Intermittent distributed power supply planning method based on multi-scene analysis

Abstract

The invention relates to an intermittent distributed power supply planning method based on multi-scene analysis, and belongs to the field of power distribution network planning. Performing scene reduction on a wind speed and illumination intensity time sequence scene by using a K-means clustering algorithm; and an improved cuckoo particle swarm search algorithm is adopted to solve the DG and energy storage device addressing and sizing planning model taking the minimum sum of the annual social cost, the network loss cost, the electricity purchase cost and the environmental pollution compensation cost of the power distribution system as an objective function. According to the method, the intermittent DG and the energy storage device can be scientifically and reasonably subjected to addressing and sizing planning.

Description

Technical Field

[0001] The present invention belongs to the field of distribution network planning, and in particular relates to an intermittent distributed power supply planning method based on multi-scenario analysis. Background Art

[0002] With the development of smart grids and active distribution networks, more and more distributed generation (DG) is connected to the distribution network. Since DG output is intermittent and uncertain, it increases the uncertainty and complexity of system operation and planning. Therefore, how to scientifically and reasonably plan the site selection and capacity of intermittent DG and energy storage devices has become one of the hot research issues. Summary of the invention

[0003] The purpose of the present invention is to solve the problems of the prior art and provide an intermittent distributed power supply planning method based on multi-scenario analysis. The method takes into account the intermittent DG output and load uncertainty, includes the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost in the optimization planning objective function, and establishes a corresponding multi-objective optimization planning model. The present invention also proposes a method for scenario reduction using a K-means clustering algorithm and a method for solving a planning model using an improved cuckoo particle swarm search algorithm.

[0004] To achieve the above-mentioned purpose, the technical solution of the present invention is: a method for planning intermittent distributed power sources based on multi-scenario analysis, characterized in that the wind speed and light intensity time series scenarios are reduced by using the K-means clustering algorithm, and the site selection and sizing planning model of DG and energy storage devices with the objective function of minimizing the sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost is solved by using an improved cuckoo particle swarm search algorithm.

[0005] In one embodiment of the present invention, the method comprises the following steps:

[0006] (1) Establish a DG and energy storage device site selection and sizing planning model that takes into account the minimum sum of the annual social cost of the distribution system, network loss cost, power purchase cost, and environmental pollution compensation cost as the objective function, and obtain load information, grid structure information, wind speed, light intensity data, and DG output model;

[0007] (2) Setting the parameters of the improved cuckoo particle swarm search algorithm, namely CSPSO;

[0008] (3) Using the K-means clustering algorithm to reduce the wind speed and light intensity time series scenes throughout the year, the typical time series scene data after reduction and the scene probability corresponding to each typical time series scene are obtained;

[0009] (4) Initialize the nest position of CSPSO, that is, generate the initial population for DG and energy storage device planning, including the access position and access capacity of DG and energy storage devices;

[0010] (5) Based on the grid structure information, load information, and the DG access location and access capacity in the network, the power flow calculation method is used to perform power flow calculation;

[0011] (6) Calculate the objective function value of each decision target under the corresponding planning scheme, update the position of the bird's nest according to the objective function value corresponding to the individual, then recalculate the objective function value, and compare the various objective function values ​​to select the best, and select the fitness value and optimal solution corresponding to the best individual;

[0012] (7) Determine whether the convergence condition is met; if so, go to step (8); if not, return to step (6);

[0013] (8) The parameters corresponding to the location of the bird's nest under the corresponding planning scheme are the DG optimal planning scheme required, and the DG optimal planning scheme is output.

[0014] In one embodiment of the present invention, in step (1), the objective function of the DG and energy storage device site selection and sizing planning model, which takes into account the minimum sum of the annual social cost of the distribution system, the network loss cost, the power purchase cost, and the environmental pollution compensation cost, is as follows:

[0015] minC=C sc +C buy +C loss +C env

[0016] Where C is the annual comprehensive cost of the distribution system; C sc is the annual social cost of DG and energy storage devices converted to annual cost for the distribution system; C buy is the annual electricity purchase cost of the distribution system; C loss is the annual network loss cost of the distribution system; C env Compensate for the annual environmental pollution costs of the power distribution system.

[0017] In one embodiment of the present invention, the specific calculation formulas for the annual social cost of the power distribution system, network loss cost, power purchase cost, and environmental pollution compensation cost are as follows:

[0018] 1) Annual social cost

[0019] The annual social cost is composed of the equipment investment cost C of DG and energy storage device invest , the operation and maintenance cost of DG and energy storage device C OM and the government subsidy income C for intermittent DG B composition:

[0020] C sc =C invest +C OM -C B

[0021] in,

[0022]

[0023] Where n WG 、n PV 、n BS are the number of nodes installed for wind power WG, photovoltaic power generation PV and energy storage devices; P i,WG is the rated installed capacity of the i-th node WG; P j,PV is the rated installed capacity of the PV of the jth node; P k,BS is the rated installed capacity of the energy storage device at the kth node; c t,WG 、c t,PV 、c t,BS are the investment costs of unit capacity WG, PV and energy storage device respectively; q is the economic service life of DG and energy storage device; r is the discount rate; N m is the number of seasons, take 4; d m is the number of days corresponding to the mth season; N s is the total number of scenes after scene reduction; p s is the probability corresponding to the sth typical time series scenario; c om,WG 、c om,PV 、c om,BS are the operation and maintenance costs per unit capacity of WG, PV and energy storage devices respectively; P i,s,t,WG is the actual power generation of the i-th node WG at time t in the s-th typical time sequence scenario; P j,s,t,PV is the actual power generation of the jth node PV at time t in the sth typical time sequence scenario; P k,s,t,BS is the charge and discharge power of the k-th node energy storage device at time t in the s-th typical timing scenario; c bt,WG 、c bt,PV They are the government subsidies per unit of electricity for WG and PV respectively;

[0024] 2) Annual electricity purchase cost

[0025] The annual electricity purchase cost of the distribution network refers to the cost paid by the distribution network to power generation enterprises or other power grids for purchasing electricity throughout the year. Its size can reflect the load density of a region and the region's ability to accept DG:

[0026]

[0027] Where N is the total number of nodes in the system; P j,s,t,Lis the load size of node j at time t in the sth typical timing scenario; P j,s,t,WG P is the WG output of node j at time t in the sth typical timing scenario; j,s,t,PV is the PV output of node j at time t in the sth typical time series; c e is the unit electricity price;

[0028] 3) Annual network loss cost

[0029]

[0030] Where, L is the number of network branches; I k (t) is the current of the kth branch at time t; R k is the resistance corresponding to the kth branch;

[0031] 4) Annual environmental pollution compensation cost

[0032] Environmental compensation costs include the costs of environmental degradation caused by pollutant gas emissions, ecological damage caused by the use of fossil energy for thermal power generation, and penalties for pollutant gas emissions:

[0033]

[0034] Where P f is the annual power purchase of the distribution network; M is the type of pollutants generated during traditional thermal power generation; a k is the emission intensity of the kth pollutant gas; X k Y is the environmental value conversion standard of the kth pollutant; k is the government penalty price for the emission of the kth pollutant.

