — The eigenvalue plane. The real part \(\sigma\) runs left–right and the imaginary part \(\omega\) up–down; a mode is stable in the left half-plane (\(\sigma \lt 0\)) and unstable in the right (\(\sigma \gt 0\)). The further left a mode sits, the more heavily it is damped.

Part A · Section 2

Reading the modes

What does an eigenvalue look like in a real waveform? Exactly the three cases of Figure 2: a well-damped mode dies away quickly, a poorly-damped mode rings for a long time, and an unstable mode grows.

Figure 2 — The same three modes as waveforms. A well-damped mode (\(\sigma\) well below zero) decays fast; a poorly-damped mode (\(\sigma\) just below zero) rings on; a growing mode (\(\sigma \gt 0\)) is unstable.

Two torques decide the shape. Synchronising torque pulls a generator rotor back toward synchronism after an angle disturbance; damping torque reduces the oscillation amplitude over time. A system can have plenty of synchronising torque yet poor damping — and then the oscillation lasts a long time even though the machine does not fall out of step. On the power-angle curve the synchronising-torque coefficient is the slope; it falls to zero at a \(90^\circ\) angle difference, so a positive slope (a positive synchronising-torque coefficient, with the angle below \(90^\circ\)) is the condition against aperiodic (monotonic) instability. Oscillatory small-signal stability needs something more — adequate damping torque (\(\sigma \lt 0\)) — and a poorly-damped or growing swing often needs an added damping source such as a power system stabiliser (PSS) or inverter power-oscillation damping (POD).

The mode shape comes from the eigenvectors, and it answers “who is involved?” It shows which machines, controllers or plant states participate strongly in a mode, and whether they move together or against each other. If two areas swing against each other it is an inter-area mode (typically 0.1–2 Hz, far below the 50 Hz system frequency of the UK and Europe); if one generator swings mainly against the rest of the system it is a local mode. A related tool, the participation factor, indicates which state variables are most involved in a mode — it tells you whether the mode is mainly a generator, exciter, governor, plant-controller or PLL state, so you know what to re-tune. IBGs can change mode shapes indirectly, by changing dispatch and power flows.

Two practical notes. “Small disturbance” is relative: a disturbance counts as small only if the system stays close enough to its operating point for linearisation to remain valid — a small load step or a small setpoint change qualifies, whereas a large fault that trips protection or hits the current limits does not. The test is how little the disturbance perturbs the system, not a fixed size. And a growing oscillation is hard to catch early, because it hides under the steady-state oscillations of natural load change; by the time it is obvious, corrective action may be too late. That is why small-signal stability is of growing interest to operators as IBG penetration rises.

Part A · Section 3

How IBGs affect small-signal stability

Why do IBGs create no classical rotor-angle mode? A grid-following PV or full-converter plant has no directly grid-coupled rotor angle like a synchronous machine; its ac-side behaviour is imposed by the converter controls. So it has no angle state variable in the electromechanical mode shape, and it creates no classical synchronous-machine rotor-angle mode. But that is not the same as “no modes at all”: the IBG’s own fast controls can create PLL and control modes, especially in weak grids — and those are usually the province of EMT or impedance-based analysis rather than classical electromechanical eigenvalue analysis.

Even without adding rotor-angle modes, large amounts of IBG still reshape the modes of the remaining synchronous system. They change generator dispatch, power-flow patterns, network loading, reactive support, the inertia level and the controller interactions. So IBG penetration can improve or worsen damping, depending on location, control settings and operating condition:

by shifting the dispatch of synchronous generation — critical machines may have to be kept online to hold the damping of low-frequency modes;
by changing the power flows in the transmission network;
by interacting with machines to alter the damping torque on their shafts — which depends on the inverter’s dynamics and on other fast controls (STATCOMs installed for voltage support, for example);
by changing the inter-area mode shape of the machines that are not displaced;
by reducing system inertia at high penetration.

