CN105552938A

CN105552938A - Voltage sag evaluation method for three-phase asymmetrical power distribution network

Info

Publication number: CN105552938A
Application number: CN201610105910.5A
Authority: CN
Inventors: 贾东梨; 刘科研; 盛万兴; 孟晓丽; 胡丽娟; 何开元; 叶学顺; 刁赢龙; 唐建岗; 李雅洁; 董伟杰
Original assignee: State Grid Corp of China SGCC; China Electric Power Research Institute Co Ltd CEPRI; State Grid Beijing Electric Power Co Ltd
Current assignee: State Grid Corp of China SGCC; China Electric Power Research Institute Co Ltd CEPRI; State Grid Beijing Electric Power Co Ltd
Priority date: 2016-02-26
Filing date: 2016-02-26
Publication date: 2016-05-04
Anticipated expiration: 2036-02-26
Also published as: CN105552938B

Abstract

The invention relates to a voltage sag evaluation method for a three-phase asymmetric power distribution network. The method includes: establishing a random fault model of a three-phase asymmetric power distribution network; Orthogonal transformation of the model is carried out to obtain the uncorrelated fault random model corresponding to the fault random model; the point estimation method is used to process the random variables composed of the uncorrelated fault random model and the DG random model, and the random variables of the two groups of simulation schemes are obtained; The random variables of the group simulation schemes are decomposed to obtain the random variables of the two sets of related simulation schemes corresponding to the random variables of the two sets of simulation schemes; the elements in the random variables of the two sets of related simulation schemes are respectively determined by the Cornish-Fisher series Probability density function; comprehensively consider the correlation between fault types and fault lines in the distribution network and various short-circuit faults in the distribution network to simulate the characteristics of the entire distribution network, and provide reference for taking measures to suppress voltage sags.

Description

A Method for Evaluating Voltage Sags in Three-phase Asymmetric Distribution Networks

技术领域technical field

本发明涉及电力系统电能质量技术领域，具体涉及一种三相不对称配电网络电压暂降评估方法。The invention relates to the technical field of power system power quality, in particular to a voltage sag evaluation method for a three-phase asymmetric power distribution network.

背景技术Background technique

电压暂降又称电压跌落，是指系统中某点的工频电压有效值突然下降到额定值的10％-90％，并在随后的10ms-1min的短暂持续期后恢复正常。随着基于大功率电力电子开关设备的普及和用电设备的技术更新，尤其是数控技术广泛应用于工业生产，电压暂降产生的危害越来越明显。配电网中，最严重的电压暂降问题大多由短路故障引起。电压暂降对敏感设备(例如可调速电机、精密控制设备等)的影响甚至可以和停电事故相提并论。电压暂降对工业用户造成的严重影响与危害表现的尤其突出，还可能造成人员伤亡和设备损坏。Voltage sag, also known as voltage sag, means that the effective value of power frequency voltage at a certain point in the system suddenly drops to 10%-90% of the rated value, and returns to normal after a short duration of 10ms-1min. With the popularization of switching equipment based on high-power power electronics and the technological update of electrical equipment, especially numerical control technology is widely used in industrial production, the harm caused by voltage sag is becoming more and more obvious. In the distribution network, the most serious voltage sag problems are mostly caused by short-circuit faults. The impact of voltage sag on sensitive equipment (such as adjustable speed motors, precision control equipment, etc.) can even be compared with power failure accidents. The serious impact and hazards caused by voltage sag to industrial users are particularly prominent, and may also cause casualties and equipment damage.

同其它电能质量问题一样，电压暂降问题并不是一个新问题，已有很多技术资料对其进行研究。通过对现有技术资料的查询得知，电压暂降评估是电能质量分析的一个重要方面。Like other power quality problems, the voltage sag problem is not a new problem, and there are many technical materials to study it. According to the query of existing technical materials, voltage sag evaluation is an important aspect of power quality analysis.

随着科学技术的发展，不断有新的方法引入到电压质量分析中。目前，点估计法在电能质量领域已有应用。技术1(吴蓓,张焰,陈闽江.点估计法在电压稳定性分析中的应用[J].中国电机工程学报，2008,28(25):38-43.)将点估计法引入到电压稳定性分析中，针对支路故障的随机性进行电压稳定分析，能够统一处理线路故障及节点注入功率的不确定性问题。技术2(徐培栋,肖先勇,汪颖.电压暂降频次两点估计随机评估方法[J].电力系统保护与控制,2011,39(9):1-6.)考虑敏感设备耐受电压和系统母线正常运行电压的随机性，研究电压暂降频次问题。技术1和技术2都能够在综合考虑计算精度和计算时间的情况下，获得令人满意的结果。With the development of science and technology, new methods are constantly introduced into voltage quality analysis. At present, the point estimation method has been applied in the field of power quality. Technology 1 (Wu Bei, Zhang Yan, Chen Minjiang. Application of point estimation method in voltage stability analysis [J]. Chinese Journal of Electrical Engineering, 2008,28(25):38-43.) Introduce point estimation method to voltage In the stability analysis, the voltage stability analysis is carried out for the randomness of branch faults, which can uniformly deal with the uncertainty of line faults and node injected power. Technology 2 (Xu Peidong, Xiao Xianyong, Wang Ying. Random evaluation method for two-point estimation of voltage sag frequency[J]. Power System Protection and Control, 2011,39(9):1-6.) Considering the withstand voltage of sensitive equipment and the system The randomness of the normal operating voltage of the busbar is studied to study the frequency of voltage sags. Both technology 1 and technology 2 can obtain satisfactory results under the comprehensive consideration of calculation accuracy and calculation time.

