Stability analysis method of high-voltage direct current power transmission system and nonlinear modeling method, device and equipment of network converter

Abstract

This application relates to a stability analysis method for high-voltage direct current (HVDC) transmission systems and a nonlinear modeling method, apparatus, and equipment for grid-connected converters. The nonlinear modeling method for grid-connected converters first determines voltage differential equations, voltage differential data, current differential equations, and current differential data by obtaining electrical quantity data. Then, it sequentially determines the main loop dynamic equations and periodic differential equations. By combining the voltage and current differential equations of the control loop dynamics with the main loop dynamic equations and periodic differential equations, a nonlinear differential equation for analyzing the stability of the HVDC transmission system is obtained. This nonlinear differential equation is used to analyze the stability of the HVDC transmission system, solving the problems of existing HVDC transmission systems based on modular multilevel converters where periodic time-varying dynamics and strongly nonlinear limiting behavior induce dynamic bifurcation leading to system instability, and the lack of a universal nonlinear mathematical model and efficient and accurate analysis method.

Description

Technical Field

[0001] This application relates to the field of power system modeling and analysis technology, and in particular to a stability analysis method for high voltage direct current transmission systems that considers periodic dynamics and switching limiting processes, as well as a nonlinear modeling method, apparatus and equipment for grid converters. Background Technology

[0002] Modular Multilevel Converter-based HVDC (MMC-HVDC) technology, with its significant advantages in regulation flexibility and islanded operation stability, has become a key technology for large-scale power transmission. MMC-HVDC systems based on grid-connected control modes have attracted widespread attention. However, dynamic processes triggered by grid faults often lead to transient overcurrent states in grid-connected converters, and excessively high overcurrent amplitudes or durations can cause thermal breakdown of devices. Therefore, limiting circuits are commonly integrated into the control systems of MMC-HVDC. However, these limiting circuits deeply intervene in the converter's dynamic response process and can even dominate the transient stability evolution path of the power system. The strong nonlinear characteristics of the limiting effect may induce bifurcation phenomena in the dynamic behavior of the power system, leading to instability risks. For the modeling and stability analysis of grid-type flexible DC transmission systems with controller limiting participation, existing technical solutions are usually carried out within a continuous nonlinear time-invariant framework, characterizing the dynamic behavior of the converter in an average manner. However, this approach has the following problems: First, it cannot characterize the impact of discrete processes such as limiting on the dynamic process of the actual control system; second, it cannot reveal the essential periodic time-varying behavior of grid-type flexible DC transmission systems, and cannot characterize complex operating conditions such as three-phase short circuits and single-phase short circuits in the AC power grid; third, it assumes that the periodic trajectory remains unchanged under parameter changes, making it difficult to achieve accurate stability analysis. Summary of the Invention

[0003] This application provides a stability analysis method for high-voltage direct current (HVDC) transmission systems and a nonlinear modeling method, apparatus, and equipment for grid-connected converters. These methods address the technical problem that existing HVDC transmission systems based on modular multilevel converters suffer from instability caused by induced dynamic bifurcation due to their time-varying dynamic and strongly nonlinear amplitude-limiting behavior, and lack a universal nonlinear mathematical model and efficient and accurate analysis method.

[0004] To achieve the above objectives, this application provides the following technical solution:

[0005] On the one hand, a nonlinear modeling method for grid-connected converters is provided, which is applied to high-voltage direct current transmission systems based on grid-connected converters. This nonlinear modeling method includes the following steps:

[0006] The electrical quantity data of the grid-connected converter in the high-voltage direct current transmission system are obtained. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit voltage command value, lower limit voltage command value, shaft voltage, proportional-integral integral quantity, upper limit current command value, lower limit current command value, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained.

[0007] Based on the voltage differential data, the current differential data, the grid-connected measured current, and the decoupling constant, current control proportional coefficient, and phase-locked output phase angle of the electrical quantity data, the bridge arm reference voltage of the three phases of the grid converter is obtained; based on the bridge arm reference voltage of each phase and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid converter is obtained.

[0008] Based on the bridge arm modulation signal and the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, AC / DC neutral point voltage difference, common coupling point current, bridge arm circulating current, and bridge arm differential mode voltage of each phase of the bridge arm submodule in the electrical quantity data, the main circuit dynamic equation of the grid converter is obtained.

[0009] Based on the power grid angular frequency and period time of the electrical quantity data, a periodic differential equation is obtained;

[0010] Based on the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation, a nonlinear mathematical model of the grid converter is obtained, which combines the dynamics of the main loop and the dynamics of the control loop and is expressed by nonlinear differential equations.

[0011] Optionally, based on the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation, a nonlinear mathematical model of the grid converter, which combines the dynamics of the main loop and the dynamics of the control loop and is expressed by nonlinear differential equations, is constructed. This model includes: using the left-hand side variables of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the state variables of the nonlinear differential equation; and using the right-hand side expressions of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the nonlinear vector field of the nonlinear differential equation.

[0012] Optionally, based on the reactive power, reactive power reference value, reactive power droop coefficient, upper voltage command limit, lower voltage command limit, shaft voltage, proportional-integral integral quantity, upper current command limit, lower current command limit, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained, including:

[0013] Based on the reactive power, the reactive power reference value, the reactive power droop coefficient, the upper limit of the voltage command, and the lower limit of the voltage command, the voltage command value and the voltage limiting command value of the grid converter using the reactive power droop control loop are determined.

[0014] Based on the voltage limiting command value, the shaft voltage, the proportional-integral integral, the upper limit of the current command, the lower limit of the current command, and the voltage control proportional coefficient, the current command value and the current limiting command value of the voltage control loop used in the grid converter are determined.

[0015] Based on the voltage command value, the voltage limiting command value, the voltage control integral coefficient, and the anti-integral saturation parameter, the voltage differential equation and voltage differential data of the voltage control loop in the grid converter are obtained.

[0016] Based on the current command value, the current limiting command value, the measured grid-connected current, and the current control integral coefficient, the current differential equation and current differential data of the current control loop in the grid converter are obtained.

[0017] On the other hand, a stability analysis method for a high-voltage direct current transmission system is provided, including the following steps:

[0018] The nonlinear mathematical model of the grid converter in the high voltage direct current transmission system is obtained by using the nonlinear modeling method of the grid converter described above, which is represented by nonlinear differential equations.

[0019] The nonlinear differential equation is processed using an automatic differentiation method to obtain the first Jacobian matrix of the Poincaré map;

[0020] The fixed points of the Poincaré mapping in the first Jacobian matrix are iteratively solved using the numerical extension method based on Newton-Raphson to obtain the second Jacobian matrix for accurately locating the periodic orbit.

[0021] The matrix eigenvalues ​​are calculated based on the second Jacobian matrix; the stability of the high-voltage direct current transmission system is then determined based on the matrix eigenvalues.

[0022] Optionally, the fixed points of the Poincaré mapping in the first Jacobian matrix are iteratively solved using a numerical extension method based on Newton-Raphson to obtain the second Jacobian matrix for accurately locating the periodic orbit, including:

[0023] The initial parameters of the numerical extension method based on Newton-Raphson are obtained, including the tangent vector, the given change in arc length, the initial fixed point, and the initial stability coefficient.

[0024] Based on the initial parameters, the first period prediction point of the first numerical extension is obtained;

[0025] Based on the first periodic prediction point and the first Jacobian matrix, an iterative calculation is performed to obtain a second Jacobian matrix that satisfies the iteration termination condition.

[0026] The formula for iterative calculation is as follows:

[0027] ;

[0028] The iteration termination condition is: ;

[0029] In the formula, Let be the Jacobian matrix calculated in the k-th iteration. For the periodic prediction point calculated in the k-th iteration, For the periodic prediction point calculated in the (k+1)th iteration, F( ) is the function value of the k-th iteration, and ε is the threshold of the iteration parameter.

[0030] Optionally, determining the stability of the high-voltage direct current transmission system based on the matrix eigenvalues ​​includes:

[0031] If all the eigenvalues ​​of the matrix are within the unit circle, then the stability of the high-voltage direct current transmission system is system stability.

[0032] If one of the eigenvalues ​​of the matrix is ​​not inside the unit circle, then the stability of the high-voltage direct current transmission system is unstable.

[0033] If there exists a pair of conjugate eigenvalues ​​on the unit circle among the eigenvalues ​​of the matrix, then the stability of the high-voltage direct current transmission system is that the system undergoes torus bifurcation.

[0034] If one of the eigenvalues ​​of the matrix lies on the x-axis of the unit circle, then the stability of the high-voltage direct current transmission system is that the system undergoes folding and bifurcation.

[0035] On the other hand, a nonlinear modeling device for grid converters is provided, which is applied to high-voltage direct current transmission systems based on grid converters. The nonlinear modeling device includes a data acquisition and processing module, a signal determination module, a dynamic equation determination module, a periodic equation module, and a model construction module.

