Load response characteristic grouping and clustering boundary delineation method and system

Abstract

The application discloses a load response characteristic grouping and clustering boundary delineation method and system, comprising: obtaining response data of multiple load bus nodes in voltage drop or frequency fluctuation time; constructing a load dynamic compression characteristic vector with power angle first swing response as a target based on the response data; clustering based on the load dynamic compression characteristic vector of all load bus nodes to determine multiple load groups; performing group boundary delineation on each load group, dividing the characteristic space into a core area, an overlapping fuzzy area and an outer point area based on the group boundary; performing parameter interpolation on the load bus nodes in the core area and the overlapping fuzzy area; and realizing load response characteristic grouping and clustering boundary delineation based on each load bus node and the corresponding parameters. The application can realize the migration deployment of the grouping knowledge while ensuring the continuous stability of the simulation results, and finally comprehensively improve the precision, robustness and engineering practicality level of the electromechanical transient simulation of the large power grid.

Description

Technical Field

[0001] This invention relates to the field of power system simulation and analysis technology, and more specifically, to a method and system for characterizing load response characteristics clustering and cluster boundaries. Background Technology

[0002] Electromechanical transient simulation of power systems is a core tool for power grid security and stability analysis. Its simulation accuracy largely depends on the accuracy of the load model. However, in actual power grids, hundreds or thousands of load bus nodes have significant regional and time-varying differences due to the components (such as induction motors, constant impedance, constant power, and power electronic interface loads). Their dynamic response behavior exhibits complex nonlinear characteristics and changes continuously and gradually with the operating conditions. If a single typical load model is used for the entire network, the simulation results of the power angle swing curve and system damping characteristics will deviate significantly from reality, and may even lead to misjudgment of stability margin.

[0003] To address this issue, existing technologies have primarily developed three types of load clustering modeling methods: The first type uses static partitioning based on user type or voltage level, but ignores the dynamic response differences of similar loads at different disturbance depths, resulting in overly coarse clustering granularity; the second type uses K-means or hierarchical clustering algorithms to directly cluster the active power time-series waveforms after disturbance using Euclidean distance. This type of method is sensitive to waveform phase shifts and the cluster boundaries are isotropic rigid spherical partitions, failing to reflect the anisotropic drift and continuous transition of load characteristics in the parameter space; the third type independently identifies equivalent load model parameters for each node, which, while highly accurate, involves a huge computational load and the model cannot be transferred to unobserved nodes. The common shortcomings of the aforementioned existing technologies are as follows: the feature extraction stage is not linked to the target accuracy of electromechanical transient simulation, and the extracted features contain redundant information and omit physical indicators that play a decisive role in the power angle first swing and damping characteristics; the cluster boundary adopts a hard partitioning strategy, and when the node features fall in the overlapping area between groups, a small measurement disturbance or change in the operating mode will cause a drastic jump in the model parameters, resulting in discontinuous simulation results and a lack of robustness; the boundary discrimination function does not have portability and is difficult to deploy to adjacent nodes with similar electrical structures but without measurement devices.

[0004] Therefore, there is an urgent need for a method to characterize load response characteristics as clusters and their boundaries. Summary of the Invention

[0005] This invention proposes a method and system for load response characteristic clustering and cluster boundary characterization to solve the problem of how to determine dynamic model data files suitable for electromechanical transient simulation.

[0006] To address the aforementioned problems, according to one aspect of the present invention, a method for clustering and delineating cluster boundaries of load response characteristics is provided, the method comprising: Acquire response data from multiple load bus nodes during voltage dips or frequency fluctuations; Based on the response data, a load dynamic compression feature vector is constructed with the power angle initial swing response as the target; Clustering is performed based on the load dynamic compression feature vectors of all load bus nodes to identify multiple load groups; For each load group, the group boundary is characterized, and the feature space is divided into a core region, an overlapping fuzzy region, and an outer point region based on the group boundary. Perform parameter interpolation on the load bus nodes in the core area and overlapping ambiguity area; Based on each load bus node and its corresponding parameters, load response characteristics are grouped and cluster boundaries are characterized.

[0007] Preferably, the response data includes: voltage amplitude time series {u(t)}, active power time series {p(t)}, and reactive power time series {q(t)} aligned with the same time base, wherein the value of t ranges from at least one cycle before the disturbance occurrence time T0 to the time T after the disturbance when the system enters a new steady state. _end .

[0008] Preferably, the method for constructing a load dynamic compression feature vector based on the response data, targeting the initial swing response at the work angle, includes: The voltage-active power coupling sag depth is calculated using the following method: , Where, ΔT d T0 represents the duration of the disturbance; T0 represents the time when the disturbance occurred. Active power; Voltage amplitude; The first preset time period after the disturbance clearing time T_clear is divided into four sub-intervals, and the average rate of change of active power in each sub-interval is calculated. k 1, k 2, k 3, k 4. To form a four-dimensional sub-feature characterizing the initial power recovery slope; The active-voltage two-dimensional trajectory is reduced in dimension, and the difference between the first and last points of the trajectory after embedding into the one-dimensional manifold is taken as the low-dimensional manifold embedding feature of the voltage-active trajectory. For the residual sequence of active power after removing the trend term, the logarithmic decay rate of the dominant oscillation mode is extracted using the matrix bundle method. α Determine the damping properties of the residual oscillations; where, if there are no identifiable oscillations in the sequence, then α is set to 0; The signed error of steady-state recovery deviation is calculated as follows: ε_sgn=p(T) _end )–1, where p(T)_end T represents the time T at which the system enters a new steady state after the disturbance. _end The active power; If multiple perturbation events exist, the median and interquartile range of the above features under each event are calculated to form the final feature vector V∈R. D Where D = (1 dimension each of B1~B5 + 4 dimensions of B2 segment) × (median + interquartile range) × event dimension aggregation coefficient; B1~B5 represent five features respectively: voltage-active coupling drop depth, four-dimensional sub-feature, low-dimensional manifold embedding feature of voltage-active trajectory, damping property of residual oscillation and signed error.

