Flexible direct current averaging modeling method considering negative sequence control and amplitude limiting link
By constructing a flexible DC averaging modeling method that considers negative sequence control and amplitude limiting, the problems of complex calculation and insufficient dynamic accuracy in MMC-HVDC modeling are solved, achieving efficient dynamic simulation and adaptability to large disturbances, and improving the accuracy of system stability analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- MAINTENANCE & TEST CENTRE CSG EHV POWER TRANSMISSION CO
- Filing Date
- 2025-12-05
- Publication Date
- 2026-05-12
AI Technical Summary
Existing MMC-HVDC modeling technology suffers from high computational complexity and poor scalability, making it unable to accurately characterize dynamic behavior under complex operating conditions. In particular, when negative sequence control and amplitude limiting are ignored, the dynamic accuracy is insufficient and cannot meet the needs of engineering design and stability analysis.
A flexible DC averaging modeling method considering negative sequence control and limiting circuits is constructed. The state variables are decomposed by multi-frequency coordinate transformation, a steady-state dual-loop state-space equation is established, a negative sequence current PI controller is designed and the limiting circuit is integrated to realize the dynamic characteristic characterization of the system.
It improves the accuracy of dynamic simulation, reduces computational complexity, enhances adaptability to large disturbances, and provides a more reliable basis for system stability control analysis.
Smart Images
Figure CN122019927A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power systems and their automation technology, specifically to a flexible DC averaging modeling method that considers negative sequence control and amplitude limiting. Background Technology
[0002] Modular multilevel converters (MMCs), as an advanced voltage source converter, have become a core technology in the field of high voltage direct current (HVDC) transmission due to their advantages such as high output waveform quality, low loss, and strong fault handling capabilities. With the development of power systems towards higher voltage, larger capacity, and higher power electronics, MMC-HVDCs are widely used in scenarios such as inter-regional grid interconnection and new energy grid integration, including major projects such as the State Grid Chongqing-Hubei DC project, the world's first flexible DC grid Zhangbei flexible DC project, and the Southern Power Grid Luxi back-to-back flexible DC project.
[0003] However, with the increase in voltage level and capacity of MMC-HVDC, system stability issues have become increasingly prominent. Harmonic resonance phenomena have been observed multiple times in engineering practice: resonances of 700Hz and 1800Hz have occurred in the State Grid Chongqing-Hubei DC project; high-frequency resonances of around 1500Hz have occurred during AC side charging at the Kangbao station of the Zhangbei flexible DC project; and resonances of around 1200Hz have occurred when the Luxi back-to-back flexible DC project was connected to a weak AC system. These resonance problems not only affect power quality but also pose a serious threat to the safe and stable operation of the power grid, highlighting the importance of accurate modeling and analysis of the dynamic characteristics of MMC-HVDC.
[0004] Accurate modeling of MMC-HVDC systems is fundamental for analyzing resonance mechanisms and proposing suppression strategies. Due to the periodic and time-varying steady-state solution characteristics of MMC, existing technologies often employ the harmonic state-space method for modeling. This method transforms the time-varying system into a linear time-invariant system by "frequency-increasing" the system's full-order state equations, thereby enabling harmonic characteristic analysis. However, this modeling method has significant drawbacks: firstly, the frequency-increasing dimension leads to extremely high model dimensionality, resulting in exponentially increasing computational complexity, making it difficult to apply to the simulation and analysis of large-scale power systems; secondly, the model has poor scalability and cannot flexibly adapt to MMC-HVDC systems with different topologies or control strategies.
[0005] Meanwhile, while existing averaged state-space models simplify the modeling process to some extent, they fail to fully calculate key control elements in practical engineering. Specifically: first, they neglect widely used negative-sequence control systems, which achieve voltage / current positive / negative sequence separation through a decoupled dual synchronous reference frame phase-locked loop (DDSRF-PLL), crucial for system stability under unbalanced conditions; second, they fail to consider the limiting element in the PI controller, which triggers nonlinear switching characteristics under large disturbances, directly affecting the accuracy of the system's dynamic response. These shortcomings prevent existing models from accurately characterizing the dynamic behavior of MMC-HVDC under complex operating conditions, making it difficult to meet the needs of engineering design and stability analysis.
[0006] In summary, current MMC-HVDC modeling technology faces a dual challenge: on the one hand, traditional harmonic state-space methods suffer from high computational costs and poor scalability due to frequency dimensionality increases; on the other hand, existing averaging models lack dynamic accuracy and cannot handle large disturbance scenarios due to neglecting negative-sequence control and amplitude limiting. Therefore, there is an urgent need for an MMC-HVDC state-space modeling method that balances modeling accuracy and computational efficiency to address the limitations of existing technologies in engineering applications. Summary of the Invention
[0007] To address the aforementioned issues, a flexible DC averaging modeling method considering negative-sequence control and limiting elements is proposed. By constructing an averaging state-space model containing negative-sequence control and limiting elements, the complexity of MMC-HVDC modeling calculations and insufficient dynamic accuracy are resolved.
[0008] To address the problems of existing technologies, this invention provides a flexible DC averaging modeling method considering negative sequence control and limiting elements, comprising the following steps: Step S1: Transform and construct the differential-common mode dual-loop averaged model of MMC; By using multi-frequency coordinate transformation, the time-varying state variables of the MMC period are decomposed into differential-mode components and common-mode components, and a steady-state dual-loop state-space equation is established to provide a dynamic basis for power circuit modeling for subsequent control loops. Step S2: Establish the averaged state-space model of the MMC negative-sequence control loop; For negative-sequence control systems containing DDSRF-PLL, voltage / current positive and negative sequence separation is achieved through dynamic equations. A negative-sequence current PI controller is designed and transformed to the standard dq coordinate system to fully characterize the dynamic characteristics of the negative-sequence control link. Step S3: Establish the averaged state-space model of the limiting stage; The step switching characteristics of the limiting circuit are made continuous by using a continuous approximation tool, and then integrated with the integral and output circuits of the PI controller to reflect the dynamic process of limiting under large disturbances.
