Adaptive virtual inertia for a stable electricity grid

The electrification and rapid growth of renewable energy are fundamentally changing the character of the electricity grid. Whereas stability was traditionally provided by the rotating mass of synchronous generators, converter-based resources such as wind, solar, and energy storage increasingly dominate today. The result is a structural lack of inertia, causing frequency deviations to occur more rapidly and intensely. This places new demands on the control of power electronics.

In his MSc thesis research[1] At TenneT BV under Eindhoven University of Technology, Florian Bingel focuses on this challenge with a combination of grid-forming converters, Virtual Oscillator Control (VOC), and an innovative frequency concept: Complex Frequency. The result is an adaptive control system that demonstrably contributes to frequency stability in low-inertia grids.

Grid Forming and Virtual Oscillator Control

Unlike grid-following converters, which follow the grid via a PLL, grid-forming converters act as a voltage source and actively determine voltage and frequency. Virtual Oscillator Control offers significant advantages within this category. By operating in the time domain and making direct use of local voltage and current measurements, VOC can respond to disturbances extremely quickly. For this study, an Andronov-Hopf oscillator was chosen, which is known for its robust synchronization properties and simple parameterization.

From classical frequency to complex frequency

A major bottleneck in conventional control systems is frequency measurement itself. PLLs mix local dynamics with global system behavior, which can lead to delayed or excessive power injection. Complex Frequency breaks through this by treating frequency as a complex quantity. The real part defines local dynamics, and the imaginary part defines global dynamics. This creates a sharp distinction between local and global effects in the grid.

By using Complex Frequency as the input for virtual inertia control, a converter can respond more precisely to disturbances, with less active power and a greater role for reactive power.

Adaptive virtual inertia with fuzzy logic

The optimal contribution to virtual inertia proves to be highly dependent on the grid and the type of disturbance. A fixed setting is therefore rarely ideal. In this work, this is solved with a fuzzy logic controller that continuously adjusts a single key parameter based on local frequency and RoCoF. In this way, the converter provides extra inertia only when necessary and remains restrained under normal conditions.

Results and relevance

Extensive EMT simulations on modified IEEE 9 bus systems show that this approach leads to lower frequency NADIRs, RoCoF values within ENTSO‑E limits, and robust behavior during load steps as well as symmetric and asymmetric errors. Notably, no additional complex hardware is required: a local PMU suffices.

For engineers and system designers, this research underscores a clear trend. Power electronics is evolving from a passive grid follower to an active system carrier. The integration of Complex Frequency and adaptive control strategies offers a promising perspective for stable, future-proof electricity grids.

Power Electronics & Energy Storage event

Florian Bingel will give the opening presentation for the Power Electronics and Energy Storage event on May 27, 2026, at Congress Centre 1931, 's-Hertogenbosch. Visit the website For more information.

[1] Complex Frequency-based Control for Adaptive Frequency Regulation of Grid-Forming Converters – Research Portal Eindhoven University of Technology