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Manuel Garcia

Publications and source records attributed to Manuel Garcia.

15 recordsLinked to original sources
arXiv2026

Smoothed Two-Stage Decomposition Algorithm for Solving Large-Scale Transmission and Distribution AC-OPF Problems

The integration of distributed energy resources (DERs) into the power grid has introduced new challenges to AC optimal power flow (AC-OPF) problems. Traditional OPF optimize consider transmission systems, treating distribution networks as static loads. However, the growing presence of DERs makes accurate distribution system modeling crucial for grid operations. Consequently, efficiently solving the resultant large-scale, nonconvex transmission and distribution (T&D) AC-OPF problem remains a significant challenge. This paper proposes a Smoothed Two-Stage Decomposition Optimizer (StsDOpt) to address these complexities by decomposing the T&D AC-OPF problem into a master-subproblem(s) structure, enabling parallel solving. Unlike traditional methods, StsDOpt does not rely on approximations or relaxations. It uses a smoothing technique to render the subproblems responses differentiable with respect to the master problem, leveraging the barrier problem properties inherent in primal-dual interior point methods. This approach is crucial for accurately modeling and solving distribution systems, which are multiphase, unbalanced, and nonlinear, distinguishing StsDOpt apart from other methods. Integrated into the PowerModelsITD framework, StsDOpt has been validated through numerical experiments, demonstrating reduced wall-clock solve time and increased scalability. Results highlight its efficacy as a robust, scalable solution for large-scale T&D AC-OPF problems, facilitating the reliable integration of DERs into complex T&D systems.

math.OC↗
arXiv2026

Load Block Modeling in Distribution Systems: Network Reconfiguration for Load Restoration

The distribution system restoration (DSR) problem has received considerable attention over the last decade or more. Solutions to the DSR problem identify the best set or sequence of actions to perform on a distribution circuit to restore service after a disruption. The problem is challenging from a computational perspective, with engineering constraints specific to distribution systems, such as radial operations, that are difficult to effectively model. In this paper, we revisit the model for how specific loads are shed, energized and restored--and develop a formulation that more accurately models the requirements of load shedding, load energizing and restoration in distribution systems.

eess.SY↗
arXiv2026

Exploiting block triangular submatrices in KKT systems

We propose a method for solving Karush-Kuhn-Tucker (KKT) systems that exploits block triangular submatrices by first using a Schur complement decomposition to isolate the block triangular submatrices then performing a block backsolve where only diagonal blocks of the block triangular form need to be factorized. We show that factorizing reducible symmetric-indefinite matrices with standard 1$\times$1 or 2$\times$2 pivots yields fill-in outside the diagonal blocks of the block triangular form, in contrast to our proposed method. While exploiting a block triangular submatrix has limited fill-in, unsymmetric matrix factorization methods do not reveal inertia, which is required by interior point methods for nonconvex optimization. We show that our target matrix has inertia that is known \textit{a priori}, letting us compute inertia of the KKT matrix by Sylvester's law. Finally, we demonstrate the computational advantage of this method on KKT systems from optimization problems with neural network surrogates in their constraints. Our method achieves up to 15$\times$ speedups over state-of-the-art symmetric indefinite matrix factorization methods MA57 and MA86 in a constant-hardware comparison.

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arXiv2025

Nonlinear Optimization with GPU-Accelerated Neural Network Constraints

We propose a reduced-space formulation for optimizing over trained neural networks where the network's outputs and derivatives are evaluated on a GPU. To do this, we treat the neural network as a "gray box" where intermediate variables and constraints are not exposed to the optimization solver. Compared to the full-space formulation, in which intermediate variables and constraints are exposed to the optimization solver, the reduced-space formulation leads to faster solves and fewer iterations in an interior point method. We demonstrate the benefits of this method on two optimization problems: Adversarial generation for a classifier trained on MNIST images and security-constrained optimal power flow with transient feasibility enforced using a neural network surrogate.

