Power grid frequency modulation power energy coordination control method and system based on supercapacitor

Abstract

The invention provides a power grid frequency modulation power energy coordination control method and system based on a super capacitor, and relates to the technical field of power grid frequency modulation, and the method comprises the steps: carrying out the time-frequency analysis of a collected power grid frequency signal, obtaining a frequency disturbance characteristic value, and determining power control data through combining with an electrical parameter value of a super capacitor group; and performing nonlinear programming calculation based on the power control data to obtain a power distribution sequence, dividing the power distribution sequence into a quick response section, a dynamic transition section and a steady state maintenance section according to a preset threshold value, and solving a control value by adopting an augmented Lagrange equation, recursive least square operation and a Lyapunov function respectively. Obtaining a power control instruction; and inputting a power control instruction into the disturbance observer, calculating a dynamic error value, constructing a nonsingular terminal equation, and outputting a power regulation signal in combination with recursive minimum entropy calculation and a superhelix 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 energy of power grid frequency modulation based on supercapacitors. Background Art

[0002] As the scale of grid-connected renewable energy power generation continues to expand, grid frequency fluctuations intensify. Traditional frequency modulation methods have slow response speeds and low regulation accuracy, making it difficult to meet grid frequency modulation needs. Supercapacitors have the advantages of high power density, high charge and discharge efficiency, and long cycle life, and have good application prospects in the field of grid frequency modulation. At present, supercapacitors participate in grid frequency modulation mainly using a proportional regulation strategy, that is, outputting frequency modulation power in proportion to 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 effects.

[0003] However, the existing supercapacitor frequency regulation control methods have several major problems. The lack of in-depth analysis of the frequency disturbance characteristics of the power grid makes it difficult to accurately identify the frequency change trend and disturbance law, which affects the targetedness of the frequency regulation strategy; a complete power energy coordination mechanism has not been established, and it is difficult to achieve the energy balance of the supercapacitor group while ensuring the frequency regulation effect; the control algorithm is not robust enough, and the frequency regulation performance is easily degraded when facing system parameter changes and external disturbances, affecting the stability and reliability of the control system.

[0004] In summary, it is urgent to solve the problems existing in the existing supercapacitor frequency modulation control and provide a power grid frequency modulation method based on time-frequency analysis and multi-stage coordinated control. The frequency disturbance characteristics are accurately identified by sliding Fourier transform and recursive principal component decomposition, and the segmented control strategy is adopted to achieve the coordination of power rapid response and energy balance, and the robustness of the control system is improved by combining disturbance observation and superhelical algorithm. The present invention can solve the problems in the prior art. Summary of the invention

[0005] The embodiment of the present invention provides a method and system for coordinated control of power 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] Use sliding Fourier transform 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 mobile entropy value of the frequency change matrix, and obtain the frequency dynamic association vector; recursively perform principal component decomposition on the frequency dynamic association vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount according to the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input the Kalman filter to calculate the electrical parameter value, determine the upper and lower power thresholds according to the electrical parameter value, and form power control data with the frequency modulation power compensation amount;

[0009] Based on the power control data, the power allocation sequence is determined through nonlinear programming calculation. 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 the system parameter estimation value 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, and a power control instruction is output;

[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, an initial control value is output, the initial control value is input into the recursive minimum entropy calculation unit, a correction coefficient is obtained, a superhelical algorithm operation is performed on the correction coefficient and the initial control value, and a 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 mobile entropy value of the frequency change matrix, and obtain the frequency dynamic correlation vector including:

[0013] The collected power grid frequency signal is divided into multiple time windows according to a preset time interval, and the power grid frequency signals of adjacent time windows are processed by smooth transition using a cosine function to obtain a smoothed frequency signal; wavelet decomposition is performed on the smoothed frequency signal to obtain hierarchical wavelet coefficients of multiple decomposition levels, and the energy value of each hierarchical wavelet coefficient is calculated, and the energy change rate of adjacent time windows is calculated based on the energy value; when the energy change rate is greater than a preset energy change threshold, the time window length is shortened according to a preset ratio, and the execution is repeated until the energy change rate is less than the energy change threshold, so as to obtain the optimal time window length;

[0014] Performing a sliding Fourier transform on the smoothed frequency signal based on the optimal time window length to obtain the spectral components of the frequency signal, and extracting the 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 series 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 feature matrix under each preset scale parameter; identify the mutation point in the frequency feature 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 a frequency dynamic association 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 according to the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input the Kalman filter to calculate the electrical parameter value, determine the upper and lower power thresholds according to the electrical parameter value, and form the power control data with the frequency modulation power compensation amount, including:

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

[0020] Based on a preset number of data segments, determine the first principal component eigenvalue sequence, establish an autoregressive prediction model of a preset order, use the least squares iterative algorithm to optimize the coefficients of the autoregressive prediction model, and when the difference between the coefficients calculated by two adjacent iterative calculations is less than a preset convergence threshold, determine the current iterative result 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 prediction 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, based on an exponential weighting method, the prediction deviation is used as a correction amount to update the coefficient of the autoregressive prediction model, and the first principal component eigenvalue is updated as the 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 the preset sampling period, the port voltage and charge and 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 and discharge current; the voltage and current observation data of the preset number of groups are differenced with 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 the 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 the charge and discharge current are differenced with the predicted value of the state space equation, and the covariance matrix of the process noise and the observation noise is dynamically adjusted by the 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 fast adjustment control values ​​including:

[0029] Calculate the sum of squares of deviations between the power optimization trajectory and the target power value to generate a power tracking error term, calculate the sum of squares of power changes at adjacent sampling points of the power optimization trajectory to generate a change rate constraint term, and combine 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 according to the operating parameters, determining a response time constraint according to a time constant of the operating parameters, and combining the power constraint and the response time constraint to form a dynamic constraint model;

[0031] Respectively multiplying the power constraint with the first Lagrangian multiplier to obtain a first multiplication result, multiplying the response time constraint with 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, constructing 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, iteratively solving the augmented Lagrangian function, generating the power optimization trajectory, calculating the convergence speed 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 including:

[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 form a transition section state vector, the transition section power adjustment amount is used as a transition section control input, and a discrete time-varying state space model is constructed;

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

[0039] The product of the parameter matrix to be estimated and the regression vector is used to construct a recursive prediction sequence, the real-time operation status is collected to obtain the current state observation value, and the difference between the current state observation value and the recursive prediction sequence is calculated to obtain the estimation error; the product of the transpose of the regression vector and the recursive prediction sequence is calculated to obtain a gain matrix, and the product of the gain matrix and the estimation error is used as the 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 value with the current transition state vector to obtain a first state prediction term, determining an expected 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 expected 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 a 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] In 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, and the rate of change of the energy integral value is calculated at the same time, and 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] Calculate the second-order derivative of the energy integral value, and construct a maintenance segment state matrix according to 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; construct a maintenance segment input matrix based on the response coefficient of the rate of change of the energy integral value to the system input; calculate the maintenance segment power adjustment amount as the 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 to the second matrix product to construct a state space equation;

[0048] The transposed matrix of the maintenance segment state matrix is ​​multiplied by the matrix to be determined, the product of the matrix to be determined and the maintenance segment state matrix is ​​added, and then the unit matrix is ​​added to form a Lyapunov stability equation, and the Lyapunov stability equation is solved to obtain the matrix to be determined as a symmetric positive definite matrix; a positive definite weight matrix is ​​determined according to the value range of the maintenance segment control input;

[0049] The state quadratic term is obtained by multiplying the state vector of the maintenance segment by a symmetric positive definite matrix on the left and then multiplying it by the transpose of the state vector of the maintenance segment on the right; the control integral term is obtained by multiplying the control input of the maintenance segment by a positive definite weight matrix on the left and then multiplying it by the transpose of the control input of the maintenance segment on the right; and the 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 the 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, and the super-helical algorithm operation is performed on the correction coefficient and the initial control value. The output power regulation 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 the output power of the system minus the expected power trajectory is added to the disturbance estimate to obtain a dynamic error value;

[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 surface; setting a stability parameter of the system to obtain a negative feedback gain, calculating a derivative of the non-singular terminal sliding 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] The initial control value is used as a basis for obtaining a system state sequence, the probability distribution of the system state sequence is calculated to obtain a state probability, the state probability is input into a recursive minimum entropy calculation unit, a system entropy value is calculated, a minimum entropy value is obtained by recursive operation, and a negative exponent of a difference between the system entropy value and the minimum entropy value is calculated 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] The convergence gain parameter of the superhelix algorithm is set, a superhelix state equation including the first algorithm component and the second algorithm component is constructed, an integral operation is performed on the superhelix state equation to obtain an auxiliary variable of the superhelix algorithm, and the auxiliary variable is combined 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 by using sliding Fourier transform, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the mobile entropy value of the frequency change matrix, and obtain the frequency dynamic association vector; recursively decompose the frequency dynamic association vector into principal components, output the frequency disturbance characteristic value in real time, and calculate the frequency modulation power compensation amount according to the frequency disturbance characteristic value; collect the voltage and current signals of the supercapacitor group, input the Kalman filter to calculate the electrical parameter value, determine the upper and lower power thresholds according to the electrical parameter value, and form the power control data with the frequency modulation power compensation amount;

[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; based on the fast response section, establish an augmented Lagrangian equation, 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 a system parameter estimation value and update the power control value; based on the steady-state maintenance section, construct a Lyapunov function, 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, obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power regulation 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 aforementioned method is implemented.

[0073] In an embodiment of the present invention, frequency disturbance characteristics are accurately extracted by methods such as sliding Fourier transform and recursive principal component decomposition, and accurate power compensation is performed in combination with the power characteristics of supercapacitors, thereby effectively suppressing grid frequency fluctuations and improving grid stability; based on the electrical parameters and frequency disturbance characteristics of supercapacitors, 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 supercapacitors; through means such as disturbance observers and recursive minimum entropy calculations, 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 ensured. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It 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;

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

[0076] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the 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 creative work are within the scope of protection of the present invention.

