CN113346482B - Method for predicting wide area power system frequency space-time distribution based on SFR model - Google Patents
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Abstract
The invention discloses a method for predicting frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model, which comprises the steps of establishing the high-order SFR model and predicting the inertia center frequency of the wide area power system by expanding the traditional simplified SFR model; then, a distance matrix and a path matrix between the nodes of the wide area power system are constructed and assigned with initial values, and the shortest electrical distance between any two nodes of the wide area power system, the path where the nodes are located and an inertia time constant on each line are calculated by updating the distance matrix and the path matrix iteratively; then marking the fault node, and calculating the shortest electrical distance and inertia between the per-unit fault node and each test node; and finally, calculating frequency space-time distribution factors, constructing a high-order frequency space-time distribution model of the wide area power system and predicting the frequency space-time dynamic distribution of the wide area power system in real time.
Description
Technical Field
The invention belongs to the technical field of electric power safety stability, and particularly relates to a method for predicting frequency space-time dynamic distribution of a wide area electric power system based on a high-order SFR model.
Background
At present, electric power systems in China are in complex forms of high voltage level, wide interconnection area, large system scale, high structural complexity and alternating current-direct current hybrid connection. The frequency is used as a key index for monitoring and controlling the power quality and the running state of the power system and is a key object for judging and controlling the stability of the power system, and the power grid frequency data of wide-area measurement shows that the frequency of each measuring point has obvious dynamic space-time distribution phenomenon. The establishment of the wide area system frequency space-time distribution model has great significance for improving the stability control level of the wide area interconnected power grid. When a wide area power system fails, the accurate frequency space-time dynamics not only can help to determine wind power permeability, reasonable configuration of a frequency modulation unit, spare capacity and Automatic Generation Control (AGC) parameter configuration, but also the accurate frequency space-time distribution characteristics are helpful to setting a low-frequency load shedding scheme, and frequency collapse accidents are avoided.
The frequency response of each monitoring point of the wide-area power system has space-time distribution characteristics. And a high-order frequency response model is established, the prediction precision of the system inertia center frequency is improved, and powerful theoretical support is provided for the space-time distribution characteristics of the follow-up research frequency. 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 difference of inertia of each node in the system and the difference of the speed regulator parameters thereof cause the difference of the frequency of each node, and the space-time distribution characteristic of the frequency is presented. The mapping relation between the inertia center frequency and the frequency dynamics of each monitoring point of the wide area system is mastered, the time-space dynamics of the frequency of the wide area system can be accurately predicted, a more accurate frequency switching control strategy can be formulated, and the safety and stability of the power system are improved.
In the prior art, the patent with the patent application number of "CN202010573418.7" entitled "a power system frequency space-time dynamic prediction method" is only able to predict and judge the disturbed space-time sequence of the power system, but is unable to accurately predict the frequency dynamic process of each measurement point of the system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for predicting the frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model.
