A reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradient.

Abstract

This invention discloses a reactive power optimization method for distribution networks based on the accelerated gradient alternating direction multiplier method, relating to the field of power system operation and control technology. The technical solution includes the following steps: S1, acquiring the topology and node operation data of the distribution network, and constructing an improved similarity matrix; S2, dynamically partitioning the distribution network using an adaptive spectral clustering algorithm; S3, establishing a local reactive power optimization model for each sub-region obtained from the dynamic partitioning; S4, introducing globally consistent variables for the voltage amplitude and phase angle of boundary nodes, establishing consistency coupling constraints between regions, constructing the augmented Lagrangian function for each region, and solving the local optimization problem; S5, updating the globally consistent variables using an accelerated gradient strategy; S6, calculating the original residual and dual residual. This invention achieves dynamic partitioning of the distribution network through adaptive spectral clustering, significantly improving the algorithm's convergence speed, effectively reducing system network losses, and eliminating the risk of node voltage exceeding limits.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, and in particular to a reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradient. Background Technology

[0002] As the power system accelerates its transformation towards a clean and low-carbon direction, the large-scale integration of distributed photovoltaic power has transformed the distribution network from a traditional passive unidirectional power flow network to an active bidirectional power flow network, causing problems such as frequent voltage fluctuations, reactive power imbalance, and decreased system stability, posing a severe challenge to the safe and stable operation of the distribution network.

[0003] Rational control of reactive power is crucial for ensuring system voltage quality, reducing network losses, and maintaining stable grid operation. Traditional centralized reactive power optimization methods can obtain complete information about the entire network and theoretically find the global optimal solution. However, with the expansion of distribution network scale and the continuous increase in photovoltaic penetration, centralized control methods face the following prominent problems: (1) Curse of dimensionality: As the number of nodes surges, the computational complexity of centralized global solution increases significantly, resulting in an excessive computational burden on the scheduling center, making it difficult to meet the timeliness requirements of real-time control.

[0004] (2) High communication reliability requirements: The centralized method relies on the centralized collection of real-time data from the entire network, which places extremely high demands on the reliability and bandwidth of the communication network. Any communication failure may lead to the failure of the entire network optimization.

[0005] (3) Weak response to photovoltaic fluctuations: The centralized algorithm is difficult to respond to the rapid random fluctuations in photovoltaic output in each zone in a timely manner. Under extreme conditions such as large photovoltaic power generation or sudden load changes, local node voltage over-limit problems are likely to occur.

[0006] Distributed optimization control decouples the unified optimization problem across the entire network into local optimization problems in multiple sub-regions. Each sub-region only needs to interact with its neighboring regions through limited boundary information to collaboratively converge to the global optimum, making it an effective way to overcome the aforementioned bottlenecks. The Alternating Direction Method of Multipliers (ADMM) combines the decomposition of the dual ascent method with the convergence of the augmented Lagrange method, making it suitable for parallel computing and distributed optimization, and has been widely applied to distributed optimization problems in power systems.

[0007] However, the standard ADMM algorithm suffers from drawbacks when applied to power system optimization problems with numerous nonlinear power flow constraints. These include a convergence speed heavily influenced by the choice of penalty factor and slow convergence under conditions of severe source-load fluctuations, making it difficult to fully leverage the rapid response advantage of reactive power resources in each subregion. To address these issues, there is an urgent need to research a distributed reactive power optimization method that can improve convergence speed and achieve local reactive power balance in each region. Summary of the Invention

[0008] The purpose of this invention is to provide a reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradient, in order to solve the technical problems of insufficient adaptability of existing zoning methods to the uncertainty of new energy output, as well as the computational complexity, slow response, and slow convergence speed of centralized reactive power optimization methods. This invention realizes dynamic zoning of distribution networks through adaptive spectral clustering, which significantly improves the convergence speed of the algorithm, effectively reduces system network losses, and eliminates the risk of node voltage exceeding limits.

[0009] To achieve the aforementioned objectives, the present invention employs the following technical solution: a reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients, comprising the following steps: Step S1: Obtain the topology of the distribution network, node voltage time-series data, photovoltaic power output data, rated capacity and load data of static var generators (SVG); calculate the Fréchet distance based on the time-series trajectory of each node's operating status and construct a similarity matrix; introduce an electrical distance matrix based on voltage-reactive power sensitivity; combine the regional voltage regulation capability and weightedly fuse the two to obtain an improved similarity matrix; Step S2: Based on the improved similarity matrix obtained in Step S1, the distribution network is dynamically partitioned using an adaptive spectral clustering algorithm. The optimal number of partitions K is automatically determined by the feature gap criterion, and the dominant node is identified within each partition based on the singular value entropy of the Jacobian matrix. On this basis, the probability density function of the Beta distribution is used to probabilistically model the photovoltaic output, extract typical photovoltaic output scenarios, construct a comprehensive performance index based on the expected electrical distance, and dynamically adjust the initial partitions through multi-objective greedy optimization iteration. The results of each sub-region obtained by the dynamic partitioning are used as the input for Step S3. Step S3: For each sub-region obtained by dynamic partitioning in step S2, establish a local reactive power optimization objective function and constraints with the goal of minimizing regional active power loss and node voltage deviation. The constraints include power flow balance constraints, photovoltaic reactive power output constraints, static var generator (SVG) reactive power compensation constraints, and node voltage constraints. Step S4: Introduce global consistency variables for the voltage magnitude and phase angle of boundary nodes, establish consistency coupling constraints between regions, and construct augmented Lagrangian functions for each region; solve the local optimization problem for each sub-region under the given global consistency variables and Lagrangian multipliers. Step S5: Update the global consistency variables using an accelerated gradient strategy, transforming the update of the global consistency variables into a problem of minimizing the global consistency error and solving it using gradient descent; after completing the update of the global consistency variables, iteratively update the dual variables of each sub-region using the current boundary interaction error; Step S6: Calculate the original residual and the dual residual, and determine whether they simultaneously meet the convergence threshold; if they do, output the optimal reactive power scheduling scheme for each sub-region; otherwise, return to step S4 to continue iterating.

[0010] Furthermore, in step S1, the method for obtaining the improved similarity matrix is ​​as follows: Set nodes With nodes j The state variables within the time interval [a, b] respectively constitute the trajectory. and trajectory ,node With nodes j Using parameterized velocity functions respectively α and parameterized velocity function β They move along their respective trajectories within the range [0,1], and in time... At that time, all distances The maximum value in the value represents the similarity between trajectories, the Fraser distance. Defined as: (1); In the formula: For nodes With nodes The Fréchet distance between the time-series trajectories of state variables; For nodes The time-series trajectory of state variables; For nodes The time-series trajectory of state variables; For nodes Along the trajectory The parameterized velocity function of the movement; For nodes Along the trajectory The parameterized velocity function of the movement; For time parameters; The distance function between two points; This is the infimum operator, representing the smallest lower bound that satisfies the condition; The similarity matrix between system nodes is constructed using the Frescher distance between the temporal trajectories of node running states. Its expression is: (2); In the formula: For nodes With nodes The Fréchet distance of the trajectory of the state variable; This is the similarity matrix between system nodes; This represents the total number of system nodes. Electrical distance matrix based on voltage-reactive power sensitivity The construction method is as follows: node With nodes Voltage-reactive power sensitivity Represented as: (3); In the formula: For nodes With nodes Voltage-reactive power sensitivity; For nodes The voltage amplitude; For nodes The amount of reactive power injected; node With nodes electrical distance between Defined as: (4); In the formula: For nodes With nodes Electrical distance between them; To prevent small positive numbers with a denominator of zero; A larger value indicates a tighter coupling between the two nodes, corresponding to a smaller electrical distance. Based on equations (2) and (3), the electrical distance matrix is ​​obtained. for: (5); In the formula: The electrical distance between each node pair The electrical distance matrix formed; The voltage regulation capability within a region is defined as: (6); In the formula: For the region Voltage regulation capability; For the first Each zone area; For the region Voltage regulation capability of the reactive power compensation device RPC; For the region The voltage regulation capability of the generator; (7); (8); In the formula: For the region The node with the highest voltage amplitude The maximum voltage deviation, if the voltage is within the normal allowable range, then ; For nodes The reactive power margin of the adjustable reactive power compensation device RPC; For nodes Reactive power injection to nodes Sensitivity to voltage amplitude at the location; For nodes The active power margin of the adjustable generator; For nodes Active power injection to nodes Sensitivity to voltage amplitude at the location; Similarity matrix and electrical distance matrix We perform weighted summation separately to obtain the improved similarity matrix. F Its expression is as follows: (9); Where: coefficient The range of values ​​is In dynamic partitioning, different weights are assigned to each indicator by the calculators to obtain the target partitioning results. The selection of weights is based on the Analytic Hierarchy Process (AHP). The elements in the improved similarity matrix are adjusted based on the voltage regulation capability of each partition. The reactive power compensation device (RPC) and controllable generator are partitioned according to voltage regulation requirements. The improved similarity matrix... F The element adjustment method is as follows: (10); In the formula: For nodes and nodes The similarity in their operating states and electrical connections; For the region Voltage regulation capability; For nodes The partition area it is located in.

