CN111740410A - Power system frequency space-time dynamic prediction method - Google Patents

Power system frequency space-time dynamic prediction method Download PDF

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CN111740410A
CN111740410A CN202010573418.7A CN202010573418A CN111740410A CN 111740410 A CN111740410 A CN 111740410A CN 202010573418 A CN202010573418 A CN 202010573418A CN 111740410 A CN111740410 A CN 111740410A
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power system
matrix
generator
distance
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CN111740410B (en
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易建波
黄琦
井实
张真源
李坚
樊益凤
刘振东
田丰勋
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University of Electronic Science and Technology of China
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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
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention discloses a method for dynamically predicting the frequency space-time of an electric power system, which comprises the steps of firstly constructing a distance matrix Z and a path matrix L of the electric power system and assigning initial values, then updating the distance matrix Z and the path matrix L through main row and main column elements of the shortest distance matrix Z, and further finding the shortest electrical distance between any two nodes in the electric power system and the path where the shortest electrical distance is located; on the basis, the coupling factors of the test points at the moment of the lowest frequency value under the same fault point are calculated, so that the sequence of the frequency dynamic reaching of the lowest value of each monitoring point after the power system is disturbed is predicted, the time-space dynamic distribution of the power system frequency is predicted, and the safe and stable operation of the power system is better guaranteed.

Description

Power system frequency space-time dynamic prediction method
Technical Field
The invention belongs to the technical field of electric power, and particularly relates to a frequency space-time dynamic prediction method of an electric power system.
Background
With the rapid development of national economy, the power load is continuously increased, the scale of the power grid is gradually enlarged, the frequency characteristic of the large-scale power grid is more and more complex, and the frequency space-time distribution characteristic cannot be ignored. The time-space distribution characteristics of the frequency of the power system under disturbance have great significance for the safety and stability monitoring of the power system, the operation control of the system, the disturbance analysis and the like. When the power system breaks down, the accurate frequency dynamic can help to determine the wind power permeability, the reasonable configuration of a frequency modulation unit, the spare capacity and the Automatic Generation Control (AGC) parameter configuration, and the accurate frequency dynamic characteristic is helpful to setting a low-frequency load shedding scheme to avoid frequency collapse accidents.
The frequency response of each monitoring point of the system has a time-space distribution characteristic in the dynamic process of the power grid. The uneven distribution of the units and the difference of the inertia thereof are important factors influencing the frequency space-time distribution. Since inertia is an inherent property of the power system, it represents an impedance effect of the system on external disturbances causing energy fluctuations. Therefore, when the power system is disturbed, the frequency of each node is different due to the difference of inertia of each node in the system, and the space-time distribution characteristic of the frequency is presented. The frequency distribution condition of a complex power grid is mastered, the sequence of arrival of the lowest frequency values of all measuring points in the system at any moment can be accurately predicted, a more accurate switching control strategy can be formulated, and the safety and stability of the power system are improved.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a power system frequency space-time dynamic prediction method, wherein the sequence of the dynamic arrival of the frequency of each monitoring point to the lowest value after the power system is disturbed is predicted through the coupling factor at the moment of the lowest value of the frequency, so that the power system frequency space-time dynamic distribution is predicted, and the safe and stable operation of the power system is better ensured.
