CN115545393A - Toughness-considered electric-gas coupling system fragile element identification method - Google Patents

Toughness-considered electric-gas coupling system fragile element identification method Download PDF

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CN115545393A
CN115545393A CN202210921340.2A CN202210921340A CN115545393A CN 115545393 A CN115545393 A CN 115545393A CN 202210921340 A CN202210921340 A CN 202210921340A CN 115545393 A CN115545393 A CN 115545393A
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柳志军
翁利国
施洪
周国华
陈杰
霍凯龙
李南
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Hangzhou Power Supply Co of State Grid Zhejiang Electric Power Co Ltd
Zhejiang Zhongxin Electric Power Engineering Construction Co Ltd
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Zhejiang Zhongxin Electric Power Engineering Construction Co Ltd
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Abstract

The invention discloses a toughness-considered method for identifying a fragile element of an electric-gas coupling system. The method comprises the following steps: establishing an electric-gas coupling system; establishing a target model of an electric-gas coupling system considering electric power network constraint and natural gas network constraint, and outputting a power flow value of each power transmission line in the electric power network by the target model; and establishing an element vulnerability evaluation index model of the electric-gas coupling system, and inputting and outputting the trend value of each transmission line in the power network to the vulnerability index of each transmission line in the power network, thereby realizing the identification of the vulnerable elements in the electric-gas coupling system. The method can quantitatively analyze the influence of the natural gas network on the toughness of the power network under the condition of considering the transient natural gas flow characteristics, and meanwhile, the method can enhance the control and protection of the elements by identifying key fragile elements in the power network, so that the capability of the power network for coping extreme events can be effectively improved.

Description

Toughness-considered fragile element identification method for electric-gas coupling system
Technical Field
The invention relates to a fragile element identification method, in particular to a toughness-considered fragile element identification method for an electric-gas coupling system.
Background
With the increase of the permeability of the natural gas unit and the electric gas conversion equipment in the power grid, the interaction between the power system and the natural gas network is stronger and stronger. Many power outages in power systems are caused by failures of other energy networks, and therefore, in the context of electro-pneumatic coupling, it is necessary to comprehensively consider the effects of natural gas systems when evaluating the reliability and toughness of power systems.
Currently, power system toughness is broadly defined as the ability to withstand or mitigate the effects of various types of disturbances, including the ability to anticipate, adapt to, and quickly recover from faults. Many extreme natural disasters occur, which shift the power system scheduling from reliability-based operation more to toughness-based operation. In conventional dispatch, power systems tend to be precisely planned to resist random failures of one or both components, i.e., the N-1/N-2 standard. However, failure of many elements may occur simultaneously in extreme weather, making traditional reliability scheduling approaches difficult to implement. Therefore, the toughness is often used to measure the degree of influence of extreme weather faults on the power system, so as to further improve the capability of the power system to cope with such faults.
The identification of the fragile elements in the power system is a key link for evaluating the toughness of the system, and the existing research mainly constructs an element fragile evaluation model from two aspects of a network topological structure and a system operation state. However, the current research is mainly limited to the independent operation of the power system, and does not consider the comprehensive operation characteristics of the electric-gas coupling system and the interaction effect among various energy systems. Therefore, an electro-pneumatic coupling system fragile element comprehensive evaluation framework considering transient natural gas flow characteristics is not available at present for identifying fragile elements.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a toughness-considered method for identifying a fragile element of an electric-gas coupling system. On the basis of establishing an electric-gas coupling system model, a vulnerability assessment index system is further established to identify key vulnerable elements, the influence of line and natural gas source faults on the toughness of the comprehensive system is assessed through network efficiency and system transmission efficiency indexes, and the validity of a vulnerability assessment result is verified.
The technical scheme adopted by the invention is as follows:
the fragile element identification method comprises the following steps:
step 1) establishing an electric-gas coupling system, which comprises a power network, a natural gas network and the power network, and acquiring the natural gas supply quantity and the reduction quantity of each node in the natural gas network and the active load quantity and the active load shedding quantity of each node in the power network, namely the initial running state of the electric-gas coupling system.
And 2) establishing a target model of the electric-gas coupling system considering the power network constraint and the natural gas network constraint, inputting the natural gas supply quantity and the reduction quantity of each node in the natural gas network and the active load quantity and the active load shedding quantity of each node in the power network into the target model of the electric-gas coupling system, and outputting the power flow value of each power transmission line in the power network by the target model.
And 3) establishing an element fragility evaluation index model of the electric-gas coupling system, inputting the power flow value of each power transmission line in the power network into the element fragility evaluation index model, and outputting the fragility index of each power transmission line in the power network by the element fragility evaluation index model, so that the identification of the fragile elements in the electric-gas coupling system is realized.
In the step 1), a power network in the electric-gas coupling system comprises a plurality of power nodes, each node is provided with a generator set, a natural gas generator set or a load, and the generator sets, the natural gas generator sets and the loads in the power network are connected through power transmission lines; the natural gas network comprises a plurality of natural gas nodes, each natural gas node is provided with a natural gas unit, each natural gas unit in the natural gas network is connected through a pipeline, each pipeline in the natural gas network is provided with a compressor, and the natural gas network conveys natural gas through a plurality of connected natural gas sources; each natural gas generating set in the power network is connected with the natural gas generating sets in the natural gas network through pipeline lines.
