Search Results (48)

Under carbon emission constraints, to promote low-carbon transformation and achieve the aim of carbon peaking and carbon neutrality in the energy sector, this paper constructs an operational optimization model for the coordinated operation of a virtual power plant cluster (VPPC). Considering the resource characteristics of different virtual power plants (VPPs) within a cooperative alliance, we propose a multi-VPP interaction and sharing architecture accounting for electricity–carbon interaction. An optimization model for VPPC is developed based on the asymmetric Nash bargaining theory. Finally, the proposed model is solved using an alternating-direction method of multipliers (ADMM) algorithm featuring an improved penalty factor. The research results show that P2P trading within the VPPC achieves resource optimization and allocation at a larger scale. The proposed distributed ADMM solution algorithm requires only the exchange of traded electricity volume and price among VPPs, thus preserving user privacy. Compared with independent operation, the total operation cost of the VPPC is reduced by 20.37%, and the overall proportion of new energy consumption is increased by 16.83%. The operation costs of the three VPPs are reduced by 1.12%, 20.51%, and 6.42%, respectively, while their carbon emissions are decreased by 4.47%, 5.80%, and 5.47%, respectively. In addition, the bargaining index incorporated in the proposed (point-to-point) P2P trading mechanism motivates each VPP to enhance its contribution to the alliance to achieve higher bargaining power, thereby improving the resource allocation efficiency of the entire alliance. The ADMM algorithm based on the improved penalty factor demonstrates good computational performance and achieves a solution speed increase of 15.8% compared to the unimproved version. Full article

Establishing a partnership necessitates agreeing on how to divide future profits or losses. We consider parties who wish to contract on the division of uncertain future profits. We propose to divide profits according to the Raiffa–Kalai–Smorodinsky (K-S) solution, which is the intersection point of the feasible region’s boundary and the line connecting the disagreement and ideal points. It is the only function which satisfies invariance to linear transformations, symmetry, strong Pareto optimality, and monotonicity. We formulate the general problem of designing a contract which divides uncertain future profit between the partners and determines shares of each partner. We first focus on linear and, later, non-linear contracts between two partners, providing analytical and numerical solutions for various special cases in terms of the utility functions of the partners, their beliefs, and the disagreement point. We then generalize the analysis to any number of partners. We also consider a contract which is partially based on the parties’ financial contribution to the partnership, which have a positive impact on profit. Finally, we address asymmetric K-S solutions. K-S solutions are seen to be a useful predictor of the outcome of negotiations, similar to Nash’s bargaining solution. Full article

Under the goal of “dual carbon”, the power market and carbon market are developing synergistically, which is strongly promoting the transformation of the power system in a clean and low-carbon direction. In order to realise the synergistic optimisation of multi-virtual power plants, economic and low-carbon operation, and the reasonable distribution of revenues, this paper proposes a multi-VPP power–carbon sharing operation optimisation strategy considering multiple uncertainties. Firstly, a cost model for each VPP power–carbon sharing considering the uncertainties of market electricity price and new energy output is established. Secondly, a multi-VPP power–carbon sharing operation optimisation model is established based on the Nash negotiation theory, which is then decomposed into a multi-VPP coalition cost minimisation subproblem and a revenue allocation subproblem based on asymmetric bargaining. Thirdly, the variable penalty parameter alternating directional multiplier method is used for the solution. Finally, an asymmetric bargaining method is proposed to quantify the contribution size of each participant with a nonlinear energy mapping function, and the VPPs negotiate with each other regarding the bargaining power of their electricity–carbon contribution size in the co-operation, so as to ensure a fair distribution of co-operation benefits and thus to motivate and maintain a long-term and stable co-operative relationship among the subjects. Example analyses show that the method proposed in this paper can significantly increase the revenue level of each VPP and reduce carbon emissions and, at the same time, improve the ability of VPPs to cope with uncertain risks and achieve a fair and reasonable distribution of the benefits of VPPs. Full article

In the vigorous development of the power system, to address the economic challenges of multi-microgrid systems, this paper proposes a Nash bargaining model for collaboration between microgrid operators (MGs) and a distribution system operator (DSO) under conditions of multiple uncertainties. Firstly, a model for energy transactions between multiple complementary microgrid systems and a distribution system is established. Secondly, the chance-constrained method and robust optimization method are applied to model the multiple uncertainties in renewable energy generation and electricity trading prices. Moreover, using Nash bargaining theory, a cooperative operation model between MGs and a DSO is established, which is then transformed into two subproblems: cost minimization in cooperation and revenue maximization from power trading. To protect the privacy of each participant, a distributed solution approach using the alternating direction method of multipliers (ADMM) is applied to solve these subproblems. Finally, the simulation results indicate that the benefit values of all entities have improved after cooperative operation through the proposed model. Specifically, the benefit value of MG 1 is CNY 919,974.3, MG 2 is CNY 1,420,363.2, MG 3 is CNY 790,288.3, and the DSO is CNY 26,257.2. These results demonstrate that the proposed model has favorable economic performance. Full article

