Renewable Modelling · RMS Models

RMS Models for Inverter-Based Generation

For almost every stability study the working tool is not an electromagnetic-transient solver but an RMS phasor model: a much smaller set of differential-algebraic equations in voltage and current phasors, running at millisecond steps and covering perhaps the lowest ten hertz of behaviour. This guide is about building inverter-based generation (IBG) models in that world — the averaged converter that ignores the switching, why the method is trusted on strong grids and distrusted on weak ones, the current-source interface and the fault ride-through, phase-locked-loop and anti-islanding blocks, and the local and plant-level active- and reactive-power controls — and the line past which you must hand over to an EMT tool such as EMTP®. It is the phasor companion to the EMT-models guide and the model-selection guide.

Reading time ≈ 40 min · Averaged models, fault ride-through, plant control

The previous guide opened up the physical inverter — its dc side, its ac side, its control, protection and capability functions. This guide asks a different question: how are those functions simplified so they fit inside a fast, phasor-domain dynamic model? An RMS model does not reproduce the inverter in detail; it keeps just enough of it to answer a system study. The single question this page keeps returning to is therefore: which inverter functions can a phasor model represent, and which phenomena force you to move to EMT?

How to read this page

This is the third part of the nine-part series. Parts 1–2 built the inverter and its characteristics; this part turns them into an RMS model, and the next part does the same for EMT. Read the two together: RMS is the fast, wide-area workhorse; EMT is the detailed tool you reach for when the waveform, the switching, the fast control or a weak grid decides the answer. Everything below is organised the same way as Part 1 — define a term before using it, explain each formula in words, and give a practical modelling rule.

Abbreviations used on this page

RMSRoot-mean-square (phasor) simulation

EMTElectromagnetic transient (time domain)

EMTP®Electromagnetic Transients Program

IBGInverter-based generation (or generator)

PVPhotovoltaic

WTGWind-turbine generator

DFIGDoubly-fed induction generator

DCDirect current (the dc link)

PCCPoint of common coupling (plant–grid connection point)

POIPoint of interconnection (plant metering / control point)

PLLPhase-locked loop

MPPTMaximum power point tracking

PWMPulse-width modulation

SCRShort-circuit ratio

ESCREffective short-circuit ratio

VSCVoltage-source converter

LCCLine-commutated converter

FRTFault ride-through

LVRTLow-voltage ride-through

HVRTHigh-voltage ride-through

LVPLLow-voltage power logic

ROCOFRate of change of frequency

SVCStatic VAr compensator

STATCOMStatic synchronous compensator

WECCWestern Electricity Coordinating Council

LFSM-OLimited frequency-sensitive mode — over-frequency

FFRFast frequency response

PODPower oscillation damping

TSO / DSOTransmission / distribution system operator

RESRenewable energy sources

Key idea

An RMS model solves the network as phasors — magnitude and angle at the fundamental frequency — not the instantaneous waveform. It is fast and ideal for wide-area stability, but it deliberately drops switching, harmonics and very fast transients.
The inverter becomes a controlled current source: the controls decide how much active and reactive current to inject, subject to a current limit and a chosen P/Q priority; the network receives those injections as phasors.
The model is built in three levels — the inverter/grid interface (current source, limits, PLL, FRT, protection), the local P and Q control, and the plant controller at the POI — and only the blocks a study needs are switched on.
RMS must be validated or replaced by EMT when the grid is weak, the fast converter control matters, or the answer depends on harmonics, unbalance or waveform shape. An SCR near 3 is a rough warning line, not a pass/fail test.

Key terms used on this page

01RMS / phasor model

A fundamental-frequency model that represents each sinusoid by its magnitude and angle and solves how those change with time; fast, and the standard tool for stability studies.

02Averaged model

A converter representation that drops the individual switching pulses and reproduces only the fundamental-frequency output — normally active and reactive current or power.

03Stiff dc source

The assumption that the dc-link voltage stays constant enough for the study, so the ac side can be modelled without the detailed dc-source dynamics.

04SCR / ESCR

Short-circuit ratio and its effective form: the grid strength at the connection point relative to the converter rating — low means a weak grid whose voltage is easily disturbed.

05Current-source interface

The RMS inverter model: an algebraic controlled current source that injects the commanded active and reactive current, subject to limits and protection.