[0077] The technical solution of the present invention is described in detail with specific embodiments below. 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. 1 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 sliding Fourier transform, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the mobile entropy value of the frequency change matrix, and obtain the frequency dynamic association vector; perform recursive principal component decomposition on the frequency dynamic association vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount according to 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, determine the upper and lower power thresholds according to the electrical parameter values, and form power control data with the frequency modulation power compensation amount;

[0080] In this embodiment, a sliding Fourier transform is used for time-frequency analysis, a frequency change matrix is ​​constructed, and a moving entropy value is calculated, so that a frequency dynamic correlation vector can be dynamically generated to accurately capture the changing characteristics of the power grid frequency; the frequency disturbance eigenvalues ​​are extracted in real time through recursive principal component decomposition, providing a fast and reliable frequency disturbance analysis and improving the response efficiency of frequency modulation control; the frequency modulation power compensation amount is quickly calculated according to the frequency disturbance eigenvalues ​​to ensure the timeliness and accuracy of power grid frequency regulation; a Kalman filter is used to calculate the voltage and current signals of the supercapacitor group in real time, and key electrical parameters are dynamically obtained to improve the monitoring accuracy of the capacitor status; the frequency modulation power compensation amount and the electrical parameter values ​​are combined to dynamically set the upper and lower power thresholds to realize intelligent power control and improve the robustness and operation stability of the frequency modulation system.

[0081] S102. Based on the power control data, determine the power allocation sequence through nonlinear programming calculation, and based on the power change rate of the power allocation sequence, divide it 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, establish the augmented Lagrangian equation, solve the power optimization trajectory, and output the fast adjustment control value; based on the dynamic transition section, perform recursive least squares operation, obtain the system parameter estimation value, and update the power control value; based on the steady-state maintenance section, construct the Lyapunov function, solve the energy balance deviation value, and calculate the compensation control value; perform piecewise continuous function operation on the fast adjustment control value, the power control value and the compensation control value, and output the power control instruction;

[0082] Based on the power control data, the power allocation sequence is calculated by nonlinear programming. This sequence determines the power demand of the system at different time points and converts it into executable control commands. During the calculation process, the system constraints need to be considered to ensure that the obtained allocation sequence meets the system operation 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 sections: fast response section, dynamic transition section and steady-state maintenance section;

[0084] In the fast response section, the augmented Lagrangian equation is established to solve the power optimization trajectory. The augmented Lagrangian method is a mathematical method for optimizing problems by introducing Lagrangian multipliers and combining them with system constraints. The solution will generate a fast adjustment control value to ensure that the power can reach the set target in the shortest time.

[0085] In the dynamic transition stage, the recursive least squares method is used to estimate the system parameters. This method optimizes the power control strategy by continuously updating the estimated values ​​to ensure the accuracy and stability of the power regulation process. The recursive least squares method can gradually improve the estimated values ​​through the real-time data of the system, thereby providing more accurate parameter support for the next step of power adjustment.

[0086] In the steady-state maintenance stage, a Lyapunov function is constructed to analyze the stability of the system and solve the energy balance deviation value. The Lyapunov function is used to determine whether the system can operate in a stable state, and can help calculate the energy balance deviation of the system, so as to determine whether compensation control is needed. By calculating the compensation control value, the steady-state operation of the system can be ensured without excessive fluctuations.

[0087] Finally, the fast adjustment control value, power control value and compensation control value are operated as piecewise continuous functions. This process combines the control signals of different sections to form a smooth control curve. In this way, the continuity and stability of power regulation are ensured. Finally, the output power control command will be sent to the system to ensure that the system runs efficiently and stably 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 the control accuracy; in the steady-state maintenance segment, the Lyapunov function is used to calculate the energy balance deviation and compensate the control to ensure the long-term stability and energy balance of the system; through the piecewise continuous function operation, the control results of each stage are organically combined to ensure the continuity and smoothness of the power control command 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 regulation 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 uncertainty; by performing generalized differential operations on the dynamic error value and combining it with the non-singular terminal equation, the initial control value can be quickly generated, and corrected through the recursive minimum entropy calculation unit to ensure control accuracy; the initial control value is further optimized through the superhelix algorithm, which 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 allows 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 implementation, 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 mobile entropy value of the frequency change matrix, and obtain the frequency dynamic correlation vector including:

[0092] The collected power grid frequency signal is divided into multiple time windows according to a preset time interval, and the power grid frequency signals of adjacent time windows are processed by smooth transition using a cosine function to obtain a smoothed frequency signal; wavelet decomposition is performed on the smoothed frequency signal to obtain hierarchical wavelet coefficients of multiple decomposition levels, and the energy value of each hierarchical wavelet coefficient is calculated, and the energy change rate of adjacent time windows is calculated based on the energy value; when the energy change rate is greater than a preset energy change threshold, the time window length is shortened according to a preset ratio, and the execution is repeated until the energy change rate is less than the energy change threshold, so as to obtain the optimal time window length;

[0093] Performing a sliding Fourier transform on the smoothed frequency signal based on the optimal time window length to obtain the spectral components of the frequency signal, and extracting the 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 series 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 feature matrix under each preset scale parameter; identify the mutation point in the frequency feature 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 a frequency dynamic association vector.

[0096] The industrial frequency band specifically refers to a specific frequency range around the industrial frequency (usually 50 Hz or 60 Hz), which is mainly used for the analysis and processing of power system signals. This frequency band usually contains the main frequency components related to the industrial frequency in the power grid, which is used to reflect the characteristics of the power system operation, such as voltage, load and frequency fluctuations, and is an important analysis interval for power grid signal monitoring and control.