The intensifying overexploitation of water resources and the increasing pollution discharge have exacerbated conflicts in water resource utilization, making it urgent to effectively reconcile the contradiction between water resource utilization and environmental protection. This study developed a Cost-Inclusive Multi-Objective Bargaining Methodology (CIMB), coupled with a Compromise Programming (CP) method, to address conflicts between water use and pollution discharge, considering the economic benefits and the sustainable development of water resources. A deterministic multi-objective bargaining approach was employed, with two players representing the maximization of water use benefits and the minimization of total pollution discharge. This study takes the middle and lower reaches of the Han River region as an example to optimize water resource allocation in ten cities in this area. Using the CIMB-CP model, the water use and pollution discharge for different cities were obtained, and the impact of various factors on the game outcomes was analyzed. The model results indicate that negotiation cost have a significant impact on the Nash equilibrium solution. Compared to the Cost-Exclusive Multi-Objective Bargaining Methodology (CEMB) model, the Nash equilibrium solution of the CIMB-CP model shows an approximately 0.1% decrease in economic benefits and an approximately 0.3% decrease in pollution discharge. The risk attitudes of the participants have a significant impact on the game outcomes, and decision-makers need to formulate corresponding negotiation strategies based on their own risk preferences. Full article

This paper proposes a two-stage, three-layer stochastic robust model and its solution method for a multi-energy access system (MEAS) considering different weather scenarios which are described through scenario probabilities and output uncertainties. In the first stage, based on the principle of the master–slave game, the master–slave relationship between the grid dispatch department (GDD) and the MEAS is constructed and the master–slave game transaction mechanism is analyzed. The GDD establishes a stochastic pricing model that takes into account the uncertainty of wind power scenario probabilities. In the second stage, considering the impacts of wind power and photovoltaic scenario probability uncertainties and output uncertainties, a max–max–min three-layer structured stochastic robust model for the MEAS is established and its cooperation model is constructed based on the Nash bargaining principle. A variable alternating iteration algorithm combining Karush–Kuhn–Tucker conditions (KKT) is proposed to solve the stochastic robust model of the MEAS. The alternating direction method of multipliers (ADMM) is used to solve the cooperation model of the MEAS and a particle swarm algorithm (PSO) is employed to solve the non-convex two-stage model. Finally, the effectiveness of the proposed model and method is verified through case studies. Full article

Forests are complex ecosystems that require integrated management to balance economic, social, and environmental dimensions. Conflicting objectives among stakeholders make optimal decision-making particularly challenging. This study seeks to balance the economic gains of forest harvesting with the goals of environmental conservation, with a focus on the Shafarood forest in Northern Iran. We applied multi-objective optimization and game theory to maximize the net present value (NPV) of forest harvesting while enhancing carbon sequestration. The research utilized data on stumpage prices, harvesting costs, tree density, volume per ha, growth rates, interest rates, carbon sequestration, and labour costs. Applying the epsilon-constraint method, we derived Pareto optimal solutions for a bi-objective model, and game theory was applied to negotiate between economic and environmental stakeholders. In the fifth round of bargaining, a Nash equilibrium was achieved between the two players. At this equilibrium point, the economic player achieved NPV from forest harvesting of 9001.884 (IRR 10,000/ha) and amount of carbon sequestration of 159.9383 tons/ha. Meanwhile, the environmental player achieved NPV from forest harvesting of 7861.248 (IRR 10,000/ha), along with a carbon sequestration of 159.9731 tons/ha. Results indicate significant trade-offs but reveal potential gains for both economic and environmental goals. These findings provide a robust framework for sustainable forest management and offer practical tools to support informed decision-making for diverse stakeholders. Full article

