CN104868465A - Power system grid structure reconfiguration and optimization method based on fuzzy chance constraint - Google Patents

Abstract

The invention relates to a power system grid structure reconfiguration and optimization method based on fuzzy chance constraints, which belongs to the field of power system security defense and restoration control. The power system grid structure reconfiguration and optimization method comprises a grid structure reconfiguration and optimization model establishing module and a grid structure reconfiguration and optimization algorithm module. The power system grid structure reconfiguration and optimization method adopts triangular fuzzy variables for representing line operation time and restoration reliability, defines an restoration reliability index for evaluating performance of a target grid structure, considers unit start-up time limit, establishes a grid structure reconfiguration and optimization model based on fuzzy chance constraints under the framework of the fuzzy chance constraints, adopts a solution method of combining fuzzy simulation, a crossed particle swarm optimization algorithm and a Dijkstra algorithm, optimizes and determines unit start-up sequence, and reconfigures a restoration grid structure with shortest reconfiguration time and highest reliability. According to the power system grid structure reconfiguration and optimization method based on fuzzy chance constraints, the fuzziness of operation time and restoration reliability when the line is put into operation at the grid structure reconfiguration stage is reasonably considered, the optimized and determined optimal grid structure reconfiguration scheme takes both system reconfiguration speed and safety requirements into account, and the power system grid structure reconfiguration and optimization method has more practical significance.

Description

Based on the electric power system rack reconstruction and optimization method of Fuzzy Chance Constraint

Technical field

The present invention relates to a kind of electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint, belong to power system security defence and recover control field.

Technical background

The large-scale blackout constantly occurred in recent years shows, have a power failure on a large scale be modern power systems must faced by serious threat.Along with expanding day and society the improving constantly supply of electric power dependency degree of electric power system scale, the consequence that large-scale blackout causes is also more and more serious.The main task of rack reconstruction stage makes full use of the isolated mini system recovered previous stage, selects suitable plant stand to be restored and sets of lines to merge and determine the corresponding order that puts into operation, as early as possible for important plant stand power transmission also progressively sets up stable grid structure.The quality of rack reconstruction stage System recover directly has influence on the recovery efficiency of follow-up load restoration and whole electrical network.

The groundwork of current rack reconstruct research is concentrated both ways: the determination of target net and return to the determination of concrete restoration path sequence of target net.Under study for action most using the operating time of circuit as determining that number processes, but the element related to due to rack reconstruction stage and operate numerous, concerning circuit puts into operation, its operating time has uncertainty.This point that had scholar to recognize and random number process will be made the operating time, but random distribution rule is based upon on a large amount of statisticss, and historical data probably produces deviation because data volume is not enough, thus causes result inaccurate.And in conjunction with historical data and relevant operating experience, we are often easier to the scope determined its most probable value and may distribute, this uncertain condition of operating time is more suitable for representing by fuzzy variable, and can well represent its fuzzy behaviour with membership function.Therefore, the operating time is more pressed close to theoretical actual as fuzzy variable process.Equally, recovery reliability when circuit puts into operation also has uncertainty, and different line combination causes the recovery reliability of target net entirety also different, and based on the consideration of security of system, we often wish that the target net formed has high reliability, the also rare research to this respect before.

Summary of the invention

For above-mentioned background, the present invention considers its operating time and the uncertainty recovering reliability when circuit puts into operation, and proposes a kind of electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint, to obtain the more reasonable reconfiguration scheme of rack accurately.

For achieving the above object, what this rack reconstruction and optimization method comprised rack reconstruction and optimization model sets up module and rack reconstruction and optimization algoritic module.

The foundation of so-called rack reconstruction and optimization model, triangular fuzzy variable is assumed to be by line loop operation time and recovery reliability, define the recovery reliability index of whole rack on this basis, utilization Fuzzy Chance Constrained Programming is theoretical, successfully obtain within its startup time limit with unit and start power supply for constraint, reach with the recovery of rack in reconstitution time short as far as possible reliability and be up to target, set up the fuzzy chance constrained model of rack reconstruction and optimization, to being met the rack reconfiguration scheme of certain confidence level.

So-called rack reconstruction and optimization algorithm is combined into by shortest path first, fuzzy simulation and particle cluster algorithm three part of intersecting.Namely according to the model of aforementioned foundation and the feature of rack reconstruct, the method being applicable to this model solution is proposed, adopt the intersection particle cluster algorithm based on fuzzy simulation to be destination node optimization recovery to be restored order, adopt classical dijkstra's algorithm to be node determination restoration path to be restored simultaneously.