[0011] Further, in step S2, the adaptive spectral clustering algorithm partitions the power grid and identifies dominant nodes based on the singular value entropy of the Jacobian matrix, including the following steps: Based on the improved similarity matrix in step S1F The adjacency matrix of spectral clustering is calculated using a fully connected method. ; (11); In the formula: It is an adjacency matrix; The scale parameter determines the decay rate of sample point similarity; For nodes With nodes The improved similarity matrix The obtained connection weights; The system's topology is represented by a degree matrix, where the degree of each node is determined by its adjacency matrix. The degree is calculated by adding the elements of each row, and the sum of each row is used as the diagonal element of the degree matrix. All other elements are set to 0, forming a degree matrix. As shown below: (12); In the formula: For degree matrix, Indicates the first The degree of each node, Adjacency matrix The Middle Line 1 Column elements, For the first The degree of each node; Laplace matrix L From the adjacency matrix A Sum-degree matrix D Composed of, through the degree matrix D Laplace matrix L Normalize: (13); In the formula: It is a Laplace matrix; (14); In the formula: For the normalized Laplace matrix; By sorting the feature values, the k largest feature values ​​are selected to obtain the corresponding feature vectors. In obtaining The eigenvalues ​​are sorted from smallest to largest as follows After that, the characteristic gap The calculation formula is: (15); In the formula: For the first One characteristic gap; For the normalized Laplace matrix The first one after ascending order One eigenvalue; By sequentially in the characteristic gap Find the maximum value in the sequence, and the corresponding index determines the number of optimal clusters. The calculation formula is as follows: (16); In the formula: This represents the index that minimizes the objective function. ; Dynamic zoning optimization for uncertain photovoltaic output: (1) Calculation of expected electrical distance: Nodes between any two nodes For nodes The effect is the sensitivity of node voltage to reactive power. , represented as: (17); Equation (17) represents the node The change in its own voltage and the node when reactive power changes The ratio of voltage changes reflects the degree of dynamic voltage coupling under power flow changes; In the formula: For the scene Next node For nodes The effect of voltage-reactive power sensitivity; For the scene Next node The sensitivity of reactive power changes to its own voltage amplitude; For the scene Next node Reactive power changes on nodes Sensitivity to voltage amplitude; Node in scene m and nodes Sensitivity electrical distance between Represented as: (18); In the formula: For the scene Next node and nodes The sensitivity of the electrical distance between them; For the intermediate variable in the summation; For the scene Next node For nodes The effect of voltage-reactive power sensitivity; For the scene Next node For nodes The effect of voltage-reactive power sensitivity; The larger the value, the more likely it is to be a node. For nodes The smaller the impact, the fewer nodes and nodes The greater the distance between them, the lower the degree of coupling. Using scene correction coefficients By aggregating all scenarios and considering the uncertainties of photovoltaics, the sensitivity electrical distance matrix is ​​improved. The desired electrical distance is obtained through probability-weighted aggregation. : (19); In the formula: For nodes With nodes The expected electrical distance between them; This represents the total number of typical scenarios; For the scene Scene correction coefficient; (2) Construction and weighting of comprehensive performance indicators: Construct a new modularity function based on the expected electrical distance and considering the photovoltaic probability distribution. : (20); In the formula: This is a modularity function considering the photovoltaic probability distribution based on the desired electrical distance; For nodes based on desired electrical distance With nodes Connection weights between them; For all nodes The sum of the weights of connected edges; For all nodes The sum of the weights of connected edges; This is the sum of the weights of all edges in the network; For partition indicator functions, if node With nodes In the same area ,otherwise ; Capacity matching index is The expression is: (twenty one); In the formula: The number of regions to be divided As a capacity matching index, For the first The sum of the maximum active power output of all active power sources in the region. For the first The sum of the maximum active power output of all conventional synchronous generators in the region. For the first The sum of the maximum active power output of all photovoltaic power stations in the region. For the first The sum of the maximum active power of each node load in each region; Reactive power compensation index The expression is: (twenty two); In the formula, The number of regions to be divided For the region The amount of reactive power compensation within the group; This represents the reactive power supply value of reactive power sources within the region. This represents the reactive power demand of nodes within the region. For division The average reactive power compensation amount of each region, i.e., the reactive power compensation index; The source-load curve matching index is The expression is: (twenty three); In the formula, Number of regions; The source-load curve matching index; For the first Time zone The sum of the output values ​​of internal photovoltaic systems, For the first Time zone The sum of internal working loads, The range of values ​​is , The closer the curve is to 1, the better. x With curve y The stronger the similarity, The closer to 0, the more the curve... x With curve y The weaker the similarity; A comprehensive performance index for evaluating power grids in different regions is proposed by weighting and combining the source-load curve matching degree index, the modularity index describing the expected electrical distance of photovoltaic probability distribution, the capacity matching index, and the reactive power compensation index. : (twenty four); In the formula: For comprehensive performance indicators; Modularity index The corresponding weight value; Capacity matching index The corresponding weight value; Reactive power compensation index The corresponding weight value; Source-load curve matching index The corresponding weight value; Perform multi-objective greedy optimization iterations, using static partitioning as the initial scheme, traversing adjacent sub-region pairs, and attempting boundary node migrations. If connectivity constraints are satisfied and the overall performance index is met, the optimization is successful. Improvements are accepted and adjustments are made; iterations are repeated until... Terminate when no further improvements are made, and output the final dynamic partitioning scheme; The dominant node identification method based on singular value entropy is as follows: For a power system, by performing a first-order Taylor expansion of the power flow equations, the corrected equations are obtained as follows: (25); In the formula: The active power deviation at the node; This refers to the reactive power deviation at the node. , , , The elements of the Jacobian matrix are defined in equation (26); This refers to the phase angle deviation of the node voltage. This refers to the deviation in node voltage amplitude. This refers to the node voltage amplitude. Jacobian matrix J The elements are represented as follows: (26); In the formula: The sensitivity of node active power changes to voltage phase angle; The sensitivity of node active power changes to voltage amplitude; The sensitivity of node reactive power changes to voltage phase angle; The sensitivity of node reactive power changes to voltage amplitude; For the Jacobian matrix in equation (26) Performing singular value decomposition, we obtain: (27); In the formula: Composed of left singular vectors Orthogonal matrix; For singular values A non-negative diagonal matrix formed by; Composed of right singular vectors Orthogonal matrix; Jacobian matrix The One singular value; For matrix The middle corresponds to Column vectors; For matrix The middle corresponds to Column vectors; (28); right Normalization yields the standardized form as follows: (29); In the formula: Jacobian matrix No. Normalized values ​​of the singular values; Jacobian matrix Singular value entropy Represented as: (30); In the formula: Jacobian matrix The singular value entropy.

[0012] Furthermore, in step S3, the local reactive power optimization objective function and constraints include: Sub-regions The local objective function is: (31); In the formula: This is the sum of the local objective functions of each sub-region; For the first Local objective functions for each sub-region; For the region Active network loss within the network; For the first Node voltage deviation within an autonomous sub-region; These are the weighting coefficients for the active power loss objective function; where are the weighting coefficients of the objective function for node voltage deviation, and ; For the region The internal vector of local variables; , For nodes The voltage amplitude; For nodes The voltage phase angle; For nodes The reactive power output of photovoltaics; For nodes SVG reactive power compensation; For the region Internal node set; for cross-regional connection lines, the loss is shared equally by adjacent regions; Network loss index is defined as: (32); In the formula: This represents the total active power loss of the distribution network. It is the set of all nodes in the network; For nodes With nodes The electrical conductance between them; For nodes and nodes The voltage phase angle difference; The voltage deviation index is defined as: (33) In the formula, S The set of all nodes in the network. This is a voltage deviation indicator; For nodes The nominal voltage, For nodes The upper limit of voltage; For nodes The lower limit of voltage; The power flow balance constraints in the constraints are as follows: (34); In the formula: For nodes The generator has active power output; For nodes The generator's reactive power output; For nodes The photovoltaic system is generating active power. For nodes The reactive power output of photovoltaic power; For nodes Active load; For nodes reactive load; Let be the real part of the admittance matrix. This represents the imaginary part of the admittance matrix; The photovoltaic reactive power output constraints in the constraints are as follows: (35); In the formula: For nodes The photovoltaic capacity; For nodes The photovoltaic system is generating active power. For nodes The reactive power output of photovoltaic power; The SVG reactive power compensation constraints in the constraints are as follows: (36); In the formula: For nodes The static var generator (SVG) device outputs reactive power. For nodes The upper limit of reactive power output of the Static Var Generator (SVG) device; For nodes The lower limit of reactive power output of the Static Var Generator (SVG) device; The node voltage constraints in the constraints are as follows: (37)

[0013] Furthermore, in step S4, the method for constructing the augmented Lagrangian function for each region is as follows: Introducing dual variables Construct the augmented Lagrangian function for each region: (38); In the formula: To augment the Lagrange function; For the first Lagrange multipliers for each region; As a penalty factor; For the first Boundary coupling variables of each region; It is a globally consistent variable; Let be the square of the L2 norm of the vector, and let be the sum of the squares of the elements in the vector. For the k-th sub-region after decomposition, at the t-th iteration, the locally augmented Lagrangian function of each region, given the global consistency variable... and Lagrange multipliers Under these conditions, the local optimization problem is solved independently and in parallel in each region: (39); In the formula: For the first During the nth iteration Updated values ​​of local variables in each subregion; For the first During the nth iteration Updated values ​​of the coupling variables at the boundaries of each sub-region; For the first Global consistency variables during the next iteration; For the first During the nth iteration Dual variables of each subregion; When the augmented Lagrangian function of the k-th subregion reaches its minimum, the local variables and boundary coupling variables Updated value.