This paper develops a distributed cooperative optimization model for multiple virtual power plant (VPP) operations based on multi-stage robust optimization and proposes a distributed solution methodology based on the combination of the alternating direction method of multipliers (ADMMs) and column-and-constraint generation (CCG) algorithm to solve the corresponding optimization problem. Firstly, considering the peer-to-peer (P2P) electricity transactions among multiple VPPs, a deterministic cooperative optimal operation model of multiple VPPs based on Nash bargaining is constructed. Secondly, considering the uncertainties of photovoltaic generation and load demand, as well as the non-anticipativity of real-time scheduling of VPPs in engineering, a cooperative optimal operation model of multiple VPPs based on multi-stage robust optimization is then constructed. Thirdly, the constructed model is solved using a distributed solution methodology based on the combination of the ADMM and CCG algorithms. Finally, a case study is solved. The case study results show that the proposed method can realize the optimal scheduling of renewable energy in a more extensive range, which contributes to the promotion of the local consumption of renewable energy and the improvement of the renewable energy utilization efficiency of VPPs. Compared with the traditional deterministic cooperative optimal operation method of multiple VPPs, the proposed method is more resistant to the risk of the uncertainties of renewable energy and load demand and conforms to the non-anticipativity of real-time scheduling of VPPs in engineering. In summary, the presented works strike a balance between the operational robustness and operational economy of VPPs. In addition, under the presented works, there is no need for each VPP to divulge personal private data such as photovoltaic generation and load demand to other VPPs, so the security privacy protection of each VPP can be achieved. Full article

The star-shaped trans-shipment network causes the retailer’s bargaining power to be different, which leads to the misalignment of trans-shipment profit. Aimed at this, we take retailers and the trans-shipment paths as the nodes and edges of the trans-shipment network. Based on this, we model the multilateral negotiations between the central retailer and the local retailer and adopt the Generalized Nash Bargaining game to derive the optimal solution of the value function for the incomplete trans-shipment network under the bargaining mechanism. Furthermore, we reveal the convexity of the optimal trans-shipment value function and give the condition that the allocation of the bargaining mechanism is in the core. Based on this, we introduce the concept of pairwise Nash equilibrium and show the star-shaped trans-shipment network is the optimal endogenous formation of the trans-shipment network. In practice, the central retailer should introduce as many local retailers as possible to join this trans-shipment alliance, which will achieve Pareto improvement. Meanwhile, the central retailer should order as many as possible. Finally, it is more appropriate to establish a star-shaped trans-shipment network when one retailer has stronger negotiation power compared to other retailers in a distribution system, which not only ensures the stability of the allocation of trans-shipment profits but also the stability of the trans-shipment network. Full article

Signal control, as an integral component of traffic management, plays a pivotal role in enhancing the efficiency of traffic and reducing environmental pollution. However, the majority of signal control research based on game theory primarily focuses on vehicular perspectives, often neglecting pedestrians, who are significant participants at intersections. This paper introduces a game theory-based signal control approach designed to minimize and equalize the queued vehicles and pedestrians across the different phases. The Nash bargaining solution is employed to determine the optimal green duration for each phase within a fixed cycle length. Several simulation tests were carried out by SUMO software to assess the effectiveness of this proposed approach. We select the actuated signal control approach as the baseline to demonstrate the superiority and stability of the proposed control strategy. The simulation results reveal that the proposed approach is able to reduce pedestrian and vehicle delay, vehicle queue length, fuel consumption, and CO₂ emissions under different demand levels and demand patterns. Furthermore, the proposed approach consistently achieves more equalized queue length for each lane compared to the actuated control strategy, indicating a higher degree of fairness. Full article

Unbalanced power structures can lead to an inequitable distribution of the supply chain’s profits, creating unstable supply chain relationships and serious social problems. This paper builds a two-tier newsvendor model composed of a single supplier and a single retailer and introduces Nash bargaining as a reference for fairness. We investigate (1) the impact of fairness concerns on the performance of a retailer-dominated supply chain and a manufacturer-dominated supply chain; (2) how demand uncertainty affects the inequitable state; and (3) how overestimated and underestimated values of fairness concerns affect supply chain performance when fairness concerns are private information. After solving the equilibrium solution of the Stackelberg game and Nash-bargaining games and numerical analyses, it is shown that unilateral fairness concerns by the Stackelberg leader or follower can motivate the leader to sacrifice its profit to reduce their income inequality by offering a coordinating wholesale price. Of course, it is also effective for both participants to be fair-minded as soon as their fairness sensitivity is moderate enough. However, followers’ fairness concerns are more effective at decreasing inequity, while leaders can improve social welfare, i.e., increase the entire supply chain’s efficiency as well as market scale. We also find that in a more uncertain market, fewer fairness-concerned participants are supposed to reach a relatively fair condition. In addition, we conclude that sometimes asymmetric information about fairness concerns can improve the profit share of the disadvantaged and even channel efficiency. This paper extends the study of Nash-bargaining fairness concerns to retailer-dominated newsvendor models and enriches the field, when fairness concerns are asymmetric information. Full article

