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

Abstract

The invention discloses a method for judging the stability of static voltage, comprising: collecting grid data, establishing a network node equation of a power system; obtaining an injection current expression of each node according to the network node equation and a node admittance matrix; defining Hamilton coefficient matrix, decompose the eigenvalues of the node admittance matrix and the Hamilton coefficient matrix to obtain the node voltage iteration equation; establish the voltage stability criterion according to the node voltage iteration equation; substitute the node admittance matrix and the eigenvalues of the Hamilton coefficient matrix into The expression of the criterion obtains the final form of the criterion of voltage stability, and solves the problem of low efficiency of the method of judging voltage stability in the prior art.

Description

A method and device for judging static voltage stability

technical field

The present application relates to the technical field of power system voltage stability analysis, in particular to a method for judging static voltage stability, and a device for judging static voltage stability.

Background technique

With the continuous expansion of the scale of the power system, the continuous growth of the load and the gradual implementation of the power market, the network structure has become increasingly complex, and the system has continued to develop in the direction of large units, large power grids, high voltage and long-distance power transmission. The increase of load and unit capacity and the improvement of users' requirements for power quality have put forward higher requirements for the safe operation of the power grid. While large-scale power system brings huge economic and social benefits, it also has some drawbacks: considering the constraints of environmental and economic factors, the dispatching becomes more complicated, the operation of the power system tends to be in a stable limit state, and the phenomenon of voltage instability becomes more and more prominent. , system failures and large-scale power outages cause huge losses and so on, especially the system stability problem has become the main factor that threatens the safe operation of the power grid.

In recent years, my country's power system has entered the era of large power grids, UHV, large units, and long-distance transmission. At the same time, with the rapid economic and social development, the demand for load in the power grid is increasing, and the power generation, transmission and distribution facilities are gradually approaching their limit values. Moreover, the trend of grid interconnection increases the capacity of the entire power system, coupled with high-voltage transmission, which generally increases the transmission voltage, which will lead to changes in the power flow of high-voltage transmission lines and large changes in reactive power caused by line switching. Higher requirements for reactive power, voltage regulation and control of power systems. Therefore, the research on grid voltage stability is of great significance to the traditional security and stability of power.

For a long time, people have done a lot of research on power angle stability, but neglected the research on voltage stability. In recent decades, with the development of China's power industry, the problem of grid voltage instability has become more and more prominent, and the load's perception of voltage sensitivity has continued to decline. Voltage recovery, once the power grid in the heavy load area of the system is disturbed, the probability of insufficient reactive power increases, resulting in voltage instability. Moreover, in recent years, the major regional power grids in my country's power grid have gradually been interconnected, and the rapid development of social economy has caused a sharp increase in the central load; in addition, the power system has evolved from an integrated system of power generation, transmission and distribution to an open and competitive environment. The increase in demand has made the utilization of power transmission equipment more and more intensive, and the problem of voltage stability has become more and more serious. Therefore, the research on voltage stability, the identification and monitoring of grid voltage instability is the most important thing.

At present, the research on voltage stability has made some progress. Summarizing the current research results, it can be concluded that the main technical approaches used are based on the idea of whether there is a feasible solution for the node voltage in the power grid or equivalent circuit. If the node voltage has a feasible solution, it is considered that the node voltage is stable; if the node voltage has no solution or no feasible solution, it is determined that the node voltage is unstable. The traditional voltage stability analysis method is mainly based on the Thevenin equivalent circuit tracking method. In the online calculation of this method, the network equivalent calculation needs to be performed for each load node, the calculation amount is large, and the required time is long, so the efficiency is low.

SUMMARY OF THE INVENTION

The present application provides a method for judging static voltage stability, which solves the problem of low efficiency of the method for judging voltage stability in the prior art.

The present application provides a method for judging static voltage stability, including:

Collect power grid data and establish the network node equation of the power system;

According to the network node equation and the node admittance matrix, the injection current expression of each node is obtained;

Define the Hamilton coefficient matrix, decompose the eigenvalues of the node admittance matrix and the Hamilton coefficient matrix, and obtain the node voltage iteration equation;

establishing a voltage stability criterion according to the node voltage iteration equation;

Substitute the nodal admittance matrix and the eigenvalues of the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.

Preferably, the grid data is collected, and the network node equation of the power system is established, including:

The collected power grid data includes: node voltage amplitude, phase angle, node output active power, and reactive power;

According to the collected power grid data, the network node equation of the power system is established as,

Among them, I _x +jI _y ≡I∈C ^n×1 is the node injection current column vector; e+jf=V≡[e _k +jf _k ]∈C ^n×1 is the node voltage column vector.

