Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems(HIES),which enhance energy sustainabili...Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems(HIES),which enhance energy sustainability through coordinated electricity,thermal,natural gas,and hydrogen utilization.This study proposes a two-stage distributionally robust optimization(DRO)-based scheduling method to improve the economic efficiency and reduce carbon emissions of HIES.The framework incorporates a ladder-type carbon trading mechanism to regulate emissions and implements a demand response(DR)program to adjustflexible multi-energy loads,thereby prioritizing RES consumption.Uncertainties from RES generation and load demand are addressed through an ambiguity set,enabling robust decision-making.The column-and-constraint generation(C&CG)algorithm efficiently solves the two-stage DRO model.Case studies demonstrate that the proposed method reduces operational costs by 3.56%,increases photovoltaic consumption rates by 5.44%,and significantly lowers carbon emissions compared to conventional approaches.Furthermore,the DRO framework achieves a superior balance between conservativeness and robustness over conventional stochastic and robust optimization methods,highlighting its potential to advance cost-effective,low-carbon energy systems while ensuring grid stability under uncertainty.展开更多
A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncer...A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.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
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
To meet the requirements of modern air combat,an integrated fire/flight control(IFFC)system is designed to achieve automatic precision tracking and aiming for armed helicopters and release the pilot from heavy target ...To meet the requirements of modern air combat,an integrated fire/flight control(IFFC)system is designed to achieve automatic precision tracking and aiming for armed helicopters and release the pilot from heavy target burden.Considering the complex dynamic characteristics and the couplings of armed helicopters,an improved automatic attack system is con-structed to integrate the fire control system with the flight con-trol system into a unit.To obtain the optimal command signals,the algorithm is investigated to solve nonconvex optimization problems by the contracting Broyden Fletcher Goldfarb Shanno(C-BFGS)algorithm combined with the trust region method.To address the uncertainties in the automatic attack system,the memory nominal distribution and Wasserstein distance are introduced to accurately characterize the uncertainties,and the dual solvable problem is analyzed by using the duality the-ory,conjugate function,and dual norm.Simulation results verify the practicality and validity of the proposed method in solving the IFFC problem on the premise of satisfactory aiming accu-racy.展开更多
Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This ...Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources.The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments.In this regard,the faults of stochastic optimization and traditional robust optimization can be overcome.Firstly,a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed,and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets.Then,an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem,which improves the computational efficiency of the model.Finally,the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy.They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.展开更多
A distributionally robust model predictive control(DRMPC)scheme is proposed based on neural network(NN)modeling to achieve the trajectory tracking control of robot manipulators with state and control torque constraint...A distributionally robust model predictive control(DRMPC)scheme is proposed based on neural network(NN)modeling to achieve the trajectory tracking control of robot manipulators with state and control torque constraints.First,an NN is used to fit the motion data of robot manipulators for data-driven dynamic modeling,converting it into a linear prediction model through gradients.Then,by statistically analyzing the stochastic characteristics of the NN modeling errors,a distributionally robust model predictive controller is designed based on the chance constraints,and the optimization problem is transformed into a tractable quadratic programming(QP)problem under the distributionally robust optimization(DRO)framework.The recursive feasibility and convergence of the proposed algorithm are proven.Finally,the effectiveness of the proposed algorithm is verified through numerical simulation.展开更多
The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal jo...The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information.We construct a distributionally robust optimization model and use the Karush-Kuhn-Tucker(KKT)conditions to solve the analytic formula of optimal solutions.By comparing the models with and without investing in sustainable technologies,we examine the effect of sustainable technologies on the operational management decisions of the retailer.Finally,some computational examples are applied to analyze the impact of critical factors on operational strategies,and some managerial insights are given based on the analysis results.展开更多
