arXiv subjects

Daniel K. Molzahn

Publications and source records attributed to Daniel K. Molzahn.

At least 55 records · Page 3Linked to original sources

arXiv2024

A Fault-Tolerant Distributed Termination Method for Distributed Optimization Algorithms

This paper proposes a fully distributed termination method for distributed optimization algorithms solved by multiple agents. The proposed method guarantees terminating a distributed optimization algorithm after satisfying the global termination criterion using information from local computations and neighboring agents. The proposed method requires additional iterations after satisfying the global terminating criterion to communicate the termination status. The number of additional iterations is bounded by the diameter of the communication network. This paper also proposes a fault-tolerant extension of this termination method that prevents early termination due to faulty agents or communication errors. We provide a proof of the method's correctness and demonstrate the proposed method by solving the optimal power flow problem for electric power grids using the alternating direction method of multipliers.

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arXiv2024

Fairness-aware Photovoltaic Generation Limits for Voltage Regulation in Power Distribution Networks using Conservative Linear Approximations

This paper proposes a framework for fairly curtailing photovoltaic (PV) plants in response to the over-voltage problem in PV-rich distribution networks. The framework imposes PV generation limits to avoid overvoltages. These limits are computed a day ahead of real-time operations by solving an offline stochastic optimization problem using forecasted scenarios for PV generation and load demand. The framework minimizes the overall curtailment while considering fairness by reducing disparities in curtailments among different PV owners. We model the distribution grid constraints using a conservative linear approximation (CLA) of the AC power flow equations which is computed using a set of sampled power injections from the day-ahead predicted scenarios. The proposed framework is numerically validated on a CIGRE benchmark network interfaced with a large number of PV plants. We compare the performance of the proposed framework versus an alternative formulation that does not incorporate fairness considerations. To this end, we assess tradeoffs between fairness, as quantified with the Jain Fairness Index (JFI), and the total curtailed energy.

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arXiv2024

Co-Optimization of Damage Assessment and Restoration: A Resilience-Driven Dynamic Crew Allocation for Power Distribution Systems

This study introduces a mixed-integer linear programming (MILP) model, effectively co-optimizing patrolling, damage assessment, fault isolation, repair, and load re-energization processes. The model is designed to solve a vital operational conundrum: deciding between further network exploration to obtain more comprehensive data or addressing the repair of already identified faults. As information on the fault location and repair timelines becomes available, the model allows for dynamic adaptation of crew dispatch decisions. In addition, this study proposes a conservative power flow constraint set that considers two network loading scenarios within the final network configuration. This approach results in the determination of an upper and a lower bound for node voltage levels and an upper bound for power line flows. To underscore the practicality and scalability of the proposed model, we have demonstrated its application using IEEE 123-node and 8500-node test systems, where it delivered promising results.

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arXiv2023

Managing Vehicle Charging During Emergencies via Conservative Distribution System Modeling

Combinatorial distribution system optimization problems, such as scheduling electric vehicle (EV) charging during evacuations, present significant computational challenges. These challenges stem from the large numbers of constraints, continuous variables, and discrete variables, coupled with the unbalanced nature of distribution systems. In response to the escalating frequency of extreme events impacting electric power systems, this paper introduces a method that integrates sample-based conservative linear power flow approximations (CLAs) into an optimization framework. In particular, this integration aims to ameliorate the aforementioned challenges of distribution system optimization in the context of efficiently minimizing the charging time required for EVs in urban evacuation scenarios.

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arXiv2023

AC Power Flow Informed Parameter Learning for DC Power Flow Network Equivalents

This paper presents an algorithm to optimize the parameters of power systems equivalents to enhance the accuracy of the DC power flow approximation in reduced networks. Based on a zonal division of the network, the algorithm produces a reduced power system equivalent that captures inter-zonal flows with aggregated buses and equivalent transmission lines. The algorithm refines coefficient and bias parameters for the DC power flow model of the reduced network, aiming to minimize discrepancies between inter-zonal flows in DC and AC power flow results. Using optimization methods like BFGS, L-BFGS, and TNC in an offline training phase, these parameters boost the accuracy of online DC power flow computations. In contrast to existing network equivalencing methods, the proposed algorithm optimizes accuracy over a specified range of operation as opposed to only considering a single nominal point. Numerical tests demonstrate substantial accuracy improvements over traditional equivalencing and approximation methods.

