Supercapacitor-based power grid frequency modulation power energy coordinated control method and system

Abstract

The present invention provides a method and system for coordinated control of power and energy of power grid frequency modulation based on supercapacitors, which relates to the technical field of power grid frequency modulation. The method comprises performing time-frequency analysis on a collected power grid frequency signal to obtain a frequency disturbance characteristic value, and determining power control data in combination with the electrical parameter values of a supercapacitor group; performing nonlinear programming calculation based on the power control data to obtain a power allocation sequence, and dividing the power allocation sequence into a fast response section, a dynamic transition section, and a steady-state maintenance section according to a preset threshold value, respectively solving the control value using an augmented Lagrangian equation, a recursive least squares operation, and a Lyapunov function to obtain a power control instruction; inputting the power control instruction into a disturbance observer, calculating a dynamic error value, and constructing a non-singular terminal equation, and outputting a power regulation signal in combination with a recursive minimum entropy calculation and a superhelical algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field, and in particular to a method and system for coordinated control of power frequency modulation and energy of a power grid based on a supercapacitor. Background Art

[0002] As the scale of renewable energy power generation continues to expand, grid frequency fluctuations are intensifying. Traditional frequency modulation methods have slow response speeds and low regulation accuracy, making it difficult to meet the needs of grid frequency modulation. Supercapacitors, with their advantages of high power density, high charge and discharge efficiency, and long cycle life, have promising application prospects in the field of grid frequency modulation. Currently, supercapacitors participate in grid frequency modulation mainly through a proportional regulation strategy, which outputs frequency modulation power proportionally based on the frequency deviation value. However, this simple control method makes it difficult to accurately identify frequency disturbance characteristics and does not fully consider the power and energy constraints of supercapacitors, resulting in unsatisfactory frequency modulation results.

[0003] However, the existing supercapacitor frequency modulation control methods have several major problems. The first is the lack of in-depth analysis of the frequency disturbance characteristics of the power grid, which makes it difficult to accurately identify the frequency change trend and disturbance law, affecting the targetedness of the frequency modulation strategy; the second is the lack of a complete power energy coordination mechanism, which makes it difficult to achieve the energy balance of the supercapacitor group while ensuring the frequency modulation effect; the third is the lack of robustness of the control algorithm, which makes the frequency modulation performance easily deteriorate when facing system parameter changes and external disturbances, affecting the stability and reliability of the control system.

[0004] In summary, there is an urgent need to address the problems existing in existing supercapacitor frequency modulation control and provide a grid frequency modulation method based on time-frequency analysis and multi-stage coordinated control. This method accurately identifies frequency disturbance characteristics through a sliding Fourier transform and recursive principal component decomposition, adopts a segmented control strategy to achieve coordination between rapid power response and energy balance, and combines disturbance observation with a superhelical algorithm to improve the robustness of the control system. This invention can address the problems of the prior art. Summary of the Invention

[0005] The embodiments of the present invention provide a method and system for coordinated control of power and energy of power grid frequency modulation based on supercapacitors, which can solve the problems in the prior art.

[0006] According to a first aspect of the embodiments of the present invention,

[0007] Provided is a method for coordinated control of power energy of power grid frequency modulation based on supercapacitors, comprising:

[0008] The collected power grid frequency signal is analyzed in time and frequency using a sliding Fourier transform to obtain the frequency characteristic components of each time window, construct a frequency change matrix, and calculate the moving entropy value of the frequency change matrix to obtain the frequency dynamic correlation vector. The frequency dynamic correlation vector is recursively decomposed into principal components, and the frequency disturbance eigenvalue is output in real time. The frequency modulation power compensation amount is calculated based on the frequency disturbance eigenvalue. The voltage and current signals of the supercapacitor group are collected and input into the Kalman filter to calculate the electrical parameter values. The upper and lower power thresholds are determined based on the electrical parameter values, and the power control data is formed together with the frequency modulation power compensation amount.

[0009] Based on the power control data, a power allocation sequence is determined through nonlinear programming calculations. Based on the power change rate of the power allocation sequence, the sequence is divided into a fast response section, a dynamic transition section, and a steady-state maintenance section according to a preset interval segmentation threshold. Based on the fast response section, an augmented Lagrangian equation is established to solve the power optimization trajectory and output a fast adjustment control value. Based on the dynamic transition section, a recursive least squares operation is performed to obtain system parameter estimates and update the power control value. Based on the steady-state maintenance section, a Lyapunov function is constructed to solve the energy balance deviation value and calculate the compensation control value. A piecewise continuous function operation is performed on the fast adjustment control value, the power control value, and the compensation control value to output a power control instruction.

[0010] The power control command is input into the disturbance observer, the unmodeled dynamic and external disturbance terms are calculated, the dynamic error value is determined, the generalized differential operation is performed on the dynamic error value, a non-singular terminal equation is constructed, and the initial control value is output. The initial control value is input into the recursive minimum entropy calculation unit to obtain the correction coefficient, the superhelical algorithm operation is performed on the correction coefficient and the initial control value, and the power regulation signal is output.

[0011] In an optional embodiment,

[0012] The time-frequency analysis of the collected power grid frequency signal is performed using sliding Fourier transform to obtain the frequency characteristic components of each time window, construct the frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain the frequency dynamic correlation vector including:

[0013] Divide the collected power grid frequency signal into multiple time windows according to a preset time interval, use a cosine function to perform smooth transition processing on the power grid frequency signals of adjacent time windows to obtain a smoothed frequency signal; perform wavelet decomposition on the smoothed frequency signal to obtain hierarchical wavelet coefficients of multiple decomposition levels, calculate the energy value of each hierarchical wavelet coefficient, and calculate the energy change rate of adjacent time windows based on the energy value; when the energy change rate is greater than a preset energy change threshold, shorten the time window length according to a preset ratio, and repeat the process until the energy change rate is less than the energy change threshold, thereby obtaining an optimal time window length;

[0014] Performing a sliding Fourier transform on the smoothed frequency signal based on the optimal time window length to obtain spectral components of the frequency signal, and extracting amplitude information and phase information of the working frequency band from the spectral components; arranging the amplitude information and phase information of multiple consecutive time windows in time sequence to construct a frequency change matrix, and constructing an equivalued diagonal matrix based on the autocorrelation function of the frequency change matrix; performing eigenvalue decomposition on the equivalued diagonal matrix to extract the eigenvector corresponding to the maximum eigenvalue, and reconstructing the noise reduction frequency feature matrix based on the eigenvector;

[0015] Select multiple preset scale parameters, calculate the conditional entropy value and sample entropy value of the frequency characteristic matrix under each preset scale parameter; identify the mutation point in the frequency characteristic matrix, determine the mutation interval, correspondingly determine the non-mutation interval, and use the entropy value of the adjacent non-mutation interval to replace the entropy value of the mutation interval to obtain a modified entropy value sequence; calculate the fluctuation variance of the modified entropy value sequence under each preset scale parameter, and determine the weight coefficient corresponding to each preset scale parameter based on the inverse of the fluctuation variance;

[0016] The modified entropy value sequence under each preset scale parameter is weightedly combined with the corresponding weight coefficient to obtain the frequency dynamic correlation vector.

[0017] In an optional embodiment,

[0018] Perform recursive principal component decomposition on the frequency dynamic correlation vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount based on the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input them into the Kalman filter to calculate the electrical parameter values, and determine the upper and lower power thresholds based on the electrical parameter values. These power control data, together with the frequency modulation power compensation amount, include:

[0019] Divide the frequency dynamic correlation vector into multiple data segments according to the preset number of sampling points, perform principal component decomposition on each data segment, and extract the first principal component eigenvalue with the largest variance contribution rate;

[0020] Based on a preset number of data segments, a first principal component eigenvalue sequence is determined, an autoregressive prediction model of a preset order is established, and the coefficients of the autoregressive prediction model are optimized and calculated using a least squares iterative algorithm. When the difference between the coefficients calculated from two adjacent iterative calculations is less than a preset convergence threshold, the current iterative result is determined as the optimal prediction coefficient;

[0021] Substituting the optimal prediction coefficient into the autoregressive prediction model, calculating the prediction result of the first principal component eigenvalue of the next data segment, and comparing the predicted result of the first principal component eigenvalue with the corresponding actual result of the first principal component eigenvalue to obtain the prediction deviation;

[0022] When the prediction deviation is greater than a preset deviation threshold, the prediction deviation is used as a correction amount based on an exponential weighting method to update the coefficient of the autoregressive prediction model to obtain an updated first principal component eigenvalue as a frequency disturbance eigenvalue; the frequency disturbance eigenvalue is multiplied by a preset proportional coefficient to obtain a frequency modulation power compensation amount;

[0023] According to a preset sampling period, the port voltage and charge / discharge current of the supercapacitor group are collected, and a state-space equation including equivalent series resistance, equivalent series capacitance, and remaining available capacity is constructed based on the port voltage and charge / discharge current. The voltage and current observation data of a preset number of groups are subtracted from the output value of the state-space equation to obtain an observation residual sequence;

[0024] According to a preset sampling period, the port voltage, charge and discharge current, and shell temperature of the supercapacitor group are collected; based on the port voltage and charge and discharge current, a state-space equation including equivalent series resistance, equivalent series capacitance, and remaining available capacity is constructed; the port voltage and charge and discharge current are differenced with the predicted value of the state-space equation, and the covariance matrix of process noise and observation noise is dynamically adjusted using a sliding window method to construct a Kalman filter; the state-space equation is input into the Kalman filter to calculate the equivalent series resistance, equivalent series capacitance, and remaining available capacity of the supercapacitor group;

[0025] Establishing a power constraint equation, substituting the equivalent series resistance, equivalent series capacitance, remaining available capacity, and housing temperature into the power constraint equation, and solving to obtain upper and lower power thresholds;

[0026] The power upper and lower limit thresholds and the frequency modulation power compensation amount are combined into power control data.

