Flywheel energy storage and network construction type wind power coupling frequency modulation parameter optimization method and system

Abstract

The application relates to the technical field of power system frequency control, and discloses a flywheel energy storage and network type wind power coupling frequency modulation parameter optimization method and system. The method comprises the following steps: a frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation and a flywheel energy storage power response model containing droop coefficient are established; the equivalent virtual inertia and the equivalent damping coefficient are decomposed into wind power components and flywheel components, and a to-be-optimized control parameter vector is constructed; a parameter test matrix is constructed by adopting central composite design; parameter disturbance simulation is set, and frequency performance indexes are extracted; a quadratic response surface proxy model containing main effect terms, interaction terms and quadratic terms is fitted and established; variance analysis is performed to screen key control parameters; an optimization objective function is constructed, and an optimal control parameter combination is solved to set a frequency modulation control system. The application solves the problems that control parameters depend on experience setting and frequency response performance is difficult to be uniformly optimized under multiple working conditions, and improves parameter optimization efficiency and system frequency stability.

Description

Technical Field

[0001] This application relates to the field of power system frequency control technology, and in particular to a method and system for optimizing frequency regulation parameters of flywheel energy storage and grid-connected wind power coupling. Background Technology

[0002] With the integration of a high proportion of renewable energy power systems, the system's equivalent inertia continues to decrease, making frequency stability issues increasingly prominent. Grid-connected wind turbines provide inertia support through virtual synchronous control, while flywheel energy storage participates in frequency regulation due to its rapid power response capability; the synergy of these two technologies can improve the primary frequency regulation performance of the power grid. However, the lack of a unified modeling and collaborative optimization method between the virtual inertia, damping, and droop control parameters of grid-connected wind power and the frequency regulation power of flywheel energy storage restricts the overall performance of the joint frequency regulation system.

[0003] Existing technologies have the following main shortcomings: First, wind-storage coordinated control methods based on a single time scale typically describe wind power output, energy storage power response, and system frequency deviation in a unified manner. Frequency regulation is achieved using model predictive control or virtual inertia control under a single control cycle, failing to characterize the multi-time-scale coupling characteristics between the inertia response of grid-connected wind turbines, the rapid dynamic response of energy storage, and the dynamic frequency of the power grid. Second, while hierarchical frequency regulation methods adopt an "upper-level energy management - lower-level rapid control" architecture, they only divide functions and do not systematically consider the multi-scale response differences between various physical subsystems. Third, data-driven or intelligent optimization-based frequency regulation methods typically construct decision models based on a single time-scale state space, failing to explicitly characterize the multi-scale response differences between different physical subsystems. Fourth, offline optimization methods based on parameter optimization and simulation experiments rely on high-fidelity simulation models for point-by-point calculations, failing to construct an approximate analytical model that reflects the system's input-output relationship. The computational load is enormous during multi-parameter, multi-condition optimization, making rapid design and real-time optimization difficult. The above methods empirically tune the virtual inertia coefficient, damping coefficient, and droop coefficient as independent static parameters, lacking a unified modeling and global optimization framework for the overall dynamic process of wind power "energy storage-grid". Summary of the Invention

[0004] This application provides a method and system for optimizing frequency regulation parameters coupled with flywheel energy storage and grid-connected wind power. It solves the problems of control parameters relying on empirical tuning, the fragmentation of the inertia-damping-droop mechanism, and the difficulty in uniformly optimizing frequency response performance under multiple operating conditions, thereby improving parameter optimization efficiency and system frequency stability.

[0005] In a first aspect, this application provides a method for optimizing frequency regulation parameters of flywheel energy storage coupled with grid-connected wind power, including: S1. Based on the power balance relationship between the grid-type wind turbine and the flywheel energy storage system, establish the frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation, and the flywheel energy storage power response model containing droop coefficient. S2. Decompose the equivalent virtual inertia and the equivalent damping coefficient in the frequency dynamic equation into wind power components and flywheel components, respectively. Determine the virtual inertia parameters of the grid-type wind power and the droop coefficient and flywheel energy storage frequency regulation power in the flywheel energy storage power response model according to the source of each component, and construct the control parameter vector to be optimized. S3. Using each parameter in the control parameter vector to be optimized as an experimental factor, a parameter experimental matrix is ​​constructed using a central composite design. S4. Set the parameter disturbance simulation group by group according to the parameter test matrix, and extract the corresponding frequency performance indicators, including the maximum frequency deviation, the maximum frequency change rate and the steady-state frequency deviation. S5. Using the vector of control parameters to be optimized as input and the frequency performance index as output, fit and establish a quadratic response surface surrogate model containing main effect term, interaction term and quadratic term; S6. Perform variance analysis on the quadratic response surface surrogate model and screen key control parameters based on the main effects, interaction effects and significance of the quadratic terms of each experimental factor. S7. Construct an optimization objective function by weighting and minimizing the frequency performance indicators, solve for the optimal combination of control parameters based on the quadratic response surface surrogate model, and tune the frequency regulation control system of the grid-type wind turbine and flywheel energy storage system.

[0006] Secondly, this application provides a flywheel energy storage and grid-connected wind power coupled frequency regulation parameter optimization system, used to implement the aforementioned flywheel energy storage and grid-connected wind power coupled frequency regulation parameter optimization method, including: The coupling establishment module is used to establish a frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation, and a flywheel energy storage power response model containing droop coefficient, based on the power balance relationship between the coupled grid-type wind turbine and the flywheel energy storage system. The parameter decomposition module is used to decompose the equivalent virtual inertia and the equivalent damping coefficient in the frequency dynamic equation into wind power components and flywheel components, respectively. Based on the source of each component, the virtual inertia parameters of the grid-type wind power and the droop coefficient and flywheel energy storage frequency regulation power in the flywheel energy storage power response model are determined to construct the control parameter vector to be optimized. The experimental design module is used to construct a parameter experiment matrix using central composite design, with each parameter in the vector of control parameters to be optimized as experimental factors. The disturbance simulation module is used to simulate disturbances by setting parameters one group at a time according to the parameter test matrix and extract the corresponding frequency performance indicators, including the maximum frequency deviation, the maximum frequency change rate and the steady-state frequency deviation. The model fitting module is used to fit and establish a quadratic response surface surrogate model containing main effect terms, interaction terms, and quadratic terms, using the vector of control parameters to be optimized as input and the frequency performance index as output. The variance analysis module is used to perform variance analysis on the quadratic response surface surrogate model and to screen key control parameters based on the main effects, interaction effects and significance of the quadratic terms of each experimental factor. The optimization and tuning module is used to construct an optimization objective function by weighting and minimizing the frequency performance index, solve for the optimal combination of control parameters based on the quadratic response surface surrogate model, and tune the frequency regulation and control system of the grid-type wind turbine and flywheel energy storage system.

[0007] Thirdly, this application provides a computer-readable storage medium storing instructions that, when executed by a processor, implement the aforementioned method for optimizing frequency regulation parameters of flywheel energy storage and grid-connected wind power coupling.

[0008] The beneficial effects of this application are as follows: This application proposes a method and system for optimizing frequency regulation parameters of flywheel energy storage and grid-connected wind power. Compared with the prior art, this application combines unified frequency dynamic modeling, multi-parameter coupled decomposition, central composite test design, construction of a secondary response surface proxy model, variance analysis significance test and parameter optimization solution. This can solve the technical problems of control parameters relying on empirical tuning, the fragmentation of the inertia-damping-droop mechanism, and the difficulty in uniformly optimizing frequency response performance under multiple operating conditions. Specifically, by establishing a frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient, and frequency deviation, and a flywheel energy storage power response model containing droop coefficient, the power balance relationship between grid-connected wind power and flywheel energy storage is unified into the frequency dynamic framework. This ensures that inertia, damping, and droop control are no longer designed in isolation, providing a physical basis for subsequent parameter coupling analysis. By decomposing the equivalent virtual inertia and equivalent damping coefficient into wind power components and flywheel components and constructing a vector of control parameters to be optimized, the control parameters are coupled and correlated in a unified parameter space, achieving a unified description of the parameter synergy mechanism. A parameter experiment matrix is ​​constructed through a central composite design, scientifically covering the parameter interaction area within a preset value range, providing a basis for... The quadratic response surface surrogate model provides highly informative sample data. By fitting the quadratic response surface surrogate model, complex nonlinear systems are mapped to explicit polynomial functions, replacing point-by-point calculations in high-fidelity simulation models and reducing the number of simulations in the parameter optimization process. Variance analysis is used to screen key control parameters, reducing the optimization dimensionality and avoiding interference from low-impact parameters in the optimization process. With the goal of minimizing the weighted sum of frequency performance indicators, the optimal combination of control parameters is directly solved on the surrogate model to tune the frequency modulation control system. This transforms frequency modulation parameters from empirical tuning to a systematic design based on statistical modeling and analytical optimization, reducing the amount of simulation computation while ensuring optimization accuracy, and enabling rapid optimization design and engineering deployment of control parameters. Attached Figure Description

[0009] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0010] Figure 1 This is a flowchart illustrating a method for optimizing frequency regulation parameters of flywheel energy storage coupled with grid-connected wind power in this application. Figure 2 This is a simulation structure diagram of the wind-storage DC-side collaborative system in this application; Figure 3 This is the response surface of the steady-state frequency deviation in this application as a function of the equivalent damping coefficient and the flywheel frequency modulation power; Figure 4This is a schematic diagram of the structure of a flywheel energy storage and grid-connected wind power frequency regulation parameter optimization system according to this application. Detailed Implementation

[0011] This application provides a method and system for optimizing frequency regulation parameters coupled with flywheel energy storage and grid-connected wind power. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or device that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or devices.