[0014] Furthermore, in step S5, the method for updating the globally consistent variable using the accelerated gradient strategy is as follows: The accelerated gradient strategy is used to replace the traditional arithmetic mean method for average updates, thus ensuring global consistency of variables. The update problem is transformed into minimizing the global consistency error: (40); In the formula: For the first During the nth iteration Updated values ​​of coupling variables at the boundaries of each sub-region. Indicates the consistency of global variables Find the minimum value; Applying gradient descent to the consistency error function in equation (40), we obtain the update formula for the globally consistent variable z: (41); In the formula: This refers to the gradient step size parameter; For the first The updated value of the globally consistent variable in the next iteration; After completing the global consistency variable update, the dual variables of each region are updated using the current boundary interaction error, so that each region can adjust in the next iteration to meet the global coordination requirements: (42); In the formula: For the first During the nth iteration Updated values ​​of dual variables in each subregion.

[0015] Furthermore, in step S6, the original residual and the dual residual are used as convergence criteria, including the following: Using the original residual and dual residuals As a convergence criterion, the algorithm terminates when both conditions are met simultaneously: (43); In the formula: The original residuals reflect the degree of deviation between boundary coupling variables and globally consistent variables; The dual residuals reflect the magnitude of change in global variables between two adjacent iterations; The convergence threshold of the original residual; The convergence threshold of the dual residual; the original residual It reflects the degree of deviation between boundary coupling variables and globally consistent variables, and measures the degree to which consistency constraints are satisfied; dual residuals It reflects the magnitude of change in global variables between two adjacent iterations, measures the stability of dual variable updates, and when the original residual... and dual residuals The algorithm is considered converged when both values ​​are less than a given threshold. The infinite norm represents the maximum absolute value of all elements in the vector.

[0016] Meanwhile, the present invention proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is executed, it implements the steps of the method described in the present invention.

[0017] Furthermore, the present invention proposes a computer-readable storage medium having a computer program stored thereon, the computer program being configured to implement the steps of the method described in the present invention when invoked by a processor.

[0018] Finally, the present invention provides a computer program product comprising a computer program / instructions that, when executed by a processor, implement the steps of the method described in the present invention.

[0019] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) Improve the adaptability of partitioning to photovoltaic uncertainty: This invention introduces a time-series trajectory similarity matrix based on Fraser distance, an electrical distance matrix based on voltage-reactive power sensitivity, and regional voltage regulation capability to construct an improved similarity matrix. Based on the initial partitioning of adaptive spectral clustering, the probability density function of the Beta distribution is used to probabilistically model photovoltaic output, extract typical photovoltaic output scenarios, construct a comprehensive performance index with the expected electrical distance as the core, and adopt multi-objective greedy optimization iteration to dynamically adjust the partition boundary. Compared with the static partitioning scheme that only considers electrical distance, the voltage regulation capability of each sub-region in the partition obtained by this invention is improved by 4% to 6%, enabling each partition to have a stronger autonomous adjustment capability under photovoltaic output fluctuation conditions, effectively enhancing the robustness of the partitioning scheme.

[0020] (2) Achieving adaptive determination of the optimal number of partitions and accurate identification of key nodes: This invention adopts an adaptive spectral clustering algorithm based on the feature gap criterion. By calculating the index corresponding to the largest feature gap in the eigenvalue sequence of the normalized Laplace matrix, the optimal number of partitions K is automatically determined without manual intervention. In the IEEE 33-node system example, the fourth position of the feature gap sequence achieves a maximum value of 0.3681, and the optimal number of partitions is automatically determined to be 4. The resulting partition modularity is 0.6432, which is better than the cases with 3 (0.6056) and 5 (0.6328) partitions, verifying the objectivity and accuracy of the adaptive determination. At the same time, the dominant nodes of each partition are identified based on the singular value entropy of the Jacobian matrix. The larger the singular value entropy of a node, the more uniform the influence of its load change on the system voltage and the stronger the stability. Nodes 3, 32, 6, and 15 are identified as the dominant nodes of the four partitions, providing an accurate basis for the key control of reactive power optimization in subsequent partitions.

[0021] (3) Effectively achieve local reactive power balance and significantly reduce network losses: This invention rationally divides the distribution network into several electrically coupled autonomous sub-regions through adaptive spectral clustering. Each region prioritizes calling the reactive power margin of the static var generator (SVG) and photovoltaic inverter within the region to respond to disturbances locally, reducing the cross-regional flow of reactive power. In the IEEE 33-node system simulation, compared with the centralized optimization scheme based on the improved particle swarm optimization algorithm, the total active power loss of the system of this invention is reduced from 7580.22MWh to 6535.72MWh, with a loss reduction rate of 13.8%, and the economic operation benefits are significant.

[0022] (4) This invention introduces globally consistent variables for the voltage amplitude and phase angle of boundary nodes to establish inter-regional consistency coupling constraints, ensuring that each region achieves global coordination and consistency of boundary node voltages while independently solving local optimization problems. In the IEEE 33-node system simulation, the average voltage deviation of the entire network under this invention decreased from 1.16% to 0.77%, an improvement rate of 33.8%; the voltage fluctuation index improved by 33.0%; the 1.32% node voltage over-limit risk in the original scheme was completely eliminated, and the voltage over-limit rate decreased to 0.00%, effectively ensuring the safe and stable operation of the power grid in high photovoltaic penetration scenarios. Attached Figure Description

[0023] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0024] Figure 1 This is a flowchart of the dynamic partitioning and dominant node identification process of the adaptive spectral clustering algorithm in this invention.

[0025] Figure 2This is a flowchart of the reactive power optimization process using the alternating direction multiplier method in this invention.

[0026] Figure 3 This is a sequence diagram of the feature gaps in the normalized Laplace matrix of the improved similarity matrix in this invention.

[0027] Figure 4 This is a partitioning result diagram of the IEEE 33-node distribution network adaptive spectral clustering algorithm in this invention.

[0028] Figure 5 This is a comparison chart of the 24-hour voltage range and average voltage of Scheme 1 and Scheme 2 in this invention.

[0029] Figure 6 This is a schematic diagram showing a quantitative comparison of the comprehensive indicators of reactive power optimization results between Scheme 1 and Scheme 2 of the present invention. Among them, (a) is a comparison result of the average voltage deviation; (b) is a comparison result of the voltage fluctuation; (c) is a comparison result of the total network loss of the system; and (d) is a comparison result of the voltage over-limit rate.

[0030] Figure 7 This is a comparison chart of the daily voltage changes of the dominant nodes in each partition of Scheme 1 and Scheme 2 in this invention.

[0031] Among them, (a) is the daily voltage variation curve of the dominant node 3 in partition 1; (b) is the daily voltage variation curve of the dominant node 32 in partition 2; (c) is the daily voltage variation curve of the dominant node 6 in partition 3; and (d) is the daily voltage variation curve of the dominant node 15 in partition 4. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0033] Example 1: See Figure 1 and Figure 7 This invention's method is applied to power system dispatch and control centers. For distribution networks, it sequentially completes dynamic grid zoning, dominant node identification, and reactive power optimization for each zone. Finally, it issues reactive power dispatch commands to the static var generators (SVG) and photovoltaic inverters within each zone. The overall process is as follows: Figure 1 and Figure 2 As shown, This embodiment provides a reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradient, including the following steps: Step S1: Obtain the topology of the distribution network, node voltage time-series data, photovoltaic power output data, rated capacity and load data of static var generators (SVG); calculate the Fréchet distance based on the time-series trajectory of each node's operating status and construct a similarity matrix; introduce an electrical distance matrix based on voltage-reactive power sensitivity; combine the regional voltage regulation capability and weightedly fuse the two to obtain an improved similarity matrix; Step S2: Based on the improved similarity matrix obtained in Step S1, the distribution network is dynamically partitioned using an adaptive spectral clustering algorithm. The optimal number of partitions K is automatically determined by the feature gap criterion, and the dominant node is identified within each partition based on the singular value entropy of the Jacobian matrix. On this basis, the probability density function of the Beta distribution is used to probabilistically model the photovoltaic output, extract typical photovoltaic output scenarios, construct a comprehensive performance index based on the expected electrical distance, and dynamically adjust the initial partitions through multi-objective greedy optimization iteration. The results of each sub-region obtained by the dynamic partitioning are used as the input for Step S3. Step S3: For each sub-region obtained by dynamic partitioning in step S2, establish a local reactive power optimization objective function and constraints with the goal of minimizing regional active power loss and node voltage deviation. The constraints include power flow balance constraints, photovoltaic reactive power output constraints, static var generator (SVG) reactive power compensation constraints, and node voltage constraints. Step S4: Introduce global consistency variables for the voltage magnitude and phase angle of boundary nodes, establish consistency coupling constraints between regions, and construct augmented Lagrangian functions for each region; solve the local optimization problem for each sub-region under the given global consistency variables and Lagrangian multipliers. Step S5: Update the global consistency variables using an accelerated gradient strategy, transforming the update of the global consistency variables into a problem of minimizing the global consistency error and solving it using gradient descent; after completing the update of the global consistency variables, iteratively update the dual variables of each sub-region using the current boundary interaction error; Step S6: Calculate the original residual and the dual residual, and determine whether they simultaneously meet the convergence threshold; if they do, output the optimal reactive power scheduling scheme for each sub-region; otherwise, return to step S4 to continue iterating.

