Search Results (165)

The integration of grid-forming energy storage systems (GFM-ESSs) provides essential support for the stable operation of grid-connected converters in renewable energy systems. However, GFM-ESSs may exhibit low-frequency oscillations in response to grid state variations, posing a threat to power system stability. To address this challenge, this paper proposes a fast continuous optimization method for the active power–frequency control loop of multi-VSG-based GFM-ESSs. First, a parameter coupling model for multiple VSGs is established, and an internal parameter decoupling control strategy is proposed. Subsequently, an iterative optimization model based on a gradient-based master–slave game is developed, in which the minimization of converter frequency deviation serves as the leader’s objective, while the minimization of system frequency deviation acts as the follower’s objective. Frequency fluctuations are further mitigated through tracking differentiator-based active power compensation. The effectiveness of the proposed method is validated through simulation with six GFM-ESS units integrated into a modified IEEE 33-node system featuring six renewable energy stations. Simulation results demonstrate that the proposed approach significantly suppresses frequency fluctuations while also reducing the response time and the rate of frequency change under grid disturbance conditions. Full article

To address the challenges in embodied creativity research, this study innovatively developed a new mirror game experimental paradigm based on the dual theoretical framework of embodied metaphor and enactive metaphor. From the perspective of embodied metaphor, the study investigates how “body interaction direction” (imitation vs. avoidance) influences delayed creativity. From the perspective of enactive metaphor, it examines how “body interaction type” (leader–follower vs. Joint Improvisation) shapes immediate creativity and reveals the overall effects of their interaction on creativity. Two experiments were conducted in this study: Experiment 1 focused on virtual human–machine interaction, and Experiment 2 explored real-life human–human interaction. Experiment 1 validated the synergistic effects of body interaction direction and type on individual creativity dimensions, with Joint Improvisation showing significant advantages. Experiment 2 further demonstrated that embodied and enactive metaphors exhibit significant synergistic effects on group creativity, with the leader–follower interaction pattern showing distinct value in the context of interaction effects. The general discussion highlights that embodied and enactive metaphors, as dual mechanisms, provide a theoretical breakthrough for understanding creativity, spanning human–machine and human–human interactions. Within the framework of enactive cognition, this study further expands the sense-making function of metaphor theory in creativity development. Full article

This paper presents an adaptive optimal consensus tracking control scheme for canonical nonlinear multi-agent systems (MASs) with unknown dynamics, employing an actor–critic reinforcement learning (RL) framework. The scheme integrates a sliding mode mechanism to suppress tracking errors and ensure consensus tracking between the followers and the leader. Additionally, optimal control is designed to find a Nash equilibrium in a graphical game. To address the intractability of obtaining an analytical solution for the coupled Hamilton–Jacobi–Bellman (HJB) equation, a policy iteration algorithm is utilized. Within this algorithm, a critic neural network (NN) approximates the gradient of the optimal value function, while an actor NN approximates the optimal control policy. Together, these networks form a compact actor–critic (AC) architecture that achieves optimal consensus tracking. Furthermore, the proposed method guarantees the boundedness of all closed-loop signals while ensuring consensus tracking. Finally, two simulations are conducted to verify the effectiveness and advantages of the proposed method. Full article

With grid-connected microgrids connected to power distribution networks, a hierarchical coordination scheduling framework is developed to solve the benefit allocation problem among different entities. Firstly, a bi-level master–slave game model with the power distribution network as the leader and the microgrids as the followers is proposed. For the leader, a two-stage robust optimization economic dispatch model considering wind power uncertainty is established for the power distribution network. For the followers, an optimal-scheduling model considering time-of-use pricing and load demand response is constructed. Secondly, the follower model is transformed into the equilibrium constraints of the leader model in light of the Karush–Kuhn–Tucker condition. As a result, the above bi-level master–slave game model can be converted into a single-layer robust optimization problem with mixed-integer recourse, which is solved by the nested column-and-constraint generation algorithm. Finally, the proposed model and solution method are validated via an improved IEEE 33-bus distribution network connected with three microgrids. The simulation results demonstrate that the proposed model can reduce the total operation cost by 12.42% compared with the centralized optimization model. Moreover, the load demand response and the regulation of ESSs at the real-time scheduling stage can prominently improve the operation flexibility and reduce the operation cost. Specifically, the operation cost of multiple microgrids has reduced by 21.55% when considering load demand response. In addition, the solving time for the proposed model is 627.3 s, which has the potential for practical engineering application. Full article

