Search Results (111)

Virtual power plants (VPPs) enable the efficient participation of distributed renewable energy resources in electricity markets by aggregating them. However, the profitability of VPPs is challenged by market volatility and regulatory constraints, such as price caps and imbalance penalties. This study examines the joint impact of varying price cap levels and imbalance penalty structures on the bidding strategies and revenues of VPPs. A stochastic optimization model was developed, where a three-stage scenario tree was utilized to capture the uncertainty in electricity prices and renewable generation output. Simulations were performed under various market conditions using real-world price and generation data from the Korean electricity market. The analysis reveals that higher price cap coefficients lead to greater revenue and more segmented bidding strategies, especially under asymmetric penalty structures. Segment-wise analysis of bid price–quantity pairs shows that over-bidding is preferred under upward-only penalty schemes, while under-bidding is preferred under downward-only ones. Notably, revenue improvement tapers off beyond a price cap coefficient of 0.8, which indicates that there exists an optimal threshold for regulatory design. The findings of this study suggest the need for coordination between price caps and imbalance penalties to maintain market efficiency while supporting renewable energy integration. The proposed framework also offers practical insights for market operators and policymakers seeking to balance profitability, adaptability, and stability in VPP-integrated electricity markets. Full article

The large-scale integration of renewable energy and electric vehicles(EVs) into power distribution systems presents complex operational challenges, particularly in coordinating market mechanisms with grid stability requirements. This study proposes a new dispatching method based on dynamic electricity prices to coordinate the relationship between the market and the physical characteristics of the power grid. The proposed approach introduces a multi-agent transaction model incorporating voltage regulation metrics and network loss considerations into market bidding mechanisms. For EV integration, a differentiated scheduling strategy categorizes vehicles based on usage patterns and charging elasticity. The methodological innovations primarily include an enhanced scheduling algorithm for coordinated optimization of renewable energy and energy storage, and a dynamic coordinated optimization method for EV clusters. Implemented on a modified IEEE test system, the framework demonstrates improved voltage stability through price-guided energy storage dispatch, with coordinated strategies effectively balancing peak demand management and renewable energy utilization. Case studies verify the system’s capability to align economic incentives with technical objectives, where time-of-use pricing dynamically regulates storage operations to enhance reactive power support during critical periods. This research establishes a theoretical linkage between electricity market dynamics and grid security constraints, providing system operators with a holistic tool for managing high-renewable penetration networks. By bridging market participation with operational resilience, this work contributes actionable insights for developing interoperable electricity market architectures in energy transition scenarios. Full article

This paper demonstrates that perfectly calibrating a multi-asset model to observed market prices of all basket call options is insufficient to uniquely determine the price of a best-of call option. Previous research on multi-asset option pricing has primarily focused on complete market settings or assumed specific parametric models, leaving fundamental questions about model risk and pricing uniqueness in incomplete markets inadequately addressed. This limitation has critical practical implications: derivatives practitioners who hedge best-of options using basket-equivalent instruments face fundamental distributional uncertainty that compounds the well-recognized non-linearity challenges. We establish this non-uniqueness using convex analysis (extreme ray characterization demonstrating geometric incompatibility between payoff structures), measure theory (explicit construction of distinct equivalent probability measures), and geometric analysis (payoff structure comparison). Specifically, we prove that the set of equivalent probability measures consistent with observed basket prices contains distinct measures yielding different best-of option prices, with explicit no-arbitrage bounds $[a_K,b_K]$ quantifying this uncertainty. Our theoretical contribution provides the first rigorous mathematical foundation for several empirically observed market phenomena: wide bid-ask spreads on extremal options, practitioners’ preference for over-hedging strategies, and substantial model reserves for exotic derivatives. We demonstrate through concrete examples that substantial model risk persists even with perfect basket calibration and equivalent measure constraints. For risk-neutral pricing applications, equivalent martingale measure constraints can be imposed using optimal transport theory, though this requires additional mathematical complexity via Schrödinger bridge techniques while preserving our fundamental non-uniqueness results. The findings establish that additional market instruments beyond basket options are mathematically necessary for robust exotic derivative pricing. Full article

Crowdshipping establishes a short-term connection between shippers and individual carriers, bridging the service requirements in last-mile logistics. From the perspective of a carrier operating multiple vehicles, this study considers the challenge of maximizing profits by optimizing bid strategies for delivery prices and transportation conditions in the context of bid-based crowdshipping services. We considered two types of bid strategies: a price bid that adjusts the RFQ freight charge and a multi-attribute bid that scores both price and service quality. We formulated the problem as a Markov decision process (MDP) to represent uncertain and sequential decision-making procedures. Furthermore, given the complexity of the newly proposed problem, which involves multiple vehicles, route optimizations, and multiple attributes of bids, we employed a reinforcement learning (RL) approach that learns an optimal bid strategy. Finally, numerical experiments are conducted to illustrate the superiority of the bid strategy learned by RL and to analyze the behavior of the bid strategy. A numerical analysis shows that the bid strategies learned by RL provide more rewards and lower costs than other benchmark strategies. In addition, a comparison of price-based and multi-attribute strategies reveals that the choice of appropriate strategies is situation-dependent. Full article

