CN109034467A - A kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method - Google Patents
A kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method Download PDFInfo
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Abstract
The invention discloses a kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Methods, belong to technical field of power systems, it, which is proposed, maximizes three differentiation planning economy, system restorability and Survivabilities of Networks targets while being used as bulk transmission grid optimization aim, and bulk transmission grid need to meet certain constraint condition；Bulk transmission grid multi-objective optimization question is solved using comprehensive study particle swarm algorithm, and is embedded in graph theory correcting strategy to repair the particle for being unsatisfactory for connectivity constraint.Using the optimal compromise solution solved based on the multiple target non-cooperative solution method of mixed strategy Nash Equilibrium in the solution of Pareto forward position, as optimal bulk transmission grid scheme.It uses multiple-objection optimization strategy of the invention that can plan for the differentiation of power grid and reasonable bulk transmission grid constructing plan is provided, and can preferably realize the balance of three economy, system restorability and Survivabilities of Networks objective functions.
Description
Technical field
The present invention relates to technical field of power systems, in particular to a kind of electric system disaster-resistant type bulk transmission grid multiple target is excellent
Change method.
Background technique
The extreme natural calamity to take place frequently seriously threatens the safe and reliable operation of electric system.Research shows that extreme natural
The basic reason that disaster causes large-scale blackout to occur be the existing norm for civil defense of electric power facility can not resist it is increasingly severe from
Right disaster.Further, since the difference of region locating for the elements such as substation, route and shaft tower in electric system and its importance,
Therefore, it is necessary to according to the principle of " generally improve, emphasis reinforce ", before disaster is arrived differentiation design element combat a natural disaster to mark
Standard is ensured the power demands of important power consumers by construction disaster-resistant type bulk transmission grid, and then enhances electric system rack
The stability of structure reduces the equipment repairing after loss of outage and disaster, reconstruction expenses.
The essence of disaster-resistant type bulk transmission grid be by improve critical elements norm for civil defense, composition meet topology connectivity and
The small-sized strong rack of power network safety operation constraint, for ensureing holding for responsible consumer under the emergency cases such as natural calamity
Continuous power supply.
It is mainly at present Graph-theoretical Approach and artificial intelligence approach about the searching method of bulk transmission grid.Graph-theoretical Approach is mostly root
Route different degree is evaluated according to graph theory knowledge, after the high route of different degree is successively selected into bulk transmission grid, passes through graph theory connectivity
It is required that lacking the overall evaluation to bulk transmission grid to select All other routes.Intelligent algorithm passes through building then to minimize difference
Alienation reinforces expense and carries out backbone network comprising the critical elements etc. in system as much as possible for the Optimized model of objective function
Frame search, it is adaptable, but further assessment is lacked to rack performance.
Since disaster-resistant type bulk transmission grid can not only maintain the power supply of important node and route in power grid, moreover it is possible to make after disaster
For the trunk channel for restoring the transmission of the whole network output power.In addition, it is contemplated that the destructiveness of exceedingly odious weather, bulk transmission grid search
When need to consider disaster-resistant type bulk transmission grid resist disaster ability.Therefore, the existing method about the search of disaster-resistant type bulk transmission grid
It is unable to satisfy the actual demand of bulk transmission grid search.
Summary of the invention
The purpose of the present invention is to provide a kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Methods, to realize bone
Dry rack economy, restorability, the balance of survivability.
In order to achieve the above object, the present invention uses a kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method, packet
Include following steps:
Electric system topological structure parameter, electrical characteristic parameter and economic parameters are obtained, and electric system is abstracted as
Network topological diagram G=G (E, L) filters out disaster-resistant type bulk transmission grid Gbone, interior joint collection E has m node, and sets of lines L has n
Route；
If GboneFor the disaster-resistant type bulk transmission grid filtered out, GboneBy VEAnd VLIt determines, VE、VLThe respectively m dimension two of node
The n dimension binary decision vector of system decision vector, route；
Maximum differenceization is planned into economy, maximizes system restorability and the conduct simultaneously of maximization network survivability
Disaster-resistant type bulk transmission grid GboneOptimization aim, and combine comprehensively study particle swarm algorithm optimized after disaster-resistant type backbone network
Frame.
Further, described that maximum differenceization is planned into economy, maximizes system restorability and maximization network
Survivability is used as disaster-resistant type bulk transmission grid G simultaneouslyboneOptimization aim, and combine comprehensively study particle swarm algorithm obtain optimization after
Disaster-resistant type bulk transmission grid, comprising:
The random position and speed for generating initialization particle；
Based on disaster-resistant type bulk transmission grid GboneDifferentiation plan economic goal function, calculate the corresponding disaster-resistant type bone of particle
Dry rack GboneEconomic goal functional value；
Based on disaster-resistant type bulk transmission grid GboneMaximization system restorability objective function, calculate that particle is corresponding combats a natural disaster
Type bulk transmission grid GboneMaximization system restorability target function value；
Based on disaster-resistant type bulk transmission grid GboneMaximization network survivability objective function, calculate the corresponding disaster-resistant type of particle
Bulk transmission grid GboneMaximization network survivability target function value；
Based on economy objectives functional value, maximize system restorability target function value and maximization network survivability
Target function value constructs the disaster-resistant type bulk transmission grid after the optimization in conjunction with comprehensive study particle swarm algorithm.
Further, under the premise of meeting load failure rate γ condition, to minimize reinforcing expense as the disaster-resistant type
Bulk transmission grid GboneDifferentiation plan economic goal function:
Wherein,
In formula: m dimensional vectorFor joint reinforcing cost vector, n dimensional vectorFor line length vector, k is route
Unit length reinforce expense, m dimensional vectorFor load node power vector, m ties up row vector EU=[1,1 ..., 1].
