CN110533291B - Medium voltage distribution network weak link identification method based on risk assessment - Google Patents

Medium voltage distribution network weak link identification method based on risk assessment Download PDF

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CN110533291B
CN110533291B CN201910674512.9A CN201910674512A CN110533291B CN 110533291 B CN110533291 B CN 110533291B CN 201910674512 A CN201910674512 A CN 201910674512A CN 110533291 B CN110533291 B CN 110533291B
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梁朔
陈绍南
袁智勇
高立克
秦丽文
李珊
周杨珺
俞小勇
于力
白浩
欧阳健娜
欧世锋
李克文
陈千懿
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Abstract

The invention belongs to the technical field of power distribution risk assessment and evaluation and power distribution risk identification, and particularly relates to a medium voltage distribution network weak link identification method based on risk assessment. Compared with the traditional risk assessment method, the invention innovatively provides a new modeling method for combining the fuzzy model and the traditional probability distribution model. A mixed fuzzy probability model of system peak load is provided aiming at the problems of medium-voltage line heavy overload, transformer area distribution heavy overload and the like of a distribution network, a construction method of a risk index fuzzy membership function and risk index defuzzification are provided on the basis of the traditional Monte Carlo simulation method, and the risk degree of the distribution network system is measured through the defuzzified specific quantity value of the risk index, so that the identification of weak links of the distribution network is realized. The method provided by the invention can help a power supply company to analyze the risk degree of the urban distribution network system and identify the weak links of the distribution network system, thereby providing a valuable theoretical basis for the distribution network generation decision.

Description

Medium voltage distribution network weak link identification method based on risk assessment
Technical Field
The invention belongs to the technical field of power distribution risk assessment and evaluation and power distribution risk identification, and particularly relates to a medium voltage distribution network weak link identification method based on risk assessment.
Background
In the whole power system, the power distribution network is used as a link directly connected with a power customer and directly influences the power supply of the power customer, so that the evaluation and risk assessment of the running state of the power system become the focus of attention of power supply enterprises and the power customer. The conventional common power system risk assessment method is power system risk probability assessment based on statistical analysis theoretical probability, and the most basic characteristic of the method is modeling of random factors in a power system, including randomness of fault and power failure of system elements and uncertain change of load. In fact, there are two uncertainties in the power system, randomness and ambiguity. Probabilistic models can be used for randomness, but not for ambiguity. In conventional risk assessment methods, fault data (e.g., fault frequency, repair time, and fault probability) is typically modeled by one value. Theoretically, the probability distribution of fault data is better measurable than the mean. However, modeling alone is not easy due to limited statistical records. Furthermore, such ambiguity may exist in raw fault data that cannot be represented by a probability distribution, with insufficient statistical records, but may allow the grid company to make a good judgment on the scope of the fault parameters. For all cases, a fuzzy model is required.
Disclosure of Invention
In order to solve the problems, the invention provides a method for identifying weak links of a medium voltage distribution network based on risk assessment, which has the following specific technical scheme:
a medium voltage distribution network weak link identification method based on risk assessment comprises the following steps:
s1: establishing a fuzzy model of the distribution network element fault parameters according to historical statistical data; the fuzzy models of the distribution network element fault parameters comprise a maintenance time fuzzy model, a fault rate fuzzy model and an unavailability fuzzy model;
s2: combining a traditional fuzzy model and a probability distribution model to construct a distribution network system load fuzzy probability hybrid model; the distribution network system load fuzzy probability hybrid model comprises a fuzzy model of a system peak load and a combined probability model based on a load continuous curve; s3: evaluating risk index values corresponding to given membership by adopting a Monte Carlo simulation method, establishing a membership function of the risk indexes, and calculating a total risk index according to the distribution network system load fuzzy probability hybrid model and all load levels obtained by Monte Carlo simulation;
s4: and defuzzifying the risk index membership function to obtain a specific value of the risk index.
