CN104810853B - Digraph-based islanding method of distribution network including distributed generations - Google Patents

Abstract

The invention discloses a digraph-based islanding method of distribution network including distributed generations. Virtual nodes and virtual demands are introduced to establish a distribution network digraph model with variable branch directions, and inner connectivity and radial structure of an island operation area is guaranteed. The problem that failure to independently power the island area due to unstable output of the distributed generations is solved; also solved is the major problem that islanding failure is caused due to connecting switch operability, load importance, load controllability and the like in the distribution network; an islanding scheme is of higher engineering practicality and is higher in operability.

Description

Based on digraph power distribution network containing distributed power generation isolated island division methods

Technical field

The invention belongs to power network schedule automation field, it is related to a kind of lonely based on digraph power distribution network containing distributed power generation Island division methods.

Background technology

Realize controlled isolated island to divide is to improve power supply reliability, it is to avoid the important measures of electrical network total collapse.To power distribution network For, when departing from higher level's electrical network because of failure cause, distribution region will face the risk of dead electricity.Distributed power generation (send out by photovoltaic Electricity, wind-powered electricity generation) due to directly coupling with power distribution network, after with higher level's grid disconnection, sub-load be can achieve by isolated island mode Restore electricity, be that the sufficient time is reserved in trouble hunting, caused load loss problem during energy effectively solving fault.

Current isolated island division methods mainly turn to target with load restoration total amount maximum, take into account important load amount of recovery Etc. factor；The division methods being adopted based on describe isolated island internal power balance, islet operation when network structure, because of target The difference of function and constraints and there is some difference；The method of solving model with heuristic search algorithm and intelligent algorithm is Main.The heuristic being adopted is because it is linear, the solution flow process of open loop and globally optimal solution cannot be obtained, and intelligent algorithm The uncertainty of result is led to due to randomness and the uncertainty of its solution procedure.

Existing power distribution network isolated island division methods do not fully take into account distributed power source and have the unstable spy that exerts oneself Property, ignore the closed loop design of power distribution network, the design feature of open loop operation, the key factor that impact isolated island is divided, such as load The concern such as important level, load controllability not, leads to the isolated island scheme dividing to lack operability in engineering.

Content of the invention

Present invention aims to the deficiencies in the prior art, provide and a kind of joined containing distributed power generation based on digraph Electrical network isolated island division methods.

The purpose of the present invention is achieved through the following technical solutions: a kind of is joined containing distributed power generation based on digraph Electrical network isolated island division methods, comprise the following steps:

(1) set up the simplified model of distribution networks based on node-branch road: the actual usual complex structure of distribution system, distribution Net number of devices is huge, for simplifying islanding problem description and amount of calculation, needs Distribution Network Equipment model is simplified.The present invention Bus is regarded as node, the connection equipment such as transformer between bus, circuit regards branch road as, and concrete simplification principle is as follows:

A. bus nodes: the switchyard bus in power distribution network, transformer station's 10kv bus are all reduced to bus nodes；Bus Node is divided into load bus and generating node；

B. branch road: cable branch road, overhead transmission line are treated as branch road, any bar branch road all can disconnect and closure, branch road divides For contact branch road and non-contact branch road, get in touch with the branch road that branch road refers to possess interconnection switch function.

(2) increase dummy node and virtual demand, build the electricity distribution network model based on rooted tree, specifically include following sub-step Rapid:

(2.1) simplified model of distribution networks is traveled through, bus nodes are considered as branch node or leaf node, branch road regards Side for connecting node；, as dg node, the bus nodes only carrying load, will used as load bus for the bus nodes accessing dg Power distribution network is described as with bus as node, and supply line is tree t (v, e) on side, and wherein v={ v1 ..., vn } is node set, e Set for side；

(2.2) increase dummy node and virtual demand, all of node is set up with virtual demand, increase to every branch road Directionality description and the description of folding condition, form the electricity distribution network model t'(v+v based on rooted tree₀,e∪e',s^d,s^r), wherein E' is virtual tributary set, s^dFor branch road forward direction side state set, s^rFor branch road reverse edge state set.

