CN110943479A - Wide-area transient stability control method and system based on random matrix theory - Google Patents

Wide-area transient stability control method and system based on random matrix theory Download PDF

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CN110943479A
CN110943479A CN201911165333.9A CN201911165333A CN110943479A CN 110943479 A CN110943479 A CN 110943479A CN 201911165333 A CN201911165333 A CN 201911165333A CN 110943479 A CN110943479 A CN 110943479A
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matrix
generator
generators
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standard
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CN110943479B (en
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高磊
褚晓杰
孙华东
孙智
霍承祥
李文锋
郭强
汤涌
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
China Electric Power Research Institute Co Ltd CEPRI
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State Grid Corp of China SGCC
State Grid Zhejiang Electric Power Co Ltd
China Electric Power Research Institute Co Ltd CEPRI
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers

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Abstract

The invention discloses a wide area transient stability control method and a system based on a random matrix theory, wherein the method comprises the following steps: establishing a random matrix model based on terminal voltage data of each generator in the critical cluster; processing the random matrix model based on a random matrix single-ring theorem to obtain a standard matrix; solving a characteristic root of the standard matrix, and acquiring the average spectrum radius of each hair voltage according to the characteristic root; identifying sensitive ones of the generators based on the average spectral radii of the generators; and carrying out wide-area transient stability control on the sensitive generator.

Description

Wide-area transient stability control method and system based on random matrix theory
Technical Field
The invention relates to the technical field of power transmission of power systems, in particular to a wide-area transient stability control method and system based on a random matrix theory.
Background
With the grid-connected operation of more and more large-capacity units and the interconnection of each regional power grid, especially the preliminary formation of an alternating current-direct current hybrid power grid, the power system is increasingly sensitive to interference, and the guarantee of safe and stable operation of the power system is increasingly important. When the system breaks down, the disturbance degrees of the generators in different areas of the power grid are different, so that the selection of a proper generator for control is particularly important for improving the transient stability of the system.
Although the multi-machine system after the fault can be divided into the critical machine group and the rest machine groups by the EEAC theory, the control process is very complicated because of too many machine groups in the critical machine group.
Therefore, a novel wide-area transient stability control method is needed to reduce the control difficulty.
Disclosure of Invention
The technical scheme of the invention provides a wide area transient stability control method and system based on a random matrix theory, and aims to solve the problem of how to perform wide area transient stability control based on the random matrix theory.
In order to solve the above problem, the present invention provides a wide area transient stability control method based on a random matrix theory, the method comprising:
establishing a random matrix based on terminal voltage data of each generator in the critical cluster; processing the random matrix based on a random matrix single-ring theorem to obtain a standard matrix;
solving a characteristic root of the standard matrix, and acquiring an average spectrum radius of each generator according to the characteristic root;
identifying the sensitivity of each generator in the critical cluster based on the average spectral radius of each generator;
and carrying out wide-area transient stability control on the sensitive generator.
Preferably, a random matrix model is established based on terminal voltage data of each generator in the critical cluster; processing the random matrix model based on a random matrix single-ring theorem to obtain a standard matrix; the steps further include:
(1) firstly, establishing a random matrix model by using terminal voltage data of each generator in a critical cluster as follows:
Figure BDA0002287292550000021
(2) the model is processed based on the single-ring theorem of the random matrix as follows:
Figure BDA0002287292550000022
wherein
Figure BDA0002287292550000023
To
Figure BDA0002287292550000024
A column vector formed by terminal voltage data of the 1 st to the Nth generators;
Figure BDA0002287292550000025
is a random matrix model; n is the number of generators in the critical cluster;
Figure BDA0002287292550000026
is the element of the ith row and the jth column of the transition matrix; 1, N, j 1, T;
Figure BDA0002287292550000027
Figure BDA0002287292550000028
is composed of
Figure BDA0002287292550000029
The mean value of (a);
Figure BDA00022872925500000210
is composed of
Figure BDA00022872925500000211
Standard deviation of (d);
Figure BDA00022872925500000212
is composed of
Figure BDA00022872925500000213
Has a mean value of
Figure BDA00022872925500000214
Figure BDA00022872925500000215
Is composed of
Figure BDA00022872925500000216
Has a standard deviation of
Figure BDA00022872925500000217
For transition matrix
Figure BDA00022872925500000218
Calculating to obtain the equivalent matrix of singular value
Figure BDA00022872925500000219
Figure BDA00022872925500000220
Wherein U is a unitary matrix;
Figure BDA00022872925500000221
is a transition matrix;
Figure BDA00022872925500000222
a transposed matrix which is a transition matrix; for the equivalent matrix of singular values, have
Figure BDA00022872925500000223
Consider the case of L singular value equivalence matrices,
Figure BDA00022872925500000224
is the ith singular value equivalence matrix; the matrix product is:
Figure BDA0002287292550000031
to pair
Figure BDA0002287292550000032
Performing unitization to obtain a standard matrix
Figure BDA0002287292550000033
Figure BDA0002287292550000034
Wherein i is 1,2, N,
Figure BDA0002287292550000035
n is the number of generators in the critical cluster;
Figure BDA0002287292550000036
is composed of
Figure BDA0002287292550000037
Row i of (1);
Figure BDA0002287292550000038
to
Figure BDA0002287292550000039
Is composed of
Figure BDA00022872925500000310
1 st to nth element of (a);
Figure BDA00022872925500000311
is composed of
Figure BDA00022872925500000312
Standard deviation of (d);
Figure BDA00022872925500000313
is the ith row of the standard matrix;
Figure BDA00022872925500000314
to
Figure BDA00022872925500000315
Is composed of
Figure BDA00022872925500000316
1 st to nth element of (a);
Figure BDA00022872925500000317
is a non-Hermitian matrix.