In order to achieve the above object, the present invention provides a method for predicting frequency space-time dynamics of an electrical power system, comprising the following steps:
(1) constructing a distance matrix Z and a path matrix L of the power system;
the distance matrix for constructing the power system is Z ═ Zij]n×n，zijRepresenting the electrical distance between any node i and a node j, wherein n is the number of nodes in the power system;
constructing a path matrix L ═ Lij]n×n，lijRepresenting intermediate nodes on the shortest path from the non-adjacent node i to the node j;
(2) assigning initial values to the distance matrix Z and the path matrix L;
the distance matrix Z has an initial value:
Figure BDA0002550460080000021
wherein,
Figure BDA0002550460080000022
the shortest path matrix L is assigned with an initial value:
Figure BDA0002550460080000023
wherein
Figure BDA0002550460080000024
(3) Marking main row and main column elements of the shortest distance matrix Z;
marking a row and a column from the shortest distance matrix Z at will, marking as the kth row and the kth column, wherein k belongs to [1, n ], and elements of the kth row and the kth column are marked as main row elements and main column elements;
(4) updating the distance matrix Z and the path matrix L;
updating the distance matrix Z: in the distance matrix Z, traversing all values of k from small to large, and in each value of k, starting from the first element which is not in the main row and the main column, sequentially comparing the element with the sum of any two elements in the main row and the main column, if Z isik+zkj≥zijThen element z is maintainedijThe value of (d) is unchanged; if z isik+zkj＜zijThen use zik+zkjAlternative element zij；
Updating the distance matrix L(k)Comprises the following steps:
Figure BDA0002550460080000025
(5) calculating the shortest electrical distance between any two nodes in the power system and the path where the shortest electrical distance is located;
repeating the step (4), and when k is traversed to n, obtaining an updated distance matrix Z(n)Sum path matrix L(n)(ii) a Then let node i to node j have the shortest electrical distance
Figure BDA0002550460080000026
The corresponding shortest electrical distance path is marked as Li-j-min；
(6) Calculating an inertia time constant of each line in the power system;
(6.1) selecting all generator nodes in the network topology of the power system, and recording the nodes as n in total1A plurality of; marking any one generator node as a generator starting end node, and marking the rest generators as generator terminal nodes;
(6.2) calculating the path from the starting end node of the generator to the terminal end node of each generator in combination with the step (5) and the line l on the pathi-jAn inertial time constant of (c);
Figure BDA0002550460080000031
Figure BDA0002550460080000032
Figure BDA0002550460080000033
wherein,
Figure BDA0002550460080000034
for the q-th generatorStarting node
Figure BDA0002550460080000035
To the p-th generator terminal node
Figure BDA0002550460080000036
Q is 1,2, …, n is the line set on the path of the shortest electrical distance between them1，p＝1,2,…,n1-1；
Figure BDA0002550460080000037
The starting end node of the q-th generator is distributed on a line li-jAn inertial time constant of (c); z is a radical ofijRepresents a line li-jThe electrical distance from node i to node j;
Figure BDA0002550460080000038
representing the qth generator start node
Figure BDA0002550460080000039
To the p-th generator terminal node
Figure BDA00025504600800000310
The shortest electrical distance between the two;
Figure BDA00025504600800000311
represents the inertia time constant of the qth start generator;
(6.3) calculating each line l in the power systemi-jUpper time constant of inertia Tli-j：
Figure BDA00025504600800000312
(7) Calculating the coupling factor at the moment of the lowest frequency value;
(7.1) calculating an impedance reference value ZbaseWith a reference value of inertia Tbase：
Figure BDA00025504600800000313
Figure BDA00025504600800000314
Wherein N is the number of lines in the power system;
(7.2) marking any one generator node as a fault node and the rest as test nodes in the network topology of the power system;
(7.3) the shortest electrical distance from each per unit fault node to each test node and inertia:
Figure BDA0002550460080000041
Figure BDA0002550460080000042
Figure BDA0002550460080000043
wherein,
Figure BDA0002550460080000044
for failed node vfaultTo the lambda test node
Figure BDA0002550460080000045
The shortest electrical distance between them, λ 1,2, …, n1-1；
Figure BDA0002550460080000046
For failed node vfaultTo the lambda test node
Figure BDA0002550460080000047
Per unit value of the shortest electrical distance therebetween;
Figure BDA0002550460080000048
for failed node vfaultTo the lambda test node
Figure BDA0002550460080000049
The per unit value of inertia between;
(7.4) calculating the coupling factor of each test node at the moment of the lowest frequency value
Figure BDA00025504600800000410
Figure BDA00025504600800000411
(8) Predicting power system frequency space-time dynamics
Coupling factor of test point at the moment of lowest frequency value under the same fault point
Figure BDA00025504600800000412
The smaller the value, the lowest the test point frequency is reached first, so all will be
Figure BDA00025504600800000413
The sequence T is formed from small to largedIs marked as
Figure BDA00025504600800000414
Therefore, the frequency space-time dynamic distribution of the power system is predicted.
The invention aims to realize the following steps:
the invention relates to a method for dynamically predicting the frequency space-time of an electric power system, which comprises the steps of firstly constructing a distance matrix Z and a path matrix L of the electric power system and assigning initial values, then updating the distance matrix Z and the path matrix L through main row and main column elements of the shortest distance matrix Z, and further finding the shortest electrical distance between any two nodes in the electric power system and the path where the shortest electrical distance is located; on the basis, the coupling factors of the test points at the moment of the lowest frequency value under the same fault point are calculated, so that the sequence of the frequency dynamic reaching of the lowest value of each monitoring point after the power system is disturbed is predicted, the time-space dynamic distribution of the power system frequency is predicted, and the safe and stable operation of the power system is better guaranteed.
