A wind storage heterogeneous resource collaborative configuration method based on frequency modulation capability boundary driving

Abstract

The application relates to a wind storage heterogeneous resource collaborative configuration method based on frequency modulation capability boundary driving. The method discloses the variation characteristics of the power grid strength and the system frequency safety domain in the parameter space by constructing a system linearization state space model, and makes up for the deficiency that the existing research only focuses on steady-state single-point constraints and ignores dynamic topology evolution. On this basis, the multi-dimensional frequency modulation capability boundary including the instantaneous power domain boundary, the dynamic energy domain boundary and the recovery trajectory boundary is constructed from the supply side based on the variation characteristics, and the function compensation boundary of the flywheel and the lithium battery in the heterogeneous resource is determined. Finally, the improved particle swarm algorithm based on the target function and guided by the boundary sensitivity operator is used for optimization in the multi-dimensional frequency modulation capability boundary, the heterogeneous capacity configuration scheme is obtained, the accurate configuration of the heterogeneous energy storage in the non-convex failure space is realized, and the full life cycle cost is significantly reduced while the system frequency resilience is ensured.

Description

Technical Field

[0001] This application relates to the technical field of wind-storage heterogeneous resource capacity allocation methods, and in particular to a wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving. Background Technology

[0002] Existing active frequency control strategies for wind turbines and their combined frequency regulation technologies with energy storage systems (ESS) effectively compensate for the power deficit of wind turbines during the rotor energy recovery phase, forming a complementary "wind-storage combined frequency regulation" mode. However, existing frequency regulation technologies have the following shortcomings: 1. Limited safety assessment dimensions: Existing solutions focus on quasi-steady-state indicators such as the lowest frequency point, failing to analyze and characterize the dramatic topological evolution and centripetal collapse characteristics of the frequency safety domain (SFB) under extremely weak power grids as the short-circuit ratio (SCR) decreases.

[0003] 2. Lack of identification of physical performance gaps: There is a lack of analytical expression of the "performance gap" mechanism caused by severe inertia in extremely weak power grids, which makes the system prone to irreversible instability in the early stage of disturbance due to the instantaneous over-limit of the rate of change of frequency (RoCoF).

[0004] 3. Ambiguous criteria for matching heterogeneous resources: The capability boundary mapping relationship between flywheel energy storage system (FESS) and lithium battery energy storage system (BESS) is unclear at different time scales. In particular, when dealing with the frequency "second drop" caused by wind power recovery, there is a lack of mechanism-driven configuration criteria.

[0005] 4. Optimization algorithms are prone to getting trapped in local optima: The constrained space of extremely weak power grids is characterized by high non-convexity, discontinuity and physical failure zones. Traditional heuristic algorithms (such as standard PSO) lack physical perception, and particles are prone to blindly oscillate within the failure zones or get trapped in local extrema. Summary of the Invention

[0006] This application aims to address the frequency stability degradation and security defense failure issues caused by the high coupling of extremely low short-circuit ratios and low inertia characteristics in extremely weak receiving-end power grids. It is necessary to provide a wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving, including: S1: A linearized state-space model of the system is established based on the incremental deviation of the output power of conventional generating units, wind turbines, flywheel batteries, and lithium batteries in the power grid; the trajectory evolution of the system eigenvalues ​​based on the linearized state-space model describes the variation characteristics of the grid strength and the system frequency security domain in the parameter space. S2: Based on the aforementioned change characteristics, construct a multi-dimensional frequency modulation capability boundary from the supply side, including instantaneous power domain boundary, dynamic energy domain boundary, and recovery trajectory boundary; S3: Based on the instantaneous power domain boundary, dynamic energy domain boundary, recovery trajectory boundary and grid strength, a boundary sensitivity operator is constructed, and an objective function to minimize the annualized total cost over the entire life cycle is constructed. Based on the objective function and an improved particle swarm algorithm guided by the boundary sensitivity operator, the optimization is performed in the multidimensional frequency regulation capability boundary to obtain a heterogeneous capacity configuration scheme.

