Optimized stationing method for multiplexing type electric energy quality control equipment

Abstract

The invention relates to an optimized stationing method for multiplexing type power quality control equipment, which comprises the following steps of: firstly, selecting a power distribution network provided with the multiplexing type power quality control equipment, and carrying out regional division on the power distribution network by adopting an improved k-means clustering algorithm to carry out regional control; then, an optimal configuration model of the multiplexing type electric energy quality treatment equipment is constructed with the minimum installation cost as the target, and the optimal configuration model comprises a target function and constraint conditions; and finally, solving the constructed optimal configuration model of the multiplexing type electric energy quality treatment equipment by adopting a self-adaptive ant colony optimization algorithm, and obtaining the optimal access position and capacity of the electric energy quality treatment equipment. The self-adaptive ant colony optimization algorithm refers to the idea of an elite ant colony system, the pheromone updating link is improved, the global solution space can be fully searched, and the efficiency of searching the global optimal solution is improved. The method has the functions of harmonic suppression, reactive compensation and oscillation suppression, and economic benefits can be ensured while the power distribution network treatment effect is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of power quality management and relates to a method for optimizing the deployment of multiplexed power quality management equipment. Background Art

[0002] With the large-scale access of distributed renewable energy to the distribution network, the distribution network presents significant power electronics characteristics. The intermittent and random characteristics of distributed renewable energy make the power quality problems such as harmonic pollution and voltage deviation in the distribution network prominent, and have the characteristics of interactive coupling. In addition, power quality pollution has the characteristics of high density, decentralization, and full network, which makes the power quality governance more difficult. At present, the research on power quality pollution governance has achieved certain results. Most of them are based on the idea of ​​zoning governance, which divides the distribution network into regions and optimizes the governance of each region. For the existing partitioning algorithms, the k-means clustering algorithm has been widely used in the field of partitioning because of its simplicity, ease of use and high computational efficiency. However, the algorithm searches for the optimal solution based on the greedy strategy, which is easy to fall into the local optimum and may not get the best partitioning result. In addition, for the traditional k-means clustering algorithm, the number of subclusters is randomly selected, and the number of subclusters of different sizes and densities will affect the clustering effect. As for the optimization point distribution algorithm, existing research is mostly based on artificial intelligence algorithm solutions, but traditional artificial intelligence algorithms are prone to fall into local optimality. Taking the ant colony algorithm as an example, the traditional ant colony optimization algorithm updates pheromones for all ant search paths, and the search efficiency is low. At the same time, the positive feedback effect of the algorithm makes the search easy to fall into the local optimal solution, limiting its search breadth of the solution space. Regarding the configuration of existing governance devices, current research mainly focuses on the configuration of single-type equipment for harmonic and voltage deviation problems, and does not consider the optimal configuration of multiplexed governance equipment with multiple functions, resulting in incomplete governance means and poor governance effects. Summary of the invention

[0003] In order to solve the above-mentioned shortcomings, the present invention proposes an optimization layout method for multiplexed power quality management equipment. Multiplexed power quality management equipment has the functions of harmonic control, reactive power compensation and oscillation suppression. The coordinated optimization configuration scheme of multiplexed power quality management equipment is studied, which can ensure the economic benefits while ensuring the management effect of the distribution network. The scheme adopts the improved k-means clustering algorithm to divide the distribution network into regions, and determines the optimal number of clusters by introducing the clustering effectiveness index, reduces the influence of the initial clustering center on the clustering analysis results, and avoids falling into the local optimal solution. With the lowest installation cost as the goal, considering the constraints such as the power flow equation, node injection power balance, and optimal power quality management effect, an optimization configuration model of multiplexed power quality management equipment is constructed to give full play to the harmonic control, reactive power compensation and oscillation suppression of the equipment in each region. Finally, the adaptive ant colony optimization algorithm is used to solve the constructed optimization model to obtain the optimal access location and capacity of the power quality management equipment. The adaptive ant colony optimization algorithm refers to the idea of ​​the elite ant colony system, improves the pheromone update link, can fully search the global solution space, and improve the efficiency of searching the global optimal solution.

[0004] The technical solution adopted by the present invention is:

[0005] A method for optimizing the layout of multiplexed power quality management equipment, characterized in that it includes the following steps:

[0006] Step S1: Select a distribution network for installing a multiplexed power quality management device, and use an improved k-means clustering algorithm to divide the distribution network into regions for zone management;

[0007] The improved k-means clustering algorithm refers to introducing the clustering effectiveness index D on the basis of the traditional k-means clustering algorithm. CH Determine the optimal number of clusters K_ best ;

[0008] D CH The closeness and separation are described by calculating the intra-class dispersion matrix and the inter-class dispersion matrix respectively. The calculation formula is:

[0009]

[0010] In the formula, K represents the number of subclusters divided by the data set under the clustering algorithm, and D CHk represents the CH index of the kth subcluster;

[0011] Step S2: constructing an optimal configuration model of the multiplexed power quality management equipment with the goal of minimizing the installation cost, wherein the optimal configuration model includes an objective function and constraint conditions;

[0012] Step S3: Adopting the adaptive ant colony optimization algorithm to solve the constructed optimal configuration model of the multiplexed power quality management equipment, and obtaining the optimal access location and capacity of the power quality management equipment.

