Urban electricity and heat networks(UEHN)consist of the coupling and interactions between electric power systems and district heating systems,in which the geographical and functional features of integrated energy syst...Urban electricity and heat networks(UEHN)consist of the coupling and interactions between electric power systems and district heating systems,in which the geographical and functional features of integrated energy systems are demonstrated.UEHN have been expected to provide an effective way to accommodate the intermittent and unpredictable renewable energy sources,in which the application of stochastic optimization approaches to UEHN analysis is highly desired.In this paper,we propose a chance-constrained coordinated optimization approach for UEHN considering the uncertainties in electricity loads,heat loads,and photovoltaic outputs,as well as the correlations between these uncertain sources.A solution strategy,which combines the Latin Hypercube Sampling Monte Carlo Simulation(LHSMCS)approach and a heuristic algorithm,is specifically designed to deal with the proposed chance-constrained coordinated optimization.Finally,test results on an UEHN comprised of a modified IEEE 33-bus system and a 32-node district heating system at Barry Island have verified the feasibility and effectiveness of the proposed framework.展开更多
By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all con...By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is presented.The Darboux transformation for these FDIHSs is derived.展开更多
An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low...An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low-dimensional space by performing the Proper Orthogonal Decomposition(POD)on snapshots and is coupled with the Radial Basis Function(RBF)to achieve fast prediction speed.However,due to the disparate scales in the ionized flow field,the conventional ROM usually generates spurious negative errors.Here,this issue is addressed by performing flow-solution preprocessing in logarithmic space to improve the conventional ROM.Then,extra orthogonal polynomials are introduced in the RBF interpolation to achieve additional improvement of the prediction accuracy.In addition,to construct high-efficiency snapshots,a trajectory-constrained adaptive sampling strategy based on convex hull optimization is developed.To evaluate the performance of the proposed fast prediction method,two hypersonic vehicles with classic configurations,i.e.a wave-rider and a reentry capsule,are used to validate the proposed method.Both two cases show that the proposed fast prediction method has high accuracy near the vehicle surface and the free-stream region where the flow field is smooth.Compared with the conventional ROM prediction,the prediction results are significantly improved by the proposed method around the discontinuities,e.g.the shock wave and the ionized layer.As a result,the proposed fast prediction method reduces the error of the conventional ROM by at least 45%,with a speedup of approximately 2.0×105compared to the Computational Fluid Dynamic(CFD)simulations.These test cases demonstrate that the method developed here is efficient and accurate for predicting ionized hypersonic flows.展开更多
Security-constrained unit commitment(SCUC)has been extensively studied as a key decision-making tool to determine optimal power generation schedules in the operation of electricity market.With the development of emerg...Security-constrained unit commitment(SCUC)has been extensively studied as a key decision-making tool to determine optimal power generation schedules in the operation of electricity market.With the development of emerging power grids,fruitful research results on SCUC have been obtained.Therefore,it is essential to review current work and propose future directions for SCUC to meet the needs of developing power systems.In this paper,the basic mathematical model of the standard SCUC is summarized,and the characteristics and application scopes of common solution algorithms are presented.Customized models focusing on diverse mathematical properties are then categorized and the corresponding solving methodologies are discussed.Finally,research trends in the field are prospected based on a summary of the state-of-the-art and latest studies.It is hoped that this paper can be a useful reference to support theoretical research and practical applications of SCUC in the future.展开更多
The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient f...The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.展开更多
In recent years,reinforcement learning(RL)has emerged as a solution for model-free dynamic programming problem that cannot be effectively solved by traditional optimization methods.It has gradually been applied in the...In recent years,reinforcement learning(RL)has emerged as a solution for model-free dynamic programming problem that cannot be effectively solved by traditional optimization methods.It has gradually been applied in the fields such as economic dispatch of power systems due to its strong selflearning and self-optimizing capabilities.However,existing economic scheduling methods based on RL ignore security risks that the agent may bring during exploration,which poses a risk of issuing instructions that threaten the safe operation of power system.Therefore,we propose an improved proximal policy optimization algorithm for sequential security-constrained optimal power flow(SCOPF)based on expert knowledge and safety layer to determine active power dispatch strategy,voltage optimization scheme of the units,and charging/discharging dispatch of energy storage systems.The expert experience is introduced to improve the ability to enforce constraints such as power balance in training process while guiding agent to effectively improve the utilization rate of renewable energy.Additionally,to avoid line overload,we add a safety layer at the end of the policy network by introducing transmission constraints to avoid dangerous actions and tackle sequential SCOPF problem.Simulation results on an improved IEEE 118-bus system verify the effectiveness of the proposed algorithm.展开更多