[0012] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the method for optimizing frequency regulation parameters of flywheel energy storage and grid-connected wind power coupling in this application includes: S1. Based on the power balance relationship between the grid-connected wind turbine and the flywheel energy storage system, establish the frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation, and the flywheel energy storage power response model containing droop coefficient.

[0013] In one specific embodiment, performing S1 includes the following steps: Establish the power balance relationship between grid-connected wind turbines and flywheel energy storage systems sharing a DC bus, and characterize the power balance between wind power, flywheel energy storage, and load disturbances; The power balance relationship is sorted out to obtain the frequency dynamic equation, which includes the product of the equivalent virtual inertia and the rate of change of frequency deviation, the product of the equivalent damping coefficient and the frequency deviation, and the power loss. The flywheel energy storage power response model includes the static regulation power, which is the product of the droop coefficient and the frequency deviation, and the dynamic compensation power, which tracks the rate of change of the frequency deviation. The frequency regulation process is divided into three stages: fast inertia response, dynamic recovery, and steady-state power recovery, according to the dominant order of equivalent virtual inertia, equivalent damping coefficient, and droop coefficient.

[0014] Specifically, the implementation targets are the integrated wind and energy storage system in Region 1, consisting of a 2MW grid-connected permanent magnet direct-drive wind turbine and a 0.4MW flywheel energy storage device. Both are connected to a common 1200V DC bus via turbine-side and flywheel-side converters, and then connected to a 50Hz AC grid via a grid-side converter. A 10MW synchronous generator in Region 2 is interconnected with this region via a tie line. The grid-side converter control loop collects the grid frequency f at the grid connection point with a 1ms sampling period; the flywheel-side converter control loop collects the flywheel rotor speed; and the turbine-side converter control loop collects the DC bus voltage and turbine-side output current. These three types of sampled data are processed to obtain three intermediate quantities: the grid frequency f is filtered by a moving average at a cutoff frequency of 10Hz and then subtracted from the rated frequency of 50Hz to obtain the frequency deviation Δf; the frequency deviation Δf is then differentially calculated to obtain the frequency deviation change rate dΔf / dt; and the DC bus voltage is multiplied by the turbine-side output current to obtain the wind power output. The flywheel rotor speed is converted into the flywheel electromagnetic torque to obtain the flywheel energy storage power. When establishing a power balance relationship, the wind power output power... Flywheel energy storage power With regional load disturbance power By taking the algebraic sum along the injection direction, we obtain the power loss ΔP, i.e. The power loss ΔP is converted to a per-unit value based on the rated capacity of the wind turbine unit of 2MW, and the frequency deviation Δf is converted to a per-unit value based on the rated frequency of 50Hz. The frequency deviation change rate dΔf / dt is correspondingly measured in per-unit per second, so that the quantities in the subsequent frequency dynamic equation are dimensionally consistent under the per-unit system.

[0015] By rearranging the power balance relationship, we obtain the frequency dynamic equation: In the formula, frequency deviation Δf and power deviation ΔP are both per-unit values. J is the system's equivalent virtual inertia, in seconds, formed by the virtual synchronous control of the grid-connected wind turbine and the inertial support of the flywheel energy storage. D is the system's equivalent damping coefficient, a dimensionless per-unit coefficient whose nominal value is the ratio of the base capacity of 2MW to the base frequency of 50Hz, determined by the droop control and flywheel power regulation links. The first term on the left side of the equation... The power absorbed by an inertial element that varies in frequency is expressed as the product of seconds and per unit second, and the result is the per-unit power. (Term 2) The power absorbed by the damping element is the product of a dimensionless coefficient and the per-unit frequency deviation. Since both sides of the equation represent per-unit power, the dimensions are unified to per-unit power. The power loss ΔP on the right side of the equation represents the external disturbance caused by the deviation of the driving frequency from the rated value. This equation maps the three types of power—wind power, flywheel energy storage, and load disturbance—into two state variables: frequency deviation Δf and the rate of change of frequency deviation dΔf / dt. In other words, the three types of power sampling data, after processing according to the power balance relationship, correspond to two frequency state variables, forming a unified input for subsequent parameter decomposition and disturbance simulation.

[0016] The flywheel energy storage power response model is set as follows: The model operates under a named value system, where... The droop factor, measured in megawatts per hertz, represents the frequency deviation Δf in this model, which is expressed in hertz. The rate of change of frequency deviation, dΔf / dt, is expressed in hertz per second, characterizing the power-frequency static regulation characteristics. The product of the frequency deviation Δf is the static regulation power, which is only output when the frequency deviates from the rated value; For the frequency regulation power of flywheel energy storage, the rated power of the flywheel energy storage device is taken as 0.4 MW. The reference value for the rate of change of frequency deviation is taken as 0.5 Hz / s. The product of the normalized frequency deviation rate of change and the power output is the dynamic compensation power for tracking the frequency deviation rate of change, used to provide inertial support during sudden frequency changes. The output of the flywheel energy storage power response model is constrained to within ±0.4 MW by a limiting circuit. When the calculated value exceeds the rated power, the output is set to the rated power to prevent overload of the flywheel energy storage device. The inputs to this model are the frequency deviation Δf and the frequency deviation rate of change dΔf / dt, and the output is the flywheel energy storage power command. The power command is a named value in megawatts. After being converted to a per-unit value by dividing it by the base capacity of 2MW, the power command is substituted back into the power balance relationship to change the power imbalance ΔP, which in turn changes the frequency state quantity in the frequency dynamic equation, forming a closed-loop data flow.

[0017] Based on the equivalent virtual inertia J, equivalent damping coefficient D, and droop coefficient The frequency regulation process after a load disturbance is divided into three stages based on the dominant order of the load disturbance. Stage 1 is the rapid inertia response stage, lasting from 0 to 2 seconds after the disturbance. The criterion is that the absolute value of the frequency deviation change rate is greater than 0.1 Hz / s. In this stage, the power loss ΔP is mainly balanced by the J×dΔf / dt term, the equivalent virtual inertia J determines the frequency drop rate, and the dynamic compensation power in the flywheel energy storage power response model plays a major role. Stage 2 is the dynamic recovery stage, lasting from 2 to 10 seconds. The criterion is that the absolute value of the frequency deviation change rate is not greater than 0.1 Hz / s and the absolute value of the frequency deviation is greater than 0.05 Hz. In this stage, the D×Δf term plays a dominant role, the equivalent damping coefficient D determines the decay rate of the frequency oscillation, and the static regulation power and dynamic compensation power work together. Stage 3 is the steady-state power recovery stage, lasting after 10 seconds. The criterion is that the absolute value of the frequency deviation is not greater than 0.05 Hz, and the droop coefficient in this stage... The dominant static regulation power redistributes power between wind power and flywheel energy storage, causing the frequency deviation to converge to a steady-state value. For example, when the regional load suddenly increases by 200kW at 10s, the instantaneous frequency deviation change rate reaches -0.3Hz / s, and the dynamic compensation power term of the flywheel energy storage power response model... The calculated output of +240kW discharge power suppresses frequency drop. After 2 seconds, the frequency deviation rate decays to 0.05Hz / s, entering the damping-dominated dynamic recovery phase. After 10 seconds, the droop coefficient... The product of the residual frequency deviation and the power maintained in steady state is determined by the threshold values ​​of the two state variables, frequency deviation and frequency deviation change rate. No additional disturbance type identification is required.

[0018] S2. Decompose the equivalent virtual inertia and equivalent damping coefficient in the frequency dynamic equation into wind power components and flywheel components, respectively. Determine the virtual inertia parameters of the grid-type wind power and the droop coefficient and flywheel energy storage frequency regulation power in the flywheel energy storage power response model according to the source of each component, and construct the control parameter vector to be optimized.

[0019] In one specific embodiment, performing S2 includes the following steps: The equivalent virtual inertia is decomposed into wind power component and flywheel component. The wind power component is the virtual synchronous inertia mapped by the virtual inertia parameters of grid-type wind power, and the flywheel component is the inertia support mapped by the flywheel rotor inertia. The equivalent damping coefficient is decomposed into wind power component and flywheel component. The wind power component is the droop damping mapped by the droop coefficient, and the flywheel component is the dynamic damping mapped by the flywheel energy storage frequency regulation power. The droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameters are determined according to the source of each component. The flywheel rotor inertia is an inherent parameter of the device and is not optimized. The three parameters, namely the droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameters, together with the equivalent virtual inertia and equivalent damping coefficient, are used to construct the control parameter vector to be optimized, and the value range of each parameter is determined.

