On the Coupling of Power-Related and Inner Inverter Control Loops of Grid-Forming Converter Systems

Abstract

In the last decade, different control concepts for the synchronisation of voltage-controlled power converters have been proposed in order to form converter-based power systems. The interoperability of these grid-forming power controls is often analysed based on reduced-order models covering only the slow controls or modes. In this article, the coupling of the outer, power-related and inner, inverter outputrelated control of multiple grid-forming power converter systems is analysed, based on a minimal working example. The elementary study cases each consist of a different grid-forming converter coupled with an external (and passive) grid. Here, the investigated stability problems are already manifested in the simplest possible setup. The analysis of these coupling effects is performed by modelling the system in impedancebased, state-space and phase portrait-based frameworks. In particular, small coupling impedances, like short transmission lines or small short circuit impedances, can be challenging for the controller stability of gridforming converters while the inner controls can even enhance this issue. The impact of this phenomenon and the participating subsystems are identified in this work. Thus, recommendations concerning modelling techniques and their legitimate assumptions are given. Laboratory experiments validate the performed analysis by indicating a close correlation between analytical models and experimental results. INDEX TERMSCoupling effects, grid-forming power converter, power-related control, stability analysis, voltage control.

Modeling Techniques and Stability Analysis Tools for Grid-Connected Converters

“…Also, power-related controller or synchronization unit and inner controller can be considered separately because the coupling is neglectable. So the common approach is to analyze the large-signal synchronous stability (frequency dynamics) with TD EMT equations [20], [21] and simplified symmetrical small-signal models for aiding the inner controller design [90].…”

“…Time-domain state-space model instead can also provide insights into the coupling path based on the participation factors [21]. Note that the TD state-space model is actually a series of differential equations.…”

“…By that, the phase portrait offers a visualized way to access the dynamic performance with both frequency and phase jump, while oscillation can also be confirmed when under specific disturbance. In [21], based on the DPM, the time-domain simulation and phase plane trajectory of a grid-forming converter is given for different control strategies. Combined with the impedance model and eigenvalue analysis, the coupling effect between the power-related control and inner closed-loop control is further revealed.…”

“…Moreover, with HD modeling methods, time-and frequency-domain analysis can be used in one unified model, and therefore more dedicated controllers can be designed accordingly [17], [18]. Besides these numerical analysis methods, transient stability analysis with a large signal non-linear model in phase plane provides a visualized way to analyze the stability and performance under larger disturbance [19]- [21].…”

Frequency-Domain Stability Criteria for Converter-Based Power Systems

“…Ref. [11] proposed a system model for a single grid-forming converter connected to a grid. The converter was modeled as a voltage source behind impedance and the grid was treated as a passive network.…”