The Grid Is Getting Weaker: A New Framework to Measure How Much

The Challenge of Weaker Grids

Picture a busy highway at rush hour. If one lane suddenly closes, the traffic flow adjusts—cars slow, merge, redistribute. The highway is "strong" enough to absorb the shock. Now imagine that same highway with half the cars replaced by tiny remote-controlled vehicles that respond differently to pressure, brake at different thresholds, and can't anticipate what others will do. The same disruption could cause chaos.

This is roughly what is happening to power grids worldwide. For over a century, electricity networks have relied on massive rotating machines—synchronous generators in coal plants, natural gas facilities, and nuclear stations—to keep the lights on and the system stable. These machines are heavy, literally: their massive spinning turbines and generators carry enormous physical inertia, like that sturdy highway. When something goes wrong—a generator trips offline, a lightning strike hits a transmission line—their sheer mechanical mass buys time for the system to react.

But the grid is changing faster than almost anyone predicted. Solar panels, wind turbines, and battery storage systems are now the fastest-growing sources of electricity in most countries. These devices don't spin. They convert power through power electronics—inverters—that behave fundamentally differently from synchronous machines. They're lighter, faster, and more agile, but they can also be more delicate, more sensitive to disturbances, and, in some respects, weaker.

This is the core tension at the heart of a new paper by Ignacio Ponce and Federico Milano of University College Dublin: our grids are becoming weaker even as we ask more of them. The tools we've used for a century to measure grid strength are starting to fail. And we need new ones. (Ponce & Milano, 2026)

The Science

The concept of "power system strength" sounds straightforward, but defining it precisely—and measuring it—has proven devilishly complicated. In simplest terms, strength is the ability of a system to resist changes in voltage at a given location. When something disrupts the grid, stronger systems keep voltage stable; weaker ones see it sag, surge, or oscillate dangerously.

Traditional metrics have served reasonably well in the past. The short-circuit level (SCL), for instance, measures how much current would flow if a fault shorted the system—it tells you how much "backup" capacity exists to maintain voltage during emergencies. Inertia, the kinetic energy stored in spinning generators, provides a buffer against frequency swings by releasing energy when the balance between supply and demand shifts.

But these metrics were designed for a world of predominantly synchronous generators. As grids fill with inverter-based resources (IBRs)—solar inverters, wind turbine converters, battery storage systems, and the power electronic interfaces of offshore wind farms—these old measures become less reliable. IBRs can trip faster than conventional generators, respond to disturbances in unpredictable ways, and, crucially, lack the inherent robustness of a spinning mass of metal and copper.

"Strength is commonly understood as the ability of a system to resist changes in the three-phase AC voltage at a certain location, typically reflected through variables such as the voltage magnitude, phase angle, and frequency," the authors note. But the traditional metrics that quantify this resistance "have fallen short for quantifying strength in power systems with an increasingly heterogeneous mix of devices."

Ponce and Milano's earlier work, published in IEEE Transactions on Power Systems, proposed a solution: a unified analytical framework based on the concept of "complex frequency"—a mathematical tool that treats voltage magnitude and frequency as two aspects of the same underlying phenomenon. This framework comprises twelve indicators organized into three orders of dynamics. Zero-order indicators capture how voltage magnitude and phase angle respond to current injections. First-order indicators measure how quickly those responses occur (the stiffness of the complex frequency). Second-order indicators track the acceleration of those changes.

This unified approach was theoretically elegant. It also required detailed post-disturbance data that, in practice, is rarely available before a disturbance occurs—which rather limits its utility for planning and real-time operation.

The new paper tackles this gap directly. Its central aim is translating the sophisticated theoretical framework into something engineers can actually use in the field. The authors provide simplified analytical expressions that depend only on pre-disturbance conditions, define normalized device-level metrics that allow apples-to-apples comparisons across different systems, introduce a novel "strength source" model for testing device behavior under controlled conditions, and validate everything against a real-world power system: the All-Island Irish grid.

