CN109193751B - Power grid resilience calculation method and system based on black start and load recovery process - Google Patents

Power grid resilience calculation method and system based on black start and load recovery process Download PDF

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CN109193751B
CN109193751B CN201810907019.2A CN201810907019A CN109193751B CN 109193751 B CN109193751 B CN 109193751B CN 201810907019 A CN201810907019 A CN 201810907019A CN 109193751 B CN109193751 B CN 109193751B
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unit
load
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CN109193751A (en
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朱海南
于振江
王涛
王琰
王娟娟
宋静
薛云霞
房巍
李宗璇
刘明
刘堃
陈兵兵
周玉
宋圣兰
张同军
孙言实
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State Grid Corp of China SGCC
Weifang Power Supply Co of State Grid Shandong Electric Power Co Ltd
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Weifang Power Supply Co of State Grid Shandong Electric Power Co Ltd
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    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
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Abstract

The invention relates to the technical field of power grid system recovery, and provides a power grid recovery force calculation method and a system based on black start and load recovery processes, wherein the method comprises the following steps: identifying the state of the power grid system, acquiring basic data of the power grid system, and establishing a network connection matrix M corresponding to the system; screening out power plants of available black start units in the system, and calculating the sum of weighted capacities of all available black start units in each power plant and a corresponding per unit value; generating a minimum spanning tree T1 containing all recoverable plant nodes, and calculating an average shortest distance D1 and an average shortest distance D2; calculating an average value D of D1 and D2; and calculating the ratio of the per unit value of the weighted sum of the black start unit capacity to the D, thereby providing a quantitative means for evaluating and analyzing the power grid restoring force of the power grid system after a blackout accident occurs on the basis of fully considering the black start and load recovery processes.

Description

Power grid resilience calculation method and system based on black start and load recovery process
Technical Field
The invention belongs to the technical field of power grid system recovery, and particularly relates to a power grid recovery force calculation method and system based on black start and load recovery processes.
Background
The continuous progress of the operation defense technology and the equipment manufacturing technology of the power grid system cannot keep pace with the occurrence of large-scale power failure accidents, which is fully explained in recent ten years at home and abroad. For example: in 14 days 8 months in 2003, the power failure accident which is the most serious in North America historically occurs, the power failure accident reaches many areas in the United states and Canada, the load is lost by 61.8GW, and the number of the affected people is 5000 ten thousand; in 2006, 11/4 days, the European interconnected network has a major power failure accident, the national common loss load of Germany, French, ideation and the like is about 1600 ten thousand kW, and 1500 universal households are affected; in 11 months and 10 days in 2009, the brazil and Paraguay power grids have major power failure accidents, so that three 750kV lines trip, two +/-600 kV direct current lines are locked, the brazil power grid loses about 1700 ten thousand kW of power, the power failure range reaches 12 states in the Past and most areas of the neighboring country Paraguay, and 5000 to 6000 million people are affected; in 2011, 3, 11 days, a 22GW power supply is lost due to major power failure of a power grid in Tokyo, Japan, caused by an earthquake, a power gap reaches 10GW, and the power gap cannot provide power support for a Fukuma nuclear power station which is in emergency shutdown, but the Fukuma nuclear power station does not have enough emergency power supply to support a cooling system of the Fukuma nuclear power station, so that a serious nuclear leakage crisis occurs, and a catastrophic result is caused; in 2012, 30 days and 31 days, two large-area power failure accidents occur continuously in northern and eastern areas of India, more than half of the homeland is covered, and the lives of 6 hundred million and more people are directly influenced; in China, serious large-scale power failure events occur for several times, such as 9-26 th month in 2005, and severe accidents of power failure of the whole island are caused by the fact that the Hainan power grid is attacked by typhoon 'Dawei'; in early 2008, ice disasters occurred in the power grid in south, which caused a large number of tower collapse and disconnection accidents, and caused large-area power failure accidents.
The large-scale power failure accidents bring extremely serious loss and influence to national production, life and economic development, the economic loss is extremely large, and the influence is difficult to eliminate in a long time. The statistical discovery is carried out on data of the recovery process after a plurality of times of home and abroad major power failure accidents, and the shorter the system recovery time is, the lighter the loss and influence are. The length of the system recovery time depends on whether the grid structure of the system is reasonable, the type of the load of the system station, the corresponding recovery difficulty and other factors, namely, the power failure time of the power grid after a large-scale power failure accident occurs is shortened from the viewpoint of improving the power grid recovery force. The restoring force is an important characteristic of the smart grid, and the research on the restoring force of the power grid is a necessary trend of the development of the smart grid.
At present, the research on the resilience of the power grid is still in a starting stage, the evaluation theory and the evaluation index of the resilience of the power grid are still in a low-level stage, the research on the resilience of the power grid lacks an important theoretical basis, and the guidance of disaster prevention and reduction planning and operation foundation of a power grid system is lacked.
Disclosure of Invention
The invention aims to provide a power grid resilience calculation method based on black start and load recovery processes, and aims to solve the problems that in the prior art, research on power grid resilience is still in a starting stage, an evaluation theory and an evaluation index of power grid resilience are still in a low-level stage, the research on power grid resilience lacks an important theoretical basis, and the guidance of a power grid system disaster prevention and reduction plan and an operation foundation is further lacked.
