A photovoltaic power fluctuation control method based on distributed resource clustering

Abstract

The present invention relates to a technology for coordinated control of multiple distributed resources in a distribution network, and specifically to a photovoltaic power fluctuation smoothing control method based on distributed resource clustering. A minute-level AGC control framework model is established, and the control process is divided into the calculation of the power reference value of the network point under the current control cycle, the clustering of distributed resources, and the solution of an optimization control model based on a particle swarm algorithm. An objective function and the relationship between the power fluctuation smoothing control target and the control cost are established, and the optimization control model and related constraints before and after resource clustering are clarified. Based on the control cycle and step size, a particle swarm algorithm is used to perform a rolling solution to the optimization control model, determine the minute-level control amount of the resource aggregate, and ultimately evaluate the results based on the power fluctuation rate of the network point before and after control, the control cost, and the model solution time. This control method can not only improve the control effect, but also suppress the impact of distributed photovoltaic power fluctuations on the distribution network and the main network while ensuring control economy.

Description

Technical Field

[0001] The present invention belongs to the technical field of coordinated control of multiple distributed resources in distribution networks, and in particular relates to a photovoltaic power fluctuation smoothing control method based on distributed resource clustering. Background Art

[0002] As the scale of distributed photovoltaics within distribution networks increases, the impact of photovoltaic output fluctuations on distribution networks becomes increasingly significant. Photovoltaic power fluctuations can be transmitted to the main grid through downstream nodes, affecting the safe and stable operation of the power grid. At the same time, the increase in the types and number of distributed resources has improved the controllability of distribution networks. Research on resource clustering methods has further enhanced the feasibility of distributed resources participating in power fluctuation smoothing. From the perspectives of economy and feasibility, exploring a resource collaborative control scheme based on distributed resource clustering is of great significance for improving photovoltaic absorption rates and participating in grid peak and frequency regulation. Therefore, for distribution networks with diverse control resources, studying how to achieve collaborative control of multiple types of distributed resources and rationally decompose control instructions to each controlled object based on their operating status, thereby minimizing control costs, is an important part of achieving photovoltaic power fluctuation smoothing control.

[0003] In summary, studying a resource-coordinated control scheme based on distributed resource clustering to minimize control costs and manage photovoltaic power fluctuations in distribution networks is a multi-stakeholder, efficient, and economical control method. Renewable energy generators can guarantee their own absorption rate to a certain extent; grid companies maintain safe and stable grid operation with minimal control costs; and flexible load users receive financial compensation when production conditions permit. Overall, the overall economic benefits of the source-grid-load system are improved. Summary of the Invention

[0004] In view of the problems existing in the background technology, the present invention provides a method for smoothing photovoltaic power fluctuation control in a distribution network based on distributed resource clustering.

[0005] To solve the above technical problems, the present invention adopts the following technical solution: a photovoltaic power fluctuation smoothing control method based on distributed resource clustering, comprising the following steps:

[0006] Step 1: Establish a minute-level AGC control framework model based on resource clustering and optimization algorithms.

[0007] Step 2: Build a minute-level AGC optimization control model based on the control object characteristics and control objectives, establish the connection between power fluctuation smoothing and control cost, and distinguish the optimization model and control constraints before and after resource clustering;

[0008] Step 3: Based on actual control, an optimization control model solving method based on particle swarm algorithm is proposed. The economic objective function reflecting the control cost is used as the basis for algorithm fitness evaluation. An optimization control model solving method based on resource clustering and optimization algorithm is proposed.

[0009] In the above-mentioned photovoltaic power fluctuation smoothing control method based on distributed resource clustering, establishing a minute-level AGC control framework model specifically includes the following steps:

[0010] Step 1.1: Establish a minute-level AGC control framework model;

[0011] Step 1.1.1, distribution network structure and resource parameter setting;

[0012] Step 1.1.1.1. Select the time period benchmark for the downstream power point and generate the target value within the current control cycle. Within the same control cycle, calculate the downstream power fluctuation rate based on the predictive control step size, and use it as a coupling constraint for the minute-level AGC optimization control and the power fluctuation smoothing target.

[0013] The control period T is selected as 5 minutes, and the predictive control step length T c The power of the network point at the first moment is selected as the control reference value in each control cycle.

[0014] Step 1.1.2: Use the photovoltaic forecast data at the first moment of the control cycle as clustering indicators. Use the improved K-means++ algorithm based on indicator weights to implement resource clustering. Then, perform aggregation modeling on the indicators. The aggregation model is used to determine the priority order of resource regulation, which serves as the basis for optimization control in the next stage. The specific steps are as follows:

[0015] Step 1.1.2.1. Construct a resource clustering control indicator system. Based on the resource regulation requirements of the power fluctuation smoothing goal, select appropriate control indicators from both technical and economic perspectives to establish a control indicator system that serves resource clustering.

[0016] Step 1.1.2.2: Configure clustering indicator weights. Determine the weight configuration principle based on the clustering goal and the clustering service object, and use the subjective weighting method to assign weights to each clustering indicator.

[0017] Step 1.1.2.3: Propose a K-means++ algorithm based on improved indicator weights. Based on the obtained weight configuration results, improve the sample Euclidean distance calculation method in the K-means++ algorithm to achieve clustering of distributed resources and give practical meaning to the clustering results.

[0018] Step 1.2: Solve the minute-level AGC control model;

[0019] In the second stage of the control framework, based on the power reference value of the downstream node obtained in the first stage, the control demand of the distribution network at the tth minute is determined: output increase or output decrease, and the control quantity is sent to several distributed resources in the resource aggregate according to the priority order of resource control. The output size of each resource aggregate is used as the decision variable, and the particle swarm algorithm is used to solve the optimization control model. While achieving the goals of power fluctuation smoothing control and minimizing economic costs, the dimension of decision variables is reduced; each time the optimization model solution is completed, the number of solution cycles N is calculated according to the predictive control step size and the cycle number N. c Determine whether the current control cycle has ended, and then determine whether it is necessary to update the clustering index and perform clustering and calculation for the next cycle.

