CN103607375A - Network N-1 security-region-boundary calculation and security evaluation method - Google Patents

Abstract

The invention discloses a network N-1 security-region-boundary calculation and security evaluation method and relates to the field of analysis of network security. The method includes: defining network operation work points, network N-1 security and network security regions. The method is a security evaluation method based on the security regions. The security evaluation method based on the security regions is capable of judging the security of a system rapidly without simulating N-1 events one by one and giving measurement of the security. The network N-1 security-region-boundary calculation and security evaluation method is widely applicable to undirected authorized networks such as power grids and communication networks and the like. The general security-region method which is applicable to general networks provides a basis for adjustment of work points and planning of topology and capacity when the general networks are subjected to random attacks. It is found that in the security-region method, a security-distance calculation result is highly identical with an anti-destroying-ability calculation result so that correctness of the security-domain method in security measurement is proved.

Description

A kind of N-1 security domain feature modeling and method for evaluating safety of network

Technical field

The present invention relates to Network security analysis field, particularly a kind of N-1 security domain feature modeling and method for evaluating safety of network.

Background technology

Be reliably and efficiently the target that system is pursued safely.No matter be computer network, electric power networks, city traffic network, communication network or cellular metabolism system, all need to when some component failure, still can keep normal operation by redundant path.Therefore, security reliability requires network to possess certain to cause still completing under subelement failure conditions the ability of predetermined function because of random external disturbance or malicious attack.Survivability is a typical method evaluating this ability, in recent years, has obtained studying widely and applying.

Survivability is as the important indicator of network reliability, its relevant research starts from strategic communication net, because Albert is after the paper of < < Nature > > magazine proposes in complex network field, has obtained research widely and be applied and approve in fields such as traffic, logistics and electric power afterwards.Survivabilities of Networks refers to that the node (limit) in network occurs under condition weathering or that suffer deliberately to attack, and network maintains the ability of its function ^[1].

In realizing process of the present invention, in discovery prior art, at least there is following shortcoming and defect in inventor:

No matter existing survivability research method is simulation method or analytic method ^[1]all focus on the reliability standard of weighing network with a numerical value, leave following defect: 1) amount of calculation and speed: working point and element emulation one by one one by one, amount of calculation is large, length consuming time, the demand of discontented sufficient real-time online; 2) security control: directly perceived not, be inconvenient to carry out real-time security control.3) safety evaluation effect and accuracy: can only provide safe or unsafe binary information or average after overall security desired value, information is less; Can only judge from part, can not embody whole safety allowance completely, the difference of diverse network state in the time of can not distinguishing safe operation, therefore can not accurately carry out capacity and join planning and safety evaluatio.

Summary of the invention

The technical problem underlying that the present invention solves has been to provide a kind of N-1 security domain feature modeling and method for evaluating safety of network, the method has reduced amount of calculation, has improved the speed of service, can carry out the security control intuitively of two-dimentional three-dimensional and adjustment, complete secure border information can be provided, more various working points (safe or unsafe) is described, described below:

The beneficial effect of technical scheme provided by the invention is:

N-1 security domain feature modeling and the method for evaluating safety of network, said method comprising the steps of:

(1) network operation working point, network N-1 fail safe and network security territory are defined;

Described network operation working point: represent all summits of network operating state and state vector and the operational mode on limit;

Described network N-1 fail safe: when network moves in certain network operation working point, remove any limit or summit in network, network can carry out flow reallocation to keep normal flow to transmit;

Described network security territory: in the process of operation, make all limits and summit all meet the set of the network operation working point of network N-1 fail safe for the network of determining topological sum capacity;

(2) safe evaluation method based on security domain;

Definition secure border distance B _ijfor:

D _ij=min(c _mn-f _mn)-f _ij，(v _m，v _n)∈B _ij

If D _ijbe greater than 0 explanation and still can guarantee normal transmission in network N-1 safety conditions lower network, there is no flow loss, D _ijfor the load margin of network operation working point to each border; If D _ijbe less than 0 explanation and under the safety conditions of network N-1, understand some flow loss, even loss seriously causes periods of network disruption; If D _ijequal 0 explanation under the safety conditions of network N-1 in critical condition;

If D _ijcomplete is timing, shows that network operation working point is inner at secure border, and system is current is N-1 safety;

If D _ijbe not timing entirely, show that network operation working point is outside at secure border, system is current is that N-1 is unsafe, is the D of negative value _ijthe flow value that exceeds this border for network operation working point is measured;

By two dimension or three-dimensional visualization are carried out in network security territory.

