CN113609637B - Multi-disaster power distribution network elasticity assessment method considering fault linkage - Google Patents

Multi-disaster power distribution network elasticity assessment method considering fault linkage Download PDF

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CN113609637B
CN113609637B CN202110702083.9A CN202110702083A CN113609637B CN 113609637 B CN113609637 B CN 113609637B CN 202110702083 A CN202110702083 A CN 202110702083A CN 113609637 B CN113609637 B CN 113609637B
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邢海青
俞啸玲
夏红军
郭创新
赵福林
施苗根
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Hangzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
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Abstract

The invention discloses a multi-disaster power distribution network elasticity evaluation method considering fault cascading, which comprises the following steps: step S1, modeling various disaster feature failure rates; step S2, based on sequential Monte Carlo simulation, the time sequence characteristics of the element in the disaster process are reserved, and an element running state model formed by a basic range fault rate and a characteristic fault rate is established; s3, analyzing the nonlinear association degree of the trend state characterization quantity sequences of the lines and the nodes in the N-1 scene set and the N-2 scene set through the gray theory, and establishing a coupling relation between fault scenes; s4, establishing a LLD index, an SEDT index and an economic index which comprehensively consider the load loss degree and the maximum frequency change rate of the active unbalance initial moment to form a weighted elasticity-economic space evaluation system, and carrying out elasticity evaluation by measuring the composite entropy weight Euclidean distance between the scene cluster center and the perfect elasticity point; the fault linkage in the disaster process can be prevented and inhibited, and the elasticity of the power transmission network in extreme weather is improved.

Description

Multi-disaster power distribution network elasticity assessment method considering fault linkage
Technical Field
The invention relates to the technical field of power grid index evaluation, in particular to a multi-disaster power distribution network elasticity evaluation method considering fault linkage.
Background
Elasticity is the ability of a system to resist, adapt to, and quickly recover from disturbance events. With the increasing global natural disasters, there is increasing interest in building "elastic grids" that have resilience to extreme disturbance events. As a key link for transmitting power, the power distribution network has a relatively complex structure and a larger scale, and the hidden trouble of fault cascading is particularly remarkable under the background that high fault rate of electrical elements is caused by extreme weather. The current elastic assessment method often ignores the risk of fault linkage, the assessment speed is improved through probability weighting scene results, the voltage level of the power distribution network is higher, the scale is larger, and the ignoring of the highlighted fault linkage hidden danger is unreasonable under the condition that the disaster causes the high fault rate of the element. In terms of elastic lifting strategies, power distribution networks often utilize a large number of configurable resources such as: the energy storage site selection and volume determination, load switching, user demand side response, grid reconstruction and the like are used for improving the elasticity of the power grid, the power distribution network is complex in structure and large in scale, and the elastic lifting strategy for the power distribution network cannot be directly migrated.
The existing elasticity evaluation index of the power distribution network is limited to the combination of the elasticity trapezoid area and the time index to a certain extent, and consideration of fault linkage is lacking, so that how to consider fault scene coupling and establish a more perfect elasticity index evaluation system of the multi-disaster power distribution network becomes a problem to be solved urgently.
Disclosure of Invention
The invention aims to provide a multi-disaster power distribution network elasticity assessment method considering fault linkage, which can form a weighted elasticity-economic space assessment system, and the elasticity assessment is carried out by measuring the composite entropy weight Euclidean distance between the scene cluster center and the perfect elasticity point, so that the fault linkage in the disaster process is prevented and inhibited, and the elasticity of the power distribution network under extreme weather is improved.
In order to achieve the above purpose, the invention adopts the following technical scheme: a multi-disaster power distribution network elasticity evaluation method considering fault linkage comprises the following steps:
step S1, modeling various disaster feature failure rates:
step S2, based on sequential Monte Carlo simulation, the time sequence characteristics of the element in the disaster process are reserved, and an element running state model formed by a basic range fault rate and a characteristic fault rate is established;
s3, analyzing the nonlinear association degree of the trend state characterization quantity sequences of the lines and the nodes in the N-1 scene set and the N-2 scene set through the gray theory, and establishing a coupling relation between fault scenes;
and S4, establishing LLD indexes comprehensively considering the load loss degree and the maximum frequency change rate of the active unbalance initial moment, SEDT indexes considering the system performance recovery characteristic in the disaster process and economic indexes, so as to form a weighted elasticity-economic space evaluation system, and carrying out elasticity evaluation by measuring the composite entropy weight Euclidean distance between the scene cluster center and the perfect elasticity point.
