arXiv subjects

Salvador Pineda

Publications and source records attributed to Salvador Pineda.

At least 19 recordsLinked to original sources

arXiv2026

How long is long enough? Finite-horizon approximation of energy storage scheduling problems

Energy storage scheduling problems, where a storage system is operated to maximize its profit in response to a price signal, are naturally formulated as infinite-horizon optimization problems, since storage systems operate continuously, without a foreseen end to their operation. Such problems can be solved to optimality with a rolling-horizon approach, provided that the planning horizon over which the problem is solved is long enough. Such a horizon is termed a forecast horizon. Despite its importance, the planning horizon is usually chosen arbitrarily for such applications. We introduce an easy-to-check condition that confirms whether a planning horizon is a forecast horizon, and which can be used to derive a bound on suboptimality when it is not the case. In practice, this condition enables practitioners to evaluate whether the planning horizon chosen is sufficient, thereby providing, for the first time, a practical means of evaluating and selecting planning horizons for energy storage scheduling problems. We also derive a lower bound on the minimum forecast horizon. Building on the theoretical results, we develop an algorithm to determine the minimum forecast horizon. It enables the identification, a posteriori, of the shortest planning horizon that guarantees optimal rolling-horizon decisions while avoiding unnecessary forecasting effort and computational cost. Numerical experiments illustrate the practical use of the proposed framework and investigate how storage system characteristics and electricity price patterns influence the minimum forecast horizon.

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arXiv2026

Scenario Reduction for Two-Stage Stochastic Mixed-Integer Programs

Two-stage stochastic mixed-integer programs are important tools for decision-making under uncertainty. Representing the uncertainty with many scenarios, however, can make them challenging to solve. Scenario reduction addresses this by finding a distribution supported on fewer scenarios that still yields similar optimal first-stage decisions. In this paper, we revisit the classical scenario reduction theory based on distances between probability distributions and the optimal mass transportation problem. The transportation problem's cost function captures scenario similarity and is central to the effectiveness of scenario reduction. We then review and compare various transportation cost functions from the literature and propose a new one. Using the Forward Selection Algorithm, we prove that our proposed cost function selects the best possible scenario from a given sample on the first draw with respect to the relative approximation error. To reduce the computational cost of evaluating this cost function, we further propose a hybrid algorithm with a scenario pre-selection phase. We assess solution quality and computational complexity on the two-stage stochastic unit commitment problem for small 24-bus and large 300-bus case studies. With only around five scenarios, the proposed cost function approximates the full-distribution optimum to within roughly 2.1% and 0.4% error for the small and large cases, respectively. In contrast, prevalent cost functions often need 25 scenarios or more to achieve that solution quality. The hybrid algorithm achieves similar solution quality while reducing wall-clock time by a factor of 18 and work (per Gurobi solver) by a factor of 66 on the large case study.

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arXiv2026

Towards time-variant scenario reduction for energy system optimization modeling under uncertainty

Stochastic programming has become a popular tool for supporting decision-making under uncertainty in the long-term planning of energy systems. Existing scenario reduction methods, however, are naive about the long-term temporal nature of scenarios, which limits their efficiency in reducing model size. In this paper, we overcome this inefficiency by proposing a novel time-variant scenario reduction framework that explicitly allows for varying scenario aggregations over time. As a result, scenario probabilities become time-variant, enabling not only the accurate capture of scenario realizations but also their probabilities at the time steps that drive investment decisions. This substantially increases flexibility compared to traditional time-invariant methods, which we demonstrate on a two-stage stochastic generation expansion planning problem with uncertain renewable power production.

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arXiv2026

Data-Boosted Optimization for AC Optimal Power Flow: Interior-Point and Spatial Branching Methods

The AC Optimal Power Flow (AC-OPF) problem is a non-convex, NP-hard optimization task essential for secure and economic power system operation. While interior-point methods are widely used due to their computational efficiency, spatial branching techniques offer global optimality guarantees at significantly higher computational cost. In this work, we propose data-boosted variants of both approaches that leverage historical operating data to enhance performance. Specifically, data are used to guide initialization in interior-point methods and to restrict the search region in spatial branching. This unified perspective enables a systematic assessment of how learning can accelerate both local and global optimization strategies. We conduct an extensive empirical study across networks of varying sizes under both standard conditions and modified configurations designed to induce local optima. Our results show that data-boosted strategies consistently improve convergence and reduce computation times for both approaches. However, spatial branching remains computationally demanding even with data-driven enhancements, while interior-point methods exhibit remarkable robustness, often converging to globally optimal solutions, even in challenging instances with multiple local optima. These findings highlight the practical effectiveness of modern interior-point solvers and suggest that global optimization methods for AC-OPF still face significant scalability challenges, even when augmented with data-driven guidance.

