arXiv subjects

Daniel K. Molzahn

Publications and source records attributed to Daniel K. Molzahn.

At least 19 recordsLinked to original sources

arXiv2026

Congestion Structure and Exceedance Bounds for Locational Marginal Emissions

Locational marginal emissions (LMEs) give the sensitivity of total operating carbon emissions to nodal power demand. We show that this vector with $n$ entries has a much smaller intrinsic dimension under DC optimal power flow. Within a fixed active constraint set, the LME vector lies in the span of the uniform vector and the power transfer distribution factor rows of the binding lines. Its rank $r$ is therefore at most one more than the number of binding/congested lines. This structure makes $r$ independent scalar observations necessary and sufficient for exact recovery. Across ten systems with nonzero operating emissions, from 14 to 1,354 buses, $r$ ranges from 2 to 15. For instance, on a 300 bus system, 24 dispatch simulations recover all 300 LMEs. We also derive an emissions exceedance bound under uncertain demand. The bound separates variation while the nominal active set remains unchanged, the probability of an active set change, and estimation error. Numerical results show that its usable forecast error range depends on local active set geometry.

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arXiv2026

Grid Trouble in Paradise: Uncovering Vulnerable Distributed Energy Resources and Their Grid-Level Risks

Grid-connected solar distributed energy resources (DERs), such as solar inverters and monitoring platforms, have been deployed at unprecedented scale over the past few years, with global solar capacity more than doubling since 2022. To support monitoring and control, many of these systems are Internet-connected and configured by installers or end users, yet the real-world scale of their Internet exposure and the implications for power grid operation remain poorly understood. In this paper, we present an Internet-scale evaluation of exposed and vulnerable solar DER infrastructure, and assess the risk that compromised DERs can pose to energy grids. We develop a method for accurately identifying solar DERs from Internet scanning data, and discover a diverse population of over 66,000 Internet-exposed solar DERs. We detect that at least 10,000 of these DERs may have known CVEs, such as unauthenticated monitoring and control endpoints. To assess the risk that these vulnerable DERs pose to a power grid, we use an electric grid network for Oahu, Hawaii, established and used by the power system research community, and conduct a power system analysis. Our evaluation shows that by compromising exposed DERs, attackers can cause voltage and line flow violations across multiple locations in the Oahu network, resulting in a range of consequences from degraded power quality to damaged power system components to power outages. Ultimately, our work brings to light the emerging threat of grid-connected DERs, and provides directions for improving energy security.

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arXiv2026

Targeted Power System Frequency Attack via the Selection of Maliciously Controlled Inverters

This paper studies how an adversary can execute a power system frequency attack by choosing the most effective subset of inverter-based resources (IBRs) as malicious control nodes. During the attack, the adversary controls the attacking devices to destabilize a group of designated target generators. The attack is designed by introducing an unstable oscillatory mode whose eigenvector has large components at the target generators and small components at the compromised IBRs. We formalize the optimal attacker selection problem and present an equivalent mixed-integer quadratically constrained program (MIQCP). To address this combinatorial nonconvex problem, we develop two heuristic algorithms by introducing a ranking metric. The attack process is demonstrated on a modified WSCC 179-bus system, with results verified through nonlinear dynamic simulations. We show that the proposed heuristics find optimal attacking sets in a majority of evaluated scenarios while significantly reducing the required computational time. Scenarios from the ACTIVSg500 system are used to further support our results. Finally, we discuss how selecting different eigenvalues, targets, and numbers of compromised devices impact the attack's severity.

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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

Machine Learning Guided Optimal Transmission Switching to Mitigate Wildfire Ignition Risk

To mitigate acute wildfire ignition risks, utilities de-energize power lines in high-risk areas. The Optimal Power Shutoff (OPS) problem optimizes line energization statuses to manage wildfire ignition risks through de-energizations while reducing load shedding. OPS problems are computationally challenging Mixed-Integer Linear Programs (MILPs) that must be solved rapidly and frequently in operational settings. For a particular power system, OPS instances share a common structure with varying parameters related to wildfire risks, loads, and renewable generation. This motivates the use of Machine Learning (ML) for solving OPS problems by exploiting shared patterns across instances. In this paper, we develop an ML-guided framework that quickly produces high-quality de-energization decisions by extending existing ML-guided MILP solution methods while integrating domain knowledge on the number of energized and de-energized lines. Results on a large-scale realistic California-based synthetic test system show that the proposed ML-guided method produces high-quality solutions faster than traditional optimization methods.

