CN111106607B - Method and device for judging stability of static voltage - Google Patents

Method and device for judging stability of static voltage Download PDF

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CN111106607B
CN111106607B CN201911174615.5A CN201911174615A CN111106607B CN 111106607 B CN111106607 B CN 111106607B CN 201911174615 A CN201911174615 A CN 201911174615A CN 111106607 B CN111106607 B CN 111106607B
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voltage
equation
matrix
hamilton
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CN111106607A (en
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宋墩文
刘开欣
于明
杨学涛
郁舒雁
李铮
许鹏飞
陈勇
刘英志
郅治
位士全
刘道伟
杜三恩
冯静
杨红英
蒋勇
谢家正
赵高尚
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
Guangxi Power Grid Co Ltd
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State Grid Corp of China SGCC
China Electric Power Research Institute Co Ltd CEPRI
Guangxi Power Grid Co Ltd
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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
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • 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
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • 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
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component

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Abstract

The invention discloses a method for judging the stability of static voltage, which comprises the following steps: collecting power grid data, and establishing a network node equation of the power system; obtaining an injection current expression of each node according to the network node equation and the node admittance matrix; defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation; establishing a voltage stability criterion according to the node voltage iterative equation; substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion, and solving the problem of low efficiency of the method for judging the voltage stability in the prior art.

Description

Method and device for judging stability of static voltage
Technical Field
The application relates to the technical field of voltage stability analysis of power systems, in particular to a method for judging static voltage stability, and also relates to a device for judging static voltage stability.
Background
With the continuous enlargement of the scale of the power system, the continuous increase of the load and the gradual implementation of the power market, the network structure is increasingly complex, and the system is continuously developed towards the direction of large unit, large power grid, high voltage and long distance power transmission. The increase of load and unit capacity, the improvement of the requirement of users on the quality of electric energy and the like put forward higher requirements on the safe operation of the power grid. The large power system has great economic benefit and social benefit, and simultaneously has some disadvantages: considering the constraints of environmental and economic factors, the scheduling is more complex, the operation of the power system tends to a stable limit state, the voltage instability phenomenon is increasingly highlighted, the loss caused by system faults and large-scale power failure accidents is huge, and the system stability problem especially becomes a main factor threatening the safe operation of the power grid.
In recent years, electric power systems in China have stepped into the era of large power grids, extra-high voltage, large units and long-distance power transmission. Meanwhile, with the rapid development of economy and society, the load demand in the power grid is continuously increased, and power generation, transmission and distribution facilities gradually approach the limit value. And the capacity of the whole power system is increased by the trend of grid interconnection, and the transmission voltage is generally increased by high-voltage transmission, so that the tidal current change of a high-voltage transmission line and the great change of reactive power caused by the switching of the line can be caused, and the requirements on the regulation and control of the reactive power and the voltage of the power system are higher. Therefore, the research on the problem of power grid voltage stability has important significance on the traditional safety and stability of electric power.
For a long time, people have conducted a great deal of research on the problem of power angle stability, but have neglected the research on the problem of voltage stability. In recent decades, with the development of the power industry in China, the problem of unstable voltage of a power grid becomes more and more prominent, the perception of the voltage sensitivity of a load is continuously reduced, dynamic reactive compensation cannot be realized, sudden load cannot be coped with, the voltage recovery is not facilitated, once the power grid in a heavy load area of a system is disturbed, the probability of insufficient reactive power is increased, and therefore the voltage instability phenomenon occurs. In recent years, the interconnection of power grids in various large areas of the power grid in China is gradually realized, and the high-speed development of social economy leads the central load to be increased rapidly; in addition, the power system evolves from an integrated system of power generation, power transmission and power distribution to an open and competitive environment, the increase of the demand of the power transmission capacity enables the utilization intensity of power transmission equipment to be larger and larger, the problem of voltage stability to be more and more serious, and unsafe voltage obviously becomes a main factor for limiting power transmission. Therefore, the study on the voltage stability problem, the judgment and the monitoring of the grid voltage instability are more important.
