CN114062848A - 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 the actual power grid to a complex plane coordinate system; selecting a PMU monitoring node; reordering PMU monitoring nodes according to the sequence of the electrical distance from the disturbance source from near to far; 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 out a node closest to the optimal solution in a complex plane coordinate system, namely a disturbance source of forced power oscillation; the invention has the advantages that: and the accurate positioning of the forced oscillation disturbance source is realized.
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
The forced oscillation theory is another classical theory distinguished from the negative damping mechanism, which successfully explains the problem of low frequency oscillations that occur in situations where the system is sufficiently damped, and is drawing increasing attention in the industry. The theory states that when a system is subjected to a continuous periodic power disturbance, and the frequency of the disturbance is close to the natural frequency of the system, the system is excited to undergo a large amplitude 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. Therefore, cutting off the disturbance source is the most direct and effective means for suppressing the forced oscillation, and accurate positioning of the disturbance source is the key to achieving the method.
Scholars at home and abroad have developed a series of researches on the positioning of forced oscillation disturbance sources, and the current thinking mainly includes an energy method, a traveling wave method and other methods. Document "yupinyi, mincour, chenyian, etc.. forced power oscillation disturbance source localization [ J ] based on energy function, power system automation, 2010, 34 (5): 1-6, Chen-Xie, Min-Yong, et al. Low-frequency oscillation analysis and oscillation source localization based on oscillation energy (two) oscillation source localization methods and example [ J ] Power System Automation, 2012, 36 (4): 1-5 and "Yang Dong Jun, Ding Piao, Li Su Sheng, etc.. forced power oscillation disturbance source location method based on parameter identification [ J ] power system automation, 2012, 36 (2): 26-29, the purpose of positioning the disturbance source is achieved by researching different energy variation characteristics in the disturbance process, and when the component effect determined by the non-disturbance source is large, the calculation error of the energy method is large, and accurate positioning cannot be achieved.
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 through the following technical means: a forced power oscillation disturbance source positioning method based on equivalent electrical distance comprises the following steps:
the method comprises the following steps: obtaining an equivalent electrical distance between any two nodes in a power grid;
step two: mapping each node of the actual power grid to a complex plane coordinate system according to the theory of the node equivalent electrical distance;
step three: acquiring the coupling degree of the electric connection of the generator and the coincidence nodes, and selecting PMU monitoring nodes;
step four: oscillation occurs, the frequency variation curve of each PMU monitoring node bus is analyzed, the time sequence of disturbance waves reaching each PMU monitoring node is judged, and the PMU monitoring nodes are reordered according to the sequence from near to far from the electrical distance of a 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 out a node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of the forced power oscillation.
The method is based on the equivalent electrical distance theory, and maps the actual grid nodes to a complex plane coordinate system, so that the electrical position coordination of each node is realized. Then, the coupling degree of the electrical connection between the generator and the load nodes is defined, and a plurality of PMU monitoring nodes are selected according to the index. And finally, solving the objective function to obtain an optimal solution by taking the minimum sum of squares of equivalent electrical distances from the disturbance source to be solved to each PMU monitoring point as an objective function, and finding a node closest to the optimal solution in a complex plane coordinate system, namely the disturbance source of the forced power oscillation, so as to realize the accurate positioning of the disturbance source of the forced oscillation.
Further, the first step comprises:
the equivalent electrical distance between any two nodes i, j in the power grid is the equivalent impedance Z between the two nodesij,eqAnd (c) characterizing, wherein,
wherein ,ZiiIs the ith row and ith column element, Z of the node impedance matrixijIs the i row, j column element, Z of the impedance matrixijIs the ith row and jth column element of the node impedance matrix.
Further, the second step comprises:
step 201: selecting a power grid balance node as an origin of a complex plane coordinate system, and selecting one balance node as the origin of the complex plane coordinate system if the actual power grid has a plurality of balance nodes;
step 202: generating a power grid node admittance matrix 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 obtaining the equivalent impedance Z between the node k and the origin o of the complex plane coordinate system by supposing calculationok＝Rok+jXokThen the node k is mapped to the coordinate (R) in the complex plane coordinate systemok,Xok)；
Step 205: all nodes are mapped to a complex planar coordinate system.