[0020] In the above-mentioned photovoltaic power fluctuation smoothing control method based on distributed resource clustering, building a minute-level AGC optimization control model specifically includes the following steps:

[0021] Step 2.1, establish the economic objective function of the optimization control model;

[0022] Based on the aggregation model, the priority of resource regulation is determined to establish the economic optimization goal at the aggregate level:

[0023]

[0024] Where F(t) is the total economic cost; K is the number of aggregates obtained after clustering; F cluster,k (t) is the control cost of the k-th aggregate at the t-th minute; F grid (t) is the cost of electricity purchased from the main grid at minute t;

[0025] The control cost of a single aggregate is calculated based on the actual aggregate control amount and the resource economic priority curve within each aggregate. The main grid power purchase cost is calculated as follows:

[0026]

[0027] Where, f grid The electricity purchase cost of the grid unit; is the power of the downstream node at minute t, i.e., the main network power; Δt is the duration of the calculation period;

[0028] The power of the downstream network is calculated by forward-backward substitution method under the premise of clarifying the structural parameters, load conditions and actual resource access conditions in the distribution network;

[0029] Step 2.2: Optimize the control model constraints, including the operation constraints of the distributed control resource aggregate, power balance constraints, and power fluctuation rate constraints at the downstream network. Specifically,

[0030] Step 2.2.1, Operational constraints of distributed photovoltaics;

[0031] Distributed photovoltaics should meet the following constraints:

[0032]

[0033] Where, is the total amount of distributed photovoltaic control within aggregate k at minute t; P PV,i,max is the maximum controllable amount of the i-th distributed unit;

[0034] Step 2.2.2, distributed photovoltaic energy storage operation constraints;

[0035] Meet the charging and discharging power constraints and capacity constraints:

[0036]

[0037]

[0038] Where, is the output of distributed energy storage in aggregate k at minute t; is the minimum output of the i-th distributed energy storage unit in aggregate k; is the maximum output of the i-th distributed energy storage unit in aggregate k; is the capacity of distributed energy storage in aggregate k at minute t; is the minimum capacity of the i-th distributed energy storage unit in aggregate k; is the maximum capacity of the i-th distributed energy storage unit in aggregate k;

[0039] The capacity constraint is calculated and analyzed in combination with the dynamic characteristics of the charging and discharging capacity of the cluster energy storage. Assuming that all energy storage units in the system are of the same model, the cluster charging and discharging efficiency is also the same:

[0040]

[0041]

[0042] Where η in is the charging efficiency of the energy storage unit; η out is the discharge efficiency of the energy storage unit;

[0043] Step 2.2.3, interruptible load operation constraints;

[0044] For aggregates with interruptible loads, consider their aggregate output constraints:

[0045]

[0046] Where, is the load size of distributed energy storage in aggregate k at minute t; is the minimum load power of the i-th interruptible load unit in aggregate k; is the maximum load power of the i-th interruptible load unit in aggregate k;

[0047] Step 2.2.4, power balance constraint;

[0048]

[0049] Where, P L (t) is the load power in the distribution network at minute t; P loss (t) is the power loss in the distribution network at minute t;

[0050] Step 2.2.5: Set the power fluctuation rate constraint of the network point;

[0051] Define the power fluctuation rate R of the next grid point in the tth minute Vol (t), which represents the degree of power change at the current moment relative to the previous moment; according to the distribution network structure and resource parameters simulated in the example, the power fluctuation rate constraint conditions of the down-grid point in the example are determined, and the fluctuation rate R Vol (t) Limited to 2%:

[0052]

[0053] The connection between the power fluctuation rate constraint at the downstream grid point and the economic objective function is established. The constraint is added to the economic objective function in the form of a penalty function. The coefficient representing the intensity of the penalty function is then adjusted and defined in the form of a piecewise function:

[0054]

[0055] Where β is the penalty function intensity coefficient; ΔR Vol (t) is the difference between the actual power fluctuation rate of the downlink point and the constraint value;

[0056] The economic objective function considering the power fluctuation penalty is:

[0057]

[0058] In the above-mentioned photovoltaic power fluctuation smoothing control method based on distributed resource clustering, the optimization control model solution method based on the particle swarm algorithm includes the following steps:

[0059] Step 3.1, initialization of population particle positions and velocities;

[0060] Step 3.1.1. Determine the variable dimension D of the feasible solution based on the clustering results of the distributed resources in the distribution network, which corresponds to the spatial dimension of the particles in the PSO, and set the number of particles in the population N.

[0061] Step 3.1.2: Set the upper limit of the search area X according to the aggregation index of the aggregate max and the lower bound X min , giving the maximum value V of the particle search speed Vi max and minimum value V min , and the convergence accuracy ε or the maximum number of iterations N iter , and take the value of the initial state of the particles within the constraints of position and velocity to complete the initialization of the position and velocity of the population particles;

[0062] Step 3.1.3: At the beginning of the algorithm, set the individual learning factor c1, social learning factor c2, and inertia weight ω of the population to update the particle position and velocity;

[0063] Step 3.2, calculate particle fitness;

[0064] Step 3.2.1. In each iteration, re-evaluate the fitness of each particle in the population, and update the individual optimal solution and the population optimal solution; the fitness function is represented by the economic objective function of the optimization model;

[0065] Step 3.2.2: Repeat the calculation to obtain the fitness value of each particle during each iteration, and update the individual optimal solution of the current particle and the optimal solution of the population, as well as the corresponding objective function value, to achieve the purpose of optimization;

[0066] Step 3.2.3: The individual optimal solution and the population optimal solution are expressed as follows:

[0067]

[0068] Where p i is the individual optimal solution of the particle; g is the population optimal solution of the particle; X D is the D-th dimension position characteristic of the particle;

[0069] Step 3.3, optimize convergence judgment;

[0070] Step 3.3.1. After each iteration is completed, the difference between the optimal particle fitness values of the population obtained in this iteration and the previous iteration is used to determine whether the optimization solution has converged. The convergence conditions are as follows:

[0071] |H(g(n))-H(g(n-1))|<ε (14)

[0072] Among them, ε is the convergence accuracy; H(g(n)) is the optimal fitness value of the population calculated at the nth iteration;

[0073] Step 3.3.2: If the convergence condition is met or the maximum number of iterations N has been reached iter , then the optimal particle of the current population corresponds to the optimal solution of the decision variable, realizing the optimization control process; if the convergence condition cannot be met, execute step 3.4 to update the particle position and velocity;

[0074] Step 3.4, update particle position and velocity and boundary processing;

[0075] Step 3.4.1. At the beginning of each iteration, the particle optimization speed and position are updated according to the individual optimal fitness value and the population optimal fitness value obtained in the previous iteration according to formula (15) and formula (16):