[0007] Beneficial Effects: Addressing the core challenges of the system's susceptibility to "performance gaps" caused by inertia dilution in the early stages of disturbances and "frequency secondary drops" induced by wind power withdrawal during the recovery phase, this method constructs a linearized state-space model of the system. This model reveals the variation characteristics of the grid strength and system frequency security domain in the parameter space, overcoming the shortcomings of existing research that only focuses on steady-state single-point constraints while neglecting dynamic topology evolution. Based on these variation characteristics, a multi-dimensional frequency regulation capability boundary, including instantaneous power domain boundary, dynamic energy domain boundary, and recovery trajectory boundary, is constructed from the supply side, clarifying the functional compensation boundary of flywheel and lithium battery in heterogeneous resources. Finally, based on the objective function and an improved particle swarm optimization algorithm guided by the boundary sensitivity operator, the multi-dimensional frequency regulation capability boundary is optimized to obtain a heterogeneous capacity configuration scheme. This achieves precise configuration of heterogeneous energy storage in a non-convex failure space, thereby significantly reducing the total life cycle cost while ensuring system frequency resilience. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart of the wind-storage heterogeneous resource collaborative configuration method based on frequency modulation capability boundary driven in the embodiments of this application.

[0010] Figure 2 This is a schematic diagram illustrating the variation characteristics of the system frequency security domain in the state space under power grid intensity differences in this embodiment of the application.

[0011] Figure 3 This is a sensitivity heatmap showing the impact of grid strength and disturbance power on the annualized total cost over the entire life cycle, as described in this application embodiment.

[0012] Figure 4 This diagram shows the safety and robustness verification of the method under power grid intensity fluctuations in the embodiments of this application.

[0013] Figure 5This is a comparison chart of the convergence characteristics of the method in this application embodiment with other optimization algorithms.

[0014] Figure 6 This is a heatmap showing the sensitivity of the annualized total cost over the entire life cycle under different combinations of SCR and disturbance in the embodiments of this application.

[0015] Figure 7 This is a heat map showing the coupled effects of grid strength and load disturbance on the lowest point of system frequency in the embodiments of this application.

[0016] Figure 8 This is a comparison chart showing the optimal configuration of annualized total cost for different algorithms in the embodiments of this application. Detailed Implementation

[0017] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0018] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0019] like Figure 1 As shown, this embodiment provides a method for collaborative allocation of heterogeneous wind and energy storage resources based on frequency regulation capability boundary driving, including: S1: Establish a linearized state-space model of the system based on the incremental deviation of the output power of conventional units, wind turbines, flywheel batteries, and lithium batteries in the power grid; describe the variation characteristics of the grid strength and system frequency security domain in the parameter space based on the trajectory evolution of the system eigenvalues ​​of the linearized state-space model.

[0020] Specifically, the linearized state-space model of the system includes: The dynamic evolution equation of the system's state vector is expressed as: ; ; in, The dynamic evolution of the state vector is represented by A(·), where A(·) represents the state matrix and SCR represents the grid strength. Let B represent the state vector, and let B represent the input matrix, which includes the frequency deviation rate of change, the output power increment deviation rate of the conventional generator speed governor, the output power increment deviation rate of the wind turbine generator, the output power increment deviation rate of the flywheel energy storage system, the output power increment deviation rate of the lithium battery energy storage system, and the rotor angular velocity deviation rate of the wind turbine generator. This indicates the per-unit value of the disturbance power. Indicates frequency deviation. This indicates the deviation in the incremental output power of conventional generating units. This indicates the deviation in the incremental output power of the fan. This indicates the deviation in the output power increment of the flywheel battery. This indicates the deviation in the incremental output power of the lithium battery. This indicates the angular velocity deviation of the fan rotor, where T represents transpose; The frequency deviation evolves dynamically with the state vector, and the evolution equation is as follows: ; in, This represents the dynamic evolution of frequency deviation. This represents the equivalent moment of inertia dependent on the strength of the power grid. This represents the load damping coefficient that depends on the strength of the power grid.

[0021] Furthermore, the expression for the state matrix is: ; in, This represents the droop characteristic coefficient of a conventional generator set speed governor. This represents the equivalent time constant between the governor and the prime mover of a conventional generator set. This represents the virtual inertia of the wind turbine's primary frequency control. This represents the equivalent response time constant of the active frequency regulation control loop of the wind turbine. This indicates the frequency modulation power gain of the flywheel energy storage system. This represents the equivalent control response time constant of the flywheel energy storage system. Indicates the frequency modulation power gain of a lithium battery energy storage system. This represents the equivalent control response time constant of a lithium battery energy storage system. This represents the dynamic damping coefficient of the wind turbine generator. This represents the rotor inertia constant of a wind turbine generator set.

