CN102983570A - Islanding method for power distribution network comprising distributed generation and considering interconnection switch - Google Patents

Abstract

The invention discloses an islanding method for a power distribution network comprising distributed generation (DG) and considering an interconnection switch. The method comprises the steps of obtaining a new islanding model of a power distribution system comprising the DG based on a graph model of the power distribution system, and constructing a graph model G of the power distribution system in a power-losing area after a failure. The method provides theoretical criteria for constructing the islanding method of the power distribution network comprising the DG and considering the interconnection switch, which meets an engineering demand, a solving strategy for the islanding of the power distribution network comprising a looped network structure is proposed based on the algorithm, an engineering application scope of a islanding technique comprising the DG is expanded, the defect that the existing similar technique is not applicable to the islanding of the power distribution network comprising the interconnection switch is overcome, the application scope is wider, development requirements of an intelligent power grid structure are met, the solving algorithm of the islanding of the distribution network comprising the DG and considering the interconnection switch is low in time calculation complexity, and the practical engineering demand is satisfied.

Description

A kind ofly contain distributed power generation distribution isolated island division methods for what consider interconnection switch

Technical field

The invention belongs to and contain distributed power generation distribution isolated island and divide the field, relate in particular to and a kind ofly contain distributed power generation distribution isolated island division methods for what consider interconnection switch.

Background technology

One of the purpose of building of intelligent grid is exactly " accessible being incorporated into the power networks " and " plug and play " that realization utilizes the distributed power generation (Distributed Generation, DG) of various renewable energy power generations, to reach the purpose of energy-saving and emission-reduction.A large amount of DG generally is connected with distribution system, and power distribution network has also had and the similar characteristic of power transmission network because having independently-powered power supply, such as amphicheirality, system safety stable problem and the electric power isolated island supply power mode etc. of trend.Islet operation is significant equally for the distribution system that contains DG.

Electric power isolated island supply power mode is a kind of new operational mode of distribution system after introducing distributed power generation.Under this operational mode, the certain customers of distribution system are only powered by DG, and the system that comprises this part user and DG is called as the electric power isolated island in the distribution system.After distribution system hindered stoppage in transit for some reason, for maintainer's personal safety, simultaneously for so that power distribution network is eliminated fault as early as possible, according to the relevant regulations of I EEE1547-2003, all DG in the power distribution network must be out of service in short-term.But because DG has independently-powered ability, after the Fault Isolation, can utilize the power supply of DG recovered part important load and relevant load, thereby significantly improve the power supply reliability of system.Than transmission system, the distribution system wiring is complicated, and various device quantity is huge, and manufacturer and principle are different, easier breaking down.Statistics shows that the system failure more than 95% occurs in distribution system.Therefore, along with being incorporated into the power networks of a large amount of distributed power generations, for realizing the target of following intelligent grid/highly reliable power supply of intelligent distribution, the electric power decoupled mode of power distribution network will become its important normality operational mode.

In the situation of system's dead electricity, if can independently-powered isolated island can ensure the uninterrupted of important load power supply as power supply forms take all kinds of DG, allow simultaneously load as much as possible obtain service restoration, thereby significantly promote the power supply reliability of distribution system.And the DG installation site is very flexible, dispersion, and finite capacity, how fully to effectively utilize limited distribution type electric energy, determine the best electric power isolated island take DG as power center, and in time carry out islet operation and with the synchronous operation of large electrical network, thereby bring into play to greatest extent the advantage of distributed power generation, ensure that the continued power of important load and many as far as possible loads is the key issues that realize the efficient operation of distribution system isolated island.The isolated island of present stage is divided the isolated island of the power supply interrupted district of all only having considered tree and is divided.Tree-shaped fault zone isolated island partition problem can abstractly be the tree knapsack problem, and this also is to have now to contain distributed power generation distribution isolated island division methods key problems-solving mainly for tree.But the structure of intelligent distribution will be more complicated, and interconnection switch, block switch are more, and corresponding isolated island form is then more flexible, and the tree knapsack problem is difficult to carry out abstract to its isolated island partition problem.Therefore, for giving full play to the advantage of distributed power generation, tackle the development of following intelligent distribution network, for considering the containing for distributed power generation power distribution network isolated island divides of interconnection switch effect, take out essential graph theoretic problem wherein, study corresponding derivation algorithm, and provide corresponding isolated island partition strategy and just seem particularly important.

Summary of the invention

The object of the invention is to make up the new graph theoretic problem of a class---figure knapsack problem, propose a kind of figure knapsack problem method for solving, and based on this, propose to solve the available strategy that contains distributed power generation distribution isolated island partition problem of considering interconnection switch.