[0034] Specifically, in step S1, the method for obtaining the improved similarity matrix is ​​as follows: Set nodes With nodes j The state variables within the time interval [a, b] respectively constitute the trajectory. and trajectory ,node With nodes j Using parameterized velocity functions respectively α and parameterized velocity function β They move along their respective trajectories within the range [0,1], and in time... At that time, all distances The maximum value in the value represents the similarity between trajectories, the Fraser distance. Defined as: (1); In the formula: For nodes With nodes The Fréchet distance between the time-series trajectories of state variables; For nodes The time-series trajectory of state variables; For nodes The time-series trajectory of state variables; For nodes Along the trajectory The parameterized velocity function of the movement; For nodes Along the trajectory The parameterized velocity function of the movement; For time parameters; The distance function between two points; This is the infimum operator, representing the smallest lower bound that satisfies the condition; The similarity matrix between system nodes is constructed using the Frescher distance between the temporal trajectories of node running states. Its expression is: (2); In the formula: For nodes With nodes The Fréchet distance of the trajectory of the state variable; This is the similarity matrix between system nodes; This represents the total number of system nodes. Electrical distance matrix based on voltage-reactive power sensitivity The construction method is as follows: node With nodes Voltage-reactive power sensitivity Represented as: (3); In the formula: For nodes With nodes Voltage-reactive power sensitivity; For nodes The voltage amplitude; For nodes The amount of reactive power injected; node With nodes electrical distance between Defined as: (4); In the formula: For nodes With nodes Electrical distance between them; To prevent small positive numbers with a denominator of zero; A larger value indicates a tighter coupling between the two nodes, corresponding to a smaller electrical distance. Based on equations (2) and (3), the electrical distance matrix is ​​obtained. for: (5); In the formula: The electrical distance between each node pair The electrical distance matrix formed; The voltage regulation capability within a region is defined as: (6); In the formula: For the region Voltage regulation capability; For the first Each zone area; For the region Voltage regulation capability of the reactive power compensation device RPC; For the region The voltage regulation capability of the generator; (7); (8); In the formula: For the region The node with the highest voltage amplitude The maximum voltage deviation, if the voltage is within the normal allowable range, then ; For nodes The reactive power margin of the adjustable reactive power compensation device RPC; For nodes Reactive power injection to nodes Sensitivity to voltage amplitude at the location; For nodes The active power margin of the adjustable generator; For nodes Active power injection to nodes Sensitivity to voltage amplitude at the location; Similarity matrix and electrical distance matrix We perform weighted summation separately to obtain the improved similarity matrix. F Its expression is as follows: (9); Where: coefficient The range of values ​​is In dynamic partitioning, different weights are assigned to each indicator by the calculators to obtain the target partitioning results. The selection of weights is based on the Analytic Hierarchy Process (AHP). The elements in the improved similarity matrix are adjusted based on the voltage regulation capability of each partition. The reactive power compensation device (RPC) and controllable generator are partitioned according to voltage regulation requirements. The improved similarity matrix... F The element adjustment method is as follows: (10); In the formula: For nodes and nodes The similarity in their operating states and electrical connections; For the region Voltage regulation capability; For nodes The partition area it is located in.

[0035] Specifically, in step S2, the adaptive spectral clustering algorithm partitions the power grid and identifies dominant nodes based on the singular value entropy of the Jacobian matrix, including the following steps: Based on the improved similarity matrix in step S1 F The adjacency matrix of spectral clustering is calculated using a fully connected method. ; (11); In the formula: It is an adjacency matrix; The scale parameter determines the decay rate of sample point similarity; For nodes With nodes The improved similarity matrix The obtained connection weights; The system's topology is represented by a degree matrix, where the degree of each node is determined by its adjacency matrix. The degree is calculated by adding the elements of each row, and the sum of each row is used as the diagonal element of the degree matrix. All other elements are set to 0, forming a degree matrix. As shown below: (12); In the formula: For degree matrix, Indicates the first The degree of each node, Adjacency matrix The Middle Line 1 Column elements, For the first The degree of each node; Laplace matrix L From the adjacency matrix A Sum-degree matrix D Composed of, through the degree matrix D Laplace matrix L Normalize: (13); In the formula: It is a Laplace matrix; (14); In the formula: For the normalized Laplace matrix; By sorting the feature values, the k largest feature values ​​are selected to obtain the corresponding feature vectors. In obtaining The eigenvalues ​​are sorted from smallest to largest as follows After that, the characteristic gap The calculation formula is: (15); In the formula: For the first One characteristic gap; For the normalized Laplace matrix The first one after ascending order One eigenvalue; By sequentially in the characteristic gap Find the maximum value in the sequence, and the corresponding index determines the number of optimal clusters. The calculation formula is as follows: (16); In the formula: This represents the index that minimizes the objective function. ; Dynamic zoning optimization for uncertain photovoltaic output: (1) Calculation of expected electrical distance: Nodes between any two nodes For nodes The effect is the sensitivity of node voltage to reactive power. , represented as: (17); Equation (17) represents the node The change in its own voltage and the node when reactive power changes The ratio of voltage changes reflects the degree of dynamic voltage coupling under power flow changes; In the formula: For the scene Next node For nodes The effect of voltage-reactive power sensitivity; For the scene Next node The sensitivity of reactive power changes to its own voltage amplitude; For the scene Next node Reactive power changes on nodes Sensitivity to voltage amplitude; Node in scene m and nodes Sensitivity electrical distance between Represented as: (18); In the formula: For the scene Next node and nodes The sensitivity of the electrical distance between them; For the intermediate variable in the summation; For the scene Next node For nodes The effect of voltage-reactive power sensitivity; For the scene Next node For nodes The effect of voltage-reactive power sensitivity; The larger the value, the more likely it is to be a node. For nodes The smaller the impact, the fewer nodes and nodes The greater the distance between them, the lower the degree of coupling. Using scene correction coefficients By aggregating all scenarios and considering the uncertainties of photovoltaics, the sensitivity electrical distance matrix is ​​improved. The desired electrical distance is obtained through probability-weighted aggregation. : (19); In the formula: For nodes With nodes The expected electrical distance between them; This represents the total number of typical scenarios; For the scene Scene correction coefficient; (2) Construction and weighting of comprehensive performance indicators: Construct a new modularity function based on the expected electrical distance and considering the photovoltaic probability distribution. : (20); In the formula: This is a modularity function considering the photovoltaic probability distribution based on the desired electrical distance; For nodes based on desired electrical distance With nodes Connection weights between them; For all nodes The sum of the weights of connected edges; For all nodes The sum of the weights of connected edges; This is the sum of the weights of all edges in the network; For partition indicator functions, if node With nodes In the same area ,otherwise ; Capacity matching index is The expression is: (twenty one); In the formula: The number of regions to be divided As a capacity matching index, For the first The sum of the maximum active power output of all active power sources in the region. For the first The sum of the maximum active power output of all conventional synchronous generators in the region. For the first The sum of the maximum active power output of all photovoltaic power stations in the region. For the first The sum of the maximum active power of each node load in each region; Reactive power compensation index The expression is: (twenty two); In the formula, The number of regions to be divided For the region The amount of reactive power compensation within the group; This represents the reactive power supply value of reactive power sources within the region. This represents the reactive power demand of nodes within the region. For division The average reactive power compensation amount of each region, i.e., the reactive power compensation index; The source-load curve matching index is The expression is: (twenty three); In the formula, Number of regions; The source-load curve matching index; For the first Time zone The sum of the output values ​​of internal photovoltaic systems, For the first Time zone The sum of internal working loads, The range of values ​​is , The closer the curve is to 1, the better. x With curve y The stronger the similarity, The closer to 0, the more the curve... x With curve y The weaker the similarity; A comprehensive performance index for evaluating power grids in different regions is proposed by weighting and combining the source-load curve matching degree index, the modularity index describing the expected electrical distance of photovoltaic probability distribution, the capacity matching index, and the reactive power compensation index. : (twenty four); In the formula: For comprehensive performance indicators; Modularity index The corresponding weight value; Capacity matching index The corresponding weight value; Reactive power compensation index The corresponding weight value; Source-load curve matching index The corresponding weight value; Perform multi-objective greedy optimization iterations, using static partitioning as the initial scheme, traversing adjacent sub-region pairs, and attempting boundary node migrations. If connectivity constraints are satisfied and the overall performance index is met, the optimization is successful. Improvements are accepted and adjustments are made; iterations are repeated until... Terminate when no further improvements are made, and output the final dynamic partitioning scheme; The dominant node identification method based on singular value entropy is as follows: For a power system, by performing a first-order Taylor expansion of the power flow equations, the corrected equations are obtained as follows: (25); In the formula: The active power deviation at the node; This refers to the reactive power deviation at the node. , , , The elements of the Jacobian matrix are defined in equation (26); This refers to the phase angle deviation of the node voltage. This refers to the deviation in node voltage amplitude. This refers to the node voltage amplitude. Jacobian matrix J The elements are represented as follows: (26); In the formula: The sensitivity of node active power changes to voltage phase angle; The sensitivity of node active power changes to voltage amplitude; The sensitivity of node reactive power changes to voltage phase angle; The sensitivity of node reactive power changes to voltage amplitude; For the Jacobian matrix in equation (26) Performing singular value decomposition, we obtain: (27); In the formula: Composed of left singular vectors Orthogonal matrix; For singular values A non-negative diagonal matrix formed by; Composed of right singular vectors Orthogonal matrix; Jacobian matrix The One singular value; For matrix The middle corresponds to Column vectors; For matrix The middle corresponds to Column vectors; (28); right Normalization yields the standardized form as follows: (29); In the formula: Jacobian matrix No. Normalized values ​​of the singular values; Jacobian matrix Singular value entropy Represented as: (30); In the formula: Jacobian matrix The singular value entropy.

