A magnitude-frequency operating point linear time-invariant modeling method for dfigs

Abstract

The application belongs to the technical field of electronic system modeling, and specifically discloses a linear time-invariant modeling method of amplitude-frequency operating point suitable for a DFIG, which comprises the following steps: constructing a dynamic behavior model of an asynchronous machine, a back-to-back converter and a three-phase alternating current line in a doubly-fed wind power generator, wherein the dynamic behavior model comprises a complex exponential equation in which each electrical quantity is represented by a product of a time-varying amplitude and a complex exponential; solving the amplitude dynamic equation and the angular frequency dynamic equation of each electrical quantity based on the dynamic behavior model; linearizing the amplitude dynamic equation and the angular frequency dynamic equation of each electrical quantity to obtain the linear time-invariant model of the amplitude-frequency operating point corresponding to the asynchronous machine, the back-to-back converter and the three-phase alternating current line respectively; and integrating the linear time-invariant model of the amplitude-frequency operating point corresponding to the asynchronous machine, the back-to-back converter and the three-phase alternating current line respectively to obtain the linear time-invariant model of the doubly-fed wind power generator based on the amplitude-frequency operating point.

Description

Technical Field

[0001] This application belongs to the field of electronic system modeling technology, and more specifically, relates to a linear time-invariant modeling method for amplitude-frequency operating point of a doubly fed induction generator (DFIG). Background Technology

[0002] The increasing penetration of new energy sources in power systems has led to the emergence of multi-timescale stability issues related to voltage and frequency. Meanwhile, doubly-fed induction generators (DFIGs) have become the mainstream in the wind power market due to their cost advantage. Therefore, establishing a correct linear time-invariant model for DFIGs with clearly defined physical meanings of state variables is the theoretical foundation and research prerequisite for analyzing the stability and voltage and frequency dynamic evolution mechanisms of power systems with a high proportion of DFIGs. This model provides guidance for the design of damping control systems and the optimization of operating parameters for DFIGs, and is fundamental to improving the stability of DFIG systems.

[0003] Existing small-signal modeling methods for doubly-fed induction generator (DFIG) wind turbines can be categorized into three types: quasi-steady-state modeling, impedance modeling, and dynamic phasor modeling. Quasi-steady-state modeling can only reflect the dynamic characteristics of DFIG wind turbines at lower frequencies (typically below 10Hz), making it unsuitable for current multi-timescale dynamic system analysis. Impedance modeling treats the equipment as a black box, focusing only on port characteristics, making it difficult to reveal the physical mechanisms of electromagnetic-electromechanical coupling within the equipment and failing to provide a physical basis for damping control system design. Dynamic phasor modeling essentially establishes three-phase electrical quantities in one or more rotating coordinate systems with constant frequencies. However, the state variables projected from the rotating coordinate system lack clear physical meaning. When using this method for modeling and analysis, it is usually necessary to preset the system operating frequency, i.e., set an infinite power supply, or to uniformly establish the equipment and network at a dynamic reference frequency formed by a specific network configuration, resulting in dynamic coupling between equipment and between equipment and the network, making it difficult to apply to autonomous power system scenarios lacking an infinite power supply.

[0004] The three modeling methods mentioned above are mostly for single-unit infinite bus systems or multi-unit infinite bus systems. However, the small-signal stability problem of autonomous power systems plays a crucial role in whether doubly-fed wind turbines can be successfully connected to the grid and operate stably. Therefore, existing modeling methods cannot establish a correct linear time-invariant model of doubly-fed wind turbines with clear physical meaning of state variables. Using the model obtained by existing modeling methods to analyze doubly-fed wind turbines will lead to low system stability. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the purpose of this application is to provide a linear time-invariant modeling method for amplitude-frequency operating points suitable for DFIGs. This method aims to solve the problems of existing modeling methods relying on rotating coordinate systems, making it difficult to perform physical mechanism analysis on the equipment, and requiring preset system operating frequencies, which leads to low stability of doubly-fed wind turbine systems.

[0006] To achieve the above objectives, in a first aspect, this application provides a linear time-invariant modeling method for the amplitude-frequency operating point of DFIG, comprising: A dynamic behavior model is constructed for the asynchronous motor, back-to-back converter and three-phase AC line in a doubly fed wind turbine generator. The dynamic behavior model includes complex exponential equations in which each electrical quantity is expressed as a product of time-varying amplitude and complex exponent. Based on the dynamic behavior model, the dynamic equations for the magnitude and angular frequency of each electrical quantity are solved to obtain the dynamic equations for the electrical quantity. Linearize the amplitude dynamic equations and angular frequency dynamic equations of the electrical quantities to obtain linear time-invariant models of the amplitude frequency operating points for asynchronous machines, back-to-back converters and three-phase AC lines, respectively. By integrating the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous motor, back-to-back converter, and three-phase AC line, a linear time-invariant model of the entire doubly-fed wind turbine based on the amplitude-frequency operating point is obtained.

[0007] This application expresses electrical quantities as a product of time-varying amplitude and complex exponent, and further derives the complex exponential equations for the dynamic behavior model of the electrical components. This allows electrical quantities to be uniformly described using amplitude and frequency as state characteristics, thus avoiding the problem of needing to preset a fixed reference frequency in traditional rotating coordinate system modeling. By solving the dynamic behavior model, the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity are obtained, enabling the amplitude and frequency variation processes of electrical quantities in the doubly-fed wind turbine system to be characterized separately. This provides state variables with clear physical meaning for analyzing voltage amplitude dynamics, frequency dynamics, and their interactions. Furthermore, the application linearizes and integrates the amplitude and angular frequency dynamic equations of each electrical quantity. This study constructs a linear time-invariant model of the entire doubly-fed induction generator (DFIG) wind turbine based on its amplitude and frequency operating points. This model decouples the dynamics of the DFIG equipment from the dynamics of the power system network at the modeling level, facilitating its extension to stability mechanism analysis in multi-machine system scenarios. It not only clearly characterizes the dynamic evolution of the amplitude and frequency of each of the three-phase electrical quantities of the DFIG, but also provides a fundamental model with clear physical meaning for voltage and frequency small-signal stability analysis, damping control system design in multi-machine scenarios, and operating parameter optimization. It is also applicable to autonomous power system scenarios where infinite power sources are lacking, and can support small-signal stability analysis of multi-machine grid-connected systems, thereby helping to improve the stability of DFIG wind turbine systems.