Described dummy node has the feature that

A. this node be one virtual independent of power distribution network node outside node, only pass through the virtual tributary that can cut-off with In power distribution network, each dg node is connected；Described virtual tributary refer to virtual independent of the branch road outside power distribution network, only with dg Node is connected with dummy node；

B. dummy node does not consume, sends or transfers power, the virtual tributary being connected with dg node not through-put power；

The virtual demand of node has the feature that

A., during power distribution network islet operation, each in the range of isolated island carries electrical nodes, including dg node, all has 1 unit Virtual demand；

B. only provide virtual supply by dummy node；

C. the transmission path of virtual demand is by powering branch road and virtual tributary forms；

The introducing of dummy node and virtual demand only increases the demand properties of powered node virtual, and virtual tributary is only Transfer of virtual demand, does not change the tree-like operating structure of system and running status.

When considering that interconnection switch is operable to describe distribution system normal run or islet operation in the case of radial Operating structure, introduces the related notion of digraph.Digraph has in-degree (in-degree) and out-degree (out-degree) two Attribute, uses λ respectivelyⁱⁿ(v_i)、λ^out(v_i) represent.Rooted tree (rooted tree), as the special case of digraph, can describe and join The open loop operation structure of electrical network, but when interconnection switch comes into operation it may appear that node in-degree is unsatisfactory for the feelings of rooted tree property Condition, at this moment just may need to disconnect other branch roads to ensure radial operating structure.Because rooted tree is difficult to describe branch road direction With the change of membership, the directionality description to every branch road and folding shape can be increased on the basis of digraph concept The description of state.

(3) to load, exert oneself and limit is configured, set up power distribution network electrical constraints: electrical constraints are power distribution network isolated islands Condition necessary to operation, electrical constraints at least include power balance constraint and the constraint of line transmission limit；Power balance will be expired Sufficient trend constraint, units limits, load controllability constrain three conditions, and mathematical expression is as follows:

(3.1) trend constraint

$x_i\·(p_{dgi}-p_{li})=\underset{j\&element;v_i}{\σ}{p}_{ij}---\left(1\right)$

In formula (1), x_iFor 0-1 variable, represent the electriferous state of node i, 0 expression dead electricity, 1 represents powered；p_dgiFor node The distributed power generation of i is active to exert oneself, p_liRepresent burden with power access amount in node i；j∈v_iRepresent that be connected with node i is owned Node；p_ijComputing formula such as formula (2)

p_ij=s_ij(δ_i-δ_j)/x_ij(2)

In formula (2): p_ij、x_ijFor branch road e_ijOn the active power that flows through and branch road reactance；δ_iPhase angle for node i；δ_jFor The phase angle of node j；

(3.2) load controllability constraint

With the development of load management and DSM, load controllable levels and control device are improved, Therefore load controllability is also by the key factor needing when isolated island divides to consider, that is,

${\underset{\&overbar;}{p}}_{li}\≤p_{li}\≤{\stackrel{\&overbar;}{p}}_{li}---\left(3\right)$

In formula:p _li、It is respectively the bound of the regulating power of connect load in node i；For uncontrollable load, its Bound is equal；

(3.3) dg units limits

${\underset{\&overbar;}{p}}_{dgi}\≤p_{dgi}\≤{\stackrel{\&overbar;}{p}}_{dgi}---\left(4\right)$

In formula:p _dgi、It is respectively the active bound of exerting oneself of dg of i-th node；Similar blower fan, photovoltaic etc. are easily subject to weather Impact, it is impossible to provide the dg continually and steadily exerting oneself it is impossible to be individually for isolated island block supply, needs and has continual and steady capacity The dg synthetic operation of (i.e. fm capacity)；Processing method is to remove virtual being connected between dummy node and unstable type dg Road.

