CN113077358B - Method for identifying fragile line of electric power system in response to hurricane disaster - Google Patents

Method for identifying fragile line of electric power system in response to hurricane disaster Download PDF

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CN113077358B
CN113077358B CN202110388044.6A CN202110388044A CN113077358B CN 113077358 B CN113077358 B CN 113077358B CN 202110388044 A CN202110388044 A CN 202110388044A CN 113077358 B CN113077358 B CN 113077358B
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唐文虎
连祥龙
钱瞳
李泽蓬
陈星宇
张文浩
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South China University of Technology SCUT
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Abstract

The invention discloses a method for identifying a fragile line of an electric power system for dealing with hurricane disasters, which comprises the following steps of firstly, respectively quantifying the influence of hurricane wind speed and line tide out-of-limit on line fault probability; then, the failure of the power system under an extreme disaster such as hurricane is described as a continuous disturbance process considering the continuous influence of strong wind; then, simulating the faults of the system under the disaster by adopting a Monte Carlo simulation method to obtain a large number of cascading fault accident chains; and then constructing a fault association diagram CFGPD under continuous disturbance describing a line fault sequence and loss conditions, and finally providing a fragile line identification mode based on the CFGPD. According to the method, the influence degree of the disaster on the power system is calculated from two dimensions of time and space, and the load loss of the system is greatly reduced by taking corresponding reinforcement measures on the identified fragile line, so that support is provided for disaster prevention.

Description

Method for identifying fragile line of electric power system in response to hurricane disaster
Technical Field
The invention relates to the technical field of electric power system operation and pre-disaster warning, in particular to a method for identifying a fragile line of an electric power system in response to hurricane disasters.
Background
Hurricane weather is an extreme natural disaster, and is very easy to cause large-scale faults in power system areas crossed by the hurricane weather, and the faults are specifically represented by power transmission line disconnection, insulator flashover, tower collapse of an iron tower, line self-excited vibration and the like. At present, a lot of model researches for deducing wind field wind speed according to historical meteorological data of hurricanes exist, but the universality is not high and the calculation is complicated.
In order to research the capability of the power system to cope with the hurricane disaster event, the hurricane disaster event is considered in three stages, namely before the occurrence of the hurricane disaster weather disaster, when the disaster occurs and after the occurrence of the disaster. The method has the advantages that the resistance of the system can be effectively improved through measures such as early warning and reinforcement in advance of disasters, and the method is an important link for reducing the loss of the system in the disaster process. In the actual disaster prevention process, the large-scale improvement of the lines brings huge cost, so that the weak lines of the system under the disaster are identified, and the method of improving a small number of the weak lines can improve the resistance of the system and greatly reduce the reinforcement cost. At present, researches on a fragile line identification method of an electric power system mainly focus on stability analysis of the electric power system, only aim at N-1 events, and have less fragile line identification analysis in a disaster scene.
In summary, the current vulnerable line identification based on the stability analysis of the power system is not suitable for the disaster scene analysis which may cause large-scale faults. Based on the method, the vulnerable line in the system can be identified before the hurricane disaster occurs, corresponding strengthening measures are taken for the weakest line, the aims of improving the resistance of the system and greatly reducing the strengthening cost can be achieved, disaster early warning and emergency strengthening measures are provided for electric power workers, and the system loss of the system during the hurricane disaster is reduced to the minimum.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art, provides a method for identifying fragile lines of a power system for responding to hurricane disasters, and can effectively solve the technical problems that the existing system response strategy is executed after a fault occurs, the existing method for strengthening the power grid under catastrophe is not sufficient in foresight, and identification of fragile lines of the power grid under catastrophe is lacked, wherein the identification can be realized by simultaneously considering disaster fault probability and a pre-disaster early warning enhancement strategy.
