With the widespread application of combined heat and power(CHP)units,the economic dispatch of integrated electric and district heating systems(IEHSs)has drawn increasing attention.Because the electric power system(EPS...With the widespread application of combined heat and power(CHP)units,the economic dispatch of integrated electric and district heating systems(IEHSs)has drawn increasing attention.Because the electric power system(EPS)and district heating system(DHS)are generally managed separately,the decentralized dispatch pattern is preferable for the IEHS dispatch problem.However,many common decentralized methods suffer from the drawbacks of slow and local convergence.Moreover,the uncertainties of renewable generation cannot be ignored in a decentralized pattern.Additionally,the most commonly used individual chance constraints in distributionally robust optimization cannot consider safety constraints simultaneously,so the safe operation of an IEHS cannot be guaranteed.Thus,distributionally robust joint chance constraints and robust constraints are jointly introduced into the IEHS dispatch problem in this paper to obtain a stronger safety guarantee,and a method combined with Bonferroni and conditional value at risk(CVaR)approximation is presented to transform the original model into a quadratic program.Additionally,a dynamic boundary response(DBR)-based distributed algorithm based on multiparametric programming is proposed for a fast solution.Case studies showcase the necessity of using mixed distributionally robust joint chance constraints and robust constraints,as well as the effectiveness of the DBR algorithm.展开更多
Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in un...Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.展开更多
Constraints on each node and line in power systems generally have upper and lower bounds,denoted as twosided constraints.Most existing power system optimization methods with the distributionally robust(DR)chance-const...Constraints on each node and line in power systems generally have upper and lower bounds,denoted as twosided constraints.Most existing power system optimization methods with the distributionally robust(DR)chance-constrained program treat the two-sided DR chance constraint separately,which is an inexact approximation.This letter derives an equivalent reformulation for the generic two-sided DR chance constraint under the interval moment based ambiguity set,which does not require the exact moment information.The derived reformulation is a second-order cone program(SOCP)formulation and is then applied to the optimal power flow(OPF)problem under uncertainty.Numerical results on several IEEE systems demonstrate the effectiveness of the proposed SOCP formulation and show the differences with other DR chance-constrained OPF approaches.展开更多
This paper considers the problem of supply-demand imbalances in Mobility-on-Demand(MoD)services.These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehic...This paper considers the problem of supply-demand imbalances in Mobility-on-Demand(MoD)services.These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high.To achieve this,we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing.More precisely,first travel demand is predicted using Gaussian Process Regression(GPR)which provides uncertainty bounds on the prediction.We then formulate a stochastic model predictive control(MPC)for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds.In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction,we employ a probabilistic constraining method with user-defined confidence interval,using Chance Constrained MPC(CCMPC).The benefits of the proposed method are twofold.First,travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework,allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability.Second,CCMPC can be relaxed into a Mixed-Integer-Linear-Program(MILP)and the MILP can be solved as a corresponding Linear-Program,which always admits an integral solution.Our transportation simulations show that by tuning the confidence bound on the chance constraint,close to optimal oracle performance can be achieved,with a median customer wait time reduction of 4%compared to using only the mean prediction of the GPR.展开更多
In the pharmaceutical industry,model-based prediction is a crucial stage in process development that allows pharmaceutical companies to simulate different scenarios toward improving process efficiency,reducing costs,a...In the pharmaceutical industry,model-based prediction is a crucial stage in process development that allows pharmaceutical companies to simulate different scenarios toward improving process efficiency,reducing costs,and enhancing product quality.Nevertheless,ensuring the quality of formulated pharmaceutical products through the management of raw material variations has always been a challenging task.In this work,data-driven chance-constrained recurrent neural networks(CCRNNs)are developed to address the issue arising from raw material uncertainty.Our goal is to explore how,by proactively incorporating uncertainty into the model training process,more accurate predictions and enhanced robustness can be realized.The proposed approach is tested on a fluid bed dryer(FBD)from a continuous pharmaceutical manufacturing pilot plant.The results demonstrate that CCRNN models offer more robust and accurate predictions for the critical quality attribute(CQA)-in this case,moisture content-when material variations occur,compared with conventional recurrent neural network-based models.展开更多