Further, described to be based on disaster-resistant type bulk transmission grid GboneMaximization system restorability objective function building
Process:
The node according to electric system removes front and back disaster-resistant type bulk transmission grid GboneThe change rate of efficiency measures this
The topological structure importance of node obtains node in topological structure different degree WC；
Different degree of the node in power transmission is measured using weighting trend flux matrix, the node is obtained and is passed in power
Different degree Y in defeatedE；
According to node in topological structure different degree WCWith the different degree Y in power transmissionE, obtain pitch point importance vector
ZE；
Route is measured using trend betweenness index to the active-power P for being transferred to load bus d from generator node g
The contribution of (g, d) obtains the different degree of route in the power system；
The weight of the route in the power system is measured using the weighting trend betweenness index of meter and line transmission capacity
It spends, obtains the different degree vector Z of the routeL；
Based on the disaster-resistant type bulk transmission grid GboneThe pass in key node and the sets of lines that the node is concentrated
The coverage condition of key route obtains rack coverage rate B (Gbone)；
According to pitch point importance vector ZE, route different degree vector ZLAnd rack coverage rate B (Gbone), building is based on anti-
Calamity type bulk transmission grid GboneMaximization system restorability objective function.
Further, described to be based on disaster-resistant type bulk transmission grid GboneMaximization network survivability objective function building
Journey includes:
By the disaster-resistant type bulk transmission grid GboneAfter middle removal any node, the node that is still connected in rest network is to putting down
The ratio of connection node pair in mean value and former disaster-resistant type bulk transmission grid is as network connectivity C1(Gbone)；
Based on the disaster-resistant type bulk transmission grid GboneThe difference of corresponding full-mesh network analyzes the disaster-resistant type
Bulk transmission grid GboneClose structure degree, obtain disaster-resistant type bulk transmission grid GboneEquivalent shortest path number C2(Gbone)；
According to network connectivity C1(Gbone) and equivalent shortest path number C2(Gbone), building is based on disaster-resistant type bulk transmission grid
GboneMaximization network survivability objective function:
maxC(Gbone)=μ C1(Gbone)+(1-μ)C2(Gbone)
In formula: μ is weight coefficient.
Further, further includes:
Retain the tide of constraint, network connectivty constraint and safe operation of power system based on special joint, special route
It flows equation and inequality and constraint checking is carried out to the disaster-resistant type bulk transmission grid after the optimization.
Further, if the disaster-resistant type bulk transmission grid after the optimization is unsatisfactory for network connectivty constraint, further includes:
It is carried out in comprehensive study particle swarm algorithm using the graph theory correcting strategy based on breadth-first search
Connectivity reparation obtains the one group of bulk transmission grid Pareto forward position met the requirements solution；
The bulk transmission grid pa is solved using the multiple target non-cooperative solution decision model based on mixed strategy Nash Equilibrium
Optimal compromise solution in tired support forward position solution, as the optimal disaster-resistant type bulk transmission grid under multiple target.
Further, the graph theory reparation based on breadth-first search is used in comprehensive study particle swarm algorithm
Strategy carries out connectivity reparation, and obtains the one group of bulk transmission grid Pareto forward position met the requirements solution, comprising:
Connectivity reparation is carried out using the graph theory correcting strategy based on breadth-first search, Pareto is obtained and dominates pass
System；
According to Pareto dominance relation, itself optimal location p of per generation particle is updated；
Utilize external archive QeThe disaster-resistant type bulk transmission grid met the requirements in storage particle iterative process, and outside real-time update
Portion archives Qe；
From external archive QeTwo particles of middle random selection are chosen compared with the superior by the way of binary championship as global
I-th kind of disaster-resistant type bulk transmission grid scheme g of optimal location gi, to be updated to global optimum position；
Utilize the global optimum position of all particles and the speed of itself optimal location more new particle；
The position when former generation particle is updated using the position of previous generation particle；
After loop iteration sets number, the external archive Q that will obtaineIt is solved as bulk transmission grid Pareto forward position.
Further, the graph theory correcting strategy based on breadth-first search carries out connectivity reparation, comprising:
Power grid adjacency matrix M is obtained according to the connection relationship of the disaster-resistant type bulk transmission grid interior joint after the optimizationn0, with line
Road reactance is that weight constructs weighted adjacent matrix Mw0；
According to power grid adjacency matrix Mn0And weighted adjacent matrix Mw0, seek for most short electrical distance between memory node pair
Distance matrix Md0And the path matrix P for electrical distance respective path most short between memory node pairath0；
Determine that the n of the node ties up binary decision vector V according to the position of every generation particleL, obtain new adjoining square
Battle array Mn0wWith new distance matrix Md0w；
The new adjacency matrix M is searched for using breadth-first searchn0wIn all connection pieces；
By new adjacency matrix Mn0wIn all connection pieces in the connection piece of only one node give up, after obtaining screening
Connection piece；
Using each connection piece after screening as an aggregation, and M is calculated using Floyd algorithmd0wIn all connections
Most short electrical distance between piece；
The most your pupil between all connection pieces is sought using Kruskal algorithm as weight to be connected to most short electrical distance between piece
Cheng Shu；
The repair path between two connection pieces is determined according to minimum spanning tree, and will be on the repair path of all spanning trees
Route decision variable set 1.
Further, the multiple target non-cooperative solution decision model based on mixed strategy Nash Equilibrium are as follows:
Wherein,Indicate the equilibrium solution of i-th of target, yijIt is j-th of forward position solution for i-th
The equilibrium value of a target；uiFor i-th of objective function desired value upper limit, ωiFor the importance weight of i-th of target, fijFor jth
Normalized function value of a forward position solution for i-th of target, SobFor objective function quantity, SesBefore Pareto in external archive
Along the quantity of solution.
