Flexible Impedance Calculation of Inverter-Based Resources via Descriptor State Space Models

Impedance-based models of inverter-based resources (IBR) such as wind/photovoltaic generators are widely used to study control to grid interactions. Existing methods for obtaining detailed analytic expressions of the impedance equivalents are time consuming and reliant on extensive algebraic manipulation of numerous equations. In this context, this paper presents a method for calculating impedance profiles numerically, by using a descriptor state-space (DSS) representation of the IBRs which considers all IBR control blocks modularly, so that they can be added, removed, or modified without extensive algebraic manipulations. The method is based on DSS models, which are more transparent than traditional state-space models as algebraic expressions are modeled explicitly. This modular approach speeds up the investigation of the impact of different control designs and tunings on the risk of instabilities, while preserving a high level of detail of IBR behavior and mitigating potential human error. The proposed calculation methodology is validated with detailed electromagnetic transient simulations, for single-phase and three-phase IBRs. Applications of the proposed approach are presented to illustrate its ability to assist on the efficient investigation of characteristics of different control designs, and to help identify simplified models tailored for studying specific types of instabilities at different frequency ranges.