A centralized / distributed phase modifier hybrid site selection and capacity optimization configuration method

Abstract

The present application relates to the technical field of reactive power compensation configuration of new energy direct current sending system, and discloses a centralized / distributed phase modifier hybrid site selection and capacity optimization configuration method, which performs electrical partitioning on the sending end power grid based on an improved K-means clustering algorithm, and ensures the partitioning topological connectivity through an adjacency matrix constraint; a transient voltage rise severity index is constructed to quantify the overvoltage level of each node, and a quantile method and a quartile distance are introduced to establish a partitioning two-dimensional risk grade evaluation system; differentiated hybrid site selection configuration is performed based on the partitioning risk grade; a linear response coefficient Pi is defined to perform distributed phase modifier basic capacity configuration, and a successive linear programming method is introduced to iteratively correct the capacity to approximate the optimal solution under nonlinear constraints. The present application realizes scientific hybrid site selection and accurate capacity determination of the phase modifier, effectively suppresses the transient overvoltage of the sending end power grid, and improves the system voltage stability.

Description

Technical Field

[0001] This invention relates to the field of reactive power compensation configuration technology for DC transmission systems containing new energy sources, and in particular to a method for hybrid site selection and capacity optimization configuration of centralized / distributed synchronous condensers. Background Technology

[0003] In ultra-high voltage direct current (UHVDC) transmission systems with a high proportion of wind power, the sending-end power grid exhibits typical characteristics of high-proportion power electronics. The installed capacity of wind power continues to climb, with wind power penetration exceeding 30% in some regions. Traditional spinning reserve capacity, such as synchronous generators, is relatively insufficient, and system inertia and short-circuit capacity have significantly decreased. Against this backdrop, the safe and stable operation of the sending-end power grid faces severe challenges. In particular, when the UHVDC transmission system experiences commutation failures, DC blocking, or other faults, the sending-end AC system will be subjected to enormous transient reactive power surges, leading to serious transient overvoltage problems. This could result in large-scale disconnection of wind turbines from the grid, or even grid collapse. Therefore, effectively suppressing transient overvoltages in the sending-end power grid with a high proportion of wind power has become a core engineering problem for ensuring the safe and stable operation of the UHVDC transmission system.

[0004] Currently, the reactive power compensation devices widely used in engineering mainly include Static Var Compensators (SVCs), Static Synchronous Compensators (STATCOMs), and Synchronous Condensers. Among them, Synchronous Condensers, as a rotating reactive power compensation device, have significant advantages such as fast response speed, strong reactive power output capacity, and low coupling with the power grid, making them particularly suitable for rapid suppression of transient overvoltages. However, centralized synchronous condensers have a large single-unit capacity (usually 300 Mvar), which, while providing strong voltage support at the regional power grid level, is difficult to meet the dynamic reactive power demands of local renewable energy power plants. Distributed synchronous condensers have a smaller capacity (usually 20 Mvar to 100 Mvar) and can be deployed near wind farm step-up substations for rapid on-site compensation, but the compensation capacity of a single power plant is limited. Therefore, how to rationally configure centralized and distributed synchronous condensers in the sending-end power grid to achieve complementary advantages has become a key technical direction for optimizing the reactive power compensation configuration of power grids with a high proportion of renewable energy.

[0005] Although synchronous condensers have significant technical advantages in transient voltage support, existing synchronous condenser configuration methods still have the following technical problems:

[0006] First, the lack of a systematic zoning strategy fails to reflect the differentiated electrical characteristics of regional power grids. Traditional synchronous condenser (SCDC) configuration methods typically rely on engineering experience or simple voltage sensitivity analysis for site selection, ignoring the differences in electrical characteristics across different regions of the sending-end power grid. In actual power grids, there are significant differences in renewable energy penetration rates, grid structure strength, and electrical distances from DC converter stations across different regions, resulting in drastically different requirements for SCDC configuration. Adopting a uniform configuration strategy would inevitably lead to an imbalance where some regions are overcompensated while others are undercompensated. Although some studies have attempted to use clustering algorithms such as K-means to partition the power grid, traditional clustering algorithms only divide samples based on features such as electrical distance, failing to guarantee the connectivity of the partitioning results in the topological structure, thus resulting in partitioning results that do not meet the actual operational needs of the power grid.

[0007] Second, the lack of precise quantification methods for the severity of transient overvoltages makes it difficult to identify true weak points. The severity of transient overvoltages depends not only on the magnitude of the voltage amplitude but also on the duration of the voltage exceeding the limit. Existing methods often use voltage amplitude as the sole criterion, ignoring the duration dimension and failing to comprehensively reflect the true degree of disturbance to each node under fault conditions. Furthermore, the severity of transient voltage rises at each node exhibits certain distribution characteristics within a partition. How to scientifically assess the overall trend and dispersion of transient voltage rise severity within a partition, and thus identify abnormally weak nodes within the partition, is a pressing technical challenge that needs to be addressed.

[0008] Third, the hybrid site selection of centralized and distributed synchronous condensers lacks a scientific basis for decision-making. Centralized and distributed synchronous condensers differ fundamentally in terms of capacity, response characteristics, and economics, and their applicable scenarios and configuration principles differ. Existing methods often configure them in isolation, failing to form an organic and coordinated configuration strategy. There is currently no mature technical solution for developing differentiated hybrid configuration schemes for centralized / distributed synchronous condensers based on zonal quantitative assessments and for zones with different risk levels.

[0009] Fourth, there is a lack of efficient and accurate optimization methods for the capacity configuration of distributed synchronous condensers. While the compensation effect of distributed synchronous condensers is positively correlated with their configured capacity, it is difficult to establish an analytical relationship between the capacity of the synchronous condensers and the severity of node transient voltage rise. This is mainly because transient overvoltages are significantly nonlinear, influenced by multiple factors such as the system grid structure, fault disturbance intensity, and the dynamic reactive power response of the synchronous condensers. Using only linear approximations for capacity configuration will result in large calculation errors, leading to undercompensation or overcompensation. Directly employing nonlinear optimization or time-domain simulation iteration faces problems of high computational load and low solution efficiency, making it difficult to meet the needs of engineering applications.

[0010] Therefore, those skilled in the art urgently need a complete technical solution based on improved K-means clustering partitioning, quantitative assessment of partition risk levels, differentiated mixed site selection, and hierarchical capacity optimization configuration. Summary of the Invention

[0011] The core technical problem addressed by this invention is: how to achieve a scientific and systematic hybrid site selection and capacity optimization configuration of centralized and distributed synchronous condensers in scenarios where a high proportion of wind power is transmitted via ultra-high voltage direct current (UHVDC) to effectively suppress transient overvoltages in the sending-end power grid and ensure the safe and stable operation of the DC transmission system.

[0012] For those skilled in the art, solving the aforementioned core technical problems has the following significance:

[0014] Transient overvoltage suppression is a rigid requirement to ensure the safe and stable operation of the power system. Once a large-scale grid disconnection accident of wind turbine units caused by transient overvoltage occurs, it may lead to a chain reaction, causing widespread power outages and economic losses.

[0015] To address the aforementioned core technical problems, this invention designs a centralized / distributed synchronous condenser hybrid location and capacity optimization configuration method. Its purpose is to establish a systematic methodology for synchronous condenser optimization configuration, overcoming the technical bottlenecks of traditional methods in areas such as zoning strategies, weak link identification, hybrid location decision-making, and precise capacity configuration. This provides precise and flexible technical support for voltage stability control in power grids with a high proportion of renewable energy transmission. Simultaneously, it achieves the following technical objectives:

[0016] (1) Realize differentiated zoning management of the sending-end power grid, so that the configuration of synchronous condensers can be accurately matched with the actual needs of each region;

[0017] (2) Establish a multi-dimensional quantitative evaluation system for transient overvoltages to accurately identify weak points in the system;

[0018] (3) Achieve coordinated and optimized configuration of centralized and distributed synchronous condensers to give full play to the complementary advantages of the two types of equipment;

[0019] (4) Establish an efficient capacity optimization model to significantly reduce the solution complexity while ensuring calculation accuracy, so as to meet the needs of practical engineering applications.

[0020] It should be noted that the technical solution of this invention is mainly applied to the planning, design and operation optimization of high-proportion wind power transmission systems via UHVDC. Through a systematic zoning strategy, accurate identification of weak links, scientific multi-type synchronous condenser collaborative site selection and efficient capacity optimization algorithm, it fundamentally solves the problem of transient overvoltage suppression in the sending-end power grid.

[0021] To achieve the above objectives, the specific technical solution of the present invention is a method for hybrid site selection and capacity optimization configuration of centralized / distributed synchronous condensers, the method comprising the following steps:

[0022] Step 1: Based on PSACD / EMTDC, establish a simulation model of a high-proportion wind power transmission system via ±800kV UHVDC to analyze the transient characteristics of the UHVDC transmission system under DC faults.

