CN110690716A - Method and system for positioning active splitting section of power grid based on voltage trajectory information - Google Patents

Method and system for positioning active splitting section of power grid based on voltage trajectory information Download PDF

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CN110690716A
CN110690716A CN201910760005.7A CN201910760005A CN110690716A CN 110690716 A CN110690716 A CN 110690716A CN 201910760005 A CN201910760005 A CN 201910760005A CN 110690716 A CN110690716 A CN 110690716A
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node voltage
track
voltage
space
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CN110690716B (en
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李宗翰
刘道伟
张东霞
马世英
杨红英
郑恒峰
刘洋
杨少波
赵高尚
李京
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Power Grid Corp Northeast Division
China Electric Power Research Institute Co Ltd CEPRI
Northeast Electric Power University
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Power Grid Corp Northeast Division
China Electric Power Research Institute Co Ltd CEPRI
Northeast Dianli University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
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Abstract

The invention discloses a method and a system for positioning an active splitting section of a power grid based on voltage trajectory information, wherein the method comprises the following steps: constructing a vector offset feature space of a node voltage phase track; acquiring the time sequence evolution characteristic of the node voltage when the power system is in step-out oscillation by utilizing the vector offset characteristic space of the node voltage trajectory; and according to the time sequence evolution characteristics of the node voltage, evaluating the similarity of the node voltage change based on a track clustering algorithm, and positioning one or more splitting sections by tracking the one or more splitting sections. According to the technical scheme, a time sequence evolution rule of node voltage change is extracted by constructing an offset characteristic space, the rationality of the rule is explained by a two-machine equivalent system, the similarity evaluation of node voltage tracks is realized by a track distance-based adaptive clustering algorithm, and then the splitting section is accurately positioned on line through cluster expansion and power self-balancing constraint.

Description

Method and system for positioning active splitting section of power grid based on voltage trajectory information
Technical Field
The invention relates to the technical field of transient stability control of a large power grid, in particular to a method and a system for positioning an active splitting section of the power grid based on voltage trajectory information.
Background
With the rapid development of ultrahigh voltage alternating current and direct current power grids in China, the grid pattern and the power supply structure are greatly changed, the operating characteristics of the power grids are deeply changed, the traditional power grid online safety defense concept and stability control technology taking modeling simulation and expected faults as the core are difficult to adapt to the power grid development requirements, and three defense systems for safety and stability of the current power grids face severe challenges. The out-of-step separation is used as the last defense line for ensuring the safe and stable operation of the power grid, and is one of important prevention and control measures for restraining further propagation of the power failure accident of the interconnected power grid. However, with the continuous expansion of system scale and the formation of a cross-regional interconnected power grid, the passive splitting section positioning method based on the oscillation center positioning is difficult to adapt to complex fault forms, and is very easy to cause serious consequences.
In recent years, with the popularization and application of Wide Area Measurement Systems (WAMS), high-precision real-time monitoring of the operation state of a power grid becomes possible. Active splitting methods based on online decision-making become current research hotspots, which are mainly classified into the following three categories:
(1) the method is mainly characterized in that the method comprises a network simplification method and a rapid network division method. The network simplification method sacrifices the integrity of the system in order to reduce the search scale and accelerate the solving speed, which may cause the loss of a feasible solution; the rapid network partition method can effectively avoid traversal search of feasible solutions, but the final solution often does not meet the connectivity constraint; (2) the method comprises the steps of searching a splitting section based on a slow coherent theory, extracting a dynamic mode of a power system and analyzing weak connection among clusters by constructing a singular perturbation model with double time scales, and identifying coherent clusters and weak links. However, the method needs to calculate the characteristic value and the characteristic vector, the calculation amount is too large, and the solving speed of the optimal splitting section is forced to be reduced; (3) and (4) searching a splitting section based on an intelligent algorithm. The active splitting of the power grid has higher requirements on timeliness, and the optimal splitting section needs to be calculated within a limited time. The optimal splitting section solving problem based on the optimization theory is substantially an NP-hard problem, and researches prove that the optimal splitting section solving problem does not have an accurate solution in linear time complexity, so that the searching speed and the accuracy can be improved by solving an approximate solution or converting an objective function, and the stability of an isolated island after splitting is ensured.
In the actual large power grid splitting process, the splitting section candidate space is a set of all branch circuit breaking combinations, so that the splitting scheme is increased in a geometric exponential mode along with scale improvement. For the slow coherent theory and the intelligent optimization algorithm, apart from inherent defects of the slow coherent theory and the intelligent optimization algorithm, the slow coherent theory and the intelligent optimization algorithm are limited by system scale in different degrees and face huge calculation pressure, so that the second-level solving speed of practical power grid splitting control is difficult to meet, and the slow coherent theory and the intelligent optimization algorithm can be applied to on-line operation only by further research and improvement.
Therefore, a technique is needed to realize the positioning of the active splitting section of the power grid based on the voltage trajectory information.
Disclosure of Invention
The technical scheme of the invention provides a method and a system for positioning an active splitting section of a power grid based on voltage trajectory information, so as to solve the problem of how to position the active splitting section of the power grid based on the voltage trajectory information.