06Current limiter & priority

The block enforcing the current ceiling \(I_{max}\); the P/Q priority flag decides whether active or reactive current is kept when the two cannot both fit.

07LVPL

Low-voltage power logic: caps and rate-limits the active-current command during a voltage dip so the converter does not demand impossible active power.

08Fault ride-through (LVRT / HVRT)

Staying connected through a low- or high-voltage excursion; modelled as time–voltage trip curves plus reactive-current support.

09PLL freezing

Holding the estimated angle constant when the measured voltage is too low to read reliably, so the loop does not chase a collapsed signal during a fault.

10Anti-islanding

Detecting an unintended island: passive schemes watch voltage, frequency, ROCOF or vector jump; active schemes inject a small disturbance and watch the response.

11Synthetic inertia / FFR

A fast active-power response to a frequency change; not physical inertia, and limited by stored or curtailed energy and the converter rating.

12Dynamic phasors

An emerging method that keeps RMS speed while representing unbalance and harmonics more accurately — a bridge between RMS and EMT.

Symbols and notation used on this page

\(I_P,\ I_Q\) — active- and reactive-current components (active power vs voltage / reactive-power support). \(I_x,\ I_y\) — the same current in the network solver’s rotating reference frame. \(\theta\) — angle between the converter frame and the network frame.
\(I_{max}\) — the converter current ceiling; \(I_n\) — rated current. \(dq\) — the converter’s control axes; \(xy\) — the network reference axes.
\(U_{dc}\) — dc-link voltage; \(I_{array}\) — current from the source into the dc link; \(I_{dc}\) — current drawn by the inverter from the dc link.
\(K_{LVRT},\ K_{HVRT},\ K_{HFRT}\) — the droop/gain factors that turn a voltage or frequency deviation into a current response (defined where each is used).

Section 1

What an RMS (phasor) model is

Start with the name. RMS stands for root-mean-square, but in power-system dynamic simulation an “RMS model” almost always means a phasor-domain model. A phasor represents the fundamental-frequency waveform by its magnitude and angle rather than by every instantaneous sample. It does not trace the 50 Hz sinusoid point by point; it tracks how the magnitude, angle, frequency, and the active and reactive power change with time.

The contrast with EMT makes it concrete. In an EMT model the simulator computes instantaneous voltages and currents — the actual waveform of, say, the phase-a voltage. In an RMS model the simulator assumes the waveform is essentially sinusoidal and computes its magnitude and angle instead. That assumption is what makes RMS so much faster — but it also means high-frequency switching, harmonics and very fast electromagnetic transients are not represented directly.

You will meet the phrase differential-algebraic equations for what RMS solves. It is less abstract than it sounds:

The differential equations carry the dynamic states — controllers, governors, PLL filters, dc-link states — anything with memory that evolves over time.
The algebraic equations carry the network relationships — the phasor power-flow that ties the bus voltages and currents together at each instant.
RMS simulation solves both sets together at every time step.

How far up in frequency does this reach? As a working guide, RMS studies cover phenomena up to roughly 10 Hz, with a time step of about 1–10 ms. That is not a hard universal law — it is the practical range over which the electromechanical and control dynamics normally studied in RMS remain valid. “10 Hz bandwidth” refers to how fast the quantities of interest change (the magnitude, angle and power), not to the 50 Hz carrier waveform itself, which the phasor represents as a steady sinusoid. If a phenomenon depends on switching frequency, harmonics, sub-synchronous control interaction, detailed unbalance, or very fast converter control, EMT is normally required instead.

One point is worth stating carefully, because it is easy to misread. RMS can perfectly well study system-frequency deviations — a fall to 49 Hz or a rise to 51 Hz — provided the modelling assumptions still hold. The limitation is not simply “the frequency is different from 50 Hz.” The limitation bites when waveform distortion, harmonics, fast converter dynamics or non-fundamental components begin to dominate the answer. Frequency stability is squarely an RMS problem; sub-synchronous control interaction is not.

Section 2

The averaged converter model

Why does an inverter fit into a phasor model at all? Because RMS replaces the switching converter with an averaged equivalent. Step by step:

The real inverter uses semiconductor switching driven by PWM.
RMS does not model each switching pulse.
The converter is replaced by an averaged, fundamental-frequency source.
Its output is normally the active and reactive current (or active and reactive power) it injects.
That output is then shaped by the outer controls, the current limits and the protection blocks — the very functions the previous guide described.

