A novel approach was proposed to allocate spinning reserve for dynamic economic dispatch.The proposed approach set up a two-stage stochastic programming model to allocate reserve.The model was solved using a decompose...A novel approach was proposed to allocate spinning reserve for dynamic economic dispatch.The proposed approach set up a two-stage stochastic programming model to allocate reserve.The model was solved using a decomposed algorithm based on Benders' decomposition.The model and the algorithm were applied to a simple 3-node system and an actual 445-node system for verification,respectively.Test results show that the model can save 84.5 US $ cost for the testing three-node system,and the algorithm can solve the model for 445-node system within 5 min.The test results also illustrate that the proposed approach is efficient and suitable for large system calculation.展开更多
In this paper, dynamic economic dispatch model is proposed for power systems with bulk wind power integration. The wind turbine generators are assumed to partially undertake the spinning reserve for the thermal genera...In this paper, dynamic economic dispatch model is proposed for power systems with bulk wind power integration. The wind turbine generators are assumed to partially undertake the spinning reserve for the thermal generator. A double-layer optimization model is proposed. The outer layer use the differential evolution to search for the power output of thermal generators, and the inner layer use the primal-dual interior point method to solve the OPF of the established output state. Finally, the impact of spinning reserve with wind power on power system operating is validated.展开更多
Microgrids integrate distributed renewable energy resources, controllable loads and energy storage in a more economic and reliable fashion. Battery energy storage units are essential for microgrid operation, which mak...Microgrids integrate distributed renewable energy resources, controllable loads and energy storage in a more economic and reliable fashion. Battery energy storage units are essential for microgrid operation, which make microgird become a strong coupling system in the time domain. Hence, the traditional methods of static dispatch are no longer suitable for microgrids. This paper proposes a dynamic economic dispatch method for microgrids. Considering microgrid as a discrete time system, the dynamic economic dispatch is to find the optimal control strategy for the system in finite time period. Based on this idea, the dynamic economic dispatch model for microgrids is established, and then the corresponding dynamic programming algorithm is designed. Finally, an example of microgrid is given, and the dynamic economic dispatch results are compared with that of the static dispatch. The comparison confirms the effectiveness of the proposed dynamic dispatch method.展开更多
The hydro unit economic load dispatch （ELD） is of great importance in energy conservation and emission reduction. Dynamic programming （DP） and genetic algorithm （GA） are two representative algorithms for solving...The hydro unit economic load dispatch （ELD） is of great importance in energy conservation and emission reduction. Dynamic programming （DP） and genetic algorithm （GA） are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA＇s performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.展开更多
Renewable sources of energy are being integrated into the power grids due to their economic and environmental merits as compared with the traditional fossil-fuel-fired power generation. However, their significant pene...Renewable sources of energy are being integrated into the power grids due to their economic and environmental merits as compared with the traditional fossil-fuel-fired power generation. However, their significant penetration demands a thorough research in terms of system reliability, that is, security and stability. In this paper, Security Constrained Multi Objective Dynamic Economic Dispatch (SCMODED) problem considering cubic thermal cubic cost function, wind, solar penetration, cubic transmission power losses and cubic emissions cost function as objectives is first formulated. Both HVDC and HVAC lines are included in their formulation. Various approaches like probabilistic load flow (PLF), scenario based method, participation factors and Harmony Search algorithm etc. are employed in the solution process. Security and stability effects of renewable energy (RE) penetration are investigated and analyzed. The simulated results reveal that RE penetration leads to reduced cost and emissions and increased security concerns. Further, there is increased power system instability and hence increased load shedding so as to help the power system attain steady state stability. Inclusion of HVDC lines facilitates rapid and fast control to increase the transient stability limit by the action of the converter ignition angle (CIA) and converter extinction angle (CEA).展开更多