This paper suggests a way to improve teamwork and reduce uncertainties in operations by using a game theory approach involving multiple virtual power plants(VPP).A generalized credibility-based fuzzy chance constraint...This paper suggests a way to improve teamwork and reduce uncertainties in operations by using a game theory approach involving multiple virtual power plants(VPP).A generalized credibility-based fuzzy chance constraint programming approach is adopted to address uncertainties stemming from renewable generation and load demand within individual VPPs,while robust optimization techniques manage electricity and thermal price volatilities.Building upon this foundation,a hierarchical Nash-Stackelberg game model is established across multiple VPPs.Within each VPP,a Stackelberg game resolves the strategic interaction between the operator and photovoltaic prosumers(PVP).Among VPPs,a cooperative Nash bargaining model coordinates alliance formation.The problem is decomposed into two subproblems:maximizing coalitional benefits,and allocating cooperative surpluses via payment bargaining,solved distributively using the alternating direction method of multipliers(ADMM).Case studies demonstrate that the proposed strategy significantly enhances the economic efficiency and uncertainty resilience of multi-VPP alliances.展开更多
This study proposes a two-stage photovoltaic(PV)voltage control strategy for centralized control that ignores short-term load fluctuations.In the first stage,a deterministic power flow model optimizes the 15-minute ac...This study proposes a two-stage photovoltaic(PV)voltage control strategy for centralized control that ignores short-term load fluctuations.In the first stage,a deterministic power flow model optimizes the 15-minute active cycle of the inverter and reactive outputs to reduce network loss and light rejection.In the second stage,the local control stabilizes the fluctuations and tracks the system state of the first stage.The uncertain interval model establishes a chance constraint model for the inverter voltage-reactive power local control.Second-order cone optimization and sensitivity theories were employed to solve the models.The effectiveness of the model was confirmed using a modified IEEE 33 bus example.The intraday control outcome for distributed power generation considering the effects of fluctuation uncertainty,PV penetration rate,and inverter capacity is analyzed.展开更多
Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans...Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.展开更多
Air traffic flow management has been a major means for balancing air traffic demandand airport or airspace capacity to reduce congestion and flight delays.However,unpredictable fac-tors,such as weather and equipment m...Air traffic flow management has been a major means for balancing air traffic demandand airport or airspace capacity to reduce congestion and flight delays.However,unpredictable fac-tors,such as weather and equipment malfunctions,can cause dynamic changes in airport and sectorcapacity,resulting in significant alterations to optimized flight schedules and the calculated pre-departure slots.Therefore,taking into account capacity uncertainties is essential to create a moreresilient flight schedule.This paper addresses the flight pre-departure sequencing issue and intro-duces a capacity uncertainty model for optimizing flight schedule at the airport network level.The goal of the model is to reduce the total cost of flight delays while increasing the robustnessof the optimized schedule.A chance-constrained model is developed to address the capacity uncer-tainty of airports and sectors,and the significance of airports and sectors in the airport network isconsidered when setting the violation probability.The performance of the model is evaluated usingreal flight data by comparing them with the results of the deterministic model.The development ofthe model based on the characteristics of this special optimization mechanism can significantlyenhance its performance in addressing the pre-departure flight scheduling problem at the airportnetwork level.展开更多
To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described for...To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described formally. To deal with the uncertainty fuzzy parameters brought,a chance constraint was introduced. A mathematical model was established with an objective function of minimizing intra-cell and inter-cell material handling cost. As the chance constraint of this problem could not be converted into its crisp equivalent,a hybrid simulated annealing(HSA) based on fuzzy simulation was put forward. Finally,simulation experiments were conducted under different confidence levels. Results indicated that the proposed hybrid algorithm was feasible and effective.展开更多