[0009] Preferably, clustering is performed based on the load dynamic compression feature vectors of all load bus nodes to determine multiple load groups, including: In the traditional fuzzy C-mean objective function, a regularization term guided by electromechanical transient simulation is introduced to cluster the load dynamic compression feature vectors of all load bus nodes using the improved fuzzy C-mean, thereby identifying multiple load groups. The modified objective function is as follows: in, g (V i ,c j The surrogate function, "characteristic deviation - power angle error," is pre-fitted using a small number of simulation samples and is used to quantify the error at a given node. i Classified into a group j At that time, the expected power angle simulation error caused by characteristic deviation; N is the total number of load bus nodes; C The preset number of clusters; u ij For the first i The node belongs to the first j The fuzzy membership degree of each load group satisfies and ; m For fuzzy weighted index; V i For the first i The load dynamic compression characteristic vector of each load bus node; c j For the first j Cluster center vectors of each load group; For the characteristic vector V i To cluster center c j The square of the Euclidean distance; λ It is a balancing factor.

[0010] Preferably, the group boundary characterization for each load group includes: For each load group j, its attribution boundary is constructed using the directed boundary support vector method; wherein, the attribution decision function for each load group j is: , Where Σj is the Mahalanobis distance scaling matrix of the j-th group. f j (V) represents the discrimination function for the j-th load group to the sample feature vector V. The output value is positive 1 or negative 1. Positive 1 indicates that the sample is located inside the boundary of the group, and negative 1 indicates that it is located outside the boundary. sgn(·) is the sign function. When the expression in the parentheses is greater than or equal to zero, it outputs positive 1, and when it is less than zero, it outputs negative 1. Let V be the directed boundary radius of the j-th group; V is the characteristic vector of the load node to be discriminated; a j Let be the directed boundary ellipsoid center vector of the j-th group, representing the typical position of the group in the characteristic space; This is the transpose of the characteristic deviation vector, where the superscript T indicates the transpose operation of a matrix or vector; Σj is the inverse of the Mahalanobis distance scaling matrix of the j-th group.

[0011] Preferably, the feature space is divided into a core region, an overlapping blurred region, and an outer point region based on the group boundary, including: If load group j satisfies f j (V)=1 and for all k≠j, we have f k If (V)=0, then load group j is located in the core area; If there exist at least two distinct load groups j1 and j2 such that f j1 (V)=1 and f j2 If (V)=1, then load groups j1 and j2 are located in the cross-fuzzy region; If for all load groups j, f j If (V)=0, then all load groups j are determined to be in the outer point zone.

[0012] Preferably, the parameter interpolation for the load bus nodes in the core area and the overlapping ambiguity area includes: For the load bus node in the core area, parameter interpolation is performed based on a pre-identified set of composite load model parameters Θ_j corresponding to the load group j to which the load bus node is located; For load bus nodes in the overlapping ambiguity region, their parameter θ is generated using the following constrained hybrid weighting strategy: , , in, The set of fuzzy groups to which the load bus nodes belong; For the first j The weight coefficients of each group in the interpolation of the node parameters; The standard load model parameters are pre-calibrated for the j-th group; γ is the Mahalanobis distance from the load bus node to the decision boundary of group j; γ is the sensitivity coefficient. For electromechanical transient simulation power angle error; Let be the group standard parameters of group j and their approximate sensitivity to the simulation power angle error.

[0013] Preferably, the load response characteristics are clustered and the cluster boundaries are characterized based on each load bus node and its corresponding parameters, including: Each load bus node and its corresponding parameters are compiled into a load model card format compatible with the simulation software, or directly output as a dynamic model data file of the simulation platform, so as to realize the characterization of load response characteristics clustering and cluster boundaries.

[0014] According to another aspect of the present invention, a system for clustering and characterizing load response characteristics is provided, the system comprising: The response data acquisition unit is used to acquire response data of multiple load bus nodes during voltage dips or frequency fluctuations. A feature vector construction unit is used to construct a load dynamic compression feature vector based on the response data, with the power angle initial swing response as the target. Clustering units are used to cluster based on the load dynamic compression feature vectors of all load bus nodes to identify multiple load groups; The feature space partitioning unit is used to characterize the group boundary of each load group and divide the feature space into the core area, the overlapping fuzzy area and the outer point area based on the group boundary. The parameter interpolation unit is used to perform parameter interpolation on the load bus nodes in the core area and the overlapping ambiguity area. The clustering and boundary characterization implementation unit is used to implement the clustering and boundary characterization of load response characteristics based on each load bus node and its corresponding parameters.

[0015] According to another aspect of the present invention, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any one of the methods for load response characteristic clustering and cluster boundary characterization.

[0016] According to another aspect of the present invention, the present invention provides an electronic device, comprising: The aforementioned computer-readable storage medium; and One or more processors for executing a program in the computer-readable storage medium.

[0017] This invention provides a method and system for load response characteristic clustering and cluster boundary characterization, comprising: acquiring response data of multiple load bus nodes during voltage dips or frequency fluctuations; constructing a load dynamic compression feature vector based on the response data with the power angle first swing response as the target; clustering based on the load dynamic compression feature vectors of all load bus nodes to determine multiple load groups; characterizing the group boundary for each load group, and dividing the feature space into a core region, an overlapping fuzzy region, and an outer point region based on the group boundary; performing parameter interpolation on the load bus nodes in the core region and the overlapping fuzzy region; and realizing load response characteristic clustering and cluster boundary characterization based on each load bus node and its corresponding parameters. This invention constructs a set of dynamically compressed features sensitive to the initial swing angle and damping characteristics, enabling the feature extraction process to directly serve the accuracy requirements of electromechanical transient simulation. By introducing an improved fuzzy C-means algorithm with simulation error regularization terms and a directed boundary support vector description based on Mahalanobis distance, a non-spherical ellipsoidal boundary is formed that is loose in the simulation-sensitive direction and tight in the non-sensitive direction, thus reasonably characterizing the anisotropic and continuous gradual change of load characteristics in the parameter space. By dividing the feature space into three regions—core region, overlapping fuzzy region, and outer point region—and implementing differentiated parameter assignment strategies for different regions (the core region directly uses standard parameters, while the fuzzy region uses a weighted interpolation of distance inverse ratio and sensitivity), the invention ensures the continuous and stable simulation results while enabling the transferable deployment of clustered knowledge, ultimately comprehensively improving the accuracy, robustness, and engineering practicality of large power grid electromechanical transient simulation. Attached Figure Description

