This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sam...This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sample size for any random variable. Such approach mainly consists of sample allocation, evaluation, proliferation and mutation. The former two, depending on a lower bound estimate acquired, not only decide the sample size of random variable and the importance level of each evolving B cell, but also ensure that such B cell is evaluated with low computational cost; the third makes diverse B cells participate in evolution and suppresses the influence of noise; the last, which associates with the information on population diversity and fitness inheritance, creates diverse and high-affinity B cells. Under such approach, three similar immune algorithms are derived after selecting different mutation rules. The experiments, by comparison against two valuable genetic algorithms, have illustrated that these immune algorithms are competitive optimizers capable of effectively executing noisy compensation and searching for the desired optimal reliable solution.展开更多
Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-m...Energy harvesting has been recognized as a promising technique with which to effectively reduce carbon emis-sions and electricity expenses of base stations.However,renewable energy is inherently stochastic and inter-mittent,imposing formidable challenges on reliably satisfying users'time-varying wireless traffic demands.In addition,the probability distribution of the renewable energy or users’wireless traffic demand is not always fully known in practice.In this paper,we minimize the total energy cost of a hybrid-energy-powered cellular network by jointly optimizing the energy sharing among base stations,the battery charging and discharging rates,and the energy purchased from the grid under the constraint of a limited battery size at each base station.In solving the formulated non-convex chance-constrained stochastic optimization problem,a new ambiguity set is built to characterize the uncertainties in the renewable energy and wireless traffic demands according to interval sets of the mean and covariance.Using this ambiguity set,the original optimization problem is transformed into a more tractable second-order cone programming problem by exploiting the distributionally robust optimization approach.Furthermore,a low-complexity distributionally robust chance-constrained energy management algo-rithm,which requires only interval sets of the mean and covariance of stochastic parameters,is proposed.The results of extensive simulation are presented to demonstrate that the proposed algorithm outperforms existing methods in terms of the computational complexity,energy cost,and reliability.展开更多
Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe ...Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.展开更多
Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morph...Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morphology information, Existing geological surface models suffer from high levels of uncertainty, which exposes oil and gas exploration and development to additional risk. In this paper, we achieve a reconstruction of the uncertainties associated with a geological surface using chance-constrained programming based on multisource data. We also quantifi ed the uncertainty of the modeling data and added a disturbance term to the objective function. Finally, we verifi ed the applicability of the method using both synthetic and real fault data. We found that the reconstructed geological models met geological rules and reduced the reconstruction uncertainty.展开更多
A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncert...A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.展开更多
energy management model is constructed including chance constraints of spinning reserves for the sake of guaranteeing the maximum utilization of wind power on the basis of reliability.With the available wind power cha...energy management model is constructed including chance constraints of spinning reserves for the sake of guaranteeing the maximum utilization of wind power on the basis of reliability.With the available wind power characterized by Weibull distribution,the chance constraints can be converted into deterministic ones by the derived analytical form of inverse cumulative distribution function.Although the original problem is transformed into a typical convex optimization problem,the tight coupling of constraints presents challenges to the design of distributed strategy.Therefore,we formulate the problem into a compact form with each generator unit depending on individual decision variables,instead of the common form with a decision vector being the collection of all local decision variables.Then,by developing a new initialization method and an adaptive weight matrix selection method,a distributed strategy based on tracking Alternating Direction Method of Multipliers(ADMM)is proposed to solve the model.The simulation results indicate that the proposed distributed strategy achieves comparable performance to the corresponding centralized scenario,and better performance than distributed consensus-based ADMM in the related literature.Moreover,the validity of the proposed distributed strategy is confirmed in day-ahead chance-constrained energy management with stochastic wind power.展开更多
