A power network feature analysis method and system considering line distributed parameters

Abstract

The application discloses a power network characteristic analysis method and system considering line distribution parameters, which can accurately analyze eigenvalues and oscillation modes of long power transmission line time delay dynamic process; compared with a Π type lumped parameter cascade RLC network simulating long power transmission system dynamic characteristics, the characteristic analysis model is established from the modeling of the distributed parameter transmission line, and time delay effects brought by the traveling wave equation are accurately established through a set of time delay algebraic equations, which is more in line with actual conditions in the electromagnetic transient process of the power network, and false oscillation caused by high-dimensional ordinary differential equations generated by the Π type cascade is avoided. In addition, the discrete characteristic polynomial method with an exponential term can reduce the order of the discrete model while keeping sparsity and accuracy, and improve the calculation efficiency of solving the generalized eigenvalue, so that the method is suitable for solving eigenvalues of large-scale power transmission network time delay dynamic characteristics.

Description

Technical Field

[0001] This invention belongs to the field of small-disturbance stability analysis technology in power systems, specifically relating to a power network characteristic analysis method and system that considers line distribution parameters. Background Technology

[0002] With the rapid development of power transmission networks and the continuous commissioning of long-distance AC and DC transmission projects, the oscillation characteristics of power systems and their influencing factors have changed significantly. In recent years, the power grid has experienced time-delay-related oscillation transient processes, posing a huge challenge to the safe operation of the power system.

[0003] Electromagnetic transient processes in power systems typically occur between microseconds and seconds. Generally, the distributed characteristics of transmission line parameters, the electromagnetic processes of dynamic components, and the response characteristics of a series of nonlinear components should be considered. While detailed modeling and characteristic analysis of the latter two are quite extensive, research on the impact of time delay effects caused by the distributed characteristics of transmission and transformation networks on the occurrence, development, and suppression of oscillations remains lacking. Traditional power network analysis often employs a cascaded Π-type lumped parameter circuit approach. This method is only suitable for electromechanical transients and lacks rigor in the characteristic analysis of electromagnetic transient processes. It can lead to spurious oscillations and inaccurate oscillation analysis, failing to meet the requirements for safe and stable power grid operation. Therefore, a modeling method for power network characteristic analysis that considers the distributed parameters of transmission lines is urgently needed.

[0004] The time delay characteristic is inherent to power transmission networks. The traveling wave equation, derived from the telegraph equations, reflects the relationship between voltage and current at the transmission line ports. The propagation delay of the time delay term depends on the transmission line length and propagation speed. Generally, a 50-kilometer transmission line will produce a time delay of 167 microseconds. The power network equations can be described by a set of time-delay algebraic equations. The calculation of its eigenvalues ​​ultimately reduces to solving the characteristic equation containing exponential terms, and there are generally infinitely many solutions in the complex plane. From the perspective of the system's asymptotic stability requirements, all eigenvalues ​​must lie in the left half-plane or on the imaginary axis. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a power network characteristic analysis method and system that considers line distribution parameters, which addresses the shortcomings of the prior art. This method and system can perform characteristic analysis of long transmission lines considering time delay under electromagnetic transient background, and solve the technical problem of inaccurate oscillation analysis of long transmission lines in power networks.

[0006] The present invention adopts the following technical solution:

[0007] A power network characteristic analysis method considering line distribution parameters includes the following steps:

[0008] S1. Obtain key parameters of long-distance transmission lines;

[0009] S2. Based on the key parameters of the long transmission line obtained in step S1, write the Dommel equivalent circuit model of the independent modulus lines, connect all the lines to form a power network using Kirchhoff's laws, transform the voltage and current modulus to the three-phase abc time domain using the inverse mode, and use a set of time-delay algebraic equations to represent the relationship between node voltage and node injected current.

[0010] S3. Use the time-delay algebraic equations obtained in step S2 to generate the characteristic polynomial;

[0011] S4. Solve the characteristic polynomial obtained in step S3 using the operator discretization method based on differential operators to obtain the rightmost eigenvalue of the dynamic characteristics of the power network. When the rightmost eigenvalue is a real number, the power network has a non-oscillating mode; when the rightmost eigenvalue is a positive real number, the power network is aperiodic and unstable; when the rightmost eigenvalue is a complex number, it indicates that the power network has an oscillating mode, with the positive real part representing an amplifying oscillation and the negative real part representing a damping oscillation. Furthermore, when the frequency of the external excitation source is equal to the oscillation frequency determined by the imaginary part, the power network resonates.

[0012] Preferably, in step S1, the key parameters of the long-distance transmission line include:

[0013] The power network topology, line length, positive-sequence unit inductance, capacitance and resistance, and zero-sequence data are used to obtain the diagonal modulus inductance and capacitance matrix through phase-mode transformation.

