This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its gene...This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its generalization error bound is established through the lens of uniform convergence analysis.The CVaR-based MRO can achieve the polynomial decay rate on the excess risk,which extends the generalization analysis associated with the expected risk to the risk-averse case.展开更多
Consider a risk-averse newsvendor who has an option to purchase the units that are short at an emergency purchase price after demand is realized. We use the conditional value-at-risk （CVaR） as the risk measure. The ...Consider a risk-averse newsvendor who has an option to purchase the units that are short at an emergency purchase price after demand is realized. We use the conditional value-at-risk （CVaR） as the risk measure. The aim of the study is to investigate the optimal ordering decision in such a setting under CVaR only and mean-CVaR criterions. For each case, we derive the closed-form optimal solution and perform comparative statics to show the monotonicity properties and other characteristics of the optimal decisions. We also compare our results with those of risk-neutral newsvendor.展开更多
For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,...For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,considering the stochasticity of water availability in the study area,the impact of the risk factor(λ)from a quantitative and qualitative perspective was analyzed.The chance-constrained programming(CCP)and conditional value-at-risk(CVaR)models were introduced into five important major grain production areas in Sanjiang Plain,and the crop planting structure under this condition was optimized.The results showed that,after optimization,overall benefit of cultivation increased from 42.07 billion Yuan to 42.47 billion Yuan,water consumption decreased from 15.90 billion m3 to 11.95 billion m3,the plantation benefit of unit water consumption increased from 2.65 Yuan/m3 to 3.55 Yuan/m3.Furthermore,the index of water consumption,benefit of cultivation and plantation benefit of unit water consumption showed an increasing trend with the increase of violation likelihood.However,through the quantification ofλfrom an economic perspective,the increasing ofλcould not enhance plantation benefit of unit water consumption significantly.展开更多
Due to the lack of support from the main grid,the intermittency of renewable energy sources(RESs)and the fluctuation of load will derive uncertainties to the operation of islanded microgrids(IMGs).It is crucial to all...Due to the lack of support from the main grid,the intermittency of renewable energy sources(RESs)and the fluctuation of load will derive uncertainties to the operation of islanded microgrids(IMGs).It is crucial to allocate appropriate reserve capacity for the economic and reliable operation of IMGs.With the high penetration of RESs,it faces both economic and environmental challenges if we only use spinning reserve for reserve support.To solve these problems,a multi-type reserve scheme for IMGs is proposed according to different operation characteristics of generation,load,and storage.The operation risk due to reserve shortage is modeled by the conditional value-at-risk(CVaR)method.The correlation of input variables is considered for the forecasting error modeling of RES and load,and Latin hypercube sampling(LHS)is adopted to generate the random scenarios of the forecasting error,so as to avoid the dimension disaster caused by conventional large-scale scenario sampling approaches.Furthermore,an optimal day-ahead scheduling model of joint energy and reserve considering riskbased reserve decision is established to coordinate the security and economy of the operation of IMGs.Finally,the comparison of numerical results of different schemes demonstrate the rationality and effectiveness of the proposed scheme and model.展开更多
In the competitive energy market,energy retailers are facing the uncertainties of both energy price and demand,which requires them to formulate reasonable energy purchasing and selling strategies for improving their c...In the competitive energy market,energy retailers are facing the uncertainties of both energy price and demand,which requires them to formulate reasonable energy purchasing and selling strategies for improving their competitiveness in this market.Particularly,the attractive multi-energy retail packages are the key for retailers to increase their benefit.Therefore,combined with incentive means and price signals,five types of multi-energy retail packages such as peak-valley time-of-use(TOU)price package and day-night bundled price package are designed in this paper for retailers.The iterative interactions between retailers and end-users are modeled using a bi-level model of stochastic optimization based on multi-leader multi-follower(MLMF)Stackelberg game,in which retailers are leaders and end-users are followers.Retailers make decisions to maximize the profit considering the conditional value at risk(CVaR)while end-users optimize the satisfaction of both energy comfort and economy.Besides,a distributed algorithm is proposed to obtain the Nash equilibrium of above MLMF Stackelberg game model while the particle swarm optimization(PSO)algorithm and CPLEX solver are applied to solve the optimization model for each participant(retailer or end-user).Numeral results show that the designed retail packages can increase the overall profit of retailers,and the overall satisfaction of industrial users is the highest while that of residential users is the lowest after game interaction.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
基金Supported by Education Science Planning Project of Hubei Province(2020GB198)Natural Science Foundation of Hubei Province(2023AFB523).
