When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game ...When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.展开更多
为解决区域综合能源系统中多主体利益冲突、用户侧分布式储能投资成本高昂、容量利用不均以及碳排放量较高等问题,提出一种基于云储能服务商-综合能源系统运行商(integrated energy system operators,IESO)-负荷聚合商(load aggregators...为解决区域综合能源系统中多主体利益冲突、用户侧分布式储能投资成本高昂、容量利用不均以及碳排放量较高等问题,提出一种基于云储能服务商-综合能源系统运行商(integrated energy system operators,IESO)-负荷聚合商(load aggregators,LA)联盟三层博弈的区域综合能源系统低碳运行策略。首先,构建租赁云储能的IESO与LA的能源交易框架。其次,考虑到多个理性主体对盈利最大化的诉求,建立综合能源系统三层博弈模型。第一层为以IESO为主导者、LA联盟为伴随者的主从博弈;第二层为以云储能服务商为供给者、IESO为接收者的主从博弈;第三层是LA联盟成员之间的合作博弈,并采取非对称纳什议价法分配收益。最后,利用二分法、KKT条件结合交替方向乘子法(alternating direction multiplier method,ADMM)对该模型进行求解。仿真结果表明,该策略不仅能够促进系统低碳运行,而且能够满足各主体的经济性需求。展开更多
针对多微网与上级能源网络协同优化运行的问题,提出一种基于混合博弈的社区综合能源服务商(community integrated energy service provider,CIESP)与微网群的二阶段协同运行策略。首先,构建了CIESP与微网群能源交易的基本框架;其次,针...针对多微网与上级能源网络协同优化运行的问题,提出一种基于混合博弈的社区综合能源服务商(community integrated energy service provider,CIESP)与微网群的二阶段协同运行策略。首先,构建了CIESP与微网群能源交易的基本框架;其次,针对源荷不确定性,采用蒙特卡洛法生成大量随机场景,并通过K-means聚类进行场景削减;接着,将主从博弈和合作博弈相结合,建立CIESP与微网群的混合博弈模型,其中,CIESP为领导者,以自身收益最大为目标,通过制定与微网群的能源交易价格引导微网群优化运行,微网群为跟随者,以群运行成本最小为目标,通过合作来对CIESP的定价决策进行响应;然后,基于纳什谈判理论,将模型下层各微网之间的合作博弈转化为联盟成本最小化和合作收益分配两个子问题。最后,采用差分进化算法结合交替方向乘子法对模型进行求解,算例仿真验证了所提方法能够兼顾各方利益的同时促进新能源消纳并降低碳排放。展开更多
Based on the actual experience of cooperation in the supply chain, the Nash solution of two enterprises cooperative games is given. Not only is the solution unique, but it is also stable, and neither side has the capa...Based on the actual experience of cooperation in the supply chain, the Nash solution of two enterprises cooperative games is given. Not only is the solution unique, but it is also stable, and neither side has the capability to deviate the allocation of interests from the equilibrium point. If some firm tries to withdraw from cooperation or threaten to use other particular strategy, the negotiations are likely to achieve the distribution by the threat game; The calculating method of the choice of the optimal bargaining base point and the corresponding optimal pay-off vector are given.展开更多
以能源交易为背景,针对多微电网合作中的运行优化问题,提出了基于Nash议价模型的合作博弈策略,旨在实现微电网之间的合作,以最大化整体利益,同时考虑能源交易和成本优化。首先,将各微电网视为博弈参与者,构建了基于Nash议价理论的多微...以能源交易为背景,针对多微电网合作中的运行优化问题,提出了基于Nash议价模型的合作博弈策略,旨在实现微电网之间的合作,以最大化整体利益,同时考虑能源交易和成本优化。首先,将各微电网视为博弈参与者,构建了基于Nash议价理论的多微电网合作博弈模型,通过选择能源交易策略和运行策略来影响其能源成本和效益。其次,采用交替方向乘子法(alternating direction multiplier method,ADMM)求解此多参与者优化问题,通过将原问题分解为子问题并引入乘子变量来实现迭代求解。最后,在每次迭代中,各微电网根据其局部信息更新能源交易和运行策略,并利用乘子变量进行信息交换和博弈协调,以达到全局一致性。结果表明,该策略在多微电网合作中能够实现整体性能的提升,有效促进了可再生能源的消纳水平,平衡了各参与者的利益,同时降低了能源成本。展开更多
