arXiv subjects

Juan M. Morales

Publications and source records attributed to Juan M. Morales.

At least 19 recordsLinked to original sources

arXiv2026

Wasserstein Distributionally Robust Optimization with Heterogeneous Data Sources

We study decision problems under uncertainty, where the decision-maker has access to $K$ data sources that carry {\em biased} information about the underlying risk factors. The biases are measured by the mismatch between the risk factor distribution and the $K$ data-generating distributions with respect to an optimal transport (OT) distance. In this situation the decision-maker can exploit the information contained in the biased samples by solving a distributionally robust optimization (DRO) problem, where the ambiguity set is defined as the intersection of $K$ OT neighborhoods, each of which is centered at the empirical distribution on the samples generated by a biased data source. We show that if the decision-maker has a prior belief about the biases, then the out-of-sample performance of the DRO solution can improve with $K$ -- irrespective of the magnitude of the biases. We also show that, under standard convexity assumptions, the proposed DRO problem is computationally tractable if either $K$ or the dimension of the risk factors is kept constant.

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arXiv2025

Linear and Second-order-cone Valid Inequalities for Problems with Storage

Batteries are playing an increasingly central role as distributed energy resources in the shift toward power systems dominated by renewable energy sources. However, existing battery models must invariably rely on complementarity constraints to prevent simultaneous charging and discharging, rendering models of a disjunctive nature and NP-hard. In this paper, we analyze the disjunctive structure of the battery's feasible operational set and uncover a submodularity property in its extreme power trajectories. Leveraging this structure, we propose a systematic approach to derive linear valid inequalities that define facets of the convex hull of the battery's feasible operational set, including a distinguished family that generalizes and dominates existing formulations in the literature. To evaluate the practical utility of these inequalities, we conduct computational experiments on two representative problems whose continuous relaxations frequently result in simultaneous charge and discharge: energy arbitrage under negative prices and set-point tracking. For the latter, we further introduce second-order cone inequalities that remarkably and efficiently reduce simultaneous charging and discharging. Our results highlight the potential of structured relaxations to enhance the tractability and fidelity of battery models in optimization-based energy system tools.

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arXiv2025

Distributionally Fair Peer-to-Peer Electricity Trading

Peer-to-peer energy trading platforms enable direct electricity exchanges between peers who belong to the same energy community. In a semi-decentralized system, a community manager adheres to grid restrictions while optimizing social welfare. However, with no further supervision, some peers can be discriminated against from participating in the electricity trades. To solve this issue, this paper proposes an optimization-based mechanism to enable distributionally fair peer-to-peer electricity trading. For the implementation of our mechanism, peers are grouped by energy poverty level. The proposed model aims to redistribute the electricity trades to minimize the maximum Wasserstein distance among the transaction distributions linked to the groups while limiting the sacrifice level with a predefined parameter. We demonstrate the effectiveness of our proposal using the IEEE 33-bus distribution grid, simulating an energy community with 1600 peers. Results indicate that up to 70.1% of unfairness can be eliminated by using our proposed model, even achieving a full elimination when including a non-profit community photovoltaic plant.

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arXiv2023

Data Valuation from Data-Driven Optimization

With the ongoing investment in data collection and communication technology in power systems, data-driven optimization has been established as a powerful tool for system operators to handle stochastic system states caused by weather- and behavior-dependent resources. However, most methods are ignorant to data quality, which may differ based on measurement and underlying privacy-protection mechanisms. This paper addresses this shortcoming by (i) proposing a practical data quality metric based on Wasserstein distance, (ii) leveraging a novel modification of distributionally robust optimization using information from multiple data sets with heterogeneous quality to valuate data, (iii) applying the proposed optimization framework to an optimal power flow problem, and (iv) showing a direct method to valuate data from the optimal solution. We conduct numerical experiments to analyze and illustrate the proposed model and publish the implementation open-source.

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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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arXiv2022

Distributionally Robust Optimal Power Flow with Contextual Information

In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide a tractable reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.

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arXiv2022

Cost-driven Screening of Network Constraints for the Unit Commitment Problem

In an attempt to speed up the solution of the unit commitment (UC) problem, both machine-learning and optimization-based methods have been proposed to lighten the full UC formulation by removing as many superfluous line-flow constraints as possible. While the elimination strategies based on machine learning are fast and typically delete more constraints, they may be over-optimistic and result in infeasible UC solutions. For their part, optimization-based methods seek to identify redundant constraints in the full UC formulation by exploring the feasibility region of an LP-relaxation. In doing so, these methods only get rid of line-flow constraints whose removal leaves the feasibility region of the original UC problem unchanged. In this paper, we propose a procedure to substantially increase the line-flow constraints that are filtered out by optimization-based methods without jeopardizing their appealing ability of preserving feasibility. Our approach is based on tightening the LP-relaxation that the optimization-based method uses with a valid inequality related to the objective function of the UC problem and hence, of an economic nature. The result is that the so strengthened optimization-based method identifies not only redundant line-flow constraints but also inactive ones, thus leading to more reduced UC formulations.

