CN101212141A - Optimized back-track algorithm-based capacitor switching method - Google Patents

Abstract

The invention relates to a method for switching of capacitors based on an optimization backtracking algorithm. The invention selects the optimal capacitance combination in real time according to the capacity of the compensation capacitance in the compensation device and according to the real needed compensation reactive in the power network. The method comprises the processes as follows: 1. using an artificial stack to build a solution space tree; 2. using a feasible limit function to cut the invalid search; 3. using an optimal limit function to accelerate the search. The stack is used for storing a backtracking route of the solution space tree and the limit function is used for processing the expending and backtracking of the node. The invention accelerates the search speed of a single chip microcomputer and the single chip microcomputer can process switching of capacitors with more routes to achieve the rapid and optimal control effect.

Description

Based on the capacitor switching method of optimizing back-track algorithm

Technical field

The present invention relates to a kind of capacitor switching algorithm based on the thyristor switchable capacitor principle, especially a kind of based on the capacitor switching method of optimizing back-track algorithm.

Background technology

At present, the capacitance arrangement scheme based on the reactive power compensator of thyristor switchable capacitor (TSC) principle has two kinds usually: endless form and binary mode.

Endless form is a kind of special capacity configuration scheme, also is a kind of switching control method.Under this scheme, the capacitance on the circuit all equates:

R={＜C _i, C _I+1| C _i=C _I+1, 0≤i≤N-1} formula 1

R represents the relation that capacitance exists; C _iThe compensation capacity of representing i road electric capacity; N represents always total how many contacts, road of control device, and for example N is 16, and then the contact numbering from 0 to 15.

Binary mode is meant that the capacitance on the circuit always doubles than its last road:

$R=\{<C_i,C_{i+1}>|C_i=\frac{1}{2}{C}_{i+1},0\&le;i\&le;N-1\}$ Formula 2

Control method under these two kinds of allocation plans is simple relatively.Order:

The detected reactive power of controller is the idle Q of phenomenon _Ph

The compensation capacity that after the quantification all have been thrown electric capacity is compensating reactive power Q _Cp

The reactive power that load end produces is the idle Q of load _Ld

Have: Q _Ph=Q _Ld-Q _CpUsually do not wish to occur the situation of overcompensation, because this can cause the rising of transformer secondary voltage, and capacitive reactive power transmits equally on power circuit and can increase electric energy loss.If therefore supply line's voltage raise, also can increase the power loss of capacitor itself, temperature rise is increased, influence life of capacitors.Therefore our purpose of control is at the idle Q of a certain load _LdThe compensating reactive power Q that modulated is suitable _Cp, make the idle Q of phenomenon _PhValue non-negative and minimum.

The group number that drops into electric capacity under the endless form is pressed m=Q _Ld/ C, the group number of electric capacity is represented with m.As for selecting any m electric capacity to put into operation in the electric capacity formation, generally choose according to the time of putting into operation of electric capacity, make that the time of putting into operation of each road electric capacity is balanced substantially, the bulk life time of control device is the longest like this.

The switching state of electric capacity is pressed M under the binary mode _{Targ et}=Binary (Q _Ld/ C ₀) determine.

M _TargetThe dbjective state of expression capacitor switching; C ₀The capacity of that road electric capacity of expression capacity minimum; Binary () expression is converted into binary number with a decimal number.After the conversion with M _TargetBe considered as by a series of 0,1 bit fields of forming.Wherein 0 represents the excision state, 1 expression input state.

Compensation arrangement can obtain the longest working life under the endless form, and the compensation arrangement compensation quality that can offer the best under the binary mode.More than two kinds of capacity configuration schemes all belong to special scheme, sometimes the user considers for operation of power networks situation and economy or for the consideration that effectively utilizes idle capacitance apparatus, selects the configuration of capacitance to be different from above two kinds: can be without any relation on capacity between each electric capacity.This allocation plan can be thought the popularization and the vague generalization of recycle scheme and binary scheme; These two kinds of particular arrangement can be regarded as the special case that this vague generalization is disposed.

For this on capacity can without any the relation the vague generalization allocation plan, one of traditional control method is following often 3 kinds:

1, schedule method: all the switching compound modes of the electric capacity in the electric capacity formation and bank capability thereof are made into a form by the size groups of compensation capacity, are stored in the solid-state memory.When detecting unit obtains the idle Q of phenomenon _PhThe time, it is idle to convert out load according to the electric capacity of having thrown, and reads this form.Utilize split comparison with form with this load is idle then, find optimum electric capacity combination, implement switching then.The time complexity of this method is T (n)=O (n), but space complexity is S (n)=O (2 ⁿ).Memory cell that just needs and controlled electric capacity quantity are exponential relationship.The method should not be used on the control device more than 6 road building-out capacitors.