[0008] According to the amplitude-frequency operating point linear time-invariant modeling method for DFIG provided in this application, the dynamic behavior model of the asynchronous machine includes: Three-phase stator and rotor voltage equations, three-phase stator and rotor flux linkage equations, electromagnetic torque equations, and rotor sway equations; The dynamic behavior model of the back-to-back converter includes: Active power equation, DC capacitor equation, phase-locked loop control model, machine-side controller model, and grid-side controller model; The dynamic behavior model of the three-phase AC line includes: Choke circuit equations, filter capacitor equations, and transmission line equations.

[0009] This application comprehensively covers the electromagnetic-electromechanical coupling dynamics of the asynchronous motor, the power electronic conversion and control dynamics of the back-to-back converter, and the electrical dynamics of the grid connection line in a doubly-fed wind turbine system by establishing the three-phase stator and rotor voltage equations, flux linkage equations, electromagnetic torque equations, and rotor sway equations of the asynchronous motor, the active power equations, DC capacitor equations, phase-locked loop control models, machine-side controller models, and grid-side controller models of the back-to-back converter, as well as the choke circuit equations, filter capacitor equations, and transmission line equations of the three-phase AC network. This ensures that the physical foundation for subsequent modeling steps is complete and the dynamic characteristics of each part of the system are accurately described, laying the foundation for obtaining an accurate overall system model.

[0010] According to the linear time-invariant modeling method for amplitude-frequency operating point of DFIG provided in this application, the step of solving the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity based on the dynamic behavior model includes: By taking the time derivatives of both sides of the complex exponential equation and separating the real and imaginary parts of the result, the dynamic equations for the amplitude and angular frequency of each electrical quantity are obtained.

[0011] This application obtains the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity by taking the time derivative of the complex exponential equation and separating the real and imaginary parts. This enables the amplitude and frequency change processes of electrical quantities in the doubly fed wind turbine system to be characterized separately, thereby providing state variables with clear physical meaning for analyzing voltage amplitude dynamics, frequency dynamics and their interactions.

[0012] According to the linear time-invariant modeling method for amplitude-frequency operating point of DFIG provided in this application, the step of solving the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity based on the dynamic behavior model includes: Based on the causal operation principle of physical systems and the dynamic behavior model of back-to-back converters, without taking the time derivative of the non-integral state variables of the controller in the back-to-back converter, the dynamic equations of the internal potential amplitude and angular frequency output by the controller in the back-to-back converter are solved.

[0013] Based on the causal operation principle of physical systems and the dynamic behavior model of back-to-back converters, this application identifies the non-integral state variables of the controller in the back-to-back converter. Under the constraint that the non-integral state variables are not differentiated over time, the dynamic equations of the internal potential amplitude and angular frequency of the controller output in the back-to-back converter are solved to ensure that the established model satisfies physical causality.

[0014] According to the amplitude-frequency operating point linear time-invariant modeling method for DFIG provided in this application, the method involves linearizing the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity to obtain the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous machine, back-to-back converter, and three-phase AC line, respectively. The amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, are linearized at the DC operating point to obtain linear time-invariant models of the amplitude and frequency operating points corresponding to the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively.

[0015] This application linearizes the amplitude and angular frequency dynamic equations of various electrical quantities, as well as the amplitude and angular frequency dynamic equations of the internal potential output by the controller in a back-to-back converter, at the DC operating point. This transforms the nonlinear amplitude and frequency dynamic equations into linear time-invariant small-signal equations. This linearization can be performed directly at the DC operating point at any steady-state frequency without the need to preset a specific operating frequency. This makes the resulting linear time-invariant model applicable to any steady-state frequency operating scenario, greatly expanding the applicability of the model.

[0016] According to the linear time-invariant modeling method for amplitude-frequency operating point of a DFIG provided in this application, the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, are linearized at the DC operating point to obtain linear time-invariant models for amplitude-frequency operating point of the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively. This includes: The amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, are linearized with small perturbations at the DC operating point to obtain linear time-invariant models of amplitude and frequency operating points for the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively. The linear time-invariant model of the amplitude-frequency operating point of the asynchronous machine includes small-signal equations for stator voltage, rotor voltage, stator flux linkage, rotor flux linkage, electromagnetic torque, and rotor sway. The linear time-invariant model of the amplitude-frequency operating point of the back-to-back converter includes small-signal equations for active power, DC capacitor, phase-locked loop, grid-side controller, and machine-side controller. The linear time-invariant model of the amplitude-frequency operating point of the three-phase AC line includes small-signal equations for choke circuit, filter capacitor, and transmission line.

[0017] This application transforms the nonlinear amplitude-frequency dynamic equation into a linear time-invariant small-signal equation by representing each state variable as a superposition of steady-state values ​​and small disturbances, and by ignoring second-order and higher-order small terms for linearization. This linearization can be performed directly at any steady-state frequency DC operating point without presetting a specific operating frequency, making the resulting linear time-invariant model applicable to any steady-state frequency operating scenario, thus significantly expanding the model's applicability. By establishing small-signal equations for stator voltage, rotor voltage, stator flux linkage, rotor flux linkage, electromagnetic torque, and rotor sway of the asynchronous machine; small-signal equations for active power, DC capacitance, phase-locked loop, grid-side controller, and machine-side controller of the back-to-back converter; and small-signal equations for choke circuits, filter capacitors, and transmission lines of the AC network, the application ensures that the linear time-invariant models of each sub-component of the system are complete and without omissions. The sub-models form a clear interface relationship through common state variables, facilitating the assembly of the sub-models into the overall system model in the final integration step. It also facilitates the individual analysis of the contribution and impact of each sub-component on system stability.

[0018] Secondly, this application provides a linear time-invariant modeling apparatus for the amplitude-frequency operating point of a DFIG, comprising: The module is used to construct a dynamic behavior model of the asynchronous motor, back-to-back converter and three-phase AC line in a doubly fed wind turbine. The dynamic behavior model includes complex exponential equations in which each electrical quantity is expressed as a product of time-varying amplitude and complex exponent. The solver module is used to solve for the magnitude dynamic equations and angular frequency dynamic equations of each electrical quantity based on the dynamic behavior model. The linearization module is used to linearize the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity to obtain linear time-invariant models of the amplitude frequency operating points corresponding to the asynchronous machine, back-to-back converter and three-phase AC line, respectively. The integration module is used to integrate the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous motor, back-to-back converter and three-phase AC line respectively, to obtain the overall linear time-invariant model of the doubly-fed wind turbine based on the amplitude-frequency operating point.