The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging.While joint chance-constrained methods are equipped to model the...The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging.While joint chance-constrained methods are equipped to model these complexities and uncertainties,solving these problems using traditional iterative solvers is often time-consuming,limiting their suitability for real-time applications.To overcome the shortcomings of today’s solvers,we propose a fast,scalable,and explainable machine learning-based optimization proxy.Our solution,called Learning to Optimize the Optimization of Joint Chance-Constrained Problems(LOOP−JCCP),is iteration-free and solves the underlying problem in a single-shot.Our model uses a polyhedral reformulation of the original problem to manage constraint violations and ensure solution feasibility across various scenarios through customizable probability settings.To this end,we build on our recent deterministic solution(LOOP−LC2.0)by incorporating a set aggregator module to handle uncertain sample sets of varying sizes and complexities.Our results verify the feasibility of our near-optimal solutions for joint chance-constrained power dispatch scenarios.Additionally,our feasibility guarantees increase the transparency and interpretability of our method,which is essential for operators to trust the outcomes.We showcase the effectiveness of our model in solving the stochastic energy management problem of Virtual Power Plants(VPPs).Our theoretical analysis,supported by empirical evidence,reveals strong flexibility in parameter tuning,adaptability to diverse datasets,and significantly improved computational speed.展开更多
The escalating installation of distributed generation (DG) within active distribution networks (ADNs) diminishes the reliance on fossil fuels, yet it intensifies the disparity between demand and generation across vari...The escalating installation of distributed generation (DG) within active distribution networks (ADNs) diminishes the reliance on fossil fuels, yet it intensifies the disparity between demand and generation across various regions. Moreover, due to the intermittent and stochastic characteristics, DG also introduces uncertain forecasting errors, which further increase difficulties for power dispatch. To overcome these challenges, an emerging flexible interconnection device, soft open point (SOP), is introduced. A distributionally robust chance-constrained optimization (DRCCO) model is also proposed to effectively exploit the benefits of SOPs in ADNs under uncertainties. Compared with conventional robust, stochastic and chance-constrained models, the DRCCO model can better balance reliability and economic profits without the exact distribution of uncertainties. More-over, unlike most published works that employ two individual chance constraints to approximate the upper and lower bound constraints (e.g, bus voltage and branch current limitations), joint two-sided chance constraints are introduced and exactly reformulated into conic forms to avoid redundant conservativeness. Based on numerical experiments, we validate that SOPs' employment can significantly enhance the energy efficiency of ADNs by alleviating DG curtailment and load shedding problems. Simulation results also confirm that the proposed joint two-sided DRCCO method can achieve good balance between economic efficiency and reliability while reducing the conservativeness of conventional DRCCO methods.展开更多
Moving away from fossil fuels towards renewable sources requires system operators to determine the capacity of distribution systems to safely accommodate green and distributed generation(DG).However,the DG capacity of...Moving away from fossil fuels towards renewable sources requires system operators to determine the capacity of distribution systems to safely accommodate green and distributed generation(DG).However,the DG capacity of a distribution system is often underestimated due to either overly conservative electrical demand and DG output uncertainty modelling or neglecting the recourse capability of the available components.To improve the accuracy of DG capacity assessment,this paper proposes a distributionally adjustable robust chance-constrained approach that utilises uncertainty information to reduce the conservativeness of conventional robust approaches.The proposed approach also enables fast-acting devices such as inverters to adjust to the real-time realisation of uncertainty using the adjustable robust counterpart methodology.To achieve a tractable formulation,we first define uncertain chance constraints through distributionally robust conditional value-at-risk(CVaR),which is then reformulated into convex quadratic constraints.We subsequently solve the resulting large-scale,yet convex,model in a distributed fashion using the alternating direction method of multipliers(ADMM).Through numerical simulations,we demonstrate that the proposed approach outperforms the adjustable robust and conventional distributionally robust approaches by up to 15%and 40%,respectively,in terms of total installed DG capacity.展开更多
This paper proposes an adjustable and distributionally robust chance-constrained(ADRCC) optimal power flow(OPF) model for economic dispatch considering wind power forecasting uncertainty. The proposed ADRCC-OPF model ...This paper proposes an adjustable and distributionally robust chance-constrained(ADRCC) optimal power flow(OPF) model for economic dispatch considering wind power forecasting uncertainty. The proposed ADRCC-OPF model is distributionally robust because the uncertainties of the wind power forecasting are represented only by their first-and second-order moments instead of a specific distribution assumption. The proposed model is adjustable because it is formulated as a second-order cone programming(SOCP) model with an adjustable coefficient.This coefficient can control the robustness of the chance constraints, which may be set up for the Gaussian distribution, symmetrically distributional robustness, or distributionally robust cases considering wind forecasting uncertainty. The conservativeness of the ADRCC-OPF model is analyzed and compared with the actual distribution data of wind forecasting error. The system operators can choose an appropriate adjustable coefficient to tradeoff between the economics and system security.展开更多