Meanwhile, the power system frequency space-time dynamic prediction method also has the following beneficial effects:
(1) aiming at the distribution of system inertia, a new distribution method is provided: the inertia of each generator in the system is uniformly distributed on a line where the shortest electrical distance path between the generator and the rest of the generators in the system is located, so that the processing is favorable for simulating the characteristics of an actual power grid, and the precision of frequency space-time dynamic prediction is improved;
(2) the transmission of disturbance in the system is carried by the transmission line, and the line between two nodes in the actual power grid is not a straight line in a geographic space, so that the geographic distribution of the generator in the power system is measured by the electrical distance between the two nodes in the system, and the frequency moment dynamics of the power system can be more accurately predicted;
(3) according to the invention, the frequency space-time dynamics after the power system disturbance can be rapidly predicted by constructing the coupling factor at the lowest frequency value moment.
Drawings
FIG. 1 is a flow chart of a method for power system frequency space-time dynamic prediction according to the present invention;
FIG. 2 is a diagram of an IEEE 10 machine 39 node emulation system;
FIG. 3 is an initial value of the distance matrix Z;
FIG. 4 is a distance matrix Z after the update is completed(n)；
FIG. 5 is a diagram of the path matrix L after the update is completed(n)；
FIG. 6 is a system frequency spatio-temporal distribution diagram after generator G9 generator tripping failure;
FIG. 7 is a system frequency spatio-temporal profile of generator G7 after generator tripping failure.
Detailed Description
The following description of the embodiments of the present invention is provided in order to better understand the present invention for those skilled in the art with reference to the accompanying drawings. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Examples
In the present embodiment, as shown in fig. 1, for an example of IEEE 10 machine 39 node power system simulation data, a fault description is as follows: when t is 5s, the generator G9 cuts the generator by 41 percent due to faults, the simulation time is 50s, the simulation step length is 0.0001s, and the time difference of the lowest frequency value between two monitoring points in the power system is 0.001 s, which can be regarded as the occurrence of the space-time distribution phenomenon.
The present embodiment does not take into account the influence of the transformer on the propagation of the dynamic frequency space-time distribution, that is, when the shortest electrical distance between two generators and the path where the generator is located are calculated, the monitoring node is selected as the bus node 29 after the generator passes through the transformer without considering the influence of the transformer. The monitoring nodes selected in this example are 39 (generator G1), 19 (generator G4), 23 (generator G7), 25 (generator G8) and 2 (generator G10).
The following describes in detail a power system frequency space-time dynamic prediction method according to the present invention with reference to fig. 2, as shown in fig. 1, specifically including the following steps:
s1, constructing a distance matrix Z and a path matrix L of the power system;
the distance matrix for constructing the power system is Z ═ Zij]n×n，zijThe electrical distance between any node i and a node j is represented, n is the number of nodes in the power system, and the value is 39;
constructing a path matrix L ═ Lij]n×n，lijRepresenting intermediate nodes on the shortest path from the non-adjacent node i to the node j;
s2, assigning initial values to the distance matrix Z and the path matrix L;
the distance matrix Z has an initial value:
Figure BDA0002550460080000061
wherein,
Figure BDA0002550460080000062
referring to fig. 2, the specific initial value of the distance matrix Z is shown in fig. 3, and since the matrix is too large, fig. 3 is a screenshot of the matrix in the code, where inf represents ∞, and 0.00025+0.0125i represents 0.0005+ j 0.0125;
the path matrix L is given an initial value of:
Figure BDA0002550460080000063
wherein
Figure BDA0002550460080000064
S3, marking main row and main column elements of the shortest distance matrix Z;
marking a row and a column from the shortest distance matrix Z at will, marking as the kth row and the kth column, wherein k belongs to [1, n ], and elements of the kth row and the kth column are marked as main row elements and main column elements;
s4, updating the distance matrix Z and the path matrix L;
updating the distance matrix Z: in the distance matrix Z, traversing all values of k from small to large, and in each value of k, starting from the first element which is not in the main row and the main column, sequentially comparing the element with the sum of any two elements in the main row and the main column, if Z isik+zkj≥zijThen element z is maintainedijThe value of (d) is unchanged; if z isik+zkj＜zijThen use zik+zkjAlternative element zij；
Updating the distance matrix L(k)Comprises the following steps:
Figure BDA0002550460080000065
in this embodiment, the primary row and primary column elements of the annotated distance matrix Z begin with the first row and first column.