In order to achieve the above object, the present invention provides a method for predicting frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model, which is characterized by comprising the following steps:
(1) The method for predicting the frequency space-time dynamic distribution of the wide area power system based on the high-order SFR model is characterized by comprising the following steps of:
(1) Establishing a high-order SFR model;
(1.1) expanding mechanical gain K in the traditional simplified SFR model m A first-order inertia link k/A + Ts is adopted, wherein k, A and T are all mechanical gain coefficients, and S represents an S domain; increasing excitation system damping
And wide area power system load effect damping D L To simulate damping of a wide area power system;
(1.2) setting parameters of the high-order SFR model;
wherein R is the equivalent difference adjustment coefficient of the wide area power system; t is a unit of R An equivalent reheat time constant of the wide area power system; h is the equivalent inertia time constant of the wide area power system, F H Working proportion of the equivalent high-pressure cylinder of the wide-area power system is obtained; m is the number of generators in the wide area power system; h q Rated capacity of the q generator in the wide area power system; r is q The difference adjustment coefficient of the q-th generator in the wide area power system is obtained; f Hq Working proportion of a high-pressure cylinder of a qth generator in a wide-area power system; t is Rq A reheat time constant of a qth generator in the wide area power system; m base,q Rated capacity of the q-th generator; s. the base A reference capacity for the wide area power system;
(2) Constructing a distance matrix B and a path matrix L between nodes of the wide area power system and assigning initial values to the distance matrix B and the path matrix L;
(3) And calculating the shortest electrical distance Z between any two nodes i and j of the wide area power system by iteratively updating the distance matrix B and the path matrix L i-j-min And its path L i-j-min ；
(4) Calculating each line l in the wide area power system i-j Time constant of inertia of
(5) Marking any fault node v in wide area power system fault Per-unit fault node to each test node
The shortest electrical distance therebetween
And inertia thereof
(6) Introducing frequency space-time distribution factors to part of key parameters of the high-order SFR model;
(6.1) for each test node, calculating the frequency space-time distribution factor of the equivalent inertia time constant in the high-order SFR model as follows:
wherein,
for the ith test node
The inertia space-time distribution factor of;
(6.2) for each test node, calculating the frequency space-time distribution factor of the equivalent reheating time constant in the high-order SFR model as follows:
wherein,
for the ith test node
The reheat time constant spatial-temporal distribution factor;
(6.3) for each test node, calculating a frequency space-time distribution factor of the work proportion of the medium-value high-pressure cylinder in the high-order SFR model as follows:
wherein,
for the ith test node
The work proportion space-time distribution factor of the high-pressure cylinder is calculated;
(7) Taking the high-order SFR model after the frequency space-time distribution factor is introduced as a frequency space-time distribution model of the wide area power system;
(8) Predicting the time-space dynamic distribution of the frequency by utilizing a frequency time-space distribution model of the wide area power system;
(8.1) calculating each test node after the wide area power system is disturbed
The amount of frequency variation of (a);
wherein D is g Indicating the damping of the generator and the excitation system,
representing the damping of the generator; d L Representing the load effect coefficient; p is d Is a power deficit of the wide area power system; Δ ω i Represents the ith test node
The amount of frequency variation of (a); w is a group of i Is a variable and satisfies:
ζ i is variable and satisfies:
(8.2) calculating each test node after disturbance of the wide area power system
Dynamic distribution of frequencies of (3);
f i ＝50+Δω i
wherein, f i For the ith test node
The frequency dynamics of (2).
The invention aims to realize the following steps:
the invention discloses a method for predicting frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model, which comprises the steps of establishing the high-order SFR model and predicting the inertia center frequency of the wide area power system by expanding the traditional simplified SFR model; then, a distance matrix and a path matrix between the nodes of the wide area power system are constructed and assigned with initial values, and the shortest electrical distance between any two nodes of the wide area power system, the path where the nodes are located and an inertia time constant on each line are calculated by updating the distance matrix and the path matrix iteratively; then marking the fault node, and calculating the shortest electrical distance and inertia between the per unit fault node and each test node; and finally, calculating frequency space-time distribution factors, constructing a high-order frequency space-time distribution model of the wide area power system and predicting the frequency space-time dynamic distribution of the wide area power system in real time.
Meanwhile, the method for predicting the frequency space-time dynamic distribution of the wide area power system based on the high-order SFR model has the following beneficial effects:
(1) And a high-order frequency response model is established to predict the disturbed inertia center frequency of the system, so that the model prediction precision is improved, and a powerful theoretical support is provided for the research of the subsequent frequency space-time distribution.
(2) 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 the path of the shortest electrical distance with other generators in the system, so that the process is favorable for simulating the characteristics of an actual disturbed power grid, and a powerful theoretical support is provided for the time-space distribution prediction research of the system frequency.
(3) The mapping relation between the inertia center frequency and the frequency dynamics of each measuring point of the wide area system is determined, the frequency space-time distribution factor is constructed, the frequency space-time distribution model of the wide area system is built, the frequency dynamics process of each measuring point of the wide area system can be rapidly and accurately predicted, and the space-time distribution characteristics of the frequency of the wide area system are accurately disclosed.