[0097] In a specific implementation, the power grid frequency signal is collected and preprocessed. First, the frequency signal of the power grid is collected by a sensor and stored digitally. In order to eliminate noise and interference, the collected original frequency signal is preprocessed, for example, a low-pass filter is used to remove high-frequency noise, or a Kalman filter is used for smoothing. An initial time window length is set, for example, 0.1 seconds, and the collected power 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 and select the optimal time window length for the smoothed frequency signal. 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 rate 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 the 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, 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. Perform a sliding Fourier transform on the smoothed grid frequency signal using the determined optimal time window length. In each time window, calculate the spectral components of the frequency signal, and extract the amplitude and phase information of the power frequency band (for example, 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 two features, the amplitude and phase 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 change matrix. In order to remove noise and interference in the frequency change matrix, first calculate the autocorrelation function of the frequency change matrix. Then, construct an equivalued diagonal matrix based on the autocorrelation function, where the diagonal elements are the values ​​of the autocorrelation function and the non-diagonal elements are zero. Perform eigenvalue decomposition on the equivalued diagonal matrix and extract the eigenvector corresponding to the maximum eigenvalue. Use the eigenvector to perform linear combination on the original frequency change matrix and reconstruct the frequency feature matrix after denoising.

[0101] Calculate the entropy of the frequency feature matrix and make corrections. Select multiple preset scale parameters, such as setting 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, such as by calculating the difference between the feature values ​​of adjacent time windows to determine whether there is a mutation. Determine the mutation interval and determine the non-mutation interval accordingly. 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 volatility variance of the modified entropy sequence and determine the weight coefficient. Calculate the volatility variance of the modified entropy sequence at each preset scale parameter. The volatility variance can be defined as the standard deviation of the entropy sequence. Determine the weight coefficient corresponding to each scale parameter based on the inverse of the volatility variance. For example, if the volatility variance of the entropy sequence under a certain scale parameter is small, then the corresponding weight coefficient is large.

[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 combined to finally obtain the frequency dynamic correlation vector. This vector reflects the dynamic correlation characteristics of the power grid frequency signal at different time scales.

[0104] Exemplarily, 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. Perform a sliding Fourier transform on the smoothed frequency signal, extract the amplitude and phase information of the power frequency band, and construct a frequency change matrix with 20 rows and 2 columns. After denoising the matrix, calculate the conditional entropy and sample entropy with scale parameters of 2 to 5 to obtain 4 entropy value sequences. Calculate the fluctuation variance of each entropy value sequence, and determine the weight coefficient according to the inverse. Finally, the 4 entropy value sequences are weighted and combined with the corresponding weight coefficients to obtain the frequency dynamic association 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 denoising and entropy 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 calculation, the dynamic correlation characteristics of the grid frequency can be quickly extracted, thereby improving the analysis efficiency.

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

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

[0108] Based on a preset number of data segments, determine the first principal component eigenvalue sequence, establish an autoregressive prediction model of a preset order, use the least squares iterative algorithm to optimize the coefficients of the autoregressive prediction model, and when the difference between the coefficients calculated by two adjacent iterative calculations is less than a preset convergence threshold, determine the current iterative result 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 prediction 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, based on an exponential weighting method, the prediction deviation is used as a correction amount to update the coefficient of the autoregressive prediction model, and the first principal component eigenvalue is updated as the 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 the preset sampling period, the port voltage and charge and 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 and discharge current; the voltage and current observation data of the preset number of groups are differenced with 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 the 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 the charge and discharge current are differenced with the predicted value of the state space equation, and the covariance matrix of the process noise and the observation noise is dynamically adjusted by the 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 a specific implementation, in order to achieve accurate control of supercapacitor power, this implementation proposes a supercapacitor power control method based on frequency dynamic correlation vector and Kalman filtering. The method outputs frequency disturbance characteristic values ​​in real time, calculates frequency modulation power compensation, and determines power upper and lower limit thresholds in combination with the electrical parameter values ​​of the supercapacitor, and finally forms power control data.

[0116] First, the frequency dynamic correlation vector related to the working state of the supercapacitor is collected. Assuming that data is collected every 0.1 second, 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 of which contains 100 data points.

[0117] Perform principal component decomposition on each data segment and extract the first principal component eigenvalue with the largest variance contribution rate. 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 the first principal component eigenvalue sequence of 10 data segments.

[0118] Using the first principal component eigenvalue sequence of these 10 data segments, a second-order autoregressive prediction model is established. The coefficients of the autoregressive prediction model are optimized and calculated using the least squares iterative algorithm. The convergence threshold is set to 0.001. When the difference in coefficients calculated from two adjacent iterative calculations is less than 0.001, the current iteration result is determined as the optimal prediction coefficient. Assume that the optimal prediction coefficients finally obtained are 0.8 and 0.1.

[0119] Substitute the optimal prediction coefficients 0.8 and 0.1 into the autoregressive prediction model and calculate the prediction result of the first principal component eigenvalue of the next data segment (i.e., the 11th data segment). Assume that the prediction 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. Compare the predicted result of the first principal component eigenvalue 2.7 with the corresponding actual result of the first principal component eigenvalue 2.8, and obtain a prediction deviation of 0.1.

[0120] The deviation threshold is set to 0.05. Since the predicted deviation 0.1 is greater than the deviation threshold 0.05, the predicted deviation 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 0.55.