Preferably, the step S1 includes the steps of:
s11: establishing a fuzzy model of maintenance time:
the sample average value of the fault duration may be obtained by the following formula:
Figure GDA0003660777230000011
wherein the content of the first and second substances,
Figure GDA0003660777230000021
is the average value of the fault duration and is also the point estimation value of the fault duration; r is a radical of hydrogeniIs the fault duration for the ith fault; n is the number of failures in the outage data; using the t-distribution, a confidence interval for the expected fault duration can be estimated:
assuming that μ represents the actual expected fault duration and s represents the sample standard deviation of the fault duration, for a given significance level α, a random variable can be determined
Figure GDA0003660777230000022
In the interval [ -t ]α/2(n-1),tα/2(n-1)]Has an internal probability of 1-alpha, where tα/2(n-1) is a t-distribution density function with n-1 degrees of freedom from tα/2An integrated value of (n-1) to ∞ having a value α/2, and thus:
Figure GDA0003660777230000023
can also be equivalently expressed as:
Figure GDA0003660777230000024
according to the formula (3), the value interval of the actual expected fault duration can be determined by the upper and lower bounds of the sample fault duration;
s12: establishing a fault rate fuzzy model:
the mean failure rate can be calculated by the following formula:
Figure GDA0003660777230000025
wherein the content of the first and second substances,
Figure GDA0003660777230000026
the average failure rate is also a point estimation value of the failure rate; lambdaiIs the fault duration of the ith load point; m is the number of load points;
by x2Distribution of confidence intervals, x, estimating expected failure rates2The distribution satisfies the following relationship:
x2(2F)＝2λT；(5)
wherein, lambda is the expected failure rate, T is the period, and F is the total number of failures in the period T; from equation (5) it can be derived that for a given significance level α, the probability that the failure rate λ falls within the following random confidence interval can be determined as 1- α, i.e. there is:
Figure GDA0003660777230000027
equation (6) is used to estimate the upper and lower bounds of the failure rate;
s13: establishing a fuzzy model of unavailability:
the unavailability of system components may be calculated using the following frequencies and repair times:
Figure GDA0003660777230000028
wherein f is the failure frequency of the element, and the unit: second/year; r is fault maintenance time, and the unit is hour/time; assuming that the interval of the fault frequency is [ a, b ] and the interval of the fault repairing time is [ c, d ], the value interval of the unavailability degree U can be calculated by the following formula:
Figure GDA0003660777230000031
preferably, the step of establishing the combined probability model based on the load duration curve is as follows:
(1) constructing a load continuous curve by adopting historical load data; setting N load points, dividing the created load continuous curve into N load levels, determining the load levels according to the percentage of the load and the peak load, and calculating the probability of each load level, wherein the load points among the load levels are as follows:
Figure GDA0003660777230000032
wherein, NiIs the number of load points between the ith and next levels of the load level;
the discrete probability distribution of the load curve can be represented by:
p(Li)＝pi,i＝1,2,…,n；(10)
wherein L isiRepresenting the ith load level of the element;
(2) calculating the load level L of each element by using a clustering methodiAnd a sample standard deviation, the steps are as follows:
1) choosing to calculate the initial clustering mean CiIn which C isiDenotes the ith cluster, i ═ 1,2, … …, n;
2) calculating the average value C from each load point to the cluster in the load point clusteriThe calculation formula is as follows:
Dki＝|Ci-Lk|；(11)
wherein L iskIs the kth load point, k is 1,2, … …, N; ciIs the ith clustering mean; dkiThe distance between the kth load point and the ith clustering average value is calculated;
3) the load points are redistributed according to distance and distributed to the nearest cluster, and the new cluster is calculated as follows:
Figure GDA0003660777230000033
wherein N' i is the number of load points in the ith cluster in the new cluster; c' i is the ith cluster average value in the new cluster generated after iteration;
4) repeating the steps 2) and 3) until all clusters are unchanged;
5) calculating the load level according to the following formula:
Figure GDA0003660777230000034
wherein L ispeakIs the load peak value in the load continuous curve, namely the load maximum value;
6) calculating the sample standard deviation of each load level according to the following calculation formula:
Figure GDA0003660777230000041
7) the load duration curve is modeled by adopting a combined probability model, namely a discrete probability distribution model is established for a plurality of stages of the load duration curve, and each stage is modeled by adopting a mean value and a normal distribution of a standard deviation of a sample of the mean value.
