In competitive electricity markets, the optimal bid or offer problem of a strategic agent is commonly formulated as a bi-level program and solved as a mathematical program with equilibrium constraints (MPEC). If the lower-level (LL) part of the problem can be well approximated as a convex problem, this approach leads to a global optimum. However, electricity markets are governed by non-convex (partially known) constraints and reward functions of the participating agents. In this paper, an alternative data-driven paradigm, labeled as a mathematical program with neural network constraint (MPNNC), is developed. The method uses a neural network to represent the mapping between the upper-level (agent) decisions and the lower-level (market) outcomes, i.e., it replaces the lower-level problem with a surrogate model. In the presented case studies, the proposed model is used to find the optimal load shedding strategy of a strategic load-serving entity. First, the MPNNC performance is compared to the MPEC approach, both in convex and non-convex environments, showing that the proposed MPNNC achieves similar performance to an ideal MPEC that has perfect knowledge of the simulated market environment. Then, aggregated supply curves from the Belgian spot exchange are used to assess the potential gains of using the developed model in real-life applications.@en

Exposing residential consumers to real-time pricing (RTP) can yield significant efficiency gains, but may also pose challenges due to the inherent complexity. Using an extensive spectrum of temporal granularities for retail electricity pricing, we analyze to what extent these capture the benefits of RTP while concurrently considering the influence of three distribution tariff types in distorting the pricing signal. Via a mixed complementarity model, we consider both operational and investment decisions at retail as well as wholesale levels, accounting for their interdependencies. Our analysis reveals three key findings. Firstly, we find that decreasing temporal granularity of retail electricity prices increases total system cost due to an increasingly inefficient generation mix, however, three-hourly or six-hourly pricing can approximate RTP benefits. Secondly, decreasing temporal granularity of retail electricity prices raises average offtake and lowers average injection prices for consumers due to changes in wholesale market prices as well as consumption patterns of consumers. Thirdly, capacity-based tariffs reduce system offtake peaks and associated price increases by incentivizing battery discharge during peak consumption while volumetric tariffs, over-incentivizing solar PV investments, result in highest offtake prices and injection peaks.

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This study delves into the interplay of residential electricity customers in low voltage distribution systems (LVDS) with market designs that manage local grid constraints. Within this context, residential electricity customers are self-interested agents, exposed to real-time pricing, that can invest in distributed energy resources (DER) and participate in wholesale energy as well as ancillary service market. The study specifically evaluates the trade-off between market design complexity and economic efficiency by examining market designs that employ Static Limits (SLs), Dynamic Operating Envelopes (DOEs), and Distribution Locational Marginal Pricing (DLMP) to ensure network integrity. Using a long-run equilibrium problem the study comprises both operational and investment perspective, considering feedbacks between distribution and higher voltage levels. The analysis reveals three key insights. Firstly, simpler market designs, namely SL-based and DOE-based designs, can approximate the economic efficiency of DLMP-based design, contingent on the network's characteristics. Effective in networks comprised of shorter feeders and larger consumers, the efficacy of simpler designs in approximating DLMP-based design diminishes in networks comprising longer feeders and numerous small consumers. Secondly, consumer preferences play a crucial role in DOE-based design, with consumers having a high willingness-to-pay (WTP) for grid capacity influencing economic efficiency. Thirdly, despite differences in distribution, energy, and DER investment costs, for the majority of consumers, total costs remain comparable across the three designs.

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Flow-based market coupling is a critical element of the electricity market in Europe. Transmission System Operators determine the commercial transmission capacity that can be implicitly traded in a zonal day-ahead market. However, this entails a trade-off: higher commercial transmission capacities increase market efficiency, affecting the electricity market prices, but also increase redispatch costs, affecting the network tariff. The decision on the commercial transmission capacity should optimally balance day-ahead welfare and redispatch costs, but depends on the rules and regulated incentives enforced on the TSOs. A MinRAM criterion, i.e., imposing minima for the commercial transmission capacity, is a one-size-fits-all policy without variation in time and space that unlikely leads to optimal transmission capacity allocation and is hard to tune because regulators have incomplete information. Incentive regulation is an alternative policy instrument promoting welfare-maximizing commercial transmission capacities, robust against information asymmetry. We provide a set of mathematical conditions to properly design an incentive scheme that rewards price convergence and penalizes excessive redispatch costs. Therefore, this paper serves as a stepping stone towards tapping the full potential of cross-border trade in zonal markets for policymakers, regulators, TSOs and market participants.