Do not read a single universal trend into this. A low or moderate penetration of IBG may help damping — it can lighten the net load so the largest angle difference between machines shrinks (a cited case shows the modal frequency and the damping ratio both rising as PV goes from 10% to 20%) — but a higher penetration may worsen it if it displaces well-damped synchronous machines, weakens voltage support, or creates poorly-tuned control interactions. Two cautions on the models themselves: the first-generation WECC generic IBG models and the IEC 61400-27 wind models were not built for eigenvalue analysis (they contain highly nonlinear, simplified elements, so linearising them is not trivial and sometimes fails); and beware crude displacement rules such as “3 MW of renewables → 2 MW less commitment and 1 MW less dispatch” — they lower system inertia and can create small-signal problems, so decide which machines to keep by a sensitivity analysis with respect to generator inertia. This applies whether the displaced fleet is PV, WTG or DFIG wind.

Part A · Section 4

Which functions to model for small-signal analysis

Because the analysis works with tiny increments around the operating point, the protections and limiters are ignored — they never act for such small excursions. What matters is the continuous control dynamics. Concretely, include active-power control, reactive / voltage control (Q(V)), the plant controller, the PLL if it is represented in the RMS small-signal model, POD if present, and frequency response if it affects the studied mode. Usually exclude the LVRT / HVRT trip curves, current limiters that act only during large disturbances, anti-islanding trips, protection trips, and the fast MPPT detail — unless the active-power controller dynamics are themselves part of the study. The reason for every exclusion is the same: the disturbance is too small to trigger these nonlinear functions. The governing rule is that small-signal and transient-stability studies generally use the same system and control data, so unless a functionality is needed for transient stability, it is not needed for small-signal either.

A warning about linearising discontinuous logic

Protection trips, current limiters, dead-bands and mode switches are discontinuous or strongly nonlinear. They may not linearise meaningfully at all. If the event you care about actually activates these functions, a time-domain RMS or EMT simulation is more appropriate than pure eigenvalue analysis — the study has left the small-signal world.

Read Table 1 as a small-disturbance modelling guide: a “Yes” means the function can affect the linearised dynamics around the operating point; a “No” means it normally acts only during large disturbances or protection events and should not affect a pure small-signal result.

Table 1 — Recommended IBG functionalities for a small-signal-stability study (after CIGRE Table 3.9).
Category	Functionality	Model?	Note
Control	DC source control	Yes, if the dc link is modelled
Control	Current control	No
Control	PLL	Yes
Control	MPPT	No
Protection	All protection functions	No	ignored — the analysis uses small increments around the operating point
Capability	P(f) control (over / under frequency)	No
Capability	Voltage control by reactive power, Q(V)	Yes
Capability	Voltage control by active power, P(V)	Yes
Capability	Synthetic inertia	Yes
Capability	ROCOF immunity	No
Capability	Fault ride-through (LV / HV)	No
Capability	Active behaviour during fast voltage variations	Yes	often not activated for a tiny voltage dip
Capability	Power oscillation damping (POD)	Yes

The practical message is that small-signal stability needs continuous control dynamics, not trip logic.

A small-signal study workflow

1. Define the operating point and dispatch.
2. Initialise the RMS / dynamic model.
3. Linearise the system around the operating point.
4. Calculate the eigenvalues and damping ratios.
5. Identify the critical modes below the damping threshold.
6. Use mode shapes / participation factors to find the responsible machines or controllers.
7. Repeat for different IBG penetration and dispatch cases.
8. Recommend controller tuning, POD, dispatch changes or network reinforcement if required.

Part B · Section 5

Unintentional islanding

Unintentional islanding occurs when a part of the network becomes electrically separated from the main grid but remains energised by local generation — PV, wind, battery storage or synchronous generation — with voltage and frequency held near nominal. Intentional islanding is fine; the unintentional kind is a hazard, for several reasons at once:

a safety risk to personnel working on lines believed dead;
out-of-phase reclosing when the feeder recloses onto a live, unsynchronised island;
incorrect protection operation in the separated section;
voltage and frequency drifting outside limits;
power-quality problems; and
equipment damage.

