A continuous-time modeling method and device for double high-power system node frequency

Abstract

This invention discloses a continuous-time modeling method and apparatus for node frequencies in high-voltage, high-efficiency power systems. The method first constructs a node admittance matrix based on power system network parameters, then simplifies the network by incorporating generator transient characteristics, thereby building a dynamic model of node frequency response. Next, piecewise Bernstein polynomials are introduced to represent relevant variables, and their integral mapping properties are used to transform differential equations into algebraic equations. Subsequently, constraint equations are constructed and piecewise continuity conditions are added to form a complete constraint system, and the interpolation coefficients are obtained through optimized solutions. Finally, basis functions are used to reconstruct the continuous frequency variation trajectory of all nodes, achieving a dynamic representation of node frequency response. This invention solves the problems of existing technologies, such as difficulty in characterizing the spatial differences in node frequencies, errors in discrete numerical integration, and the inability to achieve continuous-time modeling, thus failing to meet the requirements for refined frequency analysis.

Description

Technical Field

[0001] This invention relates to the field of dynamic modeling technology for power system node frequencies, and specifically to a continuous-time modeling method and apparatus for node frequencies in a high-voltage, high-efficiency power system. Background Technology

[0002] With the widespread integration of high-proportion renewable energy into the power system, the traditional grid structure dominated by synchronous generators has undergone profound changes. The system inertia distribution exhibits significant imbalances, the topology is becoming increasingly complex, and differences in frequency regulation resource allocation and response capabilities across regions are becoming increasingly prominent. Against this backdrop, the dynamic frequency characteristics of the power system have shifted from a traditional single inertial center frequency model to a node-level frequency response model with distinct spatial distribution characteristics. After experiencing load disturbances and fluctuations in renewable energy output, nodes in different regions exhibit significant differences in frequency offset amplitude, trough values, and recovery trajectories. Currently, existing frequency analysis methods primarily focus on the overall response of the system's inertial center frequency. Related dynamic simulations generally employ numerical integration methods based on discrete time steps, obtaining time-series data of the system frequency by discretizing and solving the frequency dynamic differential equations, thus providing support for power system frequency stability assessment and control strategy formulation.

[0003] However, existing technologies still have many problems to be solved in practical applications: On the one hand, existing methods focus on the overall frequency response of the system, making it difficult to accurately depict the independent frequency change trajectory of each node and failing to fully reflect the spatial differences in frequency dynamics. This may lead to the underestimation or misjudgment of the risk of local node frequency exceeding limits, posing a hidden danger to the safe and stable operation of the power system. On the other hand, discrete-time step numerical integration methods are limited by step size accuracy, making it difficult to accurately capture the dynamic process of rapid frequency changes in the early stage of disturbances. They are also prone to calculation errors due to step size accumulation. Furthermore, they do not essentially form a complete frequency response model expression at the continuous time level, making it impossible to achieve refined analysis of continuous dynamic frequency at the node level. This makes it difficult to meet the needs of power systems for accurate assessment of frequency characteristics in the context of high proportion of renewable energy access.

[0004] Therefore, there is an urgent need for a continuous-time modeling method for the node frequencies of high-voltage power systems to solve the problems that existing technologies cannot adequately characterize the spatial differences in node frequencies, have errors in discrete numerical integration and cannot achieve continuous-time modeling, and thus cannot meet the requirements for refined frequency analysis. Summary of the Invention

[0005] To address these issues, this invention provides a continuous-time modeling method and apparatus for node frequencies in high-energy-density power systems. This method solves the problems of existing methods being unable to characterize the spatial differences in node frequencies, having errors in discrete numerical integration, and being unable to achieve continuous-time modeling under conditions of high-proportion renewable energy access, thus failing to meet the requirements for refined frequency analysis.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a continuous-time modeling method for node frequencies in a dual-high-voltage power system, characterized in that it includes:

[0007] Based on the network parameters of the power system, a node admittance matrix of the power system is constructed; the node admittance matrix of the power system is simplified by network equivalence according to the transient characteristics of the generator to obtain a simplified node admittance matrix; based on the simplified node admittance matrix, a dynamic model of the node frequency response of the power system is constructed.

[0008] Piecewise Bernstein polynomials are introduced in the continuous time domain to represent load disturbances, generator output, and various state variables as functions in Bernstein polynomial form; using the integral mapping property of Bernstein polynomials, the differential equations in the dynamic model of the node frequency response are transformed into algebraic equations.

[0009] Based on the mathematical properties of the algebraic equations and Bernstein interpolation coefficients, nodal frequency response constraint equations are constructed; based on the nodal frequency response constraint equations, continuity constraints between segments are added to form a complete constraint system; by optimizing the complete constraint system, the interpolation coefficients of each nodal frequency are obtained.

[0010] Based on the interpolation coefficients of each node frequency, combined with Bernstein polynomial basis functions, the continuous frequency change trajectory of all nodes in the power system is reconstructed, and the dynamic response process of node frequency is characterized.

[0011] As a preferred scheme for continuous-time modeling of node frequencies in a high-voltage power system, during the process of network simplification of the power system node admittance matrix based on the transient characteristics of the generator, Kron simplification is performed on the power system node admittance matrix based on the transient reactance parameters of the generator; the potential nodes within the generator are equivalently embedded into the power system node admittance matrix to obtain an equivalent admittance matrix containing only the potential nodes within the generator and the load nodes, which is the simplified node admittance matrix.

[0012] As a preferred embodiment of a continuous-time modeling method for node frequencies in a dual-high power system, the node frequency response dynamic model includes: DC power flow equations, frequency-power angle equations, generator rotor motion equations, and governor equations.

[0013] The expression for the DC power flow equation is: ; ; In the formula, The change in active power injected into the generator; This represents the disturbance at the load node; This represents the change in the generator's power angle; This is the simplified equivalent susceptance matrix from the Krone model. The equivalent self-susceptance matrix of the generator node after Kron's simplification; The generator-load node mutual susceptance matrix; For load node sub-susceptance matrix; The generator node sub-susceptance matrix; The load-generator node mutual susceptance matrix;

[0014] The expression for the frequency-power angle equation is:

[0015]

[0016]

[0017] In the formula, This is the initial rated frequency of the generator; This represents the frequency change of the generator after the disturbance.

