Reactive power optimization control method, system and equipment for low-voltage power distribution system and medium

Abstract

The invention relates to the technical field of power system automation, and discloses a low-voltage power distribution system reactive power optimization control method, system, device and medium, and the method comprises the steps: constructing a power distribution system simplified network model containing virtual nodes based on observable node data and line parameters; constructing a network adjacency matrix by using a graph theory, and realizing system partitioning by combining a comprehensive sensitivity index and an improved K-means + + clustering algorithm; on the basis, a reactive power optimization model with voltage deviation, network loss and adjustment cost as multiple targets is established, and boundary node relaxation constraints are designed to improve stability; and solving by adopting a distributed ADMM algorithm to realize autonomous optimization and cooperative control of each region. According to the method, subarea reactive power control of each area can be realized under the condition of limited measurement information, and a rapid and accurate reactive power optimization scheme is provided for a low-voltage power distribution system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system automation, and in particular to a low-voltage power distribution system reactive power optimization control method, system, device and medium. BACKGROUND

[0002] With a large number of distributed power sources being connected to the low-voltage power distribution system in a dispersed manner, the randomness and volatility thereof break the traditional reactive power balance, and easily lead to local voltage out-of-limit, while the popularity of new types of loads further aggravates the voltage fluctuation and power quality deterioration problem of the low-voltage power distribution network. Ideal reactive power optimization relies on accurate perception of the real-time operation state of the entire system, however, in the actual low-voltage power distribution system, the measurement equipment is not fully covered, the data communication and quality are restricted, and the system model parameters are inaccurate, so that the data of some nodes cannot be collected in real time, and the reactive power optimization problem is increasingly prominent.

[0003] Under the condition of incomplete measurement, the traditional reactive power optimization method has great limitations, the method based on accurate physical model relies on complete network parameters and real-time measurement data, when the measurement data is missing or the model is inaccurate, the optimization result may deviate from the actual situation, and even lead to deterioration of system operation. The simple control strategy based on local measurement is single and lacks systematicness, and is difficult to cope with complex and variable operation conditions, and the optimization effect is limited, and may cause frequent action of equipment and damage the service life of equipment. SUMMARY

[0004] In view of the above existing problems, the present application provides a low-voltage power distribution system reactive power optimization control method, system, device and medium.

[0005] Therefore, the technical problem solved by the present application is that the real-time data in the power distribution system is incomplete and the prediction accuracy is not high, and the voltage of the new energy access is prone to be out of limit.

[0006] To solve the above technical problems, the present application provides the following technical scheme, a low-voltage power distribution system reactive power optimization control method, comprising: constructing a simplified model of the low-voltage power distribution system network, using the measurement data of the nodes, the line impedance parameters and the new energy access information, converting the incomplete measurement area into a simplified network with complete measurement information; based on the simplified network, using the graph theory method to describe the network topology, combining the comprehensive sensitivity to calculate the node and line weight, constructing the network matrix, and using the improved K-means clustering method to divide the low-voltage power distribution system partition; constructing a low-voltage power distribution system reactive power optimization model and a multi-objective optimization function, and designing a partition boundary node stability relaxation constraint; based on the reactive power optimization model, using the distributed ADMM algorithm to solve, and obtaining the reactive power optimization control scheme of each area.

[0007] As a preferred scheme of the low-voltage power distribution system reactive power optimization control method, the simplified network model of the low-voltage power distribution system is constructed by processing the measurement data of two adjacent measurement nodes through a power flow equation, and equivalent expressing the unknown network between the two nodes by a virtual node to obtain a simplified network structure with complete information.

[0008] As a preferred scheme of the low-voltage power distribution system reactive power optimization control method, the network matrix is constructed based on active power flow, reactive power flow and power-voltage comprehensive sensitivity, and the network adjacency matrix is fused by coupling weight indexes.

[0009] As a preferred scheme of the low-voltage power distribution system reactive power optimization control method, the low-voltage power distribution system reactive power optimization model is constructed by setting a multi-objective function with minimum voltage deviation, minimum network loss and minimum reactive power regulation cost, distributing weight coefficients to form a comprehensive optimization target, and combining a partition boundary node stability relaxation constraint to obtain a reactive power optimization model with boundary stability guarantee.

