A Generalized and Open-Source State-Space Framework to Derive Small-Signal Models for EMT dynamics of Inverter-Dominated Grids

Complex electromagnetic transient (EMT) interactions among inverters' control loops and network components have caused detrimental events. To study and prevent these EMT interactions, it is imperative to have a tool that readily synthesizes the state-space model not only for ad hoc grid cases, but rather for generic electrical grids. Using the Component Connection Method (CCM), we propose a systematic analytical framework that derives the dq-frame-based small-signal state-space model of the EMT dynamics for generic electrical grids. Most prior works apply the CCM to ad hoc grid cases or neglect devicelevel inputs. In turn, we propose for the first time definitions and analytical proofs that enable the CCM to incorporate: any generation device (e.g., grid-following and grid-forming inverters, synchronous generators, etc.), any network configuration, and all device-level inputs. Moreover, we propose guidelines that prevent the CCM from yielding state-space models that misrepresent the actual grid dynamics. We also prove the analytical conditions that guarantee the existence of the system-level state-space matrices when they are constructed via the CCM for generic electrical grids. The proposed framework is implemented as an open-source toolbox. Our toolbox reads the user-defined electrical grid in CSV files and returns not only the system-level state matrix A, but all system-level state-space matrices B, C, D. Thus, our toolbox provides an analytical platform for stability analysis, state-space control design, and model order reduction for userdefined inverter dominated grids.