Preferably, the identifying a sensitive generator in the generators based on the average spectral radius of the generator voltages further comprises:
the average spectrum radius expression is as follows:
Figure BDA00022872925500000318
wherein,
Figure BDA00022872925500000319
as a standard matrix
Figure BDA00022872925500000320
By the mean spectral radius kMSRCharacterizing each generationThe sensitivity of the machine to large disturbances in the transmission system.
Preferably, before establishing the random matrix model based on the terminal voltage data of each generator in the critical cluster, the method further includes:
when a power transmission system fails, a critical fleet is identified.
Preferably, the wide-area transient stability control of the sensitive generator further comprises:
and when the power transmission system is unstable, the generator with the highest sensitivity degree is firstly selected for wide-area transient stability control, and when the power transmission system is still unstable, the generator with the highest sensitivity degree in the rest generators is subjected to wide-area transient stability control until the power transmission system meets the stability margin.
According to another aspect of the present invention, there is provided a wide-area transient stability control system based on random matrix theory, the system comprising:
the establishing unit is used for establishing a random matrix model based on terminal voltage data of each generator in the critical cluster;
the first acquisition unit is used for processing the random matrix model based on a random matrix single-ring theorem to acquire a standard matrix;
the second acquisition unit is used for solving a characteristic root of the standard matrix and acquiring the average spectrum radius of each generator according to the characteristic root;
the identification unit is used for identifying a sensitive generator in the generators based on the average spectrum radius of each voltage;
and the control unit is used for carrying out wide-area transient stability control on the sensitive generator.
Preferably, the establishing unit is configured to establish a random matrix model based on terminal voltage data of each generator in the critical cluster; the first acquisition unit is used for processing the random matrix model based on a random matrix single-ring theorem to acquire a standard matrix; the establishing unit and the first obtaining unit are further configured to:
(1) firstly, establishing a random matrix model by using terminal voltage data of each generator in a critical cluster as follows:
Figure BDA0002287292550000041
(2) the model is processed based on the single-ring theorem of the random matrix as follows:
Figure BDA0002287292550000042
wherein
Figure BDA0002287292550000043
To
Figure BDA0002287292550000044
A column vector formed by terminal voltage data of the 1 st to the Nth generators;
Figure BDA0002287292550000045
is a random matrix model; n is the number of generators in the critical cluster;
Figure BDA0002287292550000046
is the element of the ith row and the jth column of the transition matrix; 1, N, j 1, T;
Figure BDA0002287292550000047
Figure BDA0002287292550000048
is composed of
Figure BDA0002287292550000049
The mean value of (a);
Figure BDA00022872925500000410
is composed of
Figure BDA00022872925500000411
Standard deviation of (d);
Figure BDA00022872925500000412
is composed of
Figure BDA00022872925500000413
Has a mean value of
Figure BDA00022872925500000414
Figure BDA00022872925500000415
Is composed of
Figure BDA00022872925500000416
Has a standard deviation of
Figure BDA00022872925500000417
For transition matrix
Figure BDA00022872925500000418
Calculating to obtain the equivalent matrix of singular value
Figure BDA00022872925500000419
Figure BDA0002287292550000051
Wherein U is a unitary matrix;
Figure BDA0002287292550000052
is a transition matrix;
Figure BDA0002287292550000053
a transposed matrix which is a transition matrix; for the equivalent matrix of singular values, have
Figure BDA0002287292550000054
Consider the case of L singular value equivalence matrices,
Figure BDA0002287292550000055
is the ith singular value equivalence matrix; the matrix product is:
Figure BDA0002287292550000056
to pair
Figure BDA0002287292550000057
Performing unitization to obtain a standard matrix
Figure BDA0002287292550000058
Figure BDA0002287292550000059
Wherein i is 1,2, N,
Figure BDA00022872925500000510
n is the number of generators in the critical cluster;
Figure BDA00022872925500000511
is composed of
Figure BDA00022872925500000512
Row i of (1);
Figure BDA00022872925500000513
to
Figure BDA00022872925500000514
Is composed of
Figure BDA00022872925500000515
1 st to nth element of (a);
Figure BDA00022872925500000516
is composed of
Figure BDA00022872925500000517
Standard deviation of (d);
Figure BDA00022872925500000518
is the ith row of the standard matrix;
Figure BDA00022872925500000519
to
Figure BDA00022872925500000520
Is composed of
Figure BDA00022872925500000521
1 st to nth element of (a);
Figure BDA00022872925500000522
is a non-Hermitian matrix.
Preferably, the identification unit is configured to identify a sensitive generator in the generators based on the average spectrum radius of each generator, and includes:
the average spectrum radius expression is as follows:
Figure BDA00022872925500000523
wherein,
Figure BDA00022872925500000524
as a standard matrix
Figure BDA00022872925500000525
By the mean spectral radius kMSRAnd representing the sensitivity of each generator to large disturbance of the power transmission system.
