A reactive voltage partitioning method and device considering wind power output

Abstract

The application discloses a reactive power voltage partitioning method and device considering wind power output, and the method comprises the following steps: fitting a first Gaussian mixture model of wind power reactive power output according to historical data of a wind turbine and a preset time period; establishing a second Gaussian mixture model of wind turbine node voltage according to a reactive power linear flow equation and the first Gaussian mixture model; calculating a first distance between the second Gaussian mixture models, and obtaining a Laplace matrix according to the first distance; establishing an improved modularity index according to the Laplace matrix, and merging a first partition obtained by pre-partitioning to obtain a second partition. By adopting the embodiment of the application, the randomness of the reactive power output is considered through the Gaussian mixture model; the second Gaussian mixture model representing the wind turbine node voltage is obtained, and only one flow calculation is involved, so that the calculation amount is reduced; the closeness of the internal coupling of the region is considered through the improved modularity index, and the problem of frequent re-partitioning is avoided.

Description

Technical Field

[0001] This invention relates to the field of power grid zoning technology, and in particular to a reactive voltage zoning method and apparatus that takes into account wind power output. Background Technology

[0002] To achieve the goals of "carbon peaking and carbon neutrality," renewable energy sources, primarily wind and solar power, are being widely integrated into new power systems. The output of new energy sources such as wind power is characterized by randomness, fluctuation, and intermittency. Their increasing penetration rate has led to a more complex and variable power flow in the power grid, significantly altering the system characteristics and reactive power / voltage control of the grid.

[0003] Current power system reactive power and voltage control systems divide the entire network into different regions, fully utilizing the local balance characteristics of reactive power for voltage control. Therefore, reasonable voltage control region division is a crucial foundation for achieving effective and economical voltage control. Existing voltage zoning methods mainly fall into two categories. The first category only considers network topology and structural parameters. While simple and yielding fixed results, it fails to consider actual power flow characteristics, leading to problems such as insufficient reactive power sources within regions and lines exceeding reactive power limits in practice, thus gradually being phased out. The second category, although considering system reactive power flow information, analyzes, calculates, and divides regions based only on a single typical power flow scenario. When a large amount of wind power is integrated into the power system, the randomness of wind power output causes frequent changes in system power flow. In this case, using a zoning method considering a single power flow scenario will cause individual nodes to switch back and forth between different regions, adversely affecting voltage stability control. Summary of the Invention

[0004] This invention provides a reactive voltage partitioning method and apparatus that considers wind power output, in order to solve the technical problems of frequent re-partitioning calculations and large computational load caused by considering power flow scenarios under a single operating condition in the prior art.

[0005] To address the aforementioned technical problems, embodiments of the present invention provide a reactive voltage zoning method considering wind power output, comprising:

[0006] Based on historical wind turbine data and a preset time period, a first Gaussian mixture model for wind power reactive power output is fitted.

[0007] Based on the reactive power linear power flow equation and the first Gaussian mixture model, a second Gaussian mixture model of wind turbine node voltage is established.

[0008] Calculate the first distance between the second Gaussian mixture models, and obtain the Laplacian matrix based on the first distance;

[0009] Based on the Laplace matrix, an improved modularity index is established, and then the pre-divided first partition is merged according to the improved modularity index to obtain the second partition.

[0010] This invention fits the reactive power output of wind power using a first Gaussian mixture model, which takes into account the randomness of reactive power output and avoids considering only a single power flow scenario. In addition, by utilizing the linear transformation invariance of the Gaussian mixture model, solving the linear power flow equations yields a second Gaussian mixture model representing the wind turbine node voltage. A Laplace matrix is ​​established by combining the distance between the Gaussian models. This calculation method involves only one power flow calculation, reducing the computational load while maintaining accuracy. An improved modularity index is used for region merging, taking into account the tightness of coupling within the region, thus avoiding the problem of frequent re-partitioning due to changes in power flow information.

[0011] Furthermore, the establishment of a second Gaussian mixture model for the wind turbine node voltage based on the reactive power linear power flow equation and the first Gaussian mixture model is specifically as follows:

[0012] Based on the AC power flow equation, a reactive linear power flow model is established, and the reactive power injected into the bus of the reactive linear power flow model is calculated.

[0013] Based on the stated reactive power, establish the reactive linear power flow equation;

[0014] The reactive power linear power flow equation is simplified into a linear mapping, and a second Gaussian mixture model corresponding to the wind turbine node voltage is obtained based on the linear mapping and the first Gaussian mixture model.

[0015] This invention utilizes the linear transformation invariance of the Gaussian mixture model to obtain a second Gaussian mixture model representing the wind turbine node voltage by solving the AC power flow equation and the reactive linear power flow equation. This takes into account the randomness of the wind turbine node voltage in the wind turbine output, thus avoiding the power flow scenario that only considers a single operating condition.

