The power consumption flexibility of distributed energy resources (DERs) must be aggregated to enable effective interaction with power systems. However, model heterogeneity, geographical dispersion, and the large number pose significant challenges to aggregation. This paper first models DER flexibility by explicitly incorporating heterogeneity in both state variables and available time periods, represented through polytopes of heterogeneous dimensions. The aggregation of DERs is then formulated as a standard projection maximal inner approximation (MIA) problem. To efficiently and accurately solve this problem, a novel linear programming (LP)-based algorithm is developed. Furthermore, a hierarchical framework is introduced to enable large-scale aggregation, within which a Minkowski-closed family is proven, allowing accurate and efficient secondary aggregation through vector addition. In addition, generalized operating envelopes (OEs) are proposed for distribution system operators (DSOs) to establish and communicate network constraints, enabling integration into the aggregation process without disclosing sensitive network information. Numerical experiments validate the proposed formulations and demonstrate superior accuracy and scalability of the proposed method while maintaining high computational efficiency.

Contract for Difference (CfD) have been widely adopted across various countries and regions. CfD not only enable market participants to hedge against risks in the electricity spot market but also be used by government to support the development of renewable energy and new technologies, as well as to alleviate many regulatory and external issues such as market power. This review focuses on the mechanism and practice of CfD and the analysis of key issues. Currently, the excess profit recovery mechanism embedded in government authorized CfD and the capital repatriation it generates has played a crucial role in alleviating the surging electricity costs during the electricity price crisis caused by the Russia-Ukraine conflict. Moreover, in the final draft of the European Union’s electricity market reform, government authorized CfD have become one of the mandatory measures to support the development of renewable energy. But CfD exhibit certain drawbacks. Such as traditional CfD often lead to a “produce-and-forget” effect, as it suppresses spot market price signals. Consequently, power plants may prioritize maximizing production rather than responding to market price signals, leading to misaligned incentive. Furthermore, CfD can induce strategic bidding behavior of power generators in the intraday or balancing markets, distorting the intraday and real-time market. This paper introduces the fundamental concepts, applications, key parameter design, and auction processes of CfD. Furthermore, it analyzes the critical issues associated with traditional CfD, aiming to provide valuable references for the future development and construction of CfD.

In many countries declining demand in energy-intensive industries (EIIs) such as cement, steel and aluminium is leading to industrial overcapacity. Although industrial overcapacity is traditionally envisioned as problematic and resource wasteful, it could unlock EIIs' flexibility in electricity use. Here using China's aluminium smelting industry as a case study, we evaluate the system-level cost-benefit of retaining EII overcapacity for flexible electricity use in decarbonized energy systems. We find that overcapacity can enable aluminium smelters to adopt a seasonal operation paradigm, ceasing production during winter load peaks that are exacerbated by heating electrification and renewable seasonality. This seasonal operation paradigm could reduce the investment and operational costs of China's decarbonized electricity system by 23-32 billion CNY per year (11-15% of the aluminium smelting industry's product value), sufficient to offset the increased smelter maintenance and product storage costs associated with overcapacity. It may also create labour complementarities between the aluminium and thermal power sectors.

Probabilistic intraday electricity price forecasting is becoming increasingly important for short-term power-system operation. With increasing renewable generation, demand-side flexibility, and storage assets, market participants need to adjust their positions under uncertainty closer to delivery. Continuous intraday (CID) markets support this process by providing updated price signals, helping participants manage imbalance exposure and operational risk. Unlike auction markets, CID trading in many jurisdictions is characterized by the continuous posting of buy and sell orders. This dynamic orderbook microstructure of price formation presents special challenges for price forecasting. Conventional methods represent the orderbook via domain features aggregated from buy and sell trades, or by treating it as a multivariate time series, but such representations neglect the full buy–sell interaction structure of the orderbook. This research therefore develops OrderFusion, an end-to-end and parameter-efficient probabilistic forecasting model that learns an interaction-aware representation of buy–sell dynamics. Furthermore, as quantile crossing is often a problem in probabilistic forecasting, this approach hierarchically estimates the quantiles with non-crossing constraints. Extensive experiments on CID price indices across high- and low-liquidity European markets demonstrate consistent improvements over conventional baselines, and ablation studies highlight the contributions of the main components. The methodology is available at: https://runyao-yu.github.io/OrderFusion/.