Drawings
FIG. 1 is a flow chart of a method for predicting frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model according to the present invention;
FIG. 2 is a block diagram of a high-order SFR model;
FIG. 3 is a wide area complex test system topology;
FIG. 4 is an updated distance matrix visualization map;
FIG. 5 is an updated path matrix visualization map;
FIG. 6 is a time-space dynamic diagram of the actual system frequency under the fault of the generator tripping;
FIG. 7 is a frequency spatiotemporal dynamics diagram of wide area system frequency spatiotemporal distribution model prediction tripping failure;
FIG. 8 is a plot of the actual system frequency space-time profile under a line break fault;
FIG. 9 is a frequency space-time dynamic diagram under wide area system frequency space-time distribution model prediction disconnection fault.
Detailed Description
Specific embodiments of the present invention are described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. 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
FIG. 1 is a flow chart of a method for predicting frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model.
In the present embodiment, the fault of the wide area power system is described as follows in conjunction with fig. 3: when t =5s, the generator G9 cuts 41% of the fault, the simulation time is 50s, the simulation step length is 0.0001s, and the time difference of the maximum frequency offset between two monitoring points in the wide area power system is 0.001 s, which is considered as the occurrence of the space-time distribution phenomenon.
In this embodiment, the influence of the transformer on the frequency space-time distribution is not taken into account, 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 after the generator passes through the transformer without considering the influence of the transformer. In this example, the selected monitoring nodes are bus 39 (generator G1), bus 19 (generator G4), bus 23 (generator G7), bus 25 (generator G8) and bus 2 (generator G10).
With reference to fig. 1, the method for predicting frequency space-time dynamic distribution of a wide area power system based on a high-order SFR model according to the present invention is described in detail below, and as shown in fig. 1, the method specifically includes the following steps:
s1, establishing a high-order SFR model;
s1.1, expanding mechanical gain K in traditional simplified SFR model m The method comprises the following steps that a first-order inertia link k/A + Ts is formed, wherein k, A and T are all mechanical gain coefficients, and S represents an S domain; increasing excitation system damping
And wide area power system load effect damping D L To simulate damping of a wide area power system; after the expansion is completed, the structure diagram of the high-order SFR model is shown in FIG. 2.
S1.2, setting parameters of a high-order SFR model;
wherein R is the equivalent difference adjustment coefficient of the wide area power system; t is a unit of R The time constant is the equivalent reheating time constant of the wide area power system; h is the equivalent inertia time constant of the wide area power system, F H The working proportion of the equivalent high-pressure cylinder of the wide-area power system is obtained; m is the number of generators in the wide area power system; h q The rated capacity of a q-th generator in the wide area power system; r q The difference adjustment coefficient of the q-th generator in the wide area power system is obtained; f Hq Working proportion of a high-pressure cylinder of a qth generator in a wide-area power system; t is Rq A reheating time constant of a q-th generator in the wide area power system; m base,q Rated capacity of the q-th generator; s base A reference capacity for a wide area power system;
in the embodiment, parameter setting is performed on a high-order SFR model of a wide area power system, and the setting result is shown in table 1;
TABLE 1 values of parameters for the high order SFR model
| Parameter(s) | High order SFR parameters | Parameter(s) | High order SFR parameters |
| F H | 0.4 | D g | 0.17 |
| T R | 16 | D L | 0.5 |
| T | 0.11 | k | 0.008 |
| A | 0.48 | H | 1 |
| R | 0.0555 |
TABLE 1
S2, constructing a distance matrix B and a path matrix L between nodes of the wide area power system;
taking each bus in the wide area power system as a node, and constructing a distance matrix between the nodes of the wide area power system as B = [ B ] ij ] n×n ，b ij The admittance value from the node i to the node j is represented, n is the number of the nodes in the wide area power system, and the value is 39; constructing a path matrix of L = [ L = ij ] n×n ，l ij Representing an intermediate node on a shortest path from node i to node j in the wide area power system;
s3, assigning initial values to the distance matrix B and the path matrix L;
the distance matrix B is given an initial value:
wherein,
the path matrix L is given an initial value of:
wherein,
s4, iteratively updating the distance matrix B and the path matrix L;
let k e [1, n ], initialize k =1;
the updated distance matrix B is:
the update path matrix L is:
when k = n, obtaining an updated distance matrix B (n) Sum path matrix L (n) (ii) a In the present embodiment, the updated distance matrix B (n) As shown in fig. 4; updated path matrix L (n) Is shown in fig. 5;
s5, calculating the shortest electrical distance between any two nodes of the wide area power system and the path where the shortest electrical distance is located;
according to the distance matrix B (n) Sum path matrix L (n) Calculating the shortest electrical distance Z from the node i to the node j i-j-min ：
The corresponding shortest electrical distance path is marked as L i-j-min ；
In this embodiment, 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 wide area power system is calculated is shown in fig. 5, and is:
L 29-39-min ＝{29→26→25→2→1→39}
L 29-19-min ＝{29→26→27→17→16→19}
L 29-23-min ＝{29→26→17→17→16→24→23}
L 29-25-min ＝{29→26→25}
L 29-2-min ＝{29→26→25→2}
s6, calculating an inertia time constant of each line in the wide area power system;
s6.1, in the embodiment, inertia is measured by an inertia time constant of a generator, so that all bus nodes connected with the generator are marked in a wide area power system, and the total number of the bus nodes is m; then, in the m bus nodes, one bus node is marked as a starting end node arbitrarily, and the rest bus nodes are terminal nodes;
s6.2, calculating the shortest path from each initial end node to each terminal node and a line l on the shortest path according to the method in the step S5 i-j The inertial time constant of (c);
wherein,
is the qth start node
To the p-th generator terminal node
Q =1,2, \8230, m, p =1,2, \8230, m-1;
for the q-th starting generator distributed on line l i-j An inertial time constant of (c);
represents a line l i-j An admittance value of (a);
representing the qth generator start node
To the p-th generator terminal node
The shortest electrical distance between the two;
represents the inertia time constant of the qth start generator;
represents a distance matrix B (n) Middle start end node
To terminal node
An admittance value of (1);
for example: calculating the line set l between the generator starting node 29 and the generator terminal node 39 i-j ；
L 29-39-min ＝{29→26→25→2→1→39}
l i-j ＝L 29-39-min ＝{l 29-26 ,l 26-25 ,l 25-2 ,l 2-1 ,l 1-39 }
Calculating the distribution of the generator start node 29 on the path l i-j The time constant of inertia on all lines;
s6.3, calculating each line l in the wide area power system i-j Time constant of inertia of
In this embodiment, the line l 29-26 For the purpose of example only,
in this embodiment, taking m =10, the inertia distribution on each line in the wide area power system is calculated as shown in table 2.
Table 2 shows the inertia distribution of each line in the wide area power system.
| Line | Inertia | Per unit value | Line | Inertia | Per unit value |
| l 29-26 | 18.99 | 0.4498 | l 29-26 | 11.31 | 0.2693 |
| l 26-25 | 18.99 | 0.4498 | l 5-6 | 15.20 | 0.3619 |
| l 25-2 | 21.48 | 0.5114 | l 26-27 | 14.85 | 0.3536 |
| l 2-1 | 14.64 | 0.3486 | l 27-17 | 14.85 | 0.3536 |
| l 1-39 | 14.64 | 0.3486 | l 17-16 | 26.70 | 0.6357 |
| l 2-3 | 20.10 | 0.4786 | l 16-15 | 13.78 | 0.3281 |
| l 3-4 | 8.2600 | 0.1967 | l 15-14 | 13.78 | 0.3281 |
| l 14-13 | 9.570 | 0.2279 | l 21-22 | 14.94 | 0.3558 |
| l 13-10 | 9.570 | 0.2279 | l 16-24 | 14.94 | 0.3558 |
| l 16-19 | 33.15 | 0.7893 | l 24-23 | 14.94 | 0.3558 |
TABLE 2
S7, per-unit analyzing the shortest electrical distance and inertia between the fault node and each test node;
s7.1, calculating an impedance reference value Z base With reference value of inertia T base ：
Wherein N is the number of lines in the wide area power system;
in this embodiment, m =10,n =21, and it is calculated that: z base ＝0.0005+j0.0125，T base ＝42；
S7.2, marking any node in the wide area power system as a fault node, and remaining nodes as test nodes;
in this embodiment, the test node may also select the remaining part of nodes as the test node, for example: generator node 29 is a fault node, 39, 19, 23, 25 and 2 are test nodes;
s7.3, the shortest electrical distance and inertia between the per unit fault node and each test node;
wherein,
for failed node v fault To the ith test node
The shortest electrical distance between i =1,2, \ 8230;, n-1;
for failed node v fault To the ith test node
Per unit value of the shortest electrical distance therebetween;
for failed node v fault To the ith test node
The per unit value of inertia between; per unit value of;
for failed node v fault To the ith test node
The inertia per unit value of each time;
in the present embodiment, taking the fault node 29 and the test node 39 as examples:
in the present embodiment, the shortest electrical distance and the inertia result between the per-unit fault node 39 and the test nodes 39, 19, 23, 25 and 2 are shown in table 3.