In this paper, the option pricing problem is formulated as a distributionally robust optimization problem, which seeks to minimize the worst case replication error for a given distributional uncertainty set(DUS) of th...In this paper, the option pricing problem is formulated as a distributionally robust optimization problem, which seeks to minimize the worst case replication error for a given distributional uncertainty set(DUS) of the random underlying asset returns. The DUS is defined as a Wasserstein ball centred the empirical distribution of the underlying asset returns. It is proved that the proposed model can be reformulated as a computational tractable linear programming problem. Finally, the results of the empirical tests are presented to show the significance of the proposed approach.展开更多
A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lac...A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lacks interpretability in its results,obscuring the causal relationships between data distribution characteristics and the outcomes.Furthermore,the current approach to battery type selection is not included in traditional BESS planning,hindering comprehensive optimization.To tackle these BESS planning problems,this paper presents a universal method for BESS planning,which is designed to enhance the interpretability of DRO.First,mathematical definitions of interpretable DRO(IDRO)are introduced.Next,the uncertainties in wind power,photovoltaic power,and loads are modeled by using second-order cone ambiguity sets(SOCASs).In addition,the proposed method integrates selection,sizing,and siting.Moreover,a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems.Finally,the effectiveness of the proposed method is demonstrated through case studies,offering planners richer decision-making insights.展开更多
With the adjustment of the energy structure and the rapid development of commercial complex buildings,building energy systems(BES)are playing an increasingly important role.To fully utilize smart building management t...With the adjustment of the energy structure and the rapid development of commercial complex buildings,building energy systems(BES)are playing an increasingly important role.To fully utilize smart building management techniques for coordinating and optimizing energy systems while limiting carbon emissions,this study proposes a smart building energy scheduling method based on distributionally robust optimization(DRO).First,a framework for day-ahead market interaction between the distribution grid(DG),buildings,and electric vehicles(EVs)is established.Based on the the price elasticity matrix principle,demand side management(DSM)technology is used to model the price-based demand response(PBDR)of building electricity load.Meanwhile,the thermal inertia and thermal load flexibility of the building heating system are utilized to leverage the energy storage capabilities of the heating system.Second,a Wasserstein DRO Stackelberg game model is constructed with the objective of maximizing the benefits for both buildings and EVs.This Wasserstein distributionally robust model is then transformed into a mixed-integer model by combining the Karush–Kuhn–Tucker(KKT)conditions and duality theory.Finally,the optimization effect of temperature load storage characteristics on BES flexible scheduling and the coordination of DRO indicators on the optimization results were verified through simulations.The strategy proposed in this article can reduce the total operating cost of BES by 26.37%,significantly enhancing economic efficiency and achieving electricity and heat substitution,resulting in a smoother load curve.This study provides a theoretical foundation and assurance for optimal daily energy scheduling of BES.展开更多
The integrated electricity-gas system(IEGS)is the foundation of the Energy Internet.As inevitable risk factors,the widespread blackout and large-scale energy supply disruptions represent serious threats to the IEGS.Im...The integrated electricity-gas system(IEGS)is the foundation of the Energy Internet.As inevitable risk factors,the widespread blackout and large-scale energy supply disruptions represent serious threats to the IEGS.Improving the load restoration ability of IEGS is an important measure to mitigate the harm caused by blackouts.However,the increasing penetration of wind power has posed some difficulties to IEGS load restoration.In view of this,based on distributionally robust optimization(DRO),a two-stage IEGS restoration model is developed in this paper.Through a detailed mathematical model of an electric power system(EPS)with multiple generating resources and a natural gas system(NGS)with dynamic characteristics,the supporting role of the NGS operation flexibility for IEGS restoration is fully explored and quantitatively analyzed.Through the construction of a Wasserstein metric-based ambiguity set of wind power forecast deviation,the proposed two-stage IEGS restoration model can incorporate operational risks when the uncertainty of wind power output is encountered and also take into account the flexible reserve capacity(FRC)allocation and deployment constraints.The proposed model can realize the reasonable scheduling of wind power,automatically determine the allocation of the required FRC,and optimize the load restoration schemes.Moreover,the proposed model can be converted into a mixed integer linear programming problem which can be directly solved.In the case study,the advantages of the proposed model are compared with three conventional restoration models based on two test systems,and sensitivity analysis is conducted.展开更多