[0036] The data acquisition and processing module is used to acquire the electrical quantity data of the grid-connected converter in the high-voltage direct current transmission system. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit voltage command value, lower limit voltage command value, shaft voltage, proportional-integral integral quantity, upper limit current command value, lower limit current command value, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained.

[0037] The signal determination module is used to determine, based on the voltage differential data, the current differential data, the grid-connected measured current, and the decoupling constant, current control proportional coefficient, and phase-locked output phase angle of the electrical quantity data, to obtain the bridge arm reference voltage of the three phases of the grid converter; and to determine, based on the bridge arm reference voltage of each phase and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid converter.

[0038] The dynamic equation determination module is used to determine the main circuit dynamic equation of the grid converter based on the bridge arm modulation signal and the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, AC / DC neutral point voltage difference, common coupling point current, bridge arm circulating current and bridge arm differential mode voltage of each phase of the bridge arm submodule in the electrical quantity data.

[0039] The periodic equation module is used to determine, based on the power grid angular frequency and periodic time of the electrical quantity data, a periodic differential equation;

[0040] The model building module is used to construct a nonlinear mathematical model of the grid converter based on the voltage differential equation, the current differential equation, the main circuit dynamic equation, and the periodic differential equation. This model is a combination of the main circuit dynamics and the control loop dynamics, expressed by nonlinear differential equations.

[0041] Optionally, the model building module is further configured to use the left-hand side variables of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the state variables of the nonlinear differential equation; and to use the right-hand side expressions of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the nonlinear vector field of the nonlinear differential equation.

[0042] Optionally, the data acquisition and processing module includes a voltage limiting processing submodule, a current limiting processing submodule, a voltage micro-molecule module, and a current micro-molecule module;

[0043] The voltage limiting processing submodule is used to determine, based on the reactive power, the reactive power reference value, the reactive power droop coefficient, the upper limit of the voltage command, and the lower limit of the voltage command, the voltage command value and the voltage limiting command value of the grid converter using the reactive power droop control loop.

[0044] The current limiting processing submodule is used to determine, based on the voltage limiting command value, the shaft voltage, the proportional-integral integral quantity, the upper limit value of the current command, the lower limit value of the current command, and the voltage control proportional coefficient, the current command value and the current limiting command value of the voltage control loop used by the grid converter.

[0045] The voltage micro-molecule module is used to determine, based on the voltage command value, the voltage limiting command value, the voltage control integral coefficient, and the anti-integral saturation parameter, the voltage differential equation and voltage differential data of the voltage control loop in the grid converter.

[0046] The current micro-molecule module is used to determine, based on the current command value, the current limiting command value, the grid-connected measured current, and the current control integral coefficient, the current differential equation and current differential data of the current control loop in the grid converter.

[0047] On the other hand, a terminal device is provided, including a processor and a memory;

[0048] The memory is used to store program code and transmit the program code to the processor;

[0049] The processor is configured to execute the nonlinear modeling method for grid converters described above, according to the instructions in the program code.

[0050] This paper presents a stability analysis method for a high-voltage direct current (HVDC) transmission system and a nonlinear modeling method, apparatus, and equipment for a grid-connected converter. The nonlinear modeling method for the grid-connected converter includes acquiring electrical quantity data of the grid-connected converter in the HVDC transmission system. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper voltage command limit, lower voltage command limit, shaft voltage, proportional-integral (PI) integral quantity, upper current command limit, lower current command limit, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, measured grid-connected current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained. Based on the voltage differential data, current differential data, measured grid-connected current, and decoupling constants and current control proportional coefficients of the electrical quantity data, the method further refines the model. The phase angle of the phase-locked output is determined to obtain the reference voltage of the three-phase bridge arm of the grid-connected converter. Based on the reference voltage of each phase bridge arm and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid-connected converter is obtained. Based on the bridge arm modulation signal and the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, voltage difference between AC and DC neutral points, common coupling point current, bridge arm circulating current, and bridge arm differential mode voltage of each phase bridge arm submodule in the electrical quantity data, the main loop dynamic equation of the grid-connected converter is obtained. Based on the grid angular frequency and period time of the electrical quantity data, the periodic differential equation is obtained. Based on the voltage differential equation, current differential equation, main loop dynamic equation, and periodic differential equation, a nonlinear mathematical model of the grid-connected converter is constructed, which combines the dynamics of the main loop and the dynamics of the control link and is expressed by nonlinear differential equations.

[0051] As can be seen from the above technical solutions, this application has the following advantages: The nonlinear modeling method of the grid converter first determines the voltage differential equation, voltage differential data, current differential equation, and current differential data by obtaining electrical quantity data, and then determines the main loop dynamic equation and periodic differential equation in sequence. The voltage differential equation and current differential equation of the control loop dynamic are combined with the main loop dynamic equation and periodic differential equation to obtain the nonlinear differential equation for analyzing the stability of the high voltage direct current transmission system. The stability of the high voltage direct current transmission system is analyzed through this nonlinear differential equation, which solves the technical problem that the existing high voltage direct current transmission based on modular multilevel converters has instability caused by the induced dynamic bifurcation of the periodic time-varying dynamics and strong nonlinear amplitude limiting behavior, and lacks a general nonlinear mathematical model and efficient and accurate analysis method.

[0052] This stability analysis method for high-voltage direct current (HVDC) transmission systems effectively establishes a highly accurate nonlinear mathematical model of the grid-connected converter, accurately characterizing the periodic time-varying, limiting, and switching processes of the HVDC transmission system. Then, an automatic differentiation method and a deteriorated Newton-Raphson-based numerical extension method are used to process the nonlinear differential equations of the nonlinear mathematical model. Considering the influence of stability coefficient changes on the periodic track, the matrix eigenvalues ​​that accurately assess the stability of the HVDC transmission system are obtained, enabling accurate analysis of the system's stability. This method solves the technical problem of existing HVDC transmission technologies based on modular multilevel converters using strongly nonlinear characteristics for limiting, which induces bifurcation phenomena in the system's dynamic behavior, leading to system instability.

[0053] The nonlinear modeling device for this grid converter obtains electrical quantity data through a data acquisition and processing module, a signal determination module, a dynamic equation determination module, a periodic equation module, and a model construction module. First, it determines the voltage differential equation, voltage differential data, current differential equation, and current differential data. Then, it determines the main circuit dynamic equation and periodic differential equation in sequence. By combining the voltage differential equation and current differential equation of the control loop dynamics with the main circuit dynamic equation and periodic differential equation, a nonlinear differential equation for analyzing the stability of the high-voltage direct current transmission system is obtained. The stability of the high-voltage direct current transmission system is then analyzed through this nonlinear differential equation. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of 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 only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart illustrating the steps of the nonlinear modeling method for grid converters described in the embodiments of this application;

[0056] Figure 2 This is a schematic diagram of the topology of the grid converter in the nonlinear modeling method for the grid converter described in the embodiments of this application;

[0057] Figure 3 This is a flowchart illustrating the steps of the stability analysis method for a high-voltage direct current transmission system described in the embodiments of this application.

[0058] Figure 4 This is a comparative structural diagram of the stability analysis method for the high-voltage direct current transmission system described in the embodiments of this application;

[0059] Figure 5This is an instability prediction diagram of the stability analysis method for the high-voltage direct current transmission system described in the embodiments of this application;

[0060] Figure 6 This is a simulation verification diagram of instability prediction in the stability analysis method of the high-voltage direct current transmission system described in the embodiments of this application;

[0061] Figure 7 This is a schematic diagram of the framework of the nonlinear modeling device for the grid converter described in the embodiments of this application;

[0062] Figure 8 This is a schematic diagram of the terminal device described in an embodiment of this application. Detailed Implementation

[0063] To make the inventive objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are only some embodiments of this application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0064] In the description of the embodiments of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0065] In the embodiments of this application, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this application according to the specific circumstances.

[0066] Patent terminology used in this application:

[0067] High-voltage direct current (HVDC) transmission systems are power engineering systems that use direct current to transmit high-power, long-distance electrical energy. They are mainly used for submarine cable transmission, asynchronous power grid interconnection, and clean energy grid connection.

[0068] The Newton-Raphson numerical extension method is a numerical solution strategy that combines the Newton-Raphson iterative method and extension techniques. It is mainly used to solve convergence problems in nonlinear equation systems or complex systems. Its core is to guide the iterative process to stable convergence by gradually adjusting parameters or initial conditions.

[0069] A grid-connected converter refers to a converter with grid-connected capability. A grid-connected converter can also be a converter that can independently build and maintain grid voltage and frequency.

[0070] This application provides a stability analysis method for high-voltage direct current (HVDC) transmission systems and a nonlinear modeling method, apparatus, and equipment for grid-connected converters. It solves the technical problems of existing HVDC transmission systems based on modular multilevel converters, where the time-varying dynamics and strong nonlinear amplitude limiting behavior induces dynamic bifurcation leading to system instability, and there is no general nonlinear mathematical model or efficient and accurate analysis method.

