Operation of modern power systems depends on high-quality data and forecasts. As the provision of valuable forecasts shifts to independent providers, such as renewable and distributed generators, there is a growing need for forecast-sharing markets. However, existing forecast valuation mechanisms, often inspired by game theory, overlook physical network constraints and the dispersed locations of forecast providers in realistic power systems. This work shows that widely used valuation methods, such as the Shapley value, can yield counterintuitive results when applied to load forecasting in distribution networks. Specifically, due to the location of providers and voltage constraints, less accurate forecasts may appear more valuable than precise ones, while some providers may even be penalised. Moreover, value-oriented mechanisms lack incentive compatibility, as certain providers may systematically misreport load forecasts to receive higher payments. These findings expose the limitations of existing forecast valuation approaches and suggest that incorporating accuracy-based scoring may enhance value-oriented mechanisms.

Long-term investments within the European Union have typically relied on zonal price signals, which are unable to capture locational information. This has created a motivation for resorting to locational capacity auctions in order to steer investments to appropriate locations in the grid. The current work provides an algorithm for clearing bids in the context of capacity auctions for renewable investments, while accounting for nodal network constraints at the scale of the full European power system. The corresponding monolithic optimization problem would comprise approximately 760 million variables and 1.5 billion constraints. The proposed framework models bid selection in renewable auctions as a large scale continuous two stage stochastic capacity expansion problem, subject to constraints on the amount of renewable energy that is integrated into the system. The algorithm is designed in order to tackle large scale systems with a particular emphasis on (i) volumes of renewable targets, (ii) nodal resolution, (iii) high temporal resolution and (iv) uncertainty of climate patterns. The developed algorithm relies on a variety of reformulations and decomposition techniques, and it is specifically designed to exploit high performance computing infrastructure.

Renewable ammonia production is a crucial step towards decarbonizing energy-intensive industries, but its economic viability is hindered by high capital costs and renewable resource availability. We develop a stochastic optimization framework to estimate the levelized cost of ammonia (LCOA) in any location in the world, accounting for the variability of wind and solar energy. The methodology is based on optimizing the portfolio of renewable sources and the capacity of the ammonia production facility while ensuring the three pillars of renewable fuel production: additionality, temporal matching, and geographic correlation. Formulated as a stochastic linear program, the model also accounts for inter-annual climate variability. This framework is applied to assess the economic feasibility of renewable ammonia production in Chile, identifying optimal locations for facilities based on renewable energy availability and cost. Our numerical experiments show that, depending on the discount rate utilized, the LCOA in competitive Chilean locations could range from 270 to 380 USD/tNH3 by 2040, and 250 to 350 USD/tNH3 by 2050, positioning Chile as a competitive player in the global market. Moreover, our results show that a reduction in the CAPEX of ammonia production has a greater impact on the LCOA than an improvement in electricity-to-ammonia efficiency. This underscores the importance of prioritizing the reduction of investment costs.

Power grids are enormous and complex engineering systems. Electricity produced from generators is transferred through power networks to loads that consume it. Like many other assets, electricity trading can be organized via markets, driving the operation of power grids. While the general principles for market design can support the foundation of electricity markets, many particular aspects complement such basis for accounting for intricate engineering requirements and physical laws of electric power flows. Designing electricity markets is not that obvious, and a fact is the variety of electricity market designs across the globe. The general principles for designing markets for economical operation and pricing of electricity are introduced here.

The optimal transmission switching problem (OTSP) is an NP-hard problem of changing the topology of a power grid to obtain an improved dispatch by controlling the operational status of the transmission lines. Exact solution techniques based on mixed-integer programming (MIP) like branch-and-bound (B & B) guarantee identifying global optimal solutions if they exist but are potentially intractable in realistic power grids. Heuristic methods, on the other hand, can provide tractable solution approaches but potentially cut off optimal solutions. Heuristics are implemented along with B & B in modern MIP solvers to take advantage of both approaches. This paper proposes solving the full OTSP formulation alongside parallel heuristics that generate good candidate solutions to speed up conventional B & B algorithms. The innovative aspect of this work is a new asynchronous parallel algorithmic architecture and the exploitation of domain-specific knowledge in parallel heuristics. Heuristics generate solutions asynchronously to be injected into the full OTSP solution procedure during run time. Our method is tested on 14 instances of the pglib-opf library: The largest problem consists of 13659 buses and 20467 branches. Our results show good performance for large problem instances, with consistent improvements over off-the-shelf solver performance.