[0016] Furthermore, the expression for the reactive power is:

[0017]

[0018] Among them, Q i Let B be the reactive power injected into bus i, B be the imaginary part of the system admittance matrix, and G be the real part of the system admittance matrix. ij and g ij b represents the susceptance and conductance of the series branch in the lumped parameter model of the corresponding line between bus i and bus j, respectively; ii and g ii These represent the susceptance and conductance of the parallel branch in the lumped parameter model of the line corresponding to node i, respectively.

[0019] Further, the calculation of the first distance between the second Gaussian mixture models, and the determination of the Laplacian matrix based on the first distance, specifically involves:

[0020] Based on the Wasserstein distance, a second distance is defined between the Gaussian components in the second Gaussian mixture model;

[0021] Based on the second distance, the first distance is established using a geometrically weighted average.

[0022] Based on the power system's busbars and transmission lines, establish an undirected weighted graph model;

[0023] Based on the first distance, the Laplacian matrix corresponding to the undirected weighted graph model is obtained.

[0024] This invention establishes the electrical distance through a second Gaussian mixture model, directly solves the distribution of the random variables of voltage at each node based on the probability distribution of the Gaussian model, and then constructs the Laplace matrix through an undirected weighted graph model. It involves only one power flow calculation, which reduces the amount of computation while ensuring the accuracy of the calculation.

[0025] Further, the step of obtaining the Laplacian matrix corresponding to the undirected weighted graph model based on the first distance specifically involves:

[0026] Based on the first distance, the edge weights in the undirected weighted graph model are calculated, and based on the edge weights, the Laplacian matrix corresponding to the undirected weighted graph model is obtained; wherein, the expression for the elements of the Laplacian matrix is:

[0027]

[0028] Where w is the edge weight; the function δ(i,j) is 1 when the edge (i,j) is directly connected, and 0 otherwise.

[0029] Further, the step of establishing an improved modularity index based on the Laplace matrix, and then merging the pre-divided first partitions according to the improved modularity index to obtain the second partition, specifically involves:

[0030] Based on the splitting algorithm and sensitivity matrix, load nodes are incorporated into corresponding wind turbine node partitions to form the first partition; wherein, the corresponding wind turbine node partition is the wind turbine node partition with the highest sensitivity corresponding to the load node;

[0031] Based on the Laplace matrix, an improved modularity index for the first partition is established;

[0032] Based on the improved modularity index, the connected regions in the first partition are merged to obtain the second partition.

[0033] This invention pre-partitions based on a splitting algorithm and a sensitivity matrix, without requiring manual specification of pre-partitions. This reduces computational load while improving the theoretical guarantee of pre-partitioning. When merging, merging is performed based on an improved modularity index, which reduces time complexity or computational load. The improved modularity index takes into account the tightness of coupling within the region, avoiding the problem of frequent re-partitioning due to changes in power flow information.

[0034] Further, the step of merging the connected regions in the first partition according to the improved modularity index to obtain the second partition specifically involves:

[0035] Based on the improved modularity index, the connected regions with the maximum improved modularity in the first partition are merged sequentially.

[0036] Find the partition with the highest degree of improvement, and determine the second partition based on the partition location.

[0037] This invention merges the first partition based on an improved modularity index, so that each connected region in the first partition is merged according to the tightness of its internal coupling. This has clear physical meaning and low time complexity. While reducing the amount of computation, it avoids the problem of frequent re-partitioning caused by changes in power flow information by considering the tightness of internal coupling.

[0038] Furthermore, the expression for the improved modularity index is:

[0039]

[0040] Where L is an element of the Laplacian matrix; the function δ(i,j) is 1 when the edge (i,j) is directly connected, and 0 otherwise.

[0041] Furthermore, the expression for the first Gaussian mixture model is:

[0042]

[0043]

[0044]

[0045] Among them, f X (x) is the probability density function of the first Gaussian mixture model. ω i μ is the probability generated by a Gaussian distribution. i σ is the mean. i Standard deviation x represents the reactive power output of wind power.

[0046] On the other hand, this application also provides a reactive voltage partitioning device that considers wind power output, including: a first model establishment module, a second model establishment module, a matrix solving module and a voltage partitioning module;

[0047] The first model building module is used to fit a first Gaussian mixture model of wind power reactive power output based on historical wind turbine data and a preset time period.

[0048] The second model building module is used to build a second Gaussian mixture model of the wind turbine node voltage based on the reactive power linear power flow equation and the first Gaussian mixture model.

[0049] The matrix solving module is used to calculate the first distance between the second Gaussian mixture models and to obtain the Laplacian matrix based on the first distance.

[0050] The voltage partitioning module is used to establish an improved modularity index based on the Laplace matrix, and then merge the pre-divided first partitions according to the improved modularity index to obtain the second partition.