In addition, the present invention carries out trend verification to the recovery scheme obtained by algorithm optimization, only has to be verified by trend or the scheme of each regulated quantity in allowed band is just considered as feasible.

The concrete steps of the described electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint are as follows:

Step one, represents the fuzzy uncertain amounts such as the line loop operation time related in invention with triangular fuzzy variable;

Step 2, the recovery reliability defining node to be restored also determines the recovery reliability index of whole rack further;

Step 3, successfully obtains with unit and starts power supply for constraint, reach and be up to target, set up the rack reconstruction and optimization model based on Fuzzy Chance Constraint with the recovery of rack in reconstitution time short as far as possible reliability within its startup time limit;

Step 4, solving of rack reconstruction and optimization model, further:

(1) determine black starting-up power supply and destination node to be restored and initial parameter is set, forming N _pindividual primary;

(2) loop iteration is carried out to particle, i=1:N _p;

(3) get current particle i, call the restoration path of dijkstra's algorithm search each destination node under this recovery order;

(4) to machine group node, fuzzy simulation inspection Fuzzy Chance Constraint is adopted;

(5) judging whether by inspection, is carry out (6), otherwise, utilize mutation operation to upgrade particle, return step (3) afterwards;

(6) trend verification is carried out to the particle by verification;

(7) judge whether iteration completes all particles; Be carry out (8), otherwise return step (2);

(8) fuzzy simulation calculates the fitness of particle, and determines individual extreme value p _best, global extremum g _bestand the extreme value place p of their correspondences _xbest, g _xbest;

(9) utilize cross-iteration to operate to upgrade particle;

(10) maximum times reaching iteration is judged whether; Be carry out (11), otherwise return step (2);

(11) export the node restoration path of optimal particle and correspondence, namely obtain final rack reconfiguration scheme.

Accompanying drawing explanation

Fig. 1 is the flow chart of the electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint of the present invention.

Fig. 2 is the rack reconfiguration scheme of IEEE30 node system optimum.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described in detail.

The foundation of 1 rack reconstruction and optimization model

The present invention represents the operating time of circuit with triangular fuzzy variable, and in conjunction with operating experience, for certain recoverable circuit, its operating time is between optimistic estimate value t ₁with pessimistic estimated value t ₃between, and t ₂be its most probable recovery operation time, this ambiguity of operating time can represent with triangular fuzzy variable, and its membership function is such as formula shown in (1).Ambiguity for other parameters related in literary composition all can describe by similar method and process.

In system rack reconstruction stage, for each node to be restored, think that the node of process is completely reliably on its restoration path, it recovers the recovery reliability that reliability depends primarily on contained circuit on restoration path, and think that the recovery reliability of every bar circuit is relatively independent on path, so can be the reliability of the series system be made up of restoration path by the recovery certainty equivalence of node, namely to destination node i to be restored, if the recovery reliability of jth bar circuit be on its restoration path so the recovery reliability of node i is:

${\tilde{R}}_i=\underset{j=1}{\overset{N_i}{\mathrm{\Π}}}{\tilde{R}}_{\mathrm{ij}}---\left(2\right)$

Wherein N _ifor the circuit number on node i restoration path.

And then for whole target net, it is that in rack, each destination node recovers the average of reliability within the system reconfiguration time that its index recovering reliability is evaluated in definition.Concrete definition is as follows:

$\tilde{R}=\frac{\underset{i=1}{\overset{N_1}{\mathrm{\Σ}}}{\tilde{R}}_i}{N_1}=\frac{\underset{i=1}{\overset{N_1}{\mathrm{\Σ}}}\underset{j=1}{\overset{N_i}{\mathrm{\Π}}}{\tilde{R}}_{\mathrm{ij}}}{N_1}---\left(3\right)$

Be wherein N ₁the number of destination node to be restored.

