Improved model-free adaptive flexible low-frequency power transmission oscillation suppression method

Abstract

The invention relates to the technical field of power system operation and control, and discloses an improved model-free adaptive flexible low-frequency power transmission oscillation suppression method, which performs zero-phase lag filtering on noisy signals through a nonlinear tracking differentiator, effectively solves the problem of control divergence caused by signal noise, and improves the suppression efficiency. A tight-format dynamic linearization and linear expansion state observer technology is adopted, accurate capture of dynamic characteristics of a strong nonlinear system and real-time observation and compensation of internal and external full-dimensional disturbance are achieved without dependence of a physical model, and particularly, an adaptive estimation algorithm of an output variable quantity penalty factor is introduced. The problem that model parameter identification jumps severely under the broadband oscillation working condition is solved, the robustness of a control system is enhanced, and the self-adaptive optimality of a control strategy is guaranteed and interference of long-term online operation on steady-state performance is avoided by combining parameter optimization of a cuckoo search algorithm and an event triggering mechanism of time-frequency double criteria.

Description

Technical Field

[0001] This application relates to the field of power system operation and control technology, and in particular to an improved model-free adaptive flexible low-frequency transmission oscillation suppression method. Background Technology

[0002] Flexible low-frequency power transmission technology, as a highly efficient power transmission solution, has demonstrated significant advantages in large-scale offshore wind power development and grid connection. This technology significantly reduces the charging power of submarine cables by lowering the transmission frequency from the power frequency to 20 Hz or even lower, thereby greatly increasing the transmission capacity and coverage distance of the transmission system. Modular multilevel matrix converters, as the core power conversion equipment of flexible low-frequency power transmission systems, are widely used in key interconnection links between low-frequency wind farms and the power frequency grid due to their excellent voltage and current waveform quality and flexible power regulation capabilities. With the continuous expansion of new energy grid connection, the topology of power systems is becoming increasingly complex, and the dynamic interactive coupling characteristics between power electronic equipment and the grid are becoming more pronounced, resulting in highly time-varying and uncertain system operating conditions.

[0003] However, modular multilevel matrix converter systems are typical high-order, multivariable, strongly coupled nonlinear dynamic systems. Under complex operating conditions such as weak grid access or sudden load changes, they are prone to inducing broadband oscillations ranging from subsynchronous to mid-to-high frequencies. Existing technologies typically employ model-free adaptive control methods to address the uncertainty of system parameters. While this method theoretically eliminates the reliance on precise mathematical models of the controlled object, it suffers from severe technical limitations when dealing with such broadband and severe oscillations. Specifically, traditional model-free adaptive control algorithms are extremely sensitive to measurement noise and signal abrupt changes in parameter estimation. When the system output voltage or current fluctuates drastically, the estimated values ​​of the core pseudo-partial derivative time-varying parameters often diverge due to the drastic jumps in the sampled data, leading to controller output instability. Furthermore, existing methods lack active observation and compensation mechanisms for external random disturbances and unmodeled dynamics, relying solely on output error feedback for passive adjustment. This lag in control response makes it difficult for the controller to effectively curb rapid energy dissipation in the initial stages of oscillations, seriously threatening the safe and stable operation of flexible low-frequency transmission systems. Summary of the Invention

[0004] This application proposes an improved model-free adaptive flexible low-frequency transmission oscillation suppression method to address the problems mentioned in the background art.

[0005] To achieve the above objectives, this application adopts the following technical solution: an improved model-free adaptive flexible low-frequency transmission oscillation suppression method, comprising the following steps:

[0006] Step S1: Input the voltage command signal of the flexible low-frequency transmission system to the nonlinear tracking differentiator module. The nonlinear tracking differentiator module performs smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system, and outputs the smoothed signal after filtering out random noise and the first-order differential estimate.

[0007] Step S2: The smoothed signal output in step S1 is processed using the tight-format dynamic linearization method to establish a tight-format dynamic linear data model containing time-varying parameters of pseudo-partial derivatives. Based on the tight-format dynamic linear data model, a linear extended state observer is constructed. The linear extended state observer observes the system disturbance of the flexible low-frequency transmission system, iteratively calculates and outputs the total disturbance estimate.

[0008] Step S3: Construct an adaptive pseudo-partial derivative estimator algorithm that introduces an output change penalty factor. The adaptive pseudo-partial derivative estimator algorithm adjusts the adaptive regularization weight factor so that the value of the adaptive regularization weight factor is equal to the basic weight factor plus the product of the output change penalty coefficient and the square of the system output change. The output change penalty coefficient is the output change penalty factor, which is configured as a positive gain. The value of the system output change is defined as the difference between the system output sequence at the current sampling time and the system output sequence at the previous sampling time. The adaptive pseudo-partial derivative estimator algorithm calculates the pseudo-partial derivative time-varying parameters based on the adaptive regularization weight factor and feeds back the total disturbance estimate output in step S2 to the model-free adaptive control model. The model-free adaptive control model combines the pseudo-partial derivative time-varying parameters and the total disturbance estimate to calculate the oscillation suppression control law.

[0009] Step S4: The control parameters of the model-free adaptive controller are optimized and improved based on the performance index function using the cuckoo search algorithm. The operating status of the flexible low-frequency transmission system is monitored using frequency domain criteria and time domain criteria. When the frequency domain criteria or time domain criteria trigger an oscillation signal, the oscillation suppression control law generated in step S3 is added to the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system.

[0010] Furthermore, in step S1, the specific operations of the nonlinear tracking differentiator module in performing smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system include:

[0011] The voltage command signal output from the outer loop of the flexible low-frequency power transmission system is defined as the discrete-time input sequence at the current sampling moment, and initial state values ​​are assigned to the smoothed tracking signal and the first-order differential estimator inside the nonlinear tracking differentiator module.

[0012] The key control parameters required to construct a second-order nonlinear dynamic system are set, including the system sampling period, instantaneous switching factor, and filter factor.

[0013] Configure the system sampling period as the time base parameter for discretization calculation by the nonlinear tracking differentiator module;

[0014] The instantaneous interruption factor is configured as a parameter characterizing the tracking speed response capability of the nonlinear tracking differentiator module to the discrete-time input sequence. The value of the instantaneous interruption factor is positively correlated with the tracking speed of the nonlinear tracking differentiator module.

[0015] Configure the filter factor as a parameter to adjust the filtering smoothing intensity and phase characteristics of the nonlinear tracking differentiator module;

[0016] Based on the set key control parameters, the threshold parameter system of the nonlinear tracking differentiator module is further calculated, and the nonlinear interval threshold parameter is calculated. The value of the nonlinear interval threshold parameter is equal to the product of the instantaneous interruption factor and the system sampling period.

[0017] Calculate the error segment discrimination threshold parameter. The value of the error segment discrimination threshold parameter is equal to the product of the system sampling period and the nonlinear interval threshold parameter.

[0018] A nonlinear tracking differentiator module is constructed using nonlinear interval threshold parameters and error segment discrimination threshold parameters to determine whether the system state has entered a steady-state micro-region, thus completing the initial configuration of the nonlinear tracking differentiator module.

[0019] Furthermore, in step S1, the specific operations of the nonlinear tracking differentiator module in performing smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system also include:

[0020] Within each discrete system sampling period, the tracking error and differential state quantity at the current sampling time are calculated. The value of the tracking error is equal to the difference between the smoothed tracking signal at the current sampling time and the discrete-time input sequence. The value of the differential state quantity is directly taken as the first-order differential estimate at the current sampling time.

[0021] Calculate the comprehensive error term. The value of the comprehensive error term is equal to the tracking error plus the product of the system sampling period and the differential state quantity.

[0022] The equivalent correction is calculated by constructing a nonlinear mapping relationship based on the comprehensive error term: it is determined whether the absolute value of the comprehensive error term is less than or equal to the error segment discrimination threshold parameter. If the absolute value of the comprehensive error term is less than or equal to the error segment discrimination threshold parameter, the value of the equivalent correction is equal to the differential state quantity plus the quotient of the comprehensive error term divided by the system sampling period. If the absolute value of the comprehensive error term is greater than the error segment discrimination threshold parameter, the intermediate nonlinear adjustment quantity is calculated first. The value of the intermediate nonlinear adjustment quantity is equal to the square root of the sum of the square of the nonlinear interval threshold parameter plus eight times the fast-break factor and the absolute value of the comprehensive error term. At this time, the value of the equivalent correction is equal to the product of the differential state quantity plus half of the difference between the intermediate nonlinear adjustment quantity and the nonlinear interval threshold parameter and the sign function of the comprehensive error term.

[0023] Based on this, the fastest control output is calculated: it is determined whether the absolute value of the equivalent correction is less than or equal to the nonlinear interval threshold parameter. If the absolute value of the equivalent correction is less than or equal to the nonlinear interval threshold parameter, the value of the fastest control output is equal to the negative instantaneous factor multiplied by the equivalent correction divided by the nonlinear interval threshold parameter. If the absolute value of the equivalent correction is greater than the nonlinear interval threshold parameter, the value of the fastest control output is equal to the negative instantaneous factor multiplied by the sign function of the equivalent correction.

[0024] The internal state of the nonlinear tracking differentiator module is updated discretely and iteratively using the fastest control output. The smoothed tracking signal at the next sampling time is equal to the smoothed tracking signal at the current sampling time plus the product of the system sampling period and the first-order differential estimate at the current sampling time. The first-order differential estimate at the next sampling time is equal to the first-order differential estimate at the current sampling time plus the product of the system sampling period and the fastest control output.

[0025] Furthermore, in step S2, the specific operations for processing the smoothed signal output from step S1 using the compact scheme dynamic linearization method to establish a compact scheme dynamic linear data model containing time-varying pseudo-partial derivative parameters include:

[0026] Establish a data mapping relationship between step S1 and step S2, define the smooth signal output by the nonlinear tracking differentiator module in step S1 as the system output sequence of the compact dynamic linear data model, and define the control command increment of the flexible low-frequency transmission system as the system input sequence of the compact dynamic linear data model.

[0027] Based on Cauchy's mean value theorem, the nonlinear discrete-time system of the flexible low-frequency transmission system is transformed into an equivalent form. A compact-format dynamic linear data model is constructed within each discrete system sampling period. The compact-format dynamic linear data model consists of time-varying pseudo-partial derivative parameters, system input sequence, system output sequence, and linearization error perturbation term.

[0028] In the compact dynamic linear data model, the pseudo-partial derivative time-varying parameter is defined as a dynamic gain variable characterizing the flexible low-frequency transmission system at the current operating point. The value of the pseudo-partial derivative time-varying parameter corresponds to the partial derivative of the change in the system output sequence with respect to the change in the system input sequence.

[0029] In the compact form dynamic linear data model, a linearization error perturbation term is introduced. The value of the linearization error perturbation term is equal to the sum of the model truncation error generated when the nonlinear system is equivalent to a linear data model and the dynamic deviation caused by the time-varying system parameters.

