Power Margin Ratio -- A Large-Signal System Strength Metric for Inverter-Based Resources-Dominated Power Systems

As the growing penetration of inverter-based resources (IBRs) in modern power systems, the system strength is decreasing. Due to the inherent difference in short-circuit capacity contributions of synchronous generators and inverters, the short-circuit ratio is not a one-size-fit-all metric to assess the system strength. Following the distinct dynamic behavior of the IBR in small- and large-signal disturbance, the system strength is separated accordingly. To address the large-signal system strength assessment, a control type-dependent metric, Power Margin Ratio (PMR), is proposed in this paper. PMR is defined as the ratio between the maximum power that can be injected to the system without causing any instability and the nominal power of the IBR. It can be obtained via power flow calculation with a modified algorithm. The theoretical foundation of PMR is established from the viewpoint of dynamical systems. PMR is identical to SCR for the single-plant-infinite-bus system, while presents advancement for multi-infeed power systems. Comprehensive case studies and discussions have validated that PMR reveals the large-signal system strength from a static perspective.

💡 Research Summary

The paper addresses a pressing challenge in modern power systems: as inverter‑based resources (IBRs) replace synchronous generators (SGs), the traditional metric for grid strength – the short‑circuit ratio (SCR) – becomes inadequate. SCR assumes a quasi‑linear short‑circuit current contribution, which holds for SGs but not for IBRs that are limited by over‑current protection and exhibit diverse control modes (grid‑following, grid‑supporting, grid‑forming). Moreover, the authors highlight a fundamental distinction between small‑signal (linear) and large‑signal (non‑linear) disturbances. Through EMT simulations on a single‑plant‑infinite‑bus (SPIB) test case, they demonstrate that a small fault causes a temporary voltage dip that recovers (small‑signal stability), whereas a large fault leads to a voltage collapse that does not recover (large‑signal instability). This observation invalidates the use of a single metric such as SCR for assessing both phenomena.

To fill this gap, the authors propose the Power Margin Ratio (PMR) as a large‑signal system‑strength indicator. PMR is defined as

 PMRₖ = Pₘₐₓ,ₖ / P_IBR

where Pₘₐₓ,ₖ is the maximum active power that can be injected at the point of interconnection (POI) while still allowing the power‑flow solution to converge, and P_IBR is the IBR’s nominal (or worst‑case) rating. Pₘₐₓ,ₖ is obtained by incrementally increasing the IBR’s output in a standard load‑flow routine until the solver fails to converge, thereby capturing the static power margin of the network. Crucially, the method distinguishes IBRs by their control type: GFL with P‑Q control is modeled as a “GFL (control)” node, GFL with P‑V control as a “grid‑supporting” node, and GFM as a stiff V‑θ node (treated as a PV bus in the load‑flow but with a fixed angle during the PMR calculation). This classification embeds the control‑dependent contribution of each inverter into the metric without requiring detailed internal models.

The authors analytically prove that for the SPIB configuration, PMR reduces to the conventional SCR because the Thevenin impedance of the line (X_L) fully determines both the maximum transferable power (P_max = 1/X_L) and the short‑circuit capacity. In multi‑infeed systems, however, SCR typically ignores IBR contributions (assuming zero injection), leading to an under‑estimation of grid strength. PMR, by contrast, incorporates actual or potential power injections and naturally accounts for interactions among multiple IBRs through the load‑flow solution.

From a dynamical‑systems perspective, the paper links PMR to the size of the region of attraction (ROA) of the post‑fault equilibrium. A small PMR implies a small distance between the stable equilibrium point (SEP) and the nearest unstable equilibrium point (UEP) on the P‑δ curve, which translates into a reduced ROA and a higher likelihood of losing stability under large disturbances. The authors illustrate this relationship using the equal‑area criterion on the classic P‑δ curve for the SPIB case.

Extensive case studies on networks with three and five buses, containing various mixes of GFL and GFM converters, validate the concept. Results show that increasing the proportion of GFM converters raises PMR, indicating a stronger grid. Comparisons with other SCR‑based extensions (CSCR, WSCR, ESCR) reveal that PMR uniquely captures control‑type effects and multi‑inverter interactions, whereas the other metrics either aggregate IBRs without regard to control mode or neglect interaction altogether.

The paper also candidly discusses limitations. PMR is a static, power‑flow‑based indicator; it does not model transient current waveforms, protection actions, or detailed controller dynamics, and therefore cannot guarantee stability for any specific fault scenario. It should be viewed as a quick‑assessment tool that complements, rather than replaces, detailed EMT or time‑domain simulations. Implementation may require modest modifications to conventional load‑flow algorithms to handle multiple V‑θ nodes when GFM converters are present.

In conclusion, the Power Margin Ratio offers a technology‑neutral, easily computable metric for assessing large‑signal grid strength in IBR‑dominated power systems. It aligns with SCR in simple single‑infeed cases but extends the concept to realistic multi‑infeed networks, explicitly accounting for inverter control strategies. By providing a rapid estimate of the power margin before a large disturbance, PMR can aid system operators in planning, in‑feed allocation, and the strategic deployment of grid‑forming converters, ultimately contributing to more resilient low‑carbon power grids.