To address the challenges of low-carbon economic optimization and collaborative management for multiple Virtual Power Plants (VPPs), this paper proposes a low-carbon economic optimization and collaborative management method based on a Stackelberg game framework. Firstly, a Stackelberg game model is constructed with the Distribution System Operator (DSO) as the leader and multiple VPPs as followers. The leader (DSO) guides the followers’ behavior through dynamic pricing strategies to maximize its own utility. Meanwhile, the followers (VPPs) develop energy management strategies to minimize their individual costs, taking into account factors such as energy transaction costs, fuel costs, carbon trading costs, operation and maintenance (O&M) costs, compensation costs, and renewable energy generation revenues. Furthermore, the strategy spaces of all participants are defined, and an optimization model is established subjected to constraints including energy balance, energy storage operation, power conversion, and flexible load response. The CPLEX solver and Nonlinear-based Chaotic Harris Hawks Optimization (NCHHO) algorithm are employed to solve the proposed game model. Simulation results demonstrate that the proposed method effectively facilitates collaboration between the DSO and multiple VPPs. While ensuring the safe operation of the system, it balances the profit between the DSO and VPPs, and incentivizes renewable energy consumption and indirect carbon reduction, thereby validating the effectiveness and superiority of the method and providing reliable technical support for the low-carbon collaborative operation of multiple VPPs. Full article

Integrated Demand Response (IDR) enhances the operational flexibility of Integrated Energy Systems (IES) and promotes renewable energy integration. However, limited interaction between the Integrated Energy Operator (IEO) and users during actual energy transactions can lead to biases in IDR planning, compromising user response effectiveness. To address this, this paper proposes a method for revising IDR stimulus parameters in IES based on gradient descent within a Stackelberg game framework. First, an IDR model based on consumer psychology principles is constructed to establish an IES Stackelberg game, in which the IEO acts as the leader and the load aggregator acts as the follower. Subsequently, during the game, the IEO utilizes users’ energy consumption strategies to adjust the stimulus threshold parameters of the dead zone and saturation zone along the negative gradient direction, thereby updating its decision for the next round. Furthermore, a response adjustment mechanism is designed to refine the IDR plan, enhancing its feasibility. Finally, comparative analyses across diverse scenarios demonstrate that the proposed method reduces deviations in planned IDR, thereby enhancing the low-carbon performance and renewable energy integration capacity of IES. Full article

To design Product–Service System (PSS) schemes that meet individual customer requirements, the configuration of technology systems is commonly used to select and assemble preferable modules from a predefined product and service library under certain constraints. Service delivery and realization have a significant impact on customer satisfaction in PSSs. However, existing research seldom considers the interactions between PSS configuration and service delivery. This paper focuses on two key stakeholders in PSS configuration: the product manufacturer (PSS provider) and the service providers. A bi-level optimization model based on Stackelberg game theory is proposed to configure the optimal PSS solution. Firstly, the upper-level optimization problem represents the PSS configuration as a leader to maximize customer satisfaction. Secondly, the lower-level optimization problem represents service configuration as a follower to minimize the service supply cost. Thirdly, an improved Dual-Population Co-evolutionary Hybrid Algorithm (DPC-NMHA), combining NSGA-II and MOPSO, is proposed to solve the bi-level optimization model. Finally, the feasibility and effectiveness of the proposed method are demonstrated through a case study of a refrigerator PSS configuration. Full article

The coupling of electricity, heat, and hydrogen subsystems together with carbon capture technologies introduces complex operational interactions in modern multi-energy systems. Existing game-based scheduling studies mainly focus on electricity–heat or electricity–heat–gas coupling, often neglecting hydrogen blending, carbon capture integration, and strategic coordination among heterogeneous stakeholders. To address these gaps, this study develops a game-theoretic hierarchical optimization framework for electricity–heat–hydrogen integrated energy systems incorporating carbon capture. Compared with conventional multi-energy game models, the proposed framework integrates hydrogen blending and carbon capture into a unified electricity–heat–hydrogen–carbon coupling structure, enabling coordinated low-carbon operation. A Stackelberg leader–follower structure is adopted, where the upper-level operator determines electricity and heat prices, and lower-level participants optimize generation dispatch and demand response accordingly. The bi-level model is transformed into an equivalent single-level formulation using Karush–Kuhn–Tucker conditions and solved through a hybrid particle swarm optimization–mathematical programming approach. Simulation results based on an extended IEEE 30-bus system demonstrate improved coordination, enhanced scheduling flexibility, and reduced operating costs and carbon emissions. Compared with centralized optimization, the proposed framework enables the integrated energy operator and energy supplier to achieve revenues of 3.18 × 10⁵ CNY and 3.95 × 10⁵ CNY, respectively, while reducing the load aggregator’s cost by 41.71%, confirming its effectiveness for coordinated low-carbon IES scheduling. Full article

