Juan M. Morales

University of Malaga | UMA · Department of Applied Mathematics

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 thi...

The task of state estimation faces a major challenge due to the inherent lack of real-time observability, as certain measurements can only be acquired with a delay. As a result, power systems are essentially unobservable in real time, indicating the existence of multiple states that result in identical values for the available measurements. Certain...

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 diffic...

The increased uncertainty due to the integration of stochastic renewable energy sources necessitates solving Optimal Power Flow (OPF) problems repeatedly and for a large number of scenarios. Machine learning methods hold significant potential to reduce the computing time for OPF problems by learning a mapping from varying input loads to decisions,...

Uncertainty in renewable energy generation has the potential to adversely impact the operation of electric power systems. 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 in their assumptions, caus...

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 mak...

Smart metering infrastructures collect data almost continuously in the form of fine-grained long time series. These massive data series often have common daily patterns that are repeated between similar days or seasons and shared among grouped meters. Within this context, we propose an unsupervised method to highlight individuals with abnormal dail...

The optimal power flow (OPF) is one of the fundamental mathematical tools currently used for the operation of power systems. Under certain assumptions, the power flow equations can be linearized using the power transfer distribution factors (PTDF), leading to the so-called DC-OPF. Initially formulated as a deterministic problem, the DC-OPF problem...

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 in...

Some problems in engineering, medicine and economics, among other, consist in finding the best possible decision to achieve a goal while satisfying with certain constraints. Mathematically, these decision-making problems are usually formulated as optimization problems. In this article, we shortly present the most known mathematical programs for cer...

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...

Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Non-deterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal solution if enough time is given, their use in online applications remains a great challenge due to their usu...

Mixed Integer Linear Programs (MILP) are well known to be NP-hard (Nondeterministic Polynomial-time hard) problems in general. Even though pure optimization-based methods, such as constraint generation, are guaranteed to provide an optimal solution if enough time is given, their use in online applications remains a great challenge due to their usua...

The blast wave of machine learning and artificial intelligence has also reached the power systems community, and amid the frenzy of methods and black-box tools that have been left in its wake, it is sometimes difficult to perceive a glimmer of Occam’s razor principle. In this letter, we use the unit commitment problem (UCP), an NP-hard mathematical...

We tackle the resolution of 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 $\epsilon > 0$. We use Sample Average Approximation to produce a data-driven deterministic...

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 constr...

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 mas...

The increase in distributed energy resources and flexible electricity consumers has turned TSO-DSO coordination strategies into a challenging problem. Existing decomposition/decentralized methods apply divide-and-conquer strategies to trim down the computational burden of this complex problem, but rely on access to proprietary information or fail-s...

In this paper, we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically...

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 in...

We consider a two-stage electricity market comprising a forward and a real-time settlement. The former pre-dispatches the power system following a least-cost merit order and facing an uncertain net demand, while the latter copes with the plausible deviations with respect to the forward schedule by making use of power regulation during the actual op...

We consider a two-stage electricity market comprising a forward and a real-time settlement. The former pre-dispatches the power system following a least-cost merit order and facing an uncertain net demand, while the latter copes with the plausible deviations with respect to the forward schedule by making use of power regulation during the actual op...

In recent years, feature selection has become a challenging problem in several machine learning fields, such as classification problems. Support Vector Machine (SVM) is a well-known technique applied in classification tasks. Various methodologies have been proposed in the literature to select the most relevant features in SVM. Unfortunately, all of...

Smart metering infrastructures collect data almost continuously in the form of fine-grained long time series. These massive time series often have common daily patterns that are repeated between similar days or seasons and shared between grouped meters. Within this context, we propose a method to highlight individuals with abnormal daily dependency...

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 b...

The blast wave of machine learning and artificial intelligence has also reached the power systems community, and amid the frenzy of methods and black-box tools that have been left in its wake, it is sometimes difficult to perceive a glimmer of Occam's razor principle. In this letter, we use the unit commitment problem (UCP), an NP-hard mathematical...

