CN104899353B - A kind of power quality disturbance localization method based on evidence theory - Google Patents

A kind of power quality disturbance localization method based on evidence theory Download PDF

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CN104899353B
CN104899353B CN201510223195.0A CN201510223195A CN104899353B CN 104899353 B CN104899353 B CN 104899353B CN 201510223195 A CN201510223195 A CN 201510223195A CN 104899353 B CN104899353 B CN 104899353B
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翁国庆
王强
黄飞腾
张有兵
谢路耀
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Hangzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
Zhejiang Zhongxin Electric Power Engineering Construction Co Ltd
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Zhejiang University of Technology ZJUT
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Abstract

一种基于证据融合理论的电能质量扰动源定位方法,包括:确定系统覆盖矩阵AL×N及依据扰动功率和扰动能量两种判据实现的方向判定矩阵Bv,N×1;构建表征扰动方向判定结果各影响因素的可信度函数;基于D‑S证据理论对两种不同判据各自获得的不确定扰动方向判定信息进行融合处理;基于融合后的扰动方向判定矩阵和矩阵算法进行电能质量扰动源定位决策;基于多证据源间的一致性指标进行电能质量扰动源定位结果的可信度评估。

A method for locating power quality disturbance sources based on evidence fusion theory, including: determining the system coverage matrix AL×N and the direction determination matrix B v,N×1 based on the two criteria of disturbance power and disturbance energy; The credibility function of each influencing factor of the direction judgment result; based on the D‑S evidence theory, the uncertain disturbance direction judgment information obtained by two different criteria is fused; based on the fused disturbance direction judgment matrix and matrix algorithm, the electric energy Quality disturbance source location decision-making; based on the consistency index among multiple evidence sources, the credibility evaluation of the power quality disturbance source location results is carried out.

Description

一种基于证据理论的电能质量扰动源定位方法A Power Quality Disturbance Source Location Method Based on Evidence Theory

技术领域technical field

本发明涉及一种基于证据理论并计及监测可信度的电能质量扰动源定位方法,属电气工程和电能质量领域。The invention relates to a method for locating a power quality disturbance source based on evidence theory and taking monitoring reliability into account, belonging to the fields of electrical engineering and power quality.

背景技术Background technique

近年来,随着电网中敏感设备激增及电力市场化进程不断推进,电能质量扰动造成的经济损失迅速增加,人们对责任确定的诉求日益强烈。电能质量扰动源(PowerQuality Disturbance Source,PQDS)定位,是指当目标电网区域中发生电能质量扰动事件时,通过系统中布置的电能质量监测装置(Power Quality Monitor,PQM)及电能质量监测中心对扰动信号进行采集、计算、分析和处理,进而实现PQDS确切线路或位置的智能诊断。PQDS的快速、准确定位,是电力管理部门尽快查明扰动原因、明确责任、排除扰动源、采取合理改善措施,从而保证电能质量满足用户需求的前提和基础,也是未来智能配电网中网络化电能质量监测系统(Network Power Quality Monitoring System,NPQMS)的核心高级功能之一。In recent years, with the rapid increase of sensitive equipment in the power grid and the continuous advancement of the power marketization process, the economic losses caused by power quality disturbances have increased rapidly, and people's demands for determination of responsibility have become increasingly strong. Power quality disturbance source (Power Quality Disturbance Source, PQDS) location refers to when a power quality disturbance event occurs in the target grid area, the power quality monitoring device (Power Quality Monitor, PQM) and power quality monitoring center arranged in the system detect the disturbance The signal is collected, calculated, analyzed and processed, and then the intelligent diagnosis of the exact line or position of the PQDS is realized. The rapid and accurate positioning of PQDS is the premise and basis for the power management department to find out the cause of the disturbance as soon as possible, clarify the responsibility, eliminate the source of the disturbance, and take reasonable improvement measures to ensure that the power quality meets the needs of users. One of the core advanced functions of the Network Power Quality Monitoring System (NPQMS).

当前,电能质量相关的研究热点主要集中在电能质量信号的辨识处理、电能质量评价指标、电能质量监测装置和系统的结构、电能质量优化与控制等方向,关于PQDS定位方法的研究成果较少。申请号为2013104676593和2014101006927的发明专利分别提出一种基于有限电能质量监测点的电压暂降源定位方法和通过计算故障线路两端电能质量监测节点监测到问题的时间差而对故障源进行定位方法,但其主要思路是基于故障距离测定的方式解决少量线路上具体故障位置的确定;申请号为2008100612549的发明专利提出一种基于矩阵算法原理的配电网PQDS自动定位方法,但其定位准确性过度依赖各测点PQM的扰动方向判别结果的可靠性和信息的完备性;申请号为2014105375263的发明专利提出一种基于粒子群优化算法的计及监测可信度的矩阵定位改进算法。本发明专利针对各种影响PQM扰动方向判定结果可靠性的因素、影响程度表征函数、基于多证据源的PQDS智能定位方法进行研究,建立了多种表征方向判定信息可信度函数,基于证据理论融合两种不同扰动方向判据信息实现了在部分监测信息有误情况下的PQDS的自动精确定位,并提出了运用证据源一致性构建评价函数实现定位结果的可靠性评价。At present, the research hotspots related to power quality mainly focus on the identification and processing of power quality signals, power quality evaluation indicators, power quality monitoring devices and system structures, power quality optimization and control, etc. There are few research results on PQDS positioning methods. The invention patents with the application numbers 2013104676593 and 2014101006927 proposed a voltage sag source location method based on limited power quality monitoring points and a method of locating the fault source by calculating the time difference between the power quality monitoring nodes at both ends of the fault line to detect the problem, respectively. However, its main idea is to solve the determination of specific fault locations on a small number of lines based on fault distance measurement; the invention patent with application number 2008100612549 proposes a distribution network PQDS automatic positioning method based on the principle of matrix algorithm, but its positioning accuracy is too high Relying on the reliability and completeness of the information of the disturbance direction discrimination results of the PQM of each measuring point; the invention patent with the application number 2014105375263 proposes an improved matrix positioning algorithm based on the particle swarm optimization algorithm and considering the monitoring reliability. The patent of the present invention studies various factors that affect the reliability of the PQM disturbance direction determination results, the influence degree characterization function, and the PQDS intelligent positioning method based on multiple evidence sources, and establishes a variety of characterization direction determination information credibility functions, based on evidence theory The fusion of two different disturbance direction criterion information realizes automatic and accurate positioning of PQDS when some monitoring information is wrong, and proposes to use the consistency of evidence sources to construct an evaluation function to realize the reliability evaluation of positioning results.