[0076] V i (n+1)=ωV i (n)+c1r1[p i (n)-x i (n)]+c2r2[g(n)-x i (n)] (15)

[0077] x i (n+1)=x i (n)+V i (n+1) (16)

[0078] Where c1 is the individual learning factor, which takes a value of 0.5; c2 is the social learning factor, which takes a value of 0.5; r1 and r2 are random numbers in the range of [0,1] to increase the randomness of particle optimization; ω is the weight of the particle to maintain the historical speed, which takes a value of 0.9;

[0079] Step 3.4.2: The particle position update formula includes three parts: historical experience, individual cognition and social learning. The first part ωV i (n) reflects the habit of particle movement and its own historical experience; the second part represents the impact of the particle's own memory of the optimal value on the speed of the next iteration; the third part reflects the cooperation between particles and the historical experience of the population, showing that the particles tend to approach the historical best position during the optimization process;

[0080] Step 3.4.3: After completing the update of particle velocity and position, verify the updated results according to the following formula:

[0081] X min ≤X i,d ≤X max (17)

[0082] Vmin ≤V i,d ≤V max (18)

[0083] Among them, X i,d is the d-dimensional position variable of particle i; V i,d is the d-dimensional velocity variable of particle i;

[0084] Step 3.4.4: For particles that exceed the constraint range, randomly generate a feasible solution within the constraint range to replace them.

[0085] Compared with the existing technology, the present invention has the following advantages: the present invention uses a photovoltaic power fluctuation control method based on distributed resource clustering to perform minute-level rolling optimization control on the distribution network. Taking a multi-resource aggregate as the control object, by establishing a rolling optimization control model, it can not only improve the control effect, but also suppress the impact of distributed photovoltaic power fluctuations on the distribution network and the main grid while ensuring control economy. The present invention has the following advantages:

[0086] 1. Make full use of the regulation potential of distributed resources and give full play to the controllability of the distribution network containing multiple distributed resources.

[0087] 2. Propose and adopt a clustering algorithm that considers the actual meaning of resource indicators to improve the feasibility of collaborative control of distributed resources.

[0088] 3. Based on the resource clustering results, the PSO algorithm is used to perform rolling optimization and solution of the control model to improve the control effect, reduce the control cost, and speed up the control solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 This is a flow chart of the K-means++ clustering algorithm improved based on the control index weight in an embodiment of the present invention;

[0090] Figure 2 This is a minute-level AGC control framework model based on resource clustering and optimization algorithms in an embodiment of the present invention;

[0091] Figure 3 This is a flow chart of solving an optimization control model based on a particle swarm algorithm in an embodiment of the present invention;

[0092] Figure 4 The present invention provides an IEEE-33 node power distribution network system including distributed control resources according to an embodiment of the present invention;

[0093] Figure 5 It is the resource clustering control indicator system adopted in the embodiment of the present invention;

[0094] FIG6( a ) is a comparison curve of adjustable capacity and total regulation cost according to an embodiment of the present invention;

[0095] FIG6( b ) is a comparison curve of adjustable capacity and total control cost according to an embodiment of the present invention;

[0096] Figure 7 The embodiment of the present invention is based on the particle swarm algorithm to solve the optimization control model convergence effect;

[0097] Figure 8 This is a comparison of the power of the network points before and after the optimization control of the embodiment of the present invention;

[0098] Figure 9 This is a comparison of power fluctuation rates at the downstream network points before and after optimization control according to an embodiment of the present invention;

[0099] FIG10( a ) is a curve showing the output change of polymer 1 before and after control during the control period of an embodiment of the present invention;

[0100] FIG10( b ) is a curve showing the output variation of the polymer 2 before and after control during the control period of the embodiment of the present invention. DETAILED DESCRIPTION

[0101] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0102] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0103] The present invention will be further described below with reference to specific examples, but they are not intended to limit the present invention.

[0104] This implementation takes the aggregate obtained by resource aggregation as the direct control object and proposes an optimized collaborative control scheme involving three types of distributed resources for distributed photovoltaic power fluctuation evaluation. First, a minute-level AGC control framework model based on resource clustering and optimization algorithm is established, and the control process is divided into two stages, including the calculation of the grid power reference value under the current control cycle and the clustering of distributed resources and the solution of the optimization control model based on the particle swarm algorithm. Secondly, based on the mathematical models of the three distributed resources, an economic objective function reflecting the control cost and the relationship between the power fluctuation smoothing control target and the control cost are established, and the optimization control model and related constraints before and after resource clustering are clarified; according to the control cycle and step size indicated by the control framework, the particle swarm algorithm is used to perform a rolling solution on the optimization control model to determine the minute-level regulation amount of the resource aggregate, and finally the results are evaluated by the grid power fluctuation rate, control cost and model solution time before and after control.

[0105] This embodiment is implemented through the following technical solution, a photovoltaic power fluctuation smoothing control method based on distributed resource clustering, including the following steps:

[0106] S1. Based on traditional AGC control, a minute-level AGC control framework model based on resource clustering and optimization algorithms is established. Compared with conventional AGC control, its main control object is distributed resource aggregates, which can achieve more flexible and efficient power fluctuation smoothing;

[0107] S1.1. Establishment of a minute-level AGC control framework model.

[0108] 1) Distribution network structure and resource parameter setting;

[0109] As the first stage of the control framework model, the main work is to calculate the initial power of the network point and group the resources. First, the time period benchmark of the network point power is selected to generate the target value within the current control cycle; secondly, within the same control cycle, the network point power fluctuation rate is calculated based on the predictive control step size, which serves as the coupling constraint for the minute-level AGC optimization control and the power fluctuation smoothing target. In this embodiment, the control period T is selected as 5 minutes, and the predictive control step size T is selected as 5 minutes. c The power of the network point at the first moment is selected as the control reference value in each control cycle.

[0110] At the same time, the photovoltaic forecast data at the first moment of the control cycle is used as a clustering indicator, and the K-means++ algorithm based on the improved indicator weight is used to realize resource clustering. The indicators are aggregated and modeled. The priority order of resource regulation is determined by the aggregation model, which serves as a reliable basis for the next stage of optimization control. The specific steps are as follows:

[0111] a. Build a resource clustering control indicator system. Based on the actual resource regulation requirements for power fluctuation mitigation, select appropriate control indicators from both technical and economic perspectives to establish a control indicator system that serves resource clustering.