[0071] Example 1:

[0072] Figure 1 This is a flowchart illustrating the steps of the nonlinear modeling method for a grid converter described in this application embodiment. Figure 2 This is a schematic diagram of the topology of the grid converter in the nonlinear modeling method of the grid converter described in the embodiments of this application.

[0073] like Figure 1 and Figure 2 As shown in the figure, this application provides a nonlinear modeling method for grid-connected converters, applied to high-voltage direct current transmission systems based on grid-connected converters. The nonlinear modeling method includes the following steps:

[0074] S1. Obtain the electrical quantity data of the grid-connected converter in the high-voltage direct current transmission system. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit of voltage command, lower limit of voltage command, shaft voltage, proportional-integral integral quantity, upper limit of current command, lower limit of current command, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient, determine the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter.

[0075] It should be noted that in the nonlinear modeling process of the grid-connected converter, step S1 involves first obtaining the electrical quantity data of the grid-connected converter in the HVDC transmission system. The mobile terminal can first determine the electrical quantity data required for constructing the nonlinear mathematical model of the grid-connected converter in the HVDC transmission system, and then construct the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter based on the electrical quantity data. The electrical quantity data includes the current and voltage of the grid-connected converter connected to the HVDC transmission system, as well as various parameters of the grid-connected converter itself. For example, the electrical quantity data includes reactive power Q and reactive power reference value Q. ref reactive power droop coefficient k dp Voltage command upper limit U max Voltage command lower limit U min , shaft voltage, proportional-integral integral quantity x dI Current command upper limit value I max Current command lower limit I min Voltage control proportional coefficient k pI Voltage control integral coefficient k iI Anti-integral saturation parameter K aw Measured grid-connected current and current control integral coefficient k i etc. Among them, the axis voltage includes the d-axis voltage u. d and q-axis voltage u q The measured grid-connected current includes the measured grid-connected current i along the d-axis. d Measured current i in parallel with q-axis q The voltage differential equations, voltage differential data, current differential equations, and current differential data of the grid converter include the voltage differential equations, voltage differential data, current differential equations, and current differential data of the d-axis and the voltage differential equations, voltage differential data, current differential equations, and current differential data of the q-axis, respectively.

[0076] Understandably, mobile terminals can extract electrical quantity data of grid-connected converters in HVDC transmission systems from real-time monitoring platforms, energy management systems, or dispatch data centers of the power system. This ensures that the collected data covers the computational data required to construct a nonlinear mathematical model of the grid-connected converter using nonlinear differential equations. After determining the electrical quantity data of the grid-connected converter, the mobile terminal can construct the electrical quantity data transmitted from the HVDC transmission system to the grid-connected converter. Based on this electrical quantity data, voltage and current differential equations can be used to smoothly and dynamically characterize the limiting and switching links in the grid-connected HVDC converter using a linear combination of hyperbolic tangent functions. This provides data for subsequent analysis to model the dynamics of the main circuit and control links of the grid-connected HVDC converter, thereby more accurately constructing a nonlinear mathematical model of the grid-connected converter using nonlinear differential equations. This avoids inaccurate modeling caused by the time-varying periodicity of the grid-connected converter and the limiting and switching processes in the HVDC transmission system.

[0077] In the embodiment of the application, step S1 can also first obtain the electrical quantity data of the grid-connected converter in the high-voltage direct current transmission system. The mobile terminal can first determine the electrical quantity data required to construct the nonlinear mathematical model of the grid-connected converter in the high-voltage direct current transmission system, and then construct the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter using a smooth approximation method for discontinuous processes based on the electrical quantity data. The smooth approximation method for discontinuous processes refers to approximating a non-smooth function with discontinuities or jumps using a continuously differentiable (smooth) function while preserving the key features of the original function. Smooth approximation methods include convolution approximation based on the Dirac function / kernel function, kernel density estimation, and iterative smoothing.

[0078] S2. Based on the voltage differential data, current differential data, grid-connected measured current, and electrical quantity data, the decoupling constant and phase-locked output phase angle are determined to obtain the bridge arm reference voltage of the three phases of the grid converter; based on the bridge arm reference voltage of each phase and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid converter is determined.

[0079] It should be noted that in this step S2, the mobile terminal can use the d-axis voltage differential data u determined in step S1. d d-axis current differential data x d q-axis voltage differential data u q q-axis current differential data x q d-axis grid-connected measured current i d Measured current i in parallel with q-axis q and the decoupling constant K of electrical quantity data d Current control proportional coefficient k pAfter calculating the phase angle θ of the phase-locked output, the three-phase arm reference voltages of the grid converter are obtained, providing data for calculating the arm modulation signal of each phase arm. The mobile terminal can also obtain the DC voltage rating U of each phase arm reference voltage and electrical quantity data. dc It is determined that the arm modulation signal for each phase arm in the grid converter is obtained. Among them, the arm reference voltage of the three phases of the grid converter includes the arm reference voltage u of phase a. a ref b-phase bridge arm reference voltage u b ref and the reference voltage u of the c-phase bridge arm c ref In a grid converter, the bridge arm modulation signal for each phase arm includes the upper bridge arm modulation signal n. j A and lower bridge arm modulation signal n j B In the formula, A is the upper bridge arm, B is the lower bridge arm, and j is phase a, phase b, or phase c.

[0080] It is understandable that determining the d-axis voltage differential data u... d d-axis current differential data x d q-axis voltage differential data u q q-axis current differential data x q d-axis grid-connected measured current i d Measured current i in parallel with q-axis q and the decoupling constant K of electrical quantity data d Current control proportional coefficient k p After the phase angle θ of the phase-locked output, the mobile terminal can then calculate the arm voltage reference data based on the predetermined arm voltage reference formula to obtain the three-phase arm reference voltages required for the operation of the grid-connected converter in the HVDC transmission system. Finally, the mobile terminal can calculate the determined arm reference voltage and DC voltage rating U for each phase based on the predetermined modulation signal formula. dc The calculation yields the upper arm modulation signal n for each phase of the grid-connected converter. j A and lower bridge arm modulation signal n j B This provides data for the subsequent construction of the dynamic equations of the main circuit of the grid converter, fully reflecting the dynamic changes of the main circuit in the grid converter.

[0081] In this embodiment, the bridge arm voltage reference formula is:

[0082] ;

[0083] In the formula, i d refi is the current limiting command value for the d-axis. q ref This is the current limiting command value for the q-axis.

[0084] It should be noted that the mobile terminal can determine the d-axis voltage differential data u. d d-axis current differential data x d q-axis voltage differential data u q q-axis current differential data x q d-axis grid-connected measured current i d Measured current i in parallel with q-axis q and the decoupling constant K of electrical quantity data d Current control proportional coefficient k p The phase angle θ of the phase-locked loop output can be calculated using Clarke transform and Park transform to obtain the reference voltage u of phase a bridge arm. a ref b-phase bridge arm reference voltage u b ref and the reference voltage u of the c-phase bridge arm c ref .

[0085] In this embodiment, the modulation signal formula is:

[0086] ;

[0087] In the formula, u j ref Let n be the reference voltage for the bridge arm of phase j. j A Let n be the modulation signal of the upper arm of phase j. j B is the modulation signal for the lower arm of phase j.

[0088] S3. Based on the bridge arm modulation signal and electrical quantity data, the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, AC / DC neutral point voltage difference, common coupling point current, bridge arm circulating current, and bridge arm differential mode voltage of each phase of the bridge arm submodule are determined, and the main circuit dynamic equation of the grid converter is obtained.

[0089] It should be noted that in step S3, the upper arm modulation signal n of each phase is determined based on step S2. j A Lower arm modulation signal n j B Total capacitor voltage of each phase bridge arm submodule Equivalent capacitance C eq Equivalent inductance L eq Bridge arm inductor L arm Voltage difference between AC and DC neutral points u nNCommon coupling point current i j Bridge arm circulation and bridge arm differential voltage Then, based on the determined data, the dynamic equations of the main loop of the grid converter are constructed, providing data for the subsequent construction of a nonlinear mathematical model of the grid converter, which combines the dynamics of the main loop and the dynamics of the control loop and is expressed by nonlinear differential equations. Among these, the equivalent inductance L... eq =L t +0.5L arm， L t This is the transformer inductance.

[0090] Understandably, during the process of constructing the main loop dynamic equations of the grid converter, the mobile terminal can determine the upper arm modulation signal n for each phase. j A Lower arm modulation signal n j B Total capacitor voltage of each phase bridge arm submodule Equivalent capacitance C eq Equivalent inductance L eq Bridge arm inductor L arm Voltage difference between AC and DC neutral points u nN Common coupling point current i j Bridge arm circulation and bridge arm differential voltage Subsequently, the mobile terminal can construct the main loop dynamic equation of the grid converter based on the predetermined data. The main loop dynamic equation fully reflects the internal dynamics of the grid converter and can also display the internal situation of the grid converter based on the main loop dynamic equation, providing data for analyzing the stability of the high voltage direct current transmission system.