The resource-task network (RTN) model has been widely applied to represent the technical constraints of complex industrial processes (IPs) such as steel-making, providing the basis for industrial demand response. However, the legacy RTN model contains numerous binary variables and applies different formulations for non-flexible and flexible processes, restricting its computational efficiency and applicability. To systematically improve the computational performance of IP models, we propose continuous RTN model (cRTN), a novel modeling approach that uses continuous variables to represent production tasks and progresses, which are then integrated into unified as well as computationally favorable formulations for the technical constraints in discrete IPs, including resource balance, task execution, waiting time limits, and production targets. Compared to the legacy models, cRTN features fewer binary variables, shorter solving time, and better scalability while maintaining the same accuracy. Numerical tests based on a steel plant demonstrate that cRTN is in typical cases 10 times faster than legacy models and remains tractable with increasing batch sizes, which in legacy models leads to larger problem scales and infeasible solving time. cRTN also achieves a reduction in energy costs by resolving the issue of rounding errors reported in legacy models.

Intermittent renewable energy has rapidly developed worldwide and has been required to participate in the market. Since renewable energy's fluctuating and uncertain nature will bring significant risks to the electricity spot market, the medium & long-term electricity market is receiving broad attention. Generation companies (GenCos) may distort market prices through strategic behaviors in a two-stage market composed of the medium & long-term market and the spot market. This paper establishes a mathematical problem with an equilibrium constraints (MPEC) model to simulate the strategic behaviors of GenCos in the two-stage market. The nonlinear model is linearized through the strong duality theorem and the binary expansion approach. Finally, numerical analysis shows the model's effectiveness in simulating the behaviors of strategic GenCo.

In power systems with high proportion of variable renewable energy, the scarcity of inertia and primary frequency response (IPFR) becomes a critical issue. This evolution necessitates the emergence of corresponding markets. The increasing variety of markets and the diversity of market participants have led to more complex bidding behaviors than before, which need be thoroughly studied. This paper proposes a bi-level model to analyze the bidding behaviors of a renewable-storage system (RSS) acting as a price maker in multiple markets. The nonlinear relationship between IPFR and system frequency is modeled. To depict the characteristics of IPFR and future markets, the unit commitment (UC) process is embedded. To address the nonconvexity caused by the UC process in the proposed bi-level model, a solution approach based on penalty function and dual theory is presented. The proposed model and its solution method are applied to a case study based on the IEEE30-bus system and historical operational data from the California Independent System Operator. The case study results illustrate that the proposed model can effectively characterize the complex bidding behaviors of RSS in multiple markets and validate the efficacy of the solution method.

Virtual power plants (VPPs) can aggregate distributed energy resources (DERs) to provide ancillary services for power systems, creating new profit opportunities. Ancillary services such as secondary frequency regulation require providers to have sufficient response capability to follow rapidly changing control commands. If overlooking the response requirement, the VPP will not be able to accurately measure its regulation capability, reducing its earnings in performance-based markets or risking disqualification. This paper integrates the requirement for fast-response capability into the operational framework of VPPs providing ancillary services. We leverage historical control commands to formulate chance constraints in the bidding model, mandating that the VPP’s fast-response capability meets the requirement of ancillary services with a specified probability. Case studies verify that considering fast-response capabilities can enhance VPP operation.