The European Union (EU) has a natural gas storing capacity of approximately 1100 TWh in underground reservoirs. This energy capacity, in the form of natural gas, is one million times larger than the world's largest electricity battery project. Underground gas storage (UGS) facilities offer large-scale, long-duration energy storage solutions that aid in balancing supply and demand, stabilizing gas and electricity prices, and enhancing the overall EU energy security. Energy modelers frequently rely on simplified model formulations for UGS facilities, which are akin to electrochemical battery models. In this paper, we emphasize the importance of employing appropriate UGS formulations in energy system models. First, we introduce the primary characteristics of UGS. Subsequently, we develop an optimization problem to estimate the optimal set of linear equations for adjusting the non-convex operating capacity limits of UGS. We present numerical results for various approximations and specific EU countries with UGS facilities. The findings reveal that generic battery-like models are insufficiently representative of gas storage facilities, with errors as large as 90% of the total withdrawal capacity. However, a simple two-segment piecewise linear approximation results in negligible or very low approximation errors.

The catastrophic blackout events and ever-increasing penetration of renewable power generation highlight an advanced restoration strategy to effectively and reliably employ renewable power generation to contribute to renewable power system restoration. This paper reviews the research advances of power system restoration involving large renewable peneration, and the methods of handling renewable power uncertainty during restoration are also summarized. First, the transmission system restoration processes are divided into three sequential stages: a) black-start, b) network reconfiguration and c) load restoration, and the research advances of these three restoration stages involving large renewable generation are presented. Then, the distribution system restoration assisted by multiple flexible resources, such as renewable distributed generators, remotely-controlled switches, energy storage systems, and soft open points, are reviewed with emerging techniques, including microgrids, multi-agent systems, repair crews, and mobile power sources. Furthermore, with the growing activeness and flexibility of the distribution system, the coordinated transmission and distribution system restoration and their information interactions are also discussed. Finally, for practical applications, the laboratory validations of restoration strategies using realistic power grid data, real-world restoration strategies, decision support systems, and field tests of black-start procedures are introduced to complete this literature review. Effectively deploying renewable power sources can significantly improve the power system restoration efficiency, and their inherent uncertainty should be carefully handled. Moreover, promising research trends are provided to improve the power system restoration with large renewable penetration.

Electric power systems and the companies and customers that interact with them are experiencing increasing levels of uncertainty due to factors such as renewable energy generation, market liberalization, and climate change. This raises the important question of how to make optimal decisions under uncertainty. This paper aims to provide an overview of existing methods for modeling and optimization of problems affected by uncertainty, targeted at researchers with a familiarity with power systems and optimization. We also review some important applications of optimization under uncertainty in power systems and provide an outlook to future directions of research.

In this paper the potential benefits t hat energy storage systems (ESS) can bring to distribution networks are analyzed. We propose an optimization model for the strategic allocation of ESS within a distribution system with photovoltaic (PV) generation, with the main focus on maximizing value benefits. A D istFlow formulation i s used for modeling t he AC power flow. The ESS model is based on a generic formulation that captures the charging and discharging modes' complementarity. The resulting optimization model is stated as a mixed-integer quadratically constrained program (MIQCP) problem. We evaluate the model on a modified 33-bus IEEE network considering renewable uncertainties. The obtained results show that ESS can offer various important benefits such a so verall system cost reduction, energy arbitrage, voltage profile improvement, and congestion management in distribution grids. These findings highlight the significance of utilizing ESS technologies to provide aggregated value through various grid services, extending beyond energy arbitrage alone.

In this letter, two formulations of the linear convex hull of an energy storage system (ESS) are presented. The convex hulls are constructed from the standard parameters of an ESS, namely the charging and discharging power rate capacities, charging and discharging efficiencies, and energy capacity limits. These formulations provide the tightest linear approximation of an ESS model that takes into account the complementarity of charging and discharging modes.

