arXiv subjects

Jean-Paul Watson

Publications and source records attributed to Jean-Paul Watson.

17 recordsLinked to original sources

arXiv2026

Robust Capacity Expansion under Wildfire Ignition Risk and High Renewable Penetration

In power systems, the risk of wildfire ignition has increased significantly in recent years. The impact and severity of these events on energy dispatch, as well as their societal ramifications, make wildfire prevention critical for power system planning and operation. A common intervention by system operators is to de-energize transmission lines to mitigate the risk of fire caused by equipment failures. With the growing integration of variable renewable generation, managing and preparing the system to de-energization under wildfire risk has become even more challenging. In this context, mitigation decisions such as installing battery energy storage systems and undergrounding transmission lines can reduce the risk and adverse effects associated with de-energization and renewable generation variability. This paper presents a robust optimization model to determine the optimal location of battery storage and undergrounding of transmission line investment, utilizing representative weeks and uncertainty sets to capture the temporal relationship of uncertain variables. Specifically, this paper addresses: (i) the worst-case realization of ignition risk leading to the de-energization of transmission lines, combined with the worst-case realization of renewable energy availability, and (ii) the optimal investment decisions for energy storage capacity and undergrounding of transmission lines that are exposed to ignition risk. The proposed model is formulated as a mixed-integer linear programming (MILP) problem, employing duality theory and binary decomposition to address nonlinearities, and is solved using a column-and-constraint generation algorithm. The proposed framework is evaluated on a model of the San Diego power system, demonstrating its practical effectiveness in improving the resilience to wildfire risk.

math.OC↗

arXiv2026

High-Fidelity Capacity Expansion Planning for Puerto Rico's Electric Power System

This study presents a mathematical optimization framework and analysis to inform practical long-term investment planning in Puerto Rico's electric power system. We utilize a high-resolution capacity expansion planning model to identify least-cost generation and storage investments that improve reliability. The model co-optimizes new investments with thermal retirements and includes detailed dispatch, unit commitment, fuel selection, storage operation, engineering limits, system constraints, fuel supply limits, and load balance. Key advances over prior studies on Puerto Rico's system include: (i) Nodal transmission representation at 38 kV and above; (ii) hourly chronological simulation for representative days; (iii) explicit unit commitment for existing and new thermal units with realistic ramping, minimum up and down times, and startup costs; (iv) system-wide fuel supply constraints; and (v) operational scenarios reflecting load variability, renewable availability, and high forced outage rates in legacy units. Using data from LUMA, the Puerto Rico Electric Power Authority (PREPA), U.S. Department of Energy, and public sources, the study builds representative Puerto Rico systems for 2024 and 2030, with the latter including planned generation and storage projects. It tests scenarios with different future load levels, fuel supply assumptions, planned additions, and allowed technologies. Under the study assumptions, least-cost portfolios that meet reliability targets require about 1.5 GW or more of new H-class combined cycle capacity, in addition to planned projects. These additions mainly replace unreliable legacy thermal units rather than serve new load. The new CC investments eliminate modeled load shedding in the bulk system and restore a robust reserve margin, even under stressed load and outage conditions.

math.OC↗

arXiv2026

Modeling Adversarial Wildfires for Power Grid Disruption

Electric power infrastructure faces increasing risk of damage and disruption due to wildfire. Operators of power grids in wildfire-prone regions must consider the potential impacts of unpredictable fires. However, traditional wildfire models do not effectively describe worst-case, or even high-impact, fire behavior. To address this issue, we propose a mixed-integer conic program to characterize an adversarial wildfire that targets infrastructure while respecting realistic fire spread dynamics. We design a wind-assisted fire spread set based on the Rothermel fire spread model and propose principled convex relaxations of this set, including a new relaxation of the inner product over Euclidean balls. We present test cases derived from the recent Park, Eaton, and Palisades fires in California and solve models to identify the minimum time-to-outage of multiple-element contingencies and the maximum load shed associated with a sequence of element outages caused by a realistic wildfire. We use the minimum time-to-outage values to screen contingencies and construct security-constrained optimal power flow models that promote operational resilience against wildfire.

math.OC↗

arXiv2025

From Zonal to Nodal Capacity Expansion Planning: Spatial Aggregation Impacts on a Realistic Test-Case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. This work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8,000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

math.OC↗

arXiv2025

Nodal Capacity Expansion Planning with Flexible Large-Scale Load Siting

We propose explicitly incorporating large-scale load siting into a stochastic nodal power system capacity expansion planning model that concurrently co-optimizes generation, transmission and storage expansion. The potential operational flexibility of some of these large loads is also taken into account by considering them as consisting of a set of tranches with different reliability requirements, which are modeled as a constraint on expected served energy across operational scenarios. We implement our model as a two-stage stochastic mixed-integer optimization problem with cross-scenario expectation constraints. To overcome the challenge of scalability, we build upon existing work to implement this model on a high performance computing platform and exploit scenario parallelization using an augmented Progressive Hedging Algorithm. The algorithm is implemented using the bounding features of mpisppy, which have shown to provide satisfactory provable optimality gaps despite the absence of theoretical guarantees of convergence. We test our approach to assess the value of this proactive planning framework on total system cost and reliability metrics using realistic testcases geographically assigned to San Diego and South Carolina, with datacenter and direct air capture facilities as large loads.