发明内容Contents of the invention

本发明要克服现有PQDS定位算法准确性严重依赖NPQMS中各监测点PQM扰动方向判定结果可靠性以及方向判定信息完备性的问题,综合考虑扰动信号强弱、扰动电流特征、分布式电源接入以及状态估计误差等因素对扰动方向判定可靠性的影响,提供一种基于证据融合理论的PQDS自动定位方法,实现在NPQMS中部分监测信息缺失、有误或者扰动方向判定结果不理想的情况下,仍可实现PQDS的准确定位,且可评估其定位结果的可信度。The present invention overcomes the problem that the accuracy of the existing PQDS positioning algorithm is heavily dependent on the reliability of the PQM disturbance direction determination results of each monitoring point in the NPQMS and the completeness of the direction determination information, and comprehensively considers the strength of the disturbance signal, the characteristics of the disturbance current, and the access of distributed power sources. As well as the influence of factors such as state estimation errors on the reliability of the determination of the disturbance direction, a PQDS automatic positioning method based on the evidence fusion theory is provided to realize that when some monitoring information in NPQMS is missing, wrong or the result of the determination of the disturbance direction is not ideal, Accurate positioning of PQDS can still be achieved, and the credibility of its positioning results can be evaluated.

本发明为实现上述目的,提出了一种基于证据融合理论的PQDS定位方法,如附图1所示,其过程包括如下步骤:In order to achieve the above object, the present invention proposes a PQDS positioning method based on evidence fusion theory, as shown in accompanying drawing 1, and its process includes the following steps:

1、确定系统覆盖矩阵AL×N及方向判定矩阵Bv,N×1。在含有L条线段、N个PQM的配电网络中,可分别构建用以表征所有线路与PQM位置关系的覆盖矩阵AL×N,以及用以表征系统中某位置发生扰动事件时所有监测点PQM依据扰动功率(Disturbance Power,DP)和扰动能量(Disturbance Energy,DE)这两种不同扰动方向判据实现的扰动方向判定结果的方向矩阵Bv,N×1。其中,v=1表示依据扰动功率判据;v=2表示依据扰动能量判据。AL×N和Bv,N×1中各元素aji和bv,i的赋值原则如式(1)、(2)所示。1. Determine the system coverage matrix AL×N and the direction determination matrix B v,N×1 . In a power distribution network containing L line segments and N PQMs, the coverage matrix A L×N used to represent the positional relationship between all lines and PQMs can be constructed respectively, and it can be used to represent all monitoring points when a disturbance event occurs in a certain position in the system PQM is the direction matrix B v,N×1 of the disturbance direction determination results realized based on two different disturbance direction criteria, the disturbance power (DP) and the disturbance energy (DE). Wherein, v=1 means that the criterion is based on the disturbance power; v=2 means that it is based on the criterion of the disturbance energy. The assignment principles of each element a ji and b v,i in AL ×N and B v,N×1 are shown in formulas (1) and (2).

2、构建表征扰动方向判定结果各影响因素的可信度函数。定义PQM方向判定信息“可信度”概念,分别构建表征多种可信度分项函数指标,用以描述扰动信号强弱、扰动电流特征、分布式电源接入以及虚拟PQM状态估计误差等各种因素在不同情景下对扰动方向判定结果可信度的影响程度,从而实现各监测点方向判定过程及结果的模糊量化。2. Construct the credibility function representing each influencing factor of the disturbance direction determination result. Define the concept of "credibility" of PQM direction determination information, and construct a variety of reliability sub-item function indicators to describe the strength of disturbance signals, disturbance current characteristics, distributed power access, and virtual PQM state estimation errors. The degree of influence of these factors on the credibility of the results of the disturbance direction determination under different scenarios, so as to realize the fuzzy quantification of the direction determination process and results of each monitoring point.

步骤201,构建表征扰动信号强弱的方向判定可信度函数。扰动信号特征量的强弱程度,可由监测点所测得的扰动信号特征量与系统稳定时信号特征量的相对比值来体现。据此,构建表征扰动强弱的方向判定可信度γiStep 201, constructing a direction determination credibility function that characterizes the strength of the disturbance signal. The strength of the characteristic quantity of the disturbance signal can be reflected by the relative ratio of the characteristic quantity of the disturbance signal measured at the monitoring point to the signal characteristic quantity when the system is stable. Based on this, the direction judgment credibility γ i representing the strength of the disturbance is constructed:

式中,Ev(i)表示系统稳定时第i个监测点的信号特征量;Δev(i)表示PQMi扰动信号特征量;v=1表示取特征量为扰动功率DP;v=2表示取特征量为扰动能量DE。In the formula, E v (i) represents the signal characteristic quantity of the i-th monitoring point when the system is stable; Δev (i) represents the characteristic quantity of the PQM i disturbance signal; v=1 means that the characteristic quantity is taken as the disturbance power DP; v=2 It means that the characteristic quantity is taken as the disturbance energy DE.