Efficient and low-carbon energy utilization is a crucial aspect of promoting green and sustainable development. Multi-energy microgrids, which incorporate multiple interchangeable energy types, offer effective solutions for low-carbon and efficient energy consumption. This study aims to investigate the sharing of energy and carbon in multiple multi-energy microgrids (MMEMs) to enhance their economic impact, low-carbon attributes, and the efficient utilization of renewable energy. In this paper, an energy–carbon co-sharing operation model is established, incorporating carbon capture systems (CCSs) and two-stage power-to-gas (P2G) devices within the MMEMs to actualize low-carbon operation. Furthermore, based on cooperative game theory, this paper establishes an energy–carbon co-sharing Nash negotiation model and negotiates based on the energy–carbon contribution of each subject in the cooperation as bargaining power so as to maximize both the benefits of the MMEM alliance and the distribution of the cooperation benefits. The case study results show that the overall benefits of the alliance can be increased through Nash negotiation. Energy–carbon co-sharing can effectively increase the renewable energy consumption rate of 8.34%, 8.78%, and 8.83% for each multi-energy microgrid, and the overall carbon emission reduction rate reaches 17.81%. Meanwhile, the distribution of the benefits according to the energy–carbon co-sharing contribution capacity of each entity is fairer. Full article

The increasing penetration of distributed energy resources (DERs) into distribution networks has changed the energy trading pattern in traditional electricity markets to some degree, and this will possibly cause network congestion and nodal voltage violations. This paper proposes a two-stage modeling framework for peer-to-peer (P2P) energy trading with voltage regulation services provision considered. In the first stage, direct P2P trading among prosumers, considering network congestion management, is enabled. In the second stage, prosumers provide voltage regulation services to address possible voltage violations. Aiming at maximizing social welfare, the alternative direction method of multipliers (ADMM) is applied to solve the two-stage problem. On the basis of the optimal energy solution of the two-stage problem, the energy prices of P2P transactions and the price of voltage regulation services are settled based on the Nash bargaining model. Finally, simulation results of the IEEE 33-bus power system with six prosumers included demonstrate the effectiveness of the proposed models. Full article

Due to global warming and climate change, it is essential to produce power using renewable sources, such as solar, wind, fuel cells, etc. The traditional grid shifts towards the smart grid by infusing digital communication techniques and information technology. As the current power system is shifting towards a smart grid, the utility and prosumers participate in the energy trading process. Due to the distributed nature of the smart grid, providing a fair price among them is becoming a difficult task. The article introduces a model for energy trading in a smart grid by allowing participants to negotiate in multiple stages using a game-theory-based multi-stage Nash Bargaining Solution (NBS). The model’s application of game theory enables the participants to decide on a mutually acceptable price, thereby encouraging the utility, private parties and prosumers (those who are able to generate and consume energy) to participate in the trading process. Since all parties participate in the trading procedure, greenhouse gas emissions are reduced. The proposed model also balances the benefits of consumers and producers in the final agreed fixed price. To demonstrate the efficacy of the proposed work, we compare the analytical results with feed-in-tariff (FiT) techniques in terms of consumers’ energy bills and producers’ revenue. For experimental analysis, 20 participants are considered, where the percentage reduction in the bill of each consumer and the percentage increment of revenue of each producer are compared to FiT. On average, the overall bill of the consumer is reduced by $32.8\%$, and the producers’ revenue is increased by $64.83\%$ compared to FiT. It has been shown further that the proposed model shows better performance as compared to FiT with an increase in the number of participants. The analysis of carbon emission reduction in the proposed model has been analyzed, where, for 10 participants, the carbon emission reduction is approximately 28.48 kg/kWh, and for 100 participants is 342.397 kg/kWh. Full article

The Rubinstein alternating-offers bargaining game is reconsidered, where players show fairness concerns and their fairness references are characterized by the Nash bargaining solution. The objective of this paper is to explore the impact of fairness concerns in the alternating-offer bargaining game. Alternating-offer bargaining with fairness concerns is developed. We construct a subgame perfect equilibrium and show its uniqueness. Then, it is shown that players’ payoffs in the subgame perfect equilibrium are positively related to their own fairness concern coefficient and bargaining power and negatively to the opponents’ fairness concern coefficient. Moreover, it is shown that the limited equilibrium partition depends on the ratio of discount rates of the two players when the time lapse between two offers goes to zero. Finally, the proposed model is applied to the bilateral monopoly market of professional basketball players, and some properties of equilibrium price are shown. Our result provides the implication that players should carefully weigh their own fairness concerns, bargaining power and fairness concerns of their opponents, and then make proposals, rather than simply follow the suggestion that the proposal at the current stage is higher than that at the past stages. Full article