Renewable Modelling · Long-Term Voltage Stability

Modelling IBGs for Long-Term Voltage Stability

Not every voltage problem is over in a second. Long-term voltage instability builds slowly — over seconds to tens of minutes — as on-load tap changers and over-excitation limiters chase a reactive-power balance the system can no longer hold. Inverter-based generation (IBG) sits inside that slow contest: keep it connected and it props the voltage up; let a fault trip it and the net load jumps, the tap changers fight back, and the grid can walk itself into collapse. This guide covers the phenomenon and the reactive-power balance behind it, when static analysis is enough and when it is not, a worked Nordic-system example where violating the ride-through curve collapses the system after ~150 seconds, and which IBG functions you actually need for a long-term voltage study. It follows the companion guide on large voltage deviations.

Reading time ≈ 32 min · Voltage collapse, P–V/Q–V, OLTC, LVRT & functions

This guide continues the voltage-stability thread. Where the large-voltage-deviation guide covered the fast, milliseconds-to-seconds fault response, this page moves to long-term voltage stability, and the key difference is the time scale. It is not mainly about milliseconds or first-swing behaviour: it is about the seconds to minutes after the disturbance, when on-load tap changers, over-excitation limiters, load restoration and protection actions slowly reshape the system. An inverter-based generator (IBG) is woven through that slow contest, and whether it stays connected or trips can be the difference between recovery and collapse.

What long-term voltage stability means

Long-term voltage stability asks whether the system can maintain acceptable voltages after the fast fault response is over and slower devices start acting. The problem may develop over seconds, minutes, or tens of minutes. A system can survive the initial fault but still collapse later — because of load restoration, a reactive-power shortage, OLTC action, generator limiters, or IBG disconnection.

Short-term versus long-term voltage stability

Short-term voltage stability: milliseconds to seconds; fault clearing, motor stalling, the fast converter current response; low-voltage ride-through (LVRT), current limits, the PLL and dynamic reactive current are what matter.

Long-term voltage stability (this page): seconds to tens of minutes; OLTCs, over-excitation limiters (OELs), load restoration, slow reactive-power controls and protection trips dominate; static, quasi-steady-state (QSS) and RMS dynamic methods are the usual tools.

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)

OLTCOn-load tap changer

OELOver-excitation limiter

AVRAutomatic voltage regulator

QSSQuasi-steady-state simulation

LVRT / HVRTLow- / high-voltage ride-through

FRTFault ride-through

MPPTMaximum power point tracking

PLLPhase-locked loop

TN / DNTransmission / distribution network

PVPhotovoltaic

WTGWind-turbine generator

SVCStatic VAr compensator

STATCOMStatic synchronous compensator

P(V)Active power as a function of voltage

Q(V)Reactive power as a function of voltage

ROCOFRate of change of frequency

PCCPoint of common coupling

POIPoint of interconnection

Key idea

Long-term voltage instability is slow (seconds to tens of minutes) and turns on the reactive-power balance: a system can survive the fault yet collapse later as reactive reserve runs out and voltage falls progressively.
The tap-changer trap: an OLTC raising the load voltage restores the load’s consumption, drawing more current and depressing the network voltage further — the control meant to help drives the collapse. OELs compound it by removing generator reactive support just when it is needed.
IBGs help while connected; tripping them on a fault raises the net load and the transmission-to-distribution transfer, and with OLTCs restoring downstream voltage can walk the system into collapse — the Nordic example collapses at \(t \approx 150\) s only when the IBGs disconnect.
Static P–V / Q–V analysis shows proximity; QSS or dynamic simulation shows the mechanism. Model the slow controls, the voltage protection, the current limit and the plant-level reactive / voltage control — and start from a realistic post-fault connection state.

Key terms used on this page

01Long-term voltage stability

Holding acceptable bus voltages over seconds to tens of minutes after a disturbance, as slow controls act.

02Voltage collapse

The chain reaction by which voltage instability drives part of the system to abnormally low voltage or blackout.