[0019] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory. When the program stored in the memory is executed, the processor is configured to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG described in the first aspect or any possible implementation thereof.

[0020] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG described in the first aspect or any possible implementation of the first aspect.

[0021] Fifthly, this application provides a computer program product that, when run on a processor, causes the processor to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG described in the first aspect or any possible implementation of the first aspect.

[0022] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0023] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) This application expresses electrical quantities as a product of time-varying amplitude and complex exponent, and further obtains the complex exponential equation of the dynamic behavior model of the electrical part, so that electrical quantities can be uniformly described with amplitude and frequency as state characteristics, thereby avoiding the problem of needing to preset a fixed reference frequency in traditional rotating coordinate system modeling; by solving the dynamic behavior model, the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity are obtained, so that the amplitude change process and frequency change process of electrical quantities in the doubly fed wind turbine system can be characterized separately, thereby providing state variables with clear physical meaning for analyzing voltage amplitude dynamics, frequency dynamics and their interaction; by linearizing and By integrating and constructing a linear time-invariant model of the entire doubly-fed induction generator (DFIG) based on its amplitude and frequency operating points, the dynamics of the DFIG equipment and the power system network can be decoupled at the modeling level. This facilitates the extension to stability mechanism analysis in multi-machine system scenarios. It can not only clearly characterize the dynamic evolution of the amplitude and frequency of each three-phase electrical quantity of the DFIG, but also provide a fundamental model with clear physical meaning for voltage and frequency small-signal stability analysis, damping control system design in multi-machine scenarios, and operating parameter optimization. It is also applicable to autonomous power system scenarios with the absence of infinite power sources and can support small-signal stability analysis of multi-machine grid-connected systems, thereby helping to improve the stability of DFIG systems.

[0024] (2) This application obtains the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity by taking the time derivative of the complex exponential equation and separating the real part and the imaginary part, so that the amplitude change process and frequency change process of the electrical quantity in the doubly fed wind turbine system can be characterized separately, thereby providing state variables with clear physical meaning for analyzing voltage amplitude dynamics, frequency dynamics and their interaction. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 This is a flowchart illustrating the amplitude-frequency operating point linear time-invariant modeling method for DFIG provided in this application embodiment; Figure 2 This is a schematic diagram of an asynchronous machine winding model provided in an embodiment of this application; wherein, Figure 2 (a) in the diagram represents the winding structure model of an asynchronous machine. Figure 2 (b) in the diagram is a schematic diagram of the amplitude and frequency status of electrical quantities in an asynchronous machine; Figure 3 This is a schematic diagram of the amplitude and frequency of a three-phase inductor and a three-phase capacitor provided in an embodiment of this application; wherein, Figure 3 (a) in the diagram is a schematic diagram of a three-phase capacitor circuit and its current amplitude and frequency states. Figure 3 (b) in the diagram is a schematic diagram of a three-phase inductor circuit and its current amplitude and frequency states; Figure 4 This is a schematic diagram of the internal potential amplitude and frequency of the back-to-back converter provided in the embodiments of this application; Figure 5 This is a schematic diagram comparing the time-domain waveforms of the original model and the amplitude-frequency model provided in the embodiments of this application; wherein, Figure 5 (a) in the figure is a comparison of the time-domain waveforms of electromagnetic torque. Figure 5 (b) in the figure is a comparison of the time-domain waveforms of DC voltage. Figure 5 (c) in the figure is a comparison of the time-domain waveforms of the rotor speed; Figure 6 This is a schematic diagram of the time-domain response results provided in an embodiment of this application; wherein, Figure 6 (a) in the figure represents the time-domain response of the stator flux linkage frequency. Figure 6 (b) in the figure represents the time-domain response of the rotor flux linkage frequency. Figure 6 (c) in the figure represents the time-domain response of the stator voltage frequency. Figure 6 In the figure, (d) represents the rotor voltage frequency time-domain response result. Figure 6 In the figure, (e) represents the time-domain response of the stator current at frequency. Figure 6 (f) in the figure represents the time-domain response of the rotor current frequency; Figure 7 This is a schematic diagram of the structure of the amplitude-frequency operating point linear time-invariant modeling device for DFIG provided in the embodiments of this application; Figure 8 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0028] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0029] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0030] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0031] Next, combined Figures 1-6 This application provides an example of a linear time-invariant amplitude-frequency operating point modeling method for DFIG, as described in the embodiments of this application.

[0032] Figure 1 This is a flowchart illustrating the amplitude-frequency operating point linear time-invariant modeling method for DFIG provided in this application embodiment, as shown below. Figure 1 As shown, the method includes the following steps: Step S1: Construct a dynamic behavior model of the asynchronous motor, back-to-back converter and three-phase AC line in the doubly fed wind turbine generator. The dynamic behavior model includes complex exponential equations in which each electrical quantity is expressed as a product of time-varying amplitude and complex exponent. Optionally, a dynamic behavior model of the three components in a doubly fed wind turbine system can be established based on the three-phase balance assumption and ignoring the high-frequency switching process.

[0033] Optionally, the dynamic behavior model of the asynchronous motor is used to describe the electromagnetic and electromechanical dynamic behavior of the asynchronous motor in the doubly fed wind turbine, such as the electromagnetic relationship between the voltage, current and flux linkage of each winding of the stator and rotor, the relationship between the electromagnetic torque generated by the motor and the stator and rotor currents and flux linkages, and the mechanical motion dynamics of the rotor.

[0034] Optionally, the dynamic behavior model of the back-to-back converter is used to describe the electrical and control dynamic behavior of the back-to-back converter (including the control system) in the doubly-fed wind turbine, such as the active power calculation relationship between the grid-side converter and the machine-side converter on the AC side, the voltage dynamics of the DC-side capacitor of the back-to-back converter, and the control dynamics of the machine-side converter.