Preferably, the step S3 includes the steps of:
s31: constructing fuzzy membership functions of maintenance time and failure rate of all elements of the distribution network system according to the step S1, and calculating the fuzzy membership functions of unavailability;
s32: fuzzy model for system element unavailabilityCalculating the membership function mu of each element with the same membership in the typesj(U) determining the upper and lower bounds corresponding to the unavailability degree and the membership degree:
Figure GDA0003660777230000042
s33: for a given membership degree in the system peak load fuzzy model, calculating two inverse function values of a membership degree function mu (L) under the peak load, and determining an upper boundary and a lower boundary corresponding to the membership degree of the system peak load;
s34: and calculating specific numerical values corresponding to each load level, unit MW, according to a combined probability model of the load duration curve, wherein the calculation formula is as follows:
L′i＝Li·μ-1(μ(L))；(16)
wherein, L'iIs a specific load value corresponding to the ith load level, and the unit is MW; μ (L) is a fuzzy membership function of the peak load;
s35: and (4) performing probability risk assessment on each load level obtained in the step S35 by adopting a Monte Carlo simulation method, wherein the sampling value of the system load at the first sampling is as follows:
Lil＝Xlσi+L′i；(17)
wherein, XlIs a standard normal distribution random number obtained by utilizing approximate inverse transformation; sigmaiIs the sample standard deviation of the ith load level resulting from equation (14); l is a radical of an alcoholilThe sampling value of the system load in the first sampling is obtained;
s36: calculating the total risk index of the distribution network system according to the risk index and the corresponding probability of each load level obtained by analyzing in the step S36 and by combining all the load levels obtained by the membership probability distribution model in the step S35, wherein the calculation formula is as follows:
Figure GDA0003660777230000043
s37: and repeating the steps S33-S37 on the peak load and unavailability membership functions to obtain the membership functions of the risk indexes.
Preferably, in step S4, the risk index membership function is defuzzified by using a center-of-gravity method, which includes:
Figure GDA0003660777230000044
wherein, RIaverageIs the mean value of the risk indicators; RI (Ri)mThe m domain point value in the membership function of the risk index is obtained; mu (RI)m) Is the degree of membership of the domain point; g is the set of domain points considered.
The beneficial effects of the invention are as follows: compared with the traditional risk assessment method, the invention innovatively provides a new modeling method combining the fuzzy model and the traditional probability distribution model. A mixed fuzzy probability model of system peak load is provided aiming at the problems of heavy overload of medium-voltage lines of a distribution network, heavy overload of distribution transformer of a distribution area and the like, a construction method of a fuzzy membership function of a risk index and defuzzification of the risk index are provided on the basis of the traditional Monte Carlo simulation method, and the risk degree of the distribution network system is measured through the defuzzified specific quantity value of the risk index, so that the identification of weak links of the distribution network is realized. The method provided by the invention can help a power supply company to analyze the risk degree of the urban distribution network system and identify the weak links of the distribution network system, thereby providing a valuable theoretical basis for the distribution network generation decision.
Drawings
FIG. 1 is a schematic diagram of a fuzzy membership function for failure rate;
FIG. 2 is a schematic diagram of an unavailability fuzzy membership function;
FIG. 3 is a schematic diagram of fuzzy membership functions for peak loads.
Detailed Description
For a better understanding of the present invention, reference is made to the following detailed description of the invention in conjunction with the accompanying drawings:
a method for identifying weak links of a medium voltage distribution network based on risk assessment comprises the following steps:
s1: establishing a fuzzy model of the distribution network element fault parameters according to historical statistical data; the fuzzy models of the distribution network element fault parameters comprise a maintenance time fuzzy model, a fault rate fuzzy model and an unavailability fuzzy model; the method comprises the following specific steps:
s11: establishing a fuzzy model of maintenance time:
the sample average value of the fault duration may be obtained by the following formula:
Figure GDA0003660777230000051
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003660777230000052
is the average value of the fault duration and is also the point estimation value of the fault duration; r is a radical of hydrogeniIs the fault duration of the ith fault; n is the number of failures in the outage data; using the t-distribution, a confidence interval for the expected fault duration can be estimated:
assuming that μ represents the actual expected fault duration and s represents the sample standard deviation of the fault duration, for a given significance level α, a random variable can be determined
Figure GDA0003660777230000053
In the interval [ -t [ ]α/2(n-1),tα/2(n-1)]Has an internal probability of 1-alpha, where tα/2(n-1) is a t-distribution density function with n-1 degrees of freedom from tα/2An integrated value of (n-1) to ∞ having a value α/2, so that it is possible to obtain:
Figure GDA0003660777230000054
can also be equivalently expressed as:
Figure GDA0003660777230000061
as can be seen from the formula (3), the value interval of the actual expected fault duration can be determined by the upper and lower bounds of the sample fault duration; based on the point estimates and the estimated intervals for the fault duration, a triangular membership function for the fault duration may be created.