The increasing adoption of Renewable Energy Sources (RESs), due to international energy policies mainly related to the decarbonization of electricity production, raises several operating issues for power systems, which need “flexibility” in order to guarantee reliable and secure operation. RESs can be considered examples of Distributed Energy Resources (DERs), which are typically electric power generators connected to distribution networks, including photovoltaic and wind systems, fuel cells, micro-turbines, etc., as well as energy storage systems. In this case, improved operation of power systems can be achieved through coordinated control of groups of DERs by “aggregators”, who also offer a “flexibility service” to power systems that need to be appropriately remunerated according to market rules. The implementation of the aggregator function requires the development of tools to optimally operate, control, and dispatch the DERs to define their overall flexibility as a “market product” in the form of bids. The contribution of the present paper in this field is to propose a new optimization strategy for flexibility bidding to maximize the profit of the aggregator in flexibility markets. The proposed optimal scheduling procedure accounts for important practical and technical aspects related to the DERs’ operation and their flexibility estimation. A case study is also presented and discussed to demonstrate the validity of the method; the results clearly highlight the efficacy of the proposed approach, showing a profit increase of 10% in comparison with the base case without the use of the proposed methodology. It is evident that quantitatively more significant results can be obtained when larger aggregations (more participants) are considered. Full article

Electricity markets with a high share of variable renewable energy require significant balancing reserves to ensure stability by preserving the balance of supply and demand. However, they were originally conceived for dispatchable technologies, which operate with predictable and controllable generation. As a result, adapting market mechanisms to accommodate the characteristics of variable renewables is essential for enhancing grid reliability and efficiency. This work studies the strategic behavior of a wind power producer (WPP) in the Iberian electricity market (MIBEL) and the Portuguese balancing markets (BMs), where wind farms are economically responsible for deviations and do not have support schemes. In addition to exploring current market dynamics, the study proposes new market designs for the balancing markets, with separate procurement of upward and downward secondary balancing capacity, aligning with European Electricity Regulation guidelines. The difference between market designs considers that the wind farm can hourly bid in both (New 1) or only one (New 2) balancing direction. The study considers seven strategies (S1–S7) for the participation of a wind farm in the past (S1), actual (S2 and S3), New 1 (S4) and New 2 (S5–S7) market designs. The results demonstrate that new market designs can increase the wind market value by 2% compared to the optimal scenario and by 31% compared to the operational scenario. Among the tested approaches, New 2 delivers the best operational and economic outcomes. In S7, the wind farm achieves the lowest imbalance and curtailment while maintaining the same remuneration of S4. Additionally, the difference between the optimal and operational remuneration of the WPP under the New 2 design is only 22%, indicating that this design enables the WPP to achieve remuneration levels close to the optimal case. Full article

The large-scale integration of renewable energy into power grids introduces substantial stochasticity in generation profiles and operational complexities due to electricity’s non-storable nature. These factors cause significant fluctuations in day-ahead market prices. Accurate price forecasting is crucial for market participants to optimize bidding strategies, mitigate renewable curtailment, and enhance grid sustainability. However, conventional methods struggle to address the nonlinearity, high-frequency dynamics, and multivariate dependencies inherent in electricity prices. This study proposes a novel multi-objective optimization framework combining an improved non-dominated sorting genetic algorithm II (NSGA-II) with a radial basis function (RBF) neural network. The improved NSGA-II algorithm mitigates issues of population diversity loss, slow convergence, and parameter adaptability by incorporating dynamic crowding distance calculations, adaptive crossover and mutation probabilities, and a refined elite retention strategy. Simultaneously, the RBF neural network balances prediction accuracy and model complexity through structural optimization. It is verified by the data of Singapore power market and compared with other forecasting models and error calculation methods. These results highlight the ability of the model to track the peak price of electricity and adapt to seasonal changes, indicating that the improved NSGA-II and RBF (NSGA-II-RBF) model has superior performance and provides a reliable decision support tool for sustainable operation of the power market. Full article

Aggregating and scheduling flexible resources through virtual power plants (VPPs) is a key measure used to improve the flexibility of new power systems. To maximize the regulation potential of flexible resources and achieve the efficient, unified scheduling of flexible resource clusters by VPPs, this study proposed a flexible resource aggregation method for VPPs and a bidding strategy for participation in the electricity and frequency regulation markets. First, considering the differences in the grid frequency regulation demand across periods, an improved zonotope approximation method was adopted to internally approximate the feasible region of flexible resources, thereby achieving the efficient aggregation of feasible regions. On this basis, the aggregation model was applied to the optimization model for VPPs, and a day-ahead double-layer bidding model of VPPs participating in the electricity and frequency regulation markets was proposed. The upper layer optimizes the bidding strategies to maximize the VPP revenue, while the lower layer achieves joint market clearing with the goal of maximizing social welfare. Finally, case studies were undertaken to validate the effectiveness of the proposed method. Full article