[0020] Specifically, the equivalent virtual inertia J and the equivalent damping coefficient D are decomposed according to their sources. The equivalent virtual inertia J is decomposed into wind power components. With flywheel component ,Right now Wind power components Virtual inertia parameters for grid-type wind power The mapped virtual synchronization inertia, the mapping relationship is as follows Virtual inertia parameters of grid-type wind power The time constant of the inertial element in the virtual synchronous control loop is expressed in seconds. The coefficient 2 is derived from the conversion relationship between the inertial time constant and the kinetic energy storage time under rated capacity in the oscillation equation; flywheel component. The inertia support is a mapping of the flywheel rotor inertia. The flywheel rotor inertia is an inherent parameter of the device, taken as 20 kg·m. 2 The flywheel energy storage device has 2 pole pairs and a rated speed of 3000 r / min, corresponding to a rated mechanical angular velocity of 314.16 rad / s. The kinetic energy stored in the flywheel is half the product of the flywheel rotor inertia and the square of the rated mechanical angular velocity, which is calculated to be 0.987 MJ. The inertia is based on a wind turbine rated capacity of 2 MW. Conversion, flywheel weight Equals twice the stored kinetic energy divided by the inertia reference capacity The calculated value is 0.99s. Wind power component. With flywheel component The two components correspond to an equivalent virtual inertia J, which is a total quantity. Although the components originate from different sources, their dimensions are unified to seconds. The superposition of the two components maintains the same numerical value as the equivalent virtual inertia J in the S1 frequency dynamic equation. This relates to the virtual inertia parameters of grid-type wind power. For every 0.5s change, the equivalent virtual inertia J changes by 1s, and the correspondence between the parameter and the total is a linear mapping.

[0021] The equivalent damping coefficient D is decomposed into wind power components. With flywheel component ,Right now Wind power components Sag coefficient The droop damping of the mapping, the droop coefficient The dimension is megawatts per hertz, and the droop coefficient will be used during mapping. Multiply by the rated frequency Divide by the damping reference capacity This yields the per-unit form of droop damping, i.e. In the formula, the rated frequency Take 50Hz as the reference damping capacity. Take 2MW; flywheel component Frequency regulation power for flywheel energy storage The dynamic damping of the mapping, during mapping, will adjust the frequency regulation power of the flywheel energy storage. Divide by the reference value of the rate of change of frequency deviation The equivalent power-frequency slope is obtained, and then converted to a per-unit value using the same reference. The reference value of the frequency deviation change rate in the formula Take 0.5Hz / s as the flywheel energy storage frequency regulation power. The upper limit is taken as the rated power of the flywheel energy storage device, which is 0.4 megawatts. The baseline time constant is set to 1 second. After the above mapping, the droop coefficient... With flywheel energy storage frequency modulation power The two control parameters correspond to the wind power components respectively. With flywheel component Two damping components, when superimposed, correspond to an equivalent damping coefficient D. This allows the value of the equivalent damping coefficient in S1 to be traced back to specific control parameters, including the droop coefficient. For every change of 0.08 MW / Hz, the equivalent damping coefficient D changes by 2 per unit.

[0022] Determine the droop coefficient based on the source of each component. Flywheel energy storage frequency regulation power Virtual inertia parameters of grid-connected wind power The values ​​are taken, where the flywheel rotor inertia is 20 kg·m. 2 Due to the mechanical structure of the flywheel energy storage device, the parameters are inherent to the device and will not be optimized; they are only considered as flywheel components. The calculation basis. The droop coefficient. Flywheel energy storage frequency regulation power Virtual inertia parameters of grid-type wind power The three parameters, along with the equivalent virtual inertia J and the equivalent damping coefficient D, constitute the vector of control parameters to be optimized. The values ​​of each parameter were determined as follows: the equivalent virtual inertia J ranges from 2s to 10s, corresponding to the equivalent inertia level of a high-proportion new energy power system; the equivalent damping coefficient D ranges from 1 to 20, calculated in per-unit values, consistent with the per-unit definition of the equivalent damping coefficient in the S1 frequency dynamic equation, with a nominal base value being the ratio of the base capacity of 2MW to the base frequency of 50Hz; the droop coefficient... The range is 0.2MW / Hz to 2MW / Hz, covering the primary frequency regulation droop setting range of grid-connected power sources; flywheel energy storage frequency regulation power. The range is 0.1MW to 0.4MW, with the upper limit constrained by the rated power of the flywheel energy storage device at 0.4 MW; virtual inertia parameters for grid-type wind power. The range of 0.5s to 5s corresponds to the tuneable range of the virtual synchronous control loop inertia time constant. After determining the value range, a consistency check is performed on the five parameters in the vector: (The rest of the text appears to be a continuation of the previous sentence and can be left as is.) and The equivalent virtual inertia obtained by superimposing s must fall within the range of values ​​for J, by and The equivalent damping coefficient obtained by superposition must fall within the range of D. Parameter combinations that fail verification are truncated according to the boundary of the range, ensuring that there is no numerical conflict between the parameters in the control parameter vector to be optimized and the S1 frequency dynamic equation. For example, when the virtual inertia parameter of a grid-type wind power system... Wind power component at 2s The duration is 4 seconds, with the flywheel component superimposed. The equivalent virtual inertia J is 4.99s, falling within the range of 2s to 10s; with the lower droop coefficient... Take 1MW / Hz, flywheel energy storage frequency regulation power When the wind power component is 0.4MW, The flywheel component is 25. The value is 20, which, after superposition, exceeds the upper limit of 20 for the equivalent damping coefficient D. This parameter combination is truncated to the boundary and then enters the subsequent central composite design. Each dimension of the control parameter vector θ to be optimized corresponds to a control parameter with a clear physical source. The vector as a whole serves as the experimental factor input for the S3 central composite design, realizing a bidirectional backtracking correspondence between the 5 control parameters and the 2 frequency dynamic coefficients. The equivalent virtual inertia J and equivalent damping coefficient D output from S1, after decomposition processing in this step, correspond to the 5 control parameters to be optimized, forming the unified data basis for S3 to S7.

[0023] S3. Using each parameter in the control parameter vector to be optimized as an experimental factor, a central composite design is used to construct the parameter experiment matrix.

[0024] In one specific embodiment, performing S3 includes the following steps: The equivalent virtual inertia, equivalent damping coefficient, droop coefficient, flywheel energy storage frequency regulation power and grid-type wind power virtual inertia parameters in the control parameter vector to be optimized are taken as five test factors. Within the preset value range, the actual values ​​of each test factor are normalized and coded as high level and low level. The test points are arranged in the coded factor space according to the central composite design. The test points include factor points composed of two-level combinations of each test factor, axial points on the coordinate axes of each test factor at a set distance from the center, and center points that are repeatedly arranged in the center of the factor space. A parameter test matrix is ​​generated by summarizing the parameter combinations corresponding to all test points. Each row of the parameter test matrix corresponds to a set of parameter values ​​to be simulated under disturbance.

[0025] Specifically, the equivalent virtual inertia J, equivalent damping coefficient D, and droop coefficient are represented by the control parameter vector θ to be optimized. Flywheel energy storage frequency regulation power Virtual inertia parameters of grid-connected wind power Five parameters were used as five experimental factors. Within the preset value range determined by S2, the actual values ​​of each experimental factor were normalized and coded into high and low levels. The coding employed a linear transformation. In the formula, j is the experimental factor number, ranging from 1 to 5, corresponding sequentially. , For the actual value of the j-th experimental factor, The midpoint of the range of values ​​for the j-th experimental factor. The range of values ​​for the j-th experimental factor is half-width, which is half the difference between the upper and lower limits. The axial distance is for the central composite design. Based on the range of S2, the midpoint of the equivalent virtual inertia J is 6s, and the half-width is 4s; the midpoint of the equivalent damping coefficient D is 10.5, and the half-width is 9.5; the sag coefficient... The midpoint is 1.1 MW / Hz, the half-width is 0.9 MW / Hz, and the flywheel energy storage frequency regulation power is... The midpoint is 0.25MW, the half-width is 0.15MW, and the virtual inertia parameters of the grid-type wind power are as follows: The midpoint is 2.75s and the half-width is 2.25s. After coding, the high level of each experimental factor is recorded as +1, the low level as -1, and the midpoint as 0. The five actual parameters with different dimensions are coded into five dimensionless coded variables, eliminating the dimensional differences between megawatts per hertz, seconds, and megawatts, so that each experimental factor has the same measurement scale in the factor space, providing a unified benchmark for the horizontal comparison of the quadratic response surface regression coefficients.