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arXiv2023

Optimally Managing the Impacts of Convergence Tolerance for Distributed Optimal Power Flow

The future power grid may rely on distributed optimization to determine the set-points for huge numbers of distributed energy resources. There has been significant work on applying distributed algorithms to optimal power flow (OPF) problems, which require separate computing agents to agree on shared boundary variable values. Looser tolerances for the mismatches in these shared variables generally yield faster convergence at the expense of exacerbating constraint violations, but there is little quantitative understanding of how the convergence tolerance affects solution quality. To address this gap, we first quantify how convergence tolerance impacts constraint violations when the distributed OPF generator dispatch is applied to the power system. Using insights from this analysis, we then develop a bound tightening algorithm which guarantees that operating points from distributed OPF algorithms will not result in violations despite the possibility of shared variable mismatches within the convergence tolerance. We also explore how bounding the cumulative shared variable mismatches can prevent unnecessary conservativeness in the bound tightening. The proposed approach enables control of the trade-off between computational speed, which improves as the convergence tolerance increases, and distributed OPF solution cost, which increases with convergence tolerance due to tightened constraints, while ensuring feasibility.

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arXiv2023

PowerModelsADA: A Framework for Solving Optimal Power Flow using Distributed Algorithms

This paper presents PowerModelsADA, an open-source framework for solving Optimal Power Flow (OPF) problems using Alternating Distributed Algorithms (ADA). PowerModelsADA provides a framework to test, verify, and benchmark both existing and new ADAs. This paper demonstrates use cases for PowerModelsADA and validates its implementation with multiple OPF formulations.

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arXiv2023

GreenEVT: Greensboro Electric Vehicle Testbed

The ongoing electrification of the transportation fleet will increase the load on the electric power grid. Since both the transportation network and the power grid already experience periods of significant stress, joint analyses of both infrastructures will most likely be necessary to ensure acceptable operation in the future. To enable such analyses, this paper presents an open-source testbed that jointly simulates high-fidelity models of both the electric distribution system and the transportation network. The testbed utilizes two open-source simulators, OpenDSS to simulate the electric distribution system and the microscopic traffic simulator SUMO to simulate the traffic dynamics. Electric vehicle charging links the electric distribution system and the transportation network models at vehicle locations determined using publicly available parcel data. Leveraging high-fidelity synthetic electric distribution system data from the SMART-DS project and transportation system data from OpenStreetMap, this testbed models the city of Greensboro, NC down to the household level. Moreover, the methodology and the supporting scripts released with the testbed allow adaption to other areas where high-fidelity geolocated OpenDSS datasets are available. After describing the components and usage of the testbed, we exemplify applications enabled by the testbed via two scenarios modeling the extreme stresses encountered during evacuations.

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arXiv2023

Restoring AC Power Flow Feasibility from Relaxed and Approximated Optimal Power Flow Models

To address computational challenges associated with power flow nonconvexities, significant research efforts over the last decade have developed convex relaxations and approximations of optimal power flow (OPF) problems. However, benefits associated with the convexity of these relaxations and approximations can have tradeoffs in terms of solution accuracy since they may yield voltage phasors that are inconsistent with the power injections and line flows, limiting their usefulness for some applications. Inspired by state estimation (SE) techniques, this paper proposes a new method for obtaining an AC power flow feasible point from the solution to a relaxed or approximated optimal power flow (OPF) problem. By treating the inconsistent voltage phasors, power injections, and line flows analogously to noisy measurements in a state estimation algorithm, the proposed method yields power injections and voltage phasors that are feasible with respect to the AC power flow equations while incorporating information from many quantities in the solution to a relaxed or approximated OPF problem. We improve this method by adjusting weighting terms with an approach inspired by algorithms used to train machine learning models. We demonstrate the proposed method using several relaxations and approximations. The results show up to several orders of magnitude improvement in accuracy over traditional methods.