S12: establishing a fault rate fuzzy model:
the mean failure rate can be calculated by the following formula:
Figure GDA0003660777230000062
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003660777230000063
the average failure rate is also a point estimation value of the failure rate; lambda [ alpha ]iIs the fault duration of the ith load point; m is the number of load points;
by x2Distribution of confidence intervals, x, estimating expected failure rates2The distribution satisfies the following relationship:
x2(2F)＝2λT；(5)
wherein, lambda is the expected failure rate, T is the period, and F is the total number of failures in the period T; from equation (5) it can be derived that for a given significance level α, the probability that the failure rate λ falls within the following random confidence interval can be determined as 1- α, i.e. there is:
Figure GDA0003660777230000064
equation (6) is used to estimate the upper and lower bounds of the failure rate; the triangular membership function of the fault rate shown in fig. 1 can be established by using the point estimation value and the estimated interval range of the fault rate, the membership function of the fault rate is asymmetric, generally, the distance between the point estimation value obtained by the formula (6) and the upper limit value thereof is far larger than the distance between the point estimation value and the lower limit value thereof, and the upper limit value and the lower limit value can be adjusted according to the influence of meteorological environment, operation state and the like on the fault rate. In addition, when the actual engineering calculation of the power system is carried out, the fault frequency and the fault rate are very close in numerical value and can be mutually replaced, so that the fuzzy membership function of the fault frequency can be obtained through the fuzzy membership function of the fault rate, and meanwhile, the fault rate can be used for replacing the fault frequency to participate in the calculation of the unavailability of system elements.
S13: establishing a fuzzy model of unavailability:
the unavailability of system components may be calculated using the following frequencies and repair times:
Figure GDA0003660777230000065
wherein f is the failure frequency of the element, and the unit: second/year; r is fault maintenance time, and the unit is hour/time; the fuzzy membership function of the unavailability degree can be obtained by carrying out fuzzy operation on the fuzzy membership function through the fault frequency f and the fault restoration time r. Assuming that the interval of the fault frequency is [ a, b ] and the interval of the fault repairing time is [ c, d ], the value interval of the unavailability degree U can be calculated by the following formula:
Figure GDA0003660777230000071
by multiplication of two triangular membership functions, the unavailability membership functions are no longer exactly triangular but shifted to the left, forming membership functions as shown in fig. 2.
S2: combining a traditional fuzzy model and a probability distribution model to construct a distribution network system load fuzzy probability hybrid model; the distribution network system load fuzzy probability hybrid model comprises a fuzzy model of system peak load and a combined probability model based on a load continuous curve; the method specifically comprises the following steps:
s21: establishing a fuzzy model of the peak load of the system:
for the identification of the weak link of the power distribution network based on risk identification, the peak load of the power distribution network system is focused, so that the ambiguity of the distribution network system load level fluctuation is solved, only the upper limit and the lower limit of the interval of the peak load are required to be given, and the fuzzy model of the peak load can be constructed by referring to the fuzzy model construction method provided by the step S1, so that the asymmetric triangular membership function of the peak load shown in the figure 3 can be obtained, wherein the maximum value of the maximum possible peak value of the system corresponds to when the membership degree is 1.0, and the minimum value of the maximum possible peak value of the system corresponds to when the membership degree is 0.