[0026] In a central composite design, test points are arranged in the coded factor space. These test points include three types: factor points, axial points, and center points. Factor points are vertices formed by the two-level combinations of each test factor. A total of 2 factor combinations are available for the 5 test factors. 5 =32 points, with each factor point having 5 coordinates set to +1 or -1 respectively; axial points are points on the coordinate axes of each experimental factor at a predetermined distance from the center of the factor space, with one point for each experimental factor in both the positive and negative directions of the coordinate axis, for a total of 2 × 5 = 10 points, and the axial distance α is set to 2 according to the rotatability requirement. 5 / 4The rotatability of the quadratic response surface surrogate model ensures equal prediction variances at any point within the factor space at the same distance from the center. The center point is repeatedly placed 6 times at the center of the factor space, where all coded variables are 0, to estimate random error variation and test model fit. Since the axial distance of 2.378 is greater than the coding level 1, to ensure that the actual values ​​corresponding to the axial points do not exceed the preset range determined by S2, the boundary of the actual value range is mapped to the coded value ±2.378 during the coding transformation. The actual value corresponding to the factor point coding value ±1 is the midpoint plus or minus half the width divided by 2.378. For example, the equivalent virtual inertia J at the high level corresponds to an actual value of 6 + 4 / 2.378 ≈ 7.68s, at the low level to 4.32s, and the axial point in the positive direction corresponds to an actual value of 6 + 4 = 10s, which is exactly the upper limit of the preset range. (Flywheel energy storage frequency regulation power) The negative axial point corresponds to an actual value of 0.25 - 0.15 = 0.1MW, which is exactly the lower limit of the preset value range. The inverse decoding transform is... Any combination of codes can be transformed dimension by dimension to obtain the actual parameter combination.

[0027] A parameter test matrix is ​​generated by summarizing the parameter combinations corresponding to all test points. The matrix consists of 32 + 10 + 6 = 48 rows and 5 columns. Each row corresponds to a set of parameter values ​​to be simulated under disturbance, and each column corresponds to a test factor. During matrix generation, 32 factor points, 10 axial points, and 6 center points are stored in encoded form. Then, through decoding and inverse transformation, each row is converted into actual values, forming a parameter test matrix containing 5 columns of actual values ​​for equivalent virtual inertia, equivalent damping coefficient, droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameters. The simulation order of the 48 parameter combinations is randomized to avoid the mixing of simulation platform state drift and time trends with the effects of test factors. The 6 center points are distributed at the beginning, middle, and end of the simulation order, ensuring that random error estimation covers the entire simulation process. For example, the encoded combination corresponding to a factor point in a certain row of the matrix is ​​[+1.42, -1, +1, -1, +1], which, after decoding, yields J = 8.39s, D = 6.5, ... =1.48MW / Hz MW The row 's' is written as a complete set of parameter values ​​into the two-region interconnected simulation model of S4. The parameter experiment matrix and the control parameter vector to be optimized in S2 have a row expansion relationship. The five components of vector θ correspond to the five columns of the matrix, and the 48 rows of the matrix correspond to the 48 sets of disturbance simulations in S4. The three frequency performance indicators of the maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation output by each set of simulations are attached back to the corresponding rows of the matrix, forming the input-output sample set required for the second-order response surface fitting of S5. The five experimental factors correspond to the 48 sets of parameter combinations, and the 48 sets of parameter combinations correspond to the 48 sets of frequency performance indicators.

[0028] S4. Set the parameter disturbance simulation group by group according to the parameter test matrix, and extract the corresponding frequency performance indicators, including the maximum frequency deviation, the maximum frequency change rate and the steady-state frequency deviation.

[0029] In one specific embodiment, performing S4 includes the following steps: A two-region interconnection simulation model is built, which includes a grid-type wind turbine, a flywheel energy storage system and a synchronous power source. The grid-type wind turbine and the flywheel energy storage system are connected to the same region and interconnected with the synchronous power source of the other region via a tie line. The parameter values ​​of each row in the parameter test matrix are written into the two-region interconnected simulation model one by one. The same load disturbance is applied under three working conditions: constant wind speed, flywheel energy storage capacity change and turbulent wind speed, and the frequency response curve is recorded. The maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation are extracted from the frequency response curves of each group of disturbance simulation records to form frequency performance indicators that correspond one-to-one with each row of the parameter test matrix.

[0030] Specifically, please refer to Figure 2 A two-region interconnection simulation model including a grid-type wind turbine, a flywheel energy storage system, and a synchronous power supply was built on the MATLAB / Simulink platform. Region 1 connects a 2MW grid-type permanent magnet direct-drive wind turbine and a 0.4MW flywheel energy storage device. The wind turbine is connected to the grid-side converter via a turbine-side converter and a common DC bus with a voltage of 1200V. The flywheel energy storage device is connected to the common DC bus via a flywheel-side converter. The control block diagram of the simulation model is built according to the following connection relationship. Each link in the block diagram is operated in a per-unit system, with a frequency reference value of 50Hz and a power reference value of 2MW: The grid-type control loop is composed of a virtual inertia link and a droop link connected in parallel. The virtual inertia link takes the per-unit frequency deviation as input and the inertial power as output, and its transfer function is: In the formula For the virtual inertia parameters of grid-connected wind power, coefficient 2 and S2 The mapping relationship is consistent; the drooping element is a proportional element, and the proportional gain is... In the formula The droop coefficient is... The rated frequency is 50Hz. The damping base capacity is 2MW, and the conversion method is the same as in S2. The mapping relationship is consistent; after the outputs of the two stages are superimposed, they are equivalent to a first-order inertial element in the grid-side converter. To generate wind power output, a time constant of 0.01s is used to assess the millisecond-level response characteristics of the inner loop of the strain gauge current. Since the inner loop dynamics are much faster than the frequency dynamics, this first-order element is considered equivalent. The flywheel energy storage branch generates a flywheel energy storage power command according to the flywheel energy storage power response model of S1. This power command is then passed through a ±0.4 MW limiting element and is equivalent to a first-order inertial element of the flywheel-side converter. Output flywheel energy storage power, flywheel rotor speed according to Updated every moment, in the formula The moment of inertia of the flywheel rotor is taken as 20 kg·m. 2 ω is the mechanical angular velocity of the flywheel. For the flywheel energy storage power, the lower limit of the speed is set to half of the rated speed of 3000 r / min. When the speed drops to the lower limit, the flywheel energy storage power command is reset to zero to prevent over-discharge of the flywheel. The wind power output power, flywheel energy storage power, and load disturbance power are combined into a power loss measure through the power balance node of the common DC bus. The power loss measure is then processed by a frequency dynamic link. The output frequency deviation is fed back to the virtual inertia element, the droop element, and the input of the flywheel energy storage branch to form a closed loop. This frequency dynamic element is the transfer function form of the S1 frequency dynamic equation. The equivalent virtual inertia J, equivalent damping coefficient D, and droop coefficient within the network control loop are... Flywheel energy storage frequency regulation power Virtual inertia parameters of grid-connected wind power Configure an externally writable variable interface. Region 2 is configured with a 10MW synchronous generator to simulate a traditional synchronous power supply. The synchronous generator uses a practical model with transient reactances: d-axis reactance 0.146 pu, d-axis transient reactance 0.0608 pu, q-axis reactance 0.0969 pu, q-axis transient reactance 0.06 pu, inertial time constant 3s, and a speed control system is configured. The speed control system transfer function is... In the formula, R is the droop rate, taken as 5%, and 0.2s is the time constant of the servo mechanism; the load disturbance adopts an ideal step model, and the load disturbance power is... The voltage is set to 0 before the disturbance occurs, and then rises to a set amplitude and remains constant from the moment the disturbance occurs, with a rise time not exceeding 1ms. The two regions are interconnected via a tie line to form a two-machine, two-region system. The tie line is equivalent to a lumped reactance of 0.1pu. The power transmitted via the tie line is calculated by dividing the product of the bus voltage amplitudes of the two regions by the tie line reactance and then multiplying by the sine of the power angle difference between the two regions. The simulation uses the ode23tb variable step size solver with a maximum step size of 1×10⁻⁶. -4 The total simulation duration is 60s. The frequency signal at the grid connection point is recorded at a period of 1ms after being filtered by the moving average with a cutoff frequency of 10Hz, forming the frequency response curve f(t).

[0031] The parameter values ​​of each row in the parameter experiment matrix are written into the two-region interconnection simulation model group by group. During the writing process, the five actual values ​​of each row are assigned to the five corresponding variable interfaces according to the decoding results of S3. The writing is then verified in the verification stage. and The sum of s equals the value of J in that row. and The sum equals the D value of that row. After verification, the simulation is started to ensure that the written parameters are strictly consistent with the models established by S1 and S2. The same load disturbance is applied to each set of parameters under three working conditions for disturbance simulation: Working condition 1 is a constant wind speed condition, with the wind speed maintained at 12m / s. When the system has been running stably for 10s, a 0.2 MW step load disturbance is applied to area 1; Working condition 2 is a flywheel energy storage capacity variation condition, with the same load disturbance maintained. The rated power of the flywheel energy storage device is set to three capacities: 0.4 MW, 0.3 MW, and 0.2 MW; Working condition 3 is a turbulent wind speed condition. A random wind speed sequence is generated using the von Karman turbulence model. The turbulence intensity is 10%, and the average wind speed is set to three levels: 8m / s, 10m / s, and 12m / s. The same 200kW load disturbance is applied at 10s. For each type of operating condition, the frequency response curve f(t) is recorded from 5 seconds before the disturbance to 50 seconds after the disturbance. The parameter test matrix has 48 rows corresponding to 48 sets of parameters. Each set of parameters corresponds to the frequency response curve under the three types of operating conditions. All simulations form a total of 48 sets of curves.

