arXiv subjects

Vassilis Kekatos

Publications and source records attributed to Vassilis Kekatos.

At least 19 recordsLinked to original sources

arXiv2026

Designing Grid-Aware Dynamic Specifications for Large Data Center Loads

As data center (DC) loads increasingly penetrate the power grid, there is an urgent need for grid operators to provide clear dynamic specifications to DC owners to ensure safe grid operation. To this end, we study two salient behaviors of large language model (LLM) training loads: abrupt ramps at job initiation and termination, which induce transient frequency excursions, and sustained periodic oscillations during training, which result in oscillatory steady-state behavior. For ramping loads, we show that nodal rotor frequencies can be accurately approximated by the center-of-inertia (COI) frequency and derive analytical expressions for its nadir and rate of change of frequency (RoCoF). These expressions determine allowable combinations of ramp times and steady-state load demands satisfying prescribed frequency limits. For oscillatory loads, we derive spectral specifications on their Fourier coefficients and show that the admissible coefficient set can be approximated by a polytope. We further obtain a compact representation via its maximum-volume inscribed ellipsoid, which we show is axis-aligned. Numerical tests on the WECC 179-bus system demonstrate that the resulting specifications remain valid for higher-order nonlinear dynamics. The proposed framework provides actionable specifications for regulating the dynamic behavior of large DC loads and informing load-shaping mechanisms within the data center ecosystem.

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arXiv2026

Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow

Conic programs arising in physics, quantum information, machine learning, and engineering are often defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers, the computational complexity scales unfavorably with graph size. We propose a variational quantum paradigm for solving conic programs, including quadratically constrained quadratic programs and semidefinite programs. We encode primal variables via the state of a parameterized quantum circuit (PQC) and dual variables via the probability mass function associated with a second PQC. The Lagrangian function can thus be expressed as scaled expectations of quantum observables. We pursue approximately stationary points of the Lagrangian by minimizing/maximizing the Lagrangian over the parameters of the first/second PQC. This is accomplished in a hybrid fashion: gradients are estimated using the two PQCs, while their parameters are updated classically using a primal-dual method. We propose permuting primal variables so that related observables have a banded form, enabling efficient measurement. We provide a complexity analysis that is useful to determine which problem types may enjoy quantum advantage. The framework is applied to the AC OPF problem, a large-scale optimization problem central to electric power system operation. Numerical tests on the IEEE 57-node system using PennyLane's simulator show that the proposed doubly variational quantum framework can find high-quality OPF solutions. While this demonstration does not yield a quantum speedup, the results serve as a proof-of-concept and highlight challenges toward practical quantum advantage. Although showcased for OPF, the framework has broader scope, including conic programs with many variables and constraints, problems defined over sparse graphs, and training quantum machine learning models to satisfy constraints.

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arXiv2026

Frequency-Domain Characterization of Load Demand from Electrified Highways

Electrified roadways (ER) equipped with dynamic wireless power transfer (DWPT) capabilities can patently extend the driving range and reduce the battery size of electric vehicles (EVs). However, due to the spatial arrangement of the transmitter coils in the ER, the DWPT load exhibits frequency content that could excite power system frequency dynamics. In this context, this work aims to study the spectrum of DWPT loads under different traffic conditions. Under simplifying assumptions, we develop statistical models to identify the location and relative magnitude of DWPT load harmonics. Our analysis reveals that the fundamental frequency depends on ER coil spacing and average EV speed. In the worst-case yet unlikely scenario that EVs move in a synchronized fashion, the amplitude of harmonics scales with the EV count. On the contrary, when EVs move freely, harmonics scale with the square root of the EV count. Platoon formations can accentuate harmonics. The spectral content around harmonics decreases in magnitude and increases in bandwidth with the harmonic index. The load of a single EV moving at a time-varying speed can be modeled as a frequency-modulated (FM) signal. Despite the simplifying assumptions, the derived models offer valuable insights for ER planners and grid operators. Dynamic simulations of a modified WECC model with DWPT loads synthesized from realistic EV trajectories and ER specifications corroborate some of these insights.

