CN114062848B - Forced power oscillation disturbance source positioning method and device based on equivalent electrical distance - Google Patents
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Abstract
The invention discloses a forced power oscillation disturbance source positioning method and device based on equivalent electrical distance, wherein the method comprises the following steps: obtaining an equivalent electrical distance between any two nodes in a power grid; mapping each node of an actual power grid into a complex plane coordinate system; selecting a PMU monitoring node; reordering PMU monitoring nodes in order of near-far electrical distance from disturbance source; taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as a target optimization function and solving the target optimization function to obtain an optimal solution; finding the node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of forced power oscillation; the invention has the advantages that: accurate positioning of the forced oscillation disturbance source is achieved.
Description
Technical Field
The invention relates to the field of disturbance source positioning, in particular to a forced power oscillation disturbance source positioning method and device based on equivalent electrical distance.
Background
Forced oscillation theory is another classical theory that differs from negative damping mechanisms, successfully explaining the problem of low frequency oscillations that occur when the system damping is sufficiently large, and is attracting increasing attention in the industry. This theory states that when a system is subjected to a sustained periodic power disturbance with a disturbance frequency close to the natural frequency of the system, the system is excited to undergo a large amplitude of power oscillation. The forced oscillation has the characteristics of quick oscillation starting, continuous constant-amplitude oscillation after the oscillation starting, and quick attenuation of the oscillation after the disturbance source is eliminated. Thus, cutting off the source of the disturbance is the most direct and effective means of suppressing the forced oscillation, and accurate positioning of the source of the disturbance is the key to this implementation.
The scholars at home and abroad have developed a series of researches on the positioning of forced oscillation disturbance sources, and the current thought mainly comprises an energy method, a traveling wave method and other methods. Document "bikini Min Yong, chen Lei, etc.. Forced power oscillation disturbance source localization based on energy function [ J ]. Power system automation, 2010, 34 (5): low frequency oscillation analysis and oscillation source positioning based on oscillation energy (two) oscillation source positioning method and algorithm [ J ]. Power system automation, 2012, 36 (4): 1-5., yang Dongjun, ding Jianyong, li Jisheng, etc. forced power oscillation disturbance source positioning method based on parameter identification [ J ]. Power system automation, 2012, 36 (2): the method achieves the purpose of positioning the disturbance source by researching different energy change characteristics in the disturbance process, and when the component determined by the non-disturbance source has a large effect, the energy method has a large calculation error, so that accurate positioning cannot be realized.
Disclosure of Invention
The invention aims to solve the technical problem that the method for positioning the disturbance source in the prior art cannot realize accurate positioning.
The invention solves the technical problems by the following technical means: a method for locating a disturbance source of forced power oscillation based on an equivalent electrical distance, the method comprising the steps of:
step one: obtaining an equivalent electrical distance between any two nodes in a power grid;
step two: according to the theory of the equivalent electrical distance of the nodes, mapping each node of the actual power grid into a complex plane coordinate system;
step three: acquiring the electric connection coupling degree of the generator and the coincidence node, and selecting a PMU monitoring node;
step four: the oscillation occurs, the busbar frequency variation curve of each PMU monitoring node is analyzed, the time sequence of the disturbance wave reaching each PMU monitoring node is judged, and the PMU monitoring nodes are reordered according to the sequence from near to far in the electrical distance from the disturbance source;
step five: taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as a target optimization function and solving the target optimization function to obtain an optimal solution;
step six: and finding the node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of forced power oscillation.
According to the invention, firstly, based on an equivalent electrical distance theory, the actual power grid nodes are mapped into a complex plane coordinate system, so that the electrical position coordinates of each node are realized. Then, the electric connection coupling degree of the generator and the load nodes is defined, and a plurality of PMU monitoring nodes are selected according to the index. And finally, taking the least square sum of equivalent electrical distances from the disturbance source to be solved to each PMU monitoring point as an objective function, solving the objective function to obtain an optimal solution, and finding out a node closest to the optimal solution in a complex plane coordinate system, namely the disturbance source of forced power oscillation, thereby realizing the accurate positioning of the disturbance source of forced oscillation.