Preferably, the system further comprises:
and the monitoring unit is used for identifying the critical cluster when the power transmission system has a fault.
Preferably, the control unit is configured to perform wide-area transient stability control on the sensitive generator, and is further configured to:
and when the power transmission system is unstable, the generator with the highest sensitivity degree is firstly selected for wide-area transient stability control, and when the power transmission system is still unstable, the generator with the highest sensitivity degree in the rest generators is subjected to wide-area transient stability control until the power transmission system meets the stability margin.
The technical scheme of the invention provides a wide area transient stability control method and a system based on a random matrix theory, wherein the method comprises the following steps: establishing a random matrix model based on terminal voltage data of each generator in the critical cluster; processing the random matrix model based on a random matrix single-ring theorem to obtain a standard matrix; solving a characteristic root of the standard matrix, and acquiring the average spectrum radius of each hair voltage according to the characteristic root; identifying sensitive generators of the generators based on the average spectral radii of the generators; and carrying out wide-area transient stability control on the sensitive generator. The technical scheme of the invention realizes the field actual measurement of the wide-area transient stability control method, has simple and effective implementation process and provides a solution for the convenient and accurate field actual measurement of the wide-area transient stability control method.
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A more complete understanding of exemplary embodiments of the present invention may be had by reference to the following drawings in which:
FIG. 1 is a flowchart of a wide-area transient stability control method based on random matrix theory according to a preferred embodiment of the present invention;
FIG. 2 is a wide area transient stability controller mathematical model in accordance with a preferred embodiment of the present invention;
FIG. 3 is a two-zone quadplexer model used in accordance with a preferred embodiment of the present invention;
FIG. 4 is a graph of the characteristic root distribution of two generators within a critical cluster, in accordance with a preferred embodiment of the present invention;
FIG. 5 is a graph comparing relative power angle response waveforms with and without control applied to a simulation model in accordance with a preferred embodiment of the present invention;
FIG. 6 is a flowchart of a wide-area transient stability control strategy based on random matrix theory according to a preferred embodiment of the present invention; and
fig. 7 is a structural diagram of a wide-area transient stability control system based on random matrix theory according to a preferred embodiment of the present invention.
Detailed Description
The exemplary embodiments of the present invention will now be described with reference to the accompanying drawings, however, the present invention may be embodied in many different forms and is not limited to the embodiments described herein, which are provided for complete and complete disclosure of the present invention and to fully convey the scope of the present invention to those skilled in the art. The terminology used in the exemplary embodiments illustrated in the accompanying drawings is not intended to be limiting of the invention. In the drawings, the same units/elements are denoted by the same reference numerals.
Unless otherwise defined, terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Further, it will be understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense.
Fig. 1 is a flowchart of a wide-area transient stability control method based on random matrix theory according to a preferred embodiment of the present invention. The implementation mode of the application provides a wide area transient stability control method, the application realizes the field actual measurement of the wide area transient stability control method, the implementation process is simple and effective, and a solution is provided for the convenient and accurate field actual measurement of the wide area transient stability control method. As shown in fig. 1, the present application provides a wide-area transient stability control method based on a random matrix theory, the method including:
preferably, in step 101: and establishing a random matrix model based on terminal voltage data of each generator in the critical cluster. Preferably, a random matrix model is established based on terminal voltage data of each generator in the critical cluster; processing the random matrix model based on the random matrix single-ring theorem to obtain a standard matrix, which comprises the following steps:
as shown in fig. 2, firstly, a random matrix model is established by using terminal voltage data of each generator in the critical cluster as follows:
Figure BDA0002287292550000071
the model is processed based on the single-ring theorem of the random matrix as follows:
Figure BDA0002287292550000081
wherein
Figure BDA0002287292550000082
To
Figure BDA0002287292550000083
A column vector formed by terminal voltage data of the 1 st to the Nth generators;
Figure BDA0002287292550000084
is a random matrix model; n is the number of generators in the critical cluster;
Figure BDA0002287292550000085
is the element of the ith row and the jth column of the transition matrix; 1, N, j 1, T;
Figure BDA0002287292550000086
Figure BDA0002287292550000087
is composed of
Figure BDA0002287292550000088
The mean value of (a);
Figure BDA0002287292550000089
is composed of
Figure BDA00022872925500000810
Standard deviation of (d);
Figure BDA00022872925500000811
is composed of
Figure BDA00022872925500000812
Has a mean value of
Figure BDA00022872925500000813
Figure BDA00022872925500000814
Is composed of
Figure BDA00022872925500000815
Has a standard deviation of
Figure BDA00022872925500000816
For transition matrix
Figure BDA00022872925500000817
Calculating to obtain the equivalent matrix of singular value
Figure BDA00022872925500000840
Figure BDA00022872925500000818
Wherein U is a unitary matrix;
Figure BDA00022872925500000819
is a transition matrix;
Figure BDA00022872925500000820
a transposed matrix which is a transition matrix; for the equivalent matrix of singular values, have
Figure BDA00022872925500000821
Consider the case of L singular value equivalence matrices,
Figure BDA00022872925500000822
is the ith singular value equivalence matrix; the matrix product is:
Figure BDA00022872925500000823
to pair
Figure BDA00022872925500000824
Performing unitization to obtain a standard matrix
Figure BDA00022872925500000825
Figure BDA00022872925500000826
Wherein i is 1,2, N,
Figure BDA00022872925500000827
n is the number of generators in the critical cluster;
Figure BDA00022872925500000828
is composed of
Figure BDA00022872925500000829
Row i of (1);
Figure BDA00022872925500000830
to
Figure BDA00022872925500000831
Is composed of
Figure BDA00022872925500000832
1 st to nth element of (a);
Figure BDA00022872925500000833
is composed of
Figure BDA00022872925500000834
Standard deviation of (d);
Figure BDA00022872925500000835
is the ith row of the standard matrix;
Figure BDA00022872925500000836
to
Figure BDA00022872925500000837
Is composed of
Figure BDA00022872925500000838
1 st to nth element of (a);
Figure BDA00022872925500000839
is a non-Hermitian matrix. Preferably, before establishing the random matrix model based on the terminal voltage data of each generator in the critical cluster, the method further includes: when a power transmission system fails, a critical fleet is identified.