Preferably, according to the network node equation and the node admittance matrix, the injection current expression of each node is obtained, including:

According to the network node equation, the node admittance matrix, node voltage column vector and node injection current column vector are denoted as,

Then the injected current expression of each node is,

In the formula, v _k is the amplitude of the node voltage, p _k and q _k are the active power and reactive power of the node, and k∈(1,n).

Preferably, a Hamilton coefficient matrix is defined, and eigenvalue decomposition is performed on the node admittance matrix and the Hamilton coefficient matrix to obtain the node voltage iteration equation, including:

The Hamilton coefficient matrix is defined as follows,

According to the Hamilton coefficient matrix, the network node equation can be expressed as:

Yx=H(t)x

The matrices Y and H(t) are decomposed as follows:

In the above formula, S ₁ and S ₂ are both symplectic and orthogonal matrices; λ ₁ and λ ₂ are the eigenvalues of matrices Y and H(t) respectively, namely

According to Yx=H(t)x to solve the voltage of each node of the power grid, the following node iteration equation is constructed:

Yx ^(k+1) =H(t)x ^(k) .

Preferably, the voltage stability criterion is established according to the node voltage iteration equation, including:

Substitute the matrices Y and H(t) obtained by eigenvalue decomposition into the iterative equation of node voltage to obtain

Thus, there are:

Therefore, the iterative equation Yx ^(k+1) = H(t)x ^(k) is absolutely convergent, and the conditional equation for the voltage solution is:

The above formula can be expressed as:

In the above conditional equation: μ _k , k∈(1, n) depends on the network structure and network parameters; τ _k , k∈(1, n) depends on the dynamic characteristics between the node injected power and the voltage amplitude; No matter in the case of small disturbance or large disturbance, if each node in the power grid satisfies the above conditional equation, the node voltage has a solution; otherwise, the node voltage state quantity will diverge, that is, there is no solution. Therefore, the above conditional equation can be regarded as the voltage stability. Criterion.

Preferably, the node admittance matrix and the eigenvalues of the Hamilton coefficient matrix are substituted into the criterion expression to obtain the final form of the voltage stability criterion, including:

作为电压稳定性判据，需要计算μ_k，k∈(1，n)、τ_k，k∈(1，n)；the conditional equation

As the voltage stability criterion, it is necessary to calculate μ _k , k∈(1,n), τ _k , k∈(1,n);

The expression for calculating τ _k is:

μ _k is the eigenvalue of the Hamilton matrix Y, and the calculation of the eigenvalue can be done by the following methods:

The Cholesky decomposition of the matrices G and -B can be obtained as follows:

In the above formula,

Using the above decomposition, we can get:

In the above formula, In is an _n -dimensional identity matrix;

Since both L ₁ and L ₂ are lower triangular matrices, the matrix η is also a lower triangular matrix, then:

If η _ii , i∈(1,n) are completely different from each other, then the matrix η can be diagonalized, then:

From this, the equation Y can be further decomposed into:

The eigenvalue decomposition of the W matrix can be obtained:

Finally get:

Based on the above derivation, the voltage stability criterion is expressed as:

Thus, the final form of the voltage stability criterion based on the eigenvalue decomposition of the Hamilton matrix is obtained.

The present application also provides a device for judging static voltage stability, including:

The node equation establishment unit is used to collect grid data and establish the network node equation of the power system;

an injection current expression obtaining unit, configured to obtain the injection current expression of each node according to the network node equation and the node admittance matrix;

The node voltage iteration equation acquisition unit is used to define the Hamilton coefficient matrix, and perform eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain the node voltage iteration equation;

a criterion establishing unit, configured to establish a voltage stability criterion according to the node voltage iteration equation;

The final criterion obtaining unit is used for substituting the node admittance matrix and the eigenvalues of the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.

The present application provides a method for judging static voltage stability. By collecting grid data, a network node equation of a power system is established; eigenvalue decomposition is performed on a node admittance matrix and a Hamilton coefficient matrix to obtain a node voltage iteration equation; The voltage iterative equation establishes the voltage stability criterion; the expression of the criterion is substituted into the node admittance matrix and the eigenvalues of the Hamilton coefficient matrix to obtain the final form of the voltage stability criterion, which solves the method efficiency of the prior art for judging voltage stability. low problem.