The escalating installation of distributed generation (DG) within active distribution networks (ADNs) diminishes the reliance on fossil fuels, yet it intensifies the disparity between demand and generation across vari...The escalating installation of distributed generation (DG) within active distribution networks (ADNs) diminishes the reliance on fossil fuels, yet it intensifies the disparity between demand and generation across various regions. Moreover, due to the intermittent and stochastic characteristics, DG also introduces uncertain forecasting errors, which further increase difficulties for power dispatch. To overcome these challenges, an emerging flexible interconnection device, soft open point (SOP), is introduced. A distributionally robust chance-constrained optimization (DRCCO) model is also proposed to effectively exploit the benefits of SOPs in ADNs under uncertainties. Compared with conventional robust, stochastic and chance-constrained models, the DRCCO model can better balance reliability and economic profits without the exact distribution of uncertainties. More-over, unlike most published works that employ two individual chance constraints to approximate the upper and lower bound constraints (e.g, bus voltage and branch current limitations), joint two-sided chance constraints are introduced and exactly reformulated into conic forms to avoid redundant conservativeness. Based on numerical experiments, we validate that SOPs' employment can significantly enhance the energy efficiency of ADNs by alleviating DG curtailment and load shedding problems. Simulation results also confirm that the proposed joint two-sided DRCCO method can achieve good balance between economic efficiency and reliability while reducing the conservativeness of conventional DRCCO methods.展开更多
As an effective carrier of integrated clean energy,the microgrid has attracted wide attention.The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the econom...As an effective carrier of integrated clean energy,the microgrid has attracted wide attention.The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids.This paper proposes an optimization scheme based on the distributionally robust optimization(DRO)model for a microgrid considering solar-wind correlation.Firstly,scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function;then the generated scenario results are reduced by K-means clustering;finally,the probability confidence interval of scenario distribution is constrained by 1-norm and∞-norm.The model is solved by a column-and-constraint generation algorithm.Experimental studies are conducted on a microgrid system in Jiangsu,China and the obtained scheduling solution turned out to be superior under wind and solar power uncertainties,which verifies the effectiveness of the proposed DRO model.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
Transmission network expansion can significantly improve the penetration level of renewable generation.However,existing studies have not explicitly revealed and quantified the trade-off between the investment cost and...Transmission network expansion can significantly improve the penetration level of renewable generation.However,existing studies have not explicitly revealed and quantified the trade-off between the investment cost and penetration level of renewable generation.This paper proposes a distributionally robust optimization model to minimize the cost of transmission network expansion under uncertainty and maximize the penetration level of renewable generation.The proposed model includes distributionally robust joint chance constraints,which maximize the minimum expectation of the renewable utilization probability among a set of certain probability distributions within an ambiguity set.The proposed formulation yields a twostage robust optimization model with variable bounds of the uncertain sets,which is hard to solve.By applying the affine decision rule,second-order conic reformulation,and duality,we reformulate it into a single-stage standard robust optimization model and solve it efficiently via commercial solvers.Case studies are carried on the Garver 6-bus and IEEE 118-bus systems to illustrate the validity of the proposed method.展开更多
This paper investigates the scheduling strategy of schedulable load in home energy management system(HEMS)under uncertain environment by proposing a distributionally robust optimization(DRO)method based on receding ho...This paper investigates the scheduling strategy of schedulable load in home energy management system(HEMS)under uncertain environment by proposing a distributionally robust optimization(DRO)method based on receding horizon optimization(RHO-DRO).First,the optimization model of HEMS,which contains uncertain variable outdoor temperature and hot water demand,is established and the scheduling problem is developed into a mixed integer linear programming(MILP)by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables.Combined with RHO,the MILP is solved in a rolling fashion using the latest update data related to uncertain variables.The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort.Furthermore,compared with the robust optimization(RO)method,the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users.展开更多