The fuzzy chance constrained model that the present invention sets up is as follows:

$\max \stackrel{\‾}{f}---\left(4\right)$

$\mathrm{Pos}\{\frac{\tilde{R}}{\tilde{T}}\≥\stackrel{\‾}{f}\}\≥\mathrm{\β}---\left(5\right)$

$\mathrm{Pos}\{0\≤\underset{k=1}{\overset{N_g}{\mathrm{\Σ}}}{\tilde{t}}_{\mathrm{gk}}\≤{\tilde{T}}_g\}\≥\mathrm{\α}---\left(6\right)$

$\tilde{T}=\underset{m=1}{\overset{N_E}{\mathrm{\Σ}}}{\tilde{t}}_m---\left(7\right)$

In above-mentioned model, formula (4) represents that optimization aim is the value maximizing target function target function value required by formula (5) ensures it is target function the maximum of getting when confidence level is at least β, wherein, for the time that whole rack reconstructs, namely from rack reconstruct, obtain the time starting power supply to all destination nodes, formula (7) is defined it, and the present invention's hypothesis only drops into a circuit in each step of rack reconstruction stage, so namely composition recovers the fuzzy operation time of each circuit of rack sum, the operating time due to circuit is Triangular Fuzzy Number, so also be Triangular Fuzzy Number.N _efor recovering the number of lines that rack comprises.Formula (6) guarantees moment that every platform unit is restored to be no more than it, and to start the confidence level that time limit reaches be α, wherein, and t _gkfor the fuzzy operation time of kth bar circuit on the restoration path of machine group node g, for the fuzzy startup time limit of unit g, be also set as Triangular Fuzzy Number, N _gfor the circuit number on machine group node g restoration path to be restored, N _gfor target machine group node number to be restored.

In addition, the present invention carries out trend verification to the recovery scheme obtained by algorithm optimization, only has to be verified by trend or the scheme of each regulated quantity in allowed band is just considered as feasible.

2 rack reconstruction and optimization algorithms

According to the feature of rack reconstruction stage, on the basis of known recovery target, need to obtain the recovery order of each node and corresponding restoration path.Rack reconstruction and optimization algorithm of the present invention, its main feature be by fuzzy simulation with intersect particle cluster algorithm and combine, be destination node optimization recovery to be restored order, adopt classical dijkstra's algorithm to be node determination restoration path to be restored simultaneously.

2.1 shortest path first

When optimization is reconstructed to recovery rack, utilize intersect the particle cluster algorithm recovery order different for destination node generates time, also need to determine concrete restoration path according to the recovery situation of network and node location.Especially, when adopting fuzzy simulation processing target function and constraints, the restoration path of node to be restored must be determined.So adopt the shortest path first-dijkstra's algorithm of classical topological sum circuit weights Network Based to carry out optimizing to path.

Because intercropping fuzzy number process during line loop operation is embodied by the present invention in target function and constraints condition of opportunity, thus only using the charging reactive power of every bar circuit as circuit weights.When system exists many loop lines, then get the idle minimum circuit of charging.During search, using black starting-up power supply or the initial stage black starting-up mini system starting point as each search.Especially, be accelerating algorithm search procedure, after searching restoration path for a destination node, the weights of the circuit be on restoration path be set to 0.Such process can not have an impact to choosing of restoration path.

2.2 fuzzy simulation

Fuzzy simulation relates to two aspects: the fuzzy system constraint in testing model and the For Fuzzy Objective Function in transaction module.

Due to the present invention set up model in constraints condition of opportunity for be machine group node, so employing dijkstra's algorithm be, after each destination node to be restored searches out restoration path, only fuzzy simulation inspection is carried out to machine group node to be restored.Specific practice is as follows:

(1) from fuzzy variable alpha levels cut set in produce clear variable t equably _gk', T _g';

(2) clear variable is brought in the middle of constraints condition of opportunity formula (6), if meet, thinks that this restoration path is feasible;

(3) if do not meet, then repeat step (1), (2) N time, N is the number of times of fuzzy simulation;

(4) if still constraint can not be met after N simulation, then think that machine group node can not start in the time limit at it and has efficient recovery under the restoration path obtained by this recovery order;

(5) for infeasible situation, the particle of representation node recovery order is carried out variation amendment, specific practice will not change to first by original position, i.e. priority restores by the position of machine group node in particle of inspection, is positioned at node before this node then slow astern position successively;

(6) particle after making a variation is adopted dijkstra's algorithm determination restoration path again, and repeat step (1) ~ (3).If now still return infeasible through N simulation, then think that this unit can not start in the time limit at it and recover;

(7) after to the aforementioned machine group node priority restores do not met the demands, if occur, other units do not meet the situation of constraints, then still adopt said method, repeat step (5), (6);

(8) if after multiple exchanging position, still cannot ensure that all units to be restored meet fuzzy constraint, then start the principle in time limit, the unit that the optimum choice warm start stage recovers according to meeting multicomputer as far as possible, for starting the unit recovered in the time limit, cold-start phase can not being arranged in and recovering.Only adopt dijkstra's algorithm for its search shortest path is as restoration path, and no longer consider the constraint in unit starting time limit, namely no longer fuzzy simulation inspection is carried out to it.

