arXiv subjects

Line Roald

Publications and source records attributed to Line Roald.

At least 37 records · Page 2Linked to original sources

arXiv2024

Multistage Stochastic Program for Mitigating Power System Risks under Wildfire Disruptions

The frequency of wildfire disasters has surged five-fold in the past 50 years due to climate change. Preemptive de-energization is a potent strategy to mitigate wildfire risks but substantially impacts customers. We propose a multistage stochastic programming model for proactive de-energization planning, aiming to minimize economic loss while accomplishing a fair load delivery. We model wildfire disruptions as stochastic disruptions with varying timing and intensity, introduce a cutting-plane decomposition algorithm, and test our approach on the RTS-GLMC test case. Our model consistently offers a robust and fair de-energization plan that mitigates wildfire damage costs and minimizes load-shedding losses, particularly when pre-disruption restoration is considered.

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arXiv2024

Long Solution Times or Low Solution Quality: On Trade-Offs in Choosing a Power Flow Formulation for the Optimal Power Shutoff Problem

The Optimal Power Shutoff (OPS) problem is an optimization problem that makes power line de-energization decisions in order to reduce the risk of igniting a wildfire, while minimizing the load shed of customers. This problem, with DC linear power flow equations, has been used in many studies in recent years. However, using linear approximations for power flow when making decisions on the network topology is known to cause challenges with AC feasibility of the resulting network, as studied in the related contexts of optimal transmission switching or grid restoration planning. This paper explores the accuracy of the DC OPS formulation and the ability to recover an AC-feasible power flow solution after de-energization decisions are made. We also extend the OPS problem to include variants with the AC, Second-Order-Cone, and Network-Flow power flow equations, and compare them to the DC approximation with respect to solution quality and time. The results highlight that the DC approximation overestimates the amount of load that can be served, leading to poor de-energization decisions. The AC and SOC-based formulations are better, but prohibitively slow to solve for even modestly sized networks thus demonstrating the need for new solution methods with better trade-offs between computational time and solution quality.

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arXiv2024

Cascading Blackout Severity Prediction with Statistically-Augmented Graph Neural Networks

Higher variability in grid conditions, resulting from growing renewable penetration and increased incidence of extreme weather events, has increased the difficulty of screening for scenarios that may lead to catastrophic cascading failures. Traditional power-flow-based tools for assessing cascading blackout risk are too slow to properly explore the space of possible failures and load/generation patterns. We add to the growing literature of faster graph-neural-network (GNN)-based techniques, developing two novel techniques for the estimation of blackout magnitude from initial grid conditions. First we propose several methods for employing an initial classification step to filter out safe "non blackout" scenarios prior to magnitude estimation. Second, using insights from the statistical properties of cascading blackouts, we propose a method for facilitating non-local message passing in our GNN models. We validate these two approaches on a large simulated dataset, and show the potential of both to increase blackout size estimation performance.

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arXiv2023

Multi-period Power System Risk Minimization under Wildfire Disruptions

Natural wildfire becomes increasingly frequent as climate change evolves, posing a growing threat to power systems, while grid failures simultaneously fuel the most destructive wildfires. Preemptive de-energization of grid equipment is effective in mitigating grid-induced wildfires but may cause significant power outages during natural wildfires. This paper proposes a novel two-stage stochastic program for planning preemptive de-energization and solves it via an enhanced Lagrangian cut decomposition algorithm. We model wildfire events as stochastic disruptions with random magnitude and timing. The stochastic program maximizes the electricity delivered while proactively de-energizing components over multiple time periods to reduce wildfire risks. We use a cellular automaton process to sample grid failure and wildfire scenarios driven by realistic risk and environmental factors. We test our method on an augmented version of the RTS-GLMC test case in Southern California and compare it with four benchmark cases, including deterministic, wait-and-see, and robust optimization formulations as well as a comparison with prior wildfire risk optimization. Our method reduces wildfire damage costs and load-shedding losses, and our nominal plan is robust against uncertainty perturbation.