Further, the first step includes:
any two nodes in power gridThe equivalent electrical distance between these two points is used as equivalent impedance +.>Characterization, wherein,
wherein ,is the +.>Line, th->Column element (s)/(S)>Is the->Line, th->Column element (s)/(S)>Is the +.>Line, th->Column elements.
Further, the second step includes:
step 201: selecting a power grid balance node as a complex plane coordinate system origin, and selecting one balance node as the complex plane coordinate system origin if the actual power grid has a plurality of balance nodes;
step 202: generating a node admittance matrix of the power grid according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix;
step 203: calculating equivalent impedance between each node of the power grid and the origin of the complex plane coordinate system by using the obtained node impedance matrix;
step 204: mapping each equivalent impedance to a complex plane coordinate system, and supposing calculation to obtain a nodeOrigin of complex plane coordinate system>Equivalent impedance +.>Node->The coordinates mapped into the complex plane coordinate system are (+.>）；
Step 205: all nodes are mapped to a complex plane coordinate system.
Still further, the third step includes:
by the formulaObtaining the electric connection coupling degree of the generator and the load node, wherein +.>For the set of all generator nodes in the system, +.>A set of all load nodes in the system;
the electric connection coupling degree of the generators and the load nodes of all nodes of the system is calculated offline, and the electric connection coupling degree is sequenced;
selecting a plurality of nodes with larger electric connection coupling index, combining a complex plane coordinate point distribution diagram, and selecting outThe PMU monitoring nodes meet the following requirements: monitoring node +.>Equivalent electrical distance between，/>For a set node electrical distance threshold, wherein +.>For node->Is>For node->Is defined by the vertical coordinate of (c).
Still further, the fourth step includes:
for one ofNode network, provided with->The PMU monitoring nodes, assume->For the disturbance of the coordinates of the source on the complex plane, any node is +.>The electrical distance to the disturbance source is
Sequencing the time when the disturbance wave reaches the PMU monitoring nodes, namely, reordering the PMU monitoring nodes according to the sequence from near to far in the electrical distance from the disturbance source:
。
still further, the fifth step includes:
by the formulaAnd constructing a target optimization function and solving the target optimization function to obtain an optimal solution.
The invention also provides a forced power oscillation disturbance source positioning device based on equivalent electrical distance, which comprises:
the equivalent electrical distance acquisition module is used for acquiring the equivalent electrical distance between any two nodes in the power grid;
the node mapping module is used for mapping each node of the actual power grid into a complex plane coordinate system according to the theory of the equivalent electrical distance of the node;
the monitoring point selecting module is used for acquiring the electric connection coupling degree of the generator and the coincidence node and selecting a PMU monitoring node;
the monitoring point sequencing module is used for generating oscillation, analyzing the busbar frequency variation curve of each PMU monitoring node, judging the time sequence of the disturbance wave reaching each PMU monitoring node, and re-sequencing the PMU monitoring nodes according to the sequence from near to far in electrical distance from the disturbance source;
the objective function solving module is used for taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as an objective optimization function and solving the objective optimization function to obtain an optimal solution;
and the disturbance source positioning module is used for finding out the node closest to the optimal solution in the complex plane coordinate system, namely the disturbance source of the forced power oscillation.
Further, the equivalent electrical distance acquisition module is further configured to:
any two nodes in power gridThe equivalent electrical distance between these two points is used as equivalent impedance +.>Characterization, wherein,
wherein ,is the +.>Line, th->Column element (s)/(S)>Is the->Line, th->Column element (s)/(S)>Is the +.>Line, th->Column elements.
