CN105893740B - A method of for excavating fragile node and route in electric power networks - Google Patents
A method of for excavating fragile node and route in electric power networks Download PDFInfo
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Abstract
A method of for excavating fragile node and route in electric power networks, it is characterized in that, comprehensively consider the topological property and electrical characteristic of electric power networks, the fragile node and route of power grid are excavated, comprising the following steps: establish power network model, establish network key degree index, calculate topological property criticality index and electrical characteristic criticality index, calculate comprehensive criticality index, the high fragile unit of output criticality, the high as fragile unit of the weakness numerical value.It is significant to the emergency prevention and control of cascading failure to excavate fragile unit in electric power networks so that the transmission process of electric power networks energy is quantified for the method for the present invention efficiency with higher, simple and convenient easy realization.
Description
Technical field
The invention belongs to Complex Power Network vulnerability analysis fields, and in particular to one kind is crisp in electric power networks for excavating
The method of weak bus and route.
Background technique
The existing fragility excavation about Complex Power Network is realized crucial based on electric power networks vulnerability assessment method
The process of one kind " knowledge acquisition " of the identification of link.The vulnerability assessment analysis of electric power networks mainly has to be managed based on complication system
The electric power networks vulnerability assessment of opinion, the electric power networks vulnerability assessment based on Brittleness Analysis theory, based on the electricity of Risk Theory
The methods of power network vulnerability assessment.Complex System Theory is mainly to study the complexity of network structure, in the finger of correlation theory
It leads down, we can start with from net topology structure come the method for seeking vulnerability assessment, but Complex System Theory is too laid particular stress on
It is the key that then assessment models superiority and inferiority with the actual goodness of fit often during actually combining in theory.Brittleness Analysis
The correlation theory system of theoretical Main Analysis cascading failure is mainly based upon cellular automata (cellular automata, CA)
Model.This method can effectively analyze power grid subsequent fault problem from self-organized criticality.But this method has ignored
The design feature of actual electric network can not carry out emulation experiment to correlation technique and model, thus also can not just be applied in practice.
Power Grid Vulnerability Assessment method based on Risk Theory mainly passes through definition risk form and is generally denoted as: R=Pe×Ie.In formula:
R indicates value-at-risk；PeThe probability of expression accident；IeThe consequence of expression accident.Re-define index such as: low-voltage risk, integrated risk
Etc. indexs etc., the fragile unit in power grid is recognized according to the size of value-at-risk and each risk indicator.Only this method lacks
Weary overall point of view is suitable only for the vulnerability assessment of power grid part.
Existing electric network composition fragility discrimination method generally excavated by network-based architectural characteristic, but in node
Or in the case that line status develops, the electrical characteristic when normal operation ignored due to, seems unilateral and has deviated from practical feelings
Condition.Existing implementation uses the analysis strategy or pure Steady-State Analysis of Power System strategy of pure topology, it is contemplated that electric power networks
Vulnerability analysis two extreme directions.The former carries out the node in electric network composition using topological structure as research object
Analysis, proposes node criticality evaluation index, has also set up power grid and has had the right topological model, and the latter establishes weighting power grid and estimates
Model, this model sufficiently pay attention to importance existing for element in network structure, have more to the distribution of the practical trend of system
Accurately reflection, and the criticality of system element is studied accordingly.Simultaneously the model using system lose load ratio, assessment when
It waits and more payes attention to end load demand.
Summary of the invention
The present invention is based on disadvantages mentioned above, based on Complex Networks Theory, have on Markov Chain and influence model
Effect combines, and completes modeling work based on the specific evolutionary process of electric network state.The technical program is established in complex load net
Network and Markov Chain and influence modular concept basis on, comprehensively consider unit " attribute " and its with other homogeneity units
" electrical distance " characterize " influence " of the unit on network, more accurately portray the key in electric network state evolutionary process
Unit.The present invention has carried out comprehensive description to electrical characteristic and network topology characteristic, carries out between the influence generated node
Analysis, in the case where the grade of voltage is with node type difference, effectively combining influences model and Markov Chain, establishes and realizes
Power grid analog simulation platform under real-time status, makes corresponding early warning to the normal operation of power grid.Invention propose with influence
What is carried out based on the fragile link that model has is identified as theoretical basis, can expand for multicomponent failure there is a situation where.