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arXiv2026

Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection

This work investigates the reduction of phasor measurement unit (PMU) data through low-rank matrix approximations. To reconstruct a PMU data matrix from fewer measurements, we propose the framework of interpolatory matrix decompositions (IDs). In contrast to methods relying on principal component analysis or singular value decomposition, IDs recover the complete data matrix using only a few of its rows (PMU datastreams) and/or a few of its columns (snapshots in time). This row-/column-based compression enables real-time monitoring of power transmission systems using measurements from a smaller subset of pilot datastreams, thereby minimizing communication bandwidth. The ID perspective gives a rigorous error bound on the quality of the data compression. We propose selecting the pilot measurements used in an ID via the discrete empirical interpolation method (DEIM), a greedy algorithm that aims to control the error bound. This bound yields a computable estimate of the reconstruction error during online operations. A violation of this estimate suggests a change in the system's operating conditions and thus serves as a tool for fault detection. Following a disturbance, DEIM can be used to localize the event source across all buses with high accuracy. Numerical tests on synthetic PMU data demonstrate DEIM's excellent performance in data compression and validate the proposed DEIM-based fault-detection and localization method.

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arXiv2025

Dynamic Modeling of Load Demand in Electrified Highways Based on the EV Composition

Electrified roadways (ERs) equipped with the dynamic wireless power transfer (DWPT) technology can achieve longer driving range and reduce on-board battery requirements for electric vehicles (EVs). Due to the spatial arrangement of transmitter (Tx) coils embedded into the ER pavement, the power drawn by the EV's receiver (Rx) coil is oscillatory in nature. Therefore, understanding the dynamic behavior of the total DWPT load is important for power system dynamic studies. To this end, we model the load of individual EVs in the time and frequency domains for constant EV speed. We establish that a nonlinear control scheme implemented in existing DWPT-enabled EVs exhibits milder frequency harmonics compared to its linear alternative. According to this model, the harmonics of an EV load decrease in amplitude with the Rx coil length. We further propose and analyze stochastic models for the total DWPT load served by an ER segment. Our models explain how the EV composition on the ER affects its frequency spectrum. Interestingly, we show that serving more EVs with longer Rx coils (trucks) does not necessarily entail milder harmonics. Our analytical findings are corroborated using realistic flows from a traffic simulator and offer valuable insights to grid operators and ER designers.

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arXiv2025

Learning AC Power Flow Solutions using a Data-Dependent Variational Quantum Circuit

Interconnection studies require solving numerous instances of the AC load or power flow (AC PF) problem to simulate diverse scenarios as power systems navigate the ongoing energy transition. To expedite such studies, this work leverages recent advances in quantum computing to find or predict AC PF solutions using a variational quantum circuit (VQC). VQCs are trainable models that run on modern-day noisy intermediate-scale quantum (NISQ) hardware to accomplish elaborate optimization and machine learning (ML) tasks. Our first contribution is to pose a single instance of the AC PF as a nonlinear least-squares fit over the VQC trainable parameters (weights) and solve it using a hybrid classical/quantum computing approach. The second contribution is to feed PF specifications as features into a data-embedded VQC and train the resultant quantum ML (QML) model to predict general PF solutions. The third contribution is to develop a novel protocol to efficiently measure AC-PF quantum observables by exploiting the graph structure of a power network. Preliminary numerical tests indicate that the proposed VQC models attain enhanced prediction performance over a deep neural network despite using much fewer weights. The proposed quantum AC-PF framework sets the foundations for addressing more elaborate grid tasks via quantum computing.

quant-ph↗

arXiv2025

Solving Optimal Power Flow on a Data-Budget: Feature Selection on Smart Meter Data

How much data is needed to optimally schedule distributed energy resources (DERs)? Does the distribution system operator (DSO) have to know load demands at each bus of the feeder to solve an optimal power flow (OPF)? This work exploits redundancies in OPF's structure and data to minimize the communication of such a data deluge, and explores the trade-off between data compression and the grid's performance. We propose an OPF data distillation framework involving two steps: The DSO first collects OPF data from only a subset of nodes. It subsequently reconstructs the complete OPF data from the partial ones, and feeds them into the OPF solver. Selecting and reconstructing OPF data may be performed to maximize the fidelity of the reconstructed data or the associated OPF solutions. Under the first objective, OPF data distillation is posed as a sparsity-regularized convex problem. Under the second objective, it is posed as a sparsity-regularized bilevel program. Both problems are solved using proximal gradient algorithms. The second objective is superior in approximating OPF solutions at the expense of increased complexity. Numerical tests show that it enhances the fidelity and feasibility of the reconstructed OPF solutions, which can be approximated reasonably well even from partial data.