Still further, the node mapping module is further configured to:
step 201: selecting a power grid balance node as a complex plane coordinate system origin, and selecting one balance node as the complex plane coordinate system origin if the actual power grid has a plurality of balance nodes;
step 202: generating a node admittance matrix of the power grid according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix;
step 203: calculating equivalent impedance between each node of the power grid and the origin of the complex plane coordinate system by using the obtained node impedance matrix;
step 204: mapping each equivalent impedance to a complex plane coordinate system, and supposing calculation to obtain a nodeOrigin of complex plane coordinate system>Equivalent impedance +.>Node->The coordinates mapped into the complex plane coordinate system are%）；
Step 205: all nodes are mapped to a complex plane coordinate system.
Still further, the monitoring point selection module is further configured to:
by the formulaObtaining the electric connection coupling degree of the generator and the load node, wherein +.>For the set of all generator nodes in the system, +.>For all negative in the systemA collection of load nodes;
the electric connection coupling degree of the generators and the load nodes of all nodes of the system is calculated offline, and the electric connection coupling degree is sequenced;
selecting a plurality of nodes with larger electric connection coupling index, combining a complex plane coordinate point distribution diagram, and selecting outThe PMU monitoring nodes meet the following requirements: monitoring node +.>Equivalent electrical distance between，/>For a set node electrical distance threshold, wherein +.>For node->Is>For node->Is defined by the vertical coordinate of (c).
Still further, the monitoring point ordering module is further configured to:
for one ofNode network, provided with->The PMU monitoring nodes, assume->For the coordinates of the source in the complex plane, thenAny node->The electrical distance to the disturbance source is
Sequencing the time when the disturbance wave reaches the PMU monitoring nodes, namely, reordering the PMU monitoring nodes according to the sequence from near to far in the electrical distance from the disturbance source:
。
still further, the objective function solving module is further configured to:
by the formulaAnd constructing a target optimization function and solving the target optimization function to obtain an optimal solution.
The invention has the advantages that:
(1) According to the invention, firstly, based on an equivalent electrical distance theory, the actual power grid nodes are mapped into a complex plane coordinate system, so that the electrical position coordinates of each node are realized. Then, the electric connection coupling degree of the generator and the load nodes is defined, and a plurality of PMU monitoring nodes are selected according to the index. And finally, taking the least square sum of equivalent electrical distances from the disturbance source to be solved to each PMU monitoring point as an objective function, solving the objective function to obtain an optimal solution, and finding out a node closest to the optimal solution in a complex plane coordinate system, namely the disturbance source of forced power oscillation, thereby realizing the accurate positioning of the disturbance source of forced oscillation.
(2) The method can realize the rapid and accurate positioning of the forced oscillation disturbance source (comprising the disturbance of the generator side and the load side) by only extracting the voltage waveform information of a few PMU monitoring nodes, avoids the transmission, storage and analysis of massive PMU information, and has stronger applicability to an actual power grid.
Drawings
FIG. 1 is a flow chart of a method for locating a disturbance source of forced power oscillation based on equivalent electrical distance according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a superposition principle in a method for positioning a disturbance source of forced power oscillation based on an equivalent electrical distance according to an embodiment of the present invention;
FIG. 3 is a topology structure of an IEEE 30 node system in a forced power oscillation disturbance source positioning method based on equivalent electrical distance according to an embodiment of the present invention;
FIG. 4 is a complex plane distribution diagram of an IEEE 30 node system in a forced power oscillation disturbance source positioning method based on equivalent electrical distance provided by an embodiment of the invention;
FIG. 5 is a graph showing the frequency variation of each PMU monitoring node in the method for locating a disturbance source of forced power oscillation based on equivalent electrical distance according to the embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
As shown in fig. 1, a method for positioning a disturbance source of forced power oscillation based on an equivalent electrical distance comprises the following steps:
step one: obtaining an equivalent electrical distance between any two nodes in a power grid;
step two: according to the theory of the equivalent electrical distance of the nodes, mapping each node of the actual power grid into a complex plane coordinate system;
step three: acquiring the electric connection coupling degree of the generator and the coincidence node, and selecting a PMU monitoring node;
step four: the oscillation occurs, the busbar frequency variation curve of each PMU monitoring node is analyzed, the time sequence of the disturbance wave reaching each PMU monitoring node is judged, and the PMU monitoring nodes are reordered according to the sequence from near to far in the electrical distance from the disturbance source;
step five: taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as a target optimization function and solving the target optimization function to obtain an optimal solution;
step six: and finding the node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of forced power oscillation. The following sections introduce detailed calculation procedures of the steps and final simulation experiment results.
