CN104734153A - Method of reconstructing power distribution network containing distributed power supply - Google Patents

Abstract

The invention provides a method of reconstructing a power distribution network containing a distributed power supply. A network topology adjusting module considering various load modes is established according to actual operation conditions of the power distribution network and has good practical value. Meanwhile, topological adjusting is performed by means of a binary particle swarm optimization algorithm according to features of network topology adjustment; a dynamic inertial weight adjusting mode is provided; better coordination with global convergence speed and local convergence precision is provided; optimizing effect is better; the topological adjustment results and analysis of an IEEE-33 node typical distribution system show that the method is effective and practical.

Description

A kind of Distribution Network Reconfiguration containing distributed power source

Technical field

The invention belongs to containing distributed power source power distribution network optimal control association area, particularly relate to a kind of Distribution Network Reconfiguration containing distributed power source.

Background technology

Power distribution network is sent out as contact, the important tie of transmission system and terminal use, direct terminaloriented electric power users, is to ensure one of power supply quality, the key link improving operation of power networks efficiency.In recent years, along with distributed power source is in a large amount of accesses of power distribution network, power distribution network is faced with unprecedented uncertain external environment condition, thus brings unprecedented challenge to the safe operation of power distribution network.On the one hand, distributed power source can make full use of the clean reproducible energy such as wind energy, solar energy and generate electricity, and is realizing having important practical significance in " low carbonization, the energy-saving " of electric power system; But, exerting oneself of distributed power source based on the regenerative resource such as wind energy, solar energy has the feature of intermittence and randomness, can bring the series of problems such as unbalance in trend between trend two-way flow, feeder line, the intermittent fluctuation of voltage to power distribution network, result has had a strong impact on the electric power quality of terminal use.Therefore, seek efficient optimal control means and solve the problems referred to above, can become that distributed power source is following one of the key link realizing large-scale application.

The adjustment of distribution network topology improves one of the economy of distribution network operation and the important means of reliability.Adjusted by network topology, not only can reduce network loss, balanced line load, eliminate overload, also effectively can improve power supply reliability and quality of voltage etc.In theory, the adjustment of distribution network topology is a complicated nonlinear combinatorial optimization problem.At present, distribution network topology adjustment model mainly contains static models and dynamic model.Static topological adjustment model is simple, but does not consider the feature of exerting oneself at random after distributed power source access, and the operation not meeting distribution network is actual; And dynamical topology adjusting model solution needs to carry out switching manipulation frequently, current distribution network automated level can not meet its action request, can reduce switch even initiating system fault in useful life simultaneously.Conventional distribution network topology method of adjustment roughly can be divided into two classes: one is heuritic approach, comprises optimal flow pattern, branch exchange method etc.; Two is intelligent algorithms, as Intelligentized methods such as genetic algorithm, simulated annealing, artificial neural net, particle cluster algorithms.Heuritic approach is converted into the heuristic of switch the combination operation problem of switch and singly opens problem, and challenge is simplified, and its shortcoming is that topology adjustment result and heuristic rule are in close relations, easily converges on locally optimal solution.Theoretically, Intelligentized method can converge to optimal solution, and algorithm requires more loose to initial condition and target function, implement fairly simple, but a large amount of infeasible solutions can be produced in an iterative process, there is optimal time long, be absorbed in the shortcomings such as locally optimal solution sometimes.

Summary of the invention

In order to solve the problem, the object of the present invention is to provide a kind of Distribution Network Reconfiguration containing distributed power source.

In order to achieve the above object, the Distribution Network Reconfiguration containing distributed power source provided by the invention comprises the following step performed in order:

Step 1) prepare initial data: according to power distribution network running status, collect distribution network initial data, comprise load under branch parameters, various load method and branch switch state etc.;

Step 2) algorithm parameter is set: particle cluster algorithm parameter is set, comprises population scale, inertia weight scope, accelerator coefficient and speed span etc.;

Step 3) initialization: iterations is set to 0, the all particle positions of initialization and speed, according to step 1) initial data that obtains carries out under various mode Load flow calculation, the comprehensive network harm of network within this period obtained under each group on off state by the Mathematical Modeling of distribution network topology adjustment is its initial adaptive value and history adaptive optimal control value, and the particle position of loss minimization is global optimum's particle;

