CN114709836B - AG-MOPSO-based reactive power optimization method for wind power distribution network - Google Patents
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Abstract
AG-MOPSO-based reactive power optimization method for wind-powered electricity containing power distribution network comprises the following steps: s1: establishing a probability model of wind power plant output, and converting uncertainty of wind power output into scene power in a typical scene; s2: establishing a reactive power optimization model of a power distribution network containing wind power by taking minimum active network loss and voltage deviation as objective functions, wherein the model selects the number of switching groups of reactive power compensation equipment and reactive power output of a wind turbine generator as control variables, and load node voltage as a state variable; s3: and the AG-MOPSO algorithm is used for solving a reactive power optimization model of the power distribution network containing wind power, so that the uniformity and the diversity of the Pareto front distribution are ensured. Aiming at the problems of uncertainty of grid-connected output of the wind turbine generator and poor Pareto front diversity obtained by a traditional method, the application provides a multi-target particle swarm algorithm based on a self-adaptive grid by adopting a scene analysis method based on probability occurrence, and effectively ensures uniformity and diversity of Pareto front distribution.
Description
Technical Field
The invention belongs to the technical field of wind power grids, and particularly relates to a reactive power optimization method for a wind power distribution network based on AG-MOPSO.
Background
According to the data in the global wind energy report 2019, the global wind installation capacity of the 2019 year is 651GW, wherein the land wind installation capacity is 621GW, and the sea wind installation capacity is 30GW. Wind energy is used as a clean renewable energy source, the power generation technology of the wind power generation system is rapidly developed, but due to the randomness and intermittence of wind speed, the trend distribution of a power distribution network can be changed after the wind power plant is connected with the grid, and meanwhile, the power supply quality and the stability of the system are affected.
In order to improve the power supply quality of the system and reduce the active network loss, students at home and abroad have conducted a great deal of research on the problem of multi-objective reactive power optimization of the power distribution network containing the wind power plant. The multi-objective optimization problem is converted into a single-objective optimization problem, such as Wu Xing 'reactive optimization of the offshore wind farm based on an improved genetic algorithm', the offshore wind farm is reactive optimized by adopting an improved rapid non-dominant sequencing genetic (NSGA-II) algorithm with the aim of minimum compensation capacity and minimum node voltage deviation, and the randomness and intermittence of the output of the wind turbine are not considered. The best solution of multi-target Pareto (Pareto) is also researched, the best solution can embody the relation between targets, and corresponding optimization schemes can be selected according to different requirements, such as 'multi-target reactive power optimization considering multiple wind turbines to access a power distribution network' of Wang Wenda et al, a Latin hypercube sampling method and a scene method are applied to convert a random reactive power optimization model into a deterministic trend problem under a given scene, the obtained multi-target Pareto front is analyzed, but the power factor of a fan is set to be 1, and the reactive power output of the fan is ignored.
Disclosure of Invention
Aiming at the technical problems, the invention provides a reactive power optimization method for a wind power distribution network based on AG-MOPSO, which converts an uncertainty model into multiple scene problems with different occurrence probabilities, establishes a reactive power optimization model with minimum active network loss and voltage deviation as targets, and provides a multi-target particle swarm algorithm (AG-MOPSO) based on a self-adaptive grid, thereby solving the problem of poor Pareto front diversity.
