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
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
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
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
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
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
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
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
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
In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms und...In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.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
Multi-energy microgrids,such as integrated electricity-heat-gas microgrids(IEHS-MG),have been widely recognized as one of the most convenient ways to connect wind power(WP).However,the inherent intermittency and uncer...Multi-energy microgrids,such as integrated electricity-heat-gas microgrids(IEHS-MG),have been widely recognized as one of the most convenient ways to connect wind power(WP).However,the inherent intermittency and uncertainty of WP still render serious power curtailment in the operation.To this end,this paper presents an IEHS-MG model equipped with power-to-gas technology,thermal storage,electricity storage,and an electrical boiler for improving WP utilization efficiency.Moreover,a two-stage distributionally robust economic dispatch model is constructed for the IEHSMG,with the objective of minimizing total operational costs.The first stage determines the day-ahead decisions including on/off state and set-point decisions.The second stage adjusts the day-ahead decision according to real-time WP realization.Furthermore,WP uncertainty is characterized through an Imprecise Dirichlet model(IDM)based ambiguity set.Finally,Column-and-Constraints Generation method is utilized to solve the model,which provides a day-ahead economic dispatch strategy that immunizes against the worst-case WP distributions.Case studies demonstrate the presented IEHS-MG model outperforms traditional IEHS-MG model in terms of WP utilization and dispatch economics,and that distributionally robust optimization can handle uncertainty effectively.展开更多
Achieving a low or zero carbon target is to reduce energy demand and improve energy efficiency of electricity consumers.One of the main electricity consumers in power systems is heating,ventilation,and air conditionin...Achieving a low or zero carbon target is to reduce energy demand and improve energy efficiency of electricity consumers.One of the main electricity consumers in power systems is heating,ventilation,and air conditioning systems(HVACs),which cost around 30%of the total usage in commercial buildings.This paper investigates the scheduling problem of HVAC energy consumption taking into account two uncertainties:outdoor temperature and human activities.The distributionally robust optimization approach(DROA)is extended to deal with these two uncertainties which are modeled by the proposed disjointed layered ambiguity sets according to historical data.Based on the proposed DROA method,the distributionally robust chance constraints(DRCCs)will be formulated as a nonlinear optimization problem,converted into a linear optimization problem using duality theorem and solved using SeDuMi solver.Simulation results are used to compare with existing methods,which shows the proposed DROA can decrease 2.81%and 0.14%of the electricity cost in comparison with traditional RO method and DROA based on a nest layered ambiguity set,respectively.Also,the proposed DROA decreases the number and maximum of violations from the comfort level of users.The multi-zone HVAC system model is used in the case study to verify the proposed DROA with the disjointed ambiguity set.The consecutive simulation results illustrate the proposed DROA approach can provide stable performance in a three-day scheduling period.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
A power system unit commitment(UC)problem considering uncertainties of renewable energy sources is investigated in this paper,through a distributionally robust optimization approach.We assume that the first and second...A power system unit commitment(UC)problem considering uncertainties of renewable energy sources is investigated in this paper,through a distributionally robust optimization approach.We assume that the first and second order moments of stochastic parameters can be inferred from historical data,and then employed to model the set of probability distributions.The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints,and it can be recast as a mixed-integer semidefinite programming(MI-SDP)with finite constraints.The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation.Based on the verification of strong duality of the semidefinite programming(SDP)problems,we propose a cutting plane algorithm for solving the MI-SDPs;we also introduce an SDP relaxation for the feasibility checking problem,which is an intractable biconvex optimization.Experimental results on the IEEE 6-bus system are presented,showing that without any tuning of parameters,the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general,and our method also enjoys higher reliability of dispatch operation.展开更多
A multi-energy conversion can effectively increase the utilization of renewable energy in the urban integrated energy system(UIES).Meanwhile,the uncertainties of renewable energy resources(e.g.,wind energy)also bring ...A multi-energy conversion can effectively increase the utilization of renewable energy in the urban integrated energy system(UIES).Meanwhile,the uncertainties of renewable energy resources(e.g.,wind energy)also bring increased challenges to the operation of UIES.In this study,a typical two-stage datadriven distributionally robust operation(DDRO)model based on finite scenarios is proposed for UIES including power,gas and heat networks to obtain a salient strategy from both an economic and robustness perspective.In the first stage,the forecasted information for wind power is especially included to improve the economic aspect of robust decisions.The worst probability distribution for the selected known real-time wind power scenarios can be identified in the second stage where the power differences caused by the real-time uncertainties of wind power can be mitigated by flexible regulation of energy purchasing and coupling units(such as gas turbine,power to gas equipment,electric boiler and gas boiler).Moreover,norm-1 and norm-inf co-constraints are utilized to construct a confidence set for the probability distributions of uncertain wind power.The whole two-stage model is solved by the column-and-constraint generation(CCG)algorithm.Finally,case studies are conducted to show the performance of the proposed model and various approaches.Index Terms-Data-driven methods,distributionally robust optimization,urban integrated energy system,wind power.展开更多
Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambigui...Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints.The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution.Based on the concentration inequality of Wasserstein distance,we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity.We show that with probability 1,the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution.Finally,we provide numerical evidences for the established theoretical results.展开更多
The day-ahead management schedules of hybrid energy hubs are intricate and usually exposed to various uncertainties with the penetration of renewable sources and different demands.Furthermore,it is difficult to access...The day-ahead management schedules of hybrid energy hubs are intricate and usually exposed to various uncertainties with the penetration of renewable sources and different demands.Furthermore,it is difficult to access to precise probability distribution functions and exact moment information of uncertain variables.To cope with these issues,an energy management scheme based on the distributionally robust optimization approach is developed for the energy hub.It makes no assumptions of certain probability distributions and can be implemented with limited empirical data and partial information of underlying uncertainties.The operational strategy can provide decision makers with a preliminary and robust optimal solution in the day-ahead market.Numerical results illustrate the economical benefit of the energy model,and the effectiveness of the proposed approach in chance-constrained energy management is demonstrated by comparing with other cases.Index Terms-Chance constraint,distributionally robust optimization,energy hub,energy management.展开更多
In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to...In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to achieve edge intelligence is nontrivial due to the constrained computing resources and limited training data at the network edge.To tackle these challenges,we develop a distributionally robust optimization(DRO)-based edge learning algorithm,where the uncertainty model is constructed to foster the synergy of cloud knowledge and local training.Specifically,the cloud transferred knowledge is in the form of a Dirichlet process prior distribution for the edge model parameters,and the edge device further constructs an uncertainty set centered around the empirical distribution of its local samples.The edge learning DRO problem,subject to these two distributional uncertainty constraints,is recast as a single-layer optimization problem using a duality approach.We then use an Expectation-Maximization algorithm-inspired method to derive a convex relaxation,based on which we devise algorithms to learn the edge model.Furthermore,we illustrate that the meta-learning fast adaptation procedure is equivalent to our proposed Dirichlet process prior-based approach.Finally,extensive experiments are implemented to showcase the performance gain over standard approaches using edge data only.展开更多
Information and communication technologies enable the transformation of traditional energy systems into cyber-physical energy systems(CPESs),but such systems have also become popular targets of cyberattacks.Currently,...Information and communication technologies enable the transformation of traditional energy systems into cyber-physical energy systems(CPESs),but such systems have also become popular targets of cyberattacks.Currently,available methods for evaluating the impacts of cyberattacks suffer from limited resilience,efficacy,and practical value.To mitigate their potentially disastrous consequences,this study suggests a two-stage,discrepancy-based optimization approach that considers both preparatory actions and response measures,integrating concepts from social computing.The proposed Kullback-Leibler divergence-based,distributionally robust optimization(KDR)method has a hierarchical,two-stage objective function that incorporates the operating costs of both system infrastructures(e.g.,energy resources,reserve capacity)and real-time response measures(e.g.,load shedding,demand-side management,electric vehicle charging station management).By incorporating social computing principles,the optimization framework can also capture the social behavior and interactions of energy consumers in response to cyberattacks.The preparatory stage entails day-ahead operational decisions,leveraging insights from social computing to model and predict the behaviors of individuals and communities affected by potential cyberattacks.The mitigation stage generates responses designed to contain the consequences of the attack by directing and optimizing energy use from the demand side,taking into account the social context and preferences of energy consumers,to ensure resilient,economically efficient CPES operations.Our method can determine optimal schemes in both stages,accounting for the social dimensions of the problem.An original disaster mitigation model uses an abstract formulation to develop a risk-neutral model that characterizes cyberattacks through KDR,incorporating social computing techniques to enhance the understanding and response to cyber threats.This approach can mitigate the impacts more effectively than several existing methods,even with limited data availability.To extend this risk-neutral model,we incorporate conditional value at risk as an essential risk measure,capturing the uncertainty and diverse impact scenarios arising from social computing factors.The empirical results affirm that the KDR method,which is enriched with social computing considerations,produces resilient,economically efficient solutions for managing the impacts of cyberattacks on a CPES.By integrating social computing principles into the optimization framework,it becomes possible to better anticipate and address the social and behavioral aspects associated with cyberattacks on CPESs,ultimately improving the overall resilience and effectiveness of the system’s response measures.展开更多
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 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 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 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 (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 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 by National Natural Science Foundation of China(Grant Nos.11991023 and 12371324)National Key R&D Program of China(Grant No.2022YFA1004000)。
文摘In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.
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.
