The physics underneath

Every number on this site has an equation behind it.

A state estimator is only as honest as the physics it enforces. This page is the physics — the swing equation, RoCoF, short-circuit level, reactive power, phase authority, excitation — with the actual GB numbers attached, and a note on where each one lives inside GridSim. If you only read one page before requesting an evaluation, read this one.

½·J·ω²
where inertia actually lives
0 GVA·s
FRCR 2025 minimum target
1.0 Hz/s
modern RoCoF ride-through
48.8 Hz
where LFDD starts shedding you
01 · Inertia & RoCoF

Inertia is not a service. It is a state of matter.

Every spinning mass synchronised to the grid stores kinetic energy, and when frequency moves, that energy moves first — before any controller, before any market, before any detection stage. It doesn't ask permission and it doesn't compute. It resists, because Newton said so.

Ek = ½ · J · ω²
The stored kinetic energy of a rotating machine: J is the moment of inertia (kg·m²), ω the angular velocity (rad/s). This is the reservoir the grid drinks from in the first instants of any disturbance.
H = Ek,stored / Srated
The inertia constant, in seconds: how long the machine could supply its rated power purely from its own kinetic reservoir. A number a plant engineer can feel.
df/dt = (f₀ / 2·Hsys) · (ΔP / Ssys)
The headline equation — RoCoF. Halve the inertia, double the rate of frequency fall, for the same disturbance. RoCoF and inertia are the same equation read from different sides. This is what the MECHANICAL tab's relay margins are computed against, per machine, per tick.
TechnologyTypical HContributes system inertia?
Steam turbine alternator4–7 sYes — the deep end of the pool
Gas turbine alternator4–6 sYes
Hydro alternator2–4 sYes
Wind turbine (rotor)2–3 sDecoupled — the inverter hides it from the grid
Solar PV0 sZero. There is nothing spinning

Worked example, the honest way: a 660 MW thermal unit with H = 5 s contributes 660 × 5 = 3,300 MVA·s ≈ 3.3 GVA·s the moment it synchronises — and zero the moment it doesn't. GridSim carries exactly this arithmetic per machine, then maps it: inertia-per-unit in the MECHANICAL tab, inertia-by-source in NESO RP1, the synchronous / outturn / market GVA·s split in every streamed frame.

GB system inertiaValueContext
1990s, typical300–400 GVA·sFrequency held inside ±0.2 Hz almost all the time
Today — high load, traditional plant200–280 GVA·sThe comfortable half-hours
Today — low load, high renewables120–160 GVA·sRoutine now; unthinkable in 1995
FRCR 2025 minimum target102 GVA·sThe floor the operator now plans to
Historic record low — 2019~50 GVA·sBriefly. The year the grid found out

Roughly 30 GW of coal retired between 2012 and 2024, and this table is what it took with it. The scenario engine's risk curve — 260 → 155 → 120 → 102 → 50 GVA·s — traces exactly this decline, and every counterfactual GridSim runs is pinned to a rung of it. The thing inertia really buys is time: time for governors, time for frequency response, time for a human to act. That's why the NESO RP1 tab's hero metric is literally called purchased time — seconds of ride-through at the live credible loss, recomputed every tick.

02 · Frequency control & LFDD

50.000 Hz is a promise. Here's what happens when it breaks.

The grid's frequency is the truest single measurement of its health — the balance of every generator against every kettle, resolved fifty times a second. GDA holds 392 million one-second samples of it, back to 2014. When it falls, it falls through a staircase of defences.

ThresholdWhat it means
50.0 ± 0.2 HzNormal operating band — where the grid lives almost always
49.5 HzStatutory limit — the operator is now explaining itself
49.2 HzThe line the RP1 "purchased time" metric counts down to
48.8 HzLFDD — automatic low-frequency demand disconnection begins shedding real customers, in blocks
tpurchased = Δf / RoCoF
Purchased time: seconds of ride-through from here to 49.2 Hz at the current credible-loss RoCoF. The single number a control-room shift can act on — and the hero metric of the NESO RP1 tab, computed live against the 3,600 MW Dogger Bank design basis (with the old 1,800 MW convention shown struck through).