[0032] The maximum frequency deviation, maximum rate of change of frequency, and steady-state frequency deviation are extracted from the frequency response curves of each group of disturbance simulation records. Maximum frequency deviation according to Calculate, where The rated frequency is 50Hz, and the calculation window is from the time of disturbance occurrence to 20 seconds after the disturbance; the maximum frequency change rate is calculated as follows: The frequency change rate is calculated by dividing the difference between adjacent sampling points on the frequency response curve by the sampling period of 1 ms. The calculation window is taken from the time of the disturbance to 2 seconds after the disturbance, corresponding to the fast inertial response stage divided by S1; steady-state frequency deviation. The steady-state power recovery stage is calculated based on the absolute value of the difference between the mean of the frequency response curve and the rated frequency during the 50-60s period after the disturbance. Each set of parameters was simulated under seven specific simulation conditions with the same load disturbance: ① constant wind speed (12 m / s); ② flywheel energy storage capacity variation condition, with the rated power of the flywheel energy storage device set to 0.4MW, 0.3MW, and 0.2MW, for a total of three capacity levels; ③ turbulent wind speed condition, using the von Karman turbulence model to generate a random wind speed sequence, with a turbulence intensity of 10% and average wind speeds of 8m / s, 10m / s, and 12m / s, for a total of three wind speed levels. The frequency response curve f(t) was recorded from 5s before the disturbance to 50s after the disturbance under each condition. For the same set of parameters (i.e., one row in the parameter test matrix), a disturbance simulation was performed once under each of the seven simulation conditions, and the frequency response curves were recorded. For the three indices—maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation—the maximum value from the seven simulations was taken as the representative value for each parameter combination, ensuring that the index values ​​cover the performance degradation caused by operating condition fluctuations. The 48 rows of the parameter test matrix correspond to 48 sets of parameters, and each set of parameters corresponds to the frequency response curves under the seven simulation conditions. All simulations form a total of 48 sets of curves (each set contains 7 curves, for a total of 336 simulations). The maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation are extracted from the frequency response curves recorded in each set of disturbance simulations. For example, if the maximum frequency deviation of a certain set of parameters is 0.18Hz under constant wind speed conditions and 0.24Hz under turbulent wind speed conditions, then the maximum frequency deviation index for this set of parameters is taken as 0.24Hz. The 48 parameter combinations correspond to 48 frequency performance indicators. Each frequency performance indicator contains three values: maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation. These values ​​are appended to the corresponding rows of the parameter experiment matrix to form a 48-row, 8-column sample dataset. The first 5 columns are the actual values ​​of the experimental factors, and the last 3 columns are the frequency performance indicators. This sample dataset serves as the input-output sample for the least squares regression of the S5 quadratic response surface surrogate model. Each row of the parameter experiment matrix has a closed row-to-row correspondence with the frequency response curve and the frequency performance indicators.

[0033] S5. Using the vector of control parameters to be optimized as input and the frequency performance index as output, a quadratic response surface surrogate model containing main effect terms, interaction terms, and quadratic terms is fitted and established.

[0034] In one specific embodiment, performing S5 includes the following steps: The first-order terms of each parameter in the control parameter vector to be optimized are used as the main effect term, the product term of any two parameters is used as the interaction term, and the square terms of each parameter are used as the quadratic term. The quadratic polynomial structure is constructed with the control parameter vector to be optimized as the input and the frequency performance index as the output. The parameter values ​​in each row of the parameter test matrix are subjected to least squares regression with the corresponding frequency performance index. The regression coefficients of the quadratic polynomial structure are solved, and a quadratic response surface surrogate model is fitted and established. The decision coefficient is calculated based on the residuals of the fitted values ​​of the quadratic response surface surrogate model under each set of parameter values ​​and the corresponding frequency performance index. When the decision coefficient does not meet the preset accuracy, the experimental samples are added and refitted until the decision coefficient meets the preset accuracy.

[0035] Specifically, the 48-row, 8-column sample dataset formed by S4 is used as the fitting object. The first 5 columns of the dataset are the actual values ​​of the equivalent virtual inertia, equivalent damping coefficient, droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameters after decoding each row of the parameter test matrix. The last 3 columns are the maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation corresponding to each row. Regression is performed in the encoding space, and the actual values ​​of the first 5 columns are converted into encoded variables according to the encoding transformation of S3. to ,in The corresponding coded value of the virtual inertia The coded value corresponding to the equivalent damping coefficient. The encoded value corresponding to the droop coefficient, The coded value corresponding to the frequency regulation power of flywheel energy storage. For the encoded values ​​of the virtual inertia parameters of grid-connected wind power, the encoding process eliminates the dimensional differences between seconds, megawatts per hertz, and megawatts, allowing direct horizontal comparison of the magnitudes of the regression coefficients. Subsequently, a quadratic polynomial structure is constructed using the vector of control parameters to be optimized as input and the frequency performance index as output: the first-order terms of each encoded variable... As the main effect term, it characterizes the linear effect of a single control parameter on the frequency performance index; the product term of any two encoded variables. As interaction terms, they characterize the coupling effect on frequency performance indicators when two control parameters change simultaneously. For example, the product of the equivalent virtual inertia and the droop coefficient describes the combined effect of inertia support and primary frequency modulation during the frequency recovery phase; the square terms of each coded variable... As a quadratic term, it characterizes the nonlinear saturation characteristics of frequency performance index changes as control parameters increase. For example, the square term of the equivalent virtual inertia describes the characteristic that the improvement in the maximum frequency deviation slows down as the inertia continues to increase. The quadratic polynomials corresponding to the five experimental factors contain one constant term and five main effect terms. There are 1 interaction term and 5 quadratic terms, totaling 21 regression coefficients to be determined. The structural expression is as follows: In the formula Let q be the fitted value of the q-th frequency performance index, where q takes values ​​of 1, 2, and 3, corresponding to the maximum frequency deviation, maximum rate of change of frequency, and steady-state frequency deviation, respectively; the first term on the right side of the equation... The first term is a constant, representing the baseline level of frequency performance when all control parameters are taken at the midpoint of the encoding; terms 2 through 6 are the five main effect terms. to The regression coefficients of the main effect term, for example The linear effect of individual changes in equivalent virtual inertia on frequency performance indicators is characterized; terms 7 to 16 are 10 interaction terms. to These are the regression coefficients for the interaction term; the double subscripts of the regression coefficients correspond to the two coded variables being multiplied. Term 17 through 21 consist of five quadratic terms. to These are the regression coefficients for the quadratic term. The three frequency performance indicators are each constructed with identical quadratic polynomials. One vector of control parameters to be optimized corresponds to three quadratic response surface surrogate models: the maximum frequency deviation response surface model, the maximum frequency change rate response surface model, and the steady-state frequency deviation response surface model. The three models share the same set of encoded variables, and each independently solves for a set of 21 regression coefficients.

[0036] Least square regression was performed on the parameter values ​​and corresponding frequency performance indices for each row of the parameter experiment matrix. The 48 sets of codes were expanded row by row according to a quadratic polynomial structure, assembling a 48-row, 21-column design matrix X. The 21 elements in the u-th row of the matrix were, in order, a constant term 1, the encoded values ​​of 5 linear terms, the product of 10 interaction terms, and the squared values ​​of 5 quadratic terms, where u is the test point number, ranging from 1 to 48. Each row of the design matrix corresponds one-to-one with a row of the parameter experiment matrix, and each column corresponds one-to-one with a term of the quadratic polynomial structure. Simultaneously, the 48 values ​​of the q-th frequency performance index in the sample dataset were arranged in the same row order to form a 48-row, 1-column output vector. For example, when q is 1, the output vector consists of the maximum frequency deviation corresponding to 48 sets of parameter combinations, with the dimension being Hertz. The normal equation system is established according to the least squares criterion: In the formula To design the transpose of matrix X, This is a vector of regression coefficients to be determined, consisting of 21 rows and 1 column. The 21 elements in the equation correspond sequentially to the regression coefficients of the constant term, main effect term, interaction term, and quadratic term in the structural expression. The goal is to solve this system of normal equations to minimize the sum of squared residuals between the fitted values ​​and the measured indices at all 48 experimental points. The solution process uses LU decomposition, first calculating the 21st order square matrix. Solve it again ,when When the condition number is greater than 10 to the power of 10, singular value decomposition is used to solve the problem, avoiding distortion of regression coefficients caused by ill-conditioned matrices. The above regression is performed on the three values ​​of q respectively, resulting in three sets of coefficient vectors, each containing 21 regression coefficients. Substituting these into a quadratic polynomial structure, three quadratic response surface surrogate models are fitted and established. Since the regression is completed in the encoding space, the absolute value of the regression coefficients of the main effect terms directly reflects the degree of influence of the corresponding control parameters on the frequency performance index. The sign of the regression coefficients of the interaction terms reflects the synergistic or antagonistic relationship when the two parameters change in the same direction. For example, when the interaction coefficient of the equivalent damping coefficient and the flywheel energy storage frequency regulation power is negative, it indicates that there is a superimposed effect in suppressing the maximum rate of change of frequency when both are increased simultaneously.