The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables(IBRs),which makes it necessary to consider the uncertainty...The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables(IBRs),which makes it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch(ED)programs.However,existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation(e.g.,virtual inertia and droop coefficients)in cooperation with other dispatchable resources to improve the system frequency security and dispatch reliability.This paper proposes a joint chance-constrained economic dispatch model that jointly optimizes the frequency-related inverter control,the system up/down reserves,and base-point power for the minimal total operational cost.In the proposed model,multiple dispatchable resources,including thermal units,dispatchable IBRs,and energy storage,are considered,and the(virtual)inertias,the regulation reserve allocations,and base-point power are coordinated.To ensure the system reliability,the joint chance-constraint formulation is also adopted.Additionally,since the traditional sample average approximation(SAA)method imposes a huge computational burden,a novel mix-SAA(MSAA)method is proposed to transform the original intractable model into a linear model that can be efficiently solved via commercial solvers.The case studies validate the satisfactory efficacy of the proposed ED model and demonstrate that the MSAA can save nearly 90%calculation time compared with the traditional SAA.展开更多
With the growing penetration of renewable energy,the impact of renewable uncertainties on power system secure operation is of increasing concern.Based on a recently developed linear power flow model,we formulate a cha...With the growing penetration of renewable energy,the impact of renewable uncertainties on power system secure operation is of increasing concern.Based on a recently developed linear power flow model,we formulate a chance-constrained optimal power flow(CC-OPF)in transmission networks that provides a concise way to regulate the security regarding both power and voltage behaviors under renewable uncertainties,the latter of which fails to be captured by the conventional DC power flow model.The formulated CC-OPF finds an optimal operating point for the forecasted scenario and the corresponding generation participation scheme for balancing power fluctuations such that the expectation of generation cost is minimized and the probabilities of line overloading and voltage violations are sufficiently low.The problem under the Gaussian distribution of renewable fluctuations is reformulated into a deterministic problem in the form of second-order cone programming,which can be solved efficiently.The proposed approach is also extended to the non-Gaussian uncertainty case by making use of the linear additivity of probability terms in the Gaussian mixture model.The obtained results are verified via numerical experiments on several IEEE test systems.展开更多
The load demand and distributed generation(DG)integration capacity in distribution networks(DNs)increase constantly,and it means that the violation of security constraints may occur in the future.This can be further w...The load demand and distributed generation(DG)integration capacity in distribution networks(DNs)increase constantly,and it means that the violation of security constraints may occur in the future.This can be further worsened by short-term power fluctuations.In this paper,a scheduling method based on a multi-objective chance-constrained information-gap decision(IGD)model is proposed to obtain the active management schemes for distribution system operators(DSOs)to address these problems.The maximum robust adaptability of multiple uncertainties,including the deviations of growth prediction and their relevant power fluctuations,can be obtained based on the limited budget of active management.The systematic solution of the proposed model is developed.The max term constraint in the IGD model is converted into a group of normal constraints corresponding to extreme points of the max term.Considering the stochastic characteristics and correlations of power fluctuations,the original model is equivalently reformulated by using the properties of multivariate Gaussian distribution.The effectiveness of the proposed model is verified by a modified IEEE 33-bus distribution network.The simulation result delineates a robust accommodation space to represent the adaptability of multiple uncertainties,which corresponds to an optional active management strategy set for future selection.展开更多
As battery technology matures,the battery energy storage system(BESS)becomes a promising candidate for addressing renewable energy uncertainties.BESS degradation is one of key factors in BESS operations,which is usual...As battery technology matures,the battery energy storage system(BESS)becomes a promising candidate for addressing renewable energy uncertainties.BESS degradation is one of key factors in BESS operations,which is usually considered in the planning stage.However,BESS degradations are directly affected by the depth of discharge(DoD),which is closely related to the BESS daily schedule.Specifically,the BESS life losses may be different when providing the same amount of energy under a distinct DoD.Therefore,it is necessary to develop a model to consider the effect of daily discharge on BESS degradation.In this paper,a model quantifying the nonlinear impact of DoD on BESS life loss is proposed.By adopting the chance-constrained goal programming,the degradation in day-ahead unit commitment is formulated as a multi-objective optimization problem.To facilitate an efficient solution,the model is converted into a mixed integer linear programming problem.The effectiveness of the proposed method is verified in a modified IEEE 39-bus system.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
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