[0018] Exemplary embodiments of the present invention can be more fully understood by referring to the following figures: Figure 1 A flowchart of a method for clustering and delineating the boundary of load response characteristics according to an embodiment of the present invention; Figure 2 This is an overall flowchart of determining the load model parameter list according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the load response characteristic clustering and cluster boundary characterization system 300 according to an embodiment of the present invention. Detailed Implementation

[0019] Exemplary embodiments of the invention will now be described with reference to the accompanying drawings. However, the invention may be embodied in many different forms and is not limited to the embodiments described herein. These embodiments are provided to fully and completely disclose the invention and to fully convey its scope to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the drawings is not intended to limit the invention. In the drawings, the same units / elements are referred to by the same reference numerals.

[0020] Unless otherwise stated, the terms used herein (including technical terms) have their common meaning as understood by one of ordinary skill in the art. Furthermore, it is understood that terms defined in commonly used dictionaries should be understood to have a meaning consistent with the context of their relevant field, and not to be interpreted as having an idealized or overly formal meaning.

[0021] Figure 1 This is a flowchart of a method 100 for clustering and delineating load response characteristics according to an embodiment of the present invention. Figure 1 As shown, the load response characteristic clustering and cluster boundary characterization method provided by the embodiments of the present invention constructs a set of dynamically compressed features sensitive to the first swing of the power angle and damping characteristics, so that the feature extraction process directly serves the accuracy requirements of electromechanical transient simulation. By introducing an improved fuzzy C-means algorithm with simulation error regularization terms and a directed boundary support vector description based on Mahalanobis distance, a non-spherical ellipsoidal boundary is formed that is loose in the simulation sensitive direction and tight in the non-sensitive direction, thereby reasonably characterizing the anisotropic continuous gradual change of load characteristics in the parameter space. By dividing the feature space into three types of regions: core region, overlapping fuzzy region, and outer point region, and implementing differentiated parameter assignment strategies for different regions (the core region directly uses standard parameters, and the fuzzy region uses a weighted interpolation of distance inverse ratio and sensitivity), the method ensures the continuous and stable simulation results while realizing the transferable deployment of clustering knowledge, ultimately comprehensively improving the accuracy, robustness, and engineering practicality of large power grid electromechanical transient simulation. The dynamic model data file generation method 100 for electromechanical transient simulation provided by the present invention starts from step 101. In step 101, response data of multiple load bus nodes during voltage dips or frequency fluctuations are acquired.

[0022] Preferably, the response data includes: voltage amplitude time series {u(t)}, active power time series {p(t)}, and reactive power time series {q(t)} aligned with the same time base, wherein the value of t ranges from at least one cycle before the disturbance occurrence time T0 to the time T after the disturbance when the system enters a new steady state. _end .

[0023] In this invention, voltage and active power time-series data of multiple load buses under voltage drop events are first extracted from a wide-area measurement system to construct a multi-disturbance event sample set.

[0024] Specifically, response data of N target load buses during M voltage dips or frequency fluctuations are acquired from a wide-area measurement system or a synchronous phasor measurement unit. Each sample contains voltage amplitude time series {u(t)}, active power time series {p(t)}, and reactive power time series {q(t)} aligned with the same time base, where t ranges from at least one cycle before the disturbance occurrence time T0 to the time T after the system enters a new steady state. _end The collected data is normalized so that the per-unit value of steady-state active power and the per-unit value of voltage before the disturbance are both 1.

[0025] In step 102, a load dynamic compression feature vector is constructed based on the response data, with the power angle initial swing response as the target.

[0026] Preferably, the method for constructing a load dynamic compression feature vector based on the response data, targeting the initial swing response at the work angle, includes: The voltage-active power coupling sag depth is calculated using the following method: , Where, ΔT d T0 represents the duration of the disturbance; T0 represents the time when the disturbance occurred. Active power; Voltage amplitude; The first preset time period after the disturbance clearing time T_clear is divided into four sub-intervals, and the average rate of change of active power in each sub-interval is calculated. k 1, k 2, k 3, k 4. To form a four-dimensional sub-feature characterizing the initial power recovery slope; The active-voltage two-dimensional trajectory is reduced in dimension, and the difference between the first and last points of the trajectory after embedding into the one-dimensional manifold is taken as the low-dimensional manifold embedding feature of the voltage-active trajectory. For the residual sequence of active power after removing the trend term, the logarithmic decay rate of the dominant oscillation mode is extracted using the matrix bundle method. α Determine the damping properties of the residual oscillations; where, if there are no identifiable oscillations in the sequence, then α is set to 0; The signed error of steady-state recovery deviation is calculated as follows: ε_sgn=p(T) _end )–1, where p(T) _end T represents the time T at which the system enters a new steady state after the disturbance. _end The active power; If multiple perturbation events exist, the median and interquartile range of the above features under each event are calculated to form the final feature vector V∈R. D Where D = (1 dimension each of B1~B5 + 4 dimensions of B2 segment) × (median + interquartile range) × event dimension aggregation coefficient; B1~B5 represent five features respectively: voltage-active coupling drop depth, four-dimensional sub-feature, low-dimensional manifold embedding feature of voltage-active trajectory, damping property of residual oscillation and signed error.