cs.LG↗
arXiv2025

Vehicular Communication Security: Multi-Channel and Multi-Factor Authentication

Secure and reliable communications are crucial for Intelligent Transportation Systems (ITSs), where Vehicle-to-Infrastructure (V2I) communication plays a key role in enabling mobility-enhancing and safety-critical services. Current V2I authentication relies on credential-based methods over wireless Non-Line-of-Sight (NLOS) channels, leaving them exposed to remote impersonation and proximity attacks. To mitigate these risks, we propose a unified Multi-Channel, Multi-Factor Authentication (MFA) scheme that combines NLOS cryptographic credentials with a Line-of-Sight (LOS) visual channel. Our approach leverages a challenge-response security paradigm: the infrastructure issues challenges and the vehicle's headlights respond by flashing a structured sequence containing encoded security data. Deep learning models on the infrastructure side then decode the embedded information to authenticate the vehicle. Real-world experimental evaluations demonstrate high test accuracy, reaching an average of 95% and 96.6%, respectively, under various lighting, weather, speed, and distance conditions. Additionally, we conducted extensive experiments on three state-of-the-art deep learning models, including detailed ablation studies for decoding the flashing sequence. Our results indicate that the optimal architecture employs a dual-channel design, enabling simultaneous decoding of the flashing sequence and extraction of vehicle spatial and locational features for robust authentication.

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arXiv2025

Transient Stability-Constrained OPF: Neural Network Surrogate Models and Pricing Stability

A Transient Stability-Constrained Optimal Power Flow (TSC-OPF) problem is proposed that enforces frequency stability constraints using Neural Network (NN) surrogate models. NNs are trained using a novel model-driven active sampling algorithm that iteratively generates NN training data located near the stability boundary and contained within the feasible set of the Alternating Current Optimal Power Flow (AC-OPF) problem. In the context of wholesale electricity markets, pricing structures are analyzed along with their dependencies on the selected input features to the NN surrogate model. An important insight identifies a trade-off between the accuracy of the NN surrogate model and sensible locational pricing structures. NN surrogate models for frequency stability are validated by ensuring the resulting TSC-OPF solution is stable over randomly generated load samples using a small Hawaii test case. The proposed TSC-OPF problem is shown to significantly enhance frequency stability at low computational cost and low financial cost to the system. For certain selections of NN inputs, the TSC-OPF problem is able to stabilize all load scenarios for which the solution to the AC-OPF problem resulted in instability.

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arXiv2024

Formulations and scalability of neural network surrogates in nonlinear optimization problems

We compare full-space, reduced-space, and gray-box formulations for representing trained neural networks in nonlinear constrained optimization problems. We test these formulations on a transient stability-constrained, security-constrained alternating current optimal power flow (SCOPF) problem where the transient stability criteria are represented by a trained neural network surrogate. Optimization problems are implemented in JuMP and trained neural networks are embedded using a new Julia package: MathOptAI.jl. To study the bottlenecks of the three formulations, we use neural networks with up to 590 million trained parameters. The full-space formulation is bottlenecked by the linear solver used by the optimization algorithm, while the reduced-space formulation is bottlenecked by the algebraic modeling environment and derivative computations. The gray-box formulation is the most scalable and is capable of solving with the largest neural networks tested. It is bottlenecked by evaluation of the neural network's outputs and their derivatives, which may be accelerated with a graphics processing unit (GPU). Leveraging the gray-box formulation and GPU acceleration, we solve our test problem with our largest neural network surrogate in 2.5$\times$ the time required for a simpler SCOPF problem without the stability constraint.

cs.LG↗
arXiv2024

Exact and Heuristic Approaches for the Stochastic N-k Interdiction in Power Grids

The article introduces the stochastic N-k interdiction problem for power grid operations and planning that aims to identify a subset of k components (out of N components) that maximizes the expected damage, measured in terms of load shed. Uncertainty is modeled through a fixed set of outage scenarios, where each scenario represents a subset of components removed from the grid. We formulate the stochastic N-k interdiction problem as a bi-level optimization problem and propose two algorithmic solutions. The first approach reformulates the bi-level stochastic optimization problem to a single level, mixed-integer linear program (MILP) by dualizing the inner problem and solving the resulting problem directly using a MILP solver to global optimality. The second is a heuristic cutting-plane approach, which is exact under certain assumptions. We compare these approaches in terms of computation time and solution quality using the IEEE-Reliability Test System and present avenues for future research.