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arXiv2026

The Sweet Spot of Bound Tightening for Topology Optimization

Topology optimization has emerged as a powerful and increasingly relevant strategy for enhancing the flexibility and efficiency of power system operations. However, solving these problems is computationally demanding due to their combinatorial nature and the use of big-M formulations. Optimization-based bound tightening (OBBT) is a well-known strategy to improve the solution of mixed-integer linear programs (MILPs) by computing tighter bounds for continuous variables. Yet, existing OBBT approaches in topology optimization typically relax all switching decisions in the bounding subproblems, leading to excessively loose feasible regions and limited bound improvements. In this work, we propose a topology-aware bound tightening method that uses network structure to determine which switching variables to relax. Through extensive computational experiments on the IEEE 118-bus system, we find that keeping a small subset of switching variables as binary, while relaxing the rest, strikes a sweet spot between the computational effort required to solve the bounding problems and the tightness of the resulting bounds.

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arXiv2025

Scenario Reduction for the Two-Stage Stochastic Unit Commitment Problem

The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but challenges the solution process. One way to overcome this is by using scenario reduction methods, which aim at finding a distribution supported on fewer scenarios, but leading to similar optimal first-stage decisions. In this paper, we recap the classical scenario reduction theory based on the distance of probability distributions and the optimal mass transportation problem. We then review and compare various formulations of the underlying cost function of the latter used in the literature. Using the Forward Selection Algorithm, we show that a specific formulation of the cost function can be proven to select the best possible scenario from a given sample on the first draw with respect to the Relative Approximation Error. We demonstrate this result and compare the quality of the approximation as well as the computational performance of the different cost functions using a modified version of the IEEE RTS 24-Bus System. In many cases, we find that the optimal solution of the two-stage stochastic unit commitment problem with 200 scenarios can be approximated with around 2% scenarios when using this cost function.

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arXiv2025

Unit Commitment with Cost-Oriented Temporal Resolution

Time-adaptive unit commitment (UC) has recently been investigated to reduce the scheduling costs by flexibly varying the temporal resolution, which is usually determined by clustering the net load patterns. However, there exists a misalignment between cost and net load patterns due to the discrete start-up costs and out-of-merit-order dispatch triggered by ramping and other constraints. The optimal time-adaptive resolution cannot be completely captured by clustering-based method. This paper proposes a cost-oriented method to address this misalignment by a novel bilevel optimization approach that is efficiently solved through a heuristic greedy algorithm. The impact of varying temporal resolution on the final scheduling costs are tested, based on which the temporal resolution is heuristically updated, achieving significant cost reduction without increasing the number of temporal periods. Subsequently, an improved discretized Adam optimization method together with offline warm start and online refinement strategy is proposed to efficiently search for the better temporal resolution configuration. Results show that the proposed cost-oriented UC temporal resolution determination method achieves enhanced cost efficiency.

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arXiv2025

An enhanced heuristic framework for solving the Rank Pricing Problem

The Rank Pricing Problem (RPP) is a challenging bilevel optimization problem with binary variables whose objective is to determine the optimal pricing strategy for a set of products to maximize the total benefit, given that customer preferences influence the price for each product. Traditional methods for solving RPP are based on exact approaches which may be computationally expensive. In contrast, this paper presents a novel heuristic approach that takes advantage of the structure of the problem to obtain good solutions. The proposed approach consists of two phases. Firstly, a standard heuristic is applied to get a pricing strategy. In our case, we choose to use the Variable Neighborhood Search (VNS), and the genetic algorithm. Both methodologies are very popular for their effectiveness in solving combinatorial optimization problems. The solution obtained after running these algorithms is improved in a second phase, where four different local searches are applied. Such local searches use the information of the RPP to get better solutions, that is, there is no need to solve new optimization problems. Even though our methodology does not have optimality guarantees, our computational experiments show that it outperforms Mixed Integer Program solvers regarding solution quality and computational burden.