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arXiv2023

Conditions for Estimation of Sensitivities of Voltage Magnitudes to Complex Power Injections

Voltage phase angle measurements are often unavailable from sensors in distribution networks and transmission network boundaries. Therefore, this paper addresses the conditions for estimating sensitivities of voltage magnitudes with respect to complex (active and reactive) electric power injections based on sensor measurements. These sensitivities represent submatrices of the inverse power flow Jacobian. We extend previous results to show that the sensitivities of a bus voltage magnitude with respect to active power injections are unique and different from those with respect to reactive power. The classical Newton-Raphson power flow model is used to derive a novel representation of bus voltage magnitudes as an underdetermined linear operator of the active and reactive power injections; parameterized by the bus power factors. Two conditions that ensure the existence of unique complex power injections given voltage magnitudes are established for this underdetermined linear system, thereby compressing the solution space. The first is a sufficient condition based on the bus power factors. The second is a necessary and sufficient condition based on the system eigenvalues. We use matrix completion theory to develop estimation methods for recovering sensitivity matrices with varying levels of sensor availability. Simulations verify the results and demonstrate engineering use of the proposed methods.

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arXiv2023

Two-Stage Robust Quadratic Optimization with Equalities and its Application to Optimal Power Flow

In this work, we consider two-stage quadratic optimization problems under ellipsoidal uncertainty. In the first stage, one needs to decide upon the values of a subset of optimization variables (control variables). In the second stage, the uncertainty is revealed and the rest of the optimization variables (state variables) are set up as a solution to a known system of possibly non-linear equations. This type of problem occurs, for instance, in optimization for dynamical systems, such as electric power systems as well as gas and water networks. We propose a convergent iterative algorithm to build a sequence of approximately robustly feasible solutions with an improving objective value. At each iteration, the algorithm optimizes over a subset of the feasible set and uses affine approximations of the second-stage equations while preserving the non-linearity of other constraints. We implement our approach and demonstrate its performance on Matpower instances. This paper focuses on quadratic problems, but the approach is suitable for more general setups.

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arXiv2022

Sharing the Load: Considering Fairness in De-energization Scheduling to Mitigate Wildfire Ignition Risk using Rolling Optimization

Wildfires are a threat to public safety and have increased in both frequency and severity due to climate change. To mitigate wildfire ignition risks, electric power system operators proactively de-energize high-risk power lines during "public safety power shut-off" (PSPS) events. Line de-energizations can cause communities to lose power, which may result in negative economic, health, and safety impacts. Furthermore, the same communities may repeatedly experience power shutoffs over the course of a wildfire season, which compounds these negative impacts. However, there may be many combinations of power lines whose de-energization will result in about the same reduction of system-wide wildfire risk, but the associated power outages affect different communities. Therefore, one may raise concerns regarding the fairness of de-energization decisions. Accordingly, this paper proposes a framework to select lines to de-energize in order to balance wildfire risk reduction, total load shedding, and fairness considerations. The goal of the framework is to prevent a small fraction of communities from disproportionally being impacted by PSPS events, and to instead more equally share the burden of power outages. For a geolocated test case in the southwestern United States, we use actual California demand data as well as real wildfire risk forecasts to simulate PSPS events during the 2021 wildfire season and compare the performance of various methods for promoting fairness. Our results demonstrate that the proposed formulation can provide significantly more fair outcomes with limited impacts on system-wide performance.

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arXiv2022

Optimizing Transmission Infrastructure Investments to Support Line De-energization for Mitigating Wildfire Ignition Risk

Wildfires pose a growing risk to public safety in regions like the western United States, and, historically, electric power systems have ignited some of the most destructive wildfires. To reduce wildfire ignition risks, power system operators preemptively de-energize high-risk power lines during extreme wildfire conditions as part of "Public Safety Power Shutoff" (PSPS) events. While capable of substantially reducing acute wildfire risks, PSPS events can also result in significant amounts of load shedding as the partially de-energized system may not be able to supply all customer demands. In this work, we investigate the extent to which infrastructure investments can support system operations during PSPS events by enabling reduced load shedding and wildfire ignition risk. We consider the installation of grid-scale batteries, solar PV, and line hardening or maintenance measures (e.g., undergrounding or increased vegetation management). Optimally selecting the locations, types, and sizes of these infrastructure investments requires considering the line de-energizations associated with PSPS events. Accordingly, this paper proposes a multi-period optimization formulation that locates and sizes infrastructure investments while simultaneously choosing line de-energizations to minimize wildfire ignition risk and load shedding. This formulation is evaluated using two geolocated test cases along with realistic infrastructure investment parameters and actual wildfire risk data from the US Geological Survey. We evaluate the performance of investment choices by simulating de-energization decisions for the entire 2021 wildfire season with optimized infrastructure placements. With investment decisions varying significantly for different test cases, budgets, and operator priorities, the numerical results demonstrate the proposed formulation's value in tailoring investment choices to different settings.