目前分析电压暂降的方法主要有临界距离法(技术3:M.N.Moschakis,N.D.Hatziargyriou.Analyticalcalculationandstochasticassessmentofvoltagesags[J].IEEETransactionsonPowerDelivery.2006,21(3):1727-1734.技术4:M.H.J.Bollen.Fastassessmentmethodsforvoltagesagsindistributionsystems[J].IEEETransactionsonIndustryApplications,1996,32(6):1414-1423.技术5:PadmanabhThaku,AsheeshK.Singh,RameshC.Bansal.Ananalyticalapproachforstochasticassessmentofbalancedandunbalancedvoltagesagsinlargesystems[J].IEEETransactionsonPowerDelivery,2006,21(3):1493-1500.)、故障点法以及蒙特卡洛方法(MonteCarloSimulation,MCS)。临界距离法是一种比较经典的用来评估对称故障和不对称故障引起的电压暂降的方法。故障点法仅利用几个选定点的特定故障来仿真整个电力系统的特性。蒙特卡洛方法是一种被广泛用于分析随机问题的方法。蒙特卡洛方法的采样次数与系统的规模无关，并且系统的复杂程度对其影响不大，但是蒙特卡洛方法具有静态性、计算效率低、耗时长等缺点。随着科学技术的发展，不断有新的方法引入到电压暂降分析中，比如两点法(技术6：一种有源配电网电压跌落仿真与评估方法，中国：CN201410406537.8)。两点法将随机问题转换为确定性问题，实现了对电压暂降的评估与仿真。但是，使用以上各种方法进行电压暂降评估时都是将配电网作为三相对称网络处理，未考虑配电网的三相不对称问题，但是配电网络中三相不对称现象普遍存在。现有文献资料对三相不对称的配电网电压暂降问题研究较少。At present, the methods for analyzing voltage sags mainly include the critical distance method (Technology 3: M.N.Moschakis, N.D. Hatziargyriou. Analytical calculation and stochastic assessment of voltage ags [J]. IEEETransactionsonPowerDelivery. .IEEETransactionsonIndustryApplications,1996,32(6):1414-1423.技术5:PadmanabhThaku,AsheeshK.Singh,RameshC.Bansal.Ananalyticalapproachforstochasticassessmentofbalancedandunbalancedvoltagesagsinlargesystems[J].IEEETransactionsonPowerDelivery,2006,21(3):1493-1500.)、故障点法And the Monte Carlo method (MonteCarloSimulation, MCS). The critical distance method is a classic method used to evaluate voltage sags caused by symmetrical faults and asymmetrical faults. The point-of-fault method uses only specific faults at a few selected points to simulate the behavior of the entire power system. Monte Carlo method is a widely used method for analyzing stochastic problems. The sampling times of the Monte Carlo method has nothing to do with the scale of the system, and the complexity of the system has little effect on it, but the Monte Carlo method has the disadvantages of static, low computational efficiency, and long time consumption. With the development of science and technology, new methods are continuously introduced into the analysis of voltage sags, such as the two-point method (Technology 6: A method for simulation and evaluation of voltage sags in active distribution networks, China: CN201410406537.8). The two-point method converts the random problem into a deterministic problem, and realizes the evaluation and simulation of the voltage sag. However, when using the above methods to evaluate voltage sags, the distribution network is treated as a three-phase symmetrical network, and the three-phase asymmetry of the distribution network is not considered, but the three-phase asymmetry phenomenon in the distribution network is common. . There are few studies on the voltage sag problem of three-phase asymmetric distribution network in the existing literature.

发明内容Contents of the invention

本发明提供一种三相不对称配电网络电压暂降评估方法，其目的是综合考虑配电网中故障类型与故障线路的相关性以及配电网中各种短路故障来仿真整个配电网的特性，为采取抑制电压暂降的措施提供参考，并提高配电网的供电可靠性。The invention provides a three-phase asymmetric distribution network voltage sag evaluation method, the purpose of which is to comprehensively consider the correlation between the fault type and the fault line in the distribution network and various short-circuit faults in the distribution network to simulate the entire distribution network The characteristics of the system provide a reference for taking measures to suppress voltage sags and improve the reliability of power supply in the distribution network.

本发明的目的是采用下述技术方案实现的：The object of the present invention is to adopt following technical scheme to realize:

一种三相不对称配电网络电压暂降评估方法，其改进之处在于，包括：A method for evaluating voltage sags in a three-phase asymmetric power distribution network, the improvements of which include:

(1)建立所述三相不对称配电网络的故障随机模型；(1) set up the fault stochastic model of described three-phase asymmetric power distribution network;

(2)建立所述三相不对称配电网络的DG随机模型；(2) set up the DG stochastic model of described three-phase asymmetric power distribution network;

(3)对所述故障随机模型进行正交变换，获取所述故障随机模型对应的不相关故障随机模型；(3) performing an orthogonal transformation on the fault random model to obtain an irrelevant fault random model corresponding to the fault random model;

(4)采用点估计法对所述不相关故障随机模型和DG随机模型组成的随机变量进行处理，获取两组仿真方案的随机变量；(4) adopt point estimation method to process the random variable that described irrelevant failure stochastic model and DG stochastic model form, obtain the random variable of two groups of simulation schemes;

(5)采用Choleskydecomposition方式对所述两组仿真方案的随机变量进行反分解，获取所述两组仿真方案的随机变量对应的两组相关的仿真方案的随机变量；(5) adopt Choleskydecomposition mode to decompose the random variable of described two groups of simulation schemes, obtain the random variable of two groups of related simulation schemes corresponding to the random variable of described two groups of simulation schemes;

(6)通过Cornish-Fisher级数分别确定所述两组相关的仿真方案的随机变量中元素的概率密度函数。(6) Determine the probability density functions of the elements in the random variables of the two groups of related simulation schemes respectively through the Cornish-Fisher series.

优选的，所述步骤(1)中，利用蒙特卡洛仿真方式建立所述三相不对称配电网络的故障随机模型，包括：Preferably, in the step (1), the fault stochastic model of the three-phase asymmetric power distribution network is established by means of Monte Carlo simulation, including:

(1-1)按下式建立所述三相不对称配电网络的故障线路模型：(1-1) The fault line model of the three-phase asymmetric power distribution network is established as follows:

${F f}_{L L i i n no e e} = = \{\begin{matrix} 11,, x x < < {P P}_{L L i i n no e e,, 11} \\ 22,, {P P}_{L L i i n no e e,, 22} \leq \leq x x < < {P P}_{L L i i n no e e,, 11} + + {P P}_{L L i i n no e e,, 22} \\ . . \\ . . \\ . . \\ M m,, {P P}_{L L i i n no e e,, 11} + + {P P}_{L L i i n no e e,, 22} + + ... ... + + {P P}_{L L i i n no e e,, M m - - 11} \leq \leq x x < < 11 \end{matrix} - - - - - - ((11))$

式(1)中，x为服从[0,1]均匀分布的随机数，即x～U[0,1]，F_Line为故障支路编号，M为所述三相不对称配电网络中支路总数，P_Line,i为所述三相不对称配电网络中第i条支路的故障率，i∈{1,M}，U为均匀分布函数；In formula (1), x is a random number that obeys the uniform distribution of [0,1], that is, x~U[0,1], F _Line is the number of the fault branch, and M is the number in the three-phase asymmetric distribution network The total number of branches, P _Line,i is the failure rate of the i-th branch in the three-phase asymmetric power distribution network, i∈{1,M}, U is a uniform distribution function;

(1-2)按下式建立所述三相不对称配电网络的故障位置模型：(1-2) The fault location model of the three-phase asymmetric power distribution network is established as follows:

F_Loc＝y*100％(2)F _Loc = y*100% (2)

式(2)中，y为服从[0,1]均匀分布的随机数，即y～U[0,1]，F_Loc为故障支路F_Line的故障点前支路长度与故障支路F_Line总长度之比的百分比；In formula (2), y is a random number that obeys the uniform distribution of [0,1], that is, y~U[0,1], and F _Loc is the length of the branch before the fault point of the fault branch F _Line and the length of the fault branch F Line The percentage of the ratio of the total length of _Line ;

(1-3)建立所述三相不对称配电网络的故障类型模型包括：(1-3) Establishing the fault type model of the three-phase asymmetric power distribution network includes:

若所述三相不对称配电网络的故障支路F_Line为三相，则按下式建立所述三相不对称配电网络的故障支路F_Line对应的故障类型模型：If the fault branch F _Line of the three-phase asymmetric power distribution network is three-phase, then the fault type model corresponding to the fault branch F _Line of the three-phase asymmetric power distribution network is established as follows:

${T T}_{T T y the y p p e e} = = \{\begin{matrix} 33 L L G G,, & z z < < {P P}_{33 L L G G} \\ 22 L L,, & {P P}_{33 L L G G} \leq \leq z z < < {P P}_{33 L L G G} + + {P P}_{22 L L} \\ 22 L L G G,, & {P P}_{33 L L G G} + + {P P}_{22 L L} \leq \leq z z < < {P P}_{33 L L G G} + + {P P}_{22 L L} + + {P P}_{22 L L G G} \\ L L G G,, & {P P}_{33 L L G G} + + {P P}_{22 L L} + + {P P}_{22 L L G G} \leq \leq z z < < 11 \end{matrix} - - - - - - ((33))$

式(3)中，z为服从[0,1]均匀分布的随机数，即z～U[0,1]，F_Type为所述三相不对称配电网络的故障支路F_Line对应的故障类型，3LG为三相接地短路故障类型，2L为两相相间短路故障类型，2LG为两相接地短路故障类型，LG为单相接地短路故障类型，P_3LG为三相接地短路故障发生概率，P_2L为两相相间短路故障发生概率，P_2LG为两相接地短路故障发生概率；In formula (3), z is a random number that obeys the uniform distribution of [0,1], that is, z~U[0,1], and F _Type is the fault branch F _Line corresponding to the three-phase asymmetric power distribution network Fault type, 3LG is three-phase ground short-circuit fault type, 2L is two-phase phase-to-phase short-circuit fault type, 2LG is two-phase ground short-circuit fault type, LG is single-phase ground short-circuit fault type, P _3LG is three-phase ground short-circuit fault type Occurrence probability, P _2L is the occurrence probability of two-phase phase-to-phase short-circuit fault, P _2LG is the occurrence probability of two-phase-to-ground short-circuit fault;

若所述三相不对称配电网络的故障支路F_Line为两相，则按下式建立所述三相不对称配电网络的故障支路F_Line对应的故障类型模型：If the fault branch F _Line of the three-phase asymmetric power distribution network is two phases, then the fault type model corresponding to the fault branch F _Line of the three-phase asymmetric power distribution network is established as follows:

${F f}_{T T y the y p p e e} = = \{\begin{matrix} 22 L L,, & z z < < {P P}_{22 L L} \\ 22 L L G G,, & {P P}_{22 L L} \leq \leq z z < < {P P}_{22 L L} + + {P P}_{22 L L G G} \\ L L G G,, & {P P}_{22 L L} + + {P P}_{22 L L G G} \leq \leq z z < < 11 \end{matrix} - - - - - - ((44))$

F_Type＝LG(5)。F _Type =LG(5).

(1-4)按下式建立所述三相不对称配电网络的故障持续时间模型：(1-4) The fault duration model of the three-phase asymmetric power distribution network is established as follows:

F_Dur＝μ(6)F _Dur = μ(6)

式(6)中，μ为服从期望为0.06s，标准偏差为0.01s的标准正态分布的随机数，即μ～N[0.06,0.01]，F_Dur为所述三相不对称配电网络的故障支路F_Line对应的故障持续时间；In formula (6), μ is a random number that obeys the standard normal distribution with an expectation of 0.06s and a standard deviation of 0.01s, that is, μ~N[0.06,0.01], and F _Dur is the three-phase asymmetric distribution network The fault duration corresponding to the fault branch F _Line of ;

(1-5)按下式建立所述三相不对称配电网络的故障阻抗模型：(1-5) The fault impedance model of the three-phase asymmetric power distribution network is established as follows:

F_Res＝τ(7)F _Res =τ(7)

式(7)中，τ为服从期望为5Ω，标准偏差为1Ω的标准正态分布的随机数，即τ～N[5,1]，F_Res为所述三相不对称配电网络的故障支路F_Line对应的故障阻抗。In formula (7), τ is a random number obeying the standard normal distribution with an expectation of 5Ω and a standard deviation of 1Ω, that is, τ~N[5,1], and F _Res is the fault of the three-phase asymmetric distribution network Fault impedance corresponding to branch F _Line .

优选的，所述步骤(2)中，利用蒙特卡洛仿真方式建立所述三相不对称配电网络的DG随机模型，包括：Preferably, in the step (2), the DG stochastic model of the three-phase asymmetric power distribution network is established by means of Monte Carlo simulation, including:

(2-1)风机发电系统采用一次曲线模型，风机输出功率P_wind与风速v的关系为：(2-1) The fan power generation system adopts a linear curve model, and the relationship between the fan output power P _wind and the wind speed v is:

${P P}_{w w i i n no d d} = = \{\begin{matrix} 00,, & v v < < {v v}_{c c i i},, v v > > {v v}_{c c o o} \\ a a + + b b v v,, & {v v}_{c c i i} < < v v < < {v v}_{r r} \\ {p p}_{r r},, & {v v}_{r r} < < v v < < {v v}_{c c o o} \end{matrix} - - - - - - ((88))$

式(8)中，均为常数，v_r是风机的额定风速，P_r是风机的额定功率，v_ci是风机的切入风速，v_co是风机的切出风速；In formula (8), Both are constants, v _r is the rated wind speed of the fan, P _r is the rated power of the fan, v _ci is the cut-in wind speed of the fan, v _co is the cut-out wind speed of the fan;

风电机组台数为N_wtg时，风电机组输出功率P_ω的模型为：When the number of wind turbines is N _wtg , the model of wind turbine output power P _ω is:

P_ω＝P_windN_wtg(9)P _ω ＝P _wind N _wtg (9)

当v_ci<v<v_r时，风电机组输出功率P_ω的概率密度函数的公式为：When v _ci <v<v _r , the formula of the probability density function of wind turbine output power P _ω is:

式(10)中，K为Weibull分布的形状参数，C为Weibull分布的尺度参数，f(P_ω)为风电机组有功出力的概率密度函数，Q_ω为风电机组无功出力，为功率因数；In formula (10), K is the shape parameter of the Weibull distribution, C is the scale parameter of the Weibull distribution, f(P _ω ) is the probability density function of the active output of the wind turbine, Q _ω is the reactive output of the wind turbine, is the power factor;

(2-2)光伏发电系统输出功率P_solar的模型为：(2-2) The output power P _solar model of the photovoltaic power generation system is:

P_solar＝rAη(11)P _solar =rAη(11)

式(11)中，r为辐射度，单位为W/m²，为光伏发电系统的太阳能方阵的总面积，A_m为单个电池组件的面积，M为光伏发电系统的太阳能方阵的电池组件数，为光伏发电系统的太阳能方阵的光电转换效率，η_m为单个电池组件的光电转换效率；In the formula (11), r is the radiance, the unit is W/m ² , is the total area of the solar array of the photovoltaic power generation system, A _m is the area of a single battery component, M is the number of battery components of the solar array of the photovoltaic power generation system, Be the photoelectric conversion efficiency of the solar energy square array of photovoltaic power generation system, η _m is the photoelectric conversion efficiency of single cell assembly;

光伏发电系统输出功率P_solar的概率密度函数为：The probability density function of the output power P _solar of the photovoltaic power generation system is:

$f f (({P P}_{s the s o o l l a a r r})) = = \frac{Γ Γ ((α α + + β β))}{{R R}_{s the s o o l l a a r r} Γ Γ ((α α)) Γ Γ ((β β))} {((\frac{{P P}_{s the s o o l l a a r r}}{{R R}_{s the s o o l l a a r r}}))}^{α α - - 11} {((11 - - \frac{{P P}_{s the s o o l l a a r r}}{{R R}_{s the s o o l l a a r r}}))}^{β β - - 11} - - - - - - ((1212))$

式(12)中，R_solar＝r_maxAη为光伏发电系统的太阳能方阵的最大输出功率，r_max为最大辐射度，α、β均为Beta分布形状参数。In formula (12), R _solar =r _max Aη is the maximum output power of the solar array of the photovoltaic power generation system, r _max is the maximum irradiance, and α and β are Beta distribution shape parameters.