According to the wide-area transient stability control method, the distribution of the characteristic roots of each generator is solved according to the single-loop theorem of the random matrix theory, and the average spectrum radius is used as a quantization index to identify the sensitive generator. According to the Lyapunov theory, an energy function is divided into a controlled part and an uncontrolled part, and a wide-area transient stability controller can be designed by deducing the controlled part.
The identification of the sensitive generator and the design of the wide-area transient stability controller comprise the following specific steps;
the specific steps of the identification of the sensitive generator comprise:
(1) firstly, establishing a random matrix model by using terminal voltage data of each generator in a critical cluster as follows:
Figure BDA0002287292550000091
(2) the model is processed based on the single-ring theorem of the random matrix as follows:
Figure BDA0002287292550000092
wherein i is 1, N, j is 1, T.
Figure BDA0002287292550000093
Figure BDA0002287292550000094
Is composed of
Figure BDA0002287292550000095
The mean value of (a);
Figure BDA0002287292550000096
is composed of
Figure BDA0002287292550000097
Standard deviation of (d);
Figure BDA0002287292550000098
is composed of
Figure BDA0002287292550000099
Has a mean value of
Figure BDA00022872925500000910
Figure BDA00022872925500000911
Is composed of
Figure BDA00022872925500000912
Has a standard deviation of
Figure BDA00022872925500000913
For transition matrix
Figure BDA00022872925500000914
Calculating to obtain the equivalent matrix of singular value
Figure BDA00022872925500000915
Figure BDA00022872925500000916
Where U is a unitary matrix. For the equivalent matrix of singular values, have
Figure BDA00022872925500000917
Consider the case of L singular value equivalence matrices whose matrix product is
Figure BDA00022872925500000918
To pair
Figure BDA00022872925500000919
Performing unitization to obtain a standard matrix
Figure BDA00022872925500000920
Figure BDA0002287292550000101
Wherein i is 1,2, N,
Figure BDA0002287292550000102
Figure BDA0002287292550000103
is a non-Hermitian matrix.
Preferably, at step 102: and processing the random matrix model based on a random matrix single-ring theorem to obtain a standard matrix.
Preferably, in step 103: and solving a characteristic root of the standard matrix, and acquiring the average spectrum radius of each generator according to the characteristic root. Preferably, based on the average spectral radius of each generator voltage, identifying a sensitive generator of the generators, further comprises:
the average spectral radius is expressed as:
Figure BDA0002287292550000104
wherein,
Figure BDA0002287292550000105
as a standard matrix
Figure BDA0002287292550000106
By the mean spectral radius kMSRAnd representing the sensitivity of each generator to large disturbance of the power transmission system.
The application finds the standard matrix
Figure BDA0002287292550000107
And quantitatively comparing the disturbance degree of each generator through Mean Spectral Radius (MSR), wherein the expression is as follows:
Figure BDA0002287292550000108
wherein,
Figure BDA0002287292550000109
as a standard matrix
Figure BDA00022872925500001010
Characteristic value of (1), in this context kMSRThe sensitivity of each generator to large system disturbances can be characterized. The smaller the average spectral radius, the more sensitive the generator is to system disturbances, so that sensitive generators can be identified.
Preferably, at step 104: based on the average spectral radius of each generator voltage, a sensitive generator of the generators is identified.
Preferably, at step 105: and carrying out wide-area transient stability control on the sensitive generator.
Preferably, the wide-area transient stability control of the sensitive generator further comprises: when the power transmission system is unstable, the generator with the highest sensitivity degree is selected to perform wide-area transient stability control, when the power transmission system is still unstable, the generator with the highest sensitivity degree in the rest generators is subjected to wide-area transient stability control, and the control is performed until the power transmission system meets the stability margin.
As shown in fig. 6.