This paper introduces a novel fully distributed economic power dispatch(EPD)strategy for distribution networks,integrating dynamic tariffs.A two-layer model is proposed:the first layer comprises the physical power dis...This paper introduces a novel fully distributed economic power dispatch(EPD)strategy for distribution networks,integrating dynamic tariffs.A two-layer model is proposed:the first layer comprises the physical power distribution network,including photovoltaic(PV)sources,wind turbine(WT)generators,energy storage systems(ESS),flexible loads(FLs),and other inflexible loads.The upper layer consists of agents dedicated to communication,calculation,and control tasks.Unlike previous EPD strategies,this approach incorporates dynamic tariffs derived from voltage constraints to ensure compliance with nodal voltage constraints.Addi-tionally,a fast distributed optimization algorithm with an event-triggered communication protocol has been developed to address the EPD problem effectively.Through mathematical and simulation analyses,the proposed algorithm's efficiency and rapid conver-gence capability are demonstrated.展开更多
Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods...Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods well-performed on the DEED problem,most of them fail to achieve expected results in practice due to a lack of effective trade-off mechanisms between the convergence and diversity of non-dominated optimal dispatching solutions.To address this issue,a new multi-objective solver called Multi-Objective Golden Jackal Optimization(MOGJO)algorithm is proposed to cope with the DEED problem.The proposed algorithm first stores non-dominated optimal solutions found so far into an archive.Then,it chooses the best dispatching solution from the archive as the leader through a selection mechanism designed based on elite selection strategy and Euclidean distance index method.This mechanism can guide the algorithm to search for better dispatching solutions in the direction of reducing fuel costs and pollutant emissions.Moreover,the basic golden jackal optimization algorithm has the drawback of insufficient search,which hinders its ability to effectively discover more Pareto solutions.To this end,a non-linear control parameter based on the cosine function is introduced to enhance global exploration of the dispatching space,thus improving the efficiency of finding the optimal dispatching solutions.The proposed MOGJO is evaluated on the latest CEC benchmark test functions,and its superiority over the state-of-the-art multi-objective optimizers is highlighted by performance indicators.Also,empirical results on 5-unit,10-unit,IEEE 30-bus,and 30-unit systems show that the MOGJO can provide competitive compromise scheduling solutions compared to published DEED methods.Finally,in the analysis of the Pareto dominance relationship and the Euclidean distance index,the optimal dispatching solutions provided by MOGJO are the closest to the ideal solutions for minimizing fuel costs and pollution emissions simultaneously,compared to the latest published DEED solutions.展开更多
Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based o...Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based on dual-population pseudo-parallel genetic algorithm-differential evolution is proposed in this paper.The algorithm is based on external elite archive and Pareto dominance,and it adopts the cooperative co-evolution mechanism of differential evolution and genetic algorithm.Average entropy and cubic chaoticmapping initialization strategies are proposed to increase population diversity.In the proposed method,we analyze the distribution of neighboring solutions and apply a new Pareto solution set pruning approach.Unlike traditional models,this work takes the transmission losses as an optimization target and overcomes complex model constraints through a dynamic relaxation constraint approach.To solve the uncertainty caused by integrating wind and photovoltaic energy in power system scheduling,a multi-objective dynamic environment economical dispatch model is set up that takes the system spinning reserve and network highest losses into account.In this paper,the DE algorithm is improved to form the DGAGE algorithm for the objective optimization of the overall power system,The DE algorithm part of DGAGE is combined with the JAYA algorithm to form the system scheduling HDJ algorithm for multiple energy sources connected to the grid.The effectiveness of the proposed method is demonstrated using CEC2022 and CEC2005 test functions,showing robust optimization performance.Validation on a classical 10-unit system confirms the feasibility of the proposed algorithm in addressing power system scheduling issues.This approach provides a novel solution for dynamic power dispatch systems.展开更多