[0018] The expression for the generator rotor motion equation is as follows:

[0019]

[0020] In the formula, The inertia coefficient of the generator; This represents the change in the generator's mechanical power after the disturbance. This is the damping coefficient of the generator;

[0021] The expression for the governor equation is:

[0022]

[0023] In the formula, The time constant of the generator speed governor; This is the droop coefficient of the generator speed governor.

[0024] As a preferred embodiment of a continuous-time modeling method for node frequencies in a dual-high power system, the node frequency response constraint equations include: DC power flow constraint equations, frequency-power angle constraint equations, generator rotor motion constraint equations, and generator governor constraint equations.

[0025] The expression for the DC power flow constraint equation is:

[0026]

[0027] In the formula, For the first Bernstein discretization vector of the change in active power of generator nodes in the segment; For the first Bernstein discretized vector of active power disturbance at load nodes in a segment; For the first Bernstein discretization vector of the phase angle change of the generator node in the segment;

[0028] The expression for the frequency-power angle constraint equation is:

[0029]

[0030] In the formula, For the first The initial segment Bernstein discretization vector for the phase angle change of the generator node in the segment; h is the segment time length of the piecewise Bernstein polynomial. This is the discretization transformation matrix for the frequency-phase relationship; For the first Bernstein discretization vector of the frequency change of generator nodes in the segment;

[0031] The expression for the generator rotor motion constraint equation is as follows:

[0032]

[0033] In the formula, The generator's inertia coefficient; For the first The initial segment Bernstein discretization vector of the generator node frequency change in the segment; This is the discretization transformation matrix of the rotor motion equations; For the first Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the generator damping coefficient;

[0034] The expression for the constraint equation of the generator governor is:

[0035]

[0036] In the formula, The time constant of the generator speed governor; For the first The initial segment Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the governor droop coefficient;

[0037] The expression for the continuity condition constraint between segments is:

[0038]

[0039]

[0040] In the formula, For the first The 0th Bernstein interpolation coefficient for the frequency change of the generator node in the segment; For the first The first Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The second Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The third Bernstein interpolation coefficient for the frequency change of the generator node in the segment.

[0041] As a preferred scheme for continuous-time modeling of node frequencies in a high-voltage power system, the expression for the continuous frequency variation trajectory of all nodes in the power system is:

[0042]

[0043] In the formula, It is a continuous function of the generator node frequency change over the entire time domain; T is the total number of segments in the time domain. For the first A piecewise function of the frequency variation of generator nodes within a segment; For the first The Bernstein polynomial basis function vectors corresponding to the segments.

[0044] This invention also provides a continuous-time modeling device for node frequencies in a dual-high power system, employing the above-mentioned continuous-time modeling method for node frequencies in a dual-high power system, comprising:

[0045] The node frequency response dynamic model construction module is used to construct the node admittance matrix of the power system based on the network parameters of the power system; to perform network equivalence simplification on the node admittance matrix of the power system according to the transient characteristics of the generator to obtain the simplified node admittance matrix; and to construct the node frequency response dynamic model of the power system based on the simplified node admittance matrix.

[0046] The differential equation transformation module is used to introduce piecewise Bernstein polynomials in the continuous time domain, representing load disturbances, generator output, and various state variables as functions in Bernstein polynomial form; and using the integral mapping property of Bernstein polynomials, the differential equations in the dynamic model of the node frequency response are transformed into algebraic equations.

[0047] The node frequency interpolation coefficient acquisition module is used to construct node frequency response constraint equations based on the algebraic equations and the mathematical properties of Bernstein interpolation coefficients; based on the node frequency response constraint equations, add continuity constraints between segments to form a complete constraint system; and obtain the interpolation coefficients of each node frequency by optimizing and solving the complete constraint system.

[0048] The module for restoring the continuous frequency variation trajectory of all nodes is used to calculate and restore the continuous frequency variation trajectory of all nodes in the power system based on the interpolation coefficients of each node frequency and the Bernstein polynomial basis functions, thereby characterizing the dynamic response process of the node frequency.

[0049] As a preferred embodiment of a continuous-time modeling device for node frequencies in a high-voltage power system, in the node frequency response dynamic model construction module, during the process of network equivalence simplification of the power system node admittance matrix based on the transient characteristics of the generator, Kron simplification is performed on the power system node admittance matrix based on the transient reactance parameters of the generator; the generator internal potential nodes are equivalently embedded into the power system node admittance matrix to obtain an equivalent admittance matrix containing only the generator internal potential nodes and load nodes, which is the simplified node admittance matrix.

[0050] As a preferred embodiment of a continuous-time modeling device for node frequencies in a dual-high power system, the node frequency response dynamic model construction module includes: DC power flow equations, frequency-power angle equations, generator rotor motion equations, and governor equations.

[0051] The expression for the DC power flow equation is:

[0052]

[0053]

[0054] In the formula, The change in active power injected into the generator; This represents the disturbance at the load node; This represents the change in the generator's power angle; This is the simplified equivalent susceptance matrix from the Krone model. The equivalent self-susceptance matrix of the generator node after Kron's simplification; The generator-load node mutual susceptance matrix; For load node sub-susceptance matrix; The generator node sub-susceptance matrix; The load-generator node mutual susceptance matrix;

[0055] The expression for the frequency-power angle equation is:

[0056]

[0057]

[0058] In the formula, This is the initial rated frequency of the generator; This represents the frequency change of the generator after the disturbance.

[0059] The expression for the generator rotor motion equation is as follows:

[0060]

[0061] In the formula, The inertia coefficient of the generator; This represents the change in the generator's mechanical power after the disturbance. This is the damping coefficient of the generator;

[0062] The expression for the governor equation is:

[0063]

[0064] In the formula, The time constant of the generator speed governor; This is the droop coefficient of the generator speed governor.

[0065] As a preferred embodiment of a continuous-time modeling device for node frequencies in a dual-high power system, the node frequency interpolation coefficient acquisition module includes the following node frequency response constraint equations: DC power flow constraint equation, frequency-power angle constraint equation, generator rotor motion constraint equation, and generator governor constraint equation.