The deepening operation of the carbon emission trading market has reshaped the cost–benefit structure of the power generation side. In the process of participating in the market quotation, power suppliers not only need to calculate the conventional power generation cost but also need to coordinate the superimposed impact of carbon quota accounting on operating income, which causes the power suppliers a multi-time-scale decision-making collaborative optimization problem under the interaction of the carbon market, power market, and coal market. This paper focuses on the multi-market-coupling decision optimization problem of thermal power suppliers. It proposes a collaborative bidding decision framework based on a multi-agent deep deterministic policy gradient (MADDPG). Firstly, aiming at the time-scale difference of multi-sided market decision making, a decision-making cycle coordination scheme for the carbon–electricity–coal coupling market is proposed. Secondly, upper and lower optimization models for the bidding decision making of power suppliers are constructed. Then, based on the MADDPG algorithm, the multi-generator bidding scenario is simulated to solve the optimal multi-generator bidding strategy in the carbon–electricity–coal coupling market. Finally, the multi-scenario simulation based on the IEEE-5 node system shows that the model can effectively analyze the differential influence of a multi-market structure on the bidding strategy of power suppliers, verifying the superiority of the algorithm in convergence speed and revenue optimization. Full article

China’s power generation system has undergone reforms, leading to a competitive electricity market where independent producers participate through competitive bidding. With the rise of low-carbon policies, producers must optimize bidding strategies while reducing carbon emissions, creating complex interactions with local governments. Evolutionary game theory (EGT) is well-suited to analyze these dynamics. This study begins by summarizing the fundamental concepts of electricity trading markets, including transaction models, bidding mechanisms, and carbon reduction strategies. Existing research on the application of evolutionary game theory in power markets is reviewed, with a focus on theoretical constructs such as evolutionary stable strategies and replicator dynamics. Based on this foundation, the study conducts a detailed mathematical analysis of symmetric and asymmetric two-group evolutionary game models in general market scenarios. Building upon these models, a three-group evolutionary game framework is developed to analyze interactions within power producer groups and between producers and regulators under low-carbon mechanisms. A core innovation of this study is the incorporation of a case study based on China’s electricity market, which examines the evolutionary dynamics between local governments and power producers regarding carbon reduction strategies. This includes analyzing how regulatory incentives, market-clearing prices, and demand-side factors influence producers’ bidding and emission reduction behaviors. The study also provides a detailed analysis of the bidding strategies for small, medium, and large power producers, revealing the significant impact of carbon pricing and market-clearing prices on strategic decision-making. Specifically, the study finds that small producers tend to adopt more conservative bidding strategies, aligning closely with market-clearing prices, while large producers take advantage of economies of scale, adjusting their strategies at higher capacities. The study explores the conditions under which carbon emission reduction strategies achieve stable equilibrium, as well as the implications of these equilibria for both market efficiency and environmental sustainability. The study reveals that integrating carbon reduction strategies into power market dynamics significantly impacts bidding behaviors and long-term market stability, especially under the influence of governmental penalties and incentives. The findings provide actionable insights for both power producers and policymakers, contributing to the advancement of low-carbon market theories and supporting the global transition to sustainable energy systems. Full article

Market liberalization and the growth of renewable energy sources have enabled the rise of generation companies (GENCOs) managing diverse generation portfolios, creating a dynamic market environment that necessitates innovative energy management strategies to enhance operational efficiency and economic viability. Investing in the energy storage system (ESS), which, in addition to participating in the energy and ancillary services markets and in joint operations with other GENCO facilities, can mitigate the fluctuation level from renewables and increase profits. Besides the optimal operation and bidding strategy, determining the optimal size of the ESS aligned with the GENCO’s requirements is significant for its market success. The purpose of the ESS impacts both the sizing criteria and the sizing techniques. The proposed sizing method of ESS for a GENCO daily operation mode is based on the developed optimization operation model of GENCO with utility-scale energy storage and a cost-benefit analysis. A GENCO operates in a market-oriented power system with possible penalties for undelivered energy. The proposed method considers various stochastic phenomena; therefore, the optimization calculations analyze the GENCO operation over a long period to involve multiple potential combinations of uncertainties. Numerical results validate the competencies of the presented optimization model despite many unpredictable parameters. The results showed that both the battery storage system and the pumped storage hydropower plant yield a higher net income for a specific GENCO with a mixed portfolio, regardless of the penalty clause. Considering the investment costs, the optimal sizes for both types of ESS were obtained. Full article

