To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a ...To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.展开更多
Intensity-modulated particle therapy(IMPT)with carbon ions is comparatively susceptible to various uncertainties caused by breathing motion,including range,setup,and target positioning uncertainties.To determine relat...Intensity-modulated particle therapy(IMPT)with carbon ions is comparatively susceptible to various uncertainties caused by breathing motion,including range,setup,and target positioning uncertainties.To determine relative biological effectiveness-weighted dose(RWD)distributions that are resilient to these uncertainties,the reference phase-based four-dimensional(4D)robust optimization(RP-4DRO)and each phase-based 4D robust optimization(EP-4DRO)method in carbon-ion IMPT treatment planning were evaluated and compared.Based on RWD distributions,4DRO methods were compared with 4D conventional optimization using planning target volume(PTV)margins(PTV-based optimization)to assess the effectiveness of the robust optimization methods.Carbon-ion IMPT treatment planning was conducted in a cohort of five lung cancer patients.The results indicated that the EP-4DRO method provided better robustness(P=0.080)and improved plan quality(P=0.225)for the clinical target volume(CTV)in the individual respiratory phase when compared with the PTV-based optimization.Compared with the PTV-based optimization,the RP-4DRO method ensured the robustness(P=0.022)of the dose distributions in the reference breathing phase,albeit with a slight sacrifice of the target coverage(P=0.450).Both 4DRO methods successfully maintained the doses delivered to the organs at risk(OARs)below tolerable levels,which were lower than the doses in the PTV-based optimization(P<0.05).Furthermore,the RP-4DRO method exhibited significantly superior performance when compared with the EP-4DRO method in enhancing overall OAR sparing in either the individual respiratory phase or reference respiratory phase(P<0.05).In general,both 4DRO methods outperformed the PTV-based optimization in terms of OAR sparing and robustness.展开更多
To accommodate wind power as safely as possible and deal with the uncertainties of the output power of winddriven generators,a min-max-min two-stage robust optimization model is presented,considering the unit commitme...To accommodate wind power as safely as possible and deal with the uncertainties of the output power of winddriven generators,a min-max-min two-stage robust optimization model is presented,considering the unit commitment,source-network load collaboration,and control of the load demand response.After the constraint functions are linearized,the original problem is decomposed into the main problem and subproblem as a matrix using the strong dual method.The minimum-maximum of the original problem was continuously maximized using the iterative method,and the optimal solution was finally obtained.The constraint conditions expressed by the matrix may reduce the calculation time,and the upper and lower boundaries of the original problem may rapidly converge.The results of the example show that the injected nodes of the wind farms in the power grid should be selected appropriately;otherwise,it is easy to cause excessive accommodation of wind power at some nodes,leading to a surge in reserve costs and the load demand response is continuously optimized to reduce the inverse peak regulation characteristics of wind power.Thus,the most economical optimization scheme for the worst scenario of the output power of the generators is obtained,which proves the economy and reliability of the two-stage robust optimization method.展开更多
Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-m...Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.展开更多
Reducing the impact of power outages and maintaining the power supply duration must be considered in implementing emergency energy dispatching in micro-networks.This paper studies a new emergency energy treatment meth...Reducing the impact of power outages and maintaining the power supply duration must be considered in implementing emergency energy dispatching in micro-networks.This paper studies a new emergency energy treatment method based on the robust optimal method and the industrial park micro-network with the optical energy storage system.After controlling the load input,a control strategy of adjusting and removing is proposed.Rolling optimal theory is applied to emergency energy scheduling based on a robust optimal mathematical model.A weighting factor is introduced into the optimal model to balance the importance of reducing and retaining the power supply.Uncertainty is designed to adjust the effect of uncertainty on the problem.The example shows that this method can flexibly set the weight coefficient and uncertainty value according to the actual situation so that the input of the control load can be optimized.展开更多
Metamodeling techniques have been used in robust optimization to reduce the high computational cost of the uncertainty analysis and improve the performance of robust optimization problems with computationally expensiv...Metamodeling techniques have been used in robust optimization to reduce the high computational cost of the uncertainty analysis and improve the performance of robust optimization problems with computationally expensive simulation models. Existing metamodels main focus on polynomial regression(PR), neural networks(NN) and Kriging models, these metamodels are not well suited for large-scale robust optimization problems with small size training sets and high nonlinearity. To address the problem, a reduced approximation model technique based on support vector regression(SVR) is introduced in order to improve the accuracy of metamodels. A robust optimization method based on SVR is presented for problems that involve high dimension and nonlinear. First appropriate design parameter samples are selected by experimental design theories, then the response samples are obtained from the simulations such as finite element analysis, the SVR metamodel is constructed and treated as the mean and the variance of the objective performance functions. Combining other constraints, the robust optimization model is formed which can be solved by genetic algorithm (GA). The applicability of the method developed is demonstrated using a case of two-bar structure system study. The performances of SVR were compared with those of PR, Kriging and back-propagation neural networks(BPNN), the comparison results show that the prediction accuracy of the SVR metamodel was higher than those of other metamodels under uncertainty. The robust optimization solutions are near to the real result, and the proposed method is found to be accurate and efficient for robust optimization. This reaserch provides an efficient method for robust optimization problems with complex structure.展开更多