[0091] In this embodiment of the application, the expression for the dynamic equation of the main loop is:

[0092] ;

[0093] In the formula, A in the table above represents the upper bridge arm, and B in the table above represents the lower bridge arm. This is the modulation signal for the upper (lower) bridge arm of phase j.

[0094] S4. Based on the power grid angular frequency and period time of the electrical quantity data, the periodic differential equation is obtained.

[0095] It should be noted that in constructing the periodic differential equation, step S4 is based on the periodic variables such as the grid angular frequency and periodic time determined in step S1. The mobile terminal can introduce differential equations to convert the determined periodic variables into time-independent periodic differential equations, thus realizing the construction of the periodic differential equations. Specifically, the periodic differential equations represent the trend of the grid angular frequency changing with periodic time in the HVDC transmission system. However, the periodic differential equations constructed by the nonlinear modeling method of this grid-connected converter do not contain time-dependent periodic variables, reducing the difficulty of stability analysis of the HVDC transmission system using nonlinear differential equations. In this embodiment, for the ideal AC power supply excitation in the dynamic DC main circuit of the grid-connected converter, there are explicit time-dependent periodic variables cos(ω0t) and sin(ω0t), where ω0 is the grid angular frequency and t is the periodic time corresponding to the grid angular frequency.

[0096] Understandably, the mobile terminal can determine the grid angular frequency and periodic time of the DC main circuit dynamic periodic variables of the grid-connected converter, and then convert the periodic variables into time-independent periodic differential data according to a pre-determined conversion formula. Afterward, a periodic differential equation is constructed based on the determined periodic differential data. The conversion formula is: c = cos(ω0t), s = sin(ω0t). For example, the initial grid angular frequency ω0 can be a grid angular frequency of 100p, corresponding to a periodic time T = 0.02s; then the initial periodic differential data would be c = 1, s = 0.

[0097] In this embodiment of the application, the periodic differential equation is:

[0098] ;

[0099] c and s represent periodic differential data of different values.

[0100] S5. Based on the voltage differential equation, current differential equation, main loop dynamic equation and periodic differential equation, a nonlinear mathematical model of the grid converter is constructed, which combines the dynamics of the main loop and the dynamics of the control link and is expressed by nonlinear differential equations.

[0101] It should be noted that in the nonlinear mathematical model of the grid-connected converter, which combines the dynamics of the main circuit and the control loop and is expressed using nonlinear differential equations, step S5 involves using the voltage differential equation, current differential equation, main circuit dynamic equation, and periodic differential equation determined in steps S1, S3, and S4. The mobile terminal combines the voltage and current differential equations of the control loop dynamics with the main circuit dynamic equation and periodic differential equation of the main circuit dynamics according to a pre-determined equation construction method to determine the nonlinear mathematical model of the grid-connected converter expressed using nonlinear differential equations. For example, the mobile terminal first selects the state variables of the nonlinear differential equations from the voltage, current, main circuit dynamic, and periodic differential equations, and then determines the nonlinear data from these equations. Finally, the complete nonlinear differential equations of the grid-connected converter are constructed based on the state variables and the nonlinear data. Nonlinear differential equations characterize the changing trends of discrete processes such as amplitude limiting in the actual control of grid-type converters on the dynamic processes of HVDC transmission systems. They also describe the inherent periodic time-varying behavior of grid-type converters and characterize complex operating conditions in HVDC transmission systems, such as three-phase short circuits and single-phase short circuits in the AC grid. The nonlinear data includes stability coefficients and nonlinear vector fields used to analyze the stability of HVDC transmission systems, such as the voltage control proportional coefficient k. pI Voltage control integral coefficient k iI Current control integral coefficient k i Equal stability coefficient.

[0102] It is understandable that in the process of constructing nonlinear differential equations, the state variables and nonlinear data for constructing nonlinear differential equations are determined based on the voltage differential equation, current differential equation, main loop dynamic equation, and periodic differential equation. The mobile terminal can construct nonlinear differential equations for analyzing the stability of high-voltage direct current transmission systems based on the determined state variables and nonlinear data. Through these nonlinear differential equations, this application can analyze the stability of high-voltage direct current transmission systems.

[0103] This application provides a nonlinear modeling method for grid-connected converters, comprising: acquiring electrical quantity data of the grid-connected converter in a high-voltage direct current transmission system; determining the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter based on the reactive power, reactive power reference value, reactive power droop coefficient, upper voltage command limit, lower voltage command limit, shaft voltage, proportional-integral integral quantity, upper current command limit, lower current command limit, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient; and determining the decoupling constant, current control proportional coefficient, and phase-locked output phase angle of the grid-connected converter based on the voltage differential data, current differential data, grid-connected measured current, and electrical quantity data. The reference voltages of the three-phase bridge arms are determined; based on the reference voltages of each phase bridge arm and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid converter is obtained; based on the bridge arm modulation signal and the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, AC / DC neutral point voltage difference, common coupling point current, bridge arm circulating current, and bridge arm differential mode voltage of each phase bridge arm submodule in the electrical quantity data, the main circuit dynamic equation of the grid converter is obtained; based on the grid angular frequency and period time of the electrical quantity data, the periodic differential equation is obtained; based on the voltage differential equation, current differential equation, main circuit dynamic equation, and periodic differential equation, a nonlinear mathematical model of the grid converter is constructed, which combines the dynamics of the main circuit and the dynamics of the control link and is expressed by nonlinear differential equations. This nonlinear modeling method for grid-connected converters first determines the voltage differential equation, voltage differential data, current differential equation, and current differential data by obtaining electrical quantity data. Then, the dynamic equation and periodic differential equation of the main circuit are determined sequentially. The voltage and current differential equations of the control loop dynamics are combined with the dynamic equations and periodic differential equations of the main circuit dynamics to obtain the nonlinear differential equation for analyzing the stability of the HVDC transmission system. This nonlinear differential equation is used to analyze the stability of the HVDC transmission system, solving the technical problem that the existing HVDC transmission based on modular multilevel converters suffers from instability caused by induced dynamic bifurcation due to the periodic time-varying dynamics and strong nonlinear amplitude limiting behavior, and lacks a general nonlinear mathematical model and efficient and accurate analysis method.

[0104] It should be noted that the nonlinear modeling method of this grid converter can combine the voltage differential equation and current differential equation that determine and characterize the dynamics of the control loop based on the smooth approximation method of discontinuous process with the main loop dynamic equation and periodic differential equation to obtain the nonlinear differential equation for analyzing the stability of the high voltage direct current transmission system.

[0105] In one embodiment of this application, a nonlinear mathematical model is constructed based on voltage differential equations, current differential equations, main loop dynamic equations, and periodic differential equations. This model combines the dynamics of the main loop and the dynamics of the control loop of the grid converter and is expressed using nonlinear differential equations. The model includes: using the left-hand side variables of the voltage differential equations, current differential equations, main loop dynamic equations, and periodic differential equations as state variables of the nonlinear differential equations; and using the right-hand side expressions of the voltage differential equations, current differential equations, main loop dynamic equations, and periodic differential equations as nonlinear vector fields of the nonlinear differential equations.

[0106] It should be noted that in the process of constructing the nonlinear mathematical model, based on the determined voltage differential equation, current differential equation, main loop dynamic equation, and periodic differential equation, the mobile terminal can construct a nonlinear mathematical model for analyzing the stability of the HVDC transmission system using pre-set rules. This nonlinear mathematical model analyzes the stability of the HVDC transmission system, considering not only the limiting and time-varying behavior of grid-type converters but also complex operating conditions such as those of the HVDC transmission system itself, thus improving the accuracy of the stability analysis. For example, the pre-set rules can first treat the left-hand side variables of the voltage, current, main loop dynamic equation, and periodic differential equation as the state variables of the nonlinear differential equation, and then treat the left-hand side variables of these equations as the state variables of the nonlinear differential equation, resulting in the nonlinear differential equation represented by the nonlinear mathematical model.

[0107] In the embodiments of this application, the nonlinear differential equation can be:

[0108] ;

[0109] In the formula, For state variables, The nonlinear vector field is an expression on the right-hand side of the voltage differential equation, current differential equation, main loop dynamic equation, and periodic differential equation. α is a stability parameter of interest in analyzing the stability of the HVDC transmission system and should be determined during the stability analysis.

[0110] In one embodiment of this application, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained based on the reactive power, reactive power reference value, reactive power droop coefficient, voltage command upper limit value, voltage command lower limit value, shaft voltage, proportional-integral integral quantity, current command upper limit value, current command lower limit value, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient.

[0111] Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit of voltage command value, and lower limit of voltage command value, the voltage command value and voltage limiting command value of the grid converter using the reactive power droop control loop are obtained.