The invention adopts the following specific technical scheme:
AG-MOPSO-based reactive power optimization method for wind-powered electricity containing power distribution network comprises the following steps:
s1: establishing a probability model of wind power plant output, and converting uncertainty of wind power output into scene power in a typical scene:
S1.1: the relation between the output power p w and the wind speed v obtained by the power characteristic curve of the wind turbine generator;
s1.2: dividing the output power of the wind turbine into three typical scenes;
S1.3: calculating the output power of the wind turbine generator in three typical scenes by combining the probability density function;
s1.4: the output power of the wind turbine generator in three typical scenes is multiplied by the probability of the wind turbine generator respectively and then summed to obtain the expected output power of the wind turbine generator, and the expected output power is used as the active output of the fan;
S2: establishing a reactive power optimization model of a power distribution network containing wind power by taking minimum active network loss and voltage deviation as objective functions, wherein the model selects the number of switching groups of reactive power compensation equipment and reactive power output of a wind turbine generator as control variables, and load node voltage as a state variable;
S3: based on AG-MOPSO algorithm, solving a reactive power optimization model of the power distribution network containing wind power through AG-MOPSO algorithm, and guaranteeing uniformity and diversity of Pareto front distribution:
S3.1: reading in power grid operation data, setting AG-MOPSO algorithm parameters, and encoding control variables Q CZi is the number of switching groups of the ith capacitor bank, and Q WGi is the reactive power output of the ith wind turbine generator;
s3.2: initializing the position and the speed of particles, and calculating the power flow to obtain corresponding active network loss and voltage deviation;
S3.3: taking the current particle positions as individual optimal positions pbest, judging the dominant relationship between the individual optimal positions, putting non-dominant solutions into an external archive, and determining a global optimal position gbest through a global optimal particle selection principle;
s3.4: iteratively updating the position and the speed of the particles, and generating a new solution set by tide calculation;
S3.5: determining pbest through an individual optimal particle selection principle, adding non-dominant solutions in the individual optimal particle selection principle into an external archive, maintaining the number of Pareto optimal solutions by utilizing an external archive maintenance principle, and determining gbest through a global optimal particle selection principle;
s3.6: if the algorithm reaches the maximum iteration number or meets the convergence condition, outputting the Pareto optimal solution in the external archive, otherwise, jumping to the step S3.4 to continue calculation.
Preferably, the relation between the output power p w and the wind speed v in S1.1 is:
Wherein c ci、vr、vco is cut-in wind speed, rated wind speed and cut-out wind speed respectively, and k 1＝pr(vr-vco)-1, k2＝-k1vco,pr is rated power of the wind turbine generator.
Preferably, the output power of the wind turbine generator is divided into three typical scenarios by the formula (1): the method comprises a first scene of zero output in a shutdown state, a second scene of undershot output in a state of corresponding power changing along with wind speed, and a third scene of rated output in a rated power state.
Preferably, the probability of occurrence of the three typical scenes is calculated according to a probability density function:
Wherein P 1、P2、P3 represents occurrence probability of scene one, scene two and scene three respectively, f (v) represents probability density function of Weibull distribution, K and c are the shape parameter and the scale parameter of Weibull distribution respectively;
Therefore, the output power of the wind turbine generator set corresponding to the first scene and the third scene is respectively 0 and p r, and the output power of the wind turbine generator set corresponding to the second scene is as follows:
Preferably, the active power loss f 1 and the voltage deviation f 2 in S2 are respectively:
Wherein N is the number of system nodes, i and j are node labels, G ij is branch admittance between the nodes i and j, U i and U j are voltage amplitude values of the nodes i and j respectively, theta ij is voltage phase difference of the nodes i and j, and U i.N、Ui.max and U i.min are rated voltage, maximum value and minimum value of the node i respectively;
Thus, the objective function of the reactive power optimization model of the distribution network is:
F＝min(f1,f2)。
Preferably, the equality constraint condition of the reactive power optimization model of the power distribution network is active power and reactive power balance constraint of system nodes:
Wherein, P Gi and Q Gi are respectively the active output and the reactive output of the power supply; p Li and Q Li are the active power and reactive power of the load node, respectively; q Ci is reactive compensation capacity; g ij and B ij are the conductance and susceptance between nodes i, j, respectively.
Preferably, the inequality constraint condition of the reactive power optimization model of the power distribution network comprises node voltage constraint, capacitor capacity constraint and output constraint of the wind driven generator:
Wherein, Q CZi、PWGi and Q WGi are respectively the number of capacitor switching groups, the active output and the reactive output of the fan.