S22: establishing a combined probability model based on a load duration curve, comprising the following steps of:
(1) constructing a load continuous curve by adopting historical load data; n load points are set, one point is collected every 5min for medium voltage distribution network line load data, and one point is collected every 15min for medium voltage distribution network low-voltage transformer distribution; the created load duration curve is divided into n load levels, the load levels are determined according to the percentage of load to peak load, and the probability of each load level is calculated, the load points between the load levels are:
Figure GDA0003660777230000072
wherein N isiIs the number of load points between the ith and next levels of the load level;
the discrete probability distribution of the load curve can be represented by:
p(Li)＝pi,i＝1,2,…,n；(10)
wherein L isiRepresenting the ith load level of the element;
(2) calculating the load level L of each element by using a clustering methodiAnd a sample standard deviation, the steps are as follows:
1) choosing to calculate the initial clustering mean CiIn which C isiDenotes the ith cluster, i ═ 1,2, … …, n;
2) calculating the average value C from each load point to the cluster in the load point clusteriThe calculation formula is as follows:
Dki＝|Ci-Lk|；(11)
wherein L iskThe k-th load point, k 1,2,……,N；Ciis the ith clustering mean; dkiThe distance between the kth load point and the ith clustering average value is calculated;
3) the load points are redistributed according to distance and distributed to the nearest cluster, and the new cluster is calculated as follows:
Figure GDA0003660777230000081
wherein N' i is the number of load points in the ith cluster in the new cluster; c' i is the ith cluster average value in the new clusters generated after iteration;
4) repeating the steps 2) and 3), and iterating until all clusters are unchanged;
5) calculating the load level according to the following formula:
Figure GDA0003660777230000082
wherein L ispeakIs the load peak value in the load continuous curve, namely the load maximum value;
6) calculating the sample standard deviation of each load level according to the following calculation formula:
Figure GDA0003660777230000083
7) the load duration curve is modeled by adopting a combined probability model, namely, a discrete probability distribution model is established for a plurality of stages of the load duration curve, and each stage is modeled by adopting a mean value and a sample standard deviation normal distribution thereof.
S3: evaluating risk index values corresponding to the given membership by adopting a Monte Carlo simulation method, establishing a membership function of the risk index, and calculating a total risk index according to the distribution network system load fuzzy probability hybrid model and all load levels obtained by Monte Carlo simulation; the method comprises the following specific steps:
s31: constructing fuzzy membership functions of maintenance time and failure rate of all elements of the distribution network system according to the step S1, and calculating the fuzzy membership functions of unavailability;
s32: aiming at the condition that the membership degrees in the fuzzy model of the unavailability degrees of the elements of the system are the same, calculating the membership function mu of the unavailability degrees of all the elementsj(U) determining the upper and lower bounds corresponding to the unavailability degree and the membership degree:
Figure GDA0003660777230000084
s33: for a given membership degree in the system peak load fuzzy model, calculating two inverse function values of a membership degree function mu (L) under the peak load, and determining an upper boundary and a lower boundary corresponding to the membership degree of the system peak load;
s34: and calculating specific numerical values corresponding to each load level, unit MW, according to a combined probability model of the load duration curve, wherein the calculation formula is as follows:
L′i＝Li·μ-1(μ(L))；(16)
wherein, L'iIs a specific load value corresponding to the ith load level, and the unit is MW; μ (L) is a fuzzy membership function of the peak load; l isiAt the ith load level relative to peak load;
s35: and (4) performing probability risk assessment on each load level obtained in the step (S35) by adopting a Monte Carlo simulation method, wherein when the load state of the sampling system is analyzed by adopting Monte Carlo, the randomness of the load level is considered, so that discrete probability distribution is established for multiple stages of a load curve, and each stage is modeled by adopting a mean value and a sample standard deviation normal distribution thereof. Then the sampling value of the system load at the ith sampling is:
Lil＝Xlσi+L′i；(17)
wherein, XlIs a standard normal distribution random number obtained by utilizing approximate inverse transformation; sigmaiIs a sample standard deviation of the ith load level resulting from equation (14); l is a radical of an alcoholilIs the system at the first sampling time is negativeA loaded sampling value;
s36: calculating the total risk index of the distribution network system according to the risk index and the corresponding probability of each load level analyzed in the step S36 and by combining all the load levels obtained by the membership probability distribution model in the step S35, wherein the calculation formula is as follows:
Figure GDA0003660777230000091
s37: and repeating the steps S33-S37 on the peak load and unavailability membership functions to obtain the membership functions of the risk indexes.