The specific steps of the wide-area transient stability controller design of the application include:
(1) given a nonlinear dynamical system with dx/dt ═ f (x), at equilibrium point x for a system with no control applied0In the steady state, a Lyapunov function variable V (x) may be defined, and the Lyapunov stability criterion is as follows:
Figure BDA0002287292550000111
the system energy function without applied control is as follows:
Figure BDA0002287292550000112
in the formula: c0Is a constant; miThe inertia time constant of the ith unit is obtained;
Figure BDA0002287292550000113
the angular velocity of the ith unit under the coordinate of the inertia Center (COI);
Figure BDA0002287292550000114
Figure BDA0002287292550000115
in order to not apply the mechanical power of the ith unit under control,
Figure BDA0002287292550000116
for terminal voltage of the i-th unit without control, GiiThe network self-conductance is node i;
Figure BDA0002287292550000117
Figure BDA0002287292550000118
and
Figure BDA0002287292550000119
terminal voltages, B, of the i-th and j-th units, respectivelyijCarrying out susceptance for the network;
Figure BDA00022872925500001110
Figure BDA00022872925500001111
and
Figure BDA00022872925500001112
the power angles of the i-th and j-th machine sets under the coordinates of the inertia Center (COI) are shown.
In equation (8) the derivative of the energy function is 0, i.e.
Figure BDA00022872925500001113
(2) For systems where control is applied, the Lyapunov function variable V (x) can be divided into controlled and uncontrolled portions, the derivative of which can be expressed as follows:
Figure BDA0002287292550000121
when the controlled part is dVctrlWhen the/dt is less than or equal to 0, the transient stability of the system can be improved.
When a system with wide-area transient stability control fails, the excitation voltage is composed of an excitation voltage (with the upper label of 0) and a forced excitation voltage generated by an uncontrolled part of the system, as follows:
Figure BDA0002287292550000122
in the formula: efdiThe excitation voltage after the fault is obtained;
Figure BDA0002287292550000123
excitation voltage of an uncontrolled part after a fault; eEBiThe excitation voltage generated for wide-area transient stability control.
Fault backend terminal voltage E'iIn direct proportion to the excitation voltage, i.e.
Figure BDA0002287292550000124
In the formula: ei'0Terminal voltage, Δ E ', produced by the uncontrolled part after failure'iThe terminal voltage generated for wide-area transient stability control after the fault.
The derivative of the energy function after a system failure can be expressed as follows
Figure BDA0002287292550000125
In the formula:
Figure BDA0002287292550000126
ΔPifor the ith unit P under wide-area transient stability controliAn increase;
Figure BDA0002287292550000127
ΔCijfor wide-area transient stability controlijThe amount of increase.
Will be delta PiAnd Δ CijCan be carried into (13)
Figure BDA0002287292550000131
In the formula: the generators are arranged in the sequence of the power angle from high to low, i.e. when i < j
Figure BDA0002287292550000132
Can be obtained from the above formula
Figure BDA0002287292550000133
Time dVctrlThe transient stability is improved when the/dt is less than or equal to 0.
The method and the device have the advantages that the process of screening the sensitive generators based on the random matrix theory does not depend on the structure and parameters of a specific power grid, changes of a complex system can be fully coped with, historical data can be fully utilized to establish a random matrix model, and therefore the method and the device have good response speed. The wide area transient stability controller of this application design can effectively improve system transient stability as input signal through wide area signal. According to the method, the accuracy of the wide-area transient stability control method is verified through simulation example analysis results, and the fact that the actual measurement method has strong engineering practicability is shown.
The two-zone four-machine ac/dc hybrid transmission system shown in fig. 3 is an example to further describe the embodiment of the present application in detail, but the present application is not limited to the given example.
And (3) constructing the simulation system shown in the figure 3 by utilizing a Matlab 2014a software platform. At 10s, a three-phase short fault was imposed on the system. The wide-area transient stability control experiment provided by the invention comprises the following steps:
the method comprises the following steps: when the system is in fault, a critical cluster of the system is identified through an EEAC theory, and a random matrix model is established by using terminal voltage data of each generator in the critical cluster as follows:
Figure BDA0002287292550000134
step two: the model is processed based on the single-ring theorem of the random matrix as follows:
Figure BDA0002287292550000141
wherein i is 1, N, j is 1, T.
Figure BDA0002287292550000142
Figure BDA0002287292550000143
Is composed of
Figure BDA0002287292550000144
The mean value of (a);
Figure BDA0002287292550000145
is composed of
Figure BDA0002287292550000146
Standard deviation of (d);
Figure BDA0002287292550000147
is composed of
Figure BDA0002287292550000148
Is andis provided with
Figure BDA0002287292550000149
Figure BDA00022872925500001410
Is composed of
Figure BDA00022872925500001411
Has a standard deviation of
Figure BDA00022872925500001412
For transition matrix
Figure BDA00022872925500001413
Calculating to obtain the equivalent matrix of singular value
Figure BDA00022872925500001414
Figure BDA00022872925500001415
Where U is a unitary matrix. For the equivalent matrix of singular values, have
Figure BDA00022872925500001416
Consider the case of L singular value equivalence matrices whose matrix product is
Figure BDA00022872925500001417
To pair
Figure BDA00022872925500001418
Performing unitization to obtain a standard matrix
Figure BDA00022872925500001419
Figure BDA00022872925500001420
Wherein i is 1,2, N,
Figure BDA00022872925500001421
Figure BDA00022872925500001422
is a non-Hermitian matrix.