优选的，所述步骤(3)中，利用Choleskydecomposition对所述故障随机模型进行正交变换包括：Preferably, in the step (3), utilizing Choleskydecomposition to carry out orthogonal transformation to the fault random model includes:

由所述故障随机模型中故障线路模型、故障位置模型、故障类型模型、故障持续时间模型和故障阻抗模型组成5维随机变量p＝[p₁,p₂,…,p₅]^T，所述随机变量p的期望向量为u_p＝[u₁,u₂,…,u₅]^T，所述随机变量p的协方差矩阵C_p为：The 5-dimensional random variable p=[p ₁ ,p ₂ ,…,p ₅ ] ^T is composed of the fault line model, fault location model, fault type model, fault duration model and fault impedance model in the fault random model, and the The expected vector of random variable p is u _p =[u ₁ ,u ₂ ,…,u ₅ ] ^T , and the covariance matrix C _p of said random variable p is:

${C C}_{p p} = = [\begin{matrix} {σ σ}_{{p p}_{11}}^{22} & {σ σ}_{{p p}_{11} {p p}_{22}} & {σ σ}_{{p p}_{11} {p p}_{33}} & {σ σ}_{{p p}_{11} {p p}_{44}} & {σ σ}_{{p p}_{11} {p p}_{55}} \\ {σ σ}_{{p p}_{22} {p p}_{11}} & {σ σ}_{{p p}_{22}}^{22} & {σ σ}_{{p p}_{22} {p p}_{33}} & {σ σ}_{{p p}_{22} {p p}_{44}} & {σ σ}_{{p p}_{22} {p p}_{55}} \\ {σ σ}_{{p p}_{33} {p p}_{11}} & {σ σ}_{{p p}_{33} {p p}_{22}} & {σ σ}_{{p p}_{33}}^{22} & {σ σ}_{{p p}_{33} {p p}_{44}} & {σ σ}_{{p p}_{33} {p p}_{55}} \\ {σ σ}_{{p p}_{44} {p p}_{11}} & {σ σ}_{{p p}_{44} {p p}_{22}} & {σ σ}_{{p p}_{44} {p p}_{33}} & {σ σ}_{{p p}_{44}}^{22} & {σ σ}_{{p p}_{44} {p p}_{55}} \\ {σ σ}_{{p p}_{55} {p p}_{11}} & {σ σ}_{{p p}_{55} {p p}_{22}} & {σ σ}_{{p p}_{55} {p p}_{33}} & {σ σ}_{{p p}_{55} {p p}_{44}} & {σ σ}_{{p p}_{2525}}^{22} \end{matrix}] - - - - - - ((1313))$

确定所述随机变量p的偏导系数λ₃，公式为：Determine the partial derivative coefficient λ ₃ of the random variable p, the formula is:

${λ λ}_{33} = = d d i i a a g g (({λ λ}_{{p p}_{11},, 33},, ... ...,, {λ λ}_{{p p}_{l l},, 33},, ... ... {λ λ}_{{p p}_{55},, 33})) - - - - - - ((1414))$

式(14)中，为所述随机变量p中第l个随机变量p_l的偏导系数，l∈[1,5]；In formula (14), is the partial derivative coefficient of the lth random variable p _l in the random variable p, l∈[1,5];

确定所述随机变量p的不相关矩阵q的公式为：The formula for determining the uncorrelated matrix q of the random variable p is:

q＝Bp(15)q=Bp(15)

式(15)中，B为中间矩阵；In formula (15), B is the intermediate matrix;

对所述随机变量p的协方差矩阵C_p进行正交变换，公式为：Carry out orthogonal transformation to the covariance matrix C _p of described random variable p, the formula is:

C_p＝LL^T(16)C _p =LL ^T (16)

式(16)中，L为所述协方差矩阵C_p的下三角阵；In formula (16), L is the lower triangular matrix of described covariance matrix C _p ;

则确定所述不相关矩阵q的期望向量u_q的公式为：Then the formula for determining the expected vector u _q of the uncorrelated matrix q is:

u_q＝L^-1u_p(17)u _q =L ^-1 u _p (17)

式(17)中，u_p为所述随机变量p的期望向量；In formula (17), u _p is the expectation vector of described random variable p;

确定所述不相关矩阵q中第r个元素q_r的偏导系数的公式为：Determine the partial derivative coefficient of the rth element q _r in the uncorrelated matrix q The formula is:

${λ λ}_{{q q}_{r r},, 33} = = {Σ Σ}_{l l = = 11}^{55} {(({L L}_{r r l l}^{- - 11}))}^{33} {λ λ}_{{p p}_{l l},, 33} {σ σ}_{{p p}_{l l}}^{33} - - - - - - ((1818))$

式(18)中，为所述协方差矩阵C_p的下三角阵L的第r行第l列元素，r,l∈[1,5]。In formula (18), is the element in row r and column l of the lower triangular matrix L of the covariance matrix C _p , r,l∈[1,5].

优选的，所述步骤(4)中，采用点估计法对所述三相不对称配电网络的故障随机模型和DG随机模型进行处理包括：Preferably, in the step (4), processing the fault stochastic model and the DG stochastic model of the three-phase asymmetric power distribution network using the point estimation method includes:

由所述故障随机模型中故障线路模型、故障位置模型、故障类型模型、故障持续时间模型和故障阻抗模型以及所述DG随机模型中风电机组输出功率和光伏发电系统输出功率组成7维的随机变量X＝[X_1,X₂,…,X₇]^T，设Y＝h(X)是以所述随机变量X为变量的非线性函数，为所述随机变量X中第i个随机变量的概率密度函数，i∈[1,7]；A 7-dimensional random variable is composed of the fault line model, fault location model, fault type model, fault duration model, and fault impedance model in the fault random model, as well as the wind turbine output power and photovoltaic power generation system output power in the DG stochastic model X=[X _1, X ₂ ,…,X ₇ ] ^T , suppose Y=h(X) is a non-linear function with the random variable X as a variable, is the probability density function of the i-th random variable in the random variable X, i∈[1,7];

从所述随机变量X中第i个随机变量X_i中提取两个估计点，其中，第k个估计点x_i,k计算公式为：Two estimated points are extracted from the i-th random variable X _i in the random variable X, wherein, the k-th estimated point x _i,k calculation formula is:

x_i,k＝μ_i+ξ_i,kσ_i(19)x _i,k =μ _i +ξ _i,k σ _i (19)

式(19)中，μ_i为的期望，σ_i为的标准差，ξ_i,k为x_i,k对应的位置系数，k＝1,2；In formula (19), μ _i is The expectation of σ _i is The standard deviation of , ξ _i,k is the position coefficient corresponding to x _i,k , k=1,2;