The invention is realized in such a way that a power grid resilience calculation method based on black start and load recovery processes comprises the following steps:
identifying the state of a power grid system, acquiring and calculating basic data of the power grid system, and establishing a network connection matrix M corresponding to the system based on the acquired basic data of the power grid system, wherein the basic data comprises black start unit parameters, unit parameters to be recovered, line parameters and load types;
screening out the power plants of the available black start unit in the system according to the established network connection matrix M, and calculating the sum of the weighted capacity of all the available black start units in each power plant and the corresponding per unit value
Figure GDA0003409741820000021
Generating a minimum spanning tree T1 containing all recoverable plant station nodes by taking generalized black starter group nodes generated by aggregation as root nodes, and calculating the average shortest distance D1 from the generalized black starter group nodes in the minimum spanning tree T1 to each unit group node to be recovered;
aggregating generalized black starter group nodes, each unit node to be recovered and corresponding paths in the minimum spanning tree T1 into a generalized unit node, and then calculating the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes;
calculating the average value of the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered and the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes
Figure GDA0003409741820000022
Calculating per unit value of weighted sum of black start unit capacity
Figure GDA0003409741820000023
And
Figure GDA0003409741820000024
is defined as the grid resilience based on the black start and load recovery processes.
As an improved scheme, the network connection matrix M is a square matrix, which is denoted as:
Figure GDA0003409741820000031
in the network connection matrix M, the number of rows and columns is equal to the number of available plant nodes in the system, and when there is an available tie line l between node i and node jijAnd line lijPer unit value of line reactance of xijThen element M in the network connection matrix Mij＝Mji＝(wli+wlj)/2×xij(ii) a On the contrary, if there is no available tie line between node i and node j, Mij＝MjiInfinity, whereiniFor load recovery difficulty of node i, wljLoad recovery difficulty for node j;
in the network connection matrix M, the load model of the node i is a constant impedance load proportion alpha1The motor type load ratio is1-α1The load model of the node j is a constant impedance load proportion of alpha2With a motor type load ratio of 1-alpha2；
If the node is a load node, setting the load recovery difficulty of the motor type to be 1, and setting the load recovery difficulty of the constant impedance type to be 0.5, then setting the load recovery difficulty of the node i to be wli＝0.5×α1+1×(1-α1)＝1-0.5α1(ii) a The load recovery difficulty of node j is defined as wlj＝0.5×α2+1×(1-α2)＝1-0.5α2；
If the node is a contact node and the substation represented by the contact node has no load to be restored, the load restoration difficulty coefficient wI of the contact node is 1.
As an improved scheme, the calculation formula of the sum of the weighted capacities of all available black start units in each power plant is as follows:
Figure GDA0003409741820000032
wherein,
Figure GDA0003409741820000033
k＝1,2,K,m，Pblackthe sum of the weighted capacities of the black start units of each power plant; n is the number of power plants comprising the black start unit in the system; piThe weighted capacity sum of all black start units in the ith power plant; m is the number of black start units in the ith power plant; pijFor the capacity of the jth black start unit in power plant i, cjThe coefficient of the jth black start unit in the power plant i is related to the starting sequence k of the black start unit j;
per unit value corresponding to the sum of weighted capacities of all available black start units in each power plant
Figure GDA0003409741820000034
The calculation formula of (2) is as follows:
Figure GDA0003409741820000041
wherein SB is a power base value and takes the value of 100 MVA.
As an improved scheme, the step of generating the minimum spanning tree T1 including all recoverable plant nodes by taking the generalized black starter group node generated by aggregation as a root node specifically includes the following steps:
(1) any black start unit is positioned at power plant node s0Put into the set U, i.e. U ═ s0}，TE＝{}；
(2) Judging whether the set U contains all nodes in the abstract graph G, if not, finding an edge with the minimum weight (U, V) belongs to the edges (U, V) belonging to the V-U and the edges (U, V) belonging to the E according to the network connection matrix M corresponding to the abstract graph G0,v0)；
(3) Node v0Put into the set U and put the line (U)0,v0) Put into the aggregate TE;
(4) repeating the step (2) and the step (3) to obtain a minimum spanning tree T1 containing all power plant and substation nodes in the abstract diagram G;
wherein G ═ (V, E) is an abstract graph corresponding to the power grid, G is an undirected weighted connected graph, V is a set of nodes in the abstract graph G, E is a set of lines in the abstract graph G and includes virtual lines, the line weights are per unit values of line reactance, the network connection matrix corresponding to the abstract graph G is M, and when a minimum spanning tree T1 including all nodes in the abstract graph G is (U, TE), U is a set of nodes in the tree T1, TE is a set of edges in the tree T1, and U and TE are initially empty sets.
As an improved scheme, the calculation formula of the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered is as follows:
Figure GDA0003409741820000042
wherein n is the path from the generalized black starter unit node in the tree T1 to each unit node to be recovered and includesThe number of edges of (a); liA reactance value corresponding to the ith side contained in a path from the generalized black starter unit node in the tree T1 to each unit node to be recovered; m is the number of nodes of the tree T1 containing the unit power plant to be recovered;
the calculation formula of the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the other load nodes is as follows:
Figure GDA0003409741820000043
wherein, N is the number of edges with weights not equal to 0 in the tree T2; liThe edge weight corresponding to the ith edge with the weight not equal to 0 in T2; and M is the number of the rest load nodes except the generalized unit node in T2.
Another object of the present invention is to provide a power grid restoration force calculation system based on black start and load restoration processes, the system comprising:
the basic data acquisition module is used for identifying the state of the power grid system and acquiring and calculating basic data of the power grid system, wherein the basic data comprises black start unit parameters, unit parameters to be recovered, line parameters and load types;
the network connection matrix establishing module is used for establishing a network connection matrix M corresponding to the system on the basis of the acquired basic data of the power grid system;
a first calculation module, configured to screen out power plants of the available black start unit in the system according to the established network connection matrix M, and calculate a sum of weighted capacities of all available black start units in each power plant and a corresponding per unit value
Figure GDA0003409741820000051
The minimum spanning tree generation module is used for generating a minimum spanning tree T1 containing all recoverable plant nodes by taking the generalized black starter group node generated by aggregation as a root node;
the first average shortest distance calculation module is used for calculating the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered;
the generalized unit node aggregation module is used for aggregating generalized black starter unit nodes, all unit nodes to be recovered and corresponding paths in the minimum spanning tree T1 into a generalized unit node;
the second average shortest distance calculation module is used for calculating the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to each of the rest load nodes;
an average value calculating module, configured to calculate an average value of average shortest distances D1 from the generalized black starter group node in the minimum spanning tree T1 to each unit node to be restored and average shortest distances D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes
Figure GDA0003409741820000052
A ratio calculation module for calculating the per unit value of the weighted sum of the black start unit capacity
Figure GDA0003409741820000053
And
Figure GDA0003409741820000054
is defined as the grid resilience based on the black start and load recovery processes.