In order to solve the above problem, the present invention provides a method for positioning an active splitting section of a power grid based on voltage trajectory information, the method including:
constructing a vector offset feature space of a node voltage phase track;
acquiring the time sequence evolution characteristic of the node voltage when the power system is in step-out oscillation by utilizing the vector offset characteristic space of the node voltage trajectory;
and according to the time sequence evolution characteristics of the node voltage, evaluating the similarity of the node voltage change based on a track clustering algorithm, and positioning one or more splitting sections by tracking the one or more splitting sections.
Preferably, the constructing a vector offset eigenspace of the node voltage phase trajectories comprises:
with dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdLet a node start point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) And the vector offset characteristic track of the vector between the starting point and the end point forming node i in a certain time interval is as follows:
Figure BDA0002169966440000031
constructed of
Figure BDA0002169966440000032
As a node at dl、dθ、dpJudging basis of movement direction change and speed change in a certain time interval in space;
Figure BDA0002169966440000033
component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
Preferably, the obtaining, by using a vector offset feature space of the node voltage trajectory, a time sequence evolution feature of the node voltage during step-out oscillation of the power system includes:
collecting the time sequence information of the node voltage in the power grid through a wide area measurement system, acquiring the time sequence information of the node voltage in a certain time interval, and forming a voltage phasor track group UR of all nodes in a voltage complex space in the time intervalTm：
Figure BDA0002169966440000034
In the formula (I), the compound is shown in the specification,
Figure BDA0002169966440000035
represents the m-th time interval TmInner, voltage vector of node i; and n is the number of all nodes of the power grid.
Preferably, the estimating, according to the time-series evolution characteristic of the node voltage, the similarity of the node voltage changes based on a trajectory clustering algorithm, and locating one or more splitting sections by tracking the one or more splitting sections, further includes:
selecting time sequence tracks in a preset time interval for clustering, defining the time sequence tracks as the sum of distances between points of different tracks under the same time scale, and recording the sum as DTrajThe method is used for representing the similarity degree between time sequence tracks and measuring the difference degree between different tracks; the distance between two discrete points at a certain time in the space is known as follows:
Figure BDA0002169966440000036
the distance D can be used to generalize to the inter-track distance D within a certain time intervalTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn
in the formula DnThe distance between two points at the nth moment is expressed, and n is the window length of the time sliding window;
the distance between any two tracks can be obtained by sliding the window length by one unit.
Preferably, the method further comprises the following steps:
performing cluster expansion on the neighborhood track group, and offsetting tracks of each vector in the neighborhoodPerforming secondary traversal and label assignment by applying to the neighborhood
Figure BDA0002169966440000042
Inner track vector offset trackPerforming a second traversal to find an AND in the original cluster
Figure BDA0002169966440000044
Indirectly similar and not yet assigned to the trajectory of the tag.
According to another aspect of the present invention, there is provided a system for positioning an active splitting section of a power grid based on voltage trajectory information, the system comprising:
the building unit is used for building a vector offset characteristic space of the node voltage phase track;
the acquisition unit is used for acquiring the time sequence evolution characteristics of the node voltage during the step-out oscillation of the power system by utilizing the vector offset characteristic space of the node voltage trajectory;
and the positioning unit is used for evaluating the similarity of the node voltage change based on a track clustering algorithm according to the time sequence evolution characteristics of the node voltage and positioning one or more splitting sections by tracking the one or more splitting sections.
Preferably, the construction unit is configured to construct a vector offset eigenspace of the node voltage phase trajectories, and further configured to:
with dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdLet a node start point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) And the vector offset characteristic track of the vector between the starting point and the end point forming node i in a certain time interval is as follows:
constructed of
Figure BDA0002169966440000046
As a node at dl、dθ、dpJudging basis of movement direction change and speed change in a certain time interval in space;
Figure BDA0002169966440000047
component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
Preferably, the obtaining unit is configured to obtain a time sequence evolution characteristic of the node voltage when the power system is in step-out oscillation by using a vector offset feature space of the node voltage trajectory, and is further configured to:
collecting the time sequence information of the node voltage in the power grid through a wide area measurement system, acquiring the time sequence information of the node voltage in a certain time interval, and forming a voltage phasor track group UR of all nodes in a voltage complex space in the time intervalTm：
Figure BDA0002169966440000048
In the formula (I), the compound is shown in the specification,
Figure BDA0002169966440000051
represents the m-th time interval TmInner, voltage vector of node i; and n is the number of all nodes of the power grid.
Preferably, the positioning unit is configured to evaluate similarity of changes of the node voltages based on a trajectory clustering algorithm according to a time-series evolution characteristic of the node voltages, and position one or more splitting sections by tracking the one or more splitting sections, and is further configured to:
selecting time sequence tracks in a preset time interval for clustering, defining the time sequence tracks as the sum of distances between points of different tracks under the same time scale, and recording the sum as DTrajThe method is used for representing the similarity degree between time sequence tracks and measuring the difference degree between different tracks; the distance between two discrete points at a certain time in the space is known as follows:
Figure BDA0002169966440000052
the distance D can be used to generalize to the inter-track distance D within a certain time intervalTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn
in the formula DnThe distance between two points at the nth moment is expressed, and n is the window length of the time sliding window;
the distance between any two tracks can be obtained by sliding the window length by one unit.