Due to the uncertain fluctuations of renewable energy and load power, the state variables such as bus voltages and pipeline mass flows in the combined cooling, heating, and power campus microgrid(CCHP-CMG) may exceed ...Due to the uncertain fluctuations of renewable energy and load power, the state variables such as bus voltages and pipeline mass flows in the combined cooling, heating, and power campus microgrid(CCHP-CMG) may exceed the secure operation limits. In this paper, an optimal energy flow(OEF) model for a CCHP-CMG using parameterized probability boxes(p-boxes) is proposed to describe the higher-order uncertainty of renewables and loads. In the model, chance constraints are used to describe the secure operation limits of the state variable p-boxes, and variance constraints are introduced to reduce their random fluctuation ranges. To solve this model, the chance and variance constraints are transformed into the constraints of interval cumulants(ICs) of state variables based on the p-efficient point theory and interval Cornish-Fisher expansion. With the relationship between the ICs of state variables and node power, and using the affine interval arithmetic method, the original optimization model is finally transformed into a deterministic nonlinear programming model. It can be solved by the CONOPT solver in GAMS software to obtain the optimal operation point of a CCHP-CMG that satisfies the secure operation requirements considering the higher-order uncertainty of renewables and loads. Case study on a CCHP-CMG demonstrates the correctness and effectiveness of the proposed OEF model.展开更多
An improved approach for constrained large-eddy simulations(CLES)of wall-bounded compressible transitional flows is proposed by introducing an intermittency factor.The improved model is tested and validated with compr...An improved approach for constrained large-eddy simulations(CLES)of wall-bounded compressible transitional flows is proposed by introducing an intermittency factor.The improved model is tested and validated with compressible channel flows at various Mach numbers and Reynolds numbers that are transitioning from laminar to turbulent states.The improved model is compared against traditional dynamic Smagorinsky model(DSM)and Direct Numerical Simulations(DNS),where the improved model is in better agreement with DNS results than traditional DSM model,in terms of mean velocity profiles,total Reynolds stress and total heat flux.Therefore,the proposed method can be used to accurately predict the temporal laminar-turbulent transition process of compressible wall-bounded flows.展开更多
Compressible flow past a circular cylinder at an inflow Reynolds number of 2×105 is numerically investigated by using a constrained large-eddy simulation(CLES)technique.Numerical simulation with adiabatic wall bo...Compressible flow past a circular cylinder at an inflow Reynolds number of 2×105 is numerically investigated by using a constrained large-eddy simulation(CLES)technique.Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows.Some typical and characteristic physical quantities,such as the drag coefficient,the root-mean-square lift fluctuations,the Strouhal number,the pressure and skin friction distributions around the cylinder,etc.are calculated and compared with previously reported experimental data,finer-grid large-eddy simulation(LES)data and those obtained in the present LES and detached-eddy simulation(DES)on coarse grids.It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well.Then,the effects of Mach number on the flow patterns and parameters such as the pressure,skin friction and drag coefficients,and the cylinder surface temperature are studied,with Mach number varying from 0.1 to 0.95.Nonmonotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5.Additionally,the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures.It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature.Moreover,the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point.It is inferred that the CLES approach in its current version is a useful and effective tool for sim展开更多
By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A...By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A method to construct the Lax representations for both x- and t(n)- constrained flows via reduction of the adjoint representations of the auxiliary linear problems is developed.展开更多
The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method f...The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.展开更多
首先探究了融合式翼梢小翼倾斜角、高度以及安装角对民用运输机气动特性的影响。然后基于多区域自由变形(FFD,free form deformation)技术、拉丁超立方取样方法(LHS,latin hypercube sampling)、Kriging代理模型以及改进的粒子群算法构...首先探究了融合式翼梢小翼倾斜角、高度以及安装角对民用运输机气动特性的影响。然后基于多区域自由变形(FFD,free form deformation)技术、拉丁超立方取样方法(LHS,latin hypercube sampling)、Kriging代理模型以及改进的粒子群算法构建优化设计系统,对融合式翼梢小翼应用优化系统,通过对FFD控制体框架的合理布置,实现了多个控制框架对融合式翼梢小翼的自由变形参数化设计。优化设计结果表明,设计后的融合式翼梢小翼较原始构型减阻效果有明显改善。并通过与"翼尖延伸"、"涡扩散器"和"双叉弯刀"等3种翼尖装置进行调参对比分析,得出一些对翼尖装置设计具有参考价值的结论。展开更多