Compared with prior art, there are following technical effects by the present invention: disaster-resistant type bulk transmission grid proposed by the present invention it is more
In objective optimization strategy, is resisted using maximum differenceization planning economy, maximization system restorability and maximization network and ruined
Property be used as the optimization aim of disaster-resistant type bulk transmission grid simultaneously.Wherein, economy objectives function considers the investment of differentiation planning
Expense, system restorability objective function restore the efficiency that the whole network is powered after considering disaster, and Survivabilities of Networks objective function is examined
Consider bulk transmission grid and resists the ability that further disaster is destroyed.Meanwhile using comprehensive PSO Algorithm disaster-resistant type backbone network
Frame Model for Multi-Objective Optimization obtains disaster-resistant type bulk transmission grid.Compared with single object optimization strategy, using more mesh proposed by the present invention
The disaster-resistant type bulk transmission grid that searches out of mark optimisation strategy is more comprehensive, and can preferably realize economy, system restorability and
The balance of three objective functions of Survivabilities of Networks.
Detailed description of the invention
With reference to the accompanying drawing, specific embodiments of the present invention will be described in detail:
Fig. 1 is a kind of flow diagram of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method；
Fig. 2 is the flow diagram of another electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method；
Fig. 3 is certain regional power grid topological diagram；
Fig. 4 is the Nash Equilibrium point schematic diagram that Pareto forward position solution is concentrated；
Fig. 5 is using the disaster-resistant type bulk transmission grid schematic diagram that study particle swarm algorithm and Nash Equilibrium optimize comprehensively.
Specific embodiment
In order to further explain feature of the invention, reference should be made to the following detailed description and accompanying drawings of the present invention.Institute
Attached drawing is only for reference and purposes of discussion, is not used to limit protection scope of the present invention.
As shown in Figure 1, present embodiment discloses a kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Methods, including
Following steps S1 to S3:
S1, electric system topological structure parameter, electrical characteristic parameter and economic parameters are obtained, and electric system is abstracted
For network topological diagram G=G (E, L), disaster-resistant type bulk transmission grid G is filtered outbone, interior joint collection E has m node, and sets of lines L has
N route；
It should be noted that the topological structure parameter of electric system includes the connection relationship of node and route, electrical characteristic
Parameter includes the power output of power supply node, the payload of load bus, reactance of route etc., and economic parameters includes each section Points And lines
The reinforcing expense on road.
S2, G is setboneFor the disaster-resistant type bulk transmission grid filtered out, GboneBy VEAnd VLIt determines, VE、VLThe respectively m dimension of node
The n dimension binary decision vector of binary decision vector, route；
Wherein, VE=[ve(1),…,ve(i),…,ve(m)]TIndicate that the m of node ties up binary decision vector, VL=[vl
(1),…,vl(k),…,vl(n)]TIndicate that the n of route ties up binary decision vector.Bulk transmission grid GboneBy VEAnd VLIt determines.ve
And v (i)=1l(k)=1 it respectively indicates in bulk transmission grid comprising i-th of node and kth route；veAnd v (i)=0l(k)=0
It then respectively indicates and does not include i-th of node and kth route in bulk transmission grid.
S3, maximum differenceization is planned into economy, maximizes system restorability and maximization network survivability simultaneously
As disaster-resistant type bulk transmission grid GboneOptimization aim, and combine comprehensively study particle swarm algorithm optimized after disaster-resistant type bone
Dry rack.
The present embodiment by comprehensively considering the economy of bulk transmission grid building, in rack performance system restorability and net
Frame survivability proposes maximum differenceization planning economic goal function, maximizes system restorability objective function and maximization
Survivabilities of Networks objective function, and the optimization aim as comprehensive study particle swarm algorithm simultaneously.
Learn the solution of the position representing optimized problem of particle in particle swarm algorithm, i.e. the decision variable V of route comprehensivelyL, one
All positions of a particle correspond to a kind of bulk transmission grid prioritization scheme；The speed of particle determines the search direction of algorithm.Using complete
Face study particle swarm algorithm optimizes above three objective function, constructs the disaster-resistant type bulk transmission grid of optimization, specific mistake
Journey are as follows:
The random position and speed for generating initialization particle；
Based on disaster-resistant type bulk transmission grid GboneDifferentiation plan economic goal function, calculate the corresponding disaster-resistant type bone of particle
Dry rack GboneEconomic goal functional value；
Based on disaster-resistant type bulk transmission grid GboneMaximization system restorability objective function, calculate that particle is corresponding combats a natural disaster
Type bulk transmission grid GboneMaximization system restorability target function value；
Based on disaster-resistant type bulk transmission grid GboneMaximization network survivability objective function, calculate the corresponding disaster-resistant type of particle
Bulk transmission grid GboneMaximization network survivability target function value；
Based on economy objectives functional value, maximize system restorability target function value and maximization network survivability
Target function value constructs the disaster-resistant type bulk transmission grid after the optimization in conjunction with comprehensive study particle swarm algorithm.
Above-mentioned differentiation planning economic goal function, maximization system restorability objective function, maximization network, which resist, to be ruined
The building process of property objective function is as follows:
(1) economy objectives function is constructed:
Under the premise of meeting load failure rate γ condition, to minimize reinforcing expense as the disaster-resistant type bulk transmission grid
GboneDifferentiation plan economic goal function:
Wherein,
In formula: m dimensional vectorFor joint reinforcing cost vector, n dimensional vectorFor line length vector, k is route
Unit length reinforce expense, m dimensional vectorFor load node power vector, m ties up row vector EU=[1,1 ..., 1], T is
Transposition symbol.