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

[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 (e.g., 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 the sliding window method to construct a Kalman filter. The state-space equation is input into the Kalman filter to calculate the equivalent series resistance (e.g., 0.01 ohms), equivalent series capacitance (e.g., 100 farads), and remaining available capacity (e.g., 80%) of the supercapacitor group.

[0123] A power constraint equation is established, and the equivalent series resistance of 0.01 ohm, the equivalent series capacitance of 100 farads, the remaining available capacity of 80%, and the housing temperature (e.g., 25 degrees Celsius) are substituted into the power constraint equation to solve the power upper and lower limit thresholds. Assume that the power lower limit threshold is 10 kilowatts and the power upper limit threshold is 20 kilowatts.

[0124] Finally, the power upper and lower limit 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 command value and limited to the power upper and lower limit 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 the 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 implementation, based on the fast response segment, an augmented Lagrangian equation is established to solve the power optimization trajectory, and outputting a fast adjustment control value includes:

[0127] Calculate the sum of squares of deviations between the power optimization trajectory and the target power value to generate a power tracking error term, calculate the sum of squares of power changes at adjacent sampling points of the power optimization trajectory to generate a change rate constraint term, and combine 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 according to the operating parameters, determining a response time constraint according to a time constant of the operating parameters, and combining the power constraint and the response time constraint to form a dynamic constraint model;

[0129] Respectively multiplying the power constraint with the first Lagrangian multiplier to obtain a first multiplication result, multiplying the response time constraint with 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, constructing 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, iteratively solving the augmented Lagrangian function, generating the power optimization trajectory, calculating the convergence speed 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 a specific implementation, first, the sum of squares of the difference between the power optimization trajectory and the target power value is calculated to generate an index for measuring the power tracking error. At the same time, the sum of squares of the power changes between adjacent sampling points of the power optimization trajectory is calculated to generate an index for measuring the power change rate. The power tracking error index and the power change rate index are combined to construct a composite optimization objective function, the goal of which is to minimize 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, collect the operating parameters of the system, such as load characteristics, ambient temperature, etc. Determine the upper and lower thresholds of the power constraint based on these operating parameters. For example, the power value must be between 0 and 15. At the same time, determine the response time constraint based on the time constant of the operating parameters. For example, the power change cannot be too fast, and the power change between adjacent sampling points cannot exceed 2. Combine the power constraint and the response time constraint to form a dynamic constraint model.

[0135] Then, the power constraint is multiplied by the first Lagrangian multiplier to obtain a first product result. The response time constraint is multiplied by the second Lagrangian multiplier to obtain a second product result. The first product result, the second product result and the composite optimization objective function are combined to construct an augmented Lagrangian function. The constraint violation degree is calculated, and the first Lagrangian multiplier and the second Lagrangian multiplier are updated according to 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. Then the value of the augmented Lagrangian function is 16.

[0137] Afterwards, the alternating direction multiplier method is applied to iteratively solve the augmented Lagrangian function to generate the power optimization trajectory. The convergence speed of the power optimization trajectory is calculated, and the adaptive penalty factor is determined according to the convergence speed.

[0138] Finally, the deviation between the power optimization trajectory and the target power value is calculated, and the deviation is multiplied by the proportional gain to obtain the proportional control amount. The rate of change of the power optimization trajectory is calculated, and the rate of change is 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.

[0139] For example, assuming the target power value 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; it can adapt to different operating parameters and constraints, thereby enhancing the robustness of power regulation.

[0141] In an optional implementation, based on the dynamic transition section, a recursive least squares operation is performed to obtain a system parameter estimation value, 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 form a transition section state vector, the transition section power adjustment amount is used as a transition section control input, and a discrete time-varying state space model is constructed;

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

[0145] The product of the parameter matrix to be estimated and the regression vector is used to construct a recursive prediction sequence, the real-time operation status is collected to obtain the current state observation value, and the difference between the current state observation value and the recursive prediction sequence is calculated to obtain the estimation error; the product of the transpose of the regression vector and the recursive prediction sequence is calculated to obtain a gain matrix, and the product of the gain matrix and the estimation error is used as the 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 value with the current transition state vector to obtain a first state prediction term, determining an expected 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 expected 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 a negative value of the power adjustment coefficient to obtain an updated power control value.

[0149] In a specific implementation, first, a continuous sampling sequence of real-time power values ​​in the dynamic transition section is collected, for example, a power value is collected every 0.1 seconds to obtain a power value sequence, for example: [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 change trend curve is constructed by cubic spline interpolation. This curve describes the overall trend of power change and can be used to predict future power changes. For example, a function describing the power change trend can be obtained by cubic spline interpolation.

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

[0153] The first-order differential coefficient of the real-time power value and the first-order differential coefficient of the power change amount are combined into a parameter matrix to be estimated. The first-order differential coefficient represents the rate of change of the power value or the power change amount at adjacent moments. For example, the first-order differential coefficient of the power value can be obtained 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] The product of the estimated parameter matrix and the regression vector is used to construct a recursive prediction sequence. This sequence predicts the future power value and power change. The real-time operating status is collected to obtain the current state observation value. The difference between the current state observation value 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] The transpose of the regression vector and the product of the recursive prediction sequence are calculated to obtain the gain matrix. The product of the gain matrix and the estimation error is used as the parameter correction. The parameter matrix to be estimated and the parameter correction are added to obtain the updated parameter estimate.