S5, calculating the shortest electrical distance between any two nodes in the power system and the path where the shortest electrical distance is located;
repeating the step S4, and obtaining the updated distance matrix Z when k traverses to n(n)As shown in fig. 4 and path matrix L(n)As shown in fig. 5; in FIG. 4, 0.5 in the matrix represents 0.00025+ j0.00625, 1 represents 0.0005+ j0.0125, 2 represents 0.001+ j0.025, and so on; then let node i to node j have the shortest electrical distance
Figure BDA0002550460080000071
And the path of the shortest electrical distance from the node i to the node j is recorded as Li-j-min；
In this embodiment, with reference to fig. 2 and 4, the path along which the shortest electrical distance between the generator G9 node 29 and the measurement point nodes 39, 19, 23, 25 and 2 in the power system is calculated is as follows:
L29-39-min＝{29→26→25→2→1→39}；
L29-19-min＝{29→26→27→17→16→19}；
L29-23-min＝{29→26→27→17→16→24→23}；
L29-25-min＝{29→26→25}；
L29-2-min＝{29→26→25→2}；)
s6, calculating the distribution of inertia in the power system;
s6.1, measuring inertia by using an inertia time constant of the generator, and calculating inertia distribution of each generator; all generator nodes are selected from the network topology of the power system and are recorded as n1A plurality of; marking any one generator node as a generator starting end node, and marking the rest generators as generator terminal nodes;
s6.2, calculating the path from the initial end node to each terminal node and the line l on the pathi-jTime constant of inertia above;
Figure BDA0002550460080000072
Figure BDA0002550460080000073
Figure BDA0002550460080000074
for example, a set l of lines is calculated between the 9 th generator start node 29 and the 1 st generator end node 39i-j。
L29-39-min{29→26→25→2→1→39}
li-j＝{L29-39-min}＝{l29-26,l26-25,l25-2,l2-1,l1-39}
Figure BDA0002550460080000081
Calculating the 9 th generator starting node 29 distributed in the path set li-jThe time constant of inertia on all lines;
Figure BDA0002550460080000082
s6.3, calculating the inertia distribution of all generators in the system according to the steps, and then calculating each line l in the power systemi-jUpper time constant of inertia Tli-j：
Figure BDA0002550460080000083
By a line l29-26For the purpose of example only,
Figure BDA0002550460080000084
in this embodiment, n is shown in FIG. 11The calculated inertia distribution on each line in the power system is shown in table 1, 10.
Table 1 shows the power system line inertia distribution results.
Line Inertia Line Inertia Line Inertia
L29-26 18.99 L1-39 14.64 L5-6 15.2
L26-25 18.99 L2-3 20.1 L26-27 14.85
L25-2 21.48 L3-4 8.26 L27-17 14.85
L2-1 14.64 L1-5 11.31 L17-16 26.7
L16-15 13.78 L14-13 9.57 L16-19 33.15
L15-14 13.78 L13-10 9.57 L16-21 14.94
L21-22 14.94 L16-24 14.94 L24-23 14.94
TABLE 1
S7, calculating the coupling factor at the moment of the lowest frequency value;
s7.1, calculating an impedance reference value ZbaseWith a reference value of inertia Tbase：
Figure BDA0002550460080000091
Figure BDA0002550460080000092
Wherein N is the number of lines in the power system; in the present embodiment, n1＝10，N＝21And thus calculating: zbase＝0.0005+j0.0125，Tbase＝42；
S7.2, in conjunction with fig. 2, the generator node 29 is a fault node, and 39, 19, 23, 25, and 2 are test nodes;
s7.3, the shortest electrical distance between the per-unit fault node fault point 29 to the test nodes 39, 19, 23, 25, and 2, and the inertia:
Figure BDA0002550460080000093
Figure BDA0002550460080000094
Figure BDA0002550460080000095
wherein,
Figure BDA0002550460080000096
for failed node vfaultTo the lambda test node
Figure BDA0002550460080000097
The shortest electrical distance therebetween, λ ═ 1,2, …, 5;
Figure BDA0002550460080000098
for failed node vfaultTo the lambda test node
Figure BDA0002550460080000099
Per unit value of the shortest electrical distance therebetween;
Figure BDA00025504600800000910
indicating a faulty node vfaultTo the lambda test node
Figure BDA00025504600800000911
The path of the shortest electrical distance
Figure BDA00025504600800000912
For failed node vfaultTo the lambda test node
Figure BDA00025504600800000913
The per unit value of inertia between;
taking fault node 29 and test node 39 as examples,
Figure BDA00025504600800000914
Figure BDA00025504600800000915
Figure BDA00025504600800000916
in the present embodiment, the shortest electrical distance and the inertia result between the per-unit fault node 29 and the test nodes 39, 19, 23, 25 and 2 are shown in table 2.