The object of the present invention is to provide and a kind ofly contain distributed power generation distribution isolated island division methods, described may further comprise the steps for what consider interconnection switch:

The distribution system major network breaks down, partly contain distributed power generation zone dead electricity after the Fault Isolation in the system, the power supply that the islanded system of formation take distributed power generation as power supply in time recovers the important load power supply and recover simultaneously many as far as possible loads, based on the distribution system graph model, obtain containing DG distribution system isolated island and divide new model:

$\left\{\begin{array}{c}\underset{{X,P}^{\mathrm{Gem}},Q^{\mathrm{Gen}},P^{\mathrm{Load}},Q^{\mathrm{Load}},U,T,C}{\mathrm{Max}}{c}_{\mathrm{sum}}=\underset{v=0}{\overset{n}{\mathrm{\Σ}}}{c}_v{x}_v\\ s.t.\\ 1.x_g=1\\ 2.x_v=\left\{\mathrm{0,1}\right\},v\∈V\backslash g\\ 3.x_i\≥x_v,i\∈l_{v,g},\∀v\∈V\backslash g,{\∃l}_{v,g}\∈L_{v,g}\\ 4.{\mathrm{\ΔP}}_i=\underset{j\∈S}{\mathrm{\Σ}}{U}_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}),i\∈S\\ 5.{\mathrm{\ΔQ}}_i=\underset{j\∈S}{\mathrm{\Σ}}{U}_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}),i\∈S\\ 6.{\underset{\‾}{U}}_i\≤U_i\≤{\stackrel{\‾}{U}}_i,i=\mathrm{1,2},...,n\\ 7.{\underset{\‾}{T}}_i\≤T_i\≤{\stackrel{\‾}{T}}_i,T_i\∈T\\ 8.0\≤C_i\≤{\stackrel{\‾}{C}}_i,C_i\∈C\\ 9.{\underset{\‾}{P}}_{l_{i,j}}\≤P_{l_{i,j}}\≤{\stackrel{\‾}{P}}_{l_{i,j}},l_{i,j}\∈L_L\\ 10.0\≤P_g^{\mathrm{Gen}}\≤{\stackrel{\‾}{P}}_g^{\mathrm{Gen}}\\ 11.{\underset{\‾}{Q}}_g^{\mathrm{Gen}}\≤G_g^{\mathrm{Gen}}\≤{\stackrel{\‾}{Q}}_g^{\mathrm{Gen}}\\ 12.0\≤P_i^{\mathrm{Load}}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Load}},i=\mathrm{0,1,2},...,n\\ 13.0\≤Q_i^{\mathrm{Load}}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Load}},i=\mathrm{0,1,2},...,n\end{array}\right.$

Make up the afterwards graph model G of dead electricity zone distribution system of fault:

$\left\{\begin{array}{c}\mathrm{Max}\underset{v=0}{\overset{n}{\mathrm{\Σ}}}{c}_v{x}_v\\ s.t.\underset{v\∈S\backslash g}{\mathrm{\Σ}}{d}_v\≤\left|d_g\right|\\ x_g=1\\ x_v=\left\{\mathrm{0,1}\right\},v\∈V\backslash g\\ x_i\≥x_v,i\∈l_{v,g},\∀v\∈V\backslash g,\∃l_{v,g}\∈L_{v,g}\end{array}\right.---\left(2\right)$

In the following formula (2) in each variable and the formula (1) implication to dependent variable identical.

Further, make up the graph model G contain the distributed power generation distribution system, to flow out node power for just; The demand d of each node v _vBe the injecting power of corresponding node v in the distribution, if v is tie point, namely the v node is not loaded, then d _vEqual 0; The weights c of each node v _vBe set to c _v=W _vd _v, for load bus, W _vBe the load weight of node v, the priority of load is higher, its W _vLarger; For DG node and connected node, W _v=0, corresponding c _v=0; Make that the distributed electrical source node is v ₀, make V ₀=V (v ₀), G '=G, order expansion subgraph E=v ₀, wherein, node set in V (*) the expression subgraph; Make G '=G ' v ₀, establish e _jFor among the G ' with the limit of E adjacency, j=1,2 ... k, k are total with the E adjacent side among the G ';

Make a _j=V (e _j(E ∩ e _j)), j=1,2 ... k, i.e. a _jFor among the G ' with the E adjacent node; With e _jFor the expansion limit expansion subgraph is expanded, made N _j=N (E ∪ e _j), wherein, N (*) expression subgraph all of its neighbor node set;

Structure is with N _jIn node be alternative node, H-d (e _j∪ E) as the knapsack problem of constraint of demand, forward next step to, wherein, in d (*) the expression subgraph node demand and; If with a _jBe the expansion limit to the circuit between the initial subgraph E, node 1～8 is alternative node in the accompanying drawing 2;

The optimal solution that solves this knapsack problem is S _p, then make M _j=e _j∪ E ∪ S _p, p _j=w (M _j), wherein, in w (*) the expression subgraph node weights and;

Judge whether j＜k;

Have Wherein max is Numbering j when getting maximum makes V _n=V (M _Max) (initial n=1), E=E ∪ e _Max

Judge whether d (V _n) 〉=H;

Select set { V _n| n=0,1,2,3 ... in satisfy d (V _nThe weights of)≤H and the maximum are as optimal solution, and the node in the optimal solution set consists of optimum isolated island.