[0022] Furthermore, the expression for the system's eigenvalues ​​is: ; in, Indicates the equivalent damping ratio. Indicates the undamped natural frequency. Representing the system's characteristic roots, Represents the imaginary unit; The equivalent damping ratio is directly proportional to the change in grid strength. The system frequency security domain is represented as: ; in, Represents the system frequency security domain. Indicates the rate of change of frequency. Indicates the frequency deviation limit. This represents the limit value of the rate of change of frequency.

[0023] The trajectory evolution of system eigenvalues ​​based on the linearized state-space model describes the variation characteristics of grid strength and system frequency security domain in the parameter space (system equivalent inertia J, system equivalent damping D), such as... Figure 2 As shown, it specifically includes: In a strong power grid environment, the equivalent damping ratio increases and the system characteristic root is far away from the imaginary axis. The manifold envelope of the system frequency safety domain far exceeds the limit, and the stability is dominated by the recovery time. For medium-intensity power grid environments, a decrease in the equivalent damping ratio leads to an increase in frequency deviation, and the system frequency safety domain collapses laterally toward the origin, making the maximum frequency deviation a constraint. In extremely weak power grid environments, the inertia dilution effect causes the system's eigenvalues ​​to approach the imaginary axis, and the system's frequency security domain to... When the shaft collapses vertically along its axial direction, the instantaneous rate of change of frequency exceeds the limit, and the system fails dynamically.

[0024] S2: Based on the aforementioned change characteristics, construct a multi-dimensional frequency modulation capability boundary from the supply side, including instantaneous power domain boundary, dynamic energy domain boundary, and recovery trajectory boundary.

[0025] Specifically, the steps include: The instantaneous rate of change of frequency under disturbance is strongly constrained by the equivalent rotational inertia dependent on grid strength, the equivalent time delay of the wind-storage control system, and the output power of the flywheel energy storage system. Therefore, the instantaneous power domain boundary is defined as follows: ; ; ; in, This indicates the per-unit value of the disturbance power. Indicates the equivalent delay of the flywheel energy storage system 'output power' This represents the equivalent moment of inertia dependent on the strength of the power grid. This represents the output power of the flywheel energy storage system at time t. Indicates that the flywheel energy storage system is in Maximum output power at any given time This represents the equivalent response time constant of the flywheel system; The frequency deviation limit depends on the energy difference of the disturbance process, and the dynamic energy domain boundary is defined as follows: ; in, t nadir The time point representing the quasi-steady-state equilibrium point. This indicates the per-unit value of the disturbance power. This represents the deviation of the output power increment of a conventional unit at time t. This represents the incremental deviation of the fan's output power at time t when the fan load reduction rate is a. This indicates the deviation in the output power increment of the flywheel battery. This represents the deviation in the incremental output power of the lithium battery at time t. Represents the equivalent moment of inertia. f 0 indicates the initial nominal frequency of the system; The monotonicity guarantee criterion for the frequency recovery stage is derived using the convergence region analysis method, and the disturbance power is guaranteed. If the lower time-domain frequency trajectory is greater than 0, then the recovered trajectory boundary is defined as: ; in, This indicates the output power of the lithium battery. Indicates partial derivative, The angular velocity of the fan rotor is... The output power of the fan This indicates the ramp-up rate of conventional generating units, which depends on the strength of the power grid.

[0026] Furthermore, the disturbance power The lower time-domain frequency trajectory is represented as: ; in, f ( t () indicates the disturbance power The time-domain frequency trajectory at time t. Indicates the load damping coefficient. This represents the initial phase angle.

[0027] S3: Based on the instantaneous power domain boundary, dynamic energy domain boundary, recovery trajectory boundary and grid strength, a boundary sensitivity operator is constructed, and an objective function to minimize the annualized total cost over the entire life cycle is constructed. Based on the objective function and an improved particle swarm algorithm guided by the boundary sensitivity operator, the optimization is performed in the multidimensional frequency regulation capability boundary to obtain a heterogeneous capacity configuration scheme.