Step three: solving a standard matrix
Figure BDA00022872925500001423
And quantitatively comparing the disturbance degree of each generator through Mean Spectral Radius (MSR), wherein the expression is as follows:
Figure BDA00022872925500001424
wherein,
Figure BDA00022872925500001425
as a standard matrix
Figure BDA00022872925500001426
Characteristic value of (1), in this context kMSRThe sensitivity of each generator to large system disturbances can be characterized. Generators with smaller average spectral radii are more sensitive to system disturbances.
From the characteristic root distributions of the two generators shown in FIG. 4, the average spectral radius k of the generator G1 can be determinedMSR10.134, average spectral radius k of generator G2MSR20.096. Generator G2 is a more sensitive generator because the average spectral radius of generator G2 is smaller than the average spectral radius of generator G1.
Step four: a wide-area transient stability controller is designed based on the Lyapunov theory, and a WAMS is utilized to combine a wide-area signal and a local signal as an input signal specific controller model, which is shown in figure 3. The designed controller is applied to wide-area transient stability control.
Step five: on the basis of identifying the sensitive generator, simulation comparison verification is carried out on the control of the sensitive generator in the system without applying control to the system and only the sensitive generator in the system, and the method is shown in figure 5;
as can be seen from fig. 5, when no control is applied, the system is destabilized; when control is only applied to the sensitive generators, the maximum relative power angle of each generator is 120 degrees, and the system is stable. Therefore, simulation verification of the two-region alternating current and direct current hybrid power transmission system shows that good control effect can be ensured only by performing wide-area transient stability control on the sensitive generator, and the control difficulty is reduced, so that the effectiveness of the method provided by the invention in actual system analysis is verified.
Fig. 7 is a structural diagram of a wide-area transient stability control system based on random matrix theory according to a preferred embodiment of the present invention. As shown in fig. 7, a wide-area transient stability control system based on random matrix theory includes:
the establishing unit 701 is configured to establish a random matrix model based on terminal voltage data of each generator in the critical cluster. Preferably, the establishing unit 701 is configured to establish a random matrix model based on terminal voltage data of each generator in the critical cluster; the first obtaining unit is used for processing the random matrix model based on a random matrix single-ring theorem to obtain a standard matrix, and is further used for:
firstly, establishing a random matrix model by using terminal voltage data of each generator in a critical cluster as follows:
Figure BDA0002287292550000161
the model is processed based on the single-ring theorem of the random matrix as follows:
Figure BDA0002287292550000162
wherein
Figure BDA0002287292550000163
To
Figure BDA0002287292550000164
A column vector formed by terminal voltage data of the 1 st to the Nth generators;
Figure BDA0002287292550000165
is a random matrix model; n is the number of generators in the critical cluster;
Figure BDA0002287292550000166
is the element of the ith row and the jth column of the transition matrix; 1, N, j 1, T;
Figure BDA0002287292550000167
Figure BDA0002287292550000168
is composed of
Figure BDA0002287292550000169
The mean value of (a);
Figure BDA00022872925500001610
is composed of
Figure BDA00022872925500001611
Standard deviation of (d);
Figure BDA00022872925500001612
is composed of
Figure BDA00022872925500001613
Has a mean value of
Figure BDA00022872925500001614
Figure BDA00022872925500001615
Is composed of
Figure BDA00022872925500001616
Has a standard deviation of
Figure BDA00022872925500001617
For transition matrix
Figure BDA00022872925500001618
Calculating to obtain the equivalent matrix of singular value
Figure BDA00022872925500001619
Figure BDA00022872925500001620
Wherein U is a unitary matrix;
Figure BDA00022872925500001621
is a transition matrix;
Figure BDA00022872925500001622
a transposed matrix which is a transition matrix; for the equivalent matrix of singular values, have
Figure BDA00022872925500001623
Consider the case of L singular value equivalence matrices,
Figure BDA00022872925500001624
is the ith singular value equivalence matrix; the matrix product is:
Figure BDA00022872925500001625
to pair
Figure BDA00022872925500001626
Performing unitization to obtain a standard matrix
Figure BDA00022872925500001627
Figure BDA00022872925500001628
Wherein i is 1,2, N,
Figure BDA00022872925500001629
n is the number of generators in the critical cluster;
Figure BDA00022872925500001630
is composed of
Figure BDA00022872925500001631
Row i of (1);
Figure BDA00022872925500001632
to
Figure BDA00022872925500001633
Is composed of
Figure BDA00022872925500001634
1 st to nth element of (a);
Figure BDA00022872925500001635
is composed of
Figure BDA0002287292550000171
Standard deviation of (d);
Figure BDA0002287292550000172
is the ith row of the standard matrix;
Figure BDA0002287292550000173
to
Figure BDA0002287292550000174
Is composed of
Figure BDA0002287292550000175
1 st to nth element of (a);
Figure BDA0002287292550000176
is a non-Hermitian matrix.
A first obtaining unit 702, configured to process the random matrix model based on a random matrix single-loop theorem to obtain a standard matrix.
The second obtaining unit 703 is configured to obtain a feature root of the standard matrix, and obtain an average spectrum radius of each generator according to the feature root.