In the step 2), the established target model of the electric-gas coupling system considering the power network constraint and the natural gas network constraint specifically includes the following steps:
Figure BDA0003777673300000021
wherein N is g And N e Respectively representing the number of nodes in a natural gas network and a power network;
Figure BDA0003777673300000022
and
Figure BDA0003777673300000023
respectively representing the natural gas cost and the natural gas cutting cost of the ith node in the natural gas network; a. The g,i And Δ A g,i Respectively representing the natural gas supply amount and the reduction amount of the ith node in the natural gas network;
Figure BDA0003777673300000024
and
Figure BDA0003777673300000025
respectively representing the unit cost and the load shedding cost of the jth node in the power network; l is a radical of an alcohol j And Δ L j Respectively representing the active load capacity and the active load shedding capacity of the jth node in the power network. The cost specifically represents the relevant amount of the unit itself or the quantity of natural gas or electricity consumed.
The power network constraint based on the direct current power flow is specifically as follows:
P c,j +P gas,j -L j +ΔL j -P in,j ＝0
Q c,j +Q gas,j -Q L,j +ΔQ L,j -Q in,j ＝0
Figure BDA0003777673300000026
Figure BDA0003777673300000031
Figure BDA0003777673300000032
Figure BDA0003777673300000033
Figure BDA0003777673300000034
Figure BDA0003777673300000035
Figure BDA0003777673300000036
Figure BDA0003777673300000037
wherein, P c,j And Q c,j Respectively representing the active output and the reactive output of a generator set at the j node in the power network when the j node in the power network is the generator set; p is gas,j And Q gas,j Respectively representing the active output and the reactive output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set; p is in,j And Q in,j Respectively representing net injected active output and net injected reactive output of a j-th node in the power network; q L,j And Δ Q L,j Respectively representing the reactive load capacity and the reactive load shedding capacity of the jth node in the power network; v j Representing a voltage magnitude at a jth node in the power network; g jk And B jk Respectively representing the real part and the imaginary part of the kth row and the jth column of the node admittance matrix; theta.theta. jk Representing a phase angle difference between a jth node and a kth node in the power network; f jk Representing a tidal current value of the transmission line between the jth node and the kth node in the power network; v j min And V j max Respectively representing the minimum value and the maximum value of the voltage amplitude of a jth node in the power network;
Figure BDA0003777673300000038
and
Figure BDA0003777673300000039
respectively representing the minimum value and the maximum value of the power flow value of the power transmission line between the jth node and the kth node in the power network;
Figure BDA00037776733000000310
and
Figure BDA00037776733000000311
respectively representing the minimum value and the maximum value of the active output of the generator set at the j node in the power network when the j node in the power network is the generator set;
Figure BDA00037776733000000312
and
Figure BDA00037776733000000313
respectively representing the minimum value and the maximum value of the active output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set;
Figure BDA00037776733000000314
and
Figure BDA00037776733000000315
respectively representing the minimum value and the maximum value of the reactive output of the generator set at the j node in the power network when the j node in the power network is the generator set;
Figure BDA00037776733000000316
and
Figure BDA00037776733000000317
respectively representing the minimum value and the maximum value of the reactive output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set; the jth node and the kth node in the power network are connected; a power flow value F of the transmission line between the jth node and the kth node in the power network jk Net injected active output P by jth node in the power network in,j And net injected reactive output Q in,j And (6) determining.
The natural gas network constraint considering the transient process of the natural gas flow specifically comprises the following steps:
A g,i -A gas,i -L g,i +ΔA g,i -A in,i ＝0
Figure BDA0003777673300000041
P gas,j ＝η g2p A gas,i G HV
Figure BDA0003777673300000042
Figure BDA0003777673300000043
Figure BDA0003777673300000044
Figure BDA0003777673300000045
Figure BDA0003777673300000046
Figure BDA0003777673300000047
0≤ΔA g,i ≤A g,i
0≤ΔP e,j ≤P e,j
wherein A is gas,i Representing the amount of natural gas consumed by the natural gas unit at the ith node in the natural gas network; l is g,i Representing the natural gas load capacity of the ith node in the natural gas network; the natural gas injection amount of the ith node in the natural gas network; r represents a natural gas constant; psi, d and l denote the temperature of the pipeline line connected between the ith and the w-th nodes in the natural gas networkDiameter and length; ρ is a unit of a gradient n Represents the density of natural gas under standard conditions; a. The in,i And A in,w Respectively representing the net injected natural gas amount of the ith node in the natural gas network and the w node in the natural gas network; z is a radical of formula s Representing the compressibility of natural gas; pi i And pi w Respectively representing the air pressure of an ith node in the natural gas network and the air pressure of a w node in the natural gas network; eta g2p Representing the generating efficiency of the natural gas unit; g HV Represents the thermal efficiency of natural gas; v represents the natural gas flow transport velocity in the pipeline circuit; u represents a natural gas transmission coefficient;
Figure BDA0003777673300000048
representing the average flow rate of the natural gas stream in the pipeline connected between the ith node and the w-th node in the natural gas network; h is iw Representing the power consumption of a compressor branch between an ith node and a w-th node in the natural gas network; b is a mixture of iw A compressor constant representing a compressor on a pipeline line connected between an ith node and a w-th node in the natural gas network; f. of iw And τ iw Respectively representing the natural gas flow circulating in a pipeline connected between the ith node and the w-th node in the natural gas network and the natural gas flow consumed by a compressor; z and r represent the compressor coefficient and thermodynamic coefficient, respectively; a. b and c represent a first consumption coefficient, a second consumption coefficient and a third consumption coefficient of the compressor, respectively;
Figure BDA0003777673300000051
and
Figure BDA0003777673300000052
respectively representing the minimum value and the maximum value of the natural gas supply quantity of the ith node in the natural gas network;
Figure BDA0003777673300000053
and
Figure BDA0003777673300000054
respectively representing the ith section in the natural gas networkMinimum and maximum values of natural gas pressure at the point;
Figure BDA0003777673300000055
and
Figure BDA0003777673300000056
respectively representing the minimum value and the maximum value of the compressor boost ratio of a compressor on a pipeline line connected between the ith node and the w-th node in the natural gas network; delta P e,j And P e,j Respectively representing the reduction amount and the output amount of the electric load of the jth node in the power network; the ith node in the natural gas network is connected with the jth node in the power network.