[0156] According to 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 in combination with the transition control input, the expected state value is determined. The expected state value is subtracted from the first state prediction term to obtain a state compensation value.

[0157] Calculate the product of the transpose of the input matrix estimate value and the input matrix estimate value to obtain the matrix coefficient. Calculate the product of the transpose of the input matrix estimate value and 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 and improve the robustness and reliability of the system; the recursive least squares algorithm is used, which has a small amount of calculation and is easy to implement, which can simplify the complexity of the power control system and reduce the system cost.

[0159] In an optional implementation, 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] In 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, and the rate of change of the energy integral value is calculated at the same time, and 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] Calculate the second-order derivative of the energy integral value, and construct a maintenance segment state matrix according to 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; construct a maintenance segment input matrix based on the response coefficient of the rate of change of the energy integral value to the system input; calculate the maintenance segment power adjustment amount as the 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 to the second matrix product to construct a state space equation;

[0163] The transposed matrix of the maintenance segment state matrix is ​​multiplied by the matrix to be determined, the product of the matrix to be determined and the maintenance segment state matrix is ​​added, and then the unit matrix is ​​added to form a Lyapunov stability equation, and the Lyapunov stability equation is solved to obtain the matrix to be determined as a symmetric positive definite matrix; a positive definite weight matrix is ​​determined according to the value range of the maintenance segment control input;

[0164] The state quadratic term is obtained by multiplying the state vector of the maintenance segment by a symmetric positive definite matrix on the left and then multiplying it by the transpose of the state vector of the maintenance segment on the right; the control integral term is obtained by multiplying the control input of the maintenance segment by a positive definite weight matrix on the left and then multiplying it by the transpose of the control input of the maintenance segment on the right; and the 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 the 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 a matrix or vector on the left side of another matrix or vector for multiplication in matrix or vector operations. Left multiplication is usually used to express linear transformation or some left-side operation on data.

[0169] The right multiplication specifically refers to placing a matrix or vector on the right side of another matrix or vector for multiplication in matrix or vector operations. The right multiplication is opposite to the left multiplication and is used to express the right-side operation.

[0170] The negative definiteness specifically refers to the property that the output value of a matrix or function is always less than zero under all input conditions. This means that the corresponding system or function has a decreasing or concave characteristic, which is usually used to analyze stability or determine whether a state has a specific trend.

[0171] In a specific implementation, first, a time window is set, for example, 1 second. Within the time window, the difference between the real-time power value and the reference power value is continuously calculated. These differences are accumulated to obtain the energy integral value. At the same time, the change speed of the energy integral value, that is, the change rate of the energy integral value, is calculated. The energy integral value and its change rate are respectively used as the first state quantity and the second state quantity to form a two-dimensional vector, which is called 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 of 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] Then, the maintenance segment state vector is multiplied by the maintenance segment state matrix to obtain a new vector, called the first matrix product. The maintenance segment control input is multiplied by the maintenance segment input matrix to obtain the second matrix product. The first matrix product and the second matrix product are added together to construct the state space equation.

[0174] In order to design a compensation controller, a Lyapunov function needs to be constructed. First, a symmetric positive definite matrix is ​​obtained by solving a specific matrix equation, namely the Lyapunov stability equation. The form of this equation is: the transposed matrix of the maintenance segment state matrix multiplied by the matrix to be determined, plus the product of the matrix to be determined and the maintenance segment state matrix, plus the identity matrix, equals the zero matrix. Solve this equation to obtain the matrix to be determined. According to the range of the control input of the maintenance segment, a positive definite weight matrix is ​​determined. For example, if the range of the control input is -1 to 1, the weight matrix can be set to the identity matrix.

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

[0176] The time derivative of the Lyapunov function is obtained to obtain the derivative equation. Based on the optimal control theory, the feedback control law is constructed. The feedback control law is substituted into the derivative equation, and the stability of the system is verified by judging whether the result is negative. If the result is always 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 input matrix of the maintenance segment. 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 the optimal control theory, the stability of the system is ensured, and the system can maintain stable operation even in the presence of external interference; by real-time calculation of the energy integral value, rate of change and deviation, and combining the compensation control strategy, precise control of the 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 implementation, a power control instruction is input into a disturbance observer, unmodeled dynamics 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, a correction coefficient is obtained, 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 the output power of the system minus the expected power trajectory is added to the disturbance estimate to obtain a dynamic error value;

[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 surface; setting a stability parameter of the system to obtain a negative feedback gain, calculating a derivative of the non-singular terminal sliding 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] The initial control value is used as a basis for obtaining a system state sequence, the probability distribution of the system state sequence is calculated to obtain a state probability, the state probability is input into a recursive minimum entropy calculation unit, a system entropy value is calculated, a minimum entropy value is obtained by recursive operation, and a negative exponent of a difference between the system entropy value and the minimum entropy value is calculated 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] The convergence gain parameter of the superhelix algorithm is set, a superhelix state equation including the first algorithm component and the second algorithm component is constructed, an integral operation is performed on the superhelix state equation to obtain an auxiliary variable of the superhelix algorithm, and the auxiliary variable is combined with the first algorithm component and the second algorithm component to output a power adjustment signal.