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arXiv2023

Security Constrained Optimal Power Shutoff

Electric grid faults are increasingly the source of ignition for major wildfires. To reduce the likelihood of such ignitions in high risk situations, utilities use pre-emptive deenergization of power lines, commonly referred to as Public Safety Power Shut-offs (PSPS). Besides raising challenging trade-offs between power outages and wildfire safety, PSPS removes redundancy from the network just at a time when component faults are likely to happen. This may leave the network particularly vulnerable to unexpected line faults that may occur while the PSPS is in place. Previous works have not explicitly considered the impacts of such outages. To address this gap, we propose the Security-Constrained Optimal Power Shutoff (SC-OPS) problem which uses post-contingency security constraints to model the impact of unexpected line faults when planning a PSPS. This SC-OPS model enables, for the first time, the exploration of a wide range of trade-offs between both wildfire risk and pre- and post-contingency load shedding while designing PSPS plans, providing useful insights for utilities and policy makers considering different approaches to PSPS.We demonstrate the efficacy of our model using the EPRI 39-bus test system as a case study. The results highlight the potential risks of not considering security constraints when planning PSPS and show that incorporating security constraints into the PSPS design process improves the resilience of current PSPS plans.

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arXiv2023

Optimal Design and Cascading Failure Evaluation of Remedial Action Schemes

Remedial action schemes (RAS) are often seen as an alternative to building new transmission infrastructure to relieve congestion in the system. Consequently, there has been a rapid growth in the number of RAS in electric power systems across the world. However, most RAS rely on fixed parameters and hence cannot adapt to the rapidly evolving nature of the electric grid. In this paper, an optimization framework (RAS-SCOPF) to automate the RAS design procedure is proposed. The proposed framework is a mixed integer quadratic program (MIQP) that chooses a set of optimal RAS actions and minimizes load shed when a contingency occurs. The cost of operation of the RAS-SCOPF is compared against those of standard OPF and SCOPF formulations. Moreover, the risk of cascading failure for the different formulations are evaluated using a DC power flow based cascading failure simulator (CFS). The proposed framework is applied to the RTS-96 24-bus network. The inclusion of RAS allows the system to be operated at a lower cost while preventing any contingency from evolving into cascading blackouts.

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arXiv2023

Co-optimization of power line shutoff and restoration under high wildfire ignition risk

Electric power infrastructure has ignited several of the most destructive wildfires in recent history. Preemptive power shutoffs are an effective tool to mitigate the risk of ignitions from power lines, but at the same time can cause widespread power outages. This work proposes a mathematical optimization problem to help utilities decide where and when to implement these shutoffs, as well as how to most efficiently restore power once the wildfire risk is lower. Specifically, our model co-optimizes the power shutoff (considering both wildfire risk reduction and power outages) as well as the post-event restoration efforts given constraints related to inspection and energization of lines, and is implemented as a rolling horizon optimization problem that is resolved whenever new forecasts of load and wildfire risk become available. We demonstrate our method on the IEEE RTS-GMLC test case using real wildfire risk data and forecasts from US Geological Survey, and investigate the sensitivity of the results to the forecast quality, decision horizon and system restoration budget. The software implementation is available in the open source software package PowerModelsWildfire.jl.

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arXiv2022

Efficient Representations of Radiality Constraints in Optimization of Islanding and De-Energization in Distribution Grids

Optimization of power distribution system topology is complicated by the requirement that the system be operated in a radial configuration. In this paper, we discuss existing methods for enforcing radiality constraints and introduce two new formulations that enable optimization over partially energized or islanded network topologies. The first builds on methods that use so-called parent-child constraints, but enforces those constraints on an abstracted network which enables an equivalent formulation with significantly less variables and constraints. The second formulation builds on existing approaches which directly generate constraints disallowing loops, and through an iterative approach seeks to limit the number of these constraints which must be enforced.

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arXiv2022

Recursive Restoration Refinement: A Fast Heuristic for Near-Optimal Restoration Prioritization in Power Systems

The prioritization of restoration actions after large power system outages plays a key role in how quickly power can be restored. It has been shown that fast and intuitive heuristics for restoration prioritization most often result in low-quality restoration plans. Meanwhile, mathematical optimization tools that find high-quality restoration plans are too slow to be applied to restoration planning problems of practical interest. This work makes a significant step in closing this quality vs compute time gap by proposing the Recursive Restoration Refinement heuristic for power system restoration. This heuristic is shown to produce near-optimal restoration plans up to 1,000 times faster than other state-of-the-art solution methods on a range of test cases with up to 500 buses and 700 damaged components. The potential impact of this new heuristic is demonstrated by a preliminary analysis of the key features of high-quality restoration plans. The recursive restoration refinement algorithm and other methods explored in this work have been made available as part of the open-source software package, PowerModelsRestoration, to support ongoing research in power restoration algorithms.