[0010] As a preferred scheme of the low-voltage power distribution system reactive power optimization control method, the improved K-means clustering method includes a K-means++ algorithm that selects each cluster center one by one, increases the probability P(x) of becoming the next cluster center for the sample point with greater distance D(x) from the known cluster center, and stops until k is sufficient. A data is randomly selected from the sample set as the first starting cluster center c, the distance D(x) of each sample from the known center is calculated, and the probability P(x) of each sample being selected as the next cluster center is allocated according to D(x): wherein, The above process is repeated until the value of k is satisfied. The clustering index of the clustering algorithm is set as a clustering algorithm adaptive function, the elbow rule is used to determine the number of cluster centers, for a data set of n points, the number of cluster centers is iteratively calculated from k to n, and after each clustering is completed, the sum of squares of distances of each sample to the classified cluster center is calculated and recorded, each value corresponds to a sum of squares of distances, and a trend line change trend graph of the sum of squares of distances with the horizontal axis of the number of cluster centers increasing and the vertical axis of the sum of squares of distances is drawn. The sum of squares of distances decreases until the sum of squares of distances is S(k), and the elbow point near the selected value is selected as the best value when the decreasing change buffer area of the trend line on the graph of the sum of squares of distances with the horizontal axis value increasing is suddenly slowed down.

[0011] As a preferred scheme of the low-voltage power distribution system reactive power optimization control method, the partition boundary node stability relaxation constraint includes that the partition principle meets the characteristics of strong coupling within the region and weak connection outside the region. Meanwhile, for the reactive power control mode of each partition, the control principle is "internal self-balancing, external supplement of surplus / deficiency", and in the control process, the voltage change of the boundary connection node is maintained within the set range, and the specific control principle is as follows: Wherein, t is time, T is total time step, is the voltage value of the i-th boundary node in the region g at time t, is the voltage value of the i-th boundary node in the region g at time t-1. γ is the limit value of the relaxation constraint, which is determined based on the remaining / missing reactive power of each region and the connection impedance parameter: In the formula, is the active power deviation of the region g, is the reactive power deviation of the region g, is the active power deviation of other regions connected with the boundary node in the region g, is the reactive power deviation of other regions connected with the boundary node in the region g. is the number of nodes in the region g, , is the external connection line parameter of the boundary node i; , is the external connection line parameter of other boundary nodes in the region g except node i; The limit range of the boundary node is determined by the above formula, which is the boundary relaxation constraint of the reactive power optimization control.

[0012] As a preferred scheme of the low-voltage power distribution system reactive power optimization control method, the distributed ADMM algorithm includes decomposing the reactive power optimization model into two sub-problems of continuous variables and discrete variables, updating the Lagrange multiplier by alternately optimizing the sub-problems, and combining the dynamic adjustment step strategy to improve the convergence efficiency of the algorithm. The ADMM algorithm alternately solves the sub-optimization problem: Wherein, the superscript K represents the iteration number, x is the first group of original variables, y is the second group of original variables, is the dual variable, is the augmented Lagrange function, The punishment parameter is argmin, and the iteration process is repeatedly cycled until a feasible and sufficient optimal solution is found. In each iteration process of the algorithm, the step size is dynamically adjusted based on the changes of the original residual r and the dual residual s In the formula, r is the original residual, s is the dual residual, rK and sK are the value changes of the original residual and the dual residual in the Kth iteration; When the value changes of the original residual and the dual residual are both greater than the set value Δ, it indicates that the convergence performance is good, and the original step size is maintained for the next iteration, otherwise, the step size is updated; When the original residual is much larger than the dual residual, the step size will be increased, resulting in a serious punishment of violating the original feasibility; When the dual residual is much larger than the original residual, the step size is reduced, and the convergence of the original feasibility and the dual feasibility can be alternately balanced.

[0013] The application provides a low-voltage power distribution system reactive power optimization control system.

[0014] As a preferred scheme of the low-voltage power distribution system reactive power optimization control system, the system comprises a data acquisition and simplification module, a network partition calculation module, an optimization modeling module and a distributed solving module. The data acquisition and simplification module is used to acquire the measurement data of observable nodes, line impedance parameters and new energy access information from the power distribution system, perform network simplification, and construct a simplified network model of the low-voltage power distribution system with complete measurement information. The network partition calculation module is connected with the data acquisition and simplification module, and is used to receive the simplified network model, construct a network matrix based on graph theory, and perform partition calculation on the simplified network by using an improved clustering algorithm, and output a partition result. The optimization modeling module is connected with the network partition calculation module, and is used to construct a comprehensive optimization function with voltage deviation, network loss and reactive power regulation cost as targets according to the partition result, and design stability relaxation constraints of partition boundary nodes to form a reactive power optimization model. The distributed solving module is connected with the optimization modeling module, and is used to solve the reactive power optimization model by using a distributed ADMM algorithm, calculate an optimal output scheme of reactive power equipment in each partition, and realize reactive power optimization control of the system.

[0015] The application provides a computer device, comprising a memory and a processor, the memory stores a computer program, and the processor implements steps of a low-voltage power distribution system reactive power optimization control method when executing the computer program.

[0016] The application provides a computer readable storage medium, which stores a computer program, and the computer program implements steps of a low-voltage power distribution system reactive power optimization control method when executed by a processor.