[0023] Step 2: Use the power flow correction equations of the power system to obtain the electrical distance matrix of the sending-end grid nodes;

[0024] Step 3: Introduce the system structure adjacency matrix to obtain the improved K-means clustering algorithm. Combined with the elbow rule, cluster and partition each node of the sending-end power grid to ensure that the partitioning results are coupled in electrical characteristics and connected in topology.

[0025] Step four: Introduce a transient pressure rise severity index to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and magnitude.

[0026] Step 5: Introduce the quantile method to reflect the overall trend and dispersion of the severity of transient pressure rise in nodes within the partition, establish a method for quantifying the risk level of the partition, and complete the hybrid site selection configuration of distributed / centralized synchronous condensers in the sending-end system based on the quantification results.

[0027] Step 6: Based on the quantization results of each partition, distributed synchronous condensers are preferentially configured on nodes with higher transient voltage rise severity indicators, while centralized synchronous condensers are configured on nodes with the largest sensitivity matrix columns and norms within the partition.

[0028] Step 7: To reduce computational load and improve solution speed, define the linear response coefficient Pi of the nodes and configure the basic capacity of the distributed synchronous condenser.

[0029] Step 8: Introduce the successive linear programming method to iteratively correct the distributed synchronous condenser configuration capacity of each node, gradually approximating the capacity configuration scheme under actual nonlinear constraints.

[0030] Preferably, the process of obtaining the electrical distance matrix of the sending-end power grid nodes in step two includes:

[0031] Power flow correction equations for power systems based on the Newton-Raphson method:

[0032]

[0033] ;

[0034] ;

[0035] In the formula, For Jacobian matrices, , , , These are the block elements of the Jacobian matrix. , These are the active and reactive power disturbances injected into the nodes, respectively. , This refers to the deviation of the node voltage phase angle and amplitude.

[0036] set up We can obtain: In the formula This is the reactive power-voltage sensitivity matrix;

[0037] Define nodes With nodes Electrical distance index The electrical distance matrix is ​​symmetric and normalized so that all elements are located in the interval [0,1]. The larger the element value, the closer the electrical distance between nodes.

[0038] Preferably, the process of improving the K-means clustering algorithm in step three includes:

[0039] Define the adjacency matrix based on the network topology. ,but If the nodes in the system With nodes If there are coupled branches, then =1, otherwise =0;

[0040] In each node assignment in K-means clustering, the node is only allowed to be assigned to a cluster with a connection path based on the adjacency matrix, and the cluster with the closest electrical distance is selected as the node to belong to.

[0041] Repeatedly assign and update the center until convergence, and perform topological connectivity verification on the partitioning results;

[0042] The objective function of K-means clustering is to minimize the sum of squared errors within clusters.

[0043]

[0044] In the formula, For nodes eigenvectors, For the first The center of each cluster.

[0045] Preferably, the transient pressure rise severity index in step four is calculated in the following way:

[0046] node In the fault Local transient pressure rise severity index for:

[0047]

[0048] In the formula, This is the effective value of the system voltage. For the rated voltage, [ , These are overvoltage binary meters, This refers to the number of overvoltage binary meters. This is the overvoltage threshold value. The duration of the overvoltage. and They are respectively The time above and below the threshold voltage;

[0049] Multiple fault nodes Comprehensive transient pressure rise severity index for:

[0050]

[0051] In the formula, Fault The weighting coefficients.

[0052] Preferably, the method for quantifying the risk level of a region in step five includes:

[0053] The comprehensive transient pressure rise severity index of each node Sort in ascending order and calculate the upper tertiary value. and lower thirds ;

[0054] If the comprehensive transient pressure rise severity index of more than half of the nodes in the partition is... Less than or equal to This zone is defined as a low-risk zone for transient pressure rise.

[0055] If a partition has more than half of its nodes Greater than or equal to This zone is defined as a risk zone for increased transient pressure.

[0056] The remaining area is defined as the medium-risk area for transient pressure rise;

[0057] If the proportion of partition nodes is the same in both risk zones, the partition is divided according to the principle of the most unfavorable system operation, and the partition is assigned to the relatively higher risk level.

[0058] Introducing the interquartile range, then the first... The interquartile range of nodes within each partition is:

[0059]

[0060] Assess the severity of the comprehensive transient pressure rise at nodes within the assessment zone. The degree of dispersion, where, For partitioning The upper quartile of the internal node, For partitioning The lower quartile of an internal node;

[0061] Calculate the lower third of the interquartile range for all partitions. and the third place ;

[0062] If the interquartile range of the partition is greater than or equal to If so, the partition is considered to be in the discrete region of transient pressure increase;

[0063] If the interquartile range of the partition is less than or equal to If the condition is met, the partition is considered to be in the low discrete region of transient pressure rise; otherwise, it is in the medium discrete region of transient pressure rise.

[0064] A two-dimensional assessment system is formed by cross-combining the overall transient pressure rise risk level of a zone with the discrete characteristics of transient pressure rise within the zone.

[0065] Preferably, the columns and norm of the sensitivity matrix in step six are calculated in the following manner:

[0066] Regarding the first Let there be partitions, and let their node sets be... Extracting sub-sensitivity matrices from the system reactive-voltage sensitivity matrix R :

[0067]

[0068] node The corresponding number The column and norm of the column are:

[0069]

[0070] The column and norm are used to characterize the total response of each node to voltage changes of all nodes in the partition, so as to quantify the global reactive power-voltage support capability of each node. The node with the largest column and norm is used as the centralized synchronous condenser configuration node.

[0071] Preferably, the linear response coefficient in step seven... Defined in the following way:

[0072]

[0073] In the formula, For nodes Configure transient voltage rise severity indicators before distributing synchronous condensers. For nodes Severity index of transient voltage rise after configuring distributed synchronous condensers. This is the baseline capacity for distributed synchronous condensers;

[0074] The linear response coefficient The physical meaning is the change in the severity index of transient voltage rise of a node after a distributed synchronous condenser with a unit capacity of 1 Mvar is connected;

[0075] In the basic capacity configuration, the overvoltage suppression effect of the camera is linearly additive, when the node... Configure distributed synchronous condensers with a total capacity of At that time, the severity index of the transient pressure rise at the node is approximately: .

[0076] Preferably, the basic capacity configuration in step seven satisfies the following constraints:

[0077] node Transient pressure rise severity index constraint: ,in This serves as a reference value for the severity of transient pressure rise. = 1;

[0078] partition internal nodes Constraints on the number of distributed synchronous condensers: ,and Round up to the nearest positive integer.

[0079] node The basic configuration capacity is the minimum that satisfies the above constraints. value:

[0080] .

[0081] Preferably, the capacity iteration correction process in step eight includes:

[0082] The basic capacity configuration result is used as the starting point for iterative correction. ;

[0083] In the Next iteration point At, for nodes Severity index of transient pressure rise Using a first-order Taylor expansion:

[0084]

[0085] In the formula, For the first Node at the next iteration Capacity changes affect nodes Sensitivity of transient pressure rise severity indicators This represents the total number of nodes that require capacity adjustment.

[0086] No. The capacity-corrected linear programming subproblem for the next iteration is:

[0087]

[0088]

[0089]

[0090] In the formula, The additional capacity required for the nodes, This is the upper limit for capacity increment;

[0091] The interior-point method is used to solve the above linear programming subproblem. The capacity increment obtained in the next iteration is: The updated capacity is: ;

[0092] Updated capacity The transient pressure rise severity index for each node will be recalculated. If a node meets the set conditions... If the configuration is correct, then this capacity scheme will be used as the final capacity configuration result; otherwise, the updated capacity will be used. The above process is repeated as the initial capacity for a new iteration.

[0093] Preferably, the DC fault includes commutation failure fault and DC blockage fault, and the transient characteristic analysis includes the transient overvoltage amplitude, duration and voltage response curve of the sending-end AC system.

[0094] Preferably, the quantiles in step five are calculated using the following linear interpolation method:

[0095] After sorting the samples in ascending order, the quantile positions ,in The percentage of quantiles. The total number of samples;

[0096] Will Decompose into integer parts With the decimal part quantile values ,in and They are respectively the sorted numbers The and the first Each sample value.

[0097] Preferably, the two-dimensional evaluation system forms configuration decisions through the following rules:

[0098] For zones with high risk of transient voltage spikes and high dispersion: Configure multiple centralized synchronous condensers at the electrical center nodes with the largest column and norm within the zone;

[0099] For partitions with low-risk and highly discrete transient voltage rise: Configure distributed synchronous condensers on the extreme outlier nodes with the highest transient voltage rise severity index within the partition;

[0100] For zones with medium-risk and discrete transient voltage rise: a hybrid configuration strategy is adopted, with centralized synchronous condensers configured at the zone's electrical center node, and distributed synchronous condensers configured at wind power nodes with higher transient voltage rise severity indicators.

[0101] Transient voltage rise is low-risk and low-dispersion partitioning: no need to configure a synchronous condenser.

[0102] Preferably, the upper limit of the capacity increment This constraint is set to prevent the linear approximation from failing. Its value is a predetermined percentage of the capacity of the current iteration point, used to ensure that the step size of each iteration is within the effective range of the local linear approximation.