Described state vector comprises under certain transient state and flows out the net flow on summit, the total flow value of the load capacity of the flow value on every limit, each node, the whole network;

Described operational mode refers to summit and the limit connection status in network in network;

By operational mode, determine the limit in practical application, the n dimension theorem in Euclid space vector representation that network operation working point forms with the flow value on limit, wherein n is the number on limit in network, definition n-dimensional vector is formula (1):

Z=(f ₁₂，f ₂₃，f ₁₃…f _ij) ^T (1)

In above formula, Z represents the working point vector of the flow value based on limit; f _ijrepresent the flow value on network edge, i and j represent summit.

The expression formula of network N-1 security constraint lower network security domain is shown below:

In above formula, B _ijthe path that represents flow or load reallocation process;

(v _m, v _n) be path B _ijon all limits;

C _ijexpression is by v _ito v _jcan maximum delivered quantity, i.e. limit (v _i, v _j) capacity;

F _mnrepresent the limit (v that alternate route comprises _m, v _n) on flow value;

C _mnrepresent the limit (v that alternate route comprises _m, v _n) on capability value;

Formula (3) represents that the flow on every limit can not be over the capability value on its limit under normal circumstances.

When formula (4) represents that any limit generation N-1 fault lost efficacy, the flow value on each limit comprising on its circuitous path can not surpass its capability value.

The present invention proposes general security domain feature modeling method, can make system run to the position that approaches secure border, thereby under safety conditions, greatly improve system effectiveness meeting.The present invention is based on security domain safe evaluation method can without to N-1 event one by one emulation just can judge fast security of system, and provide the tolerance of fail safe.The present invention is extensively applicable to the undirected net of having the right such as power network, communication network.The universal safety territory method that is applicable to general network that the present invention proposes, while hit by randomness for general network, the adjustment of working point and the planning of topology and capacity provide foundation.The present invention studies and finds that Calculation of Safety Distance result and the survivability result of calculation of security domain method have very high consistency, illustrates that security domain method carries out the correctness in security metrics.But territory method is obviously better than survivability aspect a lot, it can directly describe the border of safe operation, by judging whether working point obtains easily its safety information within the scope of security domain, make adjustment, control and the planning of network traffics and capacity more directly perceived, and on operation time, be much better than simulation method, be more suitable for controlling in real-time online.The reason of territory method superiority is can complete computation go out secure border, and survivability index is average to all component failure N-1 simulation results in essence, and simulation result cannot complete description N-1 secure border.

Accompanying drawing explanation

Fig. 1 is communication network network topology provided by the invention and capacity configuration figure;

Fig. 2 is power distribution network network topology provided by the invention and capacity configuration figure;

Fig. 3 is communication network f provided by the invention ₁₂and f ₁₃two-dimensional cross-section figure;

Fig. 4 is communication network safe distance provided by the invention and the anti-measurement value variation tendency comparison diagram of ruining;

Fig. 5 is power distribution network F provided by the invention ₁₉and F ₂₄safe operation region figure;

Fig. 6 is power distribution network F provided by the invention _36/37/38and F ₂₀safe operation region figure;

Fig. 7 is a kind of N-1 security domain feature modeling of network and the flow chart of method for evaluating safety.

Embodiment

For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing, embodiment of the present invention is described further in detail.

The present invention proposes a kind of security domain method towards general networking, and its starting point is different from survivability: the method computationally secure border in advance just after given network topology structure, region that can safe operation with descriptive system integral body ^[2].Application safety territory method, for any given working point, the distance that can put secure border by evaluation work is that the position of working point in security domain judges whether safety fast, and make operations staff obtain the security measure of entire system, to determine the direction and intensity of employing prevention property control measure whether and control ^[2].Security domain can, from the reliability of the angle research network different with survivability, have the inaccessiable advantage of method of survivability.