Description of drawings

1 is a schematic flowchart of a method for judging static voltage stability provided by the present application;

2 is a schematic diagram of detailed steps for judging static voltage stability using the method provided by the present application;

3 is a schematic diagram of a device for judging static voltage stability provided by the present application

Detailed ways

In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar promotions without departing from the connotation of the present application. Therefore, the present application is not limited by the specific implementation disclosed below.

FIG. 1 is a schematic flowchart of a method for judging static voltage stability provided by the present application. The method provided by the present application will be described in detail below with reference to FIG. 1 .

In step S101, grid data is collected, and a network node equation of the power system is established.

The collected grid data includes: node voltage amplitude, phase angle, node output active power, and reactive power.

The network node equation of the power system reflects the relationship between the voltage of each node and the injected current. The network node equation of the power system is established based on the collected grid data, which can be expressed as:

In the formula, I _x +jI _y ≡I∈C ^n×1 is the node injection current column vector; e+jf=V≡[ _ek +jf _k ]∈C ^n×1 is the node voltage column vector.

Step S102, according to the network node equation and the node admittance matrix, obtain the injection current expression of each node.

According to the network node equation, the node admittance matrix, node voltage column vector and node injection current column vector are denoted as,

Then the injected current expression of each node is:

In the above formula:

In the formula, v _k is the amplitude of the node voltage, p _k and q _k are the active power and reactive power of the node, and k∈(1,n).

Step S103 , 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.

The Hamilton coefficient matrix is defined as follows,

According to 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 symmetric real matrices, they can be decomposed by the following eigenvalues:

In the above formula, S ₁ and S ₂ are both symplectic and orthogonal matrices; λ ₁ and λ ₂ are the eigenvalues of matrices Y and H(t) respectively, namely

According to (8) Yx=H(t)x to solve the voltage of each node of the power grid, the following node iteration equation is constructed:

Yx ^(k+1) =H(t)x ^(k) . (12)

Step S104, establishing a voltage stability criterion according to the node voltage iteration equation.

Substitute the matrices Y and H(t) obtained by eigenvalue decomposition into the iterative equation of node voltage to obtain

Thus, there are:

Therefore, the iterative equation Yx ^(k+1) = H(t)x ^(k) is absolutely convergent, and the conditional equation for the voltage solution is:

The above formula can be expressed as:

In the above conditional equation: μ _k , k∈(1, n) depends on the network structure and network parameters; τ _k , k∈(1, n) depends on the dynamic characteristics between the node injected power and the voltage amplitude; No matter in the case of small disturbance or large disturbance, if each node in the power grid satisfies the above conditional equation, the node voltage has a solution; otherwise, the node voltage state quantity will diverge, that is, there is no solution. Therefore, the above conditional equation can be regarded as the voltage stability. Criterion.

Step S105: Substitute the node admittance matrix and the eigenvalues of the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.

作为电压稳定性判据，需要计算μ_k，k∈(1，n)、τ_k，k∈(1，n)；the conditional equation

As the voltage stability criterion, it is necessary to calculate μ _k , k∈(1,n), τ _k , k∈(1,n);

The expression for calculating τ _k is:

μ _k is the eigenvalue of the Hamilton matrix Y, and the calculation of the eigenvalue can be done by the following methods:

First, the following lemmas are introduced:

Lemma 1: In a power system, both matrices G and -B are real symmetric positive definite matrices. have real characteristics.

矩阵-B的特征值为

则依据Gerschgor in圆盘定理有：Note that the eigenvalues of matrix G are

The eigenvalues of matrix-B are

Then according to Gerschgor in the disc theorem:

because,

therefore,

i∈(1，n)，因此，矩阵G和-B均是实对称正定矩阵。Considering that in the power system, the matrices G and -B are both invertible matrices (full rank matrices), namely

i∈(1,n), therefore, the matrices G and -B are both real symmetric positive definite matrices.

The Cholesky decomposition of the matrices G and -B can be obtained as follows:

In the above formula,

Using the above decomposition, we can get:

In the above formula, In is an _n -dimensional identity matrix;

Since both L ₁ and L ₂ are lower triangular matrices, the matrix η is also a lower triangular matrix, then:

For lower triangular matrices, we have the following lemma:

这里，P称为X的特征向量矩阵，X_ii，i∈(1，n)是矩阵X的特征值。Lemma 2: Let the matrix X≡[X _ij ]∈R ^n×n be the lower triangular matrix. If the elements X _ii and i∈(1, n) on the diagonal of the matrix are completely different from each other, the matrix can be diagonalized, that is,

Here, P is called the eigenvector matrix of X, and X _ii , i∈(1, n) are the eigenvalues of the matrix X.