1. Details of the steps of the embodiment
1. Equivalent electrical distance
Modern electric power system characteristic researches are mostly based on classical complex network models, and structural characteristics of a power grid and propagation rules of fault disturbance of the power grid are researched from a network topology angle. However, the traditional network topology model cannot accurately reveal the essential characteristics of the power grid, and the electric coupling relation among all nodes of the power grid can be reflected more truly by researching the characteristics of the power grid from the electric angle, so that the method is more suitable for the practical operation of the power grid.
Any two nodes in power gridThe equivalent electrical distance between these two points can be taken as the equivalent impedance +.>Characterization, which is equal in value to the slave node +.>Injecting unit current, slave node->A unit current flows out, and the rest node currents are zero, and the node is +.>Voltage between->The expression is as follows:
(1)
the modification of formula (1) is performed by means of the superposition theorem. The schematic diagram of the superposition principle is shown in fig. 2.
The physical significance of the node impedance matrix elements of the power system is considered as follows: when the nodeInjection unit current, other nodes injection current is zero, < ->Equal in value to node->Voltage>，/>Equal in value to node->Voltage>, wherein />Is the +.>Line, th->Column element (s)/(S)>Is the->Line, th->Column elements.
From the above, it can be seen that the nodeThe equivalent impedance between them is:
(2)
2. complex plane co-ordination of grid nodes
In order to represent the electrical connection relation between all nodes of the actual power grid, all nodes of the actual power grid are mapped into a complex plane coordinate system according to the theory of the equivalent electrical distance of the nodes. Each node of the power grid corresponds to a unique coordinate point in the complex plane coordinate system, and theoretically, a situation that a plurality of power grid nodes correspond to the same complex plane coordinate point is also possible.
The complex plane coordination of the grid node comprises the following specific steps:
1) A coordinate system origin is defined. And selecting a power grid balance node as an origin of a complex plane coordinate system, and if the actual power grid has a plurality of balance nodes, only selecting one balance node as the origin.
2) A node impedance matrix is obtained. Generating a node admittance matrix of the power grid according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix.
3) And calculating the equivalent impedance between each node and the balance node. And calculating equivalent impedance between each node of the power grid and a balance node (which is selected as the origin of a coordinate system) according to the formula (2) by using the obtained node impedance matrix.
4) The complex form of the equivalent impedance value is mapped to a complex planar coordinate system. Assume that the node is calculatedAnd balance node->Equivalent impedance +.>Node->The coordinates mapped into the complex plane coordinate system are (+.>）。
5) Mapping all nodes to a complex plane coordinate system provides a basis for positioning a forced oscillation disturbance source.
3. PMU monitoring point selection
3.1 Coupling degree of generator and load node electrical connection
The continuous periodic disturbances on both the generator side and the load side are likely to induce forced power oscillations that will propagate along the grid in the form of electro-mechanical waves (much lower than the speed of light), and those nodes that are in strong electrical communication with the generator and load nodes will be more sensitive to the oscillating disturbances and are therefore a good choice for mounting PMU devices.
For one ofNode grid, note->For the set of all generator nodes in the system, +.>Is the set of all load nodes in the system. Define arbitrary node +.>The coupling degree of the electric connection with the generator and the load node is as follows:
(3)
through the butt jointAnd the sum of the equivalent impedance modulus values of the generator and the load node in the system is counted down to quantitatively describe the degree of electric coupling tightness between each node (comprising the generator and the load node) in the system and the generator and the load node. When (when)The larger the value, the tighter the electrical coupling of the node to the generator and load nodes, the more susceptible the node to disturbances on the generator side and on the load side.