The marine climate conditions are intricate and variable. In scenarios characterized by high proportions of wind and solar energy access, the uncertainty regarding the energy sources for island microgrid is significan...The marine climate conditions are intricate and variable. In scenarios characterized by high proportions of wind and solar energy access, the uncertainty regarding the energy sources for island microgrid is significantly exacerbated, presenting challenges to both the economic viability and reliability of the capacity configuration for island microgrids. To address this issue, this paper proposes a distributionally robust optimization (DRO) method for island microgrids, considering extreme scenarios of wind and solar conditions. Firstly, to address the challenge of determining the probability distribution functions of wind and solar in complex island climates, a conditional generative adversarial network (CGAN) is employed to generate a scenario set for wind and solar conditions. Then, by combining k-means clustering with an extreme scenario selection method, typical scenarios and extreme scenarios are selected from the generated scenario set, forming the scenario set for the DRO model of island microgrids. On this basis, a DRO model based on multiple discrete scenarios is constructed with the objective of minimizing the sum of investment costs, operation and maintenance costs, fuel purchase costs, penalty costs of wind and solar curtailment, and penalty costs of load loss. The model is subjected to equipment operation and power balance constraints, and solved using the columns and constraints generation (CCG) algorithm. Finally, through typical examples, the effectiveness of this paper’s method in balancing the economic viability and robustness of the configuration scheme for the island microgrid, as well as reducing wind and solar curtailment and load loss, is verified.展开更多
Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage t...Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage technology in a low-carbon society.An appropriate self-scheduling model can guarantee AA-CAES’s profit and attract investments.However,very few studies refer to the cogeneration ability of AA-CAES,which enables the possibility to trade in the electricity and heat markets at the same time.In this paper,we propose a multimarket self-scheduling model to make full use of heat produced in compressors.The volatile market price is modeled by a set of inexact distributions based on historical data through-divergence.Then,the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory,and equivalently reformulated as a mixed-integer linear program(MILP).The numerical simulation results validate the proposed method and demonstrate that participating in multienergy markets increases overall profits.The impact of uncertainty parameters is also discussed in the sensibility analysis.展开更多
Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch...Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.展开更多
基金supported by National Key Research and Development Program(2024YFE0115600).
文摘Addressing climate change and facilitating the large-scale integration of renewable energy sources(RESs)have driven the development of hydrogen-coupled integrated energy systems(HIES),which enhance energy sustainability through coordinated electricity,thermal,natural gas,and hydrogen utilization.This study proposes a two-stage distributionally robust optimization(DRO)-based scheduling method to improve the economic efficiency and reduce carbon emissions of HIES.The framework incorporates a ladder-type carbon trading mechanism to regulate emissions and implements a demand response(DR)program to adjustflexible multi-energy loads,thereby prioritizing RES consumption.Uncertainties from RES generation and load demand are addressed through an ambiguity set,enabling robust decision-making.The column-and-constraint generation(C&CG)algorithm efficiently solves the two-stage DRO model.Case studies demonstrate that the proposed method reduces operational costs by 3.56%,increases photovoltaic consumption rates by 5.44%,and significantly lowers carbon emissions compared to conventional approaches.Furthermore,the DRO framework achieves a superior balance between conservativeness and robustness over conventional stochastic and robust optimization methods,highlighting its potential to advance cost-effective,low-carbon energy systems while ensuring grid stability under uncertainty.
基金Supported by the National Natural Science Foundation of China(No.U24B20156)the National Defense Basic Scientific Research Program of China(No.JCKY2021204B051)the National Laboratory of Space Intelligent Control of China(Nos.HTKJ2023KL502005 and HTKJ2024KL502007)。
文摘A chance-constrained energy dispatch model based on the distributed stochastic model predictive control(DSMPC)approach for an islanded multi-microgrid system is proposed.An ambiguity set considering the inherent uncertainties of renewable energy sources(RESs)is constructed without requiring the full distribution knowledge of the uncertainties.The power balance chance constraint is reformulated within the framework of the distributionally robust optimization(DRO)approach.With the exchange of information and energy flow,each microgrid can achieve its local supply-demand balance.Furthermore,the closed-loop stability and recursive feasibility of the proposed algorithm are proved.The comparative results with other DSMPC methods show that a trade-off between robustness and economy can be achieved.
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.
基金supported by the National Natural Science Foundation of China(62373187)Forward-looking Layout Special Projects(ILA220591A22).