[0066] The expression for the DC power flow constraint equation is:

[0067]

[0068] In the formula, For the first Bernstein discretization vector of the change in active power of generator nodes in the segment; For the first Bernstein discretized vector of active power disturbance at load nodes in a segment; For the first Bernstein discretization vector of the phase angle change of the generator node in the segment;

[0069] The expression for the frequency-power angle constraint equation is:

[0070]

[0071] In the formula, For the first The initial segment Bernstein discretization vector for the phase angle change of the generator node in the segment; h is the segment time length of the piecewise Bernstein polynomial. This is the discretization transformation matrix for the frequency-phase relationship; For the first Bernstein discretization vector of the frequency change of generator nodes in the segment;

[0072] The expression for the generator rotor motion constraint equation is as follows:

[0073]

[0074] In the formula, The generator's inertia coefficient; For the first The initial segment Bernstein discretization vector of the generator node frequency change in the segment; This is the discretization transformation matrix of the rotor motion equations; For the first Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the generator damping coefficient;

[0075] The expression for the constraint equation of the generator governor is:

[0076]

[0077] In the formula, The time constant of the generator speed governor; For the first The initial segment Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the governor droop coefficient;

[0078] The expression for the continuity condition constraint between segments is:

[0079]

[0080]

[0081] In the formula, For the first The 0th Bernstein interpolation coefficient for the frequency change of the generator node in the segment; For the first The first Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The second Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The third Bernstein interpolation coefficient for the frequency change of the generator node in the segment.

[0082] As a preferred embodiment of a continuous-time modeling device for the node frequencies of a dual-high power system, the expression for the continuous frequency variation trajectory of all nodes in the power system within the full-node frequency continuous variation trajectory restoration module is as follows:

[0083]

[0084] In the formula, It is a continuous function of the generator node frequency change over the entire time domain; T is the total number of segments in the time domain. For the first A piecewise function of the frequency variation of generator nodes within a segment; For the first The Bernstein polynomial basis function vectors corresponding to the segments.

[0085] The present invention has the following advantages:

[0086] First, it characterizes the spatial differences in node frequencies, breaking through the limitations of traditional inertial center frequency analysis, clearly presenting the independent frequency change trajectory of each node, and avoiding the risk of misjudgment due to local over-limits.

[0087] Second, continuous-time modeling is achieved based on piecewise Bernstein polynomials, avoiding the step-size accumulation error of discrete numerical integration and capturing the rapid dynamic process in the early stage of disturbance.

[0088] Third, by using the property of integral mapping, differential equations are transformed into algebraic equations, and by combining solution space transformation, the complexity of model solving is reduced, and computational efficiency and feasibility are improved.

[0089] Fourth, the modeling process takes into account both the network distribution characteristics and the generator dynamic characteristics, and constructs a complete electromechanical coupling constraint system, providing reliable technical support for refined frequency analysis. Attached Figure Description

[0090] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0091] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0092] Figure 1 This is a flowchart illustrating a continuous-time modeling method for node frequencies in a dual-high-voltage power system provided in Embodiment 1 of the present invention.

[0093] Figure 2 This is a schematic diagram of the IEEE 39-node system topology in one possible embodiment of Embodiment 1 of the present invention;

[0094] Figure 3 This is a schematic diagram of system generator-related parameters in one possible embodiment provided in Embodiment 1 of the present invention;

[0095] Figure 4 This is a schematic diagram simulating the frequency change trajectory of the system generator node in one possible embodiment provided in Embodiment 1 of the present invention;

[0096] Figure 5 This is a schematic diagram simulating the frequency change trajectory of the system load nodes in one possible embodiment provided in Embodiment 1 of the present invention;

[0097] Figure 6 This is a schematic diagram illustrating the simulation and comparison of the generator frequency trajectory of system node 31 in one possible embodiment of the present invention, as provided in Embodiment 1 of the present invention.

[0098] Figure 7 This is a schematic diagram of the architecture of a continuous-time modeling device for node frequencies in a dual-high power system provided in Embodiment 2 of the present invention. Detailed Implementation

[0099] The following specific embodiments illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. 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.

[0100] Example 1

[0101] See Figure 1Embodiment 1 of the present invention provides a continuous-time modeling method for node frequencies in a dual-high power system, comprising the following steps:

[0102] S1. Based on the network parameters of the power system, construct the node admittance matrix of the power system; perform network equivalence simplification on the node admittance matrix of the power system according to the transient characteristics of the generator to obtain the simplified node admittance matrix; construct the node frequency response dynamic model of the power system based on the simplified node admittance matrix.

[0103] S2. Introduce piecewise Bernstein polynomials in the continuous time domain to express load disturbance, generator output and various state variables as functions in Bernstein polynomial form; use the integral mapping property of Bernstein polynomials to convert the differential equations in the dynamic model of the node frequency response into algebraic equations.

[0104] S3. Based on the mathematical properties of the algebraic equations and Bernstein interpolation coefficients, construct the node frequency response constraint equations; based on the node frequency response constraint equations, add continuity constraints between segments to form a complete constraint system; by optimizing the complete constraint system, obtain the interpolation coefficients of each node frequency.

[0105] S4. Based on the interpolation coefficients of each node frequency, combined with Bernstein polynomial basis functions, the continuous frequency change trajectory of all nodes in the power system is reconstructed, and the dynamic response process of node frequency is characterized.

[0106] In this embodiment, in step S1, a power system node admittance matrix is ​​constructed based on the network parameters of the power system; the power system node admittance matrix is ​​simplified by network equivalence according to the transient characteristics of the generator to obtain a simplified node admittance matrix; and a dynamic model of the node frequency response of the power system is constructed based on the simplified node admittance matrix.

[0107] Specifically, based on the network parameters of the power system, the node admittance matrix of the original network is first established. Considering that the resistance of transmission lines in a typical high-voltage power grid is much smaller than their reactance, and their conductance to ground can also be ignored, the conductance component in the admittance matrix is... , The elements in the code are as follows:

[0108] (1)

[0109] In the formula, For the line The reactance; express To and Connected nodes.

[0110] The nodes in the original network are divided into server nodes and load nodes. Perform matrix block processing:

[0111] (2)

[0112] In the formula, For the set of load nodes; This is a set of machine-side nodes.