[0017] The application has the following beneficial effects: the model simplification process can obtain system key nodes and line topologies by using incomplete measurement data, while ensuring main features of the power distribution system; the network adjacency matrix of the simplified model is constructed based on graph theory, and the K-means++ algorithm is combined to perform power grid partition calculation, and the partition result can more completely reflect the operation characteristics of the power distribution system, and each region has high reactive power reserve and structural stability; by using the improved distributed ADMM algorithm and combining the boundary node stability relaxation constraint, the algorithm has a faster convergence speed, and can complete internal autonomy and external interaction of each region on the basis of strong correlation within the region and weak connection outside the region, and obtain an optimal reactive power optimization control scheme. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0019] ] Figure 1 A low-voltage power distribution system reactive power optimization control method flowchart is provided for an embodiment of the application.

[0020] Figure 2 A standard IEEE39 node example system diagram of a low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the application.

[0021] Figure 3 A simplified model diagram of a low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the application.

[0022] Figure 4 A power distribution system partition calculation result diagram of a low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the application.

[0023] Figure 5 An MT reactive power output diagram of a low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the application.

[0024] Figure 6 A low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the present application.

[0025] Figure 7 A capacitor bank reactive power output schematic diagram of a low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the present application.

[0026] Figure 8 An SVG reactive power output of a low-voltage power distribution system reactive power optimization control method is provided for an embodiment of the present application. DETAILED DESCRIPTION

[0027] In order to make the above objectives, features and advantages of the present application more apparent, more comprehensible and more understandable, the specific embodiments of the present application will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should fall within the scope of protection of the present application.

[0028] Embodiment 1, with reference to Figure 1 For the first embodiment of the present application, the embodiment provides a low-voltage power distribution system reactive power optimization control method, comprising: S1: Construct a simplified model of the low-voltage power distribution system network, and convert the incomplete measurement area into a simplified network with complete measurement information by using the measurement data of the nodes, the line impedance parameters and the new energy access information.

[0029] S2: Based on the simplified network, describe the network topology by using the graph theory method, combine the comprehensive sensitivity to calculate the node and line weight, construct the network matrix, and divide the low-voltage power distribution system partition by using the improved K-means clustering method.

[0030] S3: Construct a low-voltage power distribution system reactive power optimization model and a multi-objective optimization function, and design a partition boundary node stability relaxation constraint.

[0031] S4: Based on the reactive power optimization model, solve by using the distributed ADMM algorithm to obtain the reactive power optimization control scheme of each area.

[0032] It should be noted that the embodiment takes low-voltage power distribution network reactive power optimization as the core, uses observable node measurement data and part of known line impedance parameters, combines key information such as new energy access position, quantity and capacity, constructs a low-voltage power distribution system network simplified model, converts the incomplete measurement power distribution area into a simplified network with complete measurement information; on this basis, the topology architecture of the simplified network is described by using graph theory, and the node and line weights are calculated by combining the comprehensive sensitivity, and the low-voltage power distribution system network matrix is constructed as the main basis for power distribution system partitioning, and the improved K-means clustering method is used to divide the low-voltage power distribution system partitioning quantity and partitioning node, and the partitioning result of the low-voltage power distribution system simplified network is obtained; the low-voltage power distribution system reactive power optimization model is constructed, the stability relaxation constraint of the partitioning boundary node is designed, the distributed ADMM algorithm is used to quickly calculate the voltage optimization result of the autonomous area, and finally the fast reactive power optimization control of the low-voltage power distribution system is realized.

[0033] Embodiment 2 is an embodiment of the present application, which provides a low-voltage power distribution system reactive power optimization control method based on the above-mentioned embodiment.

[0034] Further, in the embodiment of the present application, step S1 constructs a low-voltage power distribution system network simplified model, converts the incomplete measurement area into a simplified network with complete measurement information by using the measurement data of the nodes, the line impedance parameters and the new energy access information, and the specific steps include S101-S103: S101: Screening the key nodes in the power distribution system, that is, the non-virtualizable nodes. The distributed power supply nodes and the heavy load nodes in the power distribution system are defined as the key nodes of the power distribution network, which are prone to voltage problems, so in this method, such nodes cannot be deleted and must have complete measurement capability. In particular, if the number of node inflow and outflow branches exceeds 3, the node is a key node in the topology of the power flow, and also needs to be listed as a key node.

[0035] S102: On the basis of the power flow constraints of the power distribution network, combined with the position, quantity and other information of the key nodes, a virtual node is constructed to simplify the power distribution network model, and the power flow equation from the virtual node k to the key nodes i and j satisfies the following formula: In the formula, 、 is the voltage amplitude of the nodes i and j; 、 is the active and reactive power flowing out of the line ik; 、 is the resistance and reactance of the line ij.