文摘This paper analyzes the generalization of minimax regret optimization(MRO)under distribution shift.A new learning framework is proposed by injecting the measure of con-ditional value at risk(CVaR)into MRO,and its generalization error bound is established through the lens of uniform convergence analysis.The CVaR-based MRO can achieve the polynomial decay rate on the excess risk,which extends the generalization analysis associated with the expected risk to the risk-averse case.
基金Supported by the Social Science Foundation of the Ministry of Education of China (07JA630015)
文摘Consider a risk-averse newsvendor who has an option to purchase the units that are short at an emergency purchase price after demand is realized. We use the conditional value-at-risk （CVaR） as the risk measure. The aim of the study is to investigate the optimal ordering decision in such a setting under CVaR only and mean-CVaR criterions. For each case, we derive the closed-form optimal solution and perform comparative statics to show the monotonicity properties and other characteristics of the optimal decisions. We also compare our results with those of risk-neutral newsvendor.
基金National Natural Science Foundation of China(51479032,51579044)Yangtze River Scholars in Universities of Heilongjiang Province and Water Conservancy Science and Technology Project of Heilongjiang Province(201318,201503)The Outstanding Youth Fund of Heilongjiang Province(JC201402).
文摘For optimizing the water-use structure and increasing plantation benefit of unit water consumption,a multi-objective model for water resources utilization was established based on fractional programming(FP).Meanwhile,considering the stochasticity of water availability in the study area,the impact of the risk factor(λ)from a quantitative and qualitative perspective was analyzed.The chance-constrained programming(CCP)and conditional value-at-risk(CVaR)models were introduced into five important major grain production areas in Sanjiang Plain,and the crop planting structure under this condition was optimized.The results showed that,after optimization,overall benefit of cultivation increased from 42.07 billion Yuan to 42.47 billion Yuan,water consumption decreased from 15.90 billion m3 to 11.95 billion m3,the plantation benefit of unit water consumption increased from 2.65 Yuan/m3 to 3.55 Yuan/m3.Furthermore,the index of water consumption,benefit of cultivation and plantation benefit of unit water consumption showed an increasing trend with the increase of violation likelihood.However,through the quantification ofλfrom an economic perspective,the increasing ofλcould not enhance plantation benefit of unit water consumption significantly.
基金This work was supported by the National Natural Science Foundation of China(No.51777077)the Natural Science Foundation of Guangdong Province(No.2017A030313304).
文摘Due to the lack of support from the main grid,the intermittency of renewable energy sources(RESs)and the fluctuation of load will derive uncertainties to the operation of islanded microgrids(IMGs).It is crucial to allocate appropriate reserve capacity for the economic and reliable operation of IMGs.With the high penetration of RESs,it faces both economic and environmental challenges if we only use spinning reserve for reserve support.To solve these problems,a multi-type reserve scheme for IMGs is proposed according to different operation characteristics of generation,load,and storage.The operation risk due to reserve shortage is modeled by the conditional value-at-risk(CVaR)method.The correlation of input variables is considered for the forecasting error modeling of RES and load,and Latin hypercube sampling(LHS)is adopted to generate the random scenarios of the forecasting error,so as to avoid the dimension disaster caused by conventional large-scale scenario sampling approaches.Furthermore,an optimal day-ahead scheduling model of joint energy and reserve considering riskbased reserve decision is established to coordinate the security and economy of the operation of IMGs.Finally,the comparison of numerical results of different schemes demonstrate the rationality and effectiveness of the proposed scheme and model.
基金supported by the National Natural Science Foundation of China(No.52077146)the Sichuan Science and Technology Program(No.2023YFSY0032).
文摘In the competitive energy market,energy retailers are facing the uncertainties of both energy price and demand,which requires them to formulate reasonable energy purchasing and selling strategies for improving their competitiveness in this market.Particularly,the attractive multi-energy retail packages are the key for retailers to increase their benefit.Therefore,combined with incentive means and price signals,five types of multi-energy retail packages such as peak-valley time-of-use(TOU)price package and day-night bundled price package are designed in this paper for retailers.The iterative interactions between retailers and end-users are modeled using a bi-level model of stochastic optimization based on multi-leader multi-follower(MLMF)Stackelberg game,in which retailers are leaders and end-users are followers.Retailers make decisions to maximize the profit considering the conditional value at risk(CVaR)while end-users optimize the satisfaction of both energy comfort and economy.Besides,a distributed algorithm is proposed to obtain the Nash equilibrium of above MLMF Stackelberg game model while the particle swarm optimization(PSO)algorithm and CPLEX solver are applied to solve the optimization model for each participant(retailer or end-user).Numeral results show that the designed retail packages can increase the overall profit of retailers,and the overall satisfaction of industrial users is the highest while that of residential users is the lowest after game interaction.
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.