[0030] The mathematical expression logic of the compact-format dynamic linear data model is as follows: the change in the system output sequence at the next sampling time is equal to the product of the pseudo-partial derivative time-varying parameter and the change in the system input sequence at the current sampling time, plus the sum of the linearization error perturbation term, thus completing the process of transforming the strongly nonlinear system into a linear time-varying data model that depends only on the input and output data.

[0031] Furthermore, in step S2, a linear extended state observer is constructed based on the compact-format dynamic linear data model. The linear extended state observer observes the system disturbances of the flexible low-frequency transmission system, iteratively calculates and outputs the total disturbance estimate. The specific operations include:

[0032] A linear extended state observer is constructed based on a tight-form dynamic linear data model. First, the internal state variables of the linear extended state observer are defined. The internal state variables include output tracking state variables used to track the system output sequence and extended state variables used to estimate the total system disturbance.

[0033] Set the configuration parameters for the linearly extended state observer, including the observer bandwidth, observer gain coefficient, and system gain compensation factor.

[0034] Using the system sampling period determined in step S1 as the time base for discrete iterative calculation of the linear extended state observer, the output estimation error is calculated within each system sampling period. The value of the output estimation error is equal to the difference between the output tracking state variable and the smoothed signal.

[0035] The state update calculation for the linear extended state observer is as follows: the output tracking state variable at the next sampling time is equal to the output tracking state variable at the current sampling time plus the product of the system sampling period and the correction term. The correction term is calculated by adding the product of the extended state variable at the current sampling time, the system gain compensation factor, and the system input sequence, and then subtracting the product of the observer gain coefficient and the output estimation error.

[0036] The expanded state variable at the next sampling time is equal to the expanded state variable at the current sampling time plus the product of the system sampling period and the negative observer gain coefficient multiplied by the output estimation error;

[0037] Through the above iterative calculations, the output tracking state variable is corrected using the output estimation error, and the expanded state variable is used to integrally update the model mismatch inside the system and external disturbances.

[0038] The expanded state variables after iterative convergence are defined as the total disturbance estimate and output. The total disturbance estimate will serve as the data basis for feedforward compensation in subsequent steps.

[0039] Furthermore, in step S3, an adaptive pseudo-partial derivative estimator algorithm is constructed by introducing an output change penalty factor. The specific operations of the adaptive pseudo-partial derivative estimator algorithm to adjust the adaptive regularization weight factor according to the output change of the flexible low-frequency transmission system include:

[0040] An improved pseudo-partial derivative estimation criterion function is constructed, which consists of two parts: a model fitting error term and a parameter change rate constraint term.

[0041] The value of the model fitting error term is equal to the square of the difference between the system output sequence at the current sampling time and the single-step forward predicted output value;

[0042] The value of the parameter change rate constraint term is equal to the product of the square of the difference between the estimated value of the pseudo-partial derivative time-varying parameter at the current sampling time and the estimated value of the pseudo-partial derivative time-varying parameter at the previous sampling time, and the adaptive regularization weight factor.

[0043] Based on the construction of the improved pseudo-partial derivative estimation criterion function, the calculation logic of the adaptive regularization weight factor is further defined, and the adaptive regularization weight factor is configured as a time-varying parameter that changes in real time with the change of system output.

[0044] The specific numerical calculation logic of the adaptive regularization weight factor is as follows: the basic weight factor is added to the product of the output change penalty coefficient and the square of the system output change. The basic weight factor is configured as a non-zero constant and serves as the baseline value of the adaptive regularization weight factor when the system output change is zero. The output change penalty coefficient is configured as a positive gain and is used to set the proportion of the square of the system output change to the numerical contribution of the adaptive regularization weight factor. The numerical value of the system output change is defined as the difference between the system output sequence at the current sampling time and the system output sequence at the previous sampling time.

[0045] Through the above calculation logic, within each discrete system sampling period, the adaptive pseudo-partial derivative estimator algorithm updates the value of the adaptive regularization weight factor in real time based on the change in system output calculated at the current sampling time, and substitutes the updated adaptive regularization weight factor into the improved pseudo-partial derivative estimation criterion function to participate in the extreme value solution calculation.

[0046] Furthermore, in step S3, the specific operations of the adaptive pseudo-partial derivative estimator algorithm in calculating the time-varying parameters of the pseudo-partial derivatives include:

[0047] The improved pseudo-partial derivative estimation criterion function is subjected to partial derivative calculation with respect to the time-varying pseudo-partial derivative parameter, and an extreme value equation with zero derivative is established. In the process of solving the extreme value equation, a step size factor is introduced, and the real-time iterative update calculation expression of the time-varying pseudo-partial derivative parameter is derived.

[0048] Numerical calculations are performed based on the real-time iterative update calculation expression: the estimated value of the time-varying pseudo-partial derivative parameter at the current sampling time is equal to the sum of the estimated value of the time-varying pseudo-partial derivative parameter at the previous sampling time and the parameter correction term. The calculation of the parameter correction term includes numerator and denominator operations. The numerator value of the parameter correction term is equal to the step size factor multiplied by the change in system input at the previous sampling time and then multiplied by the parameter estimation error term. The value of the parameter estimation error term is equal to the change in system output at the current sampling time minus the product of the estimated value of the time-varying pseudo-partial derivative parameter at the previous sampling time and the change in system input at the previous sampling time.

[0049] The denominator value of the parameter correction term is equal to the sum of the adaptive regularization weight factor and the square of the change in system input at the previous sampling time. During the calculation of the denominator value of the parameter correction term, the adaptive regularization weight factor updated in real time is directly called to participate in the calculation. Since the adaptive regularization weight factor is located in the denominator of the parameter correction term, this calculation structure establishes an inverse numerical relationship between the magnitude of the parameter correction term and the value of the adaptive regularization weight factor.

[0050] The adaptive pseudo-partial derivative estimator algorithm performs the above calculations in each system sampling period and verifies the numerical stability of the calculation results: if the magnitude of the calculated pseudo-partial derivative time-varying parameter estimate is less than the preset minimum threshold, or if the sign of the calculated pseudo-partial derivative time-varying parameter estimate is inconsistent with the initial sign reference value, then the pseudo-partial derivative time-varying parameter estimate is forcibly reset to the initial sign reference value; otherwise, the calculation results are retained.

[0051] Furthermore, in step S3, the specific operations for calculating the oscillation suppression control law by combining the time-varying parameters of pseudo-partial derivatives and the total disturbance estimate in the model-free adaptive control model include:

[0052] Based on the compact dynamic linear data model and combined with the total disturbance estimate, the single-step forward prediction equation of the flexible low-frequency transmission system is reconstructed. In the mathematical structure of the single-step forward prediction equation, the system output sequence value at the next sampling time consists of three parts: the system output sequence at the current sampling time, the product of the time-varying parameter estimate of the pseudo-partial derivative at the current sampling time and the change in the system input at the current sampling time, and the total disturbance estimate.

[0053] Define the control criterion function for solving the control law. The control criterion function consists of the system output tracking error term and the control input change penalty term. The value of the system output tracking error term is equal to the square of the difference between the system output reference value at the next sampling time and the system output sequence at the next sampling time.

[0054] The value of the control input change penalty term is equal to the product of the square of the system input change at the current sampling time and the control input weight factor. The control input weight factor is configured as a constant parameter used to adjust the magnitude of the control input change.

[0055] Substituting the reconstructed single-step forward prediction equation into the control criterion function and differentiating it with respect to the system input sequence at the current sampling time, we obtain the final oscillation suppression control law by setting the derivative to zero: The oscillation suppression control law at the current sampling time is equal to the system input sequence at the previous sampling time plus the control increment term. The numerator of the control increment term is equal to the control step size factor multiplied by the estimated value of the time-varying pseudo-partial derivative at the current sampling time and then multiplied by the total error term. The value of the total error term is equal to the system output reference value at the next sampling time minus the system output sequence at the current sampling time minus the total disturbance estimate. The denominator of the control increment term is equal to the sum of the control input weight factor and the squares of the estimated value of the time-varying pseudo-partial derivative at the current sampling time.

[0056] By performing the above calculations, the model-free adaptive control model outputs an oscillation suppression control law that includes the reverse component of the total disturbance estimate.

[0057] Furthermore, in step S4, the specific operations of optimizing and improving the control parameters of the model-free adaptive controller based on the performance index function using the cuckoo search algorithm include:

[0058] The set of control parameters to be optimized for the improved model-free adaptive controller is determined. The set of control parameters to be optimized covers all the key adjustment variables defined in step S3. Specifically, the set of control parameters to be optimized consists of control input weighting factor, control step size factor, basic weighting factor, output change penalty coefficient, and step size factor.

[0059] A performance index function is constructed to evaluate the quality of the set of control parameters to be optimized. The performance index function is based on the time-weighted absolute error integral criterion. The numerical calculation logic of the performance index function is as follows: within the entire simulation time window, the product of the sampling time index, the system sampling period, and the absolute value of the difference between the system output reference value and the system output sequence at each sampling moment is accumulated and summed. The reciprocal of the value of the performance index function is defined as the fitness function of the Cuckoo Search algorithm.

[0060] The iterative optimization process of the cuckoo search algorithm is as follows: Initialize the host nest locations of the cuckoo population, with each host nest location representing a set of candidate control parameters to be optimized; calculate the fitness function value corresponding to each host nest location; use the Levy flight mechanism to simulate the random search path of the cuckoo to update the host nest locations, and recalculate the fitness function value corresponding to the updated host nest locations; compare the fitness function values ​​before and after the update, retain the host nest locations with larger fitness function values, discard a portion of the host nest locations with poor fitness function values ​​according to a preset probability, and randomly generate new host nest locations in the search space to replace them;

[0061] Repeat the above update and selection steps until the preset maximum number of iterations is reached. Output the parameter value corresponding to the host bird's nest position with the largest fitness function value as the global optimal control parameter set. Assign the global optimal control parameter set to the improved model-free adaptive controller to complete the optimal configuration of the control parameters.

[0062] Furthermore, in step S4, the operating status of the flexible low-frequency transmission system is monitored using frequency domain criteria and time domain criteria. When the frequency domain criteria or time domain criteria trigger an oscillation signal, the specific operation of adding the oscillation suppression control law generated in step S3 to the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system includes:

[0063] A frequency domain oscillation identification mechanism based on the sliding window fast Fourier transform algorithm is constructed, and the voltage component or current component in the voltage and current dual closed-loop control loop of the flexible low-frequency power transmission system is selected as the frequency domain monitoring signal.

[0064] Perform a sliding window fast Fourier transform operation on the frequency domain monitoring signal to obtain the amplitude spectrum distribution, and calculate the fundamental energy ratio index. The value of the fundamental energy ratio index is equal to the ratio of the energy amplitude of the zero-hertz component to the sum of the energy amplitudes of all frequency components.