After all nodes to be restored are checked by fuzzy constraint, process For Fuzzy Objective Function, specific practice is as follows:

(1) put $\stackrel{\‾}{f}=-\∞;$

(2) from fuzzy variable β horizontal cut set on evenly produce clear variable R _ij', t _m';

(3) clear variable is brought in formula (4-4), formula (4-6) and formula (4-8), try to achieve target function value f, if $\stackrel{\&OverBar;}{f}<f,$ Then put $\stackrel{\&OverBar;}{f}=f;$

(4) repeat step (2), (3) N time, N is fuzzy simulation number of times;

(5) return be the maximum of the target function of trying to achieve.

2.3 intersection particle cluster algorithms

In algorithm, particle adopts integer coding, and particle is initialized as the difference recovery order of node.The fitness function instructing particle to carry out iteration renewal in algorithm is the target function in formula (4), namely

$F=\max \stackrel{\&OverBar;}{f}---\left(8\right)$

The present invention is by particle J _irespectively with global extremum position g _xbestwith individual extreme value place p _xbestcarry out interlace operation, obtain new particle J _i'.For 5 meshed networks, suppose that node 1 is for black starting-up power supply, all the other be node to be restored, currently carry out jth time iteration, wait to intersect the particle J of renewal ₁(j)=[2 53 4], now global extremum position g _xbest=[2 34 5], individual extreme value place p _xbest=[5 23 4], the cross method so adopted is as follows:

First at g _xbestrandom selecting intersection region C in=[2 34 5] ₁=[4 5], afterwards by intersection region C ₁be added to J ₁before (j), and delete J ₁at C in (j) ₁the numeral of middle appearance, obtains particle J ₁" (j)=[4 52 3]; Then by particle J ₁" (j) and individual extreme value place p _xbest=[5 23 4] intersect, and first choose intersection region C ₂=[34], afterwards by intersection region C ₂be added to J ₁" before (j), and delete J ₁" at C in (j) ₁the numeral of middle appearance, finally obtains new particle: J ₁' (j)=[3 45 2].

The detailed implementation of the present invention is as follows:

Verify the present invention with IEEE30 bus test system, as shown in Figure 2, this system comprises 6 generators to system wiring, 40 circuits.

Wherein, machine group node 1 is as black starting-up power supply, and machine group node to be restored is [213222327], and load bus to be restored is [6101215192130]; Be limited to Triangular Fuzzy Number (10,15,20) when supposing the warm start of unit 27, the warm start time limit of all the other each units is (25,30,35); The operating time of each bar circuit is Triangular Fuzzy Number (2,2.5,3), the recovery reliability of each circuit is set as follows: wherein the recovery reliability of circuit 3-4,4-6,8-28,10-20,10-17,22-24 is (0.9,0.95,1), the recovery reliability of all the other each circuits is (0.7,0.85,1).

Other optimum configurations are as follows: particle number N _p=10, particle cluster algorithm allows the maximum times N of iteration _max=60, times N=1000 of fuzzy simulation, confidence level α, β are 0.95.During trend verification, be resumed exerting oneself of unit and get 30% of maximum output.

Adopt the present invention to be optimized rack reconfiguration scheme, finally obtain optimum rack reconfiguration scheme as shown in Figure 2.In Fig. 2, solid line is the circuit forming target net, the target net that the part that solid line connects is namely optimum.Table 1 is depicted as the recovery order of destination node and concrete restoration path.

Table 1 system node recovery order and restoration path

According to the rack restructuring procedure that table 1 provides, can find out:

(1) the warm start time limit due to machine group node 27 is shorter, so under the restriction of chance constraint, the result obtained by algorithm is preferentially recovered unit 27, and other units also all obtain startup power supply within its warm start time limit, achieves and recovers generating to greatest extent.The fuzzy expected value of the optimal objective rack reconstitution time of final acquisition is 40min.