In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many method...In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many methods of computing TS-IRPFL have been proposed.However,in practice,the method widely used to determine TS-IRPFL is based on selection and analysis of typical scenarios as well as scenario matching.First,typical scenarios are selected and analyzed to obtain accurate limits,then the scenario to be analyzed is matched with a certain typical scenario,whose limit is adopted as the forecast limit.In this paper,following the steps described above,a pragmatic method to determine TS-IRPFL is proposed.The proposed method utilizes data-driven tools to improve the steps of scenario selection and matching.First of all,we formulate a clear model of power system scenario similarity.Based on the similarity model,we develop a typical scenario selector by clustering and a scenario matcher by nearest neighbor algorithm.The proposed method is pragmatic because it does not change the existing procedure.Moreover,it is much more reasonable than the traditional method.Test results verify the validity of the method.展开更多
The classical r-matrix and Poisson structure play an important role in our studying ofintegrable systems, since they contain underlying property of the system. Recently, inter-est has developed in the study of dynamic...The classical r-matrix and Poisson structure play an important role in our studying ofintegrable systems, since they contain underlying property of the system. Recently, inter-est has developed in the study of dynamical r-matrix structure, which depends also on thedynamical variables, and associated generalized Yang-Baxter equations. However,展开更多
基金This work was supported in part by Natural Science Foundation of Jiangsu Province,China(No.BK20171433)in part by Science and Technology Project of State Grid Jiangsu Electric Power Corporation,China(No.J2018066).
文摘Urban electricity and heat networks(UEHN)consist of the coupling and interactions between electric power systems and district heating systems,in which the geographical and functional features of integrated energy systems are demonstrated.UEHN have been expected to provide an effective way to accommodate the intermittent and unpredictable renewable energy sources,in which the application of stochastic optimization approaches to UEHN analysis is highly desired.In this paper,we propose a chance-constrained coordinated optimization approach for UEHN considering the uncertainties in electricity loads,heat loads,and photovoltaic outputs,as well as the correlations between these uncertain sources.A solution strategy,which combines the Latin Hypercube Sampling Monte Carlo Simulation(LHSMCS)approach and a heuristic algorithm,is specifically designed to deal with the proposed chance-constrained coordinated optimization.Finally,test results on an UEHN comprised of a modified IEEE 33-bus system and a 32-node district heating system at Barry Island have verified the feasibility and effectiveness of the proposed framework.
基金Supported by the Chinese National Basic Research Project"Nonlinear Science"
文摘By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is presented.The Darboux transformation for these FDIHSs is derived.
基金supported by the National Natural Science Foundation of China(Nos.11902271 and 91952203)the Fundamental Research Funds for the Central Universities of China(No.G2019KY05102)111 project on“Aircraft Complex Flows and the Control”of China(No.B17037)。
文摘An improved Reduced-Order Model(ROM)is proposed based on a flow-solution preprocessing operation and a fast sampling strategy to efficiently and accurately predict ionized hypersonic flows.This ROM is generated in low-dimensional space by performing the Proper Orthogonal Decomposition(POD)on snapshots and is coupled with the Radial Basis Function(RBF)to achieve fast prediction speed.However,due to the disparate scales in the ionized flow field,the conventional ROM usually generates spurious negative errors.Here,this issue is addressed by performing flow-solution preprocessing in logarithmic space to improve the conventional ROM.Then,extra orthogonal polynomials are introduced in the RBF interpolation to achieve additional improvement of the prediction accuracy.In addition,to construct high-efficiency snapshots,a trajectory-constrained adaptive sampling strategy based on convex hull optimization is developed.To evaluate the performance of the proposed fast prediction method,two hypersonic vehicles with classic configurations,i.e.a wave-rider and a reentry capsule,are used to validate the proposed method.Both two cases show that the proposed fast prediction method has high accuracy near the vehicle surface and the free-stream region where the flow field is smooth.Compared with the conventional ROM prediction,the prediction results are significantly improved by the proposed method around the discontinuities,e.g.the shock wave and the ionized layer.As a result,the proposed fast prediction method reduces the error of the conventional ROM by at least 45%,with a speedup of approximately 2.0×105compared to the Computational Fluid Dynamic(CFD)simulations.These test cases demonstrate that the method developed here is efficient and accurate for predicting ionized hypersonic flows.