Preferably, the plurality of disaster features comprise typhoons, ice and snow and lightning; respectively modeling the characteristic fault rate of typhoons, ice and snow and lightning;
the typhoon feature fault rate modeling comprises the following steps:
the Batts model is utilized to simulate the wind speed and wind direction of each point in the influence range of the typhoon wind ring, and the formula is as follows:
v in w The wind speed is the anticlockwise tangential direction at the simulation range of the wind ring, V max For the wind speed at the most intense wind zone, R max The distance from the center of the typhoon wind ring to the maximum wind speed is r, and the distance from the range action point to the typhoon center is r; from this, the wind load N of typhoons on the system elements can be calculated w The following are provided:
the load being related to the wind speed and direction at the site of action, V 1 Is the wind speed at the action position; d (D) 1 The outer diameter of the lead at the action position; θ 1 Is the included angle between the wind direction and the wire.
Assuming similar line materials, the line length is proportional to the line impedance. And traversing and generating a system random topological tree by using a BFS algorithm, wherein the length proportion is proportional to the line impedance, and the angles grow randomly. And generating scattered points in the system topology coverage range, generating typhoon action ranges at different moments by using k-means clustering, and respectively interpolating random clustering centers and scattered point average distances by using a Hermite interpolation method to obtain typhoon center track and action radius changes.
The overhead conductor is easy to break at the highest suspension point, the stress sigma born by the section of the conductor is in direct proportion to the sum of the wind load and the gravity load of the conductor, and the bending moment M born by the root of the wire rod T Is the vector sum of the shaft wind load and the root wind load. Therefore, the reliable operation probability of the element under the external load is calculated through the function, and when the function value is greater than 0, the element can be reliably operatedThe operation probability is:
λ n ＝P{R-S＞0}
s is bending moment caused by wind load; r is the element strength; the line wire and pole failure rates can thus be obtained.
The line is equivalent to a series model of a tower and a wire, so that the failure rate of the line under typhoons is obtained:
lambda is the failure rate of line i fp,k,i Failure rate, lambda, for the kth pole of line i f1,k,i The failure rate of the kth gear wire of the line i is obtained.
The modeling of the ice and snow characteristic fault rate comprises the following steps of
The key to the design of a power line considering icing problems is to scientifically estimate the icing extremum during return, i.e. predict the maximum icing thickness that a line may have during operation, describe the extremum probability of the icing thickness of the line using Generalized Extremum (GEV) distribution, and normalize the distribution function as:
wherein alpha is i Is a location parameter; beta i Is a location parameter; k (k) i Is a shape parameter. And obtaining a parameter estimation formula of the GEV distribution by adopting an L moment estimation method in the parameter estimation of the generalized extremum distribution.
The different erection heights of the lines combined with the characteristics of the lines are different, and the working temperatures in normal operation are different, so that the extreme value of the icing thickness is also different, and a correction factor is added:
F i (x)＝k ti k hi k di F(x)
k hi ＝(h i /h 0 ) α
k di ＝1-0.126ln(d 0 /d i )
wherein F is i (x) For the icing thickness extremum distribution, k of the ith line hi 、k di The coefficients of the ice coating thickening along with the change of the height and the diameter of the lead erection are respectively; h is a 0 、d 0 Suspension height and design diameter for the design of the wire; d i The actual suspension height and diameter for the ith line. N is the total number of lines, and the temperature correction coefficient of the line can be defined by the line loss, assuming that the line loss energy is mainly converted into heat dissipation. P is p il oss is the line loss power of the ith line.
The weather condition that ice coating occurs on the surface of the overhead line is that the temperature and the surface temperature of equipment are below 0 ℃, the relative humidity of air is above 85%, and the wind speed is more than 1m/s. Based on meteorological data such as rainfall, wind speed and the like, an icing prediction model is established, and prediction correction is carried out by utilizing icing extremum distribution:
wherein the method comprises the steps ofIs the ice coating thickening amount; ρ is the ice coating density; θ is the water density; p is precipitation, mm/h, V is wind speed, m/s. τ is ice inhibition judgment value, and a random number is generated at the sampling moment to judge whether the icing thickness is increased in the sampling interval time period, so that the icing thickness is more in line with actual acceleration.
According to the metal deformation theory, when the bearing capacity of the tower or the wire reaches the limit, the bearing capacity is reduced in a multiplied way along with the increase of the strain capacity, and the damage rate of the wire is inversely proportional to the bearing capacity and is increased in a multiplied way. The line fault rate function is analyzed according to the physical action of the transmission line as follows:
wherein x is the thickness of the ice coating; d is the line design ice thickness.
The lightning characteristic fault rate modeling comprises the following steps of
A lightning stroke judgment model is built, when the lightning current amplitude reaches 15kA and the lightning stroke side distance is 50 meters, the lightning shielding failure probability reaches 80%, and the lightning current amplitude estimation is an important parameter for lightning stroke flashover calculation; the distribution function and probability density recommended by IEEE Std are as follows:
assuming that the probability density function of the distance on the lightning strike side is uniformly distributed, the distance density function on the lightning strike side can be obtained as follows:
f(C)＝1/L
wherein L is the lightning stroke side distance; taking a section of threshold value as a standard of the lightning current amplitude and the lightning stroke side distance when the lightning shielding failure probability is 80%, and judging that lightning shielding failure occurs when the lightning current amplitude is 10kA to 20kA and the lightning stroke side distance is 35m to 55 m; failure rate lambda of lightning strike t The typical visual strength is 0.1, 0.5, 1 x 100 km/h.