文摘To meet the requirements of modern air combat,an integrated fire/flight control(IFFC)system is designed to achieve automatic precision tracking and aiming for armed helicopters and release the pilot from heavy target burden.Considering the complex dynamic characteristics and the couplings of armed helicopters,an improved automatic attack system is con-structed to integrate the fire control system with the flight con-trol system into a unit.To obtain the optimal command signals,the algorithm is investigated to solve nonconvex optimization problems by the contracting Broyden Fletcher Goldfarb Shanno(C-BFGS)algorithm combined with the trust region method.To address the uncertainties in the automatic attack system,the memory nominal distribution and Wasserstein distance are introduced to accurately characterize the uncertainties,and the dual solvable problem is analyzed by using the duality the-ory,conjugate function,and dual norm.Simulation results verify the practicality and validity of the proposed method in solving the IFFC problem on the premise of satisfactory aiming accu-racy.
基金supported by the Technology Project of State Grid Jiangsu Electric Power Co.,Ltd.,China,under Grant J2020090.
文摘Virtual power plants can effectively integrate different types of distributed energy resources,which have become a new operation mode with substantial advantages such as high flexibility,adaptability,and economy.This paper proposes a distributionally robust optimal dispatch approach for virtual power plants to determine an optimal day-ahead dispatch under uncertainties of renewable energy sources.The proposed distributionally robust approach characterizes probability distributions of renewable power output by moments.In this regard,the faults of stochastic optimization and traditional robust optimization can be overcome.Firstly,a second-order cone-based ambiguity set that incorporates the first and second moments of renewable power output is constructed,and a day-ahead two-stage distributionally robust optimization model is proposed for virtual power plants participating in day-ahead electricity markets.Then,an effective solution method based on the affine policy and second-order cone duality theory is employed to reformulate the proposed model into a deterministic mixed-integer second-order cone programming problem,which improves the computational efficiency of the model.Finally,the numerical results demonstrate that the proposed method achieves a better balance between robustness and economy.They also validate that the dispatch strategy of virtual power plants can be adjusted to reduce costs according to the moment information of renewable power output.
基金Project supported by the National Natural Science Foundation of China(Nos.62273245 and 62173033)the Sichuan Science and Technology Program of China(No.2024NSFSC1486)the Opening Project of Robotic Satellite Key Laboratory of Sichuan Province of China。
文摘A distributionally robust model predictive control(DRMPC)scheme is proposed based on neural network(NN)modeling to achieve the trajectory tracking control of robot manipulators with state and control torque constraints.First,an NN is used to fit the motion data of robot manipulators for data-driven dynamic modeling,converting it into a linear prediction model through gradients.Then,by statistically analyzing the stochastic characteristics of the NN modeling errors,a distributionally robust model predictive controller is designed based on the chance constraints,and the optimization problem is transformed into a tractable quadratic programming(QP)problem under the distributionally robust optimization(DRO)framework.The recursive feasibility and convergence of the proposed algorithm are proven.Finally,the effectiveness of the proposed algorithm is verified through numerical simulation.
基金supported by the National Natural Science Foundation of China (Grant No.71702087)the Youth Innovation Science and Technology Support Program of Shandong Province Higher Education (Grant No.2021RW024)the Special Funds for Taishan Scholars,Shandong (Grant No.tsqn202103063).
文摘The cap-and-offset regulation is a practical scheme to lessen carbon emissions.The retailer selling fresh products can adopt sustainable technologies to lessen greenhouse gas emissions.We aim to analyze the optimal joint strategies on order quantity and sustainable technology investment when the retailer faces stochastic market demand and can only acquire the mean and variance of distribution information.We construct a distributionally robust optimization model and use the Karush-Kuhn-Tucker(KKT)conditions to solve the analytic formula of optimal solutions.By comparing the models with and without investing in sustainable technologies,we examine the effect of sustainable technologies on the operational management decisions of the retailer.Finally,some computational examples are applied to analyze the impact of critical factors on operational strategies,and some managerial insights are given based on the analysis results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11571061,11401075,11971092)the Fundamental Research Funds for the Central Universities(Grant No.DUT17RC(4)38)。
文摘In this paper, the option pricing problem is formulated as a distributionally robust optimization problem, which seeks to minimize the worst case replication error for a given distributional uncertainty set(DUS) of the random underlying asset returns. The DUS is defined as a Wasserstein ball centred the empirical distribution of the underlying asset returns. It is proved that the proposed model can be reformulated as a computational tractable linear programming problem. Finally, the results of the empirical tests are presented to show the significance of the proposed approach.