Table 2 shows the shortest electrical distance between the fault point and the measurement point and the inertial per unit value.
29-39 28-19 29-23 29-25 29-2
Z*/pu 5 5 6 2 3
T*/pu 2.1129 2.5843 2.5064 0.9019 1.4157
TABLE 2
S7.4, calculating the coupling factor of each test node at the moment of the lowest frequency value
Figure BDA0002550460080000101
Figure BDA0002550460080000102
In this embodiment, the lowest frequency coupling factor between fault point 29 and stations 39, 19, 23, 25 and 2 is calculated as shown in Table 3.
Table 3 shows the lowest frequency coupling factor from the fault point to the station.
29-39 29-19 29-23 29-25 29-2
td 7.112 7.5843 8.5064 2.9019 4.4157
TABLE 3
S8, predicting power system frequency space-time dynamic state
As shown in table 3, at the fault point 29, the sequence of the coupling factors of the test nodes 39, 19, 23, 25 and 2 at the time of the lowest frequency value is 25 → 2 → 39 → 19 → 23 from small to large, and the smaller the value is, the test point frequency reaches the lowest value first, so the sequence of the frequency of each test point dynamically reaching the lowest value is: g8 → G10 → G1 → G4 → G7, thereby predicting the frequency space-time dynamics of the power system.
In this embodiment, with reference to fig. 2, a refined simulation is performed by the PASAP software to obtain that there is an obvious spatial-temporal distribution phenomenon in the frequencies of the monitoring points, and the sequence of the lowest frequency value moments of the monitoring points is as follows: g8 → G10 → G1 → G4 → G7, the same order as the predicted one of the present invention, the simulation result is shown in FIG. 6.
In addition, the example also provides another fault condition, when t is 5s, the node 23 of the generator G7 generates 40% of power due to fault loss, and monitoring points are selected as a node 39 (a generator G1), a node 19 (a generator G4), a node 22 (a generator G6) and a node 29 (a generator G9). According to the method provided by the invention, the shortest electrical distance path from the generator G7 to each measuring point 39, 19, 22 and 29 can be calculated as follows:
L23-39-min＝{23→24→16→17→18→3→2→1→39}
L23-19-min＝{23→24→16→19}
L23-22-min＝{23→22}
L23-29-min＝{23→24→16→17→27→26→29}
the results of the shortest electrical distance between the per unit fault point 23 and each of the measuring points 39, 19, 22 and 29 and the inertia and frequency lowest value coupling factors thereof are shown in table 4.
Table 4 shows the shortest electrical distance between the fault point and the measurement point, its inertia, and the per unit value of the coupling factor.