The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-d...The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-dimensional curve or robust control design is used to find an accurate robust solution. However, there may exist complex interaction between parameters and practical engineering system. With the increase of the number of parameters, it is getting hard to determine high-dimensional curves and robust control methods, thus it's difficult to get the robust design solutions. In this paper, a method of global sensitivity analysis based on divided variables in groups is proposed. By making relevant variables in one group and keeping each other independent among sets of variables, global sensitivity analysis is conducted in grouped variables and the importance of parameters is evaluated by calculating the contribution value of each parameter to the total variance of system response. By ranking the importance of input parameters, relatively important parameters are chosen to conduct robust design analysis of the system. By applying this method to the robust optimization design of a real complex nonlinear system-a vehicle occupant restraint system with multi-parameter, good solution is gained and the response variance of the objective function is reduced to 0.01, which indicates that the robustness of the occupant restraint system is improved in a great degree and the method is effective and valuable for the robust design of complex nonlinear system. This research proposes a new method which can be used to obtain solutions for complex nonlinear system robust design.展开更多
In engineering practice, influencing factors including material properties,external load,dimension error and so on,are uncertain to structural fatigue life,and those uncertain factors make the structure fatigue life h...In engineering practice, influencing factors including material properties,external load,dimension error and so on,are uncertain to structural fatigue life,and those uncertain factors make the structure fatigue life have a wide dispersion. Aiming at this problem,the parametric model is built in this paper,and it is used to obtain the structural first principal stress in the module of probabilistic design system( PDS). Parameters of P-S-N are added to the parametric model,and then,the fatigue life of chosen points has been calculated automatically under the reliability of 0. 99. The fatigue life response surface model is obtained by simulation of the sampling points using Monte Carlo method. The six sigma robust optimization mathematical model of fatigue life is established with the combination of six sigma robust optimization and fatigue life response surface model. Take a railway passenger car battery hanging device as an example, and the mathematical model of optimization is established. The minimum mean and mean squared of structural fatigue life are obtained under the requirements of design fatigue life. The results show that the material has been saved by the new method,and the robustness of the fatigue life has been improved.展开更多
Probabilistic method requires a lot of sample information to describe the probability distributions of uncertain variables and has difficulty in dealing with the optimization problem with uncertain parameters which co...Probabilistic method requires a lot of sample information to describe the probability distributions of uncertain variables and has difficulty in dealing with the optimization problem with uncertain parameters which contains unsufficient information.To solve this problem,a robust optimization operation method based on information gap decision theory(IGDT) is presented considering the non-probabilistic uncertainties of parameters.By the proposed method the maximum resistance to the disturbance of uncertain parameters is achieved and the optimization strategies with uncertain parameters are presented.Finally,numerical simulation is performed on the modified IEEE-14 bus system.Numerical results show the effectiveness of the proposed approach.展开更多
This paper proposes a robust optimization framework generally for scheduling systems subject to uncertain input data, which is described by discrete scenarios. The goal of robust optimization is to hedge against the r...This paper proposes a robust optimization framework generally for scheduling systems subject to uncertain input data, which is described by discrete scenarios. The goal of robust optimization is to hedge against the risk of system performance degradation on a set of bad scenarios while maintaining an excellent expected system performance. The robustness is evaluated by a penalty function on the bad-scenario set. The bad-scenario set is identified for current solution by a threshold, which is restricted on a reasonable-value interval. The robust optimization framework is formulated by an optimization problem with two conflicting objectives. One objective is to minimize the reasonable value of threshold, and another is to minimize the measured penalty on the bad-scenario set. An approximate solution framework with two dependent stages is developed to surrogate the biobjective robust optimization problem. The approximation degree of the surrogate framework is analyzed. Finally, the proposed bad-scenario-set robust optimization framework is applied to a scenario job-shop scheduling system. An extensive computational experiment was conducted to demonstrate the effectiveness and the approximation degree of the framework. The computational results testified that the robust optimization framework can provide multiple selections of robust solutions for the decision maker. The robust scheduling framework studied in this paper can provide a unique paradigm for formulating and solving robust discrete optimization problems.展开更多
Volume variation is an uncertainty element which affects timber processing. We studied the volume variation of logs caused by quality defects in traditional timber processing and set up an optimization approach,using ...Volume variation is an uncertainty element which affects timber processing. We studied the volume variation of logs caused by quality defects in traditional timber processing and set up an optimization approach,using a robust optimization method. We used total number of acceptable boards produced to study the relationship between board thickness and raw material logs, using a heuristic search algorithm to control the variation of board volume to improve the output of boards, reduce the quantity of by-products, and lower production costs. The robust optimization method can effectively control the impact of volume variations in timber processing, reduce cutting waste as far as possible using incremental processing and increase profits, maximize the utilization ratio of timber, prevent waste in processing, cultivate the productive type of tree species and save forest resources.展开更多