随着全国碳交易市场政策落地,为充分挖掘区域综合能源系统(regional integrated energy system,RIES)低碳减排能力,提高多区域综合能源系统接入主动配电网(active distribution network,ADN)的经济交互效益,提出了考虑灵活性资源与低碳...随着全国碳交易市场政策落地,为充分挖掘区域综合能源系统(regional integrated energy system,RIES)低碳减排能力,提高多区域综合能源系统接入主动配电网(active distribution network,ADN)的经济交互效益,提出了考虑灵活性资源与低碳交互结构的区域综合能源系统联盟参与配电网调峰调度的优化调度策略。建立了以主动配电网为主体,区域综合能源系统联盟为从体的主从博弈模型。主体以最大化交互效益目标制定分时电价策略,从体成员间通过联络线实现多能共享,考虑碳交易制度以供能与碳交易成本之和最小为目标,响应主体电价策略,建立了下层多区域综合能源系统联盟合作博弈优化模型。引入包含需求响应、储能和电动汽车在内的灵活性资源,配合碳捕集-电转气耦合机组优化联盟内部各系统的低碳供能策略,满足联盟负荷需求。基于纳什议价理论完成联盟成员合作收益的分配。通过算例验证所提策略能够有效减少各区域综合能源系统碳排放,并保障主从交互经济效益。展开更多
随着分布式能源的发展,传统用户具备发电能力而成为产消者(production and consumption users,PCU)的趋势愈演愈烈,该文主要研究了同一微能网下大量产消者的协同运行问题。电价不确定性和产消者响应给微能网协同不同利益主体的PCU之间...随着分布式能源的发展,传统用户具备发电能力而成为产消者(production and consumption users,PCU)的趋势愈演愈烈,该文主要研究了同一微能网下大量产消者的协同运行问题。电价不确定性和产消者响应给微能网协同不同利益主体的PCU之间的调度带来困难。在此背景下提出考虑产消者响应与电价不确定性的微能网与产消者混合博弈优化策略。首先,构建产消者响应模型和电价不确定性模型,引入效用函数来描述PCU的满意程度,采用鲁棒优化和机会约束方法描述电价的不确定性与新能源出力的不确定性。其次,构建混合博弈模型,即上层微能网运营商(integrated energy operator,IEO)与下层PCU之间的主从博弈模型和下层PCU联盟之间的合作博弈模型。上层IEO作为主从博弈的领导者以运行成本最小化为目标,通过为产消者制定电价、热价引导产消者的用能需求;下层产消者作为跟随者,以效益最大为目标通过合作方式对IEO的决策进行产消者响应。PCU之间的合作博弈以纳什议价的方式进行,将PCU模型等效为联盟收益最大化和合作分配两个子问题。基于KKT条件利用Big-M法和Mc Cormick包络法将双层问题转换为单层混合整数线性规划问题求解主从博弈,结合交替方向乘子法(alternating direction multiplier method,ADMM)求解下层合作博弈。结果表明,该文所提策略有效协调了微能网与PCU的调度并保证了PCU合作联盟的公平性。展开更多
基金National Natural Science Foundation of China(NSFC61773142,NSFC62303136)。
文摘When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.
文摘为解决区域综合能源系统中多主体利益冲突、用户侧分布式储能投资成本高昂、容量利用不均以及碳排放量较高等问题,提出一种基于云储能服务商-综合能源系统运行商(integrated energy system operators,IESO)-负荷聚合商(load aggregators,LA)联盟三层博弈的区域综合能源系统低碳运行策略。首先,构建租赁云储能的IESO与LA的能源交易框架。其次,考虑到多个理性主体对盈利最大化的诉求,建立综合能源系统三层博弈模型。第一层为以IESO为主导者、LA联盟为伴随者的主从博弈;第二层为以云储能服务商为供给者、IESO为接收者的主从博弈;第三层是LA联盟成员之间的合作博弈,并采取非对称纳什议价法分配收益。最后,利用二分法、KKT条件结合交替方向乘子法(alternating direction multiplier method,ADMM)对该模型进行求解。仿真结果表明,该策略不仅能够促进系统低碳运行,而且能够满足各主体的经济性需求。
文摘针对多微网与上级能源网络协同优化运行的问题,提出一种基于混合博弈的社区综合能源服务商(community integrated energy service provider,CIESP)与微网群的二阶段协同运行策略。首先,构建了CIESP与微网群能源交易的基本框架;其次,针对源荷不确定性,采用蒙特卡洛法生成大量随机场景,并通过K-means聚类进行场景削减;接着,将主从博弈和合作博弈相结合,建立CIESP与微网群的混合博弈模型,其中,CIESP为领导者,以自身收益最大为目标,通过制定与微网群的能源交易价格引导微网群优化运行,微网群为跟随者,以群运行成本最小为目标,通过合作来对CIESP的定价决策进行响应;然后,基于纳什谈判理论,将模型下层各微网之间的合作博弈转化为联盟成本最小化和合作收益分配两个子问题。最后,采用差分进化算法结合交替方向乘子法对模型进行求解,算例仿真验证了所提方法能够兼顾各方利益的同时促进新能源消纳并降低碳排放。
文摘Based on the actual experience of cooperation in the supply chain, the Nash solution of two enterprises cooperative games is given. Not only is the solution unique, but it is also stable, and neither side has the capability to deviate the allocation of interests from the equilibrium point. If some firm tries to withdraw from cooperation or threaten to use other particular strategy, the negotiations are likely to achieve the distribution by the threat game; The calculating method of the choice of the optimal bargaining base point and the corresponding optimal pay-off vector are given.
