Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch...Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.展开更多
Dependence of distributed generation(DG)outputs and load plays an essential role in renewable energy accommodation.This paper presents a novel DG hosting capacity(DGHC)evaluation method for distribution networks consi...Dependence of distributed generation(DG)outputs and load plays an essential role in renewable energy accommodation.This paper presents a novel DG hosting capacity(DGHC)evaluation method for distribution networks considering highdimensional dependence relations among solar radiation,wind speed,and various load types(i.e.,commercial,residential,and industrial).First,an advanced dependence modeling method called regular vine(R-vine)is applied to capture the complex dependence structure of solar radiation,wind speed,commercial loads,industrial loads,and residential loads.Then,a chanceconstrained DGHC evaluation model is employed to figure out maximum hosting capacity of each DG and its optimal allocation plan with different operational risks.Finally,a Benders decomposition algorithm is also employed to reduce computational burden.The proposed approaches are validated using a set of historical data from China.Results show dependence among different DGs and loads has significant impact on hosting capacity.Results also suggest using the R-vine model to capture dependence among distributed energy resources(DERs)and load.This finding provides useful advice for distribution networks in installing renewable energy generations.展开更多
Electric distribution networks have to deal with issues caused by natural disasters. These problems possess unique characteristics, and their severity can make load restoration methods impotent. One solution that can ...Electric distribution networks have to deal with issues caused by natural disasters. These problems possess unique characteristics, and their severity can make load restoration methods impotent. One solution that can help in alleviating the aftermath is the use of microgrids (MGs). Employing the cumulative capacity of the generation resources through MG coupling facilitates the self-healing capability and leads to better-coordinated energy management during the restoration period, while the switching capability of the system should also be considered. In this paper, to form and schedule dynamic MGs in distribution systems, a novel model based on mixed-integer linear programming (MILP) is proposed. This approach employs graph-related theories to formulate the optimal formation of the networked MGs and management of their proper participation in the load recovery process. In addition, the Benders decomposition technique is applied to alleviate computability issues of the optimization problem. The validity and applicability of the proposed model are evaluated by several simulation studies.展开更多
Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenario...Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus system.Numerical results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.展开更多
A unified optimal power flow(OPF) model for AC/DC grids integrated with natural gas systems is proposed for the real-time scheduling of power systems.Herein, the primary physical couplings underlying this coordinated ...A unified optimal power flow(OPF) model for AC/DC grids integrated with natural gas systems is proposed for the real-time scheduling of power systems.Herein, the primary physical couplings underlying this coordinated system are modeled and investigated. In addition, the uncertainties of gas loads are considered when studying the role of gas supply for gas-fired units in power system operations. The nonlinear gas system constraints are converted to the second-order cone forms that allow for the use of the Benders decomposition techniques and the interior-point method to obtain the optimal solution. The numerical results of the modified IEEE 118-bus test system that integrates the Belgium 20-node natural gas system demonstrate the effectiveness of the proposed model. The effects of gas demand uncertainties on the optimal schedule of thermal generators are investigated as well.展开更多
Cooperation between electric power networks(EPNs)and district heating networks(DHNs)has been extensively studied under the assumption that all information exchanged is authentic.However,EPNs and DHNs belonging to diff...Cooperation between electric power networks(EPNs)and district heating networks(DHNs)has been extensively studied under the assumption that all information exchanged is authentic.However,EPNs and DHNs belonging to different entities may result in marketing fraud.This paper proposes a cooperation mechanism for integrated electricity-heat systems(IEHSs)to overcome information asymmetry.First,a fraud detection method based on multiparametric programming with guaranteed feasibility reveals the authenticity of the information.Next,all honest entities are selected to form a coalition.Furthermore,to maintain operational independence and distribute benefits fairly,Benders decomposition is enhanced to calculate Shapley values in a distributed fashion.Finally,the cooperative surplus generated by the coalition is allocated according to the marginal contribution of each entity.Numerical results show that the proposed mechanism stimulates cooperation while achieving Pareto optimality under asymmetric information.展开更多
