Dynamic state estimation of hybrid systems: Inverters that switch between grid-following and grid-forming control schemes

TL;DR

This paper addresses the discontinuous dynamics of inverter-based resources that switch between grid-following and grid-forming controls. It develops a hybrid automaton representation with guard conditions on voltage and frequency and reset maps that preserve phase, frequency, and droop references during mode transitions, and embeds this model into a hybrid extended Kalman filter using a saltation matrix to handle switching. The main contributions are the formal hybrid-system formulation for dynamic state estimation and demonstrated improvements in estimation accuracy, particularly near switching instants, compared with smooth continuous-model alternatives. The work has practical implications for decentralized estimation and control in weak-grid scenarios, with future extensions to multi-inverter networks and reachability analysis.

Abstract

This paper develops a hybrid system modeling framework for inverters that switch between grid-following and grid-forming control schemes. In particular, such inverters are modeled as hybrid automata with guard conditions on voltage and frequency, and reset maps that maintain consistent phase, frequency, and droop references during mode transitions. The hybrid model is embedded within an extended Kalman filter to assess estimation performance under explicit mode switching. Results show that the proposed framework ensures stable, well-behaved dynamics and improves state estimation, especially near switching instants, compared with smooth continuous models.

Figures (4)

• Figure 1: Inverter switching between GFL and GFM controls.
• Figure 2: Hybrid automaton model.
• Figure 3: Comparison of hybrid model formulations for GFM and GFL modes with and without reset maps.
• Figure 4: Comparison of voltage and current responses for hybrid and continuous models, showing voltage variations, voltage errors, and current errors.