As an improved scheme, the network connection matrix M is a square matrix, which is denoted as:
Figure GDA0003409741820000061
in the network connection matrix M, the number of rows and columns is equal to the number of available plant nodes in the system, and when there is an available tie line l between node i and node jijAnd line lijPer unit value of line reactance of xijThen element M in the network connection matrix Mij＝Mji＝(wli+wlj)/2×xij(ii) a On the contrary, if there is no available tie line between node i and node j, Mij＝MjiInfinity, whereiniFor load recovery difficulty of node i, wljLoad recovery difficulty for node j;
in the network connection matrix M, the load model of the node i is a constant impedance load proportion alpha1With a motor type load ratio of 1-alpha1The load model of the node j is a constant impedance load proportion of alpha2With a motor type load ratio of 1-alpha2；
If the node is a load node, setting the load recovery difficulty of the motor type to be 1, and setting the load recovery difficulty of the constant impedance type to be 0.5, then setting the load recovery difficulty of the node i to be wli＝0.5×α1+1×(1-α1)＝1-0.5α1(ii) a The load recovery difficulty of node j is defined as wlj＝0.5×α2+1×(1-α2)＝1-0.5α2；
If the node is a contact node and the substation represented by the contact node has no load to be restored, the load restoration difficulty coefficient wI of the contact node is 1.
As an improved scheme, the calculation formula of the sum of the weighted capacities of all available black start units in each power plant is as follows:
Figure GDA0003409741820000062
wherein,
Figure GDA0003409741820000063
k＝1,2,K,m，Pblackthe sum of the weighted capacities of the black start units of each power plant; n is the number of power plants comprising the black start unit in the system; piThe weighted capacity sum of all black start units in the ith power plant; m is the number of black start units in the ith power plant; pijFor the capacity of the jth black start unit in power plant i, cjCoefficient of j-th black start unit in power plant i, and black start machineThe start-up order k for group j is relevant;
per unit value corresponding to the sum of weighted capacities of all available black start units in each power plant
Figure GDA0003409741820000064
The calculation formula of (2) is as follows:
Figure GDA0003409741820000071
wherein SB is a power base value and takes the value of 100 MVA.
As an improved scheme, the minimum spanning tree generation module specifically includes:
a first placement module for placing any one of the black start units at the power plant node s0Put into the set U, i.e. U ═ s0}，TE＝{}；
A judging module, configured to judge whether the set U includes all nodes in the abstract graph G, and if the set U does not include all nodes in the abstract graph G, find an edge (U, V) with the smallest weight among all edges (U, V) belonging to U and V belonging to V-U belonging to E according to the network connection matrix M corresponding to the abstract graph G0,v0)；
A second placement module for placing the node v0Put into the set U and put the line (U)0,v0) Put into the aggregate TE;
the repeated execution module is used for repeating the execution processes of the judgment module and the second placement module to obtain a minimum spanning tree T1 containing all power plant and substation nodes in the abstract diagram G;
wherein G ═ (V, E) is an abstract graph corresponding to the power grid, G is an undirected weighted connected graph, V is a set of nodes in the abstract graph G, E is a set of lines in the abstract graph G and includes virtual lines, the line weights are per unit values of line reactance, the network connection matrix corresponding to the abstract graph G is M, and when a minimum spanning tree T1 including all nodes in the abstract graph G is (U, TE), U is a set of nodes in the tree T1, TE is a set of edges in the tree T1, and U and TE are initially empty sets.
As an improved scheme, the calculation formula of the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered is as follows:
Figure GDA0003409741820000072
wherein n is the number of edges included in a path from a generalized black starter unit node to each unit node to be recovered in the tree T1; liA reactance value corresponding to the ith side contained in a path from the generalized black starter unit node in the tree T1 to each unit node to be recovered; m is the number of nodes of the tree T1 containing the unit power plant to be recovered;
the calculation formula of the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the other load nodes is as follows:
Figure GDA0003409741820000073
wherein, N is the number of edges with weights not equal to 0 in the tree T2; liThe edge weight corresponding to the ith edge with the weight not equal to 0 in T2; and M is the number of the rest load nodes except the generalized unit node in T2.
In the embodiment of the invention, the state of the power grid system is identified, the basic data of the power grid system is obtained and calculated, and a network connection matrix M corresponding to the system is established; screening out the power plants of the available black start unit in the system, and calculating the sum of the weighted capacity of all the available black start units in each power plant and the corresponding per unit value
Figure GDA0003409741820000081
Generating a minimum spanning tree T1 containing all recoverable plant nodes, and calculating an average shortest distance D1 and an average shortest distance D2; calculating an average value D of D1 and D2; calculating per unit value of weighted sum of black start unit capacity
Figure GDA0003409741820000082
And
Figure GDA0003409741820000083
the ratio of the total power loss and the maximum power loss is calculated, and the ratio of the total power loss and the maximum power loss is calculated according to the ratio of the total power loss and the maximum power loss, so that a quantitative means is provided for evaluating and analyzing the power grid restoring force of a power grid system after a blackout accident occurs on the basis of fully considering the black start and load restoring processes, and guidance and basis are provided for pertinently developing power grid planning.