The protection meant to prevent it is loss-of-mains (LOM) protection: “loss of mains” means the generator has lost its connection to the main utility grid, and anti-islanding / LOM protection is intended to detect that condition and disconnect the generator — unless intentional islanded operation is specifically designed and permitted. Some countries require an unintentional island to be cleared within a few seconds.

The sequence is worth walking through once, because every detection method is trying to catch one of its steps:

1. The local load is supplied by the grid and the IBG together.
2. An upstream breaker opens, or the network section is disconnected (a recloser, a sectionalising switch, or the customer premises — any sub-section with both generation and load and a way to be fully isolated is a potential island).
3. The local section may remain energised by the IBG.
4. If generation and load are not balanced, voltage and / or frequency move quickly.
5. The protection detects the abnormal condition and trips.
6. If generation and load are closely balanced, detection becomes difficult — the case examined next.

Figure 3 — The unintentional-islanding sequence. A grid-connected feeder loses its upstream breaker; the IBG may keep the local island energised; voltage and frequency then drift (or an active-detection perturbation is applied) until the protection detects the abnormal condition and trips.

Part B · Section 6

Power balance and the non-detection zone

Whether an island can hide comes down to power balance at the instant of disconnection. Two mismatches matter, and they act on different quantities:

An active-power imbalance (\(\Delta P\)) changes frequency, because generation and load are not equal.
A reactive-power imbalance (\(\Delta Q\)) changes voltage, because reactive supply and demand are not equal.

The non-detection zone (NDZ) is the range of active and reactive mismatch where the islanded network’s voltage and frequency stay close enough to normal that passive protection may not detect the island quickly. A small active mismatch mainly nudges frequency; a small reactive mismatch mainly nudges voltage; and if both are closely matched, voltage and frequency stay near normal — which is exactly why islanding detection is hardest when local generation approximately equals local load (Figure 4).

Figure 4 — The non-detection zone. The island is hardest to detect near \(\Delta P = 0,\ \Delta Q = 0\), where neither frequency nor voltage moves enough to trip a passive relay; outside the shaded zone, an active mismatch moves frequency or a reactive mismatch moves voltage and the island is detected.

Reactive power is the subtle lever, and the wording matters: a reactive mismatch helps force detection rather than guaranteeing it. Most loads absorb vars, so to sustain an island the local network needs a var source — power-factor-correction capacitance, parasitic cable capacitance, or larger inverters that can produce or absorb reactive power. If reactive demand exceeds reactive supply, the island voltage falls, which cuts the voltage-dependent active load, which pushes frequency up past its limit and trips the over-frequency protection. So a reactive imbalance indirectly forces detection through the active-power balance, and the risk of a sustained island is negligible when reactive demand exceeds reactive supply.

Studies therefore run three power-balance scenarios: a generation deficit (local generation less than local load; frequency and voltage tend to fall), a generation excess (local generation more than local load; frequency and voltage tend to rise), and a matched case (generation and load close — detection hardest). A ~5–10% deficit and a ~5–10% excess are a practical study range, not a universal standard.

Two complications: rotating machines and reclosers

A synchronous or induction generator (or a motor) inside the island adds inertia, which slows the voltage and frequency drift — making the island look more like a real grid and detection harder — and it can support voltage and frequency for a short time, so its inertia, excitation and protection should be modelled if present. Inertia also raises the risk of out-of-phase reclosing, where the two separated systems drift \(180^\circ\) apart. Many distribution feeders use automatic reclosing: if the island is still energised, the feeder may reclose out of phase, the voltage-vector jump driving high transient currents that can damage machines and prime movers — and with no synchro-check at the HV / MV substation a shock-free resynchronisation is impossible. So islanding detection must operate before reclosing where that is required.

Part B · Section 7

Detecting an island

Anti-islanding protection is built into the inverter, and it comes in two families. Passive (loss-of-mains) methods watch a measured quantity and trip when it leaves a window:

Under / over-frequency — trips if the island frequency moves outside limits.
Under / over-voltage — trips if the voltage moves outside limits (including a 10-minute-mean over-voltage element, positive-sequence under-voltage, and negative- and zero-sequence over-voltage).
ROCOF — trips if the frequency changes too quickly.
Vector jump — trips on a sudden step in the voltage phase angle.
A switch to a narrow frequency band — on command or after another protection acts, the inverter applies a narrower frequency window to make detection more sensitive.
Transfer trip — a direct trip signal sent from the utility when the network is intentionally opened.