[0013] Furthermore, the step S1 further includes the following steps:

[0014]

[0015] In the formula, B k is the between-class dispersion matrix, W k is the intra-class dispersion matrix, tr(B k ), tr(W k) Respectively represent B k and W k The trace of k represents the current sub-cluster, and the sample size of the kth sub-cluster is N k , m is the number of all objects in the data set S;

[0016]

[0017] In the formula, is the sample mean vector of the ith subcluster, is the sample mean vector of the entire data set, N i is the sample size of the ith subcluster, m is the number of all objects in the dataset S, and T represents transposition;

[0018]

[0019] In the formula, x i is the i-th sample in the k-th subcluster, is the sample mean vector of the kth subcluster.

[0020] Furthermore, the step S1 specifically includes the following steps:

[0021] Step S11: inputting an original data set S including the location of power grid nodes and power flow information, wherein the original data set S is formed by sampling and collecting node voltage, current, active power, and reactive power information in an actual power grid through measurement tools;

[0022] Step S12: Select the number of sub-clusters K, the range of the number of sub-clusters is K∈[2,K max ], K from 2 to K max Cycle, K max Calculation formula:

[0023]

[0024] In the formula, int is the rounding function, and m is the number of all objects in the data set;

[0025] Step S13: Determine the initial cluster center. At the beginning of the algorithm, randomly select K sample points from the data set as the initial cluster center. These points are used as the initial center for subsequent clustering iterations.

[0026] Step S14: Based on the minimum distance principle, each sample point in the data set S is assigned to K cluster centers. The calculation formula of the minimum distance principle is:

[0027]

[0028] Where: y i represents the coordinates of sample point i, which has p dimensions; c j is the coordinate of the jth cluster center; x ik and c jk are samples y i and cluster center c j The value in the kth dimension;

[0029] Step S15: Calculate new cluster centers;

[0030] Step S16: determine whether the criterion function meets the convergence condition, if so, proceed to the next step, otherwise, return to step S14;

[0031] The convergence condition is satisfied when the cluster center is updated each time, the change between the new cluster center and the previous cluster center is calculated. If the change of all cluster centers is less than a very small threshold, that is, no longer significantly changed, the algorithm is considered to have reached convergence.

[0032]

[0033] In the formula, ε is a very small positive number;

[0034] Step S17: Calculate the clustering effectiveness index D CH , after calculating the clustering effect D of the current cluster number K CH After the index is obtained, the number of clusters K is increased, and the process returns to step S13 to recalculate D under the new number of clusters K. CH index;

[0035] Step S18: Compare D CH Get the optimal effectiveness index D CHbest , according to D CH_best Select the best number of clusters K_ best ;

[0036] Step S19: According to K_ best Cluster the data set S, output the clustering results, and complete the regional division of the distribution network.

[0037] Furthermore, the step S15 of calculating the new cluster center specifically includes the following steps:

[0038] (1) In step S14, all sample points have been assigned to a cluster, forming K clusters. For the jth cluster, let its sample point set be C j , where C j Contains all sample points belonging to this cluster;

[0039] (2) Calculate the average value of all points in the cluster: For all sample points x in the jth cluster ij (ij∈C j ), the new cluster center is the geometric center of these points, that is, their average value in each dimension, the new cluster center The calculation formula is:

[0040]

[0041] Where: |C j | represents the number of sample points in cluster j; x ij is the sample point belonging to cluster j; is the new cluster center.

[0042] Furthermore, the objective function of the optimization configuration model of the multiplexed power quality management equipment is as follows:

[0043] minC=C 1 +C 2 (9)

[0044] Where minC is the installation cost of small power quality device, C 1 is the fixed investment cost of the treatment equipment, C 2 Equipment operation and maintenance costs;

[0045] The fixed investment cost of the treatment equipment is calculated according to the equal annual output value method:

[0046]

[0047] Where: C 1 is the fixed investment cost of the governance equipment, S(i,t) is the access capacity of the governance equipment at the i-th node at time t; n is the number of nodes where the governance equipment is installed; R is the annual value coefficient of the governance equipment; r is the discount rate of the governance equipment, γ is the service life of the governance equipment; c is the unit capacity cost of the governance equipment;

[0048] The operation and maintenance costs of the treatment equipment are calculated as a percentage of the fixed investment cost:

[0049] C 2 =ηC1 (12)

[0050] In the formula, C 2 is the operation and maintenance cost of the treatment equipment, and η is the percentage of the operation and maintenance cost of the treatment equipment to the fixed investment cost.

[0051] Furthermore, the constraints of the optimization configuration model of the multiplexed power quality management equipment are as follows:

[0052] (1) Power flow equation constraints:

[0053]

[0054] Where P(i,t) and Q(i,t) are the active power and reactive power injected into node i at time t, respectively; G ij and B ij are the real and imaginary parts of the i-row and j-column in the node admittance matrix; U(i,t) and U(j,t) are the fundamental voltage amplitudes of nodes i and j, respectively; θ ij (t) is the phase difference between the two ends of branch ij at time t; n is the number of nodes in the system;

[0055] After linearization:

[0056]

[0057] In the formula, g ij and b ij are the conductance and admittance of branch ij respectively. According to the definition of admittance matrix g ij =-G ij , b ij =-B ij ;

[0058] (2) Node injection power balance constraint:

[0059]

[0060] Where P g (i, t) is the active output of the generator at node i at time t; Q g (i, t) is the reactive power output of the generator at node i at time t; P re (i, t) is the renewable energy active power output of node i at time t; Q re (i,t) is the reactive power output of new energy of node i at time t; P L (i,t) is the active load of node i at time t; Q L (i,t) is the reactive load of node i at time t; Q H (i, t) is the harmonic compensation output of the multiplexing type control device at node i at time t; Qq (i, t) is the reactive power output compensated by the multiplexing type management device of node i at time t.