Preferably, the modeling of the element operation state based on sequential Monte Carlo comprises the following steps:
the above section describes a modeling method for disaster feature failure rate, based on which an operational state model of the element is established: assuming that an element has only two operating states, normal and failed, the instantaneous state probability of the element can be calculated according to the Chapman-Kolmogorov equation by:
wherein P is W (T L )，P F (T L ) Respectively represent T L The probability that the component is in both operational and failure states at the moment. Lambda is failure rate, mu is repair rate;
the index Weibull (EW) distribution was chosen as a repair time model, a parametric model widely used for data analysis and reliability studies, and the Cumulative Distribution Function (CDF) was defined as follows:
the distribution is used to fit repair time models under different conditions by selecting different shape parameters and scale parameters. Since the disaster-induced faults herein can be attributed to some extent to atmospheric effects, alpha is selected r ＝8.4298，k r ＝8.4298，λ r = 0.1210 as fitting parameters. Maintenance time (MTTR) during the action of atmospheric factors can be obtained under the estimated parameters, the MTTR under the common equipment fault is 1.550, the MTTR under the atmospheric environment fault is 3.017, and the MTTR is increased by one time under the more normal maintenance conditions and the maintenance conditions with the influence of objective weather factors to be a more reasonable value, so that under the severe weather, disasters and disasters, the MTTR is respectively increased by one time;
the repair probability distribution uses the better-performing index Weibull distribution, so that the probability distribution can be obtained by neglecting mu:
under the disaster background, the component outage replacement rate under a certain time section is as follows:
P F ＝P FB +P FS
P F for sampling instant element transient fault probability, P FB Is caused by the action of the atmosphereThe influence of the extent causes the component outage rate, P, at this time section FS The element shutdown replacement rate under the time section is caused by the physical and chemical characteristics of the disaster.
In this scheme, decisive factor difference between them lies in that most disasters cause scope type influence to the electrical component in the action region through atmospheric environment leads to scope type weather to worsen when taking place, like thunderbolt, typhoon, the rainfall on ice and snow weather brings, scope type cooling etc. these are the commonality of this kind of disasters, and the disaster combines the materialization characteristic of self to cause characteristic influence to the electrical component simultaneously. The basic range fault rate and the disaster characteristic fault rate are established by extracting common characteristics and respective unique characteristics of common disasters, and the component outage rate under the sampling instant time section is calculated by a Chapman-Kolmogorov equation to obtain P FB And P FS 。
Modeling of disaster characteristic fault rate as described above, analyzing the brazilian power grid fault information and the statistical data of the local weather by using negative two-term regression, fitting to obtain the relationship between the atmospheric wind speed and the atmospheric discharge times and the equipment fault rate, and establishing the basic range fault rate as follows:
λ b (nt,wg)＝λ 0 exp(0.0011nt+0.0275wg)
wherein lambda is 0 For the nominal failure rate, nt is the number of thunder/atmospheric discharges that occur and wg is the atmospheric gust speed. Disaster intensities were classified into severe weather (wg=50, nt=30), disasters (wg=3000, nt=50), and major disasters (wg=5500, nt=80) according to the IEEE standard.
Because the state of the line can influence the working states of elements such as a generator, a transformer and load equipment at the node, and the disaster action intensity of the node in the disaster process is similar to that of the connecting line, the instantaneous failure probability of the node is defined as the average value of the failure rate of the topological direct-connection line:
wherein P is N P is the instantaneous failure probability of a node Li And m is the number of the direct connection lines of the physical topology of the node for the instant fault probability of the ith line. The intensity change in the disaster process is simulated by using the cooling coefficient in the annealing process:
preferably, the fault scene coupling relation modeling under the N-K scene set comprises the following steps:
the failure rate of the electrical element is lower when the electrical element normally works in the rated state, for example, the line and the generator set are often in an overload working state or the active output of the electrical element is lower than the rated value for a long time due to frequent participation of the generator set in frequency modulation working, the working life of the electrical element is far lower than that of the element in normal operation, and the trend state representation quantity s is proposed based on the failure rate:
wherein s is i The characteristic quantity of the equal trend state of the i element, m is the number of the state quantity of the i element, and gamma ikr For the current value of the kth state quantity of the i element, gamma ikn The normal working state value of the kth state quantity of the i element, N is the total number of the elements, and gamma xkn For the normal working state value of the kth state variable of the element x, the element state quantity selects a variable which can represent the operation state of the element and has lower coupling degree, preferably a linear independent variable, such as a line can select variables such as input power flow active power, power flow reactive power and the like, and a node can select variables such as node voltage, node phase angle or injection active power, injection reactive power and the like. The effective information value of each feature quantity is the degree of the element deviating from the normal working state, so that the abnormal working state degree of the element is obtained by utilizing the product aggregation feature;
n-1 and N-2 fault scene formation and other trend state characterization quantity matrix of computing systemM is the total of system componentsAnd N is the number of fault scenes.