In order to realize the purpose, the technical scheme provided by the invention is as follows: a method for identifying a fragile line of an electric power system in response to a hurricane disaster comprises the following steps:
1) establishing two transmission line fault probability models of a power transmission line of a power system, wherein the two transmission line fault probability models are caused by strong wind blowing-off and tidal current out-of-limit;
2) constructing a fault association diagram CFGPD for describing a line fault association relation according to two power transmission line fault probability models;
3) calculating a vulnerability index describing the line vulnerability based on a fault association diagram CFGPD, and performing normalization processing to obtain a line vulnerability value;
4) identifying a fragile power transmission line under hurricane disasters according to the fragile value of the line; the sequence of the lines according to the vulnerability values is the vulnerability of the lines.
In step 1), a power transmission line fault probability model of a power transmission line of a power system, which is caused by a fault due to blowing of strong wind, is as follows:
when the surface wind speed V of the line does not exceed the maximum design wind resistant wind speed VdesWhen the device is used, the element is not influenced to normally operate;
when the surface wind speed V of the line is more than or equal to 2VdesWhen the device is in use, the device is in failure and stops running;
when the surface wind speed V of the line is at the maximum design wind-resistant wind speed VdesAnd 2VdesIn between, the line fault probability p due to wind speed(w)Increases exponentially with increasing wind speed:
Figure GDA0003534630110000021
the hidden fault model of the power transmission line of the power system caused by the power flow out-of-limit has the following conditions:
the hidden fault probability of the line caused by the out-of-limit tidal current is calculated, the limit operation current of the line is influenced by the wind speed, and the mathematical expression is as follows:
Figure GDA0003534630110000031
in the formula: i is the load capacity; t isaThe maximum allowable operating temperature (DEG C) of the lead is obtained; v is the line surface wind speed (m/s);d is the outer diameter (m) of the wire; epsilon is the radiation coefficient of the wire; s is a Stefan-Boltzmann constant; t iseAmbient temperature (. degree. C.); a issIs the overhead line heat absorption coefficient; k is a radical oftThe AC/DC resistance ratio is the temperature of the overhead line; rdcFor the overhead line temperature is TaDirect current resistance per unit length (Ω/m); i issIs the intensity of sunlight (W/m)2)；
In order to highlight the influence of the wind speed on the limit operation current of the line, the part of variables need to be set to be constant values, then
Figure GDA0003534630110000032
Wherein
Figure GDA0003534630110000033
Figure GDA0003534630110000034
The limit current of the line is proportional to the square of the limit current, and the limit current of the line under the wind speed v is
Figure GDA0003534630110000035
Comprises the following steps:
Figure GDA0003534630110000036
in the formula (I), the compound is shown in the specification,
Figure GDA0003534630110000037
for the line at wind speed v0A lower limit power flow;
when line current P(v)Not exceeding limit tide
Figure GDA0003534630110000038
When the device is used, the element is not influenced and normally operates;
when the line current flows
Figure GDA0003534630110000039
When the device is in use, the device is in failure and stops running;
when line current P(v)In extreme power flow
Figure GDA00035346301100000310
And
Figure GDA00035346301100000311
in the meantime, the line fault probability p due to the power flow out-of-limit(v)Increases in a linear fashion with increasing wind speed:
Figure GDA00035346301100000312
in step 2), the fault association map CFGPD is constructed as follows:
obtaining a large amount of cascading failure accident chain data by adopting a Monte Carlo simulation method according to two transmission line failure probability models established in the step 1), and constructing a CFGPD (computational fluid dynamics) based on the data, wherein the CFGPD can be defined as an incidence matrix E belonging to Rn×n，Rn×nThe simulation method comprises the following steps of (1) obtaining a real number matrix of n multiplied by n, wherein n is the number of fault lines in all simulations; in the m-th fault chain, fault phase s is included
Figure GDA0003534630110000041
A faulty line is composed of
Figure GDA0003534630110000042
The sum of current exceeds the limit
Figure GDA0003534630110000043