[0036] Specifically, in step S3, the local reactive power optimization objective function and constraints include: Sub-regions The local objective function is: (31); In the formula: This is the sum of the local objective functions of each sub-region; For the first Local objective functions for each sub-region; For the region Active network loss within the network; For the first Node voltage deviation within an autonomous sub-region; These are the weighting coefficients for the active power loss objective function; where are the weighting coefficients of the objective function for node voltage deviation, and ; For the region The internal vector of local variables; , For nodes The voltage amplitude; For nodes The voltage phase angle; For nodes The reactive power output of photovoltaics; For nodes SVG reactive power compensation; For the region Internal node set; for cross-regional connection lines, the loss is shared equally by adjacent regions; Network loss index is defined as: (32); In the formula: This represents the total active power loss of the distribution network. It is the set of all nodes in the network; For nodes With nodes The electrical conductance between them; For nodes and nodes The voltage phase angle difference; The voltage deviation index is defined as: (33) In the formula, S The set of all nodes in the network. This is a voltage deviation indicator; For nodes The nominal voltage, For nodes The upper limit of voltage; For nodes The lower limit of voltage; The power flow balance constraints in the constraints are as follows: (34); In the formula: For nodes The generator has active power output; For nodes The generator's reactive power output; For nodes The photovoltaic system is generating active power. For nodes The reactive power output of photovoltaic power; For nodes Active load; For nodes reactive load; Let be the real part of the admittance matrix. This represents the imaginary part of the admittance matrix; The photovoltaic reactive power output constraints in the constraints are as follows: (35); In the formula: For nodes The photovoltaic capacity; For nodes The photovoltaic system is generating active power. For nodes The reactive power output of photovoltaic power; The SVG reactive power compensation constraints in the constraints are as follows: (36); In the formula: For nodes The static var generator (SVG) device outputs reactive power. For nodes The upper limit of reactive power output of the Static Var Generator (SVG) device; For nodes The lower limit of reactive power output of the Static Var Generator (SVG) device; The node voltage constraints in the constraints are as follows: (37)

[0037] Specifically, in step S4, the method for constructing the augmented Lagrangian function for each region is as follows: Introducing dual variables Construct the augmented Lagrangian function for each region: (38); In the formula: To augment the Lagrange function; For the first Lagrange multipliers for each region; As a penalty factor; For the first Boundary coupling variables of each region; It is a globally consistent variable; Let be the square of the L2 norm of the vector, and let be the sum of the squares of the elements in the vector. For the k-th sub-region after decomposition, at the t-th iteration, the locally augmented Lagrangian function of each region, given the global consistency variable... and Lagrange multipliers Under these conditions, the local optimization problem is solved independently and in parallel in each region: (39); In the formula: For the first During the nth iteration Updated values ​​of local variables in each subregion; For the first During the nth iteration Updated values ​​of the coupling variables at the boundaries of each sub-region; For the first Global consistency variables during the next iteration; For the first During the nth iteration Dual variables of each subregion; When the augmented Lagrangian function of the k-th subregion reaches its minimum, the local variables and boundary coupling variables Updated value.

[0038] Specifically, in step S5, the method for updating the globally consistent variable using the accelerated gradient strategy is as follows: By employing an accelerated gradient strategy to replace the traditional arithmetic mean method for average updates, the update of the globally consistent variable z is transformed into a problem of minimizing the globally consistent error. (40); In the formula: For the first During the nth iteration Updated values ​​of coupling variables at the boundaries of each sub-region. Indicates the consistency of global variables Find the minimum value; Applying gradient descent to the consistency error function in equation (40), we obtain the update formula for the globally consistent variable z: (41); In the formula: This refers to the gradient step size parameter; For the first The updated value of the globally consistent variable in the next iteration; After completing the global consistency variable update, the dual variables of each region are updated using the current boundary interaction error, so that each region can adjust in the next iteration to meet the global coordination requirements: (42); In the formula: For the first During the nth iteration Updated values ​​of dual variables in each subregion.

[0039] Furthermore, in step S6, the original residual and the dual residual are used as convergence criteria, including the following: Using the original residual and dual residuals As a convergence criterion, the algorithm terminates when both conditions are met simultaneously: (43); In the formula: The original residuals reflect the degree of deviation between boundary coupling variables and globally consistent variables; The dual residuals reflect the magnitude of change in global variables between two adjacent iterations; The convergence threshold of the original residual; The convergence threshold of the dual residual; the original residual It reflects the degree of deviation between boundary coupling variables and globally consistent variables, and measures the degree to which consistency constraints are satisfied; dual residuals It reflects the magnitude of change in global variables between two adjacent iterations, measures the stability of dual variable updates, and when the original residual... and dual residuals The algorithm is considered converged when both values ​​are less than a given threshold. The infinite norm represents the maximum absolute value of all elements in the vector.

[0040] Example 2: To verify the effectiveness of the method proposed in this invention, an IEEE 33-node distribution network was used as the test system. Distributed photovoltaic power sources with a rated capacity of 40kW were configured at nodes 1, 11, 12, 15, 18, 19, 27, 32, 35, and 36. SVG with a capacity of 25kVar was configured at nodes 3, 10, 21, and 25. Four zoning schemes were set up for comparative research: Option A: Only consider the spectral clustering method based on the voltage-reactive power sensitivity electrical distance matrix, without considering the temporal similarity of node operating states; Option B: A spectral clustering method that only considers the temporal similarity of node operating states, without considering electrical distance; Option C: Adopt a power grid zoning method based on non-Euclidean electrical distance; Scheme D: The method proposed in this invention comprehensively considers electrical distance based on voltage-reactive power sensitivity, timing similarity of node operating states, and regional voltage regulation capability, and iteratively optimizes the initial partition through a multi-objective greedy optimization algorithm.

[0041] Figure 3 This represents the value of the feature gap sequence based on the normalized Laplacian matrix with improved similarity matrix. Figure 3 It can be seen that the fourth characteristic gap in the characteristic gap sequence reaches the maximum value of 0.3681, and based on this, the optimal number of partitions is adaptively determined to be 4. To further verify the rationality of this number of partitions, the modularity value under different numbers of partitions is calculated: the modularity is 0.6056 when the number of partitions is 3, 0.6432 when the number of partitions is 4, and 0.6328 when the number of partitions is 5. The modularity is the largest when the number of partitions is 4, indicating that the electrical distance between nodes within the region is the smallest and the coupling degree is the strongest, while the electrical distance between regions is the largest and the coupling degree is the weakest, which meets the requirements for the partitioned operation of the distribution network and is consistent with the judgment result of the characteristic gap method.

