arXiv subjects

Deepjyoti Deka

Publications and source records attributed to Deepjyoti Deka.

At least 19 recordsLinked to original sources

arXiv2026

Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration

The proliferation of distributed energy resources (DERs) in distribution grids enables the active coordination of these assets to reduce costs and enable cleaner operations. Realizing this potential requires solving multiphase AC optimal power flow (AC-OPF) quickly across varying loads, DER availabilities, and topology reconfigurations, at much greater speed and scale than conventional nonlinear solvers. Learning-based surrogates can offer millisecond inference, yet existing methods target largely balanced transmission systems and do not scale to the multiphase, unbalanced, and reconfigurable nature of distribution feeders at utility scale. We present the Penalty + Sequential Linearized Feasibility Seeking (SLFS) algorithm, a self-supervised learning framework for multiphase distribution AC-OPF under switch-induced topology changes. Penalty+SLFS requires no labeled optimal solutions and trains directly from the AC-OPF objective and constraints through a differentiable fixed-point power flow solver, avoiding expensive label generation and admitting robust training procedures. Topology changes are handled efficiently using Sherman-Morrison-Woodbury updates of the admittance-matrix inverse, while an M-step Jacobian approximation accelerates differentiation through the power flow solver. At inference, SLFS repairs any infeasible predictions, providing feasibility guarantees with low computational overhead. On IEEE feeders ranging from 13 to 8,500 nodes, Penalty+SLFS achieves negligible optimality gaps and near-zero constraint violations, delivers up to three orders of magnitude speedups over IPOPT, and remains robust under large distributional shifts, demonstrating a viable path toward real-time, topology-aware AC-OPF for large-scale distribution grids.

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arXiv2026

Learning Discrete Decisions for MIPs with Constraint-Aware Diffusion

This paper proposes a novel learning-based approach to approximately solve instances of mixed-integer optimization problems. These problems are computationally challenging, as they require jointly determining discrete and continuous decisions while satisfying complex combinatorial constraints. The proposed method relies on a graph-based generative diffusion model that learns the discrete component of mixed-integer optimization problems while integrating a training-free feasibility projection operator directly into the reverse diffusion process to steer intermediate samples toward the feasible set throughout generation. Once the discrete decisions are generated, the remaining optimization reduces to a continuous problem that can be solved efficiently (relative to the original problem) using existing numerical methods. The resulting framework named Constrained Graph Diffusion (CGD), is problem-agnostic and can accommodate a broad class of mixed-integer optimization problems through suitable projection operators. We evaluate CGD on optimal transmission switching for ACOPF and discrete portfolio optimization, demonstrating substantial improvements in feasibility and solution quality over learning-based baselines while achieving speedups of up to $425\times$ over state-of-the-art numerical solvers for MINLPs.

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arXiv2026

Watts vs. Bytes: Turning Data Centers into Grid Assets via Storage Compute Co-Optimization

Data center interconnections increasingly face tighter peak-demand and ramp-rate limits while being expected to support grid operations. Satisfying these requirements calls for coordinated computing and energy controls, yet their joint operational and economic implications remain poorly understood. To tackle this problem, we formulate a robust day-ahead co-optimization of computing load scheduling, server dynamic voltage and frequency scaling (DVFS), and co-located battery energy storage system (BESS) dispatch. The resulting mixed-integer linear program hedges against uncertainty in fixed load and ancillary service deployment while enforcing interconnection limits on peak demand and ramp rate, ancillary service capacity commitments in reserve and flexible ramping, and workload execution constraints. Case studies using CAISO and PJM market data of a 100~MW data center with a 36~MWh/12~MW BESS show that workload scheduling, DVFS, and storage provide complementary flexibility. Under binding peak-load limits, increasing the schedulable workload share reduces mean daily operating cost by up to 20.7\%, and the daily value of storage more than doubles relative to operation under less restrictive limits. Under normal conditions, optimal BESS sizing is driven more by capital cost and cycling allowance than by energy duration alone. An 8~MW aggregate ancillary service commitment increases operational cost by only 0.4\%, whereas reserve-only requirements become infeasible at commitments as small as 4~MW. These findings show that coordinated computing and storage controls can support grid services economically under binding interconnection constraints while protecting workload delivery.