[0037] The determination coefficients are calculated based on the residuals of the fitted values ​​and corresponding frequency performance indices of the quadratic response surface surrogate model for each set of parameter values. The 48 coded combinations are then substituted one by one into the quadratic polynomial established for fitting to obtain the fitted values ​​for each experimental point. The corresponding measured index in the output vector The residuals are obtained by subtraction. Press again Calculate the determination coefficient, where The numerator is the mean of 48 measured indicators, the numerator is the sum of squared residuals, and the denominator is the sum of squared total deviations. The coefficient of determination ranges from 0 to 1, with values ​​closer to 1 indicating a higher degree of reproduction of the disturbance simulation data by the surrogate model. The preset accuracy is set to a coefficient of determination of not less than 0.9, and three quadratic response surface surrogate models are validated separately. When the coefficient of determination of any model is less than 0.9, the test point with the largest absolute value of the residual is located, and test samples are added in the neighborhood of the corresponding coded coordinates of the test point. For example, new test points are arranged along each coordinate axis with an axial distance of 0.5 centered on the point, and two duplicate points are added. After decoding the new coded combination, the corresponding frequency performance index is extracted by the perturbation simulation of S4. After expanding the sample dataset, least squares regression is re-executed until the coefficient of determination of all three models is not less than 0.9. The repeated values ​​of the six center points provide an independent estimate of the random error. The dispersion of each simulation index at the center point is mutually corroborated with the model residual: if the dispersion of the center point is small but the coefficient of determination is not up to standard, it indicates that the misfit is due to the lack of higher-order nonlinear terms, and the supplementary samples are concentrated in the curvature variation region; if the dispersion of the center point is large, it indicates that the simulation noise level has increased, and the simulation settings of S4 are checked before supplementing samples.

[0038] S6. Perform variance analysis on the quadratic response surface surrogate model and screen key control parameters based on the main effects, interactions, and significance of the quadratic terms of each experimental factor.

[0039] In one specific embodiment, performing S6 includes the following steps: Analysis of variance was performed on the quadratic response surface surrogate model, and the total variation of each item in the frequency performance index at all test points was decomposed into the variation caused by the main effect of each test factor, the variation caused by the interaction between test factors, the variation caused by the quadratic term, and the variation of random error. Calculate the ratio of the mean square of the variance of the main effect, interaction effect, and quadratic term to the mean square of the variance of random error to obtain the significance test value and the corresponding significance probability value of each term. Items with a significance probability value less than a preset significance threshold are identified as significant items, and the experimental factors corresponding to each significant item are used as key control parameters.

[0040] Specifically, using the three quadratic response surface surrogate models established by S5 fitting and 48 sets of experimental data as the analysis objects, an analysis of variance was performed on each frequency performance index. For the q-th frequency performance index, the total variation of the measured index values ​​at the 48 experimental points was calculated as the sum of squared total deviations. Calculate, where Let u be the measured index of the u-th test point. The mean of 48 measured indicators is given, and the degrees of freedom of the total variation are 48-1=47. The total variation is decomposed into two parts: model variation and random error variation. The model variation is calculated according to the regression sum of squares. Calculate, where Let be the fitted value of the quadratic response surface surrogate model at the u-th experimental point. The degrees of freedom of the model variation are 21-1=20, corresponding to the 20 model terms in the quadratic polynomial structure excluding the constant term; the random error variation is expressed as the sum of squared residuals. Calculate, where For the residual at the u-th experimental point, the degrees of freedom of the random error variation are 48-21=27. These three factors satisfy the closed-loop relationship that the total variation equals the sum of the model variation and the random error variation. The model variation is then further decomposed into the variation caused by the main effects of each experimental factor, the variation caused by the interaction between experimental factors, and the variation caused by the quadratic term. The decomposition uses a partial variance approach: for the v-th model term in the quadratic polynomial structure, where v ranges from 1 to 20, corresponding to 5 main effect terms, 10 interaction terms, and 5 quadratic terms respectively, this model term is removed from the structural expression. Then, the least squares regression of S5 is re-executed on the 48 sets of experimental data to obtain the sum of squared residuals of the reduced model. The sum of squared residuals of the reduced model is compared with the sum of squared residuals of the complete model. The difference is the variation caused by the v-th model term. Deterioration The degree of freedom is 1, for example, eliminating the equivalent virtual inertia J and the droop coefficient. The increment of the sum of squared residuals after the interaction term represents the variation caused by that interaction. One frequency performance index corresponds to the variation of 20 model terms and one random error variation, while three frequency performance indices correspond to three sets of independent ANOVA results.

[0041] After completing the variance decomposition, the ratio of the mean square of the variance of the main effects, interaction effects, and quadratic terms to the mean square of the variance of the random error is calculated to obtain the significance test value and the corresponding significance probability value of each term. The mean square of the v-th model term is... Dividing it by its degree of freedom of 1, numerically equals The mean square of random error variation is the sum of squared residuals. Divide by its degrees of freedom 27; significance test value of the v-th model term according to The significance test value is calculated as the ratio of the mean square of the random error. The value follows an F-distribution with 1 to 27 degrees of freedom. The significance probability is calculated using the cumulative distribution function of the F-distribution. This probability represents the probability of a current or larger test value occurring under the assumption that the model term has no impact on the frequency performance index. Simultaneously, the random error variation is subdivided into pure error variation and lack-of-fit variation using repeated values ​​at the six center points. Pure error variation is calculated as the sum of the squares of the differences between the measured index and its mean at the six center points, with 6-1=5 degrees of freedom. Lack-of-fit variation is the difference between random error variation and pure error variation, with 27-5=22 degrees of freedom. The ratio of the mean square of the lack-of-fit variation to the mean square of the pure error variation is used to verify whether the surrogate model has structural defects. For example, a significance probability greater than 0.05 indicates that the model structure is sufficient to reproduce frequency dynamics, and the results of each significance test are reliable.

[0042] Items with a significance probability value less than a preset significance threshold are defined as significant items. The preset significance threshold is 0.05, meaning that model items with a significance probability value less than 0.05 are considered statistically significant for the frequency performance index, while model items with a significance probability value not less than 0.05 are considered insignificant items. The experimental factors corresponding to each significant item are used as key control parameters. The corresponding rules are as follows: when a main effect item is significant, its corresponding single experimental factor is directly listed as a key control parameter; when an interaction term or quadratic term is significant, the two experimental factors multiplied by the interaction term or the experimental factor corresponding to the quadratic term are both listed as key control parameters. For example, the main effect item of the equivalent virtual inertia J, the equivalent virtual inertia J and the droop coefficient... Interaction items and virtual inertia parameters of grid-type wind power When the quadratic term is significant, the equivalent virtual inertia J and the droop coefficient are... Virtual inertia parameters of grid-connected wind power These are listed as key control parameters. The above screening is performed on three quadratic response surface surrogate models, and the union of the key control parameters obtained from each of the three frequency performance indicators is taken to form a set of key control parameters for frequency modulation control systems. For example, the equivalent virtual inertia J and droop coefficient are screened out from the maximum frequency deviation model. Steady-state frequency deviation model screens out droop coefficient With flywheel energy storage frequency modulation power At that time, the union is the equivalent virtual inertia J and the droop coefficient. With flywheel energy storage frequency modulation power There are three key control parameters, which serve as the basis for selecting the optimization variables for S7.

[0043] S7. Construct an optimization objective function by weighting and minimizing the frequency performance index, solve the optimal combination of control parameters based on the quadratic response surface surrogate model, and tune the frequency regulation control system of the grid-type wind turbine and flywheel energy storage system.

[0044] In one specific embodiment, performing S7 includes the following steps: Weighting coefficients are assigned to the maximum frequency deviation, the maximum frequency change rate, and the steady-state frequency deviation, respectively, and the optimization objective function is constructed by minimizing the weighted sum of the three frequency performance indicators. Using key control parameters as optimization variables and other experimental factors as fixed values, the objective function is solved on a quadratic response surface surrogate model under the constraints of the preset value range of each experimental factor to obtain the optimal combination of control parameters. The optimal control parameter combination is mapped to the virtual inertia control link, droop control link and flywheel power control link of the frequency modulation control system according to the source of each component, and the frequency performance index is verified under load disturbance. After the verification is passed, it is fixed and put into operation.