In the step 3, the component vulnerability assessment index model V (m) of the electric-electric coupling system is established as follows:
V(m)＝V 1 (m)(α 1 V 2 (m)+α 2 V 3 (m))
the power transmission line between the jth node and the kth node in the power network is the mth power transmission line in the power network; v 1 (m) represents the coupling vulnerability index, V, of the mth transmission line in the power network 2 (m) represents a topological vulnerability indicator, V, of the mth transmission line in the power network 3 (m) represents the operational vulnerability index, alpha, of the mth transmission line in the power network 1 And alpha 2 Respectively representing a preset first weight index and a preset second weight index.
The m-th transmission line in the power network has a coupling fragility index V 1 (m), specifically as follows:
Figure BDA0003777673300000057
wherein N is s Representing the number of natural gas sources; v s And
Figure BDA0003777673300000058
respectively representing the s-th natural gas source in each natural gas sourceThe vulnerability index and the normalization value thereof; Δ F m,s And the power flow change value of the mth transmission line in the power network is shown after the s-th natural gas source fails.
The fragility indexes of the s-th natural gas source in the natural gas sources are as follows:
Figure BDA0003777673300000059
wherein, Δ F s Representing the power flow variation of all power transmission lines in the power network; h s Representing a power flow distribution entropy of the power network; n is a radical of hydrogen pl Representing the number of transmission lines in the power network; f m,0 Showing that before the fault of the s-th natural gas source, the flow value of the m-th power transmission line in the power network is the flow value F of the power transmission line between the j-th node and the k-th node in the power network obtained in the step 2 jk ；R m,s And the power flow impact rate of the mth transmission line in the power network is shown after the s-th natural gas source fails.
Tidal current variation delta F of all transmission lines in power network s The method comprises the following steps:
Figure BDA00037776733000000510
wherein, F m,s And the flow value of the mth transmission line in the power network is shown after the mth natural gas source fails.
Power flow distribution entropy H of power network s The method comprises the following steps:
Figure BDA0003777673300000061
when the s-th natural gas source fails, the tidal current impact rate R of the m-th transmission line in the power network m,s The method comprises the following steps:
Figure BDA0003777673300000062
ΔF m,s ＝|F m,s -F m,0 |。
the topological vulnerability index V of the mth transmission line in the power network 2 (m), specifically as follows:
Figure BDA0003777673300000063
wherein N is eg And N ed Respectively representing the number of generator sets and the number of nodes where loads are located in the power network; TC (tungsten carbide) j,k Representing a line transmission capacity of a transmission line between a jth node and a kth node in the power network;
Figure BDA0003777673300000064
indicating topological vulnerability index V 2 (m) an integer variable, the integer variable being present when the mth transmission line in the power network is or is not present between the jth node and the kth node in the power network
Figure BDA0003777673300000065
Is 1 or 0.
The line transmission capacity of the transmission line between the jth node and the kth node in the power network is specifically as follows:
Figure BDA0003777673300000066
wherein S is j,k Representing the set of transmission lines, tc, between the jth and kth node in the power network m Representing the line transmission capacity of the mth transmission line in the power network.
The operation fragility index V of the mth transmission line in the power network 3 (m), specifically as follows:
Figure BDA0003777673300000067
wherein H m Representing the power flow distribution entropy of the m-th transmission line in the power network after the fault; r a,m And the power flow impact ratio of the m-th transmission line in the power network to the a-th transmission line in the power network after the m-th transmission line in the power network fails is shown.
Power flow distribution entropy H after fault of mth transmission line in power network m The method comprises the following steps:
Figure BDA0003777673300000071
the power flow impact ratio R of the m-th transmission line in the power network to the a-th transmission line in the power network after the m-th transmission line in the power network fails a,m The method comprises the following steps:
Figure BDA0003777673300000072
wherein, Δ F a,m And F a,m Respectively representing the power flow change value and the power flow value of the a-th power transmission line in the power network after the m-th power transmission line in the power network fails; f a,0 And the current value of the a-th transmission line in the power network before the m-th transmission line in the power network fails is shown.
The higher the vulnerability index of each power transmission line in the power network output by the element vulnerability evaluation index model is, the more vulnerable the power transmission line is.
The invention has the beneficial effects that:
the method can quantitatively analyze the influence of the natural gas network on the toughness of the power network under the condition of considering the transient natural gas flow characteristics. Meanwhile, the identification result of the key fragile elements of the power network can enhance the control and protection of the elements, effectively improve the response capability of the power network to extreme events, and meet the application requirement under the background of the future power-air deep coupling.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the embodiments.
As shown in fig. 1, the method for identifying fragile components of the present invention comprises the following steps:
step 1) establishing an electric-gas coupling system, which comprises a power network, a natural gas network and the power network, and acquiring the natural gas supply quantity and the reduction quantity of each node in the natural gas network and the active load quantity and the active load shedding quantity of each node in the power network, namely the initial running state of the electric-gas coupling system.