[0035] In one embodiment of the present invention, in step (1), the constraints of the DG and energy storage device site selection and sizing planning model taking into account the minimum sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost as the objective function are as follows:

[0036] 1) Power balance constraints

[0037]

[0038] Where P i is the active power of node i; Q i is the reactive power of node i; V i , V j are the voltage values ​​of node i and node j respectively; G ij and B ij are the conductance and susceptance of the line between node i and node j respectively; θ ij is the voltage phase angle difference between nodes i and j;

[0039] 2) Node DG installation capacity constraints

[0040] P DGi,min ≤P DGi ≤P DGi,max

[0041] Where P DGi is the DG installation capacity of node i; P DGi,max , P DGi,min are the upper and lower limits of DG installation capacity of node i respectively;

[0042] 3) Node voltage constraints

[0043] U imin ≤U i ≤U imax

[0044] Where U imin , U imax are the minimum and maximum values ​​of the voltage allowed at node i respectively;

[0045] 4) Branch power constraints

[0046] S ij ≤S ijmax

[0047] In the formula, S ij is the apparent power of branch ij; S ijmax is the maximum transmission power allowed by branch ij;

[0048] 5) System DG installation total capacity constraints

[0049]

[0050] Where n DG The total number of nodes installed for DG; P DG,i is the DG installation capacity of node i; η is the upper limit of DG penetration rate allowed by the system; P Lj is the load size of node j.

[0051] In one embodiment of the present invention, in step (3), K-means clustering technology is used to take 24 hours of data in a day as the clustering unit, so there are 365 original wind speed time series scenes and light intensity time series scenes throughout the year. The 365 original wind speed time series scenes and light intensity time series scenes are synchronously divided and clustered to obtain several typical time series scenes that can represent the changing characteristics of the original data.

[0052] In one embodiment of the present invention, in step (3), the specific implementation method of using the K-means clustering algorithm to reduce the wind speed time series scene is as follows:

[0053] 1) Use x i (i=1,2,3,...,N) represents the original time series scene set before reduction. First, k scenes are randomly selected from the original time series scene set as the initial clustering centers, i.e., cluster centers. The cluster center scene set is ξ1, ξ2, ξ3,..., ξ k ;

[0054] 2) Calculate the Euclidean distances from each remaining scene in the original time series scene set to the k initial cluster centers;

[0055] 3) According to the principle of proximity similarity, the remaining scenes in the original time series scene set are classified into the cluster with the closest cluster center;

[0056] 4) Calculate the average values ​​of all scenes in the k clusters after classification, take them as the new cluster centers of the k clusters, and update the cluster centers;

[0057] 5) Repeat steps 2) to 4) until the clustering results and cluster centers no longer change, and the scene reduction is completed.

[0058] In one embodiment of the present invention, in step (3), after the scene reduction, the original N original time series scenes are reduced to S representative typical time series scenes, so as to calculate the probability of each typical time series scene according to the number of original time series scenes contained in each typical time series scene set after the reduction.

[0059] In one embodiment of the present invention, after the scenario reduction in step (3) is completed, the output of wind power and photovoltaic power generation in each typical time sequence scenario is calculated based on the following two formulas:

[0060]

[0061] Where P WG is the active power output of wind power, P WGR is the rated power of wind power, v ci is the cut-in wind speed; v r is the rated wind speed; v co is the cut-out wind speed; v is the wind speed; P PV It is the active power output of photovoltaic power generation; P PVR is the rated power of photovoltaic power generation; I is the actual solar intensity; I r is the rated light intensity.

[0062] In one embodiment of the present invention, in step (2), the improved cuckoo particle swarm search algorithm integrates the particle swarm algorithm and the cuckoo algorithm, and the specific implementation steps are as follows:

[0063] Step 1: Set the algorithm parameters, including the number of bird nests n, the maximum number of iterations Gen, the discovery probability Pa, the learning factors c1, c2 and the inertia weight ω max ,ω min ; Randomly initialize a set of bird nest locations Initial Speed And evaluate its fitness value; initialize the individual extreme value of the population And assign the best individual among the individual extreme values ​​to the group extreme value

[0064] Step 2: Update the speed and position of all particles to obtain a new set of bird nests

[0065] Step 3: Calculate the updated bird nests according to the objective function of the optimization problem The corresponding fitness value and the bird's nest before the update The corresponding fitness values ​​are compared, the best ones are retained, and a new set of bird nest locations is obtained.

[0066] Step 4: Generate a random number r∈(0,1) as the probability of the host bird discovering the foreign cuckoo egg, and compare it with the preset maximum discovery probability Pa. If r>Pa, discard the corresponding nest location and generate a new nest location to replace the old one, and obtain a new set of nests.

[0067] Step 5: Re-evaluate the bird's nest based on the objective function of the optimization problem The corresponding fitness value and the location of the bird's nest Compare the corresponding fitness values, select the best one, and form a new nest location

[0068] Step 6: Extract The best quality bird's nest position is determined to see whether it meets the accuracy requirements. If it does, the algorithm ends and the global optimal position is output. If it does not, go to step 7.

[0069] Step 7: Determine whether the maximum number of iterations has been reached. If so, end the process and output the optimal value. If not, compare and Let t = t + 1, Update the individual optimal extreme value and the group optimal extreme value, and go to step 2 to continue iterative optimization.

