Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point th...Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.展开更多
This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.
The optimal planning and design of an integrated energy system(IES)is of great significance to facilitate distributed renewable energy(DRE)technology and improve the overall energy efficiency of the energy system.With...The optimal planning and design of an integrated energy system(IES)is of great significance to facilitate distributed renewable energy(DRE)technology and improve the overall energy efficiency of the energy system.With the increased penetration of distributed generation(DG),the power supply and load sides of an IES present more increased levels of uncertainties.Demand response(DR)and the energy storage system(ESS)serve as important means to shift energy supply and use across time to counter the indeterminate variations.However,the current IES planning methods are unable to effectively deal with the uncertainties of DREs and loads,and to optimize the operations of DG-DR-ESS due to the enormous possible combinations.In this paper,a new method for the optimal planning and design of an integrated energy system has been introduced and verified.The new method consists of three integrated elements.First,the method of the probability scenario has been used to model the uncertainties of the DREs and loads so as to better characterize the impact of uncertainty on the planning and design of the IES.Secondly,the optimal operation of the IES under different probability scenarios is ensured using the second-order cone optimization for quick solutions due to the simplicity of this sub-problem,serving as the bottom-level optimization.Thirdly,the optimal planning and design of IES through optimal sizing of the power generating components and ESS are performed using a special meta-model based global optimization method due to the complex,black-box,and computation intensive nature of this top-level optimization in a nested,bi-level global optimization problem.The combined approach takes full account of the interrelated operations of DG-DR-ESS under different design configurations to support a better optimal planning and design of the IES.The simulation has been carried out on an IES system modified from the IEEE 33-node distribution system.The simulation results show that the proposed method and model are effective.展开更多
文摘Abstract The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
基金Supported by the National 973-Project from MOST and Trans-Century Training Programme Foundation for the Talents by Ministry of Education and the Postdoctoral Foundation of China.
文摘This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.
基金This work was supported by the National Natural Science Foundation of China(51607170)the Key Front Science Project of Chinese Academy of Sciences(QYZDB-SSW-JSC024)the International Collaboration Programs of the Chinese Academy of Sciences and the Foreign Expert Affairs.
文摘The optimal planning and design of an integrated energy system(IES)is of great significance to facilitate distributed renewable energy(DRE)technology and improve the overall energy efficiency of the energy system.With the increased penetration of distributed generation(DG),the power supply and load sides of an IES present more increased levels of uncertainties.Demand response(DR)and the energy storage system(ESS)serve as important means to shift energy supply and use across time to counter the indeterminate variations.However,the current IES planning methods are unable to effectively deal with the uncertainties of DREs and loads,and to optimize the operations of DG-DR-ESS due to the enormous possible combinations.In this paper,a new method for the optimal planning and design of an integrated energy system has been introduced and verified.The new method consists of three integrated elements.First,the method of the probability scenario has been used to model the uncertainties of the DREs and loads so as to better characterize the impact of uncertainty on the planning and design of the IES.Secondly,the optimal operation of the IES under different probability scenarios is ensured using the second-order cone optimization for quick solutions due to the simplicity of this sub-problem,serving as the bottom-level optimization.Thirdly,the optimal planning and design of IES through optimal sizing of the power generating components and ESS are performed using a special meta-model based global optimization method due to the complex,black-box,and computation intensive nature of this top-level optimization in a nested,bi-level global optimization problem.The combined approach takes full account of the interrelated operations of DG-DR-ESS under different design configurations to support a better optimal planning and design of the IES.The simulation has been carried out on an IES system modified from the IEEE 33-node distribution system.The simulation results show that the proposed method and model are effective.