[0061] (3) Constraints on the installed capacity of each node management equipment:

[0062]

[0063] Where I(i,t) is the total compensation capacity of the multiplexing type management device of node i at time t; β(i,t) is an integer variable, which indicates the number of multiplexing type management devices connected to node i at time t; I H The capacity of a single multiplexed treatment device; is the maximum allowable access capacity of the multiplexing type management device at node i; μ is the capacity margin safety factor of the management equipment, which is generally taken as 0.98; I HCq (i,t),I HC,h (i,t) and I y (i, t) are the reactive power compensation capacity, harmonic compensation capacity, and oscillation suppression compensation capacity of node i at time t;

[0064] Convert to second-order cone form:

[0065]

[0066] In the formula, sum represents summation, and T represents matrix transpose.

[0067] (4) Optimal constraints for power quality management:

[0068] U min (i,t)≤U(i,t)≤U max (i,t) (18)

[0069]

[0070] In the formula: U(i,t), U min (i,t) and U max (i, t) are the fundamental voltage, lower limit and upper limit of fundamental voltage of node i at time t, respectively. min (i,t)=[0.96](i×h),U max (i,t)=[1.04](i×h); is the square of the hth harmonic voltage at node i at time t, H is the number of harmonics considered; THD(i,t) and THD max (i, t) are the harmonic voltage distortion rate and its maximum limit of node i at time t;

[0071] Convert to second-order cone form:

[0072]

[0073] (5) Compensation capacity constraints:

[0074]

[0075] Q q (i,t)=3U N I HCq (i,t) (22)

[0076]

[0077] Where U N is the rated working voltage of the equipment;

[0078] (6) Harmonic power flow related constraints:

[0079] I h (i,t)=I inth (i,t)-I HC,h (i,t) (24)

[0080] I h (i,t)=Y h (i,i)U h (i,t) (25)

[0081] In the formula, I h (i,t) is the hth harmonic current of node i at time t after adding the harmonic compensation device; I inth (i, t) is the hth harmonic current of node i at time t before adding the harmonic compensation device; Y h (i,i) are the diagonal elements of the harmonic admittance matrix.

[0082] Furthermore, the step S3 specifically includes the following steps:

[0083] Step S31: Initialize pheromones. Initially, a certain amount of pheromones will be initialized on all possible paths. That is, ants will form a certain amount of pheromones on all possible nodes of the reusable management device, which is equivalent to the role of marking.

[0084] Step S32: Path selection. When each ant selects the next path, it will determine the path based on the pheromone concentration on the path and the expected value of the path, such as the path length and cost. The probability formula for path selection is:

[0085]

[0086] In the formula, τ ij (t) represents the pheromone concentration on the path (i, j) at time t, η ij(t) represents the residual expectation of path (i, j) at time t, usually taking the inverse of the length of path (i, j), α and β represent the relative importance of pheromone and expectation heuristic factor respectively; J k (i) = {1,2,...,c}-tabu k represents the set of cities that ant k is allowed to choose next. k is the taboo table of ant k, recording the cities it has currently visited, s belongs to any city that ant k is allowed to choose next, τ is (t) represents the residual pheromone on the path (i, s) at time t, η is (t) represents the residual expectation degree of the path (i, s) at time t;

[0087] Step S33: path construction and constraint processing;

[0088] When constructing paths, ants will make choices based on the objective function and constraints in the optimization model. Only paths within the constraints will be retained and selected by the ants. Each path generated by an ant will go through a series of constraint checks, and only paths that meet all constraints will be used to update pheromones.

[0089] Step S34: iteration and convergence;

[0090] An elite ant system is introduced. After each iteration, additional pheromones are artificially released to the optimal solution path determined by the elite ants to increase the effect of positive feedback. The pheromone update formula is as follows:

[0091] τ ij (t+1)=(1-ρ)τ ij (t)+Δτ ij ' (27)

[0092] In the formula, τ ij (t+1) represents the residual pheromone on the path (i, j) at the next moment t, 1-ρ represents the residual coefficient of pheromone (0≤ρ<1), Δτ ij ' represents the additional increment of pheromone on the path (i, j) taken by the elite ant;

[0093] The additional increment of pheromone is adjusted according to the number of iterations. The formula is as follows:

[0094]

[0095] Where Q is a constant, which represents the total amount of pheromones released by ants on all paths they pass through. σ represents the number of elite ants. N is the current number of iterations, and T is the total number of iterations of the algorithm.