[0070] Compared with the prior art, the present invention has the following beneficial effects: the present invention uses the K-means clustering algorithm to reduce the wind speed and light intensity time series scenes, and uses the improved cuckoo particle swarm search algorithm to solve the DG and energy storage device site selection and sizing planning model with the minimum sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost as the objective function. The present invention can scientifically and reasonably carry out site selection and sizing planning for intermittent DG and energy storage devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is the relationship between wind power active output and wind speed.

[0072] Figure 2 It is the relationship between the active output of photovoltaic power generation and the light intensity.

[0073] Figure 3 This is the solution flow chart of the K-means clustering algorithm.

[0074] Figure 4 This is the calculation flow chart of CSPSO algorithm. DETAILED DESCRIPTION

[0075] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings.

[0076] The present invention provides an intermittent distributed power planning method based on multi-scenario analysis, which is characterized in that the K-means clustering algorithm is used to reduce the wind speed and light intensity time series scenarios, and an improved cuckoo particle swarm search algorithm is used to solve the DG and energy storage device site selection and sizing planning model with the minimum sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost as the objective function.

[0077] The following is the specific implementation process of the present invention.

[0078] A large number of experimental studies have shown that the variation pattern of wind speed in most areas approximately obeys the Weibull distribution, and its probability density function is shown in formula (1).

[0079]

[0080] Where k is the shape parameter of the Weibull distribution; c is the scale parameter of the Weibull distribution, and v is the wind speed.

[0081] When the wind speed is known, the wind power output model can be obtained based on the relationship between wind speed and distributed wind power generation active output power. Wind turbines are set with parameters such as cut-in wind speed, cut-out wind speed, and rated wind speed. The wind turbine can only rotate when the wind speed exceeds the cut-in wind speed. As the wind speed increases, the output power changes. When the wind speed exceeds the rated wind speed but does not exceed the cut-out wind speed, the wind power output power remains unchanged. When the wind speed exceeds the cut-out wind speed, the WG output power is 0.

[0082] Wind power active output P WG The relationship with wind speed can be expressed by a piecewise function:

[0083]

[0084] Where P WGR is the rated power of wind power, v ci is the cut-in wind speed; v r is the rated wind speed; v co To cut out wind speed.

[0085] Wind power active output curve is as follows: Figure 1 shown.

[0086] The solar radiation intensity approximately follows the Beta distribution within a certain period of time, and its probability density function is:

[0087]

[0088] In the formula, γ is the actual solar illumination intensity in a certain period of time, max is the maximum solar illumination intensity in a certain period of time, and α and β are the two shape parameters of Beta distribution.

[0089] Photovoltaic power generation is closely related to light intensity. Once the distribution function of light intensity is known, the output model of photovoltaic power generation can be obtained based on the relationship between light intensity and photovoltaic power generation output power. The photovoltaic generator set is set with a rated light intensity. When the light intensity is less than the rated value, the photovoltaic power generation output power is proportional to the light intensity; when the light intensity is greater than the rated value, the photovoltaic power generation output power remains unchanged.

[0090] Photovoltaic power generation active output P PV The relationship with light intensity can be expressed as:

[0091]

[0092] Where P PVR is the rated power of photovoltaic power generation; I is the actual solar intensity; I r is the rated light intensity.

[0093] Photovoltaic power generation active output curve Figure 2 shown.

[0094] 1. Scene reduction

[0095] The present invention adopts K-means clustering algorithm to perform synchronous scene division on large-scale original wind speed and light intensity time series data to obtain a small number of representative typical scenes.

[0096] The K-means clustering algorithm uses the Euclidean distance as the similarity partitioning index, and its specific expression is shown in formula (5).

[0097]

[0098] In the formula, S i =(x i1 ,x i2 ,…x in ),S j =(x j1 ,x j2 ,…x jn ) are n-dimensional sample data respectively.

[0099] The core idea of ​​the K-means clustering algorithm is: first randomly select k elements as the initial cluster centers, then calculate the Euclidean distances of the remaining elements to the k cluster centers, and classify each element into the cluster closest to it according to the principle of proximity similarity. Finally, take the average value in each cluster and use it as the new cluster center of each cluster, and continuously iterate and update the k cluster centers until the convergence condition is met.

[0100] In order to verify the effectiveness of clustering, the present invention verifies it by calculating the pseudo F-statistic (PFS) index under different clustering methods. For a data sample with a total number of samples of N and a dimension of D, the calculation formula of the PFS index is defined as:

[0101]

[0102] In the formula, k is the number of clustering scenes; N is the total number of samples; tr(S B ) and tr(S W ) are the traces of the inter-class scatter matrix and intra-class scatter matrix of the samples, respectively. The larger the number of clusters, the smaller the intra-class sample distance of the clustering result, and the larger the inter-class distance. The larger the PFS index value, the better the clustering result. The search range of the cluster number is By calculating and comparing the PFS index values ​​corresponding to each cluster number, a reasonable clustering result can be selected.

[0103] The present invention selects 8760 hours of wind speed and light intensity sample data of the planning area throughout the year as the original scene data for scene reduction. The typical time series scene analysis method uses K-means clustering technology to use 24 hours of data in a day as the clustering unit, so there are 365 original scenes throughout the year. The 365 original sample data are synchronously divided and clustered to obtain several time series scenes that can represent the change characteristics of the original data.

[0104] Taking the typical time series scenario of wind speed in the planned area of ​​the distribution network as an example, assuming that the total number of historical wind speed scenarios throughout the year is N, and the daily wind speed data is taken as a scenario, recorded as n (n = 1, 2...N), if each scenario has T wind speed measurement data at time, then the wind speed scenario data throughout the year can be represented by an N×T matrix. The K-means clustering algorithm is used to perform cluster analysis on the original scenario data, reducing the N original time series scenarios to S typical time series scenarios, generating an S×T matrix, each typical scenario contains N d The clustering algorithm is used to reduce the number of scenes in the original data. Although the number of scenes is reduced, the time series of the data at T moments in the day remains unchanged, ensuring the time series of the original scene data.

[0105] Use x i (i=1,2,3,...,N) represents the original data scene set before reduction. The K-means clustering algorithm is used to reduce the wind speed and light intensity data scenes. The implementation process is as follows:

[0106] 1) First, randomly select k scenes from the original scene set as the initial clustering centers, i.e., cluster centers. The cluster center scene set is ξ1, ξ2, ξ3, ..., ξ k .