Because only the fundamental output survives, one generic averaged structure can stand in for many technologies — PV, wind, storage — and the engineering lives in the control and protection wrapped around it.

The “stiff dc” assumption

Most RMS IBG models assume a stiff dc link: the dc voltage is taken to stay sufficiently constant for the study, so the ac-side inverter can be represented without modelling the detailed dc-source dynamics. This is acceptable for many short-term stability studies. It may not be acceptable when the result depends on active-power reduction, dc over-voltage, chopper operation, battery state of charge, wind recovery, or MPPT dynamics — cases revisited in Section 9.

Section 3

RMS on a weak grid

Before going further, meet the single condition that most often invalidates an RMS study: a weak grid. The measure of grid strength is the short-circuit ratio (SCR), understood as

\[ \mathrm{SCR} = \frac{\text{short-circuit power at the connection point}}{\text{converter or plant rated power}} \]

A high SCR means a strong grid: the voltage is stiff and barely moves when the converter changes its current. A low SCR means a weak grid: the voltage is sensitive, and injecting or withdrawing converter current shifts it noticeably.

Why weak grids challenge RMS: when the grid is weak, the converter current, the PLL and the network impedance interact strongly, and that interaction is fast — often faster than the phenomena an RMS model is built to capture. A phasor model can therefore hide or misrepresent a fast control instability that a full EMT model would reveal. If an effective short-circuit ratio (ESCR) is quoted, it is the SCR adjusted for the reactive effect of nearby compensation, filters or other converters (the exact adjustment depends on the definition chosen); it is used because those elements weaken the effective impedance without adding short-circuit power.

You will often see “SCR below about 3” used as the point where RMS becomes doubtful. Treat that as a rough guide, not a universal pass/fail value: the safe threshold depends strongly on the converter design and its control, differs between older LCC and modern VSC technologies, and is ultimately manufacturer- and project-specific. Even a higher SCR can pose problems. The rule of thumb is a prompt to check against EMT, not a certificate of validity.

Section 4

Phenomena that need RMS simulation

Table 1 is not a list of every possible RMS study. It shows the types of power-system phenomenon for which RMS models are normally used, because the dominant behaviour is slow enough, and close enough to the fundamental frequency, for the phasor assumption to hold. Each row links to the Chapter 3 topic where it is treated in depth.

Table 1 — Phenomena and studies typically performed with RMS-type models (after CIGRE Table 5.1).
Topic	Phenomenon	Relevant key words	Type of studies
3.2	Behaviour in response to frequency deviations	Device protection; system support; plant-level control; synthetic inertia	Frequency regulation and transient stability
3.3	Behaviour in response to large voltage excursions	Device protection against damage; fault ride-through capability; grid support	Short-term voltage stability; transient stability; provision of short-circuit current; low / high-voltage ride-through
3.4	Behaviour in response to smaller but longer voltage deviations	V/Q control; reactive-power capability below the maximum-capacity diagram; plant-level control	Long-term voltage stability
3.5	Modelling simplifications for small-disturbance stability analysis	Small-disturbance angle stability	Small-signal (small-disturbance) stability

The practical message is that RMS is a system-wide screening and stability-study tool. It is the right tool for frequency, angle and voltage stability across a large network — and it is not the tool for studying the physical switching of the inverter, which belongs to EMT.

Section 5

The three model levels

An RMS IBG model is assembled in three levels. Understanding why they exist, and how they hand signals to one another, makes the rest of the page easy to follow.

Level 1 — inverter / grid interface. The current-source interface, the current limits, the PLL, the fault ride-through logic, the protection, and (optionally) the dc-link representation. This is the block that actually injects current into the network.
Level 2 — local electrical control. The active-power control, the reactive-power or voltage control, the resulting current references, and the local measurement filtering. This decides what current the interface should inject.
Level 3 — plant controller. The aggregated plant-level P and Q control, POI voltage control, coordination with STATCOM, SVC and other plant equipment, frequency response, and active-power curtailment or dispatch.

They interact top-down as a signal flow:

Plant controller → local P / Q controller → active & reactive current references → current limiter / FRT / protection → current-source injection into the RMS network.

Figure 1 draws that flow, with the two measurement feedbacks that close the loop — the PCC voltage and frequency, and the PLL angle.