Preferably, the positioning unit is further configured to:
performing cluster expansion on the neighborhood track group, and offsetting tracks of each vector in the neighborhood
Figure BDA0002169966440000053
Performing secondary traversal and label assignment by applying to the neighborhood
Figure BDA0002169966440000054
Inner track vector offset track
Figure BDA0002169966440000055
Performing a second traversal to find an AND in the original cluster
Figure BDA0002169966440000056
Indirectly similar and not yet assigned to the trajectory of the tag.
The technical scheme of the invention provides a method and a system for positioning an active splitting section of a power grid based on voltage trajectory information, wherein the method comprises the following steps: constructing a vector offset feature space of a node voltage phase track; acquiring a time sequence evolution characteristic of the node voltage when the power system is in step-out oscillation by utilizing a vector offset characteristic space of a node voltage track; and evaluating the change of the node voltage based on a track clustering algorithm according to the time sequence evolution characteristics of the node voltage, and positioning one or more splitting sections by tracking the one or more splitting sections. The technical scheme of the invention is switched in from a brand-new visual angle of a voltage track, provides a quick positioning method of an active splitting section and aims to save the survival capability of a power grid main body. According to the technical scheme, a time sequence evolution rule of node voltage change is extracted by constructing an offset characteristic space, the rationality of the rule is explained by a two-machine equivalent system, the evaluation of the node voltage track similarity is realized by a track distance-based adaptive clustering algorithm, and then the splitting section is accurately positioned on line through cluster expansion and power self-balancing constraint. The technical scheme of the invention is independent of a mathematical model, is not limited by a system operation mode and a fault form, does not need complex calculation, has strong section connectivity, and has important significance for realizing transient stability active defense of an information-driven large power grid.
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A more complete understanding of exemplary embodiments of the present invention may be had by reference to the following drawings in which:
FIG. 1 is a flow chart of a method for locating an active splitting section of a power grid based on voltage trajectory information in accordance with a preferred embodiment of the present invention;
FIG. 2 is a schematic diagram of feature space construction according to a preferred embodiment of the present invention;
FIG. 3 is a system diagram of an IEEE-9 node in accordance with a preferred embodiment of the present invention;
FIG. 4 is a graph of a characteristic trace for a system steady after a fault in accordance with a preferred embodiment of the present invention;
FIG. 5 is a characteristic trace diagram for a post-fault system instability condition in accordance with a preferred embodiment of the present invention;
FIG. 6 is a schematic diagram of a two-machine model of a power system in accordance with a preferred embodiment of the present invention;
FIG. 7 is a graph of node voltage traces in accordance with a preferred embodiment of the present invention;
FIG. 8 is a graph of node voltage phase angles in accordance with a preferred embodiment of the present invention;
FIG. 9 is a flow chart of a clustering algorithm according to a preferred embodiment of the present invention;
FIG. 10 is a diagram illustrating a cluster expansion procedure in accordance with a preferred embodiment of the present invention;
FIG. 11 is a graph showing simulation results according to a preferred embodiment of the present invention;
FIG. 12 is a graph showing simulation results according to a preferred embodiment of the present invention;
FIG. 13 is a graph showing simulation results according to a preferred embodiment of the present invention;
FIG. 14 is a cross-sectional transition diagram illustrating active splitting according to a preferred embodiment of the present invention;
FIG. 15 is a graph of simulation results for an example of an actual grid in accordance with a preferred embodiment of the present invention; and
fig. 16 is a system configuration diagram for locating an active grid splitting section based on voltage trajectory information according to a preferred embodiment of the present invention.
Detailed Description
The exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the embodiments described herein, which are provided for complete and complete disclosure of the present invention and to fully convey the scope of the present invention to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention. In the drawings, the same units/elements are denoted by the same reference numerals.
Unless otherwise defined, terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Further, it will be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense.
Fig. 1 is a flowchart of a method for locating an active splitting section of a power grid based on voltage trajectory information according to a preferred embodiment of the present invention. In recent years, the grid pattern and the power supply structure are greatly changed, the operating characteristics of the power grid are deeply changed, the traditional power grid online safety defense concept and the stability control technology are difficult to adapt to the power grid development requirements, and the current three-defense system for the safety and the stability of the power grid faces a severe challenge. The implementation mode of the application provides a quick positioning method of an active splitting section by cutting in with a brand-new visual angle of a voltage track, and aims to save the survival capacity of a power grid main body. The method comprises the steps of extracting a time sequence evolution rule of node voltage change by constructing an offset characteristic space, evaluating the similarity of node voltage tracks by a track distance-based adaptive clustering algorithm, and accurately positioning a splitting section on line by cluster expansion and power self-balancing constraint. The effectiveness of the method is verified by the IEEE-39 calculation and the practical regional interconnected network calculation, complex calculation is not needed, time consumption is short, section connectivity is strong, and the method has a certain engineering practice value. The invention provides a novel method for quickly positioning an active splitting section of a power grid, which achieves the purpose of the invention by constructing an offset characteristic space, extracting a time sequence evolution rule of node voltage change, clustering and positioning the splitting section based on a characteristic track and adaptively adjusting an algorithm. As shown in fig. 1, a method for positioning an active splitting section of a power grid based on voltage trajectory information includes:
preferably, in step 101: and constructing a vector offset feature space of the node voltage phase locus. Preferably, constructing a vector offset eigenspace of the node voltage phase trajectories comprises:
with dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdLet a node start point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) The vector offset characteristic track of the vector forming node i between the starting point and the end point in a certain time interval is as follows:
Figure BDA0002169966440000081
constructed ofAs a node at dl、dθ、dpJudging basis of movement direction change and speed change in a certain time interval in space;component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
The voltage phase locus is a directed locus of bus voltage phasor in a complex number space in the space-time motion behavior of the power grid. The track has the characteristic of complete vector and can be regarded as continuous directional splicing of infinite direction vectors on a time scale. The method is based on the existing vector distance definition and adjacent time intervals T in a voltage complex spacem、Tm+1In the interior, 2 sections of tracks of the node i can be obtainedThe traces are shown in FIG. 2 (a). The vector offset of the 2 nd segment with respect to the 1 st segment track can be represented by dl(m+1)i、dθ(m+1)iAnd dp(m+1)iAnd (5) characterizing. Similarly, the vector offset of the 1 st segment of the track relative to the track in the previous interval can be represented by dlmi、dθmiAnd dpmiAnd (5) characterizing.