[0051] This invention fits the reactive power output of wind power using a first Gaussian mixture model, which takes into account the randomness of reactive power output and avoids considering only a single power flow scenario. In addition, by utilizing the linear transformation invariance of the Gaussian mixture model, solving the linear power flow equations yields a second Gaussian mixture model representing the wind turbine node voltage. A Laplace matrix is ​​established by combining the distance between the Gaussian models. This calculation method involves only one power flow calculation, reducing the computational load while maintaining accuracy. An improved modularity index is used for region merging, taking into account the tightness of coupling within the region, thus avoiding the problem of frequent re-partitioning due to changes in power flow information. Attached Figure Description

[0052] Figure 1 A flowchart illustrating an embodiment of the reactive voltage partitioning method considering wind power output provided by the present invention;

[0053] Figure 2 A schematic flowchart illustrating another embodiment of the reactive voltage zoning method considering wind power output provided by the present invention;

[0054] Figure 3 A schematic flowchart illustrating another embodiment of the reactive voltage zoning method considering wind power output provided by the present invention;

[0055] Figure 4 A schematic flowchart illustrating another embodiment of the reactive voltage zoning method considering wind power output provided by the present invention;

[0056] Figure 5A schematic diagram of a structural embodiment of the reactive voltage zoning device considering wind power output provided by the present invention;

[0057] Figure 6 A schematic diagram of a partition-based three-level automatic voltage control paradigm provided by the present invention;

[0058] Figure 7 A schematic diagram of the first Gaussian mixture model provided by the present invention;

[0059] Figure 8 This is a schematic diagram of the undirected weighted graph model provided by the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] To ensure the robustness of voltage partitioning in power systems under frequent power flow changes, this invention proposes a reactive voltage partitioning method and device that considers wind power output. This method is based on a linear probabilistic power flow model and complex network theory to partition the network, thereby achieving reactive voltage partitioning that takes into account power flow fluctuations and has strong robustness.

[0062] The method provided in this invention is based on power network partitioning; due to the complexity of voltage control problems, large-scale power systems currently mostly adopt a three-layer automatic voltage control framework; please refer to... Figure 6 This is a schematic diagram of a partition-based three-level automatic voltage control paradigm provided by the present invention. In this paradigm, the second-level voltage control coordinates and controls the node voltages within a specific region. It receives the central bus voltage reference signal from the third-level voltage control based on optimized scheduling and sends local voltage reference signals to all first-level voltage control units within the region, playing a coordinating role in the three-level voltage control system. Achieving reasonable voltage partitioning is the foundation of second-level voltage control and is fundamental to the safety, stability, and reactive power optimization of the voltage control system. How to comprehensively consider the connectivity characteristics of the network topology and the power flow characteristics of the power system, utilize local reactive power balancing to achieve voltage partitioning, minimize reactive power-voltage coupling between partitions, and decouple voltage control regions is a crucial foundation for second-level voltage control.

[0063] To meet the above requirements, existing technologies employ a reactive power-voltage partitioning method based on community theory. This method comprehensively considers the influence of power system topology and specific power flow characteristics, specifically including: establishing a weighted graph model of the power system network: using the actual reactive power transmission rate of nodes and lines as the weights of the undirected graph to establish a weighted graph model of the power system network; pre-partitioning based on reactive power-voltage sensitivity: obtaining the sensitivity matrix of load nodes to reactive power sources based on the system admittance matrix, pre-partitioning with each reactive power source as the center, and including each load node in the pre-partition with the highest sensitivity based on reactive power-voltage sensitivity; and clustering partitioning based on modularity index: calculating the modularity index of n pre-partitions. The calculation formula is as follows, where m is the number of nodes in the graph, and a r e is the sum of the weights of the edges within the r-th region and the weights of the edges connecting it to other regions. rr Let δ(i,j) be the sum of edge weights within the r-th region, where δ(i,j) is 1 when nodes i and j are in the same partition, and 0 otherwise. The modularity metric is expressed as:

[0064]

[0065] Calculate the modularity after merging any two contiguous partitions, and find the modularity that makes the modularity... Merge the two largest regions. Repeat the above process until the entire system is merged into one region.

[0066] However, this method models and calculates voltage partitions based on power flow scenarios under specific, typical operating conditions. When using this type of voltage partitioning method, once the system power flow changes significantly, the partitioning calculation needs to be re-performed. Nodes with large power fluctuations and their surrounding areas often change frequently between partitions, negatively impacting the continuity and stability of the control strategy. Compared to traditional power systems, new power systems have a large influx of renewable energy sources with significant power fluctuation characteristics, such as wind power, causing frequent fluctuations in system power flow. On the other hand, power electronic interfaces are widely used in new power systems. Compared to traditional power systems dominated by mechanical equipment, power electronic devices have poor voltage disturbance immunity and weak fault ride-through capability, thus requiring more significant voltage stability and minimizing rigid switching of control strategies caused by partition changes. The reactive power voltage partitioning method and device considering wind power output provided by this invention can meet the requirements of reducing computational load and avoiding frequent changes in nodes between partitions under conditions of large power fluctuations.

[0067] Example 1

[0068] Please refer to Figure 1This is a flowchart illustrating an embodiment of the reactive voltage zoning method considering wind power output provided by the present invention, mainly including steps 101-105, as follows:

[0069] Step 101: Based on the historical data of the wind turbine and the preset time period, fit the first Gaussian mixture model of the reactive power output of the wind power.