Figure 1 — Structure of an RMS IBG model. The plant controller (Level 3) sets references for the local P and Q control (Level 2); those become active/reactive current references that pass through the current limiter and the fault ride-through logic before the controlled current source (Level 1) injects current into the network. The PLL supplies the grid angle, and the protection block can trip or block the injection.

The other half of the model is Table 2, which lists the inverter components and shows, for each of the four main study types, whether that component normally needs to be represented. Read it like this: the rows are model components or functions; the columns are study types; a “Yes” means the function usually affects the answer and should be included; a “No” means it is normally unnecessary for that study. The footnote markers carry real engineering conditions, so they are spelled out in full below the table rather than left as symbols.

Table 2 — Components and their selection in RMS-type models, by study type (after CIGRE Table 5.2).
Category	Functionality	Frequency deviation	Large voltage excursion	Small & long-term voltage deviation	Unintentional islanding
Control	DC source control	No	Yes^a	No	Yes
Control	Current control	No	Yes^a	No	Yes
Control	Phase-locked loop (PLL)	No	Yes	No	Yes
Control	Maximum-power-point tracking (MPPT)	Yes^b	No	Yes	No
Protection	Reduction of maximum inverter current when the dc voltage exceeds a limit	No	Yes^a	No	Yes
Protection	Limitation of inverter current’s rate of change after a fault	No	Yes	No	Yes
Protection	Current limit	Yes	Yes	Yes	Yes
Protection	DC over-voltage protection	No	Yes^a	No	Yes
Protection	Over-voltage / under-voltage protection	No	Yes	Yes	Yes
Protection	Over-frequency / under-frequency protection	Yes	Yes	No	Yes
Protection	Protection for detecting a balanced fault	No	N/A^d	No	Yes
Protection	Protection for detecting an unbalanced short-circuit fault	No	N/A^d	No	Yes
Protection	Protection for detecting a single-line-to-ground fault	No	N/A^d	No	Yes
Protection	ROCOF tripping (trips when the frequency rate exceeds a limit)	Yes	Yes	No	Yes
Protection	Vector jump	Yes	Yes	No	Yes
Protection	Transfer trip	No	No	No	Yes
Protection	Anti-islanding active-detection method	Yes	Yes	Yes	Yes
Capability	P(f) control (over / under-frequency)	Yes	No	No	Yes^e
Capability	Voltage control by reactive power	Yes	Yes	Yes	Yes
Capability	Voltage control by active power, P(V)	No	Yes	Yes	No
Capability	Synthetic inertia	Yes	Yes	No	Yes
Capability	ROCOF immunity	Yes	No	No	Yes
Capability	Fault ride-through (LV / HV)	No	Yes	No	Yes
Capability	Reactive-power control for fast, large voltage variations	No	Yes	No	Yes
Capability	Power-oscillation damping	Yes^c	Yes^a	No	No

What the conditions behind the table markers actually mean:

a — dc-link included. Include the dc-source and dc-link dynamics only when the dc voltage or the dc-source behaviour affects the result.
b — small isolated grid. On a small isolated grid the IBG has a much stronger influence on system behaviour, so its active-power / frequency response (and MPPT) needs more detail.
c — POD design. Power-oscillation damping matters only when the plant actually has a damping controller designed for the oscillation mode in question.
d — external relay model. Where fault-detection protection is not embedded in the IBG model, an external protection-relay model may be needed instead.
e — network type. Islanding assumptions differ between MV/HV networks and LV-only isolated networks, so this changes with the network the plant sits in.

Section 6

The current-source interface and the transformation

In RMS the inverter is usually represented as a controlled current source. The higher-level controls decide how much active current and how much reactive current the inverter should inject; the network then receives those current injections as phasor quantities. The same interface serves a PV plant, a full-converter wind turbine or a DFIG (whose stator connects directly to the grid while only the rotor passes through a converter) — the primary technology changes the controls, not the interface. This is the defining simplification of an RMS IBG model, and it is worth pausing on because it is quite different from a synchronous machine.

A synchronous generator behaves like an internal voltage source behind a reactance — it holds a voltage and the network draws current from it.
An IBG RMS model is usually a controlled current source with limits — it injects a commanded current, and its own protection decides when that current is capped or cut.