[0027] In this invention, after acquiring the response data, six types of compressed feature vectors for the first swing response of the power angle are constructed, including voltage-active coupling drop depth, four-segment partition slope, manifold embedding feature, logarithmic decay rate, signed steady-state deviation, and multi-event statistical aggregation.

[0028] Unlike existing technologies that directly use raw time series or general statistics, this invention constructs a set of dynamic compression features sensitive to the generator's power angle initial swing and damping characteristics in electromechanical transient simulations, specifically including the following six components: B1: Voltage-Active Coupling Drop Depth , where ΔT d This refers to the duration of the disturbance. Unlike the traditional single maximum drop depth, this feature uses a product form to penalize both voltage and power drops simultaneously, highlighting the extreme operating point that contributes most to rotor acceleration power.

[0029] B2: Segmented characterization of the initial power recovery slope after disturbance clearing. The first 200ms after the disturbance clearing time T_clear is divided into four 50ms sub-intervals, and the average rate of change of active power is calculated for each interval. k 1, k 2, k 3, k 4. Forming four-dimensional sub-features. This segmentation method differs from a single initial recovery rate and can distinguish the nonlinear acceleration stage in the slip recovery process of the induction motor.

[0030] B3: Low-dimensional manifold embedding features of the voltage-active power trajectory. A local linear embedding method is used to reduce the dimensionality of the two-dimensional active power-voltage trajectory, and the difference between the first and last points of the trajectory after embedding into a one-dimensional manifold, δ_LLE, is taken as a feature. This feature is used to characterize the non-conservative dissipative behavior experienced by the load during transient processes.

[0031] B4: Damping properties of residual oscillations. For the residual sequence after removing the trend term from the active power, the logarithmic decay rate of the dominant oscillation mode is extracted using the matrix bundle method. α If no oscillations are identifiable in the sequence, then α is set to 0.

[0032] B5: The signed error of steady-state recovery deviation ε_sgn=p(T)_end )–1, retaining the positive or negative sign to distinguish between steady-state under-recovery (ε_sgn<0) and overshoot recovery (ε_sgn>0) of load power.

[0033] B6: Multi-event statistical aggregation. If multiple perturbation events exist, calculate the median and interquartile range for the values ​​of features B1~B5 under each event, forming the final feature vector V∈R. D Where D = (1 dimension each of B1 to B5 + 4 dimensions of B2 segment) × (median + interquartile range) × event dimension aggregation coefficient.

[0034] In step 103, clustering is performed based on the load dynamic compression feature vectors of all load bus nodes to determine multiple load groups.

[0035] Preferably, clustering is performed based on the load dynamic compression feature vectors of all load bus nodes to determine multiple load groups, including: In the traditional fuzzy C-mean objective function, a regularization term guided by electromechanical transient simulation is introduced to cluster the load dynamic compression feature vectors of all load bus nodes using the improved fuzzy C-mean, thereby identifying multiple load groups. The modified objective function is as follows: in, g (V i ,c j The surrogate function, "characteristic deviation - power angle error," is pre-fitted using a small number of simulation samples and is used to quantify the error at a given node. i Classified into a group j At that time, the expected power angle simulation error caused by characteristic deviation; N is the total number of load bus nodes; C The preset number of clusters; u ij For the first i The node belongs to the first j The fuzzy membership degree of each load group satisfies and ; m For fuzzy weighted index; V i For the first i The load dynamic compression characteristic vector of each load bus node; c j For the first j Cluster center vectors of each load group; For the characteristic vector V i To cluster center c j The square of the Euclidean distance; λ It is a balancing factor.

[0036] In step 104, the group boundary is characterized for each load group, and the feature space is divided into core area, overlapping fuzzy area and outer point area based on the group boundary.

[0037] Preferably, the group boundary characterization for each load group includes: For each load group j, its attribution boundary is constructed using the directed boundary support vector method; wherein, the attribution decision function for each load group j is: , Where Σj is the Mahalanobis distance scaling matrix of the j-th group. f j (V) represents the discrimination function for the j-th load group to the sample feature vector V. The output value is positive 1 or negative 1. Positive 1 indicates that the sample is located inside the boundary of the group, and negative 1 indicates that it is located outside the boundary. sgn(·) is the sign function. When the expression in the parentheses is greater than or equal to zero, it outputs positive 1, and when it is less than zero, it outputs negative 1. Let V be the directed boundary radius of the j-th group; V is the characteristic vector of the load node to be discriminated; a j Let be the directed boundary ellipsoid center vector of the j-th group, representing the typical position of the group in the characteristic space; This is the transpose of the characteristic deviation vector, where the superscript T indicates the transpose operation of a matrix or vector; Σj is the inverse of the Mahalanobis distance scaling matrix of the j-th group.

[0038] Preferably, the feature space is divided into a core region, an overlapping blurred region, and an outer point region based on the group boundary, including: If load group j satisfies f j (V)=1 and for all k≠j, we have f k If (V)=0, then load group j is located in the core area; If there exist at least two distinct load groups j1 and j2 such that f j1 (V)=1 and f j2 If (V)=1, then load groups j1 and j2 are located in the cross-fuzzy region; If for all load groups j, f j If (V)=0, then all load groups j are determined to be in the outer point zone.

[0039] In this invention, an improved fuzzy C-means algorithm with simulation error regularization term is used for initial soft partitioning to obtain the membership degree and cluster center of each node. Then, for each load group, a directed boundary support vector description is constructed based on Mahalanobis distance to form a non-spherical ellipsoidal boundary that is loose in the simulation sensitive direction and tight in the non-sensitive direction. The feature space is divided into a core area, an overlapping fuzzy area and an outer point area.