[0065] The fundamental frequency energy ratio index is compared with the preset frequency domain safety threshold. If the fundamental frequency energy ratio index is lower than the frequency domain safety threshold and the duration of the state where the fundamental frequency energy ratio index is lower than the frequency domain safety threshold exceeds the preset frequency domain judgment period, then the generation of a frequency domain oscillation signal is triggered.

[0066] A time-domain oscillation identification mechanism based on the discrete numerical difference method is constructed. The output signal of the voltage and current dual closed-loop control loop is selected as the time-domain monitoring signal. The first-order rate of change of the time-domain monitoring signal is calculated in the discrete time domain. The value of the first-order rate of change is equal to the absolute value of the difference between the time-domain monitoring signal at the current sampling time and the time-domain monitoring signal at the previous sampling time divided by the system sampling period. The first-order rate of change is compared with a preset time-domain safety threshold. If the first-order rate of change is greater than the time-domain safety threshold, the generation of the time-domain oscillation signal is triggered. An event-triggered oscillation suppression execution logic is constructed, and an improved model-free adaptive controller is configured to switch between background calculation state and active suppression state.

[0067] When neither the frequency domain oscillation signal nor the time domain oscillation signal is generated, the improved model-free adaptive controller maintains the background calculation state, and the value of the oscillation suppression control law generated in step S3 is not output to the voltage and current dual closed-loop control loop.

[0068] When a frequency domain oscillation signal or a time domain oscillation signal is triggered, the improved model-free adaptive controller switches to the active suppression state and immediately superimposes the oscillation suppression control law generated in step S3 onto the output of the proportional-integral controller inside the voltage and current dual closed-loop control loop of the flexible low-frequency power transmission system to participate in the modulation of the converter voltage command.

[0069] The beneficial effects of this invention are as follows:

[0070] This invention effectively solves the control divergence problem caused by signal noise by using a nonlinear tracking differentiator to perform zero-phase lag filtering on noisy signals. It adopts compact dynamic linearization and linear extended state observer technology to achieve accurate capture of the dynamic characteristics of strongly nonlinear systems and real-time observation and compensation of internal and external full-dimensional disturbances without physical model dependence. In particular, the introduction of an adaptive estimation algorithm with an output change penalty factor overcomes the problem of drastic changes in model parameter identification under wideband oscillation conditions, enhancing the robustness of the control system. Combined with the parameter optimization of the cuckoo search algorithm and the event triggering mechanism with time and frequency dual criteria, it ensures the adaptive optimality of the control strategy and avoids interference with steady-state performance from long-term online operation. Finally, it achieves accurate identification and efficient active suppression of wideband oscillations in complex power grid environments. Attached Figure Description

[0071] To more clearly illustrate the technical solutions in the embodiments of the present invention 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort:

[0072] Figure 1This is a flowchart of the method of the present invention;

[0073] Figure 2 This is a schematic diagram of the broadband oscillation suppression circuit of the flexible low-frequency power transmission system of the present invention;

[0074] Figure 3 This is a diagram illustrating the oscillation suppression effect of the FLFT system of the present invention;

[0075] Figure 4 This diagram illustrates the effect of suppressing intermediate frequency oscillations within the low-frequency side control structure of the M3C in this invention.

[0076] Figure 5 This diagram illustrates the effect of suppressing subsynchronous oscillations within the low-frequency control structure of the M3C in this invention.

[0077] Figure 6 This is a comparison chart showing the data noise disturbance suppression effects of the improved MFAC of this invention and the traditional MFAC. Detailed Implementation

[0078] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0079] Example

[0080] like Figures 1 to 6 As shown, this invention discloses an improved model-free adaptive flexible low-frequency transmission oscillation suppression method, comprising the following steps:

[0081] Step S1: Input the voltage command signal of the flexible low-frequency transmission system to the nonlinear tracking differentiator module. The nonlinear tracking differentiator module performs smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system, and outputs the smoothed signal after filtering out random noise and the first-order differential estimate.

[0082] In a preferred embodiment of the present invention, step S1, in which the nonlinear tracking differentiator module (TD) performs smooth tracking and first-order differential estimation of the voltage command signal based on a second-order nonlinear dynamic system, specifically includes:

[0083] The voltage command signal output from the outer loop of the flexible low-frequency transmission system is defined as the discrete-time input sequence at the current sampling moment. And smooth the tracking signal inside the nonlinear tracking differentiator module (TD). and first-order differential estimator Perform initial state assignment.

[0084] Among them, discrete-time input sequence It refers to the first The original noisy signal acquired at each sampling time point is smoothed and tracked. Used to characterize the system in the first Steady-state output after noise removal at any time; first-order differential estimator Used to characterize the signal in the 1st Rate of change over time; in this embodiment, the instant the system starts. Smooth tracking signal and first-order differential estimator All values ​​are initialized to 0. The initialization value of 0 ensures that the nonlinear tracking differentiator module converges from the zero energy state, avoids the numerical shock caused by the state variables being suspended at the moment of algorithm startup, and ensures the soft-start characteristics of the control system.

[0085] Define the key control parameters required to construct a second-order nonlinear dynamic system. These key control parameters include the system sampling period. Instantaneous termination factor and filter factor .

[0086] System sampling period The time base parameter configured for discretization calculation by the nonlinear tracking differentiator module; in this embodiment, the system sampling period. The preferred setting is 0.00005 seconds (i.e., 50 microseconds). This value is based on the switching frequency of the modular multilevel matrix converter (M3C) in the flexible low-frequency transmission system (typically 5kHz-10kHz) and the constraints of Shannon's sampling theorem, while also considering the computational load limit of the real-time controller. The system sampling period is 0.00005 seconds. It can ensure that the control bandwidth effectively covers a wide frequency range from 0Hz to 100Hz, while avoiding processor overload due to excessively frequent floating-point operations, thus ensuring the real-time performance of the algorithm running online.

[0087] quick-break factor The instantaneous interruption factor is a parameter configured to characterize the tracking speed response capability of the nonlinear tracking differentiator module to a discrete-time input sequence. The value of is positively correlated with the tracking speed of the nonlinear tracking differentiator module; the instantaneous interruption factor The physical equivalent of the maximum acceleration limit of a second-order dynamical system determines the smooth tracking signal. Catching up with discrete-time input sequences The speed of response to changes; in this embodiment, the instantaneous interruption factor. The preferred setting is 10000, based on the dynamic response requirements of the flexible low-frequency transmission system to the 20Hz base frequency signal. Comparative testing showed that when the instantaneous trip factor... When set to 10000, the tracking phase lag for a 20Hz sinusoidal signal is less than 1 degree, and the amplitude attenuation is less than 0.1%. Compared to the phase lag of more than 30 degrees typically produced by a traditional second-order low-pass filter at the same cutoff frequency, this is significantly better than setting the instantaneous cutoff factor. Setting the value to 10000 enables the nonlinear tracking differentiator module to achieve a tracking effect with near-zero phase lag, effectively solving the problem of directional instability of the MFAC controller caused by phase lag.

[0088] filter factor The parameters configured to adjust the filtering smoothing intensity and phase characteristics of the nonlinear tracking differentiator module are, in this embodiment, the filtering factor. The preferred setting is the system sampling period. 20 times, or 0.001 seconds, is determined based on the chattering elimination theory and experimental analysis of noise suppression ratio in discrete sliding mode control, and the filter factor. The filter window width of the system near steady state was defined and set to 0.001 seconds. This can attenuate the amplitude of high-frequency random noise to less than 5% of the original amplitude while preserving the dynamic characteristics of the signal, thus preventing high-frequency noise from inducing high-frequency chatter in the control quantity.

[0089] Based on the established key control parameters, the threshold parameter system of the nonlinear tracking differentiator module (TD) is further calculated, and the threshold parameters of the nonlinear interval are calculated. Nonlinear interval threshold parameter The value is equal to the instantaneous factor. With system sampling period The product of is calculated using the following formula: ;

[0090] In this formula, Represents the threshold parameter for nonlinear intervals. As the instantaneous tripping factor, The system sampling period is defined by this formula, which is used to determine the boundary values ​​between the linear and nonlinear regions in the system control strategy. This ensures that the system has consistent dynamic response characteristics at different sampling frequencies. In this embodiment, This parameter ensures that the system state can transition smoothly as it approaches the equilibrium point.

[0091] Calculate the error segmentation threshold parameter Error segmentation discrimination threshold parameter The value is equal to the system sampling period. With nonlinear interval threshold parameter The product of is calculated using the following formula: ;

[0092] In this formula, The threshold parameter represents the segmentation threshold for error discrimination. The system sampling period is The nonlinear interval threshold parameter obtained from the aforementioned calculation is used to further define whether the system has entered a small steady-state region, preventing the system from generating high-frequency fluctuations near the equilibrium point. In this embodiment, .

[0093] Using nonlinear interval threshold parameters Error segmentation discrimination threshold parameter Construct a nonlinear tracking differentiator (TD) module to determine whether the system state has entered the steady-state small region, and complete the initial configuration of the nonlinear tracking differentiator (TD) module.

[0094] Furthermore, in step S1, the specific operations of the nonlinear tracking differentiator module (TD) in performing smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system also include:

[0095] In each discrete system sampling period Within, calculate the tracking error at the current sampling time. With differential state quantity Tracking error The value is equal to the smoothed tracking signal at the current sampling time. Subtract discrete-time input sequence The difference, the differential state quantity The value is directly taken as the first-order differential estimator at the current sampling time. The calculation formula is as follows: ;

[0096] In this set of formulas, For the first The tracking error at any given moment reflects the degree of deviation between the current output and the input; For the first The differential state quantities at time t; these two quantities serve as state feedback and are used for subsequent calculation of the deviation input of the control system.

[0097] Calculate the comprehensive error term Comprehensive error term The value equals the tracking error. Add system sampling period With differential state quantity The product of is calculated using the following formula: ;

[0098] In this formula, This represents the comprehensive error term, which actually predicts the error trend of the system at the next sampling time. This formula is used to introduce differential negative feedback, increase the damping of the system, and thus suppress overshoot.

[0099] Based on the comprehensive error term Construct nonlinear mapping relationships to calculate equivalent correction quantities Determine the comprehensive error term Whether the absolute value is less than or equal to the error segmentation threshold parameter If the comprehensive error term The absolute value is less than or equal to the error segmentation threshold parameter Then the equivalent correction amount The value is equal to the differential state quantity. Add the comprehensive error term Divide by the system sampling period The quotient; if the comprehensive error term The absolute value is greater than the error segmentation threshold parameter First, calculate the intermediate nonlinear adjustment amount. Intermediate nonlinear adjustment amount The value is equal to the nonlinear interval threshold parameter. The square of the sum of the eight quick-break factors Combined error term The arithmetic square root of the sum of the products of absolute values, at this point, is the equivalent correction quantity. The value is equal to the differential state quantity. Add intermediate nonlinear adjustment amount Subtract the nonlinear interval threshold parameter Half of the difference and the comprehensive error term The product of sign functions is calculated using the following formula: ;

[0100] In this set of formulas, For equivalent correction amount, This is the intermediate nonlinear adjustment value. This is the sign function; this part of the logic constitutes the core of the nonlinear tracking differentiator module (TD), namely the discretized form of the fastest control synthesis function. This formula is used to adaptively select the linear convergence path or the nonlinear fastest convergence path according to the magnitude of the error, thereby eliminating phase lag while ensuring fast tracking.