[0070] Grid-connected variable-speed wind turbines generally operate in Maximum Power Point Tracking (MPPT) mode. MPPT improves the efficiency of wind energy to electricity conversion, but it lacks power smoothing capabilities. Due to the stochastic nature of primary energy sources, the active power output of wind turbines using MPPT mode exhibits significant fluctuations over time. For economic reasons, the turbines themselves generate as little reactive power as possible, converting wind energy into active power for transmission. Reactive power is supplied by local reactive power compensation devices, and the overall amount of reactive power injected is proportional to the active power output of the turbine. Therefore, from the grid connection perspective, wind power and its associated reactive power compensation devices exhibit a constant power factor, but both active and reactive power outputs fluctuate with wind speed, characteristic of a power source.

[0071] In this embodiment, the stochastic characteristics of wind power output are first described using a Gaussian mixture model based on historical wind turbine data. For the transmission network, since the line reactance is much greater than the line resistance, the system exhibits decoupling characteristics between active power / frequency and reactive power / voltage. Specifically regarding voltage and reactive power partitioning, existing research and simulation results of this method both show that the impact of wind power active power output fluctuations on the partitioning results is minimal and can be ignored. Therefore, the reactive power voltage partitioning method provided by this invention only considers the characteristics of reactive power output fluctuations at the wind power port, which is mainly provided by reactive power compensation devices, in the subsequent modeling and calculation process, and designs a partitioning algorithm based on this.

[0072] Please refer to Figure 7 This is a schematic diagram of the first Gaussian mixture model provided by the present invention, wherein the probability distribution of wind power reactive power fluctuation can be described by the Gaussian mixture model. The Gaussian mixture model is a convex combination of multiple Gaussian distribution functions and has a series of good properties of Gaussian distribution.

[0073] In this embodiment, the expression for the first Gaussian mixture model is:

[0074]

[0075]

[0076]

[0077] Among them, f X (x) is the probability density function of the first Gaussian mixture model. ω i μ is the probability generated by a Gaussian distribution. i σ is the mean. i Standard deviation x represents the reactive power output of wind power.

[0078] In this embodiment, the first Gaussian mixture model has M Gaussian components, while the random variable x, as the reactive power output of wind power, has W dimensions. Based on the historical data of the active power output of wind power and the corresponding fixed power factor, the probability distribution Gaussian mixture model of the reactive power output of wind power can be obtained by using maximum likelihood estimation with the reactive power output of wind power as the random variable.

[0079] Step 102: Based on the reactive power linear power flow equation and the first Gaussian mixture model, establish the second Gaussian mixture model of the wind turbine node voltage.

[0080] In this embodiment, based on the linear power flow model, the second Gaussian mixture distribution of the wind turbine node voltage is analytically solved using the linear transformation invariance of the Gaussian mixture model; wherein, the wind turbine node is referred to as a PQ node; the wind turbine is modeled as a PQ node that absorbs negative power from the bus.

[0081] Step 103: Calculate the first distance between the second Gaussian mixture models, and obtain the Laplacian matrix based on the first distance.

[0082] In this embodiment, the electrical distance between two wind turbine nodes or PQ nodes is characterized by a second Gaussian mixture model representing the random variable of wind turbine node voltage, and an undirected weighted graph model of the power system is established based on this model. Then, the Laplace matrix corresponding to the undirected weighted graph model is obtained.

[0083] Step 104: Based on the Laplace matrix, establish an improved modularity index, and then merge the pre-divided first partition according to the improved modularity index to obtain the second partition.

[0084] In this embodiment, the pre-division of the first partition is mainly based on the power system topology and structured parameters, without considering line power flow information, generating an initial partition with the same number of generator nodes. Then, based on the improved modularity index defined by the Laplace matrix, formal voltage partitioning is performed, and the regions of the first partition are merged to obtain the second partition.

[0085] Please refer to Figure 2 This is a flowchart illustrating another embodiment of the reactive voltage zoning method considering wind power output provided by the present invention, mainly including steps 201-203, as follows:

[0086] In this embodiment, step 102 specifically includes steps 201 to 203.

[0087] Step 201: Based on the AC power flow equation, establish a reactive power linear power flow model and calculate the reactive power injected into the bus of the reactive power linear power flow model.

[0088] In this embodiment, the expression for reactive power is:

[0089]

[0090] Among them, Q i Let B be the reactive power injected into bus i, B be the imaginary part of the system admittance matrix, and G be the real part of the system admittance matrix. ij and g ij b represents the susceptance and conductance of the series branch in the lumped parameter model of the corresponding line between bus i and bus j, respectively; ii and g ii These represent the susceptance and conductance of the parallel branch in the lumped parameter model of the line corresponding to node i, respectively.

[0091] In this embodiment, the expression for reactive power uses the assumption V during the approximation process. i ≈V j ≈1, θ ij ≈0 and G ij V i (V i -V j cosθ ij )≈G ij (V i -V j These assumptions are satisfied in actual power flow under normal circumstances.