[0040] Combination Figure 2 As shown, when using a two-stage clustering algorithm with boundary fuzziness factors to partition load groups, this invention takes the feature vectors {V_i} of all N load bus nodes as input and performs the following two-stage calculation: Stage C1: Initial soft partitioning based on improved fuzzy C-means In the traditional fuzzy C-mean objective function, a regularization term guided by electromechanical transient simulation is introduced, and the modified objective function is as follows: in, g (V i ,c j The surrogate function, "characteristic deviation - power angle error," is pre-fitted using a small number of simulation samples and is used to quantify the error at a given node. i Classified into a group j At that time, the expected power angle simulation error caused by characteristic deviation; N is the total number of load bus nodes; C The preset number of clusters (i.e., the number of load clusters); u ij For the first i The node belongs to the first j The fuzzy membership degree of each load group satisfies and ; m For fuzzy weighted index (fuzzification coefficient) m >1, usually taken m =2, controls the degree of fuzziness in the clustering results; V i For the first i The load dynamic compression characteristic vector of each load bus node ;c j For the first j Cluster center vectors of each load group ; For the characteristic vector V i To cluster center c j The squared Euclidean distance measures the similarity in the feature space; λThis is a balancing factor used to adjust the relative weight between the traditional fuzzy C-means clustering objective and the electromechanical transient simulation-guided regularization term. Its value is usually between 0.1 and 0.5, and the specific value is determined based on the trade-off between simulation accuracy requirements and cluster compactness requirements.

[0041] Stage C2: Group boundary characterization based on directed boundary support vector description For each load group j obtained in stage C1, its belonging boundary is constructed using the directed boundary support vector method. The difference between this method and the conventional SVDD is that it allows the boundary to exhibit an asymmetric, directed shape in the feature space, in order to adapt to the physical law that the load response characteristics slowly drift in the parameter space along a specific direction (such as the rotor resistance axis of an induction motor).

[0042] Specifically, for group j, starting from the cluster center c_j, a relaxation radius amplification factor β_j>1 is applied along the principal component direction, which is most sensitive to simulation error, while maintaining a compact boundary in the other orthogonal directions. The final decision function for each group j is: Where, Σ j The Mahalanobis distance scaling matrix has diagonal elements that are smaller in sensitive directions (corresponding to wider boundaries) and larger in insensitive directions (corresponding to tighter boundaries). This directed boundary differs from the isotropic SVDD hyperspheres commonly seen in the literature.

[0043] Stage C3: Hard and Ambiguous Determination of Boundary Regions Define three types of regions: Core area: f j (V)=1 and for all k≠j, we have f k (V)=0; Overlapping fuzzy region: There exist at least two distinct groups j1 and j2 such that f j1 (V)=1 and f j2 (V)=1; Outer point region: for all j, f j (V)=0.

[0044] Load bus nodes in the overlapping ambiguity zone are not subject to hard assignment, but instead enter the personalized parameter generation process in step D.

[0045] In step 105, parameter interpolation is performed on the load bus nodes in the core area and the overlapping fuzzy area.

[0046] Preferably, the parameter interpolation for the load bus nodes in the core area and the overlapping ambiguity area includes: For the load bus node in the core area, parameter interpolation is performed based on a pre-identified set of composite load model parameters Θ_j corresponding to the load group j to which the load bus node is located; For load bus nodes in the overlapping ambiguity region, their parameter θ is generated using the following constrained hybrid weighting strategy: , , in, The set of fuzzy groups to which the load bus nodes belong; For the first j The weight coefficients of each group in the interpolation of the node parameters; The standard load model parameters are pre-calibrated for the j-th group; γ is the Mahalanobis distance from the load bus node to the decision boundary of group j; γ is the sensitivity coefficient. For electromechanical transient simulation power angle error; Let be the group standard parameters of group j and their approximate sensitivity to the simulation power angle error.

[0047] In this invention, based on the partitioning results, the standard load model parameters of the corresponding group are directly assigned to the core area nodes, and the parameters are interpolated by a joint weighting strategy of distance inverse ratio and simulation sensitivity for the overlapping and ambiguous area nodes.

[0048] Each load group j corresponds to a pre-identified set of composite load model parameters Θ_j. For nodes identified as core areas in the step, Θ_j is directly used. For nodes in overlapping fuzzy areas, their parameters θ are generated using the following constrained hybrid weighting strategy: , in, The set of fuzzy groups to which the load bus nodes belong; For the first j The weight coefficient of each group in the parameter interpolation of this node is a non-negative real number. The larger the weight, the higher the proportion of the parameters of this group in the final interpolation result. The standard load model parameters pre-calibrated for the j-th group, i.e. the typical parameter values ​​uniformly adopted by the core area nodes of the group, are stored in the system's load model parameter library; γ is the Mahalanobis distance from the load bus node to the decision boundary of group j; γ is the sensitivity coefficient. For electromechanical transient simulation power angle error; Let be the group standard parameters of group j and their approximate sensitivity to the simulation power angle error.

[0049] In step 106, based on each load bus node and its corresponding parameters, load response characteristics are grouped and cluster boundaries are characterized.

[0050] Preferably, the load response characteristics are clustered and the cluster boundaries are characterized based on each load bus node and its corresponding parameters, including: Each load bus node and its corresponding parameters are compiled into a load model card format compatible with the simulation software, or directly output as a dynamic model data file of the simulation platform, so as to realize the characterization of load response characteristics clustering and cluster boundaries.

[0051] In this invention, the final output is a load model parameter file compatible with commercial simulation software such as BPA, PSASP, and PSS / E. Specifically, each load bus node and its corresponding parameter θ (standard parameters for core area nodes and interpolated parameters for fuzzy area nodes) are compiled into a load model card format compatible with commercial software such as BPA, PSASP, and PSS / E, or directly output as a dynamic model data file for the simulation platform, so as to realize the characterization of load response characteristic clustering and cluster boundaries.