cs.LG↗

arXiv2026

Not All Warm Starts Help: Benchmarking Primal-Dual Initializations for ACOPF Algorithms

Warm starts are widely used to accelerate AC optimal power flow (ACOPF) solves, but the impact of different initialization strategies has received limited systematic study, particularly for the primal-dual interior-point methods that dominate large-scale ACOPF algorithms. This paper benchmarks initialization strategies for ACOPF solved with the interior-point solver IPOPT on 19 PGLib-OPF instances (5 to 30,000 buses), testing all 15 non-empty subsets of the primal blocks $\{P_g, Q_g, V_m, V_a\}$ under oracle conditions and three DC-seeded combinations in a practical setting. The experiments show that most partial primal-plus-dual restarts increase solve time or reduce convergence reliability. Among the oracle primal-plus-dual (O-PD) configurations, only the complete restart reliably converges on every baseline-convergent case, reaching a $47.6\%$ median solve-time speedup. Twelve of the 14 partial O-PD combinations have negative median speedups, and several fail repeatedly on larger networks. Decomposing the dual into constraint and bound multipliers shows that \emph{coverage}, not the presence of duals per se, governs robustness: the full bound-multiplier vector reaches 90.7\% convergence and a $+26.8$\% median speedup, whereas block-matched coverage (oracle multipliers on some bounds, defaults on the rest) drops to 70.4\% and $-31.1$\%. Practical DC seeding sometimes helps the AC solve, but the benefit is no longer statistically significant once the DCOPF presolve cost is included in the end-to-end comparison ($p = 0.4171$). For learned warm-start methods, the results support the following target ordering: predict the full primal vector first; if only partial coverage is possible, prioritize voltage variables; and avoid partial or inconsistent dual predictions unless the primal estimate is nearly complete.

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arXiv2026

Conservative Bias Linear Power Flow Approximations: Application to Unit Commitment

Accurate modeling of power flow behavior is essential for a wide range of power system applications, yet the nonlinear and nonconvex structure of the underlying equations often limits their direct use in large-scale optimization problems. As a result, linear models are frequently adopted to improve computational tractability, though these simplifications can introduce excessive approximation error or lead to constraint violations. This paper presents a linear approximation framework, referred to as Conservative Bias Linear Approximations (CBLA), that systematically incorporates conservativeness into the approximation process. Rather than solely minimizing local linearization error, CBLA constructs linear constraints that bound the nonlinear functions of interest over a defined operating region while reducing overall approximation bias. The proposed approach maintains the simplicity of linear formulations and allows the approximation to be shaped through user-defined loss functions tailored to specific system quantities. Numerical studies demonstrate that CBLA provides more reliable and accurate approximations than conventional linearization techniques, and its integration into a unit commitment formulation results in improved feasibility and reduced operating costs.

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arXiv2026

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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arXiv2026

Ramping-aware Enhanced Flexibility Aggregation of Distributed Generation with Energy Storage in Power Distribution Networks

Power distribution networks are increasingly hosting controllable and flexible distributed energy resources (DERs) that, when aggregated, can provide ancillary support to transmission systems. However, existing aggregation schemes often ignore the ramping constraints of these DERs, which can render them impractical in real deployments. This work proposes a ramping-aware flexibility aggregation scheme, computed at the transmission-distribution boundary, that explicitly accounts for DER ramp limits and yields flexibility envelopes that are provably disaggregable. To further enhance the attainable flexibility region, we introduce a novel pre-ramping strategy, which proactively adjusts resource operating points to enlarge the aggregated flexibility envelope while preserving both network feasibility and disaggregation guarantees. The proposed method demonstrates a 5.2% to 19.2% improvement in flexibility relative to the baseline model, depending on system conditions. We validate the scheme on an IEEE-33 bus distribution system and provide formal proofs showing that both aggregation strategies are disaggregable for all feasible trajectories within the aggregate flexibility envelope.

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arXiv2026

Invertibility Conditions for the Admittance Matrices of Balanced Power Systems

The admittance matrix encodes the network topology and electrical parameters of a power system in order to relate the current injection and voltage phasors. Since admittance matrices are central to many power engineering analyses, their characteristics are important subjects of theoretical studies. This paper focuses on the key characteristic of \emph{invertibility}. Previous literature has presented an invertibility condition for admittance matrices. This paper first identifies and fixes a technical issue in the proof of this previously presented invertibility condition. This paper then extends this previous work by deriving new conditions that are applicable to a broader class of systems with lossless branches and transformers with off-nominal tap ratios.

