The continuously increasing renewable energy sources(RES)and demand response(DR)are becoming crucial sources of system flexibility.Consequently,decision-dependent uncertainties(DDUs),inter-changeably referred to as en...The continuously increasing renewable energy sources(RES)and demand response(DR)are becoming crucial sources of system flexibility.Consequently,decision-dependent uncertainties(DDUs),inter-changeably referred to as endogenous uncertainties,impose new characteristics on power system dis-patch.The DDUs faced by system operators originate from uncertain dispatchable resources such as RES units or DR,while reserve providers encounter DDUs from the uncertain reserve deployment.Thus,a systematic framework was established in this study to address robust dispatch problems with DDUs.The main contributions are drawn as follows.①The robust characterization of DDUs was unfolded with a dependency decomposition structure.②A generic DDU coping mechanism was manifested as the bilateral matching between uncertainty and flexibility.③The influence of DDU incorporation on the convexity/non-convexity of robust dispatch problems was analyzed.④Generic solution algorithms adaptive for DDUs were proposed.Under this framework,the inherent distinctions and correlations between DDUs and decision-independent uncertainties(DIUs)were revealed,laying a fundamental theoretical foundation for the economic and reliable operation of RES-dominated power systems.Illustrative applications in the source and demand sides are provided to show the significance of considering DDUs and demonstrate the proposed theoretical results.展开更多
Customary stochastic programming with recourse assumes that the probability distribution of random parameters is independent of decision variables.Recent studies demonstrated that stochastic programming models with en...Customary stochastic programming with recourse assumes that the probability distribution of random parameters is independent of decision variables.Recent studies demonstrated that stochastic programming models with endogenous uncertainty can better reflect many real-world activities and applications accompanying with decision-dependent uncertainty.In this paper,we concentrate on a class of decision-dependent two-stage stochastic programs(DTSPs)and investigate their discrete approximation.To develop the discrete approximation methods for DTSPs,we first derive the quantitative stability results for DTSPs.Based on the stability conclusion,we examine two discretization schemes when the support set of random variables is bounded,and give the rates of convergence for the optimal value and optimal solution set of the discrete approximation problem to those of the original problem.Then we extend the proposed approaches to the general situation with an unbounded support set by using the truncating technique.As an illustration of our discretization schemes,we reformulate the discretization problems under specific structures of the decision-dependent distribution.Finally,an application and numerical results are presented to demonstrate our theoretical results.展开更多
In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the c...In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the current RO framework inapplicable.This paper investigates a class of two-stage RO problems that involve decision-dependent uncertainties.We introduce a class of polyhedral uncertainty sets whose right-hand-side vector has a dependency on the here-and-now decisions and seek to derive the exact optimal wait-and-see decisions for the second-stage problem.A novel iterative algorithm based on the Benders dual decomposition is proposed where advanced optimality cuts and feasibility cuts are designed to incorporate the uncertainty-decision coupling.The computational tractability,robust feasibility and optimality,and convergence performance of the proposed algorithm are guaranteed with theoretical proof.Four motivating application examples that feature the decision-dependent uncertainties are provided.Finally,the proposed solution methodology is verified by conducting case studies on the pre-disaster highway investment problem.展开更多
A virtual battery(VB)provides a succinct interface for aggregating distributed storage-like resources(SLR)to interact with a utility-level system.To overcome the drawbacks of existing VB models,including conservatism ...A virtual battery(VB)provides a succinct interface for aggregating distributed storage-like resources(SLR)to interact with a utility-level system.To overcome the drawbacks of existing VB models,including conservatism and neglecting network constraints,this paper optimizes the power and energy parameters of VB to enlarge its flexibility region.An optimal VB is identified by a robust optimization problem with decision-dependent uncertainty.An algorithm based on the Benders decomposition is developed to solve this problem.The proposed method yields the largest VB satisfying constraints of both network and SLRs.Case studies verify the superiority of the optimal VB in terms of security guarantee and less conservatism.展开更多
基金supported by the Joint Research Fund in Smart Grid(U1966601)under cooperative agreement between the National Natural Science Foundation of China(NSFC)and State Grid Corporation of China.