[0112] b. Configure clustering indicator weights. Determine the weight configuration principle based on the clustering goals and the clustering service objects, and use the subjective weighting method to assign weights to each clustering indicator.

[0113] c. A K-means++ algorithm based on improved indicator weights is proposed. Based on the obtained weight configuration results, the sample Euclidean distance calculation method in the K-means++ algorithm is improved to achieve clustering of distributed resources and give practical meaning to the clustering results.

[0114] The K-means++ clustering algorithm process based on the improved control index weights used in this embodiment is as follows: Figure 1 shown.

[0115] S1.2 minute-level AGC control model solution;

[0116] In the second stage of the control framework, the power reference value of the downstream node obtained in the first stage is used to determine the control demand (output increase or output decrease) of the distribution network in the tth minute, and the control quantity is sent to several distributed resources in the resource aggregate according to the priority order of resource control. The output size of each resource aggregate is used as the decision variable, and the particle swarm algorithm is used to solve the optimization control model. While achieving the goal of power fluctuation smoothing control and minimizing economic cost, the dimension of decision variables is reduced as much as possible to avoid the problem of solution difficulty. Each time the optimization model is solved, the number of solutions N is calculated according to the predictive control step size and cycle number. c Determine whether the current control cycle has ended, and then determine whether it is necessary to update the clustering index and perform clustering and calculation for the next cycle.

[0117] Finally, a minute-level AGC control framework model based on resource clustering and optimization algorithm was established, such as Figure 2 shown.

[0118] S2. Build a minute-level AGC optimization control model based on the characteristics of the controlled object and the control objectives, establish the connection between power fluctuation smoothing and control cost issues, and distinguish the optimization model and control constraints before and after resource clustering;

[0119] S2.1 Establishing the economic objective function of the optimization control model

[0120] For optimization problems based on resource clustering results, in order to highlight the role of distributed control resources and resource clustering in smoothing out power fluctuations at the network point, an economic optimization objective at the aggregate level should be established based on the resource control priority obtained through clustering:

[0121]

[0122] Where F(t) – total economic cost;

[0123] K – the number of aggregates obtained after clustering;

[0124] F cluster,k (t) — the control cost of the k-th aggregate at the t-th minute;

[0125] F grid (t)——the cost of electricity purchased from the main grid at minute t.

[0126] The control cost of a single aggregate should be calculated based on the actual aggregate control amount and the resource economic priority curve within each aggregate. The main grid power purchase cost is calculated as follows:

[0127]

[0128] Where f grid ——Unit electricity purchase cost of the power grid;

[0129] ——The power of the downstream network at minute t, also known as the main network power;

[0130] Δt – duration of the calculation period.

[0131] The power of the downstream grid point needs to be calculated using the forward-backward substitution method on the premise of clarifying the structural parameters, load conditions and actual resource access conditions in the distribution network.

[0132] S2.2 Optimize control model constraints;

[0133] The constraints considered in this embodiment mainly include the operation constraints of the distributed control resource aggregation, the power balance constraints, and the power fluctuation rate constraints of the downstream network points.

[0134] 1) Distributed photovoltaic operation constraints;

[0135] As a major distributed power source in the distribution network, distributed photovoltaics generally operate near the maximum power point and only abandon the power appropriately when the power consumption is insufficient. In other words, it participates in the power balance of the distribution network as a downward adjustment resource. In this process, distributed photovoltaics should meet the following constraints:

[0136]

[0137] In the formula ——the total amount of distributed photovoltaic control within aggregate k at minute t;

[0138] P PV,i,max——The maximum controllable amount of the i-th distributed unit.

[0139] 2) Distributed energy storage operation constraints;

[0140] Aggregated distributed energy storage has a strong regulatory response capability and is a major regulatory resource for smoothing fluctuations in renewable energy. During actual operation, the aggregate generally needs to meet charging and discharging power constraints and capacity constraints:

[0141]

[0142]

[0143] In the formula ——the output of distributed energy storage in aggregate k at minute t;

[0144] ——the minimum output of the i-th distributed energy storage unit in aggregate k;

[0145] ——the maximum output of the i-th distributed energy storage unit in aggregate k;

[0146] ——the capacity of distributed energy storage in aggregate k at minute t;

[0147] ——the minimum capacity of the i-th distributed energy storage unit in aggregate k;

[0148] ——The maximum capacity of the i-th distributed energy storage unit in aggregate k.

[0149] In addition, the capacity constraint should be calculated and analyzed in combination with the dynamic characteristics of the charging and discharging capacity of the cluster energy storage. Here, it is assumed that all energy storage units in the system are of the same model, so the cluster charging and discharging efficiency is also the same.

[0150]

[0151]

[0152] Where η in ——Charging efficiency of energy storage unit;

[0153] η out ——Discharge efficiency of energy storage unit.

[0154] 3) Interruptible load operation constraints

[0155] To simplify calculation and analysis, for aggregates containing interruptible loads, only their aggregate output constraints are considered:

[0156]

[0157] In the formula ——the load of distributed energy storage in aggregate k at minute t;

[0158] ——the minimum load power of the i-th interruptible load unit in aggregate k;

[0159] ——The maximum load power of the i-th interruptible load unit in aggregate k.

[0160] 4) Power balance constraints

[0161]

[0162] Where P L (t)——load power in the distribution network at minute t;

[0163] P loss (t)——Network loss power in the distribution network at minute t.

[0164] 5) Power fluctuation rate constraints at the downstream network

[0165] First, define the power fluctuation rate R of the next grid point in the tth minute Vol (t), which represents the degree of power change at the current moment relative to the previous moment; secondly, according to the distribution network structure and resource parameters of the simulation example, the power fluctuation rate constraint conditions of the downstream network in the example are determined, in order to reduce the fluctuation rate R Vol (t) Limited to 2%.

[0166]

[0167] In addition, in order to simplify the solution of the optimization control model and establish a direct connection between the power fluctuation rate constraint at the downstream grid point and the economic objective function, this paper adds it to the economic objective function in the form of a penalty function, and then adjusts the coefficient that characterizes the intensity of the penalty function to make the objective function more reasonable. This paper defines the coefficient in the form of a piecewise function:

[0168]

[0169] Where β is the penalty function intensity coefficient;

[0170] ΔR Vol (t)——the difference between the actual power fluctuation rate of the grid point and the constraint value.