[0103] Preferably, the method further includes a step of performing an engineering rounding process on the capacity correction result: when the capacity increment after iteration converges When the value is greater than zero, the number of additional distributed synchronous condensers will be taken as... ,in It is a rounding function. This is the baseline capacity of a single distributed synchronous condenser.

[0104] Preferably, the overvoltage binary meter It includes multiple sets of threshold voltages and corresponding maximum duration combinations, used to comprehensively quantify the severity of transient overvoltage from both duration and amplitude dimensions.

[0105] Preferably, the formula for symmetric processing of the electrical distance matrix is: ,in These are the elements of the symmetric electrical distance matrix; the formula for standardizing the electrical distance matrix is: ,in This is the per-unit electrical distance value. Let be the maximum element value in matrix D.

[0106] Preferably, the main technical parameters of the simulation model of the high-proportion wind power transmission system via ±800kV UHVDC are: rated voltage at both ends of the system ±800kV, rated power 5000MW, rated DC current 3.125kA, rated voltage of AC system on the rectifier side 525kV, and rated voltage of AC system on the inverter side 525kV.

[0107] Preferably, the method further includes the step of analyzing the SSE elbow curve of the clustering partitioning results: when When the value increases The inflection point that tends to flatten out corresponds to the optimal number of clusters K, which is used to determine the number of partitions in K-means clustering.

[0108] Preferably, the present invention also discloses a centralized / distributed synchronous condenser hybrid site selection and capacity optimization configuration system, which includes:

[0109] The simulation modeling module is used to establish a simulation model of a high-proportion wind power transmission system via ±800kV UHVDC based on PSACD / EMTDC, and to analyze the transient characteristics of the UHVDC transmission system under DC faults.

[0110] The electrical distance calculation module is used to obtain the electrical distance matrix of the sending-end grid nodes using the power flow correction equations of the power system;

[0111] The clustering and partitioning module is used to introduce the system structure adjacency matrix to execute the improved K-means clustering algorithm, and combine the elbow rule to cluster and partition each node of the sending-end power grid, ensuring that the partitioning results are coupled in electrical characteristics and connected in topology.

[0112] The transient pressure rise assessment module is used to introduce transient pressure rise severity indicators to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and magnitude.

[0113] The partition risk quantification module is used to introduce the quantile method to assess the overall trend and dispersion of the severity of transient pressure rise at nodes within a partition, and to establish a method for quantifying partition risk levels.

[0114] The hybrid location module is used to perform differentiated location configurations for distributed and centralized synchronous condensers based on the quantization results of each partition.

[0115] The capacity configuration module is used to define the linear response coefficient Pi of the nodes for basic capacity configuration of distributed synchronous condensers, and introduces a successive linear programming method to iteratively correct the configuration capacity of each node.

[0116] Preferably, the capacity configuration module includes:

[0117] The basic capacity configuration submodule is used to calculate the minimum distributed synchronous condenser capacity required for each node to meet the threshold requirements of the transient pressure rise severity index based on the linear response coefficient Pi and the linear superposition assumption.

[0118] The sensitivity calculation submodule is used to calculate the partial derivative of the transient pressure rise severity index with respect to the camera capacity at each iteration point, and obtain the local linearization coefficient. ;

[0119] The linear programming solution submodule is used to construct and solve the linear programming subproblem with the objective of minimizing the capacity increment and the transient pressure rise severity index threshold as a constraint using the interior point method, and to determine the capacity increment for the current iteration.

[0120] The convergence judgment submodule is used to recalculate the transient pressure rise severity index of each node after updating the capacity scheme and compare it with the threshold. When all nodes to be corrected meet the threshold requirements, the iteration is terminated and the final capacity configuration scheme is output.

[0121] Preferably, the present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is capable of implementing the steps of the method.

[0122] Compared with the prior art, the technical solution disclosed in this invention has the following non-obvious technical features:

[0123] 1. This invention employs an improved K-means clustering algorithm with a topological connectivity constraint mechanism. Based on the traditional K-means clustering algorithm, this invention creatively introduces a system structure adjacency matrix. During the clustering iteration process, nodes are only allowed to be assigned to clusters with which they have a connection path, based on the adjacency matrix, and the topological connectivity of the partitioning results is verified. This technical feature overcomes the limitation of traditional K-means clustering, which only performs unconstrained partitioning based on feature space distance, ensuring that the partitioning results are coupled in terms of electrical characteristics and connected in terms of topological structure, thus solving the inherent defect that traditional clustering partitioning results do not conform to the actual operating topological constraints of the power grid.

[0124] 2. This invention constructs a two-dimensional risk level quantification system based on the quantile method; this invention creatively introduces the quantile method and interquartile range from statistics into the field of power system transient voltage safety assessment, and for the first time constructs a two-dimensional assessment system of "overall transient voltage rise risk level of a region" and "discrete characteristics of transient voltage rise within a region"; specifically, through the upper / lower quartiles ( / Determine the overall risk level of the zone (high / medium / low risk zone) by using the ternary digits of the interquartile range (...). / The degree of dispersion within a partition (high / medium / low dispersion zone) is determined, and the two are cross-combined to form a nine-square grid evaluation matrix; this two-dimensional quantification mechanism has not been disclosed or inspired by any existing technology;

[0125] 3. This invention adopts a differentiated hybrid location strategy based on the risk level of each zone. This invention proposes an innovative differentiated hybrid location strategy: in zones with high transient voltage rise risk and high dispersion, centralized synchronous condensers are configured on multiple electrical center nodes with the largest column and norm; in low-risk, high-dispersion zones, distributed synchronous condensers are configured for extreme outlier nodes; in medium-risk, medium-dispersion zones, a hybrid centralized and distributed configuration strategy is adopted. The core technical feature of this strategy is that the location decision depends not only on a single indicator, but also on a comprehensive judgment based on the overall risk level and internal dispersion characteristics of the zone, achieving refined configuration of "zone-specific policy, one policy per zone," which is fundamentally different from the "one-size-fits-all" configuration method in existing technologies.

[0126] 4. This invention defines a linear response coefficient and applies it in capacity configuration; this invention defines the linear response coefficient Pi of a node, whose physical meaning is the change in the severity index of transient voltage rise of the node after connecting a distributed synchronous condenser with a unit capacity (1Mvar); the definition of this coefficient adopts a local linearization approximation strategy, which transforms the complex nonlinear coupling problem into a linear representation in a local range, providing a mathematical basis for the subsequent rapid configuration of basic capacity; the definition method and application scenario of this coefficient are not recorded in the prior art;

[0127] 5. This invention constructs a hierarchical capacity optimization architecture based on successive linear programming. This invention creatively constructs a hierarchical optimization architecture of "basic capacity configuration + iterative capacity correction": the first layer performs rapid basic capacity configuration based on linear response coefficients to obtain an initial feasible solution; the second layer introduces the successive linear programming method, performing a first-order Taylor expansion on the transient pressure rise severity index at each iteration point, gradually linearizing the nonlinear constraints, and approximating the optimal capacity configuration scheme under the true nonlinear constraints through multiple iterations; in this hierarchical architecture, the construction method of the linear programming subproblem (including the upper limit constraint of capacity increment to prevent linear approximation failure), the design of the iterative convergence criterion, and the engineering processing strategy of rounding up the final capacity constitute a complete and non-obvious capacity optimization methodology.

[0128] Compared with the prior art, the present invention has the following beneficial effects:

[0129] 1. This invention ensures the rationality and connectivity of partitioning: By introducing an adjacency matrix to improve the K-means clustering algorithm, this invention overcomes the technical defect that the partitioning results of traditional clustering may not be connected, ensuring that the partitioning results reflect both electrical coupling characteristics and meet the topological connectivity requirements, thus laying a partitioning foundation that meets the actual operation requirements of the power grid for subsequent differentiated configuration;

[0130] 2. This invention achieves accurate identification of weak links: By constructing a transient voltage rise severity index, this invention comprehensively quantifies the degree of transient overvoltage disturbance of each node from two dimensions: duration and amplitude. Combined with the quantile method, it evaluates the overall trend and dispersion of transient voltage rise severity within the partition, thereby achieving accurate identification of weak links and extreme outliers in the system and avoiding the risk of misjudgment based on a single voltage amplitude criterion.

[0131] 3. This invention ensures the scientific nature of differentiated hybrid site selection: Based on the quantification results of the two-dimensional risk level of the partition, this invention establishes a mapping relationship between "partition risk level - configuration strategy", realizing differentiated hybrid site selection configuration of centralized and distributed synchronous condensers; simulation verification shows that after the site selection scheme is configured, the transient voltage rise severity index of all nodes at the sending end is effectively suppressed, and all nodes meet the threshold requirements under commutation failure fault.