math.OC↗

arXiv2025

Quantifying Metrics for Wildfire Ignition Risk from Geographic Data in Power Shutoff Decision-Making

Faults on power lines and other electric equipment are known to cause wildfire ignitions. To mitigate the threat of wildfire ignitions from electric power infrastructure, many utilities preemptively de-energize power lines, which may result in power shutoffs. Data regarding wildfire ignition risks are key inputs for effective planning of power line de-energizations. However, there are multiple ways to formulate risk metrics that spatially aggregate wildfire risk map data, and there are different ways of leveraging this data to make decisions. The key contribution of this paper is to define and compare the results of employing six metrics for quantifying the wildfire ignition risks of power lines from risk maps, considering both threshold- and optimization-based methods for planning power line de-energizations. The numeric results use the California Test System (CATS), a large-scale synthetic grid model with power line corridors accurately representing California infrastructure, in combination with real Wildland Fire Potential Index data for a full year. This is the first application of optimal power shutoff planning on such a large and realistic test case. Our results show that the choice of risk metric significantly impacts the lines that are de-energized and the resulting load shed. We find that the optimization-based method results in significantly less load shed than the threshold-based method while achieving the same risk reduction.

eess.SY↗

arXiv2024

Adaptive Power Flow Approximations with Second-Order Sensitivity Insights

The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these challenges, recent research has proposed adaptive power flow linearizations that aim to achieve accuracy over wide operating ranges. The accuracy of these approximations inherently depends on the curvature of the power flow equations within these ranges, which necessitates considering second-order sensitivities. In this paper, we leverage second-order sensitivities to both analyze and improve power flow approximations. We evaluate the curvature across broad operational ranges and subsequently utilize this information to inform the computation of various sample-based power flow approximation techniques. Additionally, we leverage second-order sensitivities to guide the development of rational approximations that yield linear constraints in optimization problems. This approach is extended to enhance accuracy beyond the limitations of linear functions across varied operational scenarios.

math.OC↗

arXiv2024

Long Duration Battery Sizing, Siting, and Operation Under Wildfire Risk Using Progressive Hedging

Battery sizing and siting problems are computationally challenging due to the need to make long-term planning decisions that are cognizant of short-term operational decisions. This paper considers sizing, siting, and operating batteries in a power grid to maximize their benefits, including price arbitrage and load shed mitigation, during both normal operations and periods with high wildfire ignition risk. We formulate a multi-scenario optimization problem for long duration battery storage while considering the possibility of load shedding during Public Safety Power Shutoff (PSPS) events that de-energize lines to mitigate severe wildfire ignition risk. To enable a computationally scalable solution of this problem with many scenarios of wildfire risk and power injection variability, we develop a customized temporal decomposition method based on a progressive hedging framework. Extending traditional progressive hedging techniques, we consider coupling in both placement variables across all scenarios and state-of-charge variables at temporal boundaries. This enforces consistency across scenarios while enabling parallel computations despite both spatial and temporal coupling. The proposed decomposition facilitates efficient and scalable modeling of a full year of hourly operational decisions to inform the sizing and siting of batteries. With this decomposition, we model a year of hourly operational decisions to inform optimal battery placement for a 240-bus WECC model in under 70 minutes of wall-clock time.

eess.SY↗

arXiv2024

Exact and Heuristic Approaches for the Stochastic N-k Interdiction in Power Grids

The article introduces the stochastic N-k interdiction problem for power grid operations and planning that aims to identify a subset of k components (out of N components) that maximizes the expected damage, measured in terms of load shed. Uncertainty is modeled through a fixed set of outage scenarios, where each scenario represents a subset of components removed from the grid. We formulate the stochastic N-k interdiction problem as a bi-level optimization problem and propose two algorithmic solutions. The first approach reformulates the bi-level stochastic optimization problem to a single level, mixed-integer linear program (MILP) by dualizing the inner problem and solving the resulting problem directly using a MILP solver to global optimality. The second is a heuristic cutting-plane approach, which is exact under certain assumptions. We compare these approaches in terms of computation time and solution quality using the IEEE-Reliability Test System and present avenues for future research.