Further, the third step includes:
by the formula
Obtaining the electric connection coupling degree of the generator and the load node, wherein omegaGFor the set of all generator nodes in the system, ΩLThe method comprises the steps of (1) collecting all load nodes in a system;
calculating the electrical connection coupling degrees of the generators and the load nodes of all the nodes of the system off line, and sequencing the electrical connection coupling degrees;
selecting a plurality of nodes with large electrical connection coupling degree indexes, combining a complex plane coordinate point distribution graph, and selecting N PMU monitoring nodes from the nodes, wherein the N PMU monitoring nodes meet the following requirements: monitoring the equivalent electrical distance between nodes i, j for any PMU
Epsilon is a set electrical distance threshold of the node, where xiIs the abscissa, y, of node iiIs the ordinate of node i.
Further, the fourth step includes:
for an N-node grid, N PMU monitoring nodes are set, and (x) is assumed0,y0) The electrical distance from any node i to the disturbance source is
Sequencing the time of the disturbance waves reaching the PMU monitoring nodes in sequence, namely, reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source:
d1≤d2≤...≤dN。
further, the fifth step includes:
by the formula
Build object optimizationAnd solving the objective optimization function to obtain an optimal solution.
The invention also provides a forced power oscillation disturbance source positioning device based on the 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 to a complex plane coordinate system according to the theory of the node equivalent electrical distance;
the monitoring point selection module is used for acquiring the coupling degree of the electric connection of the generator and the coincidence nodes and selecting PMU monitoring nodes;
the monitoring point sequencing module is used for carrying out oscillation generation, analyzing the frequency variation curve of each PMU monitoring node bus, judging the time sequence of the disturbance wave reaching each PMU monitoring node, and reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source;
the objective function solving module is used for taking the minimum sum of squares of equivalent electrical distances from the 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 a 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:
the equivalent electrical distance between any two nodes i, j in the power grid is the equivalent impedance Z between the two nodesij,eqAnd (c) characterizing, wherein,
wherein ,ZiiIs the ith row and ith column element, Z of the node impedance matrixijIs the i row, j column element, Z of the impedance matrixijIs the ith row and jth column element of the node impedance matrix.
Still further, the node mapping module is further configured to:
step 201: selecting a power grid balance node as an origin of a complex plane coordinate system, and selecting one balance node as the origin of the complex plane coordinate system if the actual power grid has a plurality of balance nodes;
step 202: generating a power grid node admittance matrix 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 obtaining the equivalent impedance Z between the node k and the origin o of the complex plane coordinate system by supposing calculationok＝Rok+jXokThen the node k is mapped to the coordinate (R) in the complex plane coordinate systemok,Xok)；
Step 205: all nodes are mapped to a complex planar coordinate system.
Furthermore, the monitoring point selecting module is further configured to:
by the formula
Obtaining the electric connection coupling degree of the generator and the load node, wherein omegaGFor the set of all generator nodes in the system, ΩLThe method comprises the steps of (1) collecting all load nodes in a system;
calculating the electrical connection coupling degrees of the generators and the load nodes of all the nodes of the system off line, and sequencing the electrical connection coupling degrees;
selecting a plurality of nodes with large electrical connection coupling degree indexes, combining a complex plane coordinate point distribution graph, and selecting N PMU monitoring nodes from the nodes, wherein the N PMU monitoring nodes meet the following requirements: monitoring the equivalent electrical distance between nodes i, j for any PMU
Epsilon is a set electrical distance threshold of the node, where xiIs the abscissa, y, of node iiIs longitudinal to node iAnd (4) coordinates.
Further, the monitoring point sorting module is further configured to:
for an N-node grid, N PMU monitoring nodes are set, and (x) is assumed0,y0) The electrical distance from any node i to the disturbance source is
Sequencing the time of the disturbance waves reaching the PMU monitoring nodes in sequence, namely, reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source:
d1≤d2≤...≤dN。
still further, the objective function solving module is further configured to:
by the formula
And constructing an objective optimization function and solving the objective optimization function to obtain an optimal solution.