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arXiv2021

The Role of Distributed Energy Resources in Distribution System Restoration

With increasing levels of distributed energy resources (DERs) connected to the grid, it is important to understand the role that DERs can play in post-disaster restoration. In this paper, we propose a two-step optimization method to identify and implement an optimal restoration schedule under different DER operating scenarios. We investigate how the presence and geographical distribution of DERs change the optimal restoration order, and assess the impacts on customers with and without DERs. In our case study using the IEEE 123 single phase distribution system, we find that optimal restoration order changes significantly when DERs are concentrated in one part of the grid. We also observe that the presence of DERs generally reduces the energy not served across all customers and can help prioritize grid reconnection of customers without DERs.

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arXiv2021

Low Frequency AC Transmission Upgrades with Optimal Frequency Selection

The advantages of operating selected transmission lines at frequencies other than the standard 50 or 60 Hz are numerous, encompassing increased power transfer capacity and better utilization of existing infrastructure. While high voltage DC (HVDC) is by far the most well-established example, there has been an emerging interest low frequency AC (LFAC) transmission in applications ranging from offshore wind to railway systems and mining. In this paper, we investigate the use of LFAC as a transmission upgrade and propose models and analysis methods to determine the optimal choice of frequency. The paper first presents an optimal power flow model with frequency as a variable, assuming modular multilevel converters for frequency conversion. Using this model, we analyze LFAC as an embedded upgrade in a transmission system using existing lines. We quantify the system-wide advantages from improved power flow control and frequency reduction and find that an LFAC upgrade achieves similar and sometimes better results compared with HVDC upgrades. Finally, we analyze the factors which determine the optimal frequency for these upgraded transmission lines, and we demonstrate the benefits of changing the frequency in response to different system topologies and operating conditions.

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arXiv2021

A Guide to Reducing Carbon Emissions through Data Center Geographical Load Shifting

Recent computing needs have lead technology companies to develop large scale, highly optimized data centers. These data centers represent large loads on electric power networks which have the unique flexibility to shift load both geographically and temporally. This paper focuses on how data centers can use their geographic load flexibility to reduce carbon emissions through clever interactions with electricity markets. Because electricity market clearing accounts for congestion and power flow physics in the electric grid, the carbon emissions associated with electricity use varies between (potentially geographically close) locations. Using our knowledge about this process, we propose a new and improved metric to guide geographic load shifting, which we refer to as the locational marginal carbon emission $λ_{\text{CO}_2}$. We compare this and three other shifting metrics on their ability to reduce carbon emissions and generation costs throughout the course of a year. Our analysis demonstrates that $λ_{\text{CO}_2}$ is more effective in reducing carbon emissions than more commonly proposed metrics that do not account for the specifics of the power grid.

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arXiv2021

Stochastic Hybrid Approximation for Uncertainty Management in Gas-Electric Systems

Gas-fired generators, with their ability to quickly ramp up and down their electricity production, play an important role in managing renewable energy variability. However, these changes in electricity production translate into variability in the consumption of natural gas, and propagate uncertainty from the electric grid to the natural gas system. To ensure that both systems are operating safely, there is an increasing need for coordination and uncertainty management among the electricity and gas networks. A challenging aspect of this coordination is the consideration of natural gas dynamics, which play an important role at the time scale of interest, but give rise to a set of non-linear and non-convex equations that are hard to optimize over even in the deterministic case. Many conventional methods for stochastic optimization cannot be used because they either incorporate a large number of scenarios directly or require the underlying problem to be convex. To address these challenges, we propose using a Stochastic Hybrid Approximation algorithm to more efficiently solve these problems and investigate several different variants of this algorithm. In a case study, we demonstrate that the proposed technique is able to quickly obtain high quality solutions and outperforms existing benchmarks such as Generalized Benders Decomposition. We demonstrate that coordinated uncertainty management that accounts for the gas system can significantly reduce both electric and gas system load shed in stressed conditions.