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arXiv2026

Coordinated Dynamic Operating Envelopes for Network-Admissible Flexibility at the Grid Edge

Dynamic operating envelopes (DOEs) provide a systematic framework to integrate the flexibility of distribution grid resources while safeguarding network limits such as line ratings and voltage bounds. However, the flexibility derived from individual DOEs is often restricted and conservative, especially when some resources can coordinate via communication with an aggregator. This paper presents a convex, geometry-aware framework for constructing DOE for distribution grid customers under partial coordination, with coordinated customers modeled through polytopal flexibility sets and non-coordinated customers through hyperrectangles. The framework additionally incorporates fairness constraints for export and import headroom allocated to the customers within the DOE design. To account for forecast uncertainty in inelastic injections, the DOE design is extended to a robust formulation for bounded uncertainty sets. Case studies on two European three-phase low-voltage feeders, a widely used test feeder and a large-scale (3589)-bus system, show that the proposed DOE construction expands aggregate flexibility while maintaining network feasibility, fairness, and robustness to forecast uncertainty. Coordinating 30% of customers increases the aggregate active-power range by approximately 25% on the test feeder, while coordinating 20 customers on the large-scale feeder increases it by approximately 43%.

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arXiv2026

Strategic Spatial Load Shifting and Market Efficiency

Large, spatially flexible electricity consumers such as data centers can reallocate demand across locations, influencing dispatch and prices in wholesale electricity markets. While flexible load is often assumed to improve system efficiency, this intuition typically relies on price-taking behavior. We study price-anticipatory spatial load shifting by modeling a large flexible consumer as a Stackelberg leader interacting with DC optimal power flow (DC-OPF) based market clearing. We show that decentralized, cost-minimizing load shifting need not align with system operating cost minimization, and that misalignment arises at boundaries between DC-OPF operating regimes, where small changes in load can induce discrete changes in marginal generators or congestion patterns. We evaluate strategic load shifting on the 73-bus RTS-GMLC test system, where findings indicate reductions in system operating cost in most hours, but misalignment in a subset of cases that are driven by redispatch at merit-order discontinuities. We find that these outcomes are primarily redistributive relative to a price-taking benchmark, reducing generator profits while lowering electricity procurement costs for both flexible and inflexible consumers, even in cases where total system operating costs increase.

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arXiv2026

Efficient Policy Adaptation for Voltage Control Under Unknown Topology Changes

Reinforcement learning (RL) has shown great potential for designing voltage control policies, but their performance often degrades under changing system conditions such as topology reconfigurations and load variations. We introduce a topology-aware online policy optimization framework that leverages data-driven estimation of voltage-reactive power sensitivities to achieve efficient policy adaptation. Exploiting the sparsity of topology-switching events, where only a few lines change at a time, our method efficiently detects topology changes and identifies the affected lines and parameters, enabling fast and accurate sensitivity updates without recomputing the full sensitivity matrix. The estimated sensitivity is subsequently used for online policy optimization of a pre-trained neural-network-based RL controller. Simulations on both the IEEE 13-bus and SCE 56-bus systems demonstrate over 90 percent line identification accuracy, using only 15 data points. The proposed method also significantly improves voltage regulation performance compared with non-adaptive policies and adaptive policies that rely on regression-based online optimization methods for sensitivity estimation.

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arXiv2025

Sparse Neural Approximations for Bilevel Adversarial Problems in Power Grids

The adversarial worst-case load shedding (AWLS) problem is pivotal for identifying critical contingencies under line outages. It is naturally cast as a bilevel program: the upper level simulates an attacker determining worst-case line failures, and the lower level corresponds to the defender's generator redispatch operations. Conventional techniques using optimality conditions render the bilevel, mixed-integer formulation computationally prohibitive due to the combinatorial number of topologies and the nonconvexity of AC power flow constraints. To address these challenges, we develop a novel single-level optimal value-function (OVF) reformulation and further leverage a data-driven neural network (NN) surrogate of the follower's optimal value. To ensure physical realizability, we embed the trained surrogate in a physics-constrained NN (PCNN) formulation that couples the OVF inequality with (relaxed) AC feasibility, yielding a mixed-integer convex model amenable to off-the-shelf solvers. To achieve scalability, we learn a sparse, area-partitioned NN via spectral clustering; the resulting block-sparse architecture scales essentially linearly with system size while preserving accuracy. Notably, our approach produces near-optimal worst-case failures and generalizes across loading conditions and unseen topologies, enabling rapid online recomputation. Numerical experiments on the IEEE 14- and 118-bus systems demonstrate the method's scalability and solution quality for large-scale contingency analysis, with an average optimality gap of 5.8% compared to conventional methods, while maintaining computation times under one minute.

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arXiv2025

A Family of Convex Models to Achieve Fairness through Dispersion Control

Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional norms, the article develops a family of parameterized convex models that regulate the dispersion of a vector of decision-variable values through its coefficient of variation. Each model has a single parameter taking values in the interval $[0,1]$. When the parameter is set to zero, the model imposes only a trivial constraint on the optimization problem; when set to one, it enforces equality of all the decision variables. As the parameter varies, the coefficient of variation is provably bounded above by a monotonic function of that parameter. The article also presents theoretical results relating the space of feasible solutions across all models. Finally, it compares the models' solution quality on a variant of the assignment problem that regulates the dispersion in the assignment costs.

