The energy sector is the backbone of economic progress in industrialized countries and the well-being of their peoples. Proof of this is the current energy crisis, where the scarcity of energy resources has triggered a large inflation in the prices of consumables, goods and services. In this context, Operations Research offers powerful tools to do more with less, mitigate the most adverse effects of climate change, and take advantage of digitalization.

This special issue of TOP (co-guest-edited by Juan M. Morales and Salvador Pineda) has brought together contributions from an internationally recognized panel of experts in the use of Operations Research to address the challenges facing the energy sector today.

A succinct description of the works included in this special issue is as follows:

A comprehensive and systematic overview of the mathematical models that have been recently proposed to optimally design pipeline networks in the energy sector is conducted in the work “Recent contributions to the optimal design of pipeline networks in the energy industry using Mathematical Programming” by Diego Cafaro, Demian J. Presser and Ignacio Grossmann. The authors provide a surfeit of mathematical programming formulations and techniques (including decomposition strategies) to cope with the combinatorial and non-linear nature of the network topology and the fluid dynamics.

Among complementarity problems in the energy sector, mathematical problems with equilibrium constraints are particularly difficult to solve due to the non-convexities caused by the reformulation of the lower-level problem using its equivalent optimality conditions. In the manuscript “Solving certain complementarity problems in power markets via convex programming”, Gonzalo Constante-Flores, Antonio J. Conejo, and Santiago Constante-Flores propose a novel algorithm to solve these complementary problems by formulating a convex approximation of the recast problem and solving it iteratively until converge is achieved.

The work “Regression markets and application to energy forecasting” by Pierre Pinson, Liyang Han and Jalal Kazempour advocates an innovative market framework for users of energy forecasts and data providers to engage in data transactions that result in better forecasts for the former and appealing economic compensations for the latter. Their framework is especially tailored to regression tasks, can be used for both batch and online forecasting, and exhibits desirable economic properties.

In the paper titled “Integrating unimodality into distributionally robust optimal power flow”, Li Bowen, Ruiwei Jiang and Johanna L Mathieu introduce a chance-constrained optimal power flow formulation (OPF) that is distributionally robust against the uncertainty in renewable power generation. To significantly reduce the usual conservatism of the so obtained OPF solution, they enforce unimodality in the moment-based ambiguity set they consider to construct their distributionally robust OPF problem. Then they review exact reformulations, approximations, and online algorithms to solve this problem and propose a new offline solution algorithm.

Chance-constrained optimization problems are also the subject of study in the manuscript “Data-driven tuning for chance constrained optimization: Analysis and extensions” by Ashley M. Hou and Line A. Roald. Here the focus is placed on an empirical methodology that relies on statistical hypothesis testing to endow a two-step tuning algorithm to solve joint chance-constrained problems with probabilistic performance guarantees. The authors also use the (joint chance-constrained) optimal power flow problem to motivate their methodology.

The work “Ambiguities and nonmonotonicities under prosumer power: Optimal distributed energy resource investment in a deregulated electricity industry” by Afzal Siddiqui and Sauleh Siddiqui proposes a bilevel model to study the problem of a collective prosumer that is able to invest in distributed energy resources. The lower level mimics the operation of the existing conventional units and the distributed energy resources planned by the upper level as a function of the installed capacity. Conventional units are modeled either considering that they participate under perfect competition or exerting market power. An additional analysis is performed to compute the optimal subsidy that should be offered to investors in distributed energy resources to attain results close to those obtained using a welfare-maximizing approach.

Román Pérez-Santalla, Miguel Carrión, and Carlos Ruiz contributes to this special issue with their work titled “Optimal pricing for electricity retailers based on data-driven consumers’ price-response”. They present a quadratic optimization model to determine the optimal price tariff to be set by a risk-averse electricity retailer. As a salient feature, they consider a sufficiently large smart-meter dataset to characterize the consumers’ behavior. The authors prove the relevance of the proposed model using a realistic case study.

The work “The impact of convexity on expansion planning in low-carbon electricity markets” by Sonja Wogrin, Diego Tejada-Arango, Stefanos Delikaraoglou, Alberto Lamadrid, and Audun Botterud investigates how convexities assumptions affect the output of expansion planning optimization models. Using a throughout analysis, they find that convexity assumptions significantly affect prices and profitability, whereas the obtained optimal technology mix is less sensitive by integrality assumptions. The authors also discuss how this impact can be exacerbated as the electricity generated by renewable energy sources increases.

The work “Day-ahead market bidding taking the balancing power market into account” written by Gro Klæboe, Anders L. Eriksrud, Jørgen Braathen, and Stein-Erik Fleten analyzes the coordinated market bidding strategy of a generation company in the Nordic electricity market. In particular, they focus on investigating the impact of the low liquidity of the Nordic balancing market on the day-ahead bidding decisions. Besides, they open a debate on how to differentiate the impact of coordinated bidding and exercise of market power on the short-term decisions made by generation companies.