[0101] Based on this, the fastest control output is calculated. Determine the equivalent correction amount Is the absolute value less than or equal to the nonlinear interval threshold parameter? If the equivalent correction amount The absolute value is less than or equal to the nonlinear interval threshold parameter Then the fastest control output quantity The value is equal to a negative instantaneous factor. Multiply by the equivalent correction amount Divide by the nonlinear interval threshold parameter The quotient; if the equivalent correction amount The absolute value is greater than the threshold parameter of the nonlinear interval. Then the fastest control output quantity The value is equal to a negative instantaneous factor. Multiply by the equivalent correction amount The sign function is calculated using the following formula: ;

[0102] In this formula, Representing the fastest control output, it is essentially the acceleration control signal of a second-order system. This formula is used to generate the control quantity that drives the system's state updates, ensuring smooth tracking of the signal. It can approximate the input signal at the fastest speed without overshoot.

[0103] Using the fastest control output Discrete iterative updates are performed on the internal state of the nonlinear tracking differentiator module (TD) to obtain the smoothed tracking signal at the next sampling time. Equal to the smoothed tracking signal at the current sampling time Add system sampling period First-order differential estimator at the current sampling time The product of the first-order differential estimator at the next sampling time. Equal to the first-order differential estimator at the current sampling time Add system sampling period With the fastest control output The product of these , the updated equation is as follows: ;

[0104] In this set of formulas, It is the updated smoothed signal for the next time step. This is the updated differential estimate for the next time step. This formula is used to complete the one-step Euler integral and outputs a smoothed signal after filtering out random noise. As the data source for step S2, high-quality reconstruction of the original noisy signal is achieved.

[0105] Step S2: The smoothed signal output in step S1 is processed using the tight-format dynamic linearization method to establish a tight-format dynamic linear data model containing time-varying parameters of pseudo-partial derivatives. Based on the tight-format dynamic linear data model, a linear extended state observer is constructed. The linear extended state observer observes the system disturbance of the flexible low-frequency transmission system, iteratively calculates and outputs the total disturbance estimate.

[0106] In a preferred embodiment of the present invention, step S2, which uses a tight-format dynamic linearization method to process the smoothed signal output in step S1 and establish a tight-format dynamic linear data model containing time-varying pseudo-partial derivative parameters, specifically includes: establishing a data mapping relationship between step S1 and step S2, and processing the smoothed signal output by the nonlinear tracking differentiator module (TD) in step S1. The system output sequence is defined as a compact form dynamic linear data model (CFDL model). Soon The control command increment of the flexible low-frequency transmission system is defined as the system input sequence of the compact-format dynamic linear data model (CFDL model). .

[0107] In this definition, the system output sequence This represents the observed output voltage of the flexible low-frequency transmission system after noise reduction and phase compensation; system input sequence This represents the increment of the voltage or current reference command applied to the converter by the control system; the system output sequence The numerical range is typically between 0 and 1.2 per unit; system input sequence Limited by the controller's output limit, it is usually between -0.1 and 0.1 per unit. Both values ​​are based on the rated operating parameters and electrical safety specifications of the flexible low-frequency transmission system. Through a well-defined data mapping, it is ensured that the compact dynamic linear data model is directly built on clean data, avoiding modeling deviations caused by original sensor noise.

[0108] Based on Cauchy's mean value theorem, an equivalent transformation is performed on the nonlinear discrete-time system of the flexible low-frequency transmission system. This transformation occurs during each discrete system sampling period. The compact-scheme dynamic linear data model (CFDL model) is built-in. The compact-scheme dynamic linear data model (CFDL model) is composed of time-varying parameters of pseudopartial derivatives. System input sequence System output sequence and linearization error perturbation term constitute.

[0109] In the compact-format dynamic linear data model (CFDL model), time-varying parameters of pseudopartial derivatives are defined. The pseudopartial derivative time-varying parameter is used as a dynamic gain variable characterizing the flexible low-frequency transmission system at the current operating point. The value corresponds to the system output sequence. The change in the system input sequence The partial derivative of the change in quantity.

[0110] Pseudopartial derivative time-varying parameter This represents the flexible low-frequency power transmission system at a specific moment. The "dynamic slope," i.e., the system's sensitivity to control input, is a time-varying parameter of the pseudo-partial derivative during the initialization phase of this embodiment. The initial value is preferably set to 0.5; during operation, this parameter changes in real time with the system operating conditions, and the range of change is usually limited to between 0.01 and 10; the initial value setting is based on the estimation of the nominal value of the open-loop gain of the M3C converter; the range of change is limited based on the Lyapunov stability theory to prevent parameter drift from causing control divergence.

[0111] Pseudopartial derivative time-varying parameter It can capture the nonlinear dynamic characteristics of the M3C converter in real time. Comparative experiments show that, compared with the fixed gain model, the pseudo-partial derivative time-varying parameter method is more effective. When the system operating point shifts significantly (such as power reversal), the model prediction error is reduced by more than 85%, thus ensuring control accuracy over a wide frequency band.

[0112] Introducing a linearization error perturbation term into the compact dynamic linear data model (CFDL model) Linearization error disturbance term The value is equal to the sum of the model truncation error generated when the nonlinear system is equivalent to a linear data model and the dynamic deviation caused by the time-varying system parameters.

[0113] Personalization error disturbance term This represents the set of uncertainties that the compact-format dynamic linear data model fails to cover, including higher-order nonlinear residuals, unmodeled dynamics, and external power grid fluctuations. This value is an unknown quantity that cannot be directly measured, but in the simulation observations of this embodiment, its amplitude is typically within... The magnitude fluctuations originate from higher-order infinitesimal remainder terms in the nonlinear Taylor expansion and external environmental disturbances, and a linearized error perturbation term is explicitly introduced. This makes the originally inaccurate linear model mathematically rigorously equivalent to the original nonlinear system, providing a theoretical interface for subsequent active compensation of this term through an observer, which is a prerequisite for achieving full-dimensional perturbation suppression.

[0114] The mathematical expression logic of the compact-format dynamic linear data model (CFDL model) is as follows: system output sequence The change at the next sampling time is equal to the time-varying parameter of the pseudo-partial derivative. With system input sequence The product of the changes at the current sampling time plus the linearization error perturbation term The sum of these factors completes the process of transforming a strongly nonlinear system into a linear time-varying data model that depends only on the input and output data.

[0115] The mathematical expression for this model is as follows: ;

[0116] In this formula, The system output sequence represents the output sequence in Time and The difference in time; The system input sequence is represented in Time and The difference in time (according to the aforementioned mapping, this is the change in the control increment); The pseudo-partial derivative is a time-varying parameter; This is the linearization error disturbance term.

[0117] This formula is used to decouple a complex nonlinear flexible low-frequency transmission system into a simple linear data relationship, providing a direct mathematical basis for subsequent model-free control.

[0118] Further, in step S2, the linear extended state observer (LESO) is constructed based on the compact-format dynamic linear data model. The LESO observes the system disturbances of the flexible low-frequency transmission system, iteratively calculates, and outputs the total disturbance estimate. The specific operations include: constructing the LESO based on the compact-format dynamic linear data model (CFDL model); firstly, defining the internal state variables of the LESO, which include variables used to track the system output sequence. Output tracking state variables And the extended state variables used to estimate the total system disturbance. .

[0119] Output tracking state variables Used to reproduce the system's output trajectory, expanding state variables It is designed as an integral element to capture and compensate for all unknown internal and external disturbances in the system in real time.

[0120] Configure the parameters for the Linear Extended State Observer (LESO), including the observer bandwidth. Observer gain coefficient and system gain compensation factor .

[0121] Among them, the observer bandwidth The bandwidth of the observer represents the cutoff frequency of the linearly extended state observer's tracking response to the disturbance signal. In this embodiment, the observer bandwidth... Preferred setting is Its value is based on frequency domain analysis and is set as the system's expected closed-loop control bandwidth ( The value should be 5-10 times the standard value. If the value is too low, the phase lag will be large; if the value is too high, the measurement noise will be amplified. It should be set to... This enables the linearly extended state observer to reproduce wideband oscillation waveforms with frequencies below 80Hz without distortion, while maintaining a sufficient attenuation rate for the high-frequency noise remaining in step S1, thus ensuring the real-time performance and purity of the disturbance estimation.

[0122] Observer gain coefficient This represents the correction strength of the observer error feedback loop, set based on the pole placement principle. Its value is derived from the pole placement method in linear system control theory, which configures the characteristic equation of the observer as follows: This parameter configuration puts the observer in a critically damped state, which avoids overshoot oscillations during the perturbation observation process and ensures the fastest convergence speed, thus guaranteeing the expansion of state variables. It can quickly lock the true disturbance value within 2-3 sampling periods.

[0123] System gain compensation factor This represents the nominal estimate of the strength of the control input in the observer model. In this embodiment, the system gain compensation factor... Set as time-varying parameters of pseudo-partial derivatives The initial value, 0.5, is based on model-assisted observation theory, although... It is time-varying, but uses fixed methods. Cooperate The extended state mechanism is sufficient to compensate for the resulting bias, and the introduction of This term allows the observer to partially know the system's control input information, reducing the need for expanding state variables. The estimation burden is reduced, and the tracking error is reduced by about 30% compared to a pure perturbation observer.

[0124] Using the system sampling period determined in step S1 As a time reference for discrete iterative calculations using the Linear Extended State Observer (LESO), in each system sampling period Within, calculate the output estimation error. Output estimation error The value is equal to the output tracking state variable. Subtract the smoothed signal output in step S1 The difference is calculated using the following formula: ;

[0125] In this formula, This represents the output estimation error; The current output tracks the state variables; This is the smoothed signal after step S1; this formula is used to generate the correction bias that drives the observer state update.

[0126] Perform state update calculations for the Linear Extended State Observer (LESO): the output at the next sampling time tracks the state variables. The output tracking state variable is equal to the current sampling time. Add system sampling period The product of the product and the correction term, the correction term being the expanded state variable at the current sampling time. Add system gain compensation factor With system input sequence The product minus the observer gain coefficient With output estimation error The product is calculated.