[0112] Based on the voltage limiting command value, shaft voltage, proportional-integral integral quantity, upper limit value of current command, lower limit value of current command, and voltage control proportional coefficient, the current command value and current limiting command value of the voltage control loop used in the grid converter are obtained.

[0113] Based on the voltage command value, voltage limiting command value, voltage control integral coefficient, and anti-integral saturation parameter, the voltage differential equation and voltage differential data of the voltage control loop in the grid converter are obtained.

[0114] Based on the current command value, current limiting command value, grid-connected measured current, and current control integral coefficient, the current differential equation and current differential data of the current control loop in the grid converter are obtained.

[0115] It should be noted that, in the process of obtaining the voltage differential equations, voltage differential data, current differential equations, and current differential data of the grid-connected converter, in order to reflect the discrete processes such as limiting in the grid-connected converter, the mobile terminal can calculate the voltage command values ​​of the d-axis and q-axis of the grid-connected converter using the reactive power droop control loop and the current command values ​​of the d-axis and q-axis using the voltage control loop, respectively, based on the electrical quantity data, the voltage command values ​​of the d-axis and q-axis, and the current command values ​​of the d-axis and q-axis, respectively, using the linear combination of the hyperbolic tangent function and the pre-set limiting voltage formula and limiting current formula, respectively, to obtain the voltage limiting command values ​​and current limiting command values ​​of the d-axis and q-axis, respectively, providing data for constructing the voltage differential equations, voltage differential data, current differential equations, and current differential data of the d-axis and q-axis. Finally, the mobile terminal can construct voltage and current differential equations for the d-axis and q-axis based on the determined voltage and current limiting command values ​​of the electrical quantity data (d-axis and q-axis). It also calculates the voltage and current differential data for the d-axis and q-axis, providing data for subsequent construction of nonlinear mathematical models. In this embodiment, the voltage and current differential equations for the d-axis and q-axis can represent the impact of discrete processes such as limiting on the dynamic process of the HVDC transmission system during the control process of the grid-type converter, improving the accuracy of analyzing the stability of the HVDC transmission system.

[0116] In this embodiment, the process of calculating the voltage command value in the reactive power droop control loop of the grid converter can be expressed by a voltage formula, which is:

[0117] ;

[0118] ;

[0119] In the formula, Q represents reactive power. ref This is a reference value for reactive power. This represents the voltage command value for the d-axis. k is the voltage command value for the q-axis. dp k is the reactive droop coefficient of the d-axis. qp is the reactive droop coefficient of the q-axis.

[0120] In this embodiment of the application, during the calculation of the voltage limiting command value using the limiting voltage formula in the grid converter voltage control loop, the function h(x) (where x is a variable) is written as h(x) = 0.5[1 + tanh(k·x)], which is a linear combination of hyperbolic tangent functions, where k is an adjustable parameter, and when x > 0... When x < 0 This is used to characterize the switching behavior introduced during the clipping process. The clipping voltage formula is:

[0121] ;

[0122] ;

[0123] In the formula, This is the voltage limiting command value for the d-axis. U is the voltage limiting command value for the q-axis. max U is the upper limit of the voltage command. min This is the lower limit of the voltage command. , , , These are the linear data for voltage limiting.

[0124] In this embodiment, the process of calculating the current command value in the voltage control loop of the grid converter can be expressed using a current formula, which is:

[0125] ;

[0126] ;

[0127] In the formula, k pI U is the voltage control proportional coefficient. d x is the axis voltage of the grid-connected converter at the d-axis. I The integral quantity of the proportional-integral term in the proportional-integral series. This is the voltage limiting command value for the d-axis. The voltage limiting command value for the q-axis, u q The q-axis voltage at the grid connection point of the grid-connected converter. This is the current command value for the d-axis. This is the current command value for the q-axis.

[0128] In this embodiment of the application, during the calculation of the current limiting command value using the limiting current formula in the voltage control loop of the grid converter, the function h(x) (where x is a variable) is written as h(x) = 0.5[1 + tanh(k·x)], which is a linear combination of hyperbolic tangent functions, where k is an adjustable parameter, and when x > 0... When x < 0 This is used to characterize the switching behavior introduced during the limiting process. The limiting current formula is:

[0129] ;

[0130] ;

[0131] In the formula, This is the current limiting command value for the d-axis. I is the current limiting command value for the q-axis. max I is the upper limit of the current command. min This is the lower limit of the current command. , , , These are the linear data for current limiting.

[0132] In this embodiment, the voltage differential equation for constructing the grid converter can be expressed as:

[0133] ;

[0134] In the formula, k iI K represents the voltage control integral coefficient of the proportional-integral element in the voltage control loop. aw As a parameter to resist integral saturation, x dI For the voltage differential data along the d-axis of the proportional-integral element in the voltage control loop, x qI This refers to the voltage differential data along the q-axis of the proportional-integral element in the voltage control loop.

[0135] In this embodiment, the current differential equation for constructing the grid converter can be expressed as:

[0136] ;

[0137] In the formula, k i Let i be the integral coefficient of the current control in the proportional-integral element of the current control loop. d Let i be the measured grid-connected current along the d-axis. q Let x be the measured grid-connected current along the q-axis. dFor the d-axis current differential data of the proportional-integral element in the current control loop, x q This refers to the differential current voltage data along the q-axis of the proportional-integral element in the current control loop.

[0138] Example 2:

[0139] Figure 3 This is a flowchart illustrating the steps of the stability analysis method for a high-voltage direct current transmission system described in an embodiment of this application.

[0140] like Figure 3 As shown in the figure, this application provides a stability analysis method for a high-voltage direct current transmission system, including the following steps:

[0141] S10. Obtain the nonlinear mathematical model of the grid converter in the high voltage direct current transmission system using nonlinear differential equations, based on the nonlinear modeling method of the grid converter described above.

[0142] It should be noted that in this step, the nonlinear modeling method of the grid converter in Example 1 is used to first obtain a nonlinear mathematical model of the grid converter in the HVDC transmission system, represented by nonlinear differential equations. This nonlinear mathematical model fully considers the characterization characteristics of the complex operating conditions of the HVDC transmission system, as well as the complex data such as the periodic time-varying behavior and amplitude limiting discrete process characteristics of the grid converter, and their relationships. This makes it highly accurate in analyzing the stability of the HVDC transmission system based on the state variables and stability coefficients of the nonlinear mathematical model, providing basic data for accurately analyzing the stability of the HVDC transmission system.

[0143] Understandably, in the process of analyzing the stability of a high-voltage direct current (HVDC) transmission system, a nonlinear mathematical model combining the dynamics of the main circuit and the control loop can be constructed using the nonlinear modeling method of the grid converter in Example 1. After determining the nonlinear mathematical model to be analyzed, the mobile terminal can convert the steady-state periodic trajectory problem of the nonlinear differential equation of the nonlinear mathematical model into a fixed-point solution in the subsequent analysis of the stability of the HVDC transmission system, thereby improving the speed of analysis and obtaining the steady-state periodic trajectory more accurately, which is convenient for analyzing the stability of the HVDC transmission system.

[0144] S20. The nonlinear differential equation is processed using an automatic differentiation method to obtain the first Jacobian matrix of the Poincaré mapping.

[0145] It should be noted that step S20 is based on the nonlinear mathematical model obtained in step S10. Then, the steady-state periodic trajectory problem of the nonlinear differential equation of the obtained nonlinear model is transformed into the discrete system fixed-point problem on the Poincaré map using the Poincaré section. The first Jacobian matrix of the Poincaré map is constructed by automatic differentiation method, which simplifies the complexity of the stability analysis of the high voltage direct current transmission system and improves the analysis speed and accuracy.

[0146] Understandably, when using automatic differentiation methods to process nonlinear differential equations, for the Poincaré mapping, let Let Σ represent the trajectory of the nonlinear differential equation of a high-voltage direct current transmission system starting from the initial condition x, where Σ is an n−1-dimensional Poincaré section intersecting the vector field f(x0, a) at x0. We can let Σ: s = 0. This is because, under the excitation of an ideal AC power source, the period T of the nonlinear differential equation is 0.02 s. Therefore, the Poincaré mapping is defined as:

[0147] ;

[0148] The trajectory expression for the nonlinear differential equation is as follows:

[0149] ;

[0150] In the formula, and Let be a point on the Poincaré section. For point In the original state space, E is an (n-1)n matrix, which is the result of removing the last row from the n-th identity matrix, representing the extraction of the first to (n-1)th elements from the state variable x. Therefore, the periodic trajectory of the nonlinear differential equation can be represented as the fixed point of the fixed-point discrete system. For the Jacobian matrix of the Poincaré mapping, it can be known from the Poincaré mapping itself that the Jacobian matrix of the Poincaré mapping can be expressed as... That is, the Jacobian matrix of the Poincaré map is related to the Jacobian matrix of the system trajectory. Let... Let A(t) be the Jacobian matrix of the system trajectory relative to the initial point x. Then, obtaining the Jacobian matrix of the system trajectory depends on solving the initial value problem of the expression of the first Jacobian matrix, where A(t) is generated by an automatic differentiation method.