2, traversal method: be the compensation capacity that calculates under all switching compound modes of electric capacity in the electric capacity formation equally, but do not generate form, but directly each and load is idle compares.For controlled n road electric capacity, need to generate 2 ⁿThe compensation capacity under the compound mode and the operation that compares.Therefore its time complexity is T (n)=O (2 ⁿ), be operated in the single-chip microcomputer of 10MPS, generally can handle 8 the tunnel and following electric capacity combination.

3, greedy algorithm: greedy algorithm is a kind of control method that has the intuition tendency, and substep provides sequence of decisions, carries out immediately once decision-making.Load is idle as optimum when judging when approaching most with the target compensating reactive power, and algorithm can not be restrained, so with the idle Q of phenomenon _PhNon-negative minimum as optimum judgement.Like this as the idle Q of phenomenon _PhWhen being worth, in not throwing the electric capacity formation, choosing compensation capacity and be not more than the idle Q of phenomenon for certain _PhAnd approach the idle Q of phenomenon most _PhElectric capacity.Advantage is: time complexity is T (n)=O (n), and for the capacitance arrangement of any multichannel, single-chip microcomputer can both be competent at; Shortcoming is: greedy algorithm not necessarily obtains optimal solution, before the quality of power supply after only guaranteeing once to move is better than action.

Obviously above-mentioned traditional method or can not get optimal solution can't satisfy high-quality control effect; That handles problems is small, and speed is slow.

Summary of the invention

The object of the present invention is to provide under a kind of capacity configuration scheme of not having any relation at capacitance, the resource overhead that bears with the monolithic function is a prerequisite, optimizes back-track algorithm, realizes the optimal control of multichannel capacitor switching, and it has overcome the deficiencies in the prior art.

The object of the present invention is achieved like this: comprise the solution space tree that makes up a plurality of nodes and a plurality of branches, each node is represented a specific capacitor switching state, and each branch is represented the transfer of a next state; Search is used the invalid search of feasible boundary function cutting from the root node of tree; Use optimum boundary function acceleration search.

Described solution space tree is set up while searching in artificial storehouse, and the transfer correspondence of a next state the pop down of a storehouse or gone out stack operation.

Described feasible boundary function is by formula $\underset{i=0}{\overset{n=1}{\mathrm{\&Sigma;}}}{x}_i{C}_i{\&le;Q}_{\mathrm{ld}}$ Determine, wherein x _iBeing the switching state of electric capacity, is 1 during throwing, is 0 when cutting; C _iIt is the compensation capacity of i road electric capacity; Q _LdThe expression load is idle.

Described optimum boundary function is by formula $\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i\&le;Q_{\mathrm{optimal}}$ Determine Q in the formula _OptimalFor prior searches to feasible and maximum separating.

The invention has the beneficial effects as follows: save the time and the space expense of single-chip microcomputer, enlarge the scale that single-chip microcomputer is handled problems, make control device can bear the more Control work of multichannel, reach quick, optimum control effect simultaneously.

Description of drawings

The invention will be further described below in conjunction with drawings and Examples.

Fig. 1 is a method of work schematic diagram of the present invention.

Embodiment

According to the present invention, be based on the process of the capacitor switching method of optimizing back-track algorithm:

One, promptly there is following relation in the compensation capacity that makes each electric capacity by contact numbering ascending order or non-descending between electric capacity:

R={＜C _i, C _I+1| C _i≤ C _I+1, 0≤i≤N-1} formula 3

Can or create mapping table and accomplish this point by the change wiring.

Two, the Mathematical Modeling of constitution optimization problem.

Variable X=(x _N-1, x _N-2... x ₁, x ₀).Wherein Constraints $\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i\&le;Q_{\mathrm{ld}},$ The idle of expression compensation must not surpass idle that load end needs.Majorized function

Seek one exactly and separate X, satisfying under the situation of constraints the functional value maximum.

Three, set up the solution space tree, this algorithm adopts back-track algorithm.Compared to branch-bound algorithm, back-track algorithm is not really set up whole tree in internal memory---and that will be S (n)=O (2 under the worst case ⁿ) space complexity.Tree limit search solution space is set up on the artificial storehouse of back-track algorithm utilization limit.The degree of depth of stack is exactly the degree of depth of binary tree, is fit to very much single-chip microcomputer.In order to simplify description,, be that example is explained back-track algorithm with 4 road electric capacity as Fig. 1.