[0042] Figure 4 This is a diagram showing the adaptive spectral clustering partitioning results of the method of this invention on an IEEE 33-node distribution network. (From...) Figure 4 As can be seen, the distribution network is divided into four sub-regions: Region 1 (blue circle) includes nodes 1, 2, 3, 4, 19, 20, 21, 22, 23, 24, and 25; Region 2 (orange circle) includes nodes 27, 28, 29, 30, 31, 32, and 33; Region 3 (green circle) includes nodes 5, 6, 7, 8, 9, 10, 11, 12, and 26; and Region 4 (purple circle) includes nodes 13, 14, 15, 16, 17, and 18. Nodes 3, 32, 6, and 15 are identified as the dominant nodes in Regions 1, 2, 3, and 4, respectively (marked with stars in the diagram). They are located at the load centers or locations with strong electrical coupling in their respective regions, and have the most significant impact on the voltage stability of their respective regions.

[0043] Table 1 compares the zoning results of the four schemes on the IEEE 33-node distribution network. Scheme A performs spectral clustering based solely on the electrical distance matrix, ignoring the temporal similarity of node operating states. This results in nodes with similar load characteristics being assigned to different zones, weakening the reactive power coordination capability within the region and increasing reactive power exchange between zones. Scheme B performs spectral clustering based solely on the temporal similarity of node operating states, ignoring electrical distance constraints. This results in nodes that are geographically distant and have weak electrical connections being assigned to the same zone, increasing the power flow of tie lines between zones and hindering local reactive power balancing.

[0044] Scheme C adopts a power grid partitioning method based on non-Euclidean electrical distance. Scheme D, based on Scheme C, further considers the temporal similarity of node operating states and regional voltage regulation capabilities. As shown in Table 1, the partitioning results of Scheme D and Scheme C are basically consistent, with the differences mainly concentrated at the partition boundaries. Scheme D improves the voltage regulation capabilities of each partition compared to Scheme C by introducing regional voltage regulation capabilities to correct the boundary nodes, resulting in stronger engineering adaptability of the partitioning results.

[0045] Table 1 Partitioning results of the IEEE 33-node system

[0046] The main difference between Scheme D and Scheme C lies in the assignment of boundary nodes between the partitions. Scheme C partitions based on non-Euclidean electrical distances, focusing on reducing the impact of voltage fluctuations under specific faults. However, it does not adequately consider the voltage regulation capabilities within each partition, resulting in some nodes with strong voltage regulation capabilities not being appropriately assigned to their corresponding partitions. The method of this invention introduces a regional voltage regulation capability index during the partitioning process to correct the assignment of boundary nodes, thus making the reactive power regulation resource allocation within each partition more balanced.

[0047] Table 2 shows the comparison results of regional voltage regulation capabilities between Scheme C and Scheme D. As shown in Table 2, in Region 1, the regional voltage regulation capability of the method of the present invention is improved by 4.6% compared to Scheme C; in Region 3, the regional voltage regulation capability of the method of the present invention is improved by 6.4% compared to Scheme C. These results indicate that by introducing a regional voltage regulation capability index to correct the zoning results, the method of the present invention enables each zone to have stronger voltage self-regulation capabilities during photovoltaic power output fluctuations and load disturbances. It can rely on reactive power regulation resources such as SVG and photovoltaic inverters within the zone to achieve autonomous voltage support, effectively reducing the demand for cross-regional reactive power transmission and ensuring the ability of each zone to maintain active and reactive power balance under extreme operating conditions.

[0048] Table 2. Regional voltage regulation capabilities of schemes C and D

[0049] Based on the partitioning results, the singular value entropy of all nodes within each partition was calculated to identify the dominant nodes in each partition. Nodes 3, 32, 6, and 15 were identified as the dominant nodes in partitions 1, 2, 3, and 4, respectively, with singular value entropies of 0.368, 0.367, 0.267, and 0.167, all of which are the maximum values ​​within their respective partitions. Combined with the IEEE 33-node distribution network structure, it can be seen that the identified dominant nodes are mostly located in load centers or areas with strong electrical coupling, and their operating states are more complex, significantly impacting system voltage stability. When these nodes experience load fluctuations or power disturbances, they easily cause significant changes in voltage amplitude and phase angle within the corresponding partitions, thus affecting the overall system operating state. Using singular value entropy can effectively identify the key nodes with the greatest impact on system stability within each partition, providing an important basis for subsequent reactive power optimization.

[0050] To verify the effectiveness of the reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradient proposed in this invention, the following schemes are set up for comparative analysis: Option 1: Adopt a reactive power optimization solution method based on an improved particle swarm optimization algorithm, with the optimization objectives of minimizing system network loss and node voltage deviation, and determine the reactive power output of SVG and photovoltaic inverter through global optimization; Solution 2: The partitioned coordinated reactive power optimization method based on the alternating direction multiplier method of accelerating gradient proposed in this invention decomposes the reactive power optimization problem of the whole network into sub-problems of each partition, realizes inter-regional coordination through boundary node voltage consistency constraints, and uses gradient acceleration strategy to update the global consistency variable.

[0051] Figure 5 The results show the comparison of the system voltage throughout the day after optimization of Scheme 1 and Scheme 2. Figure 5 The image simultaneously displays the voltage range (shaded area, with the upper and lower boundaries representing the maximum and minimum voltage values ​​of all nodes in the network, respectively) and the average voltage curve (broken line) for both schemes. Figure 5It can be seen that the voltage range of Scheme 1 (orange shading) expands significantly during peak photovoltaic output (9:00-14:00), with the upper voltage boundary exceeding the safe limit of 1.05 pu. During peak load (18:00-20:00), the lower voltage boundary approaches the safe lower limit of 0.95 pu, highlighting the problem of voltage exceeding limits. The voltage average curve of Scheme 1 (orange dashed line) fluctuates significantly, with a significant peak at 1.02 pu during 12:00-14:00, followed by a significant drop during 18:00-20:00, deviating considerably from the ideal voltage value (1.0 pu). In contrast, the voltage range of Scheme 2 (blue shading) remains within the safe range throughout the day, without any voltage exceeding limits. The voltage average curve of Scheme 2 (blue solid line) remains smooth throughout the day with minimal fluctuations, closely adhering to the ideal voltage value of 1.0 pu. The overall system voltage deviation is smaller, and the operational stability is stronger.

[0052] Figure 6 A bar chart comparing four quantitative indicators of reactive power optimization results for Scheme 1 and Scheme 2, including... Figure 6 Middle (a) to Figure 6 There are four subgraphs in the middle (d). Figure 6 (a) shows a comparison of the average voltage deviation. The average voltage deviation of Scheme 1 is 1.16%, while that of Scheme 2 is 0.77%, resulting in an improvement rate of 33.8%. Figure 6 (b) shows a comparison of voltage fluctuations. Scheme 1 has a voltage fluctuation of 1.65%, while Scheme 2 has a voltage fluctuation of 1.10%, resulting in an improvement rate of 33.0%. Figure 6 (c) shows a comparison of the total network loss of the system. The total network loss of Scheme 1 is 7580.22 MWh, while that of Scheme 2 is 6535.72 MWh, with a loss reduction rate of 13.8%. Figure 6 (d) shows the voltage over-limit rate comparison. Scheme 1 has a voltage over-limit rate of 1.32%, while Scheme 2 reduces it to 0.00%, achieving an improvement rate of 100%. The above four indicators fully verify the significant superiority of the method proposed in this invention in terms of voltage quality improvement, voltage fluctuation suppression, system loss reduction, and elimination of voltage over-limit.

[0053] Figure 7 This is a comparison curve of the daily voltage changes at the dominant nodes in each partition for Scheme 1 and Scheme 2, including... Figure 7 Middle (a) to Figure 7 There are four subgraphs in the middle (d), which correspond to the dominant node 3 of partition 1, the dominant node 32 of partition 2, the dominant node 6 of partition 3, and the dominant node 15 of partition 4. Figure 7 In the middle (a), the voltage curve of node 3 is shown throughout the day. Scheme 1 (orange dashed line) fluctuates more significantly in all time periods throughout the day, and the voltage regulation accuracy is lower; Scheme 2 (blue solid line) has a smoother voltage curve and smaller fluctuation amplitude. Figure 7In Figure (b), the voltage curve of node 32 throughout the day is shown. During the peak photovoltaic output period from 12:00 to 14:00, the voltage of Scheme 1 reaches a maximum of 1.04 pu, which is close to the safe limit of 1.05 pu, and there is a risk of exceeding the limit. The voltage of Scheme 2 is always kept stable within the safe range and does not exceed the limit. Figure 7 In Figure (c), the voltage curve of node 6 throughout the day is shown. Scheme 1 shows a significant voltage peak at 12:00, reaching 1.04 pu, and the voltage drops to 0.965 pu to 0.97 pu during the peak load period at 20:00, approaching the safety lower limit. Scheme 2 shows a significant reduction in the voltage fluctuation range throughout the day, effectively suppressing the voltage deviation during the peak photovoltaic and peak load periods. Figure 7 In the middle (d), the voltage curve of node 15 throughout the day is shown. Scheme 1 shows a significant voltage peak at 12:00, which reaches the safety limit. Scheme 2 has a smoother voltage curve throughout the day and is closer to the ideal voltage value overall.