基金supported in part by the National Natural Science Foundation of China(No.51607104)。
文摘Security-constrained unit commitment(SCUC)has been extensively studied as a key decision-making tool to determine optimal power generation schedules in the operation of electricity market.With the development of emerging power grids,fruitful research results on SCUC have been obtained.Therefore,it is essential to review current work and propose future directions for SCUC to meet the needs of developing power systems.In this paper,the basic mathematical model of the standard SCUC is summarized,and the characteristics and application scopes of common solution algorithms are presented.Customized models focusing on diverse mathematical properties are then categorized and the corresponding solving methodologies are discussed.Finally,research trends in the field are prospected based on a summary of the state-of-the-art and latest studies.It is hoped that this paper can be a useful reference to support theoretical research and practical applications of SCUC in the future.
基金supported by the National Key Research and Development Program of China(2020YFA0714300)the National Natural Science Foundation of China(62003084,62203108,62073079)+3 种基金the Natural Science Foundation of Jiangsu Province of China(BK20200355)the General Joint Fund of the Equipment Advance Research Program of Ministry of Education(8091B022114)Jiangsu Province Excellent Postdoctoral Program(2022ZB131)China Postdoctoral Science Foundation(2022M720720,2023T160105).
文摘The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.
基金supported in part by National Natural Science Foundation of China(No.52077076)in part by the National Key R&D Plan(No.2021YFB2601502)。
文摘In recent years,reinforcement learning(RL)has emerged as a solution for model-free dynamic programming problem that cannot be effectively solved by traditional optimization methods.It has gradually been applied in the fields such as economic dispatch of power systems due to its strong selflearning and self-optimizing capabilities.However,existing economic scheduling methods based on RL ignore security risks that the agent may bring during exploration,which poses a risk of issuing instructions that threaten the safe operation of power system.Therefore,we propose an improved proximal policy optimization algorithm for sequential security-constrained optimal power flow(SCOPF)based on expert knowledge and safety layer to determine active power dispatch strategy,voltage optimization scheme of the units,and charging/discharging dispatch of energy storage systems.The expert experience is introduced to improve the ability to enforce constraints such as power balance in training process while guiding agent to effectively improve the utilization rate of renewable energy.Additionally,to avoid line overload,we add a safety layer at the end of the policy network by introducing transmission constraints to avoid dangerous actions and tackle sequential SCOPF problem.Simulation results on an improved IEEE 118-bus system verify the effectiveness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China (No. 51977080)the Natural Science Foundation of Guangdong Province (No. 2022A1515010332)。
文摘Due to the uncertain fluctuations of renewable energy and load power, the state variables such as bus voltages and pipeline mass flows in the combined cooling, heating, and power campus microgrid(CCHP-CMG) may exceed the secure operation limits. In this paper, an optimal energy flow(OEF) model for a CCHP-CMG using parameterized probability boxes(p-boxes) is proposed to describe the higher-order uncertainty of renewables and loads. In the model, chance constraints are used to describe the secure operation limits of the state variable p-boxes, and variance constraints are introduced to reduce their random fluctuation ranges. To solve this model, the chance and variance constraints are transformed into the constraints of interval cumulants(ICs) of state variables based on the p-efficient point theory and interval Cornish-Fisher expansion. With the relationship between the ICs of state variables and node power, and using the affine interval arithmetic method, the original optimization model is finally transformed into a deterministic nonlinear programming model. It can be solved by the CONOPT solver in GAMS software to obtain the optimal operation point of a CCHP-CMG that satisfies the secure operation requirements considering the higher-order uncertainty of renewables and loads. Case study on a CCHP-CMG demonstrates the correctness and effectiveness of the proposed OEF model.