A novel stochastic optimal dispatch model is proposed considering medium and long-term electricity transactions for a wind power integrated energy system using chance constrained programming.The electricity contract d...A novel stochastic optimal dispatch model is proposed considering medium and long-term electricity transactions for a wind power integrated energy system using chance constrained programming.The electricity contract decomposition problem is introduced into the day-ahead optimal dispatch plan formulation progress.Considering the case that decomposition results may be not executable in the dispatch plan,a coordinated optimization strategy based on the Lagrange multiplier is proposed to eliminate the non-executable electric quantity.At the same time,the uncertainties and correlation of wind power are considered in the dispatch model,and the original stochastic dispatch problem is transformed into a mixed integer second-order cone programming problem using second-order cone relaxation and sample average approximation approach.Case study results demonstrate the validity of the proposed method.展开更多
With increasing penetration of wind energy,the variability and uncertainty of wind resources have become important factors for power systems operation.In particular,an effective method is required for identifying the ...With increasing penetration of wind energy,the variability and uncertainty of wind resources have become important factors for power systems operation.In particular,an effective method is required for identifying the stochastic range of wind power output,in order to better guide the operational security of power systems.This paper proposes a metric to determine accurate wind power output ranges so that the probability of actual wind power outputs being out of the range would be less than a small pre-defined value.A mixed-integer linear programming(MILP)based chance-constrained optimization model is proposed for efficiently determining optimal wind power output ranges,which are quantified via maximum and the minimum wind generation levels with respect to a certain time interval.The derived wind power range is then used to construct dynamic uncertainty intervals for the robust securityconstrained unit commitment(SCUC)model.A comparison with the deterministic SCUC model and the traditional robust SCUC model with presumed static uncertainty interval demonstrates that the proposed approach can offer more accurate wind power variabilities(i.e.,different variability degrees with respect to different wind power output levels at different time periods).The proposed approach is also shown to offer more effective and robust SCUC solutions,guaranteeing operational security and economics of power systems.Numerical case studies on a 6-bus system and the modified IEEE 118-bus system with realworld wind power data illustrate the effectiveness of the proposed approach.展开更多
Controlled islanding plays an essential role in preventing the blackout of power systems.Although there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable...Controlled islanding plays an essential role in preventing the blackout of power systems.Although there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable energy sources(RESs)that may cause unpredictable unbalanced power and the observabilit>T of power systems after islanding that is essential for back-up black-start measures.Therefore,a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming(MISOCCP)is proposed to address these issues.First,the uncertainty of RESs is characterized by their possibility distribution models with chance constraints,and the requirements,e.g.,system observability,for rapid back-up black-start measures are also considered.Then,a law of large numbers(LLN)based method is em-ployed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex one.Finally,case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed model.The results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.展开更多
Urban electricity and heat networks(UEHN)consist of the coupling and interactions between electric power systems and district heating systems,in which the geographical and functional features of integrated energy syst...Urban electricity and heat networks(UEHN)consist of the coupling and interactions between electric power systems and district heating systems,in which the geographical and functional features of integrated energy systems are demonstrated.UEHN have been expected to provide an effective way to accommodate the intermittent and unpredictable renewable energy sources,in which the application of stochastic optimization approaches to UEHN analysis is highly desired.In this paper,we propose a chance-constrained coordinated optimization approach for UEHN considering the uncertainties in electricity loads,heat loads,and photovoltaic outputs,as well as the correlations between these uncertain sources.A solution strategy,which combines the Latin Hypercube Sampling Monte Carlo Simulation(LHSMCS)approach and a heuristic algorithm,is specifically designed to deal with the proposed chance-constrained coordinated optimization.Finally,test results on an UEHN comprised of a modified IEEE 33-bus system and a 32-node district heating system at Barry Island have verified the feasibility and effectiveness of the proposed framework.展开更多