This paper proposes a deterministic two-stage mixed integer linear programming(TSMILP)approach to solve the reserve constrained dynamic economic dispatch(DED)problem considering valve-point effect(VPE).In stage one,th...This paper proposes a deterministic two-stage mixed integer linear programming(TSMILP)approach to solve the reserve constrained dynamic economic dispatch(DED)problem considering valve-point effect(VPE).In stage one,the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming(MILP)problem,which can be solved by commercial solvers.In stage two,based on the solution obtained in stage one,a range compression technique is proposed to make a further exploitation in the subspace of the whole solution domain.Due to the linear approximation of the transmission loss,the solution obtained in stage two dose not strictly satisfies the power balance constraint.Hence,a forward procedure is employed to eliminate the error.The simulation results on four test systems show that TSMILP makes satisfactory performances,in comparison with the existing methods.展开更多
Carbon capture and storage(CCS)systems can provide sufficient carbon raw materials for power-to-gas(P2G)systems to reduce the carbon emission of traditional coal-fired units,which helps to achieve low-carbon dispatch ...Carbon capture and storage(CCS)systems can provide sufficient carbon raw materials for power-to-gas(P2G)systems to reduce the carbon emission of traditional coal-fired units,which helps to achieve low-carbon dispatch of integrated energy systems(IESs).In this study,an extended carbon-emis-sion flow model that integrates CCS-P2G coordinated operation and low-carbon characteristics of an energy storage system(ESS)is proposed.On the energy supply side,the coupling rela-tionship between CCS and P2G systems is established to realize the low-carbon economic operation of P2G systems.On the en-ergy storage side,the concept of"state of carbon"is introduced to describe the carbon emission characteristics of the ESS to ex-ploit the potential of coordinated low-carbon dispatch in terms of both energy production and storage.In addition,a low-car-bon economic dispatch model that considers multiple uncertain-ties,including wind power output,electricity price,and load de-mands,is established.To solve the model efficiently,a parallel multidimensional approximate dynamic programming algo-rithm is adopted,while the solution efficiency is significantly im-proved over that of stochastic optimization without losing solu-tion accuracy under a multilayer parallel loop nesting frame-work.The low-carbon economic dispatch method of IESs is composed of the extended carbon emission flow model,low-car-bon economic dispatch model,and the parallel multidimension-al approximate dynamic programming algorithm.The effective-ness of the proposed method is verified on E14-H6-G6 and E57-H12-G12 systems.展开更多
基金Projects(51007047,51077087)supported by the National Natural Science Foundation of ChinaProject(2013CB228205)supported by the National Key Basic Research Program of China+1 种基金Project(20100131120039)supported by Higher Learning Doctor Discipline End Scientific Research Fund of the Ministry of Education Institution,ChinaProject(ZR2010EQ035)supported by the Natural Science Foundation of Shandong Province,China
文摘A novel approach was proposed to allocate spinning reserve for dynamic economic dispatch.The proposed approach set up a two-stage stochastic programming model to allocate reserve.The model was solved using a decomposed algorithm based on Benders' decomposition.The model and the algorithm were applied to a simple 3-node system and an actual 445-node system for verification,respectively.Test results show that the model can save 84.5 US $ cost for the testing three-node system,and the algorithm can solve the model for 445-node system within 5 min.The test results also illustrate that the proposed approach is efficient and suitable for large system calculation.
文摘In this paper, dynamic economic dispatch model is proposed for power systems with bulk wind power integration. The wind turbine generators are assumed to partially undertake the spinning reserve for the thermal generator. A double-layer optimization model is proposed. The outer layer use the differential evolution to search for the power output of thermal generators, and the inner layer use the primal-dual interior point method to solve the OPF of the established output state. Finally, the impact of spinning reserve with wind power on power system operating is validated.
文摘Microgrids integrate distributed renewable energy resources, controllable loads and energy storage in a more economic and reliable fashion. Battery energy storage units are essential for microgrid operation, which make microgird become a strong coupling system in the time domain. Hence, the traditional methods of static dispatch are no longer suitable for microgrids. This paper proposes a dynamic economic dispatch method for microgrids. Considering microgrid as a discrete time system, the dynamic economic dispatch is to find the optimal control strategy for the system in finite time period. Based on this idea, the dynamic economic dispatch model for microgrids is established, and then the corresponding dynamic programming algorithm is designed. Finally, an example of microgrid is given, and the dynamic economic dispatch results are compared with that of the static dispatch. The comparison confirms the effectiveness of the proposed dynamic dispatch method.