文摘Multi-energy microgrids,such as integrated electricity-heat-gas microgrids(IEHS-MG),have been widely recognized as one of the most convenient ways to connect wind power(WP).However,the inherent intermittency and uncertainty of WP still render serious power curtailment in the operation.To this end,this paper presents an IEHS-MG model equipped with power-to-gas technology,thermal storage,electricity storage,and an electrical boiler for improving WP utilization efficiency.Moreover,a two-stage distributionally robust economic dispatch model is constructed for the IEHSMG,with the objective of minimizing total operational costs.The first stage determines the day-ahead decisions including on/off state and set-point decisions.The second stage adjusts the day-ahead decision according to real-time WP realization.Furthermore,WP uncertainty is characterized through an Imprecise Dirichlet model(IDM)based ambiguity set.Finally,Column-and-Constraints Generation method is utilized to solve the model,which provides a day-ahead economic dispatch strategy that immunizes against the worst-case WP distributions.Case studies demonstrate the presented IEHS-MG model outperforms traditional IEHS-MG model in terms of WP utilization and dispatch economics,and that distributionally robust optimization can handle uncertainty effectively.
文摘Achieving a low or zero carbon target is to reduce energy demand and improve energy efficiency of electricity consumers.One of the main electricity consumers in power systems is heating,ventilation,and air conditioning systems(HVACs),which cost around 30%of the total usage in commercial buildings.This paper investigates the scheduling problem of HVAC energy consumption taking into account two uncertainties:outdoor temperature and human activities.The distributionally robust optimization approach(DROA)is extended to deal with these two uncertainties which are modeled by the proposed disjointed layered ambiguity sets according to historical data.Based on the proposed DROA method,the distributionally robust chance constraints(DRCCs)will be formulated as a nonlinear optimization problem,converted into a linear optimization problem using duality theorem and solved using SeDuMi solver.Simulation results are used to compare with existing methods,which shows the proposed DROA can decrease 2.81%and 0.14%of the electricity cost in comparison with traditional RO method and DROA based on a nest layered ambiguity set,respectively.Also,the proposed DROA decreases the number and maximum of violations from the comfort level of users.The multi-zone HVAC system model is used in the case study to verify the proposed DROA with the disjointed ambiguity set.The consecutive simulation results illustrate the proposed DROA approach can provide stable performance in a three-day scheduling period.
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This work was supported by the National Natural Science Foundation of China(51937005)the National Key Research and Development Program of China(2016YFB0900100).
文摘A power system unit commitment(UC)problem considering uncertainties of renewable energy sources is investigated in this paper,through a distributionally robust optimization approach.We assume that the first and second order moments of stochastic parameters can be inferred from historical data,and then employed to model the set of probability distributions.The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints,and it can be recast as a mixed-integer semidefinite programming(MI-SDP)with finite constraints.The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation.Based on the verification of strong duality of the semidefinite programming(SDP)problems,we propose a cutting plane algorithm for solving the MI-SDPs;we also introduce an SDP relaxation for the feasibility checking problem,which is an intractable biconvex optimization.Experimental results on the IEEE 6-bus system are presented,showing that without any tuning of parameters,the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general,and our method also enjoys higher reliability of dispatch operation.
基金supported by National Key Research and Development Program of China under Grant No.2019YFE0111500Science and Technology Department of Sichuan Province under Grant No.2020YFH0040National Natural Science Foundation of China under Grant No.51807125.
文摘A multi-energy conversion can effectively increase the utilization of renewable energy in the urban integrated energy system(UIES).Meanwhile,the uncertainties of renewable energy resources(e.g.,wind energy)also bring increased challenges to the operation of UIES.In this study,a typical two-stage datadriven distributionally robust operation(DDRO)model based on finite scenarios is proposed for UIES including power,gas and heat networks to obtain a salient strategy from both an economic and robustness perspective.In the first stage,the forecasted information for wind power is especially included to improve the economic aspect of robust decisions.The worst probability distribution for the selected known real-time wind power scenarios can be identified in the second stage where the power differences caused by the real-time uncertainties of wind power can be mitigated by flexible regulation of energy purchasing and coupling units(such as gas turbine,power to gas equipment,electric boiler and gas boiler).Moreover,norm-1 and norm-inf co-constraints are utilized to construct a confidence set for the probability distributions of uncertain wind power.The whole two-stage model is solved by the column-and-constraint generation(CCG)algorithm.Finally,case studies are conducted to show the performance of the proposed model and various approaches.Index Terms-Data-driven methods,distributionally robust optimization,urban integrated energy system,wind power.
基金the National Natural Science Foundation of China(Nos.11991023,11901449,11735011).
文摘Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints.The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution.Based on the concentration inequality of Wasserstein distance,we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity.We show that with probability 1,the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution.Finally,we provide numerical evidences for the established theoretical results.