[0132] 4. This invention achieves accuracy and efficiency in capacity configuration: This invention employs a hierarchical capacity optimization model, quickly obtaining an initial scheme through basic capacity configuration, and then iteratively correcting it through successive linear programming. This effectively solves the problem of accurately characterizing the nonlinear coupling relationship between the synchronous condenser capacity and the severity of transient voltage rise. Simulation results show that after capacity iteration correction, the peak transient overvoltages of nodes 10, 11, and 23 decrease by 2.48%, 1.69%, and 2.79% respectively (compared to the basic capacity configuration), and by 4.34%, 3.94%, and 6.51% respectively compared to the configuration without capacity optimization. The transient overvoltages of each weak node are effectively suppressed, and the system voltage stability is significantly improved.

[0133] 5. This invention improves computational efficiency and engineering applicability: By defining the linear response coefficient and introducing the successive linear programming method, this invention significantly reduces the computational load of nonlinear optimization. Each node converges within 10 iterations, balancing computational accuracy and solution efficiency, and has good prospects for engineering application. Attached Figure Description

[0134] Figure 1 This is a flowchart of the method described in this invention;

[0135] Figure 2 This is the simulation model of the ±800kV ultra-high voltage direct current transmission system described in this invention;

[0136] Figure 3 This is the high-proportion wind power transmission-end power grid topology described in this invention;

[0137] Figure 4 This is the elbow rule curve described in this invention;

[0138] Figure 5This is the clustering and partitioning result of the sending-end system described in this invention;

[0139] Figure 6 This is the calculation result of the transient pressure rise severity index of all nodes at the sending end as described in this invention;

[0140] Figure 7 This is the result of the quantification of risk levels in each zone and the location selection of distributed / centralized synchronous condensers as described in this invention;

[0141] Figure 8 This is an indicator of the severity of transient voltage rise at all nodes of the sending-end system after the location scheme configuration described in this invention is applied;

[0142] Figure 9 These are the voltage response curves of each wind farm node after the site selection scheme described in this invention is configured;

[0143] Figure 10 This is the result of the basic capacity configuration described in this invention;

[0144] Figure 11 These are the voltage response curves of the nodes to be optimized before and after the basic capacity optimization configuration described in this invention.

[0145] Figure 12 This is a schematic diagram of the capacity correction iterative process based on successive linear programming as described in this invention;

[0146] Figure 13 This is the convergence curve of the transient pressure rise severity index and the bar chart of capacity increment change described in this invention;

[0147] Figure 14 This is the transient voltage response curve of the node to be corrected after capacity iteration correction as described in this invention;

[0148] Figure 15 This is a schematic diagram of the system described in this invention. Detailed Implementation

[0149] The following is in conjunction with the appendix Figures 1 to 15 The main technical features and embodiments of the present invention are described in detail below;

[0150] In the technical solution of this invention, the improved adjacency matrix constraint mechanism in the K-means clustering algorithm is based on defining the adjacency matrix according to the network topology. In K-means clustering, each time a node is assigned, the node is only allowed to be assigned to a cluster with a connected path based on the adjacency matrix, and the topological connectivity of the partitioning results is verified after the assignment is completed. This mechanism is the core guarantee to ensure that the partitioning results have practical engineering significance. Traditional clustering only considers electrical distance similarity, which may assign topologically disconnected nodes to the same partition, making the partitioning results unusable. This mechanism introduces topological connectivity constraints so that the partitioning results reflect both electrical coupling characteristics and meet the actual topology of the power grid, laying a decision-making foundation that conforms to engineering practice for subsequent differentiated configuration.

[0151] In the technical solution of this invention, the two-dimensional quantification mechanism of the transient voltage rise severity index is achieved by segmenting and normalizing the area of ​​the transient voltage response curve, combined with an overvoltage binary table. From duration ( to The severity of transient voltage rise at a node under fault conditions is calculated by comprehensively considering two dimensions: the integral length and the magnitude of the voltage rise (normalized deviation relative to the threshold voltage). And obtain comprehensive indicators through multi-fault weighting. This mechanism is the core technical means to achieve accurate identification of weak links. Traditional methods only use the peak voltage amplitude as a criterion, which cannot distinguish the essential difference between "instantaneous high voltage" and "continuous overvoltage". This mechanism, by introducing time dimension integration and binary table constraints, comprehensively describes the true degree of harm of transient overvoltage, and is the quantitative basis for achieving accurate site selection and capacity optimization.

[0152] In the technical solution of this invention, the partitioned two-dimensional risk level quantification system based on the quantile method utilizes the upper tertiary quantile. and lower thirds Determine the overall risk level of a zone (high / medium / low risk zone) using the interquartile range. and its upper / lower thirds / The system determines the degree of dispersion within a partition (high / medium / low dispersion zones), and combines these determinations to form a two-dimensional evaluation matrix. This system serves as a crucial bridge connecting partitioning results with differentiated allocation strategies. Assessing only the overall risk level of a partition can obscure the dispersion characteristics of its internal nodes (such as the existence of extreme outliers in low-risk zones), while focusing solely on outliers ignores the overall regional demand. This system, through two-dimensional evaluation, simultaneously captures both the overall level on a "surface" and the abnormal dispersion at "points," providing a scientific basis for formulating refined allocation strategies based on "partition-specific policies and one policy per region."

[0153] In the technical solution of this invention, the linear response coefficient Defined as The physical meaning of this coefficient is the change in the severity index of transient voltage rise at a node after connecting a distributed synchronous condenser with a unit capacity (1Mvar). It reflects the local linearization sensitivity of the synchronous condenser capacity to overvoltage suppression near a specific operating point. This coefficient is a core parameter for balancing computational efficiency and configuration accuracy. Transient overvoltage is affected by the nonlinear coupling of multiple factors, making it extremely difficult to directly establish an accurate analytical model. This coefficient, through a local linearization approximation strategy, transforms the complex nonlinear relationship into a linear representation near a specific operating point, enabling basic capacity configuration to be quickly completed through simple arithmetic operations. This significantly reduces computational complexity and provides a feasible technical path for engineering applications.

[0154] In the technical solution of this invention, the hierarchical capacity optimization architecture (basic configuration + successive linear programming correction) is based on the linear response coefficient in the first layer. The first layer rapidly calculates the minimum required capacity of each node as an initial feasible solution using the linear superposition assumption. The second layer performs a first-order Taylor expansion on the transient pressure rise severity index at each iteration point, constructing a linear programming subproblem with the goal of minimizing capacity increment and constraints of transient pressure rise threshold and increment upper limit. This subproblem is solved iteratively using the interior-point method, successively approximating the optimal capacity configuration under the true nonlinear constraints. This architecture is the core algorithm that ensures the accuracy of capacity configuration. Relying solely on linear approximation will inevitably lead to undercompensation or overcompensation errors, while directly using nonlinear optimization or exhaustive simulation iteration results in a huge computational burden. Our organization adopts a "coarse-to-fine" layered strategy, which not only utilizes the linear model to quickly obtain good initial values, but also approximates the true nonlinear solution within a limited number of iterations (in simulation verification, each node converges within 10 iterations) through successive linear programming, achieving the best balance between computational accuracy and solution efficiency.

[0155] In the technical solution of this invention, the sensitivity matrix column and norm addressing criterion are for the first... Extract sub-sensitivity matrix from each partition Calculate the column and norm of the corresponding column for each node.

[0156] refer to Figure 1This document illustrates a flowchart of a method for hybrid site selection and capacity optimization of centralized / distributed synchronous condensers according to one or more embodiments of this application. The method is applied to the planning, design, and operation optimization of a high-proportion wind power transmission system via ±800kV UHVDC, and includes the following steps: Step 1, establishing a simulation model based on PSACD / EMTDC and analyzing transient characteristics; Step 2, obtaining the electrical distance matrix of the sending-end grid nodes using the power system flow correction equation; Step 3, introducing the system structure adjacency matrix and executing an improved K-means clustering algorithm to cluster and partition each node of the sending-end grid; Step 4, introducing a transient voltage rise severity index to quantitatively describe the severity of transient voltage rise at each node; Step 5, introducing the quantile method to establish a quantification method for partition risk levels; Step 6, performing hybrid site selection and configuration of distributed / centralized synchronous condensers based on the quantification results of each partition; Step 7, defining the linear response coefficient Pi of the nodes for basic capacity configuration of distributed synchronous condensers; Step 8, introducing a successive linear programming method to iteratively correct the capacity configuration of distributed synchronous condensers at each node.

[0157] In one or more embodiments, step one establishes a simulation model of a high-proportion wind power transmission system via ±800kV UHVDC based on PSACD / EMTDC. Specifically, the converter valves of the rectifier station and inverter station adopt a series connection of two 12-pulse converter units per pole, and the two 12-pulse valve groups are distributed according to ±(400+400)kV. Figure 2 and Figure 3 As shown, the sending end comprises a 500kV and 220kV regional power grid, consisting of 25 nodes. Doubly fed wind farms are connected at nodes 2, 5, 10, 11, 14, and 23, respectively, all using a 50-wind-turbine aggregated multiplier equivalent model. The simulation module is configured to analyze the transient characteristics of the UHVDC transmission system under DC faults, including commutation failure faults and DC blocking faults. The transient characteristic analysis includes the transient overvoltage amplitude, duration, and voltage response curve of the sending-end AC system.