[0014] Preferably, step S2 specifically includes:

[0015] S201. In the modulus domain, the phase-to-phase decoupling of the three-phase coupled transmission line is transformed into three independent modulus traveling wave equations. The transmission line is divided into two lossless lines at both ends and equivalent to the Bergeron model is used. The lumped resistance of the entire line is then distributed to the beginning, end and middle ends, and the intermediate variables are eliminated to obtain the Dommel model in the three independent modulus domains.

[0016] S202. Using Kirchhoff's laws and the network topology represented by the adjacency matrix, all equations are uniformly expressed in a set of time-delay algebraic equations, reflecting the relationship between node voltage and total injected current at the node. Inverse phase-mode transformation is used to represent the electrical quantities in the modulus domain as three-phase abc time-domain electrical quantities.

[0017] More preferably, in step S201, the Dommel model in the modulus domain is specifically as follows:

[0018]

[0019]

[0020] B M =Z M A M

[0021] Among them, Y M Let A be the modulus admittance matrix. M B is the coefficient matrix before the voltage delay term. M Z is the sparse matrix before the current delay term. M,i i = 1, 2, 3 are elements in the modified modulus wave impedance matrix, γ i i = 1, 2, 3 are the elements in the resistance correction coefficient, Z M To correct the modulus wave impedance matrix.

[0022] More preferably, in step S202, the Dommel model in the three-phase abc time domain is specifically as follows:

[0023] i(t)=Yu(t)+Au(t-τ)+Bi(t-τ)

[0024] Where Y is the admittance matrix after inverse phase transformation, A is the coefficient matrix before the voltage delay term after inverse phase transformation, B is the coefficient matrix before the current delay term after inverse phase transformation, i(t) is the current passing through both sides of the branch, u(t) is the voltage at both ends of the line, i(t-τ) is the historical current passing through both sides of the branch before time period τ, u(t) is the voltage at both ends of the branch, u(t-τ) is the historical voltage at both ends of the branch before time period τ, t is time, and τ is the transmission line propagation time.

[0025] More preferably, for grounding branches, an M×N block correlation matrix E is defined. f and E t E represents the mapping from node numbers to the beginning and end points of each branch. f (i,j) = I if and only if the i-th branch starts at the j-th node; E t (i,j) = I if and only if the i-th branch ends at the j-th node;

[0026] Suppose the system has a total of W components, and the k-th component injects a current vector i into the system. k The correlation matrix to the system node vector is L k L k (i,j) = 1 if and only if i k The j-th component is injected into node i, and the node's KCL equation is:

[0027]

[0028] Preferably, in step S3, the characteristic polynomial is specifically:

[0029] (eλτ +γ)(e λτ -1)=0

[0030] Among them, e λτ The exponential term of the characteristic equation is due to the time delay effect, and γ is the resistance correction coefficient.

[0031] Preferably, step S4 specifically includes:

[0032] S401. Select an Nth-order Chebyshev interpolation polynomial within the time delay interval, and use key interpolation points to interpolate the delay exponent term, transforming the exponent term into a conventional N+1 linear equation system.

[0033] S402. Using boundary conditions, the characteristic polynomial containing exponential terms obtained in step S401 is transformed into a problem of solving the generalized eigenvalues ​​of a square matrix, which efficiently solves the rightmost eigenvalues ​​while preserving the sparsity of the original square matrix.

[0034] More preferably, the generalized eigenvalues ​​are calculated as follows:

[0035]

[0036] For the case where the unit resistance is not zero, its discretized model is expressed as:

[0037]

[0038] Among them, Π p Let Γ be a sparse matrix, Γ be an auxiliary matrix for eigenanalysis, and v be an eigenvector. It is a vector of all 1s. Let γ be a vector with alternating distributions of 1 and -1, c1 and c2 be the polynomial coefficients introduced by interpolation, and γ be the resistance correction coefficient.

[0039] Secondly, embodiments of the present invention provide a power network characteristic analysis system that considers line distribution parameters, including:

[0040] The parameter module is used to obtain key parameters of long-distance transmission lines.

[0041] The transformation module, based on the key parameters of the long transmission line obtained by the parameter module, writes the Dommel equivalent circuit model of the independent modulus line, uses Kirchhoff's laws to connect all the lines to form a power network, uses the inverse mode to transform the voltage and current modulus to the three-phase abc time domain, and uses a set of time-delay algebraic equations to represent the relationship between node voltage and node injected current.

[0042] The generation module uses the time-delay algebraic equations obtained from the transformation module to generate the characteristic polynomial;

[0043] The analysis module uses a discretization method based on differential operators to solve the characteristic polynomial obtained from the generation module, and obtains the rightmost eigenvalue of the dynamic characteristics of the power network. When the rightmost eigenvalue is a real number, the power network has a non-oscillating mode; when the rightmost eigenvalue is a positive real number, the power network is aperiodic and unstable; when the rightmost eigenvalue is a complex number, it indicates that the power network has an oscillating mode, with the positive real part representing increasing oscillation and the negative real part representing decaying oscillation. Furthermore, when the frequency of the external excitation source is equal to the oscillation frequency determined by the imaginary part, the power network resonates.

