arXiv subjects

Georgios Tzounas

Publications and source records attributed to Georgios Tzounas.

17 recordsLinked to original sources

arXiv2026

Sparse Continuation-Based Eigenvalue Tracking for Power System DDAEs

In this paper, we formulate a continuation method for tracking eigenvalue trajectories in power system models with time-delayed measurement and control signals. Such delays are known to weaken damping and reduce stability margins if not properly accounted for in stability analysis and control design. The proposed formulation follows selected eigenpairs directly from sparse delay differential-algebraic equation (DDAE) models with one or multiple delayed variables, avoiding repeated eigensolutions as system conditions or parameters vary. The continuation parameter can represent system and control parameters, constant delay magnitudes, or parameters governing nonconstant wide-area measurement system (WAMS) delays. The proposed method is validated on a modified IEEE 39-bus system and on a real-world-scale dynamic model of the Irish transmission network, demonstrating accurate tracking of critical eigenvalue trajectories and clear computational advantages over repeated eigensolution-based analysis.

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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

On the Duality Between Quantized Time and States in Dynamic Simulation

This letter introduces a formal duality between discrete-time and quantized-state numerical methods. We interpret quantized state system (QSS) methods as integration schemes applied to a dual form of the system model, where time is seen as a state-dependent variable. This perspective enables the definition of novel QSS-based schemes inspired by classical time-integration techniques. As a proof of concept, we illustrate the idea by introducing a QSS Adams-Bashforth method applied to a test equation. We then move to demonstrate how the proposed approach can achieve notable performance improvements in realistic power system simulations.

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arXiv2025

On the Eigenvalue Tracking of Large-Scale Systems

The paper focuses on the problem of tracking eigenvalue trajectories in large-scale power system models as system parameters vary. A continuation-based formulation is presented for tracing any single eigenvalue of interest, which supports sparse matrix representations and accommodates both explicit and semi-implicit differential-algebraic models. Key implementation aspects, such as numerical integration, matrix updates, derivative approximations, and handling defective eigenvalues, are discussed in detail and practical recommendations are duly provided. The tracking approach is demonstrated through a comprehensive case study on the IEEE 39-bus system, as well as on a realistic dynamic model of the Irish transmission system.

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arXiv2025

Matrix Pencil-Based Analysis of Multirate Simulation Schemes

This paper focuses on multirate time-domain simulations of power system models. It proposes a matrix pencil-based approach to evaluate the spurious numerical deformation introduced into power system dynamics by a given multirate integration scheme. Moreover, it considers the problem of multirate partitioning and discusses a strategy for allocating state and algebraic variables to fast and slow subsystems based on modal participation factors (PFs). The suitability and features of the proposed approach are illustrated through numerical simulations that assess the accuracy effects of interfacing, as well as of various prediction and solution methods.

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arXiv2025

Stability of the Theta Method for Systems with Multiple Time-Delayed Variables

The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of delay differential algebraic equations (DDAEs) in non index-1 Hessenberg form. In particular, the paper shows that numerically stable ordinary differential equation (ODE) methods, such as the trapezoidal and the Theta method, can become unstable when applied to a power system that includes a significant number of delayed variables. Numerical stability is discussed through a scalar test delay differential equation, as well as through a matrix pencil approach that accounts for the DDAEs of any given dynamic power system model. Simulation results are presented in a case study based on the IEEE 39-bus system.

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arXiv2025

Smooth Rate Limiter Model for Power System Stability Analysis and Control

The letter proposes a smooth Rate Limiter (RL) model for power system stability analysis and control. The proposed model enables the effects of derivative bounds to be incorporated into system eigenvalue analysis, while replicating the behavior of conventional non-smooth RLs with high fidelity. In addition, it can be duly modified to enhance the system's dynamic control performance. The behavior of the proposed model is demonstrated through illustrative examples as well as through a simulation of the New York/New England 16-machine 68-bus system.

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arXiv2024

Instantaneous Frequency Estimation in Unbalanced Systems Using Affine Differential Geometry

The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on this link, a new instantaneous frequency estimation formula is proposed, which is particularly suited for unbalanced and single-phase systems. Several examples as well as measurements based on two real-world events illustrate the findings of the paper.

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arXiv2024

Instantaneous Power Theory Revisited with Classical Mechanics

The paper revisits the concepts of instantaneous active and reactive powers and provides a novel definition for basic circuit elements based on quantities utilized in classical mechanics, such as absolute and relative velocity, momentum density, angular momentum and apparent forces. The discussion leverages from recent publications by the authors that interpret the voltage and current as velocities in generalized Lagrangian coordinates. The main result of the paper is a general and compact expression for the instantaneous active and reactive power of inductances, capacitances and resistances as a multivector proportional to the generalized kinetic energy and the geometric frequency multivector. Several numerical examples considering stationary and transient sinusoidal and non-sinusoidal conditions are discussed in the case study.

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arXiv2023

Enhancing Frequency Control through Rate of Change of Voltage Feedback

This letter proposes a simple and inexpensive technique to improve the frequency control of distributed energy resources. The proposed control consists in modifying the conventional estimated bus frequency signal with an additional feedback signal that utilizes the rate of change of the voltage magnitude measured at the same bus. The case study showcases the benefits of the proposed control and compares its performance with standard frequency control schemes through time-domain simulations.