This paper considers an aggregator of Electric Vehicles (EVs) who aims to learn the aggregate power of his/her fleet while also participating in the electricity market. The proposed approach is based on a data-driven inverse optimization (IO) method, which is highly nonlinear. To overcome such a caveat, we use a two-step estimation procedure which...

This paper focuses on the day-ahead forecasting of the aggregate power of a pool of smart buildings equipped with thermostatically-controlled loads. We first propose the modeling of the aggregate behavior of its power trajectory by using a geometric approach. Specifically, we assume that the aggregate power is a homothet of a prototype building, wh...

This paper proposes a learning-based approach for the coordination of transmission and distribution operations. Given a series of observations of the nodal price and the power intake at the main substation of a distribution grid, we construct the nonincreasing piecewise constant function that best explains the response of the grid to the electricit...

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 constr...

Most of the prosumers nowadays are constrained to trade only with the supplier under a flat tariff or dynamic time-of-use price signals. This paper models and discusses the cost-saving benefits of flex-ible prosumers as members of energy communities who can exchange electricity among peers and on the wholesale markets through a community manager. A...

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 b...

Due to the new carbon neutral policies, many district heating operators start operating their combined heat and power 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 unce...

In recent years, feature selection has become a challenging problem in several machine learning fields, such as classification problems. Support Vector Machine (SVM) is a well-known technique applied in classification tasks. Various methodologies have been proposed in the literature to select the most relevant features in SVM. Unfortunately, all of...

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 mas...

In this paper we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically t...

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...

This paper focuses on the day-ahead forecasting of the aggregate power of a pool of smart buildings equipped with thermostatically-controlled loads. We first propose the modeling of the aggregate behavior of its power trajectory by using a geometric approach. Specifically, we assume that the aggregate power is a homothet of a prototype building, wh...

The transmission-constrained unit commitment (TC-UC) problem is one of the most relevant problems solved by independent system operators for the daily operation of power systems. Given its computational complexity, this problem is usually not solved to global optimality for real-size power systems. In this paper, we propose a data-driven method tha...

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 imbalanc...

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...

This paper presents a corrigendum to Theorems 2 and 3 in Siddiqui and Gabriel (Netw Spatial Econ 13(2):205–227, 2013). 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 scalari...

This paper presents a new methodology to exploit consumers' flexibility for the provision of ancillary services (AS) in the smart grid era. The proposed framework offers a control-based approach that adopts price signals as the economic driver to modulate consumers' response. In this framework, various system operators broadcast price signals indep...

The oil industry operates in a very uncertain marketplace, where uncertain conditions can engender oil production fluctuations, order cancellation, transportation delays, etc. Uncertainty may arise from several sources and inexorably affect its management by interfering in the associated decision-making, increasing costs and decreasing margins. In...

We pose the aggregator's problem as a bilevel model, where the upper level minimizes the total operation costs of the fleet of EVs, while each lower level minimizes the energy available to each vehicle for transportation given a certain charging plan. Thanks to the totally unimodular character of the constraint matrix in the lower-level problems, t...

This paper considers an aggregator of Electric Vehicles (EVs) who aims to forecast the aggregate power of her fleet. The forecasting approach is based on a data-driven inverse optimization (IO) method, which is highly nonlinear. To overcome such a caveat, we use a two-step estimation procedure which requires to solve two convex programs. Both progr...

The prospective participation of smart buildings in the electricity system is strongly related to the increasing active role of demand-side resources in the electrical grid. In addition, the growing penetration of smart meters and recent advances on home automation technologies will spur the development of new mathematical tools to help optimize th...

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 imbalanc...

The transmission-constrained unit commitment (TC-UC) problem is one of the most relevant problems solved by independent system operators for the daily operation of power systems. Given its computational complexity, this problem is usually not solved to global optimality for real-size power systems. In this paper, we propose a data-driven method tha...