9 August 2019 — the day the maths went public

A lightning strike, two near-simultaneous losses, and roughly 1.4 GW of generation gone in seconds — a good part of it distributed generation tripping on RoCoF protection that was technically conforming to its settings. RoCoF spiked near 0.5 Hz/s on a system whose 1990s ancestors rarely saw 0.1–0.2. Frequency fell to 48.8 Hz. LFDD fired. A million people, trains stranded nationwide.

That day is in the lake — as a post-event dossier the evidence engine can replay, with the recorded RoCoF and nadir it must reproduce before any counterfactual is allowed to run. The relay settings it exposed are why the MECHANICAL tab shows dual RoCoF margins per machine: the original 0.125 Hz/s setting and the relaxed 1.0 Hz/s setting, side by side. The standards were rewritten after that day. Written in blood, as the engineering recommendations say — don't add to them.

Old RoCoF relay
0.125 Hz/s
the setting that bit in 2019
Modern requirement
1.0 Hz/s
G99 / ENA TS 48 ride-through
03 · Short-circuit level

A grid's strength isn't measured in peacetime. It's measured in a fight.

Short-circuit level is the grid's immune system — how hard the network can push back at a fault. High SCL behaves like a strong, low-impedance source; low SCL behaves like a weak, easily-disturbed one. It is also, quietly, the property that makes protection, power quality and inverter stability work at all.

SCLMVA = V²nominal / ZThévenin
System strength at a node, from the network's Thévenin equivalent behind it.
IF = SF / (√3 · VLL)
Worked, so you can check it: 8,000 MVA of SCL at a 400 kV bus gives IF = (8,000×10⁶)/(√3 × 400×10³) ≈ 11,547 A — call it 11.5 kA of fault current.

The fault-current asymmetry nobody prices

A synchronous machine with subtransient reactance X″d of 0.15–0.25 pu delivers 6–8× rated current into a fault, for hundreds of milliseconds, with a DC offset that doubles the first-cycle peak. A grid-following inverter is capped at 1.1–1.3× rated by IGBT thermal limits — for cycles, not seconds. Short-circuit studies routinely assume zero fault contribution from inverter fleets. A 2 GW coal station contributed upwards of 6,500 MVA of SCL at its connection bus; its replacement, in this particular respect, contributes approximately nothing.

WhereTypical SCL
400 kV node near major generation20,000–50,000 MVA
400 kV, remote5,000–10,000 MVA
132 kV bulk supply point2,000–8,000 MVA
33 kV primary distribution200–1,500 MVA
11 kV feeder80–300 MVA
LV, dense urban10–50 MVA
LV, rural1–5 MVA
The GB trend
−40–50%
Scottish nodes vs their historic SCL minimums; major transmission nodes down from 30,000–60,000 MVA in the 1990s to 10,000–15,000 today

GridSim's network model carries the impedance data this is computed from — the same Y-bus the solver factorises is the Thévenin picture a fault study needs. When the condition query scores a bus, this is part of what it's scoring.

04 · Reactive power & voltage

Reactive power does no work. It does the thing that makes work possible.

Q is the price of admission for using AC — pay it or the voltage collapses and nothing works. The wires don't know it's "only" reactive; they get hot just the same. This is the half of the power-flow problem most dashboards ignore, and exactly half of what GridSim solves at every bus.

S² = P² + Q²  ·  cos φ = P / S
The power triangle. A motor at power factor 0.7 needs 1.43× the apparent power of a resistor doing the same real work — capacity someone has to build and carry.
ΔV ≈ R·IP + X·IQ
Voltage drop, decomposed. On HV transmission X can be 10× R — so it's the reactive current that does most of the voltage damage. This is why reactive support has to be local: send 100 MVAR from London to Glasgow and the line drinks most of it on the way.

The capacitor trap

Capacitor-bank output scales with . Exactly when you need them most — voltage sagging — they supply less. The worst possible response curve, wired into the cheapest VAR source on the network. Voltage collapse is this trap plus constant-power loads plus tap-changers all pulling the same direction, and it unwinds in seconds. GridSim's solver enforces every generator's reactive limits exactly — zero violations across all fourteen validation cases — because this is the failure mode that punishes optimism.