The controller and the network solver use different reference frames, so one coordinate transformation is needed. Before the formula, the symbols:

\(I_P\) — the active-current component, mainly associated with active-power transfer.
\(I_Q\) — the reactive-current component, mainly associated with voltage / reactive-power support.
\(I_x,\ I_y\) — the current components in the network reference frame the RMS solver works in.
\(\theta\) — the angle between the converter controller’s reference frame and the network reference frame.

The relationship is only a coordinate rotation, not a new physical law:

\[ I_x = I_Q\,\sin\theta + I_P\,\cos\theta, \qquad I_y = -\,I_Q\,\cos\theta + I_P\,\sin\theta \]

\(I_x,\ I_y\): current on the network’s rotating x–y axes
\(I_P,\ I_Q\): active and reactive current from the converter control
\(\theta\): angle of the converter (d–q) frame relative to the network (x–y) frame

In words: the converter controller thinks in active and reactive current, but the network solver needs current components in its own rotating x–y axes, so the transformation simply rotates the converter current vector into the network frame. If \(\theta = 0\) the frames are aligned and the transformation becomes trivial; as \(\theta\) changes, the same current vector has different x–y components.

Three-phase inverters normally compute power in d–q coordinates (some using positive-sequence quantities only), whereas single-phase inverters act independently on each phase. Under an unbalanced fault the three phase currents can behave quite differently, and the result cannot generally be captured by positive-sequence quantities alone — one of the reasons detailed unbalanced-fault work tends to move to EMT.

Section 7

Fault ride-through and current limiting

Take the disturbance first, then the blocks. When a voltage dip or rise occurs at the terminal or PCC, three things happen at once:

The grid code may require the IBG to stay connected through the excursion.
The converter’s current rating limits how much active and reactive current it can inject in total.
The model must therefore decide a priority: active current or reactive current, because both may not fit within the limit.

With that in mind, the blocks fall into two kinds — some are protection / ride-through envelopes (they decide connect-or-trip), and some are current-control behaviours (they shape the injected current):

The ride-through and limiting blocks

LVPL (low-voltage power logic) — a current-control behaviour. It reduces or limits the active current during low-voltage operation so the converter does not demand impossible active power when the voltage is depressed. Since active power is roughly voltage times active current, a low voltage makes active-power delivery hard within the current limit — so the active current is pulled back.
Current limiter — a current-control behaviour. It enforces the ceiling \(I_{max}\) and applies the P/Q priority.
LVRT (low-voltage ride-through) — a protection envelope. A time–voltage curve: stay connected above it, disconnect if the voltage falls below.
HVRT (high-voltage ride-through) — a protection envelope for over-voltages, with reactive-current absorption to help pull the voltage down.
ROCOF immunity — a protection-coordination behaviour that keeps the plant connected through an acceptable rate of change of frequency instead of nuisance-tripping.

Current priority — a practical example

Suppose a deep dip drives the reactive-current demand up. With only \(I_{max}\) to share:

Under reactive-current priority, the inverter first spends its limited current on voltage support (reactive current), and reduces active power if necessary.
Under active-current priority, the inverter tries to hold active power first, and voltage support is whatever current is left.

This single choice strongly affects the LVRT behaviour and the post-fault voltage recovery, which is why the RMS model must include both the current limiter and the selected priority logic.

The high-voltage reactive absorption is simply proportional to the over-voltage:

\[ \Delta I_{qHVRT} = K_{HVRT}\,\Delta U \]

\(\Delta U\): how far the terminal voltage is above the HVRT threshold
\(K_{HVRT}\): the factor that converts that voltage rise into a reactive-current response
\(\Delta I_{qHVRT}\): the additional reactive current absorbed to help reduce the over-voltage

Sign convention on this page: \(\Delta I_{qHVRT}\) is written as a positive quantity of absorbed reactive current (the inverter behaves inductively to pull the voltage down). Some tools represent the same action with the opposite sign, so always check the convention of the model you use.

Section 8

The phase-locked loop

The PLL is the converter’s synchronising mechanism. It estimates the grid-voltage angle so the inverter knows where to place its active- and reactive-current components. It is one of the most important — and most fragile — parts of the model.

In a strong grid the PLL tracks the voltage angle quickly and smoothly.
During faults or in a weak grid the voltage angle becomes distorted or uncertain.
PLL error then makes the actual active and reactive current differ from what the controller intended.
PLL freezing is used when the voltage is too low to measure the angle reliably — the estimate is held so the loop does not chase a collapsed signal.