03On-load tap changer (OLTC)

A transformer tap that steps to restore downstream voltage over tens of seconds — and can drive collapse.

04Over-excitation limiter (OEL)

Protects a generator’s field by capping excitation — which removes reactive support just when the system needs it.

05Reactive reserve

The spare reactive capability that holds voltage; a deficit is the root of voltage collapse.

06P–V (nose) curve

Receiving-end voltage against load power; the nose is the maximum loadability, beyond which no stable voltage exists.

07Q–V curve

Bus voltage against injected reactive power; its distance below zero is the bus’s reactive margin.

08Voltage-dependent load

Load whose power changes with voltage; a constant-power load is the dangerous case, drawing more current as voltage falls.

09Net load

Load minus local IBG output; when IBGs trip, net load jumps even though customer demand has not changed.

10Quasi-steady-state (QSS)

A time-domain method that assumes fast transients have settled and follows the slow devices over time.

11Q(V) / P(V) control

Reactive power, or active-power reduction, controlled as a function of the local voltage.

12Current limit

The converter current ceiling; once reached, an IBG cannot independently deliver all the requested active and reactive current.

Section 1

Long-term voltage instability: what it is

Long-term voltage instability develops from a few seconds to tens of minutes after a disturbance, driven mainly by on-load tap changers and over-excitation limiters. Most incidents follow a transmission or generation equipment outage, regardless of how severe the initial fault was; the trigger can even be a slow, sustained load build-up such as the morning ramp. Voltage stability is the ability to hold steady voltages at all buses after a disturbance, or under a gradual increase in load, and it rests on keeping the balance between load demand and generation supply.

Voltage collapse is a chain reaction, not an instant

Voltage collapse is usually not one instant but a chain reaction: the system first loses voltage margin; reactive power becomes insufficient; voltage falls; loads, OLTCs and limiters respond; their response can increase demand or reduce support; more voltage falls occur; protection trips equipment or load; and the process can end in a partial or wide-area blackout — possibly with loss of synchronism as field-current limits act.

Section 2

The reactive-power balance

Voltage stability is strongly linked to reactive power. Active power mainly transfers energy, but reactive power is needed to maintain voltage magnitude. When the network cannot supply enough reactive power locally, voltage falls; and when voltage falls, more reactive current may be required — yet generators, IBGs, STATCOMs, SVCs and capacitor banks all have limits. Once those limits are reached, the voltage can decline progressively.

There is a reason it is a local problem. Reactive power does not travel as easily as active power over long distances: supplying it from far away causes extra voltage drop and losses. So voltage stability is often a local or regional problem, and the location of the IBG reactive capability matters as much as its amount.

Voltage problems appear in heavily stressed systems. A stressed voltage-stability condition may be caused by high power transfer across long transmission paths; low local reactive reserve; a weak transmission network; a high load level; the loss of a generator, transformer, line or compensation device; a high motor load; many generators already at their reactive limits; or IBGs operating without voltage support or tripping after disturbances.

Load is not constant — and that decides collapse

Some loads reduce when voltage falls, but others try to keep their power. A constant-power load is the dangerous case for voltage stability, because it draws more current as voltage decreases; motor loads can also draw high reactive current during recovery or stalling. Voltage-dependent load simply means the active or reactive power consumed changes with voltage — a resistive load reduces power when voltage falls, whereas a controlled or constant-power load tries to keep consuming the same power. That difference strongly affects whether the system settles at a lower voltage or collapses.

Section 3

Reading P–V and Q–V curves

Two curves make the margin visible. The P–V (nose) curve shows how the receiving-end voltage changes as the load power increases (Figure 1). The upper part is the normal, stable operating region; the tip — the nose — is the maximum loadability point; and beyond it, no stable voltage solution exists for that loading. Close to the nose, a small increase in load, or a loss of reactive support, can cause a large voltage drop.