Operations scheduling of mass customized products is vital in the modern make-to-order (MTO) supply chains. In these systems, order acceptance decisions should be coordinated with available capacity in different sections of the supply chain while considering their potential correlations and interactions. One of the fundamental challenges in optimization of these systems is the computation time of solving models with multiple coupling constraints between supply chain units. This paper addresses this issue by proposing a game-based framework that decomposes the related mixed integer programming mathematical model and it is coordinated and solved using integrated game-based Alternating Direction Method of Multipliers (ADMM). The proposed Stackelberg Leader-Follower game optimizes order acceptance decisions while considering the requirements in supply, production planning, maintenance, inventory, and distribution units. To validate the efficiency of the proposed framework, the model is tested with a simulated four-layer supply chain. The results of experiments proved that decompositions of the model to smaller subsections and solving it in a distributed manner not only optimizes supply chain participating units but also coordinate their movements to achieve the global optimal solution. The proposed framework offers managers a practical decision layer that preserve local autonomy of the supply chain units and reduce their data sharing and computation burdens and concerns. Full article

This paper proposes a Stackelberg game-based collaborative optimization strategy for Park-Level Integrated Energy Systems (PIESs) operating in carbon and green certificate markets. The strategy addresses interest conflicts and low-carbon transition challenges in multi-agent optimization by integrating a carbon capture, power-to-gas, and liquid carbon dioxide energy storage technology chain. Innovatively integrates LCES into the CCS-P2G-LCES chain, achieving internal carbon cycling and energy storage. First, a market environment for PIESs integrating carbon trading and green certificate trading is constructed, and a deeply coupled low-carbon technology chain model of CCS-P2G-LCES is established to realize internal carbon resource cycling and energy time shifting. Second, a one-leader, multiple-follower Stackelberg game framework is developed with the Integrated Energy Service Provider (IESP) as the leader and the User Load Aggregator (ULA) and Electric Vehicle Aggregator (EVA) as followers. The IESP guides demand response on the user and electric vehicle sides by formulating differentiated energy prices. On this basis, a collaborative optimization dispatch model is constructed with the objective of maximizing the comprehensive revenue of the IESP. Finally, case study analysis verifies that the proposed method not only enhances operational revenue and reduces user energy costs, but also significantly reduces system carbon emissions and improves renewable energy consumption rates. The results demonstrate the feasibility and superiority of integrating market mechanisms, low-carbon technologies, and multi-agent game-based collaborative optimization. Full article

The rapid evolution of live-streaming commerce has reshaped retail supply chains, shifting market dominance from manufacturers to influential streamers. Despite this shift, the internal mechanisms of selling efforts and paid traffic acquisition remain underexplored. To bridge this theoretical gap, we develop a game-theoretic framework to model the endogenous power structure and compare the streamer-led top-tier (KS) mode and the brand-led ordinary (MS) mode. Our analytical results reveal three key theoretical insights. First, we establish strict positive monotonicity between streamer influence and equilibrium decisions. Regardless of the power structure, an increase in influence consistently drives the streamer to intensify operational inputs while simultaneously inducing the brand to raise the direct selling price. Second, consumer sensitivity acts as a positive driver of the top-tier mode. Higher sensitivity motivates the streamer to scale up sales efforts and paid-traffic volume, which corresponds to an optimal increase in the brand’s retail price. Moreover, the top-tier mode exhibits negative sensitivity to operational costs. We prove that rising costs lead to a significant reduction in the streamer’s operational portfolio and, consequently, to a decrease in the brand’s price, indicating that the high-input equilibrium is constrained by cost frictions. From a managerial perspective, numerical experiments reveal not a “Consensus on Scale” but a “Conflict on Structure.” Specifically, brands maximize profit by collaborating with top-tier streamers, while streamers maximize profit by attaining top-tier influence. However, the brand receives more profit by relinquishing channel leadership with respect to the decision hierarchy. In contrast, the streamer is less profitable as a leader than as a follower due to the “leadership trap,” in which greater operational burdens outweigh first-mover advantages. Full article