Calculating the nonlinear association degree of the equal trend state characterization quantity sequences of different elements by using a gray theory:
n is the number of fault scenes, a sequence i is provided as a parent sequence, a sequence j is provided as a reference sequence, s i (k) And (4) representing the value of the equal trend state of the element i in the kth scene, wherein ρ is a resolution coefficient. Sequentially extracting corresponding element sequences as parent sequences to calculate nonlinear relevancy with other element sequences to obtain a relevancy matrix C M×M The matrix is a symmetric matrix in which the elements ζ ij Is the coefficient of association of element i with element j. Calculating the equal trend state characterization quantity of each element after each sampling, and correcting the instantaneous fault probability of the next sampling by using the association coefficient and the equal trend state characterization quantity of each current element, namely according to the association degree of other elements with the element and the degree of the abnormal working state of the element and other elements:
wherein k is ic For the associated correction coefficient of the ith element, S 1×M Vectors formed by the equal trend state characterization values of the elements in the current scene,for the transposed matrix of the ith row vector of the association matrix, the abnormal working states of the element and other elements and the association between the elements are utilized to correct the instantaneous fault probability of the next sampling by combining the sampling result of the current state, and the corrected I/O is used for correcting the instantaneous fault probability of the next sampling>Thereby establishing coupling among different fault scenes in the sampling process.
Preferably, since the traditional elasticity assessment calculates the system elasticity by considering the "elasticity trapezoid" characteristic of a single scene and the probability of occurrence of each scene, the invention considers the coupling among fault scenes in the event occurrence process in the simulation of a single event of an extreme weather event set, the probability of occurrence of a single event in a sampling time section can be changed along with the change of the scene before the time sequence, and the direct consideration of all Markov state probabilities can lead to "dimension disaster". The repair speed under extreme weather conditions is considered on the repair time model of the element, and each element has certain repair capacity in the process of extreme weather events, so that the sub-event of single element failure has self elasticity. When considering the coupling correlation of each fault event in time sequence and the repair capability during disasters, the following system performance results can be obtained:
the performance missing area index for the system elasticity assessment is as follows:
wherein: the resiience (y) is the elasticity of the system y; f (F) s,0 For the performance F of the system y under normal conditions s,i (t) is the performance curve of the system y under the extreme event i, and phi is the extreme event set; it is understood that the system loses area in extreme weather conditions relative to system performance under normal conditions.
The integration can be converted to a monte carlo integration process under sequential monte carlo simulation:
resilience i and (y) is a y system elasticity index of the events in the phi event set. F (F) s,i, And l is the system performance instantaneous value of the sequential Monte Carlo simulation first sample. The integration result may not be approximated by taking infinite limits when the sampling frequency is sufficiently high, i.e. n is sufficiently large. The performance missing area index can be seen to be the robustness index and the rapidityThe product of time indexes is evaluated by adding a robustness index and a rapidity index on the basis of a performance missing area index, which is a redundant index establishment mode, and the low-dimensional characteristic information is seriously lost by utilizing the low-dimensional characteristic of which multiplication aggregation is critical.
The invention independently extracts the load loss degree of the system and introduces transient fault state index xi RCF Constructing a load loss degree index (LLD), a System Elastic Deformation Time (SEDT) and an Economic Loss Degree (ELD) to establish an elasticity-economic space;
the loss index formula is defined as follows:
LLD index can reflect amplitude condition of system load change in disaster process, and xi RCF The maximum change rate of the frequency of the system, which occurs at the initial moment of active unbalance, is a transient fault state index which is concerned by power grid operators [24] . The reasons for considering the index are load losses with different degrees, and the transient stability influence on the system is different at the moment of unbalance of active power, so the index is used for weighting the load loss index, so that the index has both steady-state characteristic and transient characteristic of the system.