3.2 PMU monitoring point selection strategy
To better capture the forced oscillation disturbance waveform, a reasonable choice of PMU monitoring nodes is required. For a given topologyThe node power grid can select PMU monitoring nodes according to the following strategies:
1) Off-line calculating electric connection coupling degree index of generator and load nodes of all nodes of systemAnd ordering them;
2) Selecting several nodes with larger coupling index, combining with complex plane coordinate point distribution diagram, selecting outThe monitoring points meet the following requirements:
a) For any monitoring nodeEquivalent electrical distance between->，/>For a set electrical distance of the nodeA threshold value;
b) General takingAccording to the half-plane positioning principle, +.>The larger the positioning the more accurate, but in view of reducing the calculation amount, the faster the convergence process, the +.>The engineering requirements can be met by taking the proper size.
4. Disturbance source positioning based on equivalent electrical distance
According to the Geiger classical theory in seismic localization: set the seismic source asThe starting time is +.>，/>The arrival time of seismic waves of each seismic observation station is +.>The seismic source localization problem can be translated into minima for the following objective function:
(4)
wherein For the time-out residual, < >>Is->The computation of the individual stations takes place.
(5)
By means of Geiger positioning theory, the forced oscillation disturbance source positioning problem is converted into an optimization problem by assuming that the directions are at the same speed when the electromechanical wave propagates, and the minimum value is solved only by the following objective function
(6)
The square sum of the electrical distances from each monitoring point to the disturbance source is only required to be guaranteed to be minimum.
And setting constraint conditions for the optimization problem by combining the thought of the half-plane disturbance positioning method. For one ofNode network, provided with->The PMU monitoring nodes, assume->For the disturbance of the coordinates of the source on the complex plane, any node is +.>The electrical distance to the disturbance source is
(7)
The time when the disturbance wave reaches the monitoring points is sequenced, namely the monitoring points can be renumbered according to the sequence from the near to the far of the electric distance between the disturbance source and the monitoring points:
(8)
therefore, the optimization problem model to be solved is as follows:
(9)
in order to accelerate the convergence rate of the optimization problem and ensure the convergence and stability of the solution, a conjugate gradient method is adopted to calculate the minimum value of the objective function, namely the optimal solution. And finding out the node closest to the optimal solution in the complex plane coordinate system, namely the disturbance source of forced power oscillation, and realizing the accurate positioning of the disturbance source of forced oscillation.
The time sequence of the disturbance wave reaching each monitoring point is judged by adopting the following principle: when forced oscillation occurs, disturbance power injection causes system frequency to fluctuate, and the frequency variation of each node of the system presents obvious space-time distribution characteristic due to different electrical distances between each bus node and disturbance sources, network parameter differences and the like. The characteristic points out the frequency variation of each node of the systemThe response time has a time difference, the closer the electric distance from the disturbance source is, the frequency change amount is +.>The earlier the moment when the extremum is first reached. According to the principle, the invention obtains the frequency variation curve of each PMU monitoring node bus, and finally judges the time when the disturbance motor electric wave reaches each monitoring point by comparing the time when the frequency variation reaches the extremum for the first time.
2. Simulation verification
The IEEE 30 node standard test system is adopted for simulation verification, the topology structure of the IEEE 30 node system is shown in figure 3, wherein the node 1 is a balance node, namely, the origin of a complex plane coordinate system.
First, complex plane coordinates are performed on the system node, and the results are shown in table 1.
TABLE 1 IEEE 30 node System complex planar Co-ordination results
The distribution of 30 nodes of the system on a complex plane coordinate system is shown in fig. 4.