The invention has the advantages that:
(1) the method is based on the equivalent electrical distance theory, and maps the actual grid nodes to a complex plane coordinate system, so that the electrical position coordination of each node is realized. Then, the coupling degree of the electrical connection between the generator and the load nodes is defined, and a plurality of PMU monitoring nodes are selected according to the index. And finally, solving the objective function to obtain an optimal solution by taking the minimum sum of squares of equivalent electrical distances from the disturbance source to be solved to each PMU monitoring point as an objective function, and finding a node closest to the optimal solution in a complex plane coordinate system, namely the disturbance source of the forced power oscillation, so as to realize the accurate positioning of the disturbance source of the forced oscillation.
(2) The method can realize the rapid and accurate positioning of the forced oscillation disturbance source (including the disturbance at 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 strong applicability to the actual power grid.
Drawings
FIG. 1 is a flowchart of a forced power oscillation disturbance source positioning method based on an equivalent electrical distance according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a superposition principle in a forced power oscillation disturbance source positioning method based on an equivalent electrical distance according to an embodiment of the present invention;
fig. 3 is a topological structure of an IEEE 30 node system in the forced power oscillation disturbance source positioning method based on the equivalent electrical distance according to the 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 an equivalent electrical distance according to an embodiment of the present invention;
fig. 5 is a frequency variation curve of each PMU monitoring node in the forced power oscillation disturbance source positioning method based on the equivalent electrical distance according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example 1
As shown in fig. 1, a forced power oscillation disturbance source positioning method based on equivalent electrical distance includes the following steps:
the method comprises the following steps: obtaining an equivalent electrical distance between any two nodes in a power grid;
step two: mapping each node of the actual power grid to a complex plane coordinate system according to the theory of the node equivalent electrical distance;
step three: acquiring the coupling degree of the electric connection of the generator and the coincidence nodes, and selecting PMU monitoring nodes;
step four: oscillation occurs, the frequency variation curve of each PMU monitoring node bus is analyzed, the time sequence of disturbance waves reaching each PMU monitoring node is judged, and the PMU monitoring nodes are reordered according to the sequence from near to far from the electrical distance of a 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 out a node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of the forced power oscillation. The detailed calculation process of the steps and the final simulation experiment result are described in the following sections.
First, the detailed contents of each step of this embodiment
1. Equivalent electrical distance
The characteristic research of modern power systems is mostly based on a classical complex network model, and the structural characteristics of a power grid and the propagation rule of fault disturbance thereof are researched from the perspective of network topology. However, the traditional network topology model cannot accurately reveal the essential characteristics of the power grid, and the study on the characteristics of the power grid from the electrical perspective can more truly reflect the electrical coupling relation among the nodes of the power grid and better accord with the actual operation of the power grid.
The equivalent electrical distance between any two nodes i, j in the power grid can be the equivalent impedance Z between the two nodesij,eqThe representation is equal to the unit current injected from the node i and the unit current flowed from the node j in terms of value, and the voltage U between the nodes i and j is zero when the current of the rest nodes is zeroijThe expression is as follows:
and (3) modifying the formula (1) by means of a superposition theorem. The schematic diagram of the superposition principle is shown in fig. 2.
Considering the physical meaning of the power system node impedance matrix elements as follows: when the unit current is injected into the node i and the current injected into the other nodes is zero, ZiiIs equal in value to the voltage of node i
ZijIs equal in value to the voltage of node j
wherein ZiiIs the ith row and ith column element, Z of the node impedance matrixijIs the ith row and jth column element of the impedance matrix.
From the above, the equivalent impedance between the nodes i, j is:
2. complex plane coordinatization of power grid nodes
In order to represent the electrical connection relation among the nodes of the actual power grid, the 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, the situation that a plurality of power grid nodes correspond to the same complex plane coordinate point may also occur.
The complex plane coordinatization of the power 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 selecting one balance node as the origin if the actual power grid has a plurality of balance nodes.
2) A node impedance matrix is obtained. And generating a power grid node admittance matrix according to the power grid topological structure, and inverting the admittance matrix to obtain a node impedance matrix.
3) 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 a coordinate system origin) according to the formula (2) by using the obtained node impedance matrix.