The uncertainties from renewable energy sources(RESs)will not only introduce significant influences to active power dispatch,but also bring great challenges to the analysis of optimal reactive power dispatch(ORPD).To ...The uncertainties from renewable energy sources(RESs)will not only introduce significant influences to active power dispatch,but also bring great challenges to the analysis of optimal reactive power dispatch(ORPD).To address the influence of high penetration of RES integrated into active distribution networks,a distributionally robust chance constraint(DRCC)-based ORPD model considering discrete reactive power compensators is proposed in this paper.The proposed ORPD model combines a second-order cone programming(SOCP)-based model at the nominal operation mode and a linear power flow(LPF)model to reflect the system response under certainties.Then,a distributionally robust optimization(WDRO)method with Wasserstein distance is utilized to solve the proposed DRCC-based ORPD model.The WDRO method is data-driven due to the reason that the ambiguity set is constructed by the available historical data without any assumption on the specific probability distribution of the uncertainties.And the more data is available,the smaller the ambiguity would be.Numerical results on IEEE 30-bus and 123-bus systems and comparisons with the other three-benchmark approaches demonstrate the accuracy and effectiveness of the proposed model and method.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
Scalable coordination of photovoltaic(PV)inverters,considering the uncertainty in PV and load in distribution networks(DNs),is challenging due to the lack of real-time communications.Decentralized PV inverter setpoint...Scalable coordination of photovoltaic(PV)inverters,considering the uncertainty in PV and load in distribution networks(DNs),is challenging due to the lack of real-time communications.Decentralized PV inverter setpoints can be achieved to address this issue by capitalizing on the abundance of data from smart utility meters and the scalable architecture of artificial neural networks(ANNs).To this end,we first use an offline,centralized data-driven conservative convex approximation of chance-constrained optimal power flow(CVaR-OPF)in which conditional value-at-risk(CVaR)is used to compute reactive power setpoints of PV inverter,taking into account PV and load uncertainties in DNs.Following that,an artificial neural network(ANN)controller is trained for each PV inverter to emulate the optimal behavior of the centralized control setpoints of PV inverter in a decentralized fashion.Additionally,the voltage regulation performance of the developed ANN controllers is compared with other decentralized designs(local controllers)developed using model-based learning(regressionbased controller),optimization(affine feedback controller),and case-based learning(mapping)approaches.Numerical tests using real-world feeders corroborate the effectiveness of ANN controllers in voltage regulation and loss minimization.展开更多
基金supported by National Natural Science Foundation of China(52377107,52007105)and the Taishan Scholars Program.
文摘With the widespread application of combined heat and power(CHP)units,the economic dispatch of integrated electric and district heating systems(IEHSs)has drawn increasing attention.Because the electric power system(EPS)and district heating system(DHS)are generally managed separately,the decentralized dispatch pattern is preferable for the IEHS dispatch problem.However,many common decentralized methods suffer from the drawbacks of slow and local convergence.Moreover,the uncertainties of renewable generation cannot be ignored in a decentralized pattern.Additionally,the most commonly used individual chance constraints in distributionally robust optimization cannot consider safety constraints simultaneously,so the safe operation of an IEHS cannot be guaranteed.Thus,distributionally robust joint chance constraints and robust constraints are jointly introduced into the IEHS dispatch problem in this paper to obtain a stronger safety guarantee,and a method combined with Bonferroni and conditional value at risk(CVaR)approximation is presented to transform the original model into a quadratic program.Additionally,a dynamic boundary response(DBR)-based distributed algorithm based on multiparametric programming is proposed for a fast solution.Case studies showcase the necessity of using mixed distributionally robust joint chance constraints and robust constraints,as well as the effectiveness of the DBR algorithm.
基金supported by the National Natural Science Foundation of China(No.51977042)。
文摘Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.
基金This work was supported by the Natural Science Foundation of Guangdong Province(No.2021A1515012450)。
文摘Constraints on each node and line in power systems generally have upper and lower bounds,denoted as twosided constraints.Most existing power system optimization methods with the distributionally robust(DR)chance-constrained program treat the two-sided DR chance constraint separately,which is an inexact approximation.This letter derives an equivalent reformulation for the generic two-sided DR chance constraint under the interval moment based ambiguity set,which does not require the exact moment information.The derived reformulation is a second-order cone program(SOCP)formulation and is then applied to the optimal power flow(OPF)problem under uncertainty.Numerical results on several IEEE systems demonstrate the effectiveness of the proposed SOCP formulation and show the differences with other DR chance-constrained OPF approaches.
基金co-funded by Vinnova,Sweden through the project:Simulation,analysis and modeling of future efficient traffic systems.
