The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the...The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.展开更多
The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent...The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.展开更多
For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each...For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each class, and someexamples of exact invainvariant solutions are given.展开更多
We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core...We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.展开更多
In this paper, Lie point symmetries of a new(2+1)-dimensional KdV system are constructed by using the symbolic computation software Maple. Then, the one-dimensional optimal system,associated with corresponding Lie alg...In this paper, Lie point symmetries of a new(2+1)-dimensional KdV system are constructed by using the symbolic computation software Maple. Then, the one-dimensional optimal system,associated with corresponding Lie algebra, is obtained. Moreover, the reduction equations and some explicit solutions based on the optimal system are presented. Finally, the nonlinear selfadjointness is provided and conservation laws of this KdV system are constructed.展开更多
To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformati...To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides,a new conception called invariance set is raised.Moreover,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.展开更多
For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra o...For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra of the infinite Lie algebra is constructed. The reduced equations of the equations with respect to the optimal system are derived. Furthermore, the one-dimensional optimal systems of the Lie algebra admitted by the reduced equations are also constructed. Consequently, the classification of the twice optimal symmetry reductions of the equations with respect to the optimal systems is presented. The reductions show that the (1 + 2)-dimensional nonlinear Schrodinger equations can be reduced to a group of ordinary differential equations which is useful for solving the related problems of the equations.展开更多
The purpose of this paper is to find the invariant solutions of the reduction of the Navier-Stokes equations where s=z/y ((Uyy(t,s,y)-Ut(t,s,y))y-2sUsy(t,s,y))y+(s2+1)Uss(t,s,y)+2sUs=0 This equation is constructed fro...The purpose of this paper is to find the invariant solutions of the reduction of the Navier-Stokes equations where s=z/y ((Uyy(t,s,y)-Ut(t,s,y))y-2sUsy(t,s,y))y+(s2+1)Uss(t,s,y)+2sUs=0 This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Group classification of the admitted Lie algebras of this equation is obtained. Two-dimensional optimal system is constructed from classification of their subalgebras. All invariant solutions corresponding to these subalgebras are presented.展开更多
The purpose of this paper is to find the admitted Lie group of the reduction of the Navier-Stokes equationswhere using the basic Lie symmetry method. This equation is constructed from the Navier-Stokes equations risin...The purpose of this paper is to find the admitted Lie group of the reduction of the Navier-Stokes equationswhere using the basic Lie symmetry method. This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Two-dimensional optimal system is determined for symmetry algebras obtained through classification of their subalgebras. Some invariant solutions are also found.展开更多
In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the clas...In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.展开更多
In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the...In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the symmetry reductions are obtained. Finally, based on the power series method and the extended Tanh function method, some new explicit solutions of this system are constructed.展开更多
In this paper,Lie symmetry analysis method is applied to one type of mathematical physics equations named the(2+1)-dimensional fractional Hirota-Maccari system.All Lie symmetries and the corresponding conserved vector...In this paper,Lie symmetry analysis method is applied to one type of mathematical physics equations named the(2+1)-dimensional fractional Hirota-Maccari system.All Lie symmetries and the corresponding conserved vectors for the system are obtained.The one-dimensional optimai system is utilized to reduce the aimed equations with Riemann-Liouville fractional derivative to the(1+1)-dimensional fractional partial differential equations with Erdelyi-Kober fractional derivative.展开更多
In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimizatio...In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.展开更多
Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this wor...Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.展开更多
The Sine and Wormhole Energy Whale Optimization Algorithm(SWEWOA)represents an advanced solution method for resolving Optimal Power Flow(OPF)problems in power systems equipped with Flexible AC Transmission System(FACT...The Sine and Wormhole Energy Whale Optimization Algorithm(SWEWOA)represents an advanced solution method for resolving Optimal Power Flow(OPF)problems in power systems equipped with Flexible AC Transmission System(FACTS)devices which include Thyristor-Controlled Series Compensator(TCSC),Thyristor-Controlled Phase Shifter(TCPS),and Static Var Compensator(SVC).SWEWOA expands Whale Optimization Algorithm(WOA)through the integration of sine and wormhole energy features thus improving exploration and exploitation capabilities for efficient convergence in complex non-linear OPF problems.A performance evaluation of SWEWOA takes place on the IEEE-30 bus test system through static and dynamic loading scenarios where it demonstrates better results than five contemporary algorithms:Adaptive Chaotic WOA(ACWOA),WOA,Chaotic WOA(CWOA),Sine Cosine Algorithm Differential Evolution(SCADE),and Hybrid Grey Wolf Optimization(HGWO).The research shows that SWEWOA delivers superior generation cost reduction than other algorithms by reaching a minimum of 0.9%better performance.SWEWOA demonstrates superior power loss performance by achieving(P_(loss,min))at the lowest level compared to all other tested algorithms which leads to better system energy efficiency.The dynamic loading performance of SWEWOA leads to a 4.38%reduction in gross costs which proves its capability to handle different operating conditions.The algorithm achieves top performance in Friedman Rank Test(FRT)assessments through multiple performance metrics which verifies its consistent reliability and strong stability during changing power demands.The repeated simulations show that SWEWOA generates mean costs(C_(gen,min))and mean power loss values(P_(loss,min))with small deviations which indicate its capability to maintain cost-effective solutions in each simulation run.SWEWOA demonstrates great potential as an advanced optimization solution for power system operations through the results presented in this study.展开更多