[0092] In this embodiment, firstly, the system admittance matrix Y = G + jB is constructed based on the power system topology, transformer, and line parameters. This is the common foundation for most power flow calculations. Here, G and B are the real and imaginary parts of the system admittance matrix Y, respectively. If there is a line connection between buses i and j, the per-unit values ​​of the conductance and susceptance parameters of the corresponding lumped parameter model series branches are denoted as g... ij and b ij Let g be the conductance and susceptance parameters of the parallel branches of all lines connected to node i in the lumped parameter model. ii and b ii Under the above notation, the elements at position (i,j) of matrices G and B can be represented as follows:

[0093]

[0094] Step 202: Based on the reactive power, establish the reactive linear power flow equation.

[0095] In this embodiment, the expression for the reactive power linear power flow equation is:

[0096]

[0097] in, and Let represent the variable vectors of reactive power and active power, respectively; where, the matrix... M and H are defined by the following formulas:

[0098]

[0099]

[0100] In this embodiment, the subscripts S and L represent the node numbers corresponding to PV nodes and PQ nodes, respectively. All subsequent subscripts S and L in this embodiment will carry the same meaning. It should also be noted that matrices H, N, M, L and... It does not have obvious physical meaning in itself, but is only used for the purpose of simplifying the final calculation formula.

[0101] Furthermore, the variable vectors of reactive power and active power are defined by the following formulas:

[0102]

[0103] In this system, the subscripts S, L, and R represent the PV node, PQ node, or wind turbine node, and the reference node, respectively. The superscript ^ represents the new matrix obtained by removing the increment caused by parallel elements at the diagonal elements of the matrix.

[0104] Step 203: Simplify the reactive power linear power flow equation into a linear mapping, and obtain a second Gaussian mixture model corresponding to the wind turbine node voltage based on the linear mapping and the first Gaussian mixture model.

[0105] In this embodiment, the active power and voltage of the PV node remain unchanged, and the wind turbine is modeled as a PQ node absorbing negative power from the bus. Considering that active power fluctuations have little impact on reactive power voltage partitioning, it is assumed that only reactive power changes. Therefore, the above reactive power linear power flow equation can be simplified as the reactive power vector Q from the PQ node. L Voltage vector μ to load node L A linear mapping, the expression of which is:

[0106] V L =AQ L +C;

[0107] In this embodiment, when Q L ~GMM(ω,μ,σ), where ω,μ, and At that time, V L It also follows a Gaussian mixture model distribution. By utilizing the linear transformation invariance of the Gaussian mixture model, a second Gaussian mixture model of the voltages at all PQ nodes or wind turbine nodes is obtained; the expression for the second Gaussian mixture model is:

[0108]

[0109]

[0110]

[0111]

[0112] Where, ω i μ is the probability generated by a Gaussian distribution. i σ is the mean. i The standard deviation is denoted as .

[0113] This invention utilizes the linear transformation invariance of the Gaussian mixture model to obtain a second Gaussian mixture model representing the wind turbine node voltage by solving the AC power flow equation and the reactive linear power flow equation. This takes into account the randomness of the wind turbine node voltage in the wind turbine output, thus avoiding the power flow scenario that only considers a single operating condition.

[0114] Please refer to Figure 3 This is a flowchart illustrating another embodiment of the reactive voltage zoning method considering wind power output provided by the present invention, mainly including steps 301-304, as follows:

[0115] In this embodiment, step 103 specifically includes steps 301 to 304.

[0116] Step 301: Define the second distance between the Gaussian components in the second Gaussian mixture model based on the Wasserstein distance.

[0117] In this embodiment, for any two PQ node voltages, the second Gaussian mixture model V Li ~GMM(ω) i ,μ i ,σ i ) and V Lj ~GMM(ω) j ,μ j ,σ j The second distance between Gaussian components is defined according to the Wasserstein distance; where the expression for the second distance is:

[0118]

[0119] in, This represents the distance between the k-th Gaussian components.

[0120] Step 302: Based on the second distance, establish the first distance using a geometrically weighted average.

[0121] In this embodiment, based on the second distance, a first distance is established between the two second Gaussian mixture models using a geometrically weighted average; wherein the expression for the first distance is:

[0122]

[0123] Step 303: Establish an undirected weighted graph model based on the power system's busbars and transmission lines.

[0124] In this embodiment, in the undirected weighted graph model, the weight of edge (i,j) is 0 when there is no connection between the two edges, and is determined by the reciprocal of the distance between them when there is a connection. The expression for the weight is:

[0125]

[0126] Please refer to Figure 8 This is a schematic diagram of the undirected weighted graph model provided by the present invention, wherein nodes correspond to power buses, edges correspond to transmission lines, and edge weights are defined by random variables of bus voltages at both ends of the line.

[0127] Step 304: Based on the first distance, obtain the Laplacian matrix corresponding to the undirected weighted graph model.

[0128] In this embodiment, the step of obtaining the Laplacian matrix corresponding to the undirected weighted graph model based on the first distance specifically involves:

[0129] Based on the first distance, the edge weights in the undirected weighted graph model are calculated, and based on the edge weights, the Laplacian matrix corresponding to the undirected weighted graph model is obtained; wherein, the expression for the elements of the Laplacian matrix is:

[0130]

[0131] Where w is the edge weight; the function δ(i,j) is 1 when the edges (i,j) are directly connected, and 0 otherwise.