Further, described optimal solution S _pCan find the solution by dynamic programming algorithm or the branch-bound algorithm of pseudo-polynomial time O (nH).

Further, construct the some weighting connected undirected graph G (V, E, w, d) that an expression contains the distributed power generation distribution system, each node v has two parameters among the G: the node weight w _vWith node demand d _vFor such some weighted graph, take power-balance as constraint, change a figure knapsack problem take the Income Maximum that restores electricity into as the isolated island partition problem that contains in the contact Distribution Network Failure recovery process of target, can use for reference the thinking of finding the solution that contains the constraint diagram knapsack problem and find the solution.What contain the research of constraint diagram knapsack problem is how to find in the drawings to comprise an initial subgraph E ₀Node demand and satisfy the demands restriction and node weights and maximum subgraph, require simultaneously at least one associated nodes of each selected node also selected; This problem can be expressed as following linear integer optimization problem:

$\left\{\begin{array}{c}\mathrm{Max}\underset{v=V}{\mathrm{\Σ}}{w}_v{x}_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}{d}_v{x}_v\≤H\\ x_g\≥x_v,\∀v\∈V,\∃g\∈F_v\\ x_{\∈}\left\{\mathrm{0,1}\right\},\∀v\∈V\backslash E_0\\ x_v=1,\∀v\∈E_0\end{array}\right.$

In formula, x _vBe the node state variable, if v is chosen optimal solution set, x _v=1; Otherwise, x _v=0.F _vFor with the set of node v associated nodes.H is node demand and restriction.

Further, take out take power-balance as constraint, contain mathematical problem---figure knapsack problem (the Graph Knapsack Problem of contact distribution isolated island in dividing take the Income Maximum that restores electricity as target, GKP) as follows: as to construct the some weighting connected undirected graph G (V that an expression contains the distributed power generation distribution system, E, w, d), each node v has two parameters among the G: the node weight w _vWith node demand d _vFor such some weighted graph, take power-balance as constraint, divide can be described as and find how in the drawings to comprise a given node V as the contact distribution isolated island that contains of target take the Income Maximum that restores electricity ₀, node demand and satisfy the demands restriction and node weights and maximum connected subgraph are referred to as the figure knapsack problem; This figure knapsack problem can be expressed as following linear integer optimization problem:

$\left\{\begin{array}{c}\mathrm{Max}\underset{v=V}{\mathrm{\Σ}}{w}_v{x}_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}{d}_v{x}_v\≤H\\ x_v=1,v=v_0\\ x_{\∈}\left\{\mathrm{0,1}\right\},\∀v\∈V\backslash v_0\\ x_i\≥x_v,i\∈l_{v,v_0},\∀v\∈V\backslash v_0,\∃l_{v,v_0}\∈L_{v,v_0}\end{array}\right.$

In the following formula formula,

Node v and node v among the presentation graphs G ₀Between the set of node on all chains,

Be node v and node v among the figure G ₀Between node set on arbitrary chain.

The present invention has following advantage:

The method for solving that contains distributed power generation distribution isolated island partition problem of consideration contact provided by the invention, the efficient algorithm that the figure knapsack problem is found the solution in first proposition, the proposition of this algorithm contains distributed power generation power distribution network isolated island division methods based theoretical for what make up the consideration interconnection switch satisfy engineering demand, can solve the power distribution network isolated island partition problem that contains ring network structure, expand the through engineering approaches range of application that contains distributed power generation isolated island partitioning technology.Overcome existing similar technology and can't be applicable to contain the defective that interconnection switch distribution isolated island is divided, range of application is wider, more meet the requirement of intelligent grid grid structure development, simultaneously, method for solving complexity computing time that contains distributed power generation distribution isolated island partition problem of consideration contact provided by the present invention is low, satisfies actual requirement of engineering.

Description of drawings

Fig. 1 is the realization flow figure that contains distributed power generation distribution isolated island division methods that is used for considering interconnection switch that the embodiment of the invention provides;

Fig. 2 is the expander graphs for the adjacent side that contains distributed power generation distribution isolated island division methods of considering interconnection switch that the embodiment of the invention provides.

Embodiment

In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, is not intended to limit the present invention.