[0151] In this embodiment of the application, the expression for the first Jacobian matrix is:

[0152] ;

[0153] In the formula, A(t) is the automatic differentiation parameter.

[0154] In this embodiment of the application, during the processing of nonlinear differential equations using an automatic differentiation method, the automatic differentiation method is used to perform machine-precision numerical calculations on the variational equations corresponding to the nonlinear differential equations to obtain the first Jacobian matrix of the Poincaré map.

[0155] S30. The fixed points of the Poincaré mapping in the first Jacobian matrix are solved iteratively using the numerical extension method based on Newton-Raphson to obtain the second Jacobian matrix for accurately locating the periodic orbit.

[0156] It should be noted that in this step, the first Jacobian matrix is ​​first determined through step S20. The mobile terminal can solve the periodic orbit that varies with the stability coefficient according to the pre-set numerical extension method based on Newton-Raphson, until the second Jacobian matrix of the periodic orbit that is accurately located is obtained. The second Jacobian matrix can determine the stability change trend of the high voltage direct current transmission system and realize the capture of the periodic orbit that is accurately located according to the change trend of the stability coefficient.

[0157] Understandably, the numerical extension method based on the Newton-Raphson equation aims to locate the periodic trajectory of the stability coefficient variation process of the high-voltage direct current transmission system, i.e., satisfy the equation... The stability trend of the high-voltage direct current transmission system is determined by locating points on the periodic orbit and using the second Jacobian matrix of the accurately located periodic orbit. Therefore, by using a numerical extension method based on Newton-Raphson, this application can iteratively optimize the influence of points on the periodic orbit in the stability coefficient dimension from the perspective of locating the change in stability coefficient, thereby achieving interpretable analysis of the internal mechanism of complex nonlinear mathematical models.

[0158] S40. Calculate the matrix eigenvalues ​​based on the second Jacobian matrix; determine the stability of the high-voltage direct current transmission system based on the matrix eigenvalues.

[0159] It should be noted that in this step, the second Jacobian matrix is ​​determined through step S30. The mobile terminal can preset an existing formula or program for calculating the eigenvalues ​​of the matrix to calculate the eigenvalues ​​corresponding to the second Jacobian matrix. The mobile terminal can determine the stability of the high-voltage direct current transmission system based on the calculated eigenvalues ​​and a preset judgment method. Based on the fact that the periodic orbit of the second Jacobian matrix remains unchanged under changes in the stability coefficient, the stability of the high-voltage direct current transmission system can be accurately analyzed.

[0160] Understandably, in determining the stability of a high-voltage direct current (HVDC) transmission system based on matrix eigenvalues, a highly accurate nonlinear mathematical model of the grid converter is first established to accurately characterize the periodic time-varying, limiting, and switching processes of the HVDC transmission system. Then, an automatic differentiation method and a deteriorated numerical extension method based on Newton-Raphson are used to process the nonlinear differential equations of the nonlinear mathematical model. Considering the influence of stability coefficient changes on the periodic track, the matrix eigenvalues ​​that accurately assess the stability of the HVDC transmission system are obtained, thus enabling accurate analysis of the stability of the HVDC transmission system.

[0161] This application provides a stability analysis method for a high-voltage direct current (HVDC) transmission system, comprising: obtaining a nonlinear mathematical model of the grid-connected converter in the HVDC transmission system represented by nonlinear differential equations using the aforementioned nonlinear modeling method for grid-connected converters; processing the nonlinear differential equations using an automatic differentiation method to obtain the first Jacobian matrix of the Poincaré map; iteratively solving the fixed points of the Poincaré map in the first Jacobian matrix using a Newton-Raphson-based numerical extension method to obtain the second Jacobian matrix for accurately locating the periodic track; calculating the matrix eigenvalues ​​based on the second Jacobian matrix; and determining the stability of the HVDC transmission system based on the matrix eigenvalues. This stability analysis method for high-voltage direct current (HVDC) transmission systems can effectively establish a highly accurate nonlinear mathematical model of the grid converter, accurately characterizing the periodic time-varying, limiting, and switching processes of the HVDC transmission system. Then, an automatic differentiation method and a deteriorated Newton-Raphson-based numerical extension method are used to process the nonlinear differential equations of the nonlinear mathematical model. Considering the influence of stability coefficient changes on the periodic track, the matrix eigenvalues ​​that accurately assess the stability of the HVDC transmission system are obtained. This method achieves accurate analysis of the stability of the HVDC transmission system, solving the technical problems of existing HVDC transmission systems based on modular multilevel converters where periodic time-varying dynamics and strongly nonlinear limiting behavior induce dynamic bifurcation leading to system instability, and the lack of a universal nonlinear mathematical model and efficient, accurate analysis method.

[0162] In one embodiment of this application, the fixed points of the Poincaré map in the first Jacobian matrix are iteratively solved using a numerical extension method based on Newton-Raphson to obtain the second Jacobian matrix for accurately locating the periodic orbit, which includes:

[0163] The initial parameters of the numerical extension method based on Newton-Raphson are obtained. The initial parameters include the tangent vector, the given change in arc length, the initial fixed point, and the initial stability coefficient.

[0164] Based on the initial parameters, the first period prediction point of the first numerical extension is obtained;

[0165] Based on the first period prediction point and the first Jacobian matrix, an iterative calculation is performed to obtain the second Jacobian matrix that satisfies the iteration termination condition.

[0166] The formula for iterative calculation is as follows:

[0167] ;

[0168] The iteration termination condition is: ;

[0169] In the formula, Let be the Jacobian matrix calculated in the k-th iteration. For the periodic prediction point calculated in the k-th iteration, For the periodic prediction point calculated in the (k+1)th iteration, F( ) is the function value of the k-th iteration, and e is the threshold of the iteration parameter.

[0170] It should be noted that, , where x P For a point on the Poincaré section given in step S20, This is the Poincaré mapping given in step S20. And assume the function with known parameter α = α0 is... fixed point Then, the prediction point when parameter α=α1 can be determined by numerical extension. ,in:

[0171] ;

[0172] In the formula, Δs is a given change in arc length, ( , () represents the tangent vector under the initial parameters. Then, the predicted solution is obtained based on the Newton-Raphson iteration. To obtain the true solution, the iterative form is expressed using the formula for iterative calculation, which is:

[0173] ;

[0174] In the formula, ε can be set to 1e -10 When the iteration termination condition is met, it can be considered that an accurate periodic trajectory has been located. At this point, the iteration number k is denoted as k... m ,but ,in, The actual periodic trajectory, at which point the second Jacobian matrix obtained can be used to determine the stability trend of the high-voltage direct current transmission system.

[0175] In one embodiment of this application, determining the stability of a high-voltage direct current transmission system based on matrix eigenvalues ​​includes:

[0176] If all eigenvalues ​​of the matrix are inside the unit circle, then the stability of the high-voltage direct current transmission system is system stability.

[0177] If there is an eigenvalue in the matrix that is not inside the unit circle, then the stability of the high voltage direct current transmission system is unstable.

[0178] If there exists a pair of conjugate eigenvalues ​​on the unit circle among the eigenvalues ​​of the matrix, then the stability of the high-voltage direct current transmission system is that the system undergoes torus bifurcation.

[0179] If there exists an eigenvalue of the matrix that lies on the x-axis of the unit circle, then the stability of the high-voltage direct current transmission system is determined by the occurrence of system folding and bifurcation.

[0180] It should be noted that when When the eigenvalues ​​of the second Jacobian matrix are located within the unit circle, the system of the high-voltage direct current transmission system is considered to be stable. When there is a pair of conjugate eigenvalues ​​on the unit circle, the system of the high-voltage direct current transmission system is considered to be undergoing torus bifurcation. When there is an eigenvalue at the coordinate (1, 0) of the unit circle, the system of the high-voltage direct current transmission system is considered to be undergoing folding bifurcation.

[0181] Understandably, the stability analysis method for this high-voltage direct current transmission system first uses a linear combination of hyperbolic tangent functions to smoothly characterize the limiting switching element in the controller of the grid converter; secondly, it establishes a nonlinear mathematical model of the grid-type DC converter represented by nonlinear differential equations; subsequently, it constructs a discretized representation of the steady-state periodic track of the nonlinear differential equations based on the Poincaré mapping; and finally, it uses numerical extension methods to analyze the stability of the periodic track under varying stability coefficients. This approach can greatly improve the accuracy of constructing the nonlinear mathematical model of the grid converter and the stability analysis.