[0107] 2) Calculate the Euclidean distances of each remaining element in the scene set to the k initial cluster centers.

[0108] 3) According to the principle of proximity similarity, the remaining scenes are classified into the cluster with the closest cluster center.

[0109] 4) Calculate the average values ​​of all scenes in the k clusters after classification, take them as the new cluster centers of the k clusters, and update the cluster centers.

[0110] 5) Repeat steps 2 to 4 until the clustering results and cluster centers no longer change, and the scene reduction is completed.

[0111] The solution flow chart of K-means clustering algorithm is as follows: Figure 3After the scene reduction, the original N original time series scenes can be reduced to S representative typical time series scenes, and the probability of each typical scene can be calculated according to the number of original scenes included in each typical scene set after reduction.

[0112] according to Figure 3 The solution process steps shown can reduce the original scene data of wind speed and light intensity to the required typical scene data. After the scene is reduced, the output of WG and PV in each typical scene is calculated according to formula (2) and formula (4).

[0113] Since intermittent DG output is uncertain, the distribution system must have sufficient spare capacity to compensate for the randomness of the output, which limits the system's ability to accept DG in terms of both economy and safety, greatly reducing the distribution network's ability to absorb intermittent DG, thereby reducing energy utilization. While planning DG, installing a certain amount of energy storage devices and utilizing the charging and discharging of energy storage devices can suppress the volatility of DG and increase the distribution network's ability to absorb DG.

[0114] Therefore, based on the timing characteristics of DG and load, the present invention takes distribution network flow constraints, node voltage constraints, branch power constraints, DG output constraints, etc. as constraints, and establishes a DG and energy storage device site selection and capacity planning model with the annual social cost of the distribution network, network loss cost, power purchase cost and environmental pollution compensation cost as the minimum objective function. In the solution algorithm, the K-means clustering algorithm is used to reduce the wind speed and light intensity for 365 days a year, and the probability of each typical scene after reduction is obtained. In order to improve the optimization speed and accuracy of the planning model, it is proposed to use an improved cuckoo particle swarm algorithm to solve the planning model.

[0115] 2. Establishment of site selection and capacity planning model

[0116] Taking into account the timing complementary characteristics of DG, load and energy storage devices, and taking the minimum sum of the annual social cost of the distribution system, electricity purchase cost, network loss cost and environmental compensation cost as the objective function, the site selection and sizing planning model of DG and energy storage devices is established as shown in formula (7).

[0117] minC=C sc +C buy +C loss +C env (7)

[0118] Where C is the annual comprehensive cost of the distribution system; C sc is the annual social cost of DG and energy storage devices converted to annual cost for the distribution system; C buy is the annual electricity purchase cost of the distribution system; C lossis the annual network loss cost of the distribution system; C env is the annual environmental pollution compensation cost of the distribution system. The specific calculation formulas of various costs are shown in equations (8) to (15).

[0119] (1) Annual social cost

[0120] The annual social cost is mainly composed of the equipment investment cost of DG and energy storage devices C invest , the operation and maintenance cost of DG and energy storage device C OM and the government subsidy income C for intermittent DG B It consists of several parts.

[0121] C sc =C invest +C OM -C B (8)

[0122] in,

[0123]

[0124] Where n WG 、n PV 、n BS are the number of nodes installed by WG, PV and energy storage devices respectively; P i,WG is the rated installed capacity of the i-th node WG; P j,PV is the rated installed capacity of the PV of the jth node; P k,BS is the rated installed capacity of the energy storage device at the kth node; c t,WG 、c t,PV 、c t,BS are the investment costs of unit capacity WG, PV and energy storage device respectively; q is the economic service life of DG and energy storage device; r is the discount rate; N m is the number of seasons, take 4; d m is the number of days corresponding to the mth season; N s is the total number of scenes after scene reduction; p s is the probability corresponding to the sth typical scene; c om,WG 、c om,PV 、c om,BS are the operation and maintenance costs per unit capacity of WG, PV and energy storage devices respectively; P i,s,t,WG is the actual power generation of the i-th node WG at time t in the s-th scenario; P j,s,t,PV is the actual power generation of the jth node PV at time t in the sth scenario; P k,s,t,BS is the charging and discharging power of the k-th node energy storage device at time t in the s-th scenario; c bt,WG 、c bt,PV They are the government subsidies per unit of electricity for WG and PV respectively.

[0125] (2) Annual electricity purchase cost

[0126] The annual electricity purchase cost of the distribution network refers to the cost paid by the distribution network to power generation enterprises or other power grids for purchasing electricity throughout the year. Its size can reflect the load density of a region and the region's ability to accept DG. The specific model is shown in formula (12).

[0127]

[0128] Where N is the total number of nodes in the system; P j,s,t,L is the load size of node j at time t in the sth scenario; P j,s,t,WG P is the WG contribution of node j at time t in the sth scenario; j,s,t,PV is the PV output of node j at time t in the sth scenario; c e The unit electricity price.

[0129] (3) Annual network loss cost

[0130]

[0131] Where, L is the number of network branches; I k (t) is the current of the kth branch at time t; R k is the resistance corresponding to the kth branch.

[0132] (4) Annual environmental pollution compensation cost

[0133] Environmental compensation costs generally include the costs of environmental quality degradation caused by pollutant gas emissions, ecological damage caused by the use of fossil energy for thermal power generation, and penalty costs for the emission of pollutant gases (such as sulfur dioxide, carbon dioxide, carbon oxides, etc.). The specific expressions are shown in equations (14) and (15).

[0134]

[0135] Where P f is the annual power purchase of the distribution network; M is the type of pollutants generated during traditional thermal power generation; a k is the emission intensity of the kth pollutant gas (kg / MW·h); X k Y is the environmental value conversion standard of the kth pollutant (yuan / kg); k is the government penalty price for the emission of the kth pollutant (yuan / kg).

[0136] The equality constraints considered in the present invention are node power balance constraints, and the inequality constraints include node voltage constraints, branch power constraints, system DG installation total capacity constraints, and node DG installation capacity constraints.

[0137] (1) Power balance constraints

[0138]

[0139] Where P i is the active power of node i; Q i is the reactive power of node i; V i , V j are the voltage values ​​of node i and node j respectively; G ij and B ij are the conductance and susceptance of the line between node i and node j respectively; θ ij is the voltage phase angle difference between nodes i and j.