It should be noted that it is limited due to combating a natural disaster emergency worker and differentiation investment cost, so before meeting γ condition
It puts, economy objectives function is planned using the differentiation for minimizing reinforcing expense as disaster-resistant type bulk transmission grid.
(2) maximization system restorability objective function is constructed:
2-1) evaluate the importance of electric system interior joint:
The summation of most short electrical distance inverse average between nodes pair all in electric system is defined as network transmission efficiency
φ (G), to measure status of the node in network topology structure, it may be assumed that
In formula: d (i, j) indicates the most short electrical distance between node i and node j, reactance and minimal path as between node pair
The sum of reactance value of diameter.
If bulk transmission grid loses a certain key node, the efficiency of transmission decline of bulk transmission grid will lead to, therefore move according to node i
The importance of the node topology is measured except the change rate of front and back network efficiency, and then obtains node topology different degree
Vector WC, i-th of element is wi:
In formula: φ (G-Ei) it is the network transmission efficiency removed after node i.
2-2) importance of the evaluation electric system interior joint in power transmission:
Status of the node in operation of power networks state is considered, using weighting trend flux matrix YETo measure node in power
Importance in transmission:
In formula:Indicate the Hadamard product of two vectors, i.e. the corresponding element multiplication gained of two equal vectors of dimension
The new vector arrived；M dimensional vectorFor node transmission power vector, element is equal to the biography for all branches being connected with node
The sum of defeated power absolute value；M dimensional vector WGBased on and the particularity of power supply node；Indicate that m ties up power supply node
Power column vectorIn maximum element.
2-3) calculate node different degree vector ZE:
Comprehensively consider importance of the node in topological structure and power transmission, pitch point importance vector Z can be obtainedE, it may be assumed that
2-4) evaluate the importance of route in electric system:
Route in disaster-resistant type bulk transmission grid should undertake biggish power transmission effect in former network, after being just conducive in this way
Continuous system restores electricity.Here, route is measured using trend betweenness index is transferred to load bus to from generator node g
The contribution of the active-power P (g, d) of d, it may be assumed that
In formula: Zij0For the trend betweenness value of the route of connecting node i and j；min(Sg,Sd) be node g active power output Sg
With the burden with power S of node ddSmaller value in the two；Pij(g, d) is point of P (g, d) on the route of connecting node i and j
Amount.
Wherein, P (g, d) and PijThe value of (g, d) can be sought by power flow tracing algorithm, and specific solution procedure is as follows:
First pass through fair current, adverse current tracing computation obtains the sequence of electric system, backward allocation matrix TdAnd Tu:
In formula: TdijAnd TuijRespectively matrix TdAnd TuThe i-th row jth column element；PijFor the route of connecting node i and j
The active power of transmission；PjFor the sum of the active power for flowing to the node in all branches for being connected with node j；Vi(d)Indicate with
The node collection that node i is connected and power is flowed by node i；Vi(u)Expression is connected with node i and the node of power flow direction node i
Collection.
According to TuAcquire P (g, d) are as follows:
In formula: PdFor the sum of the active power for flowing to the node in all branches for being connected with node d；For TuInverse square
The d row g column element of battle array.
According to TuAnd TdTo calculate PijIn derive from generator node g part Pij,gAnd flow to the part of load bus d
Pij,d:
In formula:Indicate TuInverse matrix the i-th row g column element；Indicate TdInverse matrix the i-th row d arrange member
Element.And then acquire Pij(g, d) are as follows:
2-5) calculate the different degree vector Z of route in the power systemL:
In view of the line transmission capacity in bulk transmission grid is bigger, as the subsequent channel that restores electricity using space
It is bigger.Therefore, the importance of route is measured using the weighting trend betweenness index of meter and line transmission capacity, and then obtains line
Road different degree vector ZL。
Route different degree vector ZLK-th of element be Zk, represent the weighting trend of the kth route of connecting node i and j
Betweenness, it may be assumed that
In formula: SijFor the transmission capacity of the route of connecting node i and j；SijmaxFor the maximum transmitted of routes all in system
Capacity.
2-6) construct rack coverage rate B (Gbone):
In view of coverage condition of the bulk transmission grid to key node and critical circuits will affect entire power system restoration after disaster
The efficiency of power supply, therefore define rack coverage rate B (Gbone) are as follows:
In formula: ZE0、ZL0Node, route different degree vector respectively after normalized；Distance matrixIt stores
Node i (i=1,2 ..., m) arrives most short electrical distance d (i, the G of bulk transmission gridbone)；α is scale parameter, for adjusting d (Ei,
Gbone) to rack coverage rate B (Gbone) contribution size, d (Ei,Gbone) expression node i (i=1,2 ..., m) arrive backbone network
The most short electrical distance of frame.
(3) maximization network survivability objective function is constructed:
3-1) calculate network connectivity C1(Gbone):
Network connectivity C1(Gbone) be defined as after removing any node in network, the node being still connected in rest network
Pair average value and former network connection node pair ratio, it may be assumed that
In formula:To remove node i1Bulk transmission grid afterwards；mGFor the number of nodes of former bulk transmission grid；RijIndicate node i
With the percent continuity of j, R when node i is connected to jij=1, it is otherwise 0.Network connectivity features network when wrecking still
It is able to maintain the ability of certain connectivity.
3-2) calculate equivalent shortest path number C2(Gbone):
Based on bulk transmission grid GboneCorresponding full-mesh networkDifference analyze the close structure degree of rack.
Due to GboneWithNumber of nodes having the same, therefore the architectural difference of the two is bigger, illustrates GboneMore sparse, survivability is poorer.