S4: defuzzifying the risk index membership function to obtain a specific value of the risk index, defuzzifying the risk index membership function by adopting a gravity center method, wherein the adopted gravity center method is very similar to a weighted average concept in probability theory, and searching a balance point by calculating the weighted average of the fuzzy membership function, wherein the method comprises the following steps:
Figure GDA0003660777230000092
wherein, RIaverageIs the mean value of the risk indicators; RI (Ri)mThe m domain point value in the membership function of the risk index is obtained; mu (RI)m) Is the degree of membership of the domain point; g is the set of domain points considered.
The method provided by the invention adopts a distribution network in a certain area as an example for analysis, and the distribution network system comprises 104 nodes and 167 branches. Firstly, a fuzzy membership function of the frequency and the maintenance time of all system elements (lines and transformers) of the distribution network is established by adopting the method provided by the step S1 according to historical statistical data (fault rate and fault repair time statistical data). Then, the method provided in step S2 is adopted to construct the fuzzy model of the peak load as shown in fig. 3, and the maximum membership of the fuzzy model, i.e., the peak load L corresponding to 1.0, can be obtained according to the peak load provided by the load prediction of the distribution network system and the range of the up-down value interval thereofpeakAnd the upper and lower limits L corresponding to the membership of 01And L3Two points onDetermine a line according to L1And LpeakThe left side of the membership function of the fuzzy model triangle, i.e. a linear function in the form of y-kx + b, can be determined, and the right side of the membership function of the fuzzy model triangle can be determined according to the same principle. And a clustering method is adopted to establish a combined probability model based on a load duration curve according to historical statistical data. After the model is constructed, in order to conveniently compare, analyze and verify the effect of the invention, the invention researches and analyzes the following three scenes:
scene 1: only fuzzy models of system element fault parameters are considered, and the load curve is represented by a composite probability distribution model without considering the fuzzy model of peak load.
Scene 2: only fuzzy and probabilistic hybrid models of the load are considered, while the fault parameters of all system elements are still modeled using conventional methods (fixed average of fault frequency and repair time).
Scene 3: it is contemplated that the present invention provides fuzzy and probabilistic models including load and system component fault parameters.
The risk evaluation index selects two risk indexes of common risk index expected electricity shortage quantity (EENS) and load shedding Probability (PLC) for risk evaluation.
The results obtained after the invention is adopted are shown in the following tables 1 and 2, wherein the tables 1 and 2 respectively represent the values of EENS and PLC indexes corresponding to five membership confidence levels.
TABLE 1 Risk index EENS analysis results (MWh/year)
Figure GDA0003660777230000101
TABLE 2 Risk indices PLC analysis results (percentages)
Figure GDA0003660777230000102
The mean values of the EENS and PLC indicators, considering both randomness (probabilistic model) and ambiguity (fuzzy model), are shown in Table 3. Also included in table 3 are the means obtained using only the conventional probabilistic method without any fuzzy model, corresponding to the point with confidence of 1.0 for the membership function, for comparison with the results obtained by the proposed method.
TABLE 3 mean value of Risk indices
Risk index Scene 1 Scene 2 Scene 2 Non-fuzzification processing
EENS (MWh/year) 825.18 861.55 895.30 823.34
PLC (percent) 0.277％ 0.315％ 0.308％ 0.282％
With the variance factor of the EENS as the convergence criterion, the confidence interval is taken to be 0.05, i.e. 5%. From the viewpoint of calculation, the calculation accuracy is comparable to the calculation amount of the nine-interval model in which the peak load is normally distributed, taking into account the five membership function levels (membership degrees) of the peak load. The following results can be found: 1) the input data creates a fuzzy risk index with different membership functions. In a given example, the influence of the load ambiguity on the fuzzy range of the risk index is greater than the ambiguity of fault data of each element of the system, and the load ambiguity and the fault data of each element of the system jointly result in the maximum fuzzy range of the risk index; 2) although the membership functions of the peak load are symmetrical, the corresponding membership functions of the risk indexes are asymmetrical, and the value upper bound of the risk indexes is much larger; 3) when considering load fuzzy and the model property of system element fault parameters, the comprehensive influence of the load fuzzy and the model property on the system element fault parameters on the risk index is not simple linear superposition; 4) after defuzzification, the mean value of each risk index is close to the point value corresponding to the membership degree of 1.0, but the fuzzy range of the index is quite large. The mean of the EENS indices for the three scenarios is located to the right of the point value with degree of membership of 1.0, the mean of the PLC indices for scenarios 2 and 3 is located to the right, and scenario 1 is located to the left. For a PLC index with a degree of membership of 1.0, the closeness between the mean and the point values is not necessarily proportional to the fuzzy range of the index. The fuzzy range of the PLC index for scene 3 is larger than that of scene 2, but at a membership level of 1.0, the mean of the PLC index for scene 3 is closer to the point value than scene 2.