Currently, some progress has been made in the study of voltage stability. Summarizing the results of the current research, it can be concluded that: the main technical approach is based on the idea of whether node voltage in the power grid or the equivalent circuit can be solved. If the node voltage has a feasible solution, the node voltage is considered to be stable; if the node voltage has no solution or no feasible solution, the node voltage is determined to be unstable. The traditional voltage stability analysis method is mainly based on a Thevenin equivalent circuit tracking method. When the method is used for on-line calculation, the network equivalence calculation needs to be carried out on each load node, the calculation amount is large, the required time is long, and therefore the efficiency is low.
Disclosure of Invention
The application provides a method for judging the stability of static voltage, which solves the problem of low efficiency of the method for judging the stability of the voltage in the prior art.
The application provides a method for judging static voltage stability, which comprises the following steps:
collecting power grid data, and establishing a network node equation of the power system;
acquiring an injection current expression of each node according to the network node equation and the node admittance matrix;
defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation;
establishing a voltage stability criterion according to the node voltage iterative equation;
substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.
Preferably, the collecting the grid data and establishing a network node equation of the power system includes:
the collected power grid data comprises: the amplitude and the phase angle of the node voltage, the active power output by the node and the reactive power are calculated;
establishing a network node equation of the power system according to the collected power grid data,
Figure BDA0002289629200000021
wherein, Ix+jIy≡I∈Cn×1Is the node injection current column vector; e + jf ≡ V ≡ [ e ] }k+jfk]∈Cn×1Is a node voltage column vector.
Preferably, obtaining the injection current expression of each node according to the network node equation and the node admittance matrix includes:
according to the network node equation, a node admittance matrix, a node voltage column vector and a node injection current column vector are recorded as,
Figure BDA0002289629200000031
Figure BDA0002289629200000032
the injection current at each node is expressed as,
Figure BDA0002289629200000033
in the formula, vkIs the amplitude of the node voltage, pk、qkIs the active power and the reactive power of the node, and k belongs to (1, n).
Preferably, defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation, including:
the Hamilton coefficient matrix is defined as follows,
Figure BDA0002289629200000034
Figure BDA0002289629200000035
from the Hamilton coefficient matrix, the network node equation can be expressed as:
Yx＝H(t)x
matrices Y and h (t) are subjected to eigenvalue decomposition as follows:
Figure BDA0002289629200000036
Figure BDA0002289629200000037
in the above formula, S1、S2Are all sine matrixes and also are orthogonal matrixes; lambda [ alpha ]1、λ2Are eigenvalues of matrices Y and H (t), respectively, i.e.
Figure BDA0002289629200000041
Solving the voltage of each node of the power grid according to Yx ═ H (t) x, and then constructing the following node iterative equation:
Yx(k+1)＝H(t)x(k)。
preferably, establishing a voltage stability criterion according to the node voltage iterative equation includes:
substituting the matrixes Y and H (t) obtained by decomposing the characteristic values into a node voltage iterative equation to obtain
Figure BDA0002289629200000042
Thus, there are:
Figure BDA0002289629200000043
therefore, the iterative equation Yx(k+1)＝H(t)x(k)Absolute convergence, voltage hasThe conditional equation of the solution is:
Figure BDA0002289629200000044
the above formula can be expressed as:
Figure BDA0002289629200000045
in the above conditional equation: mu.skK ∈ (1, n) depends on the network structure and the network parameters; tau iskK ∈ (1, n) depends on the dynamic characteristics between the node injection power and the voltage amplitude; under the condition of small disturbance or large disturbance, if each node in the power grid meets the condition equation, the node voltage is solved; otherwise, the node voltage state quantity is diverged, i.e. has no solution, so that the above conditional equation can be used as the voltage stability criterion.
