The grid that hums through our cities is in the middle of a quiet revolution. It’s not just bigger or smarter; it’s different in tempo. The old era of giant spinning generators gave way to a chorus of converters, batteries, and multiport links that connect alternating current to direct current like bridges between two very different continents. In this new world, stability isn’t just about keeping turbines in step; it’s about taming a fast, intricate dance that happens in milliseconds. A MATLAB-based toolbox called STAMP, short for Small-Signal Toolbox for Analysis of Modern Power Systems, is trying to help engineers hear that dance clearly. The work comes from researchers at the CITCEA-UPC center of the Universitat Politècnica de Catalunya in Barcelona, led by Josep Arávalo-Soler, with a team of collaborators from around the campus. Their project isn’t just a software demo; it’s a blueprint for understanding how hybrid AC/DC networks behave when you push them with real-world disturbances.
STAMP is designed to bridge two stubborn gaps that have grown as power systems evolve. First, there’s the microsecond-to-millisecond electromagnetic transient world that devices operate in, driven by the fast-acting controls on inverters and HVDC links. Second, there’s the bigger, slower slew of traditional power-system dynamics focused on synchronization and power flows. Historically, engineers used RMS (root-mean-square) or quasi-static models for stability analysis, which smooth over fast transients. But as the paper’s authors show, those fast transients can no longer be ignored when converters and DC interfaces proliferate. STAMP embraces what the authors call SSA-EMT: small-signal analysis using electromagnetic transient models, capable of capturing the high-frequency interactions that matter in modern, converter-dominated grids. This is not a theoretical luxury; it’s a practical tool for diagnosing and steering stability in networks that look more like layered hybrids than a single, uniform grid.
In a field hungry for trustworthy, open tools, STAMP stands out not just for its ambition but for its accessibility. The authors lay out a clear flow: feed the tool a data sheet describing the grid and the devices, compute the operating point, automatically generate a linear state-space model that includes the network’s fast dynamics, and run a menu of analyses—modal, impedance, and passivity—to understand how the pieces might sing or screech when nudged. It’s the difference between trying to read the orchestra by listening from the back of the hall and having a conductor’s score in hand. The paper also anchors STAMP in a broader ecosystem by offering interfaces to established power-flow tools like MATPOWER and MATACDC, so engineers can situate the SSA-EMT view next to steady-state calculations. This is stability analysis for a world where every plug-in and battery matters, not just the big spinning machines.
Key idea: STAMP automates electromagnetic transient modeling and small-signal analysis for large hybrid AC/DC grids, turning a complex reality into actionable math that engineers can wield. This matters because it lets researchers ask, with confidence, how a faster controller or a new HVDC link will reshape stability across frequencies where trouble tends to hide—and it does so with a practical bridge between non-linear simulation and linear analysis for validation.
The new heartbeat of modern grids
Modern grids no longer move at a single tempo. The old rhythm—synchronous generators turning at a steady pace, with stability judged by how well the slow oscillations damp out—still matters, but it now sits on top of a structure that can respond in milliseconds. In practice, that means converter-based resources like grid-forming and grid-following voltage sources, wind and solar inverters, and even HVDC cables, all interact through fast control loops. Those loops can create converter-driven instabilities that reverberate through the network at frequencies the traditional RMS models barely touch. The paper calls this a shift from RMS to EMT modeling: from a simplified algebraic-dominant view to a full ordinary differential equation picture that captures the network’s fast dynamics.
STAMP’s job is to automate the translation from a data sheet of devices and lines into a linear model that respects these fast transients. It doesn’t pretend that every detail is inside the linear model; it hand-picks a linearization point around a realistic operating point and then uses first-order expansion to produce a small perturbation model. The result is a state-space representation that can reveal which modes are headed toward instability and which parts of the system are most involved in each mode. In other words, it’s a tool to listen to the grid’s hidden chatter and point to where that chatter could turn into trouble if the controls or topology shift too much.
The authors emphasize that this approach is especially timely because of the rise of hybrid AC/DC networks. The DC side isn’t a distant march of HVDC corridors alone; it’s a mesh that couples with the AC grid through interconnecting converters. Those devices introduce their own illnesses as well as remedies, and their fast dynamics can couple with line and filter dynamics in unexpected ways. The STAMP approach is designed to account for these cross-domain dynamics in a single framework, enabling analysts to study the stability of a hybrid network without stitching together separate models that were never meant to talk to each other.
Bottom line: the grid’s stability problem has grown more complex, but STAMP gives engineers a systemic, open, and scalable way to examine how fast electromagnetic transients interact with slower grid dynamics, all the way from microseconds up to seconds and beyond.
