In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operatio...In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operation of sets (namely, Minkowski addition) in Boolean space B<sup>n</sup> are presented. Also, sums and multisums of various “classical figures” as: sphere, layer, interval etc. are considered. The obtained results make possible to describe multisums by such characteristics of summands as: the sphere radius, weight of layer, dimension of interval etc. using the methods presented in [2], as well as possible solutions of the equation X+Y=A, where , are considered. In spite of simplicity of the statement of the problem, complexity of its solutions is obvious at once, when the connection of solutions with constructions of equidistant codes or existence the Hadamard matrices is apparent. The present paper submits certain results (statements) which are to be the ground for next investigations dealing with Minkowski summation operations of sets in Boolean space.展开更多
Development of wireless technologies provides a promising communication scheme with low operating cost and high speed.However,fragile communication channels bring negative impacts on the reliability of bidirectional c...Development of wireless technologies provides a promising communication scheme with low operating cost and high speed.However,fragile communication channels bring negative impacts on the reliability of bidirectional communication.Packet loss,the inherent attribute of communication may deteriorate control performance of distributed energy resources,affecting the profit of a virtual power plant(VPP)participating in a power market.In this paper,we present a quantitative method to analyze the effect of imperfect communication on the scheduling strategy of VPPs.In the proposed approach,a four-state discrete time Markov chain is used to model average packet loss probability.Then a two-stage dispatch scheme is proposed to maximize daily profit of a VPP with microgas-turbine,wind and electric vehicles(EVs),Meanwhile,to reduce the dimensions of the model due to large-scale EVs in the vehicle to grid(V2G)operation,a compression method of an EV cluster model is proposed based on Minkowski addition.Feasibility and effectiveness of the proposed method,including reducing the impact of data loss on the scheduling of VPPs,can significantly improve the economic efficiency of VPPs,and are verified by given cases.展开更多
文摘In many problems of combinatory analysis, operations of addition of sets are used (sum, direct sum, direct product etc.). In the present paper, as well as in the preceding one [1], some properties of addition operation of sets (namely, Minkowski addition) in Boolean space B<sup>n</sup> are presented. Also, sums and multisums of various “classical figures” as: sphere, layer, interval etc. are considered. The obtained results make possible to describe multisums by such characteristics of summands as: the sphere radius, weight of layer, dimension of interval etc. using the methods presented in [2], as well as possible solutions of the equation X+Y=A, where , are considered. In spite of simplicity of the statement of the problem, complexity of its solutions is obvious at once, when the connection of solutions with constructions of equidistant codes or existence the Hadamard matrices is apparent. The present paper submits certain results (statements) which are to be the ground for next investigations dealing with Minkowski summation operations of sets in Boolean space.
基金supported in part by the National Natural Science Foundation of China(No.52022016).
文摘Development of wireless technologies provides a promising communication scheme with low operating cost and high speed.However,fragile communication channels bring negative impacts on the reliability of bidirectional communication.Packet loss,the inherent attribute of communication may deteriorate control performance of distributed energy resources,affecting the profit of a virtual power plant(VPP)participating in a power market.In this paper,we present a quantitative method to analyze the effect of imperfect communication on the scheduling strategy of VPPs.In the proposed approach,a four-state discrete time Markov chain is used to model average packet loss probability.Then a two-stage dispatch scheme is proposed to maximize daily profit of a VPP with microgas-turbine,wind and electric vehicles(EVs),Meanwhile,to reduce the dimensions of the model due to large-scale EVs in the vehicle to grid(V2G)operation,a compression method of an EV cluster model is proposed based on Minkowski addition.Feasibility and effectiveness of the proposed method,including reducing the impact of data loss on the scheduling of VPPs,can significantly improve the economic efficiency of VPPs,and are verified by given cases.