4) The complex equivalent impedance values are mapped to a complex planar coordinate system. Supposing calculation to obtain a node k and a balance nodeEquivalent impedance Z between points ook＝Rok+jXokThen the node k is mapped to the coordinate (R) in the complex plane coordinate systemok,Xok)。
5) All the nodes are mapped to a complex plane coordinate system, and a foundation is provided for positioning a forced oscillation disturbance source.
3. PMU monitoring point selection
3.1 degree of coupling between Generator and load node Electrical connection
The continuous periodic disturbances on the generator side and the load side are both likely to induce forced power oscillations that will propagate along the grid in the form of airwaves (well below the speed of light), and those nodes that are in electrical communication with the generator and load nodes will be more sensitive to the oscillations disturbances and are therefore good choices for installing PMU devices.
For an n-node power grid, record omegaGFor the set of all generator nodes in the system, ΩLIs the set of all load nodes in the system. Defining the electrical connection coupling degree of any node i, a generator and a load node as follows:
the above equation quantitatively describes how closely each node (including generator and load nodes) in the system is electrically coupled to the generator and load nodes by taking the reciprocal of the sum of the equivalent impedance moduli of node i and the generator and load nodes in the system. When l ise,iThe larger the value, the tighter the electrical coupling of the node to the generator and load nodes, the more sensitive the node is to disturbances on both the generator side and the load side.
3.2PMU monitoring point selection strategy
In order to better capture the forced oscillation disturbance waveform, a PMU monitoring node needs to be reasonably selected. For an n-node power grid with a given topological structure, PMU monitoring nodes can be selected according to the following strategies:
1) offline calculation of electric connection coupling degree index l of generators and load nodes of all nodes of systeme,i(i ═ 1,2.. n), and sorting it;
2) selecting a plurality of nodes with larger coupling degree indexes, combining a complex plane coordinate point distribution graph, and selecting N monitoring points from the nodes, wherein the N monitoring points meet the following requirements:
a) for any monitoring of the equivalent electrical distance between nodes i, j
Epsilon is a set node electrical distance threshold value;
b) generally, N is more than or equal to 3, the positioning is more accurate when N is larger according to a semi-plane method positioning principle, but the engineering requirements can be met when N is appropriately sized in consideration of reducing the calculated amount and accelerating the convergence process.
4. Disturbance source positioning based on equivalent electrical distance
According to the Geiger classical theory in seismic positioning: let the seismic source be (x)0,y0,z0) The moment of onset is t0The arrival time of the seismic waves of the n seismic observation stations is t1,t2,...tnThen the seismic source location problem can be translated into solving the minima of the objective function:
wherein riTo the arrival time residual, TiThe calculated travel time for the ith station.
ri＝ti-t0-Ti(x0,y0,z0) (5)
By using the Geiger positioning theory, assuming that all directions are at the same speed when the electromechanical wave propagates, the positioning problem of the forced oscillation disturbance source is converted into an optimization problem, and only the minimum value needs to be solved for the following objective function
Namely, the sum of the squares of the electrical distances from each monitoring point to the disturbance source is only required to be ensured to be minimum.
And (4) setting constraint conditions for the optimization problem by combining the idea of a semi-plane disturbance positioning method. For an N-node grid, N PMU monitoring nodes are set, and (x) is assumed0,y0) The electrical distance from any node i to the disturbance source is
Sequencing the time of the disturbance waves arriving at the monitoring points in sequence, namely renumbering the monitoring points according to the sequence from near to far from the electric distance of the disturbance source:
d1≤d2≤...≤dN (8)
therefore, the optimization problem model to be solved is as follows:
in order to accelerate the convergence rate of the optimization problem and ensure the convergence and stability of the solution, the minimum value of the objective function is obtained by adopting a conjugate gradient method, namely the optimal solution. And finding out a node closest to the optimal solution in the complex plane coordinate system, namely the node is a disturbance source of the forced power oscillation, so as to realize the accurate positioning of the forced oscillation disturbance source.