[0096] The beneficial effects of the present invention are:

[0097] 1. The improved k-means clustering algorithm is used to divide the distribution network into regions, realizing the zoning management of the power quality of the distribution network; the optimal number of clusters is determined by introducing the clustering effectiveness index, reducing the influence of the initial clustering center on the clustering analysis results, avoiding falling into the local optimal solution, and improving the rationality of the zoning results;

[0098] 2. Multiplexed power quality management equipment has the functions of harmonic control, reactive power compensation and oscillation suppression. Research on the optimal configuration scheme of multiplexed power quality management equipment can ensure the distribution network management effect while ensuring economy;

[0099] 3. The adaptive ant colony optimization algorithm is used to solve the constructed optimization model. With reference to the idea of ​​the elite ant colony system, the pheromone update link is improved, which can not only fully search the global solution space, but also improve the efficiency of searching for the global optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0101] Figure 1 It is an implementation flow chart of the present invention;

[0102] Figure 2 It is the flow chart of the improved k-means clustering algorithm;

[0103] Figure 3 It is the topological structure diagram of IEEE33 node power distribution system;

[0104] Figure 4 It is the voltage level diagram of each node before and after the new energy is connected;

[0105] Figure 5 It is the voltage distortion rate diagram of each node before and after the new energy is connected;

[0106] Figure 6 It is the voltage level diagram of each node before and after the treatment device is connected;

[0107] Figure 7 It is the voltage distortion rate diagram of each node before and after the treatment device is connected; DETAILED DESCRIPTION

[0108] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0109] like Figure 1 As shown, a method for optimizing the layout of multiplexed power quality management equipment includes the following steps:

[0110] Step S1: Select a distribution network for installing a multiplexed power quality management device, and use an improved k-means clustering algorithm to divide the distribution network into regions for zone management;

[0111] It should be noted that the improved k-means clustering algorithm refers to the introduction of clustering effectiveness index D on the basis of the traditional k-means clustering algorithm. CH Determine the optimal number of clusters K _best . D CH It is an indicator based on the geometric structure of the data set samples. It evaluates the clustering results according to the statistical characteristics of the data set itself and the clustering results. CH The larger the clustering effect, the better. CH Select the optimal number of clusters. CH The closeness and separation are described by calculating the intra-class dispersion matrix and the inter-class dispersion matrix respectively. The calculation formula is:

[0112]

[0113] In the formula, K represents the number of subclusters divided by the data set under the clustering algorithm, and D CHk Represents the CH index of the kth subcluster, and the calculation formula is:

[0114]

[0115] In the formula, B k is the between-class dispersion matrix, W k is the intra-class dispersion matrix, tr(B k ), tr(W k) Respectively represent B k and W k The trace of k represents the current sub-cluster, and the sample size of the kth sub-cluster is N k , m is the number of all objects in the data set S.

[0116]

[0117] In the formula, is the sample mean vector of the ith subcluster, is the sample mean vector of the entire data set, N i is the sample size of the ith subcluster, m is the number of all objects in the dataset S, and T represents transposition.

[0118]

[0119] In the formula, x i is the i-th sample in the k-th subcluster, is the sample mean vector of the kth subcluster.

[0120] like Figure 2 As shown in the figure, the specific steps of the improved k-means clustering algorithm to divide the distribution network into regions are as follows:

[0121] Step S11: inputting the original data set S containing the grid node location and flow information, which is formed by sampling and collecting the node voltage / current, active / reactive power and other information in the actual grid through measurement tools.

[0122] Step S12: Select the number of sub-clusters K, the range of the number of sub-clusters is K∈[2,K max ], K from 2 to K max Cycle, K max Calculation formula:

[0123]

[0124] In the formula, int is the rounding function, and m is the number of all objects in the dataset.

[0125] Step S13: Determine the initial cluster center. At the beginning of the algorithm, randomly select K sample points from the data set as the initial cluster centers. These points are used as the initial centers for subsequent clustering iterations.

[0126] Step S14: Based on the minimum distance principle, each sample point in the data set S is assigned to K cluster centers. In the k-means algorithm, the commonly used distance measurement method is the Euclidean distance. For a given sample point x i and cluster center c j , the Euclidean distance between them is calculated as:

[0127]

[0128] Where: y i represents the coordinates of sample point i, which has p dimensions; c j is the coordinate of the jth cluster center; x ik and c jk The samples x are iand cluster center c j The value in the kth dimension. Assign each sample point in the data set S to K cluster centers:

[0129] First, calculate the distance between the sample and the cluster center: for each sample point x in the data set i， Calculate its correlation with all K cluster centers c 1 , c 2 , ..., c K The distance, and then select the nearest cluster center: According to the calculated distance, the sample point x i Assigned to the cluster center c closest to it j .

[0130] Step S15: Calculate new cluster centers;

[0131] Step S16: Determine whether the criterion function meets the convergence condition. If so, proceed to the next step. Otherwise, return to step S14. Each time the cluster center is updated, the change between the new cluster center and the previous cluster center is calculated. If the change of all cluster centers is less than a very small threshold, that is, no longer significantly changed, the algorithm is considered to have reached convergence.

[0132]

[0133] In the formula, ε is a very small positive number.

[0134] Step S17: Calculate the clustering effectiveness index D CH , after calculating the clustering effect D of the current cluster number K CH After the index is obtained, the number of clusters K is increased, and the process returns to step S13 to recalculate D under the new number of clusters K. CH index.

[0135] Step S18: Compare D CH Get the optimal effectiveness index D CH_best , according to D CH_best Select the best number of clusters K_ best .

[0136] Step S19: According to K _best Cluster the data set S, output the clustering results, and complete the regional division of the distribution network.

[0137] It should be noted that the step S15 of calculating the new cluster center specifically includes the following steps:

[0138] (1) In step S14, all sample points have been assigned to a cluster, forming K clusters. For the jth cluster, let its sample point set be C j , where C jContains all sample points belonging to this cluster.