[0132] In this embodiment, the Laplace matrix of the undirected weighted graph represents the connectivity and edge weights of the graph, covering all information of the undirected weighted graph. Its diagonal element ii represents the sum of the weights of all edges connected to node i, i.e., the degree of the node, and the off-diagonal element ij represents the opposite value of the weight of the line connecting nodes i and j. For example, if there is no direct connection, the value is 0.

[0133] This invention establishes the electrical distance through a second Gaussian mixture model, directly solves the distribution of the random variables of voltage at each node based on the probability distribution of the Gaussian model, and then constructs the Laplace matrix through an undirected weighted graph model. It involves only one power flow calculation, which reduces the amount of computation while ensuring the accuracy of the calculation.

[0134] Please refer to Figure 4 This is a flowchart illustrating another embodiment of the reactive voltage zoning method considering wind power output provided by the present invention, mainly including steps 401-403, as follows:

[0135] In this embodiment, step 104 specifically includes steps 401 to 403.

[0136] Step 401: Based on the splitting algorithm and sensitivity matrix, the load node is included in the corresponding wind turbine node partition to form the first partition; wherein, the corresponding wind turbine node partition is the wind turbine node partition with the highest sensitivity corresponding to the load node.

[0137] In this embodiment, the purpose of initial partitioning or establishing the first partition is to minimize the number of initial regions in the clustering partitions or the establishment of the second partition, thereby reducing the computational load. For example, if the number of regions in the first partition is n, the time complexity of clustering based on community theory or the time complexity of performing the second partition is approximately O(n^2). 2 Therefore, when there are many nodes in a power system, directly treating all nodes as initial partitions without preprocessing will lead to very inefficient, or even unacceptable, computation. For example, in a New England 10-machine, 39-node system, the number of initial regions is reduced from 39 to 10 after pre-partitioning, and the merging time is greatly reduced. Thus, the initial partitioning or the creation of the first partition is necessary.

[0138] In this embodiment, load nodes are incorporated into the corresponding wind turbine node partitions according to the splitting algorithm and the sensitivity matrix to form the first partition. Specifically, the iterative relationship is obtained according to the reactive power-voltage iterative equation of the splitting algorithm and the wind turbine nodes; the sensitivity matrix is ​​obtained according to the iterative relationship; and all load nodes are incorporated into the wind turbine node partition with the highest sensitivity according to the sensitivity matrix to form the first partition.

[0139] In this embodiment, by employing a splitting algorithm, it can be ensured that each region in the first partition has a controllable node. Furthermore, since the number of regions in the first partition is the same as the number of nodes in the generator, the number of iterations required to establish the second partition based on the improved modularity index is reduced, thus lowering the computational load.

[0140] In this embodiment, the expression for the reactive power-voltage iterative equation is:

[0141] -B LL ΔV L =ΔQ L .

[0142] In this embodiment, the expression for the iterative relationship is:

[0143]

[0144] The iterative relationship is obtained by augmenting the wind turbine nodes into the matrix.

[0145] Step 402: Based on the Laplace matrix, establish an improved modularity index for the first partition.

[0146] In this embodiment, the expression for the improved modularity index is:

[0147]

[0148] Where L is an element of the Laplacian matrix; the function δ(i,j) is 1 when the edge (i,j) is directly connected, and 0 otherwise.

[0149] In this embodiment, the improved modularity index references the definition of community modularity in complex network theory, consisting of the subtraction of two parts; both parts are positive, the first reflecting the tightness of coupling within a partition, and the second reflecting the looseness of connection between partitions. Therefore, from a physical perspective, performing partition clustering with the goal of maximizing improved modularity is essentially finding a method that makes the voltage connections within a partition as tight as possible and the voltages between partitions as uncorrelated as possible, which precisely matches the goal of voltage-controlled partitioning.

[0150] Step 403: Based on the improved modularity index, merge the connected regions in the first partition to obtain the second partition.

[0151] In this embodiment, the step of merging the connected regions in the first partition according to the improved modularity index to obtain the second partition specifically involves: merging the connected regions with the maximum improved modularity in the first partition sequentially according to the improved modularity index; finding the partition position with the maximum improved modularity; and determining the second partition based on the partition position.

[0152] In this embodiment, the improved modularity index of n pre-partitions in the first partition is first calculated. Then calculate the modularity after merging any two contiguous partitions, and find the metric that improves the modularity. Merge the two largest regions. Repeat the above process until the entire system is merged into one region.

[0153] In this embodiment, the location of the partition with the highest improved modularity can be determined using the following formula:

[0154]

[0155] In this embodiment, after determining the partition position with the largest well module size, the partition at this time is taken as the second partition; the second partition has strong robustness.

[0156] In this embodiment, other clustering algorithms based on community theory can also be used to merge the first region, such as the Balanced-Depth-Based Community Detection algorithm, which can further reduce time complexity and computational load.