按下式确定所述以所述随机变量X为变量的非线性函数Y＝h(X)的3阶矩的估计值：The estimated value of the 3rd moment of the nonlinear function Y=h(X) with the random variable X as the variable is determined as follows:

$E E. (({Y Y}^{j j})) &cong; &cong; {Σ Σ}_{i i = = 11}^{77} {Σ Σ}_{k k = = 11}^{22} {ω ω}_{i i,, k k} \times \times {[[h h (({μ μ}_{11},, {μ μ}_{22},, ... ... {μ μ}_{i i - - 11},, {x x}_{i i,, k k},, {μ μ}_{i i + + 11} ... ...,, {μ μ}_{77}))]]}^{j j} - - - - - - ((2020))$

式(20)中，j＝1,2,3，k＝1,2，i∈[1,7]，ω_i,k为x_i,k对应的权重系数，μ_i-1为的期望，μ_i+1为的期望；In formula (20), j=1,2,3, k=1,2, i∈[1,7], ω _i,k is the weight coefficient corresponding to x _i,k , μ _i-1 is The expectation of μ _i+1 is expectations;

其中，x_i,k对应的权重系数ω_i,k及位置系数ξ_i,k满足方程：Among them, the weight coefficient ω _i _{, k corresponding to x i,} k and the position coefficient ξ _{i, k} satisfy the equation:

$\{\begin{matrix} {Σ Σ}_{k k = = 11}^{22} {ω ω}_{i i,, k k} {(({ξ ξ}_{i i,, k k}))}^{j j} = = {λ λ}_{i i,, j j} & j j = = 11,, 22,, 33 \\ {Σ Σ}_{k k = = 11}^{22} {ω ω}_{i i,, k k} = = \frac{11}{77} \end{matrix} - - - - - - ((21 twenty one))$

式(21)中，λ_i,j为所述随机变量X中第i个随机变量X_i的j阶中心矩；In formula (21), λ _i,j is the j-order central moment of the i-th random variable X _i in the random variable X;

当j＝1,2时，λ_i,1＝0，λ_i,2＝1，则x_i,k对应的权重系数ω_i,k及位置系数ξ_i,k满足方程：When j=1,2, λ _i,1 =0, λ _i,2 =1, then the weight coefficient ω _i,k and the position coefficient ξ i, _{k corresponding to x i} _,k satisfy the equation:

$\{\begin{matrix} {ξ ξ}_{i i,, k k} = = \frac{{λ λ}_{i i,, 33} + + {((- - 11))}^{33 - - k k} \sqrt{2828 + + {λ λ}_{i i,, 33}^{22}}}{22} \\ {ω ω}_{i i,, k k} = = \frac{{((- - 11))}^{33 - - k k} {ξ ξ}_{i i,, 33 - - k k}^{j j}}{77 (({ξ ξ}_{i i,, 22} - - {ξ ξ}_{i i,, 11}))} = = - - \frac{{((- - 11))}^{33 - - k k} {ξ ξ}_{i i,, 33 - - k k}^{j j}}{77 \sqrt{2828 + + {λ λ}_{i i,, 33}^{22}}} \end{matrix} - - - - - - ((22 twenty two)) . .$

优选的，所述步骤(6)中，设Y_i为所述两组相关的仿真方案的随机变量中第i个元素，i∈[1,14]，则通过Cornish-Fisher级数分别确定所述两组相关的仿真方案的随机变量中元素的概率密度函数的公式为：Preferably, in the step (6), let Y _i be the i-th element in the random variables of the two groups of relevant simulation schemes, i∈[1,14], then determine the values respectively by the Cornish-Fisher series The formula of the probability density function of the element in the random variable of the above-mentioned two groups of related simulation schemes is:

式(23)中，为ξ_i的标准正态分布概率密度函数，χ₃为三阶半不变量；In formula (23), is the standard normal distribution probability density function of _ξi , and χ3 is a _third -order semi-invariant;

其中，χ₃的值为Y_i的偏导系数，ξ_i为Y_i标准形式，公式为：Among them, the value of _χ3 is the partial derivative coefficient of Y _i , and ξ _i is the standard form of Y _i , and the formula is:

ξ_i＝(x-μ_i)/σ_i(24)ξ _i =(x-μ _i )/σ _i (24)

式(24)中，μ_i为Y_i的均值，σ_i为Y_i的方差。In formula (24), μ _i is the mean value of Y _i , and σ _i is the variance of Y _i .

本发明的有益效果：Beneficial effects of the present invention:

本发明提供的一种三相不对称配电网络电压暂降评估方法，针对配电网络不对称问题进行研究，利用乔里斯基分解以及两点估计法，将随机概率问题转化为多个确定性问题，然后采用已有配电网分析软件搭建模型，进行有源配电网的电压暂降仿真，统计电压暂降的统计量特征，分析电网中的薄弱环节，基于Cornish-Fisher级数建立各节点的电压暂降概率密度函数，计算电压暂降指标，实现对三相不对称配电网的电压暂降评估，综合考虑了配电网中故障类型与故障线路的相关性以及配电网中各种短路故障来仿真整个配电网的特性，能够适用于三相不对称网络以及三相对称网络，为采取抑制电压暂降的措施提供参考，提高配电网的供电可靠性。The present invention provides a three-phase asymmetric power distribution network voltage sag evaluation method, which studies the asymmetric problem of power distribution network, and uses Cholesky decomposition and two-point estimation method to convert random probability problems into multiple deterministic problems problem, and then use the existing distribution network analysis software to build a model, carry out the voltage sag simulation of the active distribution network, count the statistical characteristics of the voltage sag, analyze the weak links in the power grid, and establish each model based on the Cornish-Fisher series The voltage sag probability density function of the node calculates the voltage sag index, and realizes the voltage sag evaluation of the three-phase asymmetric distribution network, comprehensively considering the correlation between the fault type and the fault line in the distribution network and the distribution network. Various short-circuit faults are used to simulate the characteristics of the entire distribution network, which can be applied to three-phase asymmetrical networks and three-phase symmetrical networks, providing reference for taking measures to suppress voltage sags, and improving the reliability of power supply in the distribution network.

附图说明Description of drawings

图1是本发明一种三相不对称配电网络电压暂降评估方法的流程图。Fig. 1 is a flow chart of a method for evaluating voltage sags in a three-phase asymmetric power distribution network according to the present invention.

具体实施方式detailed description

下面结合附图对本发明的具体实施方式作详细说明。The specific implementation manners of the present invention will be described in detail below in conjunction with the accompanying drawings.

为使本发明实施例的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例，都属于本发明保护的范围。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments It is a part of embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.