A fault line caused by strong wind speed, wherein
Figure GDA0003534630110000044
According to different fault line compositions of each stage, the element E in the matrix E is correlatedijFor a faulty line LiAnd LjIs defined as:
a. s in the accident chain m(m)In the stage, if
Figure GDA0003534630110000045
I.e. all faulty lines are faults due to strong winds, then:
Figure GDA0003534630110000046
where h represents the virtual node where hurricanes affect each line,
Figure GDA0003534630110000047
for the virtual node h and the fault line L in the mth fault chainjThe associated weight of (a) is determined,
Figure GDA0003534630110000048
and
Figure GDA00035346301100000419
the total system load at the s-1 and s phases of the accident chain m respectively,
Figure GDA0003534630110000049
the number of fault lines in the z stage of the mth accident chain is shown;
b. s in the accident chain m(m)In the stage, if
Figure GDA00035346301100000410
Namely, all fault lines are faults caused by power flow out-of-limit, then:
Figure GDA00035346301100000411
in the formula (I), the compound is shown in the specification,
Figure GDA00035346301100000412
for the fault line L in the mth fault chainiAnd LjThe associated weight of (a) is determined,
Figure GDA00035346301100000413
Figure GDA00035346301100000414
set of faulty lines for stage s-1, Ls-1,1For the first fault line of the s-1 th stage, wherein the s-1 th stage has k in commons-1The fault line is connected to the fault line,
Figure GDA00035346301100000415
the number of fault lines in the s-1 stage of the mth fault chain is determined;
c. s in the accident chain m(m)In the stage, if
Figure GDA00035346301100000416
And is
Figure GDA00035346301100000417
Then:
Figure GDA00035346301100000418
Figure GDA0003534630110000051
finally, eijCan be expressed as:
Figure GDA0003534630110000052
in the formula, M is the total number of accident chains.
In step 3), a calculation formula for calculating a vulnerability indicator describing line vulnerability is as follows:
Figure GDA0003534630110000053
in the formula, DiAs a vulnerability index, eijFor fault line L in fault correlation diagram CFGPDiAnd LjThe associated weight of (a); n is a line with a fault common to all simulationsThe number of the cells; to DiThe values after normalization were:
Figure GDA0003534630110000054
Dmin、Dmaxthe minimum and maximum values of the vulnerability index.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. firstly, respectively quantifying the influence of hurricane wind speed and line load flow threshold on line fault probability; then, the fault condition of the power system under an extreme disaster such as hurricane is described as a continuous disturbance process considering the continuous influence of strong wind; then, simulating the faults of the system under the disaster by adopting a Monte Carlo simulation method to obtain a large number of cascading fault accident chains; and then constructing a fault association diagram (CFGPD) under continuous disturbance describing the line fault sequence and the loss condition, and finally providing a fragile line identification mode based on the CFGPD. The method can calculate the influence degree of the disaster on the power system from two aspects of time dimension and space dimension, and can greatly reduce the load loss of the system and provide support for disaster prevention by taking corresponding reinforcement measures on the identified fragile lines.
2. The method is based on the Monte Carlo simulation method, can combine the power grid data and consider the time sequence influence of hurricanes, simulates the fault condition of the system when the hurricane disaster arrives, and the fault form of the line is expressed as the fault caused by blowing-off of strong wind and line current out-of-limit, so that the fault model of the system is more reasonable.
3. The method of the invention describes the incidence relation among fault lines based on CFGPD constructed by accident chains, and the weighted in-degree of the nodes represents the importance degree of the nodes in the CFGPD, namely the vulnerability of the corresponding lines in the system. Corresponding enhancement measures are taken for the identified fragile lines, so that the load loss of the system can be greatly reduced, and guidance is provided for pre-disaster early warning reinforcement measures.
4. The method has good foresight and load reduction effects, can effectively improve the capability of the power system to resist hurricane disasters, and has certain guiding significance for the early warning and reinforcing operation processes of the power system before the hurricane disasters come.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a schematic diagram of a power system cascading failure in a hurricane scenario for a specific case.
