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
Probabilistic load flow(PLF)algorithm has been regained attention,because the large-scale wind power integration into the grid has increased the uncertainty of the stable and safe operation of the power system.The PLF...Probabilistic load flow(PLF)algorithm has been regained attention,because the large-scale wind power integration into the grid has increased the uncertainty of the stable and safe operation of the power system.The PLF algorithm is improved with introducing the power performance of double-fed induction generators(DFIGs)for wind turbines(WTs)under the constant power factor control and the constant voltage control in this paper.Firstly,the conventional Jacobian matrix of the alternating current(AC)load flow model is modified,and the probability distributions of the active and reactive powers of the DFIGs are derived by combining the power performance of the DFIGs and the Weibull distribution of wind speed.Then,the cumulants of the state variables in power grid are obtained by improved PLF model and more accurate power probability distributions.In order to generate the probability density function(PDF)of the nodal voltage,Gram-Charlier,Edgeworth and Cornish-Fisher expansions based on the cumulants are applied.Finally,the effectiveness and accuracy of the improved PLF algorithm is demonstrated in the IEEE 14-RTS system with wind power integration,compared with the results of Monte Carlo(MC)simulation using deterministic load flow calculation.展开更多
Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to ana...Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to analyze the performance of several schemes for simulating correlated variables combined with the point estimate method(PEM).Unlike the existing works that considering one single scheme combined with Monte Carlo simulation(MCS) or PEM,by neglecting the correlation among random input variables,four schemes were presented for disposing the dependence of correlated random variables,including Nataf transformation /polynomial normal transformation(PINT) combined with orthogonal transformation(OT) / elementary transformation(ET).Combining with the 2m+1 approach of PEM,a space transformation-based formulation was proposed and adopted for solving the PLF.The proposed approach is applied in the modified IEEE 30-bus system while considering correlated wind generations and load demands.Numerical results show the effectiveness of the proposed approach compared with those obtained from the MCS.Results also show that the scheme of combining Nataf transformation and ET with PEM provides the best performance.展开更多
The increasing penetration of wind power brings great uncertainties into power systems,which poses challenges to system planning and operation.This paper proposes a novel probabilistic load flow(PLF)method based on cl...The increasing penetration of wind power brings great uncertainties into power systems,which poses challenges to system planning and operation.This paper proposes a novel probabilistic load flow(PLF)method based on clustering technique to handle large fluctuations from large-scale wind power integration.The traditional cumulant method(CM)for PLF is based on the linearization of load flow equations around the operation point,therefore resulting in significant errors when input random variables have large fluctuations.In the proposed method,the samples of wind power and loads are first generated by the inverse Nataf transformation and then clustered using an improved K-means algorithm to obtain input variable samples with small variances in each cluster.With such pre-processing,the cumulant method can be applied within each cluster to calculate cumulants of output random variables with improved accuracy.The results obtained in each cluster are combined according to the law of total probability to calculate the final cumulants of output random variables for the whole samples.The proposed method is validated on modified IEEE 9-bus and 118-bus test achieve a better performance with the consideration of both traditional CM,2 m+1 point estimate method(PEM),Monte Carlo simulation(MCS)and Latin hypercube sampling(LHS)based MCS,the proposed method can achieve a better performance with the consideration of bothcomputational efficiency and accuracy.展开更多
Clustering approaches are one of the probabilistic load flow(PLF)methods in distribution networks that can be used to obtain output random variables,with much less computation burden and time than the Monte Carlo simu...Clustering approaches are one of the probabilistic load flow(PLF)methods in distribution networks that can be used to obtain output random variables,with much less computation burden and time than the Monte Carlo simulation(MCS)method.However,a challenge of the clustering methods is that the statistical characteristics of the output random variables are obtained with low accuracy.This paper presents a hybrid approach based on clustering and Point estimate methods.In the proposed approach,first,the sample points are clustered based on the𝑙-means method and the optimal agent of each cluster is determined.Then,for each member of the population of agents,the deterministic load flow calculations are performed,and the output variables are calculated.Afterward,a Point estimate-based PLF is performed and the mean and the standard deviation of the output variables are obtained.Finally,the statistical data of each output random variable are modified using the Point estimate method.The use of the proposed method makes it possible to obtain the statistical properties of output random variables such as mean,standard deviation and probabilistic functions,with high accuracy and without significantly increasing the burden of calculations.In order to confirm the consistency and efficiency of the proposed method,the 10-,33-,69-,85-,and 118-bus standard distribution networks have been simulated using coding in Python®programming language.In simulation studies,the results of the proposed method have been compared with the results obtained from the clustering method as well as the MCS method,as a criterion.展开更多
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.