The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the u...The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult.Therefore,it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties.In this framework,the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties.The robust control problem is translated into the optimal control problem,where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function.The optimal control method is used to solve the robust control problem.The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties.The simulation and experimental results demonstrate the performance of the designed control scheme.The performance indices such as integral absolute error(IAE),integral square error(ISE),integral time absolute error(ITAE),and integral time square error(ITSE)are compared for both uncertainties to showcase the robustness of the designed control scheme.展开更多
The literature on multi-attribute optimization for renewable energy source(RES)placement in deregulated power markets is extensive and diverse in methodology.This study focuses on the most relevant publications direct...The literature on multi-attribute optimization for renewable energy source(RES)placement in deregulated power markets is extensive and diverse in methodology.This study focuses on the most relevant publications directly addressing the research problem at hand.Similarly,while the body of work on optimal location and sizing of renewable energy generators(REGs)in balanced distribution systems is substantial,only the most pertinent sources are cited,aligning closely with the study’s objective function.A comprehensive literature review reveals several key research areas:RES integration,RES-related optimization techniques,strategic placement of wind and solar generation,and RES promotion in deregulated powermarkets,particularly within transmission systems.Furthermore,the optimal location and sizing of REGs in both balanced and unbalanced distribution systems have been extensively studied.RESs demonstrate significant potential for standalone applications in remote areas lacking conventional transmission and distribution infrastructure.Also presents a thorough review of current modeling and optimization approaches for RES-based distribution system location and sizing.Additionally,it examines the optimal positioning,sizing,and performance of hybrid and standalone renewable energy systems.This paper provides a comprehensive review of current modeling and optimization approaches for the location and sizing of Renewable Energy Sources(RESs)in distribution systems,focusing on both balanced and unbalanced networks.展开更多
This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are de...This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.展开更多
Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,s...Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,so it can handle optimal control problems effectively.This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno(T-S)fuzzy systems.Based on learner systems,an expert system is constructed,where the learner system only knows the expert system's optimal control policy.To reconstruct the unknown cost function,we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known.The developed model-based learning algorithm is consists of two learning stages:an inner reinforcement learning loop and an outer inverse optimal control loop.The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy.Then,to eliminate the requirement that the system dynamics must be known,a data-driven integral learning algorithm is presented.It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable.Finally,we apply the proposed fuzzy optimal control to the truck-trailer system,and the computer simulation results verify the effectiveness of the presented approach.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11075055 and 11275072)the Innovative Research Team Program of the National Natural Science Foundation of China(Grant No.61021004)+1 种基金the National High Technology Research and Development Program of China(Grant No.2011AA010101)the Shanghai Knowledge Service Platform for Trustworthy Internet of Things,China(Grant No.ZF1213)
文摘The nonlocal symmetry of the mKdV equation is obtained from the known Lax pair; it is successfully localized to Lie point symmetries in the enlarged space by introducing suitable auxiliary dependent variables. For the closed prolongation of the nonlocal symmetry, the details of the construction for a one-dimensional optimal system are presented. Furthermore, using the associated vector fields of the obtained symmetry, we give the reductions by the one-dimensional sub-algebras and the explicit analytic interaction solutions between cnoidal waves and kink solitary waves, which provide a way to study the interactions among these types of ocean waves. For some of the interesting solutions, the figures are given to show their properties.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11375090,11275072 and 11435005+3 种基金Research Fund for the Doctoral Program of Higher Education of China under Grant No.20120076110024the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No.61321064Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213the Zhejiang Provincial Natural Science Foundation of China under Grant No.LY14A010005
文摘The one-dimensional optimal system for the Lie symmetry group of the(2+1)-dimensional Wu–Zhan equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlev integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady cas of the Wu–Zhang equation.