[0182] Figure 4 This is a comparative structural diagram of the stability analysis method for the high-voltage direct current transmission system described in the embodiments of this application. Figure 5 This is an instability prediction diagram of the stability analysis method for the high-voltage direct current transmission system described in the embodiments of this application. Figure 6 This is a simulation verification diagram of instability prediction in the stability analysis method for the high-voltage direct current transmission system described in this application embodiment. Figure 4 In the figure, (a) the AC voltage drops to 0.92 pu at t=3s; (b) a three-phase ground fault on the AC side at t=3s with a ground inductance of 2.5H; (c) a single-phase ground fault on the AC side at t=3s with a ground inductance of 1.04H. The figures show a comparison between the simulated values ​​of the positive-sequence d-axis voltage and d-axis current, and the simulated values ​​of the DC-side current of the MMC, and the calculated values ​​from the differential equation model under these three scenarios. Figure 5 In Figure (a), the system experiences a three-phase symmetrical short-circuit ground fault, with a ground inductance of L.f,TP (b) The figure shows that a short-circuit ground fault occurred in phase A of the system, and the grounding inductance is L. f,SP The prediction results of the system instability point are given using the Poincaré mapping and numerical continuation in two cases.

[0183] In this application embodiment, the stability analysis method of the high-voltage direct current transmission system is verified through the following examples. For instance, a system is built in PSCAD / EMTDC as follows: Figure 2 The simplified simulation model of a grid-connected converter in a real high-voltage direct current transmission system is shown. The rated power is 2250MW. The control system is based on an outer loop control mode of power synchronous loop (PSL) and active power drop loop (APDL). The inner loop control includes positive and negative sequence voltage inner loops and current inner loops. Figure 4 As shown, the solution results of the differential equation mathematical model proposed by the stability analysis method for this high-voltage direct current transmission system are highly consistent with the simulation results. Figure 5 As shown, the solid line represents stability and the dashed line represents instability. It can be seen that under the three-phase symmetrical short-circuit condition, the system at L... f,TP =1.3H and L f,TP Instability occurs at 2.4H; under single-phase short circuit conditions, the high-voltage direct current transmission system becomes unstable at 1.03H. Figure 6 right Figure 5 The analysis results were verified by simulation, where φ PSL This represents the phase angle output by the power synchronization link. At t=3s, a three-phase inductive ground fault of 3H occurs in the HVDC transmission system, and the HVDC transmission system remains stable; subsequently, at t=4s, the fault inductance becomes 2.3H, at which point the HVDC transmission system, due to L... f,TP Instability occurs when φ is less than 2.4H. PSL A small oscillation occurs; at t=5s, the fault inductance is further adjusted to 1.2H. At this time, the high-voltage direct current transmission system is affected by L. f,TP It becomes unstable when the value is less than 1.3H. Figure 5 Figure (b) shows the waveform under a single-phase short circuit. At t=3s, a 1.5H inductive ground fault occurs in phase A of the HVDC transmission system, and the HVDC transmission system remains stable; at t=4s, the grounding inductance is adjusted to 0.9H, which is less than 1.03H, and the HVDC transmission system becomes unstable. It can be seen that the stability analysis results given by the stability analysis method for this HVDC transmission system are highly consistent with the simulation results.

[0184] Example 3:

[0185] Figure 7This is a schematic diagram of the nonlinear modeling device for the grid converter described in the embodiments of this application.

[0186] like Figure 7 As shown, this application provides a nonlinear modeling device for a grid converter, which is applied to a high-voltage direct current transmission system based on a grid converter. The nonlinear modeling device includes a data acquisition and processing module 10, a signal determination module 20, a dynamic equation determination module 30, a periodic equation module 40, and a model construction module 50.

[0187] The data acquisition and processing module 10 is used to acquire electrical quantity data of grid-connected converters in high-voltage direct current transmission systems. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit of voltage command, lower limit of voltage command, shaft voltage, proportional-integral integral quantity, upper limit of current command, lower limit of current command, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained.

[0188] The signal determination module 20 is used to determine the bridge arm reference voltage of the three phases of the grid converter based on the voltage differential data, current differential data, grid-connected measured current and electrical quantity data, decoupling constant, current control proportional coefficient and phase-locked output phase angle; and to determine the bridge arm modulation signal of each phase bridge arm in the grid converter based on the bridge arm reference voltage of each phase and the DC voltage rated value of the electrical quantity data.

[0189] The dynamic equation determination module 30 is used to determine the main circuit dynamic equation of the grid converter based on the bridge arm modulation signal and electrical quantity data, including the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, voltage difference between AC and DC neutral points, common coupling point current, bridge arm circulating current, and bridge arm differential mode voltage of each phase bridge arm submodule.

[0190] The periodic equation module 40 is used to determine and obtain the periodic differential equation based on the power grid angular frequency and period time of the electrical quantity data.

[0191] The model building module 50 is used to construct a nonlinear mathematical model of the grid converter based on the voltage differential equation, current differential equation, main loop dynamic equation and periodic differential equation, which is a combination of the main loop dynamic and the control loop dynamic and expressed by nonlinear differential equation.

[0192] It should be noted that the content of the modules in the device of Embodiment 3 has already been described in the steps of the method of Embodiment 1, and the content of the nonlinear modeling device module of the grid converter will not be repeated in this embodiment. In this embodiment, the nonlinear modeling device of the grid converter obtains electrical quantity data through the data acquisition and processing module, signal determination module, dynamic equation determination module, periodic equation module and model construction module to first determine the voltage differential equation, voltage differential data, current differential equation and current differential data, and then determine the main circuit dynamic equation and periodic differential equation in sequence. The voltage differential equation and current differential equation of the control loop dynamic are combined with the main circuit dynamic equation and periodic differential equation to obtain the nonlinear differential equation for analyzing the stability of the high voltage direct current transmission system. The stability of the high voltage direct current transmission system is analyzed through this nonlinear differential equation.

[0193] In this embodiment, the model building module 50 is further configured to use the left-hand side variables of the voltage differential equation, current differential equation, main loop dynamic equation, and periodic differential equation as state variables of the nonlinear differential equation; and to use the right-hand side expressions of the voltage differential equation, current differential equation, main loop dynamic equation, and periodic differential equation as nonlinear vector fields of the nonlinear differential equation.

[0194] In this embodiment of the application, the data acquisition and processing module 10 includes a voltage limiting processing submodule, a current limiting processing submodule, a voltage micro-molecule module, and a current micro-molecule module;

[0195] The voltage limiting processing submodule is used to determine the voltage command value and voltage limiting command value of the grid converter using the reactive power droop control loop based on reactive power, reactive power reference value, reactive power droop coefficient, upper voltage command value and lower voltage command value.

[0196] The current limiting processing submodule is used to determine the current command value and current limiting command value of the voltage control loop used in the grid converter based on the voltage limiting command value, shaft voltage, proportional-integral integral quantity, upper limit value of current command, lower limit value of current command, and voltage control proportional coefficient.

[0197] The voltage differential module is used to determine the voltage differential equation and voltage differential data of the voltage control loop in the grid converter based on the voltage command value, voltage limiting command value, voltage control integral coefficient and anti-integral saturation parameter.

[0198] The current differential module is used to determine the current differential equation and current differential data of the current control loop in the grid converter based on the current command value, current limiting command value, grid-connected measured current and current control integral coefficient.

[0199] Example 4:

[0200] Figure 8 This is a schematic diagram of the terminal device described in an embodiment of this application.

[0201] like Figure 8 As shown, this application provides a terminal device, including a processor and a memory;

[0202] Memory is used to store program code and transfer the program code to the processor;

[0203] The processor is used to execute the nonlinear modeling method for the grid converter described above according to the instructions in the program code.

[0204] It should be noted that the processor is used to execute the steps in the above-described embodiment of a nonlinear modeling method for a grid converter according to the instructions in the program code. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the above-described system / device embodiments.

[0205] For example, a computer program can be divided into one or more modules / units, one or more of which are stored in memory and executed by a processor to complete this application. One or more modules / units can be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in a terminal device.

[0206] Terminal devices can be computing devices such as desktop computers, laptops, handheld computers, and cloud servers. Terminal devices may include, but are not limited to, processors and memory. Those skilled in the art will understand that this does not constitute a limitation on the terminal device, which may include more or fewer components than illustrated, or combinations of certain components, or different components. For example, a terminal device may also include input / output devices, network access devices, buses, etc.

[0207] The processor 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, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0208] Memory can be an internal storage unit of a terminal device, such as a hard drive or RAM. Memory can also be an external storage device, such as a plug-in hard drive, SmartMedia Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, memory can include both internal and external storage units. Memory is used to store computer programs and other programs and data required by the terminal device. Memory can also be used to temporarily store data that has been output or will be output.