Assessing building demand response (DR) potentials typically involves modeling building thermodynamics and conducting simulations. However, this approach requires detailed parameters or operational data for each building and becomes impractical at the provincial and national levels. Here, we propose DPAAS, a data-driven building DR potential assessment frame-work that combines artificial intelligence (AI) technology with advanced building energy simulation techniques. The framework envisions using readily available multimodal data sources to assess DR potential at scale, with machine learning models at its core to map building parameters to DR potentials. To validate the critical machine learning component of this framework, we conduct numerical tests using the Comstock dataset. Results show that the ML models can predict DR potentials with median errors of less than 10% for load shedding and 14% for load shifting, demonstrating the feasibility of the framework's core mechanism. This validation of the ML approach, combined with established methods for building data collection and processing, suggests that DPAAS could potentially enable cost-effective DR potential assessment at scale.

Battery characteristics are highly thermal-sensitive, making the battery temperature one of the crucial parameters that affect battery energy storage system (BESS) cost. This paper introduces a coordinated energy-temperature management for BESS that allows adjustable BESS temperature and accounts for the temperature effects on battery power capability and degradation. These effects are characterized as thermal sensitivities and are simplified for incorporation into optimization problems. The proposed management optimizes battery energy and temperature simultaneously and minimizes the total thermal-sensitive cost of BESS, which includes energy arbitrage revenue, heating and cooling energy cost, and battery degradation cost. To handle the bilinear and polynomial terms introduced by thermal sensitivities, an enhanced piecewise McCormick relaxation based on percentile partitioning is proposed to convert the optimization into a mixed-integer quadratic problem. The proposed management is validated to improve BESS income by adaptively controlling the energy and temperature under different climate conditions.

Exploring the potential of electrolytic aluminum loads (EALs) for demand response helps address the challenges of integrating renewable energy into power systems. However, most existing EAL models fail to consider thermal balance constraints and cost characteristics comprehensively. Recent studies attempting to address this issue still face difficulties in balancing modeling accuracy and computational efficiency, limiting their application in large-scale scheduling scenarios. This paper proposes an improved EAL modeling method that introduces more accurate thermal balance constraints by considering the dynamic variations in reaction energy and heat dissipation. We employ piecewise linearization and time decoupling techniques to handle nonlinear constraints and discontinuous cost functions. Case studies demonstrate that the improved model yields more reliable operation strategies by maintaining electrolyte temperatures within safe ranges during prolonged power regulation. By embedding EAL’s complex energy-material-temperature conversion mechanisms into a computationally efficient optimization framework, this work helps EALs better participate in real-world grid interaction scenarios.

Virtual power plants (VPPs) are important for coordinating the rapidly growing portfolios of distributed energy resources (DERs) and enabling them to deliver multiple services to higher-level electricity markets. However, profit allocation procedures for VPP participants become increasingly difficult to design in an incentive-compatible manner, owing to the increased market power of DERs within each VPP relative to their direct participation in wholesale markets. In this paper, we introduce translation symmetry in electricity markets and apply it to VPP aggregation of DERs for market participation to design an incentive-compatible profit allocation method. Under the stated assumptions, we prove that this translation symmetry induces an inductive property: once incentive compatibility holds at an upper level, it propagates to the internal settlements between the VPP and its constituent DERs, thereby supporting incentive compatibility throughout the hierarchy. We further show that service prices are invariant across levels, which helps preserve competitive conditions and enables transparent value assessment. Theoretical analysis and case studies illustrate how this translation-symmetry-based approach can enable incentive-compatible profit allocation when aggregating DERs to provide multiple services.

In order to ensure generation capacity adequacy under the power market environment, remuneration mechanisms have been introduced to compensate grid-supporting resources and allocate the cost to electricity consumers. However, the current remuneration mechanism takes rough allocation approaches that result in unnecessary loss of social welfare. This work proposes a novel cost allocation mechanism to cope with the deadweight loss in social welfare. Based on the theory of Ramsey Pricing, cost recovery target is described as a constraint and embedded in the power market clearing model. To address the challenges of direct application of Ramsey Pricing in power market, the proposed model is reformulated as a bilevel optimization problem and then reduced and linearized to a single layer mixed integer linear programming model. Case study is conducted to verify the validity of the proposed framework, and the results show that the proposed mechanism can achieve the allocation goal precisely, while inducing less deadweight loss compared with the traditional average allocation method and peak load contribution method.