Suppose that the distribution system major network breaks down, partly contain distributed power generation zone dead electricity after the Fault Isolation in the system, therefore can form the power supplies that the islanded system take distributed power generation as power supply in time recovers important load power supply and the many as far as possible loads of simultaneously recovery.Optimum isolated island scheme should satisfy the following basic demand: 1) satisfy the electric constraints such as power-balance, voltage, equipment ampacity; 2) important load preferentially obtains service restoration, and the load total amount that restores electricity is many as far as possible; 3) via net loss of isolated island scheme is as far as possible little; 4) impact of consideration controllable burden and uncontrollable load.For realizing these purposes, based on above-mentioned distribution system graph model, the present invention has provided and has contained DG distribution system isolated island division new model shown in the following formula (1).

$\left\{\begin{array}{c}\underset{{X,P}^{\mathrm{Gem}},Q^{\mathrm{Gen}},P^{\mathrm{Load}},Q^{\mathrm{Load}},U,T,C}{\mathrm{Max}}{c}_{\mathrm{sum}}=\underset{v=0}{\overset{n}{\mathrm{\Σ}}}{c}_v{x}_v\\ s.t.\\ 1.x_g=1\\ 2.x_v=\left\{\mathrm{0,1}\right\},v\∈V\backslash g\\ 3.x_i\≥x_v,i\∈l_{v,g},\∀v\∈V\backslash g,{\∃l}_{v,g}\∈L_{v,g}\\ 4.{\mathrm{\ΔP}}_i=\underset{j\∈S}{\mathrm{\Σ}}{U}_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}),i\∈S\\ 5.{\mathrm{\ΔQ}}_i=\underset{j\∈S}{\mathrm{\Σ}}{U}_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}),i\∈S\\ 6.{\underset{\‾}{U}}_i\≤U_i\≤{\stackrel{\‾}{U}}_i,i=\mathrm{1,2},...,n\\ 7.{\underset{\‾}{T}}_i\≤T_i\≤{\stackrel{\‾}{T}}_i,T_i\∈T\\ 8.0\≤C_i\≤{\stackrel{\‾}{C}}_i,C_i\∈C\\ 9.{\underset{\‾}{P}}_{l_{i,j}}\≤P_{l_{i,j}}\≤{\stackrel{\‾}{P}}_{l_{i,j}},l_{i,j}\∈L_L\\ 10.0\≤P_g^{\mathrm{Gen}}\≤{\stackrel{\‾}{P}}_g^{\mathrm{Gen}}\\ 11.{\underset{\‾}{Q}}_g^{\mathrm{Gen}}\≤G_g^{\mathrm{Gen}}\≤{\stackrel{\‾}{Q}}_g^{\mathrm{Gen}}\\ 12.0\≤P_i^{\mathrm{Load}}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Load}},i=\mathrm{0,1,2},...,n\\ 13.0\≤Q_i^{\mathrm{Load}}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Load}},i=\mathrm{0,1,2},...,n\end{array}\right.---\left(1\right)$

The target function of formula (1) is illustrated in realizes total power supply Income Maximum on the basis of satisfying all kinds of security constraints: because the load weights of high priority are higher, so can preferentially obtain service restoration; Simultaneously, owing to the low load of priority is also included within the target function, so also embodied the purpose that allows load restoration as much as possible power.Wherein, n is the maximum numbering of node among the figure.Variable x _vWhether the node v in the presentation graphs is selected in the optimum isolated island scheme: if node v is selected, and x then _v=1; Otherwise, x then _v=0.V is the set of node among the figure, and g is DG node among the figure; S is node set in the isolated island scheme; In the formula (1) 1 _{I, j}Branch road for connected node i and j in the system; L _LThe set of fingers in the system, L _L={ 1 _{I, j}| i, j=1,2 ... n}; P ^Gen, Q ^Gen, P ^LoadAnd Q ^LoadMeritorious, the reactive power set of generator and the load of node connection.U, T and C are respectively the node voltage amplitudes, adjustable transformer and the set of capacitor group.Constraint 3 retrains for being communicated with, wherein, and L _{V, G}Aisled set between expression node v and the node G, l _{V, G}Be arbitrary set of fingers that path is included between node v and the node G; U _i,

U _i Be respectively voltage magnitude and the bound of node i.

Be respectively transmission power value and the bound thereof of branch road (circuit and transformer), wherein

Be respectively that distributed power generation output is meritorious, reactive power and the active power upper limit thereof, reactive power bound; δ _IjBe the phase angle difference between node i and the j.

The load that is respectively node i is meritorious, reactive power and meritorious, the reactive power upper limit, and

It is meritorious and idle that value equals respectively to implement the load of isolated island division during the moment.T _i,

T _iBe respectively application of adjustable tap and the bound thereof of i platform transformer.C _i,

Be respectively i capacitor group number and the adjustable upper limit thereof.First constraint explanation DG node is selected in the optimum isolated island scheme; The 3rd constraint representation, for arbitrary node v, if v is selected in the final isolated island, then v must be connected with the DG node, and all nodes on a certain chain between v and the G are all with selected.