[0113] To further construct a network model that reflects the dynamic characteristics of the generator, it is necessary to connect the generator terminal nodes to the generator internal potential nodes. To expand upon this. Regarding the first... The generator unit can connect a generator transient reactance in series between its terminal node and internal potential node. Forming the extended admittance matrix .right Perform matrix block processing:

[0114] (3)

[0115] In the formula, .

[0116] right Simplify Kron by eliminating machine-side nodes. The node equations for the extended network are shown below:

[0117] (4)

[0118] Injecting current into the terminal node Then we have:

[0119] (5)

[0120] remember ,but .Bundle Reply to the and From the nodal equations, we can obtain:

[0121] (6)

[0122] (7)

[0123] Rearrange equations (6) and (7) into matrix form:

[0124] (8)

[0125] The equivalent admittance matrix obtained by Kron As shown below:

[0126] (9)

[0127] in, ; ; ; .

[0128] In the formula, The generator-load node mutual susceptance matrix; For load node sub-susceptance matrix; The generator node sub-susceptance matrix; This is the load-generator node mutual susceptance matrix.

[0129] In this embodiment, the node frequency response dynamic model includes: DC power flow equation, frequency-power angle equation, generator rotor motion equation, and governor equation;

[0130] The DC power flow equations after the equivalent network is disturbed are as follows:

[0131] (10)

[0132] In the formula, The change in active power injected into the generator; This represents the disturbance at the load node; This represents the change in the generator's power angle; This represents the change in phase angle at the load node.

[0133] Gaussian elimination is performed on equation (10) to eliminate... variable, It can be represented as follows:

[0134] (11)

[0135] (12)

[0136] In the formula, This is the simplified equivalent susceptance matrix from the Krone model. This is the equivalent self-susceptance matrix of the generator node after Kron simplification.

[0137] The expression for the frequency-power angle equation is:

[0138] (13)

[0139] In the formula, , This is the initial rated frequency of the generator; This represents the frequency change of the generator after the disturbance.

[0140] The expression for the generator rotor's motion equation is:

[0141] (14)

[0142] In the formula, The inertia coefficient of the generator; This represents the change in the generator's mechanical power after the disturbance. This is the damping coefficient of the generator.

[0143] The expression for the governor equation is:

[0144] (15)

[0145] In the formula, The time constant of the generator speed governor; This is the droop coefficient of the generator speed governor.

[0146] In this embodiment, in step S2, a piecewise Bernstein polynomial is introduced in the continuous time domain to represent load disturbance, generator output and various state variables as functions in Bernstein polynomial form; using the integral mapping property of Bernstein polynomial, the differential equations in the dynamic model of the node frequency response are converted into algebraic equations.

[0147] Specifically, piecewise Bernstein polynomials are used to model load disturbances, generator output, and various state variables in continuous time, ensuring that all dynamic variables have a unified polynomial expression throughout the simulation period. Utilizing the integral mapping property of Bernstein polynomials, the original differential equation constraints are equivalently transformed into linear algebraic equations, thus forming a continuous-time mathematical model that is easy to solve.

[0148] Specifically, this embodiment, based on piecewise Bernstein polynomials, uniformly represents load disturbance, generator output, and state variables such as power angle and frequency as continuous-time functions. The continuous-time functions of load disturbance power, generator injected power, mechanical power, generator power angle, and frequency are respectively... , , , as well as The entire simulation cycle is divided into several time periods, and within each time period, the following is adopted: The Bernstein polynomial represents each variable in continuous time.

[0149] by For example, let a certain time interval of this continuous-time function be... , . The basis function vector of the Bernstein polynomial is :

[0150] (16)

[0151] In the formula, Let be the combination number, representing the number of combinations from . Select from elements The number of ways to combine elements.

[0152] Bundle Time period normalized to Above, there is:

[0153] (17)

[0154] In the formula, ,for In time period The interpolation coefficient vector; where , .

[0155] The continuous-time functions of the other variables can be represented in the same way.

[0156] In this embodiment, the Bernstein polynomial has good integral mapping properties, which can equivalently map the integral operation of a continuous-time function to a linear transformation relationship in the interpolation coefficient space, as follows:

[0157] (18)

[0158] In the formula, for The integral mapping matrix of the Bernstein polynomial of order 1.

[0159] Utilizing the aforementioned integral mapping properties, the continuous-time differential equations contained in the nodal frequency response model can be directly transformed into algebraic constraint equations with interpolation coefficients as variables, thereby achieving algebraic reconstruction of the differential equations and enhancing the solvability of the model. Taking the frequency-power angle equation (13) as an example, on the continuous time scale:

[0160] (19)

[0161] Normalize the time period of equation (19) to Above, there is:

[0162] (20)

[0163] From 0 to Integrate points:

[0164] (twenty one)

[0165] Right now:

[0166] (twenty two)

[0167] Applying the properties of equations (17) and (18), equation (22) can be transformed into:

[0168] (twenty three)

[0169] in, .

[0170] Eliminate both sides Finally, we obtain the discrete algebraic equation equivalent to the continuous differential equation in equation (19):

[0171] (twenty four)

[0172] Similarly, by processing the generator rotor motion equation (14) and the governor equation (15) in the same way as described above, we can obtain:

[0173] (25)

[0174] (26)

[0175] In this embodiment, in step S3, a node frequency response constraint equation is constructed based on the mathematical properties of the algebraic equation and the Bernstein interpolation coefficients; based on the node frequency response constraint equation, continuity constraints between segments are added to form a complete constraint system; and the interpolation coefficients of each node frequency are obtained by optimizing and solving the complete constraint system.

[0176] Specifically, based on the mathematical properties of Bernstein polynomials, the solution space of the nodal frequency response model is transformed, converting all differential-algebraic equations in the model into linear algebraic equations expressed by interpolation coefficients, thereby reducing the overall solution complexity of the model. Furthermore, continuity conditions between segments are added to form a complete nodal frequency response constraint system.

[0177] Under the constraints of the interpolation coefficient space, the continuous-time modeling problem of node frequencies can be represented as an optimization problem in algebraic space. By calling the optimization solver, the Bernstein interpolation coefficients of dynamic variables such as node frequencies can be obtained.