[0035] Optionally, a dynamic behavior model of a three-phase AC line is used to describe the electrical dynamic behavior of the connection line between the doubly-fed wind turbine and the power grid, such as the relationship between the choke line current, the filter capacitor voltage, and the transmission line current.

[0036] Optionally, since the spatial vector form of the three-phase electrical quantities in the established dynamic behavior model of the doubly-fed generator has time-varying amplitude and time-varying frequency characteristics, it can be expressed as a product of time-varying amplitude and complex exponent, thereby realizing a unified expression of the three-phase electrical quantities.

[0037] Step S2: Based on the dynamic behavior model, solve for the dynamic equations of the amplitude and angular frequency of each electrical quantity. Optionally, the dynamic behavior model is solved to obtain two independent equations for each electrical quantity: the amplitude dynamic equation and the angular frequency dynamic equation. The amplitude dynamic equation describes how the amplitude changes, and the angular frequency dynamic equation describes how the frequency changes.

[0038] Step S3: Linearize the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity to obtain the linear time-invariant model of the amplitude frequency operating point corresponding to the asynchronous machine, back-to-back converter and three-phase AC line respectively. Since the obtained dynamic equations for the amplitude and angular frequency of each electrical quantity are nonlinear, they are difficult to analyze. Furthermore, since the amplitude and frequency are DC quantities in steady state, linearization at the DC operating point can yield a linear time-invariant model.

[0039] Step S4: Integrate the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous motor, back-to-back converter, and three-phase AC line respectively to obtain the overall linear time-invariant model of the doubly-fed wind turbine based on the amplitude-frequency operating point.

[0040] The amplitude-frequency operating point linear time-invariant modeling method for DFIG provided in this application expresses electrical quantities as a product of time-varying amplitude and complex exponent, and further derives the complex exponential equation of the dynamic behavior model of the electrical components. This allows electrical quantities to be uniformly described using amplitude and frequency as state characteristics, thus avoiding the problem of needing to preset a fixed reference frequency in traditional rotating coordinate system modeling. By solving the dynamic behavior model, the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity are obtained, enabling the amplitude and frequency change processes of electrical quantities in the doubly-fed wind turbine system to be characterized separately. This provides state variables with clear physical meaning for analyzing voltage amplitude dynamics, frequency dynamics, and their interactions. Through the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, the method further enhances the understanding of the dynamics of the electrical components. By linearizing and integrating the dynamic equations of angular frequency, a linear time-invariant model of the entire doubly-fed induction generator (DFIG) wind turbine based on the amplitude-frequency operating point is constructed. This decouples the dynamics of the DFIG equipment from the dynamics of the power system network at the modeling level, facilitating its extension to stability mechanism analysis in multi-machine system scenarios. It can not only clearly characterize the dynamic evolution of the amplitude and frequency of each of the three-phase electrical quantities of the DFIG wind turbine, but also provide a fundamental model with clear physical meaning for voltage and frequency small-signal stability analysis, damping control system design in multi-machine scenarios, and operating parameter optimization. It is also applicable to autonomous power system scenarios where infinite power sources are lacking, and can support small-signal stability analysis of multi-machine grid-connected systems, thereby helping to improve the stability of DFIG wind turbine systems.

[0041] In some embodiments, the dynamic behavior model of an asynchronous machine includes: Three-phase stator and rotor voltage equations, three-phase stator and rotor flux linkage equations, electromagnetic torque equations, and rotor sway equations; The dynamic behavior model of back-to-back converters includes: Active power equation, DC capacitor equation, phase-locked loop control model, machine-side controller model, and grid-side controller model; The dynamic behavior model of a three-phase AC circuit includes: Choke circuit equations, filter capacitor equations, and transmission line equations.

[0042] Figure 2 This is a schematic diagram of the asynchronous machine winding model provided in the embodiments of this application, as shown below. Figure 2 As shown, where, Figure 2 (a) in the diagram represents the winding structure model of an asynchronous machine. Figure 2(b) is a schematic diagram of the amplitude and frequency states of electrical quantities in an asynchronous generator. It assumes that spatial harmonics are ignored, the three-phase windings are symmetrical, and they differ by 120° electrical angles in space. The resulting magnetomotive force is distributed sinusoidally along the air gap. Nonlinear saturation of the magnetic circuit is ignored, and the self-inductance and mutual inductance of each winding are considered to be related to the operating point of the magnetic circuit, but are constant values ​​related to the operating point. Core losses are ignored. Rotor parameters are all converted to the stator side. It is stipulated that the stator and rotor windings of the doubly-fed wind turbine adopt the conventions of electric motors. Under these assumptions, the equivalent physical model of the asynchronous generator in a doubly-fed wind turbine can be expressed as follows: Figure 2 The winding model shown is in form. Figure 2 In (a), the stator winding axis 、 、 The rotor windings are stationary in space, symmetrically distributed with a 120° difference in angle; the rotor winding axes... 、 、 They are also symmetrically distributed and move with the rotor at an angular velocity Since it rotates in space, the dynamic behavior model of the asynchronous machine in the three-phase coordinate system can be described by the following set of equations: Three-phase stator and rotor voltage time-domain differential equations: , .

[0043] in, =d / dt , , These are the instantaneous values ​​of the magnetic flux linkage of the three-phase stator and rotor windings, respectively. , These are the instantaneous values ​​of the three-phase phase voltages of the stator and rotor, respectively. , These are the instantaneous values ​​of the three-phase currents of the stator and rotor, respectively. , These are the stator and rotor winding resistances, respectively.

[0044] Three-phase stator and rotor flux linkage equations: , .

[0045] in, , , ; In the formula, Here is the stator self-inductance matrix. For the rotor self-inductance matrix, The mutual inductance matrix of the stator and rotor. For the mutual inductance matrix of the stator and rotor, The stator mutual inductance value corresponding to the maximum mutual inductance flux linked with one phase winding of the stator. The rotor mutual inductance value corresponding to the maximum mutual inductance flux linked with one phase winding of the rotor, and the two satisfy the relationship. = , , These are the stator and rotor leakage inductances, respectively. The rotor electrical angle is given.

[0046] Electromagnetic torque equation: ; Rotor oscillation equation: ; in, For electromagnetic torque, The input mechanical drive torque, The moment of inertia of the wind turbine generator set. The damping torque coefficient is proportional to the rotational speed. The rotor angular frequency, denoted as the number of rotor pole pairs.