基金supported by the National Natural Science Foundation of China(No.51977046)。
文摘A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lacks interpretability in its results,obscuring the causal relationships between data distribution characteristics and the outcomes.Furthermore,the current approach to battery type selection is not included in traditional BESS planning,hindering comprehensive optimization.To tackle these BESS planning problems,this paper presents a universal method for BESS planning,which is designed to enhance the interpretability of DRO.First,mathematical definitions of interpretable DRO(IDRO)are introduced.Next,the uncertainties in wind power,photovoltaic power,and loads are modeled by using second-order cone ambiguity sets(SOCASs).In addition,the proposed method integrates selection,sizing,and siting.Moreover,a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems.Finally,the effectiveness of the proposed method is demonstrated through case studies,offering planners richer decision-making insights.
基金funded by the National Natural Science Foundation of China(52008014)the Fundamental Research Funds for the Central Universities(JKF-20240037)supported by the“111 Center”and Beihang World TOP University Cooperation Program.
文摘With the adjustment of the energy structure and the rapid development of commercial complex buildings,building energy systems(BES)are playing an increasingly important role.To fully utilize smart building management techniques for coordinating and optimizing energy systems while limiting carbon emissions,this study proposes a smart building energy scheduling method based on distributionally robust optimization(DRO).First,a framework for day-ahead market interaction between the distribution grid(DG),buildings,and electric vehicles(EVs)is established.Based on the the price elasticity matrix principle,demand side management(DSM)technology is used to model the price-based demand response(PBDR)of building electricity load.Meanwhile,the thermal inertia and thermal load flexibility of the building heating system are utilized to leverage the energy storage capabilities of the heating system.Second,a Wasserstein DRO Stackelberg game model is constructed with the objective of maximizing the benefits for both buildings and EVs.This Wasserstein distributionally robust model is then transformed into a mixed-integer model by combining the Karush–Kuhn–Tucker(KKT)conditions and duality theory.Finally,the optimization effect of temperature load storage characteristics on BES flexible scheduling and the coordination of DRO indicators on the optimization results were verified through simulations.The strategy proposed in this article can reduce the total operating cost of BES by 26.37%,significantly enhancing economic efficiency and achieving electricity and heat substitution,resulting in a smoother load curve.This study provides a theoretical foundation and assurance for optimal daily energy scheduling of BES.
基金supported by the National Natural Science Foundation of China,"Research on hierarchical regulation,interaction mechanism and market transaction of regional energy network based on energy cell-tissue architecture",under Grant U1866206.
文摘The integrated electricity-gas system(IEGS)is the foundation of the Energy Internet.As inevitable risk factors,the widespread blackout and large-scale energy supply disruptions represent serious threats to the IEGS.Improving the load restoration ability of IEGS is an important measure to mitigate the harm caused by blackouts.However,the increasing penetration of wind power has posed some difficulties to IEGS load restoration.In view of this,based on distributionally robust optimization(DRO),a two-stage IEGS restoration model is developed in this paper.Through a detailed mathematical model of an electric power system(EPS)with multiple generating resources and a natural gas system(NGS)with dynamic characteristics,the supporting role of the NGS operation flexibility for IEGS restoration is fully explored and quantitatively analyzed.Through the construction of a Wasserstein metric-based ambiguity set of wind power forecast deviation,the proposed two-stage IEGS restoration model can incorporate operational risks when the uncertainty of wind power output is encountered and also take into account the flexible reserve capacity(FRC)allocation and deployment constraints.The proposed model can realize the reasonable scheduling of wind power,automatically determine the allocation of the required FRC,and optimize the load restoration schemes.Moreover,the proposed model can be converted into a mixed integer linear programming problem which can be directly solved.In the case study,the advantages of the proposed model are compared with three conventional restoration models based on two test systems,and sensitivity analysis is conducted.
基金supported in part by the Science and Technology Development Fund,Macao,China(File no.SKL-IOTSC2021-2023(UM)&0076/2019/AMJ&003/2020/AKP)the Science and Technology Department of Sichuan Province(File no.2020YFH0191).