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FIG. 1 is a flow chart of an implementation of a power grid resilience calculation method based on black start and load recovery processes provided by the present invention;
FIG. 2 is a diagram of an IEEE30 node system architecture provided by the present invention;
FIG. 3 is a block diagram of a power grid resilience computing system based on black start and load restoration processes provided by the present invention;
FIG. 4 is a block diagram of a minimum spanning tree generation module provided by the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 shows an implementation flowchart of a power grid resilience calculation method based on black start and load recovery processes, which specifically includes the following steps:
in step S101, a state of a power grid system is identified, basic data for calculating the power grid system is obtained, and a network connection matrix M corresponding to the system is established based on the obtained basic data of the power grid system, where the basic data includes black-start unit parameters, unit parameters to be recovered, line parameters, and load types, and the black-start unit parameters include black-start unit capacity, number, and distribution.
The process of identifying the state of the power grid system comprises the following steps: and screening out the load types of the power transmission and transformation equipment still available in the system recovery process and the recoverable load station, finally acquiring all available power transmission and transformation equipment in the system, and establishing an available equipment table in the recovery process of the power grid after a power failure accident occurs.
In step S102, the power plants of the black start unit available in the system are screened out according to the established network connection matrix M, and the sum of the weighted capacities of all the black start units available in each power plant and the corresponding per unit value are calculated
Figure GDA0003409741820000091
The invention provides a method for calculating the power grid restoring force based on black start and load restoring processes, which comprehensively considers factors such as a power grid load restoring process after a large-scale power failure accident of a power grid, load sites in the power grid, load types and the like.
In the embodiment of the invention, when a network connection matrix M corresponding to a power grid system is established, a power plant and a transformer substation in the power grid system are used as nodes, M is a square matrix, and the number of rows and columns is equal to the number of available plant nodes in the power grid system; let the load model of node i be constant impedance and load ratio be alpha1With a motor type load ratio of 1-alpha1The load model of the node j is a constant impedance load proportion of alpha2With a motor type load ratio of 1-alpha2；
In the load model of a load node, if the constant impedance load proportion is higher, the load of the node is easier to recover successfully; conversely, the greater the difficulty of load recovery. Therefore, the difficulty of load restoration of the load node can be reflected on the weight of the line;
if one node is a load node, assuming that the load recovery difficulty of the motor type is 1 and the load recovery difficulty of the constant impedance type is 0.5, the load recovery difficulty of the node i is wli＝0.5×α1+1×(1-α1)＝1-0.5α1(ii) a The load recovery difficulty of node j is defined as wlj＝0.5×α2+1×(1-α2)＝1-0.5α2；
If a node is a contact node and the substation represented by the node has no load to be restored, the load restoration difficulty coefficient wI of the node is considered to be 1.
When there is a call line l available between node i and node j in the systemijAnd line lijPer unit value of line reactance of xijThen connect the elements M in the matrix Mij＝Mji＝(wli+wlj)/2×xij(ii) a On the contrary, if there is no available tie line between node i and node j in the system, Mij＝Mji＝∞；
For a system with n sites, the corresponding connection matrix M is in the following form:
Figure GDA0003409741820000101
wherein, for any element MijAnd MjiIn the presence of Mij＝Mji。
In this embodiment, the line l is calculatedijPer unit value x of line reactance ofijTime, reference value SBTaken as 100MVA, UBAnd taking the standard voltage of each voltage class.
On the basis, the calculation formula of the sum of the weighted capacities of all available black start units in each power plant is as follows:
Figure GDA0003409741820000102
wherein,
Figure GDA0003409741820000103
k＝1,2,K,m，Pblackthe sum of the weighted capacities of the black start units of each power plant; n is the number of power plants comprising the black start unit in the system; piThe weighted capacity sum of all black start units in the ith power plant; m is the number of black start units in the ith power plant; pijFor the capacity of the jth black start unit in power plant i, cjThe coefficient of the j th black start unit in the power plant i and the starting times of the j black start unitSequence k is related;
per unit value corresponding to the sum of weighted capacities of all available black start units in each power plant
Figure GDA0003409741820000104
The calculation formula of (2) is as follows:
Figure GDA0003409741820000105
wherein SB is a power base value and takes the value of 100 MVA.
In step S103, taking the generalized black starter group node generated by aggregation as a root node, generating a minimum spanning tree T1 including all recoverable plant nodes, and calculating an average shortest distance D1 from the generalized black starter group node in the minimum spanning tree T1 to each unit node to be recovered.
The recovery process of the power grid system after a large-area power failure accident comprises a black start stage, a grid frame reconstruction stage and a load recovery stage;
in the black start stage, the available black start unit in the power grid system is started firstly, and after the black start unit is started successfully, required starting power is provided for the rest units without self-starting capability, so that the units are restarted and connected to the grid;
in the network frame reconstruction stage, important power transmission lines and important load stations in a power grid system are gradually restored, a strong network frame is established, and a foundation is laid for subsequent load restoration;
in the load recovery stage, large-scale load recovery is carried out on the basis of early recovery, the power failure load is recovered as soon as possible, and the power failure time of the system is shortened. In the whole recovery process, no-load charging is carried out on the power-off line, so that the power-off line is charged again, which is the more critical and important content; the reactance of the line can be used as an index to reflect the difficulty of different lines in recovery, and the smaller the reactance of the line is, the smaller the difficulty of successful recovery of the line is.
In this embodiment, the calculation formula of the average shortest distance D1 from the generalized black starter crew node in the minimum spanning tree T1 to each to-be-recovered crew node is:
Figure GDA0003409741820000111
wherein n is the number of edges included in a path from a generalized black starter unit node to each unit node to be recovered in the tree T1; liA reactance value corresponding to the ith side contained in a path from the generalized black starter unit node in the tree T1 to each unit node to be recovered; and m is the number of nodes containing the unit power plant to be recovered in the tree T1.
In step S104, the generalized black starter group nodes, the to-be-restored unit nodes and the corresponding paths in the minimum spanning tree T1 are aggregated into a generalized unit node, and then an average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the rest of the load nodes is calculated.