The time sequence of the disturbance wave reaching each monitoring point is judged by adopting the following principle: the disturbance power injection when the forced oscillation occurs will cause the system frequency to fluctuate, and the frequency variation of each node of the system presents obvious space-time distribution characteristics due to different electrical distances between each bus node and a disturbance source, network parameter difference and the like. The characteristic indicates that the frequency variation delta f of each node of the system has a time difference in response time, and the closer the frequency variation delta f is to the electrical distance of the disturbance source, the earlier the time when the frequency variation delta f reaches an extreme value for the first time. According to the principle, the bus frequency variation curve of each PMU monitoring node is obtained, and the time when the frequency variation reaches the extreme value for the first time is compared, so that the time when the jamming motor electric waves reach each monitoring point is judged.
Second, simulation verification
Simulation verification is performed by adopting an IEEE 30 node standard test system, and the topological structure of the IEEE 30 node system is shown in figure 3, wherein a node 1 is a balanced node, namely the origin of a complex plane coordinate system.
First, the system node is subjected to complex plane coordinatization, and the result is shown in table 1.
TABLE 1 complex plane coordinate result of IEEE 30 node system
The distribution of 30 nodes in the system on a complex plane coordinate system is shown in figure 4.
Then, selecting a PMU monitoring node. Calculating the electric connection coupling degree l of the generator and the load node of each node of the systemeAnd arranged in descending order, see table 2. As can be seen from the calculation results in the table, the electrical connection coupling degree of the 6 nodes {6, 1, 9, 22, 2, 25} with the generator and the load node is large, and it can be known from the electrical distance distribution characteristics of fig. 4 that the distance between the node 2 and the nodes 1 and 6 is short, the node 2 can be eliminated, and finally, the 5 nodes {6, 1, 9, 22, 25} can be selected as PMU monitoring points.
TABLE 2 electric connection coupling degree of generator and load node of each node of system
And then, building a simulation model of the IEEE 30 node system in PSD-BPA software. The system has an oscillation mode with a frequency of 0.91 Hz. A periodic power disturbance with frequency of 0.91Hz and amplitude of 100% of the original mechanical power of the prime mover is applied to the prime mover side of the generator at node 11 to excite forced power oscillation of the system. The voltage angle variation curves at 5 PMU monitoring nodes obtained by time domain simulation are shown in FIG. 5.
Therefore, the time sequence of arrival of disturbance motor electric waves at three monitoring points after oscillation occurs is as follows: 9 → 6 → 22 → 1 → 25.
Solving the optimization problem shown in the formula (9) results in the optimal solution being (0.0361,0.4495), and the complex plane coordinates of the node 11 being (0.0339,0.4305), the distance deviation between the two is only 4.4%, which proves that the node 11 is the disturbance source. Therefore, the simulation example effectively verifies the effectiveness of the positioning method provided by the invention.
According to the technical scheme, the actual power grid nodes are mapped to the complex plane coordinate system based on the equivalent electrical distance theory, and the electrical position coordination of each node is realized. Then, the coupling degree of the electrical connection between the generator and the load nodes is defined, and a plurality of PMU monitoring nodes are selected according to the index. And finally, solving the objective function to obtain an optimal solution by taking the minimum sum of squares of equivalent electrical distances from the disturbance source to be solved to each PMU monitoring point as an objective function, and finding a node closest to the optimal solution in a complex plane coordinate system, namely the disturbance source of the forced power oscillation, so as to realize the accurate positioning of the disturbance source of the 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, where the device includes:
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 to a complex plane coordinate system according to the theory of the node equivalent electrical distance;
the monitoring point selection module is used for acquiring the coupling degree of the electric connection of the generator and the coincidence nodes and selecting PMU monitoring nodes;
the monitoring point sequencing module is used for carrying out oscillation generation, analyzing the frequency variation curve of each PMU monitoring node bus, judging the time sequence of the disturbance wave reaching each PMU monitoring node, and reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source;
the objective function solving module is used for taking the minimum sum of squares of equivalent electrical distances from the 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 a 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 obtaining module is further configured to:
the equivalent electrical distance between any two nodes i, j in the power grid is the equivalent impedance Z between the two nodesij,eqAnd (c) characterizing, wherein,
wherein ,ZiiIs the ith row and ith column element, Z of the node impedance matrixijIs the i row, j column element, Z of the impedance matrixijIs the ith row and jth column element of the node impedance matrix.