Formula (1) is extensive 0-1 nature of nonlinear integral programming problem, and the solving complexity of problems is higher, and this also is the immediate cause that existing similar document all adopts " search+adjust " thinking.Here " search+adjust " refers to form the as far as possible little initial isolated island of power difference according to search strategy, then takes reasonably adjusting measure to realize the reasonable operation of isolated island.

It is as follows to make up after the fault graph model G of dead electricity zone distribution system: to flow out node power for just.The demand d of each node v among the figure _vBe the injecting power of corresponding node v in the distribution, if v is tie point (being not load of v node), then d _vEqual 0.The weights c of each node v among the figure _vBe set to c _v=W _vd _v, for load bus, W _vBe the load weight of node v, the priority of load is higher, its W _vLarger; For DG node and connected node, W _v=0, corresponding c _v=0.Following given first is as shown in the formula the Mathematical Modeling of the optimum subtree problem shown in (2).

$\left\{\begin{array}{c}\mathrm{Max}\underset{v=0}{\overset{n}{\mathrm{\Σ}}}{c}_v{x}_v\\ s.t.\underset{v\∈S\backslash g}{\mathrm{\Σ}}{d}_v\≤\left|d_g\right|\\ x_g=1\\ x_v=\left\{\mathrm{0,1}\right\},v\∈V\backslash g\\ x_i\≥x_v,i\∈l_{v,g},\∀v\∈V\backslash g,\∃l_{v,g}\∈L_{v,g}\end{array}\right.---\left(2\right)$

In the following formula (2) in each variable and the formula (1) implication to dependent variable identical.

Can obtain containing distributed power generation distribution system isolated island by solution formula (2) and consist of scheme, can obtain by the Optimal Power Flow control problem of finding the solution isolated island in the case the optimal adjustment scheme of isolated island.If g=v ₀, optimum subtree problem is above-mentioned figure knapsack problem shown in the formula (2).Fig. 1 is the algorithm flow chart that the figure knapsack problem is found the solution, and as shown in the figure, this method comprises 9 steps altogether:

Make V ₀=V (v ₀), G '=G, order expansion subgraph E=v ₀Wherein, node set in V (*) presentation graphs;

Make G '=G ' v ₀If e _jFor among the G ' with the limit of E adjacency, j=1,2 ... k, k are total with the E adjacent side among the G '.Make a _j=V (e _j| (E ∩ e _j)), j=1,2 ... k.Be a _jFor among the G ' with the E adjacent node;

With e _j(initial j=1) expands the expansion subgraph for the expansion limit, as shown in Figure 2, makes N _j=N (E ∪ e _j);

Structure is with N _jIn node be alternative node, H-d (e _j∪ E) as the knapsack problem of constraint of demand, forwards next step to; As shown in Figure 1, if with a _jBe the expansion limit to the circuit between the initial subgraph E, node 1～8 is alternative node among the figure;

The optimal solution that solves this knapsack problem is S _p, then make M _j=e _j∪ E ∪ S _p, p _j=w (M _j);

Judge whether j＜k, if so, then j=j+1 turns back to Step3; Otherwise, then enter Step7;

Have

Wherein max is

Numbering j when getting maximum makes V _n=V (M _Max) (initial n=1), E=E ∪ e _Max

Judge whether d (V _n) 〉=H if so, then forwards Step9 to, otherwise, n=n+1 is then arranged, forward Step2 to;

Select set { V _n| n=0,1,2,3 ... in satisfy d (V _nThe weights of)≤H and the maximum are as optimal solution, and the node in the optimal solution set consists of optimum subgraph.

Finish.

Fig. 2 is the expander graphs of adjacent side.

The technical scheme that the present invention intends adopting is as follows:

The knapsack problem (Graph Constrained Knapsack Problem, GCKP) that contains constraint diagram can be considered as considering to exist between the alternate item the more general 0-1 knapsack problem of form of incidence relation.

As shown in Figure 2, construct a some weighting connected undirected graph G (V, E, w, d), each node v has two parameters among the G: the node weight w _vWith node demand d _vFor such some weighted graph, what contain the research of constraint diagram knapsack problem is how to find in the drawings to comprise an initial subgraph E ₀Node demand and satisfy the demands restriction and node weights and maximum subgraph, require simultaneously at least one associated nodes (may there be a plurality of associated nodes in it) of each selected node also selected.This problem can be expressed as following linear integer optimization problem:

$\left\{\begin{array}{c}\mathrm{Max}\underset{v=V}{\mathrm{\Σ}}{w}_v{x}_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}{d}_v{x}_v\≤H\\ x_g\≥x_v,\∀v\∈V,\∃g\∈F_v\\ x_{\∈}\left\{\mathrm{0,1}\right\},\∀v\∈V\backslash E_0\\ x_v=1,\∀v\∈E_0\end{array}\right.---\left(3\right)$

In formula (3), x _vBe the node state variable, if v is chosen optimal solution set, x _v=1; Otherwise, x _v=0.F _vFor with the set of node v associated nodes.H is node demand and restriction.