Security domain research starts from power system security territory.More than recent two decades Lai，Yi China, make a gift of prosperous academician for the researcher of representative has obtained a series of important achievement in this field, comprise static state/dynamic security domain model ^[3-4], security domain character ^[2]with visual ^[5], and obtained successful Application in safety analysis, evaluation, early warning, control and the risk analysis of actual power transmission network at home and abroad.Although security domain is theoretical, there is lot of advantages, except electric power system, really do not extend to other field at present.Power distribution network net capability is theoretical in recent years ^[6]and power distribution network security domain ^[7]appear as the application of security domain beyond the electric power system provide may: literary composition [8] finds that by analog simulation method trouble free service point and dangerous working point obviously exist the phenomenon of boundary, critical point fitting result in border shows that security domain border is to approach very much linearity, can a series of hyperplane, consist of approx, net capability TSC point is a critical working point on security domain Hyperplanar boundary just ^[8].

The present invention provides a kind of new security domain towards general networking (Security Region, SR) method.Referring to Fig. 7, first, the universal safety domain model and the territory absorbing boundary equation that for the undirected net of having the right, have proposed, can analytically describe security domain border.Secondly, further provide the method for evaluating safety based on security domain, the method is carried out evaluate safety by calculating the position of present operating point in security domain, thereby realizes the target of maximum performance system effectiveness under certain margin of safety.

101: network operation working point, network N-1 fail safe and network security territory (SR) are defined;

The reliability requirement network of network not only can work, and also can maintain the original function of network when meeting with outside strike (random or targetedly).These explanation networks are not only paid close attention to the fail safe under static state, but also pay close attention to the fail safe of network when current intelligence is hit.And this method mainly concentrates on the limit removed in network or the simulation method of node is carried out the variation of observation grid and then obtains reliability index.These are similar to the N-1 security criterion that electric power system is followed always.So just like giving a definition:

Define 1 network operation working point: represent all summits of network operating state and state vector and the operational mode on limit.

Wherein, state vector comprises under certain transient state and flows out the net flow on summit, the total flow value of the load capacity of the flow value on every limit, each node, the whole network, other state vector except the flow value on every limit can be tried to achieve by the flow value on limit, so only represent the state of network operation point with the flow value on limit in Practical Calculation.Operational mode refers to summit and the limit connection status in network in network.

By operational mode, determine the limit in practical application, the n dimension theorem in Euclid space vector representation that network operation working point forms with the flow value on limit, wherein n is the number on limit in network, definition n-dimensional vector is formula (1):

Z=(f ₁₂，f ₂₃，f ₁₃...f _ij) ^T (1)

In above formula, Z represents the working point vector of the flow value based on limit; f _ijrepresent the flow value on network edge, i and j represent summit.

For example: in Fig. 1, provided a communication network network topology structure, from Fig. 1 can, 1,2,3,4 and 5 is summit, the line between each summit is limit, for example: the line between summit 1 and 2 is denoted as (v ₁, v ₂), f ₁₂equal 20, f ₂₃equal 10, f ₁₃equal 10, f ₁₄equal 10, f ₁₅equal 15, by that analogy, can show that network operation working point is:

Z=(f ₁₂，f ₂₃，f ₁₃，f ₁₄，f ₂₄，f ₃₄，f ₁₅，f ₄₅) ^T=(20，10，10，10，5，15，15，20) ^T

Define 2 network N-1 fail safes: when network moves in certain network operation working point, remove any limit or summit in network, network can carry out flow reallocation to keep normal flow to transmit (flow that is each limit is no more than this edge capacity value, and time is configured capability value by setting up network).

If meet above-mentioned condition in certain network operation working point, being called network is N-1 safety in this network operation working point, otherwise is unsafe.

Define 3 network security territories (SR): for the network of determining topological sum capacity, in the process of operation, make all limits and summit all meet the set of the network operation working point of network N-1 fail safe.

What the present invention proposed is the modelling of security domain:

If W is (f _ij)≤0 represents constraints, and security domain is the set that meets all working point of constraints, can be expressed as formula (2):

Ω _SR={Z|W(f _ij)≤0，(v _i，v _j)∈A} (2)

Wherein A is the set on limit in network; (v _i, v _j) represent by vertex v _iv to the limit _ja limit.