math.OC↗

arXiv2021

A K-Nearest Neighbor Heuristic for Real-Time DC Optimal Transmission Switching

While transmission switching is known to reduce power generation costs, the difficulty of solving even DC optimal transmission switching (DCOTS) has prevented optimal transmission switching from becoming commonplace in real-time power systems operation. In this paper, we present a k-nearest neighbors (KNN) heuristic for DCOTS which relies on the insight that, for routine operations on a fixed network, the DCOTS solutions for similar load profiles and generation cost profiles will likely turn off similar sets of lines. We take a data-driven approach and assume that we have DCOTS solutions for many historical instances, which is realistic given that the problem is solved every 5 minutes in practice. Given a new instance, we find a set of "close" instances from the past and return the best of their solutions for the new instance. We present a case study on 7 test networks ranging in size from 118 to 3,375 buses. We compare the proposed heuristic to DCOTS heuristics from the literature, commercial solver heuristics, and a simple greedy local search algorithm. In most cases, we find better quality solutions in less computational time. In addition, the computational time is within the limits imposed by real-time operations, even on larger networks. Last, we present an empirical study of our training data to understand why the heuristic works well.

math.OC↗

arXiv2019

Mape_Maker: A Scenario Creator

We describe algorithms for creating probabilistic scenarios for the situation when the underlying forecast methodology is modeled as being more (or less) accurate than it has been historically. Such scenarios can be used in studies that extend into the future and may need to consider the possibility that forecast technology will improve. Our approach can also be used to generate alternative realizations of renewable energy production that are consistent with historical forecast accuracy, in effect serving as a method for creating families of realistic alternatives -- which are often critical in simulation-based analysis methodologies

stat.AP↗

arXiv2018

Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints

We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage optimization-based bounds tightening, second-order cone relaxations, and piecewise outer approximations to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

math.OC↗

arXiv2017

Scalable Planning for Energy Storage in Energy and Reserve Markets

Energy storage can facilitate the integration of renewable energy resources by providing arbitrage and ancillary services. Jointly optimizing energy and ancillary services in a centralized electricity market reduces the system's operating cost and enhances the profitability of energy storage systems. However, achieving these objectives requires that storage be located and sized properly. We use a bi-level formulation to optimize the location and size of energy storage systems which perform energy arbitrage and provide regulation services. Our model also ensures the profitability of investments in energy storage by enforcing a rate of return constraint. Computational tractability is achieved through the implementation of a primal decomposition and a subgradient-based cutting-plane method. We test the proposed approach on a 240-bus model of the Western Electricity Coordinating Council (WECC) system and analyze the effects of different storage technologies, rate of return requirements, and regulation market policies on ES participation on the optimal storage investment decisions. We also demonstrate that the proposed approach outperforms exact methods in terms of solution quality and computational performance.

math.OC↗

arXiv2016

Contingency-Constrained Unit Commitment With Intervening Time for System Adjustments

The N-1-1 contingency criterion considers the con- secutive loss of two components in a power system, with intervening time for system adjustments. In this paper, we consider the problem of optimizing generation unit commitment (UC) while ensuring N-1-1 security. Due to the coupling of time periods associated with consecutive component losses, the resulting problem is a very large-scale mixed-integer linear optimization model. For efficient solution, we introduce a novel branch-and-cut algorithm using a temporally decomposed bilevel separation oracle. The model and algorithm are assessed using multiple IEEE test systems, and a comprehensive analysis is performed to compare system performances across different contingency criteria. Computational results demonstrate the value of considering intervening time for system adjustments in terms of total cost and system robustness.

math.OC↗

arXiv2016

A Comparison of Policies on the Participation of Storage in U.S. Frequency Regulation Markets

Because energy storage systems have better ramping characteristics than traditional generators, their participation in frequency regulation should facilitate the balancing of load and generation. However, they cannot sustain their output indefinitely. System operators have therefore implemented new frequency regulation policies to take advantage of the fast ramps that energy storage systems can deliver while alleviating the problems associated with their limited energy capacity. This paper contrasts several U.S. policies that directly affect the participation of energy storage systems in frequency regulation and compares the revenues that the owners of such systems might achieve under each policy.

math.OC↗

arXiv2015

Efficient Representation of Uncertainty for Stochastic Economic Dispatch

Stochastic economic dispatch models address uncertainties in forecasts of renewable generation output by considering a finite number of realizations drawn from a stochastic process model, typically via Monte Carlo sampling. Accurate evaluations of expectations or higher-order moments for quantities of interest, e.g., generating cost, can require a prohibitively large number of samples. We propose an alternative to Monte Carlo sampling based on Polynomial Chaos expansions. These representations are based on sparse quadrature methods, and enable accurate propagation of uncertainties in model parameters. We also investigate a method based on Karhunen-Loeve expansions that enables us to efficiently represent uncertainties in renewable energy generation. Considering expected production cost, we demonstrate that the proposed approach can yield several orders of magnitude reduction in computational cost for solving stochastic economic dispatch relative to Monte Carlo sampling, for a given target error threshold.

cs.CE↗

arXiv2014

Contingency-Constrained Unit Commitment with Post-Contingency Corrective Recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an N-k-e reliability criterion. This reliability criterion is a generalization of the well-known $N$-$k$ criterion, and dictates that at least $(1-e_ j)$ fraction of the total system demand must be met following the failures of $k$ or fewer system components. We refer to this problem as the Contingency-Constrained Unit Commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network, which demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.

math.OC↗