文摘An improved approach for constrained large-eddy simulations(CLES)of wall-bounded compressible transitional flows is proposed by introducing an intermittency factor.The improved model is tested and validated with compressible channel flows at various Mach numbers and Reynolds numbers that are transitioning from laminar to turbulent states.The improved model is compared against traditional dynamic Smagorinsky model(DSM)and Direct Numerical Simulations(DNS),where the improved model is in better agreement with DNS results than traditional DSM model,in terms of mean velocity profiles,total Reynolds stress and total heat flux.Therefore,the proposed method can be used to accurately predict the temporal laminar-turbulent transition process of compressible wall-bounded flows.
基金support from National Natural Science Foundation of China(Grants No.91130001 and No.11221061)supported by the National Basic Research Program of China(Grant No.2009CB724101)support from National Science Foundation for Postdoctoral Scientists of China(Grant No.2012M520109).
文摘Compressible flow past a circular cylinder at an inflow Reynolds number of 2×105 is numerically investigated by using a constrained large-eddy simulation(CLES)technique.Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows.Some typical and characteristic physical quantities,such as the drag coefficient,the root-mean-square lift fluctuations,the Strouhal number,the pressure and skin friction distributions around the cylinder,etc.are calculated and compared with previously reported experimental data,finer-grid large-eddy simulation(LES)data and those obtained in the present LES and detached-eddy simulation(DES)on coarse grids.It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well.Then,the effects of Mach number on the flow patterns and parameters such as the pressure,skin friction and drag coefficients,and the cylinder surface temperature are studied,with Mach number varying from 0.1 to 0.95.Nonmonotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5.Additionally,the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures.It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature.Moreover,the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point.It is inferred that the CLES approach in its current version is a useful and effective tool for sim
文摘By using the constraint relating potential and eigenfunctions, the decomposition of each equation in the Boussinesq hierarchy into two commuting finite-dimensional integrable Hamiltonian system (FDIHS) is presented. A method to construct the Lax representations for both x- and t(n)- constrained flows via reduction of the adjoint representations of the auxiliary linear problems is developed.
基金Supported by the National Basic Research Project forNonlinear Sciences and the Doctorate DissertationFoundation of Tsinghua University
文摘The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.
文摘首先探究了融合式翼梢小翼倾斜角、高度以及安装角对民用运输机气动特性的影响。然后基于多区域自由变形(FFD,free form deformation)技术、拉丁超立方取样方法(LHS,latin hypercube sampling)、Kriging代理模型以及改进的粒子群算法构建优化设计系统,对融合式翼梢小翼应用优化系统,通过对FFD控制体框架的合理布置,实现了多个控制框架对融合式翼梢小翼的自由变形参数化设计。优化设计结果表明,设计后的融合式翼梢小翼较原始构型减阻效果有明显改善。并通过与"翼尖延伸"、"涡扩散器"和"双叉弯刀"等3种翼尖装置进行调参对比分析,得出一些对翼尖装置设计具有参考价值的结论。
基金This work was supported by National Key R&D Program of China(2018YFB0904500)and State Grid Corporation of China。
文摘In practical power systems,operators generally keep interface flowing under the transient stability constrained with interface real power flow limits(TS-IRPFL)to guarantee transient stability of the system.Many methods of computing TS-IRPFL have been proposed.However,in practice,the method widely used to determine TS-IRPFL is based on selection and analysis of typical scenarios as well as scenario matching.First,typical scenarios are selected and analyzed to obtain accurate limits,then the scenario to be analyzed is matched with a certain typical scenario,whose limit is adopted as the forecast limit.In this paper,following the steps described above,a pragmatic method to determine TS-IRPFL is proposed.The proposed method utilizes data-driven tools to improve the steps of scenario selection and matching.First of all,we formulate a clear model of power system scenario similarity.Based on the similarity model,we develop a typical scenario selector by clustering and a scenario matcher by nearest neighbor algorithm.The proposed method is pragmatic because it does not change the existing procedure.Moreover,it is much more reasonable than the traditional method.Test results verify the validity of the method.
基金National Basic Research Project 'Nonlinear Sciences'.
文摘The classical r-matrix and Poisson structure play an important role in our studying ofintegrable systems, since they contain underlying property of the system. Recently, inter-est has developed in the study of dynamical r-matrix structure, which depends also on thedynamical variables, and associated generalized Yang-Baxter equations. However,