Figure 1 — The P–V nose curve. The stable upper branch, the nose (maximum loadability), and the unstable lower branch; the horizontal distance from the operating point to the nose is the stability margin — how far the system can be loaded before it collapses.

The Q–V curve answers the reactive question directly: how much reactive-power margin a bus has (Figure 2). A positive margin means reactive support is still available; a low or negative margin means the bus is voltage-weak. Q–V curves help identify where reactive compensation is most effective, and they make “proximity” concrete — a contingency that shrinks the margin moves the bus closer to collapse.

Figure 2 — The Q–V curve and reactive margin. The distance the curve dips below the \(Q = 0\) line is the bus’s reactive-power margin; a contingency raises the curve (dashed), shrinking the margin and moving the weak bus closer to collapse.

Those two curves map onto the two questions any voltage-stability analysis has to answer. Proximity asks “how close are we to voltage collapse?” and is read from the P–V and Q–V margins. Mechanism asks “why does the collapse occur, and what sequence of controls and protections causes it?” The rule that follows is simple: static studies are good for proximity; dynamic studies are needed for mechanism.

Section 4

The tap-changer trap and the limiters

The core mechanism is worth seeing step by step. If the load demand rises above the maximum power the source can deliver, trying to control power by varying the load becomes unstable: increasing the load admittance actually reduces the power consumed. With a constant-admittance load the system may simply settle at a lower-than-normal voltage. But most load is fed through an OLTC transformer, and then the trap springs:

Transmission voltage falls.
Distribution voltage also falls.
The OLTC senses the low secondary-side (distribution) voltage.
The OLTC changes tap to restore the distribution voltage.
Restoring the distribution voltage increases the load consumption.
The increased load draws more current from the weakened transmission system.
Transmission voltage falls further.
The OLTC takes another tap step — and the process can become unstable.

Figure 3 — The tap-changer trap. The OLTC, trying to restore the distribution voltage, restores the load’s consumption too; the extra current depresses the transmission voltage further, the OLTC steps again, and the loop can run to collapse.

This is why an OLTC is not a detail you can leave out. An OLTC can be the engine of long-term voltage collapse, and leaving it out of the model may produce a false stable result, because the simulated load never gets restored to its pre-disturbance level.

Over-excitation limiters and generator reactive limits

A synchronous generator can supply reactive power only up to its thermal and field-current limits. Before it reaches that limit, its automatic voltage regulator (AVR) can help hold the voltage; after the limit, the machine can no longer behave like an unlimited voltage source, and the bus changes from voltage-controlled to reactive-power-limited behaviour — reducing the stability margin. The over-excitation limiter (OEL) enforces that limit: if the generator is pushed to supply too much reactive power for too long, the OEL reduces excitation to protect the rotor field winding. This protects the machine but removes voltage support exactly when the system needs it most — so OEL action can convert a recoverable low-voltage event into a voltage collapse.

Section 5

Static, QSS or dynamic?

Do not choose static or dynamic analysis on software convenience — choose it on the question. Because the long-term dynamics are slow, much can be assessed with static power-flow methods; but a static picture holds only until the automatic controls start acting, after which time-domain methods are needed. Quasi-steady-state (QSS) is a time-domain method for long-term voltage stability that assumes the fast transients have settled while it follows the slow devices — OLTCs, limiters, thermostatic loads and switched shunts — over time; it is faster than full dynamic simulation but still preserves the chronology of slow events. Full dynamic simulation is needed when both fast and slow behaviours interact, or when the post-fault state depends on whether the ride-through, protection or current-limit behaviour was represented correctly.

Table 1 — Static, QSS and full dynamic methods for long-term voltage stability.
Aspect	Static (power-flow)	QSS	Full dynamic
Best for	Wide screening, P–V / Q–V margins, many scenarios	Chronology of slow controls over minutes	Fast–slow interaction, protection / control coordination
Speed	Fast	Fast	Slower
Control timing captured	No — breaks down once controls act	Slow controls yes; fast dynamics assumed settled	Yes, fast and slow
Question answered	Proximity	Mechanism (slow)	Mechanism (full)

Which method, when

Use static analysis when the question is voltage margin, many scenarios need screening, and the timing of controls is not decisive.