[0186] The unmodeled dynamics specifically refer to the dynamic characteristics of the system that are not included in the model due to simplification or neglect of certain complex factors during the modeling process. These characteristics may come from high-frequency oscillations, small nonlinearities, unconsidered environmental effects, or unexpressed system dynamic behaviors. Unmodeled dynamics are usually the source of the difference between the actual behavior of the system and the model prediction results, and their impact needs to be reduced through estimation and compensation.

[0187] The non-singular terminal sliding surface specifically refers to a mathematical design method for sliding mode control in a control system. Through a specific construction method, it ensures that the control system achieves rapid convergence on the sliding surface and reaches a stable state. Its non-singularity is reflected in the avoidance of singularity problems in traditional sliding methods during the sliding control process, and the terminal characteristics are reflected in the control system being able to reach the sliding surface within a limited time and eventually tend to a stable state. This sliding surface design helps to improve the accuracy and robustness of system control.

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

[0189] First, the power control command and the system output power are input into a disturbance observer. The disturbance observer contains the observer gain and the auxiliary observation quantity, and the observed output is obtained by running the disturbance observer state equation. Assume that the power control command is 10kW, the system output power is 9.8kW, the observer gain is set to 0.5, and the initial value of the auxiliary observation quantity is 0. By running the disturbance observer state equation, the observed output is 0.1kW.

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

[0191] Then, generalized differential operation is performed 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 -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 surface. Assuming the power function exponent is 1.5, the non-singular terminal sliding surface is -0.15kW 1.5+(-0.01kW / s). Set the stability parameters of the system, for example, the negative feedback gain is 0.8, and calculate the derivative of the non-singular terminal sliding surface. Multiply the 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] The initial control value is used as the basis for obtaining the system state sequence, and the probability distribution of the system state sequence is calculated to obtain the state probability. For example, by statistically analyzing historical data, the state probability is 0.9. The state probability is input into the recursive minimum entropy calculation unit to calculate the system entropy value. The minimum entropy value is obtained by recursive operation. For example, the system entropy value is calculated to be 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 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 of the superhelical algorithm, for example, the convergence gain is 0.5. Construct a superhelical state equation including the first algorithm component and the second algorithm component. Integrate the superhelical state equation to obtain the auxiliary variable of the superhelical algorithm. Combine the auxiliary variable with the first algorithm component and the second algorithm component to output a power adjustment signal. For example, assuming that 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 power 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 comprises:

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

[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; based on the fast response section, establish an augmented Lagrangian equation, 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 a system parameter estimation value and update the power control value; based on the steady-state maintenance section, construct a Lyapunov function, 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, obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power regulation 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 aforementioned method 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 power and energy based on supercapacitors, characterized in that: include: Use sliding Fourier transform 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 mobile entropy value of the frequency change matrix, and obtain the frequency dynamic association vector; recursively perform principal component decomposition on the frequency dynamic association vector, output the frequency disturbance eigenvalue in real time, and calculate the frequency modulation power compensation amount according to the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input the Kalman filter to calculate the electrical parameter value, determine the upper and lower power thresholds according to the electrical parameter value, and form power control data with the frequency modulation power compensation amount; Based on the power control data, the power allocation sequence is determined through nonlinear programming calculation. 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, the 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 the system parameter estimation value 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, the power control value and the 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, an initial control value is output, the initial control value is input into the recursive minimum entropy calculation unit, a correction coefficient is obtained, a superhelical algorithm operation is performed on the correction coefficient and the initial control value, and a 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 mobile entropy value of the frequency change matrix, and obtain the frequency dynamic correlation vector including: The collected power grid frequency signal is divided into multiple time windows according to a preset time interval, and the power grid frequency signals of adjacent time windows are processed by smooth transition using a cosine function to obtain a smoothed frequency signal; wavelet decomposition is performed on the smoothed frequency signal to obtain hierarchical wavelet coefficients of multiple decomposition levels, and the energy value of each hierarchical wavelet coefficient is calculated, and the energy change rate of adjacent time windows is calculated based on the energy value; when the energy change rate is greater than a preset energy change threshold, the time window length is shortened according to a preset ratio, and the execution is repeated until the energy change rate is less than the energy change threshold, so as to obtain the optimal time window length; Performing a sliding Fourier transform on the smoothed frequency signal based on the optimal time window length to obtain the spectral components of the frequency signal, and extracting the 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 series 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 feature matrix under each preset scale parameter; identify the mutation point in the frequency feature 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 a frequency dynamic association 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 according to the frequency disturbance eigenvalue; collect the voltage and current signals of the supercapacitor group, input the Kalman filter to calculate the electrical parameter value, determine the upper and lower power thresholds according to the electrical parameter value, and form the power control data with the frequency modulation power compensation amount, including: The frequency dynamic correlation vector is divided into multiple data segments according to the preset number of sampling points, and principal component decomposition is performed on each data segment to extract the first principal component eigenvalue with the largest variance contribution rate; Based on a preset number of data segments, determine the first principal component eigenvalue sequence, establish an autoregressive prediction model of a preset order, use the least squares iterative algorithm to optimize the coefficients of the autoregressive prediction model, and when the difference between the coefficients calculated by two adjacent iterative calculations is less than a preset convergence threshold, determine the current iterative result 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 prediction 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, based on an exponential weighting method, the prediction deviation is used as a correction amount to update the coefficient of the autoregressive prediction model, and the first principal component eigenvalue is updated as the frequency disturbance eigenvalue; the frequency disturbance eigenvalue is multiplied by a preset proportional coefficient to obtain a frequency modulation power compensation amount; According to the preset sampling period, the port voltage and charge and 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 and discharge current; the voltage and current observation data of the preset number of groups are differenced with 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 the 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 the charge and discharge current are differenced with the predicted value of the state space equation, and the covariance matrix of the process noise and the observation noise is dynamically adjusted by the 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, characterized in that: Based on the fast response segment, the augmented Lagrangian equation is established to solve the power optimization trajectory and output fast adjustment control values ​​including: Calculate the sum of squares of deviations between the power optimization trajectory and the target power value to generate a power tracking error term, calculate the sum of squares of power changes at adjacent sampling points of the power optimization trajectory to generate a change rate constraint term, and combine 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 according to the operating parameters, determining a response time constraint according to a time constant of the operating parameters, and combining the power constraint and the response time constraint to form a dynamic constraint model; Respectively multiplying the power constraint with the first Lagrangian multiplier to obtain a first multiplication result, multiplying the response time constraint with 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, constructing 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, iteratively solving the augmented Lagrangian function, generating the power optimization trajectory, calculating the convergence speed 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, characterized in that: 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 including: 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 form a transition section state vector, the transition section power adjustment amount is used as a transition section control input, and a discrete time-varying state space model is constructed; The first-order differential coefficient of the real-time power value and the first-order differential coefficient of the power variation constitute a parameter matrix to be estimated, and the transition stage state vector and the transition stage control input constitute a regression vector; The product of the parameter matrix to be estimated and the regression vector is used to construct a recursive prediction sequence, the real-time operation status is collected to obtain the current state observation value, and the difference between the current state observation value and the recursive prediction sequence is calculated to obtain the estimation error; the product of the transpose of the regression vector and the recursive prediction sequence is calculated to obtain a gain matrix, and the product of the gain matrix and the estimation error is used as the 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 value with the current transition state vector to obtain a first state prediction term, determining an expected 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 expected 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 a 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: In 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, and the rate of change of the energy integral value is calculated at the same time, and 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; Calculate the second-order derivative of the energy integral value, and construct a maintenance segment state matrix according to 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; construct a maintenance segment input matrix based on the response coefficient of the rate of change of the energy integral value to the system input; calculate the maintenance segment power adjustment amount as the 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 to the second matrix product to construct a state space equation; The transposed matrix of the maintenance segment state matrix is ​​multiplied by the matrix to be determined, the product of the matrix to be determined and the maintenance segment state matrix is ​​added, and then the unit matrix is ​​added to form a Lyapunov stability equation, and the Lyapunov stability equation is solved to obtain the matrix to be determined as a symmetric positive definite matrix; a positive definite weight matrix is ​​determined according to the value range of the maintenance segment control input; The state quadratic term is obtained by multiplying the state vector of the maintenance segment by a symmetric positive definite matrix on the left and then multiplying it by the transpose of the state vector of the maintenance segment on the right; the control integral term is obtained by multiplying the control input of the maintenance segment by a positive definite weight matrix on the left and then multiplying it by the transpose of the control input of the maintenance segment on the right; and the 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 the 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, and the super-helical algorithm operation is performed on the correction coefficient and the initial control value. The output power regulation 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 the output power of the system minus the expected power trajectory is added to the disturbance estimate to obtain a dynamic error value; 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 surface; setting a stability parameter of the system to obtain a negative feedback gain, calculating a derivative of the non-singular terminal sliding 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; The initial control value is used as a basis for obtaining a system state sequence, the probability distribution of the system state sequence is calculated to obtain a state probability, the state probability is input into a recursive minimum entropy calculation unit, a system entropy value is calculated, a minimum entropy value is obtained by recursive operation, and a negative exponent of a difference between the system entropy value and the minimum entropy value is calculated 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; The convergence gain parameter of the superhelix algorithm is set, a superhelix state equation including the first algorithm component and the second algorithm component is constructed, an integral operation is performed on the superhelix state equation to obtain an auxiliary variable of the superhelix algorithm, and the auxiliary variable is combined 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 described in 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 by using sliding Fourier transform, obtain the frequency characteristic components of each time window, construct a frequency change matrix, calculate the mobile entropy value of the frequency change matrix, and obtain the frequency dynamic association vector; recursively decompose the frequency dynamic association vector into principal components, output the frequency disturbance characteristic value in real time, and calculate the frequency modulation power compensation amount according to the frequency disturbance characteristic value; collect the voltage and current signals of the supercapacitor group, input the Kalman filter to calculate the electrical parameter value, determine the upper and lower power thresholds according to the electrical parameter value, and form the power control data with the frequency modulation power compensation amount; 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, solve the power optimization trajectory, and output a fast adjustment control value; based on the dynamic transition section, perform a recursive least squares operation, obtain a system parameter estimation value, 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, the power control value and the 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, obtain the correction coefficient, perform superhelical algorithm operation on the correction coefficient and the initial control value, and output the power regulation 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 described in 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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