LevelNominalStatutory range (ESQCR 2002)
LV at consumer terminals230 V+10% / −6% (216–253 V)
Distribution HV11 kV±6% typical
Sub-transmission33 kV±6% to ±10%, site-dependent
Transmission132–275 kV±5% typical
Super Grid400 kV±5% typical

The machinery that holds those bands runs on a strict timescale hierarchy: AVRs in single-digit milliseconds, STATCOMs and inverter droop in sub-seconds, on-load tap-changers walking their ±10% range in 16 or 32 steps over minutes, capacitor switching over hours. The gb-full model carries 1,383 live OLTCs in its control loop — the solved GB state ends with 953 taps off-nominal and every bus inside 0.980–1.046 pu. That is what "electrically proofed" means in practice.

AVR — milliseconds OLTC — ±10%, 16/32 steps 953 taps off-nominal, solved
05 · Phase authority

Steel sets the phase. Software follows it.

The whole AC grid is one giant cooperative agreement about where in the cycle "now" is — and something physical has to anchor that agreement. Pull a synchronous rotor a few degrees ahead of the network and it pushes power out; the rotor angle is the reference, enforced by megatonnes of spinning steel.

Grid-following inverters lock onto that reference with a phase-locked loop — passengers, not drivers. Grid-forming inverters hold a reference in a control-loop register: driving, but with fault current of 1.1–1.3× rated for a few cycles, against a synchronous machine's 6–8× for as long as its excitation says so. In 2019, inverters tripped not because they were broken, but because the phase reference they'd been freeloading off vanished.

Real phase authority and real inertia are the same property viewed from two angles — which is why GridSim refuses to treat either as a single system-wide scalar. Every machine in the model has an angle; every angle is solved; the map shows you whose steel is actually holding the reference at any half-hour you care to replay.

Device classPhase behaviourFault contribution
Synchronous machine Decides — rotor angle is the reference, physically 6–8× rated, hundreds of ms
Grid-following inverter Follows — PLL tracks someone else's reference 1.1–1.3× rated, cycles
Grid-forming inverter Emulates — reference lives in a register 1.5–2× rated, a few cycles
"Phase isn't something you measure. It's something something gets to decide. That something better be made of steel."
06 · Excitation & the capability curve

The rotor's field is the lever the grid pulls on.

One DC field winding governs a synchronous machine's terminal voltage, its reactive output, and its fault response. Understand the excitation system and the P-Q capability diagram stops being a compliance drawing and starts being a map of what the machine can actually do for the grid.

Vt = Ef − j·Xs·Ia
Terminal voltage against internal EMF: raise the field, raise Ef, and the machine leans on the grid harder.
Q = (Vt / Xs) · (Ef·cos δ − Vt)
The reactive dial: Ef > Vt and the machine is over-excited, supplying VARs; Ef < Vt and it absorbs them. Typical synchronous capability spans roughly ±0.6 to ±0.9 per-unit Q across most of the active-power range.

During a close-in fault the AVR drives a boost of roughly 2× rated field current for 5–10 seconds before thermal limits intervene — a deep copper-and-iron thermal envelope no silicon device replicates. Static excitation responds in single-digit milliseconds; the over- and under-excitation limiters (OEL/UEL) are the fences that keep the AVR from cooking the rotor or sliding out of synchronism.

The teardrop, live in the product

The P-Q capability diagram is a teardrop bounded by four thermal realities: rotor copper heating (over-excitation), stator copper heating (current), stator end-region heating (under-excitation), and the static stability limit. GridSim's MECHANICAL tab draws it per machine, per tick, with the operating point inside it — and when the solver's Q-limit logic pins a generator at Qmax and switches its bus PV→PQ, that event lands in the math ladder with the bus number and the pass it happened on.

Zero reactive-limit violations across all fourteen validation cases isn't a slogan; it's this diagram, enforced at every bus, every solve.