We cannot analyze the architectural vulnerability of power grid and lump together with traditional Power System Stability Analysis, be based on
When the method progress architectural vulnerability of complex network is analyzed, the size of its trend is not paid close attention to excessively, but should be coke
Point focusing feature intrinsic in structure.It is known that the conveying of electric energy is issued from generator, adjacent bear first is flowed through
Lotus, then electrical energy transportation to distant place load.So it is single using watt level as the standard distinguished, it is excessively unilateral.Therefore, in order to
Reduce influence of the failed transmission path to result, the present invention not only allows for the practical electricity characteristic of node and route, simultaneously also
The topological structure for considering node and route excavates the fragile node and route of power grid.
In analysis electrical characteristic, the present invention selects susceptance for weight.It is main to consider two aspects: first is that susceptance can embody
Electrical distance between two o'clock, i.e. susceptance between two o'clock are bigger, and two node spaces distance is closer, is exactly load section in other words
Point distance power generation node is closer, which is in trend upstream, and the trend undertaken is bigger, and the load node is more important；Two
The case where being for grid disconnection, is expressed as 0 with susceptance, is if being indicated with impedance if phase connecting lines are removed between two o'clock
∞。
In order to achieve the above-mentioned object of the invention, the present invention provides following technical schemes:
A method of for excavating fragile node and route in electric power networks, which is characterized in that comprehensively consider power network
The topological property and electrical characteristic of network excavate the fragile node and route of power grid, comprising the following steps:
Step 1, power network model is established, describes electric power networks with weighted adjacent matrix W are as follows:
ω in formulaijFor the susceptance of side i-j, N indicates the load bus collection in power grid；
Step 2, network key degree index is established, characterizes the different degree index of route in electric power networks using side betweenness,
Using the susceptance of branch as the weight of route, electrical distance is converted by the connection distance between node；With route betweenness to node
As support, the important of node is codetermined by the harmonic form of the route betweenness of the weighting degree and all neighbours' routes of node
Degree；
Step 3, topological property criticality index and electrical characteristic criticality index are calculated, wherein calculate the topology of route
Characteristic criticality index and electrical characteristic criticality the following steps are included:
Node is divided into load bus and power generation two class of node by step 3.1.1；
Step 3.1.2 calculates the topology weight λ of routeij, define topology weight λijIt is numerically equal to the side of route i-j
Betweenness Bij,
Wherein, ij indicates load bus pair, δjk(lij) and δjkIt respectively indicates by route lijShortest path number and institute
There is shortest path number；
Step 3.1.3 can make every effort to the electrical characteristic weight of route according to power generation-load bus to maximum bearing load
Wherein, YijIndicate route i-j from susceptance；Indicate that load bus i and load bus j arrives power generation section respectively
The minimum value of the impedance matrix shortest path of point g and g ', then the susceptance being converted by formula (4), Zi-gIndicate that load bus i is arrived
The total impedance of power generation node g；PiIndicate the bearing load ability of node,It is expressed as between load bus i and power generation node g
Maximum bearing load ability；The maximum bearing load ability that load bus j is expressed as between the node g ' that generates electricity, tool
Body expression formula is as follows:
Step 3.1.4 finds out the criticality of each route i-j
Ij indicates load bus pair, λijIndicate topology weight,Indicate electrical characteristic weight；
Topological property criticality index and the electrical characteristic criticality of calculate node the following steps are included:
Node is divided into load bus and power generation two class of node by step 3.2.1；
Step 3.2.2 acquires node i benchmark degreeDiIt is the degree of node i,<k>is entire electric power networks