[0052] This invention achieves a reasonable expression of the continuous and gradual change process of load response characteristics by deeply coupling the cluster boundary characterization with the electromechanical transient simulation target, which significantly improves the simulation accuracy and model transferability.

[0053] Compared with the prior art, the present invention has the following significant technical effects: (1) Deep coupling between feature extraction and simulation target: Among the six types of features constructed in this invention, B1 (coupled drop depth) directly corresponds to the acceleration power of the power angle swing, the four-segment partition slope of B2 corresponds to the nonlinear process of slip recovery of the induction motor, and the manifold embedding feature of B3 reflects the load dissipation characteristics. These features are not general statistics, but are compressed expressions customized for the generator rotor motion equation in electromechanical transient simulation, and have clear physical meaning.

[0054] (2) Asymmetric and directed description capability of cluster boundaries: The directed boundary support vector description adopted in this invention overcomes the defect that the traditional SVDD spherical boundary cannot characterize the directionality of load parameter drift by setting a loose boundary in the simulation sensitive direction and keeping a tight boundary in the non-sensitive direction, making the number of boundary nodes more reasonable and avoiding fuzzy areas that are too large or too small.

[0055] (3) Introduction of simulation sensitivity feedback through boundary node parameter interpolation: In the weighting strategy of step D of this invention, in addition to the inverse distance ratio, a parameter-error sensitivity coefficient is also embedded, so that the model parameters of the boundary nodes not only depend on their geometric position in the feature space, but also on the degree of influence of the group of parameters on the final simulation results, forming a closed loop of "feature space → parameter space → simulation error → parameter adjustment".

[0056] (4) Strong engineering practicality: This invention is based on data that can be obtained from PMU / WAMS, does not rely on unobservable state variables, and the boundary decision function after training can be transferred to unmeasured nodes with similar electrical distances (by replacing V in Mahalanobis distance with the feature estimate of that node), reducing global measurement dependence.

[0057] Figure 3 This is a schematic diagram of the load response characteristic clustering and grouping boundary characterization system 300 according to an embodiment of the present invention. Figure 3 As shown, the load response characteristic clustering and boundary characterization system 300 provided in this embodiment of the invention includes: a response data acquisition unit 301, a feature vector construction unit 302, a clustering unit 303, a feature space partitioning unit 304, a parameter interpolation unit 305, and a clustering and boundary characterization implementation unit 306.

[0058] Preferably, the response data acquisition unit 301 is used to acquire response data of multiple load bus nodes during voltage dips or frequency fluctuations.

[0059] Preferably, the response data includes: voltage amplitude time series {u(t)}, active power time series {p(t)}, and reactive power time series {q(t)} aligned with the same time base, wherein the value of t ranges from at least one cycle before the disturbance occurrence time T0 to the time T after the disturbance when the system enters a new steady state. _end .

[0060] Preferably, the feature vector construction unit 302 is used to construct a load dynamic compression feature vector based on the response data, with the power angle initial swing response as the target.

[0061] Preferably, the feature vector construction unit 302 constructs a load dynamic compression feature vector based on the response data, targeting the initial swing response at the work angle, including: The voltage-active power coupling sag depth is calculated using the following method: , Where, ΔT d T0 represents the duration of the disturbance; T0 represents the time when the disturbance occurred. Active power; Voltage amplitude; The first preset time period after the disturbance clearing time T_clear is divided into four sub-intervals, and the average rate of change of active power in each sub-interval is calculated. k 1, k 2, k 3, k 4. To form a four-dimensional sub-feature characterizing the initial power recovery slope; The active-voltage two-dimensional trajectory is reduced in dimension, and the difference between the first and last points of the trajectory after embedding into the one-dimensional manifold is taken as the low-dimensional manifold embedding feature of the voltage-active trajectory. For the residual sequence of active power after removing the trend term, the logarithmic decay rate of the dominant oscillation mode is extracted using the matrix bundle method. α Determine the damping properties of the residual oscillations; where, if there are no identifiable oscillations in the sequence, then α is set to 0; The signed error of steady-state recovery deviation is calculated as follows: ε_sgn=p(T) _end )–1, where p(T) _end T represents the time T at which the system enters a new steady state after the disturbance. _end The active power; If multiple perturbation events exist, the median and interquartile range of the above features under each event are calculated to form the final feature vector V∈R. D Where D = (1 dimension each of B1~B5 + 4 dimensions of B2 segment) × (median + interquartile range) × event dimension aggregation coefficient; B1~B5 represent five features respectively: voltage-active coupling drop depth, four-dimensional sub-feature, low-dimensional manifold embedding feature of voltage-active trajectory, damping property of residual oscillation and signed error.

[0062] Preferably, the clustering unit 303 is used to perform clustering based on the load dynamic compression feature vector of all load bus nodes to determine multiple load groups.

[0063] Preferably, the clustering unit 303 performs clustering based on the load dynamic compression feature vectors of all load bus nodes to determine multiple load groups, including: In the traditional fuzzy C-mean objective function, a regularization term guided by electromechanical transient simulation is introduced to cluster the load dynamic compression feature vectors of all load bus nodes using the improved fuzzy C-mean, thereby identifying multiple load groups. The modified objective function is as follows: in, g (V i ,c j The surrogate function, "characteristic deviation - power angle error," is pre-fitted using a small number of simulation samples and is used to quantify the error at a given node. i Classified into a group j At that time, the expected power angle simulation error caused by characteristic deviation; N is the total number of load bus nodes; C The preset number of clusters; u ij For the first i The node belongs to the firstj The fuzzy membership degree of each load group satisfies and ; m For fuzzy weighted index; V i For the first i The load dynamic compression characteristic vector of each load bus node; c j For the first j Cluster center vectors of each load group; For the characteristic vector V i To cluster center c j The square of the Euclidean distance; λ It is a balancing factor.

[0064] Preferably, the feature space partitioning unit 304 is used to delineate the group boundary for each load group, and divide the feature space into a core area, an overlapping fuzzy area, and an outer point area based on the group boundary.