[0027] In an optional embodiment,

[0028] Based on the fast response segment, the augmented Lagrangian equation is established to solve the power optimization trajectory and output the fast adjustment control value including:

[0029] Calculating the sum of squares of deviations between the power optimization trajectory and the target power value to generate a power tracking error term, calculating the sum of squares of power changes at adjacent sampling points of the power optimization trajectory to generate a change rate constraint term, and combining the power tracking error term and the change rate constraint term to construct a composite optimization objective function;

[0030] Collecting operating parameters, determining upper and lower thresholds of power constraints based on the operating parameters, determining a response time constraint based on a time constant of the operating parameters, and combining the power constraint and the response time constraint to form a dynamic constraint model;

[0031] Multiplying the power constraint by the first Lagrangian multiplier to obtain a first multiplication result, multiplying the response time constraint by the second Lagrangian multiplier to obtain a second multiplication result, combining the first multiplication result and the second multiplication result with the composite optimization objective function to construct an augmented Lagrangian function, calculating the degree of constraint violation, and updating the first Lagrangian multiplier and the second Lagrangian multiplier;

[0032] Applying an alternating direction multiplier method to iteratively solve the augmented Lagrangian function to generate the power optimization trajectory, calculating the convergence rate of the power optimization trajectory and determining an adaptive penalty factor;

[0033] The deviation between the power optimization trajectory and the target power value is calculated and multiplied by the proportional gain to obtain the proportional control amount. The rate of change of the power optimization trajectory is calculated and multiplied by the differential gain to obtain the differential control amount. The proportional control amount and the differential control amount are combined and output to form a fast adjustment control value.

[0034] In an optional embodiment,

[0035] Based on the dynamic transition section, a recursive least squares operation is performed to obtain the estimated values of the system parameters. The power control value is updated by:

[0036] Collecting a continuous sampling sequence of real-time power values in a dynamic transition section, calculating power differences between adjacent sampling points in the continuous sampling sequence, and obtaining a power variation sequence;

[0037] Based on the power variation sequence, a power variation trend curve is constructed by using a cubic spline interpolation method. The real-time power value and the corresponding power variation are combined into a transition state vector. The transition power adjustment amount is used as a transition control input to construct a discrete time-varying state space model.

[0038] The first-order differential coefficient of the real-time power value and the first-order differential coefficient of the power variation are combined into a parameter matrix to be estimated, and the transition stage state vector and the transition stage control input are combined into a regression vector;

[0039] A recursive prediction sequence is constructed by multiplying the parameter matrix to be estimated and the regression vector, real-time operating status is collected to obtain a current state observation value, and the difference between the current state observation value and the recursive prediction sequence is calculated to obtain an estimation error; a gain matrix is obtained by multiplying the transpose of the regression vector and the recursive prediction sequence, and the product of the gain matrix and the estimation error is used as a parameter correction amount;

[0040] Adding the parameter matrix to be estimated and the parameter correction amount to obtain an updated parameter estimate; decomposing the updated parameter estimate to obtain a state matrix estimate and an input matrix estimate;

[0041] Multiplying the state matrix estimate by the current transition state vector to obtain a first state prediction term, determining a desired state value based on the current transition state vector and in combination with a transition control input, and subtracting the first state prediction term from the desired state value to obtain a state compensation value;

[0042] Calculate the product of the transpose of the input matrix estimate value and the input matrix estimate value to obtain a matrix coefficient, calculate the product of the transpose of the input matrix estimate value and the state compensation value to obtain a compensation coefficient; divide the compensation coefficient by the matrix coefficient to obtain a power adjustment coefficient, and take the negative value of the power adjustment coefficient to obtain an updated power control value.

[0043] In an optional embodiment,

[0044] Based on the steady-state maintenance segment, the Lyapunov function is constructed to solve the energy balance deviation value and calculate the compensation control value including:

[0045] Within a preset integration time window, the difference between the real-time power value and the reference power value is calculated and integrated to obtain an energy integral value. The rate of change of the energy integral value is also calculated. The energy integral value is used as a first state quantity, and the rate of change of the energy integral value is used as a second state quantity to form a maintenance segment state vector.

[0046] Calculating the second-order derivative of the energy integral value, constructing a maintenance segment state matrix based on the relationship between the energy integral value, the rate of change of the energy integral value, and the second-order derivative of the energy integral value; constructing a maintenance segment input matrix based on the response coefficient of the rate of change of the energy integral value to the system input; and calculating a maintenance segment power adjustment amount as a maintenance segment control input based on the deviation between the maintenance segment state matrix and the energy integral value;

[0047] multiplying the maintenance segment state vector by the maintenance segment state matrix to form a first matrix product, multiplying the maintenance segment control input by the maintenance segment input matrix to form a second matrix product, and adding the first matrix product and the second matrix product to construct a state space equation;

[0048] The Lyapunov stability equation is constructed by multiplying the transposed matrix of the maintenance segment state matrix by the matrix to be determined, adding the product of the matrix to be determined and the maintenance segment state matrix, and then adding the identity matrix. The Lyapunov stability equation is solved to obtain the matrix to be determined as a symmetric positive definite matrix; and a positive definite weight matrix is determined according to the value range of the maintenance segment control input.

[0049] A state quadratic term is obtained by multiplying the maintenance segment state vector by a symmetric positive definite matrix on the left and then multiplying it by the transpose of the maintenance segment state vector on the right; a control integral term is obtained by multiplying the maintenance segment control input by a positive definite weight matrix on the left and then multiplying it by the transpose of the maintenance segment control input on the right; and a Lyapunov function is constructed by adding the state quadratic term and the control integral term.

[0050] Taking the time derivative of the Lyapunov function to obtain a derivative equation, constructing a feedback control law based on optimal control theory, substituting the feedback control law into the derivative equation, and verifying the stability of the system by calculating the negative definiteness of the result;

[0051] Calculating the difference between the energy integral value and a preset expected energy level to obtain an energy balance deviation, and calculating the rate of change of the energy balance deviation over time to obtain a deviation change rate;

[0052] The energy balance deviation is multiplied by a first compensation gain to obtain a first compensation amount, and the deviation change rate is multiplied by a second compensation gain to obtain a second compensation amount, wherein the first compensation gain is greater than the ratio of the minimum eigenvalue of the symmetric positive definite matrix to the norm of the maintenance segment input matrix, and the second compensation gain is greater than the ratio of the norm of the positive definite weight matrix to the minimum eigenvalue of the symmetric positive definite matrix; the first compensation amount and the second compensation amount are added to obtain a compensation control value.

[0053] In an optional embodiment,

[0054] The power control command is input into the disturbance observer, the unmodeled dynamic and external disturbance terms are calculated, the dynamic error value is determined, the generalized differential operation is performed on the dynamic error value, a non-singular terminal equation is constructed, and the initial control value is output. The initial control value is input into the recursive minimum entropy calculation unit to obtain the correction coefficient. The super spiral algorithm operation is performed on the correction coefficient and the initial control value. The output power adjustment signal includes:

[0055] Inputting the power control command and the output power of the system into the disturbance observer, constructing a disturbance observer state equation including an observer gain and an auxiliary observation quantity, and running the disturbance observer state equation to obtain an observation output;

[0056] Based on the observed output, unmodeled dynamic and external disturbance terms are calculated to obtain a disturbance estimate, and a dynamic error value is obtained by subtracting a desired power trajectory from the output power of the system and adding the result to the disturbance estimate.

[0057] performing a generalized differential operation on the dynamic error value to obtain a differential error value, combining the differential error value with a power function of the dynamic error value to construct a non-singular terminal sliding mode surface; setting a stability parameter of the system to obtain a negative feedback gain, calculating a derivative of the non-singular terminal sliding mode surface, multiplying the corresponding derivative by the negative feedback gain to construct a reaching law, and calculating a ratio of the reaching law to the input gain to obtain an initial control value;

[0058] Using the initial control value as a basis for obtaining a system state sequence, calculating the probability distribution of the system state sequence to obtain a state probability, inputting the state probability into a recursive minimum entropy calculation unit to calculate a system entropy value, obtaining a minimum entropy value through recursive operation, and calculating a negative exponent of the difference between the system entropy value and the minimum entropy value to obtain a correction coefficient;

[0059] Multiplying the correction coefficient and the initial control value to obtain a first algorithm component, constructing a power function and a sign function of the non-singular terminal sliding mode surface, and combining them to obtain a second algorithm component;

[0060] Set the convergence gain parameter of the supercoil algorithm, construct a supercoil state equation containing the first algorithm component and the second algorithm component, perform an integral operation on the supercoil state equation to obtain an auxiliary variable of the supercoil algorithm, and combine the auxiliary variable with the first algorithm component and the second algorithm component to output a power adjustment signal.

[0061] According to a second aspect of the embodiments of the present invention,

[0062] Provided is a supercapacitor-based power grid frequency modulation power energy coordinated control system, comprising:

[0063] The first unit is used to perform time-frequency analysis on the collected power grid frequency signal using a sliding Fourier transform, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain a frequency dynamic correlation vector; perform recursive principal component decomposition on the frequency dynamic correlation vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount based on the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input them into the Kalman filter to calculate the electrical parameter values, and determine the upper and lower power thresholds based on the electrical parameter values, which together with the frequency modulation power compensation amount form power control data;

[0064] The second unit is used to determine the power allocation sequence based on the power control data through nonlinear programming calculation, and divide the power allocation sequence into a fast response section, a dynamic transition section, and a steady-state maintenance section according to a preset interval segmentation threshold based on the power change rate of the power allocation sequence; establish an augmented Lagrangian equation based on the fast response section, solve the power optimization trajectory, and output a fast adjustment control value; perform a recursive least squares operation based on the dynamic transition section to obtain system parameter estimates and update the power control value; construct a Lyapunov function based on the steady-state maintenance section, solve the energy balance deviation value, and calculate the compensation control value; perform piecewise continuous function operations on the fast adjustment control value, the power control value, and the compensation control value, and output a power control instruction;

[0065] The third unit is used to input the power control command into the disturbance observer, calculate the unmodeled dynamic and external disturbance terms, determine the dynamic error value, perform generalized differential operation on the dynamic error value, construct a non-singular terminal equation, output the initial control value, input the initial control value into the recursive minimum entropy calculation unit to obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power adjustment signal.