We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used; we deployed the state-of-the-art Soft Actor–Critic (SAC) algorithm for the deep learning part. The SAC algorithm is an off-policy entropy maximization algorithm more suitable for tackling complex, high-dimensional problems with continuous state and action spaces, like those in optimal market-making (MM). We introduce the optimal MM problem considered, where we detail all the deterministic and stochastic processes that go into setting up an environment to simulate this strategy. Here, we also provide an in-depth overview of the jump-diffusion pricing dynamics used and our method for dealing with adverse selection within the limit order book, and we highlight the working parts of our optimization problem. Next, we discuss the training and testing results, where we provide visuals of how important deterministic and stochastic processes such as the bid/ask prices, trade executions, inventory, and the reward function evolved. Our study includes an analysis of simulated and real data. We include a discussion on the limitations of these results, which are important points for most diffusion style models in this setting. Full article

There have been limited empirical studies that aimed to establish the tenability of the stationarity assumption in recurrent construction bidding, and thus the need for and importance of allowing for continuity in bidding models remain unexplored. This study examined the bidding trends of individual contractors according to their level of experience in recurrent bidding, to test the tenability of the stationarity assumption. The data sample was a past bidding dataset of Singapore public sector construction projects over a five-year period between 2017 and 2021, with over 8000 bidding records from more than 900 contractors. The results show that there were statistically significant changes in the contractors’ bidding trends, irrespective of their level of experience in recurrent bidding and different time periodicities, ranging between 10 and 20 months. Thus, the stationarity assumption that contractors behave in a probabilistically consistent way over time, regardless of changing conditions, was untenable for the data sample involved. The observed changes in the contractors’ bidding trends cannot be regarded as random, but represent a continuous strategic process in response to changes in market forces. It is postulated that the possible causes of changes vary among individual contractors, in which there are a set of varying internal and external factors they consider at the time of bidding. The findings have implications for future bidding modelling attempts, in allowing for continuity in recurrent bidding. Contractors should systematically review and re-optimize their bidding strategy by leveraging their historical bidding data and bidding feedback information from clients, since their potential competitors will do the same thing for recurrent bidding. Full article

With the transformation of the energy structure, the integration of numerous small-scale, widely distributed renewable energy sources into the power grid has introduced operational safety challenges. To enhance the operational competitiveness, the virtual power plant (VPP) has emerged to aggregate and manage these distributed energy resources (DERs). However, current research on the VPP’s frequency modulation performance and bidding strategy remains insufficient in the joint market of electrical energy and frequency modulation (FM) ancillary services, with inadequate coordination of internally distributed resources. To fully leverage the flexibility of VPPs and incentivize their participation in electricity market operations, this paper investigates game-based bidding strategies and internal distributed resources allocation methods for VPPs in the joint market for electrical energy and frequency ancillary services. Firstly, the regulatory performance indicators of VPPs participating in the joint market and develops the corresponding market-clearing model. Secondly, to address the competition among distributed resources within VPPs, a master-slave game approach is innovatively employed to optimize the VPP’s trading strategies. This method ensures the rational allocation of electricity consumption among distributed energy resources within the VPP and derives the optimized bidding prices and quantities for both the VPP and its internal members. Finally, the case study shows that the proposed trading strategy provides effective bidding strategies for distributed energy resources participating in the joint market for energy and frequency regulation ancillary services. It enhances the regulatory performance of VPPs in the energy-frequency regulation market, ensures the profitability of distributed energy resources, and contributes to the economically stable operation of the market. Full article

Against the backdrop of a “dual-carbon” strategy, the use of photovoltaic storage charging stations (PSCSs), as an effective way to aggregate and manage electric vehicles, new energy sources, and energy storage, will be an important primary component of the electricity market. The operational characteristics of the aggregated resources within a PSCS determine its bidding space, which has an important influence on its bidding strategy. In this paper, a novel bidding space model is constructed for PSCSs, which dynamically integrates electric vehicles, photovoltaic generation, and energy storage. A two-stage bidding strategy for multiple PSCSs is established, with stage I aiming at achieving the lowest cost for the power purchased by a PSCS to optimize the power generation and power plan and stage II aiming at achieving the lowest cost of the grid operator’s power purchase to optimize the system’s power balance. Thirdly, the two-stage model is transformed into a single-layer, mixed-integer linear programming problem using dyadic theory and Karush–Kuhn–Tucker (KKT) conditions, enabling the derivation of the optimal bidding strategy. Finally, the example analysis verifies that the proposed model can achieve a reduction in the PSCS’s day-ahead power purchase cost and flexibly dispatch each resource within the PSCS to maximize revenue, as well as reducing power consumption behavior during peak tariff hours, to enhance the market power of the PSCS in the electricity market. Full article