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arXiv2021

Distributionally robust stochastic programs with side information based on trimmings -- Extended version

We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsic error in the process of inferring conditional information from limited joint data. We show that our approach is computationally as tractable as the standard (without side information) Wasserstein-metric-based DRO and enjoys performance guarantees. Furthermore, our DRO framework can be conveniently used to address data-driven decision-making problems under contaminated samples and naturally produces distributionally robust versions of some local nonparametric predictive methods, such as Nadaraya-Watson kernel regression and $K$-nearest neighbors, which are often used in the context of conditional stochastic optimization. Finally, the theoretical results are illustrated using a single-item newsvendor problem and a portfolio allocation problem with side information.

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arXiv2021

An exact dynamic programming approach to segmented isotonic regression

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on dynamic programming and is built on the basis that said curve-fitting task can be tackled as a shortest-path type of problem. Numerical results on synthetic and realistic data sets reveal that our algorithm is able to provide the globally optimal monotone stepwise curve fit for samples with thousands of data points in less than a few hours. Furthermore, the algorithm gives a certificate on the optimality gap of any incumbent solution it generates. From a practical standpoint, this piece of research is motivated by the roll-out of smart grids and the increasing role played by the small flexible consumption of electricity in the large-scale integration of renewable energy sources into current power systems. Within this context, our algorithm constitutes an useful tool to generate bidding curves for a pool of small flexible consumers to partake in wholesale electricity markets.

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arXiv2021

Partition-based Distributionally Robust Optimization via Optimal Transport with Order Cone Constraints

In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the distribution of the uncertain parameters, which is provided by: (1) sample data and (2) a-priori information on the order among the probabilities that the true data-generating distribution assigns to some regions of its support set. This type of order is enforced by means of order cone constraints and can encode a wide range of information on the shape of the probability distribution of the uncertain parameters such as information related to monotonicity or multi-modality. We seek decisions that are distributionally robust. In a number of practical cases, the resulting distributionally robust optimization (DRO) problem can be reformulated as a finite convex problem where the a-priori information translates into linear constraints. In addition, our method inherits the finite-sample performance guarantees of the Wasserstein-metric-based DRO approach proposed by Mohajerin Esfahani and Kuhn (Math Program 171(1-2):115-166. https://doi.org/10.1007/s10107-017-1172-1, 2018), while generalizing this and other popular DRO approaches. Finally, we have designed numerical experiments to analyze the performance of our approach with the newsvendor problem and the problem of a strategic firm competing à la Cournot in a market.

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arXiv2020

An Efficient Robust Approach to the Day-ahead Operation of an Aggregator of Electric Vehicles

The growing use of electric vehicles (EVs) may hinder their integration into the electricity system as well as their efficient operation due to the intrinsic stochasticity associated with their driving patterns. In this work, we assume a profit-maximizer EV-aggregator who participates in the day-ahead electricity market. The aggregator accounts for the technical aspects of each individual EV and the uncertainty in its driving patterns. We propose a hierarchical optimization approach to represent the decision-making of this aggregator. The upper level models the profit-maximizer aggregator's decisions on the EV-fleet operation, while a series of lower-level problems computes the worst-case EV availability profiles in terms of battery draining and energy exchange with the market. Then, this problem can be equivalently transformed into a mixed-integer linear single-level equivalent given the totally unimodular character of the constraint matrices of the lower-level problems and their convexity. Finally, we thoroughly analyze the benefits of the hierarchical model compared to the results from stochastic and deterministic models.

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arXiv2020

Running on empty: Recharge dynamics from animal movement data

Vital rates such as survival and recruitment have always been important in the study of population and community ecology. At the individual level, physiological processes such as energetics are critical in understanding biomechanics and movement ecology and also scale up to influence food webs and trophic cascades. Although vital rates and population-level characteristics are tied with individual-level animal movement, most statistical models for telemetry data are not equipped to provide inference about these relationships because they lack the explicit, mechanistic connection to physiological dynamics. We present a framework for modeling telemetry data that explicitly includes an aggregated physiological process associated with decision making and movement in heterogeneous environments. Our framework accommodates a wide range of movement and physiological process specifications. We illustrate a specific model formulation in continuous-time to provide direct inference about gains and losses associated with physiological processes based on movement. Our approach can also be extended to accommodate auxiliary data when available. We demonstrate our model to infer mountain lion (in Colorado, USA) and African buffalo (in Kruger National Park, South Africa) recharge dynamics.