[0066] According to a third aspect of the embodiments of the present invention,

[0067] An electronic device is provided, comprising:

[0068] processor;

[0069] a memory for storing processor-executable instructions;

[0070] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0071] According to a fourth aspect of the embodiments of the present invention,

[0072] A computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0073] In an embodiment of the present invention, frequency disturbance characteristics are accurately extracted through methods such as sliding Fourier transform and recursive principal component decomposition, and precise power compensation is performed in combination with the power characteristics of the supercapacitor, thereby effectively suppressing grid frequency fluctuations and improving grid stability; based on the electrical parameters and frequency disturbance characteristics of the supercapacitor, nonlinear programming and segmented control strategies are adopted to achieve optimal distribution of supercapacitor power output, improve energy utilization efficiency, and extend the service life of the supercapacitor; through means such as disturbance observer and recursive minimum entropy calculation, the influence of unmodeled dynamics and external disturbances is effectively suppressed, the robustness and anti-interference ability of the system are enhanced, and the stability and reliability of the control system are guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 Schematic diagram of the flow of a method for coordinated control of power energy of power grid frequency modulation based on supercapacitors according to an embodiment of the present invention;

[0075] Figure 2 This is a structural diagram of a supercapacitor-based grid frequency modulation power energy coordinated control system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0077] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0078] Figure 1 FIG is a flow chart of a method for coordinated control of power energy of power grid frequency modulation based on supercapacitors according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0079] S101. Perform time-frequency analysis on the collected power grid frequency signal using a sliding Fourier transform to obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain a frequency dynamic correlation vector; perform recursive principal component decomposition on the frequency dynamic correlation vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount based on the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor bank, input them into a Kalman filter to calculate the electrical parameter values, and determine the upper and lower power thresholds based on the electrical parameter values, which together with the frequency modulation power compensation amount form the power control data;

[0080] In this embodiment, a sliding Fourier transform is used for time-frequency analysis to construct a frequency change matrix and calculate the moving entropy value, which can dynamically generate a frequency dynamic correlation vector and accurately capture the changing characteristics of the grid frequency. The frequency disturbance eigenvalues are extracted in real time through recursive principal component decomposition to provide fast and reliable frequency disturbance analysis and improve the response efficiency of frequency modulation control. The frequency modulation power compensation amount is quickly calculated based on the frequency disturbance eigenvalues to ensure the timeliness and accuracy of grid frequency regulation. A Kalman filter is used to perform real-time calculation of the voltage and current signals of the supercapacitor group to dynamically obtain key electrical parameters and improve the monitoring accuracy of the capacitor status. The frequency modulation power compensation amount and electrical parameter values are combined to dynamically set the upper and lower power thresholds to realize intelligent power control and improve the robustness and operational stability of the frequency modulation system.

[0081] S102. Based on the power control data, a power allocation sequence is determined through nonlinear programming calculations. Based on the power change rate of the power allocation sequence, the sequence is divided into a rapid response segment, a dynamic transition segment, and a steady-state maintenance segment according to a preset interval segmentation threshold. Based on the rapid response segment, an augmented Lagrange equation is established to solve the power optimization trajectory and output a rapid adjustment control value. Based on the dynamic transition segment, a recursive least squares operation is performed to obtain system parameter estimates and update the power control value. Based on the steady-state maintenance segment, a Lyapunov function is constructed to solve the energy balance deviation value and calculate the compensation control value. A piecewise continuous function operation is performed on the rapid adjustment control value, the power control value, and the compensation control value to output a power control instruction.

[0082] Based on the power control data, a nonlinear programming method is used to calculate a power allocation sequence. This sequence determines the system's power requirements at different time points and is converted into executable control commands. During the calculation process, system constraints must be considered to ensure that the resulting allocation sequence meets system operating specifications.

[0083] According to the power change rate of the power allocation sequence and the preset interval segmentation threshold, the system operation process is divided into three different control segments: fast response segment, dynamic transition segment and steady-state maintenance segment;

[0084] In the fast-response phase, the augmented Lagrangian equation is used to solve the power optimization trajectory. The augmented Lagrangian method is a mathematical optimization method that introduces Lagrangian multipliers and combines them with system constraints. The solution generates a fast-adjusting control value to ensure that the power reaches the set target in the shortest possible time.

[0085] During the dynamic transition phase, recursive least squares estimation is used to estimate system parameters. This method continuously updates the estimated values to optimize the power control strategy, ensuring the accuracy and stability of the power regulation process. Recursive least squares estimation gradually improves the estimated values using real-time system data, providing more accurate parameter support for the next power adjustment.

[0086] During the steady-state maintenance phase, a Lyapunov function is constructed to analyze the system's stability and determine the energy balance deviation. This function determines whether the system can operate in a stable state and helps calculate the energy balance deviation, thereby determining whether compensatory control is necessary. By calculating the compensatory control value, the system can maintain steady-state operation without excessive fluctuations.

[0087] Finally, the rapid adjustment control value, power control value, and compensation control value are subjected to piecewise continuous function calculations. This process combines the control signals from different sections to form a smooth control curve. This ensures the continuity and stability of power regulation. Ultimately, the output power control command is fed into the system to ensure efficient and stable operation according to the optimized trajectory.

[0088] In this embodiment, precise segmentation is achieved through the power change rate and interval segmentation threshold, and targeted methods are adopted for different response stages to improve the flexibility and targeting of the control strategy; the power optimization trajectory is calculated in the fast response segment, and the adjustment control value is quickly provided to ensure that the system can quickly respond to changes in power demand; the recursive least squares method is used to update the system parameters in the dynamic transition segment to maintain the real-time and adaptability of the control strategy and improve control accuracy; in the steady-state maintenance segment, the Lyapunov function is used to calculate the energy balance deviation and compensate for the control to ensure the long-term stability and energy balance of the system; through piecewise continuous function operation, the control results of each stage are organically combined to ensure the continuity and smoothness of the power control instructions and achieve efficient and reliable overall power regulation.

[0089] S103. Input the power control command into the disturbance observer, calculate the unmodeled dynamic and external disturbance terms, determine the dynamic error value, perform generalized differential operation on the dynamic error value, construct a non-singular terminal equation, output the initial control value, input the initial control value into the recursive minimum entropy calculation unit, obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power adjustment signal.

[0090] In this embodiment, by inputting power control instructions into the disturbance observer, the unmodeled dynamics and external disturbance terms in the system can be effectively calculated, ensuring that the system can timely identify and adjust external interference and internal uncertainties; performing generalized differential operations on the dynamic error value, combined with the non-singular terminal equation, can quickly generate the initial control value, and correct it through the recursive minimum entropy calculation unit to ensure control accuracy; further optimizing the initial control value through the superhelix algorithm can effectively improve the stability and response speed of the power regulation signal, so that the system can cope with complex dynamic changes; the comprehensive application of multiple optimization algorithms enables the system to remain stable in the face of disturbances and changes, improve the robustness and efficiency of power control, and ensure the smooth operation of the system.

[0091] In an optional embodiment, a sliding Fourier transform is used to perform time-frequency analysis on the collected power grid frequency signal, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain the frequency dynamic correlation vector including:

[0092] Divide the collected power grid frequency signal into multiple time windows according to a preset time interval, use a cosine function to perform smooth transition processing on the power grid frequency signals of adjacent time windows to obtain a smoothed frequency signal; perform wavelet decomposition on the smoothed frequency signal to obtain hierarchical wavelet coefficients of multiple decomposition levels, calculate the energy value of each hierarchical wavelet coefficient, and calculate the energy change rate of adjacent time windows based on the energy value; when the energy change rate is greater than a preset energy change threshold, shorten the time window length according to a preset ratio, and repeat the process until the energy change rate is less than the energy change threshold, thereby obtaining an optimal time window length;

[0093] Performing a sliding Fourier transform on the smoothed frequency signal based on the optimal time window length to obtain spectral components of the frequency signal, and extracting amplitude information and phase information of the working frequency band from the spectral components; arranging the amplitude information and phase information of multiple consecutive time windows in time sequence to construct a frequency change matrix, and constructing an equivalued diagonal matrix based on the autocorrelation function of the frequency change matrix; performing eigenvalue decomposition on the equivalued diagonal matrix to extract the eigenvector corresponding to the maximum eigenvalue, and reconstructing the noise reduction frequency feature matrix based on the eigenvector;

[0094] Select multiple preset scale parameters, calculate the conditional entropy value and sample entropy value of the frequency characteristic matrix under each preset scale parameter; identify the mutation point in the frequency characteristic matrix, determine the mutation interval, correspondingly determine the non-mutation interval, and use the entropy value of the adjacent non-mutation interval to replace the entropy value of the mutation interval to obtain a modified entropy value sequence; calculate the fluctuation variance of the modified entropy value sequence under each preset scale parameter, and determine the weight coefficient corresponding to each preset scale parameter based on the inverse of the fluctuation variance;

[0095] The modified entropy value sequence under each preset scale parameter is weightedly combined with the corresponding weight coefficient to obtain the frequency dynamic correlation vector.

[0096] The power frequency band specifically refers to a specific frequency range surrounding the industrial frequency (typically 50 Hz or 60 Hz), primarily used for analyzing and processing power system signals. This frequency band typically contains the primary power frequency components of the power grid, reflecting the characteristics of power system operation, such as voltage, load, and frequency fluctuations. It is a crucial analysis range for power grid signal monitoring and control.

[0097] In a specific embodiment, the grid frequency signal is collected and preprocessed. First, the frequency signal of the grid is collected using a sensor and stored digitally. In order to eliminate noise and interference, the collected original frequency signal is preprocessed, for example, using a low-pass filter to remove high-frequency noise, or using a Kalman filter for smoothing. An initial time window length is set, for example, 0.1 seconds, and the collected grid frequency signal is divided into a series of continuous time windows. In order to ensure a smooth transition of the frequency signal between adjacent time windows, a cosine function is used to perform weighted averaging on the edge data of adjacent time windows. For example, 5% of the data at the edge of adjacent time windows can be taken for cosine weighted smoothing.

[0098] Perform wavelet decomposition on the smoothed frequency signal and select the optimal time window length. Perform wavelet decomposition on the smoothed frequency signal, and the decomposition level can be set to 3 layers or more to obtain detailed information at different frequency scales. Calculate the energy value of the wavelet coefficients at each decomposition level. Compare the energy change rates of adjacent time windows, for example, calculate the ratio of the energy difference between the current time window and the previous time window to the energy of the previous time window. If the energy change rate is greater than a preset threshold, for example, set to 0.05, it means that the current time window length is too long and contains large frequency fluctuation information, and the time window length needs to be shortened. Shorten the time window length by a preset ratio, for example, shorten it to 0.8 times the original ratio, then re-smooth and wavelet decomposition, and calculate the energy change rate again. Repeat this process until the energy change rate is less than the preset threshold, and finally obtain the optimal time window length, for example, 0.05 seconds.

[0099] Perform a sliding Fourier transform and construct a frequency change matrix. Using the determined optimal time window length, perform a sliding Fourier transform on the smoothed grid frequency signal. Within each time window, calculate the spectral components of the frequency signal and extract the amplitude and phase information of the power frequency band (e.g., around 50 Hz or 60 Hz). Arrange the amplitude and phase information of multiple consecutive time windows in chronological order to construct a frequency change matrix. For example, if each time window extracts the amplitude and phase features of the power frequency band, then for N time windows, a frequency change matrix with N rows and 2 columns will be obtained.

[0100] Perform denoising on the frequency variation matrix. To remove noise and interference from the frequency variation matrix, first calculate the autocorrelation function of the frequency variation matrix. Then, construct an equidiagonal matrix based on the autocorrelation function, where the diagonal elements are the values of the autocorrelation function and the off-diagonal elements are zero. Perform eigenvalue decomposition on the equidiagonal matrix and extract the eigenvector corresponding to the largest eigenvalue. Use this eigenvector to linearly combine the original frequency variation matrix to reconstruct the denoised frequency feature matrix.