[0045] Specifically, weighting coefficients are assigned to the maximum frequency deviation, the maximum rate of frequency change, and the steady-state frequency deviation, respectively. , , The sum of the three weighting coefficients is 1, and their values ​​are determined according to the power grid frequency control requirements: the maximum frequency deviation directly determines whether the lowest frequency point after the disturbance triggers a low-frequency load shedding action, and the weighting coefficients are allocated accordingly. The maximum frequency change rate is set to 0.5; this represents the frequency sag rate, which affects the operational risk of relay protection and inverter grid-connected protection, and is assigned a weighting coefficient. The value is set to 0.3; the steady-state frequency deviation characterizes the frequency recovery level after the first frequency modulation, and a weighting coefficient is assigned. We set the value to 0.2. Since the three frequency performance indicators have different dimensions, before constructing the objective function, we normalize the fitted values ​​of each indicator according to allowable limits: the maximum frequency deviation limit is 0.5Hz, the maximum frequency change rate limit is 1Hz / s, and the steady-state frequency deviation limit is 0.2Hz. Normalization is achieved by dividing the fitted value by the corresponding limit to obtain the dimensionless ratio. We then construct the optimization objective function by minimizing the weighted sum of the normalized three frequency performance indicators. In the formula , , The fitted values, in order, are the maximum frequency deviation response surface model, the maximum frequency change rate response surface model, and the steady-state frequency deviation response surface model. All three fitted values ​​are encoded variables. to The objective function Φ, after weighted summation, is still a quadratic function of the encoded variables. One set of encoded variable values ​​corresponds to one objective function value. The five components of the encoded variables correspond one-to-one with the five components of the S2 control parameter vector θ to be optimized after encoding transformation.

[0046] The objective function is solved using key control parameters as optimization variables and other experimental factors as fixed values. The coded components of the optimization variables are treated as free variables. The coded components corresponding to non-key control parameters are fixed at the midpoint of the coded value 0, which corresponds to the midpoint of the value range of each experimental factor determined in S2. For example, S6 selects the equivalent virtual inertia J and the droop coefficient. With flywheel energy storage frequency modulation power When it is a critical control parameter, , , Virtual inertia parameters of grid-type wind power are free variables. corresponding We set the value to 0, i.e., take the midpoint 2.75s. However, it should be noted that the equivalent damping coefficient D is not an independent variable, but is determined by D. according to and The values ​​of D are calculated in real time, therefore D is not used as an independent optimization variable and is always calculated in real time by the mapping relationship. The constraint condition is that the values ​​of each free variable do not exceed the preset value range determined by S2. According to the encoding transformation of S3, it is converted into encoding constraints, that is, the encoding value of each free variable is between -2.378 and +2.378, corresponding to the lower limit and upper limit of the actual value. Since the objective function Φ is a quadratic function and the constraint is an interval constraint, the solution adopts the effective set method of quadratic programming: the initial point is taken as the midpoint 0 of the encoding of all free variables, the iteration process searches along the negative gradient direction of the objective function, the free variables that touch the interval boundary are added to the effective set and fixed at the boundary, the iteration termination condition is set to the difference between the objective function values ​​of two adjacent iterations being less than 10 to the power of -6, the maximum number of iterations is set to 200, and when the termination condition is met, the optimal encoding value of each free variable is output to form the optimal encoding combination. For example, the solution is obtained as follows: , , After finding the optimal encoding value, it is compared with a fixed value. , The optimal 5-dimensional code combination is then combined and converted into actual values ​​dimension by dimension according to the inverse decoding transformation of S3 to obtain the optimal control parameter combination. One quadratic programming problem corresponds to one set of optimal control parameter combinations.

[0047] The optimal control parameter combination is mapped to the corresponding control loop of the frequency regulation control system according to the source of each component. Virtual inertia parameters for grid-type wind power. The optimal value is written into the inertia time constant of the virtual inertia control loop through the mapping relationship of S2. The optimal value of the equivalent virtual inertia J is subtracted from the flywheel component to obtain the wind power component, which is used to verify the tuning range of the virtual inertia control loop; droop coefficient The optimal value is written into the droop control loop to determine the power-frequency static regulation characteristics; flywheel energy storage frequency regulation power The optimal value is written into the flywheel power control loop to determine the upper limit of the dynamic compensation power amplitude. After mapping, the optimal control parameter combination is written into the two-region interconnected simulation model built by S4, and the same 200kW step load disturbance as S4 is applied. The frequency performance index is verified under three operating conditions: constant wind speed, flywheel energy storage capacity change, and turbulent wind speed. The verification criteria are that the maximum frequency deviation does not exceed 0.5Hz, the maximum frequency change rate does not exceed 1Hz / s, and the steady-state frequency deviation does not exceed 0.2Hz. The verification is passed when all three operating conditions meet the verification criteria, and the optimal control parameter combination is solidified into the frequency regulation control system of the grid-type wind turbine and flywheel energy storage system. If any operating condition does not meet the criteria, the weight coefficient of the corresponding index is increased and the quadratic programming solution is re-executed. For example, when the maximum frequency change rate exceeds the limit under the turbulent wind speed condition, the... Increase the value from 0.3 to 0.4 and proportionally decrease the remaining weight coefficients, then recalculate until the verification passes.

[0048] Please see Figure 3 , Figure 3 The figure represents the response surface of steady-state frequency deviation as a function of the equivalent damping coefficient and the flywheel frequency modulation power. The horizontal axis represents the equivalent damping coefficient and the flywheel frequency modulation power, respectively, and the vertical axis represents the steady-state frequency deviation. This figure visually shows that as the equivalent damping coefficient increases and the flywheel frequency modulation power increases, the steady-state frequency deviation exhibits a non-linear decreasing trend. There is a positive synergistic effect between the two in suppressing the steady-state frequency deviation, and the surface exhibits the bending characteristics of a quadratic surface. This figure confirms the rationality of the quadratic response surface surrogate model used in this application and clearly visualizes the main effects and interaction of the two parameters, equivalent damping and flywheel frequency modulation power.

[0049] Please see Figure 4 The following describes a flywheel energy storage and grid-connected wind power frequency regulation parameter optimization system according to an embodiment of this application. The flywheel energy storage and grid-connected wind power frequency regulation parameter optimization system includes: The coupling establishment module is used to establish a frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation, and a flywheel energy storage power response model containing droop coefficient, based on the power balance relationship between the coupled grid-type wind turbine and the flywheel energy storage system. The parameter decomposition module is used to decompose the equivalent virtual inertia and equivalent damping coefficient in the frequency dynamic equation into wind power components and flywheel components, respectively. Based on the source of each component, the virtual inertia parameters of the grid-type wind power and the droop coefficient and flywheel energy storage frequency regulation power in the flywheel energy storage power response model are determined, and the vector of control parameters to be optimized is constructed. The experimental design module is used to construct a parameter experiment matrix using central composite design, with each parameter in the vector of control parameters to be optimized as experimental factors. The disturbance simulation module is used to simulate disturbances by setting parameters one by one according to the parameter test matrix, and extract the corresponding frequency performance indicators, including the maximum frequency deviation, the maximum rate of frequency change and the steady-state frequency deviation. The model fitting module is used to fit and establish a quadratic response surface surrogate model containing main effect terms, interaction terms, and quadratic terms, with the vector of control parameters to be optimized as input and the frequency performance index as output. The analysis of variance module is used to perform analysis of variance on the quadratic response surface surrogate model and to screen key control parameters based on the main effects, interactions and significance of quadratic terms of each experimental factor. The optimization and tuning module is used to construct the optimization objective function by weighting and minimizing the frequency performance index, solve the optimal combination of control parameters based on the quadratic response surface surrogate model, and tune the frequency regulation and control system of the grid-type wind turbine and flywheel energy storage system.

[0050] Through the collaborative efforts of the aforementioned components, this system achieves a transformation in the design approach for frequency regulation control parameters of grid-connected wind turbines and flywheel energy storage systems, shifting from a combination of empirical directional statistical modeling and analytical optimization. Specifically: The frequency dynamic equation output by the coupling module is coupled with the flywheel energy storage power response model, providing a unified physical basis for the parameter decomposition module. The parameter decomposition module traces the equivalent virtual inertia and equivalent damping coefficient back to specific control parameters according to their component sources, constructs a vector of control parameters to be optimized, and determines their value range. This vector is then used by the experimental design module to generate a parameter test matrix based on the central composite design. The disturbance simulation module performs disturbance simulations under various operating conditions group by group according to the parameter test matrix and extracts frequency performance indicators. The resulting input-output sample dataset is then used by the model fitting module to regress and establish a quadratic response surface surrogate model. The variance analysis module examines the significance of the main effects, interactions, and quadratic terms of each experimental factor based on the quadratic response surface surrogate model, and selects key control parameters to reduce the optimization dimensionality. The optimization tuning module uses the key control parameters as optimization variables to solve for the optimal combination of control parameters on the quadratic response surface surrogate model, and maps it to the virtual inertia control link, droop control link, and flywheel power control link of the frequency modulation control system according to the component sources determined by the parameter decomposition module. After verification, the module is fixed for operation. The data flow between modules is closed-loop, with the output of the previous module serving as the input of the next. The frequency modulation parameter optimization process can be completed continuously without manual intervention, reducing the amount of simulation calculation while ensuring optimization accuracy, thus improving parameter optimization efficiency and system frequency stability.