Step 4) speed and location updating: based on above-mentioned algorithm parameter, carry out particle rapidity and location updating by particle rapidity and location updating formula, and check particle position upgrade after each variable whether out-of-limit, if a certain variable is out-of-limit, then get its corresponding limit value;

Step 5) radial verification: whether the network configuration under the Switch State Combination in Power Systems that the particle position after checksum update is corresponding meets radial constraint, if some particle does not meet, reinitializes this particle, until all meet radial constraint;

Step 6) calculate adaptive value: namely calculate state variable under various load method of network under the corresponding on off state of each particle and active power loss, and verify the constraint whether particle meets node voltage, branch current, if meet constraint, by its adaptive value of calculated with mathematical model of distribution network topology adjustment; If do not met, add penalty function to adaptive value;

Step 7) upgrade optimal location: the more history optimal location of new particle and global optimum's particle position;

Step 8) inertia weight adjustment: according to dynamic inertia weight adjustable strategies dynamic conditioning inertia weight w;

Step 9) terminate to judge: if meet termination condition, as reached maximum permission iterations, then stop and Output rusults; Otherwise iterations adds 1, forward step 4 to) proceed.

In step 3) in, the Mathematical Modeling of described distribution network topology adjustment is:

$\begin{array}{cc}\min & F=\underset{k=1}{\overset{M}{\mathrm{\Σ}}}{P}_{\mathrm{loss}}^k\·\mathrm{\Δ}{t}^k\end{array}---\left(1\right)$

In formula, M is considered load method number; △ t ^kfor the percent coefficient of kth kind load method shared time in topological regulation time section; for the network active loss under kth kind load method, specific formula for calculation is:

$P_{\mathrm{loss}}^k=\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{R}_{b_i}(P_{b_i}^{k2}+Q_{b_i}^{k2})/U_{\mathrm{bi}}^{k2}---\left(2\right)$

In formula, L is the branch road sum in network; with branch road b is flow through under being respectively kth kind load method _iactive power and reactive power; for branch road b _ibranch resistance; for branch road b under kth kind load method _iterminal voltage; Then F is the comprehensive network loss in this time period;

In topological adjustment process, for each topological Adjusted Option, the power flow equation of the distribution network considered:

$S_i^k=P_i^k+j{Q}_i^k={\stackrel{\·}{U}}_i^k\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\stackrel{*}{Y}}_{\mathrm{ij}}{\stackrel{*}{U}}_j^k---\left(3\right)$

(i＝1,2,…,N；k＝1,2,…,M)

In formula, it is the injecting power of kth kind load method lower node i; with be respectively injection active power and the reactive power of kth kind load method lower node i; it is the voltage phasor of kth kind load method lower node i; Y _ijit is the element of network node admittance matrix; N is system node number.

In step 4) in, described particle position and speed more new formula are as follows:

$v_{i,d}^{t+1}=\mathrm{\ω}{v}_{i,d}^t+c_1{r}_1(p{\mathrm{Best}}_{i,d}-x_{i,d}^t)+c_2{r}_2(g{\mathrm{Best}}_d-x_d^t)---\left(4\right)$

$\left\{\begin{array}{cc}{x}_{i,d}^{t+1}=1& r<\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)\\ x_{i,d}^{t+1}=0& r\&GreaterEqual;\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)\end{array}\right.---\left(5\right)$

In formula, x _i,dand v _i,dthe d being respectively particle i ties up position and velocity component; ω is inertia weight; c ₁, c ₂for accelerator coefficient; R, r ₁, r ₂for the random number between [0,1]; PBest _i,dwith gBest _dbe respectively history optimal location and the population optimum particle position of particle i; Saturated in order to prevent, speed is generally limited in interval [-4,4]; Sigmoid function representation is as follows:

$\mathrm{Sigmoid}\left(x\right)=\frac{1}{1+e^{-x}}---\left(6\right);$

Because the switch participating in topology adjustment only exists opening and closing two states, therefore adopt binary particle swarm algorithm more suitable; Particle position represents the folding condition (0 representative is opened, and 1 representative is closed) of switch, then each particle represents a kind of Switch State Combination in Power Systems; Accordingly, particle rapidity represents that correspondence position gets the probability of 0 or 1; In order to make its more realistic requirement, the Sigmoid function getting speed is transformed on [0,1], carries out the selection of on off state with this.