Preferably, the Pareto optimal solution in the external archive is obtained through construction of an adaptive grid:
for the optimization problem of m objective functions, an m-dimensional objective space is formed, grids with 2m boundaries are required to be set, and the upper and lower boundaries of the grids on the mth objective of the kth iteration are defined And/>The method comprises the following steps of:
Wherein, And/>Respectively the maximum value and the minimum value of the mth objective function, and h is the expansion coefficient; because of the iteration process,/>And/>Is continuously changed, so that the grid boundary can be adaptively adjusted to better reflect the distribution condition of the solution, and further, the function value/>, is obtainedThe corresponding grid coordinates are:
Wherein, For the grid size of the mth objective function of the kth iteration, g is the number of divided grids, and [ (· ] is a rounding function), the number of Pareto optimal solutions in each grid can be calculated according to the formula, and the density information of particles in the grid is reflected.
Preferably, the selection of the optimal particles is mainly the selection of the individual optimal position pbest and the global optimal position gbest:
Selecting non-dominant particles as pbest by judging the dominant relationship between the current particle position and the optimal position of the historical individual, and randomly selecting if the non-dominant particles are not dominant; to ensure uniformity of Pareto front distribution, gbest is selected by adopting density information of particles, and the probability of selecting the ith grid in the kth iteration is as follows:
wherein G is the number of grids containing particles, For the number of particles in the ith grid of the kth iteration, the formula represents that the smaller the number of particles in the grid is, the larger the value of P i k is, and the larger the P i k is, the larger the probability that the grid is selected is, and after the grid is determined, one particle in the grid is randomly selected as a global optimal position gbest.
Preferably, to limit the size of the external archive storing non-dominant solutions and to reduce the computational complexity, the maximum number of stores is set:
Firstly, judging the dominant relation between a new non-dominant solution and a solution in an external file, and reserving the non-dominant solution in the new non-dominant solution;
Then checking whether the external file size exceeds the maximum storage number, if so, deleting the non-dominant solution by adopting the density information of particles and a roulette mechanism, wherein the probability of selecting an ith grid is as follows:
Wherein G is the number of grids containing particles, N i is the number of particles in the ith grid, the formula represents that the more the number of particles in the grid, the larger the value of P i is, and the larger the probability is selected;
finally randomly deleting a particle from the selected grid; the process of deleting is repeated until the external file library does not exceed the maximum number of stores.
The beneficial effects of the invention are as follows:
(1) The method adopts a scene analysis method based on probability occurrence to convert the uncertainty model into multiple scenes with different occurrence probabilities, and solves the uncertainty of grid-connected output of the wind turbine.
(2) According to the AG-MOPSO algorithm, on the basis of a multi-target reactive power optimization model of the power distribution network in comprehensive consideration of system economy and stability, reactive power compensation of the doubly-fed wind driven generator is fully utilized, so that node voltage is kept above 0.94p.u, and the network loss reduction rate is above 60%.
(3) The AG-MOPSO algorithm has higher convergence speed than the NSGA-II algorithm, has short average calculation time, and can obtain a Pareto front with better distribution and better result. In addition, the Pareto optimal solution set is obtained under the condition of taking the economical efficiency of system operation and the electric energy quality of the power distribution network into consideration, and has certain guiding significance for the selection of the system operation optimization scheme.
(4) The reactive power optimization model and the multi-objective optimization algorithm can be suitable for the condition of other distributed energy networking, and have wide application prospect.
Drawings
FIG. 1 is a power characteristic of a wind turbine;
FIG. 2 is a schematic diagram of two objective function adaptive grids and boundaries;
FIG. 3 is a flow chart of the multi-objective reactive power optimization solution of the present invention;
FIG. 4 is a schematic diagram of a modified IEEE33 node power distribution system with wind power in accordance with a preferred embodiment;
FIG. 5 is a graph showing a comparison of the distribution of multi-objective optimized Pareto fronts verified by two algorithms according to a preferred embodiment;
fig. 6 is a schematic diagram of node voltages before and after optimization of the improved IEEE 33 node system.