[0139] (2) Calculate the average value of all points in the cluster: For all sample points x in the jth cluster i (i∈C j ), the new cluster center is the geometric center of these points, that is, their average value in each dimension. The new cluster center The calculation formula is:

[0140]

[0141] Where: |C j | represents the number of sample points in cluster j; x i is the sample point belonging to cluster j; is the new cluster center.

[0142] Step S2: constructing an optimal configuration model of the multiplexed power quality management equipment with the goal of minimizing the installation cost, wherein the optimal configuration model includes an objective function and constraint conditions;

[0143] Objective function: minimum power quality device installation cost minC;

[0144] minC=C 1 +C 2 (9)

[0145] Where, C is the total investment cost; C 1 is the fixed investment cost of the treatment equipment; C 2 Equipment operation and maintenance costs.

[0146] The fixed investment cost of the treatment equipment is calculated according to the equal annual output value method:

[0147]

[0148] Where: S(i,t) is the access capacity of the governance equipment at the i-th node at time t; n is the number of nodes where the governance equipment is installed; R is the annual value coefficient of the governance equipment; r and γ are the discount rate and service life of the governance equipment respectively; c is the unit capacity cost of the governance equipment. In the embodiment of the present invention, r = 6%, γ = 20, and c = 200 yuan / kVA.

[0149] The operation and maintenance costs of the treatment equipment are calculated as a percentage of the fixed investment cost:

[0150] C 2 =ηC 1 (12)

[0151] Wherein, η is the percentage of the operation and maintenance cost of the treatment equipment to the fixed investment cost, and in the embodiment of the present invention, η=5%.

[0152] The constraints of the optimization configuration model of the multiplexed power quality management equipment are as follows:

[0153] (1) Power flow equation constraints:

[0154]

[0155] Where P(i,t) and Q(i,t) are the active power and reactive power injected by node i at time t, respectively; G ij and B ij are the real and imaginary parts of the i-row and j-column in the node admittance matrix respectively; U(i,t) and U(j,t) are the voltage amplitudes of nodes i and j; θ ij (t) is the phase difference between the two ends of branch ij at time t; n is the number of nodes in the system.

[0156] After linearization:

[0157]

[0158] In the formula, g ij and b ij are the conductance and admittance of branch ij respectively. According to the definition of admittance matrix g ij =-G ij , b ij =-B ij .

[0159] (2) Node injection power balance constraint:

[0160]

[0161] Where P g (i, t) is the active output of the generator at node i at time t; Q g (i, t) is the reactive power output of the generator at node i at time t; P re (i, t) is the renewable energy active power output of node i at time t; Q re (i,t) is the reactive power output of new energy of node i at time t; P L (i,t) is the active load of node i at time t; Q L (i,t) is the reactive load of node i at time t; Q H (i, t) is the harmonic compensation output of the multiplexing type control device at node i at time t; Q q (i, t) is the reactive power output compensated by the multiplexing type management device of node i at time t.

[0162] (3) Constraints on the installed capacity of each node management equipment:

[0163]

[0164] Where I(i,t) is the total compensation capacity of the multiplexing type management device of node i at time t; β(i,t) is an integer variable, which indicates the number of multiplexing type management devices connected to node i at time t; I H The capacity of a single multiplexed treatment device; is the maximum allowable access capacity of the multiplexing type management device at node i; μ is the capacity margin safety factor of the management equipment, which is generally taken as 0.98; I Hcq (i,t),I HC,h (i,t) and I y (i,t) are the reactive power compensation capacity, harmonic compensation capacity and oscillation suppression compensation capacity of node i at time t.

[0165] Convert to second-order cone form:

[0166]

[0167] In the formula, sum represents summation, and T represents matrix transpose.

[0168] (4) Optimal constraints for power quality management:

[0169] The fundamental voltage and total voltage distortion rate of each node meet the national standards GB / T 12325-2008 and GB / T14549-93:

[0170] U min (i,t)≤U(i,t)≤U max (i,t) (18)

[0171]

[0172] In the formula: U(i,t), U min (i,t) and U max (i, t) are the fundamental voltage, lower limit and upper limit of fundamental voltage of node i at time t, respectively. min (i,t)=[0.96](i×h),U max (i,t)=[1.04](i×h); is the square of the hth harmonic voltage at node i at time t, H is the number of harmonics considered; THD(i,t) and THD max (i, t) are the harmonic voltage distortion rate and its maximum limit of node i at time t.

[0173] Convert to second-order cone form:

[0174]

[0175] (5) Compensation capacity constraints:

[0176]

[0177] Q q (i,t)=3U N I HCq (i,t) (22)

[0178]

[0179] Where U N is the rated working voltage of the equipment.

[0180] (6) Harmonic power flow related constraints:

[0181] I h (i,t)=I inth (i,t)-I HC,h (i,t) (24)

[0182] I h (i,t)=Y h (i,i)U h (i,t) (25)

[0183] In the formula, I h (i,t) is the hth harmonic current of node i at time t after adding the harmonic compensation device; I inth (i, t) is the hth harmonic current of node i at time t before adding the harmonic compensation device; Y h (i,i) are the diagonal elements of the harmonic admittance matrix.

[0184] Step S3: Adopting the adaptive ant colony optimization algorithm to solve the constructed optimal configuration model of the multiplexed power quality management equipment, and obtaining the optimal access location and capacity of the power quality management equipment.