In the present application dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdAs shown in fig. 2 (b). And set a starting point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) The Vector offset feature Trajectory (VVMCT) of a Vector between two points constituting a node i in a certain time interval is:
Figure BDA0002169966440000084
constructed by the formula (1)Can be regarded as a node at dl-dθ-dpAnd judging the change of the moving direction and the change of the speed in a certain time interval in the space.
Figure BDA0002169966440000086
Component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
Preferably, at step 102: the method for acquiring the time sequence evolution characteristics of the node voltage during the out-of-step oscillation of the power system by utilizing the vector offset characteristic space of the node voltage trajectory comprises the following steps:
collecting time sequence information of node voltage in the power grid through a wide area measurement system, acquiring the time sequence information of the node voltage in a certain time interval, and forming a voltage phasor track group UR of all nodes in a voltage complex space in the time intervalTm：
Figure BDA0002169966440000087
In the formula (I), the compound is shown in the specification,
Figure BDA0002169966440000091
represents the m-th time interval TmInner, voltage vector of node i; and n is the number of all nodes of the power grid.
The time sequence information of the node voltage in the power grid can be acquired through the wide area measurement system. By obtaining the node voltage time sequence information in a certain time interval, the voltage phasor track group UR of all the nodes in the voltage complex space in the time interval can be formedTm：
Figure BDA0002169966440000092
In the formula (I), the compound is shown in the specification,
Figure BDA0002169966440000093
represents the voltage vector of the node i in the mth time interval Tm; and n is the number of all nodes of the power grid.
In order to illustrate the necessity of constructing the offset feature space and verify the validity of the method, the IEEE 9 node system shown in fig. 3 is taken as an example in the present application, and the node voltage motion conditions of the system after the fault in two forms, namely, the stable state and the unstable state, are analyzed.
1) Three-phase short circuit faults occur at 50% of the positions of the connecting lines between the buses 2 and 4, the fault lines are cut off after 0.1s, and the system is kept stable. Based on the above method, the motion process of the node voltage in the transient process 1s is projected to the feature space, and the trajectories in the feature space and the three feature tangential planes are shown in fig. 4. The motion tracks of all nodes in the system form 1 characteristic track cluster, no obvious layering classification phenomenon occurs, and the track of the cluster has motion convergence, which shows that all nodes generally keep the consistency of motion directions from the moment of fault removal, so that the system starts to transit to the next stable operation point; if the observation is carried out by cutting in different characteristic planes, the difference between the tracks in the clusters explains the relative swing in the movement process of the nodes, so that the difference of the direction, the speed and the offset on the position exists between the nodes.
2) Three-phase short circuit faults occur at 50% of the positions on the connecting lines between the buses 2 and 4, after 0.16s, the fault lines are cut off, and the generator G1 and the system are out of step. The feature space and the trajectories within the three feature tangential planes are shown in fig. 5. The motion tracks of all nodes in the system form 2 track clusters, and an obvious classification phenomenon occurs; if observation is carried out by cutting in from different characteristic planes, the two clusters of tracks are always kept at a certain distance on three attributes, and the difference in the motion process of the two clusters of tracks indicates the difference of node motion in the system, so that the method is a specific expression of system instability.
The aggregation effect shown in fig. 5 is regressed to the network topology of the system, and it is not difficult to find that 4 tracks in the sibling track cluster ② are respectively G1, Bus1, Bus4 and Bus5, a cut-set section can be formed exactly in space, and G1 in the cut-set is a destabilizing unit.
The trajectory in the offset feature space substantially represents the offset attribute of continuous motion of the node in a certain period, and is a concrete embodiment of continuous accumulation of motion offset. Because the similarity of the offset attributes essentially represents the motion similarity, it is necessary to extract the time sequence evolution rule of the node voltage variation by using the offset feature space as a medium and observe the aggregation condition of the traces.
When a serious fault occurs in an actual complex power grid, more than one area threatening the safety of the main grid is possible, and the stability of the main grid can be effectively ensured only by splitting a plurality of power transmission sections urgently. Therefore, the accurate positioning of the multiple splitting sections plays an extremely important role in improving the survival capability of the complex power grid in the face of serious faults. The invention realizes the similarity evaluation of node motion by analyzing the motion conditions of node voltages of a simple system under two typical stable forms and based on a characteristic space, and the aggregation condition of the track cluster can provide important reference for disconnection control.