[0051] This application also provides a computer-readable storage medium, which can be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when the instructions are executed on a computer, cause the computer to perform the steps of the method for optimizing frequency regulation parameters of flywheel energy storage and grid-connected wind power coupling.

[0052] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the methods and systems described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0053] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for optimizing frequency regulation parameters of flywheel energy storage coupled with grid-connected wind power, characterized in that, include: S1. Based on the power balance relationship between the grid-type wind turbine and the flywheel energy storage system, establish the frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation, and the flywheel energy storage power response model containing droop coefficient. S2. Decompose the equivalent virtual inertia and the equivalent damping coefficient in the frequency dynamic equation into wind power components and flywheel components, respectively. Determine the virtual inertia parameters of the grid-type wind power and the droop coefficient and flywheel energy storage frequency regulation power in the flywheel energy storage power response model according to the source of each component, and construct the control parameter vector to be optimized. S3. Using each parameter in the control parameter vector to be optimized as an experimental factor, a parameter experimental matrix is ​​constructed using a central composite design. S4. Set the parameter disturbance simulation group by group according to the parameter test matrix, and extract the corresponding frequency performance indicators, including the maximum frequency deviation, the maximum frequency change rate and the steady-state frequency deviation. S5. Using the vector of control parameters to be optimized as input and the frequency performance index as output, fit and establish a quadratic response surface surrogate model containing main effect term, interaction term and quadratic term; S6. Perform variance analysis on the quadratic response surface surrogate model and screen key control parameters based on the main effects, interaction effects and significance of the quadratic terms of each experimental factor. S7. Construct an optimization objective function by weighting and minimizing the frequency performance indicators, solve for the optimal combination of control parameters based on the quadratic response surface surrogate model, and tune the frequency regulation control system of the grid-type wind turbine and flywheel energy storage system.

2. The method according to claim 1, characterized in that, S1 includes: Establish the power balance relationship between grid-connected wind turbines and flywheel energy storage systems sharing a DC bus, and characterize the power balance between wind power, flywheel energy storage, and load disturbances; The power balance relationship is organized to obtain the frequency dynamic equation, which includes the product of the equivalent virtual inertia and the rate of change of frequency deviation, the product of the equivalent damping coefficient and the frequency deviation, and the power loss. The flywheel energy storage power response model includes static regulation power, which is the product of droop coefficient and frequency deviation, and dynamic compensation power, which tracks the rate of change of frequency deviation. The frequency regulation process is divided into three stages: fast inertia response, dynamic recovery, and steady-state power recovery, according to the dominant order of the equivalent virtual inertia, the equivalent damping coefficient, and the droop coefficient.

3. The method according to claim 1, characterized in that, S2 includes: The equivalent virtual inertia is decomposed into wind power component and flywheel component. The wind power component is the virtual synchronous inertia mapped by the virtual inertia parameters of the grid-type wind power, and the flywheel component is the inertia support mapped by the flywheel rotor inertia. The equivalent damping coefficient is decomposed into wind power component and flywheel component. The wind power component is the droop damping mapped by the droop coefficient, and the flywheel component is the dynamic damping mapped by the flywheel energy storage frequency regulation power. The droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameters are determined according to the source of each component. The flywheel rotor inertia is an inherent parameter of the device and is not optimized. The three parameters, namely the droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameters, together with the equivalent virtual inertia and equivalent damping coefficient, are used to construct the control parameter vector to be optimized, and the value range of each parameter is determined.

4. The method according to claim 1, characterized in that, S3 includes: The equivalent virtual inertia, equivalent damping coefficient, droop coefficient, flywheel energy storage frequency regulation power, and grid-type wind power virtual inertia parameter in the control parameter vector to be optimized are taken as five test factors. Within the preset value range, the actual values ​​of each test factor are normalized and encoded as high level and low level. The test points are arranged in the coded factor space according to the central composite design. The test points include factor points composed of two-level combinations of each test factor, axial points on the coordinate axes of each test factor at a set distance from the center, and center points that are repeatedly arranged in the center of the factor space. A parameter test matrix is ​​generated by summarizing the parameter combinations corresponding to all test points. Each row of the parameter test matrix corresponds to a set of parameter values ​​to be simulated under disturbance.

5. The method according to claim 1, characterized in that, S4 includes: A two-region interconnection simulation model is built, which includes a grid-type wind turbine, a flywheel energy storage system and a synchronous power source. The grid-type wind turbine and the flywheel energy storage system are connected to the same region and interconnected with the synchronous power source of the other region via a tie line. Write the parameter values ​​of each row in the parameter test matrix into the two-region interconnection simulation model one by one, and apply the same load disturbance under three working conditions: constant wind speed, flywheel energy storage capacity change and turbulent wind speed, and record the frequency response curve. The maximum frequency deviation, maximum frequency change rate, and steady-state frequency deviation are extracted from the frequency response curves of each group of disturbance simulation records to form frequency performance indicators that correspond one-to-one with each row of the parameter test matrix.

6. The method according to claim 1, characterized in that, S5 includes: The first-order terms of each parameter in the control parameter vector to be optimized are used as the main effect term, the product term of any two parameters is used as the interaction term, and the square terms of each parameter are used as the quadratic term. A quadratic polynomial structure is constructed with the control parameter vector to be optimized as the input and the frequency performance index as the output. The parameter values ​​in each row of the parameter test matrix are subjected to least squares regression with the corresponding frequency performance index. The regression coefficients of the quadratic polynomial structure are solved, and a quadratic response surface surrogate model is fitted and established. The determination coefficient is calculated based on the fitting value of the quadratic response surface surrogate model under each set of parameter values ​​and the residual of the corresponding frequency performance index. When the determination coefficient does not meet the preset accuracy, the experimental samples are added for refitting until the determination coefficient meets the preset accuracy.

7. The method according to claim 1, characterized in that, S6 includes: Analysis of variance was performed on the quadratic response surface surrogate model, and the total variation of each item in the frequency performance index at all test points was decomposed into the variation caused by the main effect of each test factor, the variation caused by the interaction between test factors, the variation caused by the quadratic term, and the variation of random error. The mean square of the variances of the main effects, interaction effects, and quadratic terms is calculated as the ratio of the mean square of the variance of the random error to obtain the significance test value and the corresponding significance probability value of each term. The items whose significance probability value is less than the preset significance threshold are identified as significant items, and the experimental factors corresponding to each significant item are used as the key control parameters.

8. The method according to claim 1, characterized in that, S7 includes: Weighting coefficients are assigned to the maximum frequency deviation, the maximum frequency change rate, and the steady-state frequency deviation, respectively, and the optimization objective function is constructed by minimizing the weighted sum of the three frequency performance indicators. Using the key control parameters as optimization variables and the other experimental factors as fixed values, the objective function is solved on the quadratic response surface surrogate model under the constraints of the preset value range of each experimental factor to obtain the optimal combination of control parameters; The optimal control parameter combination is mapped to the virtual inertia control link, droop control link and flywheel power control link of the frequency modulation control system according to the source of each component, and the frequency performance index is verified under load disturbance. After the verification is passed, it is fixed and put into operation.

9. A flywheel energy storage and grid-connected wind power coupling frequency regulation parameter optimization system, used to implement the flywheel energy storage and grid-connected wind power coupling frequency regulation parameter optimization method as described in any one of claims 1 to 8, characterized in that, include: The coupling establishment module is used to establish a frequency dynamic equation containing equivalent virtual inertia, equivalent damping coefficient and frequency deviation, and a flywheel energy storage power response model containing droop coefficient, based on the power balance relationship between the coupled grid-type wind turbine and the flywheel energy storage system. The parameter decomposition module is used to decompose the equivalent virtual inertia and the equivalent damping coefficient in the frequency dynamic equation into wind power components and flywheel components, respectively. Based on the source of each component, the virtual inertia parameters of the grid-type wind power and the droop coefficient and flywheel energy storage frequency regulation power in the flywheel energy storage power response model are determined to construct the control parameter vector to be optimized. The experimental design module is used to construct a parameter experiment matrix using central composite design, with each parameter in the vector of control parameters to be optimized as experimental factors. The disturbance simulation module is used to simulate disturbances by setting parameters one group at a time according to the parameter test matrix and extract the corresponding frequency performance indicators, including the maximum frequency deviation, the maximum frequency change rate and the steady-state frequency deviation. The model fitting module is used to fit and establish a quadratic response surface surrogate model containing main effect terms, interaction terms, and quadratic terms, using the vector of control parameters to be optimized as input and the frequency performance index as output. The variance analysis module is used to perform variance analysis on the quadratic response surface surrogate model and to screen key control parameters based on the main effects, interaction effects and significance of the quadratic terms of each experimental factor. The optimization and tuning module is used to construct an optimization objective function by weighting and minimizing the frequency performance index, solve for the optimal combination of control parameters based on the quadratic response surface surrogate model, and tune the frequency regulation and control system of the grid-type wind turbine and flywheel energy storage system.

10. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is executed by the processor, it implements a method for optimizing frequency regulation parameters of flywheel energy storage and grid-type wind power coupling as described in any one of claims 1 to 8.

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