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arXiv2025

The value of storage in electricity distribution: The role of markets

Electricity distribution companies deploy battery storage to defer grid upgrades by reducing peak demand. In deregulated jurisdictions, such storage often sits idle because regulatory constraints bar participation in electricity markets. Here, we develop an optimization framework that, to our knowledge, provides the first formal model of market participation constraints within storage investment and operation planning. Applying the framework to a Massachusetts case study, we find that market participation delivers similar savings as peak demand reduction. Under current conditions, market participation does not increase storage investment, but at very low storage costs, could incentivize deployment beyond local distribution needs. This might run contrary to the separation of distribution from generation in deregulated markets. Our framework can mitigate this concern by identifying investment levels appropriate for local distribution needs.

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arXiv2025

Stability-Constrained AC Optimal Power Flow--A Gaussian Process-Based Approach

The Alternating Current Optimal Power Flow (ACOPF) problem is a core task in power system operations, aimed at determining cost-effective generation dispatch while satisfying physical and operational constraints. However, conventional ACOPF formulations rely on steady-state models and neglect generator dynamics, which can result in operating points that are economically optimal but dynamically unstable. This paper proposes a novel, data-driven approach to incorporate generator dynamics into the ACOPF using Gaussian Process (GP) models. Specifically, it introduces an exponential surrogate function to characterize the stability of solutions to the differential equations governing synchronous generator dynamics. The exponent, which indicates whether system trajectories decay (stable) or grow (unstable), is learned as a function of the bus voltage using GP regression. Crucially, the framework enables probabilistic stability assessment to be integrated directly into the optimization process. The resulting dynamics-aware ACOPF formulation identifies operating points that satisfy both operational safety and dynamic stability criteria. Numerical experiments on the IEEE 39-bus, 57-bus, and 118-bus systems demonstrate that, compared with existing data-driven approaches, the proposed method efficiently captures generator dynamics with limited training data, yielding more reliable and robust decisions across a wide range of operating conditions.

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arXiv2025

Gaussian Processes in Power Systems: Techniques, Applications, and Future Works

The increasing integration of renewable energy sources (RESs) and distributed energy resources (DERs) has significantly heightened operational complexity and uncertainty in modern power systems. Concurrently, the widespread deployment of smart meters, phasor measurement units (PMUs) and other sensors has generated vast spatiotemporal data streams, enabling advanced data-driven analytics and decision-making in grid operations. In this context, Gaussian processes (GPs) have emerged as a powerful probabilistic framework, offering uncertainty quantification, non-parametric modeling, and predictive capabilities to enhance power system analysis and control. This paper presents a comprehensive review of GP techniques and their applications in power system operation and control. GP applications are reviewed across three key domains: GP-based modeling, risk assessment, and optimization and control. These areas serve as representative examples of how GP can be utilized in power systems. Furthermore, critical challenges in GP applications are discussed, and potential research directions are outlined to facilitate future power system operations.

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arXiv2025

Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes

Learning-based approaches are increasingly leveraged to manage and coordinate the operation of grid-edge resources in active power distribution networks. Among these, model-based techniques stand out for their superior data efficiency and robustness compared to model-free methods. However, effective model learning requires a learning-based approximator for the underlying power flow model. This study extends existing work by introducing a data-driven power flow method based on Gaussian Processes (GPs) to approximate the multiphase power flow model, by mapping net load injections to nodal voltages. Simulation results using the IEEE 123-bus and 8500-node distribution test feeders demonstrate that the trained GP model can reliably predict the nonlinear power flow solutions with minimal training data. We also conduct a comparative analysis of the training efficiency and testing performance of the proposed GP-based power flow approximator against a deep neural network-based approximator, highlighting the advantages of our data-efficient approach. Results over realistic operating conditions show that despite an 85% reduction in the training sample size (corresponding to a 92.8% improvement in training time), GP models produce a 99.9% relative reduction in mean absolute error compared to the baselines of deep neural networks.

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arXiv2024

A Parametric, Second-Order Cone Representable Model of Fairness for Decision-Making Problems

The article develops a parametric model of fairness called "$\varepsilon$-fairness" that can be represented using a single second-order cone constraint and incorporated into existing decision-making problem formulations without impacting the complexity of solution techniques. We develop the model from the fundamental result of finite-dimensional norm equivalence in linear algebra and show that this model has a closed-form relationship to an existing metric for measuring fairness widely used in the literature. Finally, a simple case study on the optimal operation of a damaged power transmission network illustrates its effectiveness.