STAMP in action
STAMP works by slicing the whole system into manageable subsystems and then weaving those subsystems back together. Each device or grid element—whether a generator, a voltage source converter, or a piece of transmission line—gets its own linear model. Those models are then interconnected according to the actual wiring of the network, producing a composite state-space model for the full system. The point of the exercise is not to replace time-domain simulations but to complement them with a linear representation that makes the stability landscape easier to scan and interpret. The math moves into the rotating reference frame, which is a standard trick in power systems to simplify dynamics by removing unnecessary time-varying angles. The global frame aligns the overall grid’s reference, while local frames track individual devices, and rotation matrices knit these perspectives together as the network interconnects.
STAMP does more than glue pieces together. It provides three complementary lenses to look for trouble. First is modal analysis, which digs into the eigenvalues of the state matrix. If any eigenvalue creeps into the right half of the complex plane, you’ve got an instability, and the associated eigenvectors tell you which states are most involved. Participation factors quantify how much each state participates in a given mode, spotlighting the likely culprits—be it the inertia of a turbine, a voltage controller in a grid-forming converter, or a fast-acting filter. This is the classic stability toolkit but applied to a model that includes fast electromagnetic dynamics across hybrid networks.
Second is impedance analysis. In the frequency domain, you can model devices as impedances and form a minor-loop gain by multiplying the grid’s impedance with a device’s admittance. The Nyquist criterion then tells you whether the loop can sustain stable operation. For three-phase systems expressed in rotating coordinates, this becomes a generalized Nyquist analysis that can handle multiple inputs and outputs. The result is a map of how the device and the grid interact across frequencies, revealing resonances and potential destabilizing frequencies.
Third is passivity analysis. A passive network, in the control-theory sense, can only dissipate energy and tends to be stable when interconnected with other passive systems. By checking the impedance’s frequency response for positive semi-definite Hermitian properties, STAMP can flag regions where a device might contribute to instability when paired with the rest of the network. In practice, this helps identify devices or control configurations that, while individually well-behaved, could produce trouble when coupled together in a hybrid AC/DC system.
What STAMP does well is provide these three angles in a single workflow, all built on an automatic pipeline. The toolbox can generate linear models for large networks with many converter-based resources, including grid-forming and grid-following modes, and it can handle user-defined blocks or black-box models if a frequency response is supplied. It also includes routines to initialize non-linear EMT models so that time-domain simulations can be used to validate linear predictions, a crucial step when you’re trying to trust a linear analysis on a real, messy system.
STAMP’s architecture is modular by design. The developers lay out a library of predefined linear models for common devices, and they provide a framework to plug in new elements. The AC grid and the DC grid get treated as subsystems that can be connected via node-interconnectors, a concept that reflects the way real buses in a network balance currents and voltages while responding to injections from other elements. The DC side relies on a three-parallel-RL representation for lines, while HVDC interconnections are captured through hybrid admittance blocks that link the AC and DC worlds. It’s a careful, principled way to capture the couplings that define modern grids while avoiding the worst of symbolic bloat or oversized math that would make the approach impractical for large systems.
STAMP isn’t just theoretical polish; it’s designed to run on real hardware datasets and to load data from familiar tools. The authors connect the toolbox to MATPOWER and MATACDC for power-flow calculations, enabling a coherent flow from steady-state operating points to linear SSA-EMT analyses. They also show how to initialize a non-linear EMT model in Simulink, which means engineers can cross-check linear predictions against full non-linear simulations, a win for both accuracy and confidence in the results. In short, STAMP makes it easier to go from “this is a plausible operating point” to a quantified statement about stability margins and risky parameter ranges.
Impact in practice: engineers can run parametric scans of controller time constants, inertia values, and HVDC settings to see how the spectrum of possible instabilities shifts across frequency. They can identify which devices are likely to participate in the most dangerous modes and prioritize tuning or hardware changes accordingly. This kind of proactive analysis is exactly what future grids will need as converter penetration grows and as we rely more on DC interfaces and fast-acting power electronics to keep the lights on.
What the case studies reveal
The paper tests STAMP against two illustrative studies that highlight both the power and the limits of the approach. The first is based on the WSCC system, a classic benchmark in power systems research. In this scenario, two traditional synchronous generators are replaced by two voltage-source converters. One operates in grid-forming mode, the other in grid-following mode, and a conventional turbine-governor and exciter model sits on the remaining generator. The aim is to see how a modern converter-rich configuration behaves under a small disturbance and how the linear model stacks up against a time-domain face-off with a nonlinear EMT model.
STAMP’s validation is robust. After solving the power flow to establish a realistic operating point, the authors compute the eigenvalues of the full state matrix. They show that the linear model captures both the slow dynamics of the rotor angles and the fast electromagnetic modes, aligning with the nonlinear simulations across a broad spectrum of timescales. The eigenvalues closest to the imaginary axis reveal which internal states are driving the most threatening modes. In a striking sensitivity study, adjusting the inertia of the synchronous machine, the grid-forming converter time constants, and the SG’s inertia and governor settings shifts the eigenvalue positions in well-predicted ways. When the GFM converter’s voltage-control time constant is shortened dramatically, two pairs of eigenvalues march toward the imaginary axis and cross it, signaling instability at around two kilohertz. The authors don’t stop at time-domain validation; they turn to the frequency domain to show that the converter’s admittance and the system’s impedance interact in a region of the spectrum where these unstable modes live, and that the combined picture explains the instability. The upshot is not merely that the model works; it’s that the tool makes it possible to see how high-frequency dynamics, once neglected, can become the bottleneck of stability in a modern grid.