Preferably, substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression to obtain a final form of the voltage stability criterion, including:
equation of condition
Figure BDA0002289629200000046
As a voltage stability criterion, it is necessary to calculate μk，k∈(1，n)、τk，k∈(1，n)；
τkThe expression calculated is:
Figure BDA0002289629200000051
μkis the eigenvalue of the Hamilton matrix Y, the eigenvalue can be calculated by the following method,
cholesky decomposition of matrices G and-B yields the following expression:
Figure BDA0002289629200000052
in the above formula, the first and second carbon atoms are,
Figure BDA0002289629200000053
the decomposition can be used for obtaining:
Figure BDA0002289629200000054
in the above formula, InIs an n-dimensional identity matrix;
Figure BDA0002289629200000055
due to L1And L2Are all lower triangular matrices, so matrix η is also a lower triangular matrix, then:
Figure BDA0002289629200000056
if etaiiI ∈ (1, n) is completely different, then the matrix η can be diagonalized, then:
Figure BDA0002289629200000057
thus, equation Y can be further decomposed into:
Figure BDA0002289629200000058
Figure BDA0002289629200000059
and (3) carrying out eigenvalue decomposition on the W matrix to obtain:
Figure BDA00022896292000000510
finally, the following can be obtained:
Figure BDA0002289629200000061
based on the above derivation, the voltage stability criterion is expressed as:
Figure BDA0002289629200000062
thus, the final form of the voltage stability criterion based on the decomposition of eigenvalues of the Hamilton matrix is obtained.
This application provides a device of judging static voltage stability simultaneously, includes:
the node equation establishing unit is used for acquiring power grid data and establishing a network node equation of the power system;
the injection current expression obtaining unit is used for obtaining the injection current expression of each node according to the network node equation and the node admittance matrix;
the node voltage iterative equation obtaining unit is used for defining a Hamilton coefficient matrix, and performing characteristic value decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation;
the criterion establishing unit is used for establishing a voltage stability criterion according to the node voltage iterative equation;
and the final criterion obtaining unit is used for substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.
The application provides a method for judging the stability of static voltage, which comprises the steps of establishing a network node equation of a power system by collecting power grid data; performing characteristic value decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iteration equation; establishing a voltage stability criterion according to the node voltage iterative equation; substituting the criterion expression into the characteristic values of the node admittance matrix and the Hamilton coefficient matrix to obtain the final form of the voltage stability criterion, and solving the problem of low efficiency of the method for judging the voltage stability in the prior art.
Drawings
FIG. 1 is a schematic flow chart illustrating a method for determining static voltage stability according to the present disclosure;
FIG. 2 is a detailed step diagram illustrating the determination of the static voltage stability using the method provided herein;
FIG. 3 is a schematic diagram of an apparatus for determining stability of static voltage according to the present application
Detailed Description
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. This application is capable of implementation in many different ways than those herein set forth and of similar import by those skilled in the art without departing from the spirit of this application and is therefore not limited to the specific implementations disclosed below.
Fig. 1 is a schematic flow chart of a method for determining static voltage stability provided by the present application, and the method provided by the present application is described in detail below with reference to fig. 1.
And S101, collecting power grid data and establishing a network node equation of the power system.
The collected power grid data comprises: the amplitude, phase angle, node output active power, and reactive power of the node voltage.
The network node equation of the power system reflects the relationship between the voltage of each node and the injection current, and is established according to the collected power grid data, and can be expressed as follows:
Figure BDA0002289629200000071
in the formula Ix+jIy≡I∈Cn×1Is the node injection current column vector; e + jf ═ V ≡ ek+jfk]∈Cn×1Is a node voltage column vector.
And S102, acquiring an injection current expression of each node according to the network node equation and the node admittance matrix.
Recording a node admittance matrix, a node voltage column vector, and a node injection current column vector according to the network node equation,
Figure BDA0002289629200000072
Figure BDA0002289629200000073
the injection current expression of each node is:
Figure BDA0002289629200000074
in the above formula:
Figure BDA0002289629200000075
in the formula, vkIs the amplitude of the node voltage, pk、qkIs the active power and the reactive power of the node, and k belongs to (1, n).
And step S103, defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation.
The Hamilton coefficient matrix is defined as follows,
Figure BDA0002289629200000081
Figure BDA0002289629200000082
from the Hamilton coefficient matrix, the network node equation (1) can be expressed as:
Yx＝H(t)x (8)
since the matrices Y and h (t) in equation (8) are symmetrical real matrices, both can be subjected to eigenvalue decomposition as follows:
Figure BDA0002289629200000083
Figure BDA0002289629200000084
in the above formula, S1、S2Are all sine matrixes and also are orthogonal matrixes; lambda [ alpha ]1、λ2Are eigenvalues of matrices Y and H (t), respectively, i.e.
