arXiv subjects

Daniel Molzahn

Publications and source records attributed to Daniel Molzahn.

7 recordsLinked to original sources

arXiv2026

PACR: Parameter-Optimized AC Power Flow Restoration for AC Feasible DCOPF Dispatch

The DC optimal power flow is widely used in power system operations because of its computational efficiency and scalability. However, DC dispatches are not guaranteed to satisfy the nonlinear AC power-flow equations or associated operational limits. This paper develops a parameterized, differentiable AC power-flow restoration method for mapping DC dispatches to AC-consistent operating points. The method incorporates distributed slack for active-power balancing and PV/PQ switching for reactive-power regulation, both implemented using smooth differentiable surrogates with tunable parameters, including slack participation factors, voltage setpoints, and regulation steepness. These parameters are trained offline by differentiating through the AC restoration equations using the implicit function theorem. Once trained, the optimized parameters are fixed and used directly during AC power-flow recovery from DC dispatches. The approach is evaluated on IEEE, ACTIVSg, and PEGASE test systems using setpoints computed by standard DC optimal power flow. Results show that the optimized restoration method improves AC feasibility recovery across various systems relative to conventional single-slack AC power-flow recovery. On the 9,241-bus case, the optimized method improves cost difference by 80% relative to the conventional recovery baseline and improves solving time relative to ACOPF by 75%.

eess.SY↗

arXiv2025

Towards AC Feasibility of DCOPF Dispatch

DC Optimal Power Flow (DCOPF) is widely utilized in power system operations due to its simplicity and computational efficiency. However, its lossless, reactive power-agnostic model often yields dispatches that are infeasible under practical operating scenarios such as the nonlinear AC power flow (ACPF) equations. While theoretical analysis demonstrates that DCOPF solutions are inherently AC-infeasible, their widespread industry adoption suggests substantial practical utility. This paper develops a unified DCOPF-ACPF pipeline to recover AC feasible solutions from DCOPF-based dispatches. The pipeline uses four DCOPF variants and applies AC feasibility recovery using both distributed slack allocation and PV/PQ switching. The main objective is to identify the most effective pipeline for restoring AC feasibility. Evaluation across over 10,000 dispatch scenarios on various test cases demonstrates that the structured ACPF model yields solutions that satisfy both the ACPF equations, and all engineering inequality constraints. In a 13,659 bus case, the mean absolute error and cost differences between DCOPF and ACOPF are reduced by 75% and 93%, respectively, compared to conventional single slack bus methods. Under extreme loading conditions, the pipeline reduces inequality constraint violations by a factor of 3 to 5.

eess.SY↗

arXiv2024

Beyond Algorithmic Fairness: A Guide to Develop and Deploy Ethical AI-Enabled Decision-Support Tools

The integration of artificial intelligence (AI) and optimization hold substantial promise for improving the efficiency, reliability, and resilience of engineered systems. Due to the networked nature of many engineered systems, ethically deploying methodologies at this intersection poses challenges that are distinct from other AI settings, thus motivating the development of ethical guidelines tailored to AI-enabled optimization. This paper highlights the need to go beyond fairness-driven algorithms to systematically address ethical decisions spanning the stages of modeling, data curation, results analysis, and implementation of optimization-based decision support tools. Accordingly, this paper identifies ethical considerations required when deploying algorithms at the intersection of AI and optimization via case studies in power systems as well as supply chain and logistics. Rather than providing a prescriptive set of rules, this paper aims to foster reflection and awareness among researchers and encourage consideration of ethical implications at every step of the decision-making process.

cs.AI↗

arXiv2024

Equitably allocating wildfire resilience investments for power grids: The curse of aggregation and vulnerability indices

Social vulnerability indices have increased traction for guiding infrastructure investment decisions to prioritize communities that need these investments most. One such plan is the Biden-Harris Justice40 initiative, which aims to guide equitable infrastructure investments by ensuring that disadvantaged communities defined by the Climate & Economic Justice Screening Tool (CEJST) receive 40% of the total benefit realized by the investment. However, there is limited research on the practicality of applying vulnerability indices like the CEJST to real-world decision-making for policy outcomes. In this paper, we study this gap by examining the effectiveness of vulnerability indices in a case study focused on power shutoff and undergrounding decisions in wildfire-prone regions. Using a mixed-integer program and a high-fidelity synthetic transmission network in Texas, we model resource allocation policies inspired by Justice40 and evaluate their impact on reducing power outages and mitigating wildfire risk for vulnerable groups. Our analysis reveals that the Justice40 framework may fail to protect certain communities facing high wildfire risk. In our case study, we show that indigenous groups are particularly impacted. We posit that this outcome is likely due to information losses from data aggregation and the use of generalized vulnerability indices. Through the use of explicit group-level protections, we are able to bound the best possible outcome for population groups that are proportionally most affected.

math.OC↗

arXiv2021

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural Networks (NNs). These NNs can be exactly transformed into Mixed Integer Linear Programs (MILPs) and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the NN. Accordingly, this paper develops a technique for training an "optimally compact" NN, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We show that the resulting NN model is more expressive than both the DC and linearized power flow approximations when embedded inside of a challenging optimization problem (i.e., the AC unit commitment problem).

cs.LG↗

arXiv2021

Fair and Reliable Reconnections for Temporary Disruptions in Electric Distribution Networks using Submodularity

Increasing reliability and reducing disruptions in supply networks are of increasing importance; for example, power outages in electricity distribution networks cost \$35-50 billion annually in the US. Motivated by the operational constraints of such networks and their rapid adoption of decentralized paradigms and self-healing components, we introduce the "minimum reconnection time" (MRT) problem. MRT seeks to reduce outage time after network disruptions by programming reconnection times of different edges (i.e., switches), while ensuring that the operating network is acyclic. We show that MRT is NP-hard and is a special case of the well-known minimum linear ordering problem (MLOP) in the submodular optimization literature. MLOP is a special case of a broader class of ordering problems that often admit polynomial time approximation algorithms. We develop the theory of kernel-based randomized rounding approaches to give a tight polynomial-time approximation for MRT, improving the state-of-the-art approximation factor for a broad class of MLOP instances. Further, motivated by the reliability incentive structure for utility companies and operational energy losses in distribution networks, we propose local search over spanning trees to balance multiple objectives simultaneously. We computationally validate our reconfiguration methods on the NREL SMART-DS Greensboro synthetic network, and show that this improves service equity by a factor of four, across industrial and residential areas.

math.OC↗

arXiv2020

DC Optimal Power Flow with Joint Chance Constraints

Managing uncertainty and variability in power injections has become a major concern for power system operators due to the increasing levels of fluctuating renewable energy connected to the grid. This work addresses this uncertainty via a joint chance-constrained formulation of the DC optimal power flow (OPF) problem, which satisfies \emph{all} the constraints \emph{jointly} with a pre-determined probability. The few existing approaches for solving joint chance-constrained OPF problems are typically either computationally intractable for large-scale problems or give overly conservative solutions that satisfy the constraints far more often than required, resulting in excessively costly operation. This paper proposes an algorithm for solving joint chance-constrained DC OPF problems by adopting an S$\ell_1$QP-type trust-region algorithm. This algorithm uses a sample-based approach that avoids making strong assumptions on the distribution of the uncertainties, scales favorably to large problems, and can be tuned to obtain less conservative results. We illustrate the performance of our method using several IEEE test cases. The results demonstrate the proposed algorithm's advantages in computational times and limited conservativeness of the solutions relative to other joint chance-constrained DC OPF algorithms.

math.OC↗