With the significant development of liquefied natural gas(LNG)rail transport,the railway system is increasingly more closely connected with the integrated electricity-natural gas system(IEGS).To coordinate the economi...With the significant development of liquefied natural gas(LNG)rail transport,the railway system is increasingly more closely connected with the integrated electricity-natural gas system(IEGS).To coordinate the economic operations of the two systems,this paper innovatively proposes a coordinated dispatch model of IEGS with LNG infrastructures and a freight railway network with LNG transport.First,an operational scheduling model of the railway network,considering energy consumption,is put forward for both LNG transmission and ordinary freight transport.Then,the coordinated dispatch problem of IEGS and the railway network is formulated into a mixed-integer linear programming model via the big M method and a modified incremental linearization approach.Finally,a bi-level optimization algorithm based on generalized benders decomposition(GBD)is presented to solve the coordinated dispatch problem due to the restrictions on exchanging private information.Case studies demonstrate the effectiveness of the proposed model and algorithm as well as the potential benefit for wind power accommodation.展开更多
Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to so...Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to solve the economic dispatch of generation power among all the generating units. The core of the two stages is how to determine the feasibility of SCUC states. The existence of ramp rate constraints and security constraints increases the difficulty of obtaining an analytical necessary and sufficient condition for determining the quasi-feasibility of SCUC states at each scheduling time. However, a numerical necessary and sufficient numerical condition is proposed and proven rigorously based on Benders Decomposition Theorem. Testing numerical example shows the effectiveness and efficiency of the condition.展开更多
With e-commerce concentrating retailers and customers onto one platform,logistics companies(e.g.,JD Logistics)have launched integrated supply chain solutions for corporate customers(e.g.,online retailers)with warehous...With e-commerce concentrating retailers and customers onto one platform,logistics companies(e.g.,JD Logistics)have launched integrated supply chain solutions for corporate customers(e.g.,online retailers)with warehousing,transportation,last-mile delivery,and other value-added services.The platform’s concentration of business flows leads to the consolidation of logistics resources,which allows us to coordinate supply chain operations across different corporate customers.This paper studies the stochastic joint replenishment problem of coordinating multiple suppliers and multiple products to gain the economies of scale of the replenishment setup cost and the warehouse inbound operational cost.To this end,we develop stochastic joint replenishment models based on the general-integer policy(SJRM-GIP)for the multi-supplier and multi-product problems and further reformulate the resulted nonlinear optimization models into equivalent mixed integer second-order conic programs(MISOCPs)when the inbound operational cost takes the square-root form.Then,we propose generalized Benders decomposition(GBD)algorithms to solve the MISOCPs by exploiting the Lagrangian duality,convexity,and submodularity of the sub-problems.To reduce the computational burden of the SJRM-GIP,we further propose an SJRM based on the power-of-two policy and extend the proposed GBD algorithms.Extensive numerical experiments based on practical datasets show that the stochastic joint replenishment across multiple suppliers and multiple products would deliver 13∼20%cost savings compared to the independent replenishment benchmark,and on average the proposed GBD algorithm based on the enhanced gradient cut can achieve more than 90%computational time reduction for large-size problem instances compared to the Gurobi solver.The power-of-two policy is capable of providing high-quality solutions with high computational efficiency.展开更多
As extreme weather events have become more frequent in recent years,improving the resilience and reliability of power systems has become an important area of concern.In this paper,a robust preventive-corrective securi...As extreme weather events have become more frequent in recent years,improving the resilience and reliability of power systems has become an important area of concern.In this paper,a robust preventive-corrective security-constrained optimal power flow(RO-PCSCOPF)model is proposed to improve power system reliability under N−k outages.Both the short-term emergency limit(STL)and the long-term operating limit(LTL)of the post-contingency power flow on the branch are considered.Compared with the existing robust corrective SCOPF model that only considers STL or LTL,the proposed ROPCSCOPF model can achieve a more reliable generation dispatch solution.In addition,this paper also summarizes and compares the solution methods for solving the N−k SCOPF problem.The computational efficiency of the classical Benders decomposition(BD)method,robust optimization(RO)method,and line outage distribution factor(LODF)method are investigated on the IEEE 24-bus Reliability Test System and 118-bus system.Simulation results show that the BD method has the worst computation performance.The RO method and the LODF method have comparable performance.However,the LODF method can only be used for the preventive SCOPF and not for the corrective SCOPF.The RO method can be used for both.展开更多