[0044] Thirdly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the power network characteristic analysis method considering line distribution parameters described above.

[0045] Fourthly, embodiments of the present invention provide an electronic device including a computer program, which, when executed by the electronic device, implements the steps of the power network characteristic analysis method considering line distribution parameters described above.

[0046] Compared with the prior art, the present invention has at least the following beneficial effects:

[0047] A power network characteristic analysis method considering distributed line parameters is proposed, capable of accurately analyzing the eigenvalues ​​and oscillation modes of the time-delay dynamic process of long-distance transmission lines. Compared to the method of simulating the dynamic characteristics of long-distance power systems using Π-type cascaded lumped-parameter RLC networks, the characteristic analysis model proposed in this invention starts from the modeling of distributed-parameter transmission lines and accurately establishes the time-delay effect caused by the traveling wave equation through a set of time-delay algebraic equations. This model better reflects the actual situation of electromagnetic transient processes in power networks and avoids spurious oscillations caused by the high-dimensional ordinary differential equations generated by Π-type cascades. The discretized characteristic polynomial method with exponential terms proposed in this invention can reduce the order of the discretized model and improve the computational efficiency of solving generalized eigenvalues ​​while maintaining sparsity and accuracy. Therefore, the method of this invention is very suitable for solving the eigenvalues ​​of the time-delay dynamic characteristics of large-scale transmission networks.

[0048] Furthermore, a Dommel model considering the distributed parameter characteristics of transmission lines in the modulus domain was constructed, which is the fundamental model for describing the dynamic characteristics of long-distance transmission lines in this invention. Compared with the conventional Π-type cascaded equivalent circuit, this model considers the distributed characteristics of inductance and capacitance and the time delay effects they bring. Through phase mode transformation, this model transforms multi-conductor transmission lines that are electromagnetically interconnected in phasor into multiple independent moduli, which can accurately describe the dynamic characteristics of long-distance transmission lines and avoid the spurious oscillations caused by the Π-type cascaded lumped parameter model, greatly improving the accuracy of the model in analyzing the dynamic characteristics of power networks. Establishing a set of time-delay algebraic equations for the entire power network after adopting wave processes is a key step in the power network characteristic analysis of this invention. The electromagnetic transient process of the power network reflects the relationship between node injected current, historical current sources, and node voltage. Due to the existence of time delay terms, this set of algebraic equations actually reflects the dynamic process of electrical quantities in an infinite-dimensional space. Therefore, based on the dynamic characteristic equations of long-distance transmission lines, constructing a set of network algebraic equations containing time-delay dynamic processes helps to further analyze the characteristics and oscillation modes of power networks.

[0049] Furthermore, writing out the characteristic polynomial of the time-delay algebraic equation system is a necessary step for the subsequent calculation of key eigenvalues ​​of the low-order discretized model, providing a mathematical model for network eigenvalue calculation.

[0050] Furthermore, the core algorithm of this invention involves selecting Chebyshev interpolation polynomials to interpolate the time delay exponent term, making the transcendental function approximately equal to a system of linear equations at the interpolation points. By selecting the Chebyshev polynomial poles as interpolation points within a fixed interval, the calculated eigenvalues ​​achieve extremely high accuracy, reaching [a certain level]. N represents the number of interpolation points; furthermore, this method can significantly reduce the order of the discretization model, making it possible to calculate the eigenvalues ​​of large-scale distributed parameter transmission networks.

[0051] Furthermore, constructing a sparse, low-order discretized eigenvalue calculation model for the entire power network is a key step in calculating eigenvalues ​​in this invention. Based on the obtained discretized model of a single time-delay variable, a discrete matrix model of the entire transmission network is established using boundary conditions and the generated characteristic polynomial. This model ensures the sparsity of the discrete matrix, facilitating computer solving for generalized eigenvalues; at the same time, it is simpler and easier to construct, making it convenient to build a discrete model of time-delay dynamics for large-scale transmission networks.

[0052] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0053] In summary, the eigenvalue analysis of the time-delay characteristics of power networks during electromagnetic transient processes more accurately reflects the dynamic characteristics of power networks compared to the original algebraic equation eigenvalue analysis of cascaded Π-type lumped circuits; obtaining key electrical data of long transmission lines is a necessary condition for performing power network characteristic analysis.

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0056] Figure 2 This is a schematic diagram of the Dommel model of the present invention;

[0057] Figure 3 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0058] Figure 4 This is a block diagram of a chip according to an embodiment of the present invention;

[0059] Figure 5 The following is an example analysis of the results when the number of discretized segments is 5, where (a) shows the approximate eigenvalue distribution of the Bergeron model and (b) shows the approximate eigenvalue distribution of the Dommel model.