When the PLL’s d-axis sits on the voltage, the current projections reduce to a clean identity that the rest of the controls rely on:

\[ i_d = i_P, \qquad i_q = -\,i_Q \]

\(i_d\): current on the PLL d-axis
\(i_q\): current on the PLL q-axis
\(i_P,\ i_Q\): active- and reactive-current commands

The minus sign is a convention from the chosen q-axis direction, not a universal physical rule. The concept that matters is that the controller maps its active/reactive current commands into the PLL reference frame; after a disturbance, while the PLL is still catching up, the delivered currents differ transiently from the commands.

Two parameters set the PLL’s character. The measurement time constant is typically \(T_m = 10\text{–}20\) ms, and the PLL gain is typically 30–60. In words: \(T_m\) is a measurement/filtering delay — a larger \(T_m\) smooths the measurement but slows the response; a higher gain makes the PLL faster but reduces the stability margin, which bites hardest on a weak grid. Real vendor PLL details are often confidential, so a generic RMS model may not reproduce exact weak-grid behaviour — another reason weak-grid studies lean on EMT and vendor models.

Section 9

MPPT, the dc source and measurement

Whether you model the dc side at all depends entirely on the study. Three cases cover most work:

Case 1 — short-term stability study. MPPT is usually held constant, the dc source is often ignored, and the stiff-dc assumption is acceptable.
Case 2 — frequency-response or active-power-curtailment study. Now the dc power availability and headroom matter, so MPPT, curtailment or storage may need to be represented.
Case 3 — dc over-voltage / chopper / momentary-cessation study. Here the dc-link dynamics must be represented; otherwise the model may miss dc over-voltage trips or the recovery behaviour that follows.

When the dc link is modelled (a PV example), the dc-capacitor relation holds the array at its operating point:

\[ U_{dc} = \frac{1}{sC}\left( I_{array} - I_{dc} \right) \]

\(U_{dc}\): dc-link voltage
\(I_{array}\): current from the source that charges the dc-link capacitor
\(I_{dc}\): current the inverter draws from the dc link
\(C\): dc-link capacitance

Reading it physically: if \(I_{array} \gt I_{dc}\) the surplus charges the capacitor and \(U_{dc}\) rises; if \(I_{array} \lt I_{dc}\) the capacitor discharges and \(U_{dc}\) falls. The \(1/s\) is integration in the Laplace/control-block sense (the capacitor accumulates net current), and a larger capacitance \(C\) slows the voltage change.

Measurements are the last interface detail. Voltage, current, power and frequency are measured and reduced to steady-state quantities; however elaborate the real filtering, it can usually be represented by a single first-order lag. The time constant is small for many quantities (0.01–0.02 s) and it should be possible to set it to zero; single-phase sensing needs a longer constant to suppress ripple, and reliable frequency measurement under disturbance needs filtering whose delay must be accounted for — a point that returns under fast frequency response.

Section 10

Protection and anti-islanding

The inverter-characteristics guide separated internal converter protection from interface / network protection. In the RMS model, both may be represented — by relay blocks or logic blocks — depending on the study. The functions you may need to include:

Under- / over-voltage protection, and under- / over-frequency protection.
Instantaneous over-voltage protection (a faster inner element).
ROCOF (rate-of-change-of-frequency) tripping.
Vector jump.
Passive anti-islanding (watching a measured quantity) and active anti-islanding (perturbing the output).
A restart / reconnection delay after a trip.

One modelling consequence is easy to miss: if the simulated time is short, a trip with a long restart delay (residential PV can take 150–300 s to reconnect) is effectively permanent for that simulation — the unit simply does not come back within the run.

Vector jump — and why it can misfire

Vector-jump protection detects a sudden step in the voltage phase angle. Such a step can occur when the network topology changes, a generator trips, or an island forms. The risk is that a genuine system disturbance can look like islanding, causing an unnecessary IBG disconnection. That tension — catching real islands without tripping on healthy system events — is exactly what the later islanding and frequency-stability pages examine.