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arXiv2025

A Scalable Approach for Safe and Robust Learning via Lipschitz-Constrained Networks

Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However, accurate methods for Lipschitz-constrained training often suffer from non-convex formulations and poor scalability due to reliance on global semidefinite programs (SDPs). In this letter, we propose a convex training framework that enforces global Lipschitz constraints via semidefinite relaxation. By reparameterizing the NN using loop transformation, we derive a convex admissibility condition that enables tractable and certifiable training. While the resulting formulation guarantees robustness, its scalability is limited by the size of global SDP. To overcome this, we develop a randomized subspace linear matrix inequalities (RS-LMI) approach that decomposes the global constraints into sketched layerwise constraints projected onto low-dimensional subspaces, yielding a smooth and memory-efficient training objective. Empirical results on MNIST, CIFAR-10, and ImageNet demonstrate that the proposed framework achieves competitive accuracy with significantly improved Lipschitz bounds and runtime performance.

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arXiv2024

Variational Quantum Eigensolver with Constraints (VQEC): Solving Constrained Optimization Problems via VQE

Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap, this work proposes a hybrid quantum-classical algorithmic paradigm termed VQEC that extends the celebrated VQE to handle optimization with constraints. As with the standard VQE, the vector of optimization variables is captured by the state of a variational quantum circuit (VQC). To deal with constraints, VQEC optimizes a Lagrangian function classically over both the VQC parameters as well as the dual variables associated with constraints. To comply with the quantum setup, variables are updated via a perturbed primal-dual method leveraging the parameter shift rule. Among a wide gamut of potential applications, we showcase how VQEC can approximately solve quadratically-constrained binary optimization (QCBO) problems, find stochastic binary policies satisfying quadratic constraints on the average and in probability, and solve large-scale linear programs (LP) over the probability simplex. Under an assumption on the error for the VQC to approximate an arbitrary probability mass function (PMF), we provide bounds on the optimality gap attained by a VQC. Numerical tests on a quantum simulator investigate the effect of various parameters and corroborate that VQEC can generate high-quality solutions.

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arXiv2024

Optimal Design of Volt/VAR Control Rules of Inverters using Deep Learning

Distribution grids are challenged by rapid voltage fluctuations induced by variable power injections from distributed energy resources (DERs). To regulate voltage, the IEEE Standard 1547 recommends each DER inject reactive power according to piecewise-affine Volt/VAR control rules. Although the standard suggests a default shape, the rule can be customized per bus. This task of optimal rule design (ORD) is challenging as Volt/VAR rules introduce nonlinear dynamics, and lurk trade-offs between stability and steady-state voltage profiles. ORD is formulated as a mixed-integer nonlinear program (MINLP), but scales unfavorably with the problem size. Towards a more efficient solution, we reformulate ORD as a deep learning problem. The idea is to design a DNN that emulates Volt/VAR dynamics. The DNN takes grid scenarios as inputs, rule parameters as weights, and outputs equilibrium voltages. Optimal rule parameters can be found by training the DNN so its output approaches unity for various scenarios. The DNN is only used to optimize rules and is never employed in the field. While dealing with ORD, we also review and expand on stability conditions and convergence rates for Volt/VAR dynamics on single- and multi-phase feeders. Tests showcase the merit of DNN-based ORD by benchmarking it against its MINLP counterpart.