[0127] Extended state variables at the next sampling time Equal to the expanded state variable at the current sampling time Add system sampling period With negative observer gain coefficient Multiply by the output estimation error The product of these factors, the mathematical expression for the above state update process is as follows: ;

[0128] In this set of formulas, These are the output tracking state variable and the extended state variable for the next time step, respectively. For the observer gain coefficient, this set of formulas utilizes an error feedback mechanism to force... Approaching the true output Thus It automatically converges to the total disturbance value of the system.

[0129] Through the above iterative calculations, the output estimation error is utilized. Track state variables in the output Corrections are made, while utilizing extended state variables. Integral updates are performed to address model mismatches within the system and external disturbances.

[0130] This iterative mechanism automatically accumulates all factors causing prediction bias using integral action. Experiments show that even with an externally applied 5% step disturbance, this mechanism can expand the state variable within 5ms. By adjusting the value to be equal to the disturbance amplitude, full-dimensional capture of unmodeled dynamics was achieved.

[0131] The expanded state variables after iterative convergence Defined as the total disturbance estimate And output the total disturbance estimate. This will serve as the data basis for feedforward compensation in subsequent steps. ;

[0132] In this formula, This is the estimated total disturbance output, which reflects the overall disturbance magnitude faced by the system at the current moment and provides an accurate quantitative basis for the subsequent controller to counteract the disturbance.

[0133] Step S3: Construct an adaptive pseudo-partial derivative estimator algorithm that introduces an output change penalty factor. The adaptive pseudo-partial derivative estimator algorithm adjusts the adaptive regularization weight factor so that the value of the adaptive regularization weight factor is equal to the basic weight factor plus the product of the output change penalty coefficient and the square of the system output change. The output change penalty coefficient is the output change penalty factor, which is configured as a positive constant gain. The value of the system output change is defined as the difference between the system output sequence at the current sampling time and the system output sequence at the previous sampling time. The adaptive pseudo-partial derivative estimator algorithm calculates the pseudo-partial derivative time-varying parameters based on the adaptive regularization weight factor and feeds back the total disturbance estimate output in step S2 to the model-free adaptive control model. The model-free adaptive control model combines the pseudo-partial derivative time-varying parameters and the total disturbance estimate to calculate the oscillation suppression control law.

[0134] Further, in step S3, an adaptive pseudo-partial derivative estimator algorithm is constructed by introducing an output change penalty factor. The specific operations of the adaptive pseudo-partial derivative estimator algorithm to adjust the adaptive regularization weight factor according to the output change of the flexible low-frequency transmission system include: constructing an improved pseudo-partial derivative estimation criterion function. Improved pseudopartial derivative estimation criterion function It consists of two parts: the model fitting error term and the parameter change rate constraint term.

[0135] To accurately identify the dynamic gain of a system under conditions of high noise and oscillation, this improved pseudo-partial derivative estimation criterion function The mathematical expression is as follows:

[0136] In this formula, The time-varying parameter representing the pseudo-partial derivative at the current sampling moment has the physical meaning of the dynamic gain of the flexible low-frequency power transmission system at a specific moment. The time-varying parameter estimate represents the pseudo-partial derivative at the previous sampling time. These represent the system output sequences at the current sampling time and the previous sampling time, respectively. That is, the system output sequence in step S2; This represents the change in system input at the previous sampling time. This represents the adaptive regularization weighting factor. This formula is used to introduce dynamic constraints on the rate of change of parameters while minimizing the model fitting error, in order to address the problem of parameter divergence in traditional algorithms under wide-frequency oscillation conditions.

[0137] The value of the model fitting error term is equal to the system output sequence at the current sampling time. The square of the difference between the output value predicted in a single step forward; the value of the parameter rate of change constraint term is equal to the time-varying parameter of the pseudo-partial derivative at the current sampling time. The time-varying parameter estimate of the pseudo-partial derivative at the previous sampling time The square of the difference between them and the adaptive regularization weight factor The product of.

[0138] In the improved pseudopartial derivative estimation criterion function Based on the existing framework, we further define the adaptive regularization weight factor. The calculation logic will adaptively regularize the weight factors. Configured to vary with system output Real-time changing time-varying parameters.

[0139] Adaptive regularization weight factor The specific numerical calculation logic is as follows: basic weight factor Add the output change penalty coefficient Changes in system output The product of the squares is calculated using the following formula:

[0140] Among them, the basic weight factor This represents the adaptive pseudo-partial derivative estimator algorithm in a flexible low-frequency power transmission system in a steady state (i.e., the change in system output). When the value approaches zero, the basic damping or inertial constraint on the update amplitude of the time-varying parameter of the pseudo-partial derivative; in this embodiment, the basic weighting factor The preferred value is 1.0, which is based on the numerical stability condition of the conventional model-free adaptive control (MFAC) algorithm (typically requiring...). (To prevent the denominator from being zero); basic weighting factor It provides basic regularization when the system output is stable, preventing computational explosion or numerical divergence caused by the denominator of the estimation algorithm approaching zero due to excessively small input changes, and ensuring the convergence accuracy of the algorithm in steady state.

[0141] Output change penalty coefficient This represents the sensitivity gain of the adaptive pseudo-partial derivative estimator algorithm to the intensity of output fluctuations in a flexible low-frequency transmission system, i.e., the strength to which the algorithm freezes parameter estimation when oscillations are detected. In this embodiment, the output change penalty coefficient is... The preferred setting is 2.0, a value optimized based on simulation tests under Gaussian white noise interference; comparative experiments show that when At that time, under strong oscillations, the parameters still have the risk of divergence; when At times, parameter updates are too delayed; when broadband oscillations occur in the flexible low-frequency transmission system... When this coefficient increases, the adaptive regularization weight factor becomes... The value increases rapidly on a quadratic basis, thus significantly increasing the penalty for parameter updates and forcing the time-varying parameter estimates of pseudo-partial derivatives to change. Maintain smoothness. Experimental data shows that setting it to 2.0 can reduce the variance of PPD estimation under strong disturbances by more than 90%, effectively avoiding system instability caused by drastic changes in controller parameters due to noise.

[0142] System output change The value is defined as the system output sequence at the current sampling time. Subtract the system output sequence from the previous sampling time. The difference.

[0143] Based on the above calculation logic, in each discrete system sampling period Internally, the adaptive pseudo-partial derivative estimator algorithm calculates the change in system output based on the current sampling time. Real-time updates of adaptive regularization weight factors The value, and the updated adaptive regularization weight factor Substituting the improved pseudo-partial derivative estimation criterion function It participates in the extreme value solution calculation.

[0144] Furthermore, in step S3, the adaptive pseudo-partial derivative estimator algorithm calculates the time-varying parameters of the pseudo-partial derivatives. The specific operations include: estimating the improved pseudo-partial derivative criterion function. Regarding the time-varying parameters of pseudopartial derivatives Perform partial derivative calculations and establish an extremum equation with zero derivative. In the process of solving the extremum equation, introduce a step size factor. The time-varying parameters of pseudopartial derivatives are derived. The expression is calculated through real-time iterative updates.

[0145] Numerical calculations are performed based on the real-time iterative update calculation expression: the estimated time-varying parameter value of the pseudo-partial derivative at the current sampling time. Equal to the time-varying parameter estimate of the pseudo-partial derivative at the previous sampling time. The sum of the parameter correction terms.

[0146] The calculation of the parameter correction term involves numerator and denominator operations. The numerator value of the parameter correction term is equal to the step size factor. Multiply by the change in system input at the previous sampling time Then multiply by the parameter estimation error term, the value of which equals the change in system output at the current sampling time. Subtract the time-varying parameter estimate of the pseudo-partial derivative at the previous sampling time. Change in system input compared to the previous sampling time The product of.

[0147] The denominator of the parameter correction term is equal to the adaptive regularization weight factor. Add the change in system input at the previous sampling time The sum of squares, pseudopartial derivatives, time-varying parameters The iterative update formula is as follows: ;

[0148] In this formula, the step size factor This represents the learning rate of the adaptive pseudopartial derivative estimator algorithm, i.e., the rate at which the algorithm uses new data to correct old parameter estimates. In this embodiment, the step size factor... Set to 1.0, its value is based on the unit step size configuration of the classical gradient descent method; step size factor Setting it to 1.0 gives the algorithm standard convergence capability under general operating conditions, combined with an adaptive regularization weight factor. The algorithm can quickly track parameter changes when the system is stable (at this time). Small, large correction term), and automatically slows down the learning speed during oscillations (at this time). (Large, small correction items) achieves a balance between flexibility and robustness.

[0149] During the calculation of the denominator value of the parameter correction term, the adaptive regularization weight factor that is updated in real time is directly called. Participating in the computation, due to the adaptive regularization weight factor Located in the denominator of the parameter correction term, this calculation structure establishes the magnitude of the parameter correction term and the adaptive regularization weighting factor. The inverse proportional relationship between the values. This means that when the system oscillates, leading to... When it gets bigger, The surge causes the correction term to approach zero, thus "freezing" or "gradually changing" the parameter estimates during oscillations, significantly improving robustness.

[0150] The adaptive pseudo-partial derivative estimator algorithm performs this function in each system sampling period. Perform the above calculations internally, and verify the numerical stability of the calculation results: if the calculated time-varying parameter estimates of the pseudo-partial derivatives are... The amplitude is less than the preset minimum threshold. ,For example Or the calculated time-varying parameter estimate of the pseudo-partial derivative. The sign and the initial sign reference value If inconsistent, then the time-varying parameter estimates of the pseudo-partial derivatives will be forcibly changed. Reset to initial symbol reference value Otherwise, the calculation result is retained. This verification mechanism is used to avoid control direction mismatch caused by numerical calculation singularities or noise impacts near the zero crossing point.

[0151] Furthermore, in step S3, the model-free adaptive control model is combined with the time-varying parameters of pseudo-partial derivatives. Compared with the total disturbance estimate Calculate the oscillation suppression control law The specific operations include:

[0152] Based on a tight-scheme dynamic linear data model and combined with the total disturbance estimate The single-step forward prediction equations of the flexible low-frequency transmission system are reconstructed. In the mathematical structure of the single-step forward prediction equations, the system output sequence at the next sampling time... The value consists of three parts: the system output sequence at the current sampling time. The estimated time-varying parameter value of the pseudo-partial derivative at the current sampling time. Change in system input at the current sampling time The product of and the total disturbance estimate The reconstructed equations are as follows: ;

[0153] Here, the total disturbance estimate calculated in step S2 is explicitly stated. Substituting the predictive model, the controller is able to anticipate disturbances faced by the system and react in advance. The control criterion function for solving the control law is defined. Control criterion function It consists of a system output tracking error term and a control input change penalty term. The value of the system output tracking error term is equal to the system output reference value at the next sampling time. With the system output sequence at the next sampling time The square of the difference between them: ;

[0154] The value of the penalty term for control input change is equal to the change in system input at the current sampling time (i.e., The square of the control input weighting factor The product of.

