As the proportion of newenergy increases,the traditional cumulant method(CM)produces significant errorswhen performing probabilistic load flow(PLF)calculations with large-scale wind power integrated.Considering the wi...As the proportion of newenergy increases,the traditional cumulant method(CM)produces significant errorswhen performing probabilistic load flow(PLF)calculations with large-scale wind power integrated.Considering the wind speed correlation,a multi-scenario PLF calculation method that combines random sampling and segmented discrete wind farm power was proposed.Firstly,based on constructing discrete scenes of wind farms,the Nataf transform is used to handle the correlation between wind speeds.Then,the random sampling method determines the output probability of discrete wind power scenarios when wind speed exhibits correlation.Finally,the PLF calculation results of each scenario areweighted and superimposed following the total probability formula to obtain the final power flow calculation result.Verified in the IEEE standard node system,the absolute percent error(APE)for the mean and standard deviation(SD)of the node voltages and branch active power are all within 1%,and the average root mean square(AMSR)values of the probability curves are all less than 1%.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
Because of the randomness and uncertainty,integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow.This paper uses polynomial normal transformation me...Because of the randomness and uncertainty,integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow.This paper uses polynomial normal transformation method to deal with non-normal random variable correlation,and solves probabilistic load flow based on Kriging method.This method is a kind of smallest unbiased variance estimation method which estimates unknown information via employing a point within the confidence scope of weighted linear combination.Compared with traditional approaches which need a greater number of calculation times,long simulation time,and large memory space,Kriging method can rapidly estimate node state variables and branch current power distribution situation.As one of the generator nodes in the western Yunnan power grid,a certain wind farm is chosen for empirical analysis.Results are used to compare with those by Monte Carlo-based accurate solution,which proves the validity and veracity of the model in wind farm power modeling as output of the actual turbine through PSD-BPA.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
In this paper,a probabilistic load flow analysis technique that combines the cumulant method and Gaussian mixture approximation method is proposed.This technique overcomes the incapability of the existing series expan...In this paper,a probabilistic load flow analysis technique that combines the cumulant method and Gaussian mixture approximation method is proposed.This technique overcomes the incapability of the existing series expansion methods to approximate multimodal probability distributions.A mix of Gaussian,non-Gaussian,and discrete type probability distributions for input bus powers is considered.Probability distributions of multimodal bus voltages and line power flows pertaining to these inputs are precisely obtained without using any series expansion method.At the same time,multiple input correlations are considered.Performance of the proposed method is demonstrated in IEEE 14 and 57 bus test systems.Results are compared with cumulant and Gram Charlier expansion,cumulant and Cornish Fisher expansion,dependent discrete convolution,and Monte Carlo simulation.Effects of different correlation cases on distribution of bus voltages and line power flows are also studied.展开更多
This paper applies a cumulant-based analytical method for probabilistic load flow (PLF) assessment in transmission and distribution systems. The uncertainties pertaining to photovoltaic generations and aggregate bus l...This paper applies a cumulant-based analytical method for probabilistic load flow (PLF) assessment in transmission and distribution systems. The uncertainties pertaining to photovoltaic generations and aggregate bus load powers are probabilistically modeled in the case of transmission systems. In the case of distribution systems, the uncertainties pertaining to plug-in hybrid electric vehicle and battery electric vehicle charging demands in residential community as well as charging stations are probabilistically modeled. The probability distributions of the result variables (bus voltages and branch power flows) pertaining to these inputs are accurately established. The multiple input correlation cases are incorporated. Simultaneously, the performance of the proposed method is demonstrated on a modified Ward-Hale 6-bus system and an IEEE 14-bus transmission system as well as on a modified IEEE 69-bus radial and an IEEE 33-bus mesh distribution system. The results of the proposed method are compared with that of Monte-Carlo simulation.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supported by Basic Science Research Program through the National Natural Science Foundation of China(Grant No.61867003).
文摘As the proportion of newenergy increases,the traditional cumulant method(CM)produces significant errorswhen performing probabilistic load flow(PLF)calculations with large-scale wind power integrated.Considering the wind speed correlation,a multi-scenario PLF calculation method that combines random sampling and segmented discrete wind farm power was proposed.Firstly,based on constructing discrete scenes of wind farms,the Nataf transform is used to handle the correlation between wind speeds.Then,the random sampling method determines the output probability of discrete wind power scenarios when wind speed exhibits correlation.Finally,the PLF calculation results of each scenario areweighted and superimposed following the total probability formula to obtain the final power flow calculation result.Verified in the IEEE standard node system,the absolute percent error(APE)for the mean and standard deviation(SD)of the node voltages and branch active power are all within 1%,and the average root mean square(AMSR)values of the probability curves are all less than 1%.
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Because of the randomness and uncertainty,integration of large-scale wind farms in a power system will exert significant influences on the distribution of power flow.This paper uses polynomial normal transformation method to deal with non-normal random variable correlation,and solves probabilistic load flow based on Kriging method.This method is a kind of smallest unbiased variance estimation method which estimates unknown information via employing a point within the confidence scope of weighted linear combination.Compared with traditional approaches which need a greater number of calculation times,long simulation time,and large memory space,Kriging method can rapidly estimate node state variables and branch current power distribution situation.As one of the generator nodes in the western Yunnan power grid,a certain wind farm is chosen for empirical analysis.Results are used to compare with those by Monte Carlo-based accurate solution,which proves the validity and veracity of the model in wind farm power modeling as output of the actual turbine through PSD-BPA.
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.
文摘In this paper,a probabilistic load flow analysis technique that combines the cumulant method and Gaussian mixture approximation method is proposed.This technique overcomes the incapability of the existing series expansion methods to approximate multimodal probability distributions.A mix of Gaussian,non-Gaussian,and discrete type probability distributions for input bus powers is considered.Probability distributions of multimodal bus voltages and line power flows pertaining to these inputs are precisely obtained without using any series expansion method.At the same time,multiple input correlations are considered.Performance of the proposed method is demonstrated in IEEE 14 and 57 bus test systems.Results are compared with cumulant and Gram Charlier expansion,cumulant and Cornish Fisher expansion,dependent discrete convolution,and Monte Carlo simulation.Effects of different correlation cases on distribution of bus voltages and line power flows are also studied.
文摘This paper applies a cumulant-based analytical method for probabilistic load flow (PLF) assessment in transmission and distribution systems. The uncertainties pertaining to photovoltaic generations and aggregate bus load powers are probabilistically modeled in the case of transmission systems. In the case of distribution systems, the uncertainties pertaining to plug-in hybrid electric vehicle and battery electric vehicle charging demands in residential community as well as charging stations are probabilistically modeled. The probability distributions of the result variables (bus voltages and branch power flows) pertaining to these inputs are accurately established. The multiple input correlation cases are incorporated. Simultaneously, the performance of the proposed method is demonstrated on a modified Ward-Hale 6-bus system and an IEEE 14-bus transmission system as well as on a modified IEEE 69-bus radial and an IEEE 33-bus mesh distribution system. The results of the proposed method are compared with that of Monte-Carlo simulation.
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.