Figure BDA0002289629200000085
Solving the voltages of the nodes of the power grid according to (8) Yx ═ h (t) x, the following node iterative equations are constructed:
Yx(k+1)＝H(t)x(k)。 (12)
and step S104, establishing a voltage stability criterion according to the node voltage iterative equation.
Substituting the matrixes Y and H (t) obtained by decomposing the characteristic values into a node voltage iterative equation to obtain
Figure BDA0002289629200000086
Thus, there are:
Figure BDA0002289629200000091
therefore, the iterative equation Yx(k+1)＝H(t)x(k)The absolute convergence, the conditional equation of the voltage solution is:
Figure BDA0002289629200000092
the above formula can be expressed as:
Figure BDA0002289629200000093
in the above conditional equation: mu.skK ∈ (1, n) depends on the network structure and the network parameters; tau iskK ∈ (1, n) depends on the dynamic characteristics between the node injection power and the voltage amplitude; under the condition of small disturbance or large disturbance, if each node in the power grid meets the condition equation, the voltage of the node is solved; otherwise, the node voltage state quantity is diverged, i.e. has no solution, so that the above conditional equation can be used as the voltage stability criterion.
And S105, substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.
Equation of condition
Figure BDA0002289629200000094
As a voltage stability criterion, it is necessary to calculate μk，k∈(1，n)、τk，k∈(1，n)；
τkThe expression calculated is:
Figure BDA0002289629200000095
μkis the eigenvalue of the Hamilton matrix Y, the eigenvalue can be calculated by the following method,
the following reasoning is introduced first:
introduction 1: in the power system, the matrices G and-B are both true symmetric positive definite matrices. All have real characteristics.
Taking the eigenvalues of the matrix G as
Figure BDA0002289629200000096
The eigenvalues of matrix-B are
Figure BDA0002289629200000097
Then according to the Gerschgor in disc theorem there are:
Figure BDA0002289629200000101
Figure BDA0002289629200000102
as a result of this, it is possible to,
Figure BDA0002289629200000103
Figure BDA0002289629200000104
therefore, the temperature of the molten metal is controlled,
Figure BDA0002289629200000105
consider that in a power system, matrices G and-B are both invertible matrices (full rank matrices), i.e.
Figure BDA0002289629200000106
i ∈ (1, n), so matrices G and-B are both true symmetric positive definite matrices.
Cholesky decomposition of matrices G and-B yields the following expression:
Figure BDA0002289629200000107
Figure BDA0002289629200000108
in the above formula, the first and second carbon atoms are,
Figure BDA0002289629200000109
the decomposition can be used for obtaining:
Figure BDA00022896292000001010
in the above formula, InIs an n-dimensional identity matrix;
Figure BDA00022896292000001011
due to L1And L2Are all lower triangular matrices, so matrix η is also a lower triangular matrix, then:
Figure BDA00022896292000001012
regarding the lower triangular matrix, the following reasoning holds:
2, leading: let matrix X ≡ [ X ]ij]∈Rn×nIs a lower triangular matrix. If the element X on the diagonal of the matrixiiI.e., i ∈ (1, n) are all completely different, the matrix can be diagonalized, i.e.
Figure BDA0002289629200000111
Here, P is called the eigenvector matrix of X, XiiI ∈ (1, n) is the eigenvalue of matrix X.
According to the theory 2: if etaiiI ∈ (1, n) is completely different, then the matrix η can be diagonalized, then:
Figure BDA0002289629200000112
thus, equation Y can be further decomposed into:
Figure BDA0002289629200000113
Figure BDA0002289629200000114
performing eigenvalue decomposition on the W matrix to obtain:
Figure BDA0002289629200000115
finally, the following components are obtained:
Figure BDA0002289629200000116
based on the above derivation, the voltage stability criterion, equation (17), can be expressed as:
Figure BDA0002289629200000117
after finishing, the voltage stability criterion is expressed as:
Figure BDA0002289629200000118
thus, the final form of the voltage stability criterion based on the decomposition of eigenvalues of the Hamilton matrix is obtained.