[0060] Figure 6 The following is an example analysis of the results when the number of discretized segments is 10, where (a) shows the approximate eigenvalue distribution of the Bergeron model and (b) shows the approximate eigenvalue distribution of the Dommel model.

[0061] Figure 7 The following is an example analysis of the results when the number of discretized segments is 20, where (a) shows the approximate eigenvalue distribution of the Bergeron model and (b) shows the approximate eigenvalue distribution of the Dommel model. Detailed Implementation

[0062] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0063] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0064] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0065] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0066] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0067] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0068] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0069] This invention provides a power network characteristic analysis method that considers line distributed parameters. The equivalent circuit constructed based on the traveling wave equation fully considers the influence of distributed capacitance, inductance, and segmented lumped resistance of long transmission lines. By selecting an Nth-order Chebyshev polynomial, while preserving sparsity, the characteristic polynomial of the time-delay algebraic equation is discretized to obtain a finite number of approximate state variables, which efficiently calculates the characteristic values ​​of the power network and obtains the oscillation mode that takes into account the characteristics of the power network distributed parameters. This allows for accurate and efficient calculation of some key characteristic values ​​of the power network.

[0070] Please see Figure 1 The present invention provides a power network characteristic analysis method considering line distribution parameters, comprising the following steps:

[0071] S1. Obtain key parameters of long-distance transmission lines;

[0072] S101. Obtain input data for the equivalent transmission line model from relevant departments;

[0073] Key data for constructing an equivalent transmission line model include: power network topology, line length, positive-sequence unit inductance, capacitance and resistance, and corresponding zero-sequence data. The diagonal modulus inductance and capacitance matrices are obtained using phase-mode transformation.

[0074] S102. After obtaining the above information from relevant departments, conduct power network characteristic analysis considering line distribution parameters, perform phase mode transformation on the above raw data, and transform the mutually coupled self-inductance and mutual inductance matrices into independent modulus diagonal matrices in the modulus domain.

[0075] Generate the modulus parameter matrices, namely the modulus inductance matrix, capacitance matrix, and resistance matrix:

[0076]

[0077] Where L / C / R are the original inductance parameter matrix and capacitance parameter matrix per unit length, symmetrical full matrix; L M / C M / R M T represents the modulus inductance and capacitance parameter matrices per unit length, in a diagonal matrix; u / T i This is the modulus transformation matrix of voltage phasors and current phasors on a multi-conductor line;

[0078] Generate the modulus wave impedance matrix, correct the modulus wave impedance matrix, and the resistance correction coefficient:

[0079]

[0080]

[0081]

[0082] Where l is the line length; ZC i i = 1, 2, 3 are elements in the modulus wave impedance matrix; Z M,i i = 1, 2, 3 are elements in the modified modulus wave impedance matrix; γ i i = 1, 2, 3 are the elements in the resistance correction coefficient.

[0083] S2. Write the Dommel equivalent circuit model of the independent modulus lines, and use Kirchhoff's laws to connect all the lines to form a power network. Use inverse mode transformation to the three-phase abc time domain, and use a set of time-delay algebraic equations to represent the relationship between node voltage and node injected current.

[0084] S201. In the modulus domain, the phase-to-phase decoupling of a three-phase coupled transmission line is transformed into three independent modulus traveling wave equations. The transmission line is divided into two lossless lines at both ends and equivalent to the Bergeron model is used. Then, the lumped resistance of the entire line is distributed to the beginning, end, and middle ends, eliminating intermediate variables, resulting in three independent Dommel models in the modulus domain.

[0085] S2011. Construct a Dommel model for a single-phase line;

[0086] The Dommel model is also a distributed parameter model that does not consider the frequency-varying effects of parameters. Its modeling method is as follows: First, the transmission line is divided into two lossless segments, each represented by an equivalent Bergeron model. Then, the lumped resistance of the entire line segment is divided into four parts and connected to three points: one-quarter is connected in series at each end, and the other half is connected in series in the middle. The starting, middle, and ending points of the line are labeled k, s, and m, respectively. A schematic diagram is attached. Figure 2 As shown, its equation form is as follows:

[0087]

[0088] Where τ is the time delay of the long transmission line, I k (t-τ) and I m (t-τ) represent the historical current sources, and their expressions are as follows:

[0089]

[0090] Equation (6) can be represented using a matrix-based unified representation as follows:

[0091]

[0092] S2012. Construct the Dommel model of a single three-phase line in the modulus domain.