Taking an equivalent two-machine system as an example, the rationality of the evolution rule of the extracted node voltage change time sequence is analyzed. For convenience, it is assumed that the two potentials of the system shown in fig. 6 are equal in magnitude and the oscillation center falls at the center c, i.e., the center of symmetry. a. b is a node far away from the oscillation center and close to the sending end, d and e are nodes close to the receiving end, and X is system connection impedance.
Knowing the node voltage amplitudeThe voltage phase angle θ is arctan (Im/Re), where Re and Im are the real and imaginary parts of the voltage, respectively. Bringing it to dV/dt and d θ/dt, respectively, is:
Figure BDA0002169966440000102
the power angle difference of the two motors changes periodically within the range of 0-360 degrees, the voltage phase tracks of the nodes on the contact section are circles with different radiuses, as shown in fig. 7, and the phase angle change of each node in the oscillation process is as shown in fig. 8. Considering the symmetry of the oscillation process, the present application addresses δ at [0 °,180 ° ]]Detailed analysis of the oscillation process of (1), S in the figure1The phase angle in the corresponding oscillation process is maximum.
As can be seen from the voltage phase locus and vector relationship of fig. 7, the voltage variation amplitude at the oscillation center c is the largest. If and only if Re Im is 0, the voltage amplitude at c is zero, so the phase locus circle of the oscillation center crosses the origin, and the imaginary axis and the phase locus circle are tangent to the origin, where the phase angle at node c is 90 °.
The phase track circle of the node M is the outer boundary of the circle cluster, the voltage amplitude is kept unchanged in the oscillation process, the condition is substituted into the formula (3) and then the formula (4) to obtain the relationship between the electrical compaction and imaginary part of the node and the angular velocity direction:
Figure BDA0002169966440000104
for nodes d and e far away from the oscillation center and close to the receiving end, the phase locus circle is in the locus circle of the oscillation center c, and the closer to the c, the larger the circle radius is, and the larger the voltage change is. The phase angles of the nodes have maximum values in the oscillation process, and the formula (4) is zero to derive the formula (6) to show the extreme value point S1The tangent at (a) must cross the origin, beyond which the phase angle starts to decrease and finally to zero.
Figure BDA0002169966440000111
For nodes a and b far away from the oscillation center and close to the sending end, the phase locus circle is between the locus circles of M and c, and the closer to c, the smaller the radius of the circle, and the larger the voltage change. The phase angle of the class node monotonically increases to 180 ° during oscillation.
In combination with the above analysis: the phase locus circle of the oscillation center c is a boundary line of two types of node motions, and finally a and b which move along with the node M intersect with the virtual axis positive half shaft in the phase angle increasing process, the voltage locus of the type of node crosses the first quadrant and the second quadrant, the locus mode is relatively long, and the motion characteristics of the locus can be captured by the length distance and the position distance in the deviation characteristics. D and e which finally move along with the node N, the phase angle of the d and e has a maximum value, and an extreme point S1The tangent line of the position crosses the origin, the voltage phase track is shown to move only in the first quadrant, the included angle of two vectors in adjacent time intervals reaches a zero value in advance, and the motion characteristic of the track can be captured by the position distance and the angle distance.
The motion difference of the two types of nodes is expressed as the difference of the geometric characteristics of the phase tracks, and the motion similarity of the nodes of the same type is expressed as the similarity of the geometric characteristics of the phase tracks. By mining the geometric characteristics of the phase trajectory, extracting the time sequence evolution rule of the node state, analyzing the time-space linkage relation of the node state, further identifying the splitting section, and having feasibility.
Preferably, in step 103: according to the time sequence evolution characteristics of the node voltage, the similarity of the change of the node voltage is evaluated based on a track clustering algorithm, and one or more splitting sections are positioned by tracking the one or more splitting sections, and the method also comprises the following steps:
selecting time sequence tracks in a preset time interval for clustering, defining the time sequence tracks as the sum of distances between points of different tracks under the same time scale, and recording the sum as DTrajThe method is used for representing the similarity degree between time sequence tracks and measuring the difference degree between different tracks; the distance between two discrete points at a certain time in the space is known as follows:
Figure BDA0002169966440000112
the distance D can be used to generalize to the inter-track distance D within a certain time intervalTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn
in the formula DnThe distance between two points at the nth moment is expressed, and n is the window length of the time sliding window;
the distance between any two tracks can be obtained every time the window length slides by one unit.
Preferably, cluster expansion is performed on the neighborhood track group, and the track is shifted for each vector in the neighborhood
Figure BDA0002169966440000113
Performing secondary traversal and label assignment by applying to the neighborhoodInner track vector offset track
Figure BDA0002169966440000115
Performing a second traversal to find an AND in the original cluster
Figure BDA0002169966440000116
Indirect phase ofSimilar to and not yet assigned to the track of the tag.
According to the method, the aggregation condition of the node voltage in the feature space under different stable forms is considered, the time sequence track in the feature space is extracted through the time sliding window, the node motion similarity is evaluated on line based on the track clustering algorithm, the migration condition of the multi-splitting section is tracked in real time, and decision support is provided for splitting control of the system.