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arXiv2025

A Graph-Based Iterative Strategy for Solving the All-Line Transmission Switching Problem

The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M constants that lead to weak relaxations and significant computational challenges, particularly when all lines are switchable. In this paper, we propose a two-fold approach: first, using graph theory to derive tighter big-M values by solving a relaxed longest path problem; second, introducing an iterative algorithm that incorporates a heuristic version of the switching problem to efficiently generate low-cost feasible solutions, thereby accelerating the search for optimal solutions in the integer optimization solver. Numerical results on the 118-bus network show that the proposed methodology significantly reduces the computational burden compared to conventional approaches.

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arXiv2025

Beyond the Neural Fog: Interpretable Learning for AC Optimal Power Flow

The AC optimal power flow (AC-OPF) problem is essential for power system operations, but its non-convex nature makes it challenging to solve. A widely used simplification is the linearized DC optimal power flow (DC-OPF) problem, which can be solved to global optimality, but whose optimal solution is always infeasible in the original AC-OPF problem. Recently, neural networks (NN) have been introduced for solving the AC-OPF problem at significantly faster computation times. However, these methods necessitate extensive datasets, are difficult to train, and are often viewed as black boxes, leading to resistance from operators who prefer more transparent and interpretable solutions. In this paper, we introduce a novel learning-based approach that merges simplicity and interpretability, providing a bridge between traditional approximation methods and black-box learning techniques. Our approach not only provides transparency for operators but also achieves competitive accuracy. Numerical results across various power networks demonstrate that our method provides accuracy comparable to, and often surpassing, that of neural networks, particularly when training datasets are limited.

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arXiv2024

The Cooperative Maximal Covering Location Problem with ordered partial attractions

The Maximal Covering Location Problem (MCLP) is a classical location problem where a company maximizes the demand covered by placing a given number of facilities, and each demand node is covered if the closest facility is within a predetermined radius. In the cooperative version of the problem (CMCLP), it is assumed that the facilities of the decision maker act cooperatively to increase the customersz' attraction towards the company. In this sense, a demand node is covered if the aggregated partial attractions (or partial coverings) of open facilities exceed a threshold. In this work, we generalize the CMCLP introducing an Ordered Median function (OMf), a function that assigns importance weights to the sorted partial attractions of each customer and then aggregates the weighted attractions to provide the total level of attraction. We name this problem the Ordered Cooperative Maximum Covering Location Problem (OCMCLP). The OMf serves as a means to compute the total attraction of each customer to the company as an aggregation of ordered partial attractions and constitutes a unifying framework for CMCLP models. We introduce a multiperiod stochastic non-linear formulation for the CMCLP with an embedded assignment problem characterizing the ordered cooperative covering. For this model, two exact solution approaches are presented: a MILP reformulation with valid inequalities and an effective approach based on Generalized Benders' cuts. Extensive computational experiments are provided to test our results with randomly generated data and the problem is illustrated with a case study of locating charging stations for electric vehicles in the city of Trois-Rivières, Québec (Canada).

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arXiv2024

Unifying Chance-Constrained and Robust Optimal Power Flow for Resilient Network Operations

Uncertainty in renewable energy generation has the potential to adversely impact the operation of electric networks. Numerous approaches to manage this impact have been proposed, ranging from stochastic and chance-constrained programming to robust optimization. However, these approaches either tend to be conservative or leave the system vulnerable to low probability, high impact uncertainty realizations. To address this issue, we propose a new formulation for stochastic optimal power flow that explicitly distinguishes between "normal operation", in which automatic generation control (AGC) is sufficient to guarantee system security, and "adverse operation", in which the system operator is required to take additional actions, e.g., manual reserve deployment. The new formulation has been compared with the classical ones in a case study on the IEEE-118 and IEEE-300 bus systems. We observe that our consideration of extreme scenarios enables solutions that are more secure than typical chance-constrained formulations, yet less costly than solutions that guarantee robust feasibility with only AGC.

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arXiv2024

Decision-Oriented Learning for Future Power System Decision-Making under Uncertainty

Better forecasts may not lead to better decision-making. To address this challenge, decision-oriented learning (DOL) has been proposed as a new branch of machine learning that replaces traditional statistical loss with a decision loss to form an end-to-end model. Applications of DOL in power systems have been developed in recent years. For renewable-rich power systems, uncertainties propagate through sequential tasks, where traditional statistical-based approaches focus on minimizing statistical errors at intermediate stages but may fail to provide optimal decisions at the final stage. This paper first elaborates on the mismatch between more accurate forecasts and more optimal decisions in the power system caused by statistical-based learning (SBL) and explains how DOL resolves this problem. Secondly, this paper extensively reviews DOL techniques and their applications in power systems while highlighting their pros and cons in relation to SBL. Finally, this paper identifies the challenges to adopt DOL in the energy sector and presents future research directions.