The detailed steps for judging the stability of the static voltage by using the method provided by the application are shown in fig. 2, firstly, the basic data of the power grid are collected, and the collected data comprise: the amplitude and the phase angle of the node voltage, the active power output by the node and the reactive power are calculated; establishing a network node equation of the power system according to the collected power grid data, and obtaining an injection current expression of each node according to the network node equation and the node admittance matrix; defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix; establishing a node voltage iteration equation; establishing a voltage stability criterion according to the node voltage iterative equation; substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression; and refining the voltage stability criterion expression to obtain a final form of the voltage stability criterion.
The present application also provides an apparatus 300 for determining stability of static voltage, as shown in fig. 3, including:
the node equation establishing unit 310 is configured to collect power grid data and establish a network node equation of the power system;
an injection current expression obtaining unit 320, configured to obtain an injection current expression of each node according to the network node equation and the node admittance matrix;
the node voltage iterative equation obtaining unit 330 is configured to define a Hamilton coefficient matrix, and perform eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation;
a criterion establishing unit 340, configured to establish a voltage stability criterion according to the node voltage iterative equation;
and a final criterion obtaining unit 350, configured to substitute the eigenvalues of the node admittance matrix and the Hamilton coefficient matrix into the criterion expression to obtain a final form of the voltage stability criterion.
Finally, it should be noted that: although the present invention has been described in detail with reference to the above embodiments, it should be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention.

Claims (6)

1. A method for determining static voltage stability, comprising:
collecting power grid data, and establishing a network node equation of the power system;
obtaining an injection current expression of each node according to the network node equation and the node admittance matrix;
defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation;
establishing a voltage stability criterion according to the node voltage iterative equation;
substituting the characteristic values of the node admittance matrix and the Hamilton coefficient matrix into a criterion expression to obtain a final form of the voltage stability criterion, wherein the final form comprises the following steps:
conditional equation
Figure FDA0003622430800000011
k is an element (1, n) as a voltage stability criterion and needs to calculate muk，k∈(1，n)、τk，k∈(1，n)；
τkThe expression calculated is:
Figure FDA0003622430800000012
μkis the eigenvalue of the Hamilton matrix Y, the eigenvalue can be calculated by the following method,
cholesky decomposition of matrices G and-B yields the following expression:
Figure FDA0003622430800000013
in the above formula, the first and second carbon atoms are,
Figure FDA0003622430800000014
the decomposition can be used for obtaining:
Figure FDA0003622430800000015
in the above formula, InIs an n-dimensional identity matrix;
Figure FDA0003622430800000016
due to L1And L2Are all lower triangular matrices, so matrix η is also a lower triangular matrix, then:
Figure FDA0003622430800000017
if etaiiI ∈ (1, n) is completely different, then the matrix η can be diagonalized, then:
Figure FDA0003622430800000021
thus, equation Y can be further decomposed into:
Figure FDA0003622430800000022
Figure FDA0003622430800000023
and (3) carrying out eigenvalue decomposition on the W matrix to obtain:
Figure FDA0003622430800000024
finally, the following can be obtained:
Figure FDA0003622430800000025
based on the above derivation, the voltage stability criterion is expressed as:
Figure FDA0003622430800000026
thus, the final form of the voltage stability criterion based on the decomposition of eigenvalues of the Hamilton matrix is obtained.
2. The method of claim 1, wherein collecting grid data and establishing network node equations for the power system comprises:
the collected power grid data comprises: the amplitude and the phase angle of the node voltage, the active power output by the node and the reactive power are calculated;
establishing a network node equation of the power system according to the collected power grid data,
Figure FDA0003622430800000027
wherein, Ix+jIy≡I∈Cn×1Is the node injection current column vector; e + jf ═ V ≡ ek+jfk]∈Cn×1Is a node voltage column vector.
3. The method of claim 1, wherein obtaining the injection current expression for each node from the network node equation and the node admittance matrix comprises:
recording a node admittance matrix, a node voltage column vector, and a node injection current column vector according to the network node equation,
Figure FDA0003622430800000031
Figure FDA0003622430800000032
the injection current at each node is expressed as,
Figure FDA0003622430800000033
in the formula, vkIs the amplitude of the node voltage, pk、qkIs the active power and the reactive power of the node, and k belongs to (1, n).