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arXiv2024

Learning Networks from Wide-Sense Stationary Stochastic Processes

Complex networked systems driven by latent inputs are common in fields like neuroscience, finance, and engineering. A key inference problem here is to learn edge connectivity from node outputs (potentials). We focus on systems governed by steady-state linear conservation laws: $X_t = {L^{\ast}}Y_{t}$, where $X_t, Y_t \in \mathbb{R}^p$ denote inputs and potentials, respectively, and the sparsity pattern of the $p \times p$ Laplacian $L^{\ast}$ encodes the edge structure. Assuming $X_t$ to be a wide-sense stationary stochastic process with a known spectral density matrix, we learn the support of $L^{\ast}$ from temporally correlated samples of $Y_t$ via an $\ell_1$-regularized Whittle's maximum likelihood estimator (MLE). The regularization is particularly useful for learning large-scale networks in the high-dimensional setting where the network size $p$ significantly exceeds the number of samples $n$. We show that the MLE problem is strictly convex, admitting a unique solution. Under a novel mutual incoherence condition and certain sufficient conditions on $(n, p, d)$, we show that the ML estimate recovers the sparsity pattern of $L^\ast$ with high probability, where $d$ is the maximum degree of the graph underlying $L^{\ast}$. We provide recovery guarantees for $L^\ast$ in element-wise maximum, Frobenius, and operator norms. Finally, we complement our theoretical results with several simulation studies on synthetic and benchmark datasets, including engineered systems (power and water networks), and real-world datasets from neural systems (such as the human brain).

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arXiv2024

Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach

Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods. The implementation code for this study is available at: https://github.com/kaarthiksundar/BNN-OPF/.

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arXiv2024

Equitable Routing--Rethinking the Multiple Traveling Salesman Problem

The Multiple Traveling Salesman Problem (MTSP) extends the traveling salesman problem by assigning multiple salesmen to visit a set of targets from a common depot, with each target visited exactly once while minimizing total tour length. A common variant, the min-max MTSP, focuses on workload balance by minimizing the longest tour, but it is difficult to solve optimally due to weak linear relaxation bounds. This paper introduces two new parametric fairness-driven variants of the MTSP: the $\varepsilon$-Fair-MTSP and the $\Delta$-Fair-MTSP, which promote equitable distribution of tour lengths while controlling overall cost. The $\varepsilon$-Fair-MTSP is formulated as a mixed-integer second-order cone program, while the $\Delta$-Fair-MTSP is modeled as a mixed-integer linear program. We develop algorithms that guarantee global optimality for both formulations. Computational experiments on benchmark instances and real-world applications, including electric vehicle fleet routing, demonstrate their effectiveness. Furthermore, we show that the algorithms presented for the fairness-constrained MTSP variants can be used to obtain the Pareto front of a bi-objective optimization problem in which one objective minimizes the total tour length and the other balances the lengths of the individual tours. Overall, these fairness-constrained MTSP variants provide a practical and flexible alternative to the min-max MTSP.

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arXiv2023

Contributions of Individual Generators to Nodal Carbon Emissions

Recent shifts toward sustainable energy systems have witnessed the fast deployment of carbon-free and carbon-efficient generations across the power networks. However, the benefits of carbon reduction are not experienced evenly throughout the grid. Each generator can have distinct carbon emission rates. Due to the existence of physical power flows, nodal power consumption is met by a combination of a set of generators, while such combination is determined by network topology, generators' characteristics and power demand. This paper describes a technique based on physical power flow model, which can efficiently compute the nodal carbon emissions contributed by each single generator given the generation and power flow information. We also extend the technique to calculate both the nodal average carbon emission and marginal carbon emission rates. Simulation results validate the effectiveness of the calculations, while our technique provides a fundamental tool for applications such as carbon auditing, carbon-oriented demand management and future carbon-oriented capacity expansion.

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arXiv2023

Fairly Extreme: Minimizing Outages Equitably

This paper focuses on the problem of minimizing the outages due to extreme events on the power grid equitably among all customers of the grid. The paper presents two ways of incorporating fairness into the existing formulations that seek to minimize the total outage in the power grid. The first method is motivated by existing literature on incorporating fairness in optimization problems and this is done by modifying the problem's objective function. The second method introduces a novel notion of fairness, termed $\varepsilon$-fairness, that can be incorporated into existing problem formulations through a single second-order cone constraint. Both these methods are very general and can be used to incorporate fairness in existing planning and operational optimization problems in the power grid and beyond. Extensive computational case studies that examine the effectiveness of both these methods to characterize fairness is presented followed by conclusions and ways forward.

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