[0101] Calculate the entropy of the frequency feature matrix and make corrections. Select multiple preset scale parameters, for example, set the scale parameter to an integer from 2 to 5. For each scale parameter, calculate the conditional entropy and sample entropy of the frequency feature matrix. Identify the mutation points in the frequency feature matrix, for example, by calculating the difference in the eigenvalues between adjacent time windows to determine whether there is a mutation. Determine the mutation interval and the corresponding non-mutation interval. Use the entropy value of the adjacent non-mutation interval to replace the entropy value of the mutation interval to obtain a corrected entropy value sequence. For example, if a mutation is detected in the 5th time window, use the average of the entropy values of the 4th and 6th time windows to replace the entropy value of the 5th time window.

[0102] Calculate the fluctuation variance of the modified entropy sequence and determine the weight coefficient. Calculate the fluctuation variance of the modified entropy sequence at each preset scale parameter. The fluctuation variance can be defined as the standard deviation of the entropy sequence. Determine the weight coefficient for each scale parameter based on the inverse of the fluctuation variance. For example, if the fluctuation variance of the entropy sequence at a certain scale parameter is smaller, the corresponding weight coefficient is larger.

[0103] The frequency dynamic correlation vector is obtained by weighted combination. The modified entropy value sequence under each scale parameter and its corresponding weight coefficient are weighted together to obtain the frequency dynamic correlation vector. This vector reflects the dynamic correlation characteristics of the power grid frequency signal at different time scales.

[0104] For example, it is assumed that the collected power grid frequency signal is a sequence containing 1000 data points. The initial time window length is set to 0.1 seconds, that is, it contains 100 data points. After wavelet decomposition and energy change rate calculation, it is finally determined that the optimal time window length is 0.05 seconds, that is, it contains 50 data points. A sliding Fourier transform is performed on the smoothed frequency signal to extract the amplitude and phase information of the power frequency band, and a frequency change matrix with 20 rows and 2 columns is constructed. After denoising the matrix, the conditional entropy and sample entropy with scale parameters of 2 to 5 are calculated to obtain 4 entropy value sequences. The fluctuation variance of each entropy value sequence is calculated, and the weight coefficient is determined according to the inverse. Finally, the 4 entropy value sequences are weighted and combined with the corresponding weight coefficients to obtain the frequency dynamic correlation vector.

[0105] In this embodiment, through wavelet decomposition and optimal time window selection, subtle changes in the grid frequency can be captured more accurately, avoiding the traditional method's reliance on a fixed time window length, thereby improving the accuracy of frequency analysis; by performing noise reduction processing and entropy value correction on the frequency change matrix, the influence of noise and interference on the analysis results is effectively suppressed, thereby enhancing the robustness of the method; through sliding Fourier transform and multi-scale entropy value calculation, the dynamic correlation characteristics of the grid frequency can be quickly extracted, thereby improving the analysis efficiency.

[0106] In an optional embodiment, recursive principal component decomposition is performed on the frequency dynamic correlation vector, and the frequency disturbance eigenvalue is output in real time. The frequency modulation power compensation amount is calculated based on the frequency disturbance eigenvalue; the voltage and current signals of the supercapacitor group are collected and input into the Kalman filter to calculate the electrical parameter values. The power upper and lower limit thresholds are determined based on the electrical parameter values, and the power control data is composed of the power control data together with the frequency modulation power compensation amount.

[0107] Divide the frequency dynamic correlation vector into multiple data segments according to the preset number of sampling points, perform principal component decomposition on each data segment, and extract the first principal component eigenvalue with the largest variance contribution rate;

[0108] Based on a preset number of data segments, a first principal component eigenvalue sequence is determined, an autoregressive prediction model of a preset order is established, and the coefficients of the autoregressive prediction model are optimized and calculated using a least squares iterative algorithm. When the difference between the coefficients calculated from two adjacent iterative calculations is less than a preset convergence threshold, the current iterative result is determined as the optimal prediction coefficient;

[0109] Substituting the optimal prediction coefficient into the autoregressive prediction model, calculating the prediction result of the first principal component eigenvalue of the next data segment, and comparing the predicted result of the first principal component eigenvalue with the corresponding actual result of the first principal component eigenvalue to obtain the prediction deviation;

[0110] When the prediction deviation is greater than a preset deviation threshold, the prediction deviation is used as a correction amount based on an exponential weighting method to update the coefficient of the autoregressive prediction model to obtain an updated first principal component eigenvalue as a frequency disturbance eigenvalue; the frequency disturbance eigenvalue is multiplied by a preset proportional coefficient to obtain a frequency modulation power compensation amount;

[0111] According to a preset sampling period, the port voltage and charge / discharge current of the supercapacitor group are collected, and a state-space equation including equivalent series resistance, equivalent series capacitance, and remaining available capacity is constructed based on the port voltage and charge / discharge current. The voltage and current observation data of a preset number of groups are subtracted from the output value of the state-space equation to obtain an observation residual sequence;

[0112] According to a preset sampling period, the port voltage, charge and discharge current, and shell temperature of the supercapacitor group are collected; based on the port voltage and charge and discharge current, a state-space equation including equivalent series resistance, equivalent series capacitance, and remaining available capacity is constructed; the port voltage and charge and discharge current are differenced with the predicted value of the state-space equation, and the covariance matrix of process noise and observation noise is dynamically adjusted using a sliding window method to construct a Kalman filter; the state-space equation is input into the Kalman filter to calculate the equivalent series resistance, equivalent series capacitance, and remaining available capacity of the supercapacitor group;

[0113] Establishing a power constraint equation, substituting the equivalent series resistance, equivalent series capacitance, remaining available capacity, and housing temperature into the power constraint equation, and solving to obtain upper and lower power thresholds;

[0114] The power upper and lower limit thresholds and the frequency modulation power compensation amount are combined into power control data.

[0115] In one specific embodiment, to achieve precise control of supercapacitor power, this embodiment proposes a supercapacitor power control method based on a frequency dynamic correlation vector and Kalman filtering. This method outputs frequency disturbance eigenvalues in real time, calculates the frequency modulation power compensation, and combines the supercapacitor's electrical parameters to determine upper and lower power thresholds, ultimately forming power control data.

[0116] First, collect the frequency dynamic correlation vector related to the supercapacitor's operating state. Assuming data is collected every 0.1 seconds, a total of 1000 data points are collected to form a frequency dynamic correlation vector. These 1000 data points are divided into 10 data segments, each containing 100 data points.

[0117] Perform principal component decomposition on each data segment and extract the eigenvalue of the first principal component with the largest variance contribution. For example, by performing principal component decomposition on the first data segment, the first principal component eigenvalue is 2.5. Repeat this process to obtain a sequence of first principal component eigenvalues for 10 data segments.

[0118] Using the first principal component eigenvalue sequence of these 10 data segments, a second-order autoregressive prediction model was established. The coefficients of the autoregressive prediction model were optimized using a least-squares iterative algorithm. A convergence threshold of 0.001 was set. When the difference between the coefficients calculated between two consecutive iterations was less than 0.001, the result of the current iteration was determined as the optimal prediction coefficient. Assume that the optimal prediction coefficients ultimately obtained were 0.8 and 0.1.

[0119] Substitute the optimal prediction coefficients of 0.8 and 0.1 into the autoregressive prediction model and calculate the predicted result of the first principal component eigenvalue for the next data segment (i.e., the 11th data segment). Assume that the predicted result is 2.7. At the same time, perform principal component decomposition on the 11th data segment and obtain the actual first principal component eigenvalue of 2.8. Comparing the predicted first principal component eigenvalue of 2.7 with the corresponding actual first principal component eigenvalue of 2.8, the prediction deviation is 0.1.

[0120] Set the deviation threshold to 0.05. Since the predicted deviation of 0.1 is greater than the deviation threshold of 0.05, the predicted deviation of 0.1 is used as a correction amount based on an exponential weighting method to update the coefficients of the autoregressive prediction model. Assume that the updated coefficients are 0.85 and 0.12. The updated first principal component eigenvalue (for example, 2.75) is used as the frequency disturbance eigenvalue. Multiply the frequency disturbance eigenvalue 2.75 by the preset proportional coefficient 0.2 to obtain the frequency modulation power compensation amount of 0.55.

[0121] Next, the terminal voltage and charge / discharge current of the supercapacitor bank are collected. Assume a sampling period of 0.01 seconds. Based on the terminal voltage and charge / discharge current, a state-space equation is constructed that includes the equivalent series resistance, equivalent series capacitance, and remaining available capacity.

[0122] At the same time, the shell temperature of the supercapacitor group is collected. The voltage and current observation data of a preset number of groups (for example, 10 groups) are interpolated with the output value of the state-space equation to obtain an observation residual sequence. The covariance matrix of the process noise and the observation noise is dynamically adjusted using a sliding window method to construct a Kalman filter. The state-space equation is input into the Kalman filter to calculate the equivalent series resistance (for example, 0.01 ohms), equivalent series capacitance (for example, 100 farads), and remaining available capacity (for example, 80%) of the supercapacitor group.

[0123] Create a power constraint equation. Substitute an equivalent series resistance of 0.01 ohm, an equivalent series capacitance of 100 farads, 80% remaining available capacity, and a case temperature (e.g., 25 degrees Celsius) into the equation to solve for the upper and lower power thresholds. Assume the lower power threshold is 10 kilowatts and the upper power threshold is 20 kilowatts.

[0124] Finally, the power upper and lower thresholds of 10 kW and 20 kW and the frequency modulation power compensation amount of 0.55 are combined into power control data. For example, the compensation amount is added to the current power instruction value and limited to the power upper and lower threshold range.

[0125] In this embodiment, by calculating the frequency disturbance characteristic value and the frequency modulation power compensation amount in real time, and determining the upper and lower power thresholds in combination with the electrical parameter values of the supercapacitor, the output power of the supercapacitor can be controlled more accurately to meet the power demand of the load; by estimating the electrical parameter values of the supercapacitor in real time through the Kalman filter and using them for power control, the influence of system noise and disturbance can be effectively suppressed and the stability of the system can be enhanced; by considering the electrical parameter values and casing temperature of the supercapacitor, overcharging or over-discharging of the supercapacitor can be avoided and its service life can be extended.