文摘The escalating installation of distributed generation (DG) within active distribution networks (ADNs) diminishes the reliance on fossil fuels, yet it intensifies the disparity between demand and generation across various regions. Moreover, due to the intermittent and stochastic characteristics, DG also introduces uncertain forecasting errors, which further increase difficulties for power dispatch. To overcome these challenges, an emerging flexible interconnection device, soft open point (SOP), is introduced. A distributionally robust chance-constrained optimization (DRCCO) model is also proposed to effectively exploit the benefits of SOPs in ADNs under uncertainties. Compared with conventional robust, stochastic and chance-constrained models, the DRCCO model can better balance reliability and economic profits without the exact distribution of uncertainties. More-over, unlike most published works that employ two individual chance constraints to approximate the upper and lower bound constraints (e.g, bus voltage and branch current limitations), joint two-sided chance constraints are introduced and exactly reformulated into conic forms to avoid redundant conservativeness. Based on numerical experiments, we validate that SOPs' employment can significantly enhance the energy efficiency of ADNs by alleviating DG curtailment and load shedding problems. Simulation results also confirm that the proposed joint two-sided DRCCO method can achieve good balance between economic efficiency and reliability while reducing the conservativeness of conventional DRCCO methods.
基金supported in part by the National Natural Science Foundation of China(51977127)in part by the ShanghaiMunicipal Science and in part by the Technology Commission(19020500800)“Shuguang Program”(20SG52)Shanghai Education Development Foundation and Shanghai Municipal Education Commission.
文摘As an effective carrier of integrated clean energy,the microgrid has attracted wide attention.The randomness of renewable energies such as wind and solar power output brings a significant cost and impact on the economics and reliability of microgrids.This paper proposes an optimization scheme based on the distributionally robust optimization(DRO)model for a microgrid considering solar-wind correlation.Firstly,scenarios of wind and solar power output scenarios are generated based on non-parametric kernel density estimation and the Frank-Copula function;then the generated scenario results are reduced by K-means clustering;finally,the probability confidence interval of scenario distribution is constrained by 1-norm and∞-norm.The model is solved by a column-and-constraint generation algorithm.Experimental studies are conducted on a microgrid system in Jiangsu,China and the obtained scheduling solution turned out to be superior under wind and solar power uncertainties,which verifies the effectiveness of the proposed DRO model.
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.
基金supported by the National Natural Science Foundation of China(No.52077136)。
文摘Transmission network expansion can significantly improve the penetration level of renewable generation.However,existing studies have not explicitly revealed and quantified the trade-off between the investment cost and penetration level of renewable generation.This paper proposes a distributionally robust optimization model to minimize the cost of transmission network expansion under uncertainty and maximize the penetration level of renewable generation.The proposed model includes distributionally robust joint chance constraints,which maximize the minimum expectation of the renewable utilization probability among a set of certain probability distributions within an ambiguity set.The proposed formulation yields a twostage robust optimization model with variable bounds of the uncertain sets,which is hard to solve.By applying the affine decision rule,second-order conic reformulation,and duality,we reformulate it into a single-stage standard robust optimization model and solve it efficiently via commercial solvers.Case studies are carried on the Garver 6-bus and IEEE 118-bus systems to illustrate the validity of the proposed method.
基金supported by the National Key Research and Development Program of China(Grant No.2016YFB0901102).
文摘This paper investigates the scheduling strategy of schedulable load in home energy management system(HEMS)under uncertain environment by proposing a distributionally robust optimization(DRO)method based on receding horizon optimization(RHO-DRO).First,the optimization model of HEMS,which contains uncertain variable outdoor temperature and hot water demand,is established and the scheduling problem is developed into a mixed integer linear programming(MILP)by using the DRO method based on the ambiguity sets of the probability distribution of uncertain variables.Combined with RHO,the MILP is solved in a rolling fashion using the latest update data related to uncertain variables.The simulation results demonstrate that the scheduling results are robust under uncertain environment while satisfying all operating constraints with little violation of user thermal comfort.Furthermore,compared with the robust optimization(RO)method,the RHO-DRO method proposed in this paper has a lower conservation and can save more electricity for users.