[0178] Specifically, in this embodiment, the mathematical properties of Bernstein polynomials are used to perform a solution space transformation on equations (11), (13)-(15), reconstructing the original infinite-dimensional nonlinear model into a linear programming model on a finite-dimensional algebraic space, as follows:

[0179] (27)

[0180] In the formula, For the first Bernstein discretization vector of the change in active power of generator nodes in the segment; For the first Bernstein discretized vector of active power disturbance at load nodes in a segment; For the first Bernstein discretization vector of the phase angle change of the generator node in the segment.

[0181] (28)

[0182] In the formula, For the first The initial segment Bernstein discretization vector for the phase angle change of the generator node in the segment; h is the segment time length of the piecewise Bernstein polynomial. This is the discretization transformation matrix for the frequency-phase relationship; For the first Bernstein discretization vector of the frequency change of generator nodes in the segment;

[0183] (29)

[0184] In the formula, The generator's inertia coefficient; For the first The initial segment Bernstein discretization vector of the generator node frequency change in the segment; This is the discretization transformation matrix of the rotor motion equations; For the first Bernstein discretization vector of the change in generator mechanical power in the segment; This represents the generator damping coefficient.

[0185] (30)

[0186] In the formula, The time constant of the generator speed governor; For the first The initial segment Bernstein discretization vector of the change in generator mechanical power in the segment; This is the governor droop coefficient.

[0187] Since the integral mapping of Bernstein polynomials is an approximate expression of equivalent transformations at the numerical implementation level, slack variables are introduced to enhance the feasibility and robustness of the model in the interpolation coefficient space. Relax equation (30) as follows:

[0188] (31)

[0189] Simultaneously, the vector composed of interpolation coefficients must also satisfy the first-order continuity constraint of the continuous time curve between adjacent time periods to ensure that the magnitude and slope of the continuous time function are equal at the end of the previous time period and the beginning of the next time period. Taking generator frequency as an example, the specific first-order continuity constraint is as follows:

[0190] (32)

[0191] (33)

[0192] In the formula, For the first The 0th Bernstein interpolation coefficient for the frequency change of the generator node in the segment; For the first The first Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The second Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The third Bernstein interpolation coefficient for the frequency change of the generator node in the segment.

[0193] The interpolation coefficients of the other variables are handled in a similar manner as in equations (32) and (33).

[0194] The mathematical model for simulating the frequency trajectory at continuous time nodes can be summarized as follows, where the objective function aims to minimize the slack variables, i.e.:

[0195] (34)

[0196] The constraints include DC power flow constraint (27), frequency-power angle constraint (28), generator rotor motion equation constraint (29), generator governor equation constraint (31), and first-order continuity constraints (32) and (33).

[0197] By transforming the solution space, the continuous-time modeling problem of node frequencies in a dual-high power system is mapped from the function space to the algebraic space composed of interpolation coefficients. This transforms the originally difficult-to-solve infinite-dimensional nonlinear optimization problem into a finite-dimensional linear programming problem, which can be solved efficiently using existing commercial solvers, and obtains the interpolation coefficients for each segment of dynamic variables such as node frequencies.

[0198] In this embodiment, in step S4, the interpolation coefficients of each node frequency are used to calculate and reconstruct the continuous frequency change trajectory of all nodes in the power system, thereby characterizing the dynamic response process of the node frequency.

[0199] Specifically, the obtained node frequency interpolation coefficients are multiplied by the Bernstein polynomial basis functions to obtain the functional expression of each node frequency in the continuous time domain, thereby simulating the continuous frequency trajectory of all nodes in the power system.

[0200] In this embodiment, for time periods The frequency of the generator node can be reduced to a continuous-time function consisting of the Bernstein interpolation coefficients multiplied by their corresponding basis functions:

[0201] (35)

[0202] By splicing together the continuous-time functions constructed over all time periods, the frequency variation trajectory of the generator node can be obtained throughout the entire simulation period:

[0203] (36)

[0204] In the formula, It is a continuous function of the generator node frequency change over the entire time domain; T is the total number of segments in the time domain. For the first A piecewise function of the frequency variation of generator nodes within a segment; For the first The Bernstein polynomial basis function vectors corresponding to the segments.

[0205] Considering the power coupling characteristics between nodes, and based on the node frequency relationships in the power system network structure, the frequency of the load node can be expressed by the frequency of the generator node as follows:

[0206] (37)

[0207] By substituting the interpolation coefficients of all generator node frequencies into equation (37), the interpolation coefficients of all load node frequencies in each time period can be obtained. Furthermore, according to equations (35) and (36), the frequency change trajectory of the load nodes throughout the entire simulation cycle can be reconstructed.

[0208] In one possible implementation, a verification example is provided as follows:

[0209] This embodiment uses Figure 2 Taking the IEEE 39-node system as an example, a continuous-time simulation of the node frequency trajectory after load disturbance is performed. The system baseline capacity is set to S. base =100MVA, reference voltage is V base=345kV. This power system comprises 39 nodes. Nodes 30, 31, 32, 33, 34, 35, 36, 37, 38, and 39 are generator nodes, node 31 is the slack load node, and the remaining nodes are load nodes. The relevant parameters for the generators are as follows: Figure 3 As shown. In A load disturbance was set, increasing the load at node 15 (3.2 pu) by 10% and the load at node 25 (2.24 pu) by 15%. The frequency response of each node in the power system after the disturbance was simulated. The simulation period was 15s, and the duration of each time segment was 1s. Bernstein polynomials of order 15 were used for modeling.

[0210] Finally, this embodiment numerically verifies the proposed continuous-time modeling method for power system node frequencies using MATLAB software. By solving the continuous-time modeling model and constructing the continuous-time function expression of node frequencies, the frequency trajectory curves of each node can be obtained, where the frequency trajectory of the generator node is as follows: Figure 4 As shown, the frequency variation trajectory of the load node is as follows: Figure 5 As shown above, the results demonstrate that, within the constructed frequency modeling framework, the frequency response curves of different nodes exhibit certain differences, reflecting the spatial distribution differences in the frequency response characteristics of various nodes in the power system.