If put aside the difference of circuitous path in economy and the impact of flow loss, only consider the constraint of flux capacity, the expression formula that can obtain network N-1 security constraint lower network security domain is shown below:

In above formula, B _ijthe path that represents flow or load reallocation process;

(v _m, v _n) be path B _ijon all limits;

C _ijexpression is by v _ito v _jcan maximum delivered quantity, i.e. limit (v _i, v _j) capacity;

F _mnrepresent the limit (v that alternate route comprises _m, v _n) on flow value;

C _mnrepresent the limit (v that alternate route comprises _m, v _n) on capability value.

Formula (3) represents that the flow on every limit can not be over the capability value on its limit under normal circumstances.

When formula (4) represents that any limit generation N-1 fault lost efficacy, the flow value on each limit comprising on its circuitous path can not surpass its capability value.

By formula (3)-(4), can obtain security domain absorbing boundary equation group:

$\left\{\begin{array}{c}{f}_{\mathrm{ia}}\&le;\min (c_{\mathrm{mn}}-f_{\mathrm{mn}}),(v_m,v_n)\&Element;B_{\mathrm{ia}}\\ f_{\mathrm{ab}}\&le;\min (c_{\mathrm{mn}}-f_{\mathrm{mn}}),(v_m,v_n)\&Element;B_{\mathrm{ab}}\\ .......\\ f_{\mathrm{hj}}\&le;\min (c_{\mathrm{mn}}-f_{\mathrm{mn}}),(v_m,v_n)\&Element;B_{\mathrm{hj}}\end{array}\right.---\left(5\right)$

Wherein, a, b, h etc. also represent summit.

102: the safe evaluation method based on security domain;

1) definition secure border distance B _ijfor:

D _ij=min(c _mn-f _mn)-f _ij，(v _m，v _n)∈B _ij (6)

If D _ijbe greater than 0 explanation and still can guarantee normal transmission in network N-1 safety conditions lower network, there is no flow loss, D _ijfor the load margin of network operation working point to each border; If D _ijbe less than 0 explanation and under the safety conditions of network N-1, understand some flow loss, even loss seriously causes periods of network disruption; If D _ijequal 0 explanation under the safety conditions of network N-1 in critical condition.

If D _ijcomplete is timing, shows that network operation working point is inner at secure border, and system is current is N-1 safety.

If D _ijbe not timing entirely, show that network operation working point is outside at secure border, system is current is that N-1 is unsafe, is the D of negative value _ijthe flow value that exceeds this border for network operation working point is measured.

Above-mentioned secure border distance model not only can judge whether safety of network operation working point, also can carry out the planning of network capacity by secure border distance, make network traffics lose less or not lose as far as possible, improves the security reliability index of network.

2), by two dimension or three-dimensional visualization are carried out in network security territory, can directly by network operation working point, in the position of safety zone, carry out easily the judgement of network operation working point fail safe and the adjustment of flow.

Visualization method is other variate-value beyond fixing independent variable, formula (5) is deteriorated to the inequality group of two dimension or three-dimensional.With f _iaand f _abthe two-dimentional formula of degenerating for independent variable is:

$\left\{\begin{array}{c}{f}_{\mathrm{ia}}\&le;\min (c_{\mathrm{mn}}-f_{\mathrm{mn}}),(v_m,v_n)\&Element;B_{\mathrm{ia}}\\ f_{\mathrm{ab}}\&le;\min (c_{\mathrm{mn}}-f_{\mathrm{mn}}),(v_m,v_n)\&Element;B_{\mathrm{ab}}\\ f_{\mathrm{ia}}\&le;\min (c_{\mathrm{ia}}-f_{\mathrm{pq}}),(v_p,v_q)\&Element;Y_{\mathrm{ia}}\\ f_{\mathrm{ab}}\&le;\min (c_{\mathrm{ab}}-f_{\mathrm{pq}}),(v_p,v_q)\&Element;{\text{Y}}_{\mathrm{ab}}\end{array}\right.---\left(7\right)$

Formula (7) is with f _iaand f _abfor independent variable, the flow value on other limit is got and be take the flow value on the limit of network N-1 fail safe when constraints lower critical moves, and formula (5) deteriorates to the two-dimentional inequality shown in formula (7).Y wherein _iarepresent limit (v _i, v _a) other limit (v in network _p, v _q) need serve as other limit (v of circuitous path while there is N-1 fault _p, v _q) set; P, q also represent summit.