文摘The continuously increasing renewable energy sources(RES)and demand response(DR)are becoming crucial sources of system flexibility.Consequently,decision-dependent uncertainties(DDUs),inter-changeably referred to as endogenous uncertainties,impose new characteristics on power system dis-patch.The DDUs faced by system operators originate from uncertain dispatchable resources such as RES units or DR,while reserve providers encounter DDUs from the uncertain reserve deployment.Thus,a systematic framework was established in this study to address robust dispatch problems with DDUs.The main contributions are drawn as follows.①The robust characterization of DDUs was unfolded with a dependency decomposition structure.②A generic DDU coping mechanism was manifested as the bilateral matching between uncertainty and flexibility.③The influence of DDU incorporation on the convexity/non-convexity of robust dispatch problems was analyzed.④Generic solution algorithms adaptive for DDUs were proposed.Under this framework,the inherent distinctions and correlations between DDUs and decision-independent uncertainties(DIUs)were revealed,laying a fundamental theoretical foundation for the economic and reliable operation of RES-dominated power systems.Illustrative applications in the source and demand sides are provided to show the significance of considering DDUs and demonstrate the proposed theoretical results.
文摘Customary stochastic programming with recourse assumes that the probability distribution of random parameters is independent of decision variables.Recent studies demonstrated that stochastic programming models with endogenous uncertainty can better reflect many real-world activities and applications accompanying with decision-dependent uncertainty.In this paper,we concentrate on a class of decision-dependent two-stage stochastic programs(DTSPs)and investigate their discrete approximation.To develop the discrete approximation methods for DTSPs,we first derive the quantitative stability results for DTSPs.Based on the stability conclusion,we examine two discretization schemes when the support set of random variables is bounded,and give the rates of convergence for the optimal value and optimal solution set of the discrete approximation problem to those of the original problem.Then we extend the proposed approaches to the general situation with an unbounded support set by using the truncating technique.As an illustration of our discretization schemes,we reformulate the discretization problems under specific structures of the decision-dependent distribution.Finally,an application and numerical results are presented to demonstrate our theoretical results.
基金This work was supported by the Joint Research Fund in Smart Grid under cooperative agreement between the National Natural Science Foundation of China(NSFC)and State Grid Corporation of China(U1966601).
文摘In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the current RO framework inapplicable.This paper investigates a class of two-stage RO problems that involve decision-dependent uncertainties.We introduce a class of polyhedral uncertainty sets whose right-hand-side vector has a dependency on the here-and-now decisions and seek to derive the exact optimal wait-and-see decisions for the second-stage problem.A novel iterative algorithm based on the Benders dual decomposition is proposed where advanced optimality cuts and feasibility cuts are designed to incorporate the uncertainty-decision coupling.The computational tractability,robust feasibility and optimality,and convergence performance of the proposed algorithm are guaranteed with theoretical proof.Four motivating application examples that feature the decision-dependent uncertainties are provided.Finally,the proposed solution methodology is verified by conducting case studies on the pre-disaster highway investment problem.
基金supported by the Science and Technology Institute of China Three Gorges Corporation under Grant 202103386.
文摘A virtual battery(VB)provides a succinct interface for aggregating distributed storage-like resources(SLR)to interact with a utility-level system.To overcome the drawbacks of existing VB models,including conservatism and neglecting network constraints,this paper optimizes the power and energy parameters of VB to enlarge its flexibility region.An optimal VB is identified by a robust optimization problem with decision-dependent uncertainty.An algorithm based on the Benders decomposition is developed to solve this problem.The proposed method yields the largest VB satisfying constraints of both network and SLRs.Case studies verify the superiority of the optimal VB in terms of security guarantee and less conservatism.