This paper addresses the coordinated operation of natural gas and electricity networks considering the line pack flexibility in the natural gas pipelines.The problem is formulated as a mixed integer linear programming...This paper addresses the coordinated operation of natural gas and electricity networks considering the line pack flexibility in the natural gas pipelines.The problem is formulated as a mixed integer linear programming problem.The objective is to minimize the operation cost of natural gas and electricity networks considering the price of the natural gas supply.Benders decomposition is used to solve the formulated problem.The master problem minimizes the startup and shutdown costs as well as the operation cost of the thermal units other than the gasfired generation units in the electricity network.The first subproblem validates the feasibility of the decisions made in the master problem in the electricity network.And if there is any violation,feasibility Benders cut is generated and added to the master problem.The second subproblem ensures the feasibility of the decisions of the master problem in the natural gas transportation network considering the line pack constraints.The last sub-problem ensuresthe optimality of the natural gas network operation problem considering the demand of the gas-fired generation units and line pack.The nonlinear line pack and flow constraints in the feasibility and optimality subproblems of natural gas transportation network are linearized using Newton-Raphson technique.The presented case study shows the effectiveness of the proposed approach.It is shown that leveraging the stored gas in the natural gas pipelines would further reduce the total operation cost.展开更多
In order to facilitate the scientific management of large-sized shipping companies, fleet planning under complicated circumstances has been studied. Based on multiple influencing factors such as the techno-economic st...In order to facilitate the scientific management of large-sized shipping companies, fleet planning under complicated circumstances has been studied. Based on multiple influencing factors such as the techno-economic status of ships, the investment capacity of company, the possible purchase of new ships, the buying/selling of second-hand vessels and the chartering/renting of ships, a mixed-integer programming model for fleet planning has been established. A large-sized shipping company is utilized to make an empirical study, and Benders decomposition algorithm is employed to test the applicability of the proposed model. The result shows that the model is capable for multi-route, multi-ship and large-scaled fleet planning and thus helpful to support the decision making of large-sized shipping companies.展开更多
基金supported by the Key Research and Development Project of Guangdong Province(Grant No.2021B0101230004)the National Natural Science Foundation of China(Grant No.51977080).
文摘Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.
基金supported by the High-level Talents Introduction&Research Start-up Fund Program of Nanjing Institute of Technology(YKJ202134).
文摘Dependence of distributed generation(DG)outputs and load plays an essential role in renewable energy accommodation.This paper presents a novel DG hosting capacity(DGHC)evaluation method for distribution networks considering highdimensional dependence relations among solar radiation,wind speed,and various load types(i.e.,commercial,residential,and industrial).First,an advanced dependence modeling method called regular vine(R-vine)is applied to capture the complex dependence structure of solar radiation,wind speed,commercial loads,industrial loads,and residential loads.Then,a chanceconstrained DGHC evaluation model is employed to figure out maximum hosting capacity of each DG and its optimal allocation plan with different operational risks.Finally,a Benders decomposition algorithm is also employed to reduce computational burden.The proposed approaches are validated using a set of historical data from China.Results show dependence among different DGs and loads has significant impact on hosting capacity.Results also suggest using the R-vine model to capture dependence among distributed energy resources(DERs)and load.This finding provides useful advice for distribution networks in installing renewable energy generations.
文摘Electric distribution networks have to deal with issues caused by natural disasters. These problems possess unique characteristics, and their severity can make load restoration methods impotent. One solution that can help in alleviating the aftermath is the use of microgrids (MGs). Employing the cumulative capacity of the generation resources through MG coupling facilitates the self-healing capability and leads to better-coordinated energy management during the restoration period, while the switching capability of the system should also be considered. In this paper, to form and schedule dynamic MGs in distribution systems, a novel model based on mixed-integer linear programming (MILP) is proposed. This approach employs graph-related theories to formulate the optimal formation of the networked MGs and management of their proper participation in the load recovery process. In addition, the Benders decomposition technique is applied to alleviate computability issues of the optimization problem. The validity and applicability of the proposed model are evaluated by several simulation studies.
基金the Science and Technology Project of State Grid Corporation of China,Grant Number 5108-202304065A-1-1-ZN.