[0093] The phase-mode transformation matrix decouples the coupled three-phase transmission lines. In the modulus domain, the mathematical model of the three-phase conductors can be regarded as the mathematical model of three isolated single-phase conductors. The relationship between the three-phase voltage and current and the modulus voltage and current is taken as follows:

[0094]

[0095] Voltage and current modulus in the modulus domain and The relationship between the components can be described as follows:

[0096]

[0097] Among them, Y M Let A be the modulus admittance matrix. M B is the coefficient matrix before the voltage delay term. M The sparse matrix before the current delay term is expressed in the following forms:

[0098]

[0099]

[0100] B M =Z M A M (12)

[0101] S202. Using Kirchhoff's laws and the network topology represented by the adjacency matrix, all equations are uniformly expressed in a set of time-delay algebraic equations, reflecting the relationship between node voltage and total injected current at the node. Inverse phase-mode transformation is used to represent the electrical quantities in the modulus domain as three-phase abc time-domain electrical quantities.

[0102] Establish a Dommel model of the power network in the three-phase abc time domain. For a single line, perform inverse phase-mode transformation on voltage and current, and we have:

[0103]

[0104] Substituting the above transformation into step S201, we obtain the Dommel model in the three-phase abc time domain:

[0105] i(t)=Yu(t)+Au(t-τ)+Bi(t-τ) (14)

[0106] in, Based on this, consider a system with N nodes and M branches, where each branch connects its starting node f to its ending node t.

[0107] For the grounding branch, f = 0 or t = 0. Therefore, we define an M×N block incidence matrix E. f and Et These are the mappings from node numbers to the beginning and end of each branch, i.e., E f (i,j) = I if and only if the i-th branch starts at the j-th node, and E t (i,j) = I if and only if the i-th branch ends at the j-th node. Assume the system has W components in total, and the k-th component injects a current vector i into the system. k The correlation matrix to the system node vector is L k L k (i,j) = 1 if and only if i k If the j-th component is injected into node i, then the node KCL equation can be written as:

[0108]

[0109] S3. Using the time-delay algebraic equations obtained in step S2, generate an exact characteristic polynomial. The constant time delay term is generally described as an exponential term in the characteristic polynomial, which makes the characteristic equation a transcendental equation with infinitely many solutions in the complex plane.

[0110] Taking a single-phase line as an example, let's first look at the case where the line's distributed resistance is 0. In this case, it simplifies to a special case of the Bergeron model, and its characteristic polynomial is written as:

[0111]

[0112] The analysis of the theoretical eigenvalues ​​of equation (16) is actually a problem of finding the preimage on the complex plane. Let the eigenvalues ​​of the system be λ = x + yi, then according to the characteristic polynomial, we have:

[0113]

[0114] Since the imaginary parts on both sides of equation (17) are 0, a periodicity condition holds.

[0115] yτ p =kπ,k=0,±1,±2,… (18)

[0116] When yτ p When =(2k+1)π, k=0,±1,±2,…, If the value is never zero, then such cases need to be removed from the solution set of eigenvalues; therefore, when yτ p When =2kπ, k=0,±1,±2,…, it can be known from the fact that the real part is 0. In summary, the eigenvalue solution set of equation (16) must be a pure imaginary number with a period of 2π, that is:

[0117]

[0118] If the distributed resistance of the line is not zero, the model in step 2 degenerates into a special case of the Dommel model, whose characteristic polynomial is written as:

[0119]

[0120] To further simplify:

[0121] (e λτ +γ)(e λτ -1)=0 (21)

[0122] Solving the above equation, we can find that the distribution of the characteristic roots is:

[0123]

[0124] S4. The characteristic polynomial of the time-delay system is solved by using the operator discretization method based on differential operators, and the rightmost eigenvalue of the dynamic characteristics of the power network is obtained.

[0125] S401. Select an Nth-order Chebyshev interpolation polynomial within the time delay interval, and use key interpolation points (the roots of the Chebyshev polynomial) to interpolate the delay exponential term, transforming the exponential term into a conventional N+1 linear equation system.

[0126] An Nth-order Chebyshev polynomial is selected to fit the exponent term. Taking equation (16) as an example, for e λτ p v is in the interval [-τ, 0], and its coefficient matrix satisfies:

[0127] λΠ p c p =Γc p (twenty three)

[0128] Where Γ=[0 I N×N ];c p These are the polynomial coefficients introduced by interpolation; Π p ∈R N×(N+1) It is a sparse matrix, where the non-zero elements are:

[0129]

[0130] And because Let v and v be the boundary values ​​of the equation t=0, then:

[0131]

[0132]

[0133] S402. Using boundary conditions, the characteristic polynomial containing exponential terms obtained in step S401 is transformed into a problem of solving the generalized eigenvalues ​​of a square matrix, which efficiently solves the rightmost eigenvalues ​​while preserving the sparsity of the original square matrix.

[0134] The generalized eigenvalues ​​are calculated as follows:

[0135]

[0136] This discretization model is simple to construct and maintains the sparsity of the matrix.