[0065] Preferably, the feature space partitioning unit 304 performs group boundary characterization for each load group, including: For each load group j, its attribution boundary is constructed using the directed boundary support vector method; wherein, the attribution decision function for each load group j is: , Where Σj is the Mahalanobis distance scaling matrix of the j-th group. f j (V) represents the discrimination function for the j-th load group to the sample feature vector V. The output value is positive 1 or negative 1. Positive 1 indicates that the sample is located inside the boundary of the group, and negative 1 indicates that it is located outside the boundary. sgn(·) is the sign function. When the expression in the parentheses is greater than or equal to zero, it outputs positive 1, and when it is less than zero, it outputs negative 1. Let V be the directed boundary radius of the j-th group; V is the characteristic vector of the load node to be discriminated; a j Let be the directed boundary ellipsoid center vector of the j-th group, representing the typical position of the group in the characteristic space; This is the transpose of the characteristic deviation vector, where the superscript T indicates the transpose operation of a matrix or vector; Σj is the inverse of the Mahalanobis distance scaling matrix of the j-th group.

[0066] Preferably, the feature space partitioning unit 304 divides the feature space into a core region, an overlapping fuzzy region, and an outer point region based on the group boundary, including: If load group j satisfies f j (V)=1 and for all k≠j, we have f k If (V)=0, then load group j is located in the core area; If there exist at least two distinct load groups j1 and j2 such that f j1 (V)=1 and f j2 If (V)=1, then load groups j1 and j2 are located in the cross-fuzzy region; If for all load groups j, f j If (V)=0, then all load groups j are determined to be in the outer point zone.

[0067] Preferably, the parameter interpolation unit 305 is used to perform parameter interpolation on the load bus nodes in the core area and the overlapping ambiguity area.

[0068] Preferably, the parameter interpolation unit 305 performs parameter interpolation on the load bus nodes in the core area and the overlapping ambiguity area, including: For the load bus node in the core area, parameter interpolation is performed based on a pre-identified set of composite load model parameters Θ_j corresponding to the load group j to which the load bus node is located; For load bus nodes in the overlapping ambiguity region, their parameter θ is generated using the following constrained hybrid weighting strategy: , , in, The set of fuzzy groups to which the load bus nodes belong; For the first j The weight coefficients of each group in the interpolation of the node parameters; The standard load model parameters are pre-calibrated for the j-th group; γ is the Mahalanobis distance from the load bus node to the decision boundary of group j; γ is the sensitivity coefficient. For electromechanical transient simulation power angle error; Let be the group standard parameters of group j and their approximate sensitivity to the simulation power angle error.

[0069] Preferably, the clustering and boundary characterization implementation unit 306 is used to implement load response characteristic clustering and cluster boundary characterization based on each load bus node and its corresponding parameters.

[0070] Preferably, the clustering and boundary characterization implementation unit 306, based on each load bus node and its corresponding parameters, implements load response characteristic clustering and boundary characterization, including: Each load bus node and its corresponding parameters are compiled into a load model card format compatible with the simulation software, or directly output as a dynamic model data file of the simulation platform, so as to realize the characterization of load response characteristics clustering and cluster boundaries.

[0071] The load response characteristic clustering and cluster boundary characterization system 300 of the present invention corresponds to the load response characteristic clustering and cluster boundary characterization method 100 of another embodiment of the present invention, and will not be described again here.

[0072] According to another aspect of the present invention, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any one of the methods for load response characteristic clustering and cluster boundary characterization.

[0073] According to another aspect of the present invention, the present invention provides an electronic device, comprising: The aforementioned computer-readable storage medium; and One or more processors for executing a program in the computer-readable storage medium.

[0074] The present invention has been described with reference to a few embodiments. However, it will be apparent to those skilled in the art that other embodiments besides those disclosed above fall equivalently within the scope of the present invention.

[0075] Generally, all terms used in this invention are interpreted according to their ordinary meaning in the art, unless otherwise expressly defined herein. All references to “a / the / the [device, component, etc.]” ​​are openly interpreted as at least one instance of said device, component, etc., unless otherwise expressly stated. The steps of any method disclosed herein need not be performed in the exact order disclosed, unless explicitly stated otherwise.

[0076] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0077] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0078] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0079] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for clustering and defining cluster boundaries of load response characteristics, characterized in that, The method includes: Acquire response data from multiple load bus nodes during voltage dips or frequency fluctuations; Based on the response data, a load dynamic compression feature vector is constructed with the power angle initial swing response as the target; Clustering is performed based on the load dynamic compression feature vectors of all load bus nodes to identify multiple load groups; For each load group, the group boundary is characterized, and the feature space is divided into a core region, an overlapping fuzzy region, and an outer point region based on the group boundary. Perform parameter interpolation on the load bus nodes in the core area and overlapping ambiguity area; Based on each load bus node and its corresponding parameters, load response characteristics are grouped and cluster boundaries are characterized.

2. The method according to claim 1, characterized in that, The response data includes: voltage amplitude time series {u(t)}, active power time series {p(t)}, and reactive power time series {q(t)} aligned with the same time base, wherein the value of t ranges from at least one cycle before the disturbance occurrence time T0 to the time T after the disturbance when the system enters a new steady state. _end .