Detailed Description
The invention will be further illustrated with reference to specific examples. Unless otherwise indicated, the starting materials and methods employed in the examples of the present invention are those conventionally commercially available in the art and those conventionally used.
And (3) calculating the power flow, namely calculating the distribution of active power, reactive power and voltage in the power grid under the conditions of given power system network topology, element parameters and power generation and load parameters. The tide calculation is to determine the steady state operation state parameters of each part of the power system according to the given power grid structure, parameters, the operation conditions of the generator, the load and other elements. Typically given operating conditions are power at various power and load points in the system, pivot point voltage, balance point voltage and phase angle. The operation state parameters to be solved comprise the voltage amplitude and phase angle of each bus node of the power grid, the power distribution of each branch, the power loss of the network and the like.
AG-MOPSO algorithm, multi-objective PARTICLE SWARM algorithm based on ADAPTIVE GRIDS, multi-target particle swarm algorithm of adaptive mesh.
Example 1
AG-MOPSO-based reactive power optimization method for wind-powered electricity containing power distribution network comprises the following steps:
s1: establishing a probability model of wind power plant output, and converting uncertainty of wind power output into scene power in a typical scene:
S1.1: the relationship between the output power p w and the wind speed v obtained from the power characteristic curve of the wind turbine shown in fig. 1 is:
Wherein c ci、vr、vco is cut-in wind speed, rated wind speed and cut-out wind speed respectively, and k 1＝pr(vr-vco)-1, k2＝-k1vco,pr is rated power of the wind turbine generator.
S1.2: dividing the output power of the wind turbine into three typical scenes by the formula (1): the method comprises a first scene of zero output of a shutdown state, a second scene of less rated output of corresponding power along with wind speed change state and a third scene of rated output of a rated power state.
S1.3: calculating the output power of the wind turbine generator in three typical scenes by combining the probability density function:
in the embodiment, the actual change of the wind speed is reflected by adopting a Weibull distribution model with two parameters, and the probability density function of Weibull distribution is as follows:
k and c are respectively the shape parameter and the scale parameter of Weibull distribution, and the probability of each scene occurrence is calculated according to a probability density function and is as follows:
Wherein, P 1、P2、P3 represents the occurrence probability of scene one, scene two and scene three respectively, the output power of the wind turbine corresponding to scene one and scene three is 0 and P r respectively, and the output power of the wind turbine of scene two is:
Therefore, the scene power in three typical scenes is obtained, namely, the uncertainty of the wind power output is converted into the scene power in the typical scenes.
S1.4: and multiplying the output power of the wind turbine in three typical scenes with the probability thereof respectively, and then summing (0*P 1+Pw2*P2+Pr*P3) to obtain the expected output power of the wind turbine as the active output of the fan.
S2: the method comprises the steps of comprehensively considering the economical efficiency and stability of power grid operation, establishing a reactive power optimization model of a power distribution network containing wind power by taking the minimum active network loss and voltage deviation as objective functions, and selecting the number of switching groups of reactive power compensation equipment and the reactive power output of a wind turbine generator as control variables and the voltage of a load node as a state variable by the model.
The active network loss f 1 and the voltage deviation f 2 of the system are respectively as follows:
Wherein, N is the number of system nodes, i and j are node labels, G ij is branch admittance between nodes i and j, U i and U j are voltage amplitudes of nodes i and j, θ ij is voltage phase difference of nodes i and j, and U i.N、Ui.max and U i.min are rated voltage of node i, maximum voltage of node and minimum voltage of node.
Thus, the objective function of the reactive power optimization model of the distribution network is:
F＝min(f1,f2)。
the reactive power optimization model of the power distribution network containing wind power needs to meet the following constraint conditions:
(1) Equation constraint:
Active power and reactive power balance constraint of system nodes:
Wherein, P Gi and Q Gi are respectively the active output and the reactive output of the power supply; p Li and Q Li are the active power and reactive power of the load node, respectively; q Ci is reactive compensation capacity; g ij and B ij are the conductance and susceptance between nodes i, j, respectively.