Compared with the characteristic scatter clustering of all nodes under a certain time section, the time sequence track in a certain time interval is selected for clustering, and the time sequence evolution characteristic of the node motion is better captured. Therefore, a concept of "track distance" is proposed, which is defined as the sum of the distances between points of different tracks at the same time scale and is recorded as DTrajThe method is used for representing the similarity degree between the time sequence tracks and measuring the difference degree between different tracks. The distance between two discrete points at a certain time in the space is known as follows:
Figure BDA0002169966440000121
the distance D can be used to generalize to the inter-track distance D within a certain time intervalTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn(8)
in the formula DnIs expressed as the distance between two points at the nth time, and n is the window length of the time sliding window.
From the above analysis, it can be known that the distance between any two tracks can be obtained every time the time window slides by one unit, and the present invention provides a VVMCT clustering algorithm based on the distance, and the steps are shown in fig. 9. Of unstable power generation nodes
Figure BDA0002169966440000122
Is likely to be in contact with the partThe large track distance exists because the moving direction of the net-removing machine set is completely deviated from the main net and is linked with the net-removing machine set due to the fact that the moving speed is too highThe average track distance of the surrounding nodes is large, the nodes are higher than the clustering threshold value and cannot be clustered, and the unstable power generation nodes are isolated, which is the normal result of clustering. Therefore, the isolated track of the clustering result is optimized, and the optimization constraint purpose of the power generation nodes is set, namely, the isolated track close to the unstable power generation nodes is clustered again in space.
If the method of the application evaluates the strong association relationship between the motion trajectories with only one traversal result, the result may be too unilateral. Therefore, it is necessary to perform cluster expansion on the neighborhood track group and perform cluster expansion on each piece in the neighborhood
Figure BDA0002169966440000124
The specific steps of performing the second traversal and the label assignment are shown in fig. 10. By making a neighborhood
Figure BDA0002169966440000125
Inner track
Figure BDA0002169966440000126
Performing secondary traversal, and searching and matching in the original cluster
Figure BDA0002169966440000127
Indirectly similar and not yet assigned to the trajectory of the tag. The cluster expansion ensures the accuracy and global optimality of cluster division, and is a key step of the clustering algorithm.
According to the clustering result of the algorithm, one or more sections are positioned through boundary nodes in a cluster where a destabilizing machine is located according to the classification evaluation of the voltage locus similarity of the nodes, in a large power grid with complex topology, certain middle and load nodes with certain electrical distance from each power generation node are not obvious in locus characteristics because the middle and load nodes are far away from the destabilizing power generation node and close to an oscillation center, and the cluster can be automatically formed when clustering is carried out.
(4) Adaptive adjustment of the algorithm:
the track distance threshold epsilon and the track cluster threshold lambda are two key parameters in a clustering algorithm, and the reasonability of the values directly influences the accuracy of the result. The invention provides a parameter self-adaptive adjusting method, firstly for DTrajCarrying out weighted average on the sample space, and if the number of all tracks in the VVMCT group is n, then DTrajThe number of trajectory distances contained in the sample space Ω is:
Figure BDA0002169966440000131
in calculating DTrajThe samples with overlarge values need to be excluded during the mean value, so the samples in omega are screened, and all D are detectedTrajAfter the samples are sorted from small to large, the first 25 percent of D is extractedTrajSamples, make up the optimization space:
in the formula, N1N/4, i.e. the number of rounded optimal spatial samples, di being D in the optimal spaceTrajAnd (4) sampling. The optimization space largely preserves the threshold information because the sample spacing within each class is relatively small. Arranging the samples in the optimized space from small to large and dividing the samples into four groups of subspaces, arranging the threshold information contained in the four groups of subspaces from large to small, and obtaining a weighted average value after giving different weights to each subspace, wherein the weighted average value comprises the following steps:
Figure BDA0002169966440000133
in the formula (I), the compound is shown in the specification,
Figure BDA0002169966440000134
for the weight value of each subspace, the weight a is taken as the neighborhood of the value 1 in principle, and as the threshold information density of each subspace is sequentially decreased, the weight selection should also be sequentially decreased, which can be determined according to the operation experience of the regulation and control personnel.
If the control person wishes to split the system as small as possible, i.e. the threshold epsilon is relatively small, then a is increased1Values are taken to enhance the effect of the 1 st subspace on the optimization space, but it should be noted that too large a value will result in isolated trajectories. To sum up, this application gets: a is1，a2，a3，a41.6, 1.2, 0.8, 0.4, wherein N2＝N1And/4, the number of samples in the subspace after the whole treatment is taken.
The adaptive adjustment method of the epsilon value dynamically adjusts the target threshold according to the sample space, and realizes the adaptive adjustment of the parameters of different VVMCT groups. And if the power grid topologies are the same, the node numbers are the same, and the lambda value is unchanged. In order to adapt to different numbers of nodes in different power grid topologies, the method selects the following steps:
λ＝n/10 (12)
in the formula, lambda also needs rounding treatment. The track clustering number matched with the power grid node number can be rapidly calculated through the formula (19), so that the reasonability of the cluster threshold value is improved.