[0158] In one or more embodiments, step two configures the electrical distance calculation module to obtain the electrical distance matrix of the sending-end grid nodes using the power system power flow correction equation. Specifically, the power system power flow correction equation is first established based on the Newton-Raphson method:

[0159]

[0160] ;

[0161] ;

[0162] In the formula, For Jacobian matrices, , , , These are the block elements of the Jacobian matrix. , These are the active and reactive power disturbances injected into the nodes, respectively. , Let P be the deviation of the node voltage phase angle and amplitude. Assuming ∆P≡0, we can obtain... In the formula, R is the reactive power-voltage sensitivity matrix. The electrical distance index between node i and node j is defined. and use the formula Perform symmetry processing, then use the formula Standardize the elements so that all elements are in the interval [0,1]. The larger the element value, the closer the electrical distance between nodes.

[0163] In one or more embodiments, step three configures the clustering partitioning module to introduce a system structure adjacency matrix to execute an improved K-means clustering algorithm. Specifically, the adjacency matrix is ​​defined based on the network topology. If there is a coupled branch between node i and node j in the system, then =1, otherwise =0. The objective function of K-means clustering is to minimize the sum of squared errors within clusters:

[0164]

[0165] In the formula, For nodes eigenvectors, For the first The center of each cluster.

[0166] In K-means clustering, each time a node is assigned, the node is only allowed to be assigned to a cluster with a connected path based on the adjacency matrix, and then the cluster with the closest electrical distance is selected. For the Cluster From the adjacency matrix Extract the corresponding submatrix If a submatrix contains node subgraphs with only one topologically connected component, then the nodes within that cluster are topologically connected. Repeated assignment and center updates continue until convergence, and topological connectivity is verified on the partitioning results. The elbow rule is used to assist in obtaining the optimal number of clusters, such as... Figure 4 As shown, when The inflection point where SSE tends to level off as the value increases corresponds to the optimal number of clusters. Values, partitioning results are as follows Figure 5 As shown.

[0167] In one or more embodiments, step four describes a transient pressure rise assessment module that introduces a transient pressure rise severity index to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and amplitude. Node In the fault Local transient pressure rise severity index for:

[0168]

[0169] In the formula, This is the effective value of the system voltage. For the rated voltage, [ , These are overvoltage binary meters, This refers to the number of overvoltage binary meters. This is the overvoltage threshold value. The duration of the overvoltage. and They are respectively Time above and below threshold voltage; nodes under multiple faults Comprehensive transient pressure rise severity index In the formula Fault The weighting coefficients. For example... Figure 6 As shown, the calculation results of the transient pressure rise severity index for all 25 nodes at the sending end are presented.

[0170] In one or more embodiments, step five configures the partition risk quantification module to introduce the quantile method to reflect the overall trend and dispersion of transient pressure rise severity of nodes within a partition, establishing a partition risk level quantification method. The comprehensive transient pressure rise severity index Λi of each node is arranged in ascending order, and the quantile position is determined. ,in The percentage of quantiles. The total number of samples; Decompose into integer parts With the decimal part quantile values Calculate the upper third. and lower thirds If more than half of the nodes in the partition... Less than or equal to Define the partition as a low-risk zone for transient pressure rise; if more than half of the nodes in a partition... Greater than or equal to The partition is defined as the high-risk area of ​​transient pressure rise; the remaining area is defined as the medium-risk area of ​​transient pressure rise; if the number of nodes in the partition is equal in both risk areas, the partition is divided according to the principle of the most unfavorable system operation, and the partition is assigned to the relatively higher risk level.

[0171] Simultaneously, the interquartile range is introduced to evaluate the dispersion of nodes within a partition; The interquartile range of nodes within each partition is ,in For partitioning The upper quartile of the internal node, For partitioning The lower quartile of the internal node. Calculate the lower quartile of the interquartile range for all partitions. and the third place If the interquartile range of the partition is greater than or equal to If the interquartile range of the partition is less than or equal to 1, then the partition is considered to be in the transient pressure rise discrete region; if the interquartile range of the partition is less than or equal to 1, then the partition is considered to be in the transient pressure rise discrete region. If the transient pressure rise risk level is within a certain range, the partition is considered to be in the low-discrete transient pressure rise region; otherwise, it is in the medium-discrete transient pressure rise region. A two-dimensional assessment system is formed by cross-combining the overall transient pressure rise risk level of the partition with the discrete characteristics of transient pressure rise within the partition.

[0172] In one or more embodiments, step six configures the hybrid addressing module to perform differentiated addressing configurations for distributed and centralized synchronous condensers based on the quantization results of each partition. For the k-th partition, let its node set be... From the system reactive power-voltage sensitivity matrix Extracting the sub-sensitivity matrix :

[0173]

[0174] node The corresponding number The column and norm of the column are The column and norm are used to characterize the total response of each node to voltage changes across all nodes within a partition, thus quantifying each node's global reactive power-voltage support capability. Distributed synchronous condensers are preferentially configured on nodes with higher transient voltage rise severity indicators, while centralized synchronous condensers are configured on nodes with the largest column and norm within a partition.

[0175] In one or more embodiments, such as Figure 7As shown, the two-dimensional evaluation system forms configuration decisions based on the following rules: For partitions with high transient voltage rise risk and high dispersion (partition 1), multiple centralized synchronous condensers are configured at the electrical center nodes with the largest column and norm within the partition (nodes 2 and 4); for partitions with low transient voltage rise risk and high dispersion (partition 5), distributed synchronous condensers are configured at the extreme outlier nodes with the highest transient voltage rise severity index within the partition (node ​​23); for partitions with medium transient voltage rise risk and medium dispersion (partition 3), a hybrid configuration strategy is adopted, configuring centralized synchronous condensers at the electrical center nodes of the partition (node ​​21) and distributed synchronous condensers at wind power nodes with high transient voltage rise severity index (node ​​14); for partitions with low transient voltage rise risk and low dispersion (partition 4), no synchronous condensers are required. Figure 8 As shown, the severity of transient pressure rise at all 25 nodes of the feed-in system was effectively suppressed after the site selection scheme was configured; as Figure 9 As shown, the voltage response curves of each wind farm node under commutation failure and DC blocking faults indicate that the transient overvoltage is significantly reduced.

[0176] In one or more embodiments, step seven configures the basic capacity configuration submodule to define the linear response coefficient Pi of the node for distributed synchronous condenser basic capacity configuration. Linear response coefficient Defined in the following way:

[0177]

[0178] In the formula, For nodes Configure transient voltage rise severity indicators before distributing synchronous condensers. For nodes Severity index of transient voltage rise after configuring distributed synchronous condensers. The baseline capacity for distributed synchronous condensers is 50 Mvar per unit. Linear response coefficient. The physical meaning of is the change in the node transient voltage rise severity index after connecting a distributed synchronous condenser with a capacity of 1Mvar. In the basic capacity configuration, assuming that the overvoltage suppression effect of the synchronous condenser can be linearly additive, when the total capacity of the distributed synchronous condenser configured at node i is Si, the node transient voltage rise severity index is approximately: .

[0179] In one or more embodiments, the node The transient pressure rise severity index constraint is: ,in This serves as a reference value for the severity of transient pressure rise. = 1. Partition internal nodes Constraints on the number of distributed synchronous condensers: ,and Round up to the nearest positive integer. Node The basic configuration capacity is the minimum that satisfies the above constraints. value: .like Figure 10 As shown, the basic capacity configuration results for nodes 10, 11, and 23 are illustrated; Figure 11 As shown, the voltage response curves of the nodes to be optimized are displayed before and after the basic capacity optimization configuration.

[0180] In one or more embodiments, the process of obtaining the electrical distance matrix of the sending-end grid nodes in step two further includes: after establishing the power flow correction equations of the power system based on the Newton-Raphson method, first verifying the Jacobian matrix. The nonsingularity of, if If the matrix is ​​singular, it is recalculated using the damped Newton method; then the reactive power-voltage sensitivity matrix R is extracted from the modified equation; finally, the electrical distance matrix is ​​symmetricized and normalized.

[0181] In one or more embodiments, the improved K-means clustering algorithm in step three further includes: in response to the fact that there are connection paths between the target node and multiple candidate clusters during the clustering assignment process, selecting the cluster with the closest electrical distance to belong to; in response to the fact that there are no connection paths between the target node and any candidate cluster, temporarily marking the node as an isolated node; after all non-isolated nodes are assigned, using a depth-first search algorithm to connect the isolated node to the neighboring cluster with the shortest path; and performing graph connectivity verification on each cluster of the final partitioning result. If the node subgraph contained in the submatrix Ak has only one connected component in the topology, then it is confirmed that the nodes inside the cluster are topologically connected.