[0009] As a specific embodiment of the present invention, step S1 includes: Step S1.1: Analyze the state equations of the MMC power circuit to determine the common-mode and differential-mode components; The original state-space equations are derived based on the MMC main loop topology, and common-mode and differential-mode components are separated by harmonic analysis. Step S1.2: Apply multi-frequency Park transform to achieve system steady-state operation; Based on the harmonic characteristics of state variables, a multi-frequency Park transformation matrix is designed to transform time-varying state variables into a rotating coordinate system to achieve steady-state transformation. Step S1.3: Derive the averaged state-space equations; Substituting the coordinate transformation results into the original state equations and simplifying them, a differential-common mode dual-loop steady-state model is established to achieve average modeling of the MMC power circuit.
[0010] As a specific embodiment of the present invention, step S2 includes: Step S2.1: Construct the averaged model of DDSRF-PLL; Establish the dynamic equations of DDSRF-PLL with PI controller to achieve voltage positive and negative sequence separation and synchronous phase tracking; Step S2.2: Establish a model for separating positive and negative sequence currents; A coordinate transformation method similar to voltage separation is used to separate the positive and negative sequences of AC current, providing a feedback signal for negative sequence current control. Step S2.3: Derive the negative sequence current control loop model; A PI controller is designed based on the separated negative-sequence current component to generate a negative-sequence modulation signal and transform it to the abc coordinate system, which is then superimposed on the positive-sequence modulation signal.
[0011] As a specific embodiment of the present invention, step S3 includes: Step S3.1: Define the mathematical model for the limiting stage; Define a piecewise function to describe the limiting characteristics, and design a step switch function to characterize the limiting state; Step S3.2: Implement continuous modeling of the limiting process; The tanh activation function is used to approximate the switching function as a continuous function, thus converting the step characteristic into a continuously differentiable function. Step S3.3: Integrate the limiting model into the PI controller; A dynamic equation for limiting the integral element is established. The integral term is adjusted by a continuous switching function to synthesize a PI output with external limiting, thus distinguishing between integral limiting and output limiting logic.
[0012] As a specific embodiment of the present invention, step S1.1 includes: Step S1.1.1: Establish the original state-space equations of MMC; Based on the MMC main loop topology, differential equations for voltage and current are derived according to Kirchhoff's laws, forming a set of first-order differential equations that include state variables such as bridge arm current and capacitor voltage. Step S1.1.2: Identify the harmonic characteristics of the state variables; Harmonic analysis is performed on the steady-state solution of the original state-space equations to identify the harmonic components of each state variable.
[0013] As a specific embodiment of the present invention, step S1.2 includes: Step S1.2.1: Derive the general Park transformation matrix; Define the transformation matrix of the rotating coordinate system It includes cosine / sine terms and a zero-sequence component, and its specific form is: ; in, The first and second rows of the matrix represent the electrical angles in the rotating coordinate system. The third row represents the zero-sequence component (z-axis), realizing the conversion of three-phase AC quantities to DC quantities in the rotating coordinate system. Step S1.2.2: Differential mode component positive sequence dq transform; Based on the differential mode component harmonic characteristics identified in step S1.2.1, the following is applied: The positive-sequence Park transformation matrix is used to perform coordinate transformation on the differential mode components, separating them into the dqz coordinate system, converting the fundamental frequency positive-sequence components into DC components, and temporarily storing the third harmonic zero-sequence components on the z-axis. Step S1.2.3: Negative-sequence second harmonic transformation of common-mode components; For the DC and second harmonic negative sequence characteristics of the common-mode component, the following is applied: The negative-order Park transformation matrix transforms the common-mode components to the negative-order second harmonic dq coordinate system, thereby stabilizing the DC and second harmonic components. Step S1.2.4: Separation of the third harmonic zero-sequence component; Perform orthogonal coordinate transformation on the third harmonic zero-sequence component of the z-axis after the positive-sequence transformation, through... Decomposed into d / q axis direct current, completing the steady-state transformation of all differential mode components, where: and for The d-axis and q-axis components in a third-harmonic rotating coordinate system.
[0014] As a specific embodiment of the present invention, step S1.3 includes: Step S1.3.1: Substitute the coordinate transformation result into the original equation; Substitute the differential mode, common mode and zero-sequence component transformation results obtained from the multi-frequency Park transformation in step S1.2 into the original MMC state-space equation established in step S1.1.1 to construct a composite dynamic equation containing coordinate transformation. Step S1.3.2: Simplify the equations and ignore higher harmonics; Expanding the composite dynamic equations, and applying the high-resistance grounding condition of the secondary side of the converter transformer ( ),neglect The above higher harmonic components, after eliminating the time-varying terms in the equations, yield the steady-state equations; Step S1.3.3: Establish the differential-common mode dual-loop model; Based on the simplified steady-state equations, the dynamic equations for the differential-mode circuit and the common-mode circuit are derived respectively, forming a dual-loop structure. The dual-loop structure utilizes the modulation ratio component (…). The coupling together constitutes the averaged state-space model of the MMC power circuit.
[0015] As a specific embodiment of the present invention, step S2.1 includes: Step S2.1.1: Establish the dynamic equations of the phase-locked loop; Based on a decoupled dual-synchronous reference coordinate system phase-locked loop structure, the dynamic equations of a proportional-integral (PI) controller are designed: , ; in, For the proportional / integral coefficient of the PI controller, This represents the positive-sequence q-axis voltage component. For phase deviation, The output of the integral stage is used to track the grid frequency and phase through phase error adjustment; Step S2.1.2: Achieve separation of positive and negative sequence voltages; Phase information output by phase-locked loop The three-phase voltages are subjected to positive sequence ( ) and negative order ( The Park transform, combined with a low-pass filter to eliminate high-frequency disturbances, leads to the state-space equation of the voltage separation stage: , ; in, This is the filter cutoff frequency. The positive sequence voltage dq component. This represents the negative sequence voltage dq component, enabling the separation and extraction of positive and negative sequence voltages.
[0016] As a specific embodiment of the present invention, step S2.2 includes: Step S2.2.1: Park transformation of current signal; Using the synchronization phase output in step S2.1 The three-phase currents are subjected to positive sequence ( ) and negative order ( The Park transformation yields the current components in the dq coordinate system. (in ascending order) and (Negative order); Step S2.2.2: Derivation of the state equation for the separation process; Based on the voltage separation stage structure, a state-space equation containing a low-pass filter is designed to filter and separate the Park-transformed current signal, eliminating cross-coupling components. ; in, The filter cutoff frequency ensures the separation of the negative sequence current component. No positive order interference.