[0036] S103: The unknown network between two adjacent nodes is replaced by a virtual node, and the line impedance value of the adjacent measurement nodes before and after network simplification remains unchanged.

[0037] The unknown network in the power distribution system can be simplified into a simple power distribution network with complete information by combining the measurement voltage amplitude, power and line impedance of the key nodes in the above steps.

[0038] In an alternative embodiment, the key nodes in the power distribution system can also be screened by the electrical betweenness of the nodes, specifically, the electrical betweenness of all nodes under typical power flow is calculated, and the nodes with a betweenness higher than a set threshold are defined as key nodes together with the distributed power nodes and heavy load nodes.

[0039] In another alternative embodiment, the key nodes in the power distribution system can also be screened by the load supply radius, specifically, through topological analysis, those nodes upstream in the power supply path with a large amount of load downstream (i.e. long load supply radius or large total load) are located, and these nodes are listed as key nodes together with the distributed power nodes and heavy load nodes.

[0040] Further, in the embodiments of the present application, step S2 describes the network topology based on the simplified network using graph theory method, calculates the node and line weights in combination with the comprehensive sensitivity, constructs the network matrix, and divides the low-voltage power distribution system partition using the improved K-means clustering method, and the specific steps include S201-S203: S201: The topology of the simplified network is described using graph theory method, including nodes, lines, etc., and the connection relationship of the power system is represented by symbolic graph. The complex network composed of points and edges is defined as G=(V,E), wherein the vertex set V={1,2,…,n} constitutes the basic unit of the system, and the edge set E={(i,j),i,j∈V} describes the correlation characteristics between units.

[0041] The power grid is simplified as a weighted undirected network. For an undirected graph G, when all nodes have reachable paths, the graph is defined as having a connected characteristic. The algebraic representation in G is composed of an adjacency matrix and a Laplacian matrix, and the elements of the adjacency matrix satisfy a ij =w ij (take positive real number when (i,j)∈E, otherwise zero), and wij represents the connection weight between vertices.

[0042] S202: Based on the network simplification model, the active / reactive power-voltage sensitivity matrix is constructed to reflect the voltage operating characteristics of the power system, and normalized to construct the sensitivity weight.

[0043] The active-reactive voltage comprehensive sensitivity index is used to measure the correlation and priority ranking between subjects and within subjects. The active voltage sensitivity and the reactive voltage sensitivity are calculated based on the Jacobian matrix obtained by the power flow calculation, and the sensitivity calculation is as follows: In the formula, , is the active-reactive voltage sensitivity and the reactive voltage sensitivity.

[0044] The active sensitivity weight is derived as follows: The reactive sensitivity weight is derived as follows: The line coupling weight index of the simplified network of the low-voltage power distribution system is constructed as follows: In the formula, is the coupling weight value, and θ is the power factor angle of the system.

[0045] Therefore, the low-voltage power distribution system network adjacency matrix is: S203: The low-voltage power distribution system partition method includes the following steps: A31: Based on the graph theory model constructed above, the target of the clustering algorithm is as follows: In the formula, is the sum of the coupling weights of all nodes in the region; is the sum of the coupling weights of all nodes outside the region; λ is the partition coefficient, and a too small value is easy to cause overlapping of the divided regions, and a too large value is easy to form a large number of scattered regions.

[0046] A32: The improved K-means clustering method is used to divide the regions of the simplified network. The traditional K-means clustering algorithm needs to manually select the clustering center and needs to be considered according to human experience, and it is difficult to achieve global optimization. Meanwhile, the initialization of the clustering center will significantly affect the clustering effect. The K-means++ algorithm can adaptively select the clustering center, retains the simple and fast characteristics of the K-means clustering algorithm, and improves the universality and accuracy of the algorithm.

[0047] The K-means++ algorithm selects each cluster center one by one, and the larger the distance D(x) of a sample point from a known cluster center is, the greater the probability P(x) of the sample point becoming the next cluster center is. Until k is sufficient. The following is the specific operation and process of the algorithm: Randomly select a data from the sample set as the first starting cluster center c; Calculate the distance D(x) of each sample from the known center; according to D(x), assign each sample the probability P(x) of being selected as the next cluster center; Repeat the above process; until the value of k is satisfied.

[0048] The clustering index of the clustering algorithm is set to the adaptive function of the clustering algorithm in step A31. The elbow rule is used to determine the number of clustering centers.

[0049] For a data set of n points, iteratively calculate the number of cluster centers k from 1 to n. After each clustering is completed, the sum of the squared distances between each sample and its classified cluster center needs to be calculated and recorded. Each k value corresponds to a squared distance sum. Plot the trend chart of the broken line change of the squared distance sum with the horizontal axis of the number of clustering centers k increasing and the vertical axis of the squared distance sum.