Results of four-year experimental trials of a Gaming Lab for understanding power markets are presented in here. The main goal of Gaming Lab was to illustrate the effects of strategic behavior on electricity markets, recognize pricing mechanisms and analyse the issues that emerge from competitive electricity markets. Evidences for reproducibility of obtained results of experimental gaming are provided. Different scenarios for conducting the developed series of games are described and compared. We finally provide recommendations on Gaming Lab implementation and future developments that could enhance the Gaming Lab.

Mathematical models are just models.The desire to describe battery energy storage system (BESS) operation using computationally tractable model formulations has motivated a long-standing discussion in both the scientific and industrial communities.Linear BESS models are the most widely used so far.However, finding suitable linear BESS models has been controversial.This paper focuses on the description of linear BESS models.Four linear BESS formulations are presented, among the most popularly used.A new formulation is also proposed.The 5 BESS models are tested in 100 random BESS and 1.450 random samples of daily profiles of renewable generation.Two classical problems of power systems, namely, the set-point tracking problem and the transmission expansion planning problem, are selected for numerical analysis.Five thousand simulations are used to draw a better interpretation of each linear formulation presented and showcase specific challenges of BESS models.Practical recommendations are provided based on the findings.

Stochastic programming has been a crucial mathematical framework for many operational and planning problems in power systems. The increase of renewable generation sources in many countries has accelerated academia and practitioners’ interest in such a tool. Limitations on solving stochastic programs to optimality are well known. By far, the most common solution strategies have been focused on representing or approximating uncertainty by a finite and tractable set of scenarios. In general, no a priori optimality bound is guaranteed, or if so, it is impractical for use in real applications. We leverage recent advances in adaptive partition methods for dealing with a class of two-stage stochastic programming problems. In particular, we introduce a recently proposed generalized adaptive partition method (GAPM) that guarantees $\epsilon$-optimal solutions. We provide insights on the GAPM and propose two new algorithms. We run extensive numerical experiments for the stochastic unit commitment problem on systems of 24 and 118 buses. More than 30 indicators were benchmarked. The proposed algorithms showed better computational performance than the existing adaptive partition method in many of those indicators. Finally, conclusions and recommendations are drawn on the basis of numerical experiments.

With climate change, we have been witnessing more frequent extreme weather events causing increasingly common large-scale power outages. It is essential and urgent to improve power system resilience, which also substantially impacts the resilience of dependent infrastructures, such as water and health systems. This work investigates the enhancement of power grid resilience using proactive network-constrained economic dispatch (NCED) strategies. An extreme weather event is modeled as an attacker interdicting a selected set of transmission lines to cause overloading of remaining lines, which potentially leads to cascading failures. We define a set of resilience metrics, with the first one being a weighted number of overloaded lines immediately after the attack to capture the potential cascading chain effect, the second one predicting the worst-case value of the first metric to provide a forward-looking evaluation, and the last one assessing whether each line can be overloaded in the worst case to supply more granular awareness. We also propose a defender–attacker–defender NCED model solved by a column-and-constraint generation algorithm to optimize the defined metrics. The model can generate strategies that (1) enhances resilience without additional NCED cost; (2) further enhances resilience with a budgeted extra NCED cost; and (3) achieves a moving target defense scheme shifting the grid’s vulnerable part(s). The associated price of resilience is specifically evaluated. Results on standard test systems demonstrate the proposed methods’ effectiveness. Overall, our methods and results provide insights on the establishment of social, economic and environmental resilience by contributing to the resolution of resilience-related power and energy issues.

The need for flexible networks is an emerging challenge for power system operators (SO). The use of additional support, such as demand response (DR), must be quantified in order to offer a reliable service, given that this information is vital for demand aggregators. Thermostatically controlled loads (TCLs) are one of the most promising options among DR solutions; due to TCLs' thermal characteristics their power may be increased or reduced accounting as ancillary services. However, TCLs tend to synchronize their behavior, which may affect their capacity to provide flexibility. This paper proposes a method for quantifying TCLs' power flexibility, taking into account different scenarios, types of controllers and loads. Two control methods are compared, and a modified control algorithm is applied to the controllers under analysis to avoid TCL synchronization. The analysis was validated by simultaneously using real demand data from the UK National Grid and temperature data for the same region and time frame.