[0017] As a specific embodiment of the present invention, step S2.3 includes: Step S2.3.1: Design of negative sequence PI controller; Based on the negative sequence current component obtained in step S2.2 Design a proportional-integral (PI) controller to adjust the deviation between the current command and the feedback value, generating the dq component of the negative-sequence modulated signal: , ; in, This is a negative sequence d-axis current command. For the output of the integration stage, The signal is a negative-order d-axis modulated signal, and the q-axis is similar; Step S2.3.2: Control signal coordinate transformation; Using the synchronization phase output in step S2.1 The dq components of the negative-order modulated signal are transformed to the abc coordinate system using the inverse Park transform: ; The modulation ratio of the upper and lower arms of the MMC is formed by superimposing the positive sequence modulation signal and the circulating current suppression signal. , .
[0018] As a specific embodiment of the present invention, step S3.1 includes: Step S3.1.1: Define the piecewise function; Define including upper limit value ( ) and lower limit ( Piecewise functions: ; Where u is the input of the limiting circuit and y is the output. When the input exceeds the limit, the threshold is output; otherwise, the input signal is output directly. Step S3.1.2: Switch function logic design; Design a step switch function ( , Characterizing the amplitude limiting state: when u> hour =1, when u< hour =1, within the normal range Then the limited output can be expressed as .
[0019] As a specific embodiment of the present invention, step S3.2 includes: Step S3.2.1: Setting the parameters for the tanh activation function; Choosing the tanh activation function as the continuity tool and setting a smoothing factor The control transient characteristics, the continuous approximation of the switching function is as follows: , ; By controlling the steepness of the transition region through a smoothing factor A, a rapid transition is ensured near the threshold while maintaining the continuous differentiability of the function; Step S3.2.2: Continuity approximation of the switching function; The step switch function ( , Converting this to a continuously differentiable function and substituting it into the amplitude-limiting output expression yields: Eliminate discontinuities to achieve smooth modeling of the amplitude limiting process.
[0020] As a specific embodiment of the present invention, step S3.3 includes: Step S3.3.1: Amplitude limiting model for the integral element; Based on continuous switching function ( , Establish a dynamic equation for the integral term, and suppress integral growth through feedback adjustment when the integral term exceeds the limit: ; in, For the output of the integration stage, Input deviation for PI controller The integral coefficient is... For the amplitude limiting feedback coefficient, ( , ) is the limiting switch function for the integral element; Step S3.3.2: Combine external limiting and PI output; The integral term and the proportional term after limiting are superimposed, and then a second limiting is performed through an external limiting circuit to synthesize the PI controller output: ; in, This is the proportionality coefficient. and It serves as the external limiting threshold, distinguishing between integral limiting and output limiting logic, and accurately reflecting the dynamic process of limiting under large disturbances.
[0021] A data processing device, comprising: Memory, used to store computer programs; A processor, used to implement, when executing the computer program, a flexible DC averaging modeling method that takes into account negative sequence control and amplitude limiting elements.
[0022] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a flexible DC averaging modeling method that considers negative sequence control and a limiting element.
[0023] The advantages of this invention compared to the prior art are: 1. Improve dynamic simulation accuracy: By integrating negative sequence control into DDSRF-PLL dynamic modeling, the separation process of positive and negative sequence components under asymmetric faults is accurately reproduced. Compared with traditional models, the simulation deviation of asymmetric operating conditions is reduced, providing a more reliable analytical basis for system stability control.
[0024] 2. Reduce computational complexity: The averaged state-space method is used to replace the full-order harmonic state-space modeling. While retaining key dynamic characteristics, the model dimensionality is reduced, the computational efficiency is improved, and the real-time simulation and online analysis requirements of large-scale power systems are met.
[0025] 3. Enhanced adaptability to large disturbances: The limiting element is innovatively processed by continuous processing of the tanh function, which breaks through the accuracy limitation of the traditional step function approximation. In large disturbance scenarios such as voltage drop and power step, the transient response time constant error is reduced and the accuracy of predicting the dynamic behavior of the system is improved. Attached Figure Description
[0026] Figure 1 This is a flowchart of a flexible DC averaging modeling method that considers negative sequence control and amplitude limiting.
[0027] Figure 2 This is an MMC power circuit diagram.
[0028] Figure 3 This is a block diagram of DDSRF-PLL.
[0029] Figure 4 This is a block diagram of the positive and negative sequence current separation process.
[0030] Figure 5 This is a block diagram for negative sequence current control.
[0031] Figure 6 This is a block diagram of a PI controller. Detailed Implementation
[0032] To further understand the features, technical means, and specific objectives and functions achieved by the present invention, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.
[0033] A flexible DC averaging modeling method considering negative sequence control and limiting elements includes the following steps: Step S1: Transform and construct the differential-common-mode dual-loop averaged model of MMC; decompose the periodic time-varying state variables of MMC into differential-mode components (the harmonic composition of the differential-mode components includes the fundamental positive-sequence component and the third harmonic zero-sequence component) and common-mode components (the harmonic composition of the common-mode components includes the DC component and the third harmonic negative-sequence component) through multi-frequency coordinate transformation, and establish the steady-state dual-loop state-space equation to provide a dynamic basis for power circuit modeling for subsequent control loops.
[0034] Step S2: Establish the averaged state-space model of the MMC negative sequence control link; for the negative sequence control system containing DDSRF-PLL, realize the separation of positive and negative voltage / current through dynamic equations, design a negative sequence current PI controller and transform it to the standard dq coordinate system to fully characterize the dynamic characteristics of the negative sequence control link.
[0035] Step S3: Establish an averaged state-space model of the limiting circuit; use a continuous approximation tool to make the step switching characteristics of the limiting circuit continuous, and then integrate it with the integral and output circuits of the PI controller to reflect the dynamic process of limiting under large disturbances.
[0036] Furthermore, step S1 includes: Step S1.1: Analyze the state equations of the MMC power circuit to determine the common-mode and differential-mode components; derive the original state-space equations based on the MMC main circuit topology, and separate the common-mode and differential-mode components through harmonic analysis.