[0171] Finally, the economic objective function considering the power fluctuation penalty can be obtained as follows:

[0172]

[0173] S3. Based on actual control problems, the optimization control model solution method based on particle swarm algorithm is pointed out. The economic objective function reflecting the control cost is used as the basis for algorithm fitness evaluation, and the optimization control model solution process based on resource clustering and optimization algorithm is proposed.

[0174] Particle Swarm Optimization (PSO) is a swarm intelligence optimization algorithm with strong solving ability, fast convergence speed and good robustness. In PSO, individual particles continuously adjust their own positions and speeds with the goal of minimizing the fitness function, approaching the optimal particle, and after multiple iterations, finally find the global optimal solution that meets the convergence conditions. Because the particle swarm algorithm itself is effective and easy to implement, it is widely used in the field of power systems. This embodiment also uses this algorithm to solve the optimization control problem. After combining it with the actual problem, the specific solution method and steps are as follows:

[0175] After combining it with the actual problem, the steps of solving the optimization control model based on the particle swarm algorithm are as follows:

[0176] S3.1, initialization of population particle positions and velocities;

[0177] First, the variable dimension D of the optimized feasible solution is determined based on the clustering results of a large number of distributed resources in the distribution network, which corresponds to the spatial dimension of the particles in the PSO, and the number of swarm particles N is set. Secondly, the upper limit boundary X of the search area is set according to the aggregation index of the aggregate max and the lower bound X min , giving the maximum value V of the particle search speed Vi max and minimum value V min , and the convergence accuracy ε or the maximum number of iterations N iter , and the initial state of the particles is determined within the constraints of position and velocity to complete the initialization of the position and velocity of the swarm particles. In addition, the individual learning factor c1, social learning factor c2, and inertia weight ω of the swarm need to be set at the beginning of the algorithm to update the particle position and velocity.

[0178] S3.2, calculate particle fitness;

[0179] In each iteration, the fitness of each particle in the population needs to be re-evaluated, and the individual and population optimal solutions need to be updated. For the actual optimization problem in this article, the fitness function can be represented by the economic objective function of the optimization model. During each iteration, the fitness value of each particle is repeatedly calculated, and the individual optimal solution and the population optimal solution of the current particle are updated by comparison, along with the corresponding objective function value, to achieve the purpose of optimization. The individual optimal solution and the population optimal solution are represented as follows:

[0180]

[0181] Where p i ——Individual optimal solution of the particle;

[0182] g——the optimal solution of particle population;

[0183] X D ——The D-dimensional position characteristic of the particle.

[0184] S3.3, optimize convergence judgment;

[0185] After each iterative calculation is completed, the difference between the optimal particle fitness values of the population obtained in this iteration and the previous iteration is used to determine whether the optimization solution has converged. The convergence conditions are as follows:

[0186] |H(g(n))-H(g(n-1))|<ε (14)

[0187] Where ε is the convergence accuracy;

[0188] H(g(n))——The optimal fitness value of the population calculated at the nth iteration.

[0189] If the convergence condition is met, or the maximum number of iterations N is reached iter , then the optimal particle in the current population is the optimal solution for the corresponding decision variable, and the optimization control process can be achieved. If the convergence condition cannot be met, continue to update the particle position and velocity according to step S3.4.

[0190] S3.4, particle position and velocity update and boundary processing;

[0191] At the beginning of each iteration, the particle optimization speed and position are updated according to the following two formulas based on the individual optimal fitness value and the population optimal fitness value obtained in the previous iteration:

[0192] V i (n+1)=ωV i (n)+c1r1[p i (n)-x i (n)]+c2r2[g(n)-xi (n)] (15)

[0193] x i (n+1)=x i (n)+V i (n+1) (16)

[0194] Where c1 is the individual learning factor, which is 0.5;

[0195] c2——social learning factor, value is 0.5;

[0196] r1, r2 - random numbers in the range of [0,1], which increase the randomness of particle optimization;

[0197] ω——The weight of the particle to maintain its historical velocity, which is set to 0.9.

[0198] The particle position update formula includes three parts: historical experience, individual cognition and social learning. The first part ωV i (n) reflects the "habit" of particle movement and its own historical experience; the second part represents the impact of the particle's own memory of the optimal value on the speed of the next iteration; the third part reflects the cooperation between particles and the historical experience of the population, showing that particles tend to approach the historical best position during the optimization process.

[0199] After completing the update of the particle velocity and position, the updated results should be immediately tested according to the following formula:

[0200] X min ≤X i,d ≤X max (17)

[0201] V min ≤V i,d ≤V max (18)

[0202] where X i,d ——the d-th dimension position variable of particle i;

[0203] V i,d ——The d-dimensional velocity variable of particle i.

[0204] Certain processing measures are taken for particles that exceed the constraint range. Generally, a feasible solution can be randomly generated within the constraint range to replace them.

[0205] By solving the minute-level AGC optimization control model through the above method steps, the control amount of the control resources per minute and the corresponding optimal control economic cost can be obtained. The optimization control solution process based on the particle swarm algorithm is as follows: Figure 3 shown.

[0206] Case Analysis

[0207] 1. Distribution network and resource parameter settings;

[0208] In order to reflect the practical application significance of the present invention, distributed resources are set in a standard IEEE-33-node distribution network system, and parameters such as node load and line impedance are set to default values. At the same time, distributed photovoltaic (PV), distributed energy storage system (ESS) and interruptible load (IL) are connected to 5 nodes, 7 nodes and 26 nodes, respectively, with sizes of 100, 20 and 40 respectively. Figure 4 The background of the established distributed resource clustering is given.

[0209] In order to analyze the process of three types of controllable resources participating in the control of the distribution network, according to Figure 5 The clustering control indicator system and clustering algorithm requirements shown in Table 1 define and constrain the indicator ranges of various resources.

[0210] Table 1. Distributed resource clustering index range considering resource regulation capability

[0211]

[0212] The following describes a photovoltaic power fluctuation smoothing control method based on distributed resource clustering proposed in this embodiment and its effect through actual examples.

[0213] 2. Results and analysis of distributed resource clustering;

[0214] Based on the clustering results, the aggregated original data table after clustering is listed, and the various resources in each aggregate are counted and integrated. The results are shown in Table 2 and Table 3.