[0137] For the case where the unit resistance is not zero, its discretized model is expressed as:

[0138]

[0139] In another embodiment of the present invention, a power network feature analysis system considering line distribution parameters is provided. This system can be used to implement the above-mentioned power network feature analysis method considering line distribution parameters. Specifically, the power network feature analysis system considering line distribution parameters includes a parameter module, a transformation module, a generation module, and an analysis module.

[0140] Among them, the parameter module obtains key parameters of long-distance transmission lines;

[0141] The transformation module, based on the key parameters of the long transmission line obtained by the parameter module, writes the Dommel equivalent circuit model of the independent modulus line, uses Kirchhoff's laws to connect all the lines to form a power network, uses the inverse mode to transform the voltage and current modulus to the three-phase abc time domain, and uses a set of time-delay algebraic equations to represent the relationship between node voltage and node injected current.

[0142] The generation module uses the time-delay algebraic equations obtained from the transformation module to generate the characteristic polynomial;

[0143] The analysis module uses a discretization method based on differential operators to solve the characteristic polynomial obtained from the generation module, and obtains the rightmost eigenvalue of the dynamic characteristics of the power network. When the rightmost eigenvalue is a real number, the power network has a non-oscillating mode; when the rightmost eigenvalue is a positive real number, the power network is aperiodic and unstable; when the rightmost eigenvalue is a complex number, it indicates that the power network has an oscillating mode, with the positive real part representing increasing oscillation and the negative real part representing decaying oscillation. Furthermore, when the frequency of the external excitation source is equal to the oscillation frequency determined by the imaginary part, the power network resonates.

[0144] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of a power network characteristic analysis method considering line distribution parameters, including:

[0145] Key parameters of long-distance transmission lines are obtained. Based on these parameters, Dommel equivalent circuit models of independent modal lines are constructed. Kirchhoff's laws are used to connect all lines to form a power network. Voltage and current moduli are transformed to the three-phase abc time domain using inverse-phase mode, and the relationship between node voltage and node injected current is represented by a set of time-delay algebraic equations. Characteristic polynomials are generated using the obtained time-delay algebraic equations. The characteristic polynomials are solved using a solution operator discretization method based on differential operators. The rightmost eigenvalue of the power network's dynamic characteristics is obtained. When the rightmost eigenvalue is real, the power network exhibits non-oscillatory modes. When the rightmost eigenvalue is positive real, the power network is aperiodic and unstable. When the rightmost eigenvalue is complex, the power network exhibits oscillatory modes, with positive real parts representing amplified oscillations and negative real parts representing damped oscillations. Furthermore, when the frequency of the external excitation source equals the oscillation frequency determined by the imaginary part, the power network resonates.

[0146] In another embodiment of the present invention, a storage medium is also provided, specifically a computer-readable storage medium (memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0147] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the power network characteristic analysis method considering line distribution parameters in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps:

[0148] Key parameters of long-distance transmission lines are obtained. Based on these parameters, Dommel equivalent circuit models of independent modal lines are constructed. Kirchhoff's laws are used to connect all lines to form a power network. Voltage and current moduli are transformed to the three-phase abc time domain using inverse-phase mode, and the relationship between node voltage and node injected current is represented by a set of time-delay algebraic equations. Characteristic polynomials are generated using the obtained time-delay algebraic equations. The characteristic polynomials are solved using a solution operator discretization method based on differential operators. The rightmost eigenvalue of the power network's dynamic characteristics is obtained. When the rightmost eigenvalue is real, the power network exhibits non-oscillatory modes. When the rightmost eigenvalue is positive real, the power network is aperiodic and unstable. When the rightmost eigenvalue is complex, the power network exhibits oscillatory modes, with positive real parts representing amplified oscillations and negative real parts representing damped oscillations. Furthermore, when the frequency of the external excitation source equals the oscillation frequency determined by the imaginary part, the power network resonates.

[0149] Please see Figure 3The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the fluid composition calculation method in the reservoir stimulation wellbore of this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the fluid composition calculation system in the reservoir stimulation wellbore of this embodiment. To avoid repetition, these details are not elaborated here.

[0150] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 3 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0151] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0152] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0153] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0154] Please see Figure 4 The terminal device is a chip. In this embodiment, the chip 600 includes a processor 622, which may be one or more, and a memory 632 for storing computer programs executable by the processor 622. The computer program stored in the memory 632 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processor 622 may be configured to execute the computer program to perform the generalizable monocular absolute depth map estimation method described above.

[0155] Additionally, chip 600 may also include a power supply component 626 and a communication component 650. The power supply component 626 can be configured to perform power management of chip 600, and the communication component 650 can be configured to enable communication of chip 600, such as wired or wireless communication. Furthermore, chip 600 may also include an input / output interface 658. Chip 600 can operate on an operating system stored in memory 632.