(3.4) line transmission limit constraint

$-{\stackrel{\&overbar;}{p}}_{ij}\≤p_{ij}\≤{\stackrel{\&overbar;}{p}}_{ij}---\left(5\right)$

In formula:For branch road e_ijActive power transfer limit；

(4) set up power distribution network graphic constraint: in order to ensure effective division of power distribution network isolated island, meeting power distribution network electrically about In addition it is also necessary to set up graphic constraint on the basis of bundle.Described graphic constraint includes connectivity constraint, radial structure constraint, root knot Point structure and consistency constraint, mathematic(al) representation is as follows:

(4.1) connectivity constraint

$-x_i{f}_{li}=\underset{j\&element;v_i}{\σ}{s}_{ij}{f}_{ij},i\&notequal;0---\left(6\right)$

-n≤f_ij≤n (7)

In formula: f_liFor the virtual demand of the i-th node, if the virtual demand of each node is 1 unit；f_ijFor branch road e_ij The virtual demand of upper transmission；N is regional nodes number to be divided；s_ijFor represent branch road folding condition variable, wherein i < j, 0 Represent and disconnect, 1 represents closure；

(4.2) radial structure constraint

On the premise of ensureing islet operation area radiation shape structure, interconnection switch is carried out with operation can be neatly to institute Expect that the node restoring electricity is selected, to recover more important loads.Need to meet following constraints for this:

$\underset{i\&element;v_k}{\&sigma;}{s}_{ik}^d+\underset{j\&element;v_k}{\&sigma;}{s}_{jk}^r\&le;1---\left(8\right)$

$\underset{i\&element;v_k}{\&sigma;}{s}_{ik}^d+\underset{j\&element;v_k}{\&sigma;}{s}_{jk}^r\&greaterequal;x_k,k\&notequal;0---\left(9\right)$

$s_{ij}=s_{ij}^d+s_{ji}^r\&le;1---\left(10\right)$

Formula (9) represents in addition to root node (dummy node), and the in-degree of remaining node is more than or equal to the electriferous state of this node Value；Represent node i to the selected state in node j forward direction side,Represent node j to the selected state of reverse edge of node i, 0 represents not It is chosen, 1 represents selected；

(4.3) root node constraint

$\underset{j\&element;v_0}{\&sigma;}{s}_{0j}^d\&greaterequal;1---\left(11\right)$

$\&forall;s_{j0}^r=0,j\&element;v_0---\left(12\right)$

In formula:Represent the selected state on the positive side of the branch road that is connected with root node；Represent the branch road that is connected with root node Reverse edge selected state；

(4.4) branch road-node state consistency constraint

s_ij-1≤x_i-x_j≤1-s_ij(13)

Formula (13) represents the relevance between branch road folding condition and the electriferous state of two nodes being connected；

(5) set up the Mathematical Modeling expression with total system optimal solution as target；Described Mathematical Modeling expression is set up following On the basis of hypothesis:

A. study to as if need the distribution web area that external electrical network powers, i.e. intra-zone in the case of being incorporated into the power networks Dg exerts oneself less than load total amount；

B. the distribution web area internal memory being optimized division is needed to have the dg of fm capacity；

C. the controllable burden being divided in region has the ability continuously adjusting；

Set up power distribution network electrically and on the basis of graphic constraint, when carrying out the division of power distribution network isolated island, should preferentially recover weight Want load to power, and so that load restoration total amount is maximized as much as possible, define initial target function for this:

$\max .\underset{i\&element;v}{\&sigma;}{x}_i\&centerdot;w_i\&centerdot;p_{li}---\left(14\right)$

In formula: w_iRepresent the weight of connect load in node i, be divided into a type load, two classes to bear load by significance level Lotus and three type loads；p_liRepresent burden with power access amount in node i；Propose isolated island division methods contain integer variable, two Secondary object function and quadratic constraints, are mixed integer nonlinear programming problems (minlp), have certain solution difficulty. Model will be converted below, constraints will be relaxed, thus problem is changed into a MILP Problem (milp) is in order to solve.