More specifically, the node mapping module is further configured to:
step 201: selecting a power grid balance node as an origin of a complex plane coordinate system, and selecting one balance node as the origin of the complex plane coordinate system if the actual power grid has a plurality of balance nodes;
step 202: generating a power grid node admittance matrix 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 obtaining the equivalent impedance Z between the node k and the origin o of the complex plane coordinate system by supposing calculationok＝Rok+jXokThen node k mapsTo the complex plane coordinate system as the coordinate (R)ok,Xok)；
Step 205: all nodes are mapped to a complex planar coordinate system.
More specifically, the monitoring point selecting module is further configured to:
by the formula
Obtaining the electric connection coupling degree of the generator and the load node, wherein omegaGFor the set of all generator nodes in the system, ΩLThe method comprises the steps of (1) collecting all load nodes in a system;
calculating the electrical connection coupling degrees of the generators and the load nodes of all the nodes of the system off line, and sequencing the electrical connection coupling degrees;
selecting a plurality of nodes with large electrical connection coupling degree indexes, combining a complex plane coordinate point distribution graph, and selecting N PMU monitoring nodes from the nodes, wherein the N PMU monitoring nodes meet the following requirements: monitoring the equivalent electrical distance between nodes i, j for any PMU
Epsilon is a set electrical distance threshold of the node, where xiIs the abscissa, y, of node iiIs the ordinate of node i.
More specifically, the monitoring point sorting module is further configured to:
for an N-node grid, N PMU monitoring nodes are set, and (x) is assumed0,y0) The electrical distance from any node i to the disturbance source is
Sequencing the time of the disturbance waves reaching the PMU monitoring nodes in sequence, namely, reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source:
d1≤d2≤...≤dN。
more specifically, the objective function solving module is further configured to:
by the formula
And constructing an objective optimization function and solving the objective optimization function to obtain an optimal solution.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present 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 solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
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 of:
the method comprises the following steps: obtaining an equivalent electrical distance between any two nodes in a power grid;
step two: mapping each node of the actual power grid to a complex plane coordinate system according to the theory of the node equivalent electrical distance;
step three: acquiring the coupling degree of the electric connection of the generator and the coincidence nodes, and selecting PMU monitoring nodes;
step four: oscillation occurs, the frequency variation curve of each PMU monitoring node bus is analyzed, the time sequence of disturbance waves reaching each PMU monitoring node is judged, and the PMU monitoring nodes are reordered according to the sequence from near to far from the electrical distance of a 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 out a node closest to the optimal solution in the complex plane coordinate system, namely a disturbance source of the forced power oscillation.
2. The method for locating a disturbance source of forced power oscillation based on equivalent electrical distance as claimed in claim 1, wherein said step one comprises:
the equivalent electrical distance between any two nodes i, j in the power grid is the equivalent impedance Z between the two nodesij,eqAnd (c) characterizing, wherein,
wherein ,ZiiIs the ith row and ith column element, Z of the node impedance matrixijIs the i row, j column element, Z of the impedance matrixijIs the ith row and jth column element of the node impedance matrix.
3. The method for locating a disturbance source of forced power oscillation based on equivalent electrical distance as claimed in claim 2, wherein said step two comprises:
step 201: selecting a power grid balance node as an origin of a complex plane coordinate system, and selecting one balance node as the origin of the complex plane coordinate system if the actual power grid has a plurality of balance nodes;
step 202: generating a power grid node admittance matrix 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 obtaining the equivalent impedance Z between the node k and the origin o of the complex plane coordinate system by supposing calculationok＝Rok+jXokThen the node k is mapped to the coordinate (R) in the complex plane coordinate systemok,Xok)；
Step 205: all nodes are mapped to a complex planar coordinate system.