[0047] Optionally, the dynamic behavior model of a back-to-back converter includes: active power equations, DC capacitor equations, phase-locked loop control model, machine-side controller model, and grid-side controller model. Therefore, the dynamic behavior model of the asynchronous machine in the three-phase coordinate system can be described by the following set of equations: The active power equations are the calculation equations for the active power on the AC side of the grid-side and generator-side converters: , ; in, For the active power on the AC side of the grid-side converter, The active power on the AC side of the machine-side converter. This represents the instantaneous value of the three-phase phase voltage on the AC side of the grid-side converter. The instantaneous values ​​of the three-phase current in the choke circuit are given. This represents the instantaneous value of the three-phase phase voltage on the AC side of the machine-side converter. This represents the instantaneous value of the rotor's three-phase current.

[0048] DC capacitor equation:

[0049] in, This is the DC capacitor voltage. This refers to DC capacitance.

[0050] The time-domain expression of the phase-locked loop control model is: , , ; in, For phase-locked loop phase, , These are the proportional and integral coefficients of the phase-locked loop PI controller, respectively. for Q-axis components in the phase-locked loop coordinate system The state variable is the integral control state variable of the phase-locked loop.

[0051] The time-domain expression of the machine-side controller model is: , , , , ; in, , These are the proportional and integral coefficients of the PI controller in the machine-side current loop, respectively. , These are the proportional and integral coefficients of the outer loop controller for the engine speed. The d-axis output voltage of the machine-side converter. This refers to the q-axis output voltage of the machine-side converter. This is the reference value for the d-axis machine-side current. This is the reference value for the q-axis machine-side current. This represents the d-axis rotor current value of the phase-locked loop. This represents the q-axis rotor current value of the phase-locked loop. The integral state variable of the d-axis current loop on the machine side. The integral state variable of the q-axis current loop on the machine side. The rotor speed, This is the rotor speed command value. The outer loop integral state variable is the outer loop control variable on the machine side.

[0052] The time-domain expression of the network-side controller model is: , , , , ; in, , These are the proportional and integral coefficients of the grid-side current loop PI controller, respectively. , These are the proportional and integral coefficients of the grid-side DC voltage outer loop controller, respectively. The grid-side converter controller outputs the d-axis voltage. The grid-side converter controller outputs the q-axis voltage. This is the reference value for the d-axis grid-side current. This is the reference value for the q-axis network current. This represents the line current value of the d-axis choke coil in the phase-locked loop. This represents the circuit current value of the phase-locked loop q-axis choke. For the d-axis current loop integral state variable on the grid side, For the grid-side q-axis current loop integral state variable, This is the DC capacitor voltage. This is the DC voltage command value. The integral state variable for the outer loop control of the grid-side DC voltage.

[0053] The time-domain differential equation for the dynamic behavior model of a three-phase AC circuit is: Instantaneous value equations for a three-phase choke circuit: ; in, , , These are the three-phase instantaneous values ​​of the choke coil inductor current, the three-phase instantaneous values ​​of the filter capacitor voltage, and the three-phase instantaneous values ​​of the internal potential of the grid-side converter. and These are the choke circuit inductance and resistance, respectively.

[0054] Instantaneous value equations for the three-phase circuit of the filter capacitor: ; in, and These are the three-phase instantaneous values ​​of the AC transmission line current and the three-phase instantaneous values ​​of the stator current, respectively. It is a filter capacitor.

[0055] Instantaneous value equations for three-phase circuits of transmission lines: ; in, This represents the instantaneous three-phase equivalent power supply voltage. and For the inductance and resistance of the power transmission line.

[0056] In some embodiments, step S2 specifically includes: By taking the time derivatives of both sides of the complex exponential equation and separating the real and imaginary parts of the result, we obtain the dynamic equations for the amplitude and angular frequency of each electrical quantity.

[0057] Optionally, the spatial vector form of three-phase electrical quantities has time-varying amplitude and time-varying frequency characteristics, and can be expressed as a product of time-varying amplitude and complex exponent, thereby realizing a unified expression of three-phase electrical quantities and obtaining time-domain differential equations in complex exponential form for three-phase stator and rotor voltage equations, three-phase stator and rotor flux linkage equations, and three-phase AC line equations, as well as electromagnetic torque calculation equations and active power calculation equations.

[0058] Optionally, let the three-phase positive-sequence basis vectors be: For electrical quantities x The three-phase instantaneous values ​​are transformed into equal-amplitude space vectors, i.e. Electrical quantities x The space vector is Therefore, the space vector of each electrical quantity can be expressed as a product of magnitude and complex exponent: , , , , , , , , , , ; in, , , , , , , , , , , ; in, A This represents the space vector magnitude corresponding to the three-phase electrical quantity. θ This represents the counterclockwise rotation angle of the space vector corresponding to the three-phase electrical quantity. ω This represents the counterclockwise angular frequency of the space vector corresponding to a three-phase electrical quantity. The stator flux linkage space vector, The rotor flux linkage space vector, The stator voltage space vector, The rotor voltage space vector, The AC side voltage space vector of the grid-side converter. The space vector of the AC side voltage of the machine-side converter. The space vector of the filter capacitor voltage. The current space vector of the choke circuit. This is the space vector of the transmission line current. The stator current space vector, This is the rotor current space vector.

[0059] exist Figure 2 In (b), and This represents the magnitude and frequency of the stator voltage space vector. and Represents the magnitude and frequency of the stator current space vector. and This represents the magnitude and frequency of the stator flux linkage space vector. and This represents the magnitude and frequency of the stator voltage space vector. and Represents the magnitude and frequency of the stator current space vector. and This represents the amplitude and frequency of the rotor flux linkage space vector. Therefore, the electrical quantities in the instantaneous equations of an asynchronous machine, after being converted into space vectors, can be expressed as the corresponding dynamic amplitude and frequency.

[0060] Optionally, the instantaneous value equations for the three-phase stator voltages are as follows: By performing a space vector transformation on the instantaneous values ​​of each electrical quantity in the instantaneous value equation of the three-phase stator voltage, we obtain: Substituting the complex exponents of the space vectors of each electrical quantity, we obtain the complex exponential equation for the three-phase stator voltage: .

