arXiv subjects

Federico Milano

Publications and source records attributed to Federico Milano.

At least 19 recordsLinked to original sources

arXiv2026

On the Local and Global Nature of Frequency and Voltage Dynamics

This paper utilizes the autocorrelation of frequency and voltage measurements to identify, quantify and classify local and global properties of power system dynamics. The analysis is based on measurements with various resolutions (20 ms, 1 s, and 1 min) from several nodes of the Irish All-Island Power System (AIPS). Simulations based on stochastic differential algebraic equations on an IEEE benchmark system support conclusions drawn from real-world data.

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arXiv2026

Practical Framework for Power System Strength

A novel analytical framework for power system strength was recently introduced in the IEEE Transactions on Power Systems, providing a unified formulation for assessing voltage and frequency strength. Building upon this formulation, this paper addresses a series of practical challenges for translating the theoretical framework into a real-world application. In particular, simplified analytical solutions for network-wide bus-level strength metrics are provided, together with compact expressions to capture the impact of relevant devices on strength. In addition, novel normalized strength metrics at a device level are defined, enabling the comparison of strength across different systems. A strength source model is introduced to study the behavior of devices under varying strength conditions. Finally, the framework is implemented in a real-world study case, demonstrating its applicability and potential as a practical tool for a comprehensive strength assessment.

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arXiv2026

Frequency Quality Metrics based on Second-Order Derivative and Autocorrelation

This industry-oriented paper originates from the observation that current frequency quality metrics utilized by transmission system operators (TSOs) fail to fully capture the dynamic behavior of the grid frequency. Motivated by this gap, the paper proposes novel frequency quality metrics based on second-order dynamics and stochastic autocorrelation. Using real-world data with 0.1 s and 1 s resolution from the Irish, Great Britain and Nordic systems and running dynamic stochastic simulations, the paper shows that the proposed metrics bring new and counterintuitive insights in terms of how good or poor the frequency quality of power grids is beyond current well-known metrics. In particular, the paper shows that a power system may show good frequency quality using standard metrics and poor frequency quality using the proposed metrics. Overall, the paper contributes to improve the understanding of frequency quality.

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arXiv2026

Complex Frequency as Generalized Eigenvalue

This paper shows that the concept of complex frequency, originally introduced to characterize the dynamics of signals with complex values, constitutes a generalization of eigenvalues when applied to the states of linear time-invariant (LTI) systems. Starting from the definition of geometric frequency, which provides a geometrical interpretation of frequency in electric circuits that admits a natural decomposition into symmetric and antisymmetric components associated with amplitude variation and rotational motion, respectively, we show that complex frequency arises as its restriction to the two-dimensional Euclidean plane. For LTI systems, it is shown that the complex frequencies computed from the system's states subject to a non-isometric transformation, coincide with the original system's eigenvalues. This equivalence is demonstrated for diagonalizable systems of any order. The paper provides a unified geometric interpretation of eigenvalues, bridging classical linear system theory with differential geometry of curves. The paper also highlights that this equivalence does not generally hold for nonlinear systems. On the other hand, the geometric frequency of the system can always be defined, providing a geometrical interpretation of the system flow. A variety of examples based on linear and nonlinear circuits illustrate the proposed framework.

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arXiv2026

Rethinking Frequency Control in Power Systems

Frequency control in power systems is implemented in a hierarchical structure traditionally known as primary frequency control (PFC), secondary frequency control (SFC) and tertiary control reserve (TCR) and, some jurisdictions, include time error control (TEC) as well. This hierarchical structure has been designed around a century ago based on timescales separation, that is, approximately an order of magnitude difference between each control structure. This paper argues, based on real-world observations as well as detailed dynamic simulations on a model of the All-Island power system (AIPS) of Ireland, that this frequency control structure is not necessary in current and future converter-dominated power grids. The paper proposes to redesign this structure by removing the SFC and TCR and rely on PFC and a real-time energy market. The PFC is responsible for addressing fast power imbalances in timescales of tens of ms to few minutes (e.g., 100 ms to 5 minutes) while the real-time energy market is responsible for addressing longer imbalances in timescales of minutes to hours (e.g., 5 minutes to 1 hour). TEC, on the other hand, is considered as optional.

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arXiv2026

System-wide Dynamic Performance Metric for IBR-based Power Networks

In power networks based on Inverter-Based Resources (IBRs), fast controllers cause frequency and voltage dynamics to overlap. Thus, it becomes critical to assess the overall dynamic performance of such networks through a combined system-wide metric. This letter presents a unified metric designed to evaluate dynamic performance in such cases. The proposed metric consists of a weighted sum of local voltage phasor variations at each bus, where the weights are the complex powers injected at the buses. The proposed metric is further decomposed into device-driven and network-driven components, enabling a more comprehensive assessment of grid dynamics. A case study based on a modified version of the IEEE 39-bus system is presented, in which synchronous machines are replaced by inverter-based resources. A sensitivity analysis of the R/X ratio is utilized to evaluate the metric in conventional grids, as well as in those characterized by strong voltage-frequency coupling with complex power flows.