文摘This paper considers the problem of supply-demand imbalances in Mobility-on-Demand(MoD)services.These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high.To achieve this,we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing.More precisely,first travel demand is predicted using Gaussian Process Regression(GPR)which provides uncertainty bounds on the prediction.We then formulate a stochastic model predictive control(MPC)for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds.In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction,we employ a probabilistic constraining method with user-defined confidence interval,using Chance Constrained MPC(CCMPC).The benefits of the proposed method are twofold.First,travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework,allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability.Second,CCMPC can be relaxed into a Mixed-Integer-Linear-Program(MILP)and the MILP can be solved as a corresponding Linear-Program,which always admits an integral solution.Our transportation simulations show that by tuning the confidence bound on the chance constraint,close to optimal oracle performance can be achieved,with a median customer wait time reduction of 4%compared to using only the mean prediction of the GPR.
基金Financial support from the Engineering and Physical Sciences Research Council grant EP/V034723/1(RiFTMaP)is gratefully acknowledged.
文摘In the pharmaceutical industry,model-based prediction is a crucial stage in process development that allows pharmaceutical companies to simulate different scenarios toward improving process efficiency,reducing costs,and enhancing product quality.Nevertheless,ensuring the quality of formulated pharmaceutical products through the management of raw material variations has always been a challenging task.In this work,data-driven chance-constrained recurrent neural networks(CCRNNs)are developed to address the issue arising from raw material uncertainty.Our goal is to explore how,by proactively incorporating uncertainty into the model training process,more accurate predictions and enhanced robustness can be realized.The proposed approach is tested on a fluid bed dryer(FBD)from a continuous pharmaceutical manufacturing pilot plant.The results demonstrate that CCRNN models offer more robust and accurate predictions for the critical quality attribute(CQA)-in this case,moisture content-when material variations occur,compared with conventional recurrent neural network-based models.
基金supported by Science and Technology Project of SGCC(Research on Distributed Cooperative Control of Virtual Power Plants Based on Hybrid Game)(5700-202418337A-2-1-ZX).
文摘This paper suggests a way to improve teamwork and reduce uncertainties in operations by using a game theory approach involving multiple virtual power plants(VPP).A generalized credibility-based fuzzy chance constraint programming approach is adopted to address uncertainties stemming from renewable generation and load demand within individual VPPs,while robust optimization techniques manage electricity and thermal price volatilities.Building upon this foundation,a hierarchical Nash-Stackelberg game model is established across multiple VPPs.Within each VPP,a Stackelberg game resolves the strategic interaction between the operator and photovoltaic prosumers(PVP).Among VPPs,a cooperative Nash bargaining model coordinates alliance formation.The problem is decomposed into two subproblems:maximizing coalitional benefits,and allocating cooperative surpluses via payment bargaining,solved distributively using the alternating direction method of multipliers(ADMM).Case studies demonstrate that the proposed strategy significantly enhances the economic efficiency and uncertainty resilience of multi-VPP alliances.
基金supported by the China National Natural Science Foundation(52177082)China National Key R&D Program(2020YFC0827001)Science and Technology Project of Jilin Electric Power Co.,Ltd(2020JBGS-03).
文摘This study proposes a two-stage photovoltaic(PV)voltage control strategy for centralized control that ignores short-term load fluctuations.In the first stage,a deterministic power flow model optimizes the 15-minute active cycle of the inverter and reactive outputs to reduce network loss and light rejection.In the second stage,the local control stabilizes the fluctuations and tracks the system state of the first stage.The uncertain interval model establishes a chance constraint model for the inverter voltage-reactive power local control.Second-order cone optimization and sensitivity theories were employed to solve the models.The effectiveness of the model was confirmed using a modified IEEE 33 bus example.The intraday control outcome for distributed power generation considering the effects of fluctuation uncertainty,PV penetration rate,and inverter capacity is analyzed.
基金the supports from National Natural Science Foundation of China(61988101,62073142,22178103)National Natural Science Fund for Distinguished Young Scholars(61925305)International(Regional)Cooperation and Exchange Project(61720106008)。
文摘Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.