Then, a PMU monitoring node is selected. Calculating the electric connection coupling degree of the generator and the load node of each node of the systemAnd arranged in descending order, see table 2. As can be seen from the calculation results in the table, the electrical connection coupling degree between the 6 nodes of the nodes {6,1,9, 22,2 and 25} and the generator and load nodes is large, and as can be seen from the electrical distance distribution characteristics of fig. 4, the distances between the node 2 and the nodes 1 and 6 are relatively close, the node 2 can be removed, and finally the 5 nodes {6,1,9, 22 and 25} can be selected as PMU monitoring points.
Table 2 generator and load node electrical connection coupling for each node of the system
Then, a simulation model of the IEEE 30 node system is built in PSD-BPA software. The system has an oscillation mode with a frequency of 0.91 Hz. A periodic power disturbance with a frequency of 0.91Hz and an amplitude of 100% of the prime mover's initial mechanical power is applied to the generator prime mover side at node 11, which excites the forced power oscillation of the system. Time domain simulation results in a voltage phase angle variation curve at 5 PMU monitoring nodes, see fig. 5.
Therefore, the time sequence of the disturbance electromechanical wave reaching the three monitoring points after the oscillation occurs is as follows: 9- > 6- > 22- > 1- > 25.
Solving the optimization problem shown in the formula (9) to obtain an optimal solution (0.0361,0.4495), wherein the complex plane coordinate of the node 11 is (0.0339,0.4305), and the distance deviation between the complex plane coordinate and the node is only 4.4%, so that the node 11 is proved to be a disturbance source. Thus, the simulation example effectively verifies the effectiveness of the positioning method provided by the invention.
Through the technical scheme, the method and the device map the actual power grid nodes into the complex plane coordinate system based on the equivalent electric distance theory, so that the electric position coordinates of each node are realized. Then, the electric connection coupling degree of the generator and the load nodes is defined, and a plurality of PMU monitoring nodes are selected according to the index. And finally, taking the least square sum of equivalent electrical distances from the disturbance source to be solved to each PMU monitoring point as an objective function, solving the objective function to obtain an optimal solution, and finding out a node closest to the optimal solution in a complex plane coordinate system, namely the disturbance source of forced power oscillation, thereby realizing the accurate positioning of the disturbance source of forced oscillation.
Example 2
Based on embodiment 1, embodiment 2 of the present invention further provides a forced power oscillation disturbance source positioning device based on an equivalent electrical distance, the device comprising:
the equivalent electrical distance acquisition module is used for acquiring the equivalent electrical distance between any two nodes in the power grid;
the node mapping module is used for mapping each node of the actual power grid into a complex plane coordinate system according to the theory of the equivalent electrical distance of the node;
the monitoring point selecting module is used for acquiring the electric connection coupling degree of the generator and the coincidence node and selecting a PMU monitoring node;
the monitoring point sequencing module is used for generating oscillation, analyzing the busbar frequency variation curve of each PMU monitoring node, judging the time sequence of the disturbance wave reaching each PMU monitoring node, and re-sequencing the PMU monitoring nodes according to the sequence from near to far in electrical distance from the disturbance source;
the objective function solving module is used for taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as an objective optimization function and solving the objective optimization function to obtain an optimal solution;
and the disturbance source positioning module is used for finding out the node closest to the optimal solution in the complex plane coordinate system, namely the disturbance source of the forced power oscillation.
Specifically, the equivalent electrical distance acquisition module is further configured to:
any two nodes in power gridThe equivalent electrical distance between these two points is used as equivalent impedance +.>Characterization, wherein,
wherein ,is the +.>Line, th->Column element (s)/(S)>Is the->Line, th->Column element (s)/(S)>Is the +.>Line, th->Column elements.