[0050] The squared sum is reduced until the squared sum is.

[0051] There will be a decreasing change buffer area on the broken line graph of the squared distance sum with the horizontal axis of k value increasing. When the decreasing amplitude of the broken line suddenly slows down, select a nearby inflection point as the best k value.

[0052] In an alternative embodiment, the number of cluster centers can also be determined by the silhouette coefficient method. Specifically, the average silhouette coefficient is calculated for k from 2 to n, and the k value that maximizes the coefficient is selected as the best clustering number.

[0053] In another alternative embodiment, the number of cluster centers can also be determined by the Gap statistic method. Specifically, the difference between the clustering error of the actual data set and the clustering error of the reference data set (such as uniform distribution) is compared to determine the k value. Select the k value that maximizes the Gap statistic, which indicates that the clustering result is much better than random distribution.

[0054] A33: After obtaining the regional division result, the partition effect is evaluated by using the structural index and the functional index of the partition, which specifically includes the following steps: The modularity function of the power grid partition result is solved to quantify the partition structure quality: In the formula, A ij is the weight of edge (i, j); is the sum of the weights of the edges connected to node i; m is the sum of the weights of all edges in the network; if node i and node j are in the same region, If the structural index is greater than 0.3, the network is considered to have a good structure.

[0055] A reasonable power grid partition requires that the maximum reactive power output of the reactive power resource in the region is greater than the sum of all reactive power loads in the region. The reactive power support level is defined as a functional evaluation index: wherein, is the reactive power output of the i-th reactive power source, is the reactive power demand of the j-th load.

[0056] In an alternative embodiment, the partition structural evaluation index can also select the average internal coupling degree, specifically, the sum of the weights of all edges in each partition is calculated, and the sum of the maximum edge weights that can exist in the partition is calculated, and then the average of the ratio of the two values is calculated. The higher the value, the closer the connection within the partition.

[0057] In another alternative embodiment, the partition structural evaluation index can also select the average cutting degree, specifically, the sum of the weights of the connecting edges between all partitions and their external regions is calculated, and then divided by the sum of the weights of the connecting edges within the partition, and finally the average of all partitions is calculated. The lower the value, the weaker the connection between regions, and the better the partition effect.

[0058] Further, in the embodiments of the present application, step S3 constructs a low-voltage power distribution system reactive power optimization model and a multi-objective optimization function, and designs a partition boundary node stability relaxation constraint, the specific steps including S301-S303: S301: According to the partition result, the internal reactive power optimization target of each region is calculated, including the minimum voltage deviation, the minimum network loss and the minimum reactive power output cost, as follows: Target 1 is to minimize the node voltage deviation of each partition, as follows: In the formula, G is the region number; is the voltage of node i in region g at time t; is the reference voltage.

[0059] Target 2 is to minimize the overall network loss of the low-voltage power distribution system, as follows: Target 3 is to minimize the reactive power regulation cost within each region, as follows: For the above three reactive power optimization control objectives, when performing reactive power control, the weights need to be reasonably allocated, and generally the weights are matched in the manner of 4, 4, and 3. The final control objectives are as follows: wherein a1=4, a2=4, and a3=3.

[0060] S302: There can be more than one boundary node for each partition, and the partition principle needs to meet the characteristics of “strong coupling within the region and weak connection outside the region”; at the same time, for the reactive power control mode of each partition, the control principle is “internal self-balancing and external supplement of surplus / deficit”, and external interaction relies on the boundary connection node, so the stability of the voltage of such nodes needs to be ensured, that is, the voltage change of such nodes needs to be maintained within a certain range during the control process, which is shown as follows: wherein γ is a limit value of the relaxation constraint, which affects the stability judgment of the boundary node, and can be determined based on the residual / deficit reactive power of each region and the connection impedance parameter, as shown below: wherein is the active deviation amount of region g, is the reactive deviation amount of region g, is the active deviation amount of other regions connected to the boundary node in region g, is the reactive deviation amount of other regions connected to the boundary node in region g; is the number of nodes in region g, , is the external connection line parameter of boundary node i; , is the external connection line parameter of other boundary nodes in region g except node i.

[0061] The limit range of the boundary node is determined by the above formula, which is used as the boundary relaxation constraint of the reactive power optimization control.

[0062] S303: Other constraint conditions wherein is the active output of the distributed power supply; is the active output of the distributed photovoltaic; is the load demand; is the active network loss; is the active power of the tie line; is the reactive power of the tie line; is the SVG reactive power; is the reactive power of the distributed photovoltaic; reactive power of the distributed power supply; reactive power of the capacitor bank.