[0126] In an optional embodiment, based on the fast response segment, an augmented Lagrangian equation is established to solve the power optimization trajectory and output a fast adjustment control value, which includes:

[0127] Calculating the sum of squares of deviations between the power optimization trajectory and the target power value to generate a power tracking error term, calculating the sum of squares of power changes at adjacent sampling points of the power optimization trajectory to generate a change rate constraint term, and combining the power tracking error term and the change rate constraint term to construct a composite optimization objective function;

[0128] Collecting operating parameters, determining upper and lower thresholds of power constraints based on the operating parameters, determining a response time constraint based on a time constant of the operating parameters, and combining the power constraint and the response time constraint to form a dynamic constraint model;

[0129] Multiplying the power constraint by the first Lagrangian multiplier to obtain a first multiplication result, multiplying the response time constraint by the second Lagrangian multiplier to obtain a second multiplication result, combining the first multiplication result and the second multiplication result with the composite optimization objective function to construct an augmented Lagrangian function, calculating the degree of constraint violation, and updating the first Lagrangian multiplier and the second Lagrangian multiplier;

[0130] Applying an alternating direction multiplier method to iteratively solve the augmented Lagrangian function to generate the power optimization trajectory, calculating the convergence rate of the power optimization trajectory and determining an adaptive penalty factor;

[0131] The deviation between the power optimization trajectory and the target power value is calculated and multiplied by the proportional gain to obtain the proportional control amount. The rate of change of the power optimization trajectory is calculated and multiplied by the differential gain to obtain the differential control amount. The proportional control amount and the differential control amount are combined and output to form a fast adjustment control value.

[0132] In one specific embodiment, the sum of the squares of the differences between the power optimization trajectory and the target power value is first calculated to generate a metric for measuring the power tracking error. Simultaneously, the sum of the squares of the power changes between adjacent sampling points on the power optimization trajectory is calculated to generate a metric for measuring the rate of power change. The power tracking error metric and the power change rate metric are combined to construct a composite optimization objective function that minimizes both the power tracking error and the power change rate.

[0133] For example, assuming the target power value is 10 and the current power optimization trajectory is [8, 9, 11, 12], the power tracking error is (8-10) 2 +(9-10) 2 +(11-10) 2 +(12-10) 2 =10. The power change rate is (9-8) 2 +(11-9) 2 +(12-11) 2 = 6. The value of the composite optimization objective function is 10 + 6 = 16.

[0134] Next, the system's operating parameters, such as load characteristics and ambient temperature, are collected. Based on these operating parameters, upper and lower thresholds for the power constraint are determined. For example, the power value must be between 0 and 15. Furthermore, response time constraints are determined based on the time constants of the operating parameters. For example, power changes cannot be too rapid, and the power change between adjacent sampling points cannot exceed 2. Combining the power and response time constraints forms a dynamic constraint model.

[0135] Next, the power constraint is multiplied by the first Lagrangian multiplier to obtain the first product. The response time constraint is multiplied by the second Lagrangian multiplier to obtain the second product. The first and second product results are combined with the composite optimization objective function to construct the augmented Lagrangian function. The constraint violation degree is calculated, and the first and second Lagrangian multipliers are updated based on the constraint violation degree.

[0136] Assume that the initial value of the first Lagrangian multiplier is 0.1 and the initial value of the second Lagrangian multiplier is 0.2. If the current power optimization trajectory is [8, 9, 11, 12], the power constraint violation degree is 0 and the response time constraint violation degree is 0. The value of the augmented Lagrangian function is 16.

[0137] The alternating direction multiplier method is then applied to iteratively solve the augmented Lagrangian function to generate a power optimization trajectory. The convergence rate of the power optimization trajectory is calculated, and the adaptive penalty factor is determined based on the convergence rate.

[0138] Finally, the deviation between the power optimization trajectory and the target power value is calculated and multiplied by the proportional gain to obtain the proportional control variable. The rate of change of the power optimization trajectory is calculated and multiplied by the differential gain to obtain the differential control variable. The proportional and differential control variables are combined and output to form a fast adjustment control value.

[0139] For example, assume the target power is 10, the last value of the current power optimization trajectory is 11, the proportional gain is 0.5, the differential gain is 0.2, and the rate of change of the power optimization trajectory is 1. The proportional control amount is (11-10)×0.5=0.5, and the differential control amount is 1×0.2=0.2. The fast adjustment control value is 0.5+0.2=0.7.

[0140] In this embodiment, by minimizing the power tracking error, the method can make the actual power closer to the target power value, thereby improving the power tracking accuracy; by limiting the power change rate, the method can avoid problems such as overshoot and oscillation during the power regulation process, thereby improving the dynamic performance of power regulation; and can adapt to different operating parameters and constraints, thereby enhancing the robustness of power regulation.

[0141] In an optional implementation, performing a recursive least squares operation based on the dynamic transition section to obtain a system parameter estimate, and updating the power control value includes:

[0142] Collecting a continuous sampling sequence of real-time power values in a dynamic transition section, calculating power differences between adjacent sampling points in the continuous sampling sequence, and obtaining a power variation sequence;

[0143] Based on the power variation sequence, a power variation trend curve is constructed by using a cubic spline interpolation method. The real-time power value and the corresponding power variation are combined into a transition state vector. The transition power adjustment amount is used as a transition control input to construct a discrete time-varying state space model.

[0144] The first-order differential coefficient of the real-time power value and the first-order differential coefficient of the power variation are combined into a parameter matrix to be estimated, and the transition stage state vector and the transition stage control input are combined into a regression vector;

[0145] A recursive prediction sequence is constructed by multiplying the parameter matrix to be estimated and the regression vector, real-time operating status is collected to obtain a current state observation value, and the difference between the current state observation value and the recursive prediction sequence is calculated to obtain an estimation error; a gain matrix is obtained by multiplying the transpose of the regression vector and the recursive prediction sequence, and the product of the gain matrix and the estimation error is used as a parameter correction amount;

[0146] Adding the parameter matrix to be estimated and the parameter correction amount to obtain an updated parameter estimate; decomposing the updated parameter estimate to obtain a state matrix estimate and an input matrix estimate;

[0147] Multiplying the state matrix estimate by the current transition state vector to obtain a first state prediction term, determining a desired state value based on the current transition state vector and in combination with a transition control input, and subtracting the first state prediction term from the desired state value to obtain a state compensation value;

[0148] Calculate the product of the transpose of the input matrix estimate value and the input matrix estimate value to obtain a matrix coefficient, calculate the product of the transpose of the input matrix estimate value and the state compensation value to obtain a compensation coefficient; divide the compensation coefficient by the matrix coefficient to obtain a power adjustment coefficient, and take the negative value of the power adjustment coefficient to obtain an updated power control value.

[0149] In one embodiment, first, a continuous sampling sequence of real-time power values within the dynamic transition section is collected. For example, a power value is collected every 0.1 seconds to obtain a power value sequence, such as [10.1, 10.3, 10.5, 10.7, 10.9, 11.1].

[0150] Next, the power difference between adjacent sampling points in the continuous sampling sequence is calculated to obtain a power variation sequence. For example, the power variation sequence corresponding to the above power value sequence is: [0.2, 0.2, 0.2, 0.2, 0.2].

[0151] Then, based on the power change sequence, a power trend curve is constructed using cubic spline interpolation. This curve describes the overall trend of power changes and can be used to predict future power changes. For example, cubic spline interpolation can produce a function that describes the power trend.

[0152] The real-time power value and the corresponding power change form a transition state vector, and the transition power adjustment value is used as the transition control input to construct a discrete time-varying state space model. For example, if the current power value is 10.5, the power change is 0.2, and the power adjustment value is 0.1, then a state vector of [10.5, 0.2] and a control input of 0.1 can be constructed.

[0153] The first-order difference coefficients of the real-time power values and the first-order difference coefficients of the power change are combined into a parameter matrix to be estimated. The first-order difference coefficients represent the rate of change of the power value or power change between adjacent moments. For example, the first-order difference coefficients of the power value can be calculated by dividing the difference between two adjacent power values by the time interval. The transition state vector and the transition control input are combined into a regression vector.

[0154] A recursive prediction sequence is constructed by multiplying the parameter matrix to be estimated by the regression vector. This sequence predicts future power values and power changes. Real-time operating status is collected to obtain the current state observation. The difference between the current state observation and the recursive prediction sequence is calculated to obtain the estimation error. For example, if the predicted power value is 10.8 and the actual observed power value is 10.7, the estimation error is 0.1.

[0155] Calculate the transpose of the regression vector and the product of the recursive prediction sequence to obtain the gain matrix. The product of the gain matrix and the estimation error is used as the parameter correction. Add the parameter matrix to be estimated and the parameter correction to obtain the updated parameter estimate.

[0156] Based on the updated parameter estimates, the state matrix estimate and the input matrix estimate are decomposed. The state matrix estimate is multiplied by the current transition state vector to obtain a first state prediction term. Based on the current transition state vector and the transition control input, a desired state value is determined. The first state prediction term is subtracted from the desired state value to obtain a state compensation value.

[0157] Calculate the transpose of the input matrix estimate and the product of the input matrix estimate to obtain the matrix coefficient. Calculate the transpose of the input matrix estimate and the product of the state compensation value to obtain the compensation coefficient. Divide the compensation coefficient by the matrix coefficient to obtain the power adjustment coefficient. Negate the power adjustment coefficient to obtain the updated power control value.

[0158] In this embodiment, by estimating system parameters in real time and adjusting the power control value according to parameter changes, the system power can be controlled more accurately, power fluctuations can be reduced, and the system operation can be made more stable; the control strategy can be adjusted according to the characteristics of the dynamic transition section, so that the system can quickly adapt to environmental changes, thereby improving the robustness and reliability of the system; and the recursive least squares algorithm is used, which has a small amount of calculation and is easy to implement, can simplify the complexity of the power control system and reduce system costs.

[0159] In an optional embodiment, based on the steady-state maintenance segment, constructing a Lyapunov function, solving the energy balance deviation value, and calculating the compensation control value include:

[0160] Within a preset integration time window, the difference between the real-time power value and the reference power value is calculated and integrated to obtain an energy integral value. The rate of change of the energy integral value is also calculated. The energy integral value is used as a first state quantity, and the rate of change of the energy integral value is used as a second state quantity to form a maintenance segment state vector.

[0161] Calculating the second-order derivative of the energy integral value, constructing a maintenance segment state matrix based on the relationship between the energy integral value, the rate of change of the energy integral value, and the second-order derivative of the energy integral value; constructing a maintenance segment input matrix based on the response coefficient of the rate of change of the energy integral value to the system input; and calculating a maintenance segment power adjustment amount as a maintenance segment control input based on the deviation between the maintenance segment state matrix and the energy integral value;

[0162] multiplying the maintenance segment state vector by the maintenance segment state matrix to form a first matrix product, multiplying the maintenance segment control input by the maintenance segment input matrix to form a second matrix product, and adding the first matrix product and the second matrix product to construct a state space equation;

[0163] The Lyapunov stability equation is constructed by multiplying the transposed matrix of the maintenance segment state matrix by the matrix to be determined, adding the product of the matrix to be determined and the maintenance segment state matrix, and then adding the identity matrix. The Lyapunov stability equation is solved to obtain the matrix to be determined as a symmetric positive definite matrix; and a positive definite weight matrix is determined according to the value range of the maintenance segment control input.