[0157] This invention pre-partitions based on a splitting algorithm and a sensitivity matrix, without requiring manual specification of pre-partitions. This reduces computational load while improving the theoretical guarantee of pre-partitioning. When merging, merging is performed based on an improved modularity index, which reduces time complexity or computational load. The improved modularity index takes into account the tightness of coupling within the region, avoiding the problem of frequent re-partitioning due to changes in power flow information.

[0158] This invention merges the first partition based on an improved modularity index, so that each connected region in the first partition is merged according to the tightness of its internal coupling. This has clear physical meaning and low time complexity. While reducing the amount of computation, it avoids the problem of frequent re-partitioning caused by changes in power flow information by considering the tightness of internal coupling.

[0159] Please refer to Figure 5 This is a schematic diagram of an embodiment of the reactive voltage partitioning device considering wind power output provided by the present invention, which mainly includes: a first model establishment module 501, a second model establishment module 502, a matrix solving module 503, and a voltage partitioning module 504.

[0160] In this embodiment, the first model building module 501 is used to fit a first Gaussian mixture model of wind power reactive power output based on historical wind turbine data and a preset time period.

[0161] The second model building module 502 is used to build a second Gaussian mixture model of the wind turbine node voltage based on the reactive power linear power flow equation and the first Gaussian mixture model.

[0162] In this embodiment, the second model establishment module 502 includes: a first model establishment unit, an equation establishment unit, and a second model establishment unit; the first model establishment unit is used to establish a reactive power linear power flow model based on the AC power flow equation, and to obtain the reactive power injected into the bus of the reactive power linear power flow model; the equation establishment unit is used to establish a reactive power linear power flow equation based on the reactive power; the second model establishment unit is used to simplify the reactive power linear power flow equation into a linear mapping, and to obtain a second Gaussian mixture model corresponding to the wind turbine node voltage based on the linear mapping and the first Gaussian mixture model.

[0163] The matrix solving module 503 is used to calculate the first distance between the second Gaussian mixture models and to obtain the Laplacian matrix based on the first distance.

[0164] In this embodiment, the matrix solving module 503 includes: a first distance establishment unit, a second distance establishment unit, a second model establishment unit, and a matrix extraction unit; the first distance establishment unit is used to define a second distance between Gaussian components in the second Gaussian mixture model based on the Wasserstein distance; the second distance establishment unit is used to establish the first distance based on the second distance using a geometrically weighted average; the second model establishment unit is used to establish an undirected weighted graph model based on the power system's buses and transmission lines; and the matrix extraction unit is used to extract the Laplacian matrix corresponding to the undirected weighted graph model based on the first distance.

[0165] The voltage partitioning module 504 is used to establish an improved modularity index based on the Laplace matrix, and then merge the pre-divided first partitions according to the improved modularity index to obtain the second partition.

[0166] In this embodiment, the voltage partitioning module 504 includes: a first partitioning establishment unit, an index establishment unit, and a second partitioning establishment unit; the first partitioning establishment unit is used to incorporate load nodes into corresponding wind turbine node partitions according to a splitting algorithm and a sensitivity matrix to form the first partition; wherein, the corresponding wind turbine node partition is the wind turbine node partition with the highest sensitivity corresponding to the load node; the index establishment unit is used to establish an improved modularity index for the first partition according to the Laplace matrix; the second partitioning establishment unit is used to merge each connected region in the first partition according to the improved modularity index to obtain the second partition.

[0167] This invention fits the reactive power output of wind power using a first Gaussian mixture model, which takes into account the randomness of reactive power output and avoids considering only a single power flow scenario. In addition, by utilizing the linear transformation invariance of the Gaussian mixture model, solving the linear power flow equations yields a second Gaussian mixture model representing the wind turbine node voltage. A Laplace matrix is ​​established by combining the distance between the Gaussian models. This calculation method involves only one power flow calculation, reducing the computational load while maintaining accuracy. An improved modularity index is used for region merging, taking into account the tightness of coupling within the region, thus avoiding the problem of frequent re-partitioning due to changes in power flow information.

[0168] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention for those skilled in the art.

Claims

1. A reactive voltage partitioning method considering wind power output, characterized in that, include: Based on historical wind turbine data and a preset time period, a first Gaussian mixture model for wind power reactive power output is fitted. Based on the reactive power linear power flow equation and the first Gaussian mixture model, a second Gaussian mixture model of wind turbine node voltage is established. Calculate the first distance between the second Gaussian mixture models, and obtain the Laplacian matrix based on the first distance; Based on the Laplace matrix, an improved modularity index is established, and then based on the improved modularity index, the pre-divided first partition is merged to obtain the second partition; Specifically, the establishment of a second Gaussian mixture model for wind turbine node voltage based on the reactive power linear power flow equation and the first Gaussian mixture model is as follows: Based on the AC power flow equation, a reactive linear power flow model is established, and the reactive power injected into the bus of the reactive linear power flow model is calculated. Based on the stated reactive power, establish the reactive linear power flow equation; The reactive power linear power flow equation is simplified into a linear mapping, and a second Gaussian mixture model corresponding to the wind turbine node voltage is obtained based on the linear mapping and the first Gaussian mixture model. The calculation of the first distance between the second Gaussian mixture models, and the determination of the Laplacian matrix based on the first distance, specifically involves: Based on the Wasserstein distance, a second distance is defined between the Gaussian components in the second Gaussian mixture model; Based on the second distance, the first distance is established using a geometrically weighted average. Based on the power system's busbars and transmission lines, establish an undirected weighted graph model; Based on the first distance, the Laplacian matrix corresponding to the undirected weighted graph model is obtained; The expression for the improved modularity index is: ； in, Elements of the Laplace matrix; function On the side The value is 1 when directly connected, otherwise it is 0.