In the step 1), a power network in the electric-gas coupling system comprises a plurality of power nodes, each node is provided with a generator set, a natural gas generator set or a load, and the generator sets, the natural gas generator sets and the loads in the power network are connected through power transmission lines; the natural gas network comprises a plurality of natural gas nodes, each natural gas node is provided with a natural gas unit, each natural gas unit in the natural gas network is connected through a pipeline, each pipeline in the natural gas network is provided with a compressor, and the natural gas network conveys natural gas through a plurality of connected natural gas sources; each natural gas generating set in the power network is connected with the natural gas generating set in the natural gas network through a pipeline.
And 2) establishing a target model of the electric-gas coupling system considering the power network constraint and the natural gas network constraint, inputting the natural gas supply quantity and the reduction quantity of each node in the natural gas network and the active load quantity and the active load shedding quantity of each node in the power network into the target model of the electric-gas coupling system, and outputting the load flow value of each power transmission line in the power network by the target model.
In the step 2), the established target model of the electric-gas coupling system considering the power network constraint and the natural gas network constraint is as follows:
Figure BDA0003777673300000081
wherein N is g And N e Respectively representing the number of nodes in a natural gas network and a power network;
Figure BDA0003777673300000082
and
Figure BDA0003777673300000083
respectively representing the natural gas cost and the natural gas cutting cost of the ith node in the natural gas network; a. The g,i And Δ A g,i Respectively representing the natural gas supply amount and the reduction amount of the ith node in the natural gas network;
Figure BDA0003777673300000084
and
Figure BDA0003777673300000085
respectively representing the unit cost and the load shedding cost of the jth node in the power network; l is j And Δ L j Respectively representing the active load capacity and the active load shedding capacity of the jth node in the power network. The cost specifically represents the relevant amount of the unit itself or the quantity of natural gas or electricity consumed.
The power network constraint based on the direct current power flow is specifically as follows:
P c,j +P gas,j -L j +ΔL j -P in,j ＝0
Q c,j +Q gas,j -Q L,j +ΔQ L,j -Q in,j ＝0
Figure BDA0003777673300000086
Figure BDA0003777673300000087
Figure BDA0003777673300000088
Figure BDA0003777673300000089
Figure BDA00037776733000000810
Figure BDA00037776733000000811
Figure BDA00037776733000000812
Figure BDA00037776733000000813
wherein, P c,j And Q c,j Respectively representing the active output and the reactive output of a generator set at the j node in the power network when the j node in the power network is the generator set; p gas,j And Q gas,j Respectively representing the active output and the reactive output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set; p is in,j And Q in,j Respectively representing net injected active output and net injected reactive output of a jth node in the power network; q L,j And Δ Q L,j Respectively representing the reactive load capacity and the reactive load shedding capacity of the jth node in the power network; v j Representing a voltage magnitude at a jth node in the power network; g jk And B jk Respectively representing the real part and the imaginary part of the kth row and the jth column of the node admittance matrix; theta.theta. jk Representing a phase angle difference between a jth node and a kth node in the electrical power network; f jk Representing transmission lines between jth and kth nodes in an electrical power networkThe tidal current value of (c); v j min And V j max Respectively representing the minimum value and the maximum value of the voltage amplitude of a jth node in the power network;
Figure BDA0003777673300000091
and
Figure BDA0003777673300000092
respectively representing the minimum value and the maximum value of the power flow value of the power transmission line between the jth node and the kth node in the power network;
Figure BDA0003777673300000093
and
Figure BDA0003777673300000094
respectively representing the minimum value and the maximum value of the active output of the generator set at the j node in the power network when the j node in the power network is the generator set;
Figure BDA0003777673300000095
and
Figure BDA0003777673300000096
respectively representing the minimum value and the maximum value of the active output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set;
Figure BDA0003777673300000097
and
Figure BDA0003777673300000098
respectively representing the minimum value and the maximum value of the reactive output of the generator set at the j node in the power network when the j node in the power network is the generator set;
Figure BDA0003777673300000099
and
Figure BDA00037776733000000910
respectively representing the minimum value and the maximum value of the reactive output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set; the jth node and the kth node in the power network are connected; a power flow value F of the transmission line between the jth node and the kth node in the power network jk Net injected active output P by jth node in power network in,j And net injected reactive output Q in,j And (6) determining.
The natural gas network constraints considering the natural gas flow transient process are specifically as follows:
A g,i -A gas,i -L g,i +ΔA g,i -A in,i ＝0
Figure BDA00037776733000000911
P gas,j ＝η g2p A gas,i G HV
Figure BDA00037776733000000912
Figure BDA00037776733000000913
Figure BDA00037776733000000914
Figure BDA00037776733000000915
Figure BDA0003777673300000101
Figure BDA0003777673300000102
0≤ΔA g,i ≤A g,i
0≤ΔP e,j ≤P e,j
wherein A is gas,i Representing the amount of natural gas consumed by the natural gas unit at the ith node in the natural gas network; l is a radical of an alcohol g,i Representing the natural gas load capacity of the ith node in the natural gas network; the natural gas injection amount of the ith node in the natural gas network; r represents a natural gas constant; psi, d and l denote the temperature, diameter and length of the pipeline lines connected between the ith and w-th nodes in the natural gas network; rho n Represents the density of natural gas under standard conditions; a. The in,i And A in,w Respectively representing the net injected natural gas amount of the ith node in the natural gas network and the w node in the natural gas network; z is a radical of formula s Representing the compressibility of natural gas; pi i And pi w Respectively representing the air pressure of an ith node in the natural gas network and the air pressure of a w node in the natural gas network; eta g2p Representing the power generation efficiency of the natural gas unit; g HV Represents the thermal efficiency of natural gas; v represents the natural gas flow transport velocity in the pipeline circuit; u represents a natural gas transmission coefficient;
Figure BDA0003777673300000103
representing the average flow rate of the natural gas stream in the pipeline connected between the ith node and the w-th node in the natural gas network; h is iw Representing the power consumed by a compressor branch between the ith node and the w-th node in the natural gas network; b iw A compressor constant representing a compressor on a pipeline line connected between an ith node and a w-th node in the natural gas network; f. of iw And τ iw Respectively representing the natural gas flow circulating in a pipeline connected between the ith node and the w-th node in the natural gas network and the natural gas flow consumed by a compressor; z and r represent the compressor coefficient and the thermodynamic coefficient, respectively; a. b and c represent the first consumption coefficient and the second consumption coefficient of the compressor respectivelyNumber and third consumption coefficient;
Figure BDA0003777673300000104
and
Figure BDA0003777673300000105
respectively representing the minimum value and the maximum value of the natural gas supply quantity of the ith node in the natural gas network;
Figure BDA0003777673300000106
and
Figure BDA0003777673300000107
respectively representing the minimum value and the maximum value of the natural gas pressure of the ith node in the natural gas network;
Figure BDA0003777673300000108
and
Figure BDA0003777673300000109
respectively representing the minimum value and the maximum value of the compressor boosting ratio of a compressor on a pipeline line connected between the ith node and the w-th node in the natural gas network; delta P e,j And P e,j Respectively representing the reduction amount and the output amount of the electric load of the jth node in the power network; the ith node in the natural gas network is connected with the jth node in the power network.