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arXiv2025

A Decomposition Method for Solving Sensitivity-Based Distributed Optimal Power Flow

Efficiently solving large-scale optimal power flow (OPF) problems is challenging due to the high dimensionality and interconnectivity of modern power systems. Decomposition methods offer a promising solution via partitioning large problems into smaller subproblems that can be solved in parallel, often with local information. These approaches reduce computational burden and improve flexibility by allowing agents to manage their local models. This article introduces a decomposition method that enables a distributed solution to OPF problems. The proposed method solves OPF problems with a sensitivity-based formulation using the alternating direction method of multipliers (ADMM) algorithm. We also propose a distributed method to compute system-wide sensitivities without sharing local parameters. This approach facilitates scalable optimization while satisfying global constraints and limiting data sharing. We demonstrate the effectiveness of the proposed approach using a large set of test systems and compare its performance against existing decomposition methods. The results show that the proposed method significantly outperforms the typical phase-angle formulation with a 14-times faster computation speed on average.

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arXiv2025

Improving the Accuracy of DC Optimal Power Flow Formulations via Parameter Optimization

DC Optimal Power Flow (DC-OPF) problems optimize the generators' active power setpoints while satisfying constraints based on the DC power flow linearization. The computational tractability advantages of DC-OPF problems come at the expense of inaccuracies relative to AC Optimal Power Flow (AC-OPF) problems that accurately model the nonlinear steady-state behavior of power grids. This paper proposes an algorithm that significantly improves the accuracy of the generators' active power setpoints from DC-OPF problems with respect to the corresponding AC-OPF problems over a specified range of operating conditions. Using sensitivity information in a machine learning-inspired methodology, this algorithm tunes coefficient and bias parameters in the DC power flow approximation to improve the accuracy of the resulting DC-OPF solutions. Employing the Truncated Newton Conjugate-Gradient (TNC) method, a Quasi-Newton optimization technique, this parameter tuning occurs during an offline training phase, with the resulting parameters then used in online computations. Numerical results underscore the algorithm's efficacy with accuracy improvements in squared two-norm and $\infty$-norm losses of up to $90\%$ and $79\%$, respectively, relative to traditional DC-OPF formulations.

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arXiv2025

Certifying the Nonexistence of Feasible Path Between Power System Operating Points

By providing the optimal operating point that satisfies both the power flow equations and engineering limits, the optimal power flow (OPF) problem is central to power systems operations. While extensive research has focused on computing high-quality OPF solutions, assessing the feasibility of transitioning between operating points remains challenging since the feasible spaces of OPF problems may consist of multiple disconnected components. It is not possible to transition between operating points in different disconnected components without violating OPF constraints. To identify such situations, this paper introduces an algorithm for certifying the infeasibility of transitioning between two operating points within an OPF feasible space. As an indication of potential disconnectedness, the algorithm first seeks an infeasible point on the line connecting a pair of feasible points. The algorithm then certifies disconnectedness by using convex relaxation and bound tightening techniques to show that all points on the plane that is normal to this line are infeasible. Using this algorithm, we provide the first certifications of disconnected feasible spaces for a variety of OPF test cases.

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arXiv2025

Optimizing Parameters of the LinDistFlow Power Flow Approximation for Distribution Systems

The DistFlow model accurately represents power flows in distribution systems, but the model's nonlinearities result in computational challenges for many applications. Accordingly, a linear approximation known as \mbox{LinDistFlow} (and its three-phase extension LinDist3Flow) is commonly employed. This paper introduces a parameter optimization algorithm for enhancing the accuracy of this approximation for both balanced single-phase equivalent and unbalanced three-phase distribution network models, with the goal of aligning the outputs more closely with those from the nonlinear DistFlow model. Using sensitivity information, our algorithm optimizes the LinDistFlow approximation's coefficient and bias parameters to minimize discrepancies in predictions of voltage magnitudes relative to the nonlinear DistFlow model. The parameter optimization algorithm employs the Truncated Newton Conjugate-Gradient (TNC) method to fine-tune coefficients and bias parameters during an offline training phase to improve the LinDistFlow approximation's accuracy. % in optimization applications. Numerical results underscore the algorithm's efficacy, showcasing accuracy improvements in $L_{1}$-norm and $L_{\infty}$-norm losses of up to $92\%$ and $88\%$, respectively, relative to the traditional LinDistFlow model. We also assess how the optimized parameters perform under changes in the network topology and demonstrate the optimized LinDistFlow approximation's efficacy in a hosting capacity optimization problem.

