arXiv subjects

Cameron Khanpour

Publications and source records attributed to Cameron Khanpour.

6 recordsLinked to original sources

arXiv2026

Zero-Sum Power Factor Games

Variable active power injections arising from device behavior or compromised dispatch complicate voltage regulation in electric power networks with distributed energy resources (DERs). An operator can limit the resulting voltage deviations by remotely selecting DER reactive power parameters before observing the active power injections. IEEE Standard 1547-2018 specifies constant power factor as one such control mode, coupling each device's reactive power to its realized active power. Using a linear voltage model, we formulate the operator's decision as a robust minimax problem in which the operator minimizes the largest feasible aggregate voltage deviation. We solve this problem by expressing the power factor decisions through continuous reactive to active power ratios and exactly decomposing the payoff according to the signs of the voltage deviations. When every feasible voltage residual remains on its initial side of nominal, the resulting ratios cancel each injection's contribution and yield a closed form minimax strategy. We identify realistic DER ratings for which this strategy applies and quantify the regulation capacity lost under restricted power factor ranges. Numerical tests check the cancellation computation, solve the complete minimax problem directly at a representative DER rating, and compare the linear voltage predictions with nonlinear AC power flow.

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arXiv2026

Proving the Limits of Quantum Power Flow

This letter proves realistic grid properties limit the applicability of quantum computers for power flow. Grids that split into two large regions meeting at only a few buses, common in transmission networks, force the pseudo condition number of the DC susceptance matrix to grow polynomially in the network size, and long chains of lines bridging such regions force quadratic growth. This rigorously verifies the empirical results of recent work. We also show that the theory holds without model information with high probability for independent bounded random line susceptances. Combined with query and tomography lower bounds, this precludes end-to-end quantum advantage for DC power flow at every readout level, and these obstructions persist through AC power flow, optimal power flow, and unit commitment. All proofs are formally verified in Lean 4.

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arXiv2026

Making Every Bit Count for $A$-Optimal State Estimation

We study the problem of controlling how a limited communication bandwidth budget is allocated across heterogeneously quantized sensor measurements. The performance criterion is the trace of the error covariance matrix of the linear minimum mean square error (LMMSE) state estimator, i.e., an $A$-optimal design criterion. Minimizing this criterion with a bit budget constraint yields a nonconvex optimization problem. We derive a formula that reduces each evaluation of the gradient to a single Cholesky factorization. This enables efficient optimization by both a projection-free Frank-Wolfe method (with a computable convergence certificate) and an interior point method with L-BFGS Hessian approximation over the problem's continuous relaxation. A largest remainder rounding procedure recovers integer bit allocations with a bound on the quality of the rounded solution. Numerical experiments in IEEE power grid test cases with up to 300 buses compare both solvers and demonstrate that the analytic gradient is the key computational enabler for both methods. Additionally, the heterogeneous bit allocation is compared to standard uniform bit allocation on the 500 bus IEEE power grid test case.

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arXiv2025

Admittance Matrix Concentration Inequalities for Understanding Uncertain Power Networks

This paper presents conservative probabilistic bounds for the spectrum of the admittance matrix and classical linear power flow models under uncertain network parameters; for example, probabilistic line contingencies. Our proposed approach imports tools from probability theory, such as concentration inequalities for random matrices. This provides a theoretical framework for understanding error bounds of common approximations of the AC power flow equations under parameter uncertainty, including the DC and LinDistFlow approximations. Additionally, we show that the upper bounds scale as functions of nodal criticality. This network-theoretic quantity captures how uncertainty concentrates at critical nodes for use in contingency analysis. We validate these bounds on IEEE test networks, demonstrating that they correctly capture the scaling behavior of spectral perturbations up to conservative constants.

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arXiv2024

Exploring the Use of Contingency for Nuclear Electrical Studies

This paper examines the use of contingency analysis for a nuclear power plant to determine its potential benefits for the nuclear industry. Various N-1 contingencies were analyzed for a model of an existing nuclear plant, primarily inspecting voltage violations resulting from a failure. Remedial Actions Schemes were suggested to support the reduction of voltage violations in the event of a failure within the system. Many of the schemes presented were solved by existing redundancies and protection schemes that have been provided through the use of industry standard bounding analysis in the design process. This paper proposes the future use of real-time contingency analysis for nuclear power plants, conducted using constantly updating voltage, current, and power measurements through the system. This will provide real-time information of the system and can serve as historical data to reduce the analysis needed for pending design changes in the plant.

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arXiv2024

Quantitative and Qualitative Evaluation of NLM and Wavelet Methods in Image Enhancement

This paper presents a comprehensive analysis of image denoising techniques, primarily focusing on Non-local Means (NLM) and Daubechies Soft Wavelet Thresholding, and their efficacy across various datasets. These methods are applied to the CURE-OR, CURE-TSD, CURE-TSR, SSID, and Set-12 datasets, followed by an evaluation using Image Quality Assessment (IQA) metrics PSNR, SSIM, CW-SSIM, UNIQUE, MS-UNIQUE, CSV, and SUMMER. The results indicate that NLM and Wavelet Thresholding perform optimally on Set12 and SIDD datasets, attributed to their ability to effectively handle general additive and multiplicative noise masks. However, their performance on CURE datasets is limited due to the presence of complex distortions like Dirty Lens and Codec Error, which these methods are not well-suited to address. Analysis between NLM and Wavelet Thresholding shows that while NLM generally offers superior visual quality, Wavelet Thresholding excels in specific IQA metrics, particularly SUMMER, due to its enhancement in the frequency domain as opposed to NLM's spatial domain approach.

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