And 3) establishing an element fragility evaluation index model of the electric-gas coupling system, inputting the power flow value of each power transmission line in the power network into the element fragility evaluation index model, and outputting the fragility index of each power transmission line in the power network by the element fragility evaluation index model, so that the identification of the fragile element in the electric-gas coupling system is realized.
In step 3, the established component vulnerability assessment index model V (m) of the electrical-electrical coupling system is as follows:
V(m)＝V 1 (m)(α 1 V 2 (m)+α 2 V 3 (m))
wherein, between the jth node and the kth node in the power networkThe power transmission line of (1) is the mth power transmission line in the power network; v 1 (m) represents the coupling vulnerability index, V, of the mth transmission line in the power network 2 (m) represents a topological vulnerability indicator, V, of the mth transmission line in the power network 3 (m) represents the operational vulnerability index, alpha, of the mth transmission line in the power network 1 And alpha 2 Respectively representing a preset first weight index and a preset second weight index.
Coupling fragility index V of mth power transmission line in power network 1 (m), specifically as follows:
Figure BDA0003777673300000111
wherein, N s Representing the number of natural gas sources; v s And
Figure BDA0003777673300000112
respectively representing the vulnerability index and the normalization value of the s-th natural gas source in each natural gas source; Δ F m,s And the power flow change value of the mth transmission line in the power network is shown after the s-th natural gas source fails.
The fragility indexes of the s-th natural gas source in the natural gas sources are as follows:
Figure BDA0003777673300000113
wherein, Δ F s Representing the power flow variation of all transmission lines in the power network; h s Representing a power flow distribution entropy of the power network; n is a radical of pl Representing the number of transmission lines in the power network; f m,0 Showing that before the fault of the s-th natural gas source, the flow value of the m-th power transmission line in the power network is the flow value F of the power transmission line between the j-th node and the k-th node in the power network obtained in the step 2 jk ；R m,s Indicating the mth transmission line in the power network after the fault of the s-th natural gas sourceTidal current impact rate; .
Tidal current variation delta F of all transmission lines in power network s The method comprises the following steps:
Figure BDA0003777673300000114
wherein, F m,s And the flow value of the mth transmission line in the power network is shown after the mth natural gas source fails.
Power flow distribution entropy H of power network s The method comprises the following steps:
Figure BDA0003777673300000115
when the s-th natural gas source fails, the tidal current impact rate R of the m-th transmission line in the power network m,s The method comprises the following steps:
Figure BDA0003777673300000121
ΔF m,s ＝|F m,s -F m,0 |。
topological vulnerability index V of mth power transmission line in power network 2 (m), specifically as follows:
Figure BDA0003777673300000122
wherein N is eg And N ed Respectively representing the number of generator sets and the number of nodes where loads are located in the power network; TC (tungsten carbide) j,k Representing a line transmission capacity of a transmission line between a jth node and a kth node in the power network;
Figure BDA0003777673300000123
indicating topological vulnerability index V 2 (m) integer variable when the m-th transmission line in the power network is located in orInteger variable not located between jth node and kth node in the power network
Figure BDA0003777673300000124
Is 1 or 0.
The line transmission capacity of the transmission line between the jth node and the kth node in the power network is specifically as follows:
Figure BDA0003777673300000125
wherein S is j,k Representing the set of transmission lines, tc, between the jth node and the kth node in the power network m Representing the line transmission capacity of the mth transmission line in the power network.
Operation fragility index V of mth transmission line in power network 3 (m), specifically as follows:
Figure BDA0003777673300000126
wherein H m Representing the power flow distribution entropy of the m-th transmission line in the power network after the fault; r a,m And the power flow impact ratio of the m-th transmission line in the power network to the a-th transmission line in the power network after the m-th transmission line in the power network fails is shown.
Power flow distribution entropy H after fault of mth power transmission line in power network m The method comprises the following steps:
Figure BDA0003777673300000127
the power flow impact ratio R of the m-th transmission line in the power network to the a-th transmission line in the power network after the m-th transmission line in the power network fails a,m The method comprises the following steps:
Figure BDA0003777673300000128
wherein, Δ F a,m And F a,m Respectively representing the power flow change value and the power flow value of the a-th power transmission line in the power network after the m-th power transmission line in the power network fails; f a,0 And the current value of the a-th transmission line in the power network before the m-th transmission line in the power network fails is represented.