[0182] In one or more embodiments, the partition risk level quantification method in step five further includes: responding to the partition within... Less than or equal to The number of nodes and Greater than or equal to If the number of nodes is the same, the partition is classified into a relatively higher risk level based on the principle of least adverse system operation; and in response to the fact that the interquartile range of all partitions is located at... and Between these, the one with the closest dispersion will be selected. The partition is defined as a region with medium to high dispersion, and the region with the closest dispersion is selected. The partition is defined as the low-discrete region.

[0183] In one or more embodiments, step eight configures the capacity correction module to iteratively correct the distributed synchronous condenser configuration capacity of each node using a successive linear programming method. The basic capacity configuration result is used as the starting point for iterative correction. In the first Next iteration point At, for nodes Severity index of transient pressure rise Using a first-order Taylor expansion:

[0184]

[0185] In the formula, For the first Node at the next iteration Capacity changes affect nodes Sensitivity of transient pressure rise severity indicators This represents the total number of nodes requiring capacity adjustment. The capacity-corrected linear programming subproblem for the next iteration is:

[0186]

[0187]

[0188]

[0189] In the formula, The additional capacity required for the nodes, The upper limit of capacity increment is set as a constraint to prevent linear approximation failure. Its value is a predetermined percentage (e.g., 10%-20%) of the capacity at the current iteration point, used to ensure that the step size of each iteration is within the effective range of the local linear approximation. The interior-point method is used to solve the above linear programming subproblem, by constructing a barrier function within the feasible region and iteratively approximating the optimal solution along the central path. In the... The capacity increment obtained in the next iteration is: The updated capacity is: In the updated capacity The transient pressure rise severity index for each node will be recalculated. If the node meets the requirements... If the configuration is correct, then this capacity scheme will be used as the final capacity configuration result; otherwise, the updated capacity will be used. The above process is repeated as the initial capacity for a new iteration. For example... Figure 12 As shown, a schematic diagram of the capacity iterative correction process is illustrated; as Figure 13 As shown, the convergence curve of the transient pressure rise severity index and the bar chart of capacity increment change are displayed. Node 10 converges in the 8th iteration, node 11 converges in the 6th iteration, and node 23 converges in the 9th iteration.

[0190] In one or more embodiments, the capacity iteration correction process in step eight further includes a sub-step of performing engineering rounding on the capacity correction result: when the capacity increment after iteration converges When the value is greater than zero, the number of additional distributed synchronous condensers will be taken as... ,in It is a rounding function. This is the baseline capacity of a single distributed synchronous condenser. For example... Figure 14 As shown, the transient voltage response curves of nodes 10, 11, and 23 to be corrected after capacity iteration correction all meet the threshold requirements.

[0191] In one or more embodiments, the cluster allocation logic under the adjacency matrix constraint of the improved K-means clustering algorithm in step three is implemented in the following manner:

[0192] First, obtain the currently unassigned nodes. adjacency vector ,in =1 indicates a node With nodes There are coupled branches; then, for each candidate cluster Check if a node exists. Make =1, if it exists, then compute the node. to cluster center Euclidean distance Next, among all candidate clusters that satisfy the connectivity condition, select... The smallest cluster is used as a node. The node is assigned to a specific cluster; if no candidate cluster satisfies the connectivity condition, the node is marked as a pending node. After all available nodes in this round are assigned, a breadth-first search algorithm is used to find the neighboring cluster with the shortest path to the pending node and merge them; finally, after all nodes are assigned, the cluster centers are updated. The process involves repeated assignment and updates until the cluster centers no longer change, and then using graph theory to verify the connectivity of the partitioning results.

[0193] In one or more embodiments, the comprehensive calculation of the transient pressure rise severity index in step four is implemented in the following manner:

[0194] First, for each fault Get nodes transient voltage response curve and the corresponding overvoltage binary table [ , ]( =1,2,…, Then, for each threshold voltage in the binary table... Detection Higher than Time interval [ ];

[0195] Next, the normalized integral area is calculated for each time interval, with the denominator for piecewise normalization being... or ;

[0196] Then, the normalized integral surfaces of each time interval are accumulated to obtain the nodes. In the fault Local transient pressure rise severity index Finally, the local indicators under multiple faults are weighted by coefficients. Perform a weighted summation to obtain the nodes. Comprehensive transient pressure rise severity index ,in The value is determined based on the probability of the fault occurring.

[0197] In one or more embodiments, the iterative solution of the successive linear programming method in step eight is implemented in the following manner:

[0198] First, obtain the set of nodes to be corrected. (i.e., the severity of transient pressure rise exceeds the threshold after basic capacity configuration) (nodes with =1), initialize the iteration counter =0, capacity vector The result of the basic capacity configuration;

[0199] Then, at the iteration point At this point, the sensitivity matrix is ​​calculated using the small perturbation method. That is, for each node Apply small capacity increments (e.g., 1Mvar), obtained through time-domain simulation. The change in is used to calculate the partial derivative;

[0200] Next, construct a linear programming subproblem with capacity increment. Minimize the objective function, with As a constraint, with Define the variable boundaries;

[0201] Then, the interior-point method is used to solve the linear programming subproblem to obtain the optimal capacity increment. Finally, update the capacity vector. And obtain the updated results through time-domain simulation. If all All meet If the iteration converges, the final capacity configuration result is output; otherwise, let... And repeat the above process.

[0202] In one or more embodiments, to ensure data consistency and calculation repeatability during transient voltage simulation and capacity iteration, the simulation verification module uses a read-write lock mechanism to perform storage and retrieval operations on time-domain simulation data. Specifically, this includes: acquiring a mutex lock on the data storage area before the start of each iteration of the time-domain simulation; and reading the current capacity configuration scheme. The simulation configuration file below; the set of nodes to be corrected. For each node, time-domain simulation is performed to obtain the transient voltage response curve; the peak transient voltage and transient voltage rise severity index of each node are extracted from the simulation results. The simulation results are written to the data storage area by node number index; the mutex lock is released. During sensitivity calculations, a semaphore mechanism is used to control the concurrency of parallel perturbation calculation tasks, preventing excessive parallel tasks from causing competition for computing resources.

[0203] In one or more embodiments, in response to a failure to pass connectivity verification of the clustering partitioning result, an error handling process is executed, wherein the error handling process includes at least one of the following operations: increasing the cluster number K and re-executing the clustering algorithm, forcibly merging isolated nodes using a minimum path merging strategy, outputting an alarm log for partitioning failure, and terminating the subsequent configuration process. Additionally, in response to the successive linear programming iterations exceeding a preset maximum number of iterations (e.g., 20 iterations) without convergence, an error handling process is executed, including: outputting the current capacity configuration scheme as a suboptimal solution, recording the number of the non-converged node and its transient pressure rise severity index, and issuing an alarm prompt requesting manual intervention.

[0204] refer to Figure 15 This document illustrates a schematic diagram of a centralized / distributed synchronous condenser hybrid site selection and capacity optimization configuration system according to one or more embodiments of this application. The system is applied to the planning, design, and operation optimization of a high-proportion wind power transmission system via ±800kV UHVDC, and includes the following modules: simulation modeling module, electrical distance calculation module, clustering and partitioning module, transient voltage rise assessment module, partition risk quantification module, hybrid site selection module, and capacity configuration module.

[0205] In one or more embodiments, the simulation modeling module is configured to establish a high-proportion wind power transmission system via ±800kV UHVDC based on PSACD / EMTDC, and analyze the transient characteristics of the UHVDC transmission system under DC faults. Specifically, the module includes a simulation model construction unit and a transient characteristic analysis unit, wherein the simulation model construction unit is used to establish, for example, a simulation model building unit and a transient characteristic analysis unit. Figure 2 and Figure 3 The simulation model of the sending-end power grid shown contains 25 nodes. The transient characteristic analysis unit is used to obtain the transient overvoltage amplitude, duration and voltage response curve under commutation failure fault and DC blocking fault.

[0206] In one or more embodiments, the electrical distance calculation module is configured to obtain the electrical distance matrix of the sending-end grid nodes using the power system power flow correction equations. Specifically, the module includes a power flow calculation unit and a distance matrix construction unit, wherein the power flow calculation unit solves the power system power flow correction equations based on the Newton-Raphson method:

[0207]

[0208] ;

[0209] ;

[0210] In the formula, For Jacobian matrices, , , , These are the block elements of the Jacobian matrix. , These are the active and reactive power disturbances injected into the nodes, respectively. , The deviation of the phase angle and amplitude of the node voltage

[0211] and set Derive the reactive power-voltage sensitivity matrix The distance matrix construction unit is used to define electrical distance indices. and perform symmetry processing. and per-unit processing Generate a standardized electrical distance matrix.