Fault field boost
2× / 5–10 s
the thermal envelope of copper
Static AVR response
~ms
single-digit milliseconds
07 · Harmonics & stiffness

A clean waveform is an outcome, not a goal.

Total harmonic distortion measures how far the grid has drifted from its 50 Hz ideal — and the stiffer the network at a point (the higher its SCL), the more harmonic current it can absorb without the voltage waveform deforming. Waveform quality and system strength are the same story told at different frequencies.

THD = √(V₂² + V₃² + V₄² + …) / V₁
Everything that isn't the fundamental, as a fraction of the fundamental. The 5th, 7th, 11th and 13th are the troublesome ones on three-phase; eddy-current losses scale with frequency squared, so those harmonics drive 25×, 49× and 121× the loss density of the fundamental. Every 10 °C above design halves insulation life.
Voltage levelG5/5 THD limit
LV (<1 kV)5%
MV (1–35 kV)4%
HV (35–230 kV)3%
EHV (230 kV+)2%

The orientation scale engineers actually use: under 1% is exceptional, 1–3% is a healthy HV network, 3–5% tolerable, 5–8% uncomfortable, beyond 8% an operational problem. And the cautionary physics: a capacitor that looks like 100 Ω at 50 Hz looks like 20 Ω at the 5th harmonic — parallel resonance can amplify one harmonic until the capacitor fails. The compliance stack that polices all of this (G5/5 for harmonics, P28 for flicker, G98/G99/G100 for connections) exists because each rule is the codified memory of an incident.

08 · Settlement & the money

The grid runs on physics. It settles in half-hours.

Everything commercial on the GB grid resolves to the 30-minute settlement period — 48 of them a day, except the two days a year the clocks change and there are 46 or 50. GDA anchors every one of them to UTC correctly, which sounds trivial until you've debugged a dataset that doesn't.

SETTLEMENT
Meters record energy in 30-minute intervals; readings flow to Elexon, the central administrator; imbalance volumes are computed per balancing group — contracted versus actual — and cash-settled under the Balancing and Settlement Code. GDA carries ~84 Elexon/BMRS streams: notifications, bids, offers, acceptances, metered volumes per BM unit.
GSP GROUPS
Fourteen groups, lettered A–N (no I, no O — they look like digits): Eastern to the Highlands. The gb-full model's fourteen licence areas map onto this geography, bus by bus.
CONSTRAINTS
When the network can't move the power the market scheduled, the operator pays to re-dispatch — constraint payments run to billions per year, boundary by boundary. GridSim models the ETYS corridors (B4, B6, B7, B8, SEIMP) with their real MW limits, and the OPERATOR tab shows each binding constraint with its £ cost, per settlement period.
THE TRIAD
Three half-hours of peak winter demand that set the following year's transmission charges — the reason hospital diesels used to fire up on cold January evenings. Retired by the Targeted Charging Review in 2022; alive forever in the historical record, where GDA keeps it.

The market-physics gap, measured

Put the physics and the invoice on the same axis and interesting things fall out. One representative settlement period, reconstructed action by action through the bid-offer ladder: £2.65 million of balancing spend to move 271 MW net — across 993 separate actions. The weekly gap runs to nine figures.

This is what the MARKET tab streams alongside every solved frame: imbalance price, BSUoS, net imbalance volume, every interconnector flow — the money side of the same half-hour whose voltages you're looking at. Replay-only, horizon-guarded, and therefore useless for trading — which is precisely why you can publish research built on it.

Periods / day
48
46 or 50 on DST days
Elexon streams
~84
in the lake
One period's balancing
£2.65m
993 actions, replayed
The point

Five properties. One kind of machine.

Inertia, phase authority, short-circuit level, reactive capability, damping — five views of the same synchronous-mass property, and the five things the modern grid is quietly running out of. A tool that lumps them into system-wide scalars can't see the problem, let alone measure it. GridSim carries each one per machine and per bus, solves them together at machine epsilon, and replays how they've actually moved, half-hour by half-hour, since the records begin.

Resistance, not response. Measured, not asserted. That's the physics case for the licence.