The application provides a new method for rapidly positioning an information-driven active splitting section of a power grid, which has the following characteristics:
d constructed in this applicationl-dθ-dpCharacteristic space psidThe deviation attribute of the node motion track can be effectively represented, the time-space dynamics characteristics of a power grid and the time sequence evolution rule of node voltage change are reflected, and the rationality of the rule is explained through a two-machine equivalent system;
the self-adaptive clustering algorithm based on the track distance is provided, the data-driven node motion similarity classification evaluation is substantial, the method is independent of a model, is not limited by a system operation mode and a fault form, and is high in applicability;
according to the method, the migration condition of the splitting section is tracked in real time through the sliding time window, the calculation is simple, the evaluation timeliness is good, the survival capability of a main body of the power grid is effectively saved, and meanwhile, the online requirement of active splitting of the large power grid is met.
Fig. 16 is a system configuration diagram for locating an active grid splitting section based on voltage trajectory information according to a preferred embodiment of the present invention. The application provides a system for positioning power grid initiative splitting section based on voltage track information, the system includes:
and the constructing unit 601 is used for constructing a vector offset feature space of the node voltage phase trajectory. Preferably, the construction unit 601 is configured to construct a vector offset eigenspace of the node voltage phase trajectories, and further configured to:
with dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdLet a node start point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) The vector offset characteristic track of the vector forming node i between the starting point and the end point in a certain time interval is as follows:
constructed of
Figure BDA0002169966440000142
As a node at dl、dθ、dpJudging basis of movement direction change and speed change in a certain time interval in space;
Figure BDA0002169966440000143
component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
The obtaining unit 602 is configured to obtain a time sequence evolution characteristic of the node voltage during step-out oscillation of the power system by using a vector offset characteristic space of a node voltage trajectory. Preferably, the obtaining unit 602 is configured to obtain a time-sequence evolution characteristic of the node voltage when the power system is out-of-step oscillated, by using a vector offset feature space of the node voltage trajectory, and further configured to:
collecting time sequence information of node voltage in the power grid through a wide area measurement system, acquiring the time sequence information of the node voltage in a certain time interval, and forming a voltage phasor track group UR of all nodes in a voltage complex space in the time intervalTm：
Figure BDA0002169966440000151
In the formula (I), the compound is shown in the specification,
Figure BDA0002169966440000152
represents the m-th time interval TmInner, voltage vector of node i; and n is the number of all nodes of the power grid.
And the positioning unit 603 is configured to evaluate similarity of node voltage changes based on a trajectory clustering algorithm according to a time sequence evolution characteristic of the node voltage, and position one or more splitting sections by tracking the one or more splitting sections.
Preferably, the positioning unit 603 is configured to evaluate a change of the node voltage based on a trajectory clustering algorithm according to a time-series evolution characteristic of the node voltage, and position the one or more splitting sections by tracking the one or more splitting sections, and further configured to:
selecting time sequence tracks in a preset time interval for clustering, defining the time sequence tracks as the sum of distances between points of different tracks under the same time scale, and recording the sum as DTrajThe method is used for representing the similarity degree between time sequence tracks and measuring the difference degree between different tracks; the distance between two discrete points at a certain time in the space is known as follows:
Figure BDA0002169966440000153
can be promoted by using the distance DTo a distance between the tracks within a certain time interval, DTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn
in the formula DnThe distance between two points at the nth moment is expressed, and n is the window length of the time sliding window;
the distance between any two tracks can be obtained every time the window length slides by one unit.
Preferably, the positioning unit 603 is further configured to:
performing cluster expansion on the neighborhood track group, and offsetting tracks of each vector in the neighborhood
Figure BDA0002169966440000154
Performing secondary traversal and label assignment by applying to the neighborhood
Figure BDA0002169966440000155
Inner track vector offset track
Figure BDA0002169966440000156
Performing a second traversal to find an AND in the original clusterIndirectly similar and not yet assigned to the trajectory of the tag.
The system 600 for positioning an active splitting section of a power grid based on voltage trajectory information in the preferred embodiment of the present invention corresponds to the method 100 for positioning an active splitting section of a power grid based on voltage trajectory information in the preferred embodiment of the present invention, and is not described herein again.
The invention has been described with reference to a few embodiments. However, other embodiments of the invention than the one disclosed above are equally possible within the scope of the invention, as would be apparent to a person skilled in the art from the appended patent claims.
Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a/an/the [ device, component, etc ]" are to be interpreted openly as referring to at least one instance of said device, component, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.

Claims (10)

1. A method for locating an active splitting section of a power grid based on voltage trajectory information, the method comprising:
constructing a vector offset feature space of a node voltage phase track;
acquiring the time sequence evolution characteristic of the node voltage when the power system is in step-out oscillation by utilizing the vector offset characteristic space of the node voltage trajectory;
and according to the time sequence evolution characteristics of the node voltage, evaluating the similarity of the node voltage change based on a track clustering algorithm, and positioning one or more splitting sections by tracking the one or more splitting sections.