[0164] A state quadratic term is obtained by multiplying the maintenance segment state vector by a symmetric positive definite matrix on the left and then multiplying it by the transpose of the maintenance segment state vector on the right; a control integral term is obtained by multiplying the maintenance segment control input by a positive definite weight matrix on the left and then multiplying it by the transpose of the maintenance segment control input on the right; and a Lyapunov function is constructed by adding the state quadratic term and the control integral term.

[0165] Taking the time derivative of the Lyapunov function to obtain a derivative equation, constructing a feedback control law based on optimal control theory, substituting the feedback control law into the derivative equation, and verifying the stability of the system by calculating the negative definiteness of the result;

[0166] Calculating the difference between the energy integral value and a preset expected energy level to obtain an energy balance deviation, and calculating the rate of change of the energy balance deviation over time to obtain a deviation change rate;

[0167] The energy balance deviation is multiplied by a first compensation gain to obtain a first compensation amount, and the deviation change rate is multiplied by a second compensation gain to obtain a second compensation amount, wherein the first compensation gain is greater than the ratio of the minimum eigenvalue of the symmetric positive definite matrix to the norm of the maintenance segment input matrix, and the second compensation gain is greater than the ratio of the norm of the positive definite weight matrix to the minimum eigenvalue of the symmetric positive definite matrix; the first compensation amount and the second compensation amount are added to obtain a compensation control value.

[0168] The left multiplication specifically refers to placing one matrix or vector on the left side of another matrix or vector in a matrix or vector operation to perform a multiplication operation. Left multiplication is usually used to express linear transformations or perform some left-side operation on data.

[0169] The term "right multiplication" specifically refers to placing one matrix or vector on the right side of another matrix or vector in a matrix or vector operation to perform a multiplication operation. Right multiplication is in the opposite direction of left multiplication and is used to express the right-hand operation.

[0170] Negative definiteness refers to the property of a matrix or function where the output is always less than zero for all inputs. This indicates that the corresponding system or function has decreasing or concave characteristics and is often used to analyze stability or determine whether a state has a specific trend.

[0171] In one specific embodiment, a time window is first set, for example, one second. Within this time window, the difference between the real-time power value and the reference power value is continuously calculated. These differences are accumulated to obtain an energy integral value. Simultaneously, the rate of change of the energy integral value, i.e., the rate of change of the energy integral value, is calculated. The energy integral value and its rate of change are used as the first and second state quantities, respectively, to form a two-dimensional vector, referred to as the maintenance segment state vector.

[0172] Next, calculate the rate of change of the rate of change of the energy integral value, that is, the second-order derivative of the energy integral value. Based on the relationship between the energy integral value, its rate of change and the second-order derivative, construct a 2×2 matrix, called the maintenance segment state matrix. For example, if the second-order derivative is equal to the linear combination of the energy integral value and the rate of change, then the elements of the matrix are the combination coefficients. At the same time, determine the impact of the system input on the rate of change of the energy integral value and express it as a coefficient to form the maintenance segment input matrix. Based on the deviation between the maintenance segment state matrix and the energy integral value (that is, the difference between the energy integral value and the expected value), calculate the maintenance segment power adjustment amount as the maintenance segment control input.

[0173] Next, multiply the sustain segment state vector by the sustain segment state matrix to obtain a new vector, called the first matrix product. Multiply the sustain segment control input by the sustain segment input matrix to obtain the second matrix product. Add the first and second matrix products to construct the state space equation.

[0174] To design a compensation controller, a Lyapunov function must be constructed. First, a symmetric positive definite matrix is obtained by solving a specific matrix equation, the Lyapunov stability equation. This equation is formulated as follows: the transpose of the maintaining segment state matrix multiplied by the desired matrix, plus the product of the desired matrix and the maintaining segment state matrix, plus the identity matrix, equals the zero matrix. Solving this equation yields the desired matrix. A positive definite weight matrix is determined based on the range of the maintaining segment control input. For example, if the control input range is -1 to 1, the weight matrix can be set to the identity matrix.

[0175] Multiply the state vector of the maintenance segment on the left by a symmetric positive definite matrix and then on the right by the transpose of the maintenance segment state vector to obtain a scalar, called the state quadratic term. Multiply the control input of the maintenance segment on the left by a positive definite weight matrix and then on the right by the transpose of the maintenance segment control input. This is then integrated over the time window to obtain another scalar, called the control integral term. The state quadratic term and the control integral term are added together to construct the Lyapunov function.

[0176] Taking the time derivative of the Lyapunov function yields the derivative equation. Based on optimal control theory, a feedback control law is constructed. Substituting the feedback control law into the derivative equation, the system stability is verified by determining whether the result is negative. If the result is consistently negative, the system is stable.

[0177] Finally, the difference between the energy integral value and the preset expected energy level is calculated to obtain the energy balance deviation. The rate of change of the energy balance deviation over time is calculated to obtain the deviation change rate. The energy balance deviation is multiplied by the first compensation gain to obtain the first compensation amount. The deviation change rate is multiplied by the second compensation gain to obtain the second compensation amount. The value of the first compensation gain is greater than the ratio of the minimum eigenvalue of the symmetric positive definite matrix to the norm of the maintenance segment input matrix. The value of the second compensation gain is greater than the ratio of the norm of the positive definite weight matrix to the minimum eigenvalue of the symmetric positive definite matrix. The first compensation amount and the second compensation amount are added to obtain the compensation control value. For example, if the energy balance deviation is 0.1, the deviation change rate is 0.01, the first compensation gain is 10, and the second compensation gain is 5, then the compensation control value is 1.05.

[0178] In this embodiment, by constructing a Lyapunov function and designing a compensation controller based on optimal control theory, the stability of the system is guaranteed, and the system can maintain stable operation even in the presence of external interference; by calculating the energy integral value, rate of change and deviation in real time, and combining it with a compensation control strategy, precise control of energy balance is achieved, energy fluctuations are reduced, and energy utilization efficiency is improved; the design of the controller based on the steady-state maintenance segment simplifies the complexity of the control algorithm, reduces the computational burden, and facilitates practical application.

[0179] In an optional embodiment, a power control command is input into a disturbance observer, unmodeled dynamic and external disturbance terms are calculated, a dynamic error value is determined, a generalized differential operation is performed on the dynamic error value, a non-singular terminal equation is constructed, an initial control value is output, the initial control value is input into a recursive minimum entropy calculation unit to obtain a correction coefficient, a superhelical algorithm operation is performed on the correction coefficient and the initial control value, and the output power adjustment signal includes:

[0180] Inputting the power control command and the output power of the system into the disturbance observer, constructing a disturbance observer state equation including an observer gain and an auxiliary observation quantity, and running the disturbance observer state equation to obtain an observation output;

[0181] Based on the observed output, unmodeled dynamic and external disturbance terms are calculated to obtain a disturbance estimate, and a dynamic error value is obtained by subtracting a desired power trajectory from the output power of the system and adding the result to the disturbance estimate.

[0182] performing a generalized differential operation on the dynamic error value to obtain a differential error value, combining the differential error value with a power function of the dynamic error value to construct a non-singular terminal sliding mode surface; setting a stability parameter of the system to obtain a negative feedback gain, calculating a derivative of the non-singular terminal sliding mode surface, multiplying the corresponding derivative by the negative feedback gain to construct a reaching law, and calculating a ratio of the reaching law to the input gain to obtain an initial control value;

[0183] Using the initial control value as a basis for obtaining a system state sequence, calculating the probability distribution of the system state sequence to obtain a state probability, inputting the state probability into a recursive minimum entropy calculation unit to calculate a system entropy value, obtaining a minimum entropy value through recursive operation, and calculating a negative exponent of the difference between the system entropy value and the minimum entropy value to obtain a correction coefficient;

[0184] Multiplying the correction coefficient and the initial control value to obtain a first algorithm component, constructing a power function and a sign function of the non-singular terminal sliding mode surface, and combining them to obtain a second algorithm component;

[0185] Set the convergence gain parameter of the supercoil algorithm, construct a supercoil state equation containing the first algorithm component and the second algorithm component, perform an integral operation on the supercoil state equation to obtain an auxiliary variable of the supercoil algorithm, and combine the auxiliary variable with the first algorithm component and the second algorithm component to output a power adjustment signal.

[0186] Unmodeled dynamics specifically refer to dynamic characteristics of a system that are not included in the model due to simplifications or omissions of complex factors during the modeling process. These characteristics may arise from high-frequency oscillations, small nonlinearities, unaccounted environmental effects, or system dynamics that are not explicitly expressed. Unmodeled dynamics are often the source of discrepancies between the actual system behavior and the model's predictions, and their impact needs to be mitigated through estimation and compensation.

[0187] The non-singular terminal sliding surface refers to a mathematical design method used in sliding mode control within a control system. Through a specific construction method, it ensures that the control system converges quickly on the sliding surface and reaches a stable state. Its non-singularity is reflected in the fact that the sliding mode control process avoids the singularity problem found in traditional sliding mode methods, and its terminal characteristic is reflected in the fact that the control system can reach the sliding surface within a finite time and ultimately reach a stable state. This sliding surface design helps improve the accuracy and robustness of system control.

[0188] A power regulation method whose core idea is to use a disturbance observer to estimate the unmodeled dynamics of the system and external disturbances, and combine it with non-singular terminal sliding mode control and superhelical algorithm to achieve precise control of the system output power.

[0189] First, the power control command and the system's output power are input into a disturbance observer. This disturbance observer consists of an observer gain and an auxiliary observation. The observed output is obtained by running the disturbance observer state equation. Assume the power control command is 10 kW, the system output power is 9.8 kW, the observer gain is set to 0.5, and the auxiliary observation is initialized to 0. Running the disturbance observer state equation yields an observed output of 0.1 kW.

[0190] Next, the unmodeled dynamic and external disturbance terms are calculated based on the observed output to obtain a disturbance estimate. For example, by analyzing the trend of the observed output, the disturbance can be estimated to be 0.05 kW. The system's output power is subtracted from the desired power trajectory and then added to the disturbance estimate to obtain the dynamic error value. Assuming the desired power trajectory is 10 kW, the dynamic error value is 9.8 kW - 10 kW + 0.05 kW = -0.15 kW.