[0215] Table 2. Results of distributed resource clustering in the implementation example

[0216]

[0217]

[0218] Table 3. Statistics of resource indicators within the aggregate

[0219]

[0220] As shown in Tables 2 and 3, clustering results based on the definitions of positive and negative indicators across aggregates indicate that the positive indicators representing technical control are ranked as: Aggregate 1 > Aggregate 2; the negative indicators representing economic control are ranked as: Aggregate 2 > Aggregate 1. Furthermore, a comparison of the same type of regulated resources within different aggregates shows the same ranking: the technical and economic indicators of the resources within Aggregate 1 are superior to those of the distributed PV resources within Aggregate 2. Therefore, the differences in regulation performance between aggregates can be determined, and the priority of regulation can be concluded: when regulating distributed resources to smooth grid power fluctuations, prioritizing the distributed resources within Aggregate 1 can better meet technical and economic requirements.

[0221] For non-clustered resource control scenarios, the demand control amount is generally decomposed in an evenly distributed manner, that is, the required control amount is distributed to each control resource in proportion to its capacity. This control method ignores the economic requirements of the control process. In order to further distinguish the control priority of resources within an aggregate based on the priority between aggregates, this embodiment sorts the resources within the same aggregate according to the economic cost, draws a relationship curve between the aggregate control amount and the total control cost based on the resource controllable capacity and unit control cost, and divides the aggregate control amount into two situations: adjustable and adjustable according to resource characteristics. The adjustable increase scenario corresponds to energy storage discharge or interruptible load interruption, and the adjustable decrease scenario corresponds to energy storage charging and distributed photovoltaic curtailment. The resulting adjustable capacity-total control cost comparison curve is shown in Figure 6(a), and the adjustable capacity-total control cost comparison curve is shown in Figure 6(b).

[0222] Figures 6(a) and 6(b) show the control capacity-control cost curves for the two aggregates before and after resource economic ranking in the downward adjustment scenario, and before and after economic ranking in the upward adjustment scenario, respectively. It is not difficult to see from the two adjustment scenarios that, regardless of whether the resources are economically ranked, the total control cost of aggregate 1 is always lower than that of aggregate 2, which once again proves the effectiveness and correctness of the above clustering results. In addition, whether in the upward or downward adjustment scenario, for the same aggregate with the same capacity, the total control cost after economic ranking is lower than before economic ranking. In the upward adjustment scenario, the control capacity-control cost curves of the two aggregates show a clear turning point. This is because the unit control cost of distributed energy storage and interruptible load in the upward adjustment resources is significantly different.

[0223] In summary, we can draw the following conclusions:

[0224] (1) Using the weight-based improved K-means++ algorithm to cluster distributed resources can achieve a certain clustering effect and conform to the principle of weight configuration;

[0225] (2) For the situation in the implementation example, among the aggregates, the distributed resource control performance within aggregate 1 is superior, and aggregate 1 should be selected as the main control object first. Within the aggregate, the unit control cost of each resource should be adjusted in ascending order, that is, the resource with the lowest cost should be adjusted first;

[0226] In order to further illustrate the role of clustering in the problem of distributed photovoltaic power fluctuation smoothing, it is necessary to further apply it in the actual distribution network analysis.

[0227] 3. Control plan implementation process and effect verification;

[0228] Based on the control framework in the invention content, the optimization problem within a control period is solved based on the clustering results. The control period T is 5 minutes and the control step length T is 0. c For 1 minute, the number of control steps is N c To achieve the power fluctuation smoothing effect, we first need to select the power reference value P of the next grid point. ref According to the distributed photovoltaic forecast data in each control cycle, the grid power per minute before the control is calculated by forward-backward substitution, and then the grid power fluctuation rate is obtained as the coupling constraint of the optimization control and power fluctuation smoothing objectives. At the same time, the grid power at the first moment of the cycle is used as the smoothing reference value of this cycle. After calculation, the grid power reference value P of this example is ref It is 3241.92kW.

[0229] Secondly, based on the photovoltaic forecast data at t=1, the resources in the distribution network are clustered and the priority order of resource regulation is determined. pcc With reference value P ref The control demand is determined by the relationship between the size of the aggregates. For the allocation of control demand between aggregates, the PSO algorithm is used to optimize the solution with economy as the goal and power fluctuation as the constraint. For the allocation of control demand within an aggregate, the economic ranking of resources within each aggregate is used to determine the distribution.

[0230] First, draw a curve graph of the relationship between the fitness function of the PSO algorithm and the number of iterations, as shown in Figure 7 As shown in Figure 2, the convergence effect of the PSO algorithm in solving the actual optimization control model can be judged. Figure 7 It can be seen that the algorithm reaches convergence at the 46th iteration, which proves the effectiveness of the PSO algorithm in solving optimal control problems.

[0231] According to the above work, we finally get the following Figure 8 The power comparison of the lower network point before and after the control is shown, as well as Figure 9The figure shows the comparison of power fluctuation rate at the lower grid point before and after control.

[0232] It is not difficult to see from the figure that the photovoltaic power fluctuation control method based on distributed resource clustering adopted in this embodiment can effectively smooth the power fluctuation of the grid point. On the one hand, the grid point power at each time point in the control cycle is controlled within the period power reference value P ref Around 100 kW, the maximum fluctuation before and after control decreased from 174.71 kW to 65.92 kW. Furthermore, the minute-by-minute fluctuation rate of the downstream power point during the control period was consistently below 2%, whereas before control, it exceeded 2% at three points. The absolute value of the maximum fluctuation rate after control was 1.998%, a decrease of 6.099% compared to before control. This satisfied the constraints imposed by the optimized control model on downstream power fluctuations and achieved good control results. Furthermore, because the control model only considers the economic penalty for exceeding the fluctuation constraints, the control amount at t = 5 is relatively small, effectively achieving power fluctuation smoothing while also considering the control cost.

[0233] 4. Verification of the application effect of resource clustering;

[0234] Based on the solution of the optimization model, we focus on analyzing and verifying the role of resource clustering. First, we draw the output change curves of the two aggregates before and after control within a control cycle, as shown in Figure 10(a) and Figure 10(b), and make a corresponding aggregate control scale;

[0235] Table 4. Aggregate total control scale (“-” sign indicates output reduction)

[0236]

[0237] As can be seen from Figures 10(a) and 10(b), during this control period, the regulation amount of aggregate 1 is much greater than that of aggregate 2, that is, the regulation amount required by the distribution network system is basically borne by aggregate 1, and the output curves of aggregate 2 before and after control are basically coincident. This is because the power fluctuation of the downstream grid caused by photovoltaic fluctuations is small, so the regulation amount obtained by the optimization algorithm does not exceed the regulation capacity of aggregate 1. At the same time, this also indirectly illustrates the regulation advantage of aggregate 1 over aggregate 2, and proves the priority conclusion given in the distributed resource clustering results and analysis.