[0185] The specific steps are as follows:

[0186] Step S31: The ant colony algorithm imitates the behavior of ants foraging. The path selection is completed by combining pheromones and heuristic information. Initialize the pheromone. Initially, a certain amount of pheromone will be initialized on all possible paths (i.e., solution space). That is to say, ants will form a certain amount of pheromone on all possible nodes of the reusable management device, which is equivalent to the role of marking.

[0187] Step S32: Path selection: When each ant chooses the next path, it will determine it based on the pheromone concentration on the path and the expected value of the path (such as factors such as path length and cost). The probability of path selection is:

[0188]

[0189] In the formula, τ ij (t) represents the pheromone concentration on the path (i, j) at time t, η ij (t) represents the residual expectation of path (i, j) at time t, which is usually the inverse of the length of path (i, j). α and β represent the relative importance of pheromone and expectation heuristic factors, respectively.

[0190] These steps mean that all ants will randomly construct paths and leave a certain amount of pheromone. The paths with short paths (i.e., objective function: lower cost) generally have more residual pheromones.

[0191] Step S33: path construction and constraint processing;

[0192] When constructing paths, ants will make choices based on the objective function and constraints in the optimization model. Only paths within the constraints will be retained and selected by the ants. Each solution (i.e., path) generated by an ant will undergo a series of constraint checks, and only solutions that satisfy all constraints will be used to update pheromones.

[0193] Step S34: Iteration and convergence.

[0194] An elite ant system is introduced. After each iteration, additional pheromones are artificially released to the optimal solution path determined by the elite ants to increase the effect of positive feedback. The pheromone update formula is as follows:

[0195] τ ij (t+1)=(1-ρ)τ ij (t)+Δτ ij ' (27)

[0196] In the formula, τ ij (t+1) represents the residual pheromone on the path (i, j) at the next moment t, 1-ρ represents the residual coefficient of pheromone (0≤ρ<1), Δτ ij ' represents the additional increment of pheromone on the path (i, j) taken by the elite ant.

[0197] At the same time, the additional increment formula of pheromone is adjusted according to the number of iterations. The specific formula is as follows:

[0198]

[0199] Where Q is a constant, which represents the total amount of pheromones released by ants on all paths they pass through. σ represents the number of elite ants. N is the current number of iterations, and T is the total number of iterations of the algorithm.

[0200] In each iteration, after all ants complete path selection and update pheromones, the system will evaluate the quality of the path based on the objective function value (i.e., installation cost). The best path (i.e., the path with the lowest current cost) will become the current optimal solution. The path corresponding to the optimal solution has the most residual pheromones after multiple iterations. Through multiple iterations and the accumulation of pheromones, most ants will eventually choose the path of the global optimal solution, thereby finding the best access location and capacity configuration for power quality management equipment.

[0201] In order to enable those skilled in the art to better understand the present invention, the example analysis includes the following components:

[0202] 1. Case description and simulation results analysis

[0203] The present invention takes the power quality pollution control of a single period as an example, and adopts the IEEE33 node system as a case analysis to verify the effectiveness of the reusable power quality capacity configuration strategy proposed in the present invention. Figure 3 The IEEE33 node topology diagram containing new energy is shown. The 7th, 14th, 22nd, 25th, and 30th nodes of the system are connected to distributed power sources with capacities of 0.2MW, 0.1MW, 0.3MW, 0.1MW, and 0.2MW, respectively, and each distributed power source is equipped with 0.3MW of energy storage. The present invention takes the 5th, 7th, 11th, and 13th harmonics as examples, and the injection of each harmonic current of the distributed new energy access node is shown in Table 1.

[0204] Table 1 Harmonic current injection levels of distributed new energy nodes

[0205]

[0206] Through fundamental wave power flow calculation and harmonic wave power flow calculation, the per unit voltage and harmonic distortion rate of each node in the IEEE33 node system before governance can be obtained, such as Figure 4 and Figure 5 As shown in Figure 1, the voltage per unit value of the generator node is set to 1. Figure 4 and Figure 5 It can be seen that after the access of new energy, the node voltage of the adjacent nodes can be significantly improved, and the voltage distortion rate of the access node also increases.

[0207] In order to improve the voltage level of each node and reduce the harmonic voltage distortion rate of the entire network, it is planned to connect several multiplexed power quality management devices to 33 nodes. In order to determine the layout and capacity configuration of the management device, the improved ant colony optimization algorithm described above is used to solve the optimization model. In the improved ant colony algorithm, the initial population size is 100, and the optimal access location and capacity of the multiplexed power quality management device are obtained. The simulation results are as follows: Figure 6 , Figure 7 And as shown in Table 2.

[0208] Table 2 Optimization configuration results of MPQCD in the improved ant colony optimization algorithm strategy

[0209]

[0210] It can be seen from Table 2 that to achieve the expected power quality control effect (U min i max And THD i <THD max ), it is necessary to connect multiplexed power quality management devices to nodes 8, 14, 17, 24 and 33 respectively to perform reactive power compensation on node voltage, harmonic resonance and harmonic distortion rate. Figure 6 and Figure 7 It can be seen that after connecting to the management device, the voltage level of each node increases significantly, and the voltage distortion rate can be maintained below 4%.

