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.

A probabilistic power flow calculation method considering the uncertainty of the static frequency characteristic

In a power system, power generation and load have frequency response characteristics, which randomly fluctuate with changes in operating status. This study investigates a probabilistic power flow method that considers the unit and load uncertainty of the static frequency characteristic. Firstly, a calculation model is established on the basis of the characteristics of the frequency modulation performance of the unit and load. Then a calculation method is developed using the concept of dynamic power flow in order to determine the probability distribution of the active power flow of each line under the occurrence of a fault in the system. In the method, Monte Carlo sampling with the semi-invariant method is applied for analysis and calculation. The IEEE-30-buses system is taken as an example to analyze the impact of different responses of units on the power flow distribution of various branches. The method discussed herein is compared with the Monte Carlo simulation method to verify its effectiveness.

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.

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.

Three-Phase Optimal Power Flow for Study of PV Plant Distributed Impact on Distribution Systems

This paper presents a TOPF （three-phase optimal power flow） model that represents photovoltaic systems. The PV plant is modeled in the TOPF as active and reactive power source. Reactive power can be generated or absorbed using the available capacity and the adjustable power factor of the inverter. The reduction of unbalance voltage and losses in the distribution systems is obtained by actions of reactive power control of the inverter. The TOPF is formulated by current balance equations and the PV systems are modeled via an equivalent circuit. The primal-dual interior point method is used to obtain the optimal operating points for the systems for different scenarios of solar irradiance and temperature, thus providing a detailed view of the impact of photovoltaic distributed generation.

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.

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.

Unified probabilistic gas and power flow

The natural gas system and electricity system are coupled tightly by gas turbines in an integrated energy system. The uncertainties of one system will not only threaten its own safe operation but also be likely to have a significant impact on the other. Therefore, it is necessary to study the variation of state variables when random fluctuations emerge in the coupled system. In this paper, a multislack-bus model is proposed to calculate the power and gas flow in the coupled system. A unified probabilistic power and gas flow calculation, in which the cumulant method and Gram–Charlier expansion are applied, is first presented to obtain the distribution of state variables after considering the effects of uncertain factors. When the variation range of random factors is too large, a new method of piecewise linearization is put forward to achieve a better fitting precision of probability distribution. Compared to the Monte Carlo method, the proposed method can reduce computation time greatly while reaching a satisfactory accuracy.The validity of the proposed methods is verified in a coupled system that consists of a 15-node natural gas system and the IEEE case24 power system.

Probabilistic Optimal Power Flow of an AC/DC System with a Multiport Current Flow Controller

To evaluate the impact of the randomness and correlation of photovoltaic(PV)and load on AC/DC systems with a multiport current flow controller(M-CFC),this paper proposes a probabilistic optimal power flow calculation for AC/DC systems,based on a nonparametric kernel density estimation.First,according to the M-CFC model,the DC power flow calculation method with M-CFC was inferred,and its influence on line loss was analyzed.Second,a nonparametric kernel density estimation with an adaptive bandwidth is used to accurately describe the probability distribution of the PV and load,and correlation samples of the PV and load are obtained by the mixed copula function.Then an optimization model that considers system loss and static security is established,and a fast nondominated sorting genetic algorithm based on the elite strategy(NSGA-II)is used to calculate the multi-objective probability optimal power flow of the AC/DC system.Finally,a case study is performed on a modified IEEE39 bus system using measured PV and load data.We verified that the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty,and M-CFC can improve the static security of the system.

Probabilistic Optimal Power Flow Considering the Dependence of Multiple Wind Farms Using Pair Diffusive Kernel Copula