The methodology proceeds in stages. First, the researchers derive simplified versions of the twelve strength indicators by assuming that post-disturbance values are approximately equal to pre-disturbance values—essentially treating the system state as unchanged by the perturbation for the purpose of calculating strength. While this introduces some approximation error, the authors argue it produces results consistent with established practice, comparable to how engineers calculate maximum and minimum short-circuit currents using standardized assumptions.

Next, they derive "strength components" for a range of relevant devices—synchronous generators, power electronic converters, static loads, and induction machines—showing how each device type contributes to (or detracts from) overall system strength. This involves applying a systematic procedure to each device's mathematical model, identifying the terms that determine how its current injection responds to voltage changes, and extracting the coefficients that populate the strength metric calculations.

The analytical framework is then extended to a network-wide assessment, where the interaction between devices through the grid's impedance matrix determines the overall strength at each bus. Finally, the strength source model provides a means to impose arbitrary strength conditions on test systems—a controllable external equivalent that lets researchers study device behavior under precisely specified strength levels without needing to construct a full physical system.

What They Found

The simplified analytical solutions that Ponce and Milano derive are striking in their elegance. After assuming that pre- and post-disturbance states are approximately equal—a reasonable approximation for initial strength assessment—they arrive at a remarkably compact set of equations. The zero-order strength matrix at each bus becomes simply the inverse of the pre-disturbance voltage multiplied by the equivalent impedance matrix of the network. First and second-order metrics follow analogous patterns, differing only in which order of the equivalent impedance matrix enters the calculation.

These equations reveal something important: the entire twelve-indicator strength assessment, which initially required complex post-disturbance calculations, reduces to quantities that can be computed from the standard power flow solution—the baseline operating state of the network—and the network's impedance characteristics.

The authors' analysis of how different device types contribute to strength yields equally important insights. For synchronous machines—the workhorses of conventional power systems—they find that the first-order strength indicator is effectively zero. This means the complex frequency (the rate of change of voltage magnitude and phase) remains continuous when disturbances occur. In physical terms, the spinning mass of a synchronous generator naturally prevents abrupt jumps in frequency. This is a fundamental property that engineers have exploited for decades without necessarily quantifying it.

But the moment you introduce inverter-based resources, this picture changes. Power electronic converters can exhibit non-zero first-order strength components, which means the complex frequency can jump discontinuously when the system is perturbed. "In case a device introduces a non-null first-order strength component, it will challenge the continuous nature of the first-order complex frequency," the authors write. This discontinuity is not inherently catastrophic, but it does represent a fundamentally different dynamic regime—one that traditional stability tools were not designed to handle.

The second-order indicators tell a similarly nuanced story. Synchronous machines do contribute to second-order strength (because their acceleration characteristics are captured in the mathematics), meaning the rate of change of frequency can shift suddenly after a disturbance. But the magnitude and sign of this contribution depends on how the machine is controlled, its current operating point, and the characteristics of its excitation system. IBRs, depending on their control architecture, can either enhance or degrade this second-order strength.

To make sense of these abstract relationships, the researchers developed a "strength source"—a mathematical construct that acts as an external network with specified strength levels. This allows them to test how specific devices behave when subjected to precisely controlled strength conditions. In tests with a representative power electronic converter, they found that the device's performance varied systematically with the strength ratio (the ratio of active to reactive current strength components). Under weak conditions, the converter's Phase-Locked Loop (PLL)—the control mechanism that synchronizes the converter's internal oscillation with the grid—exhibited larger frequency deviations and longer recovery times. Under strong conditions, these deviations were muted.