[0063] is the injected active and reactive power of node i at time t; is the voltage phase angle difference of nodes i and j; is the voltage value of nodes i and j; is the conductance and susceptance of branch ij; is the upper and lower limit of the active and reactive power of the distributed power supply; is the upper and lower limit of the active and reactive power of the distributed photovoltaic; is the upper and lower limit of the reactive power of the SVG; is the upper and lower limit of the number of CB groups that can be put into node i; is the upper and lower limit of the voltage of node i; is the number of CB groups put into node i at time t; is the maximum adjustable number of CBs per day at node i.

[0064] Further, in the embodiments of the present application, step S4 is solved based on the reactive power optimization model using the distributed ADMM algorithm to obtain the reactive power optimization control scheme of each region, and the specific content includes: Based on the constructed reactive power control model of the power distribution system, a distributed optimization model of the power distribution system is formed through the distributed ADMM algorithm. The ADMM algorithm can decompose a complex model into a series of sub-problems for independent optimization, and each sub-problem takes the coupling constraint as a boundary constraint and a sub-problem objective function penalty term, and solves each sub-problem to obtain the optimization solution of each independent sub-problem.

[0065] The augmented Lagrangian function of the low-voltage power distribution system reactive power optimization control model is as follows: is the penalty parameter, x is the local variable of each partition, y is the global variable, and λ is the Lagrange multiplier.

[0066] The ADMM algorithm alternately solves the sub-optimization problem: wherein the superscript K represents the iteration number, x is the first group of original variables, y is the second group of original variables, is the dual variable, is the augmented Lagrangian function, is the penalty parameter, is the variable value for which the objective function takes the minimum value; the iteration process is continuously looped until a feasible and sufficient optimal solution is found;​​ Consider in each iteration of the algorithm, based on the original residual r and the dual residual s before and after the change, the dynamic adjustment of the step size.

[0067] In the formula, The original residual is r, The dual residual is s, , The value change of the Kth iteration original residual and the dual residual is Δr and Δs respectively; When the value changes of the original residual and the dual residual are both greater than the set value Δ, it indicates that the convergence performance is good, and the original step size is maintained for the next iteration, otherwise, the step size is updated; When the original residual is much larger than the dual residual, the step size will be increased, resulting in a serious punishment of violating the original feasibility; When the dual residual is much larger than the original residual, the step size is reduced, and the convergence of the original feasibility and the dual feasibility can be balanced alternately.

[0068] In an optional embodiment, the dynamic adjustment of the step size can also be realized by fixed interval and simple proportion of Specifically, every fixed number of iterations, check the ratio of the 2-norm of the original residual and the dual residual. If the ratio exceeds an upper threshold, multiply the penalty parameter by a fixed magnification factor; if the ratio is lower than a lower threshold, multiply the penalty parameter by a fixed reduction factor; otherwise, keep the penalty parameter unchanged.

[0069] In another optional embodiment, the dynamic adjustment of the step size can also be realized by the residual change trend. In each iteration, calculate the ratio of the current residual to the previous residual (i.e. the change rate). If the original residual continues to rise or does not decrease in consecutive iterations, increase the step size by a fixed step size ; if the dual residual continues to rise or does not decrease in consecutive iterations, decrease the step size by a fixed step size . If both change smoothly or tend to converge, keep the step size unchanged.

[0070] Embodiment 3, which is different from the first two embodiments, is a third embodiment of the application. The embodiment also provides a low-voltage power distribution system reactive power optimization control system, comprising: a data acquisition and simplification module, a network partition calculation module, an optimization modeling module, and a distributed solving module; The data acquisition and simplification module is used to obtain the measurement data of the observable nodes, the line impedance parameters and the new energy access information from the power distribution system, and perform network simplification to construct a low-voltage power distribution system simplified network model with complete measurement information; ​a network partition computing module connected to the data acquisition and simplification module, configured to receive the simplified network model, construct a network matrix based on graph theory, and perform partition calculation on the simplified network by using an improved clustering algorithm, and output a partition result; an optimization modeling module connected to the network partition computing module, configured to construct a comprehensive optimization function with voltage deviation, network loss and reactive power regulation cost as targets according to the partition result, and design stability relaxation constraints for boundary nodes of the partitions to form a reactive power optimization model; a distributed solving module connected to the optimization modeling module, configured to solve the reactive power optimization model by using a distributed ADMM algorithm, calculate an optimal output scheme of the reactive power equipment in each partition, and realize reactive power optimization control of the system.

[0071] The embodiment also provides an electronic device, including a memory and a processor; the memory is used to store computer executable instructions, and the processor is used to execute the computer executable instructions to realize the low-voltage power distribution system reactive power optimization control method provided in the above embodiment.

[0072] The embodiment also provides a storage medium, which stores a computer program, and the program is executed by a processor to realize the low-voltage power distribution system reactive power optimization control method provided in the above embodiment.