(2) Inequality constraint:
the method comprises the following steps of node voltage constraint, capacitor capacity constraint and output constraint of the wind driven generator:
Wherein, Q CZi、PWGi and Q WGi are respectively the number of capacitor switching groups, the active output and the reactive output of the fan.
S3: the AG-MOPSO algorithm is provided, as shown in fig. 3, the reactive power optimization model of the power distribution network containing wind power is solved through the AG-MOPSO algorithm, and uniformity and diversity of Pareto front distribution are guaranteed:
In order to obtain the Pareto optimal solution in the external archive, an adaptive grid is firstly established: for the optimization problem of m objective functions, an m-dimensional objective space is formed, grids with 2m boundaries are required to be set, and the upper and lower boundaries of the grids on the mth objective of the kth iteration are defined And/>The method comprises the following steps of:
Wherein, And/>Respectively the maximum value and the minimum value of the mth objective function, and h is the expansion coefficient; because of the iteration process,/>And/>The grid boundary is changed continuously, so that the grid boundary can be adjusted adaptively to better reflect the distribution condition of the solution, and a grid schematic diagram of the two objective functions of the embodiment is shown in fig. 2. Further, a function value/>The corresponding grid coordinates are:
Wherein, For the grid size of the mth objective function of the kth iteration, g is the number of divided grids, and [ (· ] is a rounding function), the number of Pareto optimal solutions in each grid can be calculated according to the formula, and the density information of particles in the grid is reflected.
S3.1: reading in power grid operation data, setting AG-MOPSO algorithm parameters, and encoding control variablesQ CZi is the number of switching groups of the ith capacitor bank, and Q WGi is the reactive power output of the ith wind turbine generator;
s3.2: initializing the position and the speed of particles, and calculating the power flow to obtain corresponding active network loss and voltage deviation;
S3.3: taking the current particle positions as individual optimal positions pbest, judging the dominant relationship between the individual optimal positions, putting non-dominant solutions into an external archive, and determining a global optimal position gbest through a global optimal particle selection principle;
s3.4: iteratively updating the position and the speed of the particles, and generating a new solution set by tide calculation;
S3.5: determining pbest through an individual optimal particle selection principle, adding non-dominant solutions in the individual optimal particle selection principle into an external archive, maintaining the number of Pareto optimal solutions by utilizing an external archive maintenance principle, and determining gbest through a global optimal particle selection principle;
the selection of optimal particles is mainly the selection of individual optimal positions pbest and global optimal positions gbest:
Selecting non-dominant particles as pbest by judging the dominant relationship between the current particle position and the optimal position of the historical individual, and randomly selecting if the non-dominant particles are not dominant; to ensure uniformity of Pareto front distribution, gbest is selected by adopting density information of particles, and the probability of selecting the ith grid in the kth iteration is as follows:
wherein G is the number of grids containing particles, For the number of particles in the ith grid of the kth iteration, the formula represents that the smaller the number of particles in the grid is, the larger the value of P i k is, and the larger the P i k is, the larger the probability that the grid is selected is, and after the grid is determined, one particle in the grid is randomly selected as a global optimal position gbest.
To limit the size of the external archive storing non-dominant solutions and reduce the computational complexity, the maximum number of stores is set:
Firstly, judging the dominant relation between a new non-dominant solution and a solution in an external file, and reserving the non-dominant solution in the new non-dominant solution;
Then checking whether the external file size exceeds the maximum storage number, if so, deleting the non-dominant solution by adopting the density information of particles and a roulette mechanism, wherein the probability of selecting an ith grid is as follows:
Wherein G is the number of grids containing particles, N i is the number of particles in the ith grid, the formula represents that the more the number of particles in the grid, the larger the value of P i is, and the larger the probability is selected;
finally randomly deleting a particle from the selected grid; the process of deleting is repeated until the external file library does not exceed the maximum number of stores.