步骤202,构建表征扰动电流特征的方向判定可信度函数。不平衡扰动源引起的扰动在影响系统三相平衡度的同时,还会存在一定的零序电流,其幅值大小与该PQM相对于扰动点的位置密切相关:若扰动点位于PQM的后向区域,则检测到的零序电流幅值较大;若扰动点位于PQM的前向区域,则零序电流较小。据此,构建表征不平衡扰动时扰动电流特征的方向判定可信度SiStep 202, constructing a direction determination credibility function that characterizes the characteristics of the disturbance current. While the disturbance caused by the unbalanced disturbance source affects the three-phase balance of the system, there will also be a certain zero-sequence current, and its amplitude is closely related to the position of the PQM relative to the disturbance point: if the disturbance point is located in the backward direction of the PQM area, the amplitude of the detected zero-sequence current is larger; if the disturbance point is located in the forward area of PQM, the zero-sequence current is smaller. Based on this, the direction determination reliability S i that characterizes the disturbance current characteristics during unbalanced disturbance is constructed:

其中, in,

式中,I0(i)为监测点i的零序电流均方根值;bi表示PQMi处的扰动方向判定结果;βi为I0(i)与系统中所有监测点I0(i)平均值的比值;a为常量,为使得Si在[1~0.9]区间内一般取2.2~2.5。In the formula, I 0 (i) is the RMS value of the zero-sequence current at monitoring point i; b i represents the result of the determination of the disturbance direction at PQM i ; β i is the difference between I 0 (i) and all monitoring points I 0 ( i) The ratio of the average value; a is a constant, and generally takes 2.2-2.5 in order to make S i within the interval [1-0.9].

步骤203,构建表征扰动能量波动特征的方向判定可信度函数。扰动源定位时,DE波动特征从某种程度上间接反映了该点扰动方向误判的可能性。拟定以下扰动方向判定原则:若DE波形初始峰值与最终值符号不同或者DE符号时刻变化,则该监测点扰动方向判定结果可信度降低。据此,构建表征扰动能量波动特征的方向判定结果可信度θiStep 203, constructing a direction determination credibility function that characterizes disturbance energy fluctuation characteristics. When the disturbance source is located, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction at this point to some extent. The following principle for determining the direction of disturbance is proposed: if the initial peak value of the DE waveform is different from the sign of the final value or the sign of DE changes momentarily, the credibility of the result of the determination of the disturbance direction of the monitoring point will be reduced. Based on this, the credibility θ i of the direction judgment result that characterizes the disturbance energy fluctuation characteristics is constructed:

式中,σ为可信度值,取值范围为0.5~0.75;DE0(i)为第i个监测点DE波形初始峰值;DER(i)为第i个监测点DE终值;sgn为符号函数。In the formula, σ is the reliability value, and the value range is 0.5-0.75; DE 0 (i) is the initial peak value of the DE waveform at the i -th monitoring point; DE R (i) is the final value of the DE waveform at the i-th monitoring point; sgn is a symbolic function.

步骤204,构建表征虚拟PQM点状态估计误差的方向判定可信度函数。由于状态估计误差引入,虚拟PQM点的扰动方向判定可信度可能降低。据此,构建表征虚拟PQM点的方向判定结果可信度ξiStep 204, constructing a direction determination credibility function that characterizes the state estimation error of the virtual PQM point. Due to the introduction of state estimation errors, the reliability of the determination of the disturbance direction of the virtual PQM point may be reduced. According to this, the credibility ξi of the direction judgment result representing the virtual PQM point is constructed:

其中, in,

式中,Ui为置信度u对应的不确定度;x1、x2为虚拟PQM测点i依据测点z1、z2的状态估计结果;为其对应的量测函数;di为其相对偏移量;f(di)为其对应的构造函数。In the formula, U i is the uncertainty corresponding to the confidence u; x 1 and x 2 are the state estimation results of the virtual PQM measuring point i based on the measuring points z 1 and z 2 ; is its corresponding measurement function; d i is its relative offset; f(d i ) is its corresponding constructor.

3、基于证据融合理论的PQDS自动定位。D-S证据理论具有处理不确定信息的能力,基于D-S证据理论的PQDS定位,组合依据扰动功率和扰动能量这两种不同判据各自获得的不确定扰动方向判定信息,使得扰动源定位更准确、可信。3. PQDS automatic positioning based on evidence fusion theory. The D-S evidence theory has the ability to deal with uncertain information. Based on the PQDS positioning of the D-S evidence theory, the combination of the uncertain disturbance direction determination information obtained according to the two different criteria of disturbance power and disturbance energy makes the disturbance source positioning more accurate and reliable. letter.

步骤301,构建目标识别框架。设目标配电网有N个PQM,给每个PQM配置一个编号形成由数组gi构成的识别框架Θ:Step 301, building an object recognition framework. Assuming that the target distribution network has N PQMs, assign a number to each PQM to form an identification frame Θ composed of an array g i :

Θ={gi|i=1,2,3,...,N} (7)Θ={g i |i=1,2,3,...,N} (7)

步骤302,构建基本信度分配函数。从γi、Si、θi及ξi多个角度综合考虑,构建综合的可信度函数。考虑两点:由于在定位由不平衡扰动源引起的扰动时Si才能参与信度配置,此时Si、θi可能出现交集造成重复的概率下降,因此对Si、θi进行平均概率处理,以避免信度急速减小;为避免出现γi大于1的情况,采用最小值函数处理方式。据此,构建综合可信度函数W(i):Step 302, constructing a basic reliability assignment function. A comprehensive credibility function is constructed from the perspectives of γ i , S i , θ i and ξ i . Consider two points: Since S i can participate in the reliability configuration when locating the disturbance caused by the unbalanced disturbance source, at this time S i and θ i may overlap and cause the probability of repetition to decrease, so the average probability of S i and θ i In order to avoid a rapid decrease in reliability; in order to avoid the situation that γ i is greater than 1, the minimum value function processing method is adopted. Accordingly, the comprehensive credibility function W(i) is constructed:

式中,min为最小值函数;μ为电压不平衡度系数,因系统正常电压不平衡度范围为2%~4%,取μ=0.04为界点。In the formula, min is the minimum value function; μ is the voltage unbalance degree coefficient, because the normal voltage unbalance degree of the system ranges from 2% to 4%, take μ=0.04 as the boundary point.