[0211] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.​​

Claims

1. A method for optimizing the layout of multiplexed power quality management equipment, characterized in that: The following steps are involved: Step S1: Select a distribution network for installing a multiplexed power quality management device, and use an improved k-means clustering algorithm to divide the distribution network into regions for zone management; The improved k-means clustering algorithm refers to introducing the clustering effectiveness index D on the basis of the traditional k-means clustering algorithm. CH Determine the optimal number of clusters K _best ; D CH The closeness and separation are described by calculating the intra-class dispersion matrix and the inter-class dispersion matrix respectively. The calculation formula is: In the formula, K represents the number of subclusters divided by the data set under the clustering algorithm, and D CHk represents the CH index of the kth subcluster; Step S2: Establishing an optimal configuration model of the multiplexed power quality management equipment with the goal of minimizing the installation cost, wherein the optimal configuration model includes an objective function and constraint conditions; Step S3: Adopting the adaptive ant colony optimization algorithm to solve the constructed optimal configuration model of the multiplexed power quality management equipment, and obtaining the optimal access location and capacity of the power quality management equipment.

2. The method for optimizing the layout of multiplexed power quality management equipment according to claim 1, characterized in that: The step S1 further comprises the following steps: In the formula, B k is the between-class dispersion matrix, W k is the intra-class dispersion matrix, tr(B k ), tr(W k ) represent B k and W k The trace of k represents the current sub-cluster, and the sample size of the kth sub-cluster is N k , m is the number of all objects in the data set S; In the formula, is the sample mean vector of the ith subcluster, is the sample mean vector of the entire data set, N i is the sample size of the ith subcluster, m is the number of all objects in the dataset S, and T represents transposition; In the formula, x i is the i-th sample in the k-th subcluster, is the sample mean vector of the kth subcluster.

3. The method for optimizing the layout of multiplexed power quality management equipment according to claim 2, characterized in that: The step S1 specifically includes: Step S11: inputting an original data set S including the location of power grid nodes and power flow information, wherein the original data set S is formed by sampling and collecting node voltage, current, active power, and reactive power information in an actual power grid through measurement tools; Step S12: Select the number of sub-clusters K, the range of the number of sub-clusters is K∈[2,K max ], K from 2 to K max Cycle, K max Calculation formula: In the formula, int is the rounding function, and m is the number of all objects in the data set; Step S13: Determine the initial cluster center. At the beginning of the algorithm, randomly select K sample points from the data set as the initial cluster center. These points are used as the initial center for subsequent clustering iterations. Step S14: Based on the minimum distance principle, each sample point in the data set S is assigned to K cluster centers. The calculation formula of the minimum distance principle is: Where: y i represents the coordinates of sample point i, which has p dimensions; c j is the coordinate of the jth cluster center; x ik and c jk The samples x are i and cluster center c j The value in the kth dimension; Step S15: Calculate new cluster centers; Step S16: determine whether the criterion function meets the convergence condition, if so, proceed to the next step, otherwise, return to step S14; The convergence condition is satisfied when the cluster center is updated each time, the change between the new cluster center and the previous cluster center is calculated. If the change of all cluster centers is less than a very small threshold (i.e., no longer significantly changed), the algorithm is considered to have reached convergence. In the formula, ε is a very small positive number; Step S17: Calculate the clustering effectiveness index D CH , after calculating the clustering effect D of the current cluster number K CH After the index is obtained, the number of clusters K is increased, and the process returns to step S13 to recalculate D under the new number of clusters K. CH index; Step S18: Compare D CH Get the optimal effectiveness index D CH_best , according to D CH_best Select the best number of clusters K_ best ; Step S19: According to K best Cluster the data set S, output the clustering results, and complete the regional division of the distribution network.

4. The method for optimizing the layout of multiplexed power quality management equipment according to claim 3, characterized in that: The step S15 of calculating the new cluster center includes: (1) In step S14, all sample points have been assigned to a cluster, forming K clusters. For the jth cluster, let its sample point set be C j , where C j Contains all sample points belonging to this cluster; (2) Calculate the average value of all points in the cluster. For all sample points x in the jth cluster, i (i∈C j ), the new cluster center is the geometric center of these points, that is, their average value in each dimension, the new cluster center The calculation formula is: Where: |C j | represents the number of sample points in cluster j; x i is the sample point belonging to cluster j; is the new cluster center.

5. The method for optimizing the layout of multiplexed power quality management equipment according to claim 2, characterized in that: The objective function of the optimization configuration model of the multiplexed power quality management equipment includes: minC=C1+C2 (9) In the formula, minC is the installation cost of the small power quality device, C1 is the fixed investment cost of the treatment equipment, and C2 is the equipment operation and maintenance cost; The fixed investment cost of the treatment equipment is calculated according to the equal annual output value method: Where: S(i,t) is the access capacity of the governance equipment at the i-th node at time t; n is the number of nodes where the governance equipment is installed; R is the equal annual value coefficient of the governance equipment; r and γ are the discount rate and service life of the governance equipment, respectively; c is the unit capacity cost of the governance equipment; The operation and maintenance costs of the treatment equipment are calculated as a percentage of the fixed investment cost: C2=ηC1 (12) Where η is the percentage of the operation and maintenance cost of the treatment equipment to the fixed investment cost.