基金supported in part by the National Key Research and Development Program of China(2016YFB0901900)in part by NSF of China under Grants No.61731012,61922058NSF of Shanghai Municipality of China under Grant No.18ZR1419900.
文摘The day-ahead management schedules of hybrid energy hubs are intricate and usually exposed to various uncertainties with the penetration of renewable sources and different demands.Furthermore,it is difficult to access to precise probability distribution functions and exact moment information of uncertain variables.To cope with these issues,an energy management scheme based on the distributionally robust optimization approach is developed for the energy hub.It makes no assumptions of certain probability distributions and can be implemented with limited empirical data and partial information of underlying uncertainties.The operational strategy can provide decision makers with a preliminary and robust optimal solution in the day-ahead market.Numerical results illustrate the economical benefit of the energy model,and the effectiveness of the proposed approach in chance-constrained energy management is demonstrated by comparing with other cases.Index Terms-Chance constraint,distributionally robust optimization,energy hub,energy management.
基金This work was supported in part by NSF under Grant CPS-1739344,ARO under grant W911NF-16-1-0448the DTRA under Grant HDTRA1-13-1-0029Part of this work will appear in the Proceedings of 40th IEEE International Conference on Distributed Computing Systems(ICDCS),Singapore,July 8-10,2020。
文摘In order to meet the real-time performance requirements,intelligent decisions in Internet of things applications must take place right here right now at the network edge.Pushing the artificial intelligence frontier to achieve edge intelligence is nontrivial due to the constrained computing resources and limited training data at the network edge.To tackle these challenges,we develop a distributionally robust optimization(DRO)-based edge learning algorithm,where the uncertainty model is constructed to foster the synergy of cloud knowledge and local training.Specifically,the cloud transferred knowledge is in the form of a Dirichlet process prior distribution for the edge model parameters,and the edge device further constructs an uncertainty set centered around the empirical distribution of its local samples.The edge learning DRO problem,subject to these two distributional uncertainty constraints,is recast as a single-layer optimization problem using a duality approach.We then use an Expectation-Maximization algorithm-inspired method to derive a convex relaxation,based on which we devise algorithms to learn the edge model.Furthermore,we illustrate that the meta-learning fast adaptation procedure is equivalent to our proposed Dirichlet process prior-based approach.Finally,extensive experiments are implemented to showcase the performance gain over standard approaches using edge data only.
基金supported in part by the New Generation Artificial Intelligence Development Plan of China(2015–2030)(Grants No.2021ZD0111205)the National Natural Science Foundation of China(Grants No.72025404,No.71621002,No.71974187)+1 种基金Beijing Natural Science Foundation(L192012)Beijing Nova Program(Z201100006820085).
文摘Information and communication technologies enable the transformation of traditional energy systems into cyber-physical energy systems(CPESs),but such systems have also become popular targets of cyberattacks.Currently,available methods for evaluating the impacts of cyberattacks suffer from limited resilience,efficacy,and practical value.To mitigate their potentially disastrous consequences,this study suggests a two-stage,discrepancy-based optimization approach that considers both preparatory actions and response measures,integrating concepts from social computing.The proposed Kullback-Leibler divergence-based,distributionally robust optimization(KDR)method has a hierarchical,two-stage objective function that incorporates the operating costs of both system infrastructures(e.g.,energy resources,reserve capacity)and real-time response measures(e.g.,load shedding,demand-side management,electric vehicle charging station management).By incorporating social computing principles,the optimization framework can also capture the social behavior and interactions of energy consumers in response to cyberattacks.The preparatory stage entails day-ahead operational decisions,leveraging insights from social computing to model and predict the behaviors of individuals and communities affected by potential cyberattacks.The mitigation stage generates responses designed to contain the consequences of the attack by directing and optimizing energy use from the demand side,taking into account the social context and preferences of energy consumers,to ensure resilient,economically efficient CPES operations.Our method can determine optimal schemes in both stages,accounting for the social dimensions of the problem.An original disaster mitigation model uses an abstract formulation to develop a risk-neutral model that characterizes cyberattacks through KDR,incorporating social computing techniques to enhance the understanding and response to cyber threats.This approach can mitigate the impacts more effectively than several existing methods,even with limited data availability.To extend this risk-neutral model,we incorporate conditional value at risk as an essential risk measure,capturing the uncertainty and diverse impact scenarios arising from social computing factors.The empirical results affirm that the KDR method,which is enriched with social computing considerations,produces resilient,economically efficient solutions for managing the impacts of cyberattacks on a CPES.By integrating social computing principles into the optimization framework,it becomes possible to better anticipate and address the social and behavioral aspects associated with cyberattacks on CPESs,ultimately improving the overall resilience and effectiveness of the system’s response measures.