The higher the vulnerability index of each transmission line in the power network output by the element vulnerability evaluation index model is, the more vulnerable the transmission line is.
After an element vulnerability assessment index model is established, the power transmission line in the power network is attacked in sequence, and the impact of element faults on the system toughness is measured and calculated based on the toughness assessment index of the electric-gas coupling system, wherein the specific expression is as follows:
1) Network efficiency
Network efficiency E between kth and jth nodes in an electrical power network k,j The method comprises the following steps:
Figure BDA0003777673300000131
wherein d is k,j Representing the shortest distance between the kth node and the jth node in the power network.
The overall efficiency E of the power network is an average efficiency of all node pairs therein, and is specifically as follows:
Figure BDA0003777673300000132
the network efficiency index E (y) after the y-th attack on the power transmission line in the power network is specifically as follows:
Figure BDA0003777673300000133
wherein, ω is k And omega j Respectively representing the weight coefficients of a kth node and a jth node in the power network;
Figure BDA0003777673300000134
represents the shortest electrical distance between the kth node and the jth node in the power network under the y-th attack.
2) System transmission efficiency
The system transmission efficiency Γ (y) reflects the change of the load side in the power network before and after the y-th attack, which is as follows:
Figure BDA0003777673300000135
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003777673300000136
representing the number of islands on the load side in the power network after the y-th attack;
Figure BDA0003777673300000137
representing the number of load nodes in the u th island; l is a radical of an alcohol y (j) And L 0 (j) The score is the load level of the jth load node in the current and initial states.
The specific embodiment of the invention is as follows:
1. an electric-gas coupling system is established in which an IEEE30 node power network and a Belgium-20 node natural gas network are coupled with each other. The natural gas power generating units of nodes 1, 8 and 13 in the IEEE30 node power network are connected to nodes 10, 7 and 16 of the natural gas power generating units, respectively, while the remaining power generating units in the power network are assumed to be conventional units. And inputting original data, and solving by using a target model of the electric-pneumatic coupling system to obtain an initial running state.
2. According to the transmission line vulnerability identification method, the vulnerability index of each line is further calculated, and table 1 shows the screened lines with the vulnerability rank 10.
Table 1 fragile line identification results
Vulnerability ranking Line serial number Comprehensive degree of weakness
1 6 0.168
2 8 0.114
3 9 0.108
4 10 0.106
5 2 0.093
6 28 0.079
7 5 0.067
8 23 0.052
9 9 0.051
10 16 0.018
From table 1, it can be found that the vulnerability index values of different lines are significantly different, which means that the proposed identification method has strong distinctiveness, and can effectively identify the most vulnerable line.
3. In order to further verify the validity of the fragile result, two modes of attacks including random attack and deliberate attack are sequentially carried out on each line so as to test the toughness of the system. The result shows that all lines with the highest vulnerability indexes have faults under the deliberate attack. Table 2 and table 3 show the network efficiency and the transmission efficiency of the power network, respectively.
Table 2 network efficiency under different attack modes
Figure BDA0003777673300000141
Figure BDA0003777673300000151
Table 3 transmission efficiency in different attack modes
Order of attack Intention of the userAttack mode Random attack pattern
1 0.980 1
2 0.973 1
3 0.940 0.987
4 0.940 0.987
5 0.844 0.987
6 0.724 0.880
7 0.653 0.868
8 0.523 0.838
9 0.453 0.838
10 0.432 0.838
As can be seen from table 2, the network efficiency of the system only drops by 90% under 10 random attacks. But under deliberate attacks, the network efficiency of the system drops rapidly by 20%, indicating that the identification of critical vulnerable lines is critical to the overall system performance. From table 3, it can be seen that the system transmission efficiency can be reduced to below 50% under 10 times of deliberate attacks, while the lowest system transmission efficiency is as high as 82% under random attacks. Thus, the results show that there is a strong correlation between overall system transmission efficiency and toughness of the identified fragile lines.

Claims (9)

1. A toughness-considered method for identifying a fragile element of an electro-pneumatic coupling system is characterized by comprising the following steps: the method comprises the following steps:
step 1) establishing an electric-gas coupling system which comprises a power network, a natural gas network and the power network, and acquiring the natural gas supply quantity and the reduction quantity of each node in the natural gas network and the active load quantity and the active load shedding quantity of each node in the power network;
step 2) establishing a target model of the electric-gas coupling system considering power network constraints and natural gas network constraints, inputting the natural gas supply quantity and the reduction quantity of each node in the natural gas network and the active load quantity and the active load shedding quantity of each node in the power network into the target model of the electric-gas coupling system, and outputting the load flow value of each power transmission line in the power network by the target model;
and 3) establishing an element fragility evaluation index model of the electric-gas coupling system, inputting the power flow value of each power transmission line in the power network into the element fragility evaluation index model, and outputting the fragility index of each power transmission line in the power network by the element fragility evaluation index model, so that the identification of the fragile element in the electric-gas coupling system is realized.
2. The method of claim 1, wherein the step of identifying the fragile component of the electro-pneumatic coupling system comprises: in the step 1), an electric power network in the electric-gas coupling system comprises a plurality of electric power nodes, each node is provided with a generator set, a natural gas generator set or a load, and the generator sets, the natural gas generator sets and the loads in the electric power network are connected through electric transmission lines; the natural gas network comprises a plurality of natural gas nodes, each natural gas node is provided with a natural gas unit, each natural gas unit in the natural gas network is connected through a pipeline, each pipeline in the natural gas network is provided with a compressor, and the natural gas network conveys natural gas through a plurality of connected natural gas sources; and each natural gas generator set in the power network is connected with the natural gas generator sets in the natural gas network through pipeline lines.