Average degree；The side betweenness of all neighbours' route i-j of node i is acquired, wherein j ∈ Γ (i), then acquires opening up for line support node
Flutter weight λi；λiIt indicates by the criticality of the side betweenness support node i benchmark degree of all neighbours' route i-j of node i, wherein j ∈
Γ (i), specific formula is as follows:
Step 3.2.3 can make every effort to the electrical characteristic weight W of node according to power generation-load bus to maximum bearing loadi G,
Wherein,It is the minimum impedance group that every a pair of of power generation-load bus pair is acquired by dijkstra shortest path algorithm
Be combined diameter, by formula (9) reconvert at susceptance；Indicate " power generation-load " node to the minimum impedance path between i-g
Total impedance；It is expressed as load bus i and power generation node g maximum bearing load ability；
Step 3.2.4: the criticality of each node is found out
Wherein, λiFor topology weight, Wi GIndicate electrical characteristic weight；
Step 4, comprehensive criticality index is calculated；
According to the criticality of routeCalculate line influence matrix element dij, and be defined as route fragile degree and refer to
Mark
According to the criticality of nodeSeek line influence matrix element di, and it is defined as node the weakness
Step 5, according to node or the vulnerability inder of route, by the weakness descending sort, it is believed that the weakness
The unit of descending sort top 10 is fragile unit, the high fragile unit of output criticality.
Compared with prior art, of the invention to have the advantages that
The present invention is based on model and markovian method is influenced, based on Complex Networks Theory, to Markov
Chain and influence model are effectively combined, and modeling work is completed based on the specific evolutionary process of electric network state, are carried out corresponding
Calculating, finally acquire the criticality size of grid nodes, by this algorithm efficiency with higher, simple and convenient easy realization.
Based on transmission line of electricity betweenness and node degree, the impact factor grid node is defined, and to electric power networks
Two characteristics having: electrical characteristic and topological property give sufficient consideration, then comment the weaker overall of power grid
Estimate, this case that only pay close attention to relationship between node topology line to previous topology controlment has made and having made up.To electricity
Gas criticality and equivalent topologies criticality carry out integrated treatment, and the influence generated between complete paired node carries out quantitative description, builds
It is vertical to realize that, with the system mode evolutionary model being actually consistent, method is simple and feasible.Method of the invention enables electric power networks
The transmission process of amount is quantified, and fragile unit is significant to the emergency prevention and control of cascading failure in excavation electric power networks,
Detailed description of the invention
Fig. 1 is IEEE-39 node system；
Fig. 2 is the method for the present invention flow chart；
Fig. 3 is the distribution of the criticality of route；
Fig. 4 is the criticality distribution map of node；
Fig. 5 is the distribution map of vulnerable line；
Fig. 6 is the distribution map of fragile node；
Fig. 7 is route criticality calculation flow chart；
Fig. 8 is node criticality calculation flow chart.
Specific embodiment
In the following, the invention will be further described with reference to the drawings and specific embodiments.
Fragile unit is significant to the emergency prevention and control of cascading failure in excavation power network, and method proposed by the present invention makes
The transmission process of energy is quantified, and is tested on the IEEE-39 node system network of standard, as shown in Fig. 1.
Simulation result shows that the vulnerable line that the present invention excavates is located at mostly on the important passway for transmitting electricity of system, the fragile section excavated
Point has its biggish carrying distributional effects to energy transfer.Fig. 1 is the topological structure of IEEE-39 node standard test system,
Network node shares 39, and 46, route, wherein power generation node NG=10, load bus NL=29.It proposes through the invention
Fragile source method for digging, IEEE-39 node standard test system is analyzed, each route and each node have been obtained
Criticality.