文摘以能源交易为背景,针对多微电网合作中的运行优化问题,提出了基于Nash议价模型的合作博弈策略,旨在实现微电网之间的合作,以最大化整体利益,同时考虑能源交易和成本优化。首先,将各微电网视为博弈参与者,构建了基于Nash议价理论的多微电网合作博弈模型,通过选择能源交易策略和运行策略来影响其能源成本和效益。其次,采用交替方向乘子法(alternating direction multiplier method,ADMM)求解此多参与者优化问题,通过将原问题分解为子问题并引入乘子变量来实现迭代求解。最后,在每次迭代中,各微电网根据其局部信息更新能源交易和运行策略,并利用乘子变量进行信息交换和博弈协调,以达到全局一致性。结果表明,该策略在多微电网合作中能够实现整体性能的提升,有效促进了可再生能源的消纳水平,平衡了各参与者的利益,同时降低了能源成本。
文摘随着全国碳交易市场政策落地,为充分挖掘区域综合能源系统(regional integrated energy system,RIES)低碳减排能力,提高多区域综合能源系统接入主动配电网(active distribution network,ADN)的经济交互效益,提出了考虑灵活性资源与低碳交互结构的区域综合能源系统联盟参与配电网调峰调度的优化调度策略。建立了以主动配电网为主体,区域综合能源系统联盟为从体的主从博弈模型。主体以最大化交互效益目标制定分时电价策略,从体成员间通过联络线实现多能共享,考虑碳交易制度以供能与碳交易成本之和最小为目标,响应主体电价策略,建立了下层多区域综合能源系统联盟合作博弈优化模型。引入包含需求响应、储能和电动汽车在内的灵活性资源,配合碳捕集-电转气耦合机组优化联盟内部各系统的低碳供能策略,满足联盟负荷需求。基于纳什议价理论完成联盟成员合作收益的分配。通过算例验证所提策略能够有效减少各区域综合能源系统碳排放,并保障主从交互经济效益。
文摘随着分布式能源的发展,传统用户具备发电能力而成为产消者(production and consumption users,PCU)的趋势愈演愈烈,该文主要研究了同一微能网下大量产消者的协同运行问题。电价不确定性和产消者响应给微能网协同不同利益主体的PCU之间的调度带来困难。在此背景下提出考虑产消者响应与电价不确定性的微能网与产消者混合博弈优化策略。首先,构建产消者响应模型和电价不确定性模型,引入效用函数来描述PCU的满意程度,采用鲁棒优化和机会约束方法描述电价的不确定性与新能源出力的不确定性。其次,构建混合博弈模型,即上层微能网运营商(integrated energy operator,IEO)与下层PCU之间的主从博弈模型和下层PCU联盟之间的合作博弈模型。上层IEO作为主从博弈的领导者以运行成本最小化为目标,通过为产消者制定电价、热价引导产消者的用能需求;下层产消者作为跟随者,以效益最大为目标通过合作方式对IEO的决策进行产消者响应。PCU之间的合作博弈以纳什议价的方式进行,将PCU模型等效为联盟收益最大化和合作分配两个子问题。基于KKT条件利用Big-M法和Mc Cormick包络法将双层问题转换为单层混合整数线性规划问题求解主从博弈,结合交替方向乘子法(alternating direction multiplier method,ADMM)求解下层合作博弈。结果表明,该文所提策略有效协调了微能网与PCU的调度并保证了PCU合作联盟的公平性。