In step 5) in, for meeting radial structure constraint, in distribution network, each loop must have and only have a switch opens, and the switch number namely opened must equal loop number; Must ensure that distribution network can not have electric power " isolated island ", then all branch switchs not on any loop must be all closed simultaneously; In order to reduce the probability that infeasible solution produces, location updating formula (6) changes into:

$r_{i,d}=\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)-r---\left(7\right)$

In formula, r is the random number on [0,1]; K is the set of all switches belonging to same loop with switch d; Formula (7), (8) can guarantee that the switch number opened equals loop number, effectively reduce the generation probability of infeasible Switch State Combination in Power Systems.

In step 6) in, described branch current and node voltage retrain as follows:

$\left\{\begin{array}{cc}{I^k}_{b_i}\&le;{I^k}_{b_i.\max }& (i=\mathrm{1,2},...,L)\\ U_{j.\min }\&le;{U^k}_j\&le;U_{j.\max }& (j=\mathrm{1,2},...,N)\end{array}\right.---\left(9\right)$

(k＝1,2,…,M)

In formula, with be respectively branch road b _ielectric current and its upper limit; U _j.maxand U _j.minfor node j allows upper voltage limit and lower limit.

In step 8) in, in the stage, the described method according to dynamic inertia weight adjustable strategies adjustment inertia weight is:

According to the rate of change of global optimum in searching process, the inertia weight ω curve of linear decrease superposes a random component, changes single Serial regulation pattern, use particle cluster algorithm can regulate the convergence capabilities of self better according to evolution information; First a rate of change g is defined:

$g=\frac{f\left(t\right)-f(t-10)}{f(t-10)}---\left(10\right)$

In formula, f (t) represents the global optimum of population in t generation, then g is the rate of change of population global optimum within evolution 10 generation;

Inertia weight ω presses following formula self-adaptative adjustment:

$\mathrm{\&omega;}=\left\{\begin{array}{cc}{\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{{\mathrm{Iter}}_{\max }}\&times;\mathrm{Iter}+r/4.0& g\&GreaterEqual;0.05\\ {\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{{\mathrm{Iter}}_{\max }}\&times;\mathrm{Iter}-r/4.0& g<0.05\end{array}\right.---\left(11\right)$

In formula, ω _maxand ω _minmaximum and the minimum value of inertia weight ω respectively; Iter and Iter _maxcurrent iteration number of times and maximum iteration time respectively; R is for being uniformly distributed in the random number between [0,1].

Distribution Network Reconfiguration containing distributed power source provided by the invention, from the practical operation situation of distribution network, establishes a kind of distribution network topology adjustment model considering multiple load method, has good practical value.Simultaneously, according to the feature of distribution network topology adjustment, have employed Binary Particle Swarm Optimization and carry out topology adjustment, and propose a kind of dynamic inertia weight adjustment mode, the speed of global convergence and the precision of local convergence can be coordinated better, there is good optimizing effect.The topology of IEEE-33 node typical power distribution system adjusts validity and the practicality of result and analytical proof this method.

Accompanying drawing explanation

Fig. 1 is the flow chart of the Distribution Network Reconfiguration containing distributed power source provided by the invention.

Fig. 2 is IEEE-33 Node power distribution system schematic diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments, the Distribution Network Reconfiguration containing distributed power source provided by the invention is described in detail.

As shown in Figure 1, the Distribution Network Reconfiguration containing distributed power source provided by the invention comprises the following step performed in order:

Step 1) prepare initial data: according to power distribution network running status, collect distribution network initial data, comprise load under branch parameters, various load method and branch switch state etc.;

Step 2) algorithm parameter is set: particle cluster algorithm parameter is set, comprises population scale, inertia weight scope, accelerator coefficient and speed span etc.;

Step 3) initialization: iterations is set to 0, the all particle positions of initialization and speed, according to step 1) initial data that obtains carries out under various mode Load flow calculation, the comprehensive network harm of network within this period obtained under each group on off state by the Mathematical Modeling of distribution network topology adjustment is its initial adaptive value and history adaptive optimal control value, and the particle position of loss minimization is global optimum's particle;

Step 4) speed and location updating: based on above-mentioned algorithm parameter, carry out particle rapidity and location updating by particle rapidity and location updating formula, and check particle position upgrade after each variable whether out-of-limit, if a certain variable is out-of-limit, then get its corresponding limit value;

Step 5) radial verification: whether the network configuration under the Switch State Combination in Power Systems that the particle position after checksum update is corresponding meets radial constraint, if some particle does not meet, reinitializes this particle, until all meet radial constraint;