2. The method of claim 1, the constructing a vector offset eigenspace of node voltage phase trajectories, comprising:
with dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdLet a node start point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) And the vector offset characteristic track of the vector between the starting point and the end point forming node i in a certain time interval is as follows:
Figure FDA0002169966430000011
constructed of
Figure FDA0002169966430000012
As a node at dl、dθ、dpJudging basis of movement direction change and speed change in a certain time interval in space;component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
3. The method of claim 1, wherein the obtaining the time-sequence evolution characteristic of the node voltage during the out-of-step oscillation of the power system by using the vector offset feature space of the node voltage trajectory comprises:
collecting the time sequence information of the node voltage in the power grid through a wide area measurement system, acquiring the time sequence information of the node voltage in a certain time interval, and forming a voltage phasor track group UR of all nodes in a voltage complex space in the time intervalTm：
Figure FDA0002169966430000014
In the formula (I), the compound is shown in the specification,
Figure FDA0002169966430000021
represents the m-th time interval TmInner, voltage vector of node i; and n is the number of all nodes of the power grid.
4. The method of claim 1, wherein the estimating the similarity of the node voltage changes based on a trajectory clustering algorithm according to the time-series evolution characteristics of the node voltages, and the locating of one or more splitting sections through tracking of the one or more splitting sections further comprises:
selecting time sequence tracks in a preset time interval for clustering, defining the time sequence tracks as the sum of distances between points of different tracks under the same time scale, and recording the sum as DTrajThe method is used for representing the similarity degree between time sequence tracks and measuring the difference degree between different tracks; has already been used forThe distance between two discrete points at a certain time in the space is known as follows:
the distance D can be used to generalize to the inter-track distance D within a certain time intervalTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn
in the formula DnThe distance between two points at the nth moment is expressed, and n is the window length of the time sliding window;
the distance between any two tracks can be obtained by sliding the window length by one unit.
5. The method of claim 4, further comprising:
performing cluster expansion on the neighborhood track group, and offsetting tracks of each vector in the neighborhood
Figure FDA0002169966430000023
Performing secondary traversal and label assignment by applying to the neighborhood
Figure FDA0002169966430000024
Inner track vector offset track
Figure FDA0002169966430000025
Performing a second traversal to find an AND in the original cluster
Figure FDA0002169966430000026
Indirectly similar and not yet assigned to the trajectory of the tag.
6. A system for locating an active splitting section of a power grid based on voltage trajectory information, the system comprising:
the building unit is used for building a vector offset characteristic space of the node voltage phase track;
the acquisition unit is used for acquiring the time sequence evolution characteristics of the node voltage during the step-out oscillation of the power system by utilizing the vector offset characteristic space of the node voltage trajectory;
and the positioning unit is used for evaluating the similarity of the node voltage change based on a track clustering algorithm according to the time sequence evolution characteristics of the node voltage and positioning one or more splitting sections by tracking the one or more splitting sections.
7. The system of claim 6, the construction unit to construct a vector offset eigenspace of node voltage phase trajectories, further to:
with dl、dθ、dpRespectively serving as x, y and z coordinate axes of a three-dimensional space, and constructing a vector offset feature space psi of a node voltage phase trackdLet a node start point VmiThe coordinate is (d)lmi，dθmi，dpmi) End point V(m+1)iThe coordinate is (d)l(m+1)i，dθ(m+1)i，dp(m+1)i) And the vector offset characteristic track of the vector between the starting point and the end point forming node i in a certain time interval is as follows:
Figure FDA0002169966430000031
constructed of
Figure FDA0002169966430000032
As a node at dl、dθ、dpJudging basis of movement direction change and speed change in a certain time interval in space;
Figure FDA0002169966430000033
component values in the x, y, and z axes characterize the rate, direction, and position magnitudes of node offsets, respectively.
8. The system of claim 6, wherein the obtaining unit is configured to obtain a time sequence evolution characteristic of the node voltage during step-out oscillation of the power system by using a vector offset feature space of the node voltage trajectory, and further configured to:
collecting the time sequence information of the node voltage in the power grid through a wide area measurement system, acquiring the time sequence information of the node voltage in a certain time interval, and forming a voltage phasor track group UR of all nodes in a voltage complex space in the time intervalTm：
In the formula (I), the compound is shown in the specification,represents the m-th time interval TmInner, voltage vector of node i; and n is the number of all nodes of the power grid.
9. The system of claim 6, wherein the positioning unit is configured to evaluate similarity of changes of the node voltages based on a trajectory clustering algorithm according to a time-series evolution characteristic of the node voltages, and to position one or more separation sections by tracking the one or more separation sections, and further configured to:
selecting time sequence tracks in a preset time interval for clustering, defining the time sequence tracks as the sum of distances between points of different tracks under the same time scale, and recording the sum as DTrajThe method is used for representing the similarity degree between time sequence tracks and measuring the difference degree between different tracks; the distance between two discrete points at a certain time in the space is known as follows:
Figure FDA0002169966430000036
the distance D can be used to generalize to the inter-track distance D within a certain time intervalTrajIs calculated as follows:
DTraj＝D1+D2+···+Dn
in the formula DnThe distance between two points at the nth moment is expressed, and n is the window length of the time sliding window;
the distance between any two tracks can be obtained by sliding the window length by one unit.
10. The system of claim 9, the positioning unit further to:
performing cluster expansion on the neighborhood track group, and offsetting tracks of each vector in the neighborhood
Figure FDA0002169966430000041
Performing secondary traversal and label assignment by applying to the neighborhood
Figure FDA0002169966430000042
Inner track vector offset track
Figure FDA0002169966430000043
Performing a second traversal to find an AND in the original cluster
Figure FDA0002169966430000044
Indirectly similar and not yet assigned to the trajectory of the tag.
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