The transmission-constrained unit commitment (TC-UC) problem is one of the most relevant problems solved by independent system operators for the daily operation of power systems. Given its computational complexity, this problem is usually not solved to global optimality for real-size power systems. In this paper, we propose a data-driven method tha...

Demand response (DR) will be an inevitable part of the future power system operation to compensate for stochastic variations of the ever-increasing renewable generation. A solution to achieve DR is to broadcast dynamic prices to customers at the edge of the grid. However, appropriate models are needed to estimate the potential flexibility of differ...

The short-term operation of a power system is usually planned by solving a day-ahead unit commitment problem. Due to historical reasons, the commitment of the power generating units is decided over a time horizon typically consisting of the 24 hourly periods of a day. In this paper, we show that, as a result of the increasing penetration of intermi...

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: i) sample data and ii)a-priori information ab...

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 proposed stochastic dispatch models that co-optimize these services provide the most efficient solution in terms of expec...

The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity conditions are reformulated using additional binary variables and large enough constants (big-Ms) to cast the...

Demand response (DR) will be an inevitable part of the future power system operation to compensate for stochastic variations of the ever-increasing renewable generation. A solution to achieve DR is to broadcast dynamic prices to customers at the edge of the grid. However, appropriate models are needed to estimate the potential flexibility of differ...

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....

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....

Demand flexibility will be an inevitable part of the future power system operation to compensate stochastic variations of ever-increasing renewable generation. One way to achieve demand flexibility is to provide time-varying prices to customers at the edge of the grid. However, appropriate models are needed to estimate the potential flexibility of...

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 i...

The short-term operation of a power system is usually planned by solving a day-ahead unit commitment problem. Due to historical reasons, the commitment of the power generating units is decided over a time horizon typically consisting of the 24 hourly periods of a day. In this paper, we show that, as a result of the increasing penetration of intermi...

The most common procedure to solve a linear bilevel problem in the PES community is, by far, to transform it into an equivalent single-level problem by replacing the lower level with its KKT optimality conditions. Then, the complementarity conditions are reformulated using additional binary variables and large enough constants (big-Ms) to cast the...

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...

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination...

To reduce the computational burden of capacity expansion models, power system operations are commonly accounted for in these models using representative time periods of the planning horizon such as hours, days or weeks. However, the validity of these time-period aggregation approaches to determine the capacity expansion plan of future power systems...

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 proposed stochastic dispatch models that co-optimize these services provide the most efficient solution in terms of expec...

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination...

Many optimization models in engineering are formulated as bilevel problems. Bilevel optimization problems are mathematical programs where a subset of variables is constrained to be an optimal solution of another mathematical program. Due to the lack of optimization software that can directly handle and solve bilevel problems, most existing solution...

This paper approaches the tactical distribution planning in the downstream oil supply chain (DOSC) under uncertain market conditions by using robust optimization (RO). The tactical RO model makes use of general polyhedral uncertainty sets, which encompass the so-called ramping constraints. These restrain the maximum variation in the random paramete...

Spatio-temporal problems exist in many areas of knowledge and disciplines ranging from biology to engineering and physics. However, solution strategies based on classical statistical techniques often fall short due to the large number of parameters that are to be estimated and the huge amount of data that need to be handled. In this paper we apply...

In this paper we seek to optimally operate a retailer that, on one side, aggregates a group of price-responsive loads and on the other, submits block-wise demand bids to the day-ahead and real-time markets. Such a retailer/aggregator needs to tackle uncertainty both in customer behavior and wholesale electricity markets. The goal in our design is t...

We consider the problem of forecasting the aggregate demand of a pool of price-responsive consumers of electricity. The price-response of the aggregation is modeled by an optimization problem that is characterized by a set of marginal utility curves and minimum and maximum power consumption limits. The task of estimating these parameters is address...