Section 11

Local control: active and reactive power

The local (component-level) control watches the IBG’s power output, terminal voltage and frequency, and computes the active- and reactive-current commands the interface then delivers. Reactive control comes in two kinds that act on different time scales — and both may be present at once:

Static (slow) reactive control — for normal operation: fixed power factor, fixed reactive power, Q(V), or voltage control. It responds to slow changes in the operating point.
Dynamic reactive-current support — a fast response during voltage dips or swells, usually required by grid codes. It overrides the static control while the disturbance lasts.

The dynamic support injects reactive current in proportion to the voltage deviation:

\[ I_{qLVRT} = I_{qini} + K_{LVRT}\,\frac{\Delta U}{U_{ini}}\,I_n \]

\(I_{qini}\): the pre-fault reactive current
\(\dfrac{\Delta U}{U_{ini}}\): the per-unit voltage deviation (drop or rise) relative to the pre-fault voltage
\(K_{LVRT}\): the gain / droop factor setting how aggressively reactive current is injected (typically 0 to 10)
\(I_n\): rated current, which scales the response

Critical caveat: the result must still respect the total current limit \(I_{max}\). The formula gives the requested reactive current, but it cannot be read on its own — the current limiter and the P/Q priority decide what is actually delivered when the request would exceed the ceiling.

The same coupling shapes the active-power control. In external-reference mode the active power tracks a command with some delay; in voltage-dependent mode the active current follows a measured voltage (used mainly for long-term dynamics and voltage-rise mitigation). But active and reactive current cannot be chosen independently once the current limit is reached: if reactive current rises during a fault, active current may have to fall. That is why the RMS model must always include the current limiter and the selected priority logic — the two controls are only independent while there is spare current.

Section 12

Plant-level control

The step up from local to plant control is the appearance of an aggregated quantity. The two levels differ clearly:

Local control acts at a single inverter or turbine / converter.
The plant controller measures the aggregated power and voltage at the point of interconnection (POI), and sends references to many inverters.
It may coordinate with STATCOM, SVC, capacitor banks, transformer taps or other plant equipment.
It is essential for utility-scale PV, wind and battery-storage studies.

A note on two similar terms. The PCC (point of common coupling) is the compliance / connection point between the plant and the grid; the POI (point of interconnection) is used here for the plant controller’s metering and control point. In many plants they are effectively the same busbar; this page uses PCC for the grid-connection point and POI for the plant-controller reference, and keeps to that throughout.

The reference example is the WECC centralised plant controller. WECC is the Western Electricity Coordinating Council, and its generic renewable models are widely used RMS model structures for renewable plants: excellent for bulk-system studies, but they may not reproduce vendor-specific fast controls in a weak-grid EMT study. On the active-power side, IBGs are increasingly asked to provide services once left to synchronous machines — and one of them needs care:

Synthetic inertia and fast frequency response

Synthetic inertia is not physical inertia. It is a control response computed from measured ROCOF or frequency deviation, so it requires stored or curtailed energy to deliver, and it is limited by the converter current rating, the available headroom, the dc-source capability and the recovery strategy. Because frequency cannot be measured instantly (filtering and transducer delay intervene), the honest term is fast frequency response (FFR) — which may take the form of an inertia-like action or a fast droop-like active-power injection. Renewable energy sources (RES) without storage have little readily available FFR unless short-term storage is added.

Requirements differ from one system operator (TSO or DSO) to the next, and where a plant provides a regulated inertial response the profile is prescribed. Table 3 is not a generic inverter-capability table — it is a specific recommended inertial-response profile from Hydro-Québec. Treat it as an example of the kind of grid-code or utility requirement a plant controller may need to represent.

Table 3 — Recommended inertial-response profile, Hydro-Québec (after CIGRE Table 5.3).
Parameter	Proportional function (closed loop)	Step function (open loop)
Dead-band	≤ 0.3 Hz	≤ 0.5 Hz
Active-power contribution	≥ 6%
Duration of active-power contribution	≥ 10 s
Activation time	≤ 1 s
Transition time for maximum generation reduction	≥ 3.5 s
Maximum generation reduction during recovery	≤ 20%

The key modelling point is not the exact numbers; it is that an active-power response has a magnitude, a duration, an activation threshold and a recovery behaviour — four things your model must be able to reproduce. The over-frequency limit works the same way. LFSM-O (limited frequency-sensitive mode, over-frequency — the “HFRT” subscript below stands for the high-frequency response, not a ride-through) reduces the active current as the frequency climbs past a start value:

\[ I_{pHFRT} = I_{pini} + K_{HFRT}\left( f - f_{start} \right) \]

\(I_{pini}\): the active current at the start of the over-frequency response
\(f\): the measured system frequency
\(f_{start}\): the frequency at which active-current reduction begins
\(K_{HFRT}\): a negative factor, so the active current falls as the frequency rises

Because \(K_{HFRT}\) is negative, this is an over-frequency droop: it reduces generation as the frequency climbs above \(f_{start}\), helping to arrest a high frequency.