ξ RCF The calculation mode of (2) is as follows:
wherein: ΔP im Absolute value of the active unbalance of the system; n (N) G The number of generators in operation; h n And (3) withThe inertia constant and the upper limit of the output of the nth generator; f (f) 0 Rated frequency for the system;
the system elastic deformation time index formula is defined as follows:
the economic loss index formula is defined as follows:
the SEDT index can reflect the time of the system in the elastic deformation process, t gap For the time interval between two samplings, t dura For duration of disasters, sigma d Is an elastic deformation state judgment parameter, when F s,i,l ＜F s,0 - ζ time sigma d =1, i.e. the system is judged to be in an elastically deformed state, whereas σ is the opposite d =0. ζ is a margin parameter. The economic loss index (ELD) is established by load shedding penalty and element repair cost (such as unit start-stop cost), wherein N D For the number of load elements, m ci Cutting out a unit load cost for an i-component, usually in relation to the importance of the load, P cDi To cut out the load, N b For the number of start-stop units, C bk For the start-stop expense of k units, P Di I total element load; an elasticity-economy space is thus created, which is defined as the set of all event elasticity assessment performances of the system with the goals of robustness, rapidity, economy, etc. And generating an extreme weather event set of a corresponding grade type according to the actual proportion according to the meteorological environment in which the system is located. The single point in the elastic space corresponds to a single extreme weather event in the whole simulation event set, the coordinates of the single point are three indexes normalized by the whole event set, the perfect elastic point is located at the space origin, the weighted Euclidean distance between the space position of the system in a certain event scene and the perfect elastic point is calculated, the weighted Euclidean distance between the center of the system performance point cluster and the perfect elastic point is obtained by using the average distance of the whole simulation event set, and the weighted Euclidean distance is mapped to [0, 100]Elasticity of the interval computing system:
wherein LLD is i ，SEDT i ，ELD i Elastic-economic coordinates, σ, of system y in the event of i, respectively 1 ，σ 2 ，σ 3 And the composite entropy weight calculation values of the three indexes are respectively obtained. The calculation mode is that 3000 extreme weather events are simulated, typhoons, ice and snow, lightning disasters and the like are generated in proportion, and as the research main body is the disaster event, three grades of severe weather, disasters and big disasters are generated according to the proportion of 2:5:3, an elastic-economic space coordinate sequence is calculated, and indexes are standardized and sigma is used 1 The following are examples:
wherein m is the number of indexes,entropy of information contained for the i-th set of index sequences,Y ij the proportion of the ith sample under the jth index, n is the number of samples under the single index, k 1 In order to adjust the factor, the degree of attention to the index is reflected, and a fine adjustment function is performed, and in general, 1 is taken, for example, in a disaster, the economic index has a high information entropy, but the economic efficiency is not a factor of priority at this time, and the weight of the economic index can be properly reduced by using the factor.
The beneficial effects of the invention are as follows: the invention provides a multi-disaster power distribution network elasticity assessment method considering fault linkage, which carries out multi-disaster power distribution network performance simulation, uses sequential Monte Carlo simulation to reserve time sequence characteristics of elements in a disaster process, establishes a coupling relation between fault scenes through gray theory analysis lines and nodes under N-1 and N-2 scene sets and other nonlinear relativity of trend state characterization quantity sequences, establishes LLD indexes comprehensively considering the load loss degree and the frequency maximum change rate of active imbalance initial moments, SEDT indexes considering the system performance recovery characteristics in the disaster process and economic indexes, and forms a weighted elasticity-economic space assessment system, and carries out elasticity assessment by measuring the composite entropy weight Euclidean distance between the scene cluster center and perfect elastic points; and the fault linkage in the disaster process is prevented and inhibited, and the elasticity of the power distribution network in extreme weather is improved.
Drawings
Fig. 1 is a flowchart of a method for evaluating elasticity of a multi-disaster power distribution network considering fault cascading.
Fig. 2 is a schematic diagram of a power system state considering fault scenario coupling.
Fig. 3 is a random typhoon scene graph.
FIG. 4 is a graph showing simulation results of the performance of the ice and snow, lightning and typhoon system under a disaster.
FIG. 5 is a graph of the extreme weather event set in the elastic-economic space coordinate distribution of the IEEE118 node system.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and examples, it being understood that the detailed description herein is merely a preferred embodiment of the present invention, which is intended to illustrate the present invention, and not to limit the scope of the invention, as all other embodiments obtained by those skilled in the art without making any inventive effort fall within the scope of the present invention.
Examples: as shown in fig. 1, a flowchart of a method for evaluating elasticity of a multi-disaster power distribution network considering fault cascading includes the following steps:
step S1, modeling various disaster feature failure rates: the disaster features comprise typhoons, ice and snow and lightning; respectively modeling the characteristic fault rate of typhoons, ice and snow and lightning;
the method comprises the steps of simulating wind speed and wind direction of each point in a typhoon circle influence range by using a Batts model, generating scattered points in a system topology coverage area, generating typhoon action ranges at different moments by using k-means clustering, and respectively interpolating a random clustering center and scattered point average distances by using a Hermite interpolation method to obtain typhoon center track and action radius changes. The line is equivalent to a series model of a tower and a wire, so that the failure rate of the line under typhoons is obtained:
characteristic failure rate of ice and snow:
the line fault rate function is analyzed according to the physical action of the transmission line as follows:
wherein x is the thickness of the ice coating; d is the line design ice thickness.
Lightning characteristic failure rate:
the distribution function and probability density are as follows:
assuming that the probability density function of the distance on the lightning strike side is uniformly distributed, the distance density function on the lightning strike side can be obtained as follows:
f(C)＝1/L
taking typhoons as an example, a typhoon simulation scene graph is shown in fig. 3.