[0191] Then, perform a generalized differential operation on the dynamic error value to obtain the differential error value. For example, by calculating the rate of change of the dynamic error value, the differential error value is obtained to be -0.01kW / s. The differential error value is combined with the power function of the dynamic error value to construct a non-singular terminal sliding mode surface. Assuming the power function exponent is 1.5, the non-singular terminal sliding mode surface is -0.15kW. 1.5+(-0.01kW / s). Set the system's stability parameters, for example, a negative feedback gain of 0.8, and calculate the derivative of the nonsingular terminal sliding surface. Multiply this derivative by the negative feedback gain to construct the reaching law. Finally, calculate the ratio of the reaching law to the input gain to obtain the initial control value. Assuming the input gain is 1, the initial control value is 0.012.

[0192] Using the initial control value as the basis for obtaining the system state sequence, calculate the probability distribution of the system state sequence to obtain the state probability. For example, by statistically analyzing historical data, the state probability is 0.9. Input the state probability into the recursive minimum entropy calculation unit to calculate the system entropy value. The minimum entropy value is obtained through recursive operation. For example, the calculated system entropy value is 0.5 and the minimum entropy value is 0.2. Calculate the negative exponent of the difference between the system entropy value and the minimum entropy value to obtain the correction coefficient. For example, the correction coefficient is exp(-(0.5-0.2)) = 0.74.

[0193] Multiply the correction coefficient by the initial control value to obtain the first algorithm component. For example, the first algorithm component is 0.74×0.012=0.00888. Construct the power function and sign function of the non-singular terminal sliding mode surface and combine them to obtain the second algorithm component. For example, the second algorithm component is abs(-0.15kW) 0.5 ×sign(-0.15kW)=-0.1225.

[0194] Set the convergence gain parameter for the supercoil algorithm, for example, to 0.5. Construct a supercoil state equation containing the first and second algorithm components. Integrate the supercoil state equation to obtain an auxiliary variable for the supercoil algorithm. Combine the auxiliary variable with the first and second algorithm components to output a power adjustment signal. For example, if the auxiliary variable is 0.1, the power adjustment signal is 0.1 + 0.00888 - 0.1225 = -0.01362.

[0195] In this embodiment, the unmodeled dynamics and external disturbances of the system are accurately estimated through the disturbance observer, and combined with the non-singular terminal sliding mode control and the superhelical algorithm, the influence of the disturbance can be effectively suppressed and the power regulation accuracy can be improved; the non-singular terminal sliding mode control has the characteristics of fast convergence and robustness to parameter uncertainty, and the superhelical algorithm further enhances the robustness of the system, enabling it to cope with more complex working conditions; the introduction of the recursive minimum entropy calculation unit optimizes the parameters of the controller, improves the control performance of the system, and enables the system output power to quickly and accurately track the desired power trajectory.

[0196] Figure 2 FIG. 1 is a schematic diagram of a structure of a grid frequency modulation power energy coordinated control system based on supercapacitors according to an embodiment of the present invention. Figure 2 As shown, the system includes:

[0197] The first unit is used to perform time-frequency analysis on the collected power grid frequency signal using a sliding Fourier transform, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain a frequency dynamic correlation vector; perform recursive principal component decomposition on the frequency dynamic correlation vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount based on the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input them into the Kalman filter to calculate the electrical parameter values, and determine the upper and lower power thresholds based on the electrical parameter values, which together with the frequency modulation power compensation amount form power control data;

[0198] The second unit is used to determine the power allocation sequence based on the power control data through nonlinear programming calculation, and divide the power allocation sequence into a fast response section, a dynamic transition section, and a steady-state maintenance section according to a preset interval segmentation threshold based on the power change rate of the power allocation sequence; establish an augmented Lagrangian equation based on the fast response section, solve the power optimization trajectory, and output a fast adjustment control value; perform a recursive least squares operation based on the dynamic transition section to obtain system parameter estimates and update the power control value; construct a Lyapunov function based on the steady-state maintenance section, solve the energy balance deviation value, and calculate the compensation control value; perform piecewise continuous function operations on the fast adjustment control value, the power control value, and the compensation control value, and output a power control instruction;

[0199] The third unit is used to input the power control command into the disturbance observer, calculate the unmodeled dynamic and external disturbance terms, determine the dynamic error value, perform generalized differential operation on the dynamic error value, construct a non-singular terminal equation, output the initial control value, input the initial control value into the recursive minimum entropy calculation unit to obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power adjustment signal.

[0200] According to a third aspect of the embodiments of the present invention,

[0201] An electronic device is provided, comprising:

[0202] processor;

[0203] a memory for storing processor-executable instructions;

[0204] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0205] According to a fourth aspect of the embodiments of the present invention,

[0206] A computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0207] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0208] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for coordinated control of power frequency modulation and energy of a power grid based on supercapacitors, characterized in that: include: The collected power grid frequency signal is analyzed in time and frequency using a sliding Fourier transform to obtain the frequency characteristic components of each time window, construct a frequency change matrix, and calculate the moving entropy value of the frequency change matrix to obtain the frequency dynamic correlation vector. The frequency dynamic correlation vector is recursively decomposed into principal components, and the frequency disturbance eigenvalue is output in real time. The frequency modulation power compensation amount is calculated based on the frequency disturbance eigenvalue. The voltage and current signals of the supercapacitor group are collected and input into the Kalman filter to calculate the electrical parameter values. The upper and lower power thresholds are determined based on the electrical parameter values, and the power control data is formed together with the frequency modulation power compensation amount. Based on the power control data, a power allocation sequence is determined through nonlinear programming calculations. Based on the power change rate of the power allocation sequence, it is divided into a fast response section, a dynamic transition section, and a steady-state maintenance section according to a preset interval segmentation threshold. Based on the fast response section, an augmented Lagrangian equation is established to solve the power optimization trajectory and output a fast adjustment control value. Based on the dynamic transition section, a recursive least squares operation is performed to obtain system parameter estimates and update the power control value. Based on the steady-state maintenance segment, a Lyapunov function is constructed to solve the energy balance deviation value and calculate the compensation control value; a piecewise continuous function operation is performed on the fast adjustment control value, power control value and compensation control value to output the power control instruction; The power control command is input into the disturbance observer, the unmodeled dynamic and external disturbance terms are calculated, the dynamic error value is determined, the generalized differential operation is performed on the dynamic error value, a non-singular terminal equation is constructed, and the initial control value is output. The initial control value is input into the recursive minimum entropy calculation unit to obtain the correction coefficient, the superhelical algorithm operation is performed on the correction coefficient and the initial control value, and the power regulation signal is output.

2. The method according to claim 1, characterized in that The time-frequency analysis of the collected power grid frequency signal is performed using sliding Fourier transform to obtain the frequency characteristic components of each time window, construct the frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain the frequency dynamic correlation vector including: Divide the collected power grid frequency signal into multiple time windows according to a preset time interval, use a cosine function to perform smooth transition processing on the power grid frequency signals of adjacent time windows to obtain a smoothed frequency signal; perform wavelet decomposition on the smoothed frequency signal to obtain hierarchical wavelet coefficients of multiple decomposition levels, calculate the energy value of each hierarchical wavelet coefficient, and calculate the energy change rate of adjacent time windows based on the energy value; when the energy change rate is greater than a preset energy change threshold, shorten the time window length according to a preset ratio, and repeat the process until the energy change rate is less than the energy change threshold, thereby obtaining an optimal time window length; Performing a sliding Fourier transform on the smoothed frequency signal based on the optimal time window length to obtain spectral components of the frequency signal, and extracting amplitude information and phase information of the working frequency band from the spectral components; arranging the amplitude information and phase information of multiple consecutive time windows in time sequence to construct a frequency change matrix, and constructing an equivalued diagonal matrix based on the autocorrelation function of the frequency change matrix; performing eigenvalue decomposition on the equivalued diagonal matrix to extract the eigenvector corresponding to the maximum eigenvalue, and reconstructing the noise reduction frequency feature matrix based on the eigenvector; Select multiple preset scale parameters, calculate the conditional entropy value and sample entropy value of the frequency characteristic matrix under each preset scale parameter; identify the mutation point in the frequency characteristic matrix, determine the mutation interval, correspondingly determine the non-mutation interval, and use the entropy value of the adjacent non-mutation interval to replace the entropy value of the mutation interval to obtain a modified entropy value sequence; calculate the fluctuation variance of the modified entropy value sequence under each preset scale parameter, and determine the weight coefficient corresponding to each preset scale parameter based on the inverse of the fluctuation variance; The modified entropy value sequence under each preset scale parameter is weightedly combined with the corresponding weight coefficient to obtain the frequency dynamic correlation vector.

3. The method according to claim 1, characterized in that Perform recursive principal component decomposition on the frequency dynamic correlation vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount based on the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input them into the Kalman filter to calculate the electrical parameter values, and determine the upper and lower power thresholds based on the electrical parameter values. These power control data, together with the frequency modulation power compensation amount, include: Divide the frequency dynamic correlation vector into multiple data segments according to the preset number of sampling points, perform principal component decomposition on each data segment, and extract the first principal component eigenvalue with the largest variance contribution rate; Based on a preset number of data segments, a first principal component eigenvalue sequence is determined, an autoregressive prediction model of a preset order is established, and the coefficients of the autoregressive prediction model are optimized and calculated using a least squares iterative algorithm. When the difference between the coefficients calculated from two adjacent iterative calculations is less than a preset convergence threshold, the current iterative result is determined as the optimal prediction coefficient; Substituting the optimal prediction coefficient into the autoregressive prediction model, calculating the prediction result of the first principal component eigenvalue of the next data segment, and comparing the predicted result of the first principal component eigenvalue with the corresponding actual result of the first principal component eigenvalue to obtain the prediction deviation; When the prediction deviation is greater than a preset deviation threshold, the prediction deviation is used as a correction amount based on an exponential weighting method to update the coefficient of the autoregressive prediction model to obtain an updated first principal component eigenvalue as a frequency disturbance eigenvalue; the frequency disturbance eigenvalue is multiplied by a preset proportional coefficient to obtain a frequency modulation power compensation amount; According to a preset sampling period, the port voltage and charge / discharge current of the supercapacitor group are collected, and a state-space equation including equivalent series resistance, equivalent series capacitance, and remaining available capacity is constructed based on the port voltage and charge / discharge current. The voltage and current observation data of a preset number of groups are subtracted from the output value of the state-space equation to obtain an observation residual sequence; According to a preset sampling period, the port voltage, charge and discharge current, and shell temperature of the supercapacitor group are collected; based on the port voltage and charge and discharge current, a state-space equation including equivalent series resistance, equivalent series capacitance, and remaining available capacity is constructed; the port voltage and charge and discharge current are differenced with the predicted value of the state-space equation, and the covariance matrix of process noise and observation noise is dynamically adjusted using a sliding window method to construct a Kalman filter; the state-space equation is input into the Kalman filter to calculate the equivalent series resistance, equivalent series capacitance, and remaining available capacity of the supercapacitor group; Establishing a power constraint equation, substituting the equivalent series resistance, equivalent series capacitance, remaining available capacity, and housing temperature into the power constraint equation, and solving to obtain upper and lower power thresholds; The power upper and lower limit thresholds and the frequency modulation power compensation amount are combined into power control data.