According to formula (7), can draw with f _iaand f _abtwo-dimentional relation figure, the fail safe that the position by working point in X-Y scheme can intuitive judgment working point.Example X-Y scheme as shown in Figure 3, dash area is the region of N-1 safe operation, dash area is outward the region of the dangerous operation of N-1, is the set of the network operation working point of critical operation on border.

It is independent variable that three-dimensional visualization method just be take the flow value on three limits, and security domain absorbing boundary equation group is deteriorated to three-dimensional inequality group, and all the other are equal to two-dimensional visualization method, repeat no more.

One, communication network case

1, example basic condition

The communication network of five nodes of take is example, and business demand is some imaginary data, and business demand matrix is as table 1:

Table 1 business demand matrix table

Setting shortest path alternate route is shown in table 2, network topology and capacity configuration as shown in Figure 1:

The shortest alternate route of table 2

2, the invention process step

1) security domain feature modeling

Communication network is taken no account of node capacity restriction, and according to universal safety territory expression formula, the security domain border expression formula of communication network example is suc as formula shown in (8):

$\left\{\begin{array}{c}{f}_{12}\&le;\min (c_{13}-f_{13},c_{23}-f_{23})\\ f_{23}\&le;\min (c_{24}-f_{24},c_{34}-f_{34})\\ f_{13}\&le;\min (c_{12}-f_{12},c_{23}-f_{23})\\ f_{14}\&le;\min (c_{12}-f_{12},c_{24}-f_{24})\\ f_{24}\&le;\min (c_{23}-f_{23},c_{34}-f_{34})\\ f_{34}\&le;\min (c_{23}-f_{23},c_{24}-f_{24})\\ {\mathrm{<figure-callout\; id="15"\; label="f"\; filenames="HDA0000403426810000011.png,HDA0000403426810000021.png"\; state="\{\{state\}\}">f</figure-callout>}}_{15}\&le;\min (c_{14}-f_{14},c_{45}-f_{45})\\ f_{45}\&le;\min (c_{14}-f_{14},c_{15}-f_{15})\end{array}\right.---\left(7\right)$

Formula (7) has showed the relation of flow and capacity and other link flows on every link of the whole network, has described the safety zone of this communication network operation by 8 boundary conditions.

2) safety evaluatio

For example, to unsafe network operation working point 1, according to network operation working point 1 initial data and formula (6), can calculate the safe distance of each link, as shown in table 3:

The unsafe network operation of table 3 working point 1

As can be seen from Table 3: outside link 2,4, during other any link failure, the whole network business all can not be without the transmission of losing, corresponding to safe distance D _ijall be less than 0, this working point is the unsafe network operation of N-1 working point, and obtains except link 2,4 by the method for emulation, and other link simulation result all can not be passed through, with safe distance result be consistent, safe distance D is described _ijbeing less than 0 link security emulation verification can not pass through; The business summation that the network based on link of this network operation working point transmits ^[9]be 145.

Again for example, for the network operation working point 2 of safety, according to network operation working point 2 initial data and formula (6), can calculate the safe distance of each link, as shown in table 4:

The network operation working point 2 of table 4 safety

When N-1 occurs for all links as seen from Table 4, business can be by circuitous path without the transmission of losing, and has certain allowance, and this network operation working point is safe network operation working point, safe distance D _ijbe greater than 0, corresponding link N-1 emulation verification can be passed through.The Network summation of this network operation working point is 75.

Again for example, for the network operation working point 3 of criticality safety, according to initial data and formula (6), can calculate the safe distance of each link, as shown in table 5:

The network operation working point 3 of table 5 criticality safety

8 safe distance Dij have 7 to be 0 as seen from Table 5, although D14 is not 0, are positioned on the capacity-constrained border of link 1,2,2,4.Simulation method is verified as critical passing through, and augmented flow does not just pass through arbitrarily., also illustrate that the method for security domain and the methods and results of N-1 emulation are consistent.Can find out that the business summation that the network based on link of this network operation working point transmits is 105.

Be more than by ask for safe distance mode judge whether safety of working point.Absorbing boundary equation by communication network can find out, the secure border of the security domain of this network is comprised of 8 hyperplane, so also can carry out by the two-dimensional cross-section of security domain the judgement of more vivid fail safe and the adjustment of working point.

