Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate b...Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.展开更多
Correlations among random variables make significant impacts on probabilistic load flow(PLF)calculation results.In the existing studies,correlation coefficients or Gaussian copula are usually used to model the correla...Correlations among random variables make significant impacts on probabilistic load flow(PLF)calculation results.In the existing studies,correlation coefficients or Gaussian copula are usually used to model the correlations,while vine copula,which describes the complex dependence structure(DS)of random variables,is seldom discussed since it brings in much heavier computational burdens.To overcome this problem,this paper proposes an efficient PLF method considering input random variables with complex DS.Specifically,the Rosenblatt transformation(RT)is used to transform vine copula⁃based correlated variables into independent ones;and then the sparse polynomial chaos expansion(SPCE)evaluates output random variables of PLF calculation.The effectiveness of the proposed method is verified using the IEEE 123⁃bus system.展开更多
A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector...A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector machine(SVM)is applied for the spot forecast of wind power generation.The probability density function(PDF)of the SVM forecast error is predicted by sparse Bayesian learning(SBL),and the spot forecast result is corrected according to the error expectation obtained.The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression(DCCMR)model to describe the correlation among the errors.And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function.Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.52109010)the Postdoctoral Science Foundation of China(Grant No.2021M701047)the China National Postdoctoral Program for Innovative Talents(Grant No.BX20200113).
文摘Copula functions have been widely used in stochastic simulation and prediction of streamflow.However,existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months.To address this limitation,this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations.This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas.The up-to-down sequential method,which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach,was used to determine the structures of multivariate Dvine copulas.The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station,the inflow control station of the Longyangxia Reservoir in the Yellow River Basin.The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow.This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.
基金Fundamental Research Funds for the Central Universities,China(No.2232020D⁃53)。
文摘Correlations among random variables make significant impacts on probabilistic load flow(PLF)calculation results.In the existing studies,correlation coefficients or Gaussian copula are usually used to model the correlations,while vine copula,which describes the complex dependence structure(DS)of random variables,is seldom discussed since it brings in much heavier computational burdens.To overcome this problem,this paper proposes an efficient PLF method considering input random variables with complex DS.Specifically,the Rosenblatt transformation(RT)is used to transform vine copula⁃based correlated variables into independent ones;and then the sparse polynomial chaos expansion(SPCE)evaluates output random variables of PLF calculation.The effectiveness of the proposed method is verified using the IEEE 123⁃bus system.
基金This work is supported by National Natural Science Foundation of China(No.51007047,No.51077087)Shandong Provincial Natural Science Foundation of China(No.20100131120039)National High Technology Research and Development Program of China(863 Program)(No.2011AA05A101).
文摘A novel multi-dimensional scenario forecast approach which can capture the dynamic temporal-spatial interdependence relation among the outputs of multiple wind farms is proposed.In the proposed approach,support vector machine(SVM)is applied for the spot forecast of wind power generation.The probability density function(PDF)of the SVM forecast error is predicted by sparse Bayesian learning(SBL),and the spot forecast result is corrected according to the error expectation obtained.The copula function is estimated using a Gaussian copula-based dynamic conditional correlation matrix regression(DCCMR)model to describe the correlation among the errors.And the multidimensional scenario is generated with respect to the estimated marginal distributions and the copula function.Test results on three adjacent wind farms illustrate the effectiveness of the proposed approach.