The present invention is not limited to the above-described embodiments, which are merely preferred embodiments of the present invention, and the present invention is not limited thereto, and any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A method for identifying weak links of a medium voltage distribution network based on risk assessment is characterized by comprising the following steps: the method comprises the following steps:
s1: establishing a fuzzy model of the distribution network element fault parameters according to historical statistical data; the fuzzy models of the distribution network element fault parameters comprise a fuzzy model of maintenance time, a fuzzy model of fault rate and a fuzzy model of unavailability; the method comprises the following steps:
s11: establishing a fuzzy model of maintenance time:
the sample average value of the fault duration may be obtained by the following formula:
Figure FDA0003598785120000011
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003598785120000012
is the average value of the fault duration and is also the point estimation value of the fault duration; r isiIs the fault duration for the ith fault; n is the number of failures in the outage data; using the t-distribution, a confidence interval for the expected fault duration can be estimated:
assuming that μ represents the actual expected fault duration and s represents the sample standard deviation of the fault duration, for a given significance level α, a random variable can be determined
Figure FDA0003598785120000013
In the interval [ -t [ ]α/2(n-1),tα/2(n-1)]Has an internal probability of 1-alpha, where tα/2(n-1) is a t-distribution density function with n-1 degrees of freedom from tα/2An integrated value of (n-1) to ∞ having a value α/2, and thus:
Figure FDA0003598785120000014
can also be equivalently expressed as:
Figure FDA0003598785120000015
as can be seen from the formula (3), the value interval of the actual expected fault duration can be determined by the upper and lower bounds of the sample fault duration;
s12: establishing a fault rate fuzzy model:
the mean failure rate can be calculated by the following formula:
Figure FDA0003598785120000016
wherein the content of the first and second substances,
Figure FDA0003598785120000017
the average failure rate is also a point estimation value of the failure rate; lambda [ alpha ]iIs the fault duration of the ith load point; m is the number of load points;
by x2Distribution of confidence intervals, x, for estimating expected failure rates2The distribution satisfies the following relationship:
x2(2F)＝2λT； (5)
wherein, λ is expected failure rate, T is period, and F is total number of failures in period T; from equation (5) it can be derived that for a given significance level α, the probability that the failure rate λ falls within the following random confidence interval can be determined as 1- α, i.e. as:
Figure FDA0003598785120000021
equation (6) is used to estimate the upper and lower bounds of the failure rate;
s13: establishing a fuzzy model of unavailability:
the unavailability of system components can be calculated using the following frequencies and repair times:
Figure FDA0003598785120000022
wherein f is the failure frequency of the element, and the unit: the next time/year; r is fault maintenance time, and the unit is hour/time; assuming that the interval of the fault frequency is [ a, b ] and the interval of the fault repairing time is [ c, d ], the value interval of the unavailability degree U can be calculated by the following formula:
Figure FDA0003598785120000023
s2: combining a traditional fuzzy model and a probability distribution model to construct a distribution network system load fuzzy probability hybrid model; the distribution network system load fuzzy probability hybrid model comprises a fuzzy model of system peak load and a combined probability model based on a load continuous curve; the steps of establishing the combined probability model based on the load duration curve are as follows:
(1) constructing a load continuous curve by adopting historical load data; setting N load points, dividing the created load continuous curve into N load levels, determining the load levels according to the percentage of the load and the peak load, and calculating the probability of each load level, wherein the load points among the load levels are as follows:
Figure FDA0003598785120000024
wherein N isiIs the number of load points between the ith and next levels of the load level;
the discrete probability distribution of the load curve can be represented by:
p(Li)＝pi,i＝1,2,L,n； (10)
wherein L isiRepresenting the ith load level of the element;
(2) calculating load level L of each element by clustering methodiAnd a sample standard deviation, the steps are as follows:
1) choosing to calculate the initial clustering mean CiIn which C isiDenotes the ith cluster, i ═ 1,2, … …, n;
2) calculating the average value C from each load point to the cluster in the load point clusteriThe calculation formula is as follows:
Dki＝|Ci-Lk|； (11)
wherein L iskIs the kth load point, k is 1,2, … …, N; ciIs the ith cluster mean; dkiThe distance between the kth load point and the ith clustering average value is calculated;
3) the load points are redistributed according to distance and distributed to the nearest cluster, and the new cluster is calculated as follows:
Figure FDA0003598785120000031
wherein N' i is the number of load points in the ith cluster in the new cluster; c' i is the ith cluster average value in the new clusters generated after iteration;
4) repeating the steps 2) and 3), and iterating until all clusters are unchanged;
5) calculating the load level according to the following formula:
Figure FDA0003598785120000032
wherein L ispeakIs the load peak value in the load continuous curve, namely the load maximum value;
6) calculating the sample standard deviation of each load level according to the following calculation formula:
Figure FDA0003598785120000033
7) the load duration curve is modeled by adopting a combined probability model, namely a discrete probability distribution model is established for a plurality of stages of the load duration curve, and each stage is modeled by adopting a mean value and a sample standard deviation normal distribution;
s3: evaluating risk index values corresponding to given membership by adopting a Monte Carlo simulation method, establishing a membership function of the risk indexes, and calculating a total risk index according to the distribution network system load fuzzy probability hybrid model and all load levels obtained by Monte Carlo simulation; the method comprises the following steps:
s31: constructing a fuzzy membership function of maintenance time and a fuzzy membership function of failure rate of all elements of the distribution network system according to the step S1, and calculating a fuzzy membership function of unavailability;
s32: for system componentsCalculating the membership function mu of each element under the condition that the membership degrees in the unavailability fuzzy model are the samej(U) determining the upper and lower bounds corresponding to the unavailability degree and the membership degree:
Figure FDA0003598785120000034
s33: for a given membership degree in the system peak load fuzzy model, calculating two inverse function values of a membership degree function mu (L) under the peak load, and determining an upper boundary and a lower boundary corresponding to the membership degree of the system peak load; the method specifically comprises the following steps: constructing an asymmetric triangular membership function of the peak load, namely the peak load L corresponding to mu (L) and the maximum membership degree of 1.0peakAnd the upper and lower limits L corresponding to the membership degree of 01And L3；
The highest limit L when the membership degree is 03And a minimum limit L1Substituting to obtain two inverse function values of mu (L) to obtain corresponding upper and lower bounds;
s34: and calculating specific numerical values corresponding to each load level, unit MW, according to a combined probability model of the load duration curve, wherein the calculation formula is as follows:
L′i＝Li·μ-1(μ(L))； (16)
wherein, L'iIs a specific load numerical value corresponding to the ith load level, and the unit is MW; μ (L) is a fuzzy membership function of the peak load;
s35: and (4) performing probability risk assessment on each load level obtained in the step (S35) by adopting a Monte Carlo simulation method, wherein the sampling value of the system load during the first sampling is as follows:
Lil＝Xlσi+L′i； (17)
wherein XlIs a standard normal distribution random number obtained by utilizing approximate inverse transformation; sigmaiIs the sample standard deviation of the ith load level resulting from equation (14); l isilThe sampling value of the system load in the first sampling is obtained;
s36: calculating the total risk index of the distribution network system according to the risk index and the corresponding probability of each load level obtained by analyzing in the step S36 and by combining all the load levels obtained by the membership probability distribution model in the step S35, wherein the calculation formula is as follows:
Figure FDA0003598785120000041
s37: repeating the steps S33-S37 on the peak load and unavailability membership functions to obtain membership functions of the risk indexes;
s4: defuzzifying the membership function of the risk index to obtain a specific value of the risk index; and (3) defuzzifying the risk index membership function by adopting a gravity center method, which specifically comprises the following steps:
Figure FDA0003598785120000042
wherein, RIaverageIs the mean value of the risk indicators; RI (Ri)mThe m domain point value in the risk index membership function is used as the value; mu (RI)m) For the m-th domain point value RI in the membership function of the risk indicatormDegree of membership of; g is the set of domain points considered.
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