[0028] In this embodiment, a boundary sensitivity operator is constructed based on the instantaneous power domain boundary, dynamic energy domain boundary, recovery trajectory boundary, and grid strength, including: ; in, S SCR Represents the boundary sensitivity operator. B R Indicates the instantaneous power domain boundary. B f Represents the boundary of the dynamic energy domain. B rec The boundary of the recovery trajectory is represented by SCR, which represents the grid strength (i.e., the short-circuit ratio of the grid), and T represents the transpose.

[0029] Furthermore, the expression for the objective function is: ; ; ; ; ; ; in, C total This represents the annualized total cost over the entire life cycle. C cap This indicates annualized capital expenditure. C opex Indicates operation and maintenance costs. C curt This indicates the cost of wind curtailment compensation. C deg Indicates the cost of energy storage degradation. C pen This represents adaptive default penalty, r represents the discount rate, L represents the total lifespan, F represents the flywheel, and B represents the lithium battery. This indicates the unit power of the flywheel or lithium battery. This indicates the capacity cost of the flywheel or lithium battery. μ k This represents the annual maintenance coefficient. This represents the price compensation coefficient per unit of wind curtailment energy. This represents the rated total installed capacity of the wind farm, and 'a' represents the wind turbine derating rate. C B,repl This represents the benchmark for battery replacement costs. This represents the magnitude of the change in state of charge caused by the t-th charge-discharge cycle. N cycle (DoD) indicates the maximum number of cycles under DoD. γ (SCR) represents the dynamic weight mapping coefficient, and SCR represents the grid strength. Vio (·) represents the default function, which compares each boundary with the corresponding preset conditions (such as instantaneous power limit, dynamic time-varying boundary, recovery deviation boundary). If the boundary exceeds the preset conditions, the default term is a normalized value of the relative proportion of the boundary exceeding the corresponding preset conditions; otherwise, the default term is 0. This represents the default weight corresponding to the instantaneous power domain boundary. This represents the default weight corresponding to the boundary of the dynamic energy domain. This represents the default weight corresponding to the recovery trajectory boundary, where T represents the number of years in the entire lifecycle. P k Indicates the first k Configuration power of energy storage resources E k Indicates the first k The capacity of energy storage resources; DoD represents the depth of discharge. The constraints include: Instantaneous inertia safety constraints are expressed as: ; Dynamic energy balance constraints are expressed as: ; in, This indicates the maximum frequency deviation. The second-order drop constraint is represented as: ; in, E BESS Indicates the capacity of the lithium battery. This represents the maximum ramp rate of conventional generating units, dependent on grid strength. t rec Indicates the target time point for frequency transient recovery. This represents the equivalent power deficit function caused by the rotor kinetic energy withdrawal during the transient recovery phase of a wind turbine generator, expressed by the wind turbine load factor. α angular velocity of the fan rotor ω t And time t together determine it.

[0030] Furthermore, the process of obtaining a heterogeneous capacity configuration scheme includes: Step 1; Define the position vector of the particle and the search space. The position vector of the i-th particle is denoted as: , This indicates the output power of the flywheel energy storage system. This indicates the output power of the lithium battery. E BESSdenoted by , where 'a' represents the capacity of the lithium battery, 'a' represents the wind turbine load reduction rate, and 'T' represents transposition; the search space is dynamically limited by the boundary of the multi-dimensional frequency modulation capability.

[0031] Step 2: Obtain the grid strength SCR, system equivalent inertia J, system equivalent damping D, and per-unit disturbance power ΔP. L .

[0032] Step 3: Population initialization. A Gaussian distribution is used to force 70% of the particles to be distributed along the multidimensional frequency tuning capability boundary. This prevents the particle swarm from entering the dynamic failure region during initialization and ensures that the algorithm has the ability to detect performance gaps from the initial stage. The adjustment formula is as follows: ; in, This represents the initial position of the j-th particle, and rand(·) represents a random function. L b Indicates the upper boundary of the boundary. U b Indicates the lower boundary of the boundary. λ Indicating mechanism guiding factor, N (0, σ 2 ) represents a Gaussian perturbation. X crit =[ J crit , D crit [] indicates the critical point. J crit This represents the critical value of the system's equivalent inertia. D crit This represents the critical value of the system's equivalent damping.