Fig. 2 is the flow chart of the method for the present invention, and Fig. 7 is the route criticality calculation process of the method for the present invention, according to process
It calculates as follows:
Step 1: the topology weight λ of route is calculated according to formula (2)ijAs a result as follows:
The topology weight of each route of 1 IEEE39 of table
Step 2: by formula (3), the electrical spy of route can be made every effort to maximum bearing load according to " power generation-load " node
Property weight
The electrical weight of each route of 2 IEEE39 of table
Step 3: the criticality of each route i-j is found out according to formula (6)
The criticality of each route of 3 IEEE39 of table
| Route label | Criticality | Route label | Criticality |
| 1-2 | 53.64369 | 14-15 | 89.65814 |
| 1-39 | 35.4219 | 15-16 | 106.7224 |
| 2-3 | 39.63217 | 16-17 | 106.1319 |
| 2-25 | 48.99811 | 16-19 | 70.74202 |
| 2-30 | 9.221461 | 16-21 | 51.24757 |
| 3-4 | 67.25122 | 16-24 | 55.31836 |
| 3-18 | 22.68962 | 17-18 | 48.16736 |
| 4-5 | 88.30108 | 17-27 | 56.88899 |
| 4-14 | 79.90026 | 19-20 | 38.25019 |
| 5-6 | 67.94035 | 19-33 | 19.52532 |
| 5-8 | 36.37434 | 20-34 | 15.84068 |
| 6-7 | 16.27386 | 21-22 | 37.33032 |
| 6-11 | 24.79881 | 22-23 | 4.442469 |
| 6-31 | 19.39286 | 22-35 | 20.22042 |
| 7-8 | 17.92882 | 23-24 | 33.99259 |
| 8-9 | 24.00225 | 23-36 | 18.52173 |
| 9-39 | 25.27176 | 25-26 | 42.24672 |
| 10-11 | 16.41808 | 25-37 | 16.0309 |
| 10-13 | 40.78539 | 26-27 | 49.39853 |
| 10-32 | 19.19741 | 26-28 | 21.4722 |
| 11-12 | 8.781543 | 26-29 | 44.22785 |
| 12-13 | 18.40801 | 28-29 | 1.248222 |
| 13-14 | 67.24124 | 29-38 | 24.52675 |
Step 4: the vulnerability inder d of each route is acquired according to (11)ij。
The vulnerability inder of each route of 4 IEEE39 of table
By upper table it will be seen that the vulnerability inder of route route outstanding is 15-16,16-17 etc., from its distribution
Can be more very clear on figure, the fragile degree distribution map of route is as shown in Figure 3.
The vulnerability inder of our foundation routes, by route descending sort, the route for coming top 10 is as shown in the table:
Each vulnerable line identification result of 5 IEEE39 of table
| Sequence | The method of the present invention |
| 1 | 15-16 |
| 2 | 16-17 |
| 3 | 14-15 |
| 4 | 4-5 |
| 5 | 4-14 |
| 6 | 16-19 |
| 7 | 5-6 |
| 8 | 3-4 |
| 9 | 13-14 |
| 10 | 17-27 |
By Fig. 1, it can be seen that, power plant conveys electric energy to load area, wherein 15-16,16-17,16-24,5-6,13-
14, the routes such as 2-3 are all the critical circuits of load center.