基金funded by the National Natural Science Foundation of China(Grant/Award Numbers:52177107 and 52222704)Science and Technology Project of Tianjin Municipality,China(22JCZDJC00780).
文摘The marine climate conditions are intricate and variable. In scenarios characterized by high proportions of wind and solar energy access, the uncertainty regarding the energy sources for island microgrid is significantly exacerbated, presenting challenges to both the economic viability and reliability of the capacity configuration for island microgrids. To address this issue, this paper proposes a distributionally robust optimization (DRO) method for island microgrids, considering extreme scenarios of wind and solar conditions. Firstly, to address the challenge of determining the probability distribution functions of wind and solar in complex island climates, a conditional generative adversarial network (CGAN) is employed to generate a scenario set for wind and solar conditions. Then, by combining k-means clustering with an extreme scenario selection method, typical scenarios and extreme scenarios are selected from the generated scenario set, forming the scenario set for the DRO model of island microgrids. On this basis, a DRO model based on multiple discrete scenarios is constructed with the objective of minimizing the sum of investment costs, operation and maintenance costs, fuel purchase costs, penalty costs of wind and solar curtailment, and penalty costs of load loss. The model is subjected to equipment operation and power balance constraints, and solved using the columns and constraints generation (CCG) algorithm. Finally, through typical examples, the effectiveness of this paper’s method in balancing the economic viability and robustness of the configuration scheme for the island microgrid, as well as reducing wind and solar curtailment and load loss, is verified.
基金supported in part by National Key R&D Program of China(2020YFD1100500)National Natural Science Foundation of China(under Grant 51621065 and 51807101)in part by State Grid Anhui Electric Power Co.,Ltd.Science and Technology Project“Research on grid-connected operation and market mechanism of compressed air energy storage”under Grant 521205180021.
文摘Advanced adiabatic compressed air energy storage(AA-CAES)has the advantages of large capacity,long service time,combined heat and power generation(CHP),and does not consume fossil fuels,making it a promising storage technology in a low-carbon society.An appropriate self-scheduling model can guarantee AA-CAES’s profit and attract investments.However,very few studies refer to the cogeneration ability of AA-CAES,which enables the possibility to trade in the electricity and heat markets at the same time.In this paper,we propose a multimarket self-scheduling model to make full use of heat produced in compressors.The volatile market price is modeled by a set of inexact distributions based on historical data through-divergence.Then,the self-scheduling model is cast as a robust risk constrained program by introducing Stackelberg game theory,and equivalently reformulated as a mixed-integer linear program(MILP).The numerical simulation results validate the proposed method and demonstrate that participating in multienergy markets increases overall profits.The impact of uncertainty parameters is also discussed in the sensibility analysis.
基金supported by the Key Research and Development Project of Guangdong Province(Grant No.2021B0101230004)the National Natural Science Foundation of China(Grant No.51977080).
文摘Multi-terminal voltage source converter-based highvoltage direct current(VSC-MTDC)transmission technology has become an important mode for connecting adjacent offshore wind farms(OWFs)to power systems.Optimal dispatch of an OWF cluster connected by the VSC-MTDC can improve economic operation under the uncertainty of wind speeds.A two-stage distributionally robust optimal dispatch(DROD)model for the OWF cluster connected by VSC-MTDC is established.The first stage in this model optimizes the unit commitment of wind turbines to minimize mechanical loss cost of units under the worst joint probability distribution(JPD)of wind speeds,while the second stage searches for the worst JPD of wind speeds in the ambiguity set(AS)and optimizes active power output of wind turbines to minimize the penalty cost of the generation deviation and active power loss cost of the system.Based on the Kullback–Leibler(KL)divergence distance,a data-driven AS is constructed to describe the uncertainty of wind speed,considering the correlation between wind speeds of adjacent OWFs in the cluster by their joint PD.The original solution of the two-stage DROD model is transformed into the alternating iterative solution of the master problem and the sub-problem by the column-and-constraint generation(C&CG)algorithm,and the master problem is decomposed into a mixedinteger linear programming and a continuous second-order cone programming by the generalized Benders decomposition method to improve calculation efficiency.Finally,case studies on an actual OWF cluster with three OWFs demonstrate the correctness and efficiency of the proposed model and algorithm.