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arXiv2020

Feature-driven Improvement of Renewable Energy Forecasting and Trading

Inspired from recent insights into the common ground of machine learning, optimization and decision-making, this paper proposes an easy-to-implement, but effective procedure to enhance both the quality of renewable energy forecasts and the competitive edge of renewable energy producers in electricity markets with a dual-price settlement of imbalances. The quality and economic gains brought by the proposed procedure essentially stem from the utilization of valuable predictors (also known as features) in a data-driven newsvendor model that renders a computationally inexpensive linear program. We illustrate the proposed procedure and numerically assess its benefits on a realistic case study that considers the aggregate wind power production in the Danish DK1 bidding zone as the variable to be predicted and traded. Within this context, our procedure leverages, among others, spatial information in the form of wind power forecasts issued by transmission system operators (TSO) in surrounding bidding zones and publicly available in online platforms. We show that our method is able to improve the quality of the wind power forecast issued by the Danish TSO by several percentage points (when measured in terms of the mean absolute or the root mean square error) and to significantly reduce the balancing costs incurred by the wind power producer.

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arXiv2019

Approximate Bayesian inference for a "steps and turns" continuous-time random walk observed at regular time intervals

The study of animal movement is challenging because it is a process modulated by many factors acting at different spatial and temporal scales. Several models have been proposed which differ primarily in the temporal conceptualization, namely continuous and discrete time formulations. Naturally, animal movement occurs in continuous time but we tend to observe it at fixed time intervals. To account for the temporal mismatch between observations and movement decisions, we used a state-space model where movement decisions (steps and turns) are made in continuous time. The movement process is then observed at regular time intervals. As the likelihood function of this state-space model turned out to be complex to calculate yet simulating data is straightforward, we conduct inference using a few variations of Approximate Bayesian Computation (ABC). We explore the applicability of these methods as a function of the discrepancy between the temporal scale of the observations and that of the movement process in a simulation study. We demonstrate the application of this model to a real trajectory of a sheep that was reconstructed in high resolution using information from magnetometer and GPS devices. Our results suggest that accurate estimates can be obtained when the observations are less than 5 times the average time between changes in movement direction. The state-space model used here allowed us to connect the scales of the observations and movement decisions in an intuitive and easy to interpret way. Our findings underscore the idea that the time scale at which animal movement decisions are made needs to be considered when designing data collection protocols, and that sometimes high-frequency data may not be necessary to have good estimates of certain movement processes.

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arXiv2018

Enabling Active/Passive Electricity Trading in Dual-Price Balancing Markets

In electricity markets with a dual-pricing scheme for balancing energy, controllable production units typically participate in the balancing market as "active" actors by offering regulating energy to the system, while renewable stochastic units are treated as "passive" participants that create imbalances and are subject to less competitive prices. Against this background, we propose an innovative market framework whereby the participant in the balancing market is allowed to act as an active agent (i.e., a provider of regulating energy) in some trading intervals and as a passive agent (i.e., a user of regulating energy) in some others. To illustrate and evaluate the proposed market framework, we consider the case of a virtual power plant (VPP) that trades in a two-settlement electricity market composed of a day-ahead and a dual-price balancing market. We formulate the optimal market offering problem of the VPP as a three-stage stochastic program, where uncertainty is in the day-ahead electricity prices, balancing prices and the power output from the renewable units. Computational experiments show that the VPP expected revenues can increase substantially compared to an active-only or passive-only participation, and in the paper we discuss how the variability of the stochastic sources affects the balancing market participation choice.

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arXiv2018

Setting Reserve Requirements to Approximate the Efficiency of the Stochastic Dispatch

This paper deals with the problem of clearing sequential electricity markets under uncertainty. We consider the European approach, where reserves are traded separately from energy to meet exogenous reserve requirements. Recently pro- posed stochastic dispatch models that co-optimize these services provide the most efficient solution in terms of expected operating costs by computing reserve needs endogenously. However, these models are incompatible with existing market designs. This paper proposes a new method to compute reserve requirements that bring the outcome of sequential markets closer to the stochastic energy and reserves co-optimization in terms of cost efficiency. Our method is based on a stochastic bilevel program that implicitly improves the inter-temporal coordination of energy and reserve markets, but remains compatible with the European market design. We use two standard IEEE reliability test cases to illustrate the benefit of intelligently setting operating reserves in single and multiple reserve control zones.

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arXiv2018

A two-phase stochastic programming approach to biomass supply planning for combined heat and power plants

Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power (CHP) plants using different types of biomass instead of fossil fuel. The contracts with the biomass suppliers are negotiated months in advance and involve many uncertainties from the energy producer's side. The demand for biomass is uncertain at that time, and heat demand and electricity prices vary drastically during the planning period. Furthermore, the optimal operation of combined heat and power plants has to consider the existing synergies between the power and heating systems. We propose a solution method using stochastic optimization to support the biomass supply planning for combined heat and power plants. Our two-phase approach determines mid-term decisions about biomass supply contracts as well as short-term decisions regarding the optimal production of the producer to ensure profitability and feasibility. We present results based on two realistic test cases.

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