The calculation formula of the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes is as follows:
Figure GDA0003409741820000112
wherein, N is the number of edges with weights not equal to 0 in the tree T2; liThe edge weight corresponding to the ith edge with the weight not equal to 0 in T2; and M is the number of the rest load nodes except the generalized unit node in T2.
In the embodiment of the invention, when the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered and the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes are calculated, the line weighted reactance of the corresponding type is fully considered, and the line weighted reactance is taken as the weight to be calculated.
In step S105, an average value of the average shortest distances D1 from the generalized black starter group node in the minimum spanning tree T1 to each unit node to be restored and the average shortest distances D2 from the generalized unit node in the minimum spanning tree T1 to the remaining load nodes is calculated
Figure GDA0003409741820000121
In the embodiment of the invention, the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered and the average value of the shortest distances D2 from the generalized unit node in the T2 to each load node are calculated
Figure GDA0003409741820000122
The calculation formula is as follows:
Figure GDA0003409741820000123
the minimum spanning tree searched from the abstract graph G ═ (V, E) is T1 ═ (U, TE). V is the set of all plant station nodes in the abstract graph G, E is the set of all edges in the abstract graph G, and U is equal to V; TE is the set of edges contained in tree T1; in order to aggregate the generalized black starter group nodes in T1, each to-be-recovered unit node, and the paths between the two nodes into a generalized unit node, the weight of the edge included in the path from the generalized black starter group node to each to-be-recovered unit node may be set to 0, and the node in T1 is set to be a tree T2 after aggregation.
In step S106, a per unit value of the weighted sum of the black start unit capacities is calculated
Figure GDA0003409741820000124
And
Figure GDA0003409741820000125
is defined as the grid resilience based on the black start and load recovery processes.
The calculation formula of the ratio is as follows:
Figure GDA0003409741820000126
in the embodiment of the present invention, the step of generating the minimum spanning tree T1 including all recoverable plant nodes by using the generalized black starter group node generated by aggregation as a root node specifically includes the following steps:
(1) any black start unit is positioned at power plant node s0Put into the set U, i.e. U ═ s0}，TE＝{}；
(2) Judging whether the set U contains all nodes in the abstract graph G, if not, finding an edge with the minimum weight (U, V) belongs to the edges (U, V) belonging to the V-U and the edges (U, V) belonging to the E according to the network connection matrix M corresponding to the abstract graph G0,v0)；
(3) Node v0Put into the set U and put the line (U)0,v0) Put into the aggregate TE;
(4) repeating the step (2) and the step (3) to obtain a minimum spanning tree T1 containing all power plant and substation nodes in the abstract diagram G;
wherein G ═ (V, E) is an abstract graph corresponding to the power grid, G is an undirected weighted connected graph, V is a set of nodes in the abstract graph G, E is a set of lines in the abstract graph G and includes virtual lines, the line weights are per unit values of line reactance, the network connection matrix corresponding to the abstract graph G is M, and when a minimum spanning tree T1 including all nodes in the abstract graph G is (U, TE), U is a set of nodes in the tree T1, TE is a set of edges in the tree T1, and U and TE are initially empty sets.
In this embodiment, in the system recovery process, the black start unit node is the starting point of the whole recovery process, and provides the starting power for the unit to be recovered, and then after all the units are connected to the grid, provides the power supply for the load node again. Therefore, in the network connection matrix M, the black starter group node may be regarded as a root node. For a system with a plurality of black starter group nodes, the black starter group nodes can be connected by virtual lines with reactance values of 0, namely, all power plants containing the unit to be recovered are aggregated into a generalized black starter group node.
In the embodiment of the invention, the existing available sites of the black start unit are searched in the power grid system;
and performing aggregation operation on the searched available black-start unit sites to generate generalized black-start unit nodes, wherein the black-start unit nodes are starting points for restoring the whole power grid system, and one or more black-start unit nodes are provided.
In the embodiment of the invention, the modified IEEE30 node system is taken as an example for simulation calculation, and the calculation flow of the power grid resilience in the black start and load recovery process is fully considered; the modified IEEE30 node system structure diagram is shown in fig. 2; wherein, the power plant that is located node 1 contains 3 black start unit, and the power plant that is located node 25 contains 2 black start unit, and its unit capacity and corresponding unit start-up sequence are shown as follows:
Figure GDA0003409741820000131
the modified IEEE30 node system contains 41 lines in total, and the line reactance is shown in the following table:
Figure GDA0003409741820000132
Figure GDA0003409741820000141
the nodes with the load conforming to the modified IEEE30 node system and the load types thereof are shown in the following table:
Figure GDA0003409741820000142
in the embodiment of the present invention, the edges included in the set TE are shown in the following table:
serial number Line Serial number Line
1 1-2 15 22-24
2 2-5 16 25-27
3 5-7 17 17-16
4 7-6 18 10-20
5 6-8 19 20-19
6 6-4 20 19-18
7 4-3 21 18-15
8 6-28 22 15-12
9 6-9 23 12-13
10 9-10 24 15-14
11 10-21 25 15-23
12 21-22 26 25-26
13 10-17 27 27-29
14 9-11 28 29-30
The paths from the generalized black starter group nodes in the T1 to the nodes of each unit to be recovered comprise 6 lines from 1-2, 2-5, 5-7, 7-6, 6-9, 9-10, 10-20, 20-19, 19-18, 18-15, 15-12, 12-13, 10-21, 21-22, 15-23 and 25-27, and the average shortest distance D1 from the generalized black starter group nodes in the tree T1 to the nodes of each unit to be recovered is equal to
D1＝0.3851；
And setting the node in the T1 as a tree T2 after aggregation, wherein the number of lines in the path from the generalized unit node in the T2 to the rest load nodes is 4-3, 6-4, 6-8, 6-28, 9-11, 10-17, 15-14, 17-16, 22-24, 25-26, 27-29 and 29-30, and the total number is 12. The number of the load nodes in the T2 is 12, and the average shortest distance D2 from the generalized unit node in the T2 to the rest load nodes is as follows:
D2＝0.1569；
thus, the average value is calculated:
Figure GDA0003409741820000151
further, the ratio is calculated: res＝5.66。
Fig. 3 is a block diagram illustrating a structure of a power grid restoring force calculation system based on black start and load restoring processes according to an embodiment of the present invention, where only portions related to the embodiment of the present invention are shown for convenience of description.