Active distribution networks (ADN) have grown considerably in recent years. Distributed energy resources present in ADNs can provide flexibility to the power system through TSO/DSO coordination, i.e., at the interface node (feeder) between the transmission and distribution network. This paper addresses the issue of calculating multi-period flexibility regions of the ADNs. Flexibility regions are tightly dependent between periods and conditioned on the actual deployment of such flexibilities in real-time. The existing state-of-the-art has not provided a robust methodology for building multi-period flexible regions. We present a new mathematical framework based on a non-iterative formulation that considers the multi-period flexibility boundary points in a single optimization problem. The proposed methodology is evaluated on IEEE standard test networks and compared with the most widely used methods in the literature.

The optimal transmission switching problem (OTSP) is an NP-hard problem of changing the topology of a power grid to obtain an improved dispatch by controlling the operational status of the transmission lines. Exact solution techniques based on mixed-integer programming (MIP) like branch-and-bound (B&B) guarantee identifying global optimal solutions if they exist but are potentially intractable in realistic power grids. Heuristic methods, on the other hand, can provide tractable solution approaches but potentially cut off optimal solutions. Heuristics are implemented along with B&B in modern MIP solvers to take advantage of both approaches. This paper proposes solving the full OTSP formulation alongside parallel heuristics that generate good candidate solutions to speed up conventional B&B algorithms. The innovative aspect of this work is a new asynchronous parallel algorithmic architecture and the exploitation of domain-specific knowledge in parallel heuristics. Heuristics generate solutions asynchronously to be injected into the full OTSP solution procedure during run time. Our method is tested on 14 instances of the pglib-opf library: The largest problem consists of 13659 buses and 20467 branches. Our results show good performance for large problem instances, with consistent improvements over off-the-shelf solver performance.

This work discusses the importance of a holistic data model for power systems modelling and analysis. We analyse the current landscape of methods, tools available and data required. We present a data model for simulations and analyses and outline how it could be extended to accommodate other already existing tools. For power systems modelling, we use the Julia Programming Language and its highly capable ecosystem for optimization. Regarding analyses, we conduct tests using an easily dèployable web-service based on Spring Boot and PostgreSQL. A standardised data format is used for data exchange. Visualization is facilitated by JavaScript, Leaflet and OpenStreetMap.

Worldwide commitments to net zero greenhouse emissions have accelerated investments in renewable energy resources. The requirements for operating and planning power systems are becoming stringent because of the need to take into account the uncertainty associated with renewable generation. Several modeling frameworks that consider the inherent uncertainty in the operation and planning of the power system have been extensively studied. Stochastic optimization has been the most popular approach among these frameworks due to its intuitive representation, especially when formulated using discrete probabilistic scenarios to represent the random variables. Although many scenarios representing all possible uncertain operating conditions would be needed to accurate evaluate stochastic operation and planning models, the size of the scenario set impacts computational complexity, posing a significant tradeoff between uncertainty detail representation and computational tractability. During the last decade, a large body of research has focused on developing new scenario aggregation methods to derive reduced scenario sets that show properties similar to the original scenario set while decreasing computational burden. This review provides an up-to-date, comprehensive classification and analysis of the literature related to scenario aggregation methods for addressing power system optimization problems. First, we present a general framework and the aggregation methodologies. Then, the main studies related to temporal and spatial scenario aggregation are described, followed by a bibliometric analysis of the main publication sources, authors, and application problems. Finally, we provide a numerical analysis and discuss 16 aggregation methods for the transmission expansion planning problem. Finally, recommendations, opportunities, and conclusions are discussed.

Power system network topology reconfiguration can reduce the cost of relieving network congestion. In this work, N-1 Security-Constrained Optimal Power Flow that utilizes substation reconfiguration and busbar splitting is introduced. A column-and-constraint generation decomposition technique is proposed to accelerate the solution process. The proposed models are tested on 5-bus, 39-bus, and 118-bus systems. Results show that post-contingency busbar splitting is not only useful in reducing the operating cost, but it can be crucial to improving system security.