At the 0th layer of this full binary tree, be a root node, the state that sets out of expression search, this moment, 4 electric capacity were for cutting entirely.The node expansion for the first time in the 1st layer of setting out finishes, and the highest road electric capacity is carried out switching accept or reject, and at the i floor n-i road electric capacity is carried out switching accordingly and accepts or rejects; And contained the 0 road all Switching Strategy to the whole space of end n floor to n-i road electric capacity from the i floor.The switching to this road electric capacity is represented in path 1 or 0 respectively, the Switching Strategy of the value representation electric capacity of node.

Four, search

Suppose: the quantity n=4 of electric capacity

The compensation capacity G of electric capacity _i=[30,20,20,10] Kvar

The idle Q of load _Ld=35kvar.

With constraints $\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i\&le;Q_{\mathrm{ld}}$ As feasible gauge function, use this function can stop the dilated node that can not obtain feasible solution, with the search tree of cutting infeasible solution.For example under the strategy of the node C1 (1100) on the m layer (m=2 here), compensated $Q_{\mathrm{cp}}=\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i$ Idle amount.Calculate under the C1 node $Q_{\mathrm{cp}}=\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i=50>35=Q_{\mathrm{ld}},$ So with the C1 node is feasible solution of the impossible generation of subtree of root.Therefore there is no need to search for downwards from C1, the C1 node has been killed by feasible boundary function.In addition in the boundary function $Q_{\mathrm{cp}}=\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i$ Be not that repeatedly addition is finished.In fact, because the expansion of node is still recalled all and is carried out by turn in the back-track algorithm, so a new W _CpAlways on initial value, do a sub-addition or subtraction and obtain, very efficient.

Algorithm is performed such:

1, searches for from root node A1 (0000), at this moment Q _Cp=0.

2, because A1 is that a feasible node (not killed by the boundary function) is so be expanded to left child B1.While Q _Cp=30, so Q _Cp＜Q _LdThe B1 node is not killed by the boundary function as can be known.The B1 node is to comprise feasible solution certainly in the subtree of root.So continue expansion.

3, the left child C1 from the B1 dilated node to it, Q at this moment _Cp=50＞Q _Ld, the C1 node is killed by the boundary function.Expression C1 node is not comprise feasible solution in the subtree of root.

4, date back to the B1 node from a C1 that dies for the sake of honour, to the C2 node, current moving do not change Q from the B1 dilated node _CpSo C2 is a movable joint point.

5, from the C2 dilated node to the D3 node, the D3 node is killed by the boundary function.

6, date back to the C2 node from the D3 node, to the D4 node, the D4 node does not change Q from the C2 dilated node _CpSo D4 is a movable joint point.

7, from the D4 dilated node to the E7 node, the E7 node is killed by the boundary function.

8, date back to D4 from E7, be expanded to E8 from D4.E8 is not killed by the boundary function, and E8 is a leaf node simultaneously.So found first feasible solution E8.

9, date back to A1 from E8 always, expand to right subtree from A1 then.Carry out same operation, can obtain other feasible solution.

10, relatively more all feasible solution, obtaining separating of income maximum is optimal solution.

This algorithm has been set up the storehouse of a n unit depth.Root node is at first stacked, when a node need be expanded, will be expanded a pop down.When using the boundary function, " reading " stack top element, when recalling, " ejection " stack top element.When stack is sky, finish search.

Used time of back-track algorithm is always less than traversal.Because traversal is equivalent to search for each leaf node, can give up to fall infeasible node and recall, giving up simultaneously with this node is the search of the subtree of root; Under worst case, optimal solution is the full situation of throwing of electric capacity.Only use the back-track algorithm of feasible boundary function also can travel through each leaf node this moment, however, and to compensation capacity as the leaf node of basic operation

Calculating, with respect to the traversal, do the n sub-addition, as long as and back-track algorithm is done a sub-addition or subtraction.

Unite the back-track algorithm that uses optimum boundary function: seeing in last example, is a feasible solution if electric capacity is thrown (1111) entirely.The boundary function can not kill any one node in the solution space so.That is to say that back-track algorithm has to search for whole solution space.But this obviously is redundant, because in a single day 1111 become feasible solution (satisfying constraints), can provide than its bigger compensation capacity without any a kind of separating, so there is no need other subtree of removal search.The search that the back-track algorithm of optimizing can be extruded these redundancies, only remaining necessary procedure.