It is as follows that the present invention's definition is used for containing the figure knapsack problem (Graph KnapsackProblem, GKP) of getting in touch with the division of distribution isolated island: construct a some weighting connected undirected graph G (V, E, w, d), each node v has two parameters among the G: the node weight w _vWith node demand d _vFor such some weighted graph, the research of figure knapsack problem be how to find in the drawings to comprise a given node V ₀, node demand and satisfy the demands restriction and node weights and maximum connected subgraph.This problem can be expressed as following linear integer optimization problem:

$\left\{\begin{array}{c}\mathrm{Max}\underset{v=V}{\mathrm{\Σ}}{w}_v{x}_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}{d}_v{x}_v\≤H\\ x_v=1,v=v_0\\ x_{\∈}\left\{\mathrm{0,1}\right\},\∀v\∈V\backslash v_0\\ x_i\≥x_v,i\∈l_{v,v_0},\∀v\∈V\backslash v_0,\∃l_{v,v_0}\∈L_{v,v_0}\end{array}\right.---\left(4\right)$

In the following formula (4), Node v and node v among the presentation graphs G ₀Between the set of node on all chains, Be node v and node v among the figure G ₀Between node set on arbitrary chain.

The optimum subgraph problem that contains in the division of distributed power generation distribution system isolated island as shown in Equation (2) is a figure knapsack problem, with reference to [document 1G Bo rradaile, B Heeringa, and G Wilfong.Theknapsack problem with neighbour constraints, Journal of DiscreteAlgorithms, 2012,16:224-235], what the present invention proposed the described consideration interconnection switch of a greedy approximate optimum algorithm solution formula (2) contains the optimum subgraph problem of distributed power generation distribution system isolated island in dividing.This algorithm is by obtaining the approximate optimal solution of optimum subgraph problem to the continuous expansion of initial subgraph, idiographic flow is as follows:

1) makes up the graph model in dead electricity zone after the major network fault: to flow out node power for just.The demand d of each node v among the figure _vBe the injecting power of corresponding node v in the distribution, if v is tie point (being not load of v node), then d _vEqual 0.The weights c of each node v among the figure _vBe set to c _v=W _vd _v, for load bus, W _vBe the load weight of node v, the priority of load is higher, its W _vLarger; For DG node and connected node, W _v=0, corresponding c _v=0.

2) make that the distributed electrical source node is v ₀

3) make V ₀=V (v ₀), G '=G, order expansion subgraph E=v ₀Wherein, node set in V (*) presentation graphs.

4) make G '=G ' v ₀If e _jFor among the G ' with the limit of E adjacency, j=1,2 ... k, k are total with the E adjacent side among the G '.Make a _j=V (e _j| (E ∩ e _j)), j=1,2 ... k.Be a _jFor among the G ' with the E adjacent node.

5) with e _j(initial j=1) expands the expansion subgraph for the expansion limit, makes N _j=N (E ∪ e _j).

6) structure is with N _jIn node be alternative node, H-d (e _j∪ E) as the knapsack problem of constraint of demand, forwards step 5) to.As shown in Figure 1, if with a _jBe the expansion limit to the circuit between the initial subgraph E, node 1～8 is alternative node among the figure.

7) optimal solution that solves this knapsack problem is S _p, then make M _j=e _j∪ E ∪ S _p, p _j=w (M _j).Forward step 6) to.

8) if j＜k, j=j+1 turns back to step 3); Otherwise, Wherein max is

Numbering j when getting maximum makes V _n=V (M _Max) (initial n=1), E=E ∪ e _Max

9) if d is (V _n) 〉=H forwards step 8) to, otherwise n=n+1 forwards step 2 to).

10) select set { V _n| n=0,1,2,3 ... in satisfy d (V _nThe weights of)≤H and the maximum are as optimal solution, and the node in the optimal solution set consists of optimum subgraph.

At method step 5) knapsack problem can find the solution by dynamic programming algorithm or the branch-bound algorithm of pseudo-polynomial time O (nH).Finding the solution of knapsack problem also is to affect this method principal element of computing time, and therefore, the Time Calculation complexity that the present invention puies forward power distribution network isolated island division methods is O (nH), meets the engineering calculation requirement.