Because being quadric form on the right side of formula (2), it is unfavorable for solving, so needing formula (2) to be carried out drop time process.Consider When branch road between node i and node j disconnects, δ_iAnd δ_jBetween no longer may have correlation, therefore can be by formula (2) and formula (5) Change into following form:

(s_ij-1)m≤p_ij-(δ_i-δ_j)/x_ij≤(1-s_ij)m (15)

$-s_{ij}{\stackrel{\&overbar;}{p}}_{ij}\&le;p_{ij}\&le;s_{ij}{\stackrel{\&overbar;}{p}}_{ij}---\left(16\right)$

In formula: m is a sufficiently large positive number, takes m=2/x_ij；As branch road e_ijDuring disconnection, s_ij=0, formula (15) be Formula form, formula (16) is of equal value with formula (2)；As branch road e_ijDuring closure, s_ij=1, formula (15) is of equal value with formula (2).

Formula (2)～formula (4) is changed into following form respectively:

$p_{dgi}-p_{li}=\underset{j\&element;v_i}{\&sigma;}{p}_{ij}---\left(17\right)$

$x_i{\underset{\&overbar;}{p}}_{li}\&le;p_{li}\&le;x_i{\stackrel{\&overbar;}{p}}_{li}---\left(18\right)$

$x_i{\underset{\&overbar;}{p}}_{dgi}\&le;p_{dgi}\&le;x_i{\stackrel{\&overbar;}{p}}_{dgi}---\left(19\right)$

When node is in power failure state, x_i=0, p_li=0, that is, the connect load of node i is removed；When node be in powered During state, x_i=1, therefore formula (18) is of equal value with formula (3)；Formula (19) can obtain in the same manner.

Formula (6)～formula (7) is changed into following form:

$-f_{li}=\underset{j\&element;v_i}{\&sigma;}{f}_{ij},i\&notequal;0---\left(20\right)$

x_i·1≤f_li≤x_i1, i ≠ 0 (21)

-s_ijn≤f_ij≤s_ijn (22)

Object function changes into the most at last:

$max.\underset{i\&element;v}{\&sigma;}{w}_i\&centerdot;p_{li}---\left(23\right)$

(6) after founding mathematical models, solved by cplex, obtained believable isolated island splitting scheme.

After above-mentioned model conversation, control variables is branch road forward and reverse side stateDg exerts oneself p_dgiNegative with controlled Lotus access amount p_li.This is a typical Mixed integer linear programming, such that it is able to effectively be solved using cplex, Obtain believable isolated island splitting scheme.

The invention has the beneficial effects as follows: the present invention propose a kind of based on digraph power distribution network containing distributed power generation isolated island Division methods, by introducing dummy node and virtual demand, establish the power distribution network Directed Graph Model of branch road direction-agile it is ensured that Connectedness in islet operation region and radial structure.Not only solve because distributed power source is exerted oneself unstable and leads to The problem of isolated island block supply cannot be stood alone as, and solve in power distribution network because interconnection switch operability, load are important etc. Level, load controllability etc. lead to isolated island to divide the significant problem losing efficacy, the isolated island scheme of division closing to reality in engineering, more There is operability.

Brief description

Fig. 1 is the flow chart of the present invention；

Fig. 2 is the distribution net work structure illustraton of model adding dummy node；

Fig. 3 is virtual demand transmission path figure during islet operation；

Fig. 4 is that there is interconnection switch figure in isolated island region；

There is interconnection switch figure in Fig. 5 isolated island between region；

Fig. 6 contains the 69 Node power distribution system figures of dg；

Fig. 7 does not consider the isolated island splitting scheme figure of interconnection switch and dg type；

The isolated island splitting scheme that Fig. 8 is drawn based on branch and bound method；

Fig. 9 considers the isolated island splitting scheme figure of interconnection switch；

Figure 10 considers the isolated island splitting scheme of interconnection switch and dg type；

Figure 11 several isolated island division methods compare.

Specific embodiment

With specific embodiment, the present invention is described in further detail below in conjunction with the accompanying drawings.

The flow chart based on digraph power distribution network containing distributed power generation isolated island division methods for the present invention is as shown in Figure 1.? When setting up the simplification electricity distribution network model based on bus-branch road, there are different embodiments.For actual distribution line, can root According to power connection ground row preferred process.For single loop or double loop switchyard, all switchyard can be treated as load section Point processed, linked up by branch road between switchyard, if certain switchyard has normal off point, we this switchyard with another The branch road of side is processed as interconnection switch.