[0140] (2) Node DG installation capacity constraints

[0141] P DGi,min ≤P DGi ≤P DGi,max (17)

[0142] Where P DGi is the DG installation capacity of node i; P DGi,max , P DGi,min are the upper and lower limits of the DG installation capacity of node i respectively.

[0143] (3) Node voltage constraints

[0144] U imin ≤U i ≤U imax (18)

[0145] Where U imin , U imax are the minimum and maximum allowed voltages at node i, respectively.

[0146] (4) Branch power constraints

[0147] S ij ≤S ijmax (19)

[0148] In the formula, S ij is the apparent power of branch ij; S ijmax is the maximum transmission power allowed for branch ij.

[0149] (5) System DG installation total capacity constraints

[0150]

[0151] Where n DG The total number of nodes installed for DG; P DG,iis the DG installation capacity of node i; η is the upper limit of DG penetration rate allowed by the system; P Lj is the load size of node j.

[0152] 3. Improved Cuckoo Particle Swarm Optimization

[0153] The basic idea of ​​the cuckoo algorithm is based on the cuckoo's brooding parasitism and the Lévy flight behavior of birds. During the algorithm iteration process, the location of the bird's nest is updated through Lévy flight. At the same time, according to the idea that the original host discovers the cuckoo's eggs in the cuckoo's brooding parasitism, part of the solution is discarded and updated. The path position update formula for the cuckoo to explore the next generation of bird nests is shown in formula (21).

[0154]

[0155] The path position update process is actually a Markov chain, and the next generation of bird nest positions is only determined by the current generation of bird nest positions (the first term of Equation 21) and the search direction (the second term of Equation 21). and are the positions of the ith bird nest in the t+1th generation and the tth generation respectively; α (α>0) is the step length control value, is a point-to-point multiplication; Levy(λ) represents a random search path, and its moving step length obeys the Levy probability distribution, that is:

[0156]

[0157] Lévy distribution is a complex process. When the cuckoo algorithm is searching, its step length varies randomly. Sometimes the step length is short, sometimes it is long, but most of the step lengths are short, and there are fewer long step lengths. Lévy flight seems to be chaotic, but the distance and offset angle of each flight follow a certain probability statistical distribution. In the cuckoo algorithm, the calculation formula of the random step length is obtained through the Mantegna rule, and its specific expression is shown in formula (23).

[0158]

[0159] Where s is the random search path; β = 1.5

[65] ; u and v are normal distributions obeying the forms of equation (24) and equation (25) respectively.

[0160]

[0161] Combining the above formulas, the update formula for the cuckoo's nest is:

[0162]

[0163] In the formula, α0 is a constant, generally α0 = 0.01; represents the location of the optimal bird's nest of the current generation; Γ is the standard Gamma function.

[0164] If the host bird finds foreign cuckoo eggs in the nest, the nest position update formula is:

[0165]

[0166] Where r is the scaling factor, which is a random number uniformly distributed in the interval (0,1); are two solutions chosen randomly but different from each other.

[0167] The principle and optimization steps of Cuckoo Algorithm

[0168] In nature, the nest parasitism behavior of cuckoos is random. In order to simulate this behavior, Yang Xin-she and Suash Deb made the following three ideal assumptions:

[0169] 1) Each cuckoo lays only one egg at a time and places it in a randomly selected bird's nest;

[0170] 2) Among a group of randomly selected bird nests, the nests with high-quality eggs will be retained for the next generation;

[0171] 3) The number of available host bird nests is fixed. The probability that a host bird discovers an alien cuckoo egg is Pa∈(0,1). After discovering the cuckoo egg, the host bird either pushes it out of the nest or abandons the nest and builds a new one.

[0172] Regarding the last assumption, it is actually to set a critical value Pa. After the position is updated, a random number r∈(0,1) is used to compare with Pa. If r is greater than Pa, it can be considered that the host bird has found foreign cuckoo eggs, and the cuckoo needs to find a new host nest to store new cuckoo eggs. For an optimization problem, the cuckoo search algorithm maps the cuckoo eggs to a feasible solution to the actual optimization problem when mapping the actual optimization problem. The new cuckoo eggs obtained by the algorithm update represent the new feasible solution to the optimization problem, which means that the new nest positions obtained by the Levy random flight update represent new feasible solutions. In the process of finding the optimal nest, the cuckoo eggs will continuously replace the inferior solutions in the nest with better solutions.

[0173] Based on the above three assumptions, the steps of the cuckoo algorithm can be summarized as follows:

[0174] Step 1: Set the population size to n, the dimension of the problem to D, the maximum number of iterations to Gen and the maximum discovery probability to Pa, and randomly initialize a set of initial bird nest locations X in the feasible domain. i =(x1,x2…x n ), calculate the fitness function value of each bird's nest position, and record the optimal objective function value and the corresponding bird's nest position;

[0175] Step 2: Keep the best nest position of the previous generation, and iteratively update all nest positions according to formula (21). Evaluate the fitness value of each nest after the update, and compare it with the fitness value of each nest before the update. Use the nest position with better fitness to replace the nest position with lower fitness, and keep it as the current best nest position;

[0176] Step 3: Generate a random number R in the interval (0,1), and compare the random number R with the maximum discovery probability Pa. If R>Pa, update the location of the bird's nest according to formula (27), otherwise, the location of the bird's nest remains unchanged. Evaluate the fitness value of the updated bird's nest location and compare it with the optimal value before the update. If the value is better, accept the updated bird's nest location, otherwise the location is retained;

[0177] Step 4: After step 3, a set of updated bird nest positions and their fitness values ​​are obtained. According to the objective function value, the best bird nest position is found to determine whether it meets the convergence accuracy requirement. If it meets the accuracy requirement, the global optimal value is output and the loop ends. If it does not meet the accuracy requirement, go to step 5;

[0178] Step 5: Determine whether the CS algorithm meets the maximum number of iterations. If so, end the algorithm and output the global optimal value. If the number of iterations is less than the maximum number of iterations Gen, return to step 2 to continue iterative optimization calculation until the accuracy requirement is met or the maximum number of iterations is reached.