To enhance the flexible interactions among multiple energy carriers,i.e.,electricity,thermal power and gas,a coordinated programming method for multi-energy microgrid(MEMG)system is proposed.Various energy requirement...To enhance the flexible interactions among multiple energy carriers,i.e.,electricity,thermal power and gas,a coordinated programming method for multi-energy microgrid(MEMG)system is proposed.Various energy requirements for both residential and parking loads are managed simultaneously,i.e.,electric and thermal loads for residence,and charging power and gas filling requirements for parking vehicles.The proposed model is formulated as a two-stage joint chance-constrained programming,where the first stage is a day-ahead operation problem that provides the hourly generation,conversion,and storage towards the minimization of operation cost considering the forecasting error of photovoltaic output and load demand.Meanwhile,the second stage is an on-line scheduling which adjusts the energy scheme in hourly time-scale considering the uncertainty.Simulations have demonstrated the validity of the proposed method,i.e.,collecting the flexibilities of thermal system,gas system,and parking vehicles to facilitate the operation of electrical networks.Sensitivity analysis shows that the proposed scheme can achieve a compromise between the operation efficiency and service quality.展开更多
Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form express...Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them.We then design a Monte Carlo algorithm,based on these estimators,to solve chance-constrained programs.Our numerical study shows that the algorithm works well,especially only with the gradient estimators.展开更多
To address uncertainty as well as transient stability constraints simultaneously in the preventive control of windfarm systems, a novel three-stage optimization strategy is established in this paper. In the first stag...To address uncertainty as well as transient stability constraints simultaneously in the preventive control of windfarm systems, a novel three-stage optimization strategy is established in this paper. In the first stage, the probabilisticmulti-objective particle swarm optimization based on the point estimate method is employed to cope with thestochastic factors. The transient security region of the system is accurately ensured by the interior point methodin the second stage. Finally, the verification of the final optimal objectives and satisfied constraints are enforcedin the last stage. Furthermore, the proposed strategy is a general framework that can combine other optimizationalgorithms. The proposed methodology is tested on the modified WSCC 9-bus system and the New England 39-bussystem. The results verify the feasibility of the method.展开更多
This paper discussed an extended model for flexibility analysis of chemical process. Under uncertainty, probability density function is used to describe uncertain parameters instead of hyper-rectangle, and chanceconst...This paper discussed an extended model for flexibility analysis of chemical process. Under uncertainty, probability density function is used to describe uncertain parameters instead of hyper-rectangle, and chanceconstrained programming is a feasible way to deal with the violation of constraints. Because the feasible region of control variables would change along with uncertain parameters, its smallest acceptable size threshold is presented to ensure the controllability condition. By synthesizing the considerations mentioned above, a modified model can describe the flexibility analysis problem more exactly. Then a hybrid algorithm, which integrates stochastic simulation and genetic algorithm, is applied to solve this model and maximize the flexibility region. Both numerical and chemical process examples are presented to demonstrate the effectiveness of the method.展开更多
To study the uncertain optimization problems on implementation schedule, time-cost trade-off and quality in enterprise resource planning （ERP） implementation, combined with program evaluation and review technique （...To study the uncertain optimization problems on implementation schedule, time-cost trade-off and quality in enterprise resource planning （ERP） implementation, combined with program evaluation and review technique （PERT）, some optimization models are proposed, which include the implementation schedule model, the timecost trade-off model, the quality model, and the implementation time-cost-quality synthetic optimization model. A PERT-embedded genetic algorithm （GA） based on stochastic simulation technique is introduced to the optimization models solution. Finally, an example is presented to show that the models and algorithm are reasonable and effective, which can offer a reliable quantitative decision method for ERP implementation.展开更多
