arXiv subjects

Steven A. Gabriel

Publications and source records attributed to Steven A. Gabriel.

7 recordsLinked to original sources

arXiv2026

Refinement of Reliability Grid Codes in the Provision of Ancillary Services

Stochastic resources such as wind farms, electric vehicle aggregators, and demand-side assets are increasingly participating as reserve providers in ancillary service markets. To manage delivery uncertainty, system operators impose minimum reliability thresholds on such providers. Energinet, the Danish transmission system operator (TSO), has pioneered this approach through the P90 requirement, requiring stochastic providers to make accepted reserve capacity bids available with at least 90% probability. Yet this threshold is set by regulatory convention, not optimization: no existing framework treats it as a design variable or characterizes the cost-reliability trade-off it governs. This paper closes that gap. We develop a bilevel optimization framework in which the TSO in the upper level sets the reliability threshold endogenously while providers in the lower levels respond through reliability-constrained bidding, with chance constraints reformulated analytically using a Weibull tail distribution. Applied to the Nordic frequency containment reserve for disturbances (FCR-D) market, the cost-optimal threshold lies below P90 in the studied cases, with cost reductions by up to 14.5% relative to the fixed standard. Dynamic hourly thresholds yield a further reduction of up to 2.4%, suggesting efficiency gains may increase in larger and more diverse reserve markets.

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arXiv2024

A New Computational Approach for Solving Linear Bilevel Programs Based on Parameter-Free Disjunctive Decomposition

Linear bilevel programs (linear BLPs) have been widely used in computational mathematics and optimization in several applications. Single-level reformulation for linear BLPs replaces the lower-level linear program with its Karush-Kuhn-Tucker optimality conditions and linearizes the complementary slackness conditions using the big-M technique. Although the approach is straightforward, it requires finding the big-M whose computation is recently shown to be NP-hard. This paper presents a disjunctive-based decomposition algorithm which does not need finding the big-Ms whereas guaranteeing that obtained solution is optimal. Our experience shows promising performance of our algorithm.

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arXiv2024

Renewable Energy Expansion under Taxes and Subsidies: A Transmission Operator's Perspective

This paper investigates the role of a transmission system operator within a carbon footprint reduction strategy incorporating carbon taxes and renewable energy generation subsidies in the decentralised energy market. This is achieved via an optimisation bi-level model in which a welfare-maximizing transmission system operator makes investments in transmission lines at the upper level while considering power market dynamics at the lower level. To account for the deregulated energy market structure, this paper assumes that the generation companies at the lower level make capacity investments as price-takers in perfect competition. Considering alternative transmission infrastructure expansion budgets, carbon emission taxes and monetary incentives for renewable energy generation capacity expansion, the impact of alternative compositions of these factors is analysed against three output factors: the share of renewable energy in the generation mix, total generation amount, and social welfare. The proposed modelling assessment is applied to an illustrative three-node instance and a case study considering a simplified representation of the energy system of the Nordic and Baltic countries. The results highlight that, under certain circumstances, renewable energy generation subsidies may lead to an increase of renewable energy in the generation mix followed by a simultaneous fall in the total generation amount. Nevertheless, when applied together, these three measures demonstrated a positive impact on all output factors within Nordics' and Baltics' energy systems. The experiments additionally suggest that considering the high value of the carbon tax does not have an impact on the output factors while the composition of high values of renewable energy generation subsidies and budget for transmission infrastructure expansion has the strongest effect.

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arXiv2024

A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.

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arXiv2021

A Hybrid Inverse Optimization-Stochastic Programming Framework for Network Protection

Disaster management is a complex problem demanding sophisticated modeling approaches. We propose utilizing a hybrid method involving inverse optimization to parameterize the cost functions for a road network's traffic equilibrium problem and employing a modified version of Fan and Liu (2010)'s two-stage stochastic model to make protection decisions using the information gained from inverse optimization. We demonstrate the framework using two types of cost functions for the traffic equilibrium problem and show that accurate parameterizations of cost functions can change spending on protection decisions in most of our experiments.

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arXiv2021

Using Inverse Optimization to Learn Cost Functions in Generalized Nash Games

As demonstrated by Ratliff et al. (2014), inverse optimization can be used to recover the objective function parameters of players in multi-player Nash games. These games involve the optimization problems of multiple players in which the players can affect each other in their objective functions. In generalized Nash equilibrium problems (GNEPs), a player's set of feasible actions is also impacted by the actions taken by other players in the game; see Facchinei and Kanzow (2010) for more background on this problem. One example of such impact comes in the form of joint/"coupled" constraints as referenced by Rosen (1965), Harker (1991), and Facchinei et al. (2007) which involve other players' variables in the constraints of the feasible region. We extend the framework of Ratliff et al. (2014) to find inverse optimization solutions for the class of GNEPs with joint constraints. The resulting formulation is then applied to a simulated multi-player transportation problem on a road network. Also, we provide some theoretical results related to this transportation problem regarding runtime of the extended framework as well as uniqueness and non-uniqueness of solutions to our simulation experiments. We see that our model recovers parameterizations that produce the same flow patterns as the original parameterizations and that this holds true across multiple networks, different assumptions regarding players' perceived costs, and the majority of restrictive capacity settings and the associated numbers of players. Code for the project can be found at: https://github.com/sallen7/IO_GNEP.

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arXiv2018

A bicriteria perspective on L-Penalty Approaches - A corrigendum to Siddiqui and Gabriel's L-Penalty Approach for Solving MPECs

This paper presents a corrigendum to Theorems 2 and 3 in Siddiqui S, Gabriel S (2013), An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application, Networks and Spatial Economics 13(2):205--227. In brief, we revise the claim that their L-penalty approach yields a solution satisfying complementarity for any positive value of L, in general. This becomes evident when interpreting the L-penalty method as a weighted-sum scalarization of a bicriteria optimization problem. We also elaborate further assumptions under which the L-penalty approach yields a solution satisfying complementarity.

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