按照基本信度分配函数定义,将W(i)归一化后得到新的可信度函数w(i)。则基本信度分配函数m(gi):According to the definition of the basic reliability assignment function, a new credibility function w(i) is obtained after W(i) is normalized. Then the basic reliability assignment function m(g i ):

步骤303,扰动方向判定可信度组合。采用扰动功率和扰动能量两种方向判据,一种方向判定判据对应一个基本信度函数分配,可分别定义两种情景下的基本信度分配函数mv,以及对应两组方向矩阵Bv,N×1。这样,可得到两组具有符号特性的扰动方向基本信度分配值m1(O)、m2(Γ):Step 303, combining the credibility of the disturbance direction determination. Using two direction criteria of disturbance power and disturbance energy, one direction judgment criterion corresponds to a basic reliability function distribution, and the basic reliability distribution function m v under two scenarios can be defined respectively, and two sets of direction matrices B v corresponding to ,N×1 . In this way, two sets of basic reliability distribution values m 1 (O) and m 2 (Γ) for the disturbance direction with sign characteristics can be obtained:

m1(O):m1(g1)b1,1,m1(g2)b1,2,...,m1(gN)b1,N (10)m 1 (O):m 1 (g 1 )b 1,1 ,m 1 (g 2 )b 1,2 ,...,m 1 (g N )b 1,N (10)

m2(Γ):m2(g1)b2,1,m2(g2)b2,2,...,m2(gN)b2,N m 2 (Γ):m 2 (g 1 )b 2,1 ,m 2 (g 2 )b 2,2 ,...,m 2 (g N )b 2,N

式中,焦元O,Γ∈Θ;bv,i为两组方向矩阵Bv,N×1的组成元素;mv(gi)表示两种情景下PQMi的方向判定可信度。In the formula, the focal element O,Γ∈Θ; b v,i are the components of two sets of direction matrices B v,N×1 ; m v (g i ) represents the credibility of the direction determination of PQM i in two scenarios.

由于融合数据带有符号特性,传统D-S证据组合规则失效。依据经典组合公式,改进后的组合规则遵循以下关系:Due to the symbolic characteristics of fusion data, the traditional D-S evidence combination rules are invalid. According to the classic combination formula, the improved combination rules follow the following relationship:

其中, in,

式中,m(P)为融合后的基本信度分配函数,其焦元P∈Θ;Kτ为冲突因子。In the formula, m(P) is the basic reliability assignment function after fusion, and its focal element P∈Θ; K τ is the conflict factor.

4、扰动源定位决策。定义融合后的扰动方向判定矩阵为MN×1,其组成元素为m(P),通过矩阵乘法运算得到基于证据融合的扰动定位矩阵C’L×14. Disturbance source location decision. Define the fused disturbance direction judgment matrix as M N×1 , and its constituent elements are m(P), and obtain the disturbance location matrix C' L×1 based on evidence fusion through matrix multiplication:

C’L×1=AL×N*MN×1 (12)C' L×1 =A L×N *M N×1 (12)

矩阵C’L×1中的各元素值c’j蕴含着系统PQDS位置信息,其唯一最大值元素c’jm=max{c’j,j=1,2,…,L}对应的PQM所在线路Ljm即为目标配电网中的PQDS所在线段。Each element value c' j in the matrix C' L×1 contains the system PQDS position information, and its unique maximum element c' jm= max{c' j ,j=1,2,...,L} corresponds to the PQM location The line L jm is the line segment of the PQDS in the target distribution network.

5、扰动源定位结果的可信度评估。为评估扰动源定位结果的可信程度,提出基于多证据源间的一致性指标进行某次定位结果的可靠性评价。设{y1,y2,...,yN}为O、Γ相同焦元组成的集合,O(yk)、Γ(yk)为其对应的基本信度值,则评价函数Hi,j5. Evaluation of the credibility of the disturbance source location results. In order to evaluate the credibility of the disturbance source location results, the reliability evaluation of a location result based on the consistency index among multiple evidence sources is proposed. Suppose {y 1 ,y 2 ,...,y N } is a set composed of the same focal elements of O and Γ, and O(y k ), Γ(y k ) are their corresponding basic reliability values, then the evaluation function H i,j :

依据评价函数Hi,j,可按照如下规则进行扰动源定位结果的可信度评估:Hi,j越大,则表示该次扰动源定位结果可信度高;相反,Hi,j越小,则定位结果可信度越低,且当Hi,j≤0.7时,则认为定位结果可信度不高。According to the evaluation function H i,j , the credibility of the disturbance source location results can be evaluated according to the following rules: the larger the H i,j , the higher the reliability of the disturbance source location results; on the contrary, the higher the H i,j Smaller, the lower the reliability of the positioning result, and when H i,j ≤ 0.7, it is considered that the reliability of the positioning result is not high.

本发明的有益效果主要表现在:1、构建了表征影响扰动方向判别可靠性的多种因素的可信度函数;2、采用D-S组合规则融合不同证据源获得的扰动方向判别可信度矩阵,最后得到综合的扰动方向判别结果;3、基于证据一致性准则实现扰动源定位结果准确性的评估。4、为实现在部分监测信息有误情况下的扰动源精确定位,提出了一种基于证据理论的电能质量扰动源定位方法。The beneficial effects of the present invention are mainly manifested in: 1. Constructing a credibility function representing various factors that affect the reliability of disturbance direction discrimination; 2. Adopting the D-S combination rule to fuse the disturbance direction discrimination credibility matrix obtained from different evidence sources, Finally, the comprehensive disturbance direction discrimination result is obtained; 3. Realize the evaluation of the accuracy of the disturbance source location result based on the evidence consistency criterion. 4. In order to realize the precise location of the disturbance source when some monitoring information is wrong, a method for locating the power quality disturbance source based on the evidence theory is proposed.

附图说明Description of drawings

图1为本发明方法的具体实施流程图。Fig. 1 is the specific implementation flowchart of the method of the present invention.

图2为一个9节点辐射型配电网的拓扑结构图。Figure 2 is a topology diagram of a 9-node radial distribution network.

图3为PQM前向区域与后向区域划分图。Figure 3 is a division diagram of the PQM forward area and backward area.

具体实施方式detailed description

下面结合实施例及附图对本发明作进一步的详细说明,但本发明的实施方式不限于此。实施例中基于证据融合理论的PQDS定位方案的总体框图如附图1所示,包括以下步骤:The present invention will be further described in detail below in conjunction with the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto. The overall block diagram of the PQDS positioning scheme based on the evidence fusion theory in the embodiment is shown in Figure 1, including the following steps:

1、确定系统覆盖矩阵AL×N及方向判定矩阵Bv,N×1。在含有L条线段、N个PQM的配电网络中,可分别构建用以表征所有线路与PQM位置关系的覆盖矩阵AL×N,以及用以表征系统中某位置发生扰动事件时所有监测点PQM依据扰动功率和扰动能量这两种不同扰动方向判据实现的扰动方向判定结果的方向矩阵Bv,N×1。AL×N和Bv,N×1中各元素aji和bv,i的赋值原则如式(1)、(2)所示。1. Determine the system coverage matrix AL×N and the direction determination matrix B v,N×1 . In a power distribution network containing L line segments and N PQMs, the coverage matrix A L×N used to represent the positional relationship between all lines and PQMs can be constructed respectively, and it can be used to represent all monitoring points when a disturbance event occurs in a certain position in the system The direction matrix B v,N×1 of the disturbance direction determination results realized by PQM based on two different disturbance direction criteria, disturbance power and disturbance energy. The assignment principles of each element a ji and b v,i in AL ×N and B v,N×1 are shown in formulas (1) and (2).

2、构建表征扰动方向判定结果各影响因素的可信度函数。定义PQM方向判定信息“可信度”概念,分别构建表征多种可信度分项函数指标,用以描述扰动信号强弱、扰动电流特征、分布式电源接入以及虚拟PQM状态估计误差等各种因素在不同情景下对扰动方向判定结果可信度的影响程度,从而实现各监测点方向判定过程及结果的模糊量化。2. Construct the credibility function representing each influencing factor of the disturbance direction determination result. Define the concept of "credibility" of PQM direction determination information, and construct a variety of reliability sub-item function indicators to describe the strength of disturbance signals, disturbance current characteristics, distributed power access, and virtual PQM state estimation errors. The degree of influence of these factors on the credibility of the results of the disturbance direction determination under different scenarios, so as to realize the fuzzy quantification of the direction determination process and results of each monitoring point.

步骤201,构建表征扰动信号强弱的方向判定可信度函数。扰动信号特征量的强弱程度,可由监测点所测得的扰动信号特征量与系统稳定时信号特征量的相对比值来体现。据此,如式(3)所示构建表征扰动强弱的方向判定可信度γiStep 201, constructing a direction determination credibility function that characterizes the strength of the disturbance signal. The strength of the characteristic quantity of the disturbance signal can be reflected by the relative ratio of the characteristic quantity of the disturbance signal measured at the monitoring point to the signal characteristic quantity when the system is stable. Accordingly, the direction determination credibility γ i representing the strength of the disturbance is constructed as shown in formula (3).

步骤202,构建表征扰动电流特征的方向判定可信度函数。不平衡扰动源引起的扰动在影响系统三相平衡度的同时,还会存在一定的零序电流,其幅值大小与该PQM相对于扰动点的位置密切相关:若扰动点位于PQM的后向区域,则检测到的零序电流幅值较大;若扰动点位于PQM的前向区域,则零序电流较小。据此,如式(4)所示构建表征不平衡扰动时扰动电流特征的方向判定可信度SiStep 202, constructing a direction determination credibility function that characterizes the characteristics of the disturbance current. While the disturbance caused by the unbalanced disturbance source affects the three-phase balance of the system, there will also be a certain zero-sequence current, and its amplitude is closely related to the position of the PQM relative to the disturbance point: if the disturbance point is located in the backward direction of the PQM area, the amplitude of the detected zero-sequence current is larger; if the disturbance point is located in the forward area of PQM, the zero-sequence current is smaller. Accordingly, as shown in formula (4), the direction determination reliability S i that characterizes the disturbance current characteristics during unbalanced disturbance is constructed.

步骤203,构建表征扰动能量波动特征的方向判定可信度函数。扰动源定位时,DE波动特征从某种程度上间接反映了该点扰动方向误判的可能性。拟定以下扰动方向判定原则:若DE波形初始峰值与最终值符号不同或者DE符号时刻变化,则该监测点扰动方向判定结果可信度降低。据此,如式(5)所示构建表征扰动能量波动特征的方向判定结果可信度θiStep 203, constructing a direction determination credibility function that characterizes disturbance energy fluctuation characteristics. When the disturbance source is located, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction at this point to some extent. The following principle for determining the direction of disturbance is proposed: if the initial peak value of the DE waveform is different from the sign of the final value or the sign of DE changes momentarily, the credibility of the result of the determination of the disturbance direction of the monitoring point will be reduced. Accordingly, the credibility θ i of the direction determination result representing the disturbance energy fluctuation characteristics is constructed as shown in formula (5).

步骤204,构建表征虚拟PQM点状态估计误差的方向判定可信度函数。由于状态估计误差引入,虚拟PQM点的扰动方向判定可信度可能降低。据此,如式(6)所示构建表征虚拟PQM点的方向判定结果可信度ξiStep 204, constructing a direction determination credibility function that characterizes the state estimation error of the virtual PQM point. Due to the introduction of state estimation errors, the reliability of the determination of the disturbance direction of the virtual PQM point may be reduced. According to this, the confidence degree ξi of the direction judgment result representing the virtual PQM point is constructed as shown in formula (6).

3、基于证据融合理论的PQDS自动定位。D-S证据理论具有处理不确定信息的能力,基于D-S证据理论的PQDS定位,组合依据扰动功率和扰动能量这两种不同判据各自获得的不确定扰动方向判定信息,使得扰动源定位更准确、可信。3. PQDS automatic positioning based on evidence fusion theory. The D-S evidence theory has the ability to deal with uncertain information. Based on the PQDS positioning of the D-S evidence theory, the combination of the uncertain disturbance direction determination information obtained according to the two different criteria of disturbance power and disturbance energy makes the disturbance source positioning more accurate and reliable. letter.

步骤301,构建目标识别框架。设目标配电网有N个PQM,给每个PQM配置一个编号形成由数组gi构成的识别框架Θ,如式(7)所示。Step 301, building an object recognition framework. Assuming that there are N PQMs in the target distribution network, assign a number to each PQM to form an identification frame Θ composed of array g i , as shown in formula (7).

步骤302,构建基本信度分配函数。从γi、Si、θi及ξi多个角度综合考虑,构建综合的可信度函数。考虑两点:由于在定位由不平衡扰动源引起的扰动时Si才能参与信度配置,此时Si、θi可能出现交集造成重复的概率下降,因此对Si、θi进行平均概率处理,以避免信度急速减小;为避免出现γi大于1的情况,采用最小值函数处理方式。据此,如式(8)所示构建综合可信度函数W(i)。Step 302, constructing a basic reliability assignment function. A comprehensive credibility function is constructed from the perspectives of γ i , S i , θ i and ξ i . Consider two points: Since S i can participate in the reliability configuration when locating the disturbance caused by the unbalanced disturbance source, at this time S i and θ i may overlap and cause the probability of repetition to decrease, so the average probability of S i and θ i In order to avoid a rapid decrease in reliability; in order to avoid the situation that γ i is greater than 1, the minimum value function processing method is adopted. Accordingly, the comprehensive credibility function W(i) is constructed as shown in formula (8).

按照基本信度分配函数定义,将W(i)归一化后得到新的可信度函数w(i),则如式(9)所示可得基本信度分配函数m(gi)。According to the definition of the basic reliability distribution function, W(i) is normalized to obtain a new credibility function w(i), then the basic reliability distribution function m(g i ) can be obtained as shown in formula (9).

步骤303,扰动方向判定可信度组合。采用扰动功率和扰动能量两种方向判据,一种方向判定判据对应一个基本信度函数分配,可分别定义两种情景下的基本信度分配函数mv,以及对应两组方向矩阵Bv,N×1。这样,如式(10)所示可得到两组具有符号特性的扰动方向基本信度分配值m1(O)、m2(Γ)。Step 303, combining the credibility of the disturbance direction determination. Using two direction criteria of disturbance power and disturbance energy, one direction judgment criterion corresponds to a basic reliability function distribution, and the basic reliability distribution function m v under two scenarios can be defined respectively, and two sets of direction matrices B v corresponding to ,N×1 . In this way, as shown in formula (10), two sets of basic reliability distribution values m 1 (O) and m 2 (Γ) for the disturbance direction with sign characteristics can be obtained.

由于融合数据带有符号特性,传统D-S证据组合规则失效。依据经典组合公式,改进后的组合规则如式(11)所示。Due to the symbolic characteristics of fusion data, the traditional D-S evidence combination rules are invalid. According to the classic combination formula, the improved combination rule is shown in formula (11).

4、扰动源定位决策。定义融合后的扰动方向判定矩阵为MN×1,其组成元素为m(P),通过如式(12)所示矩阵乘法运算得到基于证据融合的扰动定位矩阵C’L×1。C’L×1中的各元素值c’j蕴含着系统PQDS位置信息,其唯一最大值元素c’jm=max{c’j,j=1,2,…,L}对应的PQM所在线路Ljm即为目标配电网中的PQDS所在线段。4. Disturbance source location decision. The fused disturbance direction judgment matrix is defined as M N×1 , and its constituent element is m(P), and the disturbance location matrix C' L×1 based on evidence fusion is obtained through matrix multiplication as shown in formula (12). Each element value c' j in C' L×1 contains the system PQDS position information, and its unique maximum element c' jm= max{c' j ,j=1,2,...,L} corresponds to the line where the PQM is located L jm is the line segment of PQDS in the target distribution network.

5、扰动源定位结果的可信度评估。为评估扰动源定位结果的可信程度,提出基于多证据源间的一致性指标进行某次定位结果的可靠性评价。设{y1,y2,...,yN}为O、Γ相同焦元组成的集合,O(yk)、Γ(yk)为其对应的基本信度值,则可构建如式(13)所示评价函数Hi,j5. Evaluation of the credibility of the disturbance source location results. In order to evaluate the credibility of the disturbance source location results, the reliability evaluation of a location result based on the consistency index among multiple evidence sources is proposed. Suppose {y 1 ,y 2 ,...,y N } is a set composed of the same focal elements of O and Γ, and O(y k ), Γ(y k ) are their corresponding basic reliability values, then it can be constructed as Evaluation function H i,j shown in formula (13).

据此,可按照如下规则进行PQDS定位结果的可信度评估:Hi,j越大,则表示该次扰动源定位结果可信度高;相反,Hi,j越小,则定位结果可信度越低,且当Hi,j≤0.7时,则认为定位结果可信度不高。Accordingly, the credibility evaluation of the PQDS positioning results can be carried out according to the following rules: the larger the H i,j , the higher the reliability of the disturbance source positioning results; on the contrary, the smaller the H i,j , the more reliable the positioning results The lower the reliability, and when H i,j ≤0.7, the positioning result is considered to be less reliable.

以拓扑结构如图2所示的9节点10.5KV配电网系统为例进行仿真,进一步说明本发明的实施过程。系统中实配7个PQM,2个虚拟PQM,且接入了一个分布式电源DG。通过MATLAB/simulink仿真软件电力系统模块,搭建系统仿真模型。设置线路L7为扰动点,分别模拟单相接地短路、感应电机启动以及电容器投切三种典型的电压暂降扰动。Taking the 9-node 10.5KV distribution network system as shown in Fig. 2 as an example for simulation, the implementation process of the present invention is further described. The system is equipped with 7 PQMs and 2 virtual PQMs, and a distributed power supply DG is connected. Build a system simulation model through the power system module of MATLAB/simulink simulation software. The line L7 is set as the disturbance point, and three typical voltage sag disturbances are respectively simulated: single-phase ground short circuit, induction motor starting and capacitor switching.

按步骤2,分别计算单相接地、电容器投切、感应电机三种不同扰动的γi、Si、θi、ξi以及融合后信度m(P)值,如表1所示。According to step 2, the γ i , S i , θ i , ξ i and the fused reliability m(P) values of three different disturbances of single-phase grounding, capacitor switching, and induction motor are calculated respectively, as shown in Table 1.

表1 各类可信度值Table 1 Various reliability values

由于电容投切和感应电机启动均为平衡扰动源,因此,由电容投切和感应电机启动引起的扰动,无需计算Si数值。Since capacitor switching and induction motor starting are both balanced disturbance sources, there is no need to calculate the value of S i for the disturbance caused by capacitor switching and induction motor starting.

按附图2所示配电网的结构信息和PQM布置信息,根据步骤1可得系统覆盖矩阵如下:According to the structural information and PQM layout information of the distribution network shown in Figure 2, the system coverage matrix can be obtained according to step 1 as follows:

式中,数值±1分别对应各个PQM的后向区域与前向区域。以PQM3为例,展示根据配电网潮流方向将整个网络区域划分为前向区域与后向区域的方法,如附图3所示。In the formula, the value ±1 corresponds to the backward area and forward area of each PQM, respectively. Taking PQM 3 as an example, it shows the method of dividing the entire network area into a forward area and a backward area according to the power flow direction of the distribution network, as shown in Figure 3.

按照步骤4、5进行扰动源定位决策及评估定位结果的可靠程度,信度m(P)构成的方向判定矩阵MN×1与覆盖矩阵AL×N相乘,并计算评价函数Hi,j得到基于证据融合的PQDS定位方法的定位结果如表2所示。Follow steps 4 and 5 to make disturbance source location decisions and evaluate the reliability of the location results. Multiply the direction determination matrix M N×1 formed by the reliability m(P) and the coverage matrix AL×N , and calculate the evaluation function H i, j The positioning results of the PQDS positioning method based on evidence fusion are shown in Table 2.

表2 基于证据融合的PQDS定位方法的定位结果Table 2 The positioning results of the PQDS positioning method based on evidence fusion

取评价函数Hi,j=0.7为分界点,若Hi,j<0.7则认为定位结果可信度不高。表2仿真结果显示,在存在多处误判的情况下,本发明所提方法仍能对不同类型PQDS位置作出准确的判断,且定位结果的可信程度很高。某些情况下,虽误判个数较多,但证据间的一致性较高,使得Hi,j数值较高。The evaluation function H i,j =0.7 is taken as the cut-off point, and if H i,j <0.7, it is considered that the reliability of the positioning result is not high. The simulation results in Table 2 show that in the case of multiple misjudgments, the method proposed in the present invention can still make accurate judgments on the locations of different types of PQDS, and the positioning results are highly reliable. In some cases, although the number of misjudgments is large, the consistency among the evidence is high, making the H i,j value high.

如上所述,便可较好地实现本发明,上述实施例仅为本发明的典型实施例,并非用来限定本发明的实施范围,即凡依本发明内容所作的均等变化与修饰,都为本发明权利要求所要求保护的范围所涵盖。As mentioned above, the present invention can be better realized. The above-described embodiments are only typical embodiments of the present invention, and are not used to limit the scope of the present invention. The scope of protection required by the claims of the present invention is covered.

Claims (1)

1. A method for positioning a power quality disturbance source based on an evidence fusion theory, wherein the power quality disturbance source is called PQDS for short, comprises the following steps:
step 1, determining a system coverage matrix AL×NAnd a direction decision matrix Bv,N×1(ii) a In a power distribution network containing L line segments and N power quality monitoring devices, the power quality monitoring devices are called PQM for short, and a coverage matrix A for representing the position relationship between all lines and the PQM is respectively constructedL×NAnd all monitoring points PQM are used for representing the sum of disturbance power when a disturbance event occurs at a certain position in the systemDirection matrix B of disturbance direction judgment results realized by two different disturbance direction criteria of disturbance energyv,N×1The disturbance power is DP for short and the disturbance energy is DE for short; wherein v-1 represents a criterion according to disturbance power; v-2 represents criterion according to disturbance energy; a. theL×NAnd Bv,N×1Each element a injiAnd bv,iThe assignment principle of (A) is shown in formulas (1) and (2);
step 2, establishing a reliability function representing each influence factor of the disturbance direction judgment result; defining a concept of 'reliability' of the PQM direction judgment information, and respectively constructing and representing various reliability degree item function indexes for describing the influence degree of various factors of disturbance signal strength, disturbance current characteristics, distributed power supply access and virtual PQM state estimation errors on the reliability of the disturbance direction judgment result under different situations, thereby realizing the fuzzy quantization of the direction judgment process and result of each monitoring point;
step 201, constructing a direction judgment reliability function representing the strength of a disturbance signal; the intensity degree of the disturbing signal characteristic quantity can be represented by a relative ratio of the disturbing signal characteristic quantity measured by the monitoring point and the signal characteristic quantity when the system is stable; accordingly, the direction judgment reliability gamma for representing the disturbance intensity is constructedi
<mrow> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>0</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&lt;</mo> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;e</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>E</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>&lt;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;e</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>E</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0.01</mn> <mo>&amp;le;</mo> <mo>|</mo> <mfrac> <mrow> <msub> <mi>&amp;Delta;e</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>E</mi> <mi>v</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>|</mo> <mo>&amp;le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
In the formula, Ev(i) Representing the signal characteristic quantity of the ith monitoring point when the system is stable; Δ ev(i) Represents PQMiDisturbance signal characteristic quantity; v ═ 1 denotes taking the characteristic quantity as the disturbance power DP; v-2 represents taking the characteristic quantity as disturbance energy DE;
step 202, constructing a direction judgment reliability function representing disturbance current characteristics; disturbance caused by an unbalanced disturbance source affects the three-phase balance of a system, and simultaneously, certain zero-sequence current exists, and the amplitude of the zero-sequence current is closely related to the position of the PQM relative to a disturbance point: if the disturbance point is located in the backward region of the PQM, the detected zero sequence current amplitude is large; if the disturbance point is located in the forward region of the PQM, the zero sequence current is small; accordingly, the direction judgment credibility S of the disturbance current characteristic during representing the unbalanced disturbance is constructedi
<mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>-</mo> <mi>a</mi> </mrow> </msup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&gt;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&gt;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>~</mo> <mn>0.9</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>=</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>&amp;beta;</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mn>0.01</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
in the formula I0(i) The root mean square value of the zero sequence current of the monitoring point i is obtained; biRepresents PQMiβ, the determination result of the direction of the disturbanceiIs I0(i) And all monitoring points I in the system0(i) The ratio of the average values; a is a constant such that SiIn the range of [1 to 0.9]Taking 2.2-2.5 in the interval;
step 203, constructing a direction judgment credibility function representing disturbance energy fluctuation characteristics; when the disturbance source is positioned, the DE fluctuation characteristics indirectly reflect the possibility of misjudgment of the disturbance direction of the point to some extent; the following disturbance direction judgment principle is drawn up: if the DE waveform initial peak value is different from the final value symbol or the DE symbol changes at any moment, the reliability of the monitoring point disturbance direction judgment result is reduced; accordingly, the direction judgment result reliability theta representing the disturbance energy fluctuation characteristics is constructedi
<mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mn>0</mn> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>&amp;sigma;</mi> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mn>0</mn> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <msub> <mi>DE</mi> <mi>R</mi> </msub> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
In the formula, sigma is a credibility value, and the value range is 0.5-0.75; DE0(i) The DE waveform initial peak value is the ith monitoring point; DER(i) Is the end value of the DE of the ith monitoring point; sgn is a sign function;
step 204, constructing a direction judgment reliability function representing a virtual PQM point state estimation error; due to introduction of state estimation errors, ghostThe disturbance direction judgment reliability of the PQM point is possibly reduced, and accordingly, the direction judgment result reliability ξ representing the virtual PQM point is constructedi
<mrow> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mn>0</mn> <mo>&lt;</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>&amp;le;</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <mo>&amp;lsqb;</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>f</mi> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>&gt;</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Wherein,
in the formula of UiThe uncertainty corresponding to the confidence coefficient u; x is the number of1、x2Measure point i for virtual PQM based on measure point z1、z2The state estimation result of (1);as its corresponding measurement function; diIs its relative offset; f (d)i) For its corresponding constructor;
step 3, automatically positioning PQDS based on evidence fusion theory; the D-S evidence theory has the capability of processing uncertain information, and the uncertain disturbance direction judgment information obtained according to two different criteria of disturbance power and disturbance energy is combined based on the PQDS positioning of the D-S evidence theory, so that the disturbance source positioning is more accurate and credible;
step 301, constructing a target identification framework; the target power distribution network is provided with N PQMs, and each PQM is provided with a serial number to form an array giThe formed recognition framework Θ:
Θ={gi|i=1,2,3,...,N} (7)
step 302, constructing a basic credibility distribution function; from gammai、Si、θiAnd ξiComprehensively considering a plurality of angles, and constructing a comprehensive reliability function; consider two points: due to S in locating disturbances caused by unbalanced disturbance sourcesiCan participate in trust configuration, at which time Si、θiThere may be intersections causing a decrease in the probability of duplication, and thus for Si、θiCarrying out average probability processing to avoid rapid reduction of reliability; to avoid gammaiIf the value is larger than 1, adopting a minimum function processing mode; accordingly, a comprehensive reliability function w (i) is constructed:
<mrow> <mi>W</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <msub> <mi>S</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> <mn>2</mn> </mfrac> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>*</mo> <mi>min</mi> <mo>{</mo> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>&amp;mu;</mi> <mo>&amp;GreaterEqual;</mo> <mn>0.04</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mo>*</mo> <mi>min</mi> <mo>{</mo> <msub> <mi>&amp;gamma;</mi> <mi>i</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>}</mo> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>&amp;mu;</mi> <mo>&lt;</mo> <mn>0.04</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
in the formula, min is a minimum function; mu is a voltage unbalance coefficient, and because the normal voltage unbalance range of the system is 2% -4%, the point of taking mu as 0.04 is a boundary point;
normalizing W (i) according to the definition of the basic credibility distribution function to obtain a new credibility function w (i); then the basic confidence distribution function m (g)i):
303, judging a reliability combination according to the disturbance direction; two direction criteria of disturbance power and disturbance energy are adopted, one direction criterion corresponds to one basic belief function distribution, and basic belief distribution functions m under two situations are respectively definedvAnd corresponding to two sets of directional matrices Bv,N×1(ii) a Thus, two groups of disturbance direction basic reliability distribution values m with symbol characteristics are obtained1(O)、m2():
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>O</mi> <mo>)</mo> </mrow> <mo>:</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;Gamma;</mi> <mo>)</mo> </mrow> <mo>:</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>g</mi> <mi>N</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
Wherein, the focal element O is ∈ theta, bv,iTwo sets of direction matrixes Bv,N×1The constituent elements of (1); m isv(gi) Indicating PQM under two scenariosiThe direction of (1) determines the reliability;
as the fusion data has symbolic characteristics, the traditional D-S evidence combination rule fails; according to the classical combination formula, the improved combination rule follows the following relationship:
wherein,
wherein m (P) is the basic confidence distribution function after fusion, and focal elements P ∈ theta and KτIs a conflict factor;
step 4, disturbance source positioning decision; defining the merged disturbance direction decision matrix as MN×1The component element is m (P), and the disturbance positioning matrix C 'based on evidence fusion is obtained through matrix multiplication operation'L×1
C’L×1=AL×N*MN×1(12)
Matrix C'L×1Value c 'of each element of'jContains the system PQDS position information, the only maximum value element c'jm=max{c’jJ is 1,2, …, L } corresponding to PQM on the line LjmThe PQDS is a line segment of a target power distribution network;
step 5, evaluating the reliability of the positioning result of the disturbance source; in order to evaluate the credibility of the positioning result of the disturbance source, the reliability evaluation of the positioning result of a certain time is carried out based on the consistency index among the multiple evidence sources; let { y1,y2,...,yNIs a set of O and identical focal elements, O (y)k)、(yk) For its corresponding basic certainty value, the function H is evaluatedi,j
<mrow> <msub> <mi>H</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mi>exp</mi> <mo>{</mo> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>&amp;lsqb;</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>O</mi> <mo>(</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>-</mo> <mi>&amp;Gamma;</mi> <mo>(</mo> <msub> <mi>y</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&amp;rsqb;</mo> </mrow> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
According to an evaluation function Hi,jThe reliability evaluation of the disturbance source positioning result can be performed according to the following rules: hi,jThe larger the interference source is, the higher the reliability of the positioning result of the interference source is; in contrast, Hi,jThe smaller the size, the less reliable the localization result, and when Hi,jAnd if the reliability of the positioning result is less than or equal to 0.7, the reliability of the positioning result is not high.
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