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arXiv2024

Data-driven Forced Oscillation Localization using Inferred Impulse Responses

Poorly damped oscillations pose threats to the stability and reliability of interconnected power systems. In this work, we propose a comprehensive data-driven framework for inferring the sources of forced oscillation (FO) using solely synchrophasor measurements. During normal grid operations, fast-rate ambient data are collected to recover the impulse responses in the small-signal regime, without requiring the system model. When FO events occur, the source is estimated based on the frequency domain analysis by fitting the least-squares (LS) error for the FO data using the impulse responses recovered previously. Although the proposed framework is purely data-driven, the result has been established theoretically via model-based analysis of linearized dynamics under a few realistic assumptions. Numerical validations demonstrate its applicability to realistic power systems including nonlinear, higher-order dynamics with control effects using the IEEE 68-bus system, and the 240-bus system from the IEEE-NASPI FO source location contest. The generalizability of the proposed methodology has been validated using different types of measurements and partial sensor coverage conditions.

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arXiv2023

A Chance-Constrained Optimal Design of Volt/VAR Control Rules for Distributed Energy Resources

Deciding setpoints for distributed energy resources (DERs) via local control rules rather than centralized optimization offers significant autonomy. The IEEE Standard 1547 recommends deciding DER setpoints using Volt/VAR rules. Although such rules are specified as non-increasing piecewise-affine, their exact shape is left for the utility operators to decide and possibly customize per bus and grid conditions. To address this need, this work optimally designs Volt/VAR rules to minimize ohmic losses on lines while maintaining voltages within allowable limits. This is practically relevant as excessive reactive injections could reduce equipment's lifetime due to overloading. We consider a linearized single-phase grid model. Even under this setting, optimal rule design (ORD) is technically challenging as Volt/VAR rules entail mixed-integer models, stability implications, and uncertainties in grid loading. Uncertainty is handled by minimizing the average losses under voltage chance constraints. To cope with the piecewise-affine shape of the rules, we build upon our previous reformulation of ORD as a deep learning task. A recursive neural network (RNN) surrogates Volt/VAR dynamics and thanks to back-propagation, we expedite this chance-constrained ORD. RNN weights coincide with rule parameters, and are trained using primal-dual decomposition. Numerical tests corroborate the efficacy of this novel ORD formulation and solution methodology.

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arXiv2023

Optimal Design of Volt/VAR Control Rules for Inverter-Interfaced Distributed Energy Resources

The IEEE 1547 Standard for the interconnection of distributed energy resources (DERs) to distribution grids provisions that smart inverters could be implementing Volt/VAR control rules among other options. Such rules enable DERs to respond autonomously in response to time-varying grid loading conditions. The rules comprise affine droop control augmented with a deadband and saturation regions. Nonetheless, selecting the shape of these rules is not an obvious task, and the default options may not be optimal or dynamically stable. To this end, this work develops a novel methodology for customizing Volt/VAR rules on a per-bus basis for a single-phase feeder. The rules are adjusted by the utility every few hours depending on anticipated demand and solar scenarios. Using a projected gradient descent-based algorithm, rules are designed to improve the feeder's voltage profile, comply with IEEE 1547 constraints, and guarantee stability of the underlying nonlinear grid dynamics. The stability region is inner approximated by a polytope and the rules are judiciously parameterized so their feasible set is convex. Numerical tests using real-world data on the IEEE 141-bus feeder corroborate the scalability of the methodology and its explore the trade-offs of Volt/VAR control with alternatives.

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arXiv2023

Learning Distribution Grid Topologies: A Tutorial

Unveiling feeder topologies from data is of paramount importance to advance situational awareness and proper utilization of smart resources in power distribution grids. This tutorial summarizes, contrasts, and establishes useful links between recent works on topology identification and detection schemes that have been proposed for power distribution grids. The primary focus is to highlight methods that overcome the limited availability of measurement devices in distribution grids, while enhancing topology estimates using conservation laws of power-flow physics and structural properties of feeders. Grid data from phasor measurement units or smart meters can be collected either passively in the traditional way, or actively, upon actuating grid resources and measuring the feeder's voltage response. Analytical claims on feeder identifiability and detectability are reviewed under disparate meter placement scenarios. Such topology learning claims can be attained exactly or approximately so via algorithmic solutions with various levels of computational complexity, ranging from least-squares fits to convex optimization problems, and from polynomial-time searches over graphs to mixed-integer programs. Although the emphasis is on radial single-phase feeders, extensions to meshed and/or multiphase circuits are sometimes possible and discussed. This tutorial aspires to provide researchers and engineers with knowledge of the current state-of-the-art in tractable distribution grid learning and insights into future directions of work.