Negative electricity prices have become increasingly prevalent with the growing penetration of intermittent renewable energy sources worldwide. Although it is widely thought that the negative prices are primarily driven by intermittent renewable energies, the bidding decision theory behind this phenomenon remains underexplored. This paper seeks to illuminate the bidding theory of intermittent renewables under negative electricity prices through not only a theoretical model but also an empirical analysis of its real-world counterpart. First, we propose a comprehensive intermittent renewable bidding decision model considering both forward contract and spot market, as well as income from both the energy market and green energy incentive, which significantly influence bidding behavior under negative price conditions. Next, we develop a data-driven approach to estimate the model’s embedded parameters using publicly available market data, enabling direct comparison with real-world counterparts. Finally, on the basis of the proposed model, we analyze the actual bid records in comparison to the optimal bidding decisions from three perspectives: strategy, behavior, and profit. Empirical results show that the proposed model can explain 80% of the bidding strategies employed by intermittent renewable power plants in a real-world market, including suboptimal strategies. Furthermore, some empirical evidence can help understand the intrinsic relationship between bidding rationality and negative price severity.

Peer-to-peer (P2P) trading is seen as a viable solution to handle the growing number of distributed energy resources in distribution networks. However, when dealing with large-scale consumers, there are several challenges that must be addressed. One of these challenges is limited communication capabilities. Additionally, prosumers may have specific preferences when it comes to trading. Both can result in serious asynchrony in peer-to-peer trading, potentially impacting the effectiveness of negotiations and hindering convergence before the market closes. This paper introduces a connection-aware P2P trading algorithm designed for extensive prosumer trading. The algorithm facilitates asynchronous trading while respecting prosumer's autonomy in trading peer selection, an often overlooked aspect in traditional models. In addition, to optimize the use of limited connection opportunities, a smart trading peer connection selection strategy is developed to guide consumers to communicate strategically to accelerate convergence. A theoretical convergence guarantee is provided for the connection-aware P2P trading algorithm, which further details how smart selection strategies enhance convergence efficiency. Numerical studies are carried out to validate the effectiveness of the connection-aware algorithm and the performance of smart selection strategies in reducing the overall convergence time.

To cost-effectively manage the supply-demand balance of the power system, the flexibility of industrial users could be harnessed through demand-side response. To minimize the negative impact on the production of industrial users during demand-side response, general-purpose models such as the state-task network (STN) are widely used to model the energy-consuming constraints of industrial production processes. However, the required model parameters cannot be set because the required data are privately owned by industrial users and are not directly available, hindering the accurate modeling of industrial loads. In this paper, we propose production scheduling identification (PSI), an inverse-optimization-based approach for industrial load modeling under incomplete information. In PSI, industrial users’ smart meter data are used to identify production scheduling parameters, thus addressing the problem of accurate load modeling when private data are unavailable. We implemented PSI with a modified STN and proposed a practical algorithm to obtain an effective solution. Numerical tests showed that PSI can identify the model parameters of a steel powder plant and a cement plant with acceptable accuracy, using only 21 days of hourly smart meter data. Compared with accurate models established with direct access to private data, the modeling error does not exceed 8.5% and 5.2%, respectively.