[0211] To verify the consistency between the proposed method and traditional frequency analysis methods at the continuous-time modeling level, taking the generator frequency of node 31 as an example, the continuous-time frequency trajectory curve obtained in this embodiment is compared with the results of traditional frequency analysis methods. The comparison results are as follows: Figure 6 As shown in the figure, the red curve represents the frequency change trajectory simulated by the method in this embodiment, while the blue dashed line represents the frequency change trajectory simulated by the traditional method. The comparison results demonstrate that the continuous-time modeling method proposed in this embodiment maintains a high degree of consistency with the traditional method in describing the frequency dynamic characteristics, thus verifying the feasibility and effectiveness of this method in continuous-time modeling of node frequencies.

[0212] The application scenarios of this invention are as follows:

[0213] In the scenario of frequency stability assessment of a high proportion of new energy access to the power system, this invention can characterize the continuous dynamic trajectory of the frequency of each node, providing refined data support for system inertia configuration and frequency regulation strategy formulation.

[0214] In emergency analysis scenarios where the power system suffers from load disturbances or fluctuations in renewable energy output, this invention can quickly reconstruct the continuous response process of the entire node frequency, helping dispatchers to identify local frequency over-limit risks in a timely manner.

[0215] In simulation verification scenarios for power system planning, design, and upgrading, this invention can realize continuous-time modeling and analysis of node-level frequencies, providing a scientific basis for power grid topology optimization and frequency regulation resource layout.

[0216] In the optimization and improvement of dynamic simulation algorithms for power systems, this invention reduces the solution complexity by transforming differential-algebraic equations, providing a new technical path for improving simulation calculation efficiency and accuracy.

[0217] It should be noted that the method of this disclosure embodiment can be executed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method of this disclosure embodiment, and the multiple devices will interact with each other to complete the method described.

[0218] It should be noted that the above description describes some embodiments of this disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0219] Example 2

[0220] See Figure 7 Embodiment 2 of the present invention also provides a continuous-time modeling device for node frequencies in a dual-high power system, comprising:

[0221] The node frequency response dynamic model construction module 001 is used to construct the node admittance matrix of the power system based on the network parameters of the power system; to perform network equivalence simplification on the node admittance matrix of the power system according to the transient characteristics of the generator to obtain the simplified node admittance matrix; and to construct the node frequency response dynamic model of the power system based on the simplified node admittance matrix.

[0222] The differential equation transformation module 002 is used to introduce piecewise Bernstein polynomials in the continuous time domain, and to express load disturbance, generator output and various state variables as functions in Bernstein polynomial form; using the integral mapping property of Bernstein polynomials, the differential equations in the dynamic model of the node frequency response are transformed into algebraic equations.

[0223] The node frequency interpolation coefficient acquisition module 003 is used to construct a node frequency response constraint equation based on the algebraic equation and the mathematical properties of the Bernstein interpolation coefficient; based on the node frequency response constraint equation, add continuity constraints between segments to form a complete constraint system; and obtain the interpolation coefficients of each node frequency by optimizing and solving the complete constraint system.

[0224] The full-node frequency continuous change trajectory restoration module 004 is used to calculate and restore the full-node frequency continuous change trajectory of the power system based on the interpolation coefficients of each node frequency and in combination with Bernstein polynomial basis functions, thus characterizing the dynamic response process of the node frequency.

[0225] In this embodiment, in the node frequency response dynamic model construction module 001, during the process of network equivalent simplification of the power system node admittance matrix based on the transient characteristics of the generator, the power system node admittance matrix is ​​simplified using Kron based on the transient reactance parameters of the generator; the generator internal potential nodes are equivalently embedded into the power system node admittance matrix to obtain an equivalent admittance matrix containing only the generator internal potential nodes and load nodes, which is the simplified node admittance matrix.

[0226] In this embodiment, the node frequency response dynamic model construction module 001 includes: DC power flow equation, frequency-power angle equation, generator rotor motion equation, and governor equation.

[0227] The expression for the DC power flow equation is:

[0228]

[0229]

[0230] In the formula, The change in active power injected into the generator; This represents the disturbance at the load node; This represents the change in the generator's power angle; This is the simplified equivalent susceptance matrix from the Krone model. The equivalent self-susceptance matrix of the generator node after Kron's simplification; The generator-load node mutual susceptance matrix; For load node sub-susceptance matrix; The generator node sub-susceptance matrix; The load-generator node mutual susceptance matrix;

[0231] The expression for the frequency-power angle equation is:

[0232]

[0233]

[0234] In the formula, This is the initial rated frequency of the generator; This represents the frequency change of the generator after the disturbance.

[0235] The expression for the generator rotor motion equation is as follows:

[0236]

[0237] In the formula, The inertia coefficient of the generator; This represents the change in the generator's mechanical power after the disturbance. This is the damping coefficient of the generator;

[0238] The expression for the governor equation is:

[0239]

[0240] In the formula, The time constant of the generator speed governor; This is the droop coefficient of the generator speed governor.

[0241] In this embodiment, the node frequency interpolation coefficient acquisition module 003 includes the following node frequency response constraint equations: DC power flow constraint equation, frequency-power angle constraint equation, generator rotor motion constraint equation, and generator governor constraint equation.

[0242] The expression for the DC power flow constraint equation is:

[0243]

[0244] In the formula, For the first Bernstein discretization vector of the change in active power of generator nodes in the segment; For the first Bernstein discretized vector of active power disturbance at load nodes in a segment; For the first Bernstein discretization vector of the phase angle change of the generator node in the segment;

[0245] The expression for the frequency-power angle constraint equation is:

[0246]

[0247] In the formula, For the first The initial segment Bernstein discretization vector for the phase angle change of the generator node in the segment; h is the segment time length of the piecewise Bernstein polynomial. This is the discretization transformation matrix for the frequency-phase relationship; For the first Bernstein discretization vector of the frequency change of generator nodes in the segment;

[0248] The expression for the generator rotor motion constraint equation is as follows:

[0249]

[0250] In the formula, The generator's inertia coefficient; For the first The initial segment Bernstein discretization vector of the generator node frequency change in the segment; This is the discretization transformation matrix of the rotor motion equations; For the first Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the generator damping coefficient;

[0251] The expression for the constraint equation of the generator governor is:

[0252]

[0253] In the formula, The time constant of the generator speed governor; For the first The initial segment Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the governor droop coefficient;

[0254] The expression for the continuity condition constraint between segments is:

[0255]

[0256]

[0257] In the formula, For the first The 0th Bernstein interpolation coefficient for the frequency change of the generator node in the segment; For the first The first Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The second Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The third Bernstein interpolation coefficient for the frequency change of the generator node in the segment.