The second case study centers on INELFE, Europe’s long-haul HVDC interconnection between Spain and France. This real-world system includes a pair of interconnecting HVDC converters and a dual transmission-line arrangement, with one line disconnected to simulate a potential contingency. Here the analysis lands more squarely on the practical questions of reliability and resilience: does an HVDC-dominant link stay stable when a line trips or when the load shifts unexpectedly? Using STAMP, the authors show that with both lines in operation the system sits in a stable regime—the eigenvalues are safely to the left of the imaginary axis. If one line goes down, the spectrum shifts and two unstable modes emerge at frequencies near 1.8–1.9 kilohertz. The voltage waveform at the HVDC interconnection exhibits the predicted instability, and a Fourier analysis confirms the presence of high-frequency content around the same region. The impedance-based analysis mirrors this conclusion: the minor-loop gain around the destabilizing frequency crosses a critical boundary in the single-line scenario but remains non-threatening when both lines are connected. It’s a clean demonstration of how STAMP can tie together time-domain behavior, spectral content, and impedance criteria to tell a coherent stability story for a real-world HVDC link.
From these studies, a few practical takeaways emerge. First, high-frequency dynamics matter more than ever when converter-based resources proliferate. Second, stability is a property of the entire coupled system, not of a single device in isolation; a well-behaved converter can destabilize a network if its interactions with the grid are not carefully accounted for. Third, the same tool that helps diagnose problems also helps engineers design them away. By simulating how parametric changes push eigenvalues, impedance peaks, or passivity margins, STAMP can guide controller tuning, HVDC design, and topology decisions before costly field trials are undertaken. And because STAMP is openly available and designed to scale to larger networks, it offers a shared platform for researchers and industry to test ideas across a spectrum of grid configurations.
What the numbers say: the paper includes a careful accounting of computation times, showing that STAMP can handle relatively large networks with hundreds of states in a timeframe compatible with iterative studies. This matters because the theory has to meet the reality of engineering workflows, where fast feedback loops from analysis to design decisions drive project timelines. In the WSCC and INELFE demonstrations, the authors present a convincing case that the toolbox produces credible, actionable insights without requiring prohibitive computational resources.
In some sense, STAMP is a synthesis device. It takes the algebra of control theory, the geometry of impedance and Nyquist criteria, and the gritty realities of grid interconnections—AC lines, DC cables, HVDC links, shunt devices—and turns them into a coherent, testable picture of how a modern grid will respond to perturbations. The authors emphasize that while SSAs anchored in EMT provide a richer view than traditional RMS-based SSA, they also acknowledge the limitations: even a fully linearized model around a fixed operating point is an approximation, and the real world exhibits nonlinearity, switching, and operating point drift. The value of STAMP, then, is not to pretend perfection but to provide a disciplined, transparent framework for exploring stability in a world where the wrong parameter choice can produce fast, dramatic consequences. The researchers note that future work will broaden the device library, expand capabilities for optimal power flow and fault analysis, and continue to refine how non-linear EMT models can be leveraged to validate linear predictions. The ladder, in other words, keeps growing taller—and more useful.
As grids around the world race toward higher inverter penetration, tools like STAMP could become essential parts of the engineering toolkit. They offer a way to envision how a hybrid AC/DC network behaves not just under ideal weather and load, but under the inevitable fluctuations of everyday operation. That’s the practical dream: to anticipate instability before it happens, to design controllers and interfaces that keep the grid calm when the storm arrives, and to do it with an openly accessible, rigorously tested platform that invites researchers and practitioners to join the conversation.
In the end, STAMP is more than a software package. It is a language for describing a new kind of grid—one where the boundary between alternating current and direct current is not a rigid wall but a living interface that can flicker and flash with new kinds of dynamics. By giving researchers a way to map those dynamics in a clear and quantitative way, the authors are helping us move from reactive worry to proactive resilience. That’s the kind of progress we want when the lights stay on because a toolbox understood the grid’s heartbeat—and helped keep it steady.
The work behind STAMP is a collaborative effort from the CITCEA-UPC team at Universitat Politècnica de Catalunya in Barcelona, led by Josep Arávalo-Soler, with contributions from Dionysios Moutevelis, Elia Mateu-Barriendos, Onur Alican, Carlos Collados-Rodríguez, Marc Cheah-Mané, Eduardo Prieto-Araujo, and Oriol Gomis-Bellmunt. Their open-source toolbox represents a meaningful step toward more robust, transparent, and scalable stability analysis for the grid of the future.