In short-term operation of natural gas network,the impact of demand uncertainty is not negligible.To address this issue we propose a two-stage robust model for power cost minimization problem in gunbarrel natural gas ...In short-term operation of natural gas network,the impact of demand uncertainty is not negligible.To address this issue we propose a two-stage robust model for power cost minimization problem in gunbarrel natural gas networks.The demands between pipelines and compressor stations are uncertain with a budget parameter,since it is unlikely that all the uncertain demands reach the maximal deviation simultaneously.During solving the two-stage robust model we encounter a bilevel problem which is challenging to solve.We formulate it as a multi-dimensional dynamic programming problem and propose approximate dynamic programming methods to accelerate the calculation.Numerical results based on real network in China show that we obtain a speed gain of 7 times faster in average without compromising optimality compared with original dynamic programming algorithm.Numerical results also verify the advantage of robust model compared with deterministic model when facing uncertainties.These findings offer short-term operation methods for gunbarrel natural gas network management to handle with uncertainties.展开更多
Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestio...Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.展开更多
In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the c...In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the current RO framework inapplicable.This paper investigates a class of two-stage RO problems that involve decision-dependent uncertainties.We introduce a class of polyhedral uncertainty sets whose right-hand-side vector has a dependency on the here-and-now decisions and seek to derive the exact optimal wait-and-see decisions for the second-stage problem.A novel iterative algorithm based on the Benders dual decomposition is proposed where advanced optimality cuts and feasibility cuts are designed to incorporate the uncertainty-decision coupling.The computational tractability,robust feasibility and optimality,and convergence performance of the proposed algorithm are guaranteed with theoretical proof.Four motivating application examples that feature the decision-dependent uncertainties are provided.Finally,the proposed solution methodology is verified by conducting case studies on the pre-disaster highway investment problem.展开更多
To increase the robustness of the optimization solutions of the mixed-flow pump,the impeller was firstly indirectly parameterized based on the 2D blade design theory.Secondly,the robustness of the optimization solutio...To increase the robustness of the optimization solutions of the mixed-flow pump,the impeller was firstly indirectly parameterized based on the 2D blade design theory.Secondly,the robustness of the optimization solution was mathematically defined,and then calculated by Monte Carlo sampling method.Thirdly,the optimization on the mixed-flow pump′s impeller was decomposed into the optimal and robust sub-optimization problems,to maximize the pump head and efficiency and minimize the fluctuation degree of them under varying working conditions at the same time.Fourthly,using response surface model,a surrogate model was established between the optimization objectives and control variables of the shape of the impeller.Finally,based on a multi-objective genetic optimization algorithm,a two-loop iterative optimization process was designed to find the optimal solution with good robustness.Comparing the original and optimized pump,it is found that the internal flow field of the optimized pump has been improved under various operating conditions,the hydraulic performance has been improved consequently,and the range of high efficient zone has also been widened.Besides,with the changing of working conditions,the change trend of the hydraulic performance of the optimized pump becomes gentler,the flow field distribution is more uniform,and the influence degree of the varia-tion of working conditions decreases,and the operating stability of the pump is improved.It is concluded that the robust optimization method proposed in this paper is a reasonable way to optimize the mixed-flow pump,and provides references for optimization problems of other fluid machinery.展开更多
A robust optimization design method is proposed to investigate the influence of the hook position on the vertical vibration(bending)of an automobile exhaust system.A block diagram for the robustness analysis of the ex...A robust optimization design method is proposed to investigate the influence of the hook position on the vertical vibration(bending)of an automobile exhaust system.A block diagram for the robustness analysis of the exhaust system is initially constructed from the major affecting factors.Secondly,the second-order inertia force is set as the vibration excitation source of the exhaust system and the displacement of four hooks of the exhaust system is selected as the variable factor.Then tests are carried out to investigate the resulting vertical bending considering four influencing factors and three levels of analysis.Finally,a variance analysis of the vertical bending is performed.The present study provides a set of guidelines to control the key factors affecting the vibration of vehicle exhaust systems while proposing an effective method to reduce vehicle vibration and improve noise analysis。展开更多