This study employs a chance-constrained data envelopment analysis (CDEA) approach with two models (model A and model B) to decompose provincial productivity growth in Vietnamese agriculture from 1995 to 2007 into tech...This study employs a chance-constrained data envelopment analysis (CDEA) approach with two models (model A and model B) to decompose provincial productivity growth in Vietnamese agriculture from 1995 to 2007 into technological progress and efficiency change. The differences between the chance - constrained programming model A and model B are assumptions imposed on the covariance matrix. The decomposition allows us to identify the contributions of technical change and the improvement in technical efficiency to productivity growth in Vietnamese production. Sixty-one provinces in Vietnam are classified into Mekong - technology and other -technology categories. We conduct a Mann-Whitney test to verify whether the two samples, the Mekong technology province sample and the other technology sample, are drawn from the same productivity change populations. The result of the Mann-Whitney test indicates that the differences between the Mekong technology category and the other technology category from two models are more significant. Two important questions are whether some provinces in the samples could maintain their relative efficiency rank positions in comparison with the others over the study period and how to further examine the agreements between the two models. The Kruskal - Wallis test statistic shows that technical efficiency from both models for some provinces are higher than those of them in the study period. The Malmquist results show that production frontier has contracted by around 1.3 percent and 0.31 percent from chance-constrained model A and model B, respectively, a year on average over the sample period. To examine the agreements or disagreements in the total factor productivity indexes we compute the correlation between Malmquist indexes, which is positive and not very high. Thus there is a little discrepancy between the two Malmquist indexes, estimated from the chance - constrained models A and B.展开更多
基金supported in part by National Natural Science Foundation of China(Nos.61563009 and 61065010)Doctoral Fund of Ministry of Education of China(No.20125201110003)
文摘This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sample size for any random variable. Such approach mainly consists of sample allocation, evaluation, proliferation and mutation. The former two, depending on a lower bound estimate acquired, not only decide the sample size of random variable and the importance level of each evolving B cell, but also ensure that such B cell is evaluated with low computational cost; the third makes diverse B cells participate in evolution and suppresses the influence of noise; the last, which associates with the information on population diversity and fitness inheritance, creates diverse and high-affinity B cells. Under such approach, three similar immune algorithms are derived after selecting different mutation rules. The experiments, by comparison against two valuable genetic algorithms, have illustrated that these immune algorithms are competitive optimizers capable of effectively executing noisy compensation and searching for the desired optimal reliable solution.
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.
文摘Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.
基金by National Science and Technology Major Project(Grant No.2017ZX05018004004)the National Natural Science Foundation of China (No.U1562218 & 41604107).
文摘Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morphology information, Existing geological surface models suffer from high levels of uncertainty, which exposes oil and gas exploration and development to additional risk. In this paper, we achieve a reconstruction of the uncertainties associated with a geological surface using chance-constrained programming based on multisource data. We also quantifi ed the uncertainty of the modeling data and added a disturbance term to the objective function. Finally, we verifi ed the applicability of the method using both synthetic and real fault data. We found that the reconstructed geological models met geological rules and reduced the reconstruction uncertainty.
文摘A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.
基金supported by the National Natural Science Foundation of China under Grant No.62033007,61873146 and 61821004.
文摘energy management model is constructed including chance constraints of spinning reserves for the sake of guaranteeing the maximum utilization of wind power on the basis of reliability.With the available wind power characterized by Weibull distribution,the chance constraints can be converted into deterministic ones by the derived analytical form of inverse cumulative distribution function.Although the original problem is transformed into a typical convex optimization problem,the tight coupling of constraints presents challenges to the design of distributed strategy.Therefore,we formulate the problem into a compact form with each generator unit depending on individual decision variables,instead of the common form with a decision vector being the collection of all local decision variables.Then,by developing a new initialization method and an adaptive weight matrix selection method,a distributed strategy based on tracking Alternating Direction Method of Multipliers(ADMM)is proposed to solve the model.The simulation results indicate that the proposed distributed strategy achieves comparable performance to the corresponding centralized scenario,and better performance than distributed consensus-based ADMM in the related literature.Moreover,the validity of the proposed distributed strategy is confirmed in day-ahead chance-constrained energy management with stochastic wind power.
基金supported by National Science Foundation(NSF),Grant No.#2313768:“Collaborative Research:Learning-Assisted Estimation and Management of Flexible Energy Resources in Active Distribution Networks”,U.S.