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arXiv2023

Unified Numerical Stability and Accuracy Analysis of the Partitioned-Solution Approach

This paper focuses on the Partitioned-Solution Approach (PSA) employed for the Time-Domain Simulation (TDS) of dynamic power system models. In PSA, differential equations are solved at each step of the TDS for state variables, whereas algebraic equations are solved separately. The goal of this paper is to propose a novel, matrix-pencil based technique to study numerical stability and accuracy of PSA in a unified way. The proposed technique quantifies the numerical deformation that PSA-based methods introduce to the dynamics of the power system model, and allows estimating useful upper time step bounds that achieve prescribed simulation accuracy criteria. The family of Predictor-Corrector (PC) methods, which is commonly applied in practical implementations of PSA, is utilized to illustrate the proposed technique. Simulations are carried out on the IEEE 39-bus system, as well as on a 1479-bus model of the All-Island Irish Transmission System (AIITS).

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arXiv2023

Mode-Shape Deformation of Power System DAEs by Time-Domain Integration Methods

This paper studies the numerical deformation that time-domain integration (TDI) methods introduce to the shape of the coupling between the dynamic modes and variables of power system models. To this aim, we employ a small-signal stability analysis (SSSA)-based framework where such mode-shape deformation is efficiently identified by comparing the modal participation factors (PFs) of the power system model with the PFs of the discrete-time system that is derived from the application of the TDI method. The proposed approach is illustrated for TDI methods commonly used in dynamic power system calculations.

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arXiv2023

On the Emulation of Synchronous Machine Dynamics by Converter-Interfaced Generators

This paper discusses the conditions that a device needs to satisfy to replicate the behavior of a conventional synchronous machine (SM) connected to a power network. The conditions pertain to the device's stored energy, time scale of response, oscillation damping, and behavior during short-circuits. Relevant remarks for devices that do/don't satisfy these conditions are discussed through an illustrative numerical example as well as through simulation results based on a modified version of the well-known WSCC 9-bus test system.

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arXiv2022

Using Differential Geometry to Revisit the Paradoxes of the Instantaneous Frequency

This paper proposes a general framework to interpret the concept of Instantaneous Frequency (IF) in three-phase systems. The paper first recalls the conventional frequency-domain analysis based on the Fourier transform as well as the definition of IF which is based on the concept of analytic signals. The link between analytic signals and Clarke transform of three-phase voltages of an ac power system is also shown. Then the well-known five paradoxes of the IF are stated. In the second part of the paper, an approach based on a geometric interpretation of the frequency is proposed. This approach serves to revisit the five IF paradoxes and explain them through a common framework. The case study illustrates the features of the proposed framework based on a variety of examples and on a detailed model of the IEEE 39-bus system.

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arXiv2022

Small-Signal Stability Analysis of Numerical Integration Methods

The paper provides a novel framework to study the accuracy and stability of numerical integration schemes when employed for the time domain simulation of power systems. A matrix pencil-based approach is adopted to evaluate the error between the dynamic modes of the power system and the modes of the approximated discrete-time system arising from the application of the numerical method. The proposed approach can provide meaningful insights on how different methods compare to each other when applied to a power system, while being general enough to be systematically utilized for, in principle, any numerical method. The framework is illustrated for a handful of well-known explicit and implicit methods, while simulation results are presented based on the WSCC 9-bus system, as well as on a 1, 479-bus dynamic model of the All-Island Irish Transmission System.

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arXiv2021

Applications of the Frenet Frame to Electric Circuits

The paper discusses the relationships between electrical quantities, such as voltages, currents, and frequency, and geometrical ones, namely curvature and torsion. The proposed approach is based on the Frenet frame utilized in differential geometry and provides a general framework for the definition of the time derivative of electrical quantities in stationary as well as transient conditions. As a byproduct, the proposed approach unifies and generalizes the time- and phasor-domain frameworks. Other noteworthy results are a new interpretation of the link between frequency and the time derivatives of voltage and current; and a definition of the rate of change of frequency that includes the novel concept of "torsional frequency." Several numerical examples based on balanced, unbalanced, harmonically-distorted and transient voltages illustrate the findings of the paper.

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arXiv2021

Small-Signal Stability Techniques for Power System Modal Analysis, Control, and Numerical Integration

This thesis proposes novel Small-Signal Stability Analysis (SSSA)-based techniques that contribute to electric power system modal analysis, automatic control, and numerical integration. Modal analysis is a fundamental tool for power system stability analysis and control. The thesis proposes a SSSA approach to determine the Participation Factors (PFs) of algebraic variables in power system dynamic modes. The thesis also explores SSSA techniques for the design of power system controllers. The contributions on this topic are twofold: i) Investigate a promising control approach, that is to synthesize automatic regulators for power systems based on the theory of fractional calculus. ii) Propose a novel perspective on the potential impact of time delays on power system stability. Through SSSA, the thesis systematically identifies the control parameter settings for which delays in PSSs improve the damping of a power system. Both analytical and simulation-based results are presented. Finally, SSSA is utilized in the thesis to systematically propose a delay-based method to reduce the coupling of the equations of power system models for transient stability analysis. The method consists in identifying the variables that, when subjected to a delay equal to the time step of the numerical integration, leave practically unchanged the system trajectories. Such an one-step-delay approximation increases the sparsity of the system Jacobian matrices and can be used in conjunction with state-of-the-art techniques for the integration of DAEs. The proposed approach is evaluated in terms of accuracy, convergence and computational burden. Throughout the thesis, the proposed techniques are duly validated through numerical tests based on real-world network models.

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