The above only is preferred embodiment of the present invention, not in order to limiting the present invention, all any modifications of doing within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.

Claims (5)

1. One kind be used for to consider interconnection switch contain distributed power generation distribution isolated island division methods, it is characterized in that described may further comprise the steps:

   The distribution system major network breaks down, partly contain distributed power generation zone dead electricity after the Fault Isolation in the system, the power supply that the islanded system of formation take distributed power generation as power supply in time recovers the important load power supply and recover simultaneously many as far as possible loads, based on the distribution system graph model, obtain containing DG distribution system isolated island and divide new model:

   $\left\{\begin{array}{c}\underset{{X,P}^{\mathrm{Gem}},Q^{\mathrm{Gen}},P^{\mathrm{Load}},Q^{\mathrm{Load}},U,T,C}{\mathrm{Max}}{c}_{\mathrm{sum}}=\underset{v=0}{\overset{n}{\mathrm{\Σ}}}{c}_v{x}_v\\ s.t.\\ 1.x_g=1\\ 2.x_v=\left\{\mathrm{0,1}\right\},v\∈V\backslash g\\ 3.x_i\≥x_v,i\∈l_{v,g},\∀v\∈V\backslash g,{\∃l}_{v,g}\∈L_{v,g}\\ 4.{\mathrm{\ΔP}}_i=\underset{j\∈S}{\mathrm{\Σ}}{U}_i{U}_j(G_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}+B_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}),i\∈S\\ 5.{\mathrm{\ΔQ}}_i=\underset{j\∈S}{\mathrm{\Σ}}{U}_i{U}_j(G_{\mathrm{ij}}\sin {\mathrm{\δ}}_{\mathrm{ij}}-B_{\mathrm{ij}}\cos {\mathrm{\δ}}_{\mathrm{ij}}),i\∈S\\ 6.{\underset{\‾}{U}}_i\≤U_i\≤{\stackrel{\‾}{U}}_i,i=\mathrm{1,2},...,n\\ 7.{\underset{\‾}{T}}_i\≤T_i\≤{\stackrel{\‾}{T}}_i,T_i\∈T\\ 8.0\≤C_i\≤{\stackrel{\‾}{C}}_i,C_i\∈C\\ 9.{\underset{\‾}{P}}_{l_{i,j}}\≤P_{l_{i,j}}\≤{\stackrel{\‾}{P}}_{l_{i,j}},l_{i,j}\∈L_L\\ 10.0\≤P_g^{\mathrm{Gen}}\≤{\stackrel{\‾}{P}}_g^{\mathrm{Gen}}\\ 11.{\underset{\‾}{Q}}_g^{\mathrm{Gen}}\≤G_g^{\mathrm{Gen}}\≤{\stackrel{\‾}{Q}}_g^{\mathrm{Gen}}\\ 12.0\≤P_i^{\mathrm{Load}}\≤{\stackrel{\‾}{P}}_i^{\mathrm{Load}},i=\mathrm{0,1,2},...,n\\ 13.0\≤Q_i^{\mathrm{Load}}\≤{\stackrel{\‾}{Q}}_i^{\mathrm{Load}},i=\mathrm{0,1,2},...,n\end{array}\right.---\left(1\right)$

   Make up the afterwards graph model G of dead electricity zone distribution system of fault:

   $\left\{\begin{array}{c}\mathrm{Max}\underset{v=0}{\overset{n}{\mathrm{\Σ}}}{c}_v{x}_v\\ s.t.\underset{v\∈S\backslash g}{\mathrm{\Σ}}{d}_v\≤\left|d_g\right|\\ x_g=1\\ x_v=\left\{\mathrm{0,1}\right\},v\∈V\backslash g\\ x_i\≥x_v,i\∈l_{v,g},\∀v\∈V\backslash g,\∃l_{v,g}\∈L_{v,g}\end{array}\right.---\left(2\right)$

   In the following formula (2) in each variable and the formula (1) implication to dependent variable identical.
2. 2. as claimed in claim 1ly contain distributed power generation distribution isolated island division methods for what consider interconnection switch, it is characterized in that, make up the graph model G that contains the distributed power generation distribution system, to flow out node power for just; The demand d of each node v _vBe the injecting power of corresponding node v in the distribution, if v is tie point, namely the v node is not loaded, then d _vEqual 0; The weights c of each node v _vBe set to c _v=W _vd _v, for load bus, W _vBe the load weight of node v, the priority of load is higher, its W _vLarger; For DG node and connected node, W _v=0, corresponding c _v=0; Make that the distributed electrical source node is v ₀, make V ₀=V (v ₀), G '=G, order expansion subgraph E=v ₀, wherein, node set in V (*) the expression subgraph; Make G '=G ' v ₀, establish e _jFor among the G ' with the limit of E adjacency, j=1,2 ... k, k are total with the E adjacent side among the G ';