基金supported by the National Basic Research Program of China(973 Program,Grant No.2013CB036406)the National Natural Science Foundation of China(Grant No.51179044)the Research Innovation Program for College Graduates in Jiangsu Province of China(Grant No.CXZZ12-0242)
文摘The hydro unit economic load dispatch （ELD） is of great importance in energy conservation and emission reduction. Dynamic programming （DP） and genetic algorithm （GA） are two representative algorithms for solving ELD problems. The goal of this study was to examine the performance of DP and GA while they were applied to ELD. We established numerical experiments to conduct performance comparisons between DP and GA with two given schemes. The schemes included comparing the CPU time of the algorithms when they had the same solution quality, and comparing the solution quality when they had the same CPU time. The numerical experiments were applied to the Three Gorges Reservoir in China, which is equipped with 26 hydro generation units. We found the relation between the performance of algorithms and the number of units through experiments. Results show that GA is adept at searching for optimal solutions in low-dimensional cases. In some cases, such as with a number of units of less than 10, GA＇s performance is superior to that of a coarse-grid DP. However, GA loses its superiority in high-dimensional cases. DP is powerful in obtaining stable and high-quality solutions. Its performance can be maintained even while searching over a large solution space. Nevertheless, due to its exhaustive enumerating nature, it costs excess time in low-dimensional cases.
文摘Renewable sources of energy are being integrated into the power grids due to their economic and environmental merits as compared with the traditional fossil-fuel-fired power generation. However, their significant penetration demands a thorough research in terms of system reliability, that is, security and stability. In this paper, Security Constrained Multi Objective Dynamic Economic Dispatch (SCMODED) problem considering cubic thermal cubic cost function, wind, solar penetration, cubic transmission power losses and cubic emissions cost function as objectives is first formulated. Both HVDC and HVAC lines are included in their formulation. Various approaches like probabilistic load flow (PLF), scenario based method, participation factors and Harmony Search algorithm etc. are employed in the solution process. Security and stability effects of renewable energy (RE) penetration are investigated and analyzed. The simulated results reveal that RE penetration leads to reduced cost and emissions and increased security concerns. Further, there is increased power system instability and hence increased load shedding so as to help the power system attain steady state stability. Inclusion of HVDC lines facilitates rapid and fast control to increase the transient stability limit by the action of the converter ignition angle (CIA) and converter extinction angle (CEA).
文摘This paper introduces a novel fully distributed economic power dispatch(EPD)strategy for distribution networks,integrating dynamic tariffs.A two-layer model is proposed:the first layer comprises the physical power distribution network,including photovoltaic(PV)sources,wind turbine(WT)generators,energy storage systems(ESS),flexible loads(FLs),and other inflexible loads.The upper layer consists of agents dedicated to communication,calculation,and control tasks.Unlike previous EPD strategies,this approach incorporates dynamic tariffs derived from voltage constraints to ensure compliance with nodal voltage constraints.Addi-tionally,a fast distributed optimization algorithm with an event-triggered communication protocol has been developed to address the EPD problem effectively.Through mathematical and simulation analyses,the proposed algorithm's efficiency and rapid conver-gence capability are demonstrated.
基金supported by the National Natural Science Foundation of China under Grant No.61802328,61972333,and 61771415.
文摘Dynamic Economic Emission Dispatch(DEED)aims to optimize control over fuel cost and pollution emission,two conflicting objectives,by scheduling the output power of various units at specific times.Although many methods well-performed on the DEED problem,most of them fail to achieve expected results in practice due to a lack of effective trade-off mechanisms between the convergence and diversity of non-dominated optimal dispatching solutions.To address this issue,a new multi-objective solver called Multi-Objective Golden Jackal Optimization(MOGJO)algorithm is proposed to cope with the DEED problem.The proposed algorithm first stores non-dominated optimal solutions found so far into an archive.Then,it chooses the best dispatching solution from the archive as the leader through a selection mechanism designed based on elite selection strategy and Euclidean distance index method.This mechanism can guide the algorithm to search for better dispatching solutions in the direction of reducing fuel costs and pollutant emissions.Moreover,the basic golden jackal optimization algorithm has the drawback of insufficient search,which hinders its ability to effectively discover more Pareto solutions.To this end,a non-linear control parameter based on the cosine function is introduced to enhance global exploration of the dispatching space,thus improving the efficiency of finding the optimal dispatching solutions.The proposed MOGJO is evaluated on the latest CEC benchmark test functions,and its superiority over the state-of-the-art multi-objective optimizers is highlighted by performance indicators.Also,empirical results on 5-unit,10-unit,IEEE 30-bus,and 30-unit systems show that the MOGJO can provide competitive compromise scheduling solutions compared to published DEED methods.Finally,in the analysis of the Pareto dominance relationship and the Euclidean distance index,the optimal dispatching solutions provided by MOGJO are the closest to the ideal solutions for minimizing fuel costs and pollution emissions simultaneously,compared to the latest published DEED solutions.