[0238] Combine Figure 8The power fluctuation trend of the downstream network point in Figure 2 and the aggregate control amount in Table 4 are analyzed. When the downstream network point power fluctuates downward, in order to smooth the fluctuation, aggregate 1 reduces its output, which is equivalent to increasing the load power in the distribution network, thereby increasing the power purchased by the main network. For example, at t = 2, the output of aggregate 1 is reduced by 43.6413 kW, and that of aggregate 2 is reduced by 0.0651 kW, while the power of the downstream network point increases by 47.0489 kW, which has the effect of smoothing the power fluctuation.

[0239] To further validate the conclusions regarding intra-aggregate priorities, Table 5 shows the magnitude of the regulation of various resources within the aggregate during the regulation cycle. Positive values for energy storage represent load charging, while negative values represent source discharge. It is readily apparent that, for the fluctuations analyzed, distributed energy storage takes the primary responsibility for regulation in both aggregates. This is due to the lower unit regulation cost of energy storage. Based on the economic ranking results, energy storage takes priority in regulation, while distributed photovoltaics and interruptible loads are regulated last in the down-regulation and up-regulation scenarios, respectively.

[0240] Table 5. Resource control scale for various types of resources within the aggregate

[0241]

[0242]

[0243] In summary, the conclusion on resource control priority obtained in the previous section has been verified in the application and meets the goal of resource clustering.

[0244] Finally, to further illustrate the role of the distributed resource clustering-based optimization control method in the power fluctuation smoothing process, the time for solving the optimization control model with and without clustering, as well as the total economic cost of the optimization control, are compared. The results are shown in Tables 6 and 7.

[0245] Table 6. Comparison of optimization control time before and after clustering

[0246]

[0247] Table 7. Comparison of optimization control costs before and after clustering

[0248]

[0249] Obviously, the optimized control after clustering has a great advantage in both solution speed and control cost compared with the non-clustered case. This is because resource clustering not only reduces the dimension of optimization solution, but also comprehensively evaluates the control performance of a large number of distributed control resources, and takes resource control priority as the basis for smoothing power fluctuations, which significantly improves resource utilization efficiency and the reliability and economy of control. This is also in line with the ultimate goal of resource clustering, and indirectly illustrates the effectiveness and reliability of the control scheme.

[0250] The above are only preferred embodiments of the present invention and do not limit the implementation mode and protection scope of the present invention. For those skilled in the art, it should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the present invention specification should be included in the protection scope of the present invention.

Claims

1. A photovoltaic power fluctuation control method based on distributed resource clustering, characterized by: The following steps are involved: Step 1: Establish a minute-level AGC control framework model based on resource clustering and optimization algorithms. This includes the following steps: Step 1.1: Establish a minute-level AGC control framework model, including: Distribution network structure and resource parameter settings; The photovoltaic forecast data at the first moment of the control cycle is used as a clustering indicator. The K-means++ algorithm, which is improved based on indicator weights, is used to cluster resources. The indicators are then aggregated and modeled. The aggregation model is used to determine the priority order of resource regulation, which serves as the basis for optimal control in the next stage. The sample Euclidean distance calculation method in the K-means++ algorithm is improved to achieve clustering of distributed resources and give practical meaning to the clustering results. Step 1.2: Solve the minute-level AGC control model, including: In the second stage of the control framework, the power baseline value of the downstream node obtained in the first stage is used to determine the distribution network's control demand at minute t: output increase or output decrease. The control quantity is then distributed to several distributed resources within the resource aggregate according to the priority of resource control. The output of each resource aggregate is used as the decision variable, and the particle swarm algorithm is used to solve the optimal control model. This reduces the dimension of the decision variables while achieving the goals of power fluctuation smoothing and minimizing economic costs. Step 2: Build a minute-level AGC optimization control model based on the control object characteristics and control objectives, establish the connection between power fluctuation smoothing and control cost, and distinguish the optimization model and control constraints before and after resource clustering; including the following steps: Step 2.1, establish the economic objective function of the optimization control model; Based on the aggregation model, the priority of resource regulation is determined to establish the economic optimization goal at the aggregate level: Where F(t) is the total economic cost; K is the number of aggregates obtained after clustering; F cluster,k (t) is the control cost of the k-th aggregate at the t-th minute; F grid (t) is the main grid electricity purchase cost at minute t; The control cost of a single aggregate is calculated based on the actual aggregate control amount and the resource economic priority curve within each aggregate. The main grid power purchase cost is calculated as follows: Where, f grid The electricity purchase cost of the grid unit; is the power of the downstream node at minute t, i.e., the main network power; Δt is the duration of the calculation period; The power of the downstream network is calculated by forward-backward substitution method under the premise of clarifying the structural parameters, load conditions and actual resource access conditions in the distribution network; Step 2.2: Optimize the control model constraints, including the operation constraints of the distributed control resource aggregate, power balance constraints, and power fluctuation rate constraints of the downstream network points. The power fluctuation rate constraint of the lower grid point is: Define the power fluctuation rate R of the next grid point in the tth minute Vol (t), which represents the degree of power change at the current moment relative to the previous moment; according to the distribution network structure and resource parameters simulated in the example, the power fluctuation rate constraint conditions of the down-grid point in the example are determined, and the fluctuation rate R Vol (t) Limited to 2%: The connection between the power fluctuation rate constraint at the downstream grid point and the economic objective function is established. The constraint is added to the economic objective function in the form of a penalty function. The coefficient representing the intensity of the penalty function is then adjusted and defined in the form of a piecewise function: Where β is the penalty function intensity coefficient; ΔR Vol (t) is the difference between the actual power fluctuation rate of the downlink point and the constraint value; The economic objective function considering the power fluctuation penalty is: Step 3: Based on actual control, an optimization control model solving method based on particle swarm algorithm is proposed. The economic objective function reflecting the control cost is used as the basis for algorithm fitness evaluation. An optimization control model solving method based on resource clustering and optimization algorithm is proposed.