By GboneWithRegard undirected and unweighted network as, remembers GboneShortest path length between interior joint i and j is Dij(Gbone), it is most short
The quantity in path is ForLength is not more than D between interior joint i and jij(Gbone) path number
Amount.Therefore, bulk transmission grid GboneEquivalent shortest path number between interior joint i and j may be defined as:
And then obtain GboneNetwork equivalent shortest path number C2(Gbone), it may be assumed that
3-3) construct maximization network survivability objective function:
Comprehensively consider the connectivity and transmission performance of bulk transmission grid, it can be with the network connectivity C of bulk transmission grid1(Gbone)
Highest and network equivalent shortest path number C2(Gbone) at most as the objective function for measuring bulk transmission grid survivability, it may be assumed that
maxC(Gbone)=μ C1(Gbone)+(1-μ)C2(Gbone)
In formula: μ is weight coefficient.
As further preferred scheme, as shown in Fig. 2, the present embodiment is on the basis of above-described embodiment content, it is open
A kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method, includes the following steps:
S101, electric system topological structure parameter, electrical characteristic parameter and economic parameters are obtained；
S102, the random position and speed for generating initialization particle；
S103, three economy, network restoration and rack survivability targets for calculating the corresponding bulk transmission grid of particle
Functional value, the disaster-resistant type bulk transmission grid after building optimization；
S104, check whether the disaster-resistant type bulk transmission grid after optimization meets special joint, route retains constraint, network-in-dialing
Property constraint and system safety operation trend equation and inequality constraints；
If S105, being unsatisfactory for connectivity constraint, graph theory connectivity reparation is carried out；
S106, per generation particle itself optimal location p is updated according to Pareto dominance relation；
S107, external archive and global optimum position are updated；
S108, particle rapidity is updated using global optimum position and itself optimal location；
S109, after updating particle rapidity, update particle position；
S110, step S103~S109 then is repeated, until meeting the number of iterations requirement；
S111, it is selected from external archive using the multiple target non-cooperative solution decision model based on mixed strategy Nash Equilibrium
Optimal compromise is taken to solve, as optimal bulk transmission grid scheme.
Wherein, in practical applications, the bulk transmission grid optimized need to meet certain constraint condition, just can guarantee power grid
Trend is safely and steadily run.The present embodiment carries out constraint checking to the disaster-resistant type bulk transmission grid after optimization according to constraint condition,
Ensure the practicability of bulk transmission grid, specifically:
Retain the tide of constraint, network connectivty constraint and safe operation of power system based on special joint, special route
It flows equation and inequality and constraint checking is carried out to the disaster-resistant type bulk transmission grid after the optimization.
Wherein, retain constraint condition by special joint, special route to carry out about the disaster-resistant type bulk transmission grid after optimization
Beam, to ensure that the continued power of special important node and route in electric system, special joint, special route retain constraint item
Part are as follows:
In formula:The respectively position vector of special joint, the position vector of special route share msIt is a special
Node, nsThe special route of item.
It should be noted that obtained bulk transmission grid must be a network for connection, cannot there are isolated node or route.
The present embodiment is constrained by network connectivty to judge whether the disaster-resistant type bulk transmission grid after the optimization is connected to, network connectivty
Constraint condition are as follows:
φ(vl(1),…,vl(k),...,vl(n))=1
In formula: connectivity discriminant function φ=0 shows that network is not connected to, and φ=1 shows network-in-dialing.
Specifically, obtained bulk transmission grid carries out that Load flow calculation need to be carried out, and checks whether to meet power system security fortune
Whether capable trend equation and inequality constraints meet service requirement of the electric system under the bulk transmission grid method of operation:
In formula: P and Q is respectively the active and reactive power column vector of node injection；U and θ is respectively the voltage amplitude of node
Value and phase angle column vector；YAAnd YBThe respectively real and imaginary parts matrix of node admittance matrix.
As further preferred scheme, when disaster-resistant type bulk transmission grid after optimization is unsatisfactory for network connectivty constraint,
Above-mentioned steps S105: if being unsatisfactory for connectivity constraint, graph theory connectivity reparation is carried out.Include:
1) it calculates initial parameter: power grid adjacency matrix M is sought according to node connection relationshipn0, using line reactance as weight structure
Make weighted adjacent matrix Mw0, and then seek distance matrix Md0Carry out the most short electrical distance between storage node pair, seeks path matrix
Path0Come the corresponding path of most short electrical distance between memory node pair and selects one therein if there is a plurality of shortest path；
2) V is determined according to the position of every generation particleLValue, and then obtain new adjacency matrix Mn0wAnd distance matrix
Md0w；
3) modified M is searched for using breadth-first searchn0wIn all connection pieces；
4) regard each connection piece after screening as an aggregation, i.e., by updated Md0wIn in each connection piece
Node pair between distance be set to 0；
5) give up the connection piece of only one node, and M is calculated using Floyd algorithmd0wIn it is all connection pieces between it is most short
Electrical distance；
6) it using the most short electrical distance being connected between piece as weight, is sought between all connection pieces most using Kruskal algorithm
Small spanning tree；
7) the reparation relationship between connection piece is determined according to minimum spanning tree: if there is tree to be connected between two connection pieces, being looked into
Ask Md0Obtain the most short electrical distance of all nodes pair between the two connection pieces；Compare to obtain the smallest node of electrical distance
It is right, select its corresponding path matrix Path0In shortest path as the two be connected to pieces between repair path；
8) the route decision variable on the repair path of all spanning trees is set 1, i.e., the corresponding position of particle is set 1.