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Assessing the capability of a distribution grid to accommodate new solar PV installations, namely its hosting capacity (HC), has been a prevalent research topic. Although providing a technical limit to how much additional solar PV can be integrated into a distribution grid without trespassing operational limits, commonly used HC analysis (HCA) does not consider consumer preferences or the economic feasibility of installations. Using a market-based optimal power flow (MBOPF) and HCA, we compare the economic and technical limits of solar PV capacity integration in low voltage distribution systems (LVDS). Findings illustrate that (1) the PV HC computed using grid limits only does not give a complete picture of solar PV capacity integration potential, (2) linear, deterministic power flow is not a foolproof method for assessing the network-secure amount of PV, and (3) the number of technically feasible installation sites supersedes the economically feasible ones. @en

Michiel Kenis is a PhD researcher at the Energy Systems Integration & Modeling Group at the University of Leuven with a doctoral mandate from the Flemish Institute for Technological Research (VITO). He was a visiting researcher at the Massachusetts Institute of Technology. His research focuses on cross-border electricity markets. He holds a MSc in energy engineering and a MSc in policy economics, both from the University of Leuven. Luca Lanzilao completed his MSc degree in mathematical engineering from Politecnico di Torino in 2018. Currently, he is pursuing a PhD at KU Leuven. His research focuses on studying the response of the atmospheric boundary layer to wind farm forcing, with particular emphasis on meso-scale phenomena, such as gravity waves. Kenneth Bruninx received a MSc degree in energy engineering in 2011, a MSc in management, and a PhD degree in mechanical engineering in 2016, all from the University of Leuven (KU Leuven), Belgium. Currently, he is an assistant professor at the Faculty of Technology, Policy, and Management of TU Delft, Netherlands and a research fellow at the Department of Mechanical Engineering, KU Leuven, Belgium. His research interests include market design, policies, and regulation for integrated energy systems. Johan Meyers is a professor of mechanical engineering at KU Leuven since 2009. His research focuses on the simulation of turbulent flows and the atmospheric boundary layer with applications in wind energy. In 2012, he obtained an ERC grant on wind farm control and has been involved in various European projects on wind energy since. He served as the vice president of the European Academy of Wind Energy from 2017 to 2019 and as its president from 2019 to end of 2021. He has been active as an associate editor for Computers & Fluids and is currently an associate editor for Wind Energy Science. Erik Delarue received MSc and PhD degrees in mechanical engineering from the University of Leuven, Belgium, in 2005 and 2009, respectively. He is currently an associate professor with the University of Leuven, TME Branch (energy conversion) and active with EnergyVille. His research focus and expertise are on quantitative tools, supporting an efficient operation of, and transition toward, a low-carbon energy system (mathematical modeling of energy systems). Applications relate to flexibility through energy systems integration, market design, and energy policies.@en

Since 2015 available cross-border transmission capacity is determined using flow-based market coupling (FBMC) in the day-ahead electricity markets of Central Western Europe. This paper empirically estimates the effect of introducing FBMC on day-ahead electricity price convergence and cross-border exchange volumes. In the month following the introduction of FBMC, hourly cross-border exchange volumes increased by 1,700 MWh/h, while prices between countries converged by 10.4 €/MWh. Since then, observed cross-border exchange volumes decreased to 400 MWh/h below their levels before the introduction of FBMC by the end of 2017. However, when controlling for changing market conditions in the years following the introduction of FBMC, we find that FBMC still has a persistent positive effect of around 1,150 MWh/h on hourly cross-border exchange volumes and of 2 €/MWh on price convergence. Finally, we provide suggestive evidence that decreased commercial transmission capacity on critical branches might have contributed to the decline of the benefits over time. This paper is useful for policymakers, regulators, TSOs, and other stakeholders in light of the extension of FBMC to other regions as it is the target methodology for coupling market zones in the European single electricity market.@en