Manufacture variations can greatly increase the performance variability of compressor blades. Current robust design optimization methods have a critical role in reducing the adverse impact of the variations, but can b...Manufacture variations can greatly increase the performance variability of compressor blades. Current robust design optimization methods have a critical role in reducing the adverse impact of the variations, but can be affected by errors if the assumptions of the deviation models and distribution parameters are inaccurate. A new approach for robust design optimization without the employment of the deviation models is proposed. The deviation package method and the interval estimation method are exploited in this new approach. Simultaneously, a stratified strategy is used to reduce the computational cost and assure the optimization accuracy. The test case employed for this study is a typical transonic compressor blade profile, which resembles most of the manufacture features of modern compressor blades. A set of 96 newly manufactured blades was measured using a coordinate measurement machine to obtain the manufacture variations and produce a deviation package. The optimization results show that the scatter of the aerodynamic performance for the optimal robust design is 20% less than the baseline value. By comparing the optimization results obtained from the deviation package method with those obtained from widely-used methods employing the deviation model, the efficiency and accuracy of the deviation package method are demonstrated. Finally, the physical mechanisms that control the robustness of different designs were further investigated, and some statistical laws of robust design were extracted.展开更多
This paper proposes a fixed-time distributed robust optimization approach for solving economic dispatch problems.Based on an integral sliding mode control scheme,the proposed multi-agent system converges to an optimal...This paper proposes a fixed-time distributed robust optimization approach for solving economic dispatch problems.Based on an integral sliding mode control scheme,the proposed multi-agent system converges to an optimal solution to an economic dispatch problem before a fixed time.In addition,the proposed multi-agent system can suppress the disturbance in a fixed time.To reduce the cost of sliding mode controls,we propose a distributed event-triggered intermittent control which reduces the sliding mode control time by setting a control triggering rule on the basis of two boundary functions of a Lyapunov function.The simulation results of three power systems illustrate the characteristics and effectiveness of the theoretical results.展开更多
In the existing multi-period robust optimization methods for the optimal power flow in radial distribution systems,the capability of distributed generators(DGs)to regulate the reactive power,the operation costs of the...In the existing multi-period robust optimization methods for the optimal power flow in radial distribution systems,the capability of distributed generators(DGs)to regulate the reactive power,the operation costs of the regulation equipment,and the current of the shunt capacitor of the cables are not considered.In this paper,a multi-period two-stage robust scheduling strategy that aims to minimize the total cost of the power supply is developed.This strategy considers the time-ofuse price,the capability of the DGs to regulate the active and reactive power,the action costs of the regulation equipment,and the current of the shunt capacitors of the cables in a radial distribution system.Furthermore,the numbers of variables and constraints in the first-stage model remain constant during the iteration to enhance the computation efficiency.To solve the second-stage model,only the model of each period needs to be solved.Then,their objective values are accumulated,revealing that the computation rate using the proposed method is much higher than that of existing methods.The effectiveness of the proposed method is validated by actual 4-bus,IEEE 33-bus,and PG 69-bus distribution systems.展开更多
A coordinated scheduling model based on two-stage distributionally robust optimization(TSDRO)is proposed for integrated energy systems(IESs)with electricity-hydrogen hybrid energy storage.The scheduling problem of the...A coordinated scheduling model based on two-stage distributionally robust optimization(TSDRO)is proposed for integrated energy systems(IESs)with electricity-hydrogen hybrid energy storage.The scheduling problem of the IES is divided into two stages in the TSDRO-based coordinated scheduling model.The first stage addresses the day-ahead optimal scheduling problem of the IES under deterministic forecasting information,while the sec-ond stage uses a distributionally robust optimization method to determine the intraday rescheduling problem under high-order uncertainties,building upon the results of the first stage.The scheduling model also considers col-laboration among the electricity,thermal,and gas networks,focusing on economic operation and carbon emissions.The flexibility of these networks and the energy gradient utilization of hydrogen units during operation are also incor-porated into the model.To improve computational efficiency,the nonlinear formulations in the TSDRO-based coordinated scheduling model are properly linearized to obtain a Mixed-Integer Linear Programming model.The Column-Constraint Generation(C&CG)algorithm is then employed to decompose the scheduling model into a mas-ter problem and subproblems.Through the iterative solution of the master problem and subproblems,an efficient analysis of the coordinated scheduling model is achieved.Finally,the effectiveness of the proposed TSDRO-based coordinated scheduling model is verified through case studies.The simulation results demonstrate that the proposed TSDRO-based coordinated scheduling model can effectively accomplish the optimal scheduling task while consider-ing the uncertainty and flexibility of the system.Compared with traditional methods,the proposed TSDRO-based coordinated scheduling model can better balance conservativeness and robustness.展开更多
文摘To address the scheduling problem involving energy storage systems and uncertain energy,we propose a method based on multi-stage robust optimization.This approach aims to regulate the energy storage system by using a multi-stage robust optimal control method,which helps overcome the limitations of traditional methods in terms of time scale.The goal is to effectively utilize the energy storage power station system to address issues caused by unpredictable variations in environmental energy and fluctuating load throughout the day.To achieve this,a mathematical model is constructed to represent uncertain energy sources such as photovoltaic and wind power.The generalized Benders Decomposition method is then employed to solve the multi-stage objective optimization problem.By decomposing the problem into a series of sub-objectives,the system scale is effectively reduced,and the algorithm’s convergence ability is improved.Compared with other algorithms,the multi-stage robust optimization model has better economy and convergence ability and can be used to guide the power dispatching of uncertain energy and energy storage systems.