[0037] Step S1.2: Apply multi-frequency Park transform to achieve system stabilization; design a multi-frequency Park transform matrix based on the harmonic characteristics of the state variables to transform the time-varying state variables into a rotating coordinate system to achieve stabilization.
[0038] Step S1.3: Derive the averaged state-space equations; substitute the coordinate transformation results into the original state equations, simplify and establish a differential-common-mode dual-loop steady-state model to achieve averaged modeling of the MMC power circuit.
[0039] Furthermore, step S1.1 includes: Step S1.1.1: Establish the original state-space equations of MMC; based on the MMC main loop topology, derive the differential equations of voltage and current according to Kirchhoff's laws, forming a set of first-order differential equations containing state variables such as bridge arm current and capacitor voltage.
[0040] Step S1.1.2: Identify the harmonic characteristics of the state variables; perform harmonic analysis on the steady-state solution of the original state-space equations to identify the harmonic components of each state variable.
[0041] Step S1.2 includes: Step S1.2.1: Derive the general Park transformation matrix; define the transformation matrix for rotating coordinate systems. It includes cosine / sine terms and a zero-sequence component, and its specific form is: ; in, The first and second rows of the matrix represent the electrical angles in the rotating coordinate system. The third row represents the zero-sequence component (z-axis), thus realizing the conversion of three-phase AC quantities to DC quantities in the rotating coordinate system.
[0042] Step S1.2.2: Differential-mode component positive-sequence dq transform; based on the differential-mode component harmonic characteristics identified in step S1.2.1, apply... The positive-sequence Park transformation matrix is used to perform coordinate transformation on the differential mode components, separating them into the dqz coordinate system. The fundamental frequency positive-sequence components are converted into DC components, and the third harmonic zero-sequence components are temporarily stored on the z-axis.
[0043] Step S1.2.3: Common-mode component negative-sequence second harmonic conversion; Based on the DC and second harmonic negative-sequence characteristics of the common-mode component, the following steps are applied... The negative-order Park transformation matrix transforms the common-mode components to the negative-order second harmonic dq coordinate system, thereby stabilizing the DC and second harmonic components.
[0044] Step S1.2.4: Separation of the third harmonic zero-sequence component; Perform orthogonal coordinate transformation on the third harmonic zero-sequence component of the z-axis after the positive sequence transformation, through... Decomposed into d / q axis direct current, completing the steady-state transformation of all differential mode components, where: and for The d-axis and q-axis components in a third-harmonic rotating coordinate system.
[0045] Step S1.3 includes: Step S1.3.1: Substitute the coordinate transformation results into the original equation; Substitute the differential mode, common mode and zero-sequence component transformation results obtained from the multi-frequency Park transformation in step S1.2 into the original MMC state-space equation established in step S1.1.1 to construct a composite dynamic equation containing coordinate transformation.
[0046] Step S1.3.2: Simplify the equations and ignore higher harmonics; expand the composite dynamic equations and apply the high-resistance grounding condition of the secondary side of the converter transformer ( ),neglect The above higher harmonic components, after eliminating the time-varying terms in the equations, yield a steady-state equation.
[0047] Step S1.3.3: Establish a differential-mode-common-mode dual-loop model; based on the simplified steady-state equations, derive the dynamic equations for the differential-mode loop and the common-mode loop respectively, forming a dual-loop structure. The dual-loop structure is modulated by the modulation ratio component (…). The coupling together constitutes the averaged state-space model of the MMC power circuit.
[0048] Furthermore, step S2 includes: Step S2.1: Construct the averaged model of DDSRF-PLL; establish the dynamic equation of DDSRF-PLL with PI controller to achieve voltage positive and negative sequence separation and synchronous phase tracking.
[0049] Step S2.2: Establish a model for separating positive and negative sequence currents; use a coordinate transformation method similar to voltage separation to separate the positive and negative sequence of AC currents, providing feedback signals for negative sequence current control.
[0050] Step S2.3: Derive the negative sequence current control loop model; design a PI controller based on the separated negative sequence current components, generate a negative sequence modulation signal and transform it to the abc coordinate system, and superimpose it onto the positive sequence modulation signal.
[0051] Furthermore, step S2.1 includes: Step S2.1.1: Establish the dynamic equations of the phase-locked loop; based on the decoupled dual-synchronous reference coordinate system phase-locked loop structure, design the dynamic equations containing a proportional-integral (PI) controller: , ; in, For the proportional / integral coefficient of the PI controller, This represents the positive-sequence q-axis voltage component. For phase deviation, The output of the integral stage is used to track the grid frequency and phase through phase error adjustment.
[0052] Step S2.1.2: Achieve separation of positive and negative sequence voltages; utilize the phase information output by the phase-locked loop. The three-phase voltages are subjected to positive sequence ( ) and negative order ( The Park transform, combined with a low-pass filter to eliminate high-frequency disturbances, leads to the state-space equation of the voltage separation stage: , ; in, This is the filter cutoff frequency. The positive sequence voltage dq component. This represents the negative sequence voltage dq component, enabling the separation and extraction of positive and negative sequence voltages.
[0053] Step S2.2 includes: Step S2.2.1: Park transformation of the current signal; using the synchronization phase output from step S2.1 The three-phase currents are subjected to positive sequence ( ) and negative order ( The Park transformation yields the current components in the dq coordinate system. (in ascending order) and (Negative order).
[0054] Step S2.2.2: Derivation of the state-space equation for the separation stage; referencing the voltage separation stage structure, design the state-space equation containing a low-pass filter to filter and separate the Park-transformed current signal, eliminating cross-coupling components: ; in, The filter cutoff frequency ensures the separation of the negative sequence current component. No positive order interference.
[0055] Step S2.3 includes: Step S2.3.1: Negative-sequence PI controller design; based on the negative-sequence current component obtained in step S2.2. Design a proportional-integral (PI) controller to adjust the deviation between the current command and the feedback value, generating the dq component of the negative-sequence modulated signal: , ;
[0056] in, This is a negative sequence d-axis current command. For the output of the integration stage, It is a negative-sequence d-axis modulated signal, and the q-axis is similar.
[0057] Step S2.3.2: Control signal coordinate transformation; utilize the synchronization phase output in step S2.1 The dq components of the negative-order modulated signal are transformed to the abc coordinate system using the inverse Park transform: ; The modulation ratio of the upper and lower arms of the MMC is formed by superimposing the positive sequence modulation signal and the circulating current suppression signal. , .
