1、 Abstract Aimed at evaluating the severity of voltage sags in the distribution network more accurately and reasonably,a multi-index evaluation method based on comprehensive weight is proposed.Compared with the traditional methods,this method selects multiple evaluation indexes both from power supply
2、 side and electricity side to form a collection of evaluation indicators,making evaluation results more comprehensive.It employs analytic hierarchy process(AHP)and the CRITIC method to calculate a comprehensive weight,which can reflect the deep inner relation between each evaluation index,as well as
3、 their relative importance.After multiple Monte Carlo simulation,the composite score of each node is calculated,and the vulnerability area intersection of weak nodes in the network is obtained.Finally the results of an example prove that this method can accurately and effectively identify weak nodes
4、 and fragile area in network,which lays the foundation for voltage sag control.Index Terms voltage sag;collection of evaluation indicators;comprehensive empowerment;Monte Carlo.INTRODUCTION ITH the increase of sensitive load in the power system and the continuous improvement of power quality require
5、ments,the economic loss caused by voltage sags has also rapidly increased,and has become the most prominent problem in power quality 1-3.Therefore,it is very necessary to assess the severity of voltage sags in distribution networks,which can provide a basis for grid reform,equipment manufacturing,re
6、asonable load access points choosing and voltage sags mitigation.Voltage sags evaluation can be achieved by measurement methods or simulation prediction methods.The former usually requires statistics for decades or even hundreds of years,in order to ensure accuracy which makes it difficult to carry
7、out.Manuscript received June 30,2018.FAN Wenjie，is postgraduate with the Electrical Engineering Department,North China Electric Power University.E-mail:.Simulation prediction methods include critical distance method,fault point method and Monte Carlo method,of which the Monte Carlo method is the mos
8、t widely used 4.Monte Carlo method can calculate system-side indexes,including voltage sag amplitude 5-7,duration 6-7,sag energy 6,8 and frequency 7,9,together with customer-side index like the failure rate of sensitive equipment 10-14.Evaluation with system-side indices often ignores the sensitivit
9、y of the user equipment and overestimates the impact of voltage sag,while with customer-side indicator will underestimate the impact of the voltage sag 15.How to effectively combine them and accurately assess the severity of voltage sags in distribution network is still a problem.Considering the def
10、iciencies of the evaluation methods above,this paper proposes a multi-index assessment method of voltage sags based on comprehensive weights.In this assessment method,multiple evaluation indicators are selected to establish evaluation index sets,which overcomes the drawbacks of only using system-sid
11、e or customer-side indexes in the traditional evaluation methods,which is helpful to more comprehensive evaluation results.The comprehensive weight method not only fully considers the deep internal correlation among various evaluation indicators,but also reflects their relative importance and makes
12、the assessment results more reasonable.VOLTAGE SAG EVALUATION BASED ON MONTE CARLO METHOD Establishment of Failure Probability Model The first step of Monte Carlo simulation is to select the fault parameters as random variables,then to construct a probability density model,according to which can car
13、ry out random sample to determine the system fault parameters,and finally get the voltage sag indexes by calculation 16.This article selects fault XIAO Xiangning,is professor with the Electrical Engineering Department,North China Electric Power University.TAO Shun,is professor with the Electrical En
14、gineering Department,North China Electric Power University.A multi-index evaluation method of voltage sag based on the comprehensive weight FAN Wenjie,XIAO Xiangning，TAO Shun W 2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201804210000006 Pa
15、ge1/5 613 type FT,fault line FL,fault location p,fault impedance Z f and fault duration t as variables to evaluate voltage sag amplitude Unode during voltage sags.Its expression is:(),node T L fU f F F p Z t=(1)The construction of the probability density model follows reference 16 except the fault i
16、mpedance.This paper assumes that the fault impedance Z f obeys a normal distribution with an expected value of 5 and a standard deviation of 1.Evaluation process The assessment of the voltage sag severity proposed in this paper is divided into the following steps:1)Carry out Monte Carlo random estim
17、ation with MATLAB programming,to calculate voltage sag amplitude,duration,frequency,and failure rate of sensitive equipment and form an evaluation index set.2)Combine the AHP method and the CRITIC method to assign new weights to each nodes index set,and calculate the voltage sag score for each node.