For the more complicated mode of connection, such as " three pairs " wiring is it is believed that each switchyard is all connected to other Interconnection switch 4-8 in " interconnection switch " of node, such as Fig. 5 is similar to " three pairs " wiring.

For the 10kv bus in transformer station (such as 110kv, 35kv), each section of bus can be regarded as a bus section Point.

When building digraph structure, preferable following examples:

Dummy node numbering can be set to 0, uses v₀Represent (as Fig. 2).

Power distribution network can be increased with the attribute extension of branch road direction and membership: 1) every branch road (includes interconnection switch And virtual tributary) be made up of positive and negative two directed edges, available when network structure changes.Definition is little by numbering It is positive side that node points to the big node of numbering, otherwise is reverse edge.Use 0-1 variable respectivelyRepresent forward and reverse The selected state on side, 0 represents not selected, and 1 represents selected.For ensureing the radial structure of connected graph, arbitrary branch road can only Select a directed edge or select to disconnect, that is,

2) give the 0-1 variable s that every branch road characterizes branch road folding condition_ij(i < j), 0 represents disconnection, and 1 represents closure.Cause This, can obtain

3), after introducing dummy node and the concept of virtual demand, any band electrical nodes must be connected with dummy node；Here On the basis of, give the property of Directed Graph Model rooted tree, dummy node is set to root, and sets λⁱⁿ(v₀)=0, λ^out(v₀)≥1.

The forest that the isolated island scheme that power distribution network isolated island obtains after dividing is made up of one or more isolated island regions (forest).After introducing virtual demand, dummy node and the virtual tributary being connected with each dg node, due to power supply branch road Equally carry the function of transfer of virtual demand, in order to ensure the transmission path of virtual demand, powered in single isolated island region Node all will be interconnected；And dummy node, as uniquely virtual feed point, also same with some isolated island regions will be in one In connected graph, as shown in Figure 3.With it, powered Connectivity is guaranteed in islet operation region.

Improved by above, you can obtain the electricity distribution network model t'(v+v based on digraph₀,e∪e',s^d,s^r), wherein e' For virtual tributary set, s^dFor branch road forward direction side state set, s^rFor branch road reverse edge state set.

As shown in Figure 4 and Figure 5, Fig. 4 and Fig. 5 illustrates power distribution network isolated island and divides the typical network structure of latter two.In Fig. 4 There are two isolated island regions, in isolated island region 2, be equiped with interconnection switch, if but interconnection switch disconnect it will thus be seen that interconnection switch 6-7 closes, no matter interconnection switch selects positive side or reverse edge, then being unsatisfactory for remaining node in-degree except root node in addition to is 1 want Ask；If now disconnecting virtual tributary e'₀₂, make three branch road e in isolated island₅₆、e₅₇, the branch road direction head and the tail phase of interconnection switch 6-7 Connect, then can meet the property that remaining node in-degree in addition to root node is 1, but cut off the transmission path of virtual demand it is impossible to expire Virtual demand with electrical nodes in this isolated island region of foot.Rational branch road direction is as shown in Figure 4.

As can be seen from Figure 5: from the perspective of the radial operating structure of collateral security, interconnection switch 4-8 and virtual tributary e ′₀₁、e′₀₂Folding condition there is complementary relationship, that is, closure interconnection switch then need to disconnect a virtual tributary, vice versa.By Need through-put power in interconnection switch, and virtual tributary only transfer of virtual demand, and isolated island partition problem is to recover as many as possible Load be target, so inevitable choice disconnect a virtual tributary.

Understand, the simplified model of distribution networks based on digraph can be effectively ensured in islet operation region from model structure Connectedness and radial structure.

For specific electricity distribution network model, it is possible to use ampl platform is modeled, cplex algorithm bag is then called to solve This model.