Similarly, Fig. 8 is the node criticality calculation process of the method for the present invention, as follows according to workflow management:
Step 1: the topology weight λ of route is calculated according to formula (7)iAs a result as follows:
The topology weight of each node of 6 IEEE39 of table
| Nodal scheme | Topology weight | Nodal scheme | Topology weight |
| 1 | 0.072953 | 16 | 0.389306 |
| 2 | 0.220606 | 17 | 0.21985 |
| 3 | 0.215729 | 18 | 0.11 |
| 4 | 0.240705 | 19 | 0.149955 |
| 5 | 0.18303 | 20 | 0.069326 |
| 6 | 0.127101 | 21 | 0.101032 |
| 7 | 0.037468 | 22 | 0.07367 |
| 8 | 0.090126 | 23 | 0.07367 |
| 9 | 0.052178 | 24 | 0.101032 |
| 10 | 0.082217 | 25 | 0.146756 |
| 11 | 0.056841 | 26 | 0.187254 |
| 12 | 0.036461 | 27 | 0.126294 |
| 13 | 0.138637 | 28 | 0.02485 |
| 14 | 0.249761 | 29 | 0.071269 |
| 15 | 0.191515 |
Step 2: by formula (8), the electrical spy of route can be made every effort to maximum bearing load according to " power generation-load " node
Property weight Wi G
The electrical weight of each node of 7 IEEE39 of table
| Nodal scheme | Electrical weight | Nodal scheme | Electrical weight |
| 1 | 1039.968 | 16 | 660.721 |
| 2 | 305.1067 | 17 | 657.0707 |
| 3 | 352.0278 | 18 | 271.447 |
| 4 | 702.4697 | 19 | 697.3539 |
| 5 | 713.8078 | 20 | 735.3883 |
| 6 | 717.7018 | 21 | 685.2223 |
| 7 | 706.9972 | 22 | 719.9301 |
| 8 | 703.485 | 23 | 691.6105 |
| 9 | 1039.995 | 24 | 656.3223 |
| 10 | 699.9495 | 25 | 583.1034 |
| 11 | 690.9611 | 26 | 558.0139 |
| 12 | 664.7234 | 27 | 649.4691 |
| 13 | 690.5157 | 28 | 862.5342 |
| 14 | 678.7246 | 29 | 894.0381 |
| 15 | 657.1462 |
Step 3: the criticality of each route i-j is found out according to formula (10)
The each node criticality of 8 IEEE39 of table
Step 4: each node vulnerability inder d is acquired according to (12)i:
The vulnerability inder of each node of 9 IEEE39 of table
| Nodal scheme | Fragile index | Nodal scheme | Fragile index |
| 1 | 0.034051 | 16 | 0.062698 |
| 2 | 0.032072 | 17 | 0.046986 |
| 3 | 0.034068 | 18 | 0.021362 |
| 4 | 0.050834 | 19 | 0.039976 |
| 5 | 0.044684 | 20 | 0.027913 |
| 6 | 0.037337 | 21 | 0.032527 |
| 7 | 0.02012 | 22 | 0.02847 |
| 8 | 0.031128 | 23 | 0.027904 |
| 9 | 0.028798 | 24 | 0.031834 |
| 10 | 0.029656 | 25 | 0.036163 |
| 11 | 0.024499 | 26 | 0.039961 |
| 12 | 0.019246 | 27 | 0.035405 |
| 13 | 0.038249 | 28 | 0.018099 |
| 14 | 0.050899 | 29 | 0.031205 |
| 15 | 0.043856 |
Also the node list of node vulnerability inder sequence top 10 is obtained, as shown in the table:
Each fragile loads node authentication result of 10 IEEE39 of table
By upper table it will be seen that the criticality of node it is outstanding be the nodes such as 16,14,4, criticality distribution
As shown in Figure 4.
From Fig. 1 it can also be seen that power plant conveys electric energy to load area, wherein the nodes such as 16,14,4,5,17 are all negative
The key node at lotus center.They are to the distribution of electric energy trend in occupation of the status of hinge；Route criticality is compared simultaneously
As a result, it has also been discovered that, important line common end also can side embody important Node distribution, this and distinguishing in the present invention
The result that knowledge method obtains is consistent.
By means of the present invention, it is easy to more fragile route can be excavated, while it has been found that one has
The phenomenon that meaning, in the vulnerable line identified, their node serial number is continuous.So thus we can dig
It excavates a fragile path to come out, as shown in Figure 5.Similarly, in the fragile node identified, by their node serial number
It connects point into line, we can be obtained by one and excavate same fragile path (No. 3 nodes rows out with route fragility in this way
Sequence is 12 therefore is represented by dashed line), as shown in Figure 6.