[0054] In summary, the accelerated gradient alternating direction multiplier method proposed in this invention exhibits superior voltage control accuracy and stability at all four dominant nodes, verifying its effectiveness and superiority in reactive power optimization of distribution networks with high photovoltaic penetration.

[0055] Example 3: This example proposes an electronic system, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method steps of the present invention.

[0056] Example 4: This example proposes a computer-readable storage medium storing a computer program thereon. When the computer program is executed by a processor, it implements the steps of the method described in this invention, which will not be repeated here.

[0057] Example 5: This example proposes a computer program product, including a computer program / instructions. When the computer program / instructions are executed by a processor, they implement the steps of the method described in this invention, which will not be repeated here.

[0058] It should be noted that the processing flow of embodiments 2-5 corresponds to the specific steps of the method provided in embodiment 1 of the present invention, and has the corresponding functional modules and beneficial effects of the method. Technical details not described in detail in this embodiment can be found in the method provided in embodiment 1 of the present invention.

[0059] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradient, characterized in that, Includes the following steps: Step S1: Obtain the topology of the distribution network, node voltage time-series data, photovoltaic power output data, rated capacity and load data of static var generators (SVG); calculate the Fréchet distance based on the time-series trajectory of each node's operating status and construct a similarity matrix; introduce an electrical distance matrix based on voltage-reactive power sensitivity; combine the regional voltage regulation capability and weightedly fuse the two to obtain an improved similarity matrix; Step S2: Based on the improved similarity matrix obtained in Step S1, the distribution network is dynamically partitioned using an adaptive spectral clustering algorithm. The optimal number of partitions K is automatically determined by the feature gap criterion, and the dominant node is identified within each partition based on the singular value entropy of the Jacobian matrix. On this basis, the probability density function of the Beta distribution is used to probabilistically model the photovoltaic output, extract typical photovoltaic output scenarios, construct a comprehensive performance index based on the expected electrical distance, and dynamically adjust the initial partitions through multi-objective greedy optimization iteration. The results of each sub-region obtained by the dynamic partitioning are used as the input for Step S3. Step S3: For each sub-region obtained by dynamic partitioning in step S2, establish a local reactive power optimization objective function and constraints with the goal of minimizing regional active power loss and node voltage deviation. The constraints include power flow balance constraints, photovoltaic reactive power output constraints, static var generator (SVG) reactive power compensation constraints, and node voltage constraints. Step S4: Introduce global consistency variables for the voltage magnitude and phase angle of boundary nodes, establish consistency coupling constraints between regions, and construct augmented Lagrangian functions for each region; solve the local optimization problem for each sub-region under the given global consistency variables and Lagrangian multipliers. Step S5: Update the global consistency variables using an accelerated gradient strategy, transforming the update of the global consistency variables into a problem of minimizing the global consistency error and solving it using gradient descent; after completing the update of the global consistency variables, iteratively update the dual variables of each sub-region using the current boundary interaction error; Step S6: Calculate the original residual and the dual residual, and determine whether they simultaneously meet the convergence threshold; if they do, output the optimal reactive power scheduling scheme for each sub-region; otherwise, return to step S4 to continue iterating.

2. The reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients according to claim 1, characterized in that, In step S1, the method for obtaining the improved similarity matrix is ​​as follows: Set nodes With nodes j The state variables within the time interval [a, b] respectively constitute the trajectory. and trajectory ,node With nodes j Using parameterized velocity functions respectively α and parameterized velocity function β They move along their respective trajectories within the range [0,1], and in time... At that time, all distances The maximum value in the value represents the similarity between trajectories, the Fraser distance. Defined as: (1)； In the formula: For nodes With nodes The Fréchet distance between the time-series trajectories of state variables; For nodes The time-series trajectory of state variables; For nodes The time-series trajectory of state variables; For nodes Along the trajectory The parameterized velocity function of the movement; For nodes Along the trajectory The parameterized velocity function of the movement; For time parameters; The distance function between two points; This is the infimum operator, representing the smallest lower bound that satisfies the condition; The similarity matrix between system nodes is constructed using the Frescher distance between the temporal trajectories of node running states. Its expression is: (2)； In the formula: For nodes With nodes The Fréchet distance of the trajectory of the state variable; This is the similarity matrix between system nodes; This represents the total number of system nodes. Electrical distance matrix based on voltage-reactive power sensitivity The construction method is as follows: node With nodes Voltage-reactive power sensitivity Represented as: (3)； In the formula: For nodes With nodes Voltage-reactive power sensitivity; For nodes The voltage amplitude; For nodes The amount of reactive power injected; node With nodes electrical distance between Defined as: (4)； In the formula: For nodes With nodes Electrical distance between them; To prevent small positive numbers with a denominator of zero; A larger value indicates a tighter coupling between the two nodes, corresponding to a smaller electrical distance. Based on equations (2) and (3), the electrical distance matrix is ​​obtained. for: (5)； In the formula: The electrical distance between each node pair The electrical distance matrix formed; The voltage regulation capability within a region is defined as: (6)； In the formula: For the region Voltage regulation capability; For the first Each zone area; For the region Voltage regulation capability of the reactive power compensation device RPC; For the region The voltage regulation capability of the generator; (7)； (8)； In the formula: For the region The node with the highest voltage amplitude The maximum voltage deviation, if the voltage is within the normal allowable range, then ; For nodes The reactive power margin of the adjustable reactive power compensation device RPC; For nodes Reactive power injection to nodes Sensitivity to voltage amplitude at the location; For nodes The active power margin of the adjustable generator; For nodes Active power injection to nodes Sensitivity to voltage amplitude at the location; Similarity matrix and electrical distance matrix We perform weighted summation separately to obtain the improved similarity matrix. F Its expression is as follows: (9)； Where: coefficient The range of values ​​is In dynamic partitioning, different weights are assigned to each indicator by the calculators to obtain the target partitioning results. The selection of weights is based on the Analytic Hierarchy Process (AHP). The elements in the improved similarity matrix are adjusted based on the voltage regulation capability of each partition. The reactive power compensation device (RPC) and controllable generator are partitioned according to voltage regulation requirements. The improved similarity matrix... F The element adjustment method is as follows: (10)； In the formula: For nodes and nodes The similarity in their operating states and electrical connections; For the region Voltage regulation capability; For nodes The partition area it is located in.