[0073] The storage medium provided in the embodiment and the low-voltage power distribution system reactive power optimization control method provided in the above embodiment belong to the same inventive concept, and the technical details not described in the embodiment can be referred to the above embodiment, and the embodiment has the same beneficial effects as the above embodiment.

[0074] From the above description of the embodiments, those skilled in the art can clearly understand that the present application can be realized by means of software and necessary general hardware, and of course can also be realized by hardware. Based on such understanding, the technical solutions of the present application can be embodied in the form of a software product, and the computer software product can be stored in a computer readable storage medium, such as a floppy disk, a read-only memory (ROM), a random access memory (RAM), a FLASH, a hard disk or an optical disk, and includes a number of instructions to make a computer device (which can be a personal computer, a server or a network device, etc.) execute the methods of various embodiments of the present application.

[0075] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit the present application. Although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present application, and all should be covered in the scope of the claims of the present application.

[0076] Embodiment 4, refer to Figures 2-8 The low-voltage power distribution system reactive power optimization control method based on incomplete measurement data provided by the present application has the following implementation case test method steps: The standard IEEE39 node example system is used as the test system, part of the node measurement information is incomplete, the total active load of the system is 600MW, and the total reactive load is 230Mvar.

[0077] The above system is simplified by using the simplified model construction method, and the key nodes and lines are selected, and the results are shown in Figure 3 After model simplification, the original 39 nodes are simplified to a simplified system of 25 nodes, and the selection principle is to retain the generator nodes and the downstream nodes, and important load nodes.

[0078] The power distribution system is partitioned and calculated by using the partition method, and the results are shown in Figure 4 The clustering partition algorithm divides the simplified model into 5 partitions, and there is at least one common boundary node between each partition.

[0079] The partition evaluation index is shown in the following table, it can be found that the structural index is greater than 0.3, indicating that the partition has good reliability, and the reactive power reserve ratio is greater than 0, indicating that each region has sufficient reactive power support level. Structural Index F Functional Index H Zone 1 0.488 0.53 Zone 2 0.502 0.35 Zone 3 0.511 0.21 Zone 4 0.493 0.49 Zone 5 0.499 0.33

[0080] The reactive power optimization results of the test system are calculated by combining the reactive power optimization control model and the ADMM algorithm, and the results are shown in Figures 5-8 When the voltage exceeds the limit, the reactive power regulation resources provide certain output for reactive power regulation. The following figure shows the reactive power output of each device.

Claims

1. A reactive power optimization control method for a low-voltage power distribution system, characterized in that: include, A simplified model of a low-voltage power distribution system network is constructed. By utilizing the measurement data of nodes, line impedance parameters, and new energy access information, the incomplete measurement area is transformed into a simplified network with complete measurement information. Based on a simplified network, the network topology is described using graph theory, and the weights of nodes and lines are calculated by combining comprehensive sensitivity to construct a network matrix. An improved K-means clustering method is then used to divide the low-voltage power distribution system into zones. A reactive power optimization model and a multi-objective optimization function for a low-voltage power distribution system are constructed, and stability relaxation constraints for partition boundary nodes are designed. Based on the reactive power optimization model, the distributed ADMM algorithm is used to solve the problem and obtain the reactive power optimization control scheme for each region.

2. The reactive power optimization control method for a low-voltage power distribution system as described in claim 1, characterized in that: The construction of a simplified network model for a low-voltage power distribution system includes processing the measurement data of two adjacent measurement nodes through power flow equations and using virtual nodes to equivalently represent the unknown network between the two nodes, thereby obtaining a simplified network structure with complete information.

3. The reactive power optimization control method for a low-voltage power distribution system as described in claim 2, characterized in that: The construction of the network matrix includes constructing power flow weights and sensitivity weights based on active power flow, reactive power flow, and power-voltage integrated sensitivity, and then fusing them into a network adjacency matrix by coupling weight indices.

4. The reactive power optimization control method for a low-voltage power distribution system as described in claim 3, characterized in that: The construction of the reactive power optimization model for the low-voltage power distribution system includes setting a multi-objective function that minimizes voltage deviation, network loss, and reactive power regulation cost, assigning weight coefficients to form a comprehensive optimization objective, and combining the stability relaxation constraints of the partition boundary nodes to obtain a reactive power optimization model with boundary stability guarantees.