An identifying unit 704 for identifying a sensitive generator of the generators based on the average spectral radius of the respective generator voltages. Preferably, the identifying unit 704 is configured to identify a sensitive generator of the generators based on the average spectral radius of the voltage generators, and further configured to:
the average spectral radius is expressed as:
Figure BDA0002287292550000177
wherein,
Figure BDA0002287292550000178
as a standard matrix
Figure BDA0002287292550000179
By the mean spectral radius kMSRAnd representing the sensitivity of each generator to large disturbance of the power transmission system.
And a control unit 705, configured to perform wide-area transient stability control on the sensitive generator.
Preferably, the system further comprises a monitoring unit, further configured to: when a power transmission system fails, a critical fleet is identified.
Preferably, the control unit 705 is configured to perform wide-area transient stability control on the sensitive generator, and is further configured to: when the power transmission system is unstable, the generator with the highest sensitivity degree is selected to perform wide-area transient stability control, when the power transmission system is still unstable, the generator with the highest sensitivity degree in the rest generators is subjected to wide-area transient stability control, and the control is performed until the power transmission system meets the stability margin.
The wide-area transient stability control system 700 based on the random matrix theory in the preferred embodiment of the present invention corresponds to the wide-area transient stability control method 100 based on the random matrix theory in the preferred embodiment of the present invention, and is not described herein again.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The invention has been described with reference to a few embodiments. However, other embodiments of the invention than the one disclosed above are equally possible within the scope of the invention, as would be apparent to a person skilled in the art from the appended patent claims.
Generally, all terms used in the claims are to be interpreted according to their ordinary meaning in the technical field, unless explicitly defined otherwise herein. All references to "a// the [ device, component, etc ]" are to be interpreted openly as referring to at least one instance of said device, component, etc., unless explicitly stated otherwise. The steps of any method disclosed herein do not have to be performed in the exact order disclosed, unless explicitly stated.

Claims (10)

1. A wide-area transient stability control method based on random matrix theory, the method comprising:
establishing a random matrix based on terminal voltage data of each generator in the critical cluster; processing the random matrix based on a random matrix single-ring theorem to obtain a standard matrix;
solving a characteristic root of the standard matrix, and acquiring an average spectrum radius of each generator according to the characteristic root;
identifying the sensitivity of each generator in the critical cluster based on the average spectral radius of each generator;
and carrying out wide-area transient stability control on the sensitive generator.
2. The method of claim 1, wherein the random matrix model is established based on terminal voltage data of each generator in the critical cluster; processing the random matrix model based on a random matrix single-ring theorem to obtain a standard matrix; the method comprises the following steps:
(1) firstly, establishing a random matrix model by using terminal voltage data of each generator in a critical cluster as follows:
Figure FDA0002287292540000011
(2) the model is processed based on the single-ring theorem of the random matrix as follows:
Figure FDA0002287292540000012
wherein
Figure FDA0002287292540000013
To
Figure FDA0002287292540000014
A column vector formed by terminal voltage data of the 1 st to the Nth generators;
Figure FDA0002287292540000015
is a random matrix model; n is the number of generators in the critical cluster;
Figure FDA0002287292540000016
is the element of the ith row and the jth column of the transition matrix; 1, N, j 1, T;
Figure FDA0002287292540000017
Figure FDA0002287292540000018
is composed of
Figure FDA0002287292540000019
The mean value of (a);
Figure FDA00022872925400000110
is composed of
Figure FDA00022872925400000111
Standard deviation of (d);
Figure FDA00022872925400000112
is composed of
Figure FDA00022872925400000113
Has a mean value of
Figure FDA00022872925400000114
Figure FDA00022872925400000115
Is composed of
Figure FDA00022872925400000116
Has a standard deviation of
Figure FDA00022872925400000117
For transition matrix
Figure FDA00022872925400000118
Calculating to obtain the equivalent matrix of singular value
Figure FDA00022872925400000119
Figure FDA0002287292540000021
Wherein U is a unitary matrix;
Figure FDA0002287292540000022
is a transition matrix;
Figure FDA0002287292540000023
a transposed matrix which is a transition matrix; for the equivalent matrix of singular values, have
Figure FDA0002287292540000024
Consider the case of L singular value equivalence matrices,
Figure FDA0002287292540000025
is the ith singular value equivalence matrix; matrix thereofThe product is:
Figure FDA0002287292540000026
to pair
Figure FDA0002287292540000027
Performing unitization to obtain a standard matrix
Figure FDA0002287292540000028
Figure FDA0002287292540000029
Wherein i is 1,2, N,
Figure FDA00022872925400000210
n is the number of generators in the critical cluster;
Figure FDA00022872925400000211
is composed of
Figure FDA00022872925400000212
Row i of (1);
Figure FDA00022872925400000213
to
Figure FDA00022872925400000214
Is composed of
Figure FDA00022872925400000215
1 st to nth element of (a);
Figure FDA00022872925400000216
is composed of
Figure FDA00022872925400000217
Standard of (2)A difference;
Figure FDA00022872925400000218
is the ith row of the standard matrix;
Figure FDA00022872925400000219
to
Figure FDA00022872925400000220
Is composed of
Figure FDA00022872925400000221
1 st to nth element of (a);
Figure FDA00022872925400000222
is a non-Hermitian matrix.