基金supported by National Key Research and Development Program of China(No.2022YFC2401503)National Natural Science Foundation of China(Nos.11875299,61631001,U1532264,and 12005271).
文摘Intensity-modulated particle therapy(IMPT)with carbon ions is comparatively susceptible to various uncertainties caused by breathing motion,including range,setup,and target positioning uncertainties.To determine relative biological effectiveness-weighted dose(RWD)distributions that are resilient to these uncertainties,the reference phase-based four-dimensional(4D)robust optimization(RP-4DRO)and each phase-based 4D robust optimization(EP-4DRO)method in carbon-ion IMPT treatment planning were evaluated and compared.Based on RWD distributions,4DRO methods were compared with 4D conventional optimization using planning target volume(PTV)margins(PTV-based optimization)to assess the effectiveness of the robust optimization methods.Carbon-ion IMPT treatment planning was conducted in a cohort of five lung cancer patients.The results indicated that the EP-4DRO method provided better robustness(P=0.080)and improved plan quality(P=0.225)for the clinical target volume(CTV)in the individual respiratory phase when compared with the PTV-based optimization.Compared with the PTV-based optimization,the RP-4DRO method ensured the robustness(P=0.022)of the dose distributions in the reference breathing phase,albeit with a slight sacrifice of the target coverage(P=0.450).Both 4DRO methods successfully maintained the doses delivered to the organs at risk(OARs)below tolerable levels,which were lower than the doses in the PTV-based optimization(P<0.05).Furthermore,the RP-4DRO method exhibited significantly superior performance when compared with the EP-4DRO method in enhancing overall OAR sparing in either the individual respiratory phase or reference respiratory phase(P<0.05).In general,both 4DRO methods outperformed the PTV-based optimization in terms of OAR sparing and robustness.
基金supported by the Special Research Project on Power Planning of the Guangdong Power Grid Co.,Ltd.
文摘To accommodate wind power as safely as possible and deal with the uncertainties of the output power of winddriven generators,a min-max-min two-stage robust optimization model is presented,considering the unit commitment,source-network load collaboration,and control of the load demand response.After the constraint functions are linearized,the original problem is decomposed into the main problem and subproblem as a matrix using the strong dual method.The minimum-maximum of the original problem was continuously maximized using the iterative method,and the optimal solution was finally obtained.The constraint conditions expressed by the matrix may reduce the calculation time,and the upper and lower boundaries of the original problem may rapidly converge.The results of the example show that the injected nodes of the wind farms in the power grid should be selected appropriately;otherwise,it is easy to cause excessive accommodation of wind power at some nodes,leading to a surge in reserve costs and the load demand response is continuously optimized to reduce the inverse peak regulation characteristics of wind power.Thus,the most economical optimization scheme for the worst scenario of the output power of the generators is obtained,which proves the economy and reliability of the two-stage robust optimization method.
基金supported in part by the National Natural Science Foundation of China under grants 61971080,61901367in part by the Natural Science Foundation of Shaanxi Province under grant 2020JQ-844in part by the open-end fund of the Engineering Research Center of Intelligent Air-ground Integrated Vehicle and Traffic Control(ZNKD2021-001)。
文摘Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.
文摘Reducing the impact of power outages and maintaining the power supply duration must be considered in implementing emergency energy dispatching in micro-networks.This paper studies a new emergency energy treatment method based on the robust optimal method and the industrial park micro-network with the optical energy storage system.After controlling the load input,a control strategy of adjusting and removing is proposed.Rolling optimal theory is applied to emergency energy scheduling based on a robust optimal mathematical model.A weighting factor is introduced into the optimal model to balance the importance of reducing and retaining the power supply.Uncertainty is designed to adjust the effect of uncertainty on the problem.The example shows that this method can flexibly set the weight coefficient and uncertainty value according to the actual situation so that the input of the control load can be optimized.
基金supported by National Natural Science Foundation of China (Grant No.60572007)National Basic Research Program of China(973 Program,Grant No.613580202)
文摘Metamodeling techniques have been used in robust optimization to reduce the high computational cost of the uncertainty analysis and improve the performance of robust optimization problems with computationally expensive simulation models. Existing metamodels main focus on polynomial regression(PR), neural networks(NN) and Kriging models, these metamodels are not well suited for large-scale robust optimization problems with small size training sets and high nonlinearity. To address the problem, a reduced approximation model technique based on support vector regression(SVR) is introduced in order to improve the accuracy of metamodels. A robust optimization method based on SVR is presented for problems that involve high dimension and nonlinear. First appropriate design parameter samples are selected by experimental design theories, then the response samples are obtained from the simulations such as finite element analysis, the SVR metamodel is constructed and treated as the mean and the variance of the objective performance functions. Combining other constraints, the robust optimization model is formed which can be solved by genetic algorithm (GA). The applicability of the method developed is demonstrated using a case of two-bar structure system study. The performances of SVR were compared with those of PR, Kriging and back-propagation neural networks(BPNN), the comparison results show that the prediction accuracy of the SVR metamodel was higher than those of other metamodels under uncertainty. The robust optimization solutions are near to the real result, and the proposed method is found to be accurate and efficient for robust optimization. This reaserch provides an efficient method for robust optimization problems with complex structure.