基金supported by the Natural science foundation of China(NSF),under grand number 11071159.
文摘For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, classical symmetry algebra is found and 1-dimensional optimal system, up to conjugacy, is constructed. Its symmetry reductions are performed for each class, and someexamples of exact invainvariant solutions are given.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072,61021004National High Technology Research and Development Program under Grant No.2011AA010101+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213Talent Fund and K.C.Wong Magna Fund in Ningbo University
文摘We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.
基金the National Natural Science Foundation of China(Grant No.11771352,11871396)the Natural Science Foundation of Shaanxi Province(Grant No.2020JM-431)。
文摘In this paper, Lie point symmetries of a new(2+1)-dimensional KdV system are constructed by using the symbolic computation software Maple. Then, the one-dimensional optimal system,associated with corresponding Lie algebra, is obtained. Moreover, the reduction equations and some explicit solutions based on the optimal system are presented. Finally, the nonlinear selfadjointness is provided and conservation laws of this KdV system are constructed.
基金Supported by the Global Change Research Program of China under Grant No.2015CB95390National Natural Science Foundation of China under Grant Nos.11675054 and 11435005Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘To construct the one-dimensional optimal system of finite dimensional Lie algebra automatically,we develop a new Maple package One Optimal System.Meanwhile,we propose a new method to calculate the adjoint transformation matrix and find all the invariants of Lie algebra in spite of Killing form checking possible constraints of each classification.Besides,a new conception called invariance set is raised.Moreover,this Maple package is proved to be more efficiency and precise than before by applying it to some classic examples.
基金supported by the Natural science foundation of China(NSF),under grand number 11071159.
文摘For a class of (1 + 2)-dimensional nonlinear Schrodinger equations, the infinite dimensional Lie algebra of the classical symmetry group is found and the one-dimensional optimal system of an 8-dimensional subalgebra of the infinite Lie algebra is constructed. The reduced equations of the equations with respect to the optimal system are derived. Furthermore, the one-dimensional optimal systems of the Lie algebra admitted by the reduced equations are also constructed. Consequently, the classification of the twice optimal symmetry reductions of the equations with respect to the optimal systems is presented. The reductions show that the (1 + 2)-dimensional nonlinear Schrodinger equations can be reduced to a group of ordinary differential equations which is useful for solving the related problems of the equations.
文摘The purpose of this paper is to find the invariant solutions of the reduction of the Navier-Stokes equations where s=z/y ((Uyy(t,s,y)-Ut(t,s,y))y-2sUsy(t,s,y))y+(s2+1)Uss(t,s,y)+2sUs=0 This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Group classification of the admitted Lie algebras of this equation is obtained. Two-dimensional optimal system is constructed from classification of their subalgebras. All invariant solutions corresponding to these subalgebras are presented.
文摘The purpose of this paper is to find the admitted Lie group of the reduction of the Navier-Stokes equationswhere using the basic Lie symmetry method. This equation is constructed from the Navier-Stokes equations rising to a partially invariant solutions of the Navier-Stokes equations. Two-dimensional optimal system is determined for symmetry algebras obtained through classification of their subalgebras. Some invariant solutions are also found.