Table 3 is the per unit value of the shortest electrical distance and inertia between the failed node and the test point.
| 29-39 | 29-19 | 29-23 | 29-25 | 29-2 | |
| Z * / |
5 | 5 | 6 | 2 | 3 |
| T * /pu | 2.1129 | 2.5843 | 2.5064 | 0.9019 | 1.4157 |
TABLE 3
S8, introducing frequency space-time distribution factors into part of key parameters of the high-order SFR model;
s8.1, for each test node, calculating a frequency space-time distribution factor of an equivalent inertia time constant in the high-order SFR model as follows:
wherein,
for the ith test node
The inertia space-time distribution factor of;
s8.2, for each test node, calculating a frequency space-time distribution factor of an equivalent reheat time constant in the high-order SFR model as follows:
wherein,
for the ith test node
The reheat time constant spatio-temporal distribution factor;
s8.3, for each test node, calculating a frequency space-time distribution factor of the work proportion of the medium-value high-pressure cylinder in the high-order SFR model as follows:
wherein,
for the ith test node
The working proportion space-time distribution factor of the high-pressure cylinder;
s9, taking the high-order SFR model after the frequency space-time distribution factor is introduced as a frequency space-time distribution model of the wide area power system;
in the embodiment, the parameters of the high-order frequency spatiotemporal distribution model of the wide area power system calculated under the generator tripping fault are shown in table 4.
And table 4 shows the parameters of the wide area system space-time distribution model under the generator tripping fault.
| Parameter(s) | G1 | G4 | G7 | G8 | G10 |
| F H | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 |
| T R | 10.7728 | 9.3904 | 9.1024 | 25.7392 | 16.5824 |
| H | 0.7025 | 0.8592 | 1 | 0.1206 | 0.2824 |
TABLE 4
Therefore, frequency space-time distribution factors are introduced into partial coupling parameters of the high-order SFR model, and the high-order frequency space-time distribution model of the wide area power system is constructed;
s10, predicting the space-time dynamic distribution of the frequency by using a frequency space-time distribution model of the wide area power system;
s10.1, calculating each test node after the wide area power system is disturbed
Frequency change amount Δ ω of i ；
Wherein D is g Indicating the damping of the generator and the excitation system,
representing the damping of the generator; d L Representing the load effect coefficient; p d For power shortages in wide area power systemsIn this embodiment, as shown in FIG. 2, P sp For incremental power set points, only for P during many studies d Of interest, therefore P is the embodiment sp ＝0；Δω i Representing the ith test node
The amount of frequency variation of (a); w is a group of i Is variable and satisfies:
ζ i is a variable and satisfies:
s10.2, calculating each disturbed test node of the wide area power system
Dynamic distribution of frequencies of (a);
f i ＝50+Δω i
wherein f is i For the ith test node
The frequency dynamics of (2).
In this embodiment, the wide area power system frequency space-time distribution model can accurately predict the frequency dynamics of each measurement point of the system, and accurately reveal the space-time distribution characteristics of the wide area system frequency.