[0179] In the PSO algorithm, each particle corresponds to a candidate solution to the actual optimization problem. Each particle is composed of three elements: particle speed, particle position, and fitness value. The speed of the particle determines the direction of the particle's flight. The fitness value of the particle is calculated by the corresponding fitness function. The fitness function is used to measure the quality of each particle based on the decision objective function and constraint conditions. Assume that in a D-dimensional space, with x i =(x i1 ,x i2 ,x i3 ,…,x iD ) represents the position of the ith particle, v i =(v i1 ,v i2 ,v i3 ,…,viD ) represents the speed of the ith particle. In the particle swarm algorithm, particles mainly update their positions and speeds by using individual extreme values ​​and group extreme values ​​in the population. The individual extreme value refers to the optimal solution found by each particle from the positions it has experienced, that is, the individual extreme value, and the optimal solution of the population composed of all particles is the group extreme value. i =(P i1 ,P i2 ,…,P iD ) represents individual extreme value, P g =(P g1, P g2 ,…,P gD ) represents the population extreme value. These two extreme values ​​are obtained by dynamically adjusting the particle's own flight experience and the flight experience of its companions. PSO generally uses the number of iterations set in advance as the condition for judging the end based on experience.

[0180] In each iterative optimization process, each particle in the PSO algorithm uses formula (28) and formula (29) to update its position and velocity:

[0181]

[0182] Where v is the velocity of the particle; x is the position of the particle; ω is the inertia weight; d = 1, 2, ... D; i = 1, 2, ..., n; t is the current iteration number; c1 and c2 are learning factors; r1 and r2 are random numbers distributed in the interval (0, 1).

[0183] The PSO algorithm updates the positions of individual extreme values ​​and population extreme values ​​by comparing and replacing the individual extreme values ​​and group extreme values ​​of the newly generated particle swarm with the individual extreme values ​​and group extreme values ​​of the previous generation. Through continuous comparison and iteration, the population extreme value with the best fitness is obtained. The population extreme value at this time is the optimal solution to the objective function. The learning factors c1 and c2 are parameters that quantify the importance of the "self-cognition" and "social cognition" of particles. A large number of experimental experiences have shown that when c1=c2=2, the PSO convergence effect is optimal.

[69] Therefore, this paper takes c1=c2=2.

[0184] Among the parameters of the particle swarm algorithm, the role of the inertia weight constant ω is to balance the global convergence and convergence speed of the algorithm. A larger ω value will make the particles have a higher speed, making the global search ability of the particle swarm algorithm stronger and avoiding premature phenomenon; a smaller inertia weight constant ω will make the particles have a stronger local development ability and the algorithm converges faster. Therefore, in the particle swarm algorithm, many scholars improve the performance of the algorithm by adjusting the size of the inertia weight.

[0185] In order to make PSO perform a large-scale search in the early stage of algorithm search and perform a small-scale refined search as the number of iterations increases, the present invention improves the inertia weight coefficient as follows:

[0186]

[0187] Where t is the current iteration number of the algorithm; ω max is the maximum value of inertia weight; ω min is the minimum inertia weight value; Gen is the maximum number of iterations of the algorithm.

[0188] Based on the above theory, the optimization steps of the PSO algorithm can be summarized as follows:

[0189] Step 1: Set the parameters of the PSO algorithm, such as the particle population size, particle dimension D, maximum number of iterations, values ​​of learning factors c1 and c2, inertia weight ω, position search range and velocity search range of each particle, etc.

[0190] Step 2: Randomly initialize a set of particle populations in the feasible domain, mainly including the position and velocity of the particles.

[0191] Step 3: According to the objective function of the problem, evaluate the fitness function value corresponding to each initialized particle, and find the position of the individual optimal and group optimal particles in the particle population by comparison.

[0192] Step 4: According to the individual extreme values ​​and group extreme values ​​in the particle population, update the position and velocity of the next generation of particles according to formulas (28), (29) and (30).

[0193] Step 5: Calculate the fitness value of the updated particle and compare it with the individual extreme value of the particle before the update. If it is better, use the particle to replace the individual extreme value before the update; if the current state of a particle in PSO is better than the historical group extreme value during the iteration process, use the particle to replace the group extreme value.

[0194] Step 6: Determine whether the iteration termination condition is met. If the termination condition is met, go to step 7, otherwise, go back to step 4.

[0195] Step 7: The iteration terminates and the optimal solution and optimal function value are output.

[0196] In order to improve the performance of the CS algorithm, the particle update principle of the particle swarm algorithm is introduced into the cuckoo algorithm, and the particle swarm algorithm and the cuckoo search algorithm (CS algorithm) are combined to form the CSPSO algorithm. In this way, in the process of updating the nest position, it can always pursue the individual optimum and the global optimum like the particle swarm algorithm, which not only maintains the randomness of the algorithm's search, but also reduces the blindness of the search and improves the convergence speed of the algorithm. At the same time, the random elimination mechanism of the CS algorithm enables the algorithm to have a greater probability of jumping out of the local optimum, ensuring the global optimization ability of the improved algorithm.

[0197] The calculation flow chart of the improved cuckoo particle swarm algorithm is as follows: Figure 4 shown.

[0198] The optimization steps of the CSPSO algorithm can be summarized as:

[0199] Step 1: Set the algorithm parameters, including the number of bird nests n, the maximum number of iterations Gen, the discovery probability Pa, the learning factors c1, c2 and the inertia weight ω max ,ω min . Randomly initialize a set of bird nest locations Initial Speed And evaluate its fitness value. Initialize the individual extreme value of the population And assign the best individual among the individual extreme values ​​to the group extreme value

[0200] Step 2: Update the speed and position of all particles according to formulas (28), (29), and (30) to obtain a new set of bird nests

[0201] Step 3: Calculate the updated bird nests according to the objective function of the optimization problem The corresponding fitness value and the bird's nest before the update The corresponding fitness values ​​are compared, the best ones are retained, and a new set of bird nest locations is obtained.

[0202] Step 4: Generate a random number r∈(0,1) as the probability of the host bird discovering the foreign cuckoo eggs, and compare it with the preset maximum discovery probability Pa. If r>Pa, then discard the nest location and generate a new nest location according to formula (27) to replace the old one, so that a new set of nests can be obtained.

[0203] Step 5: Re-evaluate the bird's nest based on the objective function of the optimization problem The corresponding fitness value and the location of the bird's nest Compare the corresponding fitness values, select the best one, and form a new nest location

[0204] Step 6: Extract The best quality bird's nest position is determined to see whether it meets the accuracy requirements. If it does, the algorithm ends and the global optimal position is output. If it does not, go to step 7.