文摘Probabilistic load flow(PLF)algorithm has been regained attention,because the large-scale wind power integration into the grid has increased the uncertainty of the stable and safe operation of the power system.The PLF algorithm is improved with introducing the power performance of double-fed induction generators(DFIGs)for wind turbines(WTs)under the constant power factor control and the constant voltage control in this paper.Firstly,the conventional Jacobian matrix of the alternating current(AC)load flow model is modified,and the probability distributions of the active and reactive powers of the DFIGs are derived by combining the power performance of the DFIGs and the Weibull distribution of wind speed.Then,the cumulants of the state variables in power grid are obtained by improved PLF model and more accurate power probability distributions.In order to generate the probability density function(PDF)of the nodal voltage,Gram-Charlier,Edgeworth and Cornish-Fisher expansions based on the cumulants are applied.Finally,the effectiveness and accuracy of the improved PLF algorithm is demonstrated in the IEEE 14-RTS system with wind power integration,compared with the results of Monte Carlo(MC)simulation using deterministic load flow calculation.
基金National Science Foundation of China(No.61533010)the Science and Technology Commission of Shanghai Municipality,China(No.14ZR1415300)
文摘Dependence among random input variables affects importantly the results of probabilistic load flow(PLF),system economic operation,and system security.To solve this problem,the main objectiveness of the paper is to analyze the performance of several schemes for simulating correlated variables combined with the point estimate method(PEM).Unlike the existing works that considering one single scheme combined with Monte Carlo simulation(MCS) or PEM,by neglecting the correlation among random input variables,four schemes were presented for disposing the dependence of correlated random variables,including Nataf transformation /polynomial normal transformation(PINT) combined with orthogonal transformation(OT) / elementary transformation(ET).Combining with the 2m+1 approach of PEM,a space transformation-based formulation was proposed and adopted for solving the PLF.The proposed approach is applied in the modified IEEE 30-bus system while considering correlated wind generations and load demands.Numerical results show the effectiveness of the proposed approach compared with those obtained from the MCS.Results also show that the scheme of combining Nataf transformation and ET with PEM provides the best performance.
基金supported by the National Key Research and Development Program of China(No.2017YFB0903400).
文摘The increasing penetration of wind power brings great uncertainties into power systems,which poses challenges to system planning and operation.This paper proposes a novel probabilistic load flow(PLF)method based on clustering technique to handle large fluctuations from large-scale wind power integration.The traditional cumulant method(CM)for PLF is based on the linearization of load flow equations around the operation point,therefore resulting in significant errors when input random variables have large fluctuations.In the proposed method,the samples of wind power and loads are first generated by the inverse Nataf transformation and then clustered using an improved K-means algorithm to obtain input variable samples with small variances in each cluster.With such pre-processing,the cumulant method can be applied within each cluster to calculate cumulants of output random variables with improved accuracy.The results obtained in each cluster are combined according to the law of total probability to calculate the final cumulants of output random variables for the whole samples.The proposed method is validated on modified IEEE 9-bus and 118-bus test achieve a better performance with the consideration of both traditional CM,2 m+1 point estimate method(PEM),Monte Carlo simulation(MCS)and Latin hypercube sampling(LHS)based MCS,the proposed method can achieve a better performance with the consideration of bothcomputational efficiency and accuracy.
文摘Clustering approaches are one of the probabilistic load flow(PLF)methods in distribution networks that can be used to obtain output random variables,with much less computation burden and time than the Monte Carlo simulation(MCS)method.However,a challenge of the clustering methods is that the statistical characteristics of the output random variables are obtained with low accuracy.This paper presents a hybrid approach based on clustering and Point estimate methods.In the proposed approach,first,the sample points are clustered based on the𝑙-means method and the optimal agent of each cluster is determined.Then,for each member of the population of agents,the deterministic load flow calculations are performed,and the output variables are calculated.Afterward,a Point estimate-based PLF is performed and the mean and the standard deviation of the output variables are obtained.Finally,the statistical data of each output random variable are modified using the Point estimate method.The use of the proposed method makes it possible to obtain the statistical properties of output random variables such as mean,standard deviation and probabilistic functions,with high accuracy and without significantly increasing the burden of calculations.In order to confirm the consistency and efficiency of the proposed method,the 10-,33-,69-,85-,and 118-bus standard distribution networks have been simulated using coding in Python®programming language.In simulation studies,the results of the proposed method have been compared with the results obtained from the clustering method as well as the MCS method,as a criterion.