The power grid resilience computing system based on the black start and the load recovery process comprises:
the basic data acquisition module 11 is configured to identify a state of a power grid system, and acquire and calculate basic data of the power grid system, where the basic data includes a black start unit parameter, a unit parameter to be recovered, a line parameter, and a load type;
the network connection matrix establishing module 12 is configured to establish a network connection matrix M corresponding to the system based on the obtained basic data of the power grid system;
a first calculation module 13, configured to screen out the network connection matrix M according to the established network connection matrix MCalculating the sum of weighted capacities of all available black start units in each power plant and corresponding per unit value
Figure GDA0003409741820000152
The minimum spanning tree generating module 14 is configured to generate a minimum spanning tree T1 including all recoverable plant nodes by using the generalized black starter group node generated by aggregation as a root node;
a first average shortest distance calculating module 15, configured to calculate an average shortest distance D1 from a generalized black start unit node in the minimum spanning tree T1 to each unit node to be recovered;
the generalized unit node aggregation module 16 is configured to aggregate generalized black-start unit nodes, unit nodes to be recovered, and corresponding paths in the minimum spanning tree T1 into a generalized unit node;
a second average shortest distance calculating module 17, configured to calculate an average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to each of the other load nodes;
an average value calculating module 18, configured to calculate an average value of average shortest distances D1 from the generalized black starter group node in the minimum spanning tree T1 to each unit node to be restored and average shortest distances D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes
Figure GDA0003409741820000161
A ratio calculation module 19 for calculating the per unit value of the weighted sum of the black start unit capacities
Figure GDA0003409741820000162
And
Figure GDA0003409741820000163
is defined as the grid resilience based on the black start and load recovery processes.
As shown in fig. 4, the minimum spanning tree generation module 14 specifically includes:
a first placement module 20 for placing any black start unit at a power plant node s0Put into the set U, i.e. U ═ s0}，TE＝{}；
A judging module 21, configured to judge whether the set U includes all nodes in the abstract graph G, and if the set U does not include all nodes in the abstract graph G, find an edge (U, V) with the smallest weight among all the edges (U, V) belonging to U and V belonging to V-U belonging to E according to the network connection matrix M corresponding to the abstract graph G0,v0)；
A second placement module 22 for placing the node v0Put into the set U and put the line (U)0,v0) Put into the aggregate TE;
a repeated execution module 23, configured to repeat the execution flows of the determination module 21 and the second placement module 22 to obtain a minimum spanning tree T1 including all power plant and substation nodes in the abstract diagram G;
wherein G ═ (V, E) is an abstract graph corresponding to the power grid, G is an undirected weighted connected graph, V is a set of nodes in the abstract graph G, E is a set of lines in the abstract graph G and includes virtual lines, the line weights are per unit values of line reactance, the network connection matrix corresponding to the abstract graph G is M, and when a minimum spanning tree T1 including all nodes in the abstract graph G is (U, TE), U is a set of nodes in the tree T1, TE is a set of edges in the tree T1, and U and TE are initially empty sets.
In the embodiment of the invention, the state of the power grid system is identified, the basic data of the power grid system is obtained and calculated, and a network connection matrix M corresponding to the system is established; screening out the power plants of the available black start unit in the system, and calculating the sum of the weighted capacity of all the available black start units in each power plant and the corresponding per unit value
Figure GDA0003409741820000164
Generating a minimum spanning tree T1 containing all recoverable plant nodes, and calculating an average shortest distance D1 and an average shortest distance D2; calculate the average of D1 and D2
Figure GDA0003409741820000165
Calculating per unit value of weighted sum of black start unit capacity
Figure GDA0003409741820000166
And
Figure GDA0003409741820000167
the ratio of the total power to the total power of the power grid system is calculated, and the ratio of the total power to the total power of the power grid system is calculated according to the ratio of the total power to the total power of the power grid system, so that a quantitative means is provided for evaluating and analyzing the power grid restoring force of the power grid system after a blackout accident occurs on the basis of fully considering the black start and load restoring processes, and the method has the following technical effects:
(1) the method fully considers the specific black start process and the load recovery process of the power grid after a large-scale power failure accident occurs, and distinguishes the contribution of black start sets with different optimal sequences to the power grid recovery and the difficulty of different station load recovery, so that the calculation of the power grid recovery force is more objective;
(2) the invention relates to the condition that a plurality of available black start power supplies exist in a power grid system, and provides guidance for power grid partition recovery;
(3) in the invention, a Prim algorithm is used for respectively searching the minimum spanning trees containing all the unit nodes and all the nodes, so that a global optimal solution can be obtained;
(4) the calculation method of the power grid restoring force considering the black start and the load restoring process provides a method and means for quantitatively evaluating and researching the power grid restoring force problem, can conveniently find the weak point of the power grid in the aspect of improving the restoring force, and provides corresponding improvement measures;
(5) the quantitative calculation method for the power grid resilience provided by the invention provides means and basis for power grid planning aiming at improving the power grid resilience;
(6) the invention comprehensively considers the topological position of the unit to be recovered, the distribution and the load type of the load nodes, classifies the load nodes according to the recovery process in the calculation, and better accords with the recovery process after the power failure accident of the power grid;
(7) according to the invention, the topological position of a power plant where the black start unit is located, the starting priority of the black start unit and the load types of different nodes are mainly considered, so that a basis is provided for black start unit distribution optimization and grid frame optimization by taking improvement of the power grid resilience as a target.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (8)