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arXiv2024

A novel wavelet-based filtering strategy to remove powerline interference from electrocardiograms with atrial fibrillation

"Objective: The electrocardiogram (ECG) is currently the most widely used recording to diagnose cardiac disorders, including the most common supraventricular arrhythmia, such as atrial fibrillation (AF). However, different types of electrical disturbances, in which power-line interference (PLI) is a major problem, can mask and distort the original ECG morphology. This is a significant issue in the context of AF, because accurate characterization of fibrillatory waves (f-waves) is unavoidably required to improve current knowledge about its mechanisms. This work introduces a new algorithm able to reduce high levels of PLI and preserve, simultaneously, the original ECG morphology. Approach: The method is based on stationary wavelet transform shrinking and makes use of a new thresholding function designed to work successfully in a wide variety of scenarios. In fact, it has been validated in a general context with 48 ECG recordings obtained from pathological and non-pathological conditions, as well as in the particular context of AF, where 380 synthesized and 20 long-term real ECG recordings were analyzed. Main results: In both situations, the algorithm has reported a notably better performance than common methods designed for the same purpose. Moreover, its effectiveness has proven to be optimal for dealing with ECG recordings affected by AF, since f-waves remained almost intact after removing very high levels of noise. Significance: The proposed algorithm may facilitate a reliable characterization of the f-waves, preventing them from not being masked by the PLI nor distorted by an unsuitable filtering applied to ECG recordings with AF."

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arXiv2024

An Efficient Algorithm Based on Wavelet Transform to Reduce Powerline Noise From Electrocardiograms

Nowadays, the electrocardiogram (ECG) is still the most widely used signal for the diagnosis of cardiac pathologies. However, this recording is often disturbed by the powerline interference (PLI), its removal being mandatory to avoid misdiagnosis. Although a broad variety of methods have been proposed for that purpose, often they substantially alter the original signal morphology or are computationally expensive. Hence, the present work introduces a simple and efficient algorithm to suppress the PLI from the ECG. Briefly, the input signal is decomposed into four Wavelet levels and the resulting coefficients are thresholded to remove the PLI estimated from the TQ intervals. The denoised ECG signal is then reconstructed by computing the inverse Wavelet transform. The method has been validated making use of fifty 10-min length clean ECG segments obtained from the MIT BIH Normal Sinus Rhythm database, which were contaminated with a sinusoidal signal of 50 Hz and variable harmonic content. Comparing the original and denoised ECG signals through a signed correlation index, improvements between 10 - 72% have been observed with respect to common adaptive notch filtering, implemented for comparison. These results suggest that the proposed method is featured by an enhanced trade-off between noise reduction and signal morphology preservation.

eess.SP↗
arXiv2024

Time Variability of FibrillatoryWaves Energy Predicts Long-Term Outcome of Atrial Fibrillation Concomitant Surgical Ablation

Surgical ablation (SA) is the most effective procedure to terminate atrial fibrillation (AF) in patients requiring concomitant open heart surgery. However, considering the great stress provoked in the patients heart, along with the benefits of anticipating antiarrhythmic therapeutical decisions, preoperative prediction of long term failure of the procedure is an interesting clinical challenge. Hence, the present work introduces a novel algorithm to anticipate SA outcome after one year of follow up by just analyzing the surface ECG. The method firstly extracts fibrillatory waves reflected on standard lead V1 using an adaptive QRST cancellation approach. The resulting signal is then segmented into 1 s length intervals and wavelet energy is computed for all of them. Finally, the coefficient of variation of the time series obtained for the 7th scale is computed. Analyzing 20 second length preoperative ECG excerpts from 53 persistent AF patients undergoing concomitant openheart surgery, only the proposed method reported statistically significant differences between the patients who relapsed to AF and those who maintained sinus rhythm during the follow up. The algorithm also provided values of sensitivity, specificity, and accuracy between 10 and 20% better than the well established dominant atrial frequency and fibrillatory waves amplitude, thus suggesting to be a promising predictor of AF recurrence after SA.