The key weakness of passive methods is that they can fail inside the NDZ, when neither voltage nor frequency moves enough. Only some — ROCOF and vector jump in particular — are covered in detail by protection-relay standards.

ROCOF, vector jump, narrow band and transfer trip — in detail

ROCOF is the rate of change of frequency (Hz/s): it measures how quickly frequency is moving, not just its value. High ROCOF can indicate sudden islanding — but a system-wide disturbance can also produce high ROCOF, so settings must avoid nuisance-tripping during a genuine grid event where ride-through is required.
Vector jump detects a sudden step in the voltage phase angle, which happens when the local network separates — but faults, switching and system disturbances also cause phase-angle steps, so settings must be coordinated carefully.
Narrow frequency band: normal frequency protection has wider ride-through limits; after suspected islanding or a command, a narrower window makes detection more sensitive — but must not conflict with grid-code ride-through.
Transfer trip is communication-based: when the network operator intentionally separates a feeder, a trip signal is sent directly to the generator. It is reliable, but needs communication infrastructure.

Active methods run an internal algorithm that deliberately injects a small perturbation through the inverter control and watches the response. In a strong grid the perturbation is absorbed and the voltage / frequency response is small; in an island the same perturbation produces a much larger response, which lets the inverter detect the island. Active methods can therefore shrink the NDZ, but they can affect power quality if not carefully designed, and they are often manufacturer-specific.

Modelling tool: RMS or EMT, and how long to run

RMS may be sufficient when the anti-islanding method is based on phasor quantities — voltage magnitude, frequency, ROCOF or vector jump. EMT is needed when the detection method depends on waveform shape, harmonics, phase jumps at sub-cycle resolution, active-perturbation dynamics, or detailed inverter control / protection behaviour (RMS cannot represent harmonics, so a harmonic-injection method needs an EMT tool such as EMTP®). On timing: islanding detection is a short-duration study — a few cycles to a few seconds, depending on the protection standard, grid code and operator requirement. If the protection trips, the reconnection delay is usually far longer than the simulated event and can be treated as “no reconnection” during the study.

Part B · Section 8

Which functions to model for islanding

Here the list is almost complete — it is the protections that must detect the island and disconnect, so nearly every functionality matters. Include the voltage and frequency protection, ROCOF, vector jump and active anti-islanding; the reactive / voltage and frequency controls; the FRT / LVRT / HVRT ride-through logic; the current limits; the active behaviour during fast voltage and frequency variations; and the reconnection logic if the study duration requires it. Only three functions are unnecessary, and the reasons are practical: MPPT (detection completes in two or three seconds, too fast for a change in solar radiation to matter), voltage control by active power, P(V) (it activates only a few seconds after a voltage limit is crossed — after detection should already be complete), and power oscillation damping (POD) (once the network has islanded, the machine group that would swing against another is no longer there, so there is no inter-area oscillation to damp).

Read Table 2 as the mirror of Table 1: for islanding, protection and detection functions are central, so most protection and capability functions must be represented.

Table 2 — Recommended IBG functionalities for an unintentional-islanding study (after CIGRE Table 3.10).
Category	Functionality	Model?	Note
Control	DC source control	Yes
Control	Current control	Yes
Control	PLL	Yes
Control	MPPT	No	detection completes in ~2–3 s, before radiation changes matter
Protection	Reduce max inverter current on dc over-voltage	Yes
Protection	Limit inverter current rate of change after a fault	Yes
Protection	Current limit	Yes
Protection	DC over-voltage protection	Yes
Protection	Over / under-voltage protection	Yes
Protection	Over / under-frequency protection	Yes
Protection	Detecting a balanced fault	Yes
Protection	Detecting an unbalanced short-circuit fault	Yes
Protection	Detecting a single-line-to-ground fault	Yes
Protection	ROCOF tripping	Yes
Protection	Vector jump	Yes
Protection	Transfer trip	Yes
Protection	Anti-islanding active detection	Yes	not required by all utilities
Capability	P(f) control (over / under frequency)	Yes	unnecessary for LV-network islanding
Capability	Voltage control by reactive power, Q(V)	Yes
Capability	Voltage control by active power, P(V)	No	activates only seconds after a voltage limit — too late for detection
Capability	Synthetic inertia	Yes
Capability	ROCOF immunity	Yes
Capability	Fault ride-through (LV / HV)	Yes
Capability	Active behaviour during fast voltage variations	Yes
Capability	Power oscillation damping (POD)	No	no inter-area swing survives once the network has islanded