基金supported by the National Natural Science Foundation of China(Nos.U2033203,U1833126,61773203,61304190)。
文摘Air traffic flow management has been a major means for balancing air traffic demandand airport or airspace capacity to reduce congestion and flight delays.However,unpredictable fac-tors,such as weather and equipment malfunctions,can cause dynamic changes in airport and sectorcapacity,resulting in significant alterations to optimized flight schedules and the calculated pre-departure slots.Therefore,taking into account capacity uncertainties is essential to create a moreresilient flight schedule.This paper addresses the flight pre-departure sequencing issue and intro-duces a capacity uncertainty model for optimizing flight schedule at the airport network level.The goal of the model is to reduce the total cost of flight delays while increasing the robustnessof the optimized schedule.A chance-constrained model is developed to address the capacity uncer-tainty of airports and sectors,and the significance of airports and sectors in the airport network isconsidered when setting the violation probability.The performance of the model is evaluated usingreal flight data by comparing them with the results of the deterministic model.The development ofthe model based on the characteristics of this special optimization mechanism can significantlyenhance its performance in addressing the pre-departure flight scheduling problem at the airportnetwork level.
基金Supported by the National Natural Science Foundation of China(No.61273035,71471135)
文摘To adapt to the complex and changeable market environment,the cell formation problems(CFPs) and the cell layout problems(CLPs) with fuzzy demands were optimized simultaneously. Firstly,CFPs and CLPs were described formally. To deal with the uncertainty fuzzy parameters brought,a chance constraint was introduced. A mathematical model was established with an objective function of minimizing intra-cell and inter-cell material handling cost. As the chance constraint of this problem could not be converted into its crisp equivalent,a hybrid simulated annealing(HSA) based on fuzzy simulation was put forward. Finally,simulation experiments were conducted under different confidence levels. Results indicated that the proposed hybrid algorithm was feasible and effective.
基金supported by the National Natural Science Foundation of China under Grant 52377107.
文摘The issues of uncertainty and frequency security become significantly serious in power systems with the high penetration of volatile inverter-based renewables(IBRs),which makes it necessary to consider the uncertainty and frequency-related constraints in the economic dispatch(ED)programs.However,existing ED studies rarely proactively optimize the control parameters of inverter-based resources related to fast regulation(e.g.,virtual inertia and droop coefficients)in cooperation with other dispatchable resources to improve the system frequency security and dispatch reliability.This paper proposes a joint chance-constrained economic dispatch model that jointly optimizes the frequency-related inverter control,the system up/down reserves,and base-point power for the minimal total operational cost.In the proposed model,multiple dispatchable resources,including thermal units,dispatchable IBRs,and energy storage,are considered,and the(virtual)inertias,the regulation reserve allocations,and base-point power are coordinated.To ensure the system reliability,the joint chance-constraint formulation is also adopted.Additionally,since the traditional sample average approximation(SAA)method imposes a huge computational burden,a novel mix-SAA(MSAA)method is proposed to transform the original intractable model into a linear model that can be efficiently solved via commercial solvers.The case studies validate the satisfactory efficacy of the proposed ED model and demonstrate that the MSAA can save nearly 90%calculation time compared with the traditional SAA.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62403362 and 62088101in part by the Fundamental Research Funds for the Central Universities,in part by the Shanghai Municipal Science and Technology Commission Explorers Program under Grant No.24TS1401600in part by Xiaomi Fundation。
文摘With the growing penetration of renewable energy,the impact of renewable uncertainties on power system secure operation is of increasing concern.Based on a recently developed linear power flow model,we formulate a chance-constrained optimal power flow(CC-OPF)in transmission networks that provides a concise way to regulate the security regarding both power and voltage behaviors under renewable uncertainties,the latter of which fails to be captured by the conventional DC power flow model.The formulated CC-OPF finds an optimal operating point for the forecasted scenario and the corresponding generation participation scheme for balancing power fluctuations such that the expectation of generation cost is minimized and the probabilities of line overloading and voltage violations are sufficiently low.The problem under the Gaussian distribution of renewable fluctuations is reformulated into a deterministic problem in the form of second-order cone programming,which can be solved efficiently.The proposed approach is also extended to the non-Gaussian uncertainty case by making use of the linear additivity of probability terms in the Gaussian mixture model.The obtained results are verified via numerical experiments on several IEEE test systems.