4. The method of claim 1, wherein defining a Hamilton coefficient matrix, and performing eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain an iterative node voltage equation, comprises:
the Hamilton coefficient matrix is defined as follows,
Figure FDA0003622430800000034
Figure FDA0003622430800000035
according to the Hamilton coefficient matrix, the network node equation can be expressed as:
Yx＝H(t)x
matrices Y and h (t) are subjected to eigenvalue decomposition as follows:
Figure FDA0003622430800000036
Figure FDA0003622430800000037
in the above formula, S1、S2Are all sine matrixes and also are orthogonal matrixes; lambda [ alpha ]1、λ2Are eigenvalues of matrices Y and H (t), respectively, i.e.
Figure FDA0003622430800000041
Solving the voltage of each node of the power grid according to Yx ═ H (t) x, and then constructing the following node iterative equation:
Yx(k+1)＝H(t)x(k)。
5. the method of claim 1, wherein establishing a voltage stability criterion based on the node voltage iteration equation comprises:
substituting the matrixes Y and H (t) obtained by decomposing the characteristic values into a node voltage iterative equation to obtain
Figure FDA0003622430800000042
Thus, there are:
Figure FDA0003622430800000043
therefore, the iterative equation Yx(k+1)＝H(t)x(k)The absolute convergence, the conditional equation of the voltage solution is:
Figure FDA0003622430800000044
the above formula can be expressed as:
Figure FDA0003622430800000045
in the above conditional equation: mu.sk，kE (1, n) depends on the network structure and the network parameters; tau iskK ∈ (1, n) depends on the dynamic characteristics between the node injection power and the voltage amplitude; under the condition of small disturbance or large disturbance, if each node in the power grid meets the condition equation, the voltage of the node is solved; otherwise, the node voltage state quantity is diverged, i.e. has no solution, so that the above conditional equation can be used as the voltage stability criterion.
6. An apparatus for determining stability of a static voltage, comprising:
the node equation establishing unit is used for acquiring power grid data and establishing a network node equation of the power system;
the injection current expression obtaining unit is used for obtaining the injection current expression of each node according to the network node equation and the node admittance matrix;
the node voltage iterative equation obtaining unit is used for defining a Hamilton coefficient matrix, and performing characteristic value decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain a node voltage iterative equation;
the criterion establishing unit is used for establishing a voltage stability criterion according to the node voltage iterative equation;
and the final criterion obtaining unit is used for substituting the node admittance matrix and the Hamilton coefficient matrix eigenvalue into the criterion expression to obtain a final form of the voltage stability criterion, and comprises the following steps:
equation of condition
Figure FDA0003622430800000051
k is an element (1, n) as a voltage stability criterion and needs to calculate muk，k∈(1，n)、τk，k∈(1，n)；
τkThe expression calculated is:
Figure FDA0003622430800000052
μkis the eigenvalue of the Hamilton matrix YThe characteristic value can be calculated by the following method,
cholesky decomposition of matrices G and-B yields the following expression:
Figure FDA0003622430800000053
in the above formula, the first and second carbon atoms are,
Figure FDA0003622430800000054
the decomposition can be used for obtaining:
Figure FDA0003622430800000055
in the above formula, InIs an n-dimensional identity matrix;
Figure FDA0003622430800000056
due to L1And L2Are all lower triangular matrices, so matrix η is also a lower triangular matrix, then:
Figure FDA0003622430800000057
if etaiiI ∈ (1, n) is completely different, then the matrix η can be diagonalized, then:
Figure FDA0003622430800000061
thus, equation Y can be further decomposed into:
Figure FDA0003622430800000062
Figure FDA0003622430800000063
and (3) carrying out eigenvalue decomposition on the W matrix to obtain:
Figure FDA0003622430800000064
finally, the following can be obtained:
Figure FDA0003622430800000065
based on the above derivation, the voltage stability criterion is expressed as:
Figure FDA0003622430800000066
thus, the final form of the voltage stability criterion based on the decomposition of eigenvalues of the Hamilton matrix is obtained.
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