3. The method of claim 1, wherein the step of identifying the fragile component of the electro-pneumatic coupling system comprises: in the step 2), the established target model of the electric-gas coupling system considering the power network constraint and the natural gas network constraint specifically includes the following steps:
Figure FDA0003777673290000011
wherein N is g And N e Respectively representing the number of nodes in a natural gas network and a power network;
Figure FDA0003777673290000012
and
Figure FDA0003777673290000013
respectively representing the natural gas cost and the natural gas cutting cost of the ith node in the natural gas network; a. The g,i And Δ A g,i Respectively representing the natural gas supply amount and the reduction amount of the ith node in the natural gas network;
Figure FDA0003777673290000014
and
Figure FDA0003777673290000015
respectively representing the unit cost and the load shedding cost of the jth node in the power network; l is j And Δ L j Respectively representing the active load capacity and the active load shedding capacity of the jth node in the power network.
4. The identification method of the fragile element of the electro-pneumatic coupling system considering toughness as claimed in claim 3, wherein: the power network constraints are specifically as follows:
P c,j +P gas,j -L j +ΔL j -P in,j ＝0
Q c,j +Q gas,j -Q L,j +ΔQ L,j -Q in,j ＝0
Figure FDA0003777673290000021
Figure FDA0003777673290000022
V j min ≤V j ≤V j max
Figure FDA0003777673290000023
Figure FDA0003777673290000024
Figure FDA0003777673290000025
Figure FDA0003777673290000026
Figure FDA0003777673290000027
wherein, P c,j And Q c,j Respectively representing the active output and the reactive output of a generator set at the j node in the power network when the j node in the power network is the generator set; p gas,j And Q gas,j Respectively representing the active output and the reactive output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set; p is in,j And Q in,j Respectively representing net injected active output and net injected reactive output of a jth node in the power network; q L,j And Δ Q L,j Respectively representing the reactive load capacity and the reactive load shedding capacity of the jth node in the power network; v j Representing a voltage magnitude of a jth node in the electrical power network; g jk And B jk Respectively representing the real part and the imaginary part of the kth row and the jth column of the node admittance matrix; theta jk Representing a phase angle difference between a jth node and a kth node in the power network; f jk Representing a tidal current value of the transmission line between the jth node and the kth node in the power network; v j min And V j max Respectively representing the minimum value and the maximum value of the voltage amplitude of the jth node in the power network;
Figure FDA0003777673290000028
and
Figure FDA0003777673290000029
respectively representing the minimum value and the maximum value of the power flow value of the power transmission line between the jth node and the kth node in the power network;
Figure FDA00037776732900000210
and
Figure FDA00037776732900000211
respectively representing the minimum value and the maximum value of the active output of the generator set at the j node in the power network when the j node in the power network is the generator set;
Figure FDA00037776732900000212
and
Figure FDA00037776732900000213
respectively representing the minimum value and the maximum value of the active output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set;
Figure FDA0003777673290000031
and
Figure FDA0003777673290000032
respectively representing the minimum value and the maximum value of the reactive output of the generator set at the j node in the power network when the j node in the power network is the generator set;
Figure FDA0003777673290000033
and
Figure FDA0003777673290000034
respectively representing the minimum value and the maximum value of the reactive output of the natural gas generator set at the j node in the power network when the j node in the power network is the natural gas generator set; the jth node and the kth node in the power network are connected;
the natural gas network constraints are specifically as follows:
A g，i -A gas， i-L g，i +ΔA g，i -A in，i ＝0
Figure FDA0003777673290000035
P gas,j ＝η g2p A gas,i G HV
Figure FDA0003777673290000036
Figure FDA0003777673290000037
Figure FDA0003777673290000038
Figure FDA0003777673290000039
Figure FDA00037776732900000310
Figure FDA00037776732900000311
0≤ΔA g，i ≤A g，i
0≤ΔP e,j ≤P e,j
wherein A is gas,i Representing the amount of natural gas consumed by the natural gas unit at the ith node in the natural gas network; l is g,i Representing the natural gas load capacity of the ith node in the natural gas network; natural gas injection amount of ith node in natural gas network(ii) a R represents a natural gas constant; psi, d and l denote the temperature, diameter and length of the pipeline lines connected between the ith and w-th nodes in the natural gas network; ρ is a unit of a gradient n Represents the density of natural gas; a. The in,i And A in,w Respectively representing the net injected natural gas amount of the ith node in the natural gas network and the w node in the natural gas network; z is a radical of s Representing the compressibility of natural gas; pi i And pi w Respectively representing the air pressure of an ith node in the natural gas network and the air pressure of a w node in the natural gas network; eta g2p Representing the power generation efficiency of the natural gas unit; g HV Represents the thermal efficiency of natural gas; v represents the natural gas flow transport velocity in the pipeline circuit; u represents a natural gas transmission coefficient;
Figure FDA00037776732900000312
representing the average flow rate of the natural gas stream in the pipeline connected between the ith node and the w-th node in the natural gas network; h is iw Representing the power consumption of a compressor branch between an ith node and a w-th node in the natural gas network; b iw A compressor constant representing a compressor on a pipeline line connected between an ith node and a w-th node in the natural gas network; f. of iw And τ iw Respectively representing the natural gas flow circulating in a pipeline connected between the ith node and the w-th node in the natural gas network and the natural gas flow consumed by a compressor; z and r represent the compressor coefficient and thermodynamic coefficient, respectively; a. b and c represent a first consumption coefficient, a second consumption coefficient and a third consumption coefficient of the compressor, respectively;
Figure FDA0003777673290000041
and
Figure FDA0003777673290000042
respectively representing the minimum value and the maximum value of the natural gas supply quantity of the ith node in the natural gas network;
Figure FDA0003777673290000043
and
Figure FDA0003777673290000044
respectively representing the minimum value and the maximum value of the natural gas pressure of the ith node in the natural gas network;
Figure FDA0003777673290000045
and
Figure FDA0003777673290000046
respectively representing the minimum value and the maximum value of the compressor boost ratio of a compressor on a pipeline line connected between the ith node and the w-th node in the natural gas network; delta P e,j And P e,j Respectively representing the reduction amount and the output amount of the electric load of the jth node in the power network; the ith node in the natural gas network is connected with the jth node in the power network.