2. The photovoltaic power fluctuation control method based on distributed resource clustering according to claim 1 is characterized by: The distribution network structure and resource parameter settings include: Select the time period benchmark for the downstream power and generate the target value within the current control cycle. Within the same control cycle, calculate the downstream power fluctuation rate based on the predictive control step size as a coupling constraint for the minute-level AGC optimization control and the power fluctuation smoothing target. The control period T is selected as 5 minutes, and the predictive control step length T c The power of the network point at the first moment is selected as the control reference value in each control cycle. Aggregate modeling of indicators includes: Construct a resource clustering control indicator system. Based on the resource regulation requirements of power fluctuation smoothing goals, select corresponding control indicators from both technical and economic perspectives to establish a control indicator system that serves resource clustering. Configure clustering indicator weights, determine the weight configuration principle based on the clustering goals and the clustering service objects, and use the subjective weighting method to weight each clustering indicator; Propose an improved K-means++ algorithm based on indicator weights, and configure the results according to the obtained weights; Each time the optimization model is solved, the number of solutions N is calculated based on the predictive control step size and cycle c Determine whether the current control cycle has ended, and then determine whether it is necessary to update the clustering index and perform clustering and calculation for the next cycle.

3. The photovoltaic power fluctuation control method based on distributed resource clustering according to claim 1 is characterized by: The operational constraints and power balance constraints of the distributed control resource aggregate include: The operating constraints of distributed photovoltaics are: Distributed photovoltaics should meet the following constraints: Where, is the total amount of distributed photovoltaic control within aggregate k at minute t; P PV,i,max is the maximum controllable amount of the i-th distributed unit; The operating constraints of distributed photovoltaic energy storage are: Meet the charging and discharging power constraints and capacity constraints: Where, is the output of distributed energy storage in aggregate k at minute t; is the minimum output of the i-th distributed energy storage unit in aggregate k; is the maximum output of the i-th distributed energy storage unit in aggregate k; is the capacity of distributed energy storage in aggregate k at minute t; is the minimum capacity of the i-th distributed energy storage unit in aggregate k; is the maximum capacity of the i-th distributed energy storage unit in aggregate k; The capacity constraint is calculated and analyzed in combination with the dynamic characteristics of the charging and discharging capacity of the cluster energy storage. Assuming that all energy storage units in the system are of the same model, the cluster charging and discharging efficiency is also the same: Where η in is the charging efficiency of the energy storage unit; η out is the discharge efficiency of the energy storage unit; The interruptible load operation constraints are: For aggregates with interruptible loads, consider their aggregate output constraints: Where, is the load size of distributed energy storage in aggregate k at minute t; is the minimum load power of the i-th interruptible load unit in aggregate k; is the maximum load power of the i-th interruptible load unit in aggregate k; The power balance constraint is: Where, P L (t) is the load power in the distribution network at minute t; P loss (t) is the network loss power in the distribution network at minute t.

4. The photovoltaic power fluctuation control method based on distributed resource clustering according to claim 1 is characterized by: The solution method of the optimization control model based on resource clustering and optimization algorithm includes the following steps: Step 3.1, initialization of population particle positions and velocities; According to the clustering results of the distributed resources in the distribution network, the variable dimension D of the optimized feasible solution is determined, which corresponds to the spatial dimension of the particles in the PSO and sets the number of particles N in the population. Set the search area upper limit X according to the aggregate aggregation index max and the lower bound X min , giving the maximum value V of the particle search speed Vi max and minimum value V min , and the convergence accuracy ε or the maximum number of iterations N iter , and take the value of the initial state of the particles within the constraints of position and velocity to complete the initialization of the position and velocity of the population particles; At the beginning of the algorithm, the individual learning factor c1, social learning factor c2 and inertia weight ω of the population are set to update the position and velocity of the particles; Step 3.2, calculate particle fitness; In each iteration, the fitness of each particle in the population is re-evaluated, and the individual optimal solution and the population optimal solution are updated and calculated; the fitness function is represented by the economic objective function of the optimization model; The fitness value of each particle is repeatedly calculated during each iteration, and the individual optimal solution of the current particle and the optimal solution of the population are updated by comparison, as well as the corresponding objective function value, to achieve the purpose of optimization; The individual optimal solution and the population optimal solution are expressed as follows: Where p i is the individual optimal solution of the particle; g is the population optimal solution of the particle; X D is the D-th dimension position characteristic of the particle; Step 3.3, optimize convergence judgment; After each iterative calculation is completed, the difference between the optimal particle fitness values of the population obtained in this iteration and the previous iteration is used to determine whether the optimization solution has converged. The convergence conditions are as follows: |H(g(n))-H(g(n-1))|<ε (14) Among them, ε is the convergence accuracy; H(g(n)) is the optimal fitness value of the population calculated at the nth iteration; If the convergence condition is met, or the maximum number of iterations N is reached iter , then the optimal particle of the current population corresponds to the optimal solution of the decision variable, realizing the optimization control process; if the convergence condition cannot be met, execute step 3.4 to update the particle position and velocity; Step 3.4, update particle position and velocity and boundary processing; At the beginning of each iteration, the particle optimization speed and position are updated according to the individual optimal fitness value and the population optimal fitness value obtained in the previous iteration according to formula (15) and formula (16): V i (n+1)=ωV i (n)+c1r1[p i (n)-x i (n)]+c2r2[g(n)-x i (n)] (15) x i (n+1)=x i (n)+V i (n+1) (16) Where c1 is the individual learning factor, which takes a value of 0.5; c2 is the social learning factor, which takes a value of 0.5; r1 and r2 are random numbers in the range of [0,1] to increase the randomness of particle optimization; ω is the weight of the particle to maintain the historical speed, which takes a value of 0.9; The particle position update formula includes three parts: historical experience, individual cognition and social learning. The first part ωV i (n) reflects the habit of particle movement and its own historical experience; the second part represents the impact of the particle's own memory of the optimal value on the speed of the next iteration; the third part reflects the cooperation between particles and the historical experience of the population, showing that the particles tend to approach the historical best position during the optimization process; After completing the update of particle velocity and position, the updated results are tested according to the following formula: X min ≤X i,d ≤X max (17) In min ≤V i,d ≤V max (18) Among them, X i,d is the d-dimensional position variable of particle i; V i,d is the d-dimensional velocity variable of particle i; For particles that exceed the constraint range, a feasible solution is randomly generated within the constraint range to replace them.

Images