文摘In this paper, we discuss one-dimensional optimal system and the invariant solutions of Coupled Burgers’ equations. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Coupled Burgers’ equations are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Coupled Burgers’ equations corresponding to one element in one dimensional optimal system by using the invariant method. The results generalize the exact solutions of the Coupled Burgers’ equations.
文摘In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the symmetry reductions are obtained. Finally, based on the power series method and the extended Tanh function method, some new explicit solutions of this system are constructed.
文摘In this paper,Lie symmetry analysis method is applied to one type of mathematical physics equations named the(2+1)-dimensional fractional Hirota-Maccari system.All Lie symmetries and the corresponding conserved vectors for the system are obtained.The one-dimensional optimai system is utilized to reduce the aimed equations with Riemann-Liouville fractional derivative to the(1+1)-dimensional fractional partial differential equations with Erdelyi-Kober fractional derivative.
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金sponsored by R&D Program of Beijing Municipal Education Commission(KM202410009013).
文摘In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.
基金supported by the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302100)the National Natural Science Foundation of China(Grant Nos.12361131576,92265205,and 92476205).
文摘Quantum optimal control(QOC)relies on accurately modeling system dynamics and is often challenged by unknown or inaccessible interactions in real systems.Taking an unknown collective spin system as an example,this work introduces a machine-learning-based,data-driven scheme to overcome the challenges encountered,with a trained neural network(NN)assuming the role of a surrogate model that captures the system’s dynamics and subsequently enables QOC to be performed on the NN instead of on the real system.The trained NN surrogate proves effective for practical QOC tasks and is further demonstrated to be adaptable to different experimental conditions,remaining robust across varying system sizes and pulse durations.
文摘The Sine and Wormhole Energy Whale Optimization Algorithm(SWEWOA)represents an advanced solution method for resolving Optimal Power Flow(OPF)problems in power systems equipped with Flexible AC Transmission System(FACTS)devices which include Thyristor-Controlled Series Compensator(TCSC),Thyristor-Controlled Phase Shifter(TCPS),and Static Var Compensator(SVC).SWEWOA expands Whale Optimization Algorithm(WOA)through the integration of sine and wormhole energy features thus improving exploration and exploitation capabilities for efficient convergence in complex non-linear OPF problems.A performance evaluation of SWEWOA takes place on the IEEE-30 bus test system through static and dynamic loading scenarios where it demonstrates better results than five contemporary algorithms:Adaptive Chaotic WOA(ACWOA),WOA,Chaotic WOA(CWOA),Sine Cosine Algorithm Differential Evolution(SCADE),and Hybrid Grey Wolf Optimization(HGWO).The research shows that SWEWOA delivers superior generation cost reduction than other algorithms by reaching a minimum of 0.9%better performance.SWEWOA demonstrates superior power loss performance by achieving(P_(loss,min))at the lowest level compared to all other tested algorithms which leads to better system energy efficiency.The dynamic loading performance of SWEWOA leads to a 4.38%reduction in gross costs which proves its capability to handle different operating conditions.The algorithm achieves top performance in Friedman Rank Test(FRT)assessments through multiple performance metrics which verifies its consistent reliability and strong stability during changing power demands.The repeated simulations show that SWEWOA generates mean costs(C_(gen,min))and mean power loss values(P_(loss,min))with small deviations which indicate its capability to maintain cost-effective solutions in each simulation run.SWEWOA demonstrates great potential as an advanced optimization solution for power system operations through the results presented in this study.