Use QSS when the slow control sequence matters — the OLTC / OEL / load-restoration chronology — and the system evolves over minutes.

Use full dynamic RMS / EMT when the post-fault state depends on short-term dynamic behaviour, when IBG ride-through or protection affects whether units stay connected, or when motor recovery, current limits or converter behaviour affects the long-term trajectory.

RMS or EMT for the long-term run?

Long-term voltage stability is usually studied with RMS, QSS or power-flow-based tools, because the dominant time scale is slow — EMT is normally not required for the whole long-term simulation. However, an EMT tool such as EMTP® may be needed first, to validate the short-term fault response, the LVRT behaviour, the converter protection, or the weak-grid behaviour that determines the initial post-fault condition. Today’s tools run 5-to-10-minute long-term simulations efficiently.

Section 6

A worked example: the Nordic system, with and without LVRT

This example is included to show that a system can look stable immediately after the fault but still collapse later, because the post-fault long-term controls and IBG disconnections change the transmission-to-distribution power balance. A combined transmission-and-distribution model based on the Nordic system makes it concrete: the transmission network (TN) is expanded with 146 distribution networks (DNs) that replace the aggregated distribution loads. Each DN connects to the TN through two parallel OLTC transformers and contains about 100 buses, a distribution voltage regulator with its own OLTC, three PV units, three Type-3 wind turbines (WTGs) and 133 dynamically modelled loads (small induction machines plus exponential loads) — all complying with an LVRT curve. A 5-cycle three-phase fault near a transmission bus is cleared by opening the faulted line, and the system is run for 180 seconds at a half-cycle (10 ms) step.

The run is repeated twice — once where the LVRT curve is violated so the IBGs disconnect, and once with every IBG staying connected. Both cases are short-term stable, but they diverge in the long term:

1. A three-phase fault occurs near a transmission bus.
2. The fault is cleared by opening the line.
3. The fast electromechanical oscillations settle.
4. In one case, the IBGs disconnect because the LVRT curve is violated (losing roughly 140 MW).
5. The distribution networks then import more power from the transmission network.
6. The transmission voltages fall.
7. The OLTCs try to restore the distribution voltages.
8. The restored distribution voltage increases the load consumption.
9. The transmission voltage falls further.
10. The system collapses at about \(t \approx 150\) s.
11. When the IBGs stay connected, the long-term collapse is avoided.

Figure 4 — The Nordic example, two paths. When the IBGs trip on LVRT the net load jumps, the transmission voltage falls, the OLTCs restore the load, and the system collapses near 150 s; when the IBGs stay connected their local support holds the voltage and the system is long-term stable. (Study run with the RAMSES simulator, University of Liège.)

Why the LVRT outcome and the net load are central

LVRT is a short-term ride-through function, but its result matters for long-term voltage stability, because it decides whether the IBGs remain connected after the initial disturbance. Net load is the actual load minus the local generation; when IBGs trip, the net load seen by the transmission system increases suddenly even though customer demand has not changed. And that is why IBG disconnection worsens voltage stability: local active generation is lost, reactive support may be lost, the transmission import increases, the voltage drop across the network grows, the OLTCs restore the load (raising demand), and the remaining generators and compensation devices may hit their limits. The lesson is about discrete events — the chain of IBG disconnections, OLTC steps and control behaviour dictates the outcome, which is exactly why the protection mechanisms must be represented and validated in the dynamic model, not assumed.

Section 7

Linking the short- and long-term studies

A long-term voltage study usually follows a short-term one, and the link between them is the post-fault state. In order:

First simulate, or correctly represent, the short-term event.
Determine which IBGs, motors, generators, loads and compensation devices remain connected.
Use that realistic post-fault state as the initial condition for the long-term voltage-stability study.
Otherwise the long-term study may assume too much generation and voltage support are still online.