Known work point 3 is network operation working points of criticality safety operation, with link flow f ₁₂and f ₁₃for independent variable, flow value when other link flow is made as the operation of criticality safety in table 5, obtains security domain expression formula suc as formula shown in (8):

$\left\{\begin{array}{c}{f}_{12}+f_{13}\&le;30\\ f_{12}\&le;20\\ f_{13}\&le;20\end{array}\right.---\left(8\right)$

According to security domain expression formula, obtain two dimensional image as shown in Figure 3: as seen in Figure 3 at network topology and capacity link f certain in the situation that ₁₂and f ₁₃relation under N-1 security constraint.In Fig. 3, shade inside is f ₁₂and f ₁₃the network operation working point of safety, f ₁₂and f ₁₃value in the adjustment of shade interior zone, be safe; The border of shade is the network operation working point of criticality safety operation; The working point of shadow external is unsafe network operation working point.In addition, can carry out by the region of this figure the adjustment of working point, the size of regulating link traffic makes network operation working point from the dangerous safety that becomes.

3, with the contrast verification of existing survivability method

Survivability is similar to N-1 fail safe from defining, at this by the feasibility of relatively carrying out further to prove universal safety domain theory of safe distance and survivability result.The anti-safe distance of ruining measurements and calculating is herein carried out contrasting, and as shown in table 6, contrast images is shown in Fig. 4:

Table 6 network operation working point contrast table

Note: link total amount is each link flow sum; It is anti-that to ruin measurement value be the anti-measurement value of ruining based on link ^[9]

From the contrast of Fig. 4, can find out: at safe distance, approximate in 0, the value of survivability equals 1, safe distance is boundary with 0, and being greater than 0 is safe network operation working point, and it is unsafe being less than 0; Survivability take 1 as boundary, and equaling 1 o'clock all link traffic carrying capacity when fault can break-evenly transfer out, and is less than the phenomenon that there will be loss of traffic at 1 o'clock.When flow two points (working point 5 and 6) hour, survivability is 1, and safe distance is all more than or equal to 0 and difference to some extent, and now safe distance has been distinguished the fail safe of these two points better, reflects that working point 6 has larger margin of safety.

In computational speed, security domain method also has clear superiority.Adopt the larger actual power distribution network example of 114 feeder lines of 26 main transformers to calculate and show, be 0.016s the safety evaluatio computing time based on security domain, and survivability computing time is 0.676s.

Anti-ruin measurement value and safe distance value along with the change tendency of total traffic capacity is similar, the correctness of security domain theory and the applicability in general network are described.But the method for security domain can through type (7) directly obtains border and the region of safe operation, the hyperplane that the flow that obtains take limit is dimension carrys out the fail safe of evaluating network, can be by the visual adjustment of carrying out intuitively judgement and working point or capacity of security domain, this is the irreplaceable superior part of measure of survivability.

Two, power distribution network case

1, example basic condition

The grid structure of example electrical network is as shown in Figure 2: totally 4 110kV transformer stations and 75 times 10kV feeder lines, and every feeder line capacity 8.92MVA, main transformer capacity is as shown in FIG..

2, the invention process step

1) security domain feature modeling

Theoretical according to general security domain, that takes into account power distribution network example self turns band scheme, obtains border expression formula and has 82, and working point vector dimension is 82, only does partial descriptions herein, obtains local expression formula as follows according to universal safety territory expression formula:

$\left\{\begin{array}{c}{F}_{17}\&le;\min (\mathrm{RF}-F_{20},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-F_{18})\\ F_{18}\&le;\min (\mathrm{RF}-F_{19},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-F_{17})\\ F_{19}\&le;\min (\mathrm{RF}-F_{18},R_2-(F_{10}+F_{11}+F_{12}+F_{13}+F_{14}+F_{15}+F_{16}+F_{17}+F_{18})-F_{20})\\ F_{20}\&le;\min (\mathrm{RF}-F_{17},R_2-(F_{10}+F_{11}+F_{12}+F_{13}+F_{14}+F_{15}+F_{16}+F_{17}+F_{18})-F_{19})\\ F_{28}\&le;\min (\mathrm{RF}-F_{27},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-F_{29})\\ F_{29}\&le;\min (\mathrm{RF}-F_{26},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-F_{28})\\ F_{37}\&le;\min (\mathrm{RF}-F_{22},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-(F_{36}+F_{38}))\\ F_{38}\&le;\min (\mathrm{RF}-F_{23},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-(F_{36}+F_{37}))\\ F_{60}\&le;\min (\mathrm{RF}-F_{24},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-F_{61})\\ F_{61}\&le;\min (\mathrm{RF}-F_{25},R_3-(F_{19}+F_{20}+F_{21}+F_{22}+F_{23}+F_{24}+F_{25}+F_{26}+F_{27})-F_{60})\end{array}\right.---\left(9\right)$