5. The identification method of the fragile element of the electro-pneumatic coupling system considering toughness as claimed in claim 4, wherein: in the step 3, the component fragility evaluation index model V (m) of the electric-electric coupling system is established as follows:
V(m)＝V 1 (m)(α 1 V 2 (m)+α 2 V 3 (m))
the power transmission line between the jth node and the kth node in the power network is the mth power transmission line in the power network; v 1 (m) represents the coupling vulnerability index, V, of the mth transmission line in the power network 2 (m) represents a topological vulnerability indicator, V, of the mth transmission line in the power network 3 (m) represents the operational vulnerability index, alpha, of the mth transmission line in the power network 1 And alpha 2 Respectively representing a preset first weight index and a preset second weight index.
6. The identification method of the fragile element of the electro-pneumatic coupling system considering toughness as claimed in claim 5, wherein: the coupling of the mth transmission line in the power networkFragility index V 1 (m), specifically as follows:
Figure FDA0003777673290000047
wherein N is s The number of natural gas sources is represented; v s And
Figure FDA0003777673290000048
respectively representing the vulnerability index and the normalized value of the s-th natural gas source in each natural gas source; Δ F m,s The power flow change value of the mth power transmission line in the power network is shown after the mth natural gas source fails;
the fragility indexes of the s-th natural gas source in the natural gas sources are as follows:
Figure FDA0003777673290000051
wherein, Δ F s Representing the power flow variation of all transmission lines in the power network; h s Representing a power flow distribution entropy of the power network; n is a radical of pl Representing the number of transmission lines in the power network; f m,0 Showing that before the fault of the s-th natural gas source, the flow value of the m-th power transmission line in the power network is the flow value F of the power transmission line between the j-th node and the k-th node in the power network obtained in the step 2 jk ；R m,s The power flow impact rate of the mth power transmission line in the power network is shown after the mth natural gas source fails;
tidal current variation delta F of all transmission lines in power network s The method comprises the following steps:
Figure FDA0003777673290000052
wherein, F m,s Indicating that after the s natural gas source fails, power is appliedThe current value of the mth transmission line in the network;
power flow distribution entropy H of power network s The method comprises the following steps:
Figure FDA0003777673290000053
when the s-th natural gas source fails, the tidal current impact rate R of the m-th transmission line in the power network m,s The method comprises the following steps:
Figure FDA0003777673290000054
ΔF m,s ＝|F m,s -F m,0 |。
7. the identification method of the fragile element of the electro-pneumatic coupling system considering toughness as claimed in claim 5, wherein: the topological vulnerability index V of the mth transmission line in the power network 2 (m), specifically as follows:
Figure FDA0003777673290000055
wherein, N eg And N ed Respectively representing the number of generator sets and the number of nodes where loads are located in the power network; TC (tungsten carbide) j,k Representing a line transmission capacity of a transmission line between a jth node and a kth node in the power network;
Figure FDA0003777673290000056
indicating topological vulnerability index V 2 (m) an integer variable, the integer variable being present when the mth transmission line in the power network is or is not present between the jth node and the kth node in the power network
Figure FDA0003777673290000057
Is 1 or 0;
the line transmission capacity of the transmission line between the jth node and the kth node in the power network is specifically as follows:
Figure FDA0003777673290000061
wherein S is j,k Representing the set of transmission lines, tc, between the jth node and the kth node in the power network m Representing the line transmission capacity of the mth transmission line in the power network.
8. The method of claim 5, wherein the step of identifying the fragile component of the electro-pneumatic coupling system comprises: the operation fragility index V of the mth transmission line in the power network 3 (m), specifically as follows:
Figure FDA0003777673290000062
wherein H m Representing the power flow distribution entropy of the m-th transmission line in the power network after the fault; r is a,m Representing the power flow impact ratio of the m-th transmission line in the power network to the a-th transmission line in the power network after the m-th transmission line in the power network fails;
power flow distribution entropy H after fault of mth transmission line in power network m The method comprises the following steps:
Figure FDA0003777673290000063
the power flow impact ratio R of the m-th transmission line in the power network to the a-th transmission line in the power network after the m-th transmission line in the power network fails a,m The method comprises the following steps:
Figure FDA0003777673290000064
wherein, Δ F a,m And F a,m Respectively representing the power flow change value and the power flow value of the a-th power transmission line in the power network after the m-th power transmission line in the power network fails; f a,0 And the current value of the a-th transmission line in the power network before the m-th transmission line in the power network fails is shown.
9. The method of claim 1, wherein the step of identifying the fragile component of the electro-pneumatic coupling system comprises: the higher the vulnerability index of each power transmission line in the power network output by the element vulnerability evaluation index model is, the more vulnerable the power transmission line is.
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