4. The method for locating a disturbance source of forced power oscillation based on equivalent electrical distance as claimed in claim 3, wherein said step three comprises:
by the formula
Obtaining the electric connection coupling degree of the generator and the load node, wherein omegaGFor the set of all generator nodes in the system, ΩLThe method comprises the steps of (1) collecting all load nodes in a system;
calculating the electrical connection coupling degrees of the generators and the load nodes of all the nodes of the system off line, and sequencing the electrical connection coupling degrees;
selecting a plurality of nodes with large electrical connection coupling degree indexes, combining a complex plane coordinate point distribution graph, and selecting N PMU monitoring nodes from the nodes, wherein the N PMU monitoring nodes meet the following requirements: monitoring the equivalent electrical distance between nodes i, j for any PMU
Epsilon is a set electrical distance threshold of the node, where xiIs the abscissa, y, of node iiIs the ordinate of node i.
5. The method for locating a disturbance source of forced power oscillation based on equivalent electrical distance as claimed in claim 4, wherein said step four comprises:
for an N-node grid, N PMU monitoring nodes are set, and (x) is assumed0,y0) The electrical distance from any node i to the disturbance source is
Sequencing the time of the disturbance waves reaching the PMU monitoring nodes in sequence, namely, reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source:
d1≤d2≤...≤dN。
6. the method for locating a disturbance source of forced power oscillation based on equivalent electrical distance as claimed in claim 5, wherein said step five comprises:
by the formula
And constructing an objective optimization function and solving the objective optimization function to obtain an optimal solution.
7. Forced power oscillation disturbance source positioning device based on equivalent electrical distance, characterized in that the device 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 to a complex plane coordinate system according to the theory of the node equivalent electrical distance;
the monitoring point selection module is used for acquiring the coupling degree of the electric connection of the generator and the coincidence nodes and selecting PMU monitoring nodes;
the monitoring point sequencing module is used for carrying out oscillation generation, analyzing the frequency variation curve of each PMU monitoring node bus, judging the time sequence of the disturbance wave reaching each PMU monitoring node, and reordering the PMU monitoring nodes according to the sequence from near to far from the electrical distance of a disturbance source;
the objective function solving module is used for taking the minimum sum of squares of equivalent electrical distances from the 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 a node closest to the optimal solution in the complex plane coordinate system, namely the disturbance source of the forced power oscillation.
8. The equivalent electrical distance-based forced power oscillation disturbance source positioning device according to claim 7, wherein the equivalent electrical distance acquisition module is further configured to:
the equivalent electrical distance between any two nodes i, j in the power grid is the equivalent impedance Z between the two nodesij,eqAnd (c) characterizing, wherein,
wherein ,ZiiIs the ith row and ith column element, Z of the node impedance matrixijIs the i row, j column element, Z of the impedance matrixijIs the ith row and jth column element of the node impedance matrix.
9. The equivalent electrical distance-based forced power oscillation disturbance source positioning device according to claim 8, wherein the node mapping module is further configured to:
step 201: selecting a power grid balance node as an origin of a complex plane coordinate system, and selecting one balance node as the origin of the complex plane coordinate system if the actual power grid has a plurality of balance nodes;
step 202: generating a power grid node admittance matrix 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 obtaining the equivalent impedance Z between the node k and the origin o of the complex plane coordinate system by supposing calculationok＝Rok+jXokThen the node k is mapped to the coordinate (R) in the complex plane coordinate systemok,Xok)；
Step 205: all nodes are mapped to a complex planar coordinate system.
10. The equivalent electrical distance-based forced power oscillation disturbance source positioning device according to claim 9, wherein the monitoring point selection module is further configured to:
by the formula
Obtaining the electric connection coupling degree of the generator and the load node, wherein omegaGFor the set of all generator nodes in the system, ΩLThe method comprises the steps of (1) collecting all load nodes in a system;
calculating the electrical connection coupling degrees of the generators and the load nodes of all the nodes of the system off line, and sequencing the electrical connection coupling degrees;
selecting a plurality of nodes with large electrical connection coupling degree indexes, combining a complex plane coordinate point distribution graph, and selecting N PMU monitoring nodes from the nodes, wherein the N PMU monitoring nodes meet the following requirements: monitoring the equivalent electrical distance between nodes i, j for any PMU
Epsilon is a set electrical distance threshold of the node, where xiIs the abscissa, y, of node iiIs the ordinate of node i.
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