[0058] Furthermore, step S3 includes: Step S3.1: Define the mathematical model of the limiting circuit; define a piecewise function to describe the limiting characteristics, and design a step switch function to characterize the limiting state.
[0059] Step S3.2: Implement continuous modeling of the limiting stage; use the tanh activation function (a type of continuous approximation tool, specifically belonging to the smoothing function category in the linearization method of nonlinear systems, whose core function is to convert the nonlinear characteristics of the step switch of the limiting stage into a continuously differentiable function, thereby realizing accurate modeling of the limiting dynamic process of the MMC control system) to continuously approximate the switching function, converting the step characteristics into a continuously differentiable function.
[0060] Step S3.3: Integrate the limiting model into the PI controller; establish the limiting dynamic equation of the integral element, adjust the integral term through a continuous switching function, synthesize the PI output with external limiting, and distinguish between integral limiting and output limiting logic.
[0061] Furthermore, step S3.1 includes: Step S3.1.1: Define the piecewise function; define the function including the upper limit ( ) and lower limit ( Piecewise functions: ; Where u is the input of the limiting circuit and y is the output of the limiting circuit. When the input exceeds the limit, the threshold is output; otherwise, the input signal is output directly.
[0062] Step S3.1.2: Switching function logic design; design the step switching function ( , Characterizing the amplitude limiting state: when u> hour =1, when u< hour =1, within the normal range Then the limited output can be expressed as .
[0063] Step S3.2 includes: Step S3.2.1: Setting tanh activation function parameters; Select the tanh activation function as the continuity tool and set the smoothing factor. The control transient characteristics, the continuous approximation of the switching function is as follows: , ; By controlling the steepness of the transition region through a smoothing factor A, a rapid transition is ensured near the threshold while maintaining the continuous differentiability of the function.
[0064] Step S3.2.2: Continuous approximation of the switching function; approximate the step switching function ( , Converting this to a continuously differentiable function and substituting it into the amplitude-limiting output expression yields: Eliminate discontinuities to achieve smooth modeling of the amplitude limiting process.
[0065] Step S3.3 includes: Step S3.3.1: Integral stage limiting model; based on continuous switching function ( , Establish a dynamic equation for the integral term, and suppress integral growth through feedback adjustment when the integral term exceeds the limit: ; in, For the output of the integration stage, Input deviation for PI controller The integral coefficient is... For the amplitude limiting feedback coefficient, ( , ) is the limiting switch function for the integral element.
[0066] Step S3.3.2: External limiting and PI output synthesis; The integral and proportional terms after limiting are superimposed, and then a second limiting is performed through the external limiting stage to synthesize the PI controller output: ; in, This is the proportionality coefficient. and It serves as the external limiting threshold, distinguishing between integral limiting and output limiting logic, and accurately reflecting the dynamic process of limiting under large disturbances.
[0067] A data processing device includes: a memory for storing a computer program; and a processor for executing the computer program to implement a flexible DC averaging modeling method that considers negative sequence control and amplitude limiting.
[0068] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a flexible DC averaging modeling method that considers negative sequence control and a limiting element. Specific Implementation
[0069] Step S1: Construct the differential-common-mode dual-loop averaged model of MMC; decompose the periodic time-varying state variables of MMC into differential-mode and common-mode components through multi-frequency coordinate transformation, and establish the steady-state dual-loop state-space equation, that is, construct the differential-mode-common-mode dual-loop averaged model of MMC through multi-frequency Park transformation, as follows: Figure 1 This is a power circuit diagram for an MMC circuit. In the diagram: and These represent the AC side voltage and current, respectively. and These represent the currents of the upper and lower bridge arms, respectively. and These represent the voltages of the upper and lower bridge arms, respectively. and These represent the sum of the capacitor voltages of the upper and lower bridge arms, respectively. and These represent the switching functions of the k-th submodule; and These represent the capacitor voltages of the k-th submodule; and These represent the DC-side current and voltage, respectively. and These represent the modulation ratios of the upper and lower bridge arm submodules, respectively; above, x = a, b, and c.
[0070] The generalized averaging method requires extracting the main harmonic components from the variables and mapping them to rotating coordinate systems of different frequencies, thus requiring the harmonic characteristics of the bridge arm current and the bridge arm capacitor voltage.
[0071] The partial state-space model of the MMC power circuit with a periodic time-varying steady-state solution is shown in equation (1): (1); In the formula: and These are the bridge arm resistor and the bridge arm inductance, respectively. , It is the leakage inductance of the converter transformer; , It is the capacitor of the bridge arm submodule. This refers to the number of bridge arm sub-modules; , and These represent the sum of the upper / lower bridge arm currents, the submodule capacitor voltages, and the common-mode value of the modulation ratio, respectively. , and These represent the sum of the upper / lower bridge arm currents, capacitor voltages, and the differential mode value of the modulation ratio, respectively.
[0072] Based on equation (1), the harmonic characteristics and phase sequence of each state quantity in MMC can be derived, as shown in Table 1. The derivation process has been published in a large number of existing documents and will not be repeated here.
[0073] Table 1 Harmonic Characteristics of MMC State Quantities , As shown in Table 1, the three-phase differential mode in equation (1) can be transformed to the positive-sequence dq coordinate system and the three-phase common mode to the negative-sequence second harmonic dq coordinate system through Park transformation. Furthermore, the zero-sequence component of the differential mode value of the sum of the submodule capacitor voltages can be mapped to a rotating orthogonal coordinate system, thus achieving system stabilization. Taking the fourth set of state equations in equation (1) as an example: (2); In the formula: , and These are the d-axis, q-axis, and z-axis components of the differential voltage magnitude of the submodule capacitor in the positive-sequence dq coordinate system, respectively. Indicates frequency as The Park transformation matrix, This is the AC power frequency. The following text will discuss Park transform matrices for different frequencies, such as... Etc. A general expression is given here, as shown in equation (3), where q is a quantity that changes periodically with time.
[0074] (3); At this point, the fundamental frequency AC component of the submodule capacitor voltage differential mode is converted into a DC component on the dq axis, while the zero-sequence third harmonic AC component is separated onto the z-axis. Furthermore, this z-axis third harmonic AC component can be further mapped to an orthogonal third harmonic rotating coordinate system: (4); In the formula: and for The d-axis and q-axis components in a third-harmonic rotating coordinate system.