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arXiv2022

Assessing the Impacts of Nonideal Communications on Distributed Optimal Power Flow Algorithms

Power system operators are increasingly looking toward distributed optimization to address various challenges facing electric power systems. To assess their capabilities in environments with nonideal communications, this paper investigates the impacts of data quality on the performance of distributed optimization algorithms. Specifically, this paper compares the performance of the Alternating Direction Method of Multipliers (ADMM), Analytical Target Cascading (ATC), and Auxiliary Problem Principle (APP) algorithms in the context of DC Optimal Power Flow (DC OPF) problems. Using several test systems, this paper characterizes the performance of these algorithms in terms of their convergence rates and solution quality under three data quality nonidealities: (1) additive Gaussian noise, (2) bad data (large error), and (3) intermittent communication failure.

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arXiv2022

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

The optimal power flow problem is central to many tasks in the design and operation of electric power grids. This problem seeks the minimum cost operating point for an electric power grid while satisfying both engineering requirements and physical laws describing how power flows through the electric network. By additionally considering the possibility of component failures and using an accurate AC power flow model of the electric network, the security-constrained AC optimal power flow (SC-AC-OPF) problem is of paramount practical relevance. To assess recent progress in solution algorithms for SC-AC-OPF problems and spur new innovations, the U.S. Department of Energy's Advanced Research Projects Agency--Energy (ARPA-E) organized Challenge 1 of the Grid Optimization (GO) competition. This paper describes the SC-AC-OPF problem formulation used in the competition, overviews historical developments and the state of the art in SC-AC-OPF algorithms, discusses the competition, and summarizes the algorithms used by the top three teams in Challenge 1 of the GO Competition (Teams gollnlp, GO-SNIP, and GMI-GO).

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arXiv2022

A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow

With the increasing penetration of distributed energy resources, distributed optimization algorithms have attracted significant attention for power systems applications due to their potential for superior scalability, privacy, and robustness to a single point-of-failure. The Alternating Direction Method of Multipliers (ADMM) is a popular distributed optimization algorithm; however, its convergence performance is highly dependent on the selection of penalty parameters, which are usually chosen heuristically. In this work, we use reinforcement learning (RL) to develop an adaptive penalty parameter selection policy for the AC optimal power flow (ACOPF) problem solved via ADMM with the goal of minimizing the number of iterations until convergence. We train our RL policy using deep Q-learning, and show that this policy can result in significantly accelerated convergence (up to a 59% reduction in the number of iterations compared to existing, curvature-informed penalty parameter selection methods). Furthermore, we show that our RL policy demonstrates promise for generalizability, performing well under unseen loading schemes as well as under unseen losses of lines and generators (up to a 50% reduction in iterations). This work thus provides a proof-of-concept for using RL for parameter selection in ADMM for power systems applications.

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arXiv2022

Improving Distribution System Resilience by Undergrounding Lines and Deploying Mobile Generators

To improve the resilience of electric distribution systems, this paper proposes a stochastic multi-period mixed-integer linear programming model that determines where to underground distribution lines and how to coordinate mobile generators in order to serve critical loads during extreme events. The proposed model represents the service restoration process using the linearized DistFlow approximation of the AC power flow equations as well as binary variables for the undergrounding statuses of the lines, the configurations of switches, and the locations of mobile generators during each time period. The model also enforces a radial configuration of the distribution network and considers the transportation times needed to reposition the mobile generators. Using an extended version of the IEEE 123-bus test system, numerical simulations show that combining the ability to underground distribution lines with the deployment of mobile generators can significantly improve the resilience of the power supply to critical loads.

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arXiv2021

A Decomposition Algorithm for Large-Scale Security-Constrained AC Optimal Power Flow

A decomposition algorithm for solving large-scale security-constrained AC optimal power flow problems is presented. The formulation considered is the one used in the ARPA-E Grid Optimization (GO) Competition, Challenge 1, held from November 2018 through October 2019. The techniques found to be most effective in terms of performance in the challenge are presented, including strategies for contingency selection, fast contingency evaluation, handling complementarity constraints, avoiding issues related to degeneracy, and exploiting parallelism. The results of numerical experiments are provided to demonstrate the effectiveness of the proposed techniques as compared to alternative strategies.

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