The European Union (EU)'s resource adequacy framework consists of the reliability standard calculation, adequacy assessments and capacity remuneration mechanisms, three pillars which should conspire to deliver a realised adequacy in liberalised markets which is close to that which would be delivered by a central planner minimising total system costs. However, this framework is vulnerable to inconsistencies in the parameters used in each of the three pillars, making the framework internally incoherent and potentially increases system costs. We illustrate and discuss how an inconsistent choice of storage operation can lead to a sub-optimal level of adequacy. However, a consistent storage operation challenges the stated purpose of adequacy assessments in the EU which is to predict adequacy resulting from market operations. @en

Demand Response (DR) programs offer flexibility that is considered to hold significant potential for enhancing power system reliability and promoting the integration of renewable energy sources. Nevertheless, the distributed nature of DR resources presents challenges in developing scalable optimization tools. This paper explores a novel data-driven approach in which DR resources are modeled through their aggregate forecasts using Inverse Optimization. The proposed method utilizes historical price-consumption data to deduce DR price-response behavior via a flexibility curve. The model is assessed within the Belgian single imbalance market context, where a Balance Responsible Party (BRP) employs the inferred flexibility curve to optimize its strategic imbalance positions by managing DR resources through suitable real-time price signals. The accuracy of the estimated flexibility provided by the proposed algorithm is evaluated by comparing it with the XGboost method. The results demonstrate that the model can effectively capture DR behavior and generate profit from providing balancing energy. @en

This paper proposes a multi-level segmented tariff to encourage consumers to provide demand response using a battery. The aim of the tariff is to (i) properly reflect consumers’ contribution to the distribution grid cost while ensuring cost recovery for the distribution network operator and (ii) to provide consumers with a financial incentive to flatten their load profile and avoid peak demand. An optimization problem is formulated to describe how consumers can provide demand response by managing their batteries. To evaluate the effectiveness of the proposed multi-level segmented tariff, four case studies were conducted. The results indicate that the multi-level segmented tariff is the most effective in reducing coincident peak demand, with a reduction of 22%. Policymakers and regulators are recommended to consider multi-level segmented distribution tariffs, as it provides an incentive to consumers to manage their assets to provide demand response.@en

The potential contribution of short term storage technologies such as batteries to resource adequacy is becoming increasingly important in power systems with high penetrations of Variable Renewable Energy Sources (VRES). However, unlike generators, there are multiple ways in which storage may be operated to contribute to resource adequacy. We investigate storage operational strategies which result in the same amount of Expected Energy Not Served (EENS) but differing Loss of Load Expectation (LOLE) to investigate the range of LOLE possible and what factors affect this range. A case study of a Belgium-like power system using an economic dispatch model, typical of state-of-the-art adequacy assessments, results in a LOLE ranging between 2 and 6 h/yr, with the difference decreasing for greater storage duration and increasing for higher installed capacities of storage. Capacity Credits (CCs), which give the relative contribution of a resource to system adequacy, may also be affected by storage operation and the CC of storage is shown to differ by up to 30% depending on the operation and how the CC is calculated. Given these findings, it is recommended that modellers be explicit and transparent about the storage operation they assume in adequacy assessments and capacity credit calculations.@en

The market integration of hybrid off-shore projects, consisting of wind farms and transmission assets connecting different market zones, requires re-examining bidding zone definitions. Policy makers consider separate off-shore bidding zones to optimally integrate off-shore wind farms in power systems. In this paper, we apply Advanced Hybrid Coupling to include off-shore DC transmission lines in flow-based market coupling, and compare different bidding zone configurations. We find that off-shore bidding zones lead to a transfer of welfare: the producers' surplus of off-shore wind farm owners decreases as a result of a lower average price and the congestion rent for TSOs increases. Despite that an off-shore bidding zone signals transmission scarcity better, it impacts the need for support instruments for off-shore wind farms.@en