6. The method for optimizing the layout of multiplexed power quality management equipment according to claim 2, characterized in that: The constraints of the optimization configuration model of the multiplexed power quality management equipment include: (1) Power flow equation constraints: Where P(i,t) and Q(i,t) are the active power and reactive power injected by node i at time t, respectively; G ij and B ij are the real and imaginary parts of the i-row and j-column in the node admittance matrix respectively; U(i,t) and U(j,t) are the voltage amplitudes of nodes i and j; θ ij (t) is the phase difference between the two ends of branch ij at time t; n is the number of nodes in the system; After linearization: In the formula, g ij and b ij are the conductance and admittance of branch ij respectively. According to the definition of admittance matrix g ij =-G ij , b ij =-B ij ; (2) Node injection power balance constraint: Where P g (i, t) is the active output of the generator at node i at time t; Q g (i, t) is the reactive power output of the generator at node i at time t; P re (i, t) is the renewable energy active power output of node i at time t; Q re (i,t) is the reactive power output of new energy of node i at time t; P L (i,t) is the active load of node i at time t; Q L (i,t) is the reactive load of node i at time t; Q H (i, t) is the harmonic compensation output of the multiplexing type control device at node i at time t; Q q (i, t) is the reactive power output compensated by the multiplexing type management device at node i at time t; (3) Constraints on the installed capacity of each node management equipment: Where I(i,t) is the total compensation capacity of the multiplexing type management device of node i at time t; β(i,t) is an integer variable, which indicates the number of multiplexing type management devices connected to node i at time t; I H The capacity of a single multiplexed treatment device; is the maximum allowable access capacity of the multiplexing type management device at node i; μ is the capacity margin safety factor of the management equipment, which is generally taken as 0.98; I Hcq (i,t),I HC,h (i,t) and I y (i, t) are the reactive power compensation capacity, harmonic compensation capacity, and oscillation suppression compensation capacity of node i at time t; Convert to second-order cone form: In the formula, sum means summation, T means matrix transposition; (4) Optimal constraints for power quality management: U min (i,t)≤U(i,t)≤U max (i,t) (18) In the formula: U(i,t), U min (i,t) and U max (i, t) are the fundamental voltage, lower limit and upper limit of fundamental voltage of node i at time t, respectively. min (i,t)=[0.96](i×h),U max (i,t)=[1.04](i×h);U h 2 (i, t) is the square of the hth harmonic voltage at node i at time t, H is the number of harmonics considered; THD(i, t) and THD max (i, t) are the harmonic voltage distortion rate and its maximum limit of node i at time t; Convert to second-order cone form: (5) Compensation capacity constraints: Q q (i,t)=3U N I HCq (i,t) (22) Where U N is the rated working voltage of the equipment; (6) Harmonic power flow related constraints: I h (i,t)=I inth (i,t)-I HC,h (i,t) (24) I h (i,t)=Y h (i,i)U h (i,t) (25) In the formula, I h (i,t) is the hth harmonic current of node i at time t after adding the harmonic compensation device; I inth (i, t) is the hth harmonic current of node i at time t before adding the harmonic compensation device; Y h (i,i) are the diagonal elements of the harmonic admittance matrix.

7. The method for optimizing the layout of multiplexed power quality management equipment according to claim 2, characterized in that: The step S3 specifically includes: Step S31: Initialize pheromones. Initially, a certain amount of pheromones will be initialized on all possible paths. That is, ants will form a certain amount of pheromones on all possible nodes of the reusable management device, which is equivalent to the role of marking. Step S32: Path selection. When each ant selects the next path, it will determine the path based on the pheromone concentration on the path and the expected value of the path, such as the path length and cost. The probability formula for path selection is: In the formula, τ ij (t) represents the pheromone concentration on the path (i, j) at time t, η ij (t) represents the residual expectation of path (i, j) at time t, usually taking the inverse of the length of path (i, j), α and β represent the relative importance of pheromone and expectation heuristic factor respectively; J k (i) = {1,2,...,c}-tabu k represents the set of cities that ant k is allowed to choose next. k is the taboo table of ant k, recording the cities it has currently visited, s belongs to any city that ant k is allowed to choose next, τ is (t) represents the residual pheromone on the path (i, s) at time t, η is (t) represents the residual expectation degree of the path (i, s) at time t; Step S33: Path construction and constraint processing. In the process of path construction, the ants will make selections based on the objective function and constraint conditions in the optimization model. Only paths within the constraint conditions will be retained and selected by the ants. Each path generated by the ants will undergo a series of constraint condition checks, and only paths that meet all constraints will be used for pheromone updates. Step S34: Iteration and convergence.

8. The method for optimizing the layout of multiplexed power quality management equipment according to claim 7, characterized in that: The step S34 comprises: An elite ant system is introduced. After each iteration, additional pheromones are artificially released to the optimal solution path determined by the elite ants to increase the effect of positive feedback. The pheromone update formula is as follows: t ij (t+1)=(1-ρ)τ ij (t)+Δτ ij ' (27) In the formula, τ ij (t+1) represents the residual pheromone on the path (i, j) at the next moment t, 1-ρ represents the residual coefficient of pheromone (0≤ρ<1), Δτ ij ' represents the additional increment of pheromone on the path (i, j) taken by the elite ant; The additional increment of pheromone is adjusted according to the number of iterations. The formula is as follows: Where Q is a constant, which represents the total amount of pheromones released by ants on all paths they pass through. σ represents the number of elite ants. N is the current number of iterations, and T is the total number of iterations of the algorithm.

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