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arXiv2021

Steady State Modeling for Variable Frequency AC Power Flow

Advantages of operating portions of a power system at frequencies different from the standard 50 or 60 Hz have been demonstrated in the low frequency AC (LFAC) and high voltage DC (HVDC) literature. Branches constrained by stability or thermal limits can benefit from increased capacity and flexibility. Since advances in power electronics enable the choice of an operating frequency, tools are needed to make this choice. In order to quantify the advantages as functions of frequency, this paper provides models for steady state calculations with frequency as a variable and validates the modeling assumptions. It then introduces an analytical quantification of the power flow capacity of a transmission branch as a function of frequency, demonstrating different active constraints across the range of frequency. The modeling and power flow calculations are demonstrated for a practical transmission line using manufacturer data. The models presented here provide a foundation for system level studies with variable frequency using optimal power flow.

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arXiv2020

Chance-Constrained Unit Commitment with N-1 Security and Wind Uncertainty

As renewable wind energy penetration rates continue to increase, one of the major challenges facing grid operators is the question of how to control transmission grids in a reliable and a cost-efficient manner. The stochastic nature of wind forces an alteration of traditional methods for solving day-ahead and look-ahead unit commitment and dispatch. In particular, the variability of wind generation increases the risk of unexpected overloads and cascading events. To address these questions, we present an N-1 Security and Chance-Constrained Unit Commitment (SCCUC) that includes models of generation reserves that respond to wind fluctuations and component outages. We formulate the SCCUC as a mixed-integer, second-order cone problem that limits the probability of failure. We develop a modified Benders decomposition algorithm to solve the problem to optimality and present detailed case studies on the IEEE RTS-96 three-area and the IEEE 300 NESTA test systems. The case studies assess the economic impacts of contingencies and various degrees of wind power penetration and demonstrate the effectiveness and scalability of the algorithm.

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arXiv2020

Balancing Wildfire Risk and Power Outages through Optimized Power Shut-Offs

Electric grid faults can cause catastrophic wildfires, particularly in regions with high winds and low humidity. In real-time operations, electric utilities are often left with few options for wildfire risk mitigation, leading to use of disruptive measures such as proactive de-energization of equipment, frequently referred to as public safety power shut-offs. Such power shut-offs have significant impacts on customers, who experience power cuts in an attempt to protect them from fires. This work proposes the optimal power shut-off problem, an optimization model to support short-term operational decision making in the context of extreme wildfire risk. Specifically, the model optimizes grid operations to maximize the amount of power that can be delivered, while proactively minimizing the risk of wildfire ignitions by selectively de-energizing components in the grid. This is the first optimization model to consider how preventive wildfire risk measures impact both wildfire risk \emph{and} power systems reliability at a short-term, operational time-frame. The effectiveness of the method is demonstrated on an augmented version of the RTS-GMLC test case, located in Southern California, and compared against two approaches based on simple risk thresholds. The proposed optimization-based model reduces both wildfire risk and lost load shed relative to the benchmarks.

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arXiv2020

The Environmental Potential of Hyper-Scale Data Centers: Using Locational Marginal CO$_2$ Emissions to Guide Geographical Load Shifting

Increasing demand for computing has lead to the development of large-scale, highly optimized data centers, which represent large loads in the electric power network. Many major computing and internet companies operate multiple data centers spread geographically across the world. Thus, these companies have a unique ability to shift computing load, and thus electric load, geographically. This paper provides a "bottom-up" load shifting model which uses data centers' geographic load flexibility to lower CO$_2$ emissions. This model utilizes information about the locational marginal CO$_2$ footprint of the electricity at individual nodes, but does not require direct collaboration with the system operator. We demonstrate how to calculate marginal carbon emissions, and assess the efficacy of our approach compared to a setting where the data centers bid their flexibility into a centralized market. We find that data center load shifting can achieve substantial reductions in CO$_2$ emissions even with modest load shifting.

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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.

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