Efficient Probabilistic Load Flow Calculation Considering Vine Copula⁃Based Dependence Structure of Renewable Energy Generation

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.

Probabilistic Load Flow Considering Correlation between Generation, Loads and Wind Power

In this paper a procedure is established for solving the Probabilistic Load Flow in an electrical power network, considering correlation between power generated by power plants, loads demanded on each bus and power injected by wind farms. The method proposed is based on the generation of correlated series of power values, which can be used in a MonteCarlo simulation, to obtain the probability density function of the power through branches of an electrical network.

Day-Ahead Probabilistic Load Flow Analysis Considering Wind Power Forecast Error Correlation

Short-term power flow analysis has a significant influence on day-ahead generation schedule. This paper proposes a time series model and prediction error distribution model of wind power output. With the consideration of wind speed and wind power output forecast error’s correlation, the probabilistic distributions of transmission line flows during tomorrow’s 96 time intervals are obtained using cumulants combined Gram-Charlier expansion method. The probability density function and cumulative distribution function of transmission lines on each time interval could provide scheduling planners with more accurate and comprehensive information. Simulation in IEEE 39-bus system demonstrates effectiveness of the proposed model and algorithm.

Space Transformation-Based Interdependency Modelling for Probabilistic Load Flow Analysis of Power Systems

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.

Probabilistic Load Flow Algorithm with the Power Performance of Double-Fed Induction Generators

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.

Probabilistic Load Flow Calculation of Power System Integrated with Wind Farm Based on Kriging Model

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.

An improved probabilistic load flow in distribution networks based on clustering and Point estimate methods

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.

风电接入远海油气平台的规划方法

海上风电直供远海油气平台可降低发电成本和碳排放,但传统规划方法不适用于远海油气平台的负荷特性。在考虑海上油田电力系统燃气透平机组与负荷特性的基础上,建立计及风-燃-荷功率动态匹配特性的扩展概率潮流模型,提出适用于远海油气平台的风机规划方法。采用所提潮流计算方法,在满足远海油田电力系统的电压、线路载流量等约束条件下,以年发电成本与年碳排放量的综合成本最低为目标建立规划模型,并采用粒子群优化算法对模型进行求解。以我国某远海油田电力系统为例,提出针对远海油田电力系统特点的风电接入方案,算例结果表明,所提规划方法具有可行性。

考虑分布式电源时空相关及电动汽车充电负荷分布特性的有源配电网概率潮流

目前分布式电源(distribution generation,DG)和电动汽车(electric vehicle,EV)充电负荷等随机变量接入电力系统时时空特性考虑不足,会导致概率潮流计算偏离实际。因此该文提出了考虑DG时空相关及EV分布特性的有源配电网概率潮流模型。首先,利用场景生成建立时空相关的风电、光伏出力概率模型;然后,考虑路网约束和用户心理,建立考虑EV时空分布特性的负荷概率模型;最后,以Nataf变换结合奇异值分解处理相关性输入变量,运用三点估计法对概率潮流进行计算,通过Cornish-Fisher级数拟合得到累积分布函数。以IEEE-33节点系统进行测试,利用所提模型分析了DG时空相关性和EV分布特性对配电网潮流的影响。结果表明DG时空相关性主要影响系统的波动性,EV分布特性主要影响系统的运行特性。该文研究可为新型配电网的安全运行提供理论指导。

考虑源荷不确定性的电力系统薄弱环节辨识方法

【目的】随着我国新型电力系统的不断发展,新能源大规模并网极大增加了电网承受潮流冲击的可能性,系统线路的载流能力迎来严峻考验;同时,源荷不确定性的增加使得电网运行状态愈发复杂多变,基于确定性潮流的传统薄弱环节辨识技术难以达到要求,增加了电网运行控制的难度。【方法】针对以上问题,结合概率潮流算法提出基于改进熵理论的电力系统薄弱节点综合评估指标,以指标区间概率分布对节点薄弱程度进行分析。首先,基于模拟法概率潮流构建大量运行方式样本;其次,将熵理论与电网运行参数相结合,以指标区间概率密度对系统关键节点的潮流冲击分布均衡性以及电压稳定性进行有效评估。【结论】最后,在IEEE39节点系统进行仿真校验后得出结论,所提评估指标更加贴合电力系统实际运行状态,能有效降低因新型电力系统中新能源发电波动性以及负荷侧用户用电量不确定性增加对薄弱环节辨识带来的误差。

考虑电源与负荷间存在非正定相关性的概率潮流计算方法研究

随着电动汽车等新型电力系统负荷类型的出现,电源和负荷间的相关性日趋复杂,针对利用Cholesky分解完成概率潮流计算会受电力系统电源和电力系统负荷之间相关矩阵影响的问题,即随着相关矩阵维度的增加相关矩阵变为非正定,最终导致潮流计算无法进行的问题。文章提出一种新颖的处理相关性矩阵非正定的半不变量法,将修正Barzilai-Borwein梯度法与Nataf变换相结合,解决变量间相关矩阵非正定问题,并在IEEE-33节点系统中分析新型电力系统各类电源和负荷相关性对计算结果的影响,验证文章所提方法准确性。

Probabilistic load flow method considering large-scale wind power integration

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.

Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation

Distributed generation including wind turbine(WT) and photovoltaic panel increases very fast in recent years around the world, challenging the conventional way of probabilistic load flow(PLF) calculation. Reliable and efficient PLF method is required to take this chage into account.This paper studies the maximum entropy probabilistic density function reconstruction method based on cumulant arithmetic of linearized load flow formulation,and then develops a maximum entropy based PLF(MEPLF) calculation algorithm for power system integrated with wind power generation(WPG). Compared with traditional Gram–Charlier expansion based PLF(GC-PLF)calculation method, the proposed ME-PLF calculation algorithm can obtain more reliable and accurate probabilistic density functions(PDFs) of bus voltages and branch flows in various WT parameter scenarios. It can solve thelimitation of GC-PLF calculation method that mistakenly gains negative values in tail regions of PDFs. Linear dependence between active and reactive power injections of WPG can also be effectively considered by the modified cumulant calculation framework. Accuracy and efficiency of the proposed approach are validated with some test systems. Uncertainties yielded by the wind speed variations, WT locations, power factor fluctuations are considered.

Combined Cumulant and Gaussian Mixture Approximation for Correlated Probabilistic Load Flow Studies:A New Approach

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.

Cumulant-based correlated probabilistic load flowconsidering photovoltaic generation and electric vehiclecharging demand

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.

基于蒙特卡罗模拟法的柔性交直流混联配电网概率潮流计算

随着高压直流输电和新能源并网技术的快速发展,电力系统运行工况愈加复杂多变。为更好评估现代电力系统的不确定性,文中研究了分布式发电中的风力发电和太阳能发电的随机出力对配电系统电压质量的影响,提出一种能够计及风光互补特性和换流站控制特性,基于蒙特卡罗模拟求解含有电压源换流器的交直流混联系统概率潮流计算方法。首先,针对换流站不同的控制方式,给出利用交替迭代法进行常规交直流潮流的计算模型。其次,建立了考虑风力发电、太阳能发电和负荷不确定性的概率潮流计算模型。最后,在修改后的IEEE-34节点系统上采用蒙特卡洛法计算节点电压、线路功率的均值和标准差。该方法能较为准确的反映新能源固有的不确定性及穿透率的影响,并有着良好的收敛性。

高渗透率分布式电源影响下配电网极限线损计算方法

针对现有配电网极限线损研究中未能充分考虑高渗透率分布式电源(distributed generation,DG)下节点电压越限、上级系统有功平衡功率损失等情况,使得极限线损的计算考虑不周的问题,提出一种高渗透率DG影响下配电网的极限线损计算方法。首先,考虑该背景影响下的电压越限问题,设计以DG有功、无功出力的最小变化差为目标的电压调控策略,构建计及DG出力变化的极限线损模型,使其更符合实际运行情况;其次,在模糊算法原理基础上以不同渗透率为程度界限,构建半梯形隶属度函数及对应模糊规则,得到上级系统有功平衡功率损失模型,并在供电功率不足时,构建计及削负荷操作的配电网极限线损模型;最后,以改进的IEEE 33节点配电系统为例,基于概率潮流分别讨论DG并入后极限线损减小、增大2种情况,验证所提极限线损模型的有效性。

基于高斯函数-最大熵展开的风电并网系统概率潮流计算

为有效计及风电出力随机性对电网运行状态的影响,在风电并网系统中提出一种基于高斯函数-最大熵原理的改进半不变量概率潮流计算方法。首先,以高斯函数为风速分布信息的载体,在此基础上采用改进反射核密度估计,建立计及风速有界性的风电出力概率模型,以便精确地求取描述风电出力随机性的各阶矩、半不变量等数字特征。然后,基于节点电压、支路功率等状态变量的数字特征,采用高斯函数改进最大熵模型进行状态变量的分布展开,由高斯函数的数量和性质来计及输入侧风速分布形状对输出侧状态变量分布的影响。同时将所提改进最大熵模型的约束由积分形式转为代数形式,提升计算效率。最后,以IEEE30节点系统对所提方法进行测试,结果证明了所提方法的有效性、准确性。

柔性互联配电网概率潮流算法研究

随着柔性直流配电技术的快速发展,直流配电网通过电压源换流器连接交流配电网构成的柔性互联配电网已成为当前的研究热点,但到目前为止,对于不确定性分布式电源接入的柔性互联配电网概率潮流计算尚未有文献进行研究。针对缺乏这种柔性互联配电网概率潮流研究的现状,文章开展不确定性研究,在分析了几种常规概率潮流计算方法后,以三点估计法结合改进交直流交替迭代算法作为柔性互联配电网概率潮流实现算法;以Nataf变换方法结合Cholesky分解进行不确定非正态输入变量的相关性处理;以IEEE 33节点配电系统结合国内首个五端直流示范工程-直流配电中心作为算例,验证了所提算法的有效性。

基于分布式电源出力独立随机性的配电网随机潮流算法

各类型分布式发电(Distributed Generations,DGs)出力均存在显著的随机性和相关性特征。针对配电网中日益增加的分散式风力发电和分布式光伏发电,提出一种计及DGs出力随机性和相关性的三点估计随机潮流(Probabilistic Load Flow,PLF)计算方法。该方法基于三阶多项式的正态变换,对非正态多维随机变量的相关性进行数学表征和转换处理,将其转换为独立非正态多维随机变量,利用蒙特卡洛或三点估计方法求出估计值,由确定性潮流进行计算,进一步通过Gram-Charlier级数展开,拟合各支路的有功功率及对应节点电压的概率密度和分布曲线。该方法能够实现输入随机变量的解耦求解,有效提升计算效率和准确性。仿真算例结果验证了算法的正确性,为含高比例分布式发电的配电网的运行规划提供有效参考。