Carry both function sets, or the post-fault state is too optimistic

The short-term study fixes the post-fault topology — which IBGs have disconnected on ride-through or other protection, and the final control settings — so the fast fault-detection protections need not be re-included in the long-term run. But if you want to combine the short- and long-term phenomena in a single run, you must combine the functionality sets for both — the large-voltage-deviation functions and the long-term functions below. Leaving out the short-term protections while running a single long simulation carries forward an over-optimistic post-fault state (too much IBG still connected), and the long-term result comes out wrong.

Section 8

Which functions to model

The detailed milliseconds-to-seconds FRT control action is not the main subject of this page. However, the outcome of FRT — whether the IBG remains connected or trips — is essential, because it defines the post-fault starting point for the long-term study. Read Table 2 as a long-term voltage-stability modelling guide, not a universal IBG checklist: a “Yes” means the function can change the slow voltage trajectory or the post-fault connected generation / load balance.

Table 2 — Recommended IBG functionalities for a small / long-term voltage-deviation study (after CIGRE Table 3.8).
Category	Functionality	Model?	Note
Control	DC source control	No
Control	Current control	No	millisecond-scale — too fast to matter over minutes
Control	PLL	No	its effect enters through the slow P/Q controls and protection
Control	MPPT	Yes	irradiance is not constant over a 10-min-plus run; model as a change in \(P_{ref}\), not switching-level detail
Protection	Reduce max inverter current on DC over-voltage	No
Protection	Limit inverter current rate of change after a fault	No
Protection	Current limit	Yes	sustained low voltage can push the IBG into current limiting
Protection	DC over-voltage protection	No
Protection	Over / under-voltage protection	Yes	sustained low voltage can trip the under-voltage element
Protection	Over / under-frequency protection	No
Protection	Detecting a balanced fault	No	positive-sequence over-voltage protection may be used
Protection	Detecting an unbalanced short-circuit fault	No	negative-sequence over-voltage protection may be used
Protection	Detecting a single-line-to-ground fault	No	zero-sequence over-voltage protection may be used
Protection	ROCOF tripping	No
Protection	Vector jump	No
Protection	Transfer trip	No
Protection	Anti-islanding active detection	Yes	not required by all utilities
Capability	P(f) control (over / under frequency)	No
Capability	Voltage control by reactive power, Q(V)	Yes	deliberately slow, to coordinate with tap changers and compensators; also needed at plant level
Capability	Voltage control by active power, P(V)	Yes	keeps moving the post-fault operating point for a long time
Capability	Synthetic inertia	No
Capability	ROCOF immunity	No
Capability	Fault ride-through (LV / HV)	No	its outcome (connected or tripped) sets the starting point, but it is not re-run here
Capability	Active behaviour during fast voltage variations	No
Capability	Power oscillation damping	No

Why the fast controls come out and the slow ones stay in:

PLL and current control (No). The millisecond-scale PLL and inner current loops are too fast to be relevant over minutes; their outcome enters through the slower active / reactive controls, the current limits, the voltage protection and the post-fault connected status. If the grid is weak or the long-term result hinges on converter control instability, EMT or detailed dynamic validation may still be required first.
Current limit (Yes). Sustained low voltage may force the IBG to its current ceiling — and once there, the plant cannot independently provide all the requested active and reactive current; reactive support and active power may both be limited.
Over / under-voltage protection (Yes). Sustained low voltage is a long-term condition that can trip the under-voltage element, so the settings and delays can change the long-term outcome.
Q(V) and P(V) (Yes). Q(V) — reactive power as a function of voltage — is the direct voltage-support lever; P(V) — active power as a function of voltage — matters for over-voltage or low-voltage active-power reduction. Their delays and dead-bands matter because they interact with OLTC operation.