More specifically, the node mapping module is further configured to:
step 201: selecting a power grid balance node as a complex plane coordinate system origin, and selecting one balance node as the complex plane coordinate system origin if the actual power grid has a plurality of balance nodes;
step 202: generating a node admittance matrix of the power grid according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix;
step 203: calculating equivalent impedance between each node of the power grid and the origin of the complex plane coordinate system by using the obtained node impedance matrix;
step 204: mapping each equivalent impedance to a complex plane coordinate system, and supposing calculation to obtain a nodeOrigin of complex plane coordinate system>Equivalent impedance +.>Node->The coordinates mapped into the complex plane coordinate system are%）；
Step 205: all nodes are mapped to a complex plane coordinate system.
More specifically, the monitoring point selection module is further configured to:
by the formulaObtaining the electric connection coupling degree of the generator and the load node, wherein +.>For the set of all generator nodes in the system, +.>A set of all load nodes in the system;
the electric connection coupling degree of the generators and the load nodes of all nodes of the system is calculated offline, and the electric connection coupling degree is sequenced;
selecting a plurality of nodes with larger electric connection coupling index, combining a complex plane coordinate point distribution diagram, and selecting outThe PMU monitoring nodes meet the following requirements: monitoring node +.>Equivalent electrical distance between，/>For a set node electrical distance threshold, wherein +.>For node->Is>For node->Is defined by the vertical coordinate of (c).
More specifically, the monitoring point ordering module is further configured to:
for one ofNode network, provided with->The PMU monitoring nodes, assume->For the disturbance of the coordinates of the source on the complex plane, any node is +.>The electrical distance to the disturbance source is
Sequencing the time when the disturbance wave reaches the PMU monitoring nodes, namely, reordering the PMU monitoring nodes according to the sequence from near to far in the electrical distance from the disturbance source:
。
more specifically, the objective function solving module is further configured to:
by the formulaAnd constructing a target optimization function and solving the target optimization function to obtain an optimal solution.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (6)
1. The method for positioning the disturbance source of the forced power oscillation based on the equivalent electrical distance is characterized by comprising the following steps:
step one: obtaining an equivalent electrical distance between any two nodes in a power grid; any two nodes in power gridThe equivalent electrical distance between these two points is used as equivalent impedance +.>Characterization, wherein,
wherein ,is the +.>Line, th->Column element (s)/(S)>Is the->Line, th->The column elements are arranged in a row,is the +.>Line, th->Column elements;
step two: according to the theory of the equivalent electrical distance of the nodes, mapping each node of the actual power grid into a complex plane coordinate system;
step 201: selecting a power grid balance node as a complex plane coordinate system origin, and selecting one balance node as the complex plane coordinate system origin if the actual power grid has a plurality of balance nodes;
step 202: generating a node admittance matrix of the power grid according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix;
step 203: calculating equivalent impedance between each node of the power grid and the origin of the complex plane coordinate system by using the obtained node impedance matrix;
step 204: will each beEquivalent impedance is mapped to a complex plane coordinate system, and a node is obtained by supposing calculationOrigin of complex plane coordinate system>Equivalent impedance +.>Node->The coordinates mapped into the complex plane coordinate system are (+.>）；
Step 205: mapping all nodes to a complex plane coordinate system;
step three: acquiring the electric connection coupling degree of the generator and the coincidence node, and selecting a PMU monitoring node;
step four: the oscillation occurs, the busbar frequency variation curve of each PMU monitoring node is analyzed, the time sequence of the disturbance wave reaching each PMU monitoring node is judged, and the PMU monitoring nodes are reordered according to the sequence from near to far in the electrical distance from the disturbance source;
step five: taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as a target optimization function and solving the target optimization function to obtain an optimal solution;
step six: and finding the node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of forced power oscillation.
2. The method for locating a disturbance source of forced power oscillation based on an equivalent electrical distance according to claim 1, wherein said step three comprises:
by the formulaObtaining the electric connection coupling degree of the generator and the load node, wherein +.>For the set of all generator nodes in the system, +.>A set of all load nodes in the system;
the electric connection coupling degree of the generators and the load nodes of all nodes of the system is calculated offline, and the electric connection coupling degree is sequenced;
selecting a plurality of nodes with larger electric connection coupling index, combining a complex plane coordinate point distribution diagram, and selecting outThe PMU monitoring nodes meet the following requirements: monitoring node +.>Equivalent electrical distance between，/>For a set node electrical distance threshold, wherein +.>For node->Is>For node->Is defined by the vertical coordinate of (c).