Fig. 3 is a diagram of the system geographical location and hurricane path for a specific case.
Fig. 4 is a graph of system loss after elasticity enhancement measures are taken for different groups of fragile lines for a specific case.
Fig. 5 is a diagram of system loss after applying elasticity enhancement measures for the specific case of fragile lines identified by different analysis methods.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
Referring to fig. 1, the method for identifying a vulnerable line of an electric power system in response to a hurricane disaster, provided by the invention, comprises the following steps:
step 1: the method comprises the steps of dividing a power transmission line in a power system into a plurality of parts according to geographical positions, and simulating the influence of hurricane weather at different moments according to the weather intensity of a line.
Step 2: and (4) establishing a fault model of the element based on the wind speed of the line obtained in the step (1) at different moments. The line fault model includes: the fault probability of the power transmission line caused by strong wind and the hidden fault probability caused by the out-of-limit tidal current include two fault probability models of the power transmission line caused by the blowing-off of strong wind and the out-of-limit tidal current, and the fault probability of the power transmission line caused by the out-of-limit tidal current specifically comprises the following steps:
calculating the probability of disconnection fault caused by strong wind: when the surface wind speed V of the line does not exceed the maximum design wind-resistant wind speed VdesWhen the device is used, the element is not influenced to normally operate; when the surface wind speed V of the line is more than or equal to 2VdesWhen the device is in use, the device is in failure and stops running; when the surface wind speed V of the line is at the maximum design wind-resistant wind speed VdesAnd 2VdesIn the middle of the time, the air conditioner,line fault probability p due to wind speed(w)Increases exponentially with increasing wind speed:
Figure GDA0003534630110000071
the hidden fault probability calculation caused by the out-of-limit tidal current is that the maximum operation current of the line is influenced by the wind speed, and the mathematical expression is as follows:
Figure GDA0003534630110000072
in the formula: i is the calculated load capacity; t isaThe maximum allowable operating temperature (DEG C) of the lead is obtained; v is the line surface wind speed (m/s); d is the outer diameter (m) of the wire; epsilon is the radiation coefficient of the wire; s is Stefan-Boltzmann constant; t iseAmbient temperature (deg.C); a is asIs the overhead line heat absorption coefficient; k is a radical oftThe AC/DC resistance ratio is the temperature of the overhead line; rdcFor the overhead line temperature is TaDirect current resistance per unit length (Ω/m); i issIs the intensity of sunlight (W/m)2)。
In order to highlight the influence of the wind speed on the limit operation current of the line, the partial variables are set to be constant values in the method, and then
Figure GDA0003534630110000073
Wherein
Figure GDA0003534630110000074
Figure GDA0003534630110000075
The limit power flow of the line is proportional to the square of the limit current, and then the limit power flow of the line at the wind speed v is as follows:
Figure GDA0003534630110000081
in the formula (I), the compound is shown in the specification,
Figure GDA0003534630110000082
for the line at wind speed v0A lower limit power flow;
when line current P(v)Not exceeding limit tidal current
Figure GDA0003534630110000083
When the device is used, the element is not influenced to normally operate; when the line current flows
Figure GDA0003534630110000084
When the device is in use, the device is in failure and stops running; when line current P(v)In extreme power flow
Figure GDA0003534630110000085
And
Figure GDA0003534630110000086
in the meantime, the line fault probability p due to the power flow out-of-limit(v)Increases in a linear fashion with increasing wind speed:
Figure GDA0003534630110000087