In the present embodiment, the frequency dynamics of the nodes 39, 19, 23, 25 and 2 can be predicted by the parameters of the wide area power system high-order frequency space-time distribution model shown in table 4, and the space-time distribution characteristics of the wide area system frequencies are revealed.
In this embodiment, a PSASP software is used to perform a refinement simulation to obtain that the frequency of each measurement point has a significant spatial-temporal distribution phenomenon, and the simulation result is shown in fig. 6, where G8 → G10 → G1 → G4 → G7. Thus, it can be seen that the frequencies of the measured points predicted by the present invention are completely consistent with those of the actual system, and the error is extremely small, the predicted result is shown in fig. 7, and the error analysis table is shown in table 5.
Table 5 is an error analysis table of frequency dynamics under the cutter failure;
| G1 | G4 | G7 | G8 | G10 | |
| actual system frequency maximum offset time/s | 7.6474 | 9.020 | 9.0653 | 7.4946 | 7.5738 |
| Time/s of maximum offset of frequency of space-time distribution model | 8.6615 | 9.2457 | 9.8046 | 5.6304 | 6.6487 |
| Absolute error/s | 1.0141 | 0.2257 | 0.7397 | 1.8642 | 0.9251 |
| Actual system frequency steady state value/Hz | 49.9273 | 49.9273 | 49.9273 | 49.9273 | 49.9273 |
| Frequency steady state value/s of space-time distribution model | 49.9432 | 49.9433 | 49.9433 | 49.9418 | 49.9428 |
| Absolute error/Hz | 0.0159 | 0.016 | 0.016 | 0.0145 | 0.0155 |
| Relative error/%) | 0.0318 | 0.032 | 0.032 | 0.029 | 0.031 |
TABLE 5
In addition, the present example also provides another fault situation, line i at t =5s 15-16 Three-phase disconnection fault occurs at a node 15, the simulation time is 50s, the simulation step length is 0.0001s, and monitoring points are selected as a bus 19 (a generator G4), a bus 25 (a generator G8), a bus 29 (a generator G9) and a bus 2 (a generator G10).
The model built according to the invention can calculate the shortest electrical distance from the node 15 to each of the measurement points 19, 25, 29 and 2 as:
L 15-19-min ＝{15→16→19}
L 15-25-min ＝{15→14→4→3→2→25}
L 15-29-min ＝{15→16→17→27→26→29}
L 15-2-min ＝{15→14→4→3→2}
the shortest electrical distance from the per-unit fault point 15 to each of the measuring points 19, 25, 29 and 2 and its inertia are shown in table 6.
Table 6 shows the shortest electrical distance between the fault point and the measurement point and its inertia.
| 15-19 | 15-25 | 15-29 | 15-2 | |
| Z * / |
2 | 5 | 5 | 4 |
| T * /pu | 1.1173 | 1.7171 | 2.1230 | 1.2057 |
TABLE 6
In the present embodiment, the parameters of the wide area system spatio-temporal distribution model are calculated as shown in table 7.
Table 7 is the wide area system spatio-temporal distribution model parameters under the disconnection fault.
| Parameter(s) | G4 | G8 | G9 | G10 |
| F H | 0.4 | 0.4 | 0.4 | 0.4 |
| T R | 22.32 | 12.5184 | 10.736 | 17.2704 |
| H | 0.9336 | 1.0824 | 1.1653 | 0.9856 |
TABLE 7
The PSASP software is used for carrying out fine simulation to obtain the space-time distribution phenomenon of the frequency of each measuring point, G4 → G10 → G8 → G9, and the simulation result is shown in figure 8. The frequency of each measuring point obtained by the wide area system frequency space-time distribution model is completely consistent with that of an actual system, the error is extremely small, the prediction result is shown in a figure 9, and an error analysis table is shown in a table 8.