基金Supported by National Natural Science Foundation of China(Grant No.51275164)
文摘The current research of complex nonlinear system robust optimization mainly focuses on the features of design parameters, such as probability density functions, boundary conditions, etc. After parameters study, high-dimensional curve or robust control design is used to find an accurate robust solution. However, there may exist complex interaction between parameters and practical engineering system. With the increase of the number of parameters, it is getting hard to determine high-dimensional curves and robust control methods, thus it's difficult to get the robust design solutions. In this paper, a method of global sensitivity analysis based on divided variables in groups is proposed. By making relevant variables in one group and keeping each other independent among sets of variables, global sensitivity analysis is conducted in grouped variables and the importance of parameters is evaluated by calculating the contribution value of each parameter to the total variance of system response. By ranking the importance of input parameters, relatively important parameters are chosen to conduct robust design analysis of the system. By applying this method to the robust optimization design of a real complex nonlinear system-a vehicle occupant restraint system with multi-parameter, good solution is gained and the response variance of the objective function is reduced to 0.01, which indicates that the robustness of the occupant restraint system is improved in a great degree and the method is effective and valuable for the robust design of complex nonlinear system. This research proposes a new method which can be used to obtain solutions for complex nonlinear system robust design.
基金National Natural Science Foundation of Liaoning Province,China(No.2014028020)Liaoning Province Education Administration Project,China(No.L2013182)+1 种基金Railw ay Corporation Project,China(No.2014J004-N)Dalian Science and Technology Project,China(No.2015A11GX026)
文摘In engineering practice, influencing factors including material properties,external load,dimension error and so on,are uncertain to structural fatigue life,and those uncertain factors make the structure fatigue life have a wide dispersion. Aiming at this problem,the parametric model is built in this paper,and it is used to obtain the structural first principal stress in the module of probabilistic design system( PDS). Parameters of P-S-N are added to the parametric model,and then,the fatigue life of chosen points has been calculated automatically under the reliability of 0. 99. The fatigue life response surface model is obtained by simulation of the sampling points using Monte Carlo method. The six sigma robust optimization mathematical model of fatigue life is established with the combination of six sigma robust optimization and fatigue life response surface model. Take a railway passenger car battery hanging device as an example, and the mathematical model of optimization is established. The minimum mean and mean squared of structural fatigue life are obtained under the requirements of design fatigue life. The results show that the material has been saved by the new method,and the robustness of the fatigue life has been improved.
基金National Natural Science Foundation of China(No.61533010)Science and Technology Commission of Shanghai Municipality,China(No.14ZR1415300)
文摘Probabilistic method requires a lot of sample information to describe the probability distributions of uncertain variables and has difficulty in dealing with the optimization problem with uncertain parameters which contains unsufficient information.To solve this problem,a robust optimization operation method based on information gap decision theory(IGDT) is presented considering the non-probabilistic uncertainties of parameters.By the proposed method the maximum resistance to the disturbance of uncertain parameters is achieved and the optimization strategies with uncertain parameters are presented.Finally,numerical simulation is performed on the modified IEEE-14 bus system.Numerical results show the effectiveness of the proposed approach.
基金supported by National Natural Science Foundation of China(60874076,61273182,61273040)the Shanghai Rising-Star Program(15QA1402000)
文摘This paper proposes a robust optimization framework generally for scheduling systems subject to uncertain input data, which is described by discrete scenarios. The goal of robust optimization is to hedge against the risk of system performance degradation on a set of bad scenarios while maintaining an excellent expected system performance. The robustness is evaluated by a penalty function on the bad-scenario set. The bad-scenario set is identified for current solution by a threshold, which is restricted on a reasonable-value interval. The robust optimization framework is formulated by an optimization problem with two conflicting objectives. One objective is to minimize the reasonable value of threshold, and another is to minimize the measured penalty on the bad-scenario set. An approximate solution framework with two dependent stages is developed to surrogate the biobjective robust optimization problem. The approximation degree of the surrogate framework is analyzed. Finally, the proposed bad-scenario-set robust optimization framework is applied to a scenario job-shop scheduling system. An extensive computational experiment was conducted to demonstrate the effectiveness and the approximation degree of the framework. The computational results testified that the robust optimization framework can provide multiple selections of robust solutions for the decision maker. The robust scheduling framework studied in this paper can provide a unique paradigm for formulating and solving robust discrete optimization problems.