[0156] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0157] Case Analysis

[0158] To verify the effectiveness of the method proposed in this invention, this case study selects a single transmission line and compares the accuracy of the Bergeron model and the Dommel model using the method proposed in this invention with the true feature values ​​when the Chebyshev discretization number is 5, 10, and 20.

[0159] When N=5, such as Figure 5 As shown, after removing the pseudo-eigenvalues, the approximate eigenvalues ​​generated by the method of the present invention basically coincide with the true eigenvalues ​​under low-frequency conditions. This method can be used to analyze the oscillation of power networks under low-frequency conditions.

[0160] When N=10, such as Figure 6As shown, after removing the pseudo-eigenvalues, the approximate eigenvalues ​​generated by the method of the present invention basically coincide with the true eigenvalues ​​under medium and low frequency conditions, and the error between them and the true eigenvalues ​​is greatly reduced. The method of this invention is used to analyze the oscillation of power networks under medium and low frequency conditions.

[0161] When N=20, such as Figure 7 As shown, after removing pseudo-eigenvalues, the approximate eigenvalues ​​generated by the method of this invention highly coincide with the true eigenvalues ​​under high, medium and low frequency conditions. This method can be used to analyze the oscillation of the full-frequency power network under the premise of a high number of discretization segments.

[0162] Based on the above experimental results, given the model, in longitudinal comparison, the more Chebyshev interpolation points there are, the higher the order of the system and the more accurate the fit with the true key feature values. At the same time, the discretized model will generate pseudo feature values ​​at high frequencies. These pseudo feature values ​​are not key feature values ​​and can be ignored.

[0163] In summary, this invention provides a power network characteristic analysis method and system considering distributed line parameters, capable of accurately analyzing the eigenvalues ​​and oscillation modes of the time-delay dynamic process of long-distance transmission lines. Compared to the method of simulating the dynamic characteristics of long-distance power systems using Π-type cascaded lumped-parameter RLC networks, the characteristic analysis model starts from the modeling of distributed-parameter transmission lines and accurately establishes the time-delay effect caused by the traveling wave equation through a set of time-delay algebraic equations. This model better reflects the actual situation of electromagnetic transient processes in power networks and avoids spurious oscillations caused by the high-dimensional ordinary differential equations generated by Π-type cascades. Furthermore, the discretization method using characteristic polynomials with exponential terms can reduce the order of the discretized model while maintaining sparsity and accuracy, improving the computational efficiency for solving generalized eigenvalues, and is suitable for solving the eigenvalues ​​of the time-delay dynamic characteristics of large-scale transmission networks.

[0164] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0165] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0166] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0167] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0168] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0169] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0170] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0171] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can 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, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0172] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0173] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0174] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A power network characteristic analysis method considering line distribution parameters, characterized in that, Includes the following steps: S1. Obtain key parameters of long-distance transmission lines; S2. Based on the key parameters of the long transmission line obtained in step S1, write the Dommel equivalent circuit model of the independent modulo lines. Use Kirchhoff's laws to connect all the lines to form a power network. Use inverse mode to transform the voltage and current moduli to the three-phase abc time domain, and use a system of time-delay algebraic equations to represent the relationship between node voltage and node injected current, specifically: S201. In the modulus domain, the phase-to-phase decoupling of the three-phase coupled transmission line is transformed into three independent modulus traveling wave equations. The transmission line is divided into two lossless lines at both ends and equivalent to the Bergeron model is used. The lumped resistance of the entire line is then distributed to the beginning, end and middle ends, and the intermediate variables are eliminated to obtain the Dommel model in the three independent modulus domains. S202. Using Kirchhoff's laws and the network topology represented by the adjacency matrix, all equations are uniformly expressed in the time-delay algebraic equation system, reflecting the relationship between node voltage and total injected current at the node, and the electrical quantities in the modulus domain are expressed as three-phase abc time-domain electrical quantities by using inverse phase modulus transformation. S3. Use the time-delay algebraic equations obtained in step S2 to generate the characteristic polynomial; S4. Solve the characteristic polynomial obtained in step S3 using the operator discretization method based on differential operators to obtain the rightmost eigenvalue of the dynamic characteristics of the power network. When the rightmost eigenvalue is a real number, the power network has a non-oscillating mode; when the rightmost eigenvalue is a positive real number, the power network is aperiodic and unstable; when the rightmost eigenvalue is a complex number, it indicates that the power network has an oscillating mode, with the positive real part representing amplified oscillation and the negative real part representing damped oscillation. Furthermore, when the frequency of the external excitation source is equal to the oscillation frequency determined by the imaginary part, the power network resonates.

2. The power network characteristic analysis method considering line distribution parameters according to claim 1, characterized in that, In step S1, the key parameters of the long-distance transmission line include: The power network topology, line length, positive-sequence unit inductance, capacitance and resistance, and zero-sequence data are used to obtain the diagonal modulus inductance and capacitance matrix through phase-mode transformation.