3. The reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients according to claim 2, characterized in that, In step S2, the adaptive spectral clustering algorithm partitions the power grid and identifies dominant nodes based on the singular value entropy of the Jacobian matrix, including the following steps: Based on the improved similarity matrix in step S1 F The adjacency matrix of spectral clustering is calculated using a fully connected method. ; (11)； In the formula: It is an adjacency matrix; The scale parameter determines the decay rate of sample point similarity; For nodes With nodes The improved similarity matrix The obtained connection weights; The system's topology is represented by a degree matrix, where the degree of each node is determined by its adjacency matrix. The degree is calculated by adding the elements of each row, and the sum of each row is used as the diagonal element of the degree matrix. All other elements are set to 0, forming a degree matrix. As shown below: (12)； In the formula: For degree matrix, Indicates the first The degree of each node, Adjacency matrix The Middle Line number Column elements, For the first The degree of each node; Laplace matrix L From the adjacency matrix A Sum-degree matrix D Composed of, through the degree matrix D Laplace matrix L Normalize: (13)； In the formula: It is a Laplace matrix; (14)； In the formula: For the normalized Laplace matrix; By sorting the feature values, the k largest feature values ​​are selected to obtain the corresponding feature vectors. In obtaining The eigenvalues ​​are sorted from smallest to largest as follows After that, the characteristic gap The calculation formula is: (15)； In the formula: For the first One characteristic gap; For the normalized Laplace matrix The first one after ascending order One eigenvalue; By sequentially in the characteristic gap Find the maximum value in the sequence, and the corresponding index determines the number of optimal clusters. The calculation formula is as follows: (16)； In the formula: This represents the index that minimizes the objective function. ; Dynamic zoning optimization for uncertain photovoltaic output: (1) Calculation of expected electrical distance: Nodes between any two nodes For nodes The effect is the sensitivity of node voltage to reactive power. , is represented as: (17)； Equation (17) represents the node The change in its own voltage and the node when reactive power changes The ratio of voltage changes reflects the degree of dynamic voltage coupling under power flow changes; In the formula: For the scene Next node For nodes The effect of voltage-reactive power sensitivity; For the scene Next node The sensitivity of reactive power changes to its own voltage amplitude; For the scene Next node Reactive power changes on nodes Sensitivity to voltage amplitude; Node in scene m and nodes Sensitivity electrical distance between Represented as: (18)； In the formula: For the scene Next node and nodes The sensitivity of the electrical distance between them; For the intermediate variable in the summation; For the scene Next node For nodes The effect of voltage-reactive power sensitivity; For the scene Next node For nodes The effect of voltage-reactive power sensitivity; The larger the value, the more likely it is to be a node. For nodes The smaller the impact, the fewer nodes and nodes The greater the distance between them, the lower the degree of coupling. Using scene correction coefficients By aggregating all scenarios and considering the uncertainties of photovoltaics, the sensitivity electrical distance matrix is ​​improved. The desired electrical distance is obtained through probability-weighted aggregation. : (19)； In the formula: For nodes With nodes The expected electrical distance between them; This represents the total number of typical scenarios; For the scene Scene correction coefficient; (2) Construction and weighting of comprehensive performance indicators: Construct a new modularity function based on the expected electrical distance and considering the photovoltaic probability distribution. : (20)； In the formula: This is a modularity function considering the photovoltaic probability distribution based on the desired electrical distance; For nodes based on desired electrical distance With nodes Connection weights between them; For all nodes The sum of the weights of connected edges; For all nodes The sum of the weights of connected edges; This is the sum of the weights of all edges in the network; For partition indicator functions, if node With nodes In the same area ,otherwise ; Capacity matching index is The expression is: (21)； In the formula: The number of regions to be divided As a capacity matching index, For the first The sum of the maximum active power output of all active power sources in the region. For the first The sum of the maximum active power output of all conventional synchronous generators in the region. For the first The sum of the maximum active power output of all photovoltaic power stations in the region. For the first The sum of the maximum active power of each node load in each region; Reactive power compensation index The expression is: (22)； In the formula, The number of regions to be divided For the region The amount of reactive power compensation within the group; The reactive power supply value of reactive power sources within the region; This represents the reactive power demand of nodes within the region. For division The average reactive power compensation amount of each region, i.e., the reactive power compensation index. The source-load curve matching index is The expression is: (23)； In the formula, For the number of regions; The source-load curve matching index; For the first Time zone The sum of the output values ​​of internal photovoltaic systems, For the first Time zone The sum of internal active loads; A comprehensive performance index for evaluating power grids in different regions is proposed by weighting and combining the source-load curve matching degree index, the modularity index describing the expected electrical distance of photovoltaic probability distribution, the capacity matching index, and the reactive power compensation index. : (24)； In the formula: For comprehensive performance indicators; Modularity index The corresponding weight value; Capacity matching index The corresponding weight value; Reactive power compensation index The corresponding weight value; Source-load curve matching index The corresponding weight value; Perform multi-objective greedy optimization iterations, using static partitioning as the initial scheme, traversing adjacent sub-region pairs, and attempting boundary node migrations. If connectivity constraints are satisfied and the overall performance index is met, the optimization is successful. Improvements are accepted and adjustments are made; iterations are repeated until... Terminate when no further improvements are made, and output the final dynamic partitioning scheme; The dominant node identification method based on singular value entropy is as follows: For a power system, by performing a first-order Taylor expansion of the power flow equations, the corrected equations are obtained as follows: (25)； In the formula: The active power deviation at the node; This refers to the reactive power deviation at the node. , , , The elements of the Jacobian matrix are defined in equation (26); This refers to the phase angle deviation of the node voltage. This refers to the deviation in node voltage amplitude. This refers to the node voltage amplitude. Jacobian matrix J The elements are represented as follows: (26)； In the formula: The sensitivity of node active power changes to voltage phase angle; The sensitivity of node active power changes to voltage amplitude; The sensitivity of node reactive power changes to voltage phase angle; The sensitivity of node reactive power changes to voltage amplitude; For the Jacobian matrix in equation (26) Performing singular value decomposition, we obtain: (27)； In the formula: Composed of left singular vectors Orthogonal matrix; For singular values A non-negative diagonal matrix formed by; Composed of right singular vectors Orthogonal matrix; Jacobian matrix The One singular value; For matrix The middle corresponds to Column vectors; For matrix The middle corresponds to Column vectors; (28)； right Normalization yields the standardized form as follows: (29)； In the formula: Jacobian matrix No. Normalized values ​​of the singular values; Jacobian matrix Singular value entropy Represented as: (30)； In the formula: Jacobian matrix The singular value entropy.

4. The reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients according to claim 3, characterized in that, In step S3, the local reactive power optimization objective function and constraints include: Sub-regions The local objective function is: (31)； In the formula: This is the sum of the local objective functions of each sub-region; For the first Local objective functions for each sub-region; For the region Active network loss within the network; For the first Node voltage deviation within an autonomous sub-region; These are the weighting coefficients for the active power loss objective function; where are the weighting coefficients of the objective function for node voltage deviation, and ; For the region The internal vector of local variables; , For nodes The voltage amplitude; For nodes The voltage phase angle; For nodes The reactive power output of photovoltaics; For nodes SVG reactive power compensation; For the region Internal node set; for cross-regional connection lines, the loss is shared equally by adjacent regions; Network loss index is defined as: (32)； In the formula: This represents the total active power loss of the distribution network. It is the set of all nodes in the network; For nodes With nodes The electrical conductance between them; For nodes and nodes The voltage phase angle difference; The voltage deviation index is defined as: (33)； In the formula, S The set of all nodes in the network. This is a voltage deviation indicator; For nodes The nominal voltage, For nodes The upper limit of voltage; For nodes The lower limit of voltage; The power flow balance constraints in the constraints are as follows: (34)； In the formula: For nodes The generator has active power output; For nodes The generator's reactive power output; For nodes The photovoltaic system is generating active power. For nodes The reactive power output of photovoltaic power; For nodes Active load; For nodes reactive load; Let be the real part of the admittance matrix. This represents the imaginary part of the admittance matrix; The photovoltaic reactive power output constraints in the constraints are as follows: (35)； In the formula: For nodes The photovoltaic capacity; For nodes The photovoltaic system is generating active power. For nodes The reactive power output of photovoltaic power; The SVG reactive power compensation constraints in the constraints are as follows: (36)； In the formula: For nodes The static var generator (SVG) device outputs reactive power. For nodes The upper limit of reactive power output of the Static Var Generator (SVG) device; For nodes The lower limit of reactive power output of the Static Var Generator (SVG) device; The node voltage constraints in the constraints are as follows: (37)。 5. The reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients according to claim 4, characterized in that, In step S4, the method for constructing the augmented Lagrangian function for each region is as follows: Introducing dual variables Construct the augmented Lagrangian function for each region: (38)； In the formula: To augment the Lagrange function; For the first Lagrange multipliers for each region; As a penalty factor; For the first Boundary coupling variables of each region; It is a globally consistent variable; Let be the square of the L2 norm of the vector, and let be the sum of the squares of the elements in the vector. For the k-th sub-region after decomposition, at the t-th iteration, the locally augmented Lagrangian function of each region, given the global consistency variable... and Lagrange multipliers Under these conditions, the local optimization problem is solved independently and in parallel in each region: (39)； In the formula: For the first During the nth iteration Updated values ​​of local variables in each subregion; For the first During the nth iteration Updated values ​​of the coupling variables at the boundaries of each sub-region; For the first Global consistency variables during the next iteration; For the first During the nth iteration Dual variables of each subregion; When the augmented Lagrangian function of the k-th subregion reaches its minimum, the local variables and boundary coupling variables Updated value.

6. The reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients according to claim 5, characterized in that, In step S5, the method for updating the globally consistent variables using the accelerated gradient strategy is as follows: By employing an accelerated gradient strategy to replace the traditional arithmetic mean method for average updates, the update of the globally consistent variable z is transformed into a problem of minimizing the globally consistent error. (40)； In the formula: For the first During the nth iteration Updated values ​​of coupling variables at the boundaries of each sub-region. Indicates the consistency of global variables Find the minimum value; Applying gradient descent to the consistency error function in equation (40), we obtain the update formula for the globally consistent variable z: (41)； In the formula: This refers to the gradient step size parameter; For the first The updated value of the globally consistent variable in the next iteration; After completing the global consistency variable update, the dual variables of each region are updated using the current boundary interaction error, so that each region can adjust in the next iteration to meet the global coordination requirements: (42)； In the formula: For the first During the nth iteration The updated values ​​of dual variables in each subregion.

7. The reactive power optimization method for distribution networks based on the alternating direction multiplier method of accelerating gradients according to claim 6, characterized in that, In step S6, the original residual and the dual residual are used as convergence criteria, including the following: Using the original residual and dual residual As a convergence criterion, the algorithm terminates when both conditions are met simultaneously: (43)； In the formula: The original residuals reflect the degree of deviation between boundary coupling variables and globally consistent variables; The dual residuals reflect the magnitude of change in global variables between two adjacent iterations; The convergence threshold of the original residual; The convergence threshold of the dual residual; the original residual It reflects the degree of deviation between boundary coupling variables and globally consistent variables, and measures the degree to which consistency constraints are satisfied; dual residuals It reflects the magnitude of change in global variables between two adjacent iterations, measures the stability of dual variable updates, and when the original residual... and dual residual The algorithm is considered converged when both values ​​are less than a given threshold. The infinite norm represents the maximum absolute value of all elements in the vector.

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