Grid-Forming Inverters & Virtual Synchronous Machines
"Who holds the frequency when nothing is spinning?"
In this episode
We re-derive why grid frequency has always been pinned to spinning mass — the swing equation, the inertia constant H, droop control, and the power-angle relation P = (V₁V₂/X)·sin δ. Then we look at what inverter-based renewables did to that picture: as synchronous machines are displaced, system inertia falls, the rate-of-change-of- frequency steepens, and frequency nadirs deepen. The fix is a controls distinction the whole field now turns on — grid-following inverters (a PLL locked to the grid, behaving as a current source that needs a stiff grid) versus grid-forming inverters (a voltage source that sets its own angle, can black-start, and can island). The centerpiece is the virtual synchronous machine: implementing the swing equation in firmware so a battery emulates rotor inertia — with the battery supplying the kinetic energy the inverter doesn't physically have.
Lesson map
- ObjectiveThree goals: re-derive where frequency comes from, understand "low inertia," and nail the grid-following vs. grid-forming distinction.
- The refresherSynchronous generators, the swing equation, inertia constant H, droop, and the power-angle relation.
- What changedInverter-based resources carry no rotating mass → falling inertia, steeper RoCoF, deeper nadirs (SA 2016, GB Aug 2019).
- The mechanismGrid-following (PLL + current source) vs. grid-forming (voltage source behind an impedance); why followers destabilize in weak grids.
- Virtual synchronous machineThe swing equation as firmware; "inertia became a config parameter"; the battery cashes the check.
- Industry standard + self-testIEEE 2800, grid-forming mandates, and two exercises.
Key concepts
Self-test
1 · The inertia crisis in one calculation
For a system with combined inertia of about H ≈ 4 s and a sudden generation-loss event of known per-unit size, use the swing equation to estimate the initial RoCoF before any governor or inverter responds. Now halve the system inertia (renewables displacing spinning machines) and recompute — RoCoF doubles. That doubling is the inertia crisis.
2 · Why followers fall over
Explain why a PLL-based grid-following inverter goes unstable as the short-circuit ratio drops (the grid gets weak), while a grid-forming inverter does not. The key: the follower depends on a stiff external voltage to lock onto; the grid-former creates the voltage reference itself.
Warm up in CircuitQuEEst
The matching undergraduate foundations are quests in CircuitQuEEst, the free, offline Android app for learning EE (download the APK). Play these first, then come back for the graduate-level version:
- Power Systems — Three-Phase Power · Renewable Energy Integration: the grid this episode puts under stress.
- Renewable Energy — Grid-Tie Inverters: an inverter that synchronizes to the grid is grid-following; this episode is about the ones that lead instead.
- Power Electronics — PWM Control: how an inverter actually synthesizes the voltage a grid-former imposes.
Go deeper
- IEEE 2800-2022 — interconnection & interoperability requirements for inverter-based resources.
- UNIFI Consortium — specifications for grid-forming inverter behavior.
- Hornsdale Power Reserve — flagship grid-forming battery providing synthetic inertia in South Australia.
- South Australia 2016 & Great Britain Aug-2019 events — low-inertia, fast-RoCoF case studies.
Typical H values (2–9 s) are representative ranges; see the primary sources above for specifics. Hornsdale was built in 2017 as grid-following and upgraded to grid-forming operation around 2022.