Section 13

Limits and where this is heading

Six practical threads define the frontier of RMS IBG modelling:

Parameter identification — controller and protection parameters differ by manufacturer and even by product, so no universal set exists.
Confidentiality — the filtering behind key measurements and the exact detection logic are often undisclosed, so generic models approximate them.
Aggregation — representing many small distributed IBGs with diverse parameters by a single equivalent model is a genuine open problem.
Unbalanced operation — low-voltage distribution is frequently unbalanced, which positive-sequence RMS models capture poorly.
Dynamic phasors — a promising middle path that keeps RMS speed while representing unbalance and harmonics far better.
Validation against measurements — commissioning tests and field traces remain the ultimate check.

The stance that follows from all six: an engineer should not assume a generic RMS model is valid just because it runs. It must be checked against vendor data, grid-code requirements, commissioning tests, or an EMT benchmark — especially where the connection is weak or the controls are important.

Section 14

Common mistakes

The traps that most often catch an RMS IBG study — each one a theme from the sections above:

Six traps to avoid

Using RMS for a very weak-grid converter interaction without EMT validation.
Forgetting the current limit and P/Q priority during fault ride-through, so the injected currents exceed what the converter could really deliver.
Treating synthetic inertia as real inertia, and ignoring its energy and rating limits.
Assuming the MPPT and dc source are always irrelevant — they are not, for frequency-response, curtailment and dc over-voltage studies.
Ignoring protection and reconnection delays, so a plant that would trip and stay off is modelled as riding through.
Using a generic RMS model for vendor-specific behaviour without validation against the real controls.

Key points

An RMS IBG model is not a detailed inverter

It is a fast, phasor-domain representation of the behaviours that matter to the chosen study — current injection, P and Q control, limits, protection, and plant-level functions. It solves differential-algebraic equations (dynamic states plus the network phasor relationships) over roughly the lowest 10 Hz, at a 1–10 ms step; it replaces the switching converter with an averaged current source under a stiff-dc assumption; it is built in three levels from the current-source interface, through the local P and Q control, to the plant controller at the POI. It is excellent for bulk stability studies — frequency, voltage and angle — but it must be validated or replaced by EMT when weak-grid, fast-control, harmonic, unbalanced or switching behaviour determines the answer.

This page prepares the RMS modelling foundation. The next part explains EMT models, where the waveform, the switching, the fast control and the weak-grid interactions can all be represented in detail — and the model-selection guide ties the RMS-versus-EMT choice together. For the physical inverter behind all of this, return to the inverter-characteristics guide.

References

The CIGRE/CIRED joint working-group brochure on inverter-based generation is the primary reference; the WECC second-generation generic renewable-energy-system models underpin the local and plant-level control blocks; IEC 61400-27-1 is the interfacing standard for wind-turbine models; and the Hydro-Québec transmission requirements are the source for the inertial-response profile.

CIGRE/CIRED Joint Working Group, Modelling of Inverter-Based Generation for Power System Dynamic Studies. CIGRE Technical Brochure.
WECC Renewable Energy Modeling Task Force, Second-Generation Generic Renewable Energy System Models (REGC / REEC / REPC / WTG modules). Western Electricity Coordinating Council.
IEC 61400-27-1, Wind Energy Generation Systems — Part 27-1: Electrical Simulation Models. International Electrotechnical Commission.
Hydro-Québec TransEnergie, Transmission Provider Technical Requirements for the Connection of Power Plants to the Hydro-Québec Transmission System — inertial-response provisions.

Part 3 Reading now

RMS Models for Inverter-Based Generation

How the inverter’s behaviour is simplified into an RMS / phasor model, and where that simplification holds.

Series progress 3 of 12

Part 4

EMT Models for Inverter-Based Generation

Electromagnetic-transient modelling: the Dommel method, switching, inverter detail levels and system strength.