[0258] In this embodiment, the expression for the continuous frequency change trajectory of all nodes in the power system in the full-node frequency continuous change trajectory restoration module 004 is as follows:

[0259]

[0260] In the formula, It is a continuous function of the generator node frequency change over the entire time domain; T is the total number of segments in the time domain. For the first A piecewise function of the frequency variation of generator nodes within a segment; For the first The Bernstein polynomial basis function vectors corresponding to the segments.

[0261] It should be noted that the information interaction and execution process between the modules of the above system are based on the same concept as the method embodiment in Embodiment 1 of this application, and the resulting technical effects are the same as those in the method embodiment of this application. For details, please refer to the description in the method embodiment shown above in this application, and it will not be repeated here.

[0262] Example 3

[0263] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium storing program code for a continuous-time modeling method of node frequencies in a dual-high power system. The program code includes instructions for executing the continuous-time modeling method of node frequencies in a dual-high power system according to Embodiment 1 or any possible implementation thereof.

[0264] Computer-readable storage media can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0265] Example 4

[0266] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0267] The processor and the memory communicate with each other via a bus; the memory stores program instructions that can be executed by the processor, and the processor can execute the continuous-time modeling method for node frequencies of a dual-high power system by calling the program instructions.

[0268] Specifically, a processor can be implemented in hardware or software. When implemented in hardware, the processor can be a logic circuit, an integrated circuit, etc. When implemented in software, the processor can be a general-purpose processor that reads software code stored in memory. This memory can be integrated into the processor or located outside the processor and exist independently.

[0269] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable system. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0270] It is obvious to those skilled in the art that the modules or steps of the present invention described above can be implemented using general-purpose computing systems. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Optionally, they can be implemented using program code executable by a computing system, thereby storing them in a storage system for execution by the computing system. In some cases, the steps shown or described can be performed in a different order than those presented herein, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0271] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A continuous-time modeling method for node frequencies in a dual-high-voltage power system, characterized in that, include: Based on the network parameters of the power system, construct the node admittance matrix of the power system; The node admittance matrix of the power system is simplified by network equivalence based on the transient characteristics of the generator to obtain the simplified node admittance matrix; a dynamic model of the node frequency response of the power system is constructed based on the simplified node admittance matrix. Piecewise Bernstein polynomials are introduced in the continuous time domain to represent load disturbances, generator output, and various state variables as functions in Bernstein polynomial form; using the integral mapping property of Bernstein polynomials, the differential equations in the dynamic model of the node frequency response are transformed into algebraic equations. Based on the mathematical properties of the algebraic equations and Bernstein interpolation coefficients, nodal frequency response constraint equations are constructed; based on the nodal frequency response constraint equations, continuity constraints between segments are added to form a complete constraint system; by optimizing the complete constraint system, the interpolation coefficients of each nodal frequency are obtained. Based on the interpolation coefficients of each node frequency, combined with Bernstein polynomial basis functions, the continuous frequency change trajectory of all nodes in the power system is reconstructed, and the dynamic response process of node frequency is characterized.

2. The continuous-time modeling method for node frequencies in a dual-high-voltage power system according to claim 1, characterized in that, In the process of simplifying the power system node admittance matrix based on the transient characteristics of the generator, the power system node admittance matrix is ​​simplified using Kron based on the transient reactance parameters of the generator. By embedding the generator internal potential nodes into the power system node admittance matrix, an equivalent admittance matrix containing only the generator internal potential nodes and load nodes is obtained, which is the simplified node admittance matrix.

3. The continuous-time modeling method for node frequencies in a dual-high-voltage power system according to claim 2, characterized in that, The node frequency response dynamic model includes: DC power flow equation, frequency-power angle equation, generator rotor motion equation, and governor equation; The expression for the DC power flow equation is: ； ； In the formula, The change in active power injected into the generator; This represents the disturbance at the load node; This represents the change in the generator's power angle; This is the simplified equivalent susceptance matrix from the Krone model. The equivalent self-susceptance matrix of the generator node after Kron's simplification; The generator-load node mutual susceptance matrix; For load node sub-susceptance matrix; The generator node sub-susceptance matrix; The load-generator node mutual susceptance matrix; The expression for the frequency-power angle equation is: ； ； In the formula, This is the initial rated frequency of the generator; This represents the frequency change of the generator after the disturbance. The expression for the generator rotor motion equation is as follows: ； In the formula, The inertia coefficient of the generator; This represents the change in the generator's mechanical power after the disturbance. This is the damping coefficient of the generator; The expression for the governor equation is: ； In the formula, The time constant of the generator speed governor; This is the droop coefficient of the generator speed governor.

4. The continuous-time modeling method for node frequencies in a dual-high-voltage power system according to claim 3, characterized in that, The node frequency response constraint equations include: DC power flow constraint equations, frequency-power angle constraint equations, generator rotor motion constraint equations, and generator governor constraint equations. The expression for the DC power flow constraint equation is: ； In the formula, For the first Bernstein discretization vector of the change in active power of generator nodes in the segment; For the first Bernstein discretized vector of active power disturbance at load nodes in a segment; For the first Bernstein discretization vector of the phase angle change of the generator node in the segment; The expression for the frequency-power angle constraint equation is: ； In the formula, For the first The initial segment Bernstein discretization vector for the phase angle change of the generator node in the segment; h is the segment time length of the piecewise Bernstein polynomial. This is the discretization transformation matrix for the frequency-phase relationship; For the first Bernstein discretization vector of the frequency change of generator nodes in the segment; The expression for the generator rotor motion constraint equation is as follows: ； In the formula, The generator's inertia coefficient; For the first The initial segment Bernstein discretization vector of the generator node frequency change in the segment; This is the discretization transformation matrix of the rotor motion equations; For the first Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the generator damping coefficient; The expression for the constraint equation of the generator governor is: ； In the formula, The time constant of the generator speed governor; For the first The initial segment Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the governor droop coefficient; The expression for the continuity condition constraint between segments is: ； ； In the formula, For the first The 0th Bernstein interpolation coefficient for the frequency change of the generator node in the segment; For the first The first Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The second Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The third Bernstein interpolation coefficient for the frequency change of the generator node in the segment.