Table 8 is an error analysis table of frequency dynamics under the disconnection fault;
| G4 | G8 | G9 | G10 | |
| actual system frequency maximum offset time/s | 5.3243 | 5.5463 | 5.8242 | 5.4562 |
| Time/s of maximum frequency offset of space-time distribution model | 5.3352 | 5.4446 | 5.6355 | 5.3338 |
| Absolute error/s | 0.0109 | 0.1017 | 0.1887 | 0.1224 |
| Actual system frequency steady state value/Hz | 49.8756 | 49.8756 | 49.8756 | 49.8756 |
| Frequency steady state value/s of space-time distribution model | 49.8743 | 49.8760 | 49.8762 | 49.8754 |
| Absolute error/Hz | 0.0013 | 0.0004 | 0.0006 | 0.0002 |
| Relative error/%) | 0.0026 | 0.0008 | 0.0012 | 0.0004 |
TABLE 8
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. The method for predicting the frequency space-time dynamic distribution of the wide area power system based on the high-order SFR model is characterized by comprising the following steps of:
(1) Establishing a high-order SFR model;
(1.1) expanding mechanical gain K in the traditional simplified SFR model m A first-order inertia link k/A + Ts is adopted, wherein k, A and T are all mechanical gain coefficients, and S represents an S domain; increasing excitation system damping
And wide area power system load effect damping D L To simulate damping of a wide area power system;
(1.2) setting parameters of the high-order SFR model;
wherein R is the equivalent difference adjusting coefficient of the wide area power system; t is R An equivalent reheat time constant of the wide area power system; h is the equivalent inertia time constant of the wide area power system, F H Working proportion of the equivalent high-pressure cylinder of the wide-area power system is obtained; m is the number of generators in the wide area power system; h q Rated capacity of the q generator in the wide area power system; r is q A difference adjustment coefficient of a q-th generator in the wide area power system is obtained; f Hq Working proportion of a high-pressure cylinder of a qth generator in a wide-area power system; t is a unit of Rq A reheat time constant of a qth generator in the wide area power system; m is a group of base,q Rated capacity of the q-th generator; s base A reference capacity for a wide area power system;
(2) Constructing a distance matrix B and a path matrix L between nodes of the wide area power system and assigning initial values to the distance matrix B and the path matrix L;
(3) And calculating the shortest electrical distance Z between any two nodes i and j of the wide area power system by iteratively updating the distance matrix B and the path matrix L i-j-min And its path L i-j-min ；
(4) Calculating each line l in the wide area power system i-j Time constant of inertia of
(5) Marking any fault node v in wide area power system fault Per unit fault node to each test node
The shortest electrical distance between
And inertia thereof
(6) Introducing frequency space-time distribution factors to part of key parameters of the high-order SFR model;
(6.1) for each test node, calculating the frequency space-time distribution factor of the equivalent inertia time constant in the high-order SFR model as follows:
wherein,
for the ith test node
The inertia space-time distribution factor of (c);
(6.2) for each test node, calculating the frequency space-time distribution factor of the equivalent reheating time constant in the high-order SFR model as follows:
wherein,
for the ith test node
The reheat time constant spatial-temporal distribution factor;
(6.3) for each test node, calculating a frequency space-time distribution factor of the work proportion of the medium-value high-pressure cylinder in the high-order SFR model as follows:
wherein,
for the ith test node
The working proportion space-time distribution factor of the high-pressure cylinder;
(7) Taking the high-order SFR model after the frequency space-time distribution factor is introduced as a frequency space-time distribution model of the wide area power system;
(8) Predicting the time-space dynamic distribution of the frequency by utilizing a frequency time-space distribution model of the wide area power system;
(8.1) calculating each test node after the wide area power system is disturbed
The amount of frequency variation of (a);
wherein D is g Indicating the damping of the generator and the excitation system,
representing the damping of the generator; d L Representing the load effect coefficient; p d Is a power deficit of the wide area power system; Δ ω i Representing the ith test node
Amount of frequency change of；W i Is variable and satisfies:
ζ i is variable and satisfies:
(8.2) calculating each test node after disturbance of the wide area power system
Dynamic distribution of frequencies of (a);
f i ＝50+Δω i
wherein f is i For the ith test node
The frequency dynamics of (2).
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