Step 6) calculate adaptive value: namely calculate state variable under various load method of network under the corresponding on off state of each particle and active power loss, and verify the constraint whether particle meets node voltage, branch current, if meet constraint, by its adaptive value of calculated with mathematical model of distribution network topology adjustment; If do not met, add penalty function to adaptive value;

Step 7) upgrade optimal location: the more history optimal location of new particle and global optimum's particle position;

Step 8) inertia weight adjustment: according to dynamic inertia weight adjustable strategies dynamic conditioning inertia weight w;

Step 9) terminate to judge: if meet termination condition, as reached maximum permission iterations, then stop and Output rusults; Otherwise iterations adds 1, forward step 4 to) proceed.

In step 3) in, the Mathematical Modeling of described distribution network topology adjustment is:

$\begin{array}{cc}\min & F=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{P}_{\mathrm{loss}}^k\&CenterDot;\mathrm{\&Delta;}{t}^k\end{array}---\left(1\right)$

This Mathematical Modeling to reduce system losses for target, and considers multiple load method; In formula, M is considered load method number; △ t ^kfor the percent coefficient of kth kind load method shared time in topological regulation time section; for the network active loss under kth kind load method, specific formula for calculation is:

$P_{\mathrm{loss}}^k=\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{R}_{b_i}(P_{b_i}^{k2}+Q_{b_i}^{k2})/U_{\mathrm{bi}}^{k2}---\left(2\right)$

In formula, L is the branch road sum in network; with branch road b is flow through under being respectively kth kind load method _iactive power and reactive power; for branch road b _ibranch resistance; for branch road b under kth kind load method _iterminal voltage; Then F is the comprehensive network loss in this time period.

In topological adjustment process, for each topological Adjusted Option, the power flow equation of the distribution network considered:

$S_i^k=P_i^k+j{Q}_i^k={\stackrel{\&CenterDot;}{U}}_i^k\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{*}{Y}}_{\mathrm{ij}}{\stackrel{*}{U}}_j^k---\left(3\right)$

(i＝1,2,…,N；k＝1,2,…,M)

In formula, it is the injecting power of kth kind load method lower node i; with be respectively injection active power and the reactive power of kth kind load method lower node i; it is the voltage phasor of kth kind load method lower node i; Y _ijit is the element of network node admittance matrix; N is system node number.

In step 4) in, described particle position and speed more new formula are as follows:

$v_{i,d}^{t+1}=\mathrm{\&omega;}{v}_{i,d}^t+c_1{r}_1(p{\mathrm{Best}}_{i,d}-x_{i,d}^t)+c_2{r}_2(g{\mathrm{Best}}_d-x_d^t)---\left(4\right)$

$\left\{\begin{array}{cc}{x}_{i,d}^{t+1}=1& r<\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)\\ x_{i,d}^{t+1}=0& r\&GreaterEqual;\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)\end{array}\right.---\left(5\right)$

In formula, x _i,dand v _i,dthe d being respectively particle i ties up position and velocity component; ω is inertia weight; c ₁, c ₂for accelerator coefficient; R, r ₁, r ₂for the random number between [0,1]; PBest _{i, d}with gBest _dbe respectively history optimal location and the population optimum particle position of particle i; Saturated in order to prevent, speed is generally limited in interval [-4,4]; Sigmoid function representation is as follows:

$\mathrm{Sigmoid}\left(x\right)=\frac{1}{1+e^{-x}}---\left(6\right);$

Because the switch participating in topology adjustment only exists opening and closing two states, therefore adopt binary particle swarm algorithm more suitable; Particle position represents the folding condition (0 representative is opened, and 1 representative is closed) of switch, then each particle represents a kind of Switch State Combination in Power Systems; Accordingly, particle rapidity represents that correspondence position gets the probability of 0 or 1; In order to make its more realistic requirement, the Sigmoid function getting speed is transformed on [0,1], carries out the selection of on off state with this.

In step 5) in, for meeting radial structure constraint, in distribution network, each loop must have and only have a switch opens, and the switch number namely opened must equal loop number; Must ensure that distribution network can not have electric power " isolated island ", then all branch switchs not on any loop must be all closed simultaneously; In order to reduce the probability that infeasible solution produces, location updating formula (6) changes into:

$r_{i,d}=\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)-r---\left(7\right)$

In formula, r is the random number on [0,1]; K is the set of all switches belonging to same loop with switch d; Formula (7), (8) can guarantee that the switch number opened equals loop number, effectively reduce the generation probability of infeasible Switch State Combination in Power Systems.