(2) target net finally obtained contains part circuit 4-6,10-20 and the 22-24 with higher reliability of setting in advance, these circuits is included into the reason of target net, does a simple analysis for circuit 10-20.For destination node 19, as can be seen from the network site residing for it, the destination node 10 or 15 that can be closed on by it is recovered it by path 10-20-19 or 15-18-19.So when node 10 and 15 was all restored, only from shortest path, because the weights of path 15-18-19 are less, so this paths is more excellent before node 19.But, what these chapters and sections were sought is have the high rack recovering reliability, circuit 10-20 has higher recovery reliability, so the result obtained by algorithm is preferentially recovered node 10, and select to be recovered node 19 by path 10-20-19, to reaching higher recovery reliability, this is consistent with expected results.The circuit analyzing other high reliability is not included into the reason of rack, and the first is higher due to the weights of circuit own, is not adopted based on during dijkstra's algorithm searching route; It two is because node is recovered the recovery reliability that certainty equivalence is series system by this model, although so certain shortest path contains the higher circuit of recovery reliability sometimes, cause because circuit on path is more destination node to recover reliability and reduce and abandoned.

By analyzing, describe the present invention by the line loop operation time with recover reliability to do fuzzy number process be reasonable.The method proposed not only can effectively according to recovery situation and the topological structure of electrical network, reasonably optimize the recovery order of node, start power supply for unit as much as possible provides and meet certain confidence level, the target net simultaneously making optimization obtain has higher recovery reliability, is conducive to the safe operation of rack reconstruction stage system.In addition, the theoretical frame that the present invention proposes has certain versatility, can be used to process that rack reconstruction stage relates to that other have the uncertain factor of ambiguity, also can further consider this thinking expansive approach other stage to black starting-up.

Claims (5)

1., based on an electric power system rack reconstruction and optimization method for Fuzzy Chance Constraint, what it is characterized in that the method comprises rack reconstruction and optimization model sets up module and rack reconstruction and optimization algoritic module.

2. the electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint according to claim 1, it is characterized in that, rack reconstruction and optimization model set up module, triangular fuzzy variable is assumed to be by line loop operation time and recovery reliability, define the recovery reliability index of whole rack on this basis, utilization Fuzzy Chance Constrained Programming is theoretical, successfully obtain within its startup time limit with unit and start power supply for constraint, reach with the recovery of rack in reconstitution time short as far as possible reliability and be up to target, set up the fuzzy chance constrained model of rack reconstruction and optimization, to being met the rack reconfiguration scheme of certain confidence level.

3. the electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint according to claim 1, is characterized in that, rack reconstruction and optimization algoritic module, is combined into by shortest path first, fuzzy simulation and particle cluster algorithm three part of intersecting.Namely according to the model of aforementioned foundation and the feature of rack reconstruct, the method being applicable to this model solution is proposed, adopt the intersection particle cluster algorithm based on fuzzy simulation to be destination node optimization recovery to be restored order, adopt classical dijkstra's algorithm to be node determination restoration path to be restored simultaneously.

4. the electric power system rack reconstruction and optimization method based on Fuzzy Chance Constraint according to claim 1, it is characterized in that, trend verification is carried out to the recovery scheme obtained by algorithm optimization, only has and to be verified by trend or the scheme of each regulated quantity in allowed band is just considered as feasible.

5., based on an electric power system rack reconstruction and optimization method for Fuzzy Chance Constraint, it is characterized in that, described concrete steps are as follows:

Step one, represents the fuzzy uncertain amounts such as the line loop operation time related in invention with triangular fuzzy variable;

Step 2, the recovery reliability defining node to be restored also determines the recovery reliability index of whole rack further;

Step 3, successfully obtains with unit and starts power supply for constraint, reach and be up to target, set up the rack reconstruction and optimization model based on Fuzzy Chance Constraint with the recovery of rack in reconstitution time short as far as possible reliability within its startup time limit;

Step 4, solving of rack reconstruction and optimization model, further:

(1) determine black starting-up power supply and destination node to be restored and initial parameter is set, forming N _pindividual primary;

(2) loop iteration is carried out to particle, i=1:N _p;

(3) get current particle i, call the restoration path of dijkstra's algorithm search each destination node under this recovery order;

(4) to machine group node, fuzzy simulation inspection Fuzzy Chance Constraint is adopted;

(5) judging whether by inspection, is carry out (6), otherwise, utilize mutation operation to upgrade particle, return step (3) afterwards;

(6) trend verification is carried out to the particle by verification;

(7) judge whether iteration completes all particles; Be carry out (8), otherwise return step (2);

(8) fuzzy simulation calculates the fitness of particle, and determines individual extreme value p _best, global extremum g _bestand the extreme value place p of their correspondences _sbest, g _sbest;

(9) utilize cross-iteration to operate to upgrade particle;

(10) maximum times reaching iteration is judged whether; Be carry out (11), otherwise return step (2);

(11) export the node restoration path of optimal particle and correspondence, namely obtain final rack reconfiguration scheme.