Step S2, based on sequential Monte Carlo simulation, the time sequence characteristics of the element in the disaster process are reserved, and an element running state model formed by a basic range fault rate and a characteristic fault rate is established;
in this embodiment, index Weibull (EW) distribution is selected as a repair time model, and the component outage replacement rate under a certain time section can be obtained under a disaster background as follows:
P F ＝P FB +P FS
the basic range fault rate and the disaster characteristic fault rate are established by extracting common characteristics and respective unique characteristics of common disasters, and the basic range fault rate is established as follows:
λ b (nt,wg)＝λ 0 exp(0.0011nt+0.0275wg)
because the state of the line can influence the working states of elements such as a generator, a transformer and load equipment at the node, and the disaster action intensity of the node in the disaster process is similar to that of the connecting line, the instantaneous failure probability of the node is defined as the average value of the failure rate of the topological direct-connection line:
wherein P is N P is the instantaneous failure probability of a node Li And m is the number of the direct connection lines of the physical topology of the node for the instant fault probability of the ith line. The intensity change in the disaster process is simulated by using the cooling coefficient in the annealing process:
the simulation results of the performance of the ice and snow, lightning and typhoon system under the disaster are shown in figure 4.
S3, analyzing the nonlinear association degree of the trend state characterization quantity sequences of the lines and the nodes in the N-1 scene set and the N-2 scene set through the gray theory, and establishing a coupling relation between fault scenes;
n-1 and N-2 fault scene formation and other trend state characterization quantity matrix of computing systemCalculating the nonlinear association degree of the equal trend state characterization quantity sequences of different elements by using a gray theory;
and correcting the instantaneous fault probability of the next sampling according to the association degree of other elements and the degree of abnormal working states of the elements and the elements:
combining the sampling result of the current state, correcting the instantaneous fault probability of the next sampling by utilizing the abnormal working states of the self and other elements and the association between the elements, and correctingThereby establishing the coupling between different fault scenes in the sampling process; as shown in fig. 2, a diagram of the coupling relationship between the system performance and different fault scenarios is shown.
S4, establishing LLD indexes comprehensively considering the load loss degree and the maximum frequency change rate of the active unbalance initial moment, SEDT indexes considering the system performance recovery characteristic in the disaster process and economic indexes, so as to form a weighted elasticity-economic space evaluation system, and carrying out elasticity evaluation by measuring the composite entropy weight Euclidean distance between the scene cluster center and the perfect elasticity point;
in the embodiment, the load loss degree of the system is independently extracted and the transient fault state index xi is introduced RCF Building a load loss degree index (LLD), a System Elastic Deformation Time (SEDT) and an Economic Loss Degree (ELD), and building an elastic-economic space, wherein the indexes are defined as follows:
thus, an elasticity-economy space is established, which is defined as the set of all event elasticity assessment performances of the system under the targets of robustness, rapidity, economy and the like:
the evaluation results of the indexes under single simulation of different types of extreme weather under the heavy disaster are shown in table 1:
TABLE 1 results before normalization of various indicators under single simulation of extreme weather of different intensities and different types
The elastic-economic space assessment system can intuitively represent the event set in space by using weighted mathematical distances, and provides guidance for further improvement of the system through distribution of event assessment results as shown in fig. 5.
The above embodiments are preferred embodiments of the method for evaluating elasticity of a multi-disaster power distribution network considering fault linkage, and are not intended to limit the scope of the invention, which includes but is not limited to the embodiments, and equivalent changes of shape and structure according to the invention are all within the scope of the invention.

Claims (8)

1. The elasticity evaluation method of the multi-disaster power distribution network considering fault linkage is characterized by comprising the following steps of:
step S1, modeling various disaster feature failure rates;
step S2, based on sequential Monte Carlo simulation, the time sequence characteristics of the element in the disaster process are reserved, and an element running state model formed by a basic range fault rate and a characteristic fault rate is established;
s3, analyzing the nonlinear association degree of the trend state characterization quantity sequences of the lines and the nodes in the N-1 scene set and the N-2 scene set through the gray theory, and establishing a coupling relation between fault scenes;
s4, establishing LLD indexes comprehensively considering the load loss degree and the maximum frequency change rate of the active unbalance initial moment, SEDT indexes considering the system performance recovery characteristic in the disaster process and economic indexes, so as to form a weighted elasticity-economic space evaluation system, and carrying out elasticity evaluation by measuring the composite entropy weight Euclidean distance between the scene cluster center and the perfect elasticity point;
step S4 includes the steps of:
the loss index formula is defined as follows:
ξ RCF for the maximum rate of change of the frequency of the system, the calculation method is as follows:
wherein: ΔP im Absolute value of the active unbalance of the system; n (N) G The number of generators in operation; h n And (3) withThe inertia constant and the upper limit of the output of the nth generator; f (f) 0 Rated frequency for the system;
the system elastic deformation time index formula is defined as follows:
the economic loss index formula is defined as follows:
the SEDT index can reflect the time of the system in the elastic deformation process, t gap For the time interval between two samplings, t dura For duration of disasters, sigma d Is an elastic deformation state judgment parameter, when F s,i,l ＜F s,0 - ζ time sigma d =1, i.e. the system is judged to be in an elastically deformed state, whereas σ is the opposite d =0; ζ is a margin parameter; ELD index is established by load shedding penalty and element repair cost, wherein N D For the number of load elements, m ci Cut out unit load cost for i component, P cDi To cut out the load, N b For the number of start-stop units, C bk For the start-stop expense of k units, P Di I total element load.