[0212] In one or more embodiments, the clustering partitioning module is configured to introduce a system structure adjacency matrix to execute an improved K-means clustering algorithm, combining the elbow rule to cluster and partition each node of the sending-end power grid, ensuring that the partitioning results are coupled in electrical characteristics and connected in topology. Specifically, this module includes an adjacency matrix construction unit, a constraint clustering allocation unit, and a connectivity verification unit. The adjacency matrix construction unit defines the adjacency matrix according to the network topology. If the nodes in the system With nodes If there are coupled branches, then =1, otherwise =0. The constrained clustering assignment unit, during each node assignment in K-means clustering, only allows the node to be assigned to a cluster with a connecting path based on the adjacency matrix, and further selects the cluster with the closest electrical distance. The objective function is... The connectivity verification unit extracts the submatrix corresponding to each cluster from the adjacency matrix A. If the node subgraph contained in the submatrix has only one connected component in the topology, then the nodes inside the cluster are confirmed to be topologically connected.

[0213] In one or more embodiments, the transient pressure rise assessment module is configured to introduce a transient pressure rise severity index to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and magnitude. Specifically, the module includes a local index calculation unit and a comprehensive index calculation unit. The local index calculation unit calculates the node's performance according to a formula. In the fault Local transient pressure rise severity index :

[0214]

[0215] In the formula, [ , This is a binary overvoltage table. The comprehensive index calculation unit weights and sums the local indices under multiple faults using a weighting coefficient δj to obtain the comprehensive transient voltage rise severity index for node i. .

[0216] In one or more embodiments, the partition risk quantification module is configured to introduce a quantile method to assess the overall trend and dispersion of transient pressure rise severity at nodes within a partition, establishing a partition risk level quantification method. Specifically, this module includes an overall trend assessment unit and a dispersion characteristic assessment unit. The overall trend assessment unit assesses the severity of transient pressure rise at each node... Arrange in ascending order and calculate the upper ternary values ​​using linear interpolation. and lower thirds Based on the nodes within the partition and and The comparison relationship determines the overall risk level of the partition (high / medium / low risk zone). The discrete feature evaluation unit calculates the first... Interquartile range of nodes within each partition And calculate the lower thirds of the interquartile range for all partitions. and the third place ,according to and and The comparison relationship determines the degree of dispersion of the partition (high / medium / low dispersion zone), and the overall risk level and the discrete characteristics are cross-combined to form a two-dimensional assessment system.

[0217] In one or more embodiments, the hybrid addressing module is configured to perform differentiated addressing configurations for distributed and centralized synchronous condensers based on the quantization results of each partition. Specifically, the module includes a column and norm calculation unit and an addressing strategy execution unit. The column and norm calculation unit calculates the system sensitivity matrix for the k-th partition. Extracting the sub-sensitivity matrix compute nodes The corresponding number Column and norm The location strategy execution unit makes location decisions based on the two-dimensional evaluation results: For partitions with high transient voltage rise risk and high dispersion, multiple centralized synchronous condensers are configured at multiple electrical center nodes with the largest column and norm; for partitions with low transient voltage rise risk and high dispersion, distributed synchronous condensers are configured at the extreme outlier nodes with the highest transient voltage rise severity index; for partitions with medium transient voltage rise risk and medium dispersion, a hybrid configuration strategy is adopted; for partitions with low transient voltage rise risk and low dispersion, no synchronous condensers need to be configured.

[0218] In one or more embodiments, the capacity configuration module is configured to define the linear response coefficients of a node. This module performs basic capacity configuration for distributed synchronous condensers and introduces a successive linear programming method to iteratively correct the configured capacity of each node. Specifically, this module includes the following sub-modules.

[0219] In one or more embodiments, the basic capacity configuration submodule is configured to calculate the minimum distributed synchronous condenser capacity required for each node to meet the transient pressure rise severity index threshold based on the linear response coefficient Pi and the linear superposition assumption. The linear response coefficient is defined as... Basic capacity configuration meets ,in =1, , Round up to the nearest positive integer.

[0220] In one or more embodiments, the sensitivity calculation submodule is configured to calculate the partial derivative of the transient pressure rise severity index with respect to the camera capacity at each iteration point to obtain the local linearization coefficient. .

[0221] In one or more embodiments, the linear programming solver submodule is configured to construct and solve a linear programming subproblem with the objective of minimizing capacity increment and constrained by a transient pressure rise severity index threshold using the interior-point method:

[0222]

[0223]

[0224]

[0225] Determine the capacity increment for this iteration. Approximate the optimal solution iteratively along the central path by constructing a barrier function within the feasible region.

[0226] In one or more embodiments, the convergence determination submodule is configured to recalculate the transient pressure rise severity index for each node after updating the capacity scheme and compare it with a threshold. The convergence determination submodule determines the severity index if all nodes to be corrected meet the threshold. The iteration terminates and the final capacity configuration scheme is output.

[0227] In one or more embodiments, the capacity configuration module further includes an engineered rounding submodule, configured to handle the capacity increment after iteration convergence. When the value is greater than zero, the number of additional distributed synchronous condensers will be taken as... ,in It is a rounding function. This is the baseline capacity of a single distributed synchronous condenser.

[0228] In one or more embodiments, the system further includes an error handling module configured to execute an error handling process in response to a failure of connectivity verification of clustering partitioning results or an excess of the number of iterations in successive linear programming beyond a preset maximum number of iterations, including at least one of the following operations: terminating the current operation, recording an error log, and performing system state rollback.

[0229] In one or more embodiments, the transient characteristic analysis unit in the simulation modeling module is configured to: in response to analyzing DC blocking faults, take the set of over-limit nodes identified under commutation failure faults as the initial set to be corrected, and carry out capacity optimization configuration of distributed synchronous condensers.

[0230] Specifically, the capacity calculation of the basic capacity configuration submodule is implemented in the following way:

[0231] First, obtain the transient voltage rise severity index of each node i to be corrected before the distributed synchronous condenser is configured. and linear response coefficient ;

[0232] Then, according to the constraints The capacity required for computational theory ;

[0233] Next, based on the configuration quantity constraints and Round up to the nearest whole number to calculate the actual number of units configured. ;

[0234] Finally, output the basic configuration capacity. .

[0235] In one or more embodiments, the interior-point method for solving the linear programming submodule is implemented as follows:

[0236] First, a barrier function is constructed to transform the constrained optimization problem into an unconstrained optimization problem; then, an initial point is selected within the feasible region.

[0237] Next, the optimal solution is searched iteratively along the Newton direction, and the obstacle parameter is reduced in each iteration;

[0238] Finally, when the barrier parameter approaches zero and the KKT conditions are satisfied, the optimal capacity increment is output. .

[0239] In one or more embodiments, to ensure the accurate transfer of time-domain simulation data among multiple modules and the version consistency of capacity configuration schemes, the data management module performs the storage and retrieval of capacity configuration schemes through a version control mechanism. Specifically, this includes: before each iteration begins, reading the current capacity scheme from the configuration storage area. After the simulation modeling module completes the transient simulation, the simulation result data is written to the simulation result storage area according to the node number index. When the convergence judgment submodule performs threshold comparison, a mutex lock is used to ensure that only one iteration process reads and modifies the capacity configuration data at any given time. When outputting the final capacity configuration scheme, the configuration scheme is solidified to a non-volatile storage medium and a unique version identifier is generated.

[0240] In one or more embodiments, in response to an anomaly in the partial derivative calculation in the sensitivity calculation submodule (such as simulation non-convergence), an error handling process is executed, wherein the error handling process includes at least one of the following operations: recalculating the sensitivity by halving the difference step size, using the sensitivity value of the previous iteration point as a replacement value, terminating the current iteration and outputting the existing optimal capacity configuration scheme. Additionally, in response to non-convergence of the interior-point method solution in the linear programming solution submodule, an error handling process is executed, including: relaxing the upper limit of the capacity increment ΔSj^max and resolving, using the simplex method as an alternative solver, recording the degree of constraint violation in the linear programming subproblem and issuing an alarm.

[0241] refer to Figures 1 to 14 This application also provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program is capable of implementing the steps of the above-described centralized / distributed synchronous condenser hybrid site selection and capacity optimization configuration method. This storage medium is applied to the planning, design, and operation optimization scenarios of high-proportion wind power transmission systems via ±800kV UHVDC transmission lines. The computer program includes components corresponding to… Figure 1 The execution instructions for each step of the method flow shown.

[0242] In one or more embodiments, when the processor executes the computer program, it performs the following operations:

[0243] First, a simulation model of a high-proportion wind power transmission system via ±800kV UHVDC is established based on PSACD / EMTDC, and the transient characteristics of the UHVDC transmission system under DC faults are analyzed.

[0244] Secondly, the electrical distance matrix of the sending-end grid nodes is obtained by using the power flow correction equation of the power system;

[0245] Then, an improved K-means clustering algorithm is executed by introducing the system structure adjacency matrix, and the elbow rule is combined to cluster and partition each node of the sending-end power grid to ensure that the partitioning results are coupled in electrical characteristics and connected in topology.

[0246] Next, a transient pressure rise severity index is introduced to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and magnitude.