本发明提供的一种三相不对称配电网络电压暂降评估方法，针对配电网络不对称问题进行研究，利用乔里斯基分解(Choleskydecomposition)以及两点估计法，将随机概率问题转化为多个确定性问题，然后采用已有配电网分析软件搭建模型，进行有源配电网的电压暂降仿真，统计电压暂降的统计量特征，分析电网中的薄弱环节，基于Cornish-Fisher级数建立各节点的电压暂降概率密度函数，计算电压暂降指标，实现对三相不对称配电网的电压暂降评估，为采取抑制电压暂降的措施提供参考，提高配电网的供电可靠性，如图1所示，包括：The present invention provides a three-phase asymmetric power distribution network voltage sag evaluation method, which studies the problem of power distribution network asymmetry, uses Cholesky decomposition (Cholesky decomposition) and two-point estimation method to convert the random probability problem into a multiple A deterministic problem, and then use the existing distribution network analysis software to build a model, carry out the voltage sag simulation of the active distribution network, count the statistical characteristics of the voltage sag, and analyze the weak links in the power grid, based on the Cornish-Fisher level Establish the voltage sag probability density function of each node, calculate the voltage sag index, realize the voltage sag evaluation of the three-phase asymmetric distribution network, provide a reference for taking measures to suppress the voltage sag, and improve the power supply of the distribution network Reliability, as shown in Figure 1, includes:

具体的，所述步骤(1)中，利用蒙特卡洛仿真方式建立所述三相不对称配电网络的故障随机模型，包括：Specifically, in the step (1), the fault stochastic model of the three-phase asymmetric power distribution network is established by means of Monte Carlo simulation, including:

${F f}_{L L i i n no e e} = = \{\begin{matrix} 11,, x x < < {P P}_{L L i i n no e e,, 11} \\ 22,, {P P}_{L L i i n no e e,, 11} \leq \leq x x < < {P P}_{L L i i n no e e,, 11} + + {P P}_{L L i i n no e e,, 22} \\ . . \\ . . \\ . . \\ M m,, {P P}_{L L i i n no e e,, 11} + + {P P}_{L L i i n no e e,, 22} + + ... ... + + {P P}_{L L i i n no e e,, M m - - 11} \leq \leq x x < < 11 \end{matrix} - - - - - - ((11))$

F_Loc＝y*100％(2)F _Loc = y*100% (2)

F_Type＝LG(5)。F _Type =LG(5).

F_Dur＝μ(6)F _Dur = μ(6)

F_Res＝τ(7)F _Res =τ(7)

所述步骤(2)中，利用蒙特卡洛仿真方式建立所述三相不对称配电网络的DG随机模型，包括：In the step (2), the DG stochastic model of the three-phase asymmetric power distribution network is established by Monte Carlo simulation, including:

P_ω＝P_windN_wtg(9)P _ω ＝P _wind N _wtg (9)

P_solar＝rAη(11)P _solar =rAη(11)

所述步骤(3)中，利用Choleskydecomposition对所述故障随机模型进行正交变换包括：In the step (3), utilizing Choleskydecomposition to carry out orthogonal transformation to the fault stochastic model includes:

q＝Bp(15)q=Bp(15)

式(15)中，B为中间矩阵；In formula (15), B is the intermediate matrix;

C_p＝LL^T(16)C _p =LL ^T (16)

u_q＝L^-1u_p(17)u _q =L ^-1 u _p (17)

所述步骤(4)中，采用点估计法对所述三相不对称配电网络的故障随机模型和DG随机模型进行处理包括：In the step (4), the processing of the fault random model and the DG random model of the three-phase asymmetrical power distribution network using the point estimation method includes:

由所述故障随机模型中故障线路模型、故障位置模型、故障类型模型、故障持续时间模型和故障阻抗模型以及所述DG随机模型中风电机组输出功率和光伏发电系统输出功率组成7维的随机变量X＝[X₁,X₂,…,X₇]^T，设Y＝h(X)是以所述随机变量X为变量的非线性函数，为所述随机变量X中第i个随机变量的概率密度函数，i∈[1,7]；A 7-dimensional random variable is composed of the fault line model, fault location model, fault type model, fault duration model, and fault impedance model in the fault random model, as well as the wind turbine output power and photovoltaic power generation system output power in the DG stochastic model X=[X ₁ ,X ₂ ,…,X ₇ ] ^T , let Y=h(X) be a nonlinear function with the random variable X as a variable, is the probability density function of the i-th random variable in the random variable X, i∈[1,7];

x_i,k＝μ_i+ξ_i,kσ_i(19)x _i,k =μ _i +ξ _i,k σ _i (19)

所述步骤(5)中，采用Choleskydecomposition方式对所述两组仿真方案的随机变量进行反分解，获取所述两组仿真方案的随机变量对应的两组相关的仿真方案的随机变量；In described step (5), adopt Choleskydecomposition mode to carry out anti-decomposition to the random variable of described two groups of simulation schemes, obtain the random variable of two groups of related simulation schemes corresponding to the random variable of described two groups of simulation schemes;

其中，所述两组仿真方案的随机变量为不相关的随机变量，不相关的随机变量无法进行仿真计算，因此需要进行反变换，将所述两组仿真方案的随机变量对应的两组相关的仿真方案的随机变量，比如：只有两相的，经过乔里斯基分解后故障类型可能为三相接地，但是这是不可能，因此要反变换回去。Wherein, the random variables of the two groups of simulation schemes are uncorrelated random variables, and the uncorrelated random variables cannot be simulated and calculated, so inverse transformation is required, and the two groups of related random variables corresponding to the random variables of the two groups of simulation schemes are For the random variables of the simulation scheme, for example, if there are only two phases, the fault type may be three-phase grounding after Cholesky decomposition, but this is impossible, so it needs to be transformed back.

所述步骤(6)中，设Y_i为所述两组相关的仿真方案的随机变量中第i个元素，i∈[1,14]，则通过Cornish-Fisher级数分别确定所述两组相关的仿真方案的随机变量中元素的概率密度函数的公式为：In the step (6), let Y _i be the i-th element in the random variables of the two groups of relevant simulation schemes, i∈[1,14], then determine the two groups respectively by the Cornish-Fisher series The formula for the probability density function of the element in the random variable of the relevant simulation scenario is:

ξ_i＝(x-μ_i)/σ_i(24)ξ _i =(x-μ _i )/σ _i (24)

最后应当说明的是：以上实施例仅用以说明本发明的技术方案而非对其限制，尽管参照上述实施例对本发明进行了详细的说明，所属领域的普通技术人员应当理解：依然可以对本发明的具体实施方式进行修改或者等同替换，而未脱离本发明精神和范围的任何修改或者等同替换，其均应涵盖在本发明的权利要求保护范围之内。Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: the present invention can still be Any modifications or equivalent replacements that do not depart from the spirit and scope of the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for assessing voltage sags in a three-phase asymmetric power distribution network, characterized in that the method comprises:

(1) set up the fault stochastic model of described three-phase asymmetric power distribution network;

(2) set up the DG stochastic model of described three-phase asymmetric power distribution network;

(3) performing an orthogonal transformation on the fault random model to obtain an irrelevant fault random model corresponding to the fault random model;

(4) adopt point estimation method to process the random variable that described irrelevant failure stochastic model and DG stochastic model form, obtain the random variable of two groups of simulation schemes;

(5) adopt Choleskydecomposition mode to decompose the random variable of described two groups of simulation schemes, obtain the random variable of two groups of relevant simulation schemes corresponding to the random variable of described two groups of simulation schemes;

(6) Determine the probability density functions of the elements in the random variables of the two groups of related simulation schemes respectively through the Cornish-Fisher series.