4. The method according to claim 1, wherein Based on the fast response segment, the augmented Lagrangian equation is established to solve the power optimization trajectory and output the fast adjustment control value including: Calculating the sum of squares of deviations between the power optimization trajectory and the target power value to generate a power tracking error term, calculating the sum of squares of power changes at adjacent sampling points of the power optimization trajectory to generate a change rate constraint term, and combining the power tracking error term and the change rate constraint term to construct a composite optimization objective function; Collecting operating parameters, determining upper and lower thresholds of power constraints based on the operating parameters, determining a response time constraint based on a time constant of the operating parameters, and combining the power constraint and the response time constraint to form a dynamic constraint model; Multiplying the power constraint by the first Lagrangian multiplier to obtain a first multiplication result, multiplying the response time constraint by the second Lagrangian multiplier to obtain a second multiplication result, combining the first multiplication result and the second multiplication result with the composite optimization objective function to construct an augmented Lagrangian function, calculating the degree of constraint violation, and updating the first Lagrangian multiplier and the second Lagrangian multiplier; Applying an alternating direction multiplier method to iteratively solve the augmented Lagrangian function to generate the power optimization trajectory, calculating the convergence rate of the power optimization trajectory and determining an adaptive penalty factor; The deviation between the power optimization trajectory and the target power value is calculated and multiplied by the proportional gain to obtain the proportional control amount. The rate of change of the power optimization trajectory is calculated and multiplied by the differential gain to obtain the differential control amount. The proportional control amount and the differential control amount are combined and output to form a fast adjustment control value.

5. The method according to claim 1, wherein Based on the dynamic transition section, a recursive least squares operation is performed to obtain the estimated values of the system parameters. The power control value is updated by: Collecting a continuous sampling sequence of real-time power values in a dynamic transition section, calculating power differences between adjacent sampling points in the continuous sampling sequence, and obtaining a power variation sequence; Based on the power variation sequence, a power variation trend curve is constructed by using a cubic spline interpolation method. The real-time power value and the corresponding power variation are combined into a transition state vector. The transition power adjustment amount is used as a transition control input to construct a discrete time-varying state space model. The first-order differential coefficient of the real-time power value and the first-order differential coefficient of the power variation are combined into a parameter matrix to be estimated, and the transition stage state vector and the transition stage control input are combined into a regression vector; A recursive prediction sequence is constructed by multiplying the parameter matrix to be estimated and the regression vector, real-time operating status is collected to obtain a current state observation value, and the difference between the current state observation value and the recursive prediction sequence is calculated to obtain an estimation error; a gain matrix is obtained by multiplying the transpose of the regression vector and the recursive prediction sequence, and the product of the gain matrix and the estimation error is used as a parameter correction amount; Adding the parameter matrix to be estimated and the parameter correction amount to obtain an updated parameter estimate; decomposing the updated parameter estimate to obtain a state matrix estimate and an input matrix estimate; Multiplying the state matrix estimate by the current transition state vector to obtain a first state prediction term, determining a desired state value based on the current transition state vector and in combination with a transition control input, and subtracting the first state prediction term from the desired state value to obtain a state compensation value; Calculate the product of the transpose of the input matrix estimate value and the input matrix estimate value to obtain a matrix coefficient, calculate the product of the transpose of the input matrix estimate value and the state compensation value to obtain a compensation coefficient; divide the compensation coefficient by the matrix coefficient to obtain a power adjustment coefficient, and take the negative value of the power adjustment coefficient to obtain an updated power control value.

6. The method according to claim 1, characterized in that Based on the steady-state maintenance segment, the Lyapunov function is constructed to solve the energy balance deviation value and calculate the compensation control value including: Within a preset integration time window, the difference between the real-time power value and the reference power value is calculated and integrated to obtain an energy integral value. The rate of change of the energy integral value is also calculated. The energy integral value is used as a first state quantity, and the rate of change of the energy integral value is used as a second state quantity to form a maintenance segment state vector. Calculating the second-order derivative of the energy integral value, constructing a maintenance segment state matrix based on the relationship between the energy integral value, the rate of change of the energy integral value, and the second-order derivative of the energy integral value; constructing a maintenance segment input matrix based on the response coefficient of the rate of change of the energy integral value to the system input; and calculating a maintenance segment power adjustment amount as a maintenance segment control input based on the deviation between the maintenance segment state matrix and the energy integral value; multiplying the maintenance segment state vector by the maintenance segment state matrix to form a first matrix product, multiplying the maintenance segment control input by the maintenance segment input matrix to form a second matrix product, and adding the first matrix product and the second matrix product to construct a state space equation; The Lyapunov stability equation is constructed by multiplying the transposed matrix of the maintenance segment state matrix by the matrix to be determined, adding the product of the matrix to be determined and the maintenance segment state matrix, and then adding the identity matrix. The Lyapunov stability equation is solved to obtain the matrix to be determined as a symmetric positive definite matrix; and a positive definite weight matrix is determined according to the value range of the maintenance segment control input. A state quadratic term is obtained by multiplying the maintenance segment state vector by a symmetric positive definite matrix on the left and then multiplying it by the transpose of the maintenance segment state vector on the right; a control integral term is obtained by multiplying the maintenance segment control input by a positive definite weight matrix on the left and then multiplying it by the transpose of the maintenance segment control input on the right; and a Lyapunov function is constructed by adding the state quadratic term and the control integral term. Taking the time derivative of the Lyapunov function to obtain a derivative equation, constructing a feedback control law based on optimal control theory, substituting the feedback control law into the derivative equation, and verifying the stability of the system by calculating the negative definiteness of the result; Calculating the difference between the energy integral value and a preset expected energy level to obtain an energy balance deviation, and calculating the rate of change of the energy balance deviation over time to obtain a deviation change rate; The energy balance deviation is multiplied by a first compensation gain to obtain a first compensation amount, and the deviation change rate is multiplied by a second compensation gain to obtain a second compensation amount, wherein the first compensation gain is greater than the ratio of the minimum eigenvalue of the symmetric positive definite matrix to the norm of the maintenance segment input matrix, and the second compensation gain is greater than the ratio of the norm of the positive definite weight matrix to the minimum eigenvalue of the symmetric positive definite matrix; the first compensation amount and the second compensation amount are added to obtain a compensation control value.

7. The method according to claim 1, characterized in that The power control command is input into the disturbance observer, the unmodeled dynamic and external disturbance terms are calculated, the dynamic error value is determined, the generalized differential operation is performed on the dynamic error value, a non-singular terminal equation is constructed, and the initial control value is output. The initial control value is input into the recursive minimum entropy calculation unit to obtain the correction coefficient. The super spiral algorithm operation is performed on the correction coefficient and the initial control value. The output power adjustment signal includes: Inputting the power control command and the output power of the system into the disturbance observer, constructing a disturbance observer state equation including an observer gain and an auxiliary observation quantity, and running the disturbance observer state equation to obtain an observation output; Based on the observed output, unmodeled dynamic and external disturbance terms are calculated to obtain a disturbance estimate, and a dynamic error value is obtained by subtracting a desired power trajectory from the output power of the system and adding the result to the disturbance estimate. performing a generalized differential operation on the dynamic error value to obtain a differential error value, combining the differential error value with a power function of the dynamic error value to construct a non-singular terminal sliding mode surface; setting a stability parameter of the system to obtain a negative feedback gain, calculating a derivative of the non-singular terminal sliding mode surface, multiplying the corresponding derivative by the negative feedback gain to construct a reaching law, and calculating a ratio of the reaching law to the input gain to obtain an initial control value; Using the initial control value as a basis for obtaining a system state sequence, calculating the probability distribution of the system state sequence to obtain a state probability, inputting the state probability into a recursive minimum entropy calculation unit to calculate a system entropy value, obtaining a minimum entropy value through recursive operation, and calculating a negative exponent of the difference between the system entropy value and the minimum entropy value to obtain a correction coefficient; Multiplying the correction coefficient and the initial control value to obtain a first algorithm component, constructing a power function and a sign function of the non-singular terminal sliding mode surface, and combining them to obtain a second algorithm component; Set the convergence gain parameter of the supercoil algorithm, construct a supercoil state equation containing the first algorithm component and the second algorithm component, perform an integral operation on the supercoil state equation to obtain an auxiliary variable of the supercoil algorithm, and combine the auxiliary variable with the first algorithm component and the second algorithm component to output a power adjustment signal.

8. A supercapacitor-based grid frequency modulation power energy coordinated control system, used to implement the method according to any one of claims 1 to 7, characterized in that: include: The first unit is used to perform time-frequency analysis on the collected power grid frequency signal using a sliding Fourier transform, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the moving entropy value of the frequency change matrix, and obtain a frequency dynamic correlation vector; perform recursive principal component decomposition on the frequency dynamic correlation vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount based on the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input them into the Kalman filter to calculate the electrical parameter values, and determine the upper and lower power thresholds based on the electrical parameter values, which together with the frequency modulation power compensation amount form power control data; The second unit is used to determine the power allocation sequence based on the power control data through nonlinear programming calculation, and divide the power allocation sequence into a fast response section, a dynamic transition section, and a steady-state maintenance section according to a preset interval segmentation threshold based on the power change rate of the power allocation sequence; based on the fast response section, establish an augmented Lagrangian equation to solve the power optimization trajectory and output a fast adjustment control value; based on the dynamic transition section, perform a recursive least squares operation to obtain system parameter estimates and update the power control value; Based on the steady-state maintenance segment, a Lyapunov function is constructed to solve the energy balance deviation value and calculate the compensation control value; a piecewise continuous function operation is performed on the fast adjustment control value, power control value and compensation control value to output the power control instruction; The third unit is used to input the power control command into the disturbance observer, calculate the unmodeled dynamic and external disturbance terms, determine the dynamic error value, perform generalized differential operation on the dynamic error value, construct a non-singular terminal equation, output the initial control value, input the initial control value into the recursive minimum entropy calculation unit to obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power adjustment signal.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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