As wind farms are commonly installed in areas with abundant wind resources,spatial dependence of wind speed among nearby wind farms should be considered when modeling a power system with large-scale wind power.In this paper,a novel bivariate non-parametric copula,and a bivariate diffusive kernel(BDK)copula are proposed to formulate the dependence between random variables.BDK copula is then applied to higher dimension using the pair-copula method and is named as pair diffusive kernel(PDK)copula,offering flexibility to formulate the complicated dependent structure of multiple random variables.Also,a quasi-Monte Carlo method is elaborated in the sampling procedure based on the combination of the Sobol sequence and the Rosen-blatt transformation of the PDK copula,to generate correlated wind speed samples.The proposed method is applied to solve probabilistic optimal power flow(POPF)problems.The effectiveness of the BDK copula is validated in copula definitions.Then,three different data sets are used in various goodness-of-fit tests to verify the superior performance of the PDK copula,which facilitates in formulating the dependence structure of wind speeds at different wind farms.Furthermore,samples obtained from the PDK copula are used to solve POPF problems,which are modeled on three modified IEEE 57-bus power systems.Compared to the Gaussian,T,and parametric-pair copulas,the results obtained from the PDK copula are superior in formulating the complicated dependence,thus solving POPF problems.

计及随机变量相关性的多点线性化概率潮流计算

为满足考虑源荷双侧强不确定性场景的“双高”电力系统潮流分析计算需求,提出一种新型的概率潮流计算方法。基于核密度估计建立输入随机变量的概率分布模型,构建Copula函数刻画多维随机输入变量间的相关性,获取更加符合系统实际运行情况的样本数据。引入多点线性化潮流计算方法,在降低非线性潮流计算量的同时减小单点线性化潮流计算的截断误差。在IEEE-30节点系统上进行算例测试,验证所提方法的准确性和有效性。

基于多项式混沌展开的交直流系统全纯嵌入概率潮流计算方法

为快速、准确量化分析风电出力不确定性对交直流电力系统潮流分布的影响,提出一种基于多项式混沌展开(PCE)的交直流电力系统全纯嵌入概率潮流计算方法。该方法首先根据风电出力的概率分布特征选择最优正交基函数,构造近似风电出力概率分布特征的PCE表达式;其次,将该PCE表达式引入交直流电力系统的全纯嵌入潮流方程中,构建基于PCE的交直流电力系统全纯嵌入概率潮流计算模型;再次,通过Galerkin投影将所构建的全纯嵌入概率潮流计算模型转化为高维确定性全纯嵌入潮流计算模型;然后,借助确定性全纯嵌入潮流模型求解方法,实现对所转化的高维确定性全纯嵌入潮流模型的求解,并根据所得PCE逼近系数计算交直流电力系统潮流的概率分布特征;最后,通过修改的PJM 5节点、IEEE 30节点和IEEE 118节点交直流测试系统算例验证所提方法的准确性和有效性。

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。

提升新能源承载能力的抽水蓄能容量配置研究

考虑区域电网可靠性和安全性指标,提出了提升新能源承载能力的抽水蓄能容量配置方法。首先,分析风电场、光伏电站实测出力数据,采用Copula理论和K-means聚类生成了考虑风光相关性的典型出力场景。其次,建立了提升区域电网新能源承载能力的抽水蓄能容量配置模型,以失负荷概率和电量不足期望指标为约束,基于风光典型出力场景评价区域电网的最大新能源承载能力,结合抽水蓄能运行模型,通过配置抽水蓄能最小装机容量提升新能源承载能力。最后,以电压越限风险和潮流越限风险指标作为安全性校验,采用概率潮流分析区域电网的运行风险。改进IEEE-39节点系统算例分析结果表明,配置抽水蓄能将可承载新能源的装机容量占比提升至64%。

考虑风光出力不确定性及相关性的配电网规划方法

新能源在电力系统中的渗透率日益提高,大大增加了电网中的不确定因素,对配电网的规划运行和控制提出了更高的要求。配电网规划是电力系统安全稳定运行的重要基石,传统配电网规划中各参数都已确定,缺乏对不确定因素的适应性。因此,提出一种基于概率潮流的配电网规划方法,首先对配电网中的不确定因素定量建模,建立源荷出力模型,其次将风速、太阳辐射与用电负荷之间的相关性用秩相关系数矩阵表征,建立计及相关性的半不变量概率潮流计算方法,最后构建以规划成本最小为目标函数,以潮流平衡、馈线容量、节点电压、网架辐射型结构为约束条件的配电网规划模型,并通过改进惯性参数与引入变异操作对粒子群算法进行改进,利用改进后的算法求解规划模型。以33节点系统为例进行仿真,结果验证了该方法能够有效降低网损,减少网络规划费用。