18、3)Rearrange the scores of all nodes and select the top 5 as the most severe voltage sag points.4)Form area of vulnerability of each node among the five nodes,the intersection of 5 areas is the fragile area of the entire network.Based on the above process,assessment flowchart is shown in Figure 1.Wri
19、te database informationExpected value of voltage magnitude,duration,frequency,and failure rate of sensitive equipment at each nodeCalculate indexes comprehensive weights and get the voltage sag scores of each node Form the intersection of five nodes areas of vulnerability As the most vulnerable area
20、 Set the number of simulationsGenerate random number x 1Generate random number x 3Generate random number x 5Generate random number x 2Generate random number x 4 Type of failure Fault location Fault duration Fault lineFault impedanceRead database information to get voltage sag magnitudeIs sampling ov
21、er?NoYes Fig.1 voltage sag severity assessment flow chart.EVALUATION INDEX SET Evaluating the severity of a voltage sag at a node is based on the characteristics of all the individual events over a period of time.The single-index evaluation method proposed by the IEEE 1564 Working Group includes sev
22、eral recommended indicators,such as the SARFI indicator,voltage sag table,voltage sag energy,and voltage sag severity 17.They provide basis for establishing evaluation index set.Supply-side indexes The voltage sag amplitude,duration and frequency are three most basic and important characteristic qua
23、ntities,which are related to each other.The amplitude of the voltage sag refers to the ratio of the rms voltage to the rms rated voltage when the sag occurs.The duration refers to the time from the start to the end of the sag,and its magnitude corresponds to a specific voltage threshold.The frequenc
24、y refers to the number of voltage sags,which depends on the specific voltage sag amplitude and duration.Customer-side index In addition to the above three basic indicators,the influence of the voltage sags on sensitive loads connected to the nodes should also be considered,that is,the failure rate o
25、f sensitive equipment.This paper quantitatively calculates the failure rates of three typical sensitive loads based on the probabilistic description of the voltage-tolerance characteristics of sensitive loads.The general voltage tolerance curve(VTC)of a sensitive load is generally rectangular,the pr
26、obabilities of falling into its normal operating area,fault area and uncertainty area can be calculated according to reference 18,which can reflect the randomness by normal distribution probability density function.COMPREHENSIVE INDEX WEIGHTS The AHP method can deal with the combination of qualitati
27、ve and quantitative problems,but due to its excessive subjectivity,the actual information of the data is easily ignored;the CRITIC method can effectively reflect the objective information,but it will be affected by the quality of the original data,and will neglect the empirical attributes,so that ca
28、use poor discrimination of the samples 19.Therefore,its necessary to combine the two to establish an optimal model for comprehensive weights.Data standardization Prior to the calculation of the subjective and objective weights of the evaluation indexes,the original data must be consistent and dimens
29、ionless 19.Based on the analysis of the voltage sag evaluation index set above,the duration,frequency,and the failure rate of sensitive equipment are positively related 2018 China International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201804210000006 Page2/5 61
30、4 to the severity of voltage sag,except the voltage sag magnitude.Therefore,u 1 is taken as a countdown to become a positive-related index,and u 1-u 4 are converted to dimensionless indexes by the extreme value processing method.The formula is as follows:*ij jijjjxmxMm=（2）Where:x ij represents the j
31、-th indicator of the i-th line;m j=minx ij;M j=maxx ij.The x ij*obtained are positive-related and non-dimensional standard data.Subjective weights based on AHP Analytic Hierarchy Process(AHP)can solve multi-objective complex problems,whose subjectivity is mainly reflected in the process of judging t
32、he relative importance of each index and constructing the judgment matrix.In this paper,the coefficient of variation method proposed in reference 19 is used to calculate the basic weights of each evaluation index first,and then the elements in the judgment matrix are determined by comparing the basi
33、c weight values of two.The coefficient of variation refers to the ratio of the degree of dispersion of a set of indicator data to its mean,that is,the ratio of the standard deviation to the average,which is denoted as CV.Let 1 11 12 1,nW w w w=be the basic weight set of the evaluation indicators,the
34、n the basic weight of the j-th indicator w 1j is:11jj njjCVwCV=(3)Compare the basic weight values of each two indicators to calculate the judgment matrix A as:1 11 1211 11 111 11 1212 12 121 11 121 1 1nnnn n nw www w ww www w w Aw www w w=(4)However,since the value of the judgment matrix is determin