文摘Stochastic unit commitment is one of the most powerful methods to address uncertainty. However, the existingscenario clustering technique for stochastic unit commitment cannot accurately select representative scenarios,which threatens the robustness of stochastic unit commitment and hinders its application. This paper providesa stochastic unit commitment with dynamic scenario clustering based on multi-parametric programming andBenders decomposition. The stochastic unit commitment is solved via the Benders decomposition, which decouplesthe primal problem into the master problem and two types of subproblems. In the master problem, the committedgenerator is determined, while the feasibility and optimality of generator output are checked in these twosubproblems. Scenarios are dynamically clustered during the subproblem solution process through the multiparametric programming with respect to the solution of the master problem. In other words, multiple scenariosare clustered into several representative scenarios after the subproblem is solved, and the Benders cut obtainedby the representative scenario is generated for the master problem. Different from the conventional stochasticunit commitment, the proposed approach integrates scenario clustering into the Benders decomposition solutionprocess. Such a clustering approach could accurately cluster representative scenarios that have impacts on theunit commitment. The proposed method is tested on a 6-bus system and the modified IEEE 118-bus system.Numerical results illustrate the effectiveness of the proposed method in clustering scenarios. Compared withthe conventional clustering method, the proposed method can accurately select representative scenarios whilemitigating computational burden, thus guaranteeing the robustness of unit commitment.
文摘A unified optimal power flow(OPF) model for AC/DC grids integrated with natural gas systems is proposed for the real-time scheduling of power systems.Herein, the primary physical couplings underlying this coordinated system are modeled and investigated. In addition, the uncertainties of gas loads are considered when studying the role of gas supply for gas-fired units in power system operations. The nonlinear gas system constraints are converted to the second-order cone forms that allow for the use of the Benders decomposition techniques and the interior-point method to obtain the optimal solution. The numerical results of the modified IEEE 118-bus test system that integrates the Belgium 20-node natural gas system demonstrate the effectiveness of the proposed model. The effects of gas demand uncertainties on the optimal schedule of thermal generators are investigated as well.
基金supported by National Natural Science Foundation of China(No.52177087).
文摘Cooperation between electric power networks(EPNs)and district heating networks(DHNs)has been extensively studied under the assumption that all information exchanged is authentic.However,EPNs and DHNs belonging to different entities may result in marketing fraud.This paper proposes a cooperation mechanism for integrated electricity-heat systems(IEHSs)to overcome information asymmetry.First,a fraud detection method based on multiparametric programming with guaranteed feasibility reveals the authenticity of the information.Next,all honest entities are selected to form a coalition.Furthermore,to maintain operational independence and distribute benefits fairly,Benders decomposition is enhanced to calculate Shapley values in a distributed fashion.Finally,the cooperative surplus generated by the coalition is allocated according to the marginal contribution of each entity.Numerical results show that the proposed mechanism stimulates cooperation while achieving Pareto optimality under asymmetric information.
基金This work was supported by the National Key Research and Development Program of China(2016YFB0901900)the National Natural Science Foundation of China(51637008).
文摘With the significant development of liquefied natural gas(LNG)rail transport,the railway system is increasingly more closely connected with the integrated electricity-natural gas system(IEGS).To coordinate the economic operations of the two systems,this paper innovatively proposes a coordinated dispatch model of IEGS with LNG infrastructures and a freight railway network with LNG transport.First,an operational scheduling model of the railway network,considering energy consumption,is put forward for both LNG transmission and ordinary freight transport.Then,the coordinated dispatch problem of IEGS and the railway network is formulated into a mixed-integer linear programming model via the big M method and a modified incremental linearization approach.Finally,a bi-level optimization algorithm based on generalized benders decomposition(GBD)is presented to solve the coordinated dispatch problem due to the restrictions on exchanging private information.Case studies demonstrate the effectiveness of the proposed model and algorithm as well as the potential benefit for wind power accommodation.
文摘Generally, the procedure for Solving Security constrained unit commitment (SCUC) problems within Lagrangian Relaxation framework is partitioned into two stages: one is to obtain feasible SCUC states;the other is to solve the economic dispatch of generation power among all the generating units. The core of the two stages is how to determine the feasibility of SCUC states. The existence of ramp rate constraints and security constraints increases the difficulty of obtaining an analytical necessary and sufficient condition for determining the quasi-feasibility of SCUC states at each scheduling time. However, a numerical necessary and sufficient numerical condition is proposed and proven rigorously based on Benders Decomposition Theorem. Testing numerical example shows the effectiveness and efficiency of the condition.
基金supported by the National Natural Science Foundation of China under Grant numbers 72271029,71871023,72061127001,and 72201121National Science and Technology Innovation 2030 Major program under Grant 2022ZD0115403.