[0155] Control input weighting factor This represents the controller's weighting of the energy consumption or actuator (M3C converter) movement, reflecting the system's preference for smooth control. In this embodiment, the control input weighting factor... The preferred setting is 15, a value based on the maximum modulation depth limit of the M3C converter and the requirement for smoothness of the control signal; control input weighting factor Setting it to 15 is the optimal balance point between rapidly suppressing oscillations and protecting converter equipment. Too small a control action, or excessively abrupt control, may lead to overmodulation; if Too large, and the system response will be slow; increase It can significantly improve system stability and limit drastic changes in control output.

[0156] Substitute the reconstructed single-step forward prediction equation into the control criterion function. and the system input sequence at the current sampling time. Taking the derivative and setting it to zero, we obtain the final oscillation suppression control law. Oscillation suppression control law at the current sampling time Equal to the system input sequence at the previous sampling time Add control increment terms.

[0157] The numerator value of the control increment term is equal to the control step size factor. Multiply by the time-varying parameter estimate of the pseudo-partial derivative at the current sampling time. Multiplying this by the total error term, the value of the total error term equals the system output reference value at the next sampling time. Subtract the system output sequence at the current sampling time Subtract the total disturbance estimate The denominator of the control increment term is equal to the control input weighting factor. Add the time-varying parameter estimate of the pseudo-partial derivative at the current sampling time The sum of squares, the oscillation suppression control law The calculation formula is as follows: ;

[0158] In this formula, the step size factor is controlled. This represents the aggressiveness or gain strength of the model-free adaptive controller in eliminating system tracking errors. In this embodiment, the control step size factor... The preferred value is 0.6, and its selection is based on the steady-state error analysis of the discrete control system. Control step size factor. Setting it to 0.6 gives the control system an overdamped characteristic, ensuring that when broadband oscillations occur, the controller can smoothly intervene and gradually eliminate the oscillations, rather than introducing new excitation sources; comparative experiments show that if set to 0.6... (Full step size) is prone to overshoot under complex operating conditions; while setting it to 0.6 can ensure convergence without overshoot and improve the safety margin of the system.

[0159] By performing the above calculations, the output of the model-free adaptive control model includes an estimate of the total disturbance. Oscillation suppression control law for reverse component In the formula This term embodies a full-dimensional disturbance cancellation mechanism; the controller not only responds to the tracking error but also directly subtracts the estimated total disturbance value. This means that the control quantity already includes the corresponding reverse compensation component before the disturbance affects the system output.

[0160] Step S4: The control parameters of the model-free adaptive controller are optimized and improved based on the performance index function using the cuckoo search algorithm. The operating status of the flexible low-frequency transmission system is monitored using frequency domain criteria and time domain criteria. When the frequency domain criteria or time domain criteria trigger an oscillation signal, the oscillation suppression control law generated in step S3 is added to the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system.

[0161] Furthermore, in step S4, the specific operations of optimizing the control parameters of the improved model-free adaptive controller based on the performance index function using the cuckoo search algorithm include: determining the set of control parameters to be optimized for the improved model-free adaptive controller. Set of control parameters to be optimized The set of control parameters to be optimized includes all key adjustment variables defined in step S3. Specifically, it is controlled by the input weighting factor. Control step size factor Basic weighting factor Output change penalty coefficient and step size factor composition, ;

[0162] In this formula, This represents the five-dimensional parameter vector to be optimized. This definition ensures that the optimization algorithm covers all key variables across the entire chain, from parameter estimation to control law calculation.

[0163] Construct a set of control parameters to be optimized Performance index function of good and bad Performance index function Constructed based on the time-weighted integral of absolute error (ITAE) criterion.

[0164] Performance index function The numerical calculation logic is as follows: within the entire simulation time window, the sampling time index for each sampling moment is calculated. System sampling period and system output reference values With system output sequence The product of the absolute values ​​of the differences between the three is summed. ;

[0165] In this formula, Represents the total number of steps in the simulation or sampling; Index of the current sampling time; The system sampling period is 0.00005s. This is the expected output reference value; This formula is used to quantify the control effect by providing the actual system output sequence. Compared to the traditional sum of squared errors criterion, the ITAE criterion introduces time weights. This imposes a heavier penalty on steady-state error, thereby forcing the Cuckoo Search algorithm to find parameter combinations that converge faster and have higher steady-state accuracy.

[0166] Performance index function The reciprocal of the value is defined as the fitness function of the cuckoo search algorithm. , ;

[0167] In this formula, To prevent extremely small positive numbers with a denominator of zero (e.g.) This formula transforms the problem of minimizing error into the problem of maximizing fitness, thus adapting to the optimization mechanism of the Cuckoo Search algorithm.

[0168] The iterative optimization process of the cuckoo search algorithm is as follows: Initialize the host nest locations of the cuckoo population. Each host's nest location Represents a set of candidate control parameters to be optimized. Calculate the location of each host bird's nest. Corresponding fitness function value The Levy flight mechanism was used to simulate the cuckoo's random search path to the host nest location. Update and recalculate the updated host nest location. Corresponding fitness function value The updated formula is as follows: ;

[0169] In this formula, Indicates the first The nest in the 1st The position of the parameter vector at the next iteration; This is the step size control variable, used to adjust the size of the search step, and is usually set to 0.01 times the problem scale; This represents point-to-point multiplication; For a random search path that follows a Lévy distribution, The Levy flight index (usually taken as 1.5) is used to simulate the random walking behavior of cuckoos searching for parasitic nests. This long-tailed jumping mechanism allows the algorithm to effectively escape local optima and conduct global exploration.

[0170] Compare the fitness function values ​​before and after the update. Preserve fitness function values Larger host nest location According to the preset probability Discard fitness function value Poor host nest locations And randomly generate new host nest locations within the search space. Replace it.

[0171] Among them, the probability of discovery This represents the probability that the host bird discovers and discards the foreign bird's egg. In this embodiment, the discovery probability is... The preferred value is 0.25, determined based on empirical parameters from the standard cuckoo search algorithm and testing of multi-peak function optimization. (Discovery probability) In the algorithm, it plays a role in balancing local exploitation and global search. If the value is too small, the algorithm is prone to getting trapped in local optima, resulting in the control parameters not being globally optimal; if... If the value is too large, the algorithm's convergence speed will be significantly slowed down. Setting it to 0.25 allows the algorithm to retain about 75% of the high-quality solutions (local development) while forcing a random reset of 25% of the solutions (global search). Experiments show that this setting reduces the convergence algebra of parameter optimization by about 40%, effectively improving the efficiency of offline parameter tuning.

[0172] Repeat the above update and selection steps until the preset maximum number of iterations is reached. Output fitness function value The largest host bird's nest location The corresponding parameter values ​​are used as the set of globally optimal control parameters. And the set of globally optimal control parameters The values ​​are assigned to the improved model-free adaptive controller to achieve optimal configuration of the control parameters.

[0173] Among them, the maximum number of iterations This represents the termination condition for the cuckoo search algorithm to perform parameter optimization calculations. In this embodiment, the maximum number of iterations is... The optimal value is set to 100 times, and its value is determined based on the fitness function. Observation of the convergence curve. Maximum number of iterations. This determines the consumption of computing resources and the accuracy of optimization. Tests show that the fitness function value usually stabilizes after about 80 iterations. Setting it to 100 iterations leaves sufficient margin to ensure that the algorithm converges to the global optimum and that the final output control parameters ensure that the system overshoot is less than 5%.

[0174] Furthermore, in step S4, the operation status of the flexible low-frequency transmission system is monitored using frequency domain and time domain criteria. When the frequency domain or time domain criteria trigger an oscillation signal, the specific operation of attaching the oscillation suppression control law generated in step S3 to the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system includes: constructing a frequency domain oscillation identification mechanism based on the sliding window fast Fourier transform algorithm, and selecting the voltage component or current component in the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system as the frequency domain monitoring signal. .

[0175] Frequency domain monitoring signal Perform a sliding window Fast Fourier Transform (FFT) operation to obtain the amplitude spectrum distribution. Calculate the fundamental frequency energy ratio index Fundamental wave energy ratio index The value is equal to the energy amplitude of the zero-hertz component. The sum of the energy amplitudes of all frequency components The ratio, ;

[0176] In this formula, DC component (i.e.) Amplitude of the fundamental component in the coordinate system; The number of FFT window points is used to quantify the purity of the fundamental component in a signal, and is a frequency domain characteristic that identifies whether oscillations occur.

[0177] Among them, the number of FFT window points The time window length and frequency resolution represent the frequency domain analysis, determining the precision of frequency domain monitoring. In this embodiment, the number of FFT window points... The optimal sampling point setting is 236 points, with a sampling frequency of 3kHz and a fundamental frequency of 3Hz. These values ​​are determined based on the 20Hz fundamental frequency characteristics of the flexible low-frequency transmission system and the measurable frequency range of 0Hz-1280Hz. Setting the number of points to 236 ensures that the frequency resolution accurately covers the sub / supersynchronous oscillation and mid-to-high frequency oscillation bands. Experimental verification shows that this point configuration ensures a frequency identification error of less than 1Hz while controlling the calculation delay to within 80ms, meeting the real-time requirements of oscillation monitoring.

[0178] The fundamental frequency energy ratio index Compared with the preset frequency domain safety threshold, if the fundamental frequency energy ratio index Below the frequency domain safety threshold and the fundamental frequency energy ratio index If the duration of the state below the frequency domain safety threshold exceeds the preset frequency domain judgment period, a frequency domain oscillation signal will be generated.

[0179] Among them, frequency domain security threshold This represents the lower limit of the fundamental frequency energy ratio during normal system operation, used to distinguish between normal fluctuations and abnormal oscillations. In this embodiment, two threshold levels are set: the warning threshold is set at 90%, and the event threshold is set at 80%. The values ​​are based on the harmonic distortion rate (THD) standard of the M3C converter under normal operating conditions. When the fundamental frequency energy ratio is lower than 90%, it indicates that the non-fundamental frequency components (i.e., oscillation components) in the system have increased significantly. Setting graded thresholds (90% triggers warning, 80% triggers control) constructs a tiered defense mechanism, which effectively prevents false triggering caused by transient disturbances in the power grid, ensures that the control strategy is only activated when there is a real risk of oscillation, and improves the reliability of the system.

[0180] A time-domain oscillation identification mechanism based on the discrete numerical difference method is constructed, and the output signal of the voltage and current dual closed-loop control loop is selected as the time-domain monitoring signal. Calculate the time-domain monitoring signal in the discrete time domain. First rate of change First-order rate of change The value is equal to the time-domain monitoring signal at the current sampling time. Time-domain monitoring signal compared to the previous sampling time The absolute value of the difference between them divided by the system sampling period , ;

[0181] The first-order rate of change With the preset time-domain security threshold For comparison, if the first rate of change Greater than the time-domain security threshold This triggers the generation of a time-domain oscillation signal.