The practical message is that an islanding model is a protection model as much as a generation model.

An islanding study workflow

1. Define the island boundary (the PCC / POI) and the disconnection event.
2. Model the local load, generation and reactive compensation.
3. Create active / reactive power-mismatch cases.
4. Include the relevant inverter protection and anti-islanding logic.
5. Include rotating generation and reclosers if present.
6. Simulate the deficit, excess and matched cases.
7. Check voltage, frequency, ROCOF, vector jump and the trip time.
8. Confirm the trip occurs before unsafe reclosing or the operator limit.
9. Repeat for credible operating conditions.

Common mistakes

The traps that most often catch a small-signal or islanding study — each a theme from the sections above:

Nine traps to avoid

Using small-signal eigenvalue analysis when protection or current limits are actually activated.
Treating the damping-ratio threshold as a universal pass / fail value.
Assuming an IBG has no impact on oscillations because it has no rotor angle.
Ignoring the plant-controller or POD dynamics in small-signal studies.
Modelling islanding without checking both active and reactive power mismatch.
Relying only on passive anti-islanding inside the NDZ.
Ignoring the automatic-reclosing time.
Forgetting that active anti-islanding may be vendor-specific.
Using RMS when the islanding method depends on harmonics or waveform detail.

Key points

Two studies, a mirror-image model

Small-signal stability studies tiny disturbances and continuous control dynamics.
Eigenvalues show whether oscillations decay (\(\sigma \lt 0\)) or grow; the damping ratio shows how quickly they decay.
Mode shapes and participation factors identify what is involved in the mode.
IBGs create no classical rotor-angle mode, but reshape the system’s damping (and can add PLL / control modes in weak grids).
Islanding is a protection / detection problem; the NDZ is where local generation and load are closely matched.
Passive methods monitor voltage, frequency, ROCOF and vector jump; active methods perturb the inverter and watch the response.
The RMS-or-EMT choice depends on the detection method and the time resolution it needs.

For the fast fault behaviour these build on, see the large-voltage-deviation and frequency-stability guides; for the control-interaction modes that need EMT or impedance analysis, the control-interaction and SSCI guide; and for the machine-versus-inverter differences, the characteristics of IBG.

References

The CIGRE/CIRED joint working-group brochure on inverter-based generation is the primary reference; the IEEE/CIGRE task-force paper defines the stability classification; the Kundur reference work provides the small-signal theory; and IEEE 1547 is the interconnection standard behind the anti-islanding requirements.

CIGRE/CIRED Joint Working Group, Modelling of Inverter-Based Generation for Power System Dynamic Studies. CIGRE Technical Brochure.
P. Kundur et al., “Definition and Classification of Power System Stability,” IEEE Transactions on Power Systems, vol. 19, no. 3, pp. 1387–1401, 2004.
P. Kundur, Power System Stability and Control. New York: McGraw-Hill, 1994.
IEEE Std 1547, Standard for Interconnection and Interoperability of Distributed Energy Resources with Associated Electric Power Systems Interfaces. IEEE.

Part 11 Reading now

Modelling IBGs for Small-Signal Stability and Islanding

Two studies with opposite needs: eigenvalue small-signal damping, and islanding detection and protection.

Series progress 11 of 12

Part 12

Control Interactions, SSCI and Model Selection

The capstone: converter-grid interaction, SSCI, impedance-based stability and the final RMS / EMT / impedance choice.