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arXiv2026

Ill-Conditioned Power Flow Analysis Using a Quantized State-Based Approach

This paper focuses on power flow analysis through the lens of the Newton flow, a continuous-time formulation of Newton's method. Within this framework, we explore how quantized-state concepts, originally developed as an alternative to time discretization, can be incorporated to govern the evolution of the Newton flow toward the power flow solution. This approach provides a novel perspective on adaptive step-size control and shows how state quantization can enhance robustness in illconditioned cases. The performance of the proposed approach is discussed with the ACTIVSg70k synthetic test system.

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arXiv2025

Instantaneous Complex Phase and Frequency: Conceptual Clarification and Equivalence between Formulations

This letter seeks to clarify the different existing definitions of both instantaneous complex phase and frequency as well as their equivalence under standard modeling assumptions considered for transmission systems, i.e. balanced positive sequence operation, sole presence of electro-mechanical transient dynamics and absence of harmonics and interharmonics. To achieve this, the two fundamental definitions, i.e., those based on either the use of (i) analytic signals or (ii) space vectors, together with the premises used for their formulation, are presented and their relationship shown. Lastly, a unified notation and terminology to avoid confusion is proposed.

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arXiv2025

Coherency Control in Power Systems

This paper proposes a coherency control strategy for Inverter-Based Resources (IBRs) to establish coherence among power system devices. Using the equivalence of the Complex Frequency (CF) of the injected currents as the definition for coherency among devices, the control enforces an output current with a proportional magnitude and a constant phase shift relative to a reference. This formulation makes the control technology-agnostic, enabling coherency with any type of resource. Case studies based on the two-area and IEEE 39-bus systems demonstrate the controller's potential to improve damping and overall dynamic behavior. The paper further evaluates practical implementation aspects including delay/noise sensitivity and the trade-off between oscillation mitigation and disturbance propagation. This work establishes coherency as a viable direct control objective for IBRs in modern power systems.

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arXiv2025

Generalized Swing Control Framework for Inverter-based Resources

This paper proposes a novel control framework designed for Inverter-Based Resources (IBRs), denoted as Generalized Swing Control (GSC). The proposed GSC framework generalizes the definition of Grid-Forming (GFM) control schemes and exploits the coupling between active and reactive power dynamics. To validate the proposed scheme, we conduct extensive time-domain simulations and small-signal analysis using a modified version of the WSCC 9-bus system and a 1479-bus dynamic model of the all-island Irish transmission system. The case studies focus on evaluating the dynamic performance of the proposed framework under different configurations, including Virtual Synchronous Machine (VSM), coupled-VSM and dual-VSM schemes. To address the nonlinear nature of power system dynamics, sensitivity analysis based on Monte Carlo methods are employed to improve parameter tuning and assess the stability of GSC configurations in the studied systems.

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arXiv2025

Coherency among Power System Devices

The paper proposes a novel general definition of coherency among power system devices of any type. The proposed approach is thus not limited to synchronous machines. With this aim, the paper shows that coherency can be formally based on the difference in the complex frequency of the current injections of any two devices electrically connected to the same grid. The proposed definition is model-agnostic, making it general and suitable for modern power systems composed of a heterogeneous mix of technologies. The paper also provides a systematic analytical procedure to study the properties that specific device models must satisfy to be coherent. Time-domain simulations are conducted in three case studies whose results illustrate the ability of our definition to evaluate coherency among any type of device.

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arXiv2025

Decentralized Approach to Detect and Eliminate Flapping Phenomena due to Flexible Resources

This paper presents a decentralized methodology for detecting and mitigating flapping phenomena in power systems, primarily caused by the operation of discrete devices. The proposed approach applies moving-window autocorrelation to local measurements, enabling each device to autonomously identify sustained oscillations. Upon detection, a probabilistic, device-specific mitigation strategy is executed. Flexible demand resources (DFRs), under-load tap changers (ULTCs), and automatic voltage regulators (AVRs) are utilised to illustrate the performance of the proposed approach to both discrete and continuous-operation devices. Results show that the proposed method is robust and properly distinguishes damped oscillations from persistent flapping, allowing devices to independently recognize problematic operating scenarios and implement corrective actions accordingly.