23-39 23-19 23-22 23-29
Z*/pu 8 3 1 6
T*/pu 3.0867 1.5007 0.2214 2.5064
td 11.0867 4.5007 1.2214 8.5064
TABLE 4
The PASAP software is used for carrying out fine simulation, the time domain simulation result is shown in figure 7, and the space-time distribution characteristic is consistent with the space-time characteristic judged by the algorithm.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (1)

1. A power system frequency space-time dynamic prediction method is characterized by comprising the following steps:
(1) constructing a distance matrix Z and a path matrix L of the power system;
the distance matrix for constructing the power system is Z ═ Zij]n×n，zijRepresenting the electrical distance between any node i and a node j, wherein n is the number of nodes in the power system;
constructing a path matrix L ═ Lij]n×n，lijRepresenting intermediate nodes on the shortest path from the non-adjacent node i to the node j;
(2) assigning initial values to the distance matrix Z and the path matrix L;
the distance matrix Z has an initial value:
Figure FDA0002550460070000011
wherein,
Figure FDA0002550460070000012
the shortest path matrix L is assigned with an initial value:
Figure FDA0002550460070000013
wherein
Figure FDA0002550460070000014
(3) Marking main row and main column elements of the shortest distance matrix Z;
marking a row and a column from the shortest distance matrix Z at will, marking as the kth row and the kth column, wherein k belongs to [1, n ], and elements of the kth row and the kth column are marked as main row elements and main column elements;
(4) updating the distance matrix Z and the path matrix L;
updating the distance matrix Z: in the distance matrix Z, traversing all values of k from small to large, and in each value of k, starting from the first element which is not in the main row and the main column, sequentially comparing the element with the sum of any two elements in the main row and the main column, if Z isik+zkj≥zijThen element z is maintainedijThe value of (d) is unchanged; if z isik+zkj＜zijThen use zik+zkjAlternative element zij；
Updating the distance matrix L(k)Comprises the following steps:
Figure FDA0002550460070000015
(5) calculating the shortest electrical distance between any two nodes in the power system and the path where the shortest electrical distance is located;
repeating the step (3), and when k traverses to n, obtaining an updated distance matrix Z(n)Sum path matrix L(n)(ii) a Then let node i to node j have the shortest electrical distance
Figure FDA0002550460070000016
The corresponding shortest electrical distance path is marked as Li-j-min；
(6) Calculating an inertia time constant of each line in the power system;
(6.1) selecting all generator nodes in the network topology of the power system, and recording the nodes as n in total1A plurality of; marking any one generator node as a generator starting end node, and marking the rest generators as generator terminal nodes;
(6.2) calculating the path from the starting end node of the generator to the terminal end node of each generator in combination with the step (5) and the line l on the pathi-jAn inertial time constant of (c);
Figure FDA0002550460070000021
Figure FDA0002550460070000022
Figure FDA0002550460070000023
wherein,
Figure FDA0002550460070000024
is the starting end node of the q-th generator
Figure FDA0002550460070000025
To the p-th generator terminal node
Figure FDA0002550460070000026
Q is 1,2, …, n is the line set on the path of the shortest electrical distance between them1，p＝1,2,…,n1-1；
Figure FDA0002550460070000027
For the q-th starting generator distributed on line li-jAn inertial time constant of (c); z is a radical ofijRepresents a line li-jThe electrical distance from node i to node j;
Figure FDA0002550460070000028
representing the qth generator start node
Figure FDA0002550460070000029
To the p-th generator terminal node
Figure FDA00025504600700000210
The shortest electrical distance between the two;
Figure FDA00025504600700000211
represents an inertia time constant of the qth start-end generator;
(6.3) calculating each line l in the power systemi-jTime constant of inertia of
Figure FDA00025504600700000212
Figure FDA00025504600700000213
(7) Calculating the coupling factor at the moment of the lowest frequency value;
(7.1) calculating an impedance reference value ZbaseWith a reference value of inertia Tbase：
Figure FDA00025504600700000214
Figure FDA00025504600700000215
Wherein N is the number of lines in the power system;
(7.2) marking any one generator node as a fault node and the rest as test nodes in the network topology of the power system;
(7.3) the shortest electrical distance from each per unit fault node to each test node and inertia:
Figure FDA0002550460070000031
Figure FDA0002550460070000032
Figure FDA0002550460070000033
wherein,
Figure FDA0002550460070000034
for failed node vfaultTo the lambda test node
Figure FDA0002550460070000035
The shortest electrical distance between them, λ 1,2, …, n1-1；
Figure FDA0002550460070000036
For failed node vfaultTo the lambda test node
Figure FDA0002550460070000037
Per unit value of the shortest electrical distance therebetween;
Figure FDA0002550460070000038
for failed node vfaultTo the lambda test node
Figure FDA0002550460070000039
The per unit value of inertia between;
(7.4) calculating the coupling factor of each test node at the moment of the lowest frequency value
Figure FDA00025504600700000310
Figure FDA00025504600700000311
(8) Predicting power system frequency space-time dynamics
Coupling factor of test point at the moment of lowest frequency value under the same fault point
Figure FDA00025504600700000312
The smaller the value, the lowest the test point frequency is reached first, so all will be
Figure FDA00025504600700000313
The sequence T is formed from small to largedIs marked as
Figure FDA00025504600700000314
Therefore, the frequency space-time dynamic distribution of the power system is predicted.
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