Kristian Skorpen

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Virtual Synchronous Generators — Grid-Forming Fundamentals

How grid-forming inverters and VSG control replace the physics of spinning machines — swing equation, ROCOF, droop control, and the GFM control family, with interactive simulations.

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Virtual Synchronous Generators — Grid-Forming Fundamentals

Power grids were stabilised for a century by the physics of heavy spinning machines. Those machines are retiring, and the inverters replacing them have no spinning mass at all. This course explains the technology closing the gap: grid-forming inverters, and in particular the Virtual Synchronous Generator (VSG) — an inverter that emulates a synchronous machine in software.

You build the subject from first principles: kinetic energy and the inertia constant, the swing equation, ROCOF and the 2019 Great Britain cascade, the PLL and why it fails in weak grids, voltage-source grid-forming behaviour, the VSG control block, droop control and its century-old governor origins, and the full grid-forming control family. Three interactive simulations let you drive the physics yourself.

Table of contents

  1. 1. Introduction
    • The conductor analogy: grid-following vs grid-forming vs VSG
    • Learning outcomes, prerequisites, notation
  2. 2. Inertia & the Swing Equation
    • Kinetic energy and the inertia constant H (with per-technology table)
    • Deriving the swing equation from Newton's law
    • ROCOF — formula and worked example
    • Interactive: swing-equation sandbox
  3. 3. Case Study: Great Britain, 9 August 2019
    • Timeline of the ROCOF cascade — 737 MW + 244 MW, 0.84 Hz/s, 1 million customers
    • The causal chain and what changed afterwards (G99, ALoMCP, Stability Pathfinder)
  4. 4. Grid-Following Control
    • The PLL: how an inverter follows the grid
    • Current-source terminal behaviour and the weak-grid instability mechanism
  5. 5. Grid-Forming Control
    • Voltage-source behaviour and the ENTSO-E Thevenin definition
    • GFL vs GFM side-by-side comparison
  6. 6. The Virtual Synchronous Generator
    • The swing equation in software — the VSG control block
    • Tuning H and D; the energy reality check
    • Inertia emulation vs Fast Frequency Response
    • Interactive: who reacts first? SG vs VSG vs FFR
  7. 7. Droop Control
    • From the governor to the droop law; the parallel sharing proof
    • Interactive: two inverters share a load step
    • Droop ↔ VSG equivalence (D'Arco & Suul)
    • Primary / secondary / tertiary hierarchy; virtual impedance
  8. 8. The Grid-Forming Control Family
    • Synchronverter, VSM/VSG, droop, dVOC, PSC — one map, five trade-offs
  9. 9. Limits & Misconceptions
    • The current limit — GFM's one hard constraint
    • Six misconceptions corrected precisely, including 'synthetic inertia'
  10. 10. Summary & Key Numbers
    • The four equations, the key-numbers table, the frequency-response ladder
    • Further reading
Order by email — 49 EUR