S3.6: if the algorithm reaches the maximum iteration number or meets the convergence condition, outputting the Pareto optimal solution in the external archive, otherwise, jumping to the step S3.4 to continue calculation.
Example 2
The effectiveness of the AG-MOPSO algorithm provided in the embodiment 1 is verified, a reactive power optimization simulation test is carried out by adopting an improved IEEE 33 node distribution system containing wind power as shown in fig. 4, 7 switchable parallel capacitors are respectively installed at nodes 5, 17, 24 and 26, each capacitor is 0.15Mvar, nodes 9 and 30 are connected into a 1.5MW double-fed wind turbine generator, the bus outlet voltage is 690V, the switching-in wind speed is 3m/s, the rated wind speed is 12m/s, the switching-out wind speed is 25m/s, and the shape parameters and the scale parameters are 2.4 and 9.5 respectively.
The scenario occurrence probability and the wind power output power calculated by the formulas (3) to (6) are shown in table 1, and thus the desired output power of the doubly-fed wind generator is 0.7088MW (0*P 1+Pw2*P2+Pr*P3 = 0.7088), and the reactive power limit is (-3.554,0.6273).
TABLE 1 scene probabilities and power
Setting AG-MOPSO algorithm parameters: the maximum iteration number is 200, the particle swarm size is 150, the maximum capacity of the external archive is 50, the learning factor c 1＝c2 =2, the inertia weight w=0.9, the expansion coefficient h=0.1 and the grid number g=8.
The improved IEEE 33 node power distribution system is subjected to reactive power optimization by adopting an existing NSGA-II algorithm and an AG-MOPSO algorithm, the two algorithms are run for 20 times, the running results are shown in a table 2, and the Pareto front edge is shown in fig. 5.
Table 2 comparison of the results of the two algorithms
As can be seen from Table 2, the AG-MOPSO algorithm is superior to the NSGA-II algorithm in terms of minimum active loss and minimum voltage deviation, and the average calculation time is shorter; meanwhile, as can be seen from fig. 5, the Pareto front obtained by the AG-MOPSO algorithm is closer to the origin and better in distribution. 3 reactive power optimization schemes of AG-MOPSO algorithm are selected, namely the solution with the minimum active network loss, the minimum voltage deviation and the middle of the Pareto front, and the control variable values corresponding to the 3 optimization schemes are shown in tables 3 and 4 respectively.
TABLE 3 control variable take-off for reactive optimization scheme
Table 4 reactive optimization scheme comparison
In the three optimization schemes of table 3, the reactive power output of the doubly-fed wind generator of the access node 30 reaches the maximum value allowed, which means that the voltage of the end node of the line is often lower, and enough reactive power is needed to increase the voltage level. As can be seen from table 4, in scheme 1, the active loss is reduced from 2.0268×10-4p.u to 3.6646×10-4p.u, and the loss reduction rate is up to 81.92%; scheme 2 minimizes the node voltage deviation of the system from 1.739×10-1p.u to 7.1338×10-5p.u, with a voltage deviation reduction of 99.96%; scheme 3 is a compromise between minimum active power loss and minimum voltage deviation, the net loss reduction rate is 78.97%, and the voltage deviation reduction rate is 98.96%. Fig. 6 shows the node voltage conditions before and after optimization of the improved IEEE 33 node system.
As can be seen from FIG. 6, compared with the non-optimization, the node voltage is above 0.94p.u by the 3 schemes, the node voltage level is effectively improved, no voltage out-of-range occurs, and the operation safety of the system is ensured, wherein the node voltage of the system in the scheme 2 is above 0.98p.u, and the voltage stability of the system is better.
Example 3
The present embodiment defines a Pareto optimal solution set:
The multi-objective optimization problem is to find a set of solutions that minimizes or maximizes two or more objective functions, i.e., pareto optimal solution sets, under the constraint conditions.