基金supported by the Fundamental Research Funds for the Central Universities(Project No.2572015CB06)Nature Science Foundation of Heilongjiang Province(LC201407)
文摘Volume variation is an uncertainty element which affects timber processing. We studied the volume variation of logs caused by quality defects in traditional timber processing and set up an optimization approach,using a robust optimization method. We used total number of acceptable boards produced to study the relationship between board thickness and raw material logs, using a heuristic search algorithm to control the variation of board volume to improve the output of boards, reduce the quantity of by-products, and lower production costs. The robust optimization method can effectively control the impact of volume variations in timber processing, reduce cutting waste as far as possible using incremental processing and increase profits, maximize the utilization ratio of timber, prevent waste in processing, cultivate the productive type of tree species and save forest resources.
基金partially supported by the National Science Foundation of China(Grants 71822105 and 91746210)。
文摘In short-term operation of natural gas network,the impact of demand uncertainty is not negligible.To address this issue we propose a two-stage robust model for power cost minimization problem in gunbarrel natural gas networks.The demands between pipelines and compressor stations are uncertain with a budget parameter,since it is unlikely that all the uncertain demands reach the maximal deviation simultaneously.During solving the two-stage robust model we encounter a bilevel problem which is challenging to solve.We formulate it as a multi-dimensional dynamic programming problem and propose approximate dynamic programming methods to accelerate the calculation.Numerical results based on real network in China show that we obtain a speed gain of 7 times faster in average without compromising optimality compared with original dynamic programming algorithm.Numerical results also verify the advantage of robust model compared with deterministic model when facing uncertainties.These findings offer short-term operation methods for gunbarrel natural gas network management to handle with uncertainties.
基金supported the National Natural Science Foundation of China (71621001, 71825004, and 72001019)the Fundamental Research Funds for Central Universities (2020JBM031 and 2021YJS203)the Research Foundation of State Key Laboratory of Rail Traffic Control and Safety (RCS2020ZT001)
文摘Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.
基金This work was supported by the Joint Research Fund in Smart Grid under cooperative agreement between the National Natural Science Foundation of China(NSFC)and State Grid Corporation of China(U1966601).
文摘In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the current RO framework inapplicable.This paper investigates a class of two-stage RO problems that involve decision-dependent uncertainties.We introduce a class of polyhedral uncertainty sets whose right-hand-side vector has a dependency on the here-and-now decisions and seek to derive the exact optimal wait-and-see decisions for the second-stage problem.A novel iterative algorithm based on the Benders dual decomposition is proposed where advanced optimality cuts and feasibility cuts are designed to incorporate the uncertainty-decision coupling.The computational tractability,robust feasibility and optimality,and convergence performance of the proposed algorithm are guaranteed with theoretical proof.Four motivating application examples that feature the decision-dependent uncertainties are provided.Finally,the proposed solution methodology is verified by conducting case studies on the pre-disaster highway investment problem.
基金National Natural Science Foundation of China(51609107)Open Subject of Provincial and Ministerial Discipline Platform of Xihua University(szjj2018-123)。
文摘To increase the robustness of the optimization solutions of the mixed-flow pump,the impeller was firstly indirectly parameterized based on the 2D blade design theory.Secondly,the robustness of the optimization solution was mathematically defined,and then calculated by Monte Carlo sampling method.Thirdly,the optimization on the mixed-flow pump′s impeller was decomposed into the optimal and robust sub-optimization problems,to maximize the pump head and efficiency and minimize the fluctuation degree of them under varying working conditions at the same time.Fourthly,using response surface model,a surrogate model was established between the optimization objectives and control variables of the shape of the impeller.Finally,based on a multi-objective genetic optimization algorithm,a two-loop iterative optimization process was designed to find the optimal solution with good robustness.Comparing the original and optimized pump,it is found that the internal flow field of the optimized pump has been improved under various operating conditions,the hydraulic performance has been improved consequently,and the range of high efficient zone has also been widened.Besides,with the changing of working conditions,the change trend of the hydraulic performance of the optimized pump becomes gentler,the flow field distribution is more uniform,and the influence degree of the varia-tion of working conditions decreases,and the operating stability of the pump is improved.It is concluded that the robust optimization method proposed in this paper is a reasonable way to optimize the mixed-flow pump,and provides references for optimization problems of other fluid machinery.
基金science and technology projects of Jiangxi Provincial Education Department(GJJ161186).