[0205] Step 7: Determine whether the maximum number of iterations has been reached. If so, end and output the optimal value. If not, compare and Let t = t + 1, Update the individual optimal extreme value and the group optimal extreme value, and go to step 2 to continue iterative optimization.

[0206] The present invention uses test functions to perform performance simulation tests on the traditional particle swarm algorithm (PSO), the standard cuckoo algorithm (CS), and the cuckoo particle swarm algorithm (CSPSO) proposed in the present invention, which combines the particle swarm algorithm and the cuckoo algorithm, and verifies the effectiveness of the improved cuckoo particle swarm algorithm by comparing and analyzing the optimization results, proving that it has better algorithm performance and optimization ability. The function names, function forms, independent variable value ranges, and theoretical extreme values ​​of the four test functions are shown in Table 1.

[0207] Table 1 Test functions

[0208]

[0209]

[0210] In order to compare the performance of the three algorithms, the population size of the algorithm was set to 50, the maximum number of iterations was set to 1000, and the three algorithms were run independently for 30 times. The optimization performance of the algorithms was compared by recording the maximum fitness value, the minimum fitness value, and the average fitness value.

[0211] Table 2 Simulation results of performance tests of various algorithms

[0212]

[0213] It can be seen from Table 2 that for Sphere function, Schwefel's function and Griewank function, the maximum fitness value, minimum fitness value and average fitness value obtained by the CSPSO algorithm simulation search are orders of magnitude higher than those of the basic CS algorithm and PSO algorithm, and the search performance is better, and a better objective function value can be searched. For Rosenbrock's function, the objective function value obtained by the CSPSO algorithm is also better than that of the CS algorithm and the PSO algorithm. This shows that the algorithm performance of the improved CSPSO algorithm proposed in the present invention is greatly improved compared with the standard CS algorithm and the traditional PSO algorithm, which verifies the effectiveness of the algorithm proposed in the present invention.

[0214] The above are preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention, as long as the resulting functions do not exceed the scope of the technical solution of the present invention, belong to the protection scope of the present invention.

Claims

1. A method for planning intermittent distributed power sources based on multi-scenario analysis, characterized in that: The K-means clustering algorithm is used to reduce the wind speed and light intensity time series scenarios, and the improved cuckoo particle swarm search algorithm is used to solve the DG and energy storage device site selection and sizing planning model with the minimum sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost as the objective function.

2. According to claim 1, a method for planning intermittent distributed power supply based on multi-scenario analysis is characterized in that: The method comprises the following steps: (1) Establish a DG and energy storage device site selection and sizing planning model that takes into account the minimum sum of the annual social cost of the distribution system, network loss cost, power purchase cost, and environmental pollution compensation cost as the objective function, and obtain load information, grid structure information, wind speed, light intensity data, and DG output model; (2) Setting the parameters of the improved cuckoo particle swarm search algorithm, namely CSPSO; (3) Using the K-means clustering algorithm to reduce the wind speed and light intensity time series scenes throughout the year, the typical time series scene data after reduction and the scene probability corresponding to each typical time series scene are obtained; (4) Initialize the nest position of CSPSO, that is, generate the initial population for DG and energy storage device planning, including the access position and access capacity of DG and energy storage devices; (5) Based on the grid structure information, load information, and the DG access location and access capacity in the network, the power flow calculation method is used to perform power flow calculation; (6) Calculate the objective function value of each decision target under the corresponding planning scheme, update the position of the bird's nest according to the objective function value corresponding to the individual, then recalculate the objective function value, and compare the objective function values ​​to select the best individual corresponding to the fitness value and the optimal solution; (7) Determine whether the convergence condition is met; if so, go to step (8); if not, return to step (6); (8) The parameters corresponding to the location of the bird's nest under the corresponding planning scheme are the DG optimal planning scheme required, and the DG optimal planning scheme is output.

3. According to claim 2, a method for planning intermittent distributed power sources based on multi-scenario analysis is characterized in that: In step (1), the objective function of the DG and energy storage device location and capacity planning model, which takes into account the minimum sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost, is as follows: minC=C sc +C buy +C loss +C env Where C is the annual comprehensive cost of the distribution system; C sc is the annual social cost of DG and energy storage devices converted to annual cost for the distribution system; C buy is the annual electricity purchase cost of the distribution system; C loss is the annual network loss cost of the distribution system; C env Compensate for the annual environmental pollution costs of the distribution system.

4. According to claim 3, a method for planning intermittent distributed power sources based on multi-scenario analysis is characterized in that: The specific calculation formulas for the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost are as follows: 1) Annual social cost The annual social cost is composed of the equipment investment cost C of DG and energy storage device invest , the operation and maintenance cost of DG and energy storage device C OM and the government subsidy income C for intermittent DG B composition: C sc =C invest +C OM -C B in, Where n WG 、n PV 、n BS are the number of nodes installed for wind power WG, photovoltaic power generation PV and energy storage devices; P i,WG is the rated installed capacity of the i-th node WG; P j,PV is the rated installed capacity of the PV of the jth node; P k,BS is the rated installed capacity of the energy storage device at the kth node; c t,WG 、c t,PV 、c t,BS are the investment costs of unit capacity WG, PV and energy storage device respectively; q is the economic service life of DG and energy storage device; r is the discount rate; N m is the number of seasons, take 4; d m is the number of days corresponding to the mth season; N s is the total number of scenes after scene reduction; p s is the probability corresponding to the sth typical time series scenario; c om,WG 、c om,PV 、c om,BS are the operation and maintenance costs per unit capacity of WG, PV and energy storage devices respectively; P i,s,t,WG is the actual power generation of the i-th node WG at time t in the s-th typical time sequence scenario; P j,s,t,PV is the actual power generation of the jth node PV at time t in the sth typical time sequence scenario; P k,s,t,BS is the charge and discharge power of the k-th node energy storage device at time t in the s-th typical timing scenario; c bt,WG 、c bt,PV are the government subsidies per unit of electricity for WG and PV respectively; 2) Annual electricity purchase cost The annual electricity purchase cost of the distribution network refers to the cost paid by the distribution network to power generation enterprises or other power grids for purchasing electricity throughout the year. Its size can reflect the load density of a region and the region's ability to accept DG: Where N is the total number of nodes in the system; P j,s,t,L is the load size of node j at time t in the sth typical timing scenario; P j,s,t,WG P is the WG output of node j at time t in the sth typical timing scenario; j,s,t,PV is the PV output of node j at time t in the sth typical time series; c e is the unit electricity price; 3) Annual network loss cost Where, L is the number of network branches; I k (t) is the current of the kth branch at time t; R k is the resistance corresponding to the kth branch; 4) Annual environmental pollution compensation cost Environmental compensation costs include the costs of environmental degradation caused by pollutant gas emissions, ecological damage caused by the use of fossil energy for thermal power generation, and penalties for pollutant gas emissions: Where P f is the annual power purchase of the distribution network; M is the type of pollutants generated during traditional thermal power generation; a k is the emission intensity of the kth pollutant gas; X k Y is the environmental value conversion standard of the kth pollutant; k is the government penalty price for the emission of the kth pollutant.