2. the method for claim 1, is characterized in that, in described step (1), utilizes the Monte Carlo simulation mode to set up the failure stochastic model of described three-phase asymmetric power distribution network, comprising:

(1-1) The fault line model of the three-phase asymmetric power distribution network is established as follows:

{F f}_{L L i i n no e e} = = \{\begin{matrix} 11,, x x < < {P P}_{L L i i n no e e,, 11} \\ 22,, {P P}_{L L i i n no e e,, 11} \leq \leq x x < < {P P}_{L L i i n no e e,, 11} + + {P P}_{L L i i n no e e,, 22} \\ . . \\ . . \\ . . \\ M m,, {P P}_{L L i i n no e e,, 11} + + {P P}_{L L i i n no e e,, 22} + + ... ... + + {P P}_{L L i i n no e e,, M m - - 11} \leq \leq x x < < 11 \end{matrix} - - - - - - ((11))

In formula (1), x is a random number that obeys the uniform distribution of [0,1], that is, x~U[0,1], F _Line is the number of the fault branch, and M is the number in the three-phase asymmetric distribution network The total number of branches, P _Line,i is the failure rate of the i-th branch in the three-phase asymmetric power distribution network, i∈{1,M}, U is a uniform distribution function;

(1-2) The fault location model of the three-phase asymmetric power distribution network is established as follows:

F _Loc = y*100% (2)

In formula (2), y is a random number that obeys the uniform distribution of [0,1], that is, y~U[0,1], and F _Loc is the length of the branch before the fault point of the fault branch F _Line and the length of the fault branch F Line The percentage of the ratio of the total length of _Line ;

(1-3) Establishing the fault type model of the three-phase asymmetric power distribution network includes:

If the fault branch F _Line of the three-phase asymmetric power distribution network is three-phase, then the fault type model corresponding to the fault branch F _Line of the three-phase asymmetric power distribution network is established as follows:

{F f}_{T T y the y p p e e} = = \{\begin{matrix} 33 L L G G,, & z z < < {P P}_{33 L L G G} \\ 22 L L,, & {P P}_{33 L L G G} \leq \leq z z < < {P P}_{33 L L G G} + + {P P}_{22 L L} \\ 22 L L G G,, & {P P}_{33 L L G G} + + {P P}_{22 L L} \leq \leq z z < < {P P}_{33 L L G G} + + {P P}_{22 L L} + + {P P}_{22 L L G G} \\ L L G G,, & {P P}_{33 L L G G} + + {P P}_{22 L L} + + {P P}_{22 L L G G} \leq \leq z z < < 11 \end{matrix} - - - - - - ((33))

In formula (3), z is a random number that obeys the uniform distribution of [0,1], that is, z~U[0,1], and F _Type is the fault branch F _Line corresponding to the three-phase asymmetric power distribution network Fault type, 3LG is three-phase ground short-circuit fault type, 2L is two-phase phase-to-phase short-circuit fault type, 2LG is two-phase ground short-circuit fault type, LG is single-phase ground short-circuit fault type, P _3LG is three-phase ground short-circuit fault type Occurrence probability, P _2L is the occurrence probability of two-phase phase-to-phase short-circuit fault, P _2LG is the occurrence probability of two-phase-to-ground short-circuit fault;

If the fault branch F _Line of the three-phase asymmetric power distribution network is two phases, then the fault type model corresponding to the fault branch F _Line of the three-phase asymmetric power distribution network is established as follows:

{F f}_{T T y the y p p e e} = = \{\begin{matrix} 22 L L,, & z z < < {P P}_{22 L L} \\ 22 L L G G,, & {P P}_{22 L L} \leq \leq z z < < {P P}_{22 L L} + + {P P}_{22 L L G G} \\ L L G G,, & {P P}_{22 L L} + + {P P}_{22 L L G G} \leq \leq z z < < 11 \end{matrix} - - - - - - ((44))

F _Type =LG(5).

(1-4) The fault duration model of the three-phase asymmetric power distribution network is established as follows:

F _Dur = μ(6)

In formula (6), μ is a random number that obeys the standard normal distribution with an expectation of 0.06s and a standard deviation of 0.01s, that is, μ~N[0.06,0.01], and F _Dur is the three-phase asymmetric distribution network The fault duration corresponding to the fault branch F _Line of ;

(1-5) The fault impedance model of the three-phase asymmetric power distribution network is established as follows:

F _Res =τ(7)

In formula (7), τ is a random number obeying the standard normal distribution with an expectation of 5Ω and a standard deviation of 1Ω, that is, τ~N[5,1], and F _Res is the fault of the three-phase asymmetric distribution network Fault impedance corresponding to branch F _Line .

3. the method for claim 1, is characterized in that, in described step (2), utilizes Monte Carlo simulation mode to set up the DG stochastic model of described three-phase asymmetric power distribution network, comprising:

(2-1) The fan power generation system adopts a linear curve model, and the relationship between the fan output power P _wind and the wind speed v is:

{P P}_{w w i i n no d d} = = \{\begin{matrix} 00,, & v v < < {v v}_{c c i i},, v v > > {v v}_{c c o o} \\ a a + + b b v v,, & {v v}_{c c i i} < < v v < < {v v}_{r r} \\ {p p}_{r r},, & {v v}_{r r} < < v v < < {v v}_{c c o o} \end{matrix} - - - - - - ((88))

In formula (8), Both are constants, v _r is the rated wind speed of the fan, P _r is the rated power of the fan, v _ci is the cut-in wind speed of the fan, v _co is the cut-out wind speed of the fan;

When the number of wind turbines is N _wtg , the model of wind turbine output power P _ω is:

P _ω ＝P _wind N _wtg (9)

When v _ci <v<v _r , the formula of the probability density function of wind turbine output power P _ω is:

In formula (10), K is the shape parameter of the Weibull distribution, C is the scale parameter of the Weibull distribution, f(P _ω ) is the probability density function of the active output of the wind turbine, Q _ω is the reactive output of the wind turbine, is the power factor;

(2-2) The output power P _solar model of the photovoltaic power generation system is:

P _solar =rAη(11)

In the formula (11), r is the radiance, the unit is W/m ² , is the total area of the solar array of the photovoltaic power generation system, A _m is the area of a single battery component, M is the number of battery components of the solar array of the photovoltaic power generation system, Be the photoelectric conversion efficiency of the solar energy square array of photovoltaic power generation system, η _m is the photoelectric conversion efficiency of single cell assembly;

The probability density function of the output power P _solar of the photovoltaic power generation system is:

f f (({P P}_{s the s o o l l a a r r})) = = \frac{Γ Γ ((α α + + β β))}{{R R}_{s the s o o l l a a r r} Γ Γ ((α α)) Γ Γ ((β β))} {((\frac{{P P}_{s the s o o l l a a r r}}{{R R}_{s the s o o l l a a r r}}))}^{α α - - 11} {((11 - - \frac{{P P}_{s the s o o l l a a r r}}{{R R}_{s the s o o l l a a r r}}))}^{β β - - 11} - - - - - - ((1212))

In formula (12), R _solar =r _max Aη is the maximum output power of the solar array of the photovoltaic power generation system, r _max is the maximum irradiance, and α and β are Beta distribution shape parameters.