[0182] Time-domain security threshold This represents the maximum permissible instantaneous rate of change of the time-domain monitoring signal, physically corresponding to the maximum permissible derivative of voltage or current. In this embodiment, this value is set to 1.5 times the derivative of the system's steady-state fluctuation amplitude. Its value is determined based on noise tolerance calculated using numerical difference and sensitivity analysis to sudden high-frequency oscillations, representing the time-domain safety threshold. As a supplement to the frequency domain criterion, it compensates for the window delay in FFT calculation. Experiments show that in the event of a sudden large-amplitude oscillation fault, the time domain criterion can be triggered quickly within 3ms after the oscillation occurs (i.e., within 3-5 sampling periods), which is more than 50ms faster than the frequency domain criterion, thus minimizing the impact of oscillation on the equipment.

[0183] Construct event-triggered oscillation suppression execution logic, and configure the improved model-free adaptive controller to switch between background computation state and active suppression state; when neither frequency domain oscillation signal nor time domain oscillation signal is generated, the improved model-free adaptive controller maintains the background computation state, and the oscillation suppression control law generated in step S3 is applied. The value is not output to the voltage and current dual closed-loop control loop. At this time, the actual additional control quantity... When a frequency domain oscillation signal or a time domain oscillation signal is triggered, the improved model-free adaptive controller switches to active suppression state and immediately applies the oscillation suppression control law generated in step S3. The output of the proportional-integral controller within the voltage-current dual closed-loop control circuit of the flexible low-frequency transmission system is superimposed on the converter voltage command modulation. The superposition formula is as follows: ;

[0184] In this formula, The final control commands are sent to the M3C modulator; The logic, which is the output of the original PI controller, enables the on-demand activation of the oscillation suppression strategy. This ensures timely suppression when oscillations occur and avoids the potential impact of additional control on steady-state performance during normal system operation.

[0185] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An improved model-free adaptive flexible low-frequency transmission oscillation suppression method, characterized in that, Includes the following steps: Step S1: Input the voltage command signal of the flexible low-frequency transmission system to the nonlinear tracking differentiator module. The nonlinear tracking differentiator module performs smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system, and outputs the smoothed signal after filtering out random noise and the first-order differential estimate. Step S2: The smoothed signal output in step S1 is processed using the tight-format dynamic linearization method to establish a tight-format dynamic linear data model containing time-varying parameters of pseudo-partial derivatives. Based on the tight-format dynamic linear data model, a linear extended state observer is constructed. The linear extended state observer observes the system disturbance of the flexible low-frequency transmission system, iteratively calculates and outputs the total disturbance estimate. Step S3: Construct an adaptive pseudo-partial derivative estimator algorithm that introduces an output change penalty factor. The adaptive pseudo-partial derivative estimator algorithm adjusts the adaptive regularization weight factor so that the value of the adaptive regularization weight factor is equal to the basic weight factor plus the product of the output change penalty coefficient and the square of the system output change. The output change penalty coefficient is the output change penalty factor, which is configured as a positive gain. The value of the system output change is defined as the difference between the system output sequence at the current sampling time and the system output sequence at the previous sampling time. The adaptive pseudo-partial derivative estimator algorithm calculates the pseudo-partial derivative time-varying parameters based on the adaptive regularization weight factor and feeds back the total disturbance estimate output in step S2 to the model-free adaptive control model. The model-free adaptive control model combines the pseudo-partial derivative time-varying parameters and the total disturbance estimate to calculate the oscillation suppression control law. Step S4: The control parameters of the model-free adaptive controller are optimized and improved based on the performance index function using the cuckoo search algorithm. The operating status of the flexible low-frequency transmission system is monitored using frequency domain criteria and time domain criteria. When the frequency domain criteria or time domain criteria trigger an oscillation signal, the oscillation suppression control law generated in step S3 is added to the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system.

2. The improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 1, characterized in that, In step S1, the specific operations of the nonlinear tracking differentiator module in performing smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system include: The voltage command signal output from the outer loop of the flexible low-frequency power transmission system is defined as the discrete-time input sequence at the current sampling moment, and initial state values ​​are assigned to the smoothed tracking signal and the first-order differential estimator inside the nonlinear tracking differentiator module. The key control parameters required to construct a second-order nonlinear dynamic system are set, including the system sampling period, instantaneous switching factor, and filter factor. Configure the system sampling period as the time base parameter for discretization calculation by the nonlinear tracking differentiator module; The instantaneous interruption factor is configured as a parameter characterizing the tracking speed response capability of the nonlinear tracking differentiator module to the discrete-time input sequence. The value of the instantaneous interruption factor is positively correlated with the tracking speed of the nonlinear tracking differentiator module. Configure the filter factor as a parameter to adjust the filtering smoothing intensity and phase characteristics of the nonlinear tracking differentiator module; Based on the set key control parameters, the threshold parameter system of the nonlinear tracking differentiator module is further calculated, and the nonlinear interval threshold parameter is calculated. The value of the nonlinear interval threshold parameter is equal to the product of the instantaneous interruption factor and the system sampling period. Calculate the error segment discrimination threshold parameter. The value of the error segment discrimination threshold parameter is equal to the product of the system sampling period and the nonlinear interval threshold parameter. A nonlinear tracking differentiator module is constructed using nonlinear interval threshold parameters and error segment discrimination threshold parameters to determine whether the system state has entered a steady-state micro-region, thus completing the initial configuration of the nonlinear tracking differentiator module.

3. The improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 2, characterized in that, In step S1, the specific operations of the nonlinear tracking differentiator module in performing smooth tracking and first-order differential estimation of the voltage command signal based on the second-order nonlinear dynamic system also include: Within each discrete system sampling period, the tracking error and differential state quantity at the current sampling time are calculated. The value of the tracking error is equal to the difference between the smoothed tracking signal at the current sampling time and the discrete-time input sequence. The value of the differential state quantity is directly taken as the first-order differential estimate at the current sampling time. Calculate the comprehensive error term. The value of the comprehensive error term is equal to the tracking error plus the product of the system sampling period and the differential state quantity. The equivalent correction is calculated by constructing a nonlinear mapping relationship based on the comprehensive error term: it is determined whether the absolute value of the comprehensive error term is less than or equal to the error segment discrimination threshold parameter. If the absolute value of the comprehensive error term is less than or equal to the error segment discrimination threshold parameter, the value of the equivalent correction is equal to the differential state quantity plus the quotient of the comprehensive error term divided by the system sampling period. If the absolute value of the comprehensive error term is greater than the error segment discrimination threshold parameter, the intermediate nonlinear adjustment quantity is calculated first. The value of the intermediate nonlinear adjustment quantity is equal to the square root of the sum of the square of the nonlinear interval threshold parameter plus eight times the fast-break factor and the absolute value of the comprehensive error term. At this time, the value of the equivalent correction is equal to the product of the differential state quantity plus half of the difference between the intermediate nonlinear adjustment quantity and the nonlinear interval threshold parameter and the sign function of the comprehensive error term. Based on this, the fastest control output is calculated: it is determined whether the absolute value of the equivalent correction is less than or equal to the nonlinear interval threshold parameter. If the absolute value of the equivalent correction is less than or equal to the nonlinear interval threshold parameter, the value of the fastest control output is equal to the negative instantaneous factor multiplied by the equivalent correction divided by the nonlinear interval threshold parameter. If the absolute value of the equivalent correction is greater than the nonlinear interval threshold parameter, the value of the fastest control output is equal to the negative instantaneous factor multiplied by the sign function of the equivalent correction. The internal state of the nonlinear tracking differentiator module is updated discretely and iteratively using the fastest control output. The smoothed tracking signal at the next sampling time is equal to the smoothed tracking signal at the current sampling time plus the product of the system sampling period and the first-order differential estimate at the current sampling time. The first-order differential estimate at the next sampling time is equal to the first-order differential estimate at the current sampling time plus the product of the system sampling period and the fastest control output.

4. The improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 1, characterized in that, In step S2, the smoothed signal output from step S1 is processed using the compact scheme dynamic linearization method. The specific operations for establishing a compact scheme dynamic linear data model containing time-varying pseudo-partial derivative parameters include: Establish a data mapping relationship between step S1 and step S2, define the smooth signal output by the nonlinear tracking differentiator module in step S1 as the system output sequence of the compact dynamic linear data model, and define the control command increment of the flexible low-frequency transmission system as the system input sequence of the compact dynamic linear data model. Based on Cauchy's mean value theorem, the nonlinear discrete-time system of the flexible low-frequency transmission system is transformed into an equivalent form. A compact-format dynamic linear data model is constructed within each discrete system sampling period. The compact-format dynamic linear data model consists of time-varying pseudo-partial derivative parameters, system input sequence, system output sequence, and linearization error perturbation term. In the compact dynamic linear data model, the pseudo-partial derivative time-varying parameter is defined as a dynamic gain variable characterizing the flexible low-frequency transmission system at the current operating point. The value of the pseudo-partial derivative time-varying parameter corresponds to the partial derivative of the change in the system output sequence with respect to the change in the system input sequence. In the compact form dynamic linear data model, a linearization error perturbation term is introduced. The value of the linearization error perturbation term is equal to the sum of the model truncation error generated when the nonlinear system is equivalent to a linear data model and the dynamic deviation caused by the time-varying system parameters. The mathematical expression logic of the compact-format dynamic linear data model is as follows: the change in the system output sequence at the next sampling time is equal to the product of the pseudo-partial derivative time-varying parameter and the change in the system input sequence at the current sampling time, plus the sum of the linearization error perturbation term, thus completing the process of transforming the strongly nonlinear system into a linear time-varying data model that depends only on the input and output data.

5. An improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 4, characterized in that, In step S2, a linear extended state observer is constructed based on the compact-format dynamic linear data model. The linear extended state observer observes the system disturbances of the flexible low-frequency transmission system, iteratively calculates and outputs the total disturbance estimate. The specific operations include: A linear extended state observer is constructed based on a tight-form dynamic linear data model. First, the internal state variables of the linear extended state observer are defined. The internal state variables include output tracking state variables used to track the system output sequence and extended state variables used to estimate the total system disturbance. Set the configuration parameters for the linearly extended state observer, including the observer bandwidth, observer gain coefficient, and system gain compensation factor. Using the system sampling period determined in step S1 as the time base for discrete iterative calculation of the linear extended state observer, the output estimation error is calculated within each system sampling period. The value of the output estimation error is equal to the difference between the output tracking state variable and the smoothed signal. The state update calculation for the linear extended state observer is as follows: the output tracking state variable at the next sampling time is equal to the output tracking state variable at the current sampling time plus the product of the system sampling period and the correction term. The correction term is calculated by adding the product of the extended state variable at the current sampling time, the system gain compensation factor, and the system input sequence, and then subtracting the product of the observer gain coefficient and the output estimation error. The expanded state variable at the next sampling time is equal to the expanded state variable at the current sampling time plus the product of the system sampling period and the negative observer gain coefficient multiplied by the output estimation error; Through the above iterative calculations, the output tracking state variable is corrected using the output estimation error, and the expanded state variable is used to integrally update the model mismatch inside the system and external disturbances. The expanded state variables after iterative convergence are defined as the total disturbance estimate and output. The total disturbance estimate will serve as the data basis for feedforward compensation in subsequent steps.