5. The reactive power optimization control method for a low-voltage power distribution system as described in claim 4, characterized in that: The improved K-means clustering method includes the K-means++ algorithm, which selects each cluster center one by one and increases the probability P(x) of a sample point that is further away from the known cluster center by a larger distance D(x), until k is sufficient. Randomly select a data point from the sample set as the first initial cluster center c, calculate the distance D(x) between each sample and the known centers, and assign the probability P(x) of each sample being selected as the next cluster center based on D(x): in, For the set of all data points, repeat the above process until the value of k is satisfied; The clustering metric of the clustering algorithm is set as an adaptive function. The elbow rule is used to determine the number of cluster centers. For a dataset of n points, the number of cluster centers is calculated iteratively. from For each clustering iteration up to n, the sum of squared distances from each sample to its assigned cluster center needs to be calculated and recorded. The value corresponds to a sum of squared distances, plotted as the number of cluster centers along the horizontal axis. A line graph showing the trend of the sum of squared distances along the vertical axis as the value increases; The sum of squares decreases until The sum of squares is , along the horizontal axis As the value increases, within the buffer zone of the decreasing change on the line graph of the sum of squares, when the rate of decrease in the line suddenly slows down, select a nearby inflection point as the optimal value. value.

6. The reactive power optimization control method for a low-voltage power distribution system as described in claim 5, characterized in that: The stability relaxation constraint of the partition boundary node includes that the partitioning principle satisfies the characteristics of "strong coupling within the region and weak connection outside the region"; Meanwhile, for the reactive power control method of each zone, the control principle is "internal self-balancing, with external supplementation for surplus / deficit". When interacting with externally, it relies on boundary connection nodes. During the control process, the voltage changes of these nodes are maintained within the set range, as shown below: Where t is time and T is the total number of time steps. Let be the voltage value of the i-th boundary node in region g at time t. Let be the voltage value of the i-th boundary node in region g at time t-1; γ is the constraint value for relaxation, determined based on the residual / missing reactive power and connection impedance parameters of each region: In the formula, Let be the active power deviation in region g. Let g be the reactive power deviation in region g. This represents the active power deviation in other regions connected to the boundary nodes within non-region g. For non-region g, the reactive power deviation is the amount of reactive power deviation in other regions connected to the boundary node. Let g be the number of nodes in region g. , The parameters of the external connections of boundary node i; , For the line parameters connecting other boundary nodes of region g, excluding node i; The boundary node's limitation range is determined by the above formula, serving as the boundary relaxation constraint for reactive power optimization control.

7. The reactive power optimization control method for a low-voltage power distribution system as described in claim 6, characterized in that: The distributed ADMM algorithm includes decomposing the reactive power optimization model into two sub-problems: continuous variables and discrete variables. It improves the algorithm's convergence efficiency by alternately optimizing the sub-problems and updating the Lagrange multipliers, combined with a dynamic step size adjustment strategy. The ADMM algorithm uses the alternating multiplier method to solve the sub-optimization problems separately: Where the superscript K represents the iteration number, x is the first set of original variables, and y is the second set of original variables. As dual variables, To augment the Lagrange function, For penalty parameters, The variable values ​​are used to find the minimum value of the objective function; the iterative process continues until a feasible and sufficiently optimal solution is found. Consider dynamically adjusting the step size based on the changes in the original residual r and the dual residual s during each iteration of the algorithm. In the formula, For the original residual, For dual residuals, , For the changes in the values ​​of the original residual and the dual residual in the Kth iteration; If the changes in the values ​​of both the original residual and the dual residual are greater than the set value Δ, it indicates that the convergence performance is good, and the original step size is maintained for the next iteration; otherwise, the step size is updated. When the original residual is much larger than the dual residual, the step size will increase, resulting in a severe penalty for violating the original feasibility. When the dual residual is much larger than the original residual, the step size decreases, and the convergence of the original feasibility and the dual feasibility can be alternately balanced.

8. A reactive power optimization control system for a low-voltage power distribution system, employing the reactive power optimization control method for a low-voltage power distribution system as described in any one of claims 1 to 7, characterized in that, include: The module includes a data acquisition and simplification module, a network partitioning calculation module, an optimization modeling module, and a distributed solution module. The data acquisition and simplification module is used to acquire measurement data of observable nodes, line impedance parameters and new energy access information from the power distribution system, and perform network simplification to construct a simplified network model of the low-voltage power distribution system with complete measurement information. The network partitioning calculation module is connected to the data acquisition and simplification module. It is used to receive the simplified network model, construct a network matrix based on graph theory, and perform partitioning calculation on the simplified network using an improved clustering algorithm, and output the partitioning results. The optimization modeling module is connected to the network partitioning calculation module. It is used to construct a comprehensive optimization function with voltage deviation, network loss and reactive power regulation cost as objectives based on the partitioning results, and design stability relaxation constraints for partition boundary nodes to form a reactive power optimization model. The distributed solution module, connected to the optimization modeling module, is used to solve the reactive power optimization model using the distributed ADMM algorithm, calculate the optimal power output scheme of reactive power equipment within each partition, and realize the reactive power optimization control of the system.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the reactive power optimization control method for a low-voltage power distribution system according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the reactive power optimization control method for a low-voltage power distribution system according to any one of claims 1 to 7.

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