[0061] Optionally, the instantaneous value equation of the three-phase rotor voltage is: By performing a space vector transformation on the instantaneous values ​​of each electrical quantity in the instantaneous value equation of the three-phase rotor voltage, we obtain: Substituting the complex exponents of the space vectors of each electrical quantity, we obtain the complex exponential equation for the three-phase rotor voltage: .

[0062] Optionally, the instantaneous equation for the three-phase stator flux linkage is: Multiply the instantaneous value equations of the three-phase stator flux linkage by 2 on both sides. / 3 yielded: Acting on vectors Matrix on It will degenerate into an equivalent scalar, that is , Similarly, After substituting and converting to spatial vector form, we get: The simplified complex exponential equation for the three-phase stator flux linkage is: .

[0063] Optionally, the instantaneous equation for the three-phase stator flux linkage is: Multiply the instantaneous value equation of the three-phase rotor flux linkage by 2 on both sides. / 3 yielded: , acting on vector Matrix on L rr It will degenerate into an equivalent scalar, that is , Similarly, After substituting and converting to spatial vector form, we get: The simplified complex exponential equation for the three-phase rotor flux linkage is: .

[0064] Figure 3 This is a schematic diagram of the amplitude and frequency of the three-phase inductor and three-phase capacitor provided in the embodiments of this application, as shown below. Figure 3 As shown, Figure 3 (a) in the diagram is a schematic diagram of a three-phase capacitor circuit and its current amplitude and frequency states. Figure 3 (b) is a schematic diagram of a three-phase inductor circuit and its current amplitude and frequency states. Figure 3 In (a), Represents the space vector of three-phase inductor current. and This represents the amplitude and frequency of the three-phase inductor current. Figure 3 In (b), Represents the space vector of three-phase capacitor voltage. and The amplitude and frequency of the three-phase capacitor voltage are represented. The spatial vector dynamics of the electrical quantities of the three-phase energy storage elements can be expressed as the corresponding amplitude and frequency dynamics. The process of deriving the time-domain equations of the amplitude and frequency of the electrical quantities of each energy storage element from the instantaneous value expression of the three-phase network is as follows: Multiply both sides of the instantaneous value equation of the three-phase network by 2 on the left. / 3 yielded: ; ; .

[0065] After simplification, we obtain the complex exponential equation for the three-phase circuit: ; ; .

[0066] Optionally, the equation for calculating electromagnetic torque is: , ; Optionally, the active power calculation equation is: , , , .

[0067] Expanding the complex exponential equation, which is in complex exponential form on both sides, with respect to time, and separating the real and imaginary parts of the result, yields time-domain differential equations for the amplitude and angular frequency of the stator and rotor flux linkages, stator and rotor currents, choke line currents, filter capacitor voltages, and transmission line currents, where: The time-domain equations for the stator flux linkage amplitude and angular frequency are as follows: , , , ; in, The angle between the stator voltage and the stator flux linkage space vector. The angle between the stator current and the stator flux linkage space vector is denoted as .

[0068] The time-domain equations for the rotor flux amplitude and angular frequency are: , , , ; in, The angle between the rotor voltage and the rotor flux linkage space vector is denoted as . The angle between the rotor current and the rotor flux linkage space vector is denoted as .

[0069] The time-domain equations for the stator current amplitude and angular frequency are as follows: , , , ; in, The angle between the stator flux linkage and the stator current space vector is denoted as . The angle between the rotor current and the stator current space vector in stator coordinates.

[0070] The time-domain equations for the rotor current amplitude and angular frequency are as follows: , , , ; in, The angle between the rotor flux linkage and the rotor current space vector is denoted as . The angle between the space vectors of the stator current and the rotor current in rotor coordinates.

[0071] The time-domain equations for the current amplitude and angular frequency of the choke circuit are as follows: , , , ; in, The angle between the filter capacitor voltage and the space vector of the choke circuit current is given. It is the angle between the internal potential of the grid-side converter and the space vector of the choke line current.

[0072] The time-domain equations for the voltage amplitude and angular frequency of the filter capacitor are as follows: , , , , ; in, The angle between the space vectors of the transmission line current and the filter capacitor voltage. The angle between the space vectors of the choke circuit current and the filter capacitor voltage. It is the angle between the space vectors of the stator current and the filter capacitor voltage.

[0073] The time-domain equations for the current amplitude and angular frequency of the transmission line are as follows: , , , ; in, The angle between the equivalent power supply voltage and the space vector of the transmission line current. This is the angle between the voltage of the filter capacitor and the space vector of the transmission line current.

[0074] In some embodiments, step S2 specifically includes: Based on the causal operation principle of physical systems and the dynamic behavior model of back-to-back converters, without taking the time derivative of the non-integral state variables of the controller in the back-to-back converter, the dynamic equations of the internal potential amplitude and angular frequency output of the controller in the back-to-back converter are solved.

[0075] Without taking the time derivative of the non-integral state variables, the time-domain equations for the phase-locked loop angular frequency, the time-domain equations for the internal potential amplitude of the grid-side and machine-side controller outputs, and the time-domain equations for the angular frequency are calculated, where: The dynamic time-domain equation for the phase-locked loop angular frequency is: , , ; Figure 4 This is a schematic diagram of the potential amplitude and frequency of the back-to-back converter provided in the embodiments of this application, as shown below. Figure 4 As shown, the machine-side converter generates dynamic values ​​of rotor internal potential amplitude and rotor internal potential angular frequency at the AC interface, while the grid-side converter generates dynamic values ​​of grid-side internal potential amplitude and internal potential angular frequency at the AC interface. and This indicates the amplitude and frequency of the machine-side voltage. and This represents the amplitude and frequency of the grid-side voltage, assuming the controller operates at a rotation frequency of... In the coordinate system, PI control is performed, and the general expression for the two converters at the AC interface is: , , ; Therefore, the time-domain equations for the potential amplitude and angular frequency within the grid-side converter controller are as follows: , , , , , , , ; The time-domain equations for the potential amplitude and angular frequency within the generator-side converter controller are as follows: , , , , , , .

[0076] In some embodiments, step S3 specifically includes: Step S31: Linearize the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, at the DC operating point to obtain linear time-invariant models of amplitude and frequency operating points corresponding to the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively.