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arXiv2024

Learning-Assisted Optimization for Transmission Switching

The design of new strategies that exploit methods from Machine Learning to facilitate the resolution of challenging and large-scale mathematical optimization problems has recently become an avenue of prolific and promising research. In this paper, we propose a novel learning procedure to assist in the solution of a well-known computationally difficult optimization problem in power systems: The Direct Current Optimal Transmission Switching (DC-OTS) problem. The DC-OTS problem consists in finding the configuration of the power network that results in the cheapest dispatch of the power generating units. With the increasing variability in the operating conditions of power grids, the DC-OTS problem has lately sparked renewed interest, because operational strategies that include topological network changes have proved to be effective and efficient in helping maintain the balance between generation and demand. The DC-OTS problem includes a set of binaries that determine the on/off status of the switchable transmission lines. Therefore, it takes the form of a mixed-integer program, which is NP-hard in general. In this paper, we propose an approach to tackle the DC-OTS problem that leverages known solutions to past instances of the problem to speed up the mixed-integer optimization of a new unseen model. Although our approach does not offer optimality guarantees, a series of numerical experiments run on a real-life power system dataset show that it features a very high success rate in identifying the optimal grid topology (especially when compared to alternative competing heuristics), while rendering remarkable speed-up factors.

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arXiv2024

Tight Big-Ms for Optimal Transmission Switching

This paper addresses the Optimal Transmission Switching (OTS) problem in electricity networks, which aims to find an optimal power grid topology that minimizes system operation costs while satisfying physical and operational constraints. Existing methods typically convert the OTS problem into a Mixed-Integer Linear Program (MILP) using big-M constants. However, the computational performance of these approaches relies significantly on the tightness of these big-Ms. In this paper, we propose an iterative tightening strategy to strengthen the big-Ms by efficiently solving a series of bounding problems that account for the economics of the OTS objective function through an upper-bound on the generating cost. We also discuss how the performance of the proposed tightening strategy is enhanced if reduced line capacities are considered. Using the 118-bus test system we demonstrate that the proposed methodology outperforms existing approaches, offering tighter bounds and significantly reducing the computational burden of the OTS problem.

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arXiv2024

Practical Framework for Problem-Based Learning in an Introductory Circuit Analysis Course

Introductory courses on electric circuits at undergraduate level are usually presented in quite abstract terms, with questions and problems quite far from practical problems. This causes the students have difficulties to apply that theory to solve practical technical problems. On the other hand, electric circuits are everywhere in our lives, so we have plenty of real practical problems. Here we compile a selection of practical contexts suited for implementing Problem Based Learning approach in an introductory course on circuit analysis. And some examples describing the gamification process that uses these problems to build single-player role-playing games that fulfil the course contents and scheduling. The key point of the assessment and how it is related to the progress in the game is also described.

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arXiv2023

Tight and Compact Sample Average Approximation for Joint Chance-constrained Problems with Applications to Optimal Power Flow

In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k-envelopes, can be computed offline using polynomial-time algorithms, and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically-constrained version of the DC Optimal Power Flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system's constraints be lower than some parameter $ε> 0$. In a series of numerical experiments which involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best-performing convex inner approximations currently available in the literature.

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arXiv2023

Prescribing net demand for two-stage electricity generation scheduling

We consider a two-stage generation scheduling problem comprising a forward dispatch and a real-time re-dispatch. The former must be conducted facing an uncertain net demand that includes non-dispatchable electricity consumption and renewable power generation. The latter copes with the plausible deviations with respect to the forward schedule by making use of balancing power during the actual operation of the system. Standard industry practice deals with the uncertain net demand in the forward stage by replacing it with a good estimate of its conditional expectation (usually referred to as a point forecast), so as to minimize the need for balancing power in real time. However, it is well known that the cost structure of a power system is highly asymmetric and dependent on its operating point, with the result that minimizing the amount of power imbalances is not necessarily aligned with minimizing operating costs. In this paper, we propose a bilevel program to construct, from the available historical data, a prescription of the net demand that does account for the power system's cost asymmetry. Furthermore, to accommodate the strong dependence of this cost on the power system's operating point, we use clustering to tailor the proposed prescription to the foreseen net-demand regime. By way of an illustrative example and a more realistic case study based on the European power system, we show that our approach leads to substantial cost savings compared to the customary way of doing.

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