To represent the cross-border exchange capacities defined by the flow-based approach in the European resource adequacy assessments, transmission system operators currently employ a data-driven methodology that consists of sequential clustering and correlation steps. This methodology entails assumptions and simplifications within both clustering and correlation analyses that may lead to an erroneous representation of import-export capacities in the subsequent adequacy assessments. While the first stage of this methodology can be improved by leveraging a clustering technique tailored to adequacy assessments, the correlation step presents a poor performance in terms of accuracy and scalability. To address the latter challenges, this paper proposes a supervised learning-based model that can enhance the mapping between several relevant explanatory variables and the pre-clustered flow-based domains, leading to a more accurate representation of the flow-based domains in adequacy assessments. Furthermore, the current paper leverages supervised learning to develop a single-step approach that directly maps the selected explanatory variables to the flow-based domains using the K-Nearest Neighbors algorithm, eliminating the clustering step. This circumvents inaccuracies introduced by the significant intra-cluster discrepancies due to numerous shapes and forms of the flow-based domains and enables an enhanced modeling of the flow-based domains in adequacy assessments. In an extensive case study, we demonstrate that the proposed single-step model can significantly improve the accuracy of adequacy assessments, compared to the best-in-class result obtained by the two-step set-up. Moreover, the proposed single-step model involves no hyper-parameters, eliminates the computational complexity of the two-step set-up, and efficiently upscales to integrate the new zones joining to the flow-based market coupling. @en

Kenneth Bruninx is an assistant professor at the Faculty of Technology, Policy & Management of the TU Delft. He is also a research fellow at the Faculty of Engineering Sciences of KU Leuven. His research focuses on energy policy and energy market design for integrated, decarbonized energy systems. He holds a MSc in management, a MSc in energy engineering, and a PhD in mechanical engineering from KU Leuven. Jorge A. Moncada is a postdoctoral research fellow of the Research Foundation-Flanders (FWO) at the KU Leuven and EnergyVille. His research interests focus on understanding the socio-technical dynamics of low-carbon transitions by combining insights from the behavioral sciences and neo-institutional economics with advances in agent-based modeling. He holds a MSc in chemical engineering from the National University of Colombia, a Professional Doctorate in engineering (PDEng) and a PhD in energy system analysis and modeling from TU Delft. Marten Ovaere is an assistant professor at the Department of Economics of Ghent University and is funded by the Research Foundation- Flanders ( FWO). He is also a fellow at the Yale Center for Business and the Environment. His research interests lie in energy and environmental economics, with a focus on electricity markets, carbon pricing, and renewable energy. Marten holds a MSc in economics, a MSc in energy engineering, and a PhD in economics from KU Leuven.@en

This paper formulates an energy community's centralized optimal bidding and scheduling problem as a time-series scenario-driven stochastic optimization model, building on real-life measurement data. In the presented model, a surrogate battery storage system with uncertain state-of-charge (SoC) bounds approximates the portfolio's aggregated flexibility. First, it is emphasized in a stylized analysis that risk-based energy constraints are highly beneficial (compared to chance-constraints) in coordinating distributed assets with unknown costs of constraint violation, as they limit both violation magnitude and probability. The presented research extends state-of-the-art models by implementing a worst-case conditional value at risk (WCVaR) based constraint for the storage SoC bounds. Then, an extensive numerical comparison is conducted to analyze the trade-off between out-of-sample violations and expected objective values, revealing that the proposed WCVaR based constraint shields significantly better against extreme out-of-sample outcomes than the conditional value at risk based equivalent. To bypass the non-trivial task of capturing the underlying time and asset-dependent uncertain processes, real-life measurement data is directly leveraged for both imbalance market uncertainty and load forecast errors. For this purpose, a shape-based clustering method is implemented to capture the input scenarios' temporal characteristics. @en

This paper presents new risk-based constraints for the participation of an energy community in day-ahead and real-time energy markets. Forming communities offers indeed an effective way to manage the risk of the overall portfolio by pooling individual resources and associated uncertainties. However, the diversity of flexible resources and the related userspecific comfort constraints make it difficult to properly represent flexibility requirements and to monetize constraint violations. To address these issues, we propose a new risk-aware probabilistic enforcement of flexibility constraints using the conditional-valueat- risk (CVaR). Next, an extended version of the model is introduced to mitigate the distributional ambiguity faced by the community manager when new sites with limited information are embedded in the portfolio. This is achieved by defining the worstcase CVaR based-constraint (WCVaR-BC) that differentiates the CVaR value among different sub-clusters of clients. Both reformulations are linear, thus allowing to tackle large-scale stochastic problems. The proposed risk-based constraints are then trained and evaluated on real data collected from several industrial sites. Our findings indicate that using the WCVaRBC leads to systematically higher out-of-sample reliability, while decreasing the exposure to extreme outcomes. @en