基金funded by the Major Humanities and Social Sciences Research Projects in Zhejiang Higher Education Institutions,grant number 2023QN131National Innovation Training Program Project in China,grant number 202410451009.
文摘Considering the special features of dynamic environment economic dispatch of power systems with high dimensionality,strong coupling,nonlinearity,and non-convexity,a GA-DE multi-objective optimization algorithm based on dual-population pseudo-parallel genetic algorithm-differential evolution is proposed in this paper.The algorithm is based on external elite archive and Pareto dominance,and it adopts the cooperative co-evolution mechanism of differential evolution and genetic algorithm.Average entropy and cubic chaoticmapping initialization strategies are proposed to increase population diversity.In the proposed method,we analyze the distribution of neighboring solutions and apply a new Pareto solution set pruning approach.Unlike traditional models,this work takes the transmission losses as an optimization target and overcomes complex model constraints through a dynamic relaxation constraint approach.To solve the uncertainty caused by integrating wind and photovoltaic energy in power system scheduling,a multi-objective dynamic environment economical dispatch model is set up that takes the system spinning reserve and network highest losses into account.In this paper,the DE algorithm is improved to form the DGAGE algorithm for the objective optimization of the overall power system,The DE algorithm part of DGAGE is combined with the JAYA algorithm to form the system scheduling HDJ algorithm for multiple energy sources connected to the grid.The effectiveness of the proposed method is demonstrated using CEC2022 and CEC2005 test functions,showing robust optimization performance.Validation on a classical 10-unit system confirms the feasibility of the proposed algorithm in addressing power system scheduling issues.This approach provides a novel solution for dynamic power dispatch systems.
基金supported by Guangdong Yudean Group Co.LTD,Guangzhou 510630,China.
文摘This paper proposes a deterministic two-stage mixed integer linear programming(TSMILP)approach to solve the reserve constrained dynamic economic dispatch(DED)problem considering valve-point effect(VPE).In stage one,the nonsmooth cost function and the transmission loss are piecewise linearized and consequently the DED problem is formulated as a mixed integer linear programming(MILP)problem,which can be solved by commercial solvers.In stage two,based on the solution obtained in stage one,a range compression technique is proposed to make a further exploitation in the subspace of the whole solution domain.Due to the linear approximation of the transmission loss,the solution obtained in stage two dose not strictly satisfies the power balance constraint.Hence,a forward procedure is employed to eliminate the error.The simulation results on four test systems show that TSMILP makes satisfactory performances,in comparison with the existing methods.
基金This work was supported by the Chinese Postdoctoral Science Foundation(No.2023M734092)National Natural Science Foundation of China(No.52107111)Shandong Provincial Natural Science Foundation of China(No.ZR2022ME219)。
文摘Carbon capture and storage(CCS)systems can provide sufficient carbon raw materials for power-to-gas(P2G)systems to reduce the carbon emission of traditional coal-fired units,which helps to achieve low-carbon dispatch of integrated energy systems(IESs).In this study,an extended carbon-emis-sion flow model that integrates CCS-P2G coordinated operation and low-carbon characteristics of an energy storage system(ESS)is proposed.On the energy supply side,the coupling rela-tionship between CCS and P2G systems is established to realize the low-carbon economic operation of P2G systems.On the en-ergy storage side,the concept of"state of carbon"is introduced to describe the carbon emission characteristics of the ESS to ex-ploit the potential of coordinated low-carbon dispatch in terms of both energy production and storage.In addition,a low-car-bon economic dispatch model that considers multiple uncertain-ties,including wind power output,electricity price,and load de-mands,is established.To solve the model efficiently,a parallel multidimensional approximate dynamic programming algo-rithm is adopted,while the solution efficiency is significantly im-proved over that of stochastic optimization without losing solu-tion accuracy under a multilayer parallel loop nesting frame-work.The low-carbon economic dispatch method of IESs is composed of the extended carbon emission flow model,low-car-bon economic dispatch model,and the parallel multidimension-al approximate dynamic programming algorithm.The effective-ness of the proposed method is verified on E14-H6-G6 and E57-H12-G12 systems.