6. The improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 1, characterized in that, In step S3, an adaptive pseudo-partial derivative estimator algorithm is constructed by introducing an output change penalty factor. The specific operations of the adaptive pseudo-partial derivative estimator algorithm to adjust the adaptive regularization weight factor according to the output change of the flexible low-frequency transmission system include: An improved pseudo-partial derivative estimation criterion function is constructed, which consists of two parts: a model fitting error term and a parameter change rate constraint term. The value of the model fitting error term is equal to the square of the difference between the system output sequence at the current sampling time and the single-step forward predicted output value; The value of the parameter change rate constraint term is equal to the product of the square of the difference between the estimated value of the pseudo-partial derivative time-varying parameter at the current sampling time and the estimated value of the pseudo-partial derivative time-varying parameter at the previous sampling time, and the adaptive regularization weight factor. Based on the construction of the improved pseudo-partial derivative estimation criterion function, the calculation logic of the adaptive regularization weight factor is further defined, and the adaptive regularization weight factor is configured as a time-varying parameter that changes in real time with the change of system output. The specific numerical calculation logic of the adaptive regularization weight factor is as follows: the basic weight factor is added to the product of the output change penalty coefficient and the square of the system output change. The basic weight factor is configured as a non-zero constant and serves as the baseline value of the adaptive regularization weight factor when the system output change is zero. The output change penalty coefficient is configured as a positive gain and is used to set the proportion of the square of the system output change to the numerical contribution of the adaptive regularization weight factor. The numerical value of the system output change is defined as the difference between the system output sequence at the current sampling time and the system output sequence at the previous sampling time. Through the above calculation logic, within each discrete system sampling period, the adaptive pseudo-partial derivative estimator algorithm updates the value of the adaptive regularization weight factor in real time based on the change in system output calculated at the current sampling time, and substitutes the updated adaptive regularization weight factor into the improved pseudo-partial derivative estimation criterion function to participate in the extreme value solution calculation.

7. An improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 6, characterized in that, In step S3, the specific operations of the adaptive pseudo-partial derivative estimator algorithm to calculate the time-varying parameters of the pseudo-partial derivatives include: The improved pseudo-partial derivative estimation criterion function is subjected to partial derivative calculation with respect to the time-varying pseudo-partial derivative parameter, and an extreme value equation with zero derivative is established. In the process of solving the extreme value equation, a step size factor is introduced, and the real-time iterative update calculation expression of the time-varying pseudo-partial derivative parameter is derived. Numerical calculations are performed based on the real-time iterative update calculation expression: the estimated value of the time-varying pseudo-partial derivative parameter at the current sampling time is equal to the sum of the estimated value of the time-varying pseudo-partial derivative parameter at the previous sampling time and the parameter correction term. The calculation of the parameter correction term includes numerator and denominator operations. The numerator value of the parameter correction term is equal to the step size factor multiplied by the change in system input at the previous sampling time and then multiplied by the parameter estimation error term. The value of the parameter estimation error term is equal to the change in system output at the current sampling time minus the product of the estimated value of the time-varying pseudo-partial derivative parameter at the previous sampling time and the change in system input at the previous sampling time. The denominator value of the parameter correction term is equal to the sum of the adaptive regularization weight factor and the square of the change in system input at the previous sampling time. During the calculation of the denominator value of the parameter correction term, the adaptive regularization weight factor updated in real time is directly called to participate in the calculation. Since the adaptive regularization weight factor is located in the denominator of the parameter correction term, this calculation structure establishes an inverse numerical relationship between the magnitude of the parameter correction term and the value of the adaptive regularization weight factor. The adaptive pseudo-partial derivative estimator algorithm performs the above calculations in each system sampling period and verifies the numerical stability of the calculation results: if the magnitude of the calculated pseudo-partial derivative time-varying parameter estimate is less than the preset minimum threshold, or if the sign of the calculated pseudo-partial derivative time-varying parameter estimate is inconsistent with the initial sign reference value, then the pseudo-partial derivative time-varying parameter estimate is forcibly reset to the initial sign reference value; otherwise, the calculation results are retained.

8. An improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 7, characterized in that, In step S3, the specific operations of calculating the oscillation suppression control law by combining the time-varying parameters of pseudo-partial derivatives and the total disturbance estimate in the model-free adaptive control model include: Based on the compact dynamic linear data model and combined with the total disturbance estimate, the single-step forward prediction equation of the flexible low-frequency transmission system is reconstructed. In the mathematical structure of the single-step forward prediction equation, the system output sequence value at the next sampling time consists of three parts: the system output sequence at the current sampling time, the product of the time-varying parameter estimate of the pseudo-partial derivative at the current sampling time and the change in the system input at the current sampling time, and the total disturbance estimate. Define the control criterion function for solving the control law. The control criterion function consists of the system output tracking error term and the control input change penalty term. The value of the system output tracking error term is equal to the square of the difference between the system output reference value at the next sampling time and the system output sequence at the next sampling time. The value of the control input change penalty term is equal to the product of the square of the system input change at the current sampling time and the control input weight factor. The control input weight factor is configured as a constant parameter used to adjust the magnitude of the control input change. Substituting the reconstructed single-step forward prediction equation into the control criterion function and differentiating it with respect to the system input sequence at the current sampling time, we obtain the final oscillation suppression control law by setting the derivative to zero: The oscillation suppression control law at the current sampling time is equal to the system input sequence at the previous sampling time plus the control increment term. The numerator of the control increment term is equal to the control step size factor multiplied by the estimated value of the time-varying pseudo-partial derivative at the current sampling time and then multiplied by the total error term. The value of the total error term is equal to the system output reference value at the next sampling time minus the system output sequence at the current sampling time minus the total disturbance estimate. The denominator of the control increment term is equal to the sum of the control input weight factor and the squares of the estimated value of the time-varying pseudo-partial derivative at the current sampling time. By performing the above calculations, the model-free adaptive control model outputs an oscillation suppression control law that includes the reverse component of the total disturbance estimate.

9. An improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 8, characterized in that, In step S4, the specific operations of optimizing and improving the control parameters of the model-free adaptive controller based on the performance index function using the cuckoo search algorithm include: The set of control parameters to be optimized for the improved model-free adaptive controller is determined. The set of control parameters to be optimized covers all the key adjustment variables defined in step S3. Specifically, the set of control parameters to be optimized consists of control input weighting factor, control step size factor, basic weighting factor, output change penalty coefficient, and step size factor. A performance index function is constructed to evaluate the quality of the set of control parameters to be optimized. The performance index function is based on the time-weighted absolute error integral criterion. The numerical calculation logic of the performance index function is as follows: within the entire simulation time window, the product of the sampling time index, the system sampling period, and the absolute value of the difference between the system output reference value and the system output sequence at each sampling moment is accumulated and summed. The reciprocal of the value of the performance index function is defined as the fitness function of the Cuckoo Search algorithm. The iterative optimization process of the cuckoo search algorithm is as follows: Initialize the host nest locations of the cuckoo population, with each host nest location representing a set of candidate control parameters to be optimized; calculate the fitness function value corresponding to each host nest location; use the Levy flight mechanism to simulate the random search path of the cuckoo to update the host nest locations, and recalculate the fitness function value corresponding to the updated host nest locations; compare the fitness function values ​​before and after the update, retain the host nest locations with larger fitness function values, discard a portion of the host nest locations with poor fitness function values ​​according to a preset probability, and randomly generate new host nest locations in the search space to replace them; Repeat the above update and selection steps until the preset maximum number of iterations is reached. Output the parameter value corresponding to the host bird's nest position with the largest fitness function value as the global optimal control parameter set. Assign the global optimal control parameter set to the improved model-free adaptive controller to complete the optimal configuration of the control parameters.

10. An improved model-free adaptive flexible low-frequency transmission oscillation suppression method according to claim 9, characterized in that, In step S4, the operating status of the flexible low-frequency transmission system is monitored using frequency domain criteria and time domain criteria. When the frequency domain criteria or time domain criteria trigger an oscillation signal, the specific operation of adding the oscillation suppression control law generated in step S3 to the voltage and current dual closed-loop control loop of the flexible low-frequency transmission system includes: A frequency domain oscillation identification mechanism based on the sliding window fast Fourier transform algorithm is constructed, and the voltage component or current component in the voltage and current dual closed-loop control loop of the flexible low-frequency power transmission system is selected as the frequency domain monitoring signal. Perform a sliding window fast Fourier transform operation on the frequency domain monitoring signal to obtain the amplitude spectrum distribution, and calculate the fundamental energy ratio index. The value of the fundamental energy ratio index is equal to the ratio of the energy amplitude of the zero-hertz component to the sum of the energy amplitudes of all frequency components. The fundamental frequency energy ratio index is compared with the preset frequency domain safety threshold. If the fundamental frequency energy ratio index is lower than the frequency domain safety threshold and the duration of the state where the fundamental frequency energy ratio index is lower than the frequency domain safety threshold exceeds the preset frequency domain judgment period, then the generation of a frequency domain oscillation signal is triggered. A time-domain oscillation identification mechanism based on the discrete numerical difference method is constructed. The output signal of the voltage and current dual closed-loop control loop is selected as the time-domain monitoring signal. The first-order rate of change of the time-domain monitoring signal is calculated in the discrete time domain. The value of the first-order rate of change is equal to the absolute value of the difference between the time-domain monitoring signal at the current sampling time and the time-domain monitoring signal at the previous sampling time divided by the system sampling period. The first-order rate of change is compared with a preset time-domain safety threshold. If the first-order rate of change is greater than the time-domain safety threshold, the generation of the time-domain oscillation signal is triggered. An event-triggered oscillation suppression execution logic is constructed, and an improved model-free adaptive controller is configured to switch between background calculation state and active suppression state. When neither the frequency domain oscillation signal nor the time domain oscillation signal is generated, the improved model-free adaptive controller maintains the background calculation state, and the value of the oscillation suppression control law generated in step S3 is not output to the voltage and current dual closed-loop control loop. When a frequency domain oscillation signal or a time domain oscillation signal is triggered, the improved model-free adaptive controller switches to the active suppression state and immediately superimposes the oscillation suppression control law generated in step S3 onto the output of the proportional-integral controller inside the voltage and current dual closed-loop control loop of the flexible low-frequency power transmission system to participate in the modulation of the converter voltage command.

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