The Irish grid case study provides the framework's most compelling validation. Analyzing the All-Island Irish system (which, as of the study, derives roughly 60% of its generation from renewables, including substantial offshore wind), the researchers computed strength metrics across all major buses. The results reveal significant spatial variation. The Dublin area, dense with load and generation, showed consistently higher strength levels—the system is literally more robust near major population centers. More remote areas, particularly in the west and northwest where much of the wind generation is located but transmission infrastructure is sparser, exhibited lower strength levels. This finding aligns with practical concerns about weak grids in areas with high renewable penetration but limited grid investment.

Zero-Order Voltage Strength Across Irish Grid Buses

Label	Value
Dublin Area	4.2
Cork Area	3.1
Galway/West	1.8
Offshore Wind (East)	2.4
Belfast Area	3.5

Data from Ponce & Milano (2026), All-Island Irish System Case Study

First-Order Frequency Strength Metrics

Label	Value
Active Current (Sρ·ıp)	0.42
Reactive Current (Sρ·ıq)	0.38
Active Current (Sω·ıp)	0.55
Reactive Current (Sω·ıq)	0.48

Data from Ponce & Milano (2026), All-Island Irish System Case Study

The second-order strength metric Sγ_ıp—which captures how the rate of change of frequency responds to active current injections—reveals particularly interesting patterns. High values (indicating strong coupling between current injections and frequency acceleration) tend to cluster near synchronous generators and at buses with high short-circuit ratios. Lower values appear in regions dominated by inverter-based generation, consistent with the theoretical predictions about how IBRs alter system dynamics.

Perhaps most significantly, the researchers demonstrate that their normalized device-level metrics enable meaningful comparisons across systems. A strength indicator expressed in absolute terms (say, volts per ampere) means little without context. But the same indicator normalized relative to the system average or to a reference bus provides actionable information: how does this device or location compare to others? Is it stronger or weaker than the norm? By what factor?

Why This Changes Things

The implications of this research ripple outward in several directions, but the most profound may be conceptual: this framework treats voltage magnitude and frequency not as separate phenomena to be managed by separate tools, but as aspects of a single underlying property—the complex frequency of the three-phase AC waveform. For over a century, power system engineers have studied voltage stability and frequency stability as distinct disciplines, using distinct metrics and distinct control systems. Ponce and Milano's framework suggests these distinctions are somewhat artificial—a product of historical accident rather than fundamental physics.

"Both variables are ultimately properties of the same three-phase AC voltage waveform," they note, "this motivates the development of a unified strength assessment framework." This unification matters because the devices filling our grids don't respect these disciplinary boundaries. An inverter-based resource responding to a disturbance will affect both voltage and frequency simultaneously, in ways that traditional decoupled analysis cannot capture.

The practical consequences of this conceptual shift are potentially significant for how grids are planned and operated. If engineers can calculate twelve strength indicators (or even a subset) that capture the full spectrum of voltage-frequency behavior, they gain a far more nuanced picture of grid health than any single legacy metric provides. The short-circuit level tells you something about fault current capacity. The inertia constant tells you something about frequency response. The new framework's indicators tell you about how voltage magnitude, phase, frequency, and their rates of change will all respond to a given perturbation—across multiple time scales, from milliseconds to seconds.

The simplified expressions are particularly important because they make this sophistication accessible. A practicing engineer doesn't need to run detailed dynamic simulations to estimate strength at a given bus. They can compute it from standard power flow data and the network model—information that is almost always available, even in planning studies for future systems. This transforms the framework from a theoretical curiosity into a practical tool.

The normalized device-level metrics address an equally pressing problem: how do you compare strength across systems that differ in size, topology, and operating conditions? A short-circuit level of 5,000 amperes means very different things in a small island grid and a continental system. But normalized metrics—ratios that express local strength relative to the system average, or that benchmark devices against standardized reference conditions—enable meaningful comparison. This matters for utilities considering equipment procurement, for regulators setting interconnection requirements, and for researchers comparing case studies from different contexts.