In step 6) in, described branch current and node voltage retrain as follows:

$\left\{\begin{array}{cc}{I^k}_{b_i}\&le;{I^k}_{b_i.\max }& (i=\mathrm{1,2},...,L)\\ U_{j.\min }\&le;{U^k}_j\&le;U_{j.\max }& (j=\mathrm{1,2},...,N)\end{array}\right.---\left(9\right)$

(k＝1,2,…,M)

In formula, with be respectively branch road b _ielectric current and its upper limit; U _j.maxand U _j.minfor node j allows upper voltage limit and lower limit.

In step 8) in, the described method according to dynamic inertia weight adjustable strategies adjustment inertia weight is:

According to the rate of change of global optimum in searching process, the inertia weight ω curve of linear decrease superposes a random component, change single Serial regulation pattern, use particle cluster algorithm (PSO) that the convergence capabilities of self can be regulated better according to evolution information; First a rate of change g is defined:

$g=\frac{f\left(t\right)-f(t-10)}{f(t-10)}---\left(10\right)$

In formula, f (t) represents the global optimum of population in t generation, then g is the rate of change of population global optimum within evolution 10 generation;

Inertia weight ω presses following formula self-adaptative adjustment:

$\mathrm{\&omega;}=\left\{\begin{array}{cc}{\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{{\mathrm{Iter}}_{\max }}\&times;\mathrm{Iter}+r/4.0& g\&GreaterEqual;0.05\\ {\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{{\mathrm{Iter}}_{\max }}\&times;\mathrm{Iter}-r/4.0& g<0.05\end{array}\right.---\left(11\right)$

In formula, ω _maxand ω _minmaximum and the minimum value of inertia weight ω respectively; Iter and Iter _maxcurrent iteration number of times and maximum iteration time respectively; R is for being uniformly distributed in the random number between [0,1];

This adjustable strategies has following feature: one, and after can reaching first global search raising convergence rate, Local Search is to obtain the object of high precision solution; Its two, inertia weight ω adds random perturbation, is random by the impact making particle historical speed on present speed, the mutation operator to a certain extent in similar genetic algorithm, and this will contribute to keeping the diversity of population; Its three, dynamic conditioning inertia weight ω can be carried out according to the change of population adaptive optimal control value, global search and local search ability can be regulated more neatly, thus different optimization problems can be adapted to better.

The sample calculation analysis of the Distribution Network Reconfiguration containing distributed power source provided by the invention:

This example is random arrangement four distributed power sources on the basis of 33 Node power distribution system, and network configuration as shown in Figure 2; Its power supply point voltage is 10.5kV, and rated voltage is 10.0kV; Before topology adjustment, branch road 7-20,11-21,8-14,17-32,24-28 open; Owing to there is interconnection switch in these five branch roads, make in distribution network, to have occurred 5 loops, except the 0-1 branch road be connected with power supply point 0 can not disconnect, under the prerequisite ensureing nothing " isolated island " and loop in network, all the other all switches are all by the adjustment of participation network topology.

Adopt said method to carry out topology adjustment to this distribution system, with one day for the topology adjustment period, get three kinds of load methods; Population Size gets 50, and accelerator coefficient gets 2.05; Inertia weight upper and lower bound is respectively 1.2 and 0.4; The iterations upper limit is 100; Topology adjustment result is as shown in table 1, and the minimum node voltage amplitude before and after topology adjustment under various load method is as shown in table 2; Optimum topological Adjusted Option is that branch road 6-7,10-11,13-14,26-27,30-31 open, after optimizing, the comprehensive network loss of system within this time period have dropped 34.33%, node voltage under three kinds of load methods all meets the requirements and node minimum voltage is improved, and demonstrates validity and the practicality of this method.

The network topology adjustment result of three kinds of load methods considered by table 1

Node minimum voltage amplitude before and after the adjustment of table 2 topology

Topology adjustment result under table 3 different inertia weight adjustment mode

In order to test the effect of dynamic inertia weight adjustment, make comparisons with the binary particle swarm algorithm of inertia weight ω linear decrease; Run 20 times respectively, result is as shown in table 3; Visible, the topological adjustment algorithm of two kinds of inertia weight adjustment modes can both restrain, but the inertia weight of dynamic conditioning has better effect, and convergence in mean algebraically reduces, and the ratio converging to optimal solution improves.