文摘A robust optimization design method is proposed to investigate the influence of the hook position on the vertical vibration(bending)of an automobile exhaust system.A block diagram for the robustness analysis of the exhaust system is initially constructed from the major affecting factors.Secondly,the second-order inertia force is set as the vibration excitation source of the exhaust system and the displacement of four hooks of the exhaust system is selected as the variable factor.Then tests are carried out to investigate the resulting vertical bending considering four influencing factors and three levels of analysis.Finally,a variance analysis of the vertical bending is performed.The present study provides a set of guidelines to control the key factors affecting the vibration of vehicle exhaust systems while proposing an effective method to reduce vehicle vibration and improve noise analysis。
基金funded by the National Science and Technology Major Project, China (No. 2017-II-0001-0013)Science Center for Gas Turbine Project, China (Nos. P2022-A-II-002-001 and P2022-B-II-002-001)。
文摘Manufacture variations can greatly increase the performance variability of compressor blades. Current robust design optimization methods have a critical role in reducing the adverse impact of the variations, but can be affected by errors if the assumptions of the deviation models and distribution parameters are inaccurate. A new approach for robust design optimization without the employment of the deviation models is proposed. The deviation package method and the interval estimation method are exploited in this new approach. Simultaneously, a stratified strategy is used to reduce the computational cost and assure the optimization accuracy. The test case employed for this study is a typical transonic compressor blade profile, which resembles most of the manufacture features of modern compressor blades. A set of 96 newly manufactured blades was measured using a coordinate measurement machine to obtain the manufacture variations and produce a deviation package. The optimization results show that the scatter of the aerodynamic performance for the optimal robust design is 20% less than the baseline value. By comparing the optimization results obtained from the deviation package method with those obtained from widely-used methods employing the deviation model, the efficiency and accuracy of the deviation package method are demonstrated. Finally, the physical mechanisms that control the robustness of different designs were further investigated, and some statistical laws of robust design were extracted.
基金supported by the National Natural Science Foundation of China(Grant No.62173308)the Natural Science Foundation of Zhejiang Province of China(Grant Nos.LR20F030001 and LD19A010001)Jinhua Science and Technology Project(Grant No.2022-1-042)。
文摘This paper proposes a fixed-time distributed robust optimization approach for solving economic dispatch problems.Based on an integral sliding mode control scheme,the proposed multi-agent system converges to an optimal solution to an economic dispatch problem before a fixed time.In addition,the proposed multi-agent system can suppress the disturbance in a fixed time.To reduce the cost of sliding mode controls,we propose a distributed event-triggered intermittent control which reduces the sliding mode control time by setting a control triggering rule on the basis of two boundary functions of a Lyapunov function.The simulation results of three power systems illustrate the characteristics and effectiveness of the theoretical results.
基金supported in part by the Fundamental Research Funds for the Central Universities of China(No.PA2021GDSK0083)in part by the State Key Program of National Natural Science of China(No.51637004)in part by the National Key Research and Development Plan“Important Scientific Instruments and Equipment Development”(No.2016YFF0102200)。
文摘In the existing multi-period robust optimization methods for the optimal power flow in radial distribution systems,the capability of distributed generators(DGs)to regulate the reactive power,the operation costs of the regulation equipment,and the current of the shunt capacitor of the cables are not considered.In this paper,a multi-period two-stage robust scheduling strategy that aims to minimize the total cost of the power supply is developed.This strategy considers the time-ofuse price,the capability of the DGs to regulate the active and reactive power,the action costs of the regulation equipment,and the current of the shunt capacitors of the cables in a radial distribution system.Furthermore,the numbers of variables and constraints in the first-stage model remain constant during the iteration to enhance the computation efficiency.To solve the second-stage model,only the model of each period needs to be solved.Then,their objective values are accumulated,revealing that the computation rate using the proposed method is much higher than that of existing methods.The effectiveness of the proposed method is validated by actual 4-bus,IEEE 33-bus,and PG 69-bus distribution systems.
基金supported in part by the National Natural Science Foundation(51977181,52077180)Natural Science Foundation of Sichuan Province(2022NSFSC0027)+2 种基金Fok Ying-Tong Education Foundation of China(171104)14th Five-year Major Science and Technology Research Project of CRRC(2021CXZ021-2)Key research and development project of China National Railway Group Co.,Ltd(N2022J016-B).
文摘A coordinated scheduling model based on two-stage distributionally robust optimization(TSDRO)is proposed for integrated energy systems(IESs)with electricity-hydrogen hybrid energy storage.The scheduling problem of the IES is divided into two stages in the TSDRO-based coordinated scheduling model.The first stage addresses the day-ahead optimal scheduling problem of the IES under deterministic forecasting information,while the sec-ond stage uses a distributionally robust optimization method to determine the intraday rescheduling problem under high-order uncertainties,building upon the results of the first stage.The scheduling model also considers col-laboration among the electricity,thermal,and gas networks,focusing on economic operation and carbon emissions.The flexibility of these networks and the energy gradient utilization of hydrogen units during operation are also incor-porated into the model.To improve computational efficiency,the nonlinear formulations in the TSDRO-based coordinated scheduling model are properly linearized to obtain a Mixed-Integer Linear Programming model.The Column-Constraint Generation(C&CG)algorithm is then employed to decompose the scheduling model into a mas-ter problem and subproblems.Through the iterative solution of the master problem and subproblems,an efficient analysis of the coordinated scheduling model is achieved.Finally,the effectiveness of the proposed TSDRO-based coordinated scheduling model is verified through case studies.The simulation results demonstrate that the proposed TSDRO-based coordinated scheduling model can effectively accomplish the optimal scheduling task while consider-ing the uncertainty and flexibility of the system.Compared with traditional methods,the proposed TSDRO-based coordinated scheduling model can better balance conservativeness and robustness.