and 3, step 3: obtaining a large amount of cascading failure accident chain data by adopting a Monte Carlo simulation method according to the two transmission line failure probability models in the step 2, and constructing a failure correlation diagram CFGPD based on the data, wherein the failure correlation diagram CFGPD can be defined as a correlation matrix E epsilon Rn×n，Rn×nThe simulation method is a real matrix of n multiplied by n, and n is the number of fault lines in all simulations. In the m-th fault chain, fault phase s is included
Figure GDA0003534630110000088
A faulty line, composed of
Figure GDA0003534630110000089
The sum of current and current exceeds the limit
Figure GDA00035346301100000810
A fault line caused by strong wind speed, wherein
Figure GDA00035346301100000811
According to different fault line compositions of each stage, the element E in the correlation matrix EijFor a faulty line LiAnd LjIs defined as:
a. s in the accident chain m(m)In the stage, if
Figure GDA00035346301100000812
I.e. all faulty lines are faults due to strong winds, then:
Figure GDA00035346301100000813
where h represents the virtual node where hurricanes affect each line,
Figure GDA00035346301100000814
for the virtual node h and the fault line L in the mth fault chainjThe associated weight of (a) is determined,
Figure GDA00035346301100000815
and Ps (m)The total system load at the s-1 and s phases of the accident chain m respectively,
Figure GDA00035346301100000816
the number of fault lines in the z stage of the mth accident chain is shown;
b. s in the accident chain m(m)In the stage, if
Figure GDA0003534630110000091
Namely, all fault lines are faults caused by power flow out-of-limit, then:
Figure GDA0003534630110000092
in the formula (I), the compound is shown in the specification,
Figure GDA0003534630110000093
for the fault line L in the mth fault chainiAnd LjThe associated weight of (a) is determined,
Figure GDA0003534630110000094
Figure GDA0003534630110000095
set of faulty lines for stage s-1, Ls-1,1For the first fault line of the s-1 th stage, wherein the s-1 th stage has k in commons-1The fault line is connected to the fault line,
Figure GDA0003534630110000096
the number of fault lines in the s-1 stage of the mth fault chain is determined;
c. s in the accident chain m(m)In the phase, if
Figure GDA0003534630110000097
And is
Figure GDA0003534630110000098
Then:
Figure GDA0003534630110000099
Figure GDA00035346301100000910
finally, eijCan be expressed as:
Figure GDA00035346301100000911
in the formula, M is the total number of accident chains.
And 4, step 4: based on a fault association diagram CFGPD, calculating a vulnerability index describing the line vulnerability, wherein a calculation formula for calculating the vulnerability index describing the line vulnerability is as follows:
Figure GDA00035346301100000912
in the formula, DiAs a vulnerability index, eijFor fault line L in fault correlation diagram CFGPDiAnd LjThe associated weight of (a); to DiThe values after normalization were:
Figure GDA00035346301100000913
Dmin、Dmaxthe minimum and maximum values of the vulnerability index.
And 5: calculating line fragility value D of fault linei' the lines are sorted according to the vulnerability values of the lines, namely the vulnerability of the lines, and the vulnerable power transmission lines under the hurricane disaster can be identified according to the vulnerability values of the lines.
In the following, we use the us texas 2000 node power system data to perform example analysis to perform verification calculation of the present invention. The test system comprises 2000 nodes, 3000 transmission lines. All nodes and transmission lines in the system are assumed to be exposed to the open air environment.
The power system cascading failure in a hurricane scenario is shown in FIG. 2, which is the kth stage of the ssA faulty line can be represented as
Figure GDA0003534630110000101
h represents the virtual node influenced by hurricanes on each line, and scenes 1, 2 and 3 respectively correspond to the line fault classification conditions of a, b and c in the step 3. The power system nodes and line geographical locations and hurricane paths are shown in the left diagram of fig. 3, where a hurricane logs in from the southeast coast affecting the grid and moves in the northeast direction. The right side of fig. 3 shows the magnitude of the fault line vulnerability value, with darker line colors representing greater vulnerability values.
Table 1 lists the fragile line ordering, dividing the most fragile 60 lines into 6 groups (each group containing 10 lines) according to the size of the fragile value.