With the rapid development of the Internet of Vehicles (IoV), the explosive growth of data traffic within the system has led to a surge in demand for spectrum resources. However, the strict limitations on spectrum supply make the construction of an efficient and reasonable resource allocation scheme crucial for IoV. To maximize social benefits and improve security in the resource allocation process under IoV spectrum scarcity, this paper proposes a dynamic spectrum allocation (DSA) scheme based on a consortium blockchain framework. In this scheme, we design a demand-based vehicle priority classification method and propose a novel hybrid consensus mechanism—PhDPoR—which integrates practical byzantine fault tolerance (PBFT) and Hierarchical Delegated Proof of Reputation. Furthermore, we construct a multi-leader, multi-follower (MLMF) Stackelberg game model and utilize smart contracts to implement an immutable on-chain record of spectrum resource allocation, thereby deriving the optimal spectrum pricing and purchase strategy. Experimental results show that the proposed scheme not only effectively optimizes the utility of both supply and demand sides and improves overall social benefits while ensuring efficiency, but also significantly outperforms baseline algorithms in identifying and mitigating malicious nodes, thus verifying its feasibility and application value in complex IoV environments. Full article

As the composition of energy markets becomes increasingly diverse and distributed in character, it is difficult for traditional vertically integrated energy system (IES) structures and centralized optimization methods to stimulate coupled interactions and interactive synergies among multiple subjects. Consequently, a collaborative low-carbon scheduling strategy utilizing a leader–follower game framework is introduced for the distributed IES. Making the integrated energy system operator (IESO) a leader, distributed integrated energy supply system (DIESS) and smart user terminal (SUT) as followers, the optimal interaction operation strategy of each subject in the game process can be solved. Firstly, the overall energy interaction process of the system and the game objectives of each participant are introduced to construct a distributed collaborative optimization model with one leader and multiple followers. Secondly, the integrated demand response (IDR) and the ladder-type carbon trading scheme are considered, the two-stage operation process of the electrical gas technology (P₂G) equipment is analyzed in detail, and the genetic algorithm nested CPLEX solver is used to solve the model. Finally, the results show that this paper can provide guarantee and theoretical support for the optimal operation of the integrated energy market in terms of trading model and algorithm. Full article

To address the limitation of traditional microgrid operator-led optimization models that compromise user-side benefits, this paper proposes a novel method for the collaborative optimal operation strategy of community-based integrated energy microgrids and diversified flexible resources. The method deeply integrates user-side flexibility resources into the decision-making process. Unlike existing research that only considers electro-heat coupling, our model integrates shared energy storage services into an integrated energy system, reflecting a more realistic future application. A Stackelberg game framework is then established with the microgrid operator (MGO) as the leader and the user aggregator as the follower. The user aggregator optimizes its energy strategy by coordinating user demand response, thereby increasing the profits of both itself and the shared energy storage operator. Meanwhile, this model guides the MGO’s pricing decisions for electricity and heat, balancing interests of all stakeholders. To solve the model, a hierarchical approach that merges the Harris Hawks Optimization algorithm with the CPLEX solver is employed. Finally, simulation results demonstrate that the proposed model and strategy significantly enhance user-side revenue and flexibility, achieve a win-win outcome for the user aggregator and MGO, and lay the foundation for future shared energy storage service providers to participate in market pricing as key game entities. Full article

Electric vehicles (EVs) and renewable energy generation are widely regarded as key drivers of low-carbon transformation in the transportation and energy sectors due to their emission reduction potential and environmental benefits. However, the inherent intermittency and volatility of photovoltaic (PV) power, coupled with increasingly stochastic and disorderly EV charging demand, pose significant challenges to grid stability and local renewable energy utilization. To address these issues, this paper proposes a dynamic pricing optimization approach based on a Stackelberg game framework, in which the PV charging station operator acts as the leader and EV users as followers. Unlike conventional models, the proposed framework explicitly incorporates user psychological expectations and response deviations through a three-stage “dead-zone-linear-saturation” responsiveness structure, thereby capturing the uncertainty and partial rationality of EV charging behavior. The upper-level objective seeks to maximize operator profit and enhance PV self-consumption, while the lower-level objective minimizes user energy cost under price-responsive charging decisions. The bilevel optimization problem is solved via a differential evolution (DE) algorithm combined with YALMIP + CPLEX. Simulation results for a regional PV-EV charging station show that the proposed strategy increases PV self-consumption to about 90.5% and shifts the load peak from 18:00–20:00 to 10:00–15:00, effectively aligning charging demand with PV output. Compared with both flat and standard time-of-use (TOU) tariffs, the dynamic pricing scheme yields higher operator profit (about 7% improvement over flat pricing) while keeping total user energy expenditure essentially unchanged. In addition, the cumulative carbon reduction cost over the operating cycle is reduced by approximately 4.1% relative to flat pricing and 1.9% relative to TOU pricing, demonstrating simultaneous economic and environmental benefits of the proposed game-based dynamic pricing framework. Full article