Dynamic and Stability Studies

The decision being supported

Will the system remain synchronised after a fault; how much inertia or fast frequency response must be held; is this converter’s control stable given the short-circuit strength at its connection point; what settings should a special protection scheme use; why did that oscillation appear.

These are the questions steady-state models cannot touch, and they are the questions that have become hardest as the generation mix has changed.

A taxonomy of stability

The IEEE/CIGRE classification, revised in 2021 to add two new classes for converter-driven phenomena, is the standard map.¹

The two converter-driven classes were added because the observed events — sub-synchronous oscillations in wind-dense regions of Texas and China, control interactions at weak connection points — did not fit any of the classical categories.²

RMS versus EMT

Two simulation paradigms, and choosing wrongly is the most common error in this area.

RMS (phasor / positive-sequence) simulation assumes the network is in sinusoidal steady state at each instant, representing it algebraically by the admittance matrix while generators, controls, and loads evolve as differential equations. Time steps of 1–10 ms; the network is solved algebraically. This is the workhorse for transient and frequency stability on large systems and is what makes a 10,000-bus dynamic study feasible.

Its assumption — that network transients settle instantly relative to the phenomena of interest — is sound for synchronous machine dynamics and false for fast converter controls. RMS models cannot represent phenomena above roughly the fundamental frequency, cannot capture DC offsets or harmonics, and can miss converter instabilities entirely.

EMT (electromagnetic transient) simulation solves the network’s differential equations directly at time steps of 1–50 μs, representing instantaneous voltages and currents. It captures everything RMS discards, at a cost of two to four orders of magnitude in computation, which restricts it to small subsystems or short windows.

The practical answer is usually hybrid: an EMT representation of the area of interest coupled to an RMS or frequency-dependent network equivalent of the rest. Building a valid equivalent at the boundary is the hard part.³

The choice in a sentence: use RMS for system-wide angle, frequency, and voltage stability; use EMT for converter control interactions, weak-grid connections, HVDC, sub-synchronous resonance, and anything where the “network is a phasor” assumption is what you are testing.

The classical machine model

The minimum synchronous machine representation is the swing equation:

2H/ω_0 · d²δ/dt² = P_m − P_e − D · dδ/dt

with H the inertia constant (seconds — the time the stored kinetic energy could supply rated power), δ the rotor angle, P_m mechanical and P_e electrical power. Realistic studies use higher-order models (typically 6th order) with sub-transient reactances, plus the surrounding controls:

• AVR and exciter — regulate terminal voltage; fast excitation improves transient stability and can reduce small-signal damping.
• PSS (power system stabiliser) — added specifically to damp the oscillatory mode that fast AVRs excite. The interaction between these two is the classic worked example of control coordination in power systems.⁴
• Governor and turbine — set the frequency droop and the achievable ramp, including boiler and hydraulic dynamics; hydro units exhibit non-minimum-phase behaviour from water hammer that matters for frequency response.

Load models matter more than newcomers expect. A constant-power load draws the same power as voltage falls, worsening voltage stability; a constant-impedance load self-limits. Real load is a mix plus induction motors, which stall and draw large reactive current on voltage dips — the mechanism behind fault-induced delayed voltage recovery. Sensitivity of the result to the load model should be checked and reported as a matter of routine.⁵

What changes with inverters

Inertia falls. RoCoF after a loss of infeed rises. Systems have responded with minimum-inertia constraints, fast frequency response products with sub-second delivery, and synchronous condensers. Modelling frequency response now requires representing delivery delays explicitly, since at low inertia the difference between 0.5 s and 2 s delivery is decisive.⁶

Fault current falls. Inverters typically limit current to 1.1–1.5× rating rather than the 5–7× of a synchronous machine. Protection that relies on fault-current magnitude becomes less selective, and short-circuit studies that assume machine behaviour are wrong.

Behaviour becomes control-defined. A synchronous machine’s response is physics and is reproducible across manufacturers. An inverter’s is firmware, is manufacturer-specific, and is often proprietary. This has led to two modelling approaches, both necessary:

• Generic models — the WECC/IEC second-generation renewable energy models (REGC, REEC, REPC and their IEC 61400-27 counterparts) provide standard structures with tunable parameters, adequate for RMS system studies.⁷
• Vendor black-box EMT models — compiled, NDA-bound, and required for detailed connection studies at weak points. Practically, their integration and validation is often the schedule-critical path in a connection project.

Grid strength becomes a design constraint. The short-circuit ratio (SCR) at a connection point — system fault level divided by inverter rating — determines whether a grid-following inverter’s phase-locked loop remains stable. Below roughly SCR 3, and certainly below 2, grid-following control becomes problematic, and composite metrics such as weighted or composite SCR are needed once several inverters interact.⁸

Grid-forming control changes the picture. A grid-forming inverter imposes a voltage waveform and can provide synthetic inertia, operate at very low SCR, and in principle black-start. Deployment is progressing (notably in Australia, Great Britain, and Ireland) and specification of what “grid-forming” requires is still consolidating across grid codes — meaning the model you build today may not match the requirement that ends up applying.⁹

Method

A defensible dynamic study, in order:

1. Establish a valid steady-state base case with an AC power flow. Dynamics start from a power flow solution; if it is wrong, everything downstream is.
2. Initialise the dynamic models from that solution and verify a flat run — simulate with no disturbance and confirm nothing drifts. Failure here indicates model initialisation errors and is the most common practical problem.
3. Define the disturbance set — three-phase and single-phase faults at defined locations with defined clearing times, loss of the largest infeed, and busbar faults.
4. Simulate and assess against criteria: units remain in synchronism, voltages recover within a defined envelope, frequency stays above load-shedding thresholds, damping ratios exceed a minimum (commonly 3–5%).
5. Compute margins — critical clearing time for faults, maximum stable infeed loss, minimum inertia. A margin is far more useful than a pass/fail.
6. Validate against measurement where possible. Wide-area measurement (PMU) data allows modal identification from real events and comparison with simulated damping — increasingly the standard of evidence for model quality.¹⁰

Tooling

Commercial: PSS/E, DIgSILENT PowerFactory, PSCAD and EMTP-RV (EMT), RSCAD for real-time hardware-in-the-loop. Open: ANDES and Dynawo for RMS with well-documented model libraries, OpenIPSL (Modelica) for transparent model definitions, GridPACK for high-performance parallel dynamics.¹¹¹² The open tools are strong for research and reproducibility; connection studies almost always require the commercial ones because the vendor models are supplied for them.

Summary

Dynamics is a different modelling discipline layered on the same network: steady state supplies the starting point, and differential equations for machines, controls, and converters supply the behaviour. Choose RMS or EMT by whether the phenomenon lives below or above the fundamental. In an inverter-dominated system, inertia, fault current, and grid strength move from background assumptions to explicit constraints, and behaviour becomes a property of firmware rather than physics — which makes model provenance and validation the central practical problem.

References