5. The intermittent distributed power planning method based on multi-scenario analysis according to claim 2 is characterized in that: In step (1), the constraints of the DG and energy storage device location and capacity planning model with the minimum sum of the annual social cost of the distribution system, network loss cost, electricity purchase cost, and environmental pollution compensation cost as the objective function are as follows: 1) Power balance constraints Where P i is the active power of node i; Q i is the reactive power of node i; V i , V j are the voltage values ​​of node i and node j respectively; G ij and B ij are the conductance and susceptance of the line between node i and node j respectively; θ ij is the voltage phase angle difference between nodes i and j; 2) Node DG installation capacity constraints P DGi,min ≤P DGi ≤P DGi,max Where P DGi is the DG installation capacity of node i; P DGi,max , P DGi,min are the upper and lower limits of DG installation capacity of node i respectively; 3) Node voltage constraints IN imin ≤U i ≤U imax Where U imin , U imax are the minimum and maximum values ​​of the voltage allowed at node i respectively; 4) Branch power constraints S ij ≤S ijmax In the formula, S ij is the apparent power of branch ij; S ijmax is the maximum transmission power allowed by branch ij; 5) System DG installation total capacity constraints Where n DG The total number of nodes installed for DG; P DG,i Install capacity for the DG of node i; η is the upper limit of DG penetration rate allowed to be connected to the system; P Lj is the load size of node j.

6. The intermittent distributed power planning method based on multi-scenario analysis according to claim 2 is characterized in that: In step (3), K-means clustering technology is used to take the 24-hour data of a day as the clustering unit. There are 365 original wind speed time series scenes and light intensity time series scenes throughout the year. The 365 original wind speed time series scenes and light intensity time series scenes are synchronously divided and clustered to obtain several typical time series scenes that can represent the change characteristics of the original data.

7. The intermittent distributed power planning method based on multi-scenario analysis according to claim 2 is characterized in that: In step (3), the specific implementation method of using the K-means clustering algorithm to reduce the wind speed time series scene is as follows: 1) Use x i (i=1,2,3,...,N) represents the original time series scene set before reduction. First, k scenes are randomly selected from the original time series scene set as the initial clustering centers, i.e., cluster centers. The cluster center scene set is ξ1, ξ2, ξ3,..., ξ k ; 2) Calculate the Euclidean distances from each remaining scene in the original time series scene set to the k initial cluster centers; 3) According to the principle of proximity similarity, the remaining scenes in the original time series scene set are classified into the cluster with the closest cluster center; 4) Calculate the average values ​​of all scenes in the k clusters after classification, take them as the new cluster centers of the k clusters, and update the cluster centers; 5) Repeat steps 2) to 4) until the clustering results and cluster centers no longer change, and the scene reduction is completed.

8. The intermittent distributed power planning method based on multi-scenario analysis according to claim 2 is characterized in that: In step (3), after the scene reduction, the original N original time series scenes are reduced to S representative typical time series scenes, and the probability of each typical time series scene is calculated according to the number of original time series scenes contained in each typical time series scene set after reduction.

9. The intermittent distributed power planning method based on multi-scenario analysis according to claim 2 is characterized in that: After the scenario reduction in step (3) is completed, the output of wind power and photovoltaic power generation in each typical time sequence scenario is calculated based on the following two formulas: Where P WG is the active power output of wind power, P WGR is the wind power rated power, v ci is the cut-in wind speed; v r is the rated wind speed; v co is the cut-out wind speed; v is the wind speed; P PV It is the active power output of photovoltaic power generation; P PVR is the rated power of photovoltaic power generation; I is the actual solar intensity; I r is the rated light intensity.

10. The intermittent distributed power planning method based on multi-scenario analysis according to claim 2 is characterized in that: In step (2), the improved cuckoo particle swarm search algorithm integrates the particle swarm algorithm and the cuckoo algorithm. The specific implementation steps are as follows: Step 1: Set the algorithm parameters, including the number of bird nests n, the maximum number of iterations Gen, the discovery probability Pa, the learning factors c1, c2 and the inertia weight ω max ,ω min ; Randomly initialize a set of bird nest locations Initial Speed And evaluate its fitness value; initialize the individual extreme value of the population And assign the best individual among the individual extreme values ​​to the group extreme value Step 2: Update the speed and position of all particles to obtain a new set of bird nests Step 3: Calculate the updated bird nests according to the objective function of the optimization problem The corresponding fitness value and the bird's nest before the update The corresponding fitness values ​​are compared, the best ones are retained, and a new set of bird nest locations is obtained. Step 4: Generate a random number r∈(0,1) as the probability of the host bird discovering the foreign cuckoo egg, and compare it with the preset maximum discovery probability Pa. If r>Pa, discard the corresponding nest location and generate a new nest location to replace the old one, and obtain a new set of nests. Step 5: Re-evaluate the bird's nest based on the objective function of the optimization problem The corresponding fitness value and the location of the bird's nest Compare the corresponding fitness values, select the best one, and form a new nest location Step 6: Extract The best quality bird's nest position is determined to see whether it meets the accuracy requirements. If it does, the algorithm ends and the global optimal position is output. If it does not, go to step 7. Step 7: Determine whether the maximum number of iterations has been reached. If so, end the process and output the optimal value. If not, compare and Let t = t + 1, Update the individual optimal extreme value and the group optimal extreme value, and go to step 2 to continue iterative optimization.

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