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The Impedance Margin Ratio: An Alternative Method for Evaluating Small-Signal System Strength
Short Circuit Ratio (SCR) is a key metric used to assess the strength of power systems, particularly in the context of connecting new converters at a point of interconnection (POI). It is derived from the short-circuit capacity (SCC) ratio to the nominal power of the device connected at that POI. Mathematically, SCR can be expressed as SCR = SCC / PN, where PN is the nominal power of the device. A higher SCR indicates that the system can provide greater current during a fault, suggesting a robust ability to maintain voltage stability under perturbations. However, SCR has limitations; it is primarily a static measure that only considers fundamental frequency behaviour and does not account for the dynamic interactions of converter stations or the varying frequency responses in modern power systems, leading to potential inaccuracies in system strength assessments.
The Impedance Margin Ratio (IMR) is introduced in [1] as a new metric for evaluating small-signal system strength. It is defined as the ratio of the maximum allowed variation of the converter impedance at a POI to its original value, specifically designed to prevent oscillatory modes from shifting into the right-half plane (RHP), which indicates instability. IMR is calculated using the whole-system admittance model, which reflects the interactions among multiple apparatuses in a multi-in-feed system. The figure illustrates IMR on a complex plane, where the left side depicts the original impedance vector (yellow) and the perturbed impedance (grey), while the right side shows the corresponding mode shifts. The yellow-dashed circle marks the mode variation margin. In contrast, the red-dashed circle denotes the impedance margin, emphasizing that IMR provides a localized measure of system strength at specific frequencies.
The differences between SCR and IMR lie primarily in their definitions and applications. SCR is a static measure that focuses on fault current capacity and is primarily applicable to single-in-feed systems, while IMR is a dynamic metric that evaluates small-signal stability and accounts for the interactions of multiple converters. IMR is particularly useful in identifying weak points in the system under varying operational conditions, as it reflects the system's response to small perturbations. Moreover, while SCR can be seen as a special case of IMR when considering fundamental frequency behaviour, IMR provides a broader perspective by analyzing frequency-domain interactions and oscillatory behaviours, making it more suitable for modern power systems as the number of converters in the power system increases.
Many thanks to Puval Purgat, the original author of this summary text