4. The method according to claim 1, characterized in that, in the step (3), utilizing Choleskydecomposition to carry out orthogonal transformation to the fault stochastic model comprises:

The 5-dimensional random variable p=[p ₁ ,p ₂ ,…,p ₅ ] ^T is composed of the fault line model, fault location model, fault type model, fault duration model and fault impedance model in the fault random model, and the The expected vector of random variable p is u _p =[u ₁ ,u ₂ ,…,u ₅ ] ^T , and the covariance matrix C _p of said random variable p is:

{C C}_{p p} = = [\begin{matrix} {σ σ}_{{p p}_{11}}^{22} & {σ σ}_{{p p}_{11} {p p}_{22}} & {σ σ}_{{p p}_{11} {p p}_{33}} & {σ σ}_{{p p}_{11} {p p}_{44}} & {σ σ}_{{p p}_{11} {p p}_{55}} \\ {σ σ}_{{p p}_{22} {p p}_{11}} & {σ σ}_{{p p}_{22}}^{22} & {σ σ}_{{p p}_{22} {p p}_{33}} & {σ σ}_{{p p}_{22} {p p}_{44}} & {σ σ}_{{p p}_{22} {p p}_{55}} \\ {σ σ}_{{p p}_{33} {p p}_{11}} & {σ σ}_{{p p}_{33} {p p}_{22}} & {σ σ}_{{p p}_{33}}^{22} & {σ σ}_{{p p}_{33} {p p}_{44}} & {σ σ}_{{p p}_{33} {p p}_{55}} \\ {σ σ}_{{p p}_{44} {p p}_{11}} & {σ σ}_{{p p}_{44} {p p}_{22}} & {σ σ}_{{p p}_{44} {p p}_{33}} & {σ σ}_{{p p}_{44}}^{22} & {σ σ}_{{p p}_{44} {p p}_{55}} \\ {σ σ}_{{p p}_{55} {p p}_{11}} & {σ σ}_{{p p}_{55} {p p}_{22}} & {σ σ}_{{p p}_{55} {p p}_{33}} & {σ σ}_{{p p}_{55} {p p}_{44}} & {σ σ}_{{p p}_{2525}}^{22} \end{matrix}] - - - - - - ((1313))

Determine the partial derivative coefficient λ ₃ of the random variable p, the formula is:

λ ₃ ＝diag(λ _p1,3 ,...,λ _pl,3 ,...λ _p5,3 )(14)

In formula (14), is the partial derivative coefficient of the lth random variable p _l in the random variable p, l∈[1,5];

The formula for determining the uncorrelated matrix q of the random variable p is:

q=Bp(15)

In formula (15), B is the intermediate matrix;

Carry out orthogonal transformation to the covariance matrix C _p of described random variable p, the formula is:

C _p =LL ^T (16)

In formula (16), L is the lower triangular matrix of described covariance matrix C _p ;

Then the formula for determining the expected vector u _q of the uncorrelated matrix q is:

u _q =L ^-1 u _p (17)

In formula (17), u _p is the expectation vector of described random variable p;

Determine the partial derivative coefficient of the rth element q _r in the uncorrelated matrix q The formula is:

{λ λ}_{{q q}_{r r},, 33} = = {Σ Σ}_{l l = = 11}^{55} {(({L L}_{r r l l}^{- - 11}))}^{33} {λ λ}_{{p p}_{l l},, 33} {σ σ}_{{p p}_{l l}}^{33} - - - - - - ((1818))

In formula (18), is the element in row r and column l of the lower triangular matrix L of the covariance matrix C _p , r,l∈[1,5].

5. the method for claim 1, is characterized in that, in described step (4), adopting point estimation method to process the fault stochastic model and DG stochastic model of described three-phase asymmetric power distribution network comprises:

A 7-dimensional random variable is composed of the fault line model, fault location model, fault type model, fault duration model, and fault impedance model in the fault random model, as well as the wind turbine output power and photovoltaic power generation system output power in the DG stochastic model X=[X ₁ ,X ₂ ,…,X ₇ ] ^T , suppose Y=h(X) is a nonlinear function with the random variable X as a variable, is the probability density function of the i-th random variable in the random variable X, i∈[1,7];

Two estimated points are extracted from the i-th random variable X _i in the random variable X, wherein, the k-th estimated point x _i,k calculation formula is:

x _i,k =μ _i +ξ _i,k σ _i (19)

In formula (19), μ _i is The expectation of σ _i is The standard deviation of , ξ _i,k is the position coefficient corresponding to x _i,k , k=1,2;

The estimated value of the 3rd moment of the nonlinear function Y=h(X) with the random variable X as the variable is determined as follows:

E E. (({Y Y}^{j j})) &cong; &cong; {Σ Σ}_{i i = = 11}^{77} {Σ Σ}_{k k = = 11}^{22} {ω ω}_{i i,, k k} \times \times {[[h h (({μ μ}_{11},, {μ μ}_{22},, ... ... {μ μ}_{i i - - 11},, {x x}_{i i,, k k},, {μ μ}_{i i + + 11} ... ...,, {μ μ}_{77}))]]}^{j j} - - - - - - ((2020))

In formula (20), j=1,2,3, k=1,2, i∈[1,7], ω _i,k is the weight coefficient corresponding to x _i,k , μ _i-1 is The expectation of μ _i+1 is expectations;

Among them, the weight coefficient ω _i _{, k corresponding to x i,} k and the position coefficient ξ _{i, k} satisfy the equation:

\{\begin{matrix} {Σ Σ}_{k k = = 11}^{22} {ω ω}_{i i,, k k} {(({ξ ξ}_{i i,, k k}))}^{j j} = = {λ λ}_{i i,, j j} \\ {Σ Σ}_{k k = = 11}^{22} {ω ω}_{i i,, k k} = = \frac{11}{77} \end{matrix},, j j = = 11,, 22,, 33 - - - - - - ((21 twenty one))

In formula (21), λ _i,j is the j-order central moment of the i-th random variable X _i in the random variable X;

When j=1,2, λ _i,1 =0, λ _i,2 =1, then the weight coefficient ω _i,k and the position coefficient ξ i, _{k corresponding to x i} _,k satisfy the equation:

\{\begin{matrix} {ξ ξ}_{i i,, k k} = = \frac{{λ λ}_{i i,, 33} + + {((- - 11))}^{33 - - k k} \sqrt{2828 + + {λ λ}_{i i,, 33}^{22}}}{22} \\ {ω ω}_{i i,, k k} = = \frac{{((- - 11))}^{33 - - k k} {ξ ξ}_{i i,, 33 - - k k}^{j j}}{77 (({ξ ξ}_{i i,, 22} - - {ξ ξ}_{i i,, 11}))} = = - - \frac{{((- - 11))}^{33 - - k k} {ξ ξ}_{i i,, 33 - - k k}^{j j}}{77 \sqrt{2828 + + {λ λ}_{i i,, 33}^{22}}} \end{matrix} - - - - - - ((22 twenty two)) . .

6. the method for claim 1, is characterized in that, in described step (6), let Y _i be the ith element in the random variable of described two groups of relevant simulation schemes, i∈[1,14 ], then the formulas for determining the probability density functions of the elements in the random variables of the two groups of relevant simulation schemes respectively by the Cornish-Fisher series are:

In formula (23), is the standard normal distribution probability density function of _ξi , and χ3 is a _third -order semi-invariant;

Among them, the value of _χ3 is the partial derivative coefficient of Y _i , and ξ _i is the standard form of Y _i , and the formula is:

ξ _i =(x-μ _i )/σ _i (24)

In formula (24), μ _i is the mean value of Y _i , and σ _i is the variance of Y _i .