Claims (6)

1. containing a Distribution Network Reconfiguration for distributed power source, it is characterized in that: the described Distribution Network Reconfiguration containing distributed power source comprises the following step performed in order:

Step 1) prepare initial data: according to power distribution network running status, collect distribution network initial data, comprise load under branch parameters, various load method and branch switch state etc.;

Step 2) algorithm parameter is set: particle cluster algorithm parameter is set, comprises population scale, inertia weight scope, accelerator coefficient and speed span etc.;

Step 3) initialization: iterations is set to 0, the all particle positions of initialization and speed, according to step 1) initial data that obtains carries out under various mode Load flow calculation, the comprehensive network harm of network within this period obtained under each group on off state by the Mathematical Modeling of distribution network topology adjustment is its initial adaptive value and history adaptive optimal control value, and the particle position of loss minimization is global optimum's particle;

Step 4) speed and location updating: based on above-mentioned algorithm parameter, carry out particle rapidity and location updating by particle rapidity and location updating formula, and check particle position upgrade after each variable whether out-of-limit, if a certain variable is out-of-limit, then get its corresponding limit value;

Step 5) radial verification: whether the network configuration under the Switch State Combination in Power Systems that the particle position after checksum update is corresponding meets radial constraint, if some particle does not meet, reinitializes this particle, until all meet radial constraint;

Step 6) calculate adaptive value: namely calculate state variable under various load method of network under the corresponding on off state of each particle and active power loss, and verify the constraint whether particle meets node voltage, branch current, if meet constraint, by its adaptive value of calculated with mathematical model of distribution network topology adjustment; If do not met, add penalty function to adaptive value;

Step 7) upgrade optimal location: the more history optimal location of new particle and global optimum's particle position;

Step 8) inertia weight adjustment: according to dynamic inertia weight adjustable strategies dynamic conditioning inertia weight w;

Step 9) terminate to judge: if meet termination condition, as reached maximum permission iterations, then stop and Output rusults; Otherwise iterations adds 1, forward step 4 to) proceed.

2. the Distribution Network Reconfiguration containing distributed power source according to claim 1, is characterized in that: in step 3) in, the Mathematical Modeling of described distribution network topology adjustment is:

$\begin{array}{cc}\min & F=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{P}_{\mathrm{loss}}^k\&CenterDot;\mathrm{\&Delta;}{t}^k---\left(1\right)\end{array}$

In formula: M is considered load method number; △ t ^kfor the percent coefficient of kth kind load method shared time in topological regulation time section; for the network active loss under kth kind load method, specific formula for calculation is:

$P_{\mathrm{loss}}^k=\underset{i=1}{\overset{L}{\mathrm{\&Sigma;}}}{R}_{b_i}(P_{b_i}^{k2}+Q_{b_i}^{k2})/U_{\mathrm{bi}}^{k2}---\left(2\right)$

In formula, L is the branch road sum in network; with branch road b is flow through under being respectively kth kind load method _iactive power and reactive power; for branch road b _ibranch resistance; for branch road b under kth kind load method _iterminal voltage; Then F is the comprehensive network loss in this time period;

In topological adjustment process, for each topological Adjusted Option, the power flow equation of the distribution network considered:

$\begin{array}{c}{S}_i^k=P_i^k+j{Q}_i^k={\stackrel{.}{U}}_i^k\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}{\stackrel{*}{Y}}_{\mathrm{ij}}{\stackrel{*}{U}}_j^k\\ (i=\mathrm{1,2},...,N;k=\mathrm{1,2},...,M)\end{array}---\left(3\right)$

In formula, it is the injecting power of kth kind load method lower node i; with be respectively injection active power and the reactive power of kth kind load method lower node i; it is the voltage phasor of kth kind load method lower node i; Y _ijit is the element of network node admittance matrix; N is system node number.