TABLE 1 ordering of the most vulnerable 60 lines of the System
Figure GDA0003534630110000102
Figure GDA0003534630110000111
In order to verify that the identified line is the fragile line in the example scene, the method adopts a mode of enhancing the wind resistance or the limit operation capacity of the line in groups to carry out simulation verification. The result is shown in fig. 4, where group 0 is a scenario where no enhancements are taken to the system line. By contrast enhancement of the line system loss results of different groups, it can be seen that: when the enhancement measures are respectively taken on the lines in the group 1 and the group 2, the system load loss and the line loss are greatly reduced, wherein the group 1 reduction is most obvious, and the load loss of 13.54 percent and the line loss of 10.36 percent are reduced. In addition, after the same enhancement measures are respectively taken for the groups 1 to 6, the system loss gradually increases, which shows that the method provided by the invention can accurately identify the vulnerability of the line in the system.
By way of comparison, the present invention is also compared to two other common fragile line methods: methods based on Component Interaction Matrix (CIM) and based on Cascading Failure Graphs (CFG). The comparison result is shown in fig. 5, where INITIAL is a scenario where no enhancement is taken by the system line. The result shows that when the number of the most vulnerable 10 lines identified by the method is increased, the system load loss and the link loss are both reduced to the minimum, which shows that the method for identifying the vulnerable lines provided by the method is more advantageous. The method for identifying the fragile line of the system in the hurricane scene can be applied to the early warning stage before the hurricane, and provides the guide for strengthening the power grid operating personnel in advance so as to reduce the loss caused by the hurricane disaster.
In summary, the method can identify the vulnerable lines of the power system before hurricane disaster and improve the strength of the lines, can achieve the effect of reducing load reduction and link loss and good foresight, reinforces the reference for pre-disaster warning of the power system under natural disaster, and is worthy of popularization.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (2)

1. A method for identifying a fragile line of an electric power system in response to a hurricane disaster is characterized by comprising the following steps:
1) establishing two transmission line fault probability models of a transmission line of an electric power system, wherein the two transmission line fault probability models are caused by strong wind blowing-off and tidal current out-of-limit;
2) according to two transmission line fault probability models, constructing a fault association diagram CFGPD (computational fluid dynamics grid diagram) describing a line fault association relation, namely a mapping fault graph under persistent disturbance; the fault association graph CFGPD is constructed as follows:
obtaining a large amount of cascading failure accident chain data by adopting a Monte Carlo simulation method according to two transmission line failure probability models established in the step 1), and constructing a CFGPD (computational fluid dynamics) based on the data, wherein the CFGPD can be defined as an incidence matrix E belonging to Rn×n，Rn×nThe simulation method comprises the following steps of (1) obtaining a real number matrix of n multiplied by n, wherein n is the number of fault lines in all simulations; in the m-th fault chain, fault phase s is included
Figure FDA0003534630100000011
A faulty line, composed of
Figure FDA0003534630100000012
The sum of current and current exceeds the limit
Figure FDA0003534630100000013
Fault circuit caused by strong wind speedWherein
Figure FDA0003534630100000014
According to different fault line compositions of each stage, the element E in the correlation matrix EijFor a faulty line LiAnd LjIs defined as:
a. s in the accident chain m(m)In the stage, if
Figure FDA0003534630100000015
I.e. all faulty lines are faults due to strong winds, then:
Figure FDA0003534630100000016
where h represents the virtual node where hurricanes affect each line,
Figure FDA0003534630100000017
for the virtual node h and the fault line L in the mth fault chainjThe associated weight of (a) is determined,
Figure FDA0003534630100000018
and
Figure FDA0003534630100000019
the total system load at the s-1 and s phases of the accident chain m respectively,
Figure FDA00035346301000000110
the number of fault lines in the z stage of the mth accident chain is shown;
b. s at accident chain m(m)In the stage, if
Figure FDA00035346301000000111