The Q(V) delay, the plant controller and the current headroom

To avoid unintentional islanding, a delay can be placed on the Q(V) regulation of IBGs. That can help avoid a false islanding interaction — but if the delay is too long, the voltage support arrives after the OLTCs or other slow devices have already acted, so the delay must be coordinated with the OLTC timing and the protection settings. Two related points. Utility-scale IBG plants often regulate voltage or reactive power at the PCC / POI through a plant controller, and for long-term voltage stability that plant-level controller may matter more than the individual inverter inner loops. And an IBG can only provide reactive support within its converter current rating and capability curve: if the active-power output is high, less current headroom is available for reactive power unless the inverter is oversized or the active power is curtailed.

A long-term voltage study workflow

1. Define the disturbance or contingency.
2. Run power flow and identify the voltage-weak areas.
3. Check the P–V and Q–V margins.
4. Represent OLTCs, OELs, switched shunts, capacitor / reactor controls and the load models.
5. Determine the post-fault connected status of the IBGs from the FRT / protection assumptions.
6. Include the IBG plant voltage / reactive control, current limits and voltage protection.
7. Run a QSS / RMS dynamic simulation over several minutes.
8. Monitor bus voltages, tap positions, generator reactive limits, IBG reactive output, protection trips and load restoration.
9. Identify the collapse mechanism.
10. Test remedies — reactive compensation, OLTC blocking, voltage-control retuning, load shedding, IBG voltage support or stronger ride-through requirements.

The signals worth plotting are the ones that reveal the mechanism: the weak-bus voltages; the transmission / distribution interface power flow; the reactive-power output of the generators, IBGs, SVCs and STATCOMs; the generator field current and OEL status; the OLTC tap positions; the load active / reactive restoration; the IBG active and reactive power and its current-limit status; the voltage-protection trip signals; the switched shunt / capacitor / reactor status; and the P–V / Q–V margin where available.

Common mistakes

The traps that most often catch a long-term voltage-stability study — each a theme from the sections above:

Nine traps to avoid

Treating long-term voltage stability as only a power-flow problem when control timing matters.
Leaving OLTCs out of the model.
Leaving OELs or generator reactive limits out of the model.
Assuming IBGs stay connected after a fault without checking LVRT / protection.
Ignoring voltage-dependent and motor loads.
Ignoring current limits when requesting reactive support from IBGs.
Using static P–V / Q–V margins without checking the collapse mechanism.
Running a long-term simulation from an unrealistic post-fault state.
Modelling individual inverter inner loops in detail while omitting the plant-level voltage control.

Key points

A slow failure, driven by the controls meant to help

Long-term voltage instability can occur after the fast fault response appears stable.
The reactive-power reserve and the voltage-control limits are central.
OLTCs can unintentionally drive collapse by restoring load demand.
OELs protect generators but remove reactive support.
IBG disconnection increases net load and may remove local voltage support.
Static studies show proximity; QSS / dynamic studies show the mechanism.
RMS / QSS is normally enough for the long-term run, but EMT may be needed to validate the short-term post-fault IBG behaviour.
The model must include the slow controls, the voltage protection, the current limit and the plant-level reactive / voltage control that shape the long-term trajectory.

For the fast fault response that sets the post-fault state, see the large-voltage-deviation guide; for frequency behaviour, the frequency-stability guide; for the small-signal and islanding studies alongside this one, the small-signal and islanding guide; and for the underlying 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 used here; and the Kundur and Van Cutsem–Vournas reference works provide the voltage-stability theory and the Nordic-system studies.

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.
T. Van Cutsem and C. Vournas, Voltage Stability of Electric Power Systems. Boston: Kluwer Academic Publishers, 1998.

Part 10 Reading now

Modelling IBGs for Long-Term Voltage Stability

The slower voltage-collapse mechanism over seconds to minutes: reactive balance, tap changers and P–V/Q–V limits.

Series progress 10 of 12

Part 11

Modelling IBGs for Small-Signal Stability and Islanding

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