According to Lemma 2, if η _ii , i∈(1, n) are completely different from each other, then the matrix η can be diagonalized, then:

From this, the equation Y can be further decomposed into:

The eigenvalue decomposition of the W matrix can be obtained:

Finally get:

Based on the above derivation, the voltage stability criterion, Equation (17), can be expressed as:

After finishing, the voltage stability criterion is expressed as:

Thus, the final form of the voltage stability criterion based on the eigenvalue decomposition of the Hamilton matrix is obtained.

Using the method provided by this application, the detailed steps for judging the stability of static voltage are shown in Figure 2. First, basic data of the power grid is collected, and the collected data includes: node voltage amplitude, phase angle, node output active power, and reactive power ; Establish the network node equation of the power system according to the collected power grid data, and obtain the injection current expression of each node according to the network node equation and the node admittance matrix; Eigenvalue decomposition; establishing node voltage iteration equation; establishing voltage stability criterion according to the node voltage iteration equation; substituting the node admittance matrix and Hamilton coefficient matrix eigenvalues into the criterion expression; refining the voltage stability criterion expression to obtain the final form of the voltage stability criterion.

The present application also provides a device 300 for judging static voltage stability, as shown in FIG. 3 , including:

a node equation establishing unit 310, configured to collect grid data and establish a network node equation of the power system;

an injection current expression obtaining unit 320, configured to obtain 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 330 is used to define the Hamilton coefficient matrix, and perform eigenvalue decomposition on the node admittance matrix and the Hamilton coefficient matrix to obtain the node voltage iteration equation;

a criterion establishing unit 340, configured to establish a voltage stability criterion according to the node voltage iteration equation;

The final criterion obtaining unit 350 is used for substituting the node admittance matrix and the eigenvalues of the Hamilton coefficient matrix into the criterion expression to obtain the final form of the voltage stability criterion.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should The specific embodiments are modified or equivalently replaced, and any modification or equivalent replacement that does not depart from the spirit and scope of the present invention shall be included in the scope of the claims of the present 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

k is an element (1, n) as a voltage stability criterion and needs to calculate mu_k，k∈(1，n)、τ_k，k∈(1，n)；

τ_kThe expression calculated is:

μ_kis 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:

in the above formula, the first and second carbon atoms are,

the decomposition can be used for obtaining:

in the above formula, I_nIs an n-dimensional identity matrix;

due to L₁And L₂Are all lower triangular matrices, so matrix η is also a lower triangular matrix, then:

if eta_iiI ∈ (1, n) is completely different, then the matrix η can be diagonalized, then:

thus, equation Y can be further decomposed into:

and (3) carrying out eigenvalue decomposition on the W matrix to obtain:

finally, the following can be obtained:

based on the above derivation, the voltage stability criterion is expressed as:

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,

wherein, I_x+jI_y≡I∈C^n×1Is the node injection current column vector; e + jf ═ V ≡ e_k+jf_k]∈C^n×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,

the injection current at each node is expressed as,

in the formula, v_kIs the amplitude of the node voltage, p_k、q_kIs 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,

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:

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.

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

Thus, there are:

therefore, the iterative equation Yx^(k+1)＝H(t)x^(k)The absolute convergence, the conditional equation of the voltage solution is:

the above formula can be expressed as:

in the above conditional equation: mu.s_k，kE (1, n) depends on the network structure and the network parameters; tau is_kK ∈ (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

k is an element (1, n) as a voltage stability criterion and needs to calculate mu_k，k∈(1，n)、τ_k，k∈(1，n)；

τ_kThe expression calculated is:

μ_kis 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:

in the above formula, the first and second carbon atoms are,

the decomposition can be used for obtaining:

in the above formula, I_nIs an n-dimensional identity matrix;

due to L₁And L₂Are all lower triangular matrices, so matrix η is also a lower triangular matrix, then:

if eta_iiI ∈ (1, n) is completely different, then the matrix η can be diagonalized, then:

thus, equation Y can be further decomposed into:

and (3) carrying out eigenvalue decomposition on the W matrix to obtain:

finally, the following can be obtained:

based on the above derivation, the voltage stability criterion is expressed as:

thus, the final form of the voltage stability criterion based on the decomposition of eigenvalues of the Hamilton matrix is obtained.

Images