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arXiv2025

On the Detection of Shared Data Manipulation in Distributed Optimization

This paper investigates the vulnerability of the Alternating Direction Method of Multipliers (ADMM) algorithm to shared data manipulation, with a focus on solving optimal power flow (OPF) problems. Deliberate data manipulation may cause the ADMM algorithm to converge to suboptimal solutions. We derive a sufficient condition for detecting data manipulation based on the theoretical convergence trajectory of the ADMM algorithm. We evaluate the performance of the detection condition on three data manipulation strategies with various levels of complexity and stealth. The simplest attack sends the target values and each iteration, the second attack uses a feedback loop to find the next target values, and the last attack uses a bilevel optimization to find the target values. We then extend the three data manipulation strategies to avoid detection by the detection conditions and a neural network (NN) detection model. We also propose an adversarial NN training framework to detect shared data manipulation. We illustrate the performance of our data manipulation strategy and detection framework on OPF problems. The results show that the proposed detection condition successfully detects most of the data manipulation attacks. However, the bilevel optimization attack strategy that incorporates the detection methods may avoid being detected. Countering this, our proposed adversarial training framework detects all the instances of the bilevel optimization attack.

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arXiv2025

Efficient Network Reconfiguration by Randomized Switching

We present an algorithm that efficiently computes nearly-optimal solutions to a class of combinatorial reconfiguration problems on weighted, undirected graphs. Inspired by societally relevant applications in networked infrastructure systems, these problems consist of simultaneously finding an unreweighted sparsified graph and nodal potentials that satisfy fixed demands, where the objective is to minimize some congestion criterion, e.g., a Laplacian quadratic form. These are mixed-integer nonlinear programming problems that are NP-hard in general. To circumvent these challenges, instead of solving for a single best configuration, the proposed randomized switching algorithm seeks to design a distribution of configurations that, when sampled, ensures that congestion concentrates around its optimum. We show that the proposed congestion metric is a generalized self-concordant function in the space of switching probabilities, which enables the use of efficient and simple conditional gradient methods. We implement our algorithm and show that it outperforms a state-of-the-art commercial mixed-integer second-order cone programming (MISOCP) solver by orders of magnitude over a large range of problem sizes.

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arXiv2025

Fair Cost Allocation in Energy Communities: A DLMP-based Bilevel Optimization with a Shapley Value Approach

Energy communities (ECs) are emerging as a promising decentralized model for managing cooperative distributed energy resources (DERs). As these communities expand and their operations become increasingly integrated into the grid, ensuring fairness in allocating operating costs among participants becomes a challenge. In distribution networks, DER operations at the community level can influence Distribution Locational Marginal Prices (DLMPs), which in turn affect system's operation cost. This interdependence between local decisions and system-level pricing introduces new challenges for fair and transparent cost allocation. Despite growing interest in fairness-aware methods, most methods do not account for the impact of DLMPs. To fill this gap, we propose a bilevel optimization model in which a Community Energy Aggregator (CEA) schedules DERs across multiple ECs while a Distribution System Operator (DSO) determines DLMPs through network-constrained dispatch. Leveraging the Karush-Kuhn-Tucker (KKT) conditions and strong duality, the bilevel model is reformulated into a tractable single-level problem. We achieve fairness in the cost allocation by applying the Shapley value to quantify each community's marginal contribution to system-wide cost savings. The effectiveness of the proposed method is validated through simulations on several benchmark distribution systems.

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arXiv2025

Differentiating Through Power Flow Solutions for Admittance and Topology Control

The power flow equations relate bus voltage phasors to power injections via the network admittance matrix. These equations are central to the key operational and protection functions of power systems (e.g., optimal power flow scheduling and control, state estimation, protection, and fault location, among others). As control, optimization, and estimation of network admittance parameters are central to multiple avenues of research in electric power systems, we propose a linearization of power flow solutions obtained by implicitly differentiating them with respect to the network admittance parameters. This is achieved by utilizing the implicit function theorem, in which we show that such a differentiation is guaranteed to exist under mild conditions and is applicable to generic power systems (radial or meshed). The proposed theory is applied to derive sensitivities of complex voltages, line currents, and power flows. The developed theory of linearizing the power flow equations around changes in the complex network admittance parameters has numerous applications. We demonstrate several of these applications, such as predicting the nodal voltages when the network topology changes without solving the power flow equations. We showcase the application for continuous admittance control, which is used to increase the hosting capacity of a given distribution network.

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