[0033] Step 4: Calculate the fitness of each particle based on the objective function and boundary sensitivity operator. The calculation formula is as follows: ; in, F ( X i ) represents the fitness of the i-th particle. ，B j This represents the boundary of the instantaneous power domain, the boundary of the dynamic energy domain, or the boundary of the recovered trajectory. This represents the set of indices for the instantaneous power domain boundary, dynamic energy domain boundary, and recovered trajectory boundary; exp(·) represents the adaptive penalty term; and Dist(·) represents the Euclidean distance. This represents the coordinates of the i-th particle.

[0034] Step 5: Update the velocity and position of each particle using inertia weights; based on the classical velocity equation, introduce a boundary gradient repulsion term to prevent particles from touching the red violation boundary during the optimization process. The velocity update formula is: ; ; in, This represents the velocity of the i-th particle in the (k+1)-th iteration. This represents the inertia weight in the k-th iteration. Let represent the velocity of the i-th particle in the k-th iteration, c1 represent the first learning factor, c2 represent the second learning factor, and r1 represent the first random number, r2 represent the second random number. This represents the historical best position of the i-th particle. This represents the global optimal position of all particles. This represents the position of the i-th particle in the k-th iteration. Represents the boundary gradient repulsion term. S SCR Represents the boundary sensitivity operator. N c Indicates the number of constraint functions. This represents the m-th constraint function. Represents constraint functions gradient, ε This represents a small constant to prevent division by zero.

[0035] In this embodiment, the update formula for the inertia weight is: ; ; in, Indicates the termination value of the inertial weight. This represents the initial value of the inertia weight. Indicates the maximum number of iterations. α Indicates the illegal coupling coefficient. This indicates the degree of violation of the particle's distance from the safe domain.

[0036] Step 6: Update the archive for all particles based on the Pareto dominance criterion; for any two particles X a and X b If the following conditions are met: Then X is called a DominateX b The archive set retains only non-dominated solutions and uses crowding distance for diversity maintenance. ; in, f p(·) is a predefined first utility function; d j The crowding distance between particles, This represents the maximum value obtained based on the first utility function. This represents the minimum value obtained based on the first utility function.

[0037] Step 7: Repeat steps 4-6 until the archive size reaches the upper limit or the Pareto front stops moving in a set number of consecutive iterations. The algorithm terminates and outputs a heterogeneous capacity configuration scheme. The heterogeneous capacity configuration scheme includes the optimal output power of the flywheel energy storage system, the output power of the lithium battery, the capacity of the lithium battery, and the wind turbine load factor.

[0038] This embodiment also provides a simulation analysis experiment of the configuration method: 1. Simulation experiment configuration and system parameters; This experiment uses MATLAB R2016a software to construct a numerical simulation program for the frequency response of heterogeneous resources based on analytical kernels. To verify the effectiveness of the model under different grid strengths, two benchmark test scenarios were set up: a strong grid (SCR=8.5) and a weak grid (SCR=2.5). The frequency was 50 Hz at t=0, and a load step was applied at t=1.0s, recording the frequency trajectory over the following 20s. The specific parameter settings are shown in Table 1 below. Table 1 System Simulation Basic Parameters

[0039] Set the parameters according to the basic parameters shown in Table 1.

[0040] 2. Sensitivity analysis of system frequency stability to parameters; Sensitivity analysis aims to quantitatively describe the relationship between grid strength SCR and disturbance power ΔP. L For security domain Ω safe Geometric mapping relationship. By quantifying the coupling relationship between SCR and heterogeneous resource parameters (J, D) through multi-parameter scanning, the evolution law of security domain collapse as network strength weakens is revealed from the physical mechanism level.

[0041] 2.1 Analysis of the impact of grid strength SCR; Based on the aforementioned derivation, the boundary set {B} R B f B rec Within the parameter space of the system's equivalent inertia J and equivalent damping D, the frequency security domain distribution and boundary evolution under power grid strength differences are as follows: Figure 3 As shown.

[0042] Figure 3 It shows the work of {B} R Bf B rec The frequency modulation capability boundary formed by the envelope of nonlinear criteria such as}, and its orange shaded area is the safety region Ω under full performance constraints. safe As the SCR decreases from 8.5 to 2.5, driven by the decline in the ramp-up rate of conventional units and the surge in demand for restoring energy reserves, the area of ​​this region shrinks significantly and exhibits a centripetal collapse trend. Critical feasible point P crit As the grid strength decreases, the network drifts towards the high-parameter region, causing the steady-state parameter points under strong grid conditions to fall due to the drop in the effective support coefficient, which cannot suppress the secondary drop in frequency, eventually degenerating into the unstable region.