文摘The ever-increasing integration of stochastic renewable energy sources into power systems operation is making the supply-demand balance more challenging.While joint chance-constrained methods are equipped to model these complexities and uncertainties,solving these problems using traditional iterative solvers is often time-consuming,limiting their suitability for real-time applications.To overcome the shortcomings of today’s solvers,we propose a fast,scalable,and explainable machine learning-based optimization proxy.Our solution,called Learning to Optimize the Optimization of Joint Chance-Constrained Problems(LOOP−JCCP),is iteration-free and solves the underlying problem in a single-shot.Our model uses a polyhedral reformulation of the original problem to manage constraint violations and ensure solution feasibility across various scenarios through customizable probability settings.To this end,we build on our recent deterministic solution(LOOP−LC2.0)by incorporating a set aggregator module to handle uncertain sample sets of varying sizes and complexities.Our results verify the feasibility of our near-optimal solutions for joint chance-constrained power dispatch scenarios.Additionally,our feasibility guarantees increase the transparency and interpretability of our method,which is essential for operators to trust the outcomes.We showcase the effectiveness of our model in solving the stochastic energy management problem of Virtual Power Plants(VPPs).Our theoretical analysis,supported by empirical evidence,reveals strong flexibility in parameter tuning,adaptability to diverse datasets,and significantly improved computational speed.
基金supported in part by the Science and Technology Development Fund,Macao,China(File no.SKL-IOTSC2021-2023(UM)&0076/2019/AMJ&003/2020/AKP)the Science and Technology Department of Sichuan Province(File no.2020YFH0191).
文摘The escalating installation of distributed generation (DG) within active distribution networks (ADNs) diminishes the reliance on fossil fuels, yet it intensifies the disparity between demand and generation across various regions. Moreover, due to the intermittent and stochastic characteristics, DG also introduces uncertain forecasting errors, which further increase difficulties for power dispatch. To overcome these challenges, an emerging flexible interconnection device, soft open point (SOP), is introduced. A distributionally robust chance-constrained optimization (DRCCO) model is also proposed to effectively exploit the benefits of SOPs in ADNs under uncertainties. Compared with conventional robust, stochastic and chance-constrained models, the DRCCO model can better balance reliability and economic profits without the exact distribution of uncertainties. More-over, unlike most published works that employ two individual chance constraints to approximate the upper and lower bound constraints (e.g, bus voltage and branch current limitations), joint two-sided chance constraints are introduced and exactly reformulated into conic forms to avoid redundant conservativeness. Based on numerical experiments, we validate that SOPs' employment can significantly enhance the energy efficiency of ADNs by alleviating DG curtailment and load shedding problems. Simulation results also confirm that the proposed joint two-sided DRCCO method can achieve good balance between economic efficiency and reliability while reducing the conservativeness of conventional DRCCO methods.
文摘Moving away from fossil fuels towards renewable sources requires system operators to determine the capacity of distribution systems to safely accommodate green and distributed generation(DG).However,the DG capacity of a distribution system is often underestimated due to either overly conservative electrical demand and DG output uncertainty modelling or neglecting the recourse capability of the available components.To improve the accuracy of DG capacity assessment,this paper proposes a distributionally adjustable robust chance-constrained approach that utilises uncertainty information to reduce the conservativeness of conventional robust approaches.The proposed approach also enables fast-acting devices such as inverters to adjust to the real-time realisation of uncertainty using the adjustable robust counterpart methodology.To achieve a tractable formulation,we first define uncertain chance constraints through distributionally robust conditional value-at-risk(CVaR),which is then reformulated into convex quadratic constraints.We subsequently solve the resulting large-scale,yet convex,model in a distributed fashion using the alternating direction method of multipliers(ADMM).Through numerical simulations,we demonstrate that the proposed approach outperforms the adjustable robust and conventional distributionally robust approaches by up to 15%and 40%,respectively,in terms of total installed DG capacity.
基金co-authored by Alliance for Sustainable Energy, LLC, the manager and operator of the National Renewable Energy Laboratory for the U.S. Department of Energy (DOE) (No. DE-AC36-08GO28308)provided by U.S. DOE Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office
文摘This paper proposes an adjustable and distributionally robust chance-constrained(ADRCC) optimal power flow(OPF) model for economic dispatch considering wind power forecasting uncertainty. The proposed ADRCC-OPF model is distributionally robust because the uncertainties of the wind power forecasting are represented only by their first-and second-order moments instead of a specific distribution assumption. The proposed model is adjustable because it is formulated as a second-order cone programming(SOCP) model with an adjustable coefficient.This coefficient can control the robustness of the chance constraints, which may be set up for the Gaussian distribution, symmetrically distributional robustness, or distributionally robust cases considering wind forecasting uncertainty. The conservativeness of the ADRCC-OPF model is analyzed and compared with the actual distribution data of wind forecasting error. The system operators can choose an appropriate adjustable coefficient to tradeoff between the economics and system security.