If there is a decision vectorAnd/>Make/>And/>And is present inOr/>Then call/>Dominance/>Is marked as/>I.e./>Is the optimal decision vector.
The set of all optimal decision vectors is called Pareto optimal solution set, and its mapping on the target space is called Pareto front.
The above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.
Claims (7)
1. The AG-MOPSO-based reactive power optimization method for the wind power distribution network is characterized by comprising the following steps of:
s1: establishing a probability model of wind power plant output, and converting uncertainty of wind power output into scene power in a typical scene:
S1.1: the relation between the output power p w and the wind speed v obtained by the power characteristic curve of the wind turbine generator;
s1.2: dividing the output power of the wind turbine into three typical scenes;
S1.3: calculating the output power of the wind turbine generator in three typical scenes by combining the probability density function;
s1.4: the output power of the wind turbine generator in three typical scenes is multiplied by the probability of the wind turbine generator respectively and then summed to obtain the expected output power of the wind turbine generator, and the expected output power is used as the active output of the fan;
s2: establishing a reactive power optimization model of a power distribution network containing wind power by taking minimum active network loss and voltage deviation as objective functions, wherein the model selects the number of switching groups of reactive power compensation equipment and reactive power output of a wind turbine generator as control variables, and load node voltage as a state variable;
s3: based on AG-MOPSO algorithm, solving a reactive power optimization model of the power distribution network containing wind power through AG-MOPSO algorithm, and guaranteeing uniformity and diversity of Pareto front distribution:
S3.1: reading power grid operation data, setting AG-MOPSO algorithm parameters, and coding control variables by x= [ Q CZ1 ,QCZ2,…,QCZi ,…|QWG1 ,QWG2 ,…QWGi, … ], wherein Q CZi is the number of i-th capacitor bank switching groups, and Q WGi is the reactive power output of the i-th wind turbine generator;
s3.2: initializing the position and the speed of particles, and calculating the power flow to obtain corresponding active network loss and voltage deviation;
s3.3: taking the current particle positions as individual optimal positions pbest, judging the dominant relationship between the individual optimal positions, putting non-dominant solutions into an external archive, and determining a global optimal position gbest through a global optimal particle selection principle;
s3.4: iteratively updating the position and the speed of the particles, and generating a new solution set by tide calculation;
S3.5: determining pbest through an individual optimal particle selection principle, adding non-dominant solutions in the individual optimal particle selection principle into an external archive, maintaining the number of Pareto optimal solutions by utilizing an external archive maintenance principle, and determining gbest through a global optimal particle selection principle;
s3.6: if the algorithm reaches the maximum iteration number or meets the convergence condition, outputting a Pareto optimal solution in an external archive, otherwise, jumping to the step S3.4 to continue calculation;
The Pareto optimal solution in the external archive is obtained through construction of an adaptive grid:
For the optimization problem of m objective functions, an m-dimensional objective space is formed, grids with 2m boundaries are required to be set, and the upper and lower boundaries of the grids on the mth objective of the kth iteration are defined And/>The method comprises the following steps of:
Wherein, And/>Respectively the maximum value and the minimum value of the mth objective function, and h is the expansion coefficient; because of the iteration process,/>And/>Is continuously changed, so that the grid boundary can be adaptively adjusted to better reflect the distribution condition of the solution, and further, the function value/>The corresponding grid coordinates are:
Wherein, For the grid size of the mth objective function of the kth iteration, g is the number of divided grids, and [ (· ] is a rounding function), the number of Pareto optimal solutions in each grid can be calculated according to the formula, and the density information of particles in the grid is reflected;
The selection of the optimal particles is mainly to select an individual optimal position pbest and a global optimal position gbest:
selecting non-dominant particles as pbest by judging the dominant relationship between the current particle position and the optimal position of the historical individual, and randomly selecting if the non-dominant particles are not dominant; to ensure uniformity of Pareto front distribution, gbest is selected by adopting density information of particles, and the probability of selecting the ith grid in the kth iteration is as follows:
wherein G is the number of grids containing particles, For the number of particles in the ith grid of the kth iteration, the formula shows that the smaller the number of particles in the grid is, the larger the value of P i k is, and the larger the P i k is, the larger the probability that the grid is selected is, and after the grid is determined, one particle in the grid is randomly selected as a global optimal position gbest;
To limit the size of the external archive storing non-dominant solutions and to reduce the computational complexity, the maximum number of stores is set:
Firstly, judging the dominant relation between a new non-dominant solution and a solution in an external file, and reserving the non-dominant solution in the new non-dominant solution;
Then checking whether the external file size exceeds the maximum storage number, if yes, deleting the non-dominant solution by adopting the density information of particles and a roulette mechanism, wherein the probability of selecting an ith grid is as follows:
Wherein G is the number of grids containing particles, N i is the number of particles in the ith grid, the formula represents that the more the number of particles in the grid, the larger the value of P i is, and the larger the probability is selected;
finally randomly deleting a particle from the selected grid; the process of deleting is repeated until the external archive does not exceed the maximum number of stores.
2. The AG-MOPSO-based reactive power optimization method for a wind-powered distribution network according to claim 1, wherein the relationship between the output power p w and the wind speed v in S1.1 is:
Wherein c ci、vr、vco is the cut-in wind speed, the rated wind speed and the cut-out wind speed ,k1＝pr (vr -vco )-1,k2＝-k1vco,pr is the rated power of the wind turbine.
3. The AG-MOPSO-based reactive power optimization method for a wind power distribution network according to claim 2, wherein the output power of the wind turbine is divided into three typical scenarios by the formula (1): the method comprises a first scene of zero output in a shutdown state, a second scene of undershot output in a state of corresponding power changing along with wind speed, and a third scene of rated output in a rated power state.
4. The AG-MOPSO based reactive power optimization method for a wind power distribution network according to claim 3, wherein the probability of occurrence of said three typical scenarios is calculated according to a probability density function:
Wherein P 1、P2、P3 represents occurrence probability of a first scene, a second scene and a third scene respectively, f (v) represents probability density function of Weibull distribution, and k and c are shape parameter and scale parameter of Weibull distribution respectively;
Therefore, the output power of the wind turbine corresponding to the first scene and the third scene is 0 and p r respectively, and the output power of the wind turbine corresponding to the second scene is:
5. The AG-MOPSO-based reactive power optimization method for a wind power distribution network according to claim 1, wherein the active network loss f 1 and the voltage deviation f 2 in S2 are respectively:
Wherein N is the number of system nodes, i and j are node labels, G ij is the branch admittance between the nodes i and j, U i and U j are the voltage amplitude values of the nodes i and j respectively, theta ij is the voltage phase difference of the nodes i and j, and U i.N、Ui.max and U i.min are the rated voltage, the maximum value and the minimum value of the node voltage of the node i respectively;
Thus, the objective function of the reactive power optimization model of the distribution network is:
F＝min(f1 ,f2 )。
6. The AG-MOPSO-based reactive power optimization method for a wind power distribution network according to claim 5, wherein the equality constraint condition of the reactive power optimization model of the distribution network is the active power and reactive power balance constraint of the system node:
Wherein, P Gi and Q Gi are respectively the active output and the reactive output of the power supply; p Li and Q Li are the active power and reactive power of the load node, respectively; q Ci is reactive compensation capacity; g ij and B ij are the conductance and susceptance between nodes i, j, respectively.
7. The AG-MOPSO based reactive power optimization method of a wind power distribution network according to claim 5, wherein the inequality constraints of the reactive power optimization model of the distribution network include node voltage constraints, capacitor capacity constraints, and wind power generator output constraints:
Wherein, Q CZi、PWGi and Q WGi are respectively the capacitor switching group number, the active output and the reactive output of the fan.
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