1. A power grid resilience calculation method based on black start and load recovery processes is characterized by comprising the following steps of:
identifying the state of a power grid system, acquiring and calculating basic data of the power grid system, and establishing a network connection matrix M corresponding to the system based on the acquired basic data of the power grid system, wherein the basic data comprises black start unit parameters, unit parameters to be recovered, line parameters and load types;
screening out the power plants of the available black start unit in the system according to the established network connection matrix M, and calculating the sum of the weighted capacity of all the available black start units in each power plant and the corresponding per unit value
Figure FDA0003417338070000011
Generating a minimum spanning tree T1 containing all recoverable plant station nodes by taking generalized black starter group nodes generated by aggregation as root nodes, and calculating the average shortest distance D1 from the generalized black starter group nodes in the minimum spanning tree T1 to each unit group node to be recovered;
aggregating generalized black starter group nodes, each unit node to be recovered and corresponding paths in the minimum spanning tree T1 into a generalized unit node, and then calculating the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes;
computingThe average shortest distance D1 from the generalized black starter group node in the minimum spanning tree T1 to each unit node to be recovered and the average value of the shortest distances D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes
Figure FDA0003417338070000012
Calculating per unit value of weighted sum of black start unit capacity
Figure FDA0003417338070000013
And
Figure FDA0003417338070000014
a ratio of (a), the ratio being defined as a grid restoration force based on black start and load restoration processes;
the network connection matrix M is a square matrix, and is marked as:
Figure FDA0003417338070000015
in the network connection matrix M, the number of rows and columns is equal to the number of available plant nodes in the system, and when there is an available tie line l between node i and node jijAnd line lijPer unit value of line reactance of xijThen element M in the network connection matrix Mij＝Mji＝(wli+wlj)/2×xij(ii) a On the contrary, if there is no available tie line between node i and node j, Mij＝MjiInfinity, whereiniFor load recovery difficulty of node i, wljLoad recovery difficulty for node j;
in the network connection matrix M, the constant impedance load proportion of the node i is alpha1With a motor type load ratio of 1-alpha1The constant impedance load ratio of the node j is alpha2With a motor type load ratio of 1-alpha2；
If the node is a loadA node, setting the load recovery difficulty of the motor type to 1, setting the load recovery difficulty of the constant impedance type to 0.5, and setting the load recovery difficulty of the node i to wli＝0.5×α1+1×(1-α1)＝1-0.5α1(ii) a The load recovery difficulty of node j is defined as wlj＝0.5×α2+1×(1-α2)＝1-0.5α2；
If the node is a contact node and the substation represented by the contact node has no load to be restored, the load restoration difficulty coefficient wI of the contact node is 1.
2. The method for calculating grid restoration force based on black start and load restoration processes according to claim 1, wherein the calculation formula of the sum of the weighted capacities of all available black start units in each power plant is as follows:
Figure FDA0003417338070000021
wherein,
Figure FDA0003417338070000022
Pblackthe sum of the weighted capacities of the black start units of each power plant; n is the number of power plants comprising the black start unit in the system; piThe weighted capacity sum of all black start units in the ith power plant; m is the number of black start units in the ith power plant; pijFor the capacity of the jth black start unit in power plant i, cjThe coefficient of the jth black start unit in the power plant i is related to the starting sequence k of the black start unit j;
per unit value corresponding to the sum of weighted capacities of all available black start units in each power plant
Figure FDA0003417338070000023
The calculation formula of (2) is as follows:
Figure FDA0003417338070000024
wherein SB is a power base value and takes the value of 100 MVA.
3. The grid restoring force calculation method based on black start and load recovery processes according to claim 1, wherein the step of generating a minimum spanning tree T1 containing all recoverable plant station nodes by taking generalized black start engine group nodes generated by aggregation as root nodes specifically comprises the following steps:
(1) any black start unit is positioned at power plant node s0Put into the set U, i.e. U ═ s0}，TE＝{}；
(2) Judging whether the set U contains all nodes in the abstract graph G, if not, finding an edge with the minimum weight (U, V) belongs to the edges (U, V) belonging to the V-U and the edges (U, V) belonging to the E according to the network connection matrix M corresponding to the abstract graph G0,v0)；
(3) Node v0Put into the set U and put the line (U)0,v0) Put into the aggregate TE;
(4) repeating the step (2) and the step (3) to obtain a minimum spanning tree T1 containing all power plant and substation nodes in the abstract diagram G;
wherein G ═ (V, E) is an abstract graph corresponding to the power grid, G is an undirected weighted connected graph, V is a set of nodes in the abstract graph G, E is a set of lines in the abstract graph G and includes virtual lines, the line weights are per unit values of line reactance, the network connection matrix corresponding to the abstract graph G is M, and when a minimum spanning tree T1 including all nodes in the abstract graph G is (U, TE), U is a set of nodes in the tree T1, TE is a set of edges in the tree T1, and U and TE are initially empty sets.
4. The method for calculating power grid restoration force based on black start and load restoration processes according to claim 1, wherein the calculation formula of the average shortest distance D1 from the black start unit node in the generalized form of the minimum spanning tree T1 to each unit node to be restored is as follows:
Figure FDA0003417338070000031
wherein n is the number of edges included in a path from a generalized black starter unit node to each unit node to be recovered in the tree T1; liA reactance value corresponding to the ith side contained in a path from the generalized black starter unit node in the tree T1 to each unit node to be recovered; m is the number of nodes of the tree T1 containing the unit power plant to be recovered;
the calculation formula of the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the other load nodes is as follows:
Figure FDA0003417338070000032
wherein, N is the number of edges with weights not equal to 0 in the tree T2; liThe edge weight corresponding to the ith edge with the weight not equal to 0 in T2; and M is the number of the rest load nodes except the generalized unit node in T2.