文摘With e-commerce concentrating retailers and customers onto one platform,logistics companies(e.g.,JD Logistics)have launched integrated supply chain solutions for corporate customers(e.g.,online retailers)with warehousing,transportation,last-mile delivery,and other value-added services.The platform’s concentration of business flows leads to the consolidation of logistics resources,which allows us to coordinate supply chain operations across different corporate customers.This paper studies the stochastic joint replenishment problem of coordinating multiple suppliers and multiple products to gain the economies of scale of the replenishment setup cost and the warehouse inbound operational cost.To this end,we develop stochastic joint replenishment models based on the general-integer policy(SJRM-GIP)for the multi-supplier and multi-product problems and further reformulate the resulted nonlinear optimization models into equivalent mixed integer second-order conic programs(MISOCPs)when the inbound operational cost takes the square-root form.Then,we propose generalized Benders decomposition(GBD)algorithms to solve the MISOCPs by exploiting the Lagrangian duality,convexity,and submodularity of the sub-problems.To reduce the computational burden of the SJRM-GIP,we further propose an SJRM based on the power-of-two policy and extend the proposed GBD algorithms.Extensive numerical experiments based on practical datasets show that the stochastic joint replenishment across multiple suppliers and multiple products would deliver 13∼20%cost savings compared to the independent replenishment benchmark,and on average the proposed GBD algorithm based on the enhanced gradient cut can achieve more than 90%computational time reduction for large-size problem instances compared to the Gurobi solver.The power-of-two policy is capable of providing high-quality solutions with high computational efficiency.
基金This work was supported by the Education Department of Guangdong Province:New and Integrated Energy System Theory and Technology Research Group(No.2016KCXTD022)National Natural Science Foundation of China(No.51907031)+2 种基金Guangdong Basic and Applied Basic Research Foundation(Guangdong-Guangxi Joint Foundation)(No.2021A1515410009)China Scholarship CouncilBrunel University London BRIEF Funding。
文摘As extreme weather events have become more frequent in recent years,improving the resilience and reliability of power systems has become an important area of concern.In this paper,a robust preventive-corrective security-constrained optimal power flow(RO-PCSCOPF)model is proposed to improve power system reliability under N−k outages.Both the short-term emergency limit(STL)and the long-term operating limit(LTL)of the post-contingency power flow on the branch are considered.Compared with the existing robust corrective SCOPF model that only considers STL or LTL,the proposed ROPCSCOPF model can achieve a more reliable generation dispatch solution.In addition,this paper also summarizes and compares the solution methods for solving the N−k SCOPF problem.The computational efficiency of the classical Benders decomposition(BD)method,robust optimization(RO)method,and line outage distribution factor(LODF)method are investigated on the IEEE 24-bus Reliability Test System and 118-bus system.Simulation results show that the BD method has the worst computation performance.The RO method and the LODF method have comparable performance.However,the LODF method can only be used for the preventive SCOPF and not for the corrective SCOPF.The RO method can be used for both.
文摘This paper addresses the coordinated operation of natural gas and electricity networks considering the line pack flexibility in the natural gas pipelines.The problem is formulated as a mixed integer linear programming problem.The objective is to minimize the operation cost of natural gas and electricity networks considering the price of the natural gas supply.Benders decomposition is used to solve the formulated problem.The master problem minimizes the startup and shutdown costs as well as the operation cost of the thermal units other than the gasfired generation units in the electricity network.The first subproblem validates the feasibility of the decisions made in the master problem in the electricity network.And if there is any violation,feasibility Benders cut is generated and added to the master problem.The second subproblem ensures the feasibility of the decisions of the master problem in the natural gas transportation network considering the line pack constraints.The last sub-problem ensuresthe optimality of the natural gas network operation problem considering the demand of the gas-fired generation units and line pack.The nonlinear line pack and flow constraints in the feasibility and optimality subproblems of natural gas transportation network are linearized using Newton-Raphson technique.The presented case study shows the effectiveness of the proposed approach.It is shown that leveraging the stored gas in the natural gas pipelines would further reduce the total operation cost.
基金the Doctoral Programs Foundation ofMinistry of Education of China(No.20102125110002)
文摘In order to facilitate the scientific management of large-sized shipping companies, fleet planning under complicated circumstances has been studied. Based on multiple influencing factors such as the techno-economic status of ships, the investment capacity of company, the possible purchase of new ships, the buying/selling of second-hand vessels and the chartering/renting of ships, a mixed-integer programming model for fleet planning has been established. A large-sized shipping company is utilized to make an empirical study, and Benders decomposition algorithm is employed to test the applicability of the proposed model. The result shows that the model is capable for multi-route, multi-ship and large-scaled fleet planning and thus helpful to support the decision making of large-sized shipping companies.