基金supported by the National Natural Science Foundation of China(No.U1866207)。
文摘The load demand and distributed generation(DG)integration capacity in distribution networks(DNs)increase constantly,and it means that the violation of security constraints may occur in the future.This can be further worsened by short-term power fluctuations.In this paper,a scheduling method based on a multi-objective chance-constrained information-gap decision(IGD)model is proposed to obtain the active management schemes for distribution system operators(DSOs)to address these problems.The maximum robust adaptability of multiple uncertainties,including the deviations of growth prediction and their relevant power fluctuations,can be obtained based on the limited budget of active management.The systematic solution of the proposed model is developed.The max term constraint in the IGD model is converted into a group of normal constraints corresponding to extreme points of the max term.Considering the stochastic characteristics and correlations of power fluctuations,the original model is equivalently reformulated by using the properties of multivariate Gaussian distribution.The effectiveness of the proposed model is verified by a modified IEEE 33-bus distribution network.The simulation result delineates a robust accommodation space to represent the adaptability of multiple uncertainties,which corresponds to an optional active management strategy set for future selection.
文摘As battery technology matures,the battery energy storage system(BESS)becomes a promising candidate for addressing renewable energy uncertainties.BESS degradation is one of key factors in BESS operations,which is usually considered in the planning stage.However,BESS degradations are directly affected by the depth of discharge(DoD),which is closely related to the BESS daily schedule.Specifically,the BESS life losses may be different when providing the same amount of energy under a distinct DoD.Therefore,it is necessary to develop a model to consider the effect of daily discharge on BESS degradation.In this paper,a model quantifying the nonlinear impact of DoD on BESS life loss is proposed.By adopting the chance-constrained goal programming,the degradation in day-ahead unit commitment is formulated as a multi-objective optimization problem.To facilitate an efficient solution,the model is converted into a mixed integer linear programming problem.The effectiveness of the proposed method is verified in a modified IEEE 39-bus system.
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 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supported in part by National Key Research and Development Program of China(No.2018YFB0905000)in part by Key Research and Development Program of Shaanxi(No.2017ZDCXL-GY-02-03)。
文摘The uncertainties from renewable energy sources(RESs)will not only introduce significant influences to active power dispatch,but also bring great challenges to the analysis of optimal reactive power dispatch(ORPD).To address the influence of high penetration of RES integrated into active distribution networks,a distributionally robust chance constraint(DRCC)-based ORPD model considering discrete reactive power compensators is proposed in this paper.The proposed ORPD model combines a second-order cone programming(SOCP)-based model at the nominal operation mode and a linear power flow(LPF)model to reflect the system response under certainties.Then,a distributionally robust optimization(WDRO)method with Wasserstein distance is utilized to solve the proposed DRCC-based ORPD model.The WDRO method is data-driven due to the reason that the ambiguity set is constructed by the available historical data without any assumption on the specific probability distribution of the uncertainties.And the more data is available,the smaller the ambiguity would be.Numerical results on IEEE 30-bus and 123-bus systems and comparisons with the other three-benchmark approaches demonstrate the accuracy and effectiveness of the proposed model and method.
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 Science Foundation(No.ECCS-1847125,No.2115427)。
文摘Scalable coordination of photovoltaic(PV)inverters,considering the uncertainty in PV and load in distribution networks(DNs),is challenging due to the lack of real-time communications.Decentralized PV inverter setpoints can be achieved to address this issue by capitalizing on the abundance of data from smart utility meters and the scalable architecture of artificial neural networks(ANNs).To this end,we first use an offline,centralized data-driven conservative convex approximation of chance-constrained optimal power flow(CVaR-OPF)in which conditional value-at-risk(CVaR)is used to compute reactive power setpoints of PV inverter,taking into account PV and load uncertainties in DNs.Following that,an artificial neural network(ANN)controller is trained for each PV inverter to emulate the optimal behavior of the centralized control setpoints of PV inverter in a decentralized fashion.Additionally,the voltage regulation performance of the developed ANN controllers is compared with other decentralized designs(local controllers)developed using model-based learning(regressionbased controller),optimization(affine feedback controller),and case-based learning(mapping)approaches.Numerical tests using real-world feeders corroborate the effectiveness of ANN controllers in voltage regulation and loss minimization.