基金This work was supported in part by the National Natural Science Foundation of China(51807127)in part by the Fundamental Research Funds for Central Universities(YJ201654).
文摘A novel stochastic optimal dispatch model is proposed considering medium and long-term electricity transactions for a wind power integrated energy system using chance constrained programming.The electricity contract decomposition problem is introduced into the day-ahead optimal dispatch plan formulation progress.Considering the case that decomposition results may be not executable in the dispatch plan,a coordinated optimization strategy based on the Lagrange multiplier is proposed to eliminate the non-executable electric quantity.At the same time,the uncertainties and correlation of wind power are considered in the dispatch model,and the original stochastic dispatch problem is transformed into a mixed integer second-order cone programming problem using second-order cone relaxation and sample average approximation approach.Case study results demonstrate the validity of the proposed method.
基金supported in part by the U.S.National Science Foundation under Grant ECCS-1254310.
文摘With increasing penetration of wind energy,the variability and uncertainty of wind resources have become important factors for power systems operation.In particular,an effective method is required for identifying the stochastic range of wind power output,in order to better guide the operational security of power systems.This paper proposes a metric to determine accurate wind power output ranges so that the probability of actual wind power outputs being out of the range would be less than a small pre-defined value.A mixed-integer linear programming(MILP)based chance-constrained optimization model is proposed for efficiently determining optimal wind power output ranges,which are quantified via maximum and the minimum wind generation levels with respect to a certain time interval.The derived wind power range is then used to construct dynamic uncertainty intervals for the robust securityconstrained unit commitment(SCUC)model.A comparison with the deterministic SCUC model and the traditional robust SCUC model with presumed static uncertainty interval demonstrates that the proposed approach can offer more accurate wind power variabilities(i.e.,different variability degrees with respect to different wind power output levels at different time periods).The proposed approach is also shown to offer more effective and robust SCUC solutions,guaranteeing operational security and economics of power systems.Numerical case studies on a 6-bus system and the modified IEEE 118-bus system with realworld wind power data illustrate the effectiveness of the proposed approach.
基金the National Natural Science Foundation of China(No.51777185)National Key R&D Program of China(No.2016YFB0900100)Zhejiang University Academic Award for Outstanding Doctoral Candidates.
文摘Controlled islanding plays an essential role in preventing the blackout of power systems.Although there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable energy sources(RESs)that may cause unpredictable unbalanced power and the observabilit>T of power systems after islanding that is essential for back-up black-start measures.Therefore,a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming(MISOCCP)is proposed to address these issues.First,the uncertainty of RESs is characterized by their possibility distribution models with chance constraints,and the requirements,e.g.,system observability,for rapid back-up black-start measures are also considered.Then,a law of large numbers(LLN)based method is em-ployed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex one.Finally,case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed model.The results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.
基金This work was supported in part by Natural Science Foundation of Jiangsu Province,China(No.BK20171433)in part by Science and Technology Project of State Grid Jiangsu Electric Power Corporation,China(No.J2018066).
文摘Urban electricity and heat networks(UEHN)consist of the coupling and interactions between electric power systems and district heating systems,in which the geographical and functional features of integrated energy systems are demonstrated.UEHN have been expected to provide an effective way to accommodate the intermittent and unpredictable renewable energy sources,in which the application of stochastic optimization approaches to UEHN analysis is highly desired.In this paper,we propose a chance-constrained coordinated optimization approach for UEHN considering the uncertainties in electricity loads,heat loads,and photovoltaic outputs,as well as the correlations between these uncertain sources.A solution strategy,which combines the Latin Hypercube Sampling Monte Carlo Simulation(LHSMCS)approach and a heuristic algorithm,is specifically designed to deal with the proposed chance-constrained coordinated optimization.Finally,test results on an UEHN comprised of a modified IEEE 33-bus system and a 32-node district heating system at Barry Island have verified the feasibility and effectiveness of the proposed framework.