3. The method according to claim 1, characterized in that, Based on the response data, a load dynamic compression feature vector is constructed with the power angle initial swing response as the target, including: The voltage-active power coupling sag depth is calculated using the following method: , Where, ΔT d T0 represents the duration of the disturbance; T0 represents the time when the disturbance occurred. Active power; Voltage amplitude; The first preset time period after the disturbance clearing time T_clear is divided into four sub-intervals, and the average rate of change of active power in each sub-interval is calculated. k 1, k 2, k 3, k 4. To form a four-dimensional sub-feature characterizing the initial power recovery slope; The active-voltage two-dimensional trajectory is reduced in dimension, and the difference between the first and last points of the trajectory after embedding into the one-dimensional manifold is taken as the low-dimensional manifold embedding feature of the voltage-active trajectory. For the residual sequence of active power after removing the trend term, the logarithmic decay rate of the dominant oscillation mode is extracted using the matrix bundle method. α Determine the damping properties of the residual oscillations; where, if there are no identifiable oscillations in the sequence, then α is set to 0; The signed error of steady-state recovery deviation is calculated as follows: ε_sgn=p(T) _end )–1, where p(T) _end T represents the time T at which the system enters a new steady state after the disturbance. _end The active power; If multiple perturbation events exist, the median and interquartile range of the above features under each event are calculated to form the final feature vector V∈R. D Where D = (1 dimension each of B1~B5 + 4 dimensions of B2 segment) × (median + interquartile range) × event dimension aggregation coefficient; B1~B5 represent five features respectively: voltage-active coupling drop depth, four-dimensional sub-feature, low-dimensional manifold embedding feature of voltage-active trajectory, damping property of residual oscillation and signed error.

4. The method according to claim 1, characterized in that, Clustering is performed based on the load dynamic compression feature vectors of all load bus nodes to identify multiple load groups, including: In the traditional fuzzy C-mean objective function, a regularization term guided by electromechanical transient simulation is introduced to cluster the load dynamic compression feature vectors of all load bus nodes using the improved fuzzy C-mean, thereby identifying multiple load groups. The modified objective function is as follows: ， in, g (V i ,c j The ) is a surrogate function for "characteristic deviation - power angle error" obtained in advance through a small number of simulation samples, used to quantify the error when the node... i Classified into a group j At that time, the expected power angle simulation error caused by characteristic deviation; N is the total number of load bus nodes; C The preset number of clusters; u ij For the first i The node belongs to the first j The fuzzy membership degree of each load group satisfies and ; m For fuzzy weighted index; V i For the first i The load dynamic compression characteristic vector of each load bus node; c j For the first j Cluster center vectors of each load group; For the characteristic vector V i To cluster center c j The square of the Euclidean distance; λ It is a balancing factor.

5. The method according to claim 1, characterized in that, For each load group, the group boundary is characterized, including: For each load group j, its attribution boundary is constructed using the directed boundary support vector method; wherein, the attribution decision function for each load group j is: ， Where Σj is the Mahalanobis distance scaling matrix of the j-th group. f j (V) represents the discrimination function for the j-th load group to the sample feature vector V. The output value is positive 1 or negative 1. Positive 1 indicates that the sample is located inside the boundary of the group, and negative 1 indicates that it is located outside the boundary. sgn(·) is the sign function. When the expression in the parentheses is greater than or equal to zero, it outputs positive 1, and when it is less than zero, it outputs negative 1. Let V be the directed boundary radius of the j-th group; V is the characteristic vector of the load node to be discriminated; a j Let be the directed boundary ellipsoid center vector of the j-th group, representing the typical position of the group in the characteristic space; This is the transpose of the characteristic deviation vector, where the superscript T indicates the transpose operation of a matrix or vector; Σj is the inverse of the Mahalanobis distance scaling matrix of the j-th group.

6. The method according to claim 1, characterized in that, Based on the group boundary, the feature space is divided into a core region, an overlapping and blurred region, and an outer point region, including: If load group j satisfies f j (V)=1 and for all k≠j, we have f k If (V)=0, then load group j is located in the core area; If there exist at least two distinct load groups j1 and j2 such that f j1 (V)=1 and f j2 If (V)=1, then load groups j1 and j2 are located in the cross-fuzzy region; If for all load groups j, f j If (V)=0, then all load groups j are determined to be in the outer point zone.

7. The method according to claim 1, characterized in that, Parameter interpolation is performed on the load bus nodes in the core area and overlapping ambiguity area, including: For the load bus node in the core area, parameter interpolation is performed based on a pre-identified set of composite load model parameters Θ_j corresponding to the load group j to which the load bus node is located; For load bus nodes in the overlapping ambiguity region, their parameter θ is generated using the following constrained hybrid weighting strategy: , ， in, The set of fuzzy groups to which the load bus nodes belong; For the first j The weight coefficients of each group in the interpolation of the node parameters; The standard load model parameters are pre-calibrated for the j-th group; γ is the Mahalanobis distance from the load bus node to the decision boundary of group j; γ is the sensitivity coefficient. For electromechanical transient simulation power angle error; Let be the group standard parameters of group j and their approximate sensitivity to the simulation power angle error.

8. The method according to claim 1, characterized in that, Based on each load bus node and its corresponding parameters, load response characteristics are clustered and their boundaries are characterized, including: Each load bus node and its corresponding parameters are compiled into a load model card format compatible with the simulation software, or directly output as a dynamic model data file of the simulation platform, so as to realize the characterization of load response characteristics clustering and cluster boundaries.

9. A system for grouping and defining cluster boundaries of load response characteristics, characterized in that, The system includes: The response data acquisition unit is used to acquire response data of multiple load bus nodes during voltage dips or frequency fluctuations. A feature vector construction unit is used to construct a load dynamic compression feature vector based on the response data, with the power angle initial swing response as the target. Clustering units are used to cluster based on the load dynamic compression feature vectors of all load bus nodes to identify multiple load groups; The feature space partitioning unit is used to characterize the group boundary of each load group and divide the feature space into the core area, the overlapping fuzzy area and the outer point area based on the group boundary. The parameter interpolation unit is used to perform parameter interpolation on the load bus nodes in the core area and the overlapping ambiguity area. The clustering and boundary characterization implementation unit is used to implement the clustering and boundary characterization of load response characteristics based on each load bus node and its corresponding parameters.

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

11. An electronic device, characterized in that, include: The computer-readable storage medium as described in claim 10; as well as One or more processors for executing a program in the computer-readable storage medium.

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