eess.SP↗
arXiv2024

Spectral Distribution Complexity of the Surface Fibrillatory Waves Predicts Post-Catheter Ablation Relapse in Persistent Atrial Fibrillation

As for most of cardiac arrhythmias, atrial fibrillation (AF) is primarily treated by catheter ablation (CA). However, the mid-term recurrence rate of this procedure in persistent AF patients is still limited and the preoperative prediction of its outcome is clinically interesting to select candidates who could benefit the most from the intervention. This context encouraged the study of C0 complexity as a novel predictor, because it estimates organization of the power spectral distribution (PSD) of the fibrillatory waves (f-waves). For that purpose, the PSD was divided into two divergent components using a threshold, theta, which was considered by multiplying the mean value of the PSD by a factor, alpha, ranging between 1.5 and 2.5. On a database of 74 patients, the values of C0 complexity computed for all alpha factors reported statistically significant differences between the patients who maintained sinus rhythm and those who relapsed to AF after a follow-up of 9 months. They also showed higher values of sensitivity (Se), specificity (Sp), and accuracy (Acc) than the well known predictors of the dominant frequency (DF) and f-wave amplitude. Moreover, the combination of the DF and the C0 complexity computed with alpha = 2, via a decision tree, improved classification until values of Se, Sp and Acc of 75.33, 77.33 and 76.58%, respectively. These results manifests the relevance of the f-wave PSD distribution to anticipate CA outcome in persistent AF patients.

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arXiv2020

Requirements for Interdependent Reserve Types

As renewable energy penetration increases and system inertia levels drop, primary frequency control is becoming a critical concern in relatively small interconnections such as the Electric Reliability Council of Texas (ERCOT). To address this problem ERCOT is implementing a number of market rule changes including the introduction of a new Fast Frequency Response (FFR) reserve type to the electricity market. This FFR reserve type aims to help the traditional Primary Frequency Response (PFR) reserve type in arresting frequency decline in the event of a large generator outage. This paper derives reserve requirements to ensure sufficient reserve to arrest frequency decline before reaching the critical frequency threshold while coupling PFR reserve, FFR reserve, and system inertia. The general reserve requirement places limits on the amount of PFR reserve that can be provided by each unit based on its ramping capabilities. Two such limits are derived from first principles and another is proposed that is capable of accommodating the equivalency ratio introduced in previous work. These PFR reserve limits also provide first principles insight into equivalency ratios, which have only been studied empirically in the past. High-level insights are provided on a large Texas test case.

math.OC↗
arXiv2018

A General Economic Dispatch Problem with Marginal Losses

Standard economic dispatch problems that consider line losses are linear approximations of a non-convex economic dispatch problem formulated by fixing voltage magnitudes and assuming the decoupling of real and reactive power. This paper formulates and analyzes the general non-convex economic dispatch problem, incorporating and generalizing the Fictitious Nodal Demand (FND) model, resulting in a slack bus independent formulation that provides insight into standard formulations by pointing out commonly used but unnecessary assumptions and by deriving proper choices of "tuning parameters." The proper choice of loss allocation is derived to assign half of the losses of each transmission line to adjacent buses, justifying approaches in the literature. Line constraints are proposed in the form of voltage angle difference limits and are proven equivalent to various other line limits including current magnitude limits and mid-line power flow limits. The formulated general economic dispatch problem with marginal losses consistently models flows and loss approximation, results in approximately correct outcomes and is proven to be reference bus independent. Various approximations of this problem are compared using realistically large transmission network test cases.

math.OC↗