F wherein _irepresent distribution feeder load, be the flow value on the limit in universal network security domain theory; RF is feeder line capacity, is the capability value on limit.Visible, the secure border of distribution system can be comprised of a series of inequality, and each inequality represents a secure border, and the security domain of Fig. 2 example is that the hyperplane of being loaded by 82 feeder lines surrounds, and meets universal safety domain theory.

2) safety evaluatio

TSC ^[6]being the negative peak that power distribution network can reach under N-1 security constraint, is the working point of N-1 criticality safety.Under local feeder line TSC, permissible load value is: the load value of feeder line 17-29 is (3.16,3.16,3.46,3.46,3.1,3.1,3.1,3.46,3.46,3.46,3.46,2.79,2.79), the load value of feeder line 36-38 is (5.81,5.81,5.81), the load value of feeder line 56-80 is (3.58,3.58,5.12,5.12,4.94,4.94,4.46,4.46,4.46,4.46,4.46,4.46,4.46,4.46,2.79,2.79,2.79,2.79,2.79,2.79,1.64,1.64,1.61,1.61,3.29), unit is MVA.

To TSC working point carry out safe distance calculating, obtaining safe distance is 0.If with feeder line F ₁₉and F ₂₄for example, get F ₁₉and F ₂₄for independent variable, all the other feeder line load values are got TSC permissible load value, by formula (10) is arranged, just can obtain hyperplane that formula (10) the determines F under TSC working point ₁₉and F ₂₄projection on two-dimensional space, as shown in Figure 5:

As can be seen from Figure 5, TSC working point is positioned on secure border, corresponding to safe distance, is 0.

For example unsafe working point is verified again: on the basis of TSC, adjust load and distribute, make F ₁₉=5MVA, F ₂₄=4MVA, F ₅₂=4.8766MVA, F ₅₃=4.8766MVA, forms working point W _f1.Through calculating, the contrast that obtains safe distance and TSC working point is as shown in table 7.

Table 7W _f1working point and the contrast of TSC working point safe distance

As seen from Table 7, safe distance has occurred negative value, W _f1it is unsafe working point.The same method with two-dimensional visualization judges as shown in Figure 6:

As can be seen from Figure 6, working point W _f1be positioned at outside safety zone, identical with safe distance result of determination.According to universal safety domain theory, can make it to become safe working point by adjusting the load value of working point.

For example the working point of safety is verified again: on the basis of TSC, adjust load, make F ₁₉=3MVA, F ₂₄=2MVA, obtains working point W _f2.To this working point carry out safe distance calculating, the contrast (only having listed the safe distance value changing) as shown in table 8 that obtains safe distance and TSC working point:

Table 8W _f2working point and the contrast of TSC working point safe distance

Under TSC working point, safe distance is that 0 feeder line is at W as can be seen from Table 8 _f2working point safe distance occurred on the occasion of, W is described _f2working point is not only safe, and has certain safety allowance, safe distance D _ibe allowance value.

Checking through three class working points illustrates that general network N-1 security domain feature modeling and method for evaluating safety are also suitable in power distribution network.

Three, universal network security domain contrasts with the noun of power distribution network and communication network

The noun contrast of distribution system, universal network security domain theory and communication network is as shown in table 9:

The table 9 noun table of comparisons

List of references:

[1] Tan Yue enters, Lv Xin, Wu Jun etc. Main Scientific Issues // harmonious development and system engineering---the 15 nd Annual Meeting collection of engineering of China association of complex network survivability research. and Shanghai: Shanghai systematic science publishing house, 2008:107-114.

[2] Yu Yixin. the methodology of security domain and practicality result, University Of Tianjin's journal, 2003,36 (5): 525-528.