[0077] In some embodiments, step S31 specifically includes: The amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output of the controller in the back-to-back converter, are linearized with small perturbations at the DC operating point to obtain linear time-invariant models of amplitude frequency operating points for the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively. Among them, the amplitude-frequency operating point linear time-invariant model of the asynchronous machine includes the stator voltage small-signal equation, rotor voltage small-signal equation, stator flux linkage small-signal equation, rotor flux linkage small-signal equation, electromagnetic torque small-signal equation, and rotor sway small-signal equation. The amplitude-frequency operating point linear time-invariant model of the back-to-back converter includes the active power small-signal equation, DC capacitor small-signal equation, phase-locked loop small-signal equation, grid-side controller small-signal equation, and machine-side controller small-signal equation. The amplitude-frequency operating point linear time-invariant model of the three-phase AC line includes the choke circuit small-signal equation, filter capacitor small-signal equation, and transmission line small-signal equation.

[0078] Specifically, the time-domain small-signal equation for the stator voltage is: , , , ; Where Δ represents the disturbance of the state variable, and the superscript 0 represents the steady-state value of the state variable.

[0079] The small-signal equation of the rotor voltage in the time domain is: , , , .

[0080] The time-domain small-signal equation for the stator flux linkage is: , , , .

[0081] The small-signal equation of rotor flux linkage in the time domain is: , , , .

[0082] The small-signal equation of electromagnetic torque in the time domain is: , .

[0083] The time-domain small-signal equation of the rotor rocking equation is: .

[0084] The time-domain small-signal calculation equation for active power is: , , , .

[0085] The time-domain small-signal equation for a DC capacitor is: .

[0086] The time-domain small-signal equation of the phase-locked loop is: , ; The time-domain small-signal equation for the grid-side converter controller is: , , , , , , , .

[0087] The time-domain small-signal equation for the generator-side converter controller is: , , , , , , .

[0088] The time-domain small-signal equation for the choke circuit is: , , , .

[0089] The time-domain small-signal equation for the filter capacitor circuit is: , , , , .

[0090] The time-domain small-signal equation for a transmission line is: , , , .

[0091] By integrating the time-domain small-signal models of each part, a linear time-invariant model of the entire doubly-fed wind turbine system based on the amplitude-frequency operating point is finally obtained.

[0092] Figure 5 This is a schematic diagram comparing the time-domain waveforms of the original model and the amplitude-frequency model provided in the embodiments of this application, wherein, Figure 5 (a) in the figure is a comparison of the time-domain waveforms of electromagnetic torque. Figure 5 (b) in the figure is a comparison of the time-domain waveforms of DC voltage. Figure 5 (c) shows a comparison of the time-domain waveforms of the rotor speed. In one embodiment of this application, the original mathematical model of the doubly-fed induction generator (DFIG) system is built in MATLAB / Simulink, and the parameter settings refer to the Doubly-Fed Induction Generator (DFIG) Average Model provided by MATLAB / Simulink. For both the original mathematical model and the time-invariant mathematical model based on the amplitude-frequency operating point of the DFIG system, the per-unit value of the input mechanical torque is set to jump from -0.8 to -0.85 at 5s. The waveforms of electromagnetic power, DC capacitor voltage, and rotor angular velocity are shown below. Figure 5 As shown, the original mathematical model of the doubly fed wind turbine and the time-invariant mathematical model based on the amplitude-frequency operating point are dynamically and precisely matched, verifying the accuracy of the method provided in this application.

[0093] Figure 6 This is a schematic diagram of the time-domain response results provided in an embodiment of this application, wherein, Figure 6 (a) in the figure represents the time-domain response of the stator flux linkage frequency. Figure 6 (b) in the figure represents the time-domain response of the rotor flux linkage frequency. Figure 6 (c) in the figure represents the time-domain response of the stator voltage frequency. Figure 6 In the figure, (d) represents the rotor voltage frequency time-domain response result. Figure 6 In the figure, (e) represents the time-domain response of the stator current at frequency. Figure 6In the above embodiment, (f) represents the time-domain response result of the rotor current frequency. The equivalent power supply frequency of the doubly-fed wind turbine mathematical model based on the amplitude frequency operating point is set to step from 49.5Hz to 50Hz at the 1st second and from 50Hz to 50.5Hz at the 2nd second. The stator and rotor flux linkage frequencies, stator and rotor voltage frequencies, and stator and rotor current frequencies in the doubly-fed wind turbine model are as follows: Figure 6 As shown, the frequency state variable of the doubly fed wind turbine based on the amplitude frequency operating point can remain a DC variable under different equivalent power supply frequency settings, verifying that the overall linear time-invariant model of the doubly fed wind turbine based on the amplitude frequency operating point of this application is applicable to any steady-state frequency operating scenario.

[0094] In one embodiment of this application, the power system operates autonomously when there is no infinite power source. By establishing the doubly-fed wind turbine, network, and other grid-connected equipment at the amplitude frequency operating point, the equipment can be decoupled from each other and from the network, and can be used to analyze the impact of the doubly-fed wind turbine or other grid-connected equipment on the stability of the power system.

[0095] The following describes the amplitude-frequency operating point linear time-invariant modeling apparatus for DFIG provided in this application. The amplitude-frequency operating point linear time-invariant modeling apparatus for DFIG described below can be referred to in correspondence with the amplitude-frequency operating point linear time-invariant modeling method for DFIG described above.

[0096] Figure 7 This is a schematic diagram of a linear time-invariant modeling device for amplitude-frequency operating point suitable for DFIG provided in an embodiment of this application, as shown below. Figure 7 As shown, the device 700 includes: Module 710 is used to construct dynamic behavior models of the asynchronous motor, back-to-back converter and three-phase AC line in a doubly fed wind turbine. The dynamic behavior model includes complex exponential equations in which each electrical quantity is expressed as a product of time-varying amplitude and complex exponent. Solver module 720 is used to solve for the magnitude dynamic equations and angular frequency dynamic equations of each electrical quantity based on the dynamic behavior model; Linearization module 730 is used to linearize the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity to obtain linear time-invariant models of the amplitude frequency operating point corresponding to the asynchronous machine, back-to-back converter and three-phase AC line, respectively. The integration module 740 is used to integrate the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous machine, back-to-back converter and three-phase AC line respectively, to obtain the overall linear time-invariant model of the doubly-fed wind turbine based on the amplitude-frequency operating point.