[0043] 2.2 Analysis of the impact of disturbance power ΔPL; By traversing the (J, D) parameter space, the maximum load step disturbance ΔP that satisfies the system frequency safety red line (RoCoF < 0.8 Hz / s and Δf < 0.6 Hz) is calculated. max The carrying capacity in strong / weak network environments, for example... Figure 4 As shown in Table 2; Table 2. Quantitative Comparison of Disturbance Bearing Capacity of Typical Parameter Points under Strong / Weak Networks

[0044] Depend on Figure 4 As shown in Table 2, comparing the surfaces under different grid strengths, the weakening of SCR causes centripetal collapse of the safety domain, significantly reducing the upper limit of system disturbance resistance. Under weak grid conditions, when J < 5.0, ΔP max The performance drops at an accelerating rate as inertia decreases, forming a "RoCoF performance fault," revealing the extreme sensitivity of the low-inertia system to disturbances. Taking coordinate point (J=10, D=10) as an example, the weak network's carrying capacity decreases by approximately 27.7% compared to the strong network. The results indicate that the weak network configuration needs to introduce power-type heterogeneous resources such as flywheels to bridge the performance fault, thereby improving support margin and offsetting the performance loss caused by strong network fluctuations.

[0045] 3. Optimization configuration analysis based on boundary model; To deeply analyze the driving effect of grid strength on resource allocation, this experiment compares three schemes in an extremely weak grid (SCR=2.5) scenario: Scheme 1 (F0) adopts a fixed constraint configuration based on experience with strong grids; Scheme 2 (F1) uses a single lithium battery configuration based on nonlinear capability boundaries; Scheme 3 (F2) uses a boundary-driven method to identify "performance gaps" and achieve heterogeneous synergistic optimization of flywheel and lithium battery. The configuration results are as follows: Table 3. Result of different configuration schemes

[0046] The configuration results in Table 3 show that, in an extremely weak grid environment (SCR=2.5), Scheme F2 achieves optimal synergy between physical support and economic efficiency by accurately identifying "performance gaps." The rapid response of the 8 MW flywheel replaces approximately 77.8% of the lithium battery energy stacking in Scheme F0, reducing annualized capital expenditure by 60.0%. Furthermore, heterogeneous division of labor effectively suppresses high-rate losses in lithium batteries, significantly reducing their degradation costs compared to Scheme F1. Ultimately, while eliminating default risk, it achieves a 58.94% improvement in overall returns.

[0047] 3.1 Frequency modulation performance analysis; Time-domain simulations were performed on the optimized configuration scheme to verify its frequency modulation effect under weak network conditions. The simulation was set to occur at time t=1.0s. L = 0.15 pu step disturbance. A comparative analysis of four schemes is presented: Scheme 1 is a scheme without energy storage; Scheme 2 (S0) is a scheme based on traditional configuration methods; Scheme 3 (S1) is a scheme based on a single lithium battery; and Scheme 4 (S2) is the proposed scheme. The frequency regulation performance curves of different schemes are shown below. Figure 5 As shown in Table 4, the comprehensive indicators of the entire frequency modulation process are compared. Table 4 Comparison of Comprehensive Indicators Throughout the FM Modulation Process

[0048] Depend on Figure 5 The simulation results shown in Table 4 demonstrate that this scheme exhibits superior frequency regulation efficiency and economy through the synergy of heterogeneous resources in instantaneous power and dynamic energy domains. Under a weak grid with SCR=2.5, the flywheel energy storage system utilizes its millisecond-level response characteristics to provide inertia support, effectively suppressing the initial RoCoF; the lithium battery energy storage then smoothly takes over, raising the lowest frequency point to 49.59Hz and completely eliminating the "secondary drop" caused by wind power recovery. Compared to the high-redundancy scheme S0, this scheme only requires 10MWh of lithium battery to achieve comparable performance indicators; compared to the single lithium battery scheme S1, its economic benefits are significantly improved by 58.94%, verifying the dual advantages of the proposed synergistic strategy in ensuring the safety of extremely weak grids and improving operational efficiency.