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arXiv2023

Scalable Optimal Design of Incremental Volt/VAR Control using Deep Neural Networks

Volt/VAR control rules facilitate the autonomous operation of distributed energy resources (DER) to regulate voltage in power distribution grids. According to non-incremental control rules, such as the one mandated by the IEEE Standard 1547, the reactive power setpoint of each DER is computed as a piecewise-linear curve of the local voltage. However, the slopes of such curves are upper-bounded to ensure stability. On the other hand, incremental rules add a memory term into the setpoint update, rendering them universally stable. They can thus attain enhanced steady-state voltage profiles. Optimal rule design (ORD) for incremental rules can be formulated as a bilevel program. We put forth a scalable solution by reformulating ORD as training a deep neural network (DNN). This DNN emulates the Volt/VAR dynamics for incremental rules derived as iterations of proximal gradient descent (PGD). Analytical findings and numerical tests corroborate that the proposed ORD solution can be neatly adapted to single/multi-phase feeders.

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arXiv2023

A Quantum Approach for Stochastic Constrained Binary Optimization

Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) have been shown numerically to generate high-quality solutions to hard combinatorial problems, yet incorporating constraints to such problems has been elusive. To this end, this work puts forth a quantum heuristic to cope with stochastic binary quadratically constrained quadratic programs (QCQP). Identifying the strength of quantum circuits to efficiently generate samples from probability distributions that are otherwise hard to sample from, the variational quantum circuit is trained to generate binary-valued vectors to approximately solve the aforesaid stochastic program. The method builds upon dual decomposition and entails solving a sequence of judiciously modified standard VQE tasks. Tests on several synthetic problem instances using a quantum simulator corroborate the near-optimality and feasibility of the method, and its potential to generate feasible solutions for the deterministic QCQP too.

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arXiv2022

Fast Inverter Control by Learning the OPF Mapping using Sensitivity-Informed Gaussian Processes

Fast inverter control is a desideratum towards the smoother integration of renewables. Adjusting inverter injection setpoints for distributed energy resources can be an effective grid control mechanism. However, finding such setpoints optimally requires solving an optimal power flow (OPF), which can be computationally taxing in real time. This work proposes learning the mapping from grid conditions to OPF minimizers using Gaussian processes (GPs). This GP-OPF model predicts inverter setpoints when presented with a new instance of grid conditions. Training enjoys closed-form expressions, and GP-OPF predictions come with confidence intervals. To improve upon data efficiency, we uniquely incorporate the sensitivities (partial derivatives) of the OPF mapping into GP-OPF. This expedites the process of generating a training dataset as fewer OPF instances need to be solved to attain the same accuracy. To further reduce computational efficiency, we approximate the kernel function of GP-OPF leveraging the concept of random features, which is neatly extended to sensitivity data. We perform sensitivity analysis for the second-order cone program (SOCP) relaxation of the OPF, whose sensitivities can be computed by merely solving a system of linear equations. Extensive numerical tests using real-world data on the IEEE 13- and 123-bus benchmark feeders corroborate the merits of GP-OPF.

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arXiv2022

Dynamic Response Recovery Using Ambient Synchrophasor Data: A Synthetic Texas Interconnection Case Study

Wide-area dynamic studies are of paramount importance to ensure the stability and reliability of power grids. This paper puts forth a comprehensive framework for inferring the dynamic responses in the small-signal regime using ubiquitous fast-rate ambient data collected during normal grid operations. We have shown that the impulse response between any pair of locations can be recovered in a model-free fashion by cross-correlating angle and power flow data streams collected only at these two locations, going beyond previous work based on frequency data only. The result has been established via model-based analysis of linearized second-order swing dynamics under certain conditions. Numerical validations demonstrate its applicability to realistic power system models including nonlinear, higher-order dynamics. In particular, the case study using synthetic PMU data on a synthetic Texas Interconnection (TI) system strongly corroborates the benefit of using angle PMU data over frequency data for real-world power system dynamic modeling.

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