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。

基于源荷谐波耦合模型的数据驱动概率谐波潮流计算

随着新能源及负荷中电力电子装置的广泛应用,电力系统谐波畸变程度不断增加。同时,新能源及负荷显著的不确定特征,进一步增加了谐波分析难度。为有效评估系统不确定谐波状态,充分挖掘源荷实际运行特征,提出一种数据驱动的概率谐波潮流(probabilistic harmonic power flow,PHPF)计算方法。首先,基于实测数据,建立考虑时变特性的源荷动态谐波耦合矩阵模型(dynamic harmonic coupling matrix model,DHCMM),揭示不同时段内谐波电压与谐波电流的相互耦合关系。然后,利用实测数据挖掘源荷时变不确定特征,采用改进点估计法提取统计特性,克服变量间相互影响引起的估计偏差。最后,提出针对源荷不确定性的PHPF计算方法,对系统中时变不确定谐波进行评估。实验结果表明,基于实测数据的谐波耦合矩阵模型能够有效分析谐波源时变特性,结合源荷时变不确定功率状态,所提PHPF计算方法能够对电力系统谐波进行准确评估。

基于多保真度模型的高比例新能源配电网潮流不确定性表征方法

在能源生产和消费低碳化转型的背景下,如何量化源-荷不确定性的影响,高效、准确地实现配电网潮流不确定性表征,对配电网的安全、可靠运行具有重要意义。该文从计算效率和准确性两方面出发,将现有基于概率潮流的不确定性表征方法分为高、低保真度模型两类,综合分析了两种方法存在的问题。在此基础上,提出一种基于多保真度模型的高比例新能源配电网潮流不确定性表征方法,以实现潮流状态变量矩信息的高精度估计与概率分布函数的刻画。在矩信息估计方面,提出结合高、低保真度模型特点的最优输入样本数量分配方法,在给定总计算负担下实现了输出变量矩信息的无偏估计。在概率分布函数刻画方面,提出基于综合启动函数的概率分布函数刻画方法,利用多保真度模型提供的先验信息,提升概率分布函数拟合的准确性。通过118节点配电网的仿真计算,验证所提方法的有效性。

基于任意概率分布建模与改进混沌多项式展开的概率潮流方法

针对目前概率潮流难以兼顾准确度和速度,且缺乏有效处理任意概率分布源荷数据的手段,提出了基于任意概率分布建模策略和改进混沌多项式展开的概率潮流方法。首先,将系统输入量拟合为概率分布类型库中的概率分布,基于赤池信息量准则选取最优分布,比较最优分布和非参核密度估计的似然估计值确定最终概率分布。其次,为提升最小角回归广义混沌多项式展开的准确度,提出应用伪谱法和矩匹配法获取备选点集合,并使用组合概率窗对其筛选获得最优备选点。然后,对原始概率空间执行拉丁超立方采样获取补充配置点,并与最优备选点结合后得到最终配置点。所提方法在IEEE 30、IEEE 118节点算例中得到验证,在相近耗时下,所提方法的准确度较不确定量化计算框架UQLab推荐算法有显著提升。

考虑新能源随机波动和T接线的城市电网连锁故障风险评估

新能源的大量接入给城市电网的安全运行和重要用户可靠供电带来很大挑战,其功率的随机波动易引发电网出现连锁故障风险。提出了一种考虑新能源出力随机波动和城市电网110k V网架T接线开关投切的连锁故障风险评估方法。该方法在连锁故障发生概率和后果严重度的计算中都计及了系统状态的概率分布特性的影响,并采用基于半不变量法的概率潮流计算反映系统状态与新能源功率二者的概率分布特性之间的关系。另外,建立包含110 kV网架T接线开关投切的最小切负荷的混合整数非线性规划模型,并以最小切负荷量来表征系统在连锁故障的严重度。此优化模型通过决策故障下的各组T接线开关的投切状态,减少连锁故障下的切负荷量,进而有效降低连锁故障的风险。同时,通过机会约束描述重要用户负荷节点电压的安全运行范围,以确保重要用户负荷不停电的概率满足给定的置信水平,从而保证重要用户的安全可靠供电。最后,通过某个实际城市片区电网算例验证了所提出的连锁故障风险评估方法的正确有效性。