[0049] 4. Robustness analysis of the solution; 4.1 Economic sensitivity thermal diagram analysis; The horizontal axis of the heatmap represents the grid strength SCR ∈ [2.0, 10.0], and the vertical axis represents the load disturbance ΔP. L ∈[0.05, 0.35] pu, Figure 6 This is a heatmap of the annualized total cost sensitivity over the entire life cycle under different combinations of SCR and disturbances. The color intensity represents the annualized total cost C. total . Figure 6The quantitative analysis demonstrates the impact of grid strength (SCR) fluctuations on costs. Specifically, in strong grid areas with SCR > 6.0, costs increase linearly and slowly with disturbances, exhibiting extremely high stability. However, upon entering extremely weak grid fault areas with SCR < 3.0, to mitigate the risk of frequency exceeding limits caused by inertia collapse, the system adaptively adjusts the heterogeneous resource allocation ratio, leading to an exponential increase in costs. This verifies the robustness and superiority of the proposed solution in ensuring weak grid security and improving the economic efficiency throughout the entire life cycle.

[0050] 4.2 Security robustness verification; To verify the safety boundary of the proposed configuration scheme under different grid strengths and complex disturbances, this experiment employs a combination of extreme scenario scanning and frequency response probability envelope methods. The core of this approach lies in ensuring that the configuration point remains within the safety domain Ω during SCR fluctuations through Monte Carlo simulation and worst-case backtesting. safe internal.

[0051] Figure 7 Quantitatively, this demonstrates the effect of grid strength and load disturbance on the system's lowest frequency point f. nadir The coupling effect clearly characterizes f nadir The safe operating range boundary is >49.5Hz. As shown in the figure, in the strong grid area with SCR>6.0, the frequency drop is shallow and insensitive to the scale of disturbances, exhibiting extremely high stability. However, upon entering the extremely weak grid area with SCR<3.0, the contour density increases sharply as the grid strength decreases, indicating that the system stability is extremely sensitive to environmental fluctuations. The proposed solution effectively compensates for the frequency support capability deficiency caused by the weakening of the grid strength through the heterogeneous synergy of flywheel and lithium battery, ensuring that even under extreme conditions of extremely weak grid superimposed with the maximum disturbance, the lowest frequency point is always maintained above the 49.5Hz safety red line, strongly verifying the robustness of the proposed configuration method in ensuring frequency safety in weak grids.

[0052] 5. Algorithm performance comparison and analysis; The improved particle swarm optimization (PSO) algorithm proposed in this paper is compared with the standard PSO and genetic algorithms (GA) in a multi-dimensional performance analysis under a grid strength SCR=2.5 scenario to verify its superiority in handling nonlinear capability boundary constraints. To demonstrate the algorithm's efficiency in complex search spaces, the fitness evolution trajectories of the three algorithms under the SCR=2.5 scenario are recorded. Figure 8 As shown in Table 5, the configuration results are as follows; Table 5. Performance comparison of different algorithms in weak network scenarios (SCR=2.5)

[0053] Depend on Figure 8As shown in Table 5, the IPSO algorithm presented in this paper, thanks to the boundary sensitivity guiding factor, only requires 42 iterations to overcome the "performance gap" in weak grids, accurately locking the optimal configuration ratio of an 8.0MW flywheel to a 10.0MWh lithium battery, with a convergence speed approximately 55.8% faster than traditional algorithms. Under extremely weak grid conditions with SCR=2.5, this scheme suppresses RoCoF through flywheel instantaneous power support and utilizes lithium battery energy compensation to reduce f... nadir The frequency was increased to 49.59Hz, completely eliminating the secondary frequency drop caused by wind power recovery. Ultimately, the solution achieved zero default operation under all operating conditions with a minimum annualized cost of 3.3829 million yuan, verifying the dual superiority of heterogeneous resource collaborative configuration in ensuring the security of extremely weak networks and improving the economic efficiency throughout the entire life cycle.

[0054] The wind-storage heterogeneous resource collaborative allocation method based on frequency modulation capability boundary driving provided in this embodiment has the following beneficial effects: 1. By establishing a linearized state-space model of the system that takes into account the short-circuit ratio factor of the power grid, the physical mechanism of the frequency security domain being induced by the ramp rate of associated units