[0209] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0210] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0211] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0212] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0213] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part 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 methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0214] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A nonlinear modeling method for grid-connected converters, applied to high-voltage direct current transmission systems based on grid-connected converters, characterized in that, This nonlinear modeling method includes the following steps: The electrical quantity data of the grid-connected converter in the high-voltage direct current transmission system are obtained. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit voltage command value, lower limit voltage command value, shaft voltage, proportional-integral integral quantity, upper limit current command value, lower limit current command value, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained. Based on the voltage differential data, the current differential data, the grid-connected measured current, and the decoupling constant, current control proportional coefficient, and phase-locked output phase angle of the electrical quantity data, the bridge arm reference voltage of the three phases of the grid converter is obtained; based on the bridge arm reference voltage of each phase and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid converter is obtained. Based on the bridge arm modulation signal and the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, AC / DC neutral point voltage difference, common coupling point current, bridge arm circulating current, and bridge arm differential mode voltage of each phase of the bridge arm submodule in the electrical quantity data, the main circuit dynamic equation of the grid converter is obtained. Based on the power grid angular frequency and period time of the electrical quantity data, a periodic differential equation is obtained; Based on the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation, a nonlinear mathematical model of the grid converter is obtained, which combines the dynamics of the main loop and the dynamics of the control loop and is expressed by nonlinear differential equations.

2. The nonlinear modeling method for grid converters according to claim 1, characterized in that, Based on the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation, a nonlinear mathematical model of the grid converter, which combines the dynamics of the main loop and the dynamics of the control loop and is expressed by nonlinear differential equations, is obtained. This model includes: using the left-hand side variables of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the state variables of the nonlinear differential equation; and using the right-hand side expressions of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the nonlinear vector field of the nonlinear differential equation.

3. The nonlinear modeling method for grid converters according to claim 1, characterized in that, Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper voltage command limit, lower voltage command limit, shaft voltage, proportional-integral integral quantity, upper current command limit, lower current command limit, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained, including: Based on the reactive power, the reactive power reference value, the reactive power droop coefficient, the upper limit of the voltage command, and the lower limit of the voltage command, the voltage command value and the voltage limiting command value of the grid converter using the reactive power droop control loop are determined. Based on the voltage limiting command value, the shaft voltage, the proportional-integral integral, the upper limit of the current command, the lower limit of the current command, and the voltage control proportional coefficient, the current command value and the current limiting command value of the voltage control loop used in the grid converter are determined. Based on the voltage command value, the voltage limiting command value, the voltage control integral coefficient, and the anti-integral saturation parameter, the voltage differential equation and voltage differential data of the voltage control loop in the grid converter are obtained. Based on the current command value, the current limiting command value, the measured grid-connected current, and the current control integral coefficient, the current differential equation and current differential data of the current control loop in the grid converter are obtained.

4. A stability analysis method for a high-voltage direct current transmission system, characterized in that, Includes the following steps: The nonlinear modeling method for grid converters according to any one of claims 1-3 is used to obtain a nonlinear mathematical model of the grid converter in a high voltage direct current transmission system, expressed by nonlinear differential equations. The nonlinear differential equation is processed using an automatic differentiation method to obtain the first Jacobian matrix of the Poincaré map; The fixed points of the Poincaré mapping in the first Jacobian matrix are iteratively solved using the numerical extension method based on Newton-Raphson to obtain the second Jacobian matrix for accurately locating the periodic orbit. The eigenvalues ​​of the matrix are obtained by calculating the second Jacobian matrix. The stability of the high-voltage direct current transmission system is determined based on the eigenvalues ​​of the matrix.

5. The stability analysis method for a high-voltage direct current transmission system according to claim 4, characterized in that, The fixed points of the Poincaré mapping in the first Jacobian matrix are iteratively solved using a numerical extension method based on Newton-Raphson, resulting in the second Jacobian matrix for accurately locating the periodic orbit, which includes: The initial parameters of the numerical extension method based on Newton-Raphson are obtained, including the tangent vector, the given change in arc length, the initial fixed point, and the initial stability coefficient. Based on the initial parameters, the first period prediction point of the first numerical extension is obtained; Based on the first periodic prediction point and the first Jacobian matrix, an iterative calculation is performed to obtain a second Jacobian matrix that satisfies the iteration termination condition. The formula for iterative calculation is as follows: ； The iteration termination condition is: ; In the formula, Let be the Jacobian matrix calculated in the k-th iteration. For the periodic prediction point calculated in the k-th iteration, For the periodic prediction point calculated in the (k+1)th iteration, F( ) is the function value of the k-th iteration, and ε is the threshold of the iteration parameter.

6. The stability analysis method for a high-voltage direct current transmission system according to claim 4, characterized in that, Determining the stability of the high-voltage direct current transmission system based on the matrix eigenvalues ​​includes: If all the eigenvalues ​​of the matrix are within the unit circle, then the stability of the high-voltage direct current transmission system is system stability. If one of the eigenvalues ​​of the matrix is ​​not inside the unit circle, then the stability of the high-voltage direct current transmission system is unstable. If there exists a pair of conjugate eigenvalues ​​on the unit circle among the eigenvalues ​​of the matrix, then the stability of the high-voltage direct current transmission system is that the system undergoes torus bifurcation. If one of the eigenvalues ​​of the matrix lies on the x-axis of the unit circle, then the stability of the high-voltage direct current transmission system is that the system undergoes folding and bifurcation.

7. A nonlinear modeling device for grid-connected converters, applied to high-voltage direct current transmission systems based on grid-connected converters, characterized in that, The nonlinear modeling device includes: a data acquisition and processing module, a signal determination module, a dynamic equation determination module, a periodic equation module, and a model construction module; The data acquisition and processing module is used to acquire the electrical quantity data of the grid-connected converter in the high-voltage direct current transmission system. Based on the reactive power, reactive power reference value, reactive power droop coefficient, upper limit voltage command value, lower limit voltage command value, shaft voltage, proportional-integral integral quantity, upper limit current command value, lower limit current command value, voltage control proportional coefficient, voltage control integral coefficient, anti-integral saturation parameter, grid-connected measured current, and current control integral coefficient of the electrical quantity data, the voltage differential equation, voltage differential data, current differential equation, and current differential data of the grid-connected converter are obtained. The signal determination module is used to determine, based on the voltage differential data, the current differential data, the grid-connected measured current, and the decoupling constant, current control proportional coefficient, and phase-locked output phase angle of the electrical quantity data, to obtain the bridge arm reference voltage of the three phases of the grid converter; and to determine, based on the bridge arm reference voltage of each phase and the rated DC voltage of the electrical quantity data, the bridge arm modulation signal of each phase bridge arm in the grid converter. The dynamic equation determination module is used to determine the main circuit dynamic equation of the grid converter based on the bridge arm modulation signal and the total capacitor voltage, equivalent capacitance, equivalent inductance, bridge arm inductance, AC / DC neutral point voltage difference, common coupling point current, bridge arm circulating current and bridge arm differential mode voltage of each phase of the bridge arm sub-module in the electrical quantity data. The periodic equation module is used to determine, based on the power grid angular frequency and periodic time of the electrical quantity data, a periodic differential equation; The model building module is used to construct a nonlinear mathematical model of the grid converter based on the voltage differential equation, the current differential equation, the main circuit dynamic equation, and the periodic differential equation. This model is a combination of the main circuit dynamics and the control loop dynamics, expressed by nonlinear differential equations.

8. The nonlinear modeling device for a grid converter according to claim 7, characterized in that, The model building module is also used to take the left-hand side variables of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the state variables of the nonlinear differential equation; and to take the right-hand side expressions of the voltage differential equation, the current differential equation, the main loop dynamic equation, and the periodic differential equation as the nonlinear vector field of the nonlinear differential equation.

9. The nonlinear modeling device for a grid converter according to claim 7, characterized in that, The data acquisition and processing module includes a voltage limiting processing submodule, a current limiting processing submodule, a voltage micro-molecule module, and a current micro-molecule module; The voltage limiting processing submodule is used to determine, based on the reactive power, the reactive power reference value, the reactive power droop coefficient, the upper limit of the voltage command, and the lower limit of the voltage command, the voltage command value and the voltage limiting command value of the grid converter using the reactive power droop control loop. The current limiting processing submodule is used to determine, based on the voltage limiting command value, the shaft voltage, the proportional-integral integral quantity, the upper limit value of the current command, the lower limit value of the current command, and the voltage control proportional coefficient, the current command value and the current limiting command value of the voltage control loop used by the grid converter. The voltage micro-molecule module is used to determine, based on the voltage command value, the voltage limiting command value, the voltage control integral coefficient, and the anti-integral saturation parameter, the voltage differential equation and voltage differential data of the voltage control loop in the grid converter. The current micro-molecule module is used to determine, based on the current command value, the current limiting command value, the grid-connected measured current, and the current control integral coefficient, the current differential equation and current differential data of the current control loop in the grid converter.

10. A terminal device, characterized in that, Including the processor and memory; The memory is used to store program code and transmit the program code to the processor; The processor is configured to execute the nonlinear modeling method for grid converters as described in any one of claims 1-3 according to the instructions in the program code.

Images