[0075] Substitute into equation (2). It can be further transformed into: (5); In the formula, Defined as the following matrix: (6); Further define the matrix : (7); Next, through a frequency of The Park transform maps the three-phase common-mode values of the submodule capacitor voltage to the negative-sequence second harmonic dq coordinate system: (8); In the formula: , and These represent the d-axis, q-axis, and z-axis components of the common-mode value of the submodule capacitor voltage in the negative-sequence second harmonic dq coordinate system.
[0076] At this point, the three-phase differential-mode and common-mode values of the submodule capacitor voltage have been stabilized through coordinate transformation. Similarly, the three-phase differential-mode and common-mode values of the bridge arm current and the three-phase differential-mode and common-mode values of the modulation ratio can be stabilized using this method. Then, this transformation is applied to the three-phase state equations, as shown in equation (9): (9); In the formula: , and These are the d-axis, q-axis, and z-axis components of the differential mode value of the three-phase bridge arm current in the positive sequence dq coordinate system, respectively. , and z represents the d-axis component, q-axis component, and z-axis component of the common-mode value of the three-phase bridge arm current in the negative sequence second harmonic dq coordinate system; , and These are the d-axis and q-axis components of the differential mode value of the three-phase modulation ratio in the positive-sequence dq coordinate system, and the d-axis and q-axis components of the z-axis component in the third harmonic rotating coordinate system, respectively. , and These represent the d-axis, q-axis, and z-axis components of the three-phase modulation ratio common-mode value in the negative-sequence second harmonic dq coordinate system; "" indicates the dot product operation between two vectors.
[0077] Expand equation (9) and consider the following conditions: 1) Due to the high resistance grounding on the secondary side of the converter transformer, It is always 0; 2) Higher harmonics have no propagation path in the MMC main circuit and control circuit, so the higher trigonometric function terms are ignored, resulting in equation (10) as follows: (10); Similarly, the steady-state expressions for the remaining state equations in equation (1) can be obtained, namely, the MMC differential-common-mode two-loop averaged state-space model with constant steady-state solutions: (11); (12); (13); Step S2: Establish the averaged state-space model of the MMC negative-sequence control link. For the negative-sequence control system containing DDSRF-PLL, dynamic isolation of voltage / current positive and negative sequences is achieved through dynamic equations. A negative-sequence current PI controller is designed and transformed to the standard dq coordinate system to fully characterize the negative-sequence control link. That is, the averaged state-space model of the MMC negative-sequence control link is established, as follows: The main components of the MMC negative-sequence control loop include: a positive-negative sequence separation loop, a negative-sequence current control loop, and a modulation loop. Through these three parts, the MMC negative-sequence control loop outputs a negative-sequence modulation signal, which is superimposed with the positive-sequence modulation signal and the circulating current suppression modulation signal to form the modulation ratio of the upper and lower arms of the MMC. The following sections will perform averaged modeling of the state-space models of these three parts.
[0078] In the MMC control system, the positive and negative sequence separation of three-phase AC electrical quantities is achieved through DDSRF-PLL (direct digital synthesis reference frequency phase-locked loop, decoupled dual synchronous reference coordinate system phase-locked loop). Therefore, it is first necessary to establish an averaged state-space model of the DDSRF-PLL. Figure 2 The diagram shown is a block diagram of DDSRF-PLL. In the diagram: , and The three-phase AC voltage at the point of common coupling. and for , and The d-axis and q-axis values after the orthogonal Park transform. and for , and d-axis and q-axis values after negative-order Park transform The synchronization phase of the DDSRF-PLL output. For the power grid operating frequency, and This is the positive-sequence voltage after the positive-negative sequence separation stage. and This is the negative sequence voltage after the positive and negative sequence separation stage. This is the filter cutoff frequency.
[0079] The output of the phase-locked loop is When performing the Park transformation, It converts the three-phase signals abc to the dqz axis, while This allows the rotating coordinate system to track the phases of the three-phase signals a, b, and c. Assuming the MMC operates under three-phase symmetrical conditions, then... and It contains only direct current, while and It contains only negative-order second harmonic components. Based on the generalized averaging method, combined with... Figure 2 The block diagram yields the averaged state-space model of DDSRF-PLL: (14); In the formula: and for and The value in an orthogonal rotating coordinate system and These are the proportional and integral coefficients of the phase-locked loop PI controller. This is the output of the phase-locked loop integrator.
[0080] Figure 3 The diagram shows the block diagram of the positive and negative sequence current separation circuit. , and For the three-phase alternating current at the point of common coupling, and for , and The d-axis and q-axis values after the orthogonal Park transform. and for , and d-axis and q-axis values after negative-order Park transform For the power grid operating frequency, and This is the positive-sequence voltage after the positive-negative sequence separation stage. and This is the negative sequence voltage after the positive and negative sequence separation stage. This is the filter cutoff frequency.
[0081] The structure of the positive-sequence current separation stage is basically the same as that of the positive-sequence voltage separation stage. By analogy, the state-space model of the positive-sequence current separation stage can be obtained: (15); In the formula: and for and The value in an orthogonal rotating coordinate system.
[0082] Figure 4 The diagram shown is a block diagram for negative sequence current control. and This is the output of the negative sequence current control circuit. and for and The value is transformed to the standard dq coordinate system with an initial phase of zero.
[0083] Based on the generalized averaging method, combined with Figure 2 The block diagram yields the following averaged state-space model for negative-sequence current control: (16); Combining the state-space models of positive-sequence current control and circulating current control, we obtain the averaged state-space model of the complete MMC control system: (17); In the formula: and The output of the positive sequence current control loop is transformed to the value in the standard dq coordinate system with an initial phase of zero. and The output of the circulating current suppression circuit is transformed to the negative-sequence second harmonic dq coordinate system with an initial phase of zero. The averaging modeling of the positive-sequence current control circuit and the circulating current suppression circuit can be obtained using conventional methods, which will not be elaborated here.