If with U.S. pg＆e 69 Node power distribution system as embodiment, the validity that checking isolated island divides.In order to have The isolated island that effect simulation accesses after dg divides, and accesses 6 dg, as shown in Figure 6 in this distribution system；

Dg average output power and dg type are as shown in table 1；In this system, dg gross output is 2140kw, always active negative Lotus is 3802.9kw；Wherein dg2, dg4, dg6 have fm capacity.Load controllability and load important level are as shown in table 2； First, the weight of two, three type loads takes 100,10,1 respectively.

Table 1 pg＆e 69 node dg parameter

Unit	Place node	Exert oneself/kw	Type
				dg1	36	50	Photovoltaic
dg2	5	250	Miniature gas turbine
				dg3	19	400	Blower fan
dg4	52	1300	Fuel cell
				dg5	32	40	Photovoltaic
dg6	65	100	Miniature gas turbine

Table 2 pg＆e 69 node load controllability and important level

Assume that circuit 1-2 occurs three-phase ground fault, bus 1 and circuit 1-2 to be removed；Downstream area is broken with higher level's electrical network Open connection, run with island mode.Using the algorithm in full invention, division is optimized to fault down stream region, can obtain as The splitting scheme of Fig. 7.It can be seen from figure 7 that original system is divided into 4 isolated island regions；Disconnected branches number 9；Recover negative Lotus total amount 2139.5kw；One type load recovery rate 100%；Two type load amounts of recovery are 1618.65kw, recovery rate 56.00%.

It is as shown in Figure 8 using division result is obtained based on the method for branch-and-bound.This division result comprises 5 isolated island areas Domain；Disconnected branches number 10；Recover load total amount 2132.85kw；One type load recovery rate 100%；Two type load amounts of recovery are 1613.25kw, recovery rate 55.81%；By contrast, the splitting scheme that the present invention is given then can disconnect less branch road, recovers More important loads, also preponderate on recovering total amount.

When considering interconnection switch operability, isolated island division as shown in Figure 9 can be obtained by solving partitioning model Scheme.It can be seen in figure 9 that original system is divided into 3 isolated island regions；Disconnected branches number 9；3 interconnection switch closures (respectively interconnection switch 13-21,27-54,39-48)；Load restoration total amount 2139.5kw；One type load amount of recovery 100%；Two Type load amount of recovery is 1699.24kw, compares and does not consider that the situation of interconnection switch increased 80.09kw, recovery rate rises to 58.78%.

In the case of considering dg type, can get orphan as shown in Figure 10 by solving isolated island partitioning model in the present invention Island splitting scheme.Dg5 stably exerts oneself it is impossible to provide for photovoltaic generation, thus is divided to and dg2, dg4 the same area.The party Case load restoration total amount 2140kw；One type load amount of recovery 100%；Two type load amounts of recovery are 1673.75kw, compare and only consider The situation of interconnection switch decreases 25.49kw, recovery rate 57.90%.When considering dg type, in order that not having fm capacity Dg does not individually run in an isolated island region, and splitting scheme can be adjusted to the position of cutting load and cutting load amount；Pass through Sacrifice a part of two type loads to be connected come the dg to ensure the dg without fm capacity with there is fm capacity.

Figure 11 illustrates in the partition strategy using branch and bound method and adopts proposed by the present invention under 3 kinds of different situations During partition strategy, the amount of recovery of different brackets load.

Claims (1)

1. a kind of based on digraph power distribution network containing distributed power generation isolated island division methods it is characterised in that comprising the following steps:

(1) set up the simplified model of distribution networks based on node-branch road: bus is regarded as node, the connection equipment between bus is regarded as Branch road, described connection equipment includes transformer, circuit etc., and concrete simplification principle is as follows:

A. bus nodes: the switchyard bus in power distribution network, transformer station's 10kv bus are all reduced to bus nodes；Bus nodes It is divided into load bus and generating node；

B. branch road: cable branch road, overhead transmission line are treated as branch road, any bar branch road all can disconnect and closure, branch road is divided into connection Network branch road and non-contact branch road, described contact branch road refers to the branch road possessing interconnection switch function；