3. the Distribution Network Reconfiguration containing distributed power source according to claim 1, is characterized in that: in step 4) in, described particle position and speed more new formula are as follows:

$v_{i,d}^{t+1}=\mathrm{\&omega;}{v}_{i,d}^t+c_1{r}_1(p{\mathrm{Best}}_{i,d}-x_{i,d}^t)+c_2{r}_2(g{\mathrm{Best}}_d-x_d^t)---\left(4\right)$

$\left\{\begin{array}{cc}{x}_{i,d}^{t+1}=1& r<\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)\\ x_{i,d}^{t+1}=0& r\&GreaterEqual;\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)\end{array}\right.---\left(5\right)$

In formula, x _i,dand v _i,dthe d being respectively particle i ties up position and velocity component; ω is inertia weight; c ₁, c ₂for accelerator coefficient; R, r ₁, r ₂for the random number between [0,1]; PBest _i,dwith gBest _dbe respectively history optimal location and the population optimum particle position of particle i; Saturated in order to prevent, speed is generally limited in interval [-4,4]; Sigmoid function representation is as follows:

$\mathrm{Sigmoid}\left(x\right)=\frac{1}{1+e^{-x}}---\left(6\right);$

Because the switch participating in topology adjustment only exists opening and closing two states, therefore adopt binary particle swarm algorithm more suitable; Particle position represents the folding condition (0 representative is opened, and 1 representative is closed) of switch, then each particle represents a kind of Switch State Combination in Power Systems; Accordingly, particle rapidity represents that correspondence position gets the probability of 0 or 1; In order to make its more realistic requirement, the Sigmoid function getting speed is transformed on [0,1], carries out the selection of on off state with this.

4. the Distribution Network Reconfiguration containing distributed power source according to claim 1, it is characterized in that: in step 5) in, for meeting radial structure constraint, in distribution network, each loop must have and only have a switch opens, and the switch number namely opened must equal loop number; Must ensure that distribution network can not have electric power " isolated island ", then all branch switchs not on any loop must be all closed simultaneously; In order to reduce the probability that infeasible solution produces, location updating formula (6) changes into:

$r_{i,d}=\mathrm{Sigmoid}\left(v_{i,d}^{t+1}\right)-r---\left(7\right)$

In formula, r is the random number on [0,1]; K is the set of all switches belonging to same loop with switch d; Formula (7), (8) can guarantee that the switch number opened equals loop number, effectively reduce the generation probability of infeasible Switch State Combination in Power Systems.

5. the Distribution Network Reconfiguration containing distributed power source according to claim 1, is characterized in that: in step 6) in, described branch current and node voltage retrain as follows:

$\begin{array}{c}\left\{\begin{array}{cc}{I^k}_{b_i}\&le;{I^k}_{b_i.\max }& (i=\mathrm{1,2},...,L)\\ U_{j.\min }\&le;{U^k}_j\&le;U_{j.\max }& (j=\mathrm{1,2},...,N)\end{array},---\left(9\right)\right.\\ k=(\mathrm{1,2},...,M)\end{array}$

In formula, with be respectively branch road b _ielectric current and its upper limit; U _j.maxand U _j.minfor node j allows upper voltage limit and lower limit.

6. the Distribution Network Reconfiguration containing distributed power source according to claim 1, is characterized in that: in step 8) in, in the stage, the described method according to dynamic inertia weight adjustable strategies adjustment inertia weight is:

According to the rate of change of global optimum in searching process, the inertia weight ω curve of linear decrease superposes a random component, changes single Serial regulation pattern, use particle cluster algorithm can regulate the convergence capabilities of self better according to evolution information; First a rate of change g is defined:

$g=\frac{f\left(t\right)-f(t-10)}{f(t-10)}---\left(10\right)$

In formula, f (t) represents the global optimum of population in t generation, then g is the rate of change of population global optimum within evolution 10 generation;

Inertia weight ω presses following formula self-adaptative adjustment:

$\mathrm{\&omega;}=\left\{\begin{array}{cc}{\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{{\mathrm{Iter}}_{\max }}\&times;\mathrm{Iter}+r/4.0& g\&GreaterEqual;0.05\\ {\mathrm{\&omega;}}_{\max }-\frac{{\mathrm{\&omega;}}_{\max }-{\mathrm{\&omega;}}_{\min }}{{\mathrm{Iter}}_{\max }}\&times;\mathrm{Iter}-r/4.0& g<0.05\end{array}\right.---\left(11\right)$

In formula, ω _maxand ω _minmaximum and the minimum value of inertia weight ω respectively; Iter and Iter _maxcurrent iteration number of times and maximum iteration time respectively; R is for being uniformly distributed in the random number between [0,1].