Observe a nonterminal node Z, suppose that it is in the m layer, this facility strategy has compensated so $Q_{\mathrm{cp}}=\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i$ Idle.Node Z is any switching state that the subtree of root has contained remaining n-m road electric capacity, and certainly wherein compensating maximum is the full state of throwing of remaining n-m road electric capacity, and remaining full throwing has compensated again

In a single day arrive this leaf node from the search of Z, will compensate $Q_{\mathrm{local}\max }=\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i$ Capacity.If before to the Z node searching, searched a feasible solution Q _FirstCompare Q now _FirstAnd Q _LocalmaxIf Q _Localmax≤ Q _First, any Switching Strategy from the Z node all can not produce than the feasible solution Q that has existed so _FirstGreatly.According to majorized function, to separate under the feasible situation, value is the bigger the better.Therefore it is just nonsensical to search for Z, and the Z node is killed.

$Q_{\mathrm{local}\max }=\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i$ This basic operation seems the computing that needs T (n)=O (n) time complexity.In fact no matter to recall or expand, computing is all carried out by turn.

All need only and do a sub-addition or subtraction can be finished on the basis of initial value, time complexity is T (n)=O (2).So back-track algorithm has increased an optimum boundary function $\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i\&le;Q_{\mathrm{optimal}}.$ Q in the formula _OptimalFor prior searches to feasible and maximum separating.In the beginning of search, optimum boundary function is not carried out; After first feasible solution produced, optimum boundary function just began to carry out the task of killing node together with feasible boundary function.Optimum boundary function may not be stable, if the feasible solution that produces is Q for the first time _First, when a paths is not killed by two boundary functions, when finally making certain leaf node become feasible solution.This is separated and is Q _Second, this Q certainly _SecondCompare Q _FirstBigger, be more excellent separating.According to formula $\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i\&le;Q_{\mathrm{optimal}},$ In optimum boundary function, use bigger Q _SecondReplace Q _First, can more effectively carry out the task of killing all the other nodes.

This substitute shows separating of last search, less than new search to separate.And the generation of at every turn separating shows the through leaf node of search, and this is the time overhead maximum, should reduce the generation of new explanation as far as possible.If the number of times of replacing is a lot, show that separating of searching previously is of low quality.Also enough good separating can't be once just found in theory, all thereafter nodes can be killed.This algorithm makes the capacitance compensation capacity be R={＜C in step 1 _i, C _I+1| C _i≤ C _I+1, 0≤i≤N-1} relation.Under this relation, the appearance that can kill the optimal solution of other all nodes may be more early.May allow search speed faster.

Suppose: the quantity n=4 of electric capacity

The compensation capacity C of electric capacity _i=[30,20,20,10] Kvar

The idle Q of load _Ld=85kvar.

Search, begins one the tunnel from A1 and searches E1 according to feasible boundary function from root node A1.And find first feasible solution E1 (1111).Because it is a leaf node, so recall.This moment, optimum boundary function was waken up, and when dating back to D1, D1 is killed, and can not produce more excellent the separating than E1 because with the D1 node be in the tree of root.Continue to date back to C1, B1, A1.These nodes are all killed by optimum boundary function, and last root node is killed, and search finishes.

So the back-track algorithm after the optimization has quickened the speed of search once more.Make algorithm to the problem with identical scale, the time of processing is shorter; Perhaps in the identical time, can handle more massive problem.

Claims (5)

1. one kind based on the capacitor switching method of optimizing back-track algorithm, and comprising: make up the solution space tree of a plurality of nodes and a plurality of branches, each node is represented a specific capacitor switching state, and each branch is represented the transfer of a next state; Search is used the invalid search of feasible boundary function cutting from the root node of tree; Use optimum boundary function acceleration search.

2. as claimed in claim 1 based on the capacitor switching method of optimizing back-track algorithm, described solution space tree is set up while searching in artificial storehouse, and the transfer correspondence of a next state the pop down of a storehouse or gone out stack operation.

3. as claimed in claim 1 or 2 based on the capacitor switching method of optimizing back-track algorithm, described feasible boundary function is by formula $\underset{i=0}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i\&le;Q_{\mathrm{ld}}$ Determine, wherein x _iBeing the switching state of electric capacity, is 1 during throwing, is 0 when cutting; C _iIt is the compensation capacity of i road electric capacity; Q _LdThe expression load is idle.

4. as claimed in claim 1 or 2 based on the capacitor switching method of optimizing back-track algorithm, described optimum boundary function is by formula $\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i\&le;Q_{\mathrm{optimal}}$ Determine Q in the formula _OptimalFor prior searches to feasible and maximum separating.

5. as claimed in claim 3 based on the capacitor switching method of optimizing back-track algorithm, described optimum boundary function is by formula $\underset{i=n-m}{\overset{n-1}{\mathrm{\&Sigma;}}}{x}_i{C}_i+\underset{i=0}{\overset{n-m-1}{\mathrm{\&Sigma;}}}{C}_i\&le;Q_{\mathrm{optimal}}$ Determine Q in the formula _OptimalFor prior searches to feasible and maximum separating.