Namely, all fault lines are faults caused by power flow out-of-limit, then:
Figure FDA0003534630100000021
in the formula (I), the compound is shown in the specification,
Figure FDA0003534630100000022
for the fault line L in the mth fault chainiAnd LjThe associated weight of (a) is calculated,
Figure FDA0003534630100000023
Figure FDA0003534630100000024
set of faulty lines for stage s-1, Ls-1,1For the first fault line of the s-1 th stage, wherein the s-1 th stage has k in commons-1The fault line is connected to the fault line,
Figure FDA0003534630100000025
the number of fault lines in the s-1 stage of the mth fault chain is determined;
c. s in the accident chain m(m)In the phase, if
Figure FDA0003534630100000026
And is
Figure FDA0003534630100000027
Then:
Figure FDA0003534630100000028
Figure FDA0003534630100000029
finally, eijCan be expressed as:
Figure FDA00035346301000000210
in the formula, M is the total number of accident chains;
3) calculating a vulnerability index describing the line vulnerability based on a fault association diagram CFGPD, and performing normalization processing to obtain a line vulnerability value; the calculation formula for calculating the vulnerability index describing the line vulnerability is as follows:
Figure FDA00035346301000000211
in the formula, DiAs a vulnerability index, eijFor fault line L in fault correlation diagram CFGPDiAnd LjThe associated weight of (a); n is the number of lines with faults in all the simulations; to DiThe values after normalization were:
Figure FDA00035346301000000212
Dmin、Dmaxminimum and maximum values for the vulnerability index;
4) identifying a fragile power transmission line under hurricane disasters according to the fragile value of the line; the sequence of the lines according to the vulnerability values is the vulnerability of the lines.
2. The method of claim 1, wherein the method comprises the steps of: in step 1), a power transmission line fault probability model of a power transmission line of a power system, which is caused by a fault due to blowing of strong wind, is as follows:
when the surface wind speed V of the line does not exceed the maximum design wind resistant wind speed VdesWhen the device is used, the element is not influenced and normally operates;
when the surface wind speed V of the line is more than or equal to 2VdesWhen the device is in use, the device is in failure and stops running;
when the surface wind speed V of the line is at the maximum design wind-resistant wind speed VdesAnd 2VdesIn between, the line fault probability p due to wind speed(w)With increasing wind speedIncrease in exponential form:
Figure FDA0003534630100000031
the hidden fault model of the power transmission line of the power system caused by the power flow out-of-limit has the following conditions:
the hidden fault probability of the line caused by the out-of-limit tidal current is calculated, the limit operation current of the line is influenced by the wind speed, and the mathematical expression is as follows:
Figure FDA0003534630100000032
in the formula: i is the load capacity; t isaThe maximum allowable operating temperature of the wire; v is the line surface wind speed; d is the outer diameter of the lead; epsilon is the radiation coefficient of the wire; s is a Stefan-Boltzmann constant; t iseIs ambient temperature; a issIs the overhead line heat absorption coefficient; k is a radical oftThe AC/DC resistance ratio is the temperature of the overhead line; rdcFor the overhead line temperature is TaDc resistance per unit length of time; i issThe intensity of sunlight;
in order to highlight the influence of the wind speed on the limit operation current of the line, the part of variables need to be set to be constant values, then
Figure FDA0003534630100000033
Wherein
Figure FDA0003534630100000034
Figure FDA0003534630100000035
The limit current of the line is proportional to the square of the limit current, and the limit current of the line under the wind speed v
Figure FDA0003534630100000036
Comprises the following steps:
Figure FDA0003534630100000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003534630100000042
for the line at wind speed v0A lower limit power flow;
when line current P(v)Not exceeding limit tidal current
Figure FDA0003534630100000043
When the device is used, the element is not influenced to normally operate;
when the line current flows
Figure FDA0003534630100000044
When the device is in use, the device is in failure and stops running;
when line current P(v)In extreme power flow
Figure FDA0003534630100000045
And
Figure FDA0003534630100000046
in the meantime, the line fault probability p due to the power flow out-of-limit(v)Increases in a linear fashion with increasing wind speed:
Figure FDA0003534630100000047
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