3. The power network characteristic analysis method considering line distribution parameters according to claim 1, characterized in that, In step S201, the Dommel model in the modulus domain is specifically as follows: in, The modulus admittance matrix, This is the coefficient matrix before the voltage delay term. The sparse matrix before the current delay term. To correct the elements in the modulus wave impedance matrix, These are elements in the resistance correction factor. To correct the modulus wave impedance matrix.

4. The power network characteristic analysis method considering line distribution parameters according to claim 1, characterized in that, In step S202, the Dommel model in the three-phase abc time domain is as follows: in, The admittance matrix after inverse phase mode transformation. This is the coefficient matrix before the voltage delay term after inverse phase-mode transformation. This is the coefficient matrix before the current delay term after inverse phase transformation. The current flowing through both sides of the branch. The voltage at both ends of the line. for Historical currents passing through both sides of the branch line before the specified time period. The voltage across the branch is... for Historical voltage at both ends of the branch before the time period For time, This refers to the propagation time of the transmission line.

5. The power network characteristic analysis method considering line distribution parameters according to claim 4, characterized in that, For grounding branches, the definition is... Block association matrix and These represent the mappings from node numbers to the beginning and end points of each branch. If and only if the first i branch road j Each node is its starting point; If and only if the first i branch road j Each node is its end; Suppose the system has a total of W components, and the first... k Each component injects a current vector into the system. The correlation matrix to the system node vector is , If and only if The j Each component is injected into the node. i The node KCL equations are: 。 6. The power network characteristic analysis method considering line distribution parameters according to claim 1, characterized in that, In step S3, the characteristic polynomial is specifically: in, The exponential term of the characteristic equation is due to the time delay effect. This is the resistance correction factor.

7. The power network characteristic analysis method considering line distribution parameters according to claim 1, characterized in that, Step S4 is as follows: S401. Select an Nth-order Chebyshev interpolation polynomial within the time delay interval, and use key interpolation points to interpolate the delay exponent term, transforming the exponent term into a conventional N+1 linear equation system. S402. Using boundary conditions, the characteristic polynomial containing exponential terms obtained in step S401 is transformed into a problem of solving the generalized eigenvalues ​​of a square matrix, which efficiently solves the rightmost eigenvalues ​​while preserving the sparsity of the original square matrix.

8. The power network characteristic analysis method considering line distribution parameters according to claim 7, characterized in that, The generalized eigenvalues ​​are calculated as follows: For the case where the unit resistance is not zero, its discretized model is expressed as: in, For sparse arrays, For feature analysis auxiliary matrix, For feature vectors, It is a vector of all 1s. A vector with alternating distributions of 1 and -1. and These are the polynomial coefficients introduced by interpolation. This is the resistance correction factor.

9. A power network characteristic analysis system considering line distribution parameters, characterized in that, include: The parameter module is used to obtain key parameters of long-distance transmission lines. The transformation module, based on the key parameters of the long transmission line obtained from the parameter module, writes Dommel equivalent circuit models of the independent modulo lines. Kirchhoff's laws are used to connect all the lines to form a power network. The voltage and current moduli are transformed to the three-phase abc time domain using an inverse-phase mode, and a system of time-delay algebraic equations is used to represent the relationship between node voltage and node injected current. Specifically: In the modulus domain, the phase-to-phase decoupling of the three-phase coupled transmission line is transformed into three independent modulus traveling wave equations. The transmission line is divided into two lossless lines at both ends and equivalent to the Bergeron model is used. The lumped resistance of the entire line is then distributed to the beginning, end and middle ends, and the intermediate variables are eliminated to obtain the Dommel model in the three independent modulus domains. Using Kirchhoff's laws and the network topology represented by the adjacency matrix, all equations are uniformly expressed in a set of time-delay algebraic equations, reflecting the relationship between node voltage and total node injection current. Inverse phase-mode transformation is used to represent electrical quantities in the modulus domain as three-phase abc time-domain electrical quantities. The generation module uses the time-delay algebraic equations obtained from the transformation module to generate the characteristic polynomial; The analysis module uses a discretization method based on differential operators to solve the characteristic polynomial obtained from the generation module, and obtains the rightmost eigenvalue of the dynamic characteristics of the power network. When the rightmost eigenvalue is a real number, the power network has a non-oscillating mode; when the rightmost eigenvalue is a positive real number, the power network is aperiodic and unstable; when the rightmost eigenvalue is a complex number, it indicates that the power network has an oscillating mode, with the positive real part representing increasing oscillation and the negative real part representing decaying oscillation. Furthermore, when the frequency of the external excitation source is equal to the oscillation frequency determined by the imaginary part, the power network resonates.

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