[0097] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0098] Based on the methods in the above embodiments, Figure 8 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 8 As shown in the illustration, this application provides an electronic device that may include a processor 810, a communication interface 820, a memory 830, and a communication bus 840. The processor 810, communication interface 820, and memory 830 communicate with each other via the communication bus 840. The processor 810 can call logical instructions from the memory 830 to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG described in the above embodiment.

[0099] Furthermore, the logic instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the amplitude-frequency operating point linear time-invariant modeling method for DFIG described in the various embodiments of this application.

[0100] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG as described in the above embodiments.

[0101] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG as described in the above embodiments.

[0102] It is understood that the processor in the embodiments of this application can 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, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0103] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0104] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially 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 this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium 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 a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0105] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0106] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A linear time-invariant modeling method for the amplitude-frequency operating point of DFIG, characterized in that, include: A dynamic behavior model is constructed for the asynchronous motor, back-to-back converter and three-phase AC line in a doubly fed wind turbine generator. The dynamic behavior model includes complex exponential equations in which each electrical quantity is expressed as a product of time-varying amplitude and complex exponent. Based on the dynamic behavior model, the dynamic equations for the magnitude and angular frequency of each electrical quantity are solved to obtain the dynamic equations for the electrical quantity. Linearize the amplitude dynamic equations and angular frequency dynamic equations of the electrical quantities to obtain linear time-invariant models of the amplitude frequency operating points for the asynchronous machine, back-to-back converter and three-phase AC line, respectively. By integrating the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous motor, back-to-back converter, and three-phase AC line, a linear time-invariant model of the entire doubly-fed wind turbine based on the amplitude-frequency operating point is obtained.

2. The linear time-invariant amplitude-frequency operating point modeling method for DFIG according to claim 1, characterized in that, The dynamic behavior model of the asynchronous machine includes: Three-phase stator and rotor voltage equations, three-phase stator and rotor flux linkage equations, electromagnetic torque equations, and rotor sway equations; The dynamic behavior model of the back-to-back converter includes: Active power equation, DC capacitor equation, phase-locked loop control model, machine-side controller model, and grid-side controller model; The dynamic behavior model of the three-phase AC line includes: Choke circuit equations, filter capacitor equations, and transmission line equations.

3. The linear time-invariant amplitude-frequency operating point modeling method for DFIG according to claim 1, characterized in that, The process of solving the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity based on the dynamic behavior model includes: By taking the time derivatives of both sides of the complex exponential equation and separating the real and imaginary parts of the result, the dynamic equations for the amplitude and angular frequency of each electrical quantity are obtained.

4. The linear time-invariant modeling method for amplitude-frequency operating point applicable to DFIG as described in claim 1, characterized in that, The process of solving the amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity based on the dynamic behavior model includes: Based on the causal operation principle of physical systems and the dynamic behavior model of back-to-back converters, without taking the time derivative of the non-integral state variables of the controller in the back-to-back converter, the dynamic equations of the internal potential amplitude and angular frequency output by the controller in the back-to-back converter are solved.

5. The linear time-invariant modeling method for amplitude-frequency operating point applicable to DFIG according to claims 3 and 4, characterized in that, The linearization of the amplitude dynamic equations and angular frequency dynamic equations of the various electrical quantities to obtain linear time-invariant models of the amplitude-frequency operating points for the asynchronous machine, back-to-back converter, and three-phase AC line, respectively, includes: The amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, are linearized at the DC operating point to obtain linear time-invariant models of the amplitude and frequency operating points corresponding to the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively.

6. The linear time-invariant amplitude-frequency operating point modeling method for DFIG according to claim 5, characterized in that, The linearization of the amplitude and angular frequency dynamic equations of each electrical quantity, as well as the amplitude and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, at the DC operating point yields linear time-invariant models of the amplitude and frequency operating points for the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively, including: The amplitude dynamic equations and angular frequency dynamic equations of each electrical quantity, as well as the amplitude dynamic equations and angular frequency dynamic equations of the internal potential output by the controller in the back-to-back converter, are linearized with small perturbations at the DC operating point to obtain linear time-invariant models of amplitude and frequency operating points for the asynchronous machine, the back-to-back converter, and the three-phase AC line, respectively. The linear time-invariant model of the amplitude-frequency operating point of the asynchronous machine includes small-signal equations for stator voltage, rotor voltage, stator flux linkage, rotor flux linkage, electromagnetic torque, and rotor sway. The linear time-invariant model of the amplitude-frequency operating point of the back-to-back converter includes small-signal equations for active power, DC capacitor, phase-locked loop, grid-side controller, and machine-side controller. The linear time-invariant model of the amplitude-frequency operating point of the three-phase AC line includes small-signal equations for choke circuit, filter capacitor, and transmission line.

7. A linear time-invariant modeling device for amplitude-frequency operating point suitable for DFIG, characterized in that, include: The module is used to construct a dynamic behavior model of the asynchronous motor, back-to-back converter and three-phase AC line in a doubly fed wind turbine. The dynamic behavior model includes complex exponential equations in which each electrical quantity is expressed as a product of time-varying amplitude and complex exponent. The solver module is used to solve for the magnitude dynamic equations and angular frequency dynamic equations of each electrical quantity based on the dynamic behavior model. The linearization module is used to linearize the amplitude dynamic equation and angular frequency dynamic equation of each electrical quantity to obtain linear time-invariant models of the amplitude frequency operating points corresponding to the asynchronous machine, back-to-back converter and three-phase AC line, respectively. The integration module is used to integrate the amplitude-frequency operating point linear time-invariant models corresponding to the asynchronous motor, back-to-back converter and three-phase AC line respectively, to obtain the overall linear time-invariant model of the doubly-fed wind turbine based on the amplitude-frequency operating point.

8. An electronic device, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the amplitude-frequency operating point linear time-invariant modeling method for DFIG as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is run on the processor, the processor performs the amplitude-frequency operating point linear time-invariant modeling method for DFIG as described in any one of claims 1-6.

10. A computer program product, characterized in that, When the computer program product is run on a processor, the processor performs the amplitude-frequency operating point linear time-invariant modeling method for DFIG as described in any one of claims 1-6.

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