[3]Yu Y X，Feng F.Active power steady-state security region of power system.Sci China：Ser-A，1990，33(12)：1488-1500.

[4]Yu Y，Feng Z，Hou K，et a1.Application of dynamic equivalents in determining practical dynamic security region.Transmission and Distribution Conference and Exhibition： Asia and Pacific， 2005 IEEE／PES.IEEE，2005：1-6.

[5] Zhao Jinli, Yu Yixin, Jia Hongjie etc. the visual and realization of Static Voltage Stability Region in Cut-sets Space of Power Systems. Automation of Electric Systems, 2005,29 (5): 56-61.

[6] Xiao Jun, Gu Wenzhuo, Guo Xiaodan etc. distribution system power supply capacity model. Automation of Electric Systems, 2011,35 (24): 47-52.

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[9] Chen Jianguo etc. the survivability of network analysis and design is measured anatomy. radio engineering, 1998,28:12-1.

It will be appreciated by those skilled in the art that accompanying drawing is the schematic diagram of a preferred embodiment, the invention described above embodiment sequence number, just to describing, does not represent the quality of embodiment.

The foregoing is only preferred embodiment of the present invention, in order to limit the present invention, within the spirit and principles in the present invention not all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (3)

1. N-1 security domain feature modeling and the method for evaluating safety of network, is characterized in that, said method comprising the steps of:

(1) network operation working point, network N-1 fail safe and network security territory are defined;

Described network operation working point: represent all summits of network operating state and state vector and the operational mode on limit;

Described network N-1 fail safe: when network moves in certain network operation working point, remove any limit or summit in network, network can carry out flow reallocation to keep normal flow to transmit;

Described network security territory: in the process of operation, make all limits and summit all meet the set of the network operation working point of network N-1 fail safe for the network of determining topological sum capacity;

(2) safe evaluation method based on security domain;

Definition secure border distance B i _jfor:

Di _j=min(c _mn-f _mn)-fi _j,(v _m,v _n)∈B _ij

If Di _jbe greater than 0 explanation and still can guarantee normal transmission in network N-1 safety conditions lower network, there is no flow loss, Di _jfor the load margin of network operation working point to each border; If Di _jbe less than 0 explanation and under the safety conditions of network N-1, understand some flow loss, even loss seriously causes periods of network disruption; If Di _jequal 0 explanation under the safety conditions of network N-1 in critical condition;

If Di _jcomplete is timing, shows that network operation working point is inner at secure border, and system is current is N-1 safety;

If Di _jbe not timing entirely, show that network operation working point is outside at secure border, system is current is that N-1 is unsafe, is the Di of negative value _jthe flow value that exceeds this border for network operation working point is measured;

By two dimension or three-dimensional visualization are carried out in network security territory.

2. N-1 security domain feature modeling and the method for evaluating safety of a kind of network according to claim 1, is characterized in that,

Described state vector comprises under certain transient state and flows out the net flow on summit, the total flow value of the load capacity of the flow value on every limit, each node, the whole network;

Described operational mode refers to summit and the limit connection status in network in network;

By operational mode, determine the limit in practical application, the n dimension theorem in Euclid space vector representation that network operation working point forms with the flow value on limit, wherein n is the number on limit in network, definition n-dimensional vector is formula (1):

Z=(f ₁₂,f ₂₃,f ₁₃...fi _j) ^T(1)

In above formula, Z represents the working point vector of the flow value based on limit; f _ijrepresent the flow value on network edge, i and j represent summit.

3. N-1 security domain feature modeling and the method for evaluating safety of a kind of network according to claim 1, is characterized in that, the expression formula of network N-1 security constraint lower network security domain is shown below:

In above formula, B _ijthe path that represents flow or load reallocation process;

(v _m, v _n) be path B _ijon all limits;

C _ijexpression is by v _ito v _jcan maximum delivered quantity, i.e. limit (v _i, v _j) capacity;

F _mnrepresent the limit (v that alternate route comprises _m, v _n) on flow value;

C _mnrepresent the limit (v that alternate route comprises _m, v _n) on capability value;

Formula (3) represents that the flow on every limit can not be over the capability value on its limit under normal circumstances.

When formula (4) represents that any limit generation N-1 fault lost efficacy, the flow value on each limit comprising on its circuitous path can not surpass its capability value.

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