   Make a _j=V (e _j(E ∩ e _j)), j=1,2 ... k, i.e. a _jFor among the G ' with the E adjacent node; With e _jFor the expansion limit expansion subgraph is expanded, made N _j=N (E ∪ e _j), wherein, N (*) expression subgraph all of its neighbor node set;

   Structure is with N _jIn node be alternative node, H-d (e _j∪ E) as the knapsack problem of constraint of demand, forward next step to, wherein, in d (*) the expression subgraph node demand and; If with a _jBe the expansion limit to the circuit between the initial subgraph E, node 1～8 is alternative node in the accompanying drawing 2;

   The optimal solution that solves this knapsack problem is S _p, then make M _j=e _j∪ E ∪ S _p, p _j=w (M _j), wherein, in w (*) the expression subgraph node weights and;

   Judge whether j＜k;

   Have

   

   Wherein max is

   

   Numbering j when getting maximum makes V _n=V (M _Max) (initial n=1), E=E ∪ e _Max

   Judge whether d (V _n) 〉=H;

   Select set { V _n| n=0,1,2,3 ... in satisfy d (V _nThe weights of)≤H and the maximum are as optimal solution, and the node in the optimal solution set consists of optimum isolated island.
3. 3. as claimed in claim 1ly contain distributed power generation distribution isolated island division methods for what consider interconnection switch, it is characterized in that described optimal solution S _pCan find the solution by dynamic programming algorithm or the branch-bound algorithm of pseudo-polynomial time O (nH).
4. 4. as claimed in claim 1ly contain distributed power generation distribution isolated island division methods for what consider interconnection switch, it is characterized in that, construct the some weighting connected undirected graph G (V that an expression contains the distributed power generation distribution system, E, w, d), each node v has two parameters among the G: the node weight w _vWith node demand d _vFor such some weighted graph, take power-balance as constraint, change a figure knapsack problem take the Income Maximum that restores electricity into as the isolated island partition problem that contains in the contact Distribution Network Failure recovery process of target, can use for reference the thinking of finding the solution that contains the constraint diagram knapsack problem and find the solution.What contain the research of constraint diagram knapsack problem is how to find in the drawings one to comprise the node demand of initial subgraph E0 and satisfy the demands restriction and node weights and maximum subgraph, requires simultaneously at least one associated nodes of each selected node also selected; This problem can be expressed as following linear integer optimization problem:

   $\left\{\begin{array}{c}\mathrm{Max}\underset{v=V}{\mathrm{\Σ}}{w}_v{x}_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}{d}_v{x}_v\≤H\\ x_g\≥x_v,\∀v\∈V,\∃g\∈F_v\\ x_{\∈}\left\{\mathrm{0,1}\right\},\∀v\∈V\backslash E_0\\ x_v=1,\∀v\∈E_0\end{array}\right.$

   In formula, x _vBe the node state variable, if v is chosen optimal solution set, x _v=1; Otherwise, x _v=0.F _vFor with the set of node v associated nodes.H is node demand and restriction.
5. 5. as claimed in claim 1ly contain distributed power generation distribution isolated island division methods for what consider interconnection switch, it is characterized in that, take out take power-balance as constraint, contain mathematical problem---figure knapsack problem (the Graph Knapsack Problem of contact distribution isolated island in dividing take the Income Maximum that restores electricity as target, GKP) as follows: as to construct the some weighting connected undirected graph G (V that an expression contains the distributed power generation distribution system, E, w, d), each node v has two parameters among the G: the node weight w _vWith node demand d _vFor such some weighted graph, take power-balance as constraint, divide can be described as and find how in the drawings to comprise a given node V as the contact distribution isolated island that contains of target take the Income Maximum that restores electricity ₀, node demand and satisfy the demands restriction and node weights and maximum connected subgraph are referred to as the figure knapsack problem; This figure knapsack problem can be expressed as following linear integer optimization problem:

   $\left\{\begin{array}{c}\mathrm{Max}\underset{v=V}{\mathrm{\Σ}}{w}_v{x}_v\\ s.t.\underset{v\∈V}{\mathrm{\Σ}}{d}_v{x}_v\≤H\\ x_v=1,v=v_0\\ x_{\∈}\left\{\mathrm{0,1}\right\},\∀v\∈V\backslash v_0\\ x_i\≥x_v,i\∈l_{v,v_0},\∀v\∈V\backslash v_0,\∃l_{v,v_0}\∈L_{v,v_0}\end{array}\right.$

   In the following formula formula,

   

   Node v and node v among the presentation graphs G ₀Between the set of node on all chains,

   

   Be node v and node v among the figure G ₀Between node set on arbitrary chain.