Achieving energy sustainability requires a transition from fossil fuel-based to renewable-dominant power systems (RDPSs). However, this shift introduces significant grid stability challenges, primarily due to the reduced synchronous dynamics traditionally provided by conventional thermal power plants. To enhance RDPS resilience, grid-forming battery energy storage systems (GFM-BESSs) have emerged as a pivotal solution, emulating the dynamic behaviors of synchronous generators (SGs). With efficient bidirectional power interaction and fast response, GFM-BESSs actively enhance grid stability through virtual inertia, voltage support, enhanced synchronization, and restoration capability. In this review, we establish the GFM-BESS as a standalone and integral grid infrastructure in RDPSs. We first identify the stability risks in RDPSs and systematically examine the role of the GFM-BESS in supporting grid stability. We then investigate the coordination between multiple hierarchical control layers of the GFM-BESS, including the battery management system (BMS), power converter system (PCS), energy management system (EMS), and grid EMS (GEMS), which collectively address its operational complexities across different timescales. Based on the grid stability requirements, we evaluate the technical benefits of GFM-BESS deployment and discuss potential monetization approaches for the economic value of GFM-BESSs in RDPSs. Finally, highlighting the potential of GFM-BESSs in driving the sustainable energy transition, we conclude with a strategic road map that identifies the collaborative synergies of multiple stakeholders, from hardware manufacturers to policymakers, outlining key opportunities for future research to advance GFM-BESSs as a cornerstone of the 100% renewable energy goal.

Over the past decade, bidding in electricity markets has attracted widespread attention. Reinforcement learning (RL) has been widely used for electricity market bidding as a powerful artificial intelligence (AI) tool to make decisions under real-world uncertainties. However, current RL-based bidding methods mostly employ low-dimensional bids (LDBs), which significantly diverge from the N price-power pairs commonly used in current electricity markets. The N-pair bid format is denoted as high-dimensional bid (HDB) format, which has not been fully integrated into the existing RL-based bidding methods. The loss of flexibility of current RL-based bidding methods could greatly limit the bidding profits and make it difficult to address the increasing uncertainties caused by renewable energy generation. In this paper, we propose a framework for fully utilizing HDBs in RL-based bidding methods. First, we employ a special type of neural network called the neural network supply function (NNSF) to generate HDBs in the form of N price-power pairs. Second, we embed the NNSF into a Markov decision process (MDP) to make it compatible with most existing RL algorithms. Finally, the experiments on energy storage systems (ESSs) in the Pennsylvania-New Jersey-Maryland (PJM) real-time electricity market show that the proposed bidding method with HDBs can increase the bidding flexibility, thereby increasing the profits of state-of-the-art RL-based bidding methods.

Providing the grid-forming service (GFS) via the battery energy storage system (BESS) is essential for the increasing integration of renewable energy in modern grids. However, rapid interactions between GFS responses and battery physics pose a significant challenge in managing grid-forming BESS operations. This paper explores the grid-forming BESS management considering internal battery physics. We first develop a physics-based model that captures the authentic available power and aging dynamics of BESS during GFS provision. Based on the physics-based model, we propose a two-stage stochastic optimization problem to determine the GFS coefficients and schedule the BESS power during the day-ahead period considering uncertain grid frequency. A real-time power regulation method is further designed to implement the scheduling results, considering the practicality of both internal battery physics and external grid frequency. Case studies reveal that the proposed management can support optimal grid-forming BESS operations effectively, achieving high GFS performance and BESS profitability adaptively under various grid-side conditions and BESS statuses.

Energy storages can solve the problems of insufficient peak-shaving ability, unstable frequency and insufficient inertia in novel power system, and have a broad development prospect together with renewables. In addition to technical factors, the long-term development of energy storages also needs to consider the economic factors, clarify various values in multiple system, and compare with their investment costs. In order to solve the problems of unclear definition and rough accounting of energy storage values in previous literatures, this paper proposes an improved measurement method of energy storage alternative values. By referring to the vickery clark aloves (VCG) mechanism, this paper proposes a framework to measure the alternative value of energy storages, and calculate the contribution of energy storages to the system overall cost reduction. When measuring the overall costs, this paper uses the planning-operation two-stage joint optimization model. This model considers the inter-action of generation, network, load and storages, which can realize more accurate and reasonable economic analysis. The effectiveness of the proposed model is demonstrated based on an IEEE 5-bus system. It is found that energy storages have multiple values, such as replacing generation and transmission investments, reducing demand response and reserve costs.