文摘The electromagnetic levitation system(EMLS)serves as the most important part of any magnetic levitation system.However,its characteristics are defined by its highly nonlinear dynamics and instability.Furthermore,the uncertainties in the dynamics of an electromagnetic levitation system make the controller design more difficult.Therefore,it is necessary to design a robust control law that will ensure the system’s stability in the presence of these uncertainties.In this framework,the dynamics of an electromagnetic levitation system are addressed in terms of matched and unmatched uncertainties.The robust control problem is translated into the optimal control problem,where the uncertainties of the electromagnetic levitation system are directly reflected in the cost function.The optimal control method is used to solve the robust control problem.The solution to the optimal control problem for the electromagnetic levitation system is indeed a solution to the robust control problem of the electromagnetic levitation system under matched and unmatched uncertainties.The simulation and experimental results demonstrate the performance of the designed control scheme.The performance indices such as integral absolute error(IAE),integral square error(ISE),integral time absolute error(ITAE),and integral time square error(ITSE)are compared for both uncertainties to showcase the robustness of the designed control scheme.
文摘The literature on multi-attribute optimization for renewable energy source(RES)placement in deregulated power markets is extensive and diverse in methodology.This study focuses on the most relevant publications directly addressing the research problem at hand.Similarly,while the body of work on optimal location and sizing of renewable energy generators(REGs)in balanced distribution systems is substantial,only the most pertinent sources are cited,aligning closely with the study’s objective function.A comprehensive literature review reveals several key research areas:RES integration,RES-related optimization techniques,strategic placement of wind and solar generation,and RES promotion in deregulated powermarkets,particularly within transmission systems.Furthermore,the optimal location and sizing of REGs in both balanced and unbalanced distribution systems have been extensively studied.RESs demonstrate significant potential for standalone applications in remote areas lacking conventional transmission and distribution infrastructure.Also presents a thorough review of current modeling and optimization approaches for RES-based distribution system location and sizing.Additionally,it examines the optimal positioning,sizing,and performance of hybrid and standalone renewable energy systems.This paper provides a comprehensive review of current modeling and optimization approaches for the location and sizing of Renewable Energy Sources(RESs)in distribution systems,focusing on both balanced and unbalanced networks.
基金supported in part by the Thai Nguyen University of Technology,Vietnam.
文摘This article presents an adaptive optimal control method for a semi-active suspension system.The model of the suspension system is built,in which the components of uncertain parameters and exogenous disturbance are described.The adaptive optimal control law consists of the sum of the optimal control component and the adaptive control component.First,the optimal control law is designed for the model of the suspension system after ignoring the components of uncertain parameters and exogenous disturbance caused by the road surface.The optimal control law expresses the desired dynamic characteristics of the suspension system.Next,the adaptive component is designed with the purpose of compensating for the effects caused by uncertain parameters and exogenous disturbance caused by the road surface;the adaptive component has adaptive parameter rules to estimate uncertain parameters and exogenous disturbance.When exogenous disturbances are eliminated,the system responds with an optimal controller designed.By separating theoretically the dynamic of a semi-active suspension system,this solution allows the design of two separate controllers easily and has reduced the computational burden and the use of too many tools,thus allowing for more convenient hardware implementation.The simulation results also show the effectiveness of damping oscillations of the proposed solution in this article.
基金The National Natural Science Foundation of China(62173172).
文摘Inverse reinforcement learning optimal control is under the framework of learner-expert.The learner system can imitate the expert system's demonstrated behaviors and does not require the predefined cost function,so it can handle optimal control problems effectively.This paper proposes an inverse reinforcement learning optimal control method for Takagi-Sugeno(T-S)fuzzy systems.Based on learner systems,an expert system is constructed,where the learner system only knows the expert system's optimal control policy.To reconstruct the unknown cost function,we firstly develop a model-based inverse reinforcement learning algorithm for the case that systems dynamics are known.The developed model-based learning algorithm is consists of two learning stages:an inner reinforcement learning loop and an outer inverse optimal control loop.The inner loop desires to obtain optimal control policy via learner's cost function and the outer loop aims to update learner's state-penalty matrices via only using expert's optimal control policy.Then,to eliminate the requirement that the system dynamics must be known,a data-driven integral learning algorithm is presented.It is proved that the presented two algorithms are convergent and the developed inverse reinforcement learning optimal control scheme can ensure the controlled fuzzy learner systems to be asymptotically stable.Finally,we apply the proposed fuzzy optimal control to the truck-trailer system,and the computer simulation results verify the effectiveness of the presented approach.