[0247] Next, a quantile method is introduced to establish a method for quantifying the risk level of a region, and a hybrid location configuration of distributed / centralized synchronous condensers is executed based on the quantification results;

[0248] Then, differentiated location configuration is performed based on the quantization results of each partition;

[0249] Next, the linear response coefficient Pi of the node is defined to configure the basic capacity of the distributed synchronous condenser.

[0250] Finally, a successive linear programming method is introduced to iteratively correct the distributed synchronous condenser configuration capacity of each node.

[0251] In one or more embodiments, the storage medium includes, but is not limited to, ROM, RAM, magnetic disk, optical disk, USB flash drive, portable hard drive, etc. When a computer program is executed by a processor, it establishes, for example... Figure 2 and Figure 3 The simulation model of the ±800kV UHVDC transmission system with 25 nodes shown yields the following results: Figure 6 The results of the transient pressure rise severity index calculation are shown, and are based on... Figure 12 The iterative process shown corrects the capacity configuration step by step.

[0252] In one or more embodiments, when the computer program is executed by a processor, in response to a failure to pass the connectivity check of the clustering partitioning result, an error handling process is executed, wherein the error handling process includes at least one of the following operations: increasing the cluster number K and re-executing the clustering algorithm, applying a minimum path merging strategy to isolated nodes, outputting an alarm log for partitioning failure, and terminating the subsequent configuration process. Additionally, in response to the successive linear programming iterations exceeding a preset maximum number of iterations without convergence, the error handling process is executed, including: outputting the current capacity configuration scheme as a suboptimal solution, recording the number of the non-converged nodes and their transient pressure rise severity indicators, and issuing an alarm prompt requesting manual intervention.

[0253] The above technical solutions only embody the preferred technical solutions of the present invention. Any modifications that may be made by those skilled in the art to certain parts thereof embody the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method for hybrid site selection and capacity optimization configuration of centralized / distributed synchronous condensers, characterized in that, The method includes the following steps: Step 1: Based on PSACD / EMTDC, establish a simulation model of a high-proportion wind power transmission system via ±800kV UHVDC to analyze the transient characteristics of the UHVDC transmission system under DC faults. Step 2: Use the power flow correction equations of the power system to obtain the electrical distance matrix of the sending-end grid nodes; Step 3: Introduce the system structure adjacency matrix to obtain the improved K-means clustering algorithm. Combined with the elbow rule, cluster and partition each node of the sending-end power grid to ensure that the partitioning results are coupled in electrical characteristics and connected in topology. Step four: Introduce a transient pressure rise severity index to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and magnitude. Step 5: Introduce the quantile method to reflect the overall trend and dispersion of the severity of transient pressure rise in nodes within the partition, establish a method for quantifying the risk level of the partition, and complete the hybrid site selection configuration of distributed / centralized synchronous condensers in the sending-end system based on the quantification results. Step 6: Based on the quantization results of each partition, distributed synchronous condensers are preferentially configured on nodes with higher transient voltage rise severity indicators, while centralized synchronous condensers are configured on nodes with the largest sensitivity matrix columns and norms within the partition. Step 7: To reduce computational load and improve solution speed, define the linear response coefficients of the nodes and configure the basic capacity of the distributed synchronous condenser. Step 8: Introduce the successive linear programming method to iteratively correct the distributed synchronous condenser configuration capacity of each node, gradually approximating the capacity configuration scheme under actual nonlinear constraints.

2. The method according to claim 1, characterized in that, The process of obtaining the electrical distance matrix of the sending-end power grid nodes in step two includes: Power flow correction equations for power systems are established based on the Newton-Raphson method; Define nodes With nodes Electrical distance specifications; The electrical distance matrix is ​​symmetricized and normalized so that all elements are located in the interval [0,1]. The larger the element value, the closer the electrical distance between nodes.

3. The method according to claim 1, characterized in that, The process of improving the K-means clustering algorithm in step three includes: Define the adjacency matrix based on the network topology; In each node assignment in K-means clustering, the corresponding node is only allowed to be assigned to a cluster with a connection path based on the adjacency matrix, and the cluster with the closest electrical distance is selected as the assigned cluster. Repeatedly assign and update the center until convergence, and perform topological connectivity verification on the partitioning results.

4. The method according to claim 1, characterized in that, The method for quantifying the risk level of a region in step five includes: Arrange the comprehensive transient pressure rise severity index of each node in ascending order and calculate the upper tertiary value. and lower thirds ; If the comprehensive transient pressure rise severity index of more than half of the nodes in the partition is less than or equal to the lower third... This zone is defined as a low-risk zone for transient pressure rise. If a partition has more than half of its nodes Greater than or equal to the upper third This zone is defined as a risk zone for increased transient pressure. The remaining area is defined as the medium-risk area for transient pressure rise; If the proportion of partition nodes is the same in both risk zones, the partition is divided according to the principle of the most unfavorable system operation, and the partition is assigned to the relatively higher risk level. Introducing the interquartile range, then the first... The interquartile range of nodes within each partition is ; The dispersion of the comprehensive transient pressure rise severity index for nodes within the assessment partition is evaluated, among which, For partitioning The upper quartile of the internal node, For partitioning The lower quartile of an internal node; Calculate the lower third of the interquartile range for all partitions. and the third place ; If the interquartile range of the partition is greater than or equal to If so, the partition is considered to be in the discrete region of transient pressure increase; If the interquartile range of the partition is less than or equal to If the condition is met, the partition is considered to be in the low discrete region of transient pressure rise; otherwise, it is in the medium discrete region of transient pressure rise. A two-dimensional assessment system is formed by cross-combining the overall transient pressure rise risk level of a zone with the discrete characteristics of transient pressure rise within the zone.

5. The method according to claim 4, characterized in that, The dual-dimensional evaluation system forms configuration decisions based on the following rules: For zones with high risk of transient voltage spikes and high dispersion: Configure multiple centralized synchronous condensers at the electrical center nodes with the largest column and norm within the zone; For partitions with low-risk and highly discrete transient voltage rise: Configure distributed synchronous condensers on the extreme outlier nodes with the highest transient voltage rise severity index within the partition; For zones with medium-risk and discrete transient voltage rise: a hybrid configuration strategy is adopted, with centralized synchronous condensers configured at the zone's electrical center node, and distributed synchronous condensers configured at wind power nodes with higher transient voltage rise severity indicators. Transient voltage rise is low-risk and low-dispersion partitioning: no need to configure a synchronous condenser.

6. The method according to claim 1, characterized in that, In step six, the columns and norm of the sensitivity matrix are used to characterize the total response of each node to voltage changes of all nodes in the partition, so as to quantify the global reactive power-voltage support capability of each node. The node with the largest column and norm is used as the centralized synchronous condenser configuration node.

7. The method according to claim 1, characterized in that, The capacity iteration correction process in step eight includes: The basic capacity configuration result is used as the starting point for iterative correction; In the At the next iteration point, for the node The severity index of transient pressure rise is expressed using a first-order Taylor expansion; Confirm the The capacity-corrected linear programming subproblem of the next iteration; Using the interior-point method to solve linear programming subproblems, in the th... In the next iteration, the capacity increment is solved, and the updated capacity is obtained; Under the updated capacity, the transient pressure rise severity index of each node is recalculated. If the node meets the set conditions, the capacity scheme is used as the final capacity configuration result; otherwise, the updated capacity is used as the initial capacity for a new round of iteration, and the above process is repeated.

8. The method according to claim 1, characterized in that, It also includes the clustering partitioning results. Steps for analyzing elbow curves: When When the value increases The inflection point that tends to level off corresponds to the optimal number of clusters. The optimal cluster number is used to determine the number of partitions in a K-means cluster.

9. A centralized / distributed synchronous condenser hybrid site selection and capacity optimization configuration system, characterized in that, The system operates based on the method as described in any one of claims 1 to 8, comprising: The simulation modeling module is used to establish a simulation model of a high-proportion wind power transmission system via ±800kV UHVDC based on PSACD / EMTDC, and to analyze the transient characteristics of the UHVDC transmission system under DC faults. The electrical distance calculation module is used to obtain the electrical distance matrix of the sending-end grid nodes using the power flow correction equations of the power system; The clustering and partitioning module is used to introduce the system structure adjacency matrix to execute the improved K-means clustering algorithm, and combine the elbow rule to cluster and partition each node of the sending-end power grid, ensuring that the partitioning results are coupled in electrical characteristics and connected in topology. The transient pressure rise assessment module is used to introduce transient pressure rise severity indicators to quantitatively describe the severity of transient pressure rise at each node from two dimensions: duration and magnitude. The partition risk quantification module is used to introduce the quantile method to assess the overall trend and dispersion of the severity of transient pressure rise at nodes within a partition, and to establish a method for quantifying partition risk levels. The hybrid location module is used to perform differentiated location configurations for distributed and centralized synchronous condensers based on the quantization results of each partition. The capacity configuration module is used to define the linear response coefficients of nodes for basic capacity configuration of distributed synchronous condensers, and introduces a successive linear programming method to iteratively correct the configuration capacity of each node.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it is able to implement the steps of the method as described in any one of claims 1 to 8.

Images