From fig. 5, it is seen that this fragile path is in the center of each generator radiation, it is not only accepted
Each conveying trend for facing generator recently, while also acting as the pivotal role that energy collects, merges, distributing, converting.From Fig. 6
In we still can see, the fragile path obtained after the fragile node line excavated according to node fragility and line
What road fragility was excavated arrive the result is that identical, while also mutually confirming the reasonable validity of proposition method of the present invention.
Claims (1)
1. a kind of method for excavating fragile node and route in electric power networks, which is characterized in that comprehensively consider electric power networks
Topological property and electrical characteristic, the fragile node and route of power grid are excavated, comprising the following steps:
Step 1, power network model is established, describes electric power networks with weighted adjacent matrix W are as follows:
ω in formulaijFor the susceptance of side i-j, N indicates the load bus collection in power grid；
Step 2, network key degree index is established, using the different degree index of side betweenness characterization route in electric power networks, with branch
The connection distance between node is converted electrical distance by weight of the susceptance on road as route；Use route betweenness to node as
Support codetermines the different degree of node by the harmonic form of the route betweenness of the weighting degree and all neighbours' routes of node；
Step 3, topological property criticality index and electrical characteristic criticality index are calculated, wherein calculate the topological property of route
Criticality index and electrical characteristic criticality the following steps are included:
Node is divided into load bus and power generation two class of node by step 3.1.1；
Step 3.1.2 calculates the topology weight λ of routeij, define topology weight λijIt is numerically equal to the side betweenness of route i-j
Bij,
Wherein, ij indicates load bus pair, δjk(lij) and δjkIt respectively indicates by route lijShortest path number and it is all most
Short path number；
Step 3.1.3 can make every effort to the electrical characteristic weight of route according to power generation-load bus to maximum bearing load
Wherein, YijIndicate route i-j from susceptance；Indicate load bus i and load bus j arrive respectively power generation node g and
The minimum value of the impedance matrix shortest path of g ', then the susceptance being converted by formula (4), Zi-gIndicate that load bus i is saved to power generation
The total impedance of point g；PiIndicate the bearing load ability of node,The maximum that load bus i is expressed as between the node g that generates electricity
Bearing load ability；The maximum bearing load ability that load bus j is expressed as between the node g ' that generates electricity, embodies
Formula is as follows:
Step 3.1.4 finds out the criticality of each route i-j
Ij indicates load bus pair, λijIndicate topology weight,Indicate electrical characteristic weight；
Topological property criticality index and the electrical characteristic criticality of calculate node the following steps are included:
Node is divided into load bus and power generation two class of node by step 3.2.1；
Step 3.2.2 acquires node i benchmark degreeDiIt is the degree of node i,<k>is being averaged for entire electric power networks
Degree；The side betweenness of all neighbours' route i-j of node i is acquired, wherein j ∈ Γ (i), then acquires the topology power of line support node
Weight λi；λiIt indicates by the criticality of the side betweenness support node i benchmark degree of all neighbours' route i-j of node i, wherein j ∈ Γ
(i), specific formula is as follows:
Step 3.2.3 can make every effort to the electrical characteristic weight W of node according to power generation-load bus to maximum bearing loadi G,
Wherein,It is the minimum impedance group combining that every a pair of of power generation-load bus pair is acquired by dijkstra shortest path algorithm
Diameter, by formula (9) reconvert at susceptance；Indicate " power generation-load " node to the total of the minimum impedance path between i-g
Impedance；It is expressed as load bus i and power generation node g maximum bearing load ability；
Step 3.2.4: the criticality of each node is found out
Wherein, λiFor topology weight, Wi GIndicate electrical characteristic weight；
Step 4, comprehensive criticality index is calculated；
According to the criticality of routeCalculate line influence matrix element dij, and it is defined as route the weakness
According to the criticality of nodeSeek line influence matrix element di, and it is defined as node the weakness
Step 5, according to node or the vulnerability inder of route, by the weakness descending sort, it is believed that the weakness descending
The unit of sequence top 10 is fragile unit, the high fragile unit of output criticality.
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