3. The method of claim 2, wherein identifying the sensitive generator of the generators based on the average spectral radius of the voltage generators is expressed as:
Figure FDA00022872925400000223
wherein,
Figure FDA00022872925400000224
as a standard matrix
Figure FDA00022872925400000225
By the mean spectral radius kMSRAnd representing the sensitivity of each generator to large disturbance of the power transmission system.
4. The method of claim 1, prior to establishing the stochastic matrix model based on the generator-side voltage data of each generator in the critical cluster, further comprising:
when a power transmission system fails, a critical fleet is identified.
5. The method of claim 1, the wide-area transient-stability controlling the sensitive generator, comprising:
and when the power transmission system is unstable, the generator with the highest sensitivity degree is selected for wide-area transient stability control, and when the power transmission system is still unstable, the generator with the highest sensitivity degree in the rest generators is subjected to wide-area transient stability control until the power transmission system meets the stability margin.
6. A wide-area transient stability control system based on stochastic matrix theory, the system comprising:
the establishing unit is used for establishing a random matrix model based on terminal voltage data of each generator in the critical cluster;
the first acquisition unit is used for processing the random matrix model based on a random matrix single-ring theorem to acquire a standard matrix;
the second acquisition unit is used for solving a characteristic root of the standard matrix and acquiring the average spectrum radius of each generator according to the characteristic root;
the identification unit is used for identifying a sensitive generator in the generators based on the average spectrum radius of each voltage;
and the control unit is used for carrying out wide-area transient stability control on the sensitive generator.
7. The system according to claim 6, wherein the establishing unit is configured to establish a random matrix model based on terminal voltage data of each generator in the critical cluster; the first acquisition unit is used for processing the random matrix model based on a random matrix single-ring theorem to acquire a standard matrix; the establishing unit and the first obtaining unit are further configured to:
(1) firstly, establishing a random matrix model by using terminal voltage data of each generator in a critical cluster as follows:
Figure FDA0002287292540000031
(2) the model is processed based on the single-ring theorem of the random matrix as follows:
Figure FDA0002287292540000032
wherein
Figure FDA0002287292540000041
To
Figure FDA0002287292540000042
A column vector formed by terminal voltage data of the 1 st to the Nth generators;
Figure FDA0002287292540000043
is a random matrix model; n is the number of generators in the critical cluster;
Figure FDA0002287292540000044
is the element of the ith row and the jth column of the transition matrix; 1, N, j 1, T;
Figure FDA0002287292540000045
Figure FDA0002287292540000046
is composed of
Figure FDA0002287292540000047
The mean value of (a);
Figure FDA0002287292540000048
is composed of
Figure FDA0002287292540000049
Standard deviation of (d);
Figure FDA00022872925400000410
is composed of
Figure FDA00022872925400000411
Has a mean value of
Figure FDA00022872925400000412
Figure FDA00022872925400000413
Is composed of
Figure FDA00022872925400000414
Has a standard deviation of
Figure FDA00022872925400000415
For transition matrix
Figure FDA00022872925400000416
Calculating to obtain the equivalent matrix of singular value
Figure FDA00022872925400000417
Figure FDA00022872925400000418
Wherein U is a unitary matrix;
Figure FDA00022872925400000419
is a transition matrix;
Figure FDA00022872925400000420
a transposed matrix which is a transition matrix; for the equivalent matrix of singular values, have
Figure FDA00022872925400000421
Consider the case of L singular value equivalence matrices,
Figure FDA00022872925400000422
is the ith singular value equivalence matrix; the matrix product is:
Figure FDA00022872925400000423
to pair
Figure FDA00022872925400000424
Performing unitization to obtain a standard matrix
Figure FDA00022872925400000425
Figure FDA00022872925400000426
Wherein i is 1,2, N,
Figure FDA00022872925400000427
n is the number of generators in the critical cluster;
Figure FDA00022872925400000428
is composed of
Figure FDA00022872925400000429
Row i of (1);
Figure FDA00022872925400000430
to
Figure FDA00022872925400000431
Is composed of
Figure FDA00022872925400000432
1 st to nth element of (a);
Figure FDA00022872925400000433
is composed of
Figure FDA00022872925400000434
Standard deviation of (d);
Figure FDA00022872925400000435
is the ith row of the standard matrix;
Figure FDA00022872925400000436
to
Figure FDA00022872925400000437
Is composed of
Figure FDA00022872925400000438
1 st to nth element of (a);
Figure FDA00022872925400000439
is a non-Hermitian matrix.
8. The method of claim 7, the identifying unit for identifying sensitive ones of the generators based on the average spectral radii of the generators, comprising:
the average spectrum radius expression is as follows:
Figure FDA0002287292540000051
wherein,
Figure FDA0002287292540000052
as a standard matrix
Figure FDA0002287292540000053
By the mean spectral radius kMSRAnd representing the sensitivity of each generator to large disturbance of the power transmission system.
9. The system of claim 6, further comprising:
and the monitoring unit is used for identifying the critical cluster when the power transmission system has a fault.
10. The system of claim 6, the control unit to perform wide-area transient stability control on the sensitive generator, further to:
and when the power transmission system is unstable, the generator with the highest sensitivity degree is firstly selected for wide-area transient stability control, and when the power transmission system is still unstable, the generator with the highest sensitivity degree in the rest generators is subjected to wide-area transient stability control until the power transmission system meets the stability margin.
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