Further, above-mentioned steps S106, per generation particle itself optimal location p, tool are updated according to Pareto dominance relation
Body includes:
T+1 is defined for i-th of particle in pUpdate principle are as follows:
In formula:It indicatesIt dominatesThat is t+1 is for i-th kind of bulk transmission grid side corresponding to newly-generated particle
Three economy of case, restorability and survivability target function values, are superior to t for i-th corresponding to itself optimal particle
Three target function values of kind bulk transmission grid scheme；It indicatesIt dominatesIf the mutual insubjection of the two, generates
Random number RdIf Rd< 0.5, then
Further, above-mentioned steps S107: external archive and global optimum position are updated.It specifically includes:
External archive QeFor storing the bulk transmission grid prioritization scheme met the requirements in iterative process, i.e. Pareto is non-bad
Solution, renewal process are as follows:
If newly-generated bulk transmission grid scheme of per generation is by QeIn a certain bulk transmission grid scheme dominate, then refuse the new departure
Q is addede；If new departure and QeIn original scheme do not dominate mutually, or dominate QeIn certain schemes, then Q is added in new departuree
And remove QeIn by new departure dominate original bulk transmission grid scheme.As external archive QeScheme number be more than archives scale
CmaxWhen, then calculate QeIn scheme between crowding distance, retain before CmaxA maximum bulk transmission grid prioritization scheme of crowding distance.
Define i-th kind of bulk transmission grid scheme g of global optimum position giUpdate principle are as follows: from external archive QeIn it is random
Two particles are selected, are chosen compared with the superior by the way of binary championship as gi。
Further, above-mentioned steps S108: particle rapidity is updated using global optimum position and itself optimal location.Tool
Body includes:
According to the element value of binary sequence H, to determine the learning direction of particle, it may be assumed that
In formula:For d positions of i-th of particle in t generation, the d articles route in i-th kind of bulk transmission grid scheme is represented
Decision variable value；WithRespectively d speed of i-th of particle in t+1 generation and t generation；ω (t) is t generation
Inertia coeffeicent, the global and local search capability to equilibrium particle；c1、c2And c3For aceleration pulse；RdFor on [0,1] section
Random number；It is t for d positions of i-th of particle in global optimum position g；WithRespectively t is for itself
D positions of r-th and i-th particle in optimal location p, wherein r is generated at random, indicates the optimal location to other particles
Study；HdD-th of element in H is indicated, when p stops updating certain times NPAfterwards, then it needs to update the binary sequence generated at random
H.In ω (t) per generation, updates, more new-standard cement are as follows:
In formula: ωmaxAnd ωminThe respectively maximum value and minimum value of inertia coeffeicent；NGFor maximum number of iterations.
Preferably, the present embodiment introduces maximum speed v in study particle swarm algorithm comprehensivelymaxLimit the speed of particle,
If vmaxIt is excessive, it may cause and miss globally optimal solution；vmaxIt is too small, then it is easily trapped into locally optimal solution.The present embodiment is used and is repaired
Sigmoid function after changingIt will be on constraint of velocity to section [0,1], it may be assumed that
In formula:Indicate d speed of i-th of particle in t+1 generation.
Further, above-mentioned steps S109: after updating particle rapidity, particle position is updated.It specifically includes:
In formula:For d positions of i-th of particle in t+1 generation.
Further, above-mentioned steps S111: the multiple target non-cooperative solution decision based on mixed strategy Nash Equilibrium is used
Model chooses optimal compromise solution from external archive, as optimal bulk transmission grid scheme.Wherein it is based on mixed strategy Nash Equilibrium
Multiple target non-cooperative solution decision model, specifically:
In formula:Indicate the equilibrium solution of i-th of target, i.e., Pareto forward position disaggregation is in the mesh
The probability distribution put on；yijIt is j-th of forward position solution for the equilibrium value of i-th of target；uiFor in i-th of objective function desired value
Limit；ωiFor the importance weight of i-th of target, the numerical characteristics for concentrating objective function are solved herein according to forward position, using entropy assessment
Seek ωiValue；fijIt is j-th of forward position solution for the normalized function value of i-th of target；SobFor objective function quantity；SesFor
The quantity that Pareto forward position solves in external archive.
Then the forward position solution that will be provided with best joint equalization value, which represents, can obtain the participation of decision corresponding to highest return
The teamwork of person, i.e., optimal compromise solution:
For a further understanding of the present invention, below by taking certain simplified regional power grid as an example, to explain reality of the invention
Using.
Certain regional power grid includes 9 500kV nodes, 50 220kV nodes and 66 110kV nodes, totally 155 routes,
Its topological diagram is as shown in figure 3, the letter in Fig. 3 indicates node name, as letter r H indicates node R H.
From figure 3, it can be seen that the critical circuits identified include all 500kV routes, major part 220kV route and
A small amount of 110kV route, this matches with the general important common sense of electric system high voltage appearance grade route.
Using comprehensive study PSO Algorithm model, if in obtained per generation, is unsatisfactory for connecting without graph theory reparation
The new particle that the general character requires is up to 99.5%, is unfavorable for algorithm optimizing；And correcting strategy proposed in this paper is used to repair a nothing
Effect particle is average only to need 0.0022s, repairs quickly and greatly improve the solution space of algorithm.
It is respectively 0.1907,0.3445 and 0.4648 using the weight that entropy assessment acquires three objective functions.Selection is based on
Forward position solution in the multiple target non-cooperative solution decision model of mixed strategy Nash Equilibrium with highest joint equalization value, which is used as, to be received
Assorted equilibrium point, normalization target value are (0.5113,0.8848,0.7962), the i.e. point that circle indicates in Fig. 4.It can from Fig. 4
To find out, three target function values of Nash Equilibrium point are relatively high, closer from Pareto font solution, select the point as most
Excellent compromise solution is more reasonable.Decision scheme based on mixed strategy Nash Equilibrium is examined using non-cooperative game theory as technical foundation
Consider the tradeoff distribution character that Pareto forward position solution concentrates multiple target, can preferably accomplish the flat of interests between multiple objective functions
Weighing apparatus.