The Irish case study demonstrates that these methods aren't merely theoretical. The All-Island Irish system presents genuine challenges for traditional strength assessment: high renewable penetration, asynchronous offshore wind connections, relatively limited interconnection to neighboring grids, and a transmission network constrained by planning and geographic factors. That the framework produces interpretable results in this context—results that align with engineering intuition about where the system is strong and weak—suggests it can transfer to other systems facing similar transitions.

There are also implications for the growing concern about grid-forming inverters. Conventional inverters synchronize to the grid using PLLs that track the grid's frequency. Grid-forming inverters, by contrast, actively set the frequency, behaving more like synchronous generators. The framework's analysis of how different control architectures affect strength components suggests that grid-forming inverters could be designed to restore properties lost when synchronous machines are replaced—potentially recovering continuous frequency behavior that weaker inverter controls sacrifice.

What's Next

Several significant questions remain open. The assumption that pre- and post-disturbance states are approximately equal is a simplification whose error depends on the severity and type of disturbance. For minor perturbations, this is reasonable. For extreme events—the kind that actually threaten system stability—the error may grow. Ponce and Milano acknowledge this and suggest their simplified approach is most appropriate for preliminary assessment and planning, while more detailed analysis may require the exact solutions from their earlier work.

The framework's twelve indicators (four per dynamical order) provide rich information, but the paper offers limited guidance on which indicators matter most for specific applications. Is the zero-order strength metric (voltage stiffness) more critical for steady-state planning, while higher-order metrics become essential for dynamic stability assessment? The authors note that acceptable strength levels depend on the specific devices and control strategies present, which suggests that threshold-setting will require further research and likely system-specific calibration.

The strength source model opens interesting doors for future work. By providing a controllable external equivalent with arbitrary strength characteristics, it enables systematic study of device behavior under well-defined conditions. This could support standardization of testing protocols for inverter manufacturers, grid code development for interconnection requirements, and fundamental research on how specific control strategies affect system-level dynamics.

The Irish case study, while valuable, represents just one system. The framework's transferability to other contexts—large continental systems, small island grids, heavily industrial networks—remains to be demonstrated. Each presents unique characteristics that may require adaptation of the methods or reinterpretation of the thresholds.

And then there is the matter of time. The paper treats strength as a static property, computed from a snapshot of system conditions. But grids are dynamic: generation varies with weather, load changes through the day, equipment ages and degrades. Strength metrics computed today may not reflect conditions tomorrow. Extensions to real-time strength assessment, perhaps leveraging the data-driven approach mentioned in the earlier work, could eventually enable continuous monitoring of grid health.

Perhaps the most significant open question is institutional: how will these methods be adopted, validated, and standardized? The power industry moves deliberately, and new analytical frameworks must earn trust through extensive testing, comparison with established methods, and demonstration across diverse systems. The theoretical elegance and practical accessibility of Ponce and Milano's framework are encouraging, but the ultimate measure of success will be whether it helps engineers build and operate grids that remain stable as they continue their transformation.

The grid of the future—if it is to deliver reliable electricity while decarbonizing at the speed the climate crisis demands—will look nothing like the grid of the past. It will be populated by devices that respond faster, are distributed more widely, and can fail in new ways. Keeping that future grid stable will require tools that were unimaginable when our current metrics were developed. This framework is a promising step toward those tools. It won't solve every challenge, but it provides a new language for thinking about strength—one that acknowledges the complexity of the system we're building and gives engineers a more precise way to describe, measure, and ultimately manage it.

The highway analogy at the beginning of this piece may be apt in another way. When traffic patterns change—when more vehicles are autonomous, electric, or shared—the rules of the road must evolve. Speed limits, merging protocols, and signaling systems all require rethinking. Our power grids face a similar inflection point. The tools that got us here won't be sufficient for where we're going. Ponce and Milano's practical framework for power system strength is an early attempt to write the new rules for a grid that doesn't yet fully exist—and that we desperately need to work when it does.