2. The method for evaluating the elasticity of the power distribution network with consideration of fault cascading according to claim 1, wherein in the step S1, the plurality of disaster features comprise typhoons, ice and snow and lightning; and respectively modeling the characteristic fault rate of typhoons, ice and snow and lightning.
3. The method for evaluating the elasticity of the multi-disaster power distribution network considering fault cascading according to claim 2, wherein the modeling of the typhoon characteristic fault rate comprises the following steps:
the Batts model is utilized to simulate the wind speed and wind direction of each point in the influence range of the typhoon wind ring, and the formula is as follows:
v in w The wind speed is the anticlockwise tangential direction at the simulation range of the wind ring, V max For the wind speed at the most intense wind zone, R max The distance from the center of the typhoon wind ring to the maximum wind speed is r, and the distance from the range action point to the typhoon center is r;
calculating wind load N of typhoons acting on system elements w The following are provided:
the load being related to the wind speed and direction at the site of action, V 1 Is the wind speed at the action position; d (D) 1 The outer diameter of the lead at the action position; θ 1 Is the included angle between the wind direction and the wire;
the overhead conductor is easy to break at the highest suspension point, the stress sigma born by the section of the conductor is in direct proportion to the sum of the wind load and the gravity load of the conductor, and the bending moment M born by the root of the wire rod T Vector sum of the wind load of the pole body and the wind load of the pole root; the reliable operation probability of the element under the external load is calculated through the function, and when the function value is larger than 0, the element can reliably operate, and the probability formula is as follows:
λ n ＝P{R-S＞0}
s is bending moment caused by wind load; r is the element strength;
the line is equivalent to a series model of a tower and a wire, so that the failure rate of the line under typhoons is obtained:
lambda is the failure rate of line i fp,k,i Failure rate, lambda, for the kth pole of line i f1,k,i The failure rate of the kth gear wire of the line i is obtained.
4. The method for evaluating the elasticity of the multi-disaster power distribution network considering fault cascading according to claim 2, wherein the modeling of the ice and snow characteristic fault rate comprises the following steps:
describing the extreme value probability of the icing thickness of the line by using generalized extreme value distribution, wherein the standardized distribution function is as follows:
wherein alpha is i Is a location parameter; beta i Is a location parameter; k (k) i Is a shape parameter; adopting an L moment estimation method in the parameter estimation of the generalized extremum distribution to obtain a parameter estimation formula of GEV distribution;
the different erection heights of the lines combined with the characteristics of the lines are different, and the working temperatures in normal operation are different, so that the extreme value of the icing thickness is also different, and a correction factor is added:
F i (x)＝k ti k hi k di F(x)
k hi ＝(h i /h 0 ) α
k di ＝1-0.126ln(d 0 /d i )
wherein F is i (x) For the icing thickness extremum distribution, k of the ith line hi 、k di The coefficients of the ice coating thickening along with the change of the height and the diameter of the lead erection are respectively; h is a 0 、d 0 Suspension height and design diameter for the design of the wire; d, d i The actual suspension height and diameter for the ith line; n is the total number of lines, and the temperature correction coefficient of the lines can be defined by the line loss on the assumption that the line loss energy is mainly converted into heat dissipation; p is p iloss Line loss power for the ith line;
based on meteorological data such as rainfall, wind speed and the like, an icing prediction model is established, and prediction correction is carried out by utilizing icing extremum distribution
Wherein the method comprises the steps ofIs the ice coating thickening amount; ρ is the ice coating density; θ is the water density; p is precipitation, mm/h, V is wind speed, m/s; τ is an ice suppression judgment value;
the line fault rate function is analyzed according to the physical action of the transmission line as follows:
wherein x is the thickness of the ice coating; d is the line design ice thickness.
5. The method for evaluating the elasticity of the multi-disaster power distribution network considering fault cascading according to claim 2, wherein the modeling of the lightning stroke characteristic fault rate comprises the following steps:
since lightning current amplitude estimation is an important parameter for lightning flashover calculation; the distribution function and probability density recommended by IEEE Std are as follows:
the probability density function of the distance on the lightning strike side is uniformly distributed, and the distance density function on the lightning strike side can be obtained as follows:
f(L)＝1/L
wherein L is the lightning stroke side distance; taking a section of threshold value as a standard of the lightning current amplitude and the lightning stroke side distance when the lightning shielding failure probability is 80%, and judging that lightning shielding failure occurs when the lightning current amplitude is 10kA to 20kA and the lightning stroke side distance is 35m to 55 m; failure rate lambda of lightning strike t The typical visual strength is 0.1, 0.5, 1 x 100 km/h.