[0084] Step S3: Establish the averaged state-space model of the limiting element; use a continuous approximation tool to make the step switching characteristics of the limiting element continuous, and then integrate it with the integral and output elements of the PI controller to reflect the dynamic process of limiting under large disturbances. Specifically, establish the averaged state-space model of the limiting element as follows: To prevent overcurrent in the event of an MMC system failure, a current limit is implemented in the current control circuit. The mathematical expression for the current limit is: (18); in, and These are the upper and lower limits of the limiting circuit, respectively. u is the input of the limiting circuit, and y is the output of the limiting circuit. When the input exceeds the limit, the threshold is output; otherwise, the input signal is output directly.
[0085] Introducing a limiting switch function ( , ); when u> hour =1, when u< hour =1, within the normal range Then the limited output can be expressed as: (19); It is worth noting that, due to this time ( , ) is still a discontinuous function, therefore equation (19) is merely a non-smooth continuous function and cannot be directly integrated into the state-space model of MMC. Therefore, it is necessary to further refine () , This invention proposes a continuous approximation method for the switching function by fitting an activation function, as detailed below: (20); The limiting element in the MMC control system primarily functions within the PI controller. Its logic is as follows: when the sum of the outputs of the proportional and integral elements reaches the limiting value, the PI controller output remains within the limiting region. It's worth noting that if the output of the integral element has not yet reached the limiting value, the integral element will continue integrating until the limiting is reached. Its equivalent block diagram is shown below. Figure 5 As shown.
[0086] Combination Figure 5 The block diagram provides the state-space model of the PI controller considering the limiting element: (twenty one); In the formula: This is the output value of the integration stage. and These are the input and output values of the PI controller. and For the switching function of the integral limiter; and This is the switching function of the external limiter, where A is a large constant, taken as 10 here. 4 ; and These are the upper and lower limits of the limiter in the integration stage; and These are the upper and lower limits of the external limiter.
[0087] The above embodiments only illustrate one or more implementations of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the appended claims.
Claims
1. A flexible DC averaging modeling method considering negative sequence control and limiting elements, characterized in that, Includes the following steps: Step S1: Transform and construct the differential-common mode dual-loop averaged model of MMC; By using multi-frequency coordinate transformation, the time-varying state variables of the MMC period are decomposed into differential-mode components and common-mode components, and a steady-state dual-loop state-space equation is established to provide a dynamic basis for power circuit modeling for subsequent control loops. Step S2: Establish the averaged state-space model of the MMC negative-sequence control loop; For negative-sequence control systems containing DDSRF-PLL, voltage / current positive and negative sequence separation is achieved through dynamic equations. A negative-sequence current PI controller is designed and transformed to the standard dq coordinate system to fully characterize the dynamic characteristics of the negative-sequence control link. Step S3: Establish the averaged state-space model of the limiting stage; The step switching characteristics of the limiting circuit are made continuous by using a continuous approximation tool, and then integrated with the integral and output circuits of the PI controller to reflect the dynamic process of limiting under large disturbances.
2. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 1, characterized in that, Step S1 includes: Step S1.1: Analyze the state equations of the MMC power circuit to determine the common-mode and differential-mode components; The original state-space equations are derived based on the MMC main loop topology, and common-mode and differential-mode components are separated by harmonic analysis. Step S1.2: Apply multi-frequency Park transform to achieve system steady-state operation; Based on the harmonic characteristics of state variables, a multi-frequency Park transformation matrix is designed to transform time-varying state variables into a rotating coordinate system to achieve steady-state transformation. Step S1.3: Derive the averaged state-space equations; Substituting the coordinate transformation results into the original state equations and simplifying them, a differential-common mode dual-loop steady-state model is established to achieve average modeling of the MMC power circuit.
3. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 1, characterized in that, Step S2 includes: Step S2.1: Construct the averaged model of DDSRF-PLL; Establish the dynamic equations of DDSRF-PLL with PI controller to achieve voltage positive and negative sequence separation and synchronous phase tracking; Step S2.2: Establish a model for separating positive and negative sequence currents; A coordinate transformation method similar to voltage separation is used to separate the positive and negative sequences of AC current, providing a feedback signal for negative sequence current control. Step S2.3: Derive the negative sequence current control loop model; A PI controller is designed based on the separated negative-sequence current component to generate a negative-sequence modulation signal and transform it to the abc coordinate system, which is then superimposed on the positive-sequence modulation signal.
4. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 1, characterized in that, Step S3 includes: Step S3.1: Define the mathematical model for the limiting stage; Define a piecewise function to describe the limiting characteristics, and design a step switch function to characterize the limiting state; Step S3.2: Implement continuous modeling of the limiting process; The tanh activation function is used to approximate the switching function as a continuous function, thus converting the step characteristic into a continuously differentiable function. Step S3.3: Integrate the limiting model into the PI controller; A dynamic equation for limiting the integral element is established. The integral term is adjusted by a continuous switching function to synthesize a PI output with external limiting, thus distinguishing between integral limiting and output limiting logic.
5. A flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 2, characterized in that, Step S1.1 includes: Step S1.1.1: Establish the original state-space equations of MMC; Based on the MMC main loop topology, differential equations for voltage and current are derived according to Kirchhoff's laws, forming a set of first-order differential equations that include state variables such as bridge arm current and capacitor voltage. Step S1.1.2: Identify the harmonic characteristics of the state variables; Harmonic analysis is performed on the steady-state solution of the original state-space equations to identify the harmonic components of each state variable.
6. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 5, characterized in that, Step S1.2 includes: Step S1.2.1: Derive the general Park transformation matrix; Define the transformation matrix of the rotating coordinate system It includes cosine / sine terms and a zero-sequence component, and its specific form is: ； in, The first and second rows of the matrix represent the electrical angles in the rotating coordinate system. The third row represents the zero-sequence component (z-axis), realizing the conversion of three-phase AC quantities to DC quantities in the rotating coordinate system. Step S1.2.2: Differential mode component positive sequence dq transform; Based on the differential mode component harmonic characteristics identified in step S1.2.1, the following is applied: The positive-sequence Park transformation matrix is used to perform coordinate transformation on the differential mode components, separating them into the dqz coordinate system, converting the fundamental frequency positive-sequence components into DC components, and temporarily storing the third harmonic zero-sequence components on the z-axis. Step S1.2.3: Negative-sequence second harmonic transformation of common-mode components; For the DC and second harmonic negative sequence characteristics of the common-mode component, the following is applied: The negative-order Park transformation matrix transforms the common-mode components to the negative-order second harmonic dq coordinate system, thereby stabilizing the DC and second harmonic components. Step S1.2.4: Separation of the third harmonic zero-sequence component; Perform orthogonal coordinate transformation on the third harmonic zero-sequence component of the z-axis after the positive-sequence transformation, through... Decomposed into d / q axis direct current, completing the steady-state transformation of all differential mode components, where: and for The d-axis and q-axis components in a third-harmonic rotating coordinate system.
7. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 6, characterized in that, Step S1.3 includes: Step S1.3.1: Substitute the coordinate transformation result into the original equation; Substitute the differential mode, common mode and zero-sequence component transformation results obtained from the multi-frequency Park transformation in step S1.2 into the original MMC state-space equation established in step S1.1.1 to construct a composite dynamic equation containing coordinate transformation. Step S1.3.2: Simplify the equations and ignore higher harmonics; Expanding the composite dynamic equations, and applying the high-resistance grounding condition of the secondary side of the converter transformer ( ),neglect The above higher harmonic components, after eliminating the time-varying terms in the equations, yield the steady-state equations; Step S1.3.3: Establish the differential-common mode dual-loop model; Based on the simplified steady-state equations, the dynamic equations for the differential-mode circuit and the common-mode circuit are derived respectively, forming a dual-loop structure. The dual-loop structure utilizes the modulation ratio component (…). The coupling together constitutes the averaged state-space model of the MMC power circuit.
8. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 3, characterized in that, Step S2.1 includes: Step S2.1.1: Establish the dynamic equations of the phase-locked loop; Based on a decoupled dual-synchronous reference coordinate system phase-locked loop structure, the dynamic equations of a proportional-integral (PI) controller are designed: , ; in, For the proportional / integral coefficient of the PI controller, This represents the positive-sequence q-axis voltage component. For phase deviation, The output of the integral stage is used to track the grid frequency and phase through phase error adjustment; Step S2.1.2: Achieve separation of positive and negative sequence voltages; Phase information output by phase-locked loop The three-phase voltages are subjected to positive sequence ( ) and negative order ( The Park transform, combined with a low-pass filter to eliminate high-frequency disturbances, leads to the state-space equation of the voltage separation stage: , ; in, This is the filter cutoff frequency. The positive sequence voltage dq component. This represents the negative sequence voltage dq component, enabling the separation and extraction of positive and negative sequence voltages.
9. A flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 8, characterized in that, Step S2.2 includes: Step S2.2.1: Park transformation of current signal; Using the synchronization phase output in step S2.1 The three-phase currents are subjected to positive sequence ( ) and negative order ( The Park transformation yields the current components in the dq coordinate system. (in ascending order) and (Negative order); Step S2.2.2: Derivation of the state equation for the separation process; Based on the voltage separation stage structure, a state-space equation containing a low-pass filter is designed to filter and separate the Park-transformed current signal, eliminating cross-coupling components. ； in, The filter cutoff frequency ensures the separation of the negative sequence current component. No positive order interference.
10. A flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 9, characterized in that, Step S2.3 includes: Step S2.3.1: Design of negative sequence PI controller; Based on the negative sequence current component obtained in step S2.2 Design a proportional-integral (PI) controller to adjust the deviation between the current command and the feedback value, generating the dq component of the negative-sequence modulated signal: ， ； in, This is a negative sequence d-axis current command. For the output of the integration stage, The signal is a negative-order d-axis modulated signal, and the q-axis is similar; Step S2.3.2: Control signal coordinate transformation; Using the synchronization phase output in step S2.1 The dq components of the negative-order modulated signal are transformed to the abc coordinate system using the inverse Park transform: ； The modulation ratio of the upper and lower arms of the MMC is formed by superimposing the positive sequence modulation signal and the circulating current suppression signal. , .
11. A flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 4, characterized in that, Step S3.1 includes: Step S3.1.1: Define the piecewise function; The definition includes the upper limit value ( ) and lower limit ( Piecewise functions: ; Where u is the input of the limiting circuit and y is the output. When the input exceeds the limit, the threshold is output; otherwise, the input signal is output directly. Step S3.1.2: Switch function logic design; Design a step switch function ( , Characterizing the amplitude limiting state: when u> hour =1, when u< hour =1, within the normal range Then the limited output can be expressed as .
12. The flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 11, characterized in that, Step S3.2 includes: Step S3.2.1: Setting the parameters for the tanh activation function; Choosing the tanh activation function as the continuity tool and setting a smoothing factor The control transient characteristics, the continuous approximation of the switching function is as follows: ， ； By controlling the steepness of the transition region through a smoothing factor A, a rapid transition is ensured near the threshold while maintaining the continuous differentiability of the function; Step S3.2.2: Continuity approximation of the switching function; The step switch function ( , Converting this to a continuously differentiable function and substituting it into the amplitude-limiting output expression yields: Eliminate discontinuities to achieve smooth modeling of the amplitude limiting process.
13. A flexible DC averaging modeling method considering negative sequence control and limiting elements according to claim 12, characterized in that, Step S3.3 includes: Step S3.3.1: Amplitude limiting model for the integral element; Based on continuous switching function ( , Establish a dynamic equation for the integral term, and suppress integral growth through feedback adjustment when the integral term exceeds the limit: ； in, For the output of the integration stage, Input deviation for PI controller The integral coefficient is... For the amplitude limiting feedback coefficient, ( , ) is the limiting switch function for the integral element; Step S3.3.2: Combine external limiting and PI output; The integral term and the proportional term after limiting are superimposed, and then a second limiting is performed through an external limiting circuit to synthesize the PI controller output: ； in, This is the proportionality coefficient. and It serves as the external limiting threshold, distinguishing between integral limiting and output limiting logic, and accurately reflecting the dynamic process of limiting under large disturbances.
14. A data processing device, characterized in that, include: Memory, used to store computer programs; A processor, configured to implement the steps of a flexible DC averaging modeling method considering negative sequence control and limiting elements as described in any one of claims 1 to 13 when executing the computer program.
15. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of a flexible DC averaging modeling method considering negative sequence control and amplitude limiting as described in any one of claims 1 to 13.