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arXiv2025

Analytical Framework for Assessing Effective Regional Inertia

This paper proposes a novel formulation of effective regional inertia that explicitly accounts for both system topology and the spatial distribution of inertia. Unlike traditional approaches that model a region as an aggregated machine with an equivalent inertia, the proposed metric provides a topology-aware representation. The methodology builds on an analytical framework that extends classical slow coherency theory to address network partitioning and regional frequency stability. Based on these partitions, we develop a systematic procedure to evaluate the effective inertia of each region, enabling a more accurate interpretation of local inertial contributions, including those from virtual inertia provided by inverter-based resources (IBRs). Case studies on the IEEE 39-bus and 68-bus systems demonstrate that the integration of inertial devices does not uniformly improve system frequency response, underscoring the importance of the proposed metric for effective regional inertia assessment.

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arXiv2025

Frequency Quality Assessment of GFM and GFL Converters and Synchronous Condensers

This paper compares the impact of different conventional and emerging technologies and control strategies on frequency quality. We study, in particular, the long-term dynamic performance of grid-forming (GFM) and grid-following (GFL) inverter-based resources (IBRs) as well as conventional synchronous machines. Extensive simulations and several realistic scenarios consider both short-term and long-term aspects of frequency quality. It is shown that, while overall GFM IBRs significantly improve frequency quality, a combination of GFL IBRs providing frequency support such as wind and batteries, and synchronous condensers, might be enough to meet similar frequency quality standards. Another result of the paper is that the need for automatic generation control (AGC) becomes less clear in GFM IBR-dominated grids from a frequency quality perspective.

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arXiv2025

A Comprehensive Approach to Evaluate Frequency Control Strength of Power Systems

This paper introduces the concept of "frequency control strength" as a novel approach to understand how different real-world power systems compare to each other in terms of effectiveness and performance of system-wide frequency control. It presents a comprehensive comparison, based on measurement data, of the frequency control strength of four real-world, renewable-based, synchronous islands power systems, namely Great Britain (GB), All-Island power system (AIPS) of Ireland, and Australia (AUS) mainland and Tasmania (TAS). The strength is evaluated by means of different frequency quality metrics. The common understanding is that the bigger the capacity of a power system, the bigger its robustness with respect to events and contingencies. Here we show that this is not always the case in the context of frequency control. In fact, our study shows that mainland AUS shows the highest frequency control strength during normal operating conditions, whereas the AIPS shows the highest relative frequency control strength for abnormal system conditions. The strength is, in particular, greatly influenced by different regulatory requirements and different system/ancillary services arrangements in each jurisdiction. The paper also provides possible mitigations to improve frequency control strength through grid codes and market rules.

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arXiv2025

Analytical Framework for Power System Strength

This paper proposes a general framework to evaluate power system strength. The formulation features twelve indicators, grouped in three dynamical orders, that quantify the resistance of bus voltage phasors and their first and second order rates of change to sudden current injection changes. To quantify such changes the paper introduces a novel finite differentiation technique, that we named Delta operator, able to properly capture "jumps" of algebraic variables and utilizes the recently developed concept of complex frequency. The paper also shows how the proposed framework can be systematically applied to any system device, and provides a variety of examples based on synchronous machines, converters and loads models are given. Numerical results in a benchmark system validate the exactness of the formulation.

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arXiv2025

Quasi Steady-State Frequency

Accurate frequency estimation is critical for the control, monitoring and protection of electrical power systems, in particular, of systems with a high penetration of power electronics. This paper introduces the novel concept of Quasi Steady-State (QSS) frequency as a quantity that fills the gap between stationary and instantaneous frequency. QSS frequency coincides with the fundamental frequency of an AC voltage in any stationary conditions, including unbalanced and non-sinusoidal, and is able to capture the time-varying fundamental frequency in transient conditions. The paper also proposes a metric borrowed from fluid dynamics, namely, the time derivative of the circulation, to define the scope of validity of the QSS frequency. Analytical examples as well as a case study based on a fully-fledged EMT model of the IEEE 39-bus system serve to illustrate, respectively, the properties of the QSS frequency and its behavior in transient conditions.

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arXiv2025

Transient Slack Capability

This paper introduces the concept of Transient Slack Capability (TSC), a set of three necessary device-level conditions to ensure stability under sustained power perturbations. TSC states that a device must (1) possess sufficient stored energy; (2) a controlled input power; and (3) maintain internal energy balance and synchronization. The paper shows that the relation among the time-scales of storage, control, and power perturbation is at the core of the TSC concept. Using the port-Hamiltonian (PH) framework, these conditions are formalized and validated via simulations on an adapted model of the WSCC 9-bus system. Case studies demonstrate that TSC is achievable in both Grid-Following (GFL) and Grid-Forming (GFM) converter control schemes, provided the conditions above are satisfied. Sensitivity analysis serves to identify storage and power reserve requirements to meet Conditions 1 and 2; the impact of converter current limiters on Condition 3; and inertia-less solutions able to achieve TSC.

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