(2) increase dummy node and virtual demand, build the electricity distribution network model based on rooted tree, specifically include following sub-step:

(2.1) simplified model of distribution networks is traveled through, bus nodes are considered as branch node or leaf node, branch road is considered as even Connect the side of node；Access dg bus nodes as dg node, the bus nodes only carrying load as load bus, by distribution Net is described as with bus as node, and supply line is tree t (v, e) on side, and wherein v={ v1 ..., vn } is node set, and e is side Set；

(2.2) increase dummy node and virtual demand, all of node is set up with virtual demand, increase the direction to every branch road Property description and folding condition description, form electricity distribution network model t'(v+v based on rooted tree₀,e∪e',s^d,s^r), wherein e' is Virtual tributary set, s^dFor branch road forward direction side state set, s^rFor branch road reverse edge state set, v₀For dummy node；

Described dummy node has the feature that

A. this node be one virtual independent of power distribution network node outside node, only pass through virtual tributary and the distribution that can cut-off In net, each dg node is connected；Described virtual tributary refer to virtual independent of the branch road outside power distribution network, only with dg node It is connected with dummy node；

B. dummy node does not consume, sends or transfer power；

The virtual demand of node has the feature that

A., during power distribution network islet operation, each in the range of isolated island carries electrical nodes, including dg node, all has the void of 1 unit Plan demand；

B. only provide virtual supply by dummy node；

C. the transmission path of virtual demand is by powering branch road and virtual tributary forms；

(3) to load, exert oneself and limit is configured, set up power distribution network electrical constraints: electrical constraints at least include power balance Constraint and the constraint of line transmission limit；Power balance will meet trend constraint, units limits, load controllability three bars of constraint Part, mathematical expression is as follows:

(3.1) trend constraint

$x_i\&centerdot;(p_{dgi}-p_{li})=\underset{j\&element;v_i}{\&sigma;}{p}_{ij}---\left(1\right)$

In formula (1), x_iFor 0-1 variable, represent the electriferous state of node i, 0 expression dead electricity, 1 represents powered；p_dgiDividing for node i Cloth generating is active to exert oneself, p_liRepresent burden with power access amount in node i；j∈v_iRepresent all nodes being connected with node i； p_ijComputing formula such as formula (2)

p_ij=s_ij(δ_i-δ_j)/x_ij(2)

In formula (2): p_ij、x_ijFor branch road e_ijOn the active power that flows through and branch road reactance；δ_iPhase angle for node i；δ_jFor node j Phase angle, s_ijFor representing the variable of branch road folding condition；

(3.2) load controllability constraint

${\underset{\&overbar;}{p}}_{li}\&le;p_{li}\&le;{\stackrel{\&overbar;}{p}}_{li}---\left(3\right)$

In formula:p _li、It is respectively the bound of the regulating power of connect load in node i；For uncontrollable load, its bound Equal；

(3.3) dg units limits

${\underset{\&overbar;}{p}}_{dgi}\&le;p_{dgi}\&le;{\stackrel{\&overbar;}{p}}_{dgi}---\left(4\right)$

In formula:p _dgi、It is respectively the active bound of exerting oneself of dg of i-th node；

(3.4) line transmission limit constraint

$-{\stackrel{\&overbar;}{p}}_{ij}\&le;p_{ij}\&le;{\stackrel{\&overbar;}{p}}_{ij}---\left(5\right)$

In formula:For branch road e_ijActive power transfer limit；

(4) set up power distribution network graphic constraint: described graphic constraint includes connectivity constraint, radial structure constraint, root node knot Structure and consistency constraint, mathematic(al) representation is as follows:

(4.1) connectivity constraint

$-x_i{f}_{li}=\underset{j\&element;v_i}{\&sigma;}{s}_{ij}{f}_{ij},i\&notequal;0---\left(6\right)$

-n≤f_ij≤n (7)

In formula: f_liFor the virtual demand of the i-th node, if the virtual demand of each node is 1 unit；f_ijFor branch road e_ijUpload Defeated virtual demand；N is regional nodes number to be divided；s_ijFor representing the variable of branch road folding condition, wherein i < j, 0 expression Disconnect, 1 represents closure；