5. A grid resilience calculation system based on black start and load restoration processes, the system comprising:
the basic data acquisition module is used for identifying the state of the power grid system and acquiring and calculating basic data of the power grid system, wherein the basic data comprises black start unit parameters, unit parameters to be recovered, line parameters and load types;
the network connection matrix establishing module is used for establishing a network connection matrix M corresponding to the system on the basis of the acquired basic data of the power grid system;
a first calculation module, configured to screen out power plants of the available black start unit in the system according to the established network connection matrix M, and calculate a sum of weighted capacities of all available black start units in each power plant and a corresponding per unit value
Figure FDA0003417338070000041
The minimum spanning tree generation module is used for generating a minimum spanning tree T1 containing all recoverable plant nodes by taking the generalized black starter group node generated by aggregation as a root node;
the first average shortest distance calculation module is used for calculating the average shortest distance D1 from the generalized black starter unit node in the minimum spanning tree T1 to each unit node to be recovered;
the generalized unit node aggregation module is used for aggregating generalized black starter unit nodes, all unit nodes to be recovered and corresponding paths in the minimum spanning tree T1 into a generalized unit node;
the second average shortest distance calculation module is used for calculating the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to each of the rest load nodes;
an average value calculating module, configured to calculate an average value of average shortest distances D1 from the generalized black starter group node in the minimum spanning tree T1 to each unit node to be restored and average shortest distances D2 from the generalized unit node in the minimum spanning tree T1 to the rest load nodes
Figure FDA0003417338070000042
A ratio calculation module for calculating the per unit value of the weighted sum of the black start unit capacity
Figure FDA0003417338070000043
And
Figure FDA0003417338070000044
a ratio of (a), the ratio being defined as a grid restoration force based on black start and load restoration processes;
the network connection matrix M is a square matrix, and is marked as:
Figure FDA0003417338070000045
in the network connection matrix M, the number of rows and columns is equal to the number of available plant nodes in the system, and when there is an available tie line l between node i and node jijAnd line lijPer unit value of line reactance of xijThen element M in the network connection matrix Mij＝Mji＝(wli+wlj)/2×xij(ii) a On the contrary, if there is no available tie line between node i and node j, Mij＝MjiInfinity, whereiniFor load recovery difficulty of node i, wljLoad recovery difficulty for node j;
in the network connection matrix M, the constant impedance load proportion of the node i is alpha1With a motor type load ratio of 1-alpha1The constant impedance load ratio of the node j is alpha2With a motor type load ratio of 1-alpha2；
If the node is a load node, setting the load recovery difficulty of the motor type to be 1, and setting the load recovery difficulty of the constant impedance type to be 0.5, then setting the load recovery difficulty of the node i to be wli＝0.5×α1+1×(1-α1)＝1-0.5α1(ii) a The load recovery difficulty of node j is defined as wlj＝0.5×α2+1×(1-α2)＝1-0.5α2；
If the node is a contact node and the substation represented by the contact node has no load to be restored, the load restoration difficulty coefficient wI of the contact node is 1.
6. The system according to claim 5, wherein the sum of the weighted capacities of all available black start units in each power plant is calculated as:
Figure FDA0003417338070000051
wherein,
Figure FDA0003417338070000052
Pblackthe sum of the weighted capacities of the black start units of each power plant; n is the number of power plants comprising the black start unit in the system; piThe weighted capacity sum of all black start units in the ith power plant; m is the number of black start units in the ith power plant; pijFor the capacity of the jth black start unit in power plant i, cjThe coefficient of the jth black start unit in the power plant i is related to the starting sequence k of the black start unit j;
per unit value corresponding to the sum of weighted capacities of all available black start units in each power plant
Figure FDA0003417338070000053
The calculation formula of (2) is as follows:
Figure FDA0003417338070000054
wherein SB is a power base value and takes the value of 100 MVA.
7. The grid resilience computing system based on black start and load restoration processes according to claim 5, wherein the minimum spanning tree generation module specifically comprises:
a first placement module for placing any one of the black start units at the power plant node s0Put into the set U, i.e. U ═ s0}，TE＝{}；
A judging module, configured to judge whether the set U includes all nodes in the abstract graph G, and if the set U does not include all nodes in the abstract graph G, find an edge (U, V) with the smallest weight among all edges (U, V) belonging to U and V belonging to V-U belonging to E according to the network connection matrix M corresponding to the abstract graph G0,v0)；
A second placement module for placing the node v0Put into the set U and put the line (U)0,v0) Put into the aggregate TE;
the repeated execution module is used for repeating the execution processes of the judgment module and the second placement module to obtain a minimum spanning tree T1 containing all power plant and substation nodes in the abstract diagram G;
wherein G ═ (V, E) is an abstract graph corresponding to the power grid, G is an undirected weighted connected graph, V is a set of nodes in the abstract graph G, E is a set of lines in the abstract graph G and includes virtual lines, the line weights are per unit values of line reactance, the network connection matrix corresponding to the abstract graph G is M, and when a minimum spanning tree T1 including all nodes in the abstract graph G is (U, TE), U is a set of nodes in the tree T1, TE is a set of edges in the tree T1, and U and TE are initially empty sets.
8. The system for calculating power grid restoration force based on black start and load restoration processes according to claim 5, wherein the calculation formula of the average shortest distance D1 from the black start unit node in the generalized form of the minimum spanning tree T1 to each unit node to be restored is as follows:
Figure FDA0003417338070000061
wherein n is the number of edges included in a path from a generalized black starter unit node to each unit node to be recovered in the tree T1; liA reactance value corresponding to the ith side contained in a path from the generalized black starter unit node in the tree T1 to each unit node to be recovered; m is the number of nodes of the tree T1 containing the unit power plant to be recovered;
the calculation formula of the average shortest distance D2 from the generalized unit node in the minimum spanning tree T1 to the other load nodes is as follows:
Figure FDA0003417338070000062
wherein, N is the number of edges with weights not equal to 0 in the tree T2; liThe edge weight corresponding to the ith edge with the weight not equal to 0 in T2; and M is the number of the rest load nodes except the generalized unit node in T2.
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