The corresponding disaster-resistant type bulk transmission grid of Nash Equilibrium point as shown in figure 5, the route that marks of the dotted line of figure overstriking and
Combination of nodes as optimizes obtained disaster-resistant type bulk transmission grid.
The bulk transmission grid scheme obtained using single object optimization is the endpoint of Pareto forward position solution, the pa in corresponding diagram 4
Tired support Boundary Solutions, it is as shown in table 1 with the comparison of this paper multiple-objection optimization scheme.As it can be seen from table 1 since each single goal is excellent
The emphasis of change scheme is different, therefore obtained disaster-resistant type bulk transmission grid has bigger difference.For with the bone of economy optimal objective
Dry Optimal network frame scheme, (load for remaining 50.07%), the backbone optimized on the basis of meeting load coverage ratio γ
Route that rack is included, number of nodes are less, have restored 51 (32.9%) routes and 51 (40.8%) nodes altogether；The party
Case lays particular emphasis on the load bus and its connection line for restoring important, does not consider the recovery of whole region power system restoration power supply after disaster
Efficiency.For with the optimal bulk transmission grid prioritization scheme for optimization aim of system restorability, due to not considering economy emphatically
And survivability, optimize obtained bulk transmission grid and remain whole node and route, needs to put into biggish differentiation and reinforce
Cost.For laying particular emphasis on one integral net of building with the optimal bulk transmission grid prioritization scheme for optimization aim of Survivabilities of Networks
Network survivability can be relatively high rack, to resist the further destruction of extreme natural calamity, but to being supplied after reinforcing expense and disaster
Electricity restores efficiency and does not consider emphatically.
The comparison of table 1 single object optimization scheme and multiple-objection optimization scheme
From fig. 5, it can be seen that the disaster-resistant type bulk transmission grid obtained using the Model for Multi-Objective Optimization of the present embodiment is remained
58.1% route (90), 68.0% node (85) and 82.6% load, the parts number of reservation is moderate, illustrates the party
Case realizes higher load coverage ratio using lower expense.In addition, the bulk transmission grid remain whole 500kV elements,
Most of 220kV element and a small amount of 110kV element, substantially cover route and node important in system, and do not restore
Element it is all closer with a distance from bulk transmission grid, illustrate the grid structure be conducive to carry out calamity after whole region power grid recovery supply
Electricity.From Fig. 4 it can also be seen that the survivability that optimal compromise solves corresponding bulk transmission grid solves in Pareto forward position and ranking is concentrated to lean on
Before, this illustrates that grid structure is more reasonable, and the ability of resisting nature disaster is stronger.To sum up, with the bulk transmission grid optimisation strategy of single goal
It compares, it is anti-that the disaster-resistant type bulk transmission grid scheme that multiple-objection optimization strategy obtains has taken into account economy, system restorability and network
Ruining property considers more comprehensive.
The foregoing is merely presently preferred embodiments of the present invention, is not intended to limit the invention, it is all in spirit of the invention and
Within principle, any modification, equivalent replacement, improvement and so on be should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method characterized by comprising
Electric system topological structure parameter, electrical characteristic parameter and economic parameters are obtained, and electric system is abstracted as network
Topological diagram G=G (E, L) filters out disaster-resistant type bulk transmission grid Gbone, interior joint collection E has m node, and sets of lines L has n line
Road；
If GboneFor the disaster-resistant type bulk transmission grid filtered out, GboneBy VEAnd VLIt determines, VE、VLRespectively the m of node ties up binary system
The n dimension binary decision vector of decision vector, route；
Maximum differenceization is planned into economy, system restorability and maximization network survivability is maximized while being used as and combat a natural disaster
Type bulk transmission grid GboneOptimization aim, and combine comprehensively study particle swarm algorithm optimized after disaster-resistant type bulk transmission grid.
2. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as described in claim 1, which is characterized in that described to incite somebody to action
Maximum differenceization planning economy maximizes system restorability and maximization network survivability while being used as disaster-resistant type backbone
Rack GboneOptimization aim, and combine comprehensively study particle swarm algorithm optimized after disaster-resistant type bulk transmission grid, comprising:
The random position and speed for generating initialization particle；
Based on disaster-resistant type bulk transmission grid GboneDifferentiation plan economic goal function, calculate the corresponding disaster-resistant type backbone network of particle
Frame GboneEconomic goal functional value；
Based on disaster-resistant type bulk transmission grid GboneMaximization system restorability objective function, calculate the corresponding disaster-resistant type bone of particle
Dry rack GboneMaximization system restorability target function value；
Based on disaster-resistant type bulk transmission grid GboneMaximization network survivability objective function, calculate the corresponding disaster-resistant type backbone of particle
Rack GboneMaximization network survivability target function value；
Based on economy objectives functional value, maximize system restorability target function value and maximization network survivability target
Functional value constructs the disaster-resistant type bulk transmission grid after the optimization in conjunction with comprehensive study particle swarm algorithm.
3. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 2, which is characterized in that meeting
Under the premise of load failure rate γ condition, to minimize reinforcing expense as the disaster-resistant type bulk transmission grid GboneDifferentiation planning
Economic goal function:
Wherein,
In formula: m dimensional vectorFor joint reinforcing cost vector, n dimensional vectorFor line length vector, k is the list of route
Bit length reinforces expense, m dimensional vectorFor load node power vector, m ties up row vector EU=[1,1 ..., 1].
4. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 2, which is characterized in that the base
In disaster-resistant type bulk transmission grid GboneMaximization system restorability objective function building process:
The node according to electric system removes front and back disaster-resistant type bulk transmission grid GboneThe change rate of efficiency measures the node
Topological structure importance obtains node in topological structure different degree WC；
Different degree of the node in power transmission is measured using weighting trend flux matrix, obtains the node in power transmission
Different degree YE；
According to node in topological structure different degree WCWith the different degree Y in power transmissionE, obtain pitch point importance vector ZE；
Route is measured using trend betweenness index to the active-power P (g, d) for being transferred to load bus d from generator node g
Contribution, obtain the different degree of route in the power system；
The different degree of the route in the power system is measured using the weighting trend betweenness index of meter and line transmission capacity,
Obtain the different degree vector Z of the routeL；
Based on the disaster-resistant type bulk transmission grid GboneThe critical circuits in key node and the sets of lines that the node is concentrated
Coverage condition, obtain rack coverage rate B (Gbone)；
According to pitch point importance vector ZE, route different degree vector ZLAnd rack coverage rate B (Gbone), building is based on disaster-resistant type
Bulk transmission grid GboneMaximization system restorability objective function.
5. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 2, which is characterized in that the base
In disaster-resistant type bulk transmission grid GboneThe building process of maximization network survivability objective function include:
By the disaster-resistant type bulk transmission grid GboneAfter middle removal any node, the average value for the node pair being still connected in rest network
Ratio with the connection node pair in former disaster-resistant type bulk transmission grid is as network connectivity C1(Gbone)；
Based on the disaster-resistant type bulk transmission grid GboneThe difference of corresponding full-mesh network analyzes the disaster-resistant type backbone network
Frame GboneClose structure degree, obtain disaster-resistant type bulk transmission grid GboneEquivalent shortest path number C2(Gbone)；
According to network connectivity C1(Gbone) and equivalent shortest path number C2(Gbone), building is based on disaster-resistant type bulk transmission grid Gbone's
Maximization network survivability objective function:
maxC(Gbone)=μ C1(Gbone)+(1-μ)C2(Gbone)
In formula: μ is weight coefficient.
6. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as described in claim 1, which is characterized in that also wrap
It includes:
Retain constraint, network connectivty constraint and trend of safe operation of power system etc. based on special joint, special route
Formula and inequality carry out constraint checking to the disaster-resistant type bulk transmission grid after the optimization.
7. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 6, which is characterized in that if described
When disaster-resistant type bulk transmission grid after optimization is unsatisfactory for network connectivty constraint, further includes:
It is connected in comprehensive study particle swarm algorithm using the graph theory correcting strategy based on breadth-first search
Property reparation, obtain one group of bulk transmission grid Pareto forward position met the requirements solution；
The bulk transmission grid Pareto is solved using the multiple target non-cooperative solution decision model based on mixed strategy Nash Equilibrium
Optimal compromise solution in the solution of forward position, as the optimal disaster-resistant type bulk transmission grid under multiple target.
8. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 7, which is characterized in that described
Connectivity reparation is carried out using the graph theory correcting strategy based on breadth-first search in study particle swarm algorithm comprehensively, and is obtained
It is solved to one group of bulk transmission grid Pareto forward position met the requirements, comprising:
After carrying out connectivity reparation using the graph theory correcting strategy based on breadth-first search, is dominated and closed according to Pareto
System, updates itself optimal location p of per generation particle；
Utilize external archive QeThe disaster-resistant type bulk transmission grid met the requirements in storage particle iterative process, and shelves outside real-time update
Case Qe；
From external archive QeTwo particles of middle random selection, are chosen compared with the superior by the way of binary championship as global optimum
I-th kind of disaster-resistant type bulk transmission grid scheme g of position gi, to be updated to global optimum position；
Utilize the global optimum position of all particles and the speed of itself optimal location more new particle；
The position when former generation particle is updated using the position of previous generation particle；
After loop iteration sets number, the external archive Q that will obtaineIt is solved as bulk transmission grid Pareto forward position.
9. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 8, which is characterized in that the base
Connectivity reparation is carried out in the graph theory correcting strategy of breadth-first search, comprising:
Power grid adjacency matrix M is obtained according to the connection relationship of the disaster-resistant type bulk transmission grid interior joint after the optimizationn0, with line electricity
Resist and constructs weighted adjacent matrix M for weightw0；
According to power grid adjacency matrix Mn0And weighted adjacent matrix Mw0, seek the distance for electrical distance most short between memory node pair
Matrix Md0And the path matrix P for electrical distance respective path most short between memory node pairath0；
Determine that the n of the node ties up binary decision vector V according to the position of every generation particleL, obtain new adjacency matrix Mn0w
With new distance matrix Md0w；
The new adjacency matrix M is searched for using breadth-first searchn0wIn all connection pieces；
By new adjacency matrix Mn0wIn all connection pieces in the connection piece of only one node give up, the company after being screened
Logical piece；
Using each connection piece after screening as an aggregation, and M is calculated using Floyd algorithmd0wIn between all connection pieces
Most short electrical distance；
The minimum spanning tree between all connection pieces is sought using Kruskal algorithm as weight to be connected to most short electrical distance between piece；
The repair paths between two connection pieces are determined according to minimum spanning tree, and by the line on the repair path of all spanning trees
Road decision variable sets 1.
10. electric system disaster-resistant type bulk transmission grid Multipurpose Optimal Method as claimed in claim 8, which is characterized in that described
Multiple target non-cooperative solution decision model based on mixed strategy Nash Equilibrium are as follows:
Wherein,Indicate the equilibrium solution of i-th of target, yijIt is j-th of forward position solution for i-th of mesh
Target equilibrium value；uiFor i-th of objective function desired value upper limit, ωiFor the importance weight of i-th of target, fijBefore j-th
Along solution for the normalized function value of i-th of target, SobFor objective function quantity, SesIt is solved for Pareto forward position in external archive
Quantity.
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Application publication date: 20181218 |