6. A method for evaluating elasticity of a power distribution network in consideration of fault concatenation and multiple disaster damage according to claim 1 or 2, wherein step S2 comprises the following sub-steps:
setting a component to have only two operating states, normal and fault, according to the Chapman-Kolmogorov equation, the instantaneous state probability of the component can be calculated by the following equation:
wherein P is W (T L )，P F (T L ) Respectively represent T L Probability of the time element being in two operating states, working and failing; lambda is failure rate, mu is repair rate; the repair probability distribution uses an exponential Weibull distribution, so we can get neglecting μ:
under the disaster background, the component outage replacement rate under a certain time section is as follows:
P F ＝P FB +P FS
P F for sampling instant element transient fault probability, P FB The change rate of the components under the time section caused by the influence of the range of the disaster through the atmospheric action, P FS The element shutdown replacement rate under the time section is caused by the physical and chemical characteristic influence of the disaster;
the instantaneous failure probability of a node is defined as the mean value of the failure rates of topological direct links:
wherein P is N P is the instantaneous failure probability of a node Li The instant fault probability of the ith line is given, and m is the physical topology of the nodeThe number of direct connection lines; the intensity change in the disaster process is simulated by using the cooling coefficient in the annealing process:
7. a multi-disaster power distribution network elasticity assessment method considering fault linkage according to claim 1, 2 or 6, wherein,
in step S3, a scene coupling fault set is obtained through sequential Monte Carlo simulation by the associated coupling fault scene of the equal trend state characterization quantity:
providing an equal trend state characterization quantity s;
wherein s is i The characteristic quantity of the equal trend state of the i element, m is the number of the state quantity of the i element, and gamma ikr For the current value of the kth state quantity of the i element, gamma ikn The normal working state value of the kth state quantity of the i element, N is the total number of the elements, and gamma xkn The k state variable of the element x is a normal working state value, and the effective information value of each feature quantity is the degree of the element deviating from the normal working state, so that the abnormal working state degree of the element is obtained by utilizing the product aggregation feature;
n-1 and N-2 fault scene formation and other trend state characterization quantity matrix of computing systemM is the total number of system elements, N is the number of fault scenes; calculating nonlinear association degree and association coefficient zeta of equal trend state characterization quantity sequences of different elements by using gray theory ij The calculation formula is as follows:
n is the number of fault scenes, a sequence i is provided as a parent sequence, a sequence j is provided as a reference sequence, s i (k) The method is characterized in that the equal trend state of the element i in the kth scene represents values, and ρ is a resolution coefficient; sequentially extracting corresponding element sequences as parent sequences to calculate nonlinear relevancy with other element sequences to obtain a relevancy matrix C M×M The matrix is a symmetric matrix in which the elements ζ ij The correlation coefficient of the element i and the element j; calculating the equal trend state characterization quantity of each element after each sampling, and correcting the transient fault probability of the next sampling by using the association coefficient and the equal trend state characterization quantity of each current element:
wherein k is ic For the associated correction coefficient of the ith element, S 1×M Vectors formed by the equal trend state characterization values of the elements in the current scene,for the transposed matrix of the ith row vector of the association matrix, the abnormal working states of the element and other elements and the association between the elements are utilized to correct the instantaneous fault probability of the next sampling by combining the sampling result of the current state, and the corrected I/O is used for correcting the instantaneous fault probability of the next sampling>Thereby establishing coupling among different fault scenes in the sampling process.
8. The method for evaluating the elasticity of the multi-disaster power distribution network considering fault linkage according to claim 1, wherein the step of establishing a weighted elasticity-economy space evaluation system and evaluating the elasticity by measuring the composite entropy weight Euclidean distance between the scene cluster center and the perfect elasticity point comprises the following steps:
the single point in the elastic space corresponds to a single extreme weather event in the whole simulation event set, the coordinates of the single point are three indexes normalized by the whole event set, the perfect elastic point is located at the space origin, the weighted Euclidean distance between the space position of the system in a certain event scene and the perfect elastic point is calculated, the weighted Euclidean distance between the center of the system performance point cluster and the perfect elastic point is obtained by using the average distance of the whole simulation event set, and the weighted Euclidean distance is mapped to the elasticity of the [0, 100] interval computing system, and the formula is as follows:
wherein LLD is i ，SEDT i ，ELD i Elastic-economic coordinates, σ, of system y in the event of i, respectively 1 ，σ 2 ，σ 3 And the composite entropy weight calculation values of the three indexes are respectively obtained.
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