(4.2) radial structure constraint

$\underset{i\&element;v_k}{\&sigma;}{s}_{ik}^d+\underset{j\&element;v_k}{\&sigma;}{s}_{jk}^r\&le;1---\left(8\right)$

$\underset{i\&element;v_k}{\&sigma;}{s}_{ik}^d+\underset{j\&element;v_k}{\&sigma;}{s}_{jk}^r\&greaterequal;x_k,k\&notequal;0---\left(9\right)$

$s_{ij}=s_{ij}^d+s_{ji}^r\&le;1---\left(10\right)$

Formula (9) represents in addition to root node (dummy node), and the in-degree of remaining node is more than or equal to the electriferous state value of this node； Represent node i to the selected state in node j forward direction side,Represent node j to the selected state of reverse edge of node i, 0 represents not selected Select, 1 represents selected；

(4.3) root node constraint

$\underset{j\&element;v_0}{\mathrm{\&sigma;}}{s}_{0j}^d\&greaterequal;1---\left(11\right)$

$\&forall;s_{j0}^r=0,j\&element;v_0---\left(12\right)$

In formula:Represent the selected state on the positive side of the branch road that is connected with root node；Represent the anti-of branch road that be connected with root node Selected state to side；

(4.4) branch road-node state consistency constraint

s_ij-1≤x_i-x_j≤1-s_ij(13)

Formula (13) represents the relevance between branch road folding condition and the electriferous state of two nodes being connected；

(5) set up the Mathematical Modeling expression with total system optimal solution as target；The expression of described Mathematical Modeling set up it is assumed hereinafter that On the basis of:

A. study to as if need the distribution web area that external electrical network powers in the case of being incorporated into the power networks, that is, intra-zone dg goes out Power is less than load total amount；

B. the distribution web area internal memory being optimized division is needed to have the dg of fm capacity；

C. the controllable burden being divided in region has the ability continuously adjusting；

The initial target function of described Mathematical Modeling expression is as follows:

$max.\underset{i\&element;v}{\&sigma;}{x}_i\&centerdot;w_i\&centerdot;p_{li}---\left(14\right)$

In formula: w_iRepresent the weight of connect load in node i, by significance level, load is divided into a type load, two type loads and three Type load；p_liRepresent burden with power access amount in node i；

Line translation is entered to object function, formula (2) is carried out drop with time process, formula (2) and formula (5) are changed into following form:

(s_ij-1)m≤p_ij-(δ_i-δ_j)/x_ij≤(1-s_ij)m (15)

$-s_{ij}{\stackrel{\&overbar;}{p}}_{ij}\&le;p_{ij}\&le;s_{ij}{\stackrel{\&overbar;}{p}}_{ij}---\left(16\right)$

In formula: m is a sufficiently large positive number, takes m=2/x_ij；

Formula (2)～formula (4) is changed into following form respectively:

$p_{dgi}-p_{li}=\underset{j\&element;v_i}{\&sigma;}{p}_{ij}---\left(17\right)$

$x_i{\underset{\&overbar;}{p}}_{li}\&le;p_{li}\&le;x_i{\stackrel{\&overbar;}{p}}_{li}---\left(18\right)$

$x_i{\underset{\&overbar;}{p}}_{dgi}\&le;p_{dgi}\&le;x_i{\stackrel{\&overbar;}{p}}_{dgi}---\left(19\right)$

Formula (6)～formula (7) is changed into following form:

$-f_{li}=\underset{j\&element;v_i}{\&sigma;}{f}_{ij},i\&notequal;0---\left(20\right)$

x_i·1≤f_li≤x_i1, i ≠ 0 (21)

-s_ijn≤f_ij≤s_ijn (22)

Object function changes into the most at last:

$max.\underset{i\&element;v}{\&sigma;}{w}_i\&centerdot;p_{li}---\left(23\right)$

(6) after founding mathematical models, solved by cplex, obtained believable isolated island splitting scheme.