5. The continuous-time modeling method for node frequencies in a dual-high-voltage power system according to claim 4, characterized in that, The expression for the continuous frequency variation trajectory of all nodes in a power system is: ； In the formula, It is a continuous function of the generator node frequency change over the entire time domain; T is the total number of segments in the time domain. For the first A piecewise function of the frequency variation of generator nodes within a segment; For the first The Bernstein polynomial basis function vectors corresponding to the segments.

6. A continuous-time modeling device for node frequencies in a dual-high-voltage power system, employing the continuous-time modeling method for node frequencies in a dual-high-voltage power system as described in any one of claims 1-5, characterized in that... include: The node frequency response dynamic model construction module is used to construct the node admittance matrix of the power system based on the network parameters of the power system. The node admittance matrix of the power system is simplified by network equivalence based on the transient characteristics of the generator to obtain the simplified node admittance matrix; a dynamic model of the node frequency response of the power system is constructed based on the simplified node admittance matrix. The differential equation transformation module is used to introduce piecewise Bernstein polynomials in the continuous time domain, representing load disturbances, generator output, and various state variables as functions in Bernstein polynomial form; and using the integral mapping property of Bernstein polynomials, the differential equations in the dynamic model of the node frequency response are transformed into algebraic equations. The node frequency interpolation coefficient acquisition module is used to construct node frequency response constraint equations based on the algebraic equations and the mathematical properties of Bernstein interpolation coefficients; based on the node frequency response constraint equations, add continuity constraints between segments to form a complete constraint system; and obtain the interpolation coefficients of each node frequency by optimizing and solving the complete constraint system. The module for restoring the continuous frequency variation trajectory of all nodes is used to calculate and restore the continuous frequency variation trajectory of all nodes in the power system based on the interpolation coefficients of each node frequency and the Bernstein polynomial basis functions, thereby characterizing the dynamic response process of the node frequency.

7. The continuous-time modeling device for node frequencies in a dual-high power system according to claim 6, characterized in that, In the node frequency response dynamic model construction module, during the process of simplifying the power system node admittance matrix by network equivalence based on the generator transient characteristics, the power system node admittance matrix is ​​simplified by Kron based on the generator transient reactance parameters. By embedding the generator internal potential nodes into the power system node admittance matrix, an equivalent admittance matrix containing only the generator internal potential nodes and load nodes is obtained, which is the simplified node admittance matrix.

8. The continuous-time modeling device for node frequencies in a dual-high power system according to claim 7, characterized in that, In the node frequency response dynamic model construction module, the node frequency response dynamic model includes: DC power flow equation, frequency-power angle equation, generator rotor motion equation, and governor equation; The expression for the DC power flow equation is: ； ； In the formula, The change in active power injected into the generator; This represents the disturbance at the load node; This represents the change in the generator's power angle; This is the simplified equivalent susceptance matrix from the Krone model. The equivalent self-susceptance matrix of the generator node after Kron's simplification; The generator-load node mutual susceptance matrix; For load node sub-susceptance matrix; The generator node sub-susceptance matrix; The load-generator node mutual susceptance matrix; The expression for the frequency-power angle equation is: ； ； In the formula, This is the initial rated frequency of the generator; This represents the frequency change of the generator after the disturbance. The expression for the generator rotor motion equation is as follows: ； In the formula, The inertia coefficient of the generator; This represents the change in the generator's mechanical power after the disturbance. This is the damping coefficient of the generator; The expression for the governor equation is: ； In the formula, The time constant of the generator speed governor; This is the droop coefficient of the generator speed governor.

9. A continuous-time modeling device for node frequencies in a dual-high power system according to claim 8, characterized in that, In the node frequency interpolation coefficient acquisition module, the node frequency response constraint equations include: DC power flow constraint equations, frequency-power angle constraint equations, generator rotor motion constraint equations, and generator governor constraint equations. The expression for the DC power flow constraint equation is: ； In the formula, For the first Bernstein discretization vector of the change in active power of generator nodes in the segment; For the first Bernstein discretized vector of active power disturbance at load nodes in a segment; For the first Bernstein discretization vector of the phase angle change of the generator node in the segment; The expression for the frequency-power angle constraint equation is: ； In the formula, For the first The initial segment Bernstein discretization vector for the phase angle change of the generator node in the segment; h is the segment time length of the piecewise Bernstein polynomial. This is the discretization transformation matrix for the frequency-phase relationship; For the first Bernstein discretization vector of the frequency change of generator nodes in the segment; The expression for the generator rotor motion constraint equation is as follows: ； In the formula, The generator's inertia coefficient; For the first The initial segment Bernstein discretization vector of the generator node frequency change in the segment; This is the discretization transformation matrix of the rotor motion equations; For the first Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the generator damping coefficient; The expression for the constraint equation of the generator governor is: ； In the formula, The time constant of the generator speed governor; For the first The initial segment Bernstein discretization vector of the change in generator mechanical power in the segment; This refers to the governor droop coefficient; The expression for the continuity condition constraint between segments is: ； ； In the formula, For the first The 0th Bernstein interpolation coefficient for the frequency change of the generator node in the segment; For the first The first Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The second Bernstein interpolation coefficient for the frequency variation of the generator node in the segment; For the first The third Bernstein interpolation coefficient for the frequency change of the generator node in the segment.

10. A continuous-time modeling device for node frequencies in a dual-high power system according to claim 9, characterized in that, In the full-node frequency continuous change trajectory reconstruction module, the expression for the full-node frequency continuous change trajectory of the power system is: ； In the formula, It is a continuous function of the generator node frequency change over the entire time domain; T is the total number of segments in the time domain. For the first A piecewise function of the frequency variation of generator nodes within a segment; For the first The Bernstein polynomial basis function vectors corresponding to the segments.

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