3. The method for locating a disturbance source of forced power oscillation based on equivalent electrical distance according to claim 2, wherein said step four comprises:
for one ofNode network, provided with->The PMU monitoring nodes, assume->For the disturbance of the coordinates of the source on the complex plane, any node is +.>The electrical distance to the disturbance source is
Sequencing the time when the disturbance wave reaches the PMU monitoring nodes, namely, reordering the PMU monitoring nodes according to the sequence from near to far in the electrical distance from the disturbance source:
。
4. the method for locating a disturbance source of forced power oscillation based on an equivalent electrical distance according to claim 3, wherein said step five comprises:
by the formulaAnd constructing a target optimization function and solving the target optimization function to obtain an optimal solution.
5. Forced power oscillation disturbance source positioning device based on equivalent electrical distance, characterized in that it comprises:
the equivalent electrical distance acquisition module is used for acquiring the equivalent electrical distance between any two nodes in the power grid; the equivalent electrical distance acquisition module is further configured to:
any two nodes in power gridThe equivalent electrical distance between these two points is used as equivalent impedance +.>Characterization, wherein,
wherein ,is the +.>Line, th->Column element (s)/(S)>Is the->Line, th->Column element (s)/(S)>Is the +.>Line, th->Column elements;
the node mapping module is used for mapping each node of the actual power grid into a complex plane coordinate system according to the theory of the equivalent electrical distance of the node; the node mapping module is further configured to:
step 201: selecting a power grid balance node as a complex plane coordinate system origin, and selecting one balance node as the complex plane coordinate system origin if the actual power grid has a plurality of balance nodes;
step 202: generating a node admittance matrix of the power grid according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix;
step 203: calculating equivalent impedance between each node of the power grid and the origin of the complex plane coordinate system by using the obtained node impedance matrix;
step 204: mapping each equivalent impedance to a complex plane coordinate system, and supposing calculation to obtain a nodeOrigin of complex plane coordinate system>Equivalent impedance +.>Node->The coordinates mapped into the complex plane coordinate system are (+.>）；
Step 205: mapping all nodes to a complex plane coordinate system;
the monitoring point selecting module is used for acquiring the electric connection coupling degree of the generator and the coincidence node and selecting a PMU monitoring node;
the monitoring point sequencing module is used for generating oscillation, analyzing the busbar frequency variation curve of each PMU monitoring node, judging the time sequence of the disturbance wave reaching each PMU monitoring node, and re-sequencing the PMU monitoring nodes according to the sequence from near to far in electrical distance from the disturbance source;
the objective function solving module is used for taking the minimum sum of squares of equivalent electrical distances from a disturbance source to be solved to each PMU monitoring node as an objective optimization function and solving the objective optimization function to obtain an optimal solution;
and the disturbance source positioning module is used for finding out the node closest to the optimal solution in the complex plane coordinate system, namely the disturbance source of the forced power oscillation.
6. The equivalent electrical distance-based forced power oscillation disturbance source positioning device according to claim 5, wherein the monitoring point selection module is further configured to:
by the formulaObtaining the electric connection coupling degree of the generator and the load node, wherein +.>For the set of all generator nodes in the system, +.>A set of all load nodes in the system;
the electric connection coupling degree of the generators and the load nodes of all nodes of the system is calculated offline, and the electric connection coupling degree is sequenced;
selecting a plurality of nodes with larger electric connection coupling index, combining a complex plane coordinate point distribution diagram, and selecting outThe PMU monitoring nodes meet the following requirements: monitoring node +.>Equivalent electrical distance between，/>For a set node electrical distance threshold, wherein +.>For node->Is>For node->Is defined by the vertical coordinate of (c).
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