文摘To enhance the flexible interactions among multiple energy carriers,i.e.,electricity,thermal power and gas,a coordinated programming method for multi-energy microgrid(MEMG)system is proposed.Various energy requirements for both residential and parking loads are managed simultaneously,i.e.,electric and thermal loads for residence,and charging power and gas filling requirements for parking vehicles.The proposed model is formulated as a two-stage joint chance-constrained programming,where the first stage is a day-ahead operation problem that provides the hourly generation,conversion,and storage towards the minimization of operation cost considering the forecasting error of photovoltaic output and load demand.Meanwhile,the second stage is an on-line scheduling which adjusts the energy scheme in hourly time-scale considering the uncertainty.Simulations have demonstrated the validity of the proposed method,i.e.,collecting the flexibilities of thermal system,gas system,and parking vehicles to facilitate the operation of electrical networks.Sensitivity analysis shows that the proposed scheme can achieve a compromise between the operation efficiency and service quality.
基金the Hong Kong Research Grants Council(No.GRF 613213)。
文摘Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them.We then design a Monte Carlo algorithm,based on these estimators,to solve chance-constrained programs.Our numerical study shows that the algorithm works well,especially only with the gradient estimators.
文摘To address uncertainty as well as transient stability constraints simultaneously in the preventive control of windfarm systems, a novel three-stage optimization strategy is established in this paper. In the first stage, the probabilisticmulti-objective particle swarm optimization based on the point estimate method is employed to cope with thestochastic factors. The transient security region of the system is accurately ensured by the interior point methodin the second stage. Finally, the verification of the final optimal objectives and satisfied constraints are enforcedin the last stage. Furthermore, the proposed strategy is a general framework that can combine other optimizationalgorithms. The proposed methodology is tested on the modified WSCC 9-bus system and the New England 39-bussystem. The results verify the feasibility of the method.
文摘This paper discussed an extended model for flexibility analysis of chemical process. Under uncertainty, probability density function is used to describe uncertain parameters instead of hyper-rectangle, and chanceconstrained programming is a feasible way to deal with the violation of constraints. Because the feasible region of control variables would change along with uncertain parameters, its smallest acceptable size threshold is presented to ensure the controllability condition. By synthesizing the considerations mentioned above, a modified model can describe the flexibility analysis problem more exactly. Then a hybrid algorithm, which integrates stochastic simulation and genetic algorithm, is applied to solve this model and maximize the flexibility region. Both numerical and chemical process examples are presented to demonstrate the effectiveness of the method.
基金the National High-Tech. R & D Program for CIMS, China (2003AA413210).
文摘To study the uncertain optimization problems on implementation schedule, time-cost trade-off and quality in enterprise resource planning （ERP） implementation, combined with program evaluation and review technique （PERT）, some optimization models are proposed, which include the implementation schedule model, the timecost trade-off model, the quality model, and the implementation time-cost-quality synthetic optimization model. A PERT-embedded genetic algorithm （GA） based on stochastic simulation technique is introduced to the optimization models solution. Finally, an example is presented to show that the models and algorithm are reasonable and effective, which can offer a reliable quantitative decision method for ERP implementation.
文摘This study employs a chance-constrained data envelopment analysis (CDEA) approach with two models (model A and model B) to decompose provincial productivity growth in Vietnamese agriculture from 1995 to 2007 into technological progress and efficiency change. The differences between the chance - constrained programming model A and model B are assumptions imposed on the covariance matrix. The decomposition allows us to identify the contributions of technical change and the improvement in technical efficiency to productivity growth in Vietnamese production. Sixty-one provinces in Vietnam are classified into Mekong - technology and other -technology categories. We conduct a Mann-Whitney test to verify whether the two samples, the Mekong technology province sample and the other technology sample, are drawn from the same productivity change populations. The result of the Mann-Whitney test indicates that the differences between the Mekong technology category and the other technology category from two models are more significant. Two important questions are whether some provinces in the samples could maintain their relative efficiency rank positions in comparison with the others over the study period and how to further examine the agreements between the two models. The Kruskal - Wallis test statistic shows that technical efficiency from both models for some provinces are higher than those of them in the study period. The Malmquist results show that production frontier has contracted by around 1.3 percent and 0.31 percent from chance-constrained model A and model B, respectively, a year on average over the sample period. To examine the agreements or disagreements in the total factor productivity indexes we compute the correlation between Malmquist indexes, which is positive and not very high. Thus there is a little discrepancy between the two Malmquist indexes, estimated from the chance - constrained models A and B.