2. The reactive voltage zoning method considering wind power output as described in claim 1, characterized in that, The expression for the reactive power is: ； ； ； ； in, busbar Injected reactive power, Let be the imaginary part of the system admittance matrix. Let be the real part of the system admittance matrix. and They represent the busbars respectively. and busbar The susceptance and conductance of the series branches in the lumped parameter model of the corresponding line; and Representing nodes respectively The susceptance and conductance of parallel branches in the lumped parameter model of the corresponding line.

3. The reactive voltage zoning method considering wind power output as described in claim 1, characterized in that, The step of obtaining the Laplacian matrix corresponding to the undirected weighted graph model based on the first distance is specifically as follows: Based on the first distance, the edge weights in the undirected weighted graph model are calculated, and based on the edge weights, the Laplacian matrix corresponding to the undirected weighted graph model is obtained; wherein, the expression for the elements of the Laplacian matrix is: ； in, Edge weights; function On the side The value is 1 when directly connected, otherwise it is 0.

4. The reactive voltage zoning method considering wind power output as described in claim 1, characterized in that, The process involves establishing an improved modularity index based on the Laplace matrix, and then merging the pre-divided first partitions according to the improved modularity index to obtain the second partition. Specifically: Based on the splitting algorithm and sensitivity matrix, load nodes are incorporated into corresponding wind turbine node partitions to form the first partition; wherein, the corresponding wind turbine node partition is the wind turbine node partition with the highest sensitivity corresponding to the load node; Based on the Laplace matrix, an improved modularity index for the first partition is established; Based on the improved modularity index, the connected regions in the first partition are merged to obtain the second partition.

5. The method of claim 4, wherein the reactive voltage partitioning method considers wind power output. The step of merging connected regions in the first partition according to the improved modularity index to obtain the second partition is as follows: Based on the improved modularity index, the connected regions with the maximum improved modularity in the first partition are merged sequentially. Find the partition with the highest degree of improvement, and determine the second partition based on the partition location.

6. The reactive voltage zoning method considering wind power output as described in any one of claims 1-5, characterized in that, The expression for the first Gaussian mixture model is: ； ； ； in, Let be the probability density function of the first Gaussian mixture model. , The probability generated by the Gaussian distribution. The mean, Standard deviation , It contributes reactive power to wind power.

7. A reactive voltage partitioning device that takes into account wind power output, characterized by include: The module consists of a first model establishment module, a second model establishment module, a matrix solving module, and a voltage partitioning module. The first model building module is used to fit a first Gaussian mixture model of wind power reactive power output based on historical wind turbine data and a preset time period. The second model building module is used to build a second Gaussian mixture model of the wind turbine node voltage based on the reactive power linear power flow equation and the first Gaussian mixture model. The matrix solving module is used to calculate the first distance between the second Gaussian mixture models and to obtain the Laplacian matrix based on the first distance. The voltage partitioning module is used to establish an improved modularity index based on the Laplace matrix, and then merge the pre-divided first partitions according to the improved modularity index to obtain the second partition. The second model building module includes: a first model building unit, an equation building unit, and a second model building unit; the first model building unit is used to build a reactive power linear power flow model based on the AC power flow equation and to obtain the reactive power injected into the bus of the reactive power linear power flow model; the equation building unit is used to build a reactive power linear power flow equation based on the reactive power; the second model building unit is used to simplify the reactive power linear power flow equation into a linear mapping and to obtain a second Gaussian mixture model corresponding to the wind turbine node voltage based on the linear mapping and the first Gaussian mixture model. The matrix solving module includes: a first distance establishment unit, a second distance establishment unit, a second model establishment unit, and a matrix extraction unit; the first distance establishment unit is used to define a second distance between Gaussian components in the second Gaussian mixture model based on the Wasserstein distance; the second distance establishment unit is used to establish the first distance based on the second distance using a geometrically weighted average; the second model establishment unit is used to establish an undirected weighted graph model based on the power system's buses and transmission lines; the matrix extraction unit is used to extract the Laplacian matrix corresponding to the undirected weighted graph model based on the first distance. The expression for the improved modularity index is: ； in, Elements of the Laplace matrix; function On the side The value is 1 when directly connected, otherwise it is 0.

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