35、ed by comprehensive balance of objective data,expert opinion,and analysts knowledge,it is inevitable that consistency will not be satisfied.Therefore,consistency check and modification must be performed on the judgment matrix.When the judgment matrix satisfies the consistency,the subjective weight v
36、ector of each index after normalization is obtained by:21mnj ijiwa=(5)2321jj njjwww=(6)Where,j=1,2,3,.,n.Objective weights based on CRITIC The CRITIC method is suitable for determining the objective weights of indicators 20,which comprehensively determines the objective weights of indexes based on t
37、he variation and the conflict between indicators.The variation indicates the gap between the values of the same indicator,represented by the standard deviation.The larger the standard deviation of the indicator is,the greater the amount of information reflected and so the greater the weight is.Confl
38、iction refers to the correlation coefficient between two indicators.The smaller the correlation coefficient is,the smaller the correlation coefficient is,then the smaller the weight is.The CRITIC method determines weights as follows 20:The correlation coefficient xy between two indicators is calcula
39、ted as:()()()()12211NiiixyNNiiiiX X Y YX X Y Y=(7)The standard deviation within the same indicator is calculated as:()211NiiXXn=(8)Where,n is the number of the same index;X i,Y i are the i-th values of the two indexes respectively;X,Y are the averages of two indexes;N is the number of indexes.The am
40、ount of information contained in the j-th indicator E j is:()11nj j ijiE=(9)The objective weight of the j-th indicator W j is:4 4 41mj j jjw E E=(10)Where,m is the number of indexes.Comprehensive weights Establish an optimal model for determining the coefficients and in the integrated weight vector:
41、34 j j jw w w=+(11)Where,and satisfies:0,0,1.+=In this paper,coefficient and are determined by difference coefficient method in reference 21.First,the components of the subjective weight vector W 3 are arranged in ascending order p 1,p 2,.,p n to calculate the difference coefficient and and:2018 Chi
42、na International Conference on Electricity Distribution Tianjin,17-19 Sep.2018CICED2018 Paper No.201804210000006 Page3/5 615()122112nnT p p npnn+=+(12),11nTn=(13)SIMULATION This paper simulates and analyzes the IEEE 30-bus system.3000 times of simulation are performed on the network by MATLAB progra
43、m,and the results of voltage sag magnitude,duration and sensitive equipment failure rate of each simulation are recorded.After the simulation,for the events whose voltage sag amplitude is between 10%to 90%,calculate the expected values of all the indexes.Results of Monte Carlo simulation The results
44、 of the voltage sag magnitudes,durations,frequencies,and failure rates of various nodes are calculated,two of them are shown in Figure 2-3.It shows that the residual voltage amplitude is mostly concentrated in the range of 0.7 to 0.85 pu.,while the duration in the range of 0.150.3s.More than 80%of t
45、he node voltage sags frequency is between 5 and 9 times/year,and the sensitive equipment failure rate is 0.20.5 times/year.Fig.2 Diagram of node voltage magnitude results Fig.3 Diagram of equipment failure rate results The voltage sag level of each node is evaluated according to four indicators indi
46、vidually.The most severe nodes are shown in Table 1.Tab.1 Most sever nodes table Evaluation critics Results Amplitude 30,29 Duration 26,30 Frequency 30,29 Failure rate 26,4 Results of index weight The result of the subjective weights is W 3=0.28,0.25,0.22,0.25,while the objective weights calculated
47、based on the CRITIC method are W 5=0.20,0.16,0.14,0.50.From this,we can see that the sensitive load failure rate index is focused on measuring the endurance capacity of the equipment itself,and the conflict with the first three indicators is relatively large,so it has the largest weight;and the volt
48、age sag amplitude,duration and frequency are closely related,while the latter is largely determined by the first two,so it occupies the least weight.Using only the subjective weight method will result in the overestimation of the supply-side indxes,and ignorance of the characteristics of sensitive l
49、oads.The result of the objective weight method is similar to the comprehensive weight method.The subjective weight method can make up for the underestimation of two indexes,duration and frequency.Result of weak node ranking The severity of the voltage sags of 30 nodes is ranked.The most severe 5 nod
50、es are shown in Table 2.Tab.2 The maximum voltage sag severity node Nodes Scores 30 0.977 4 0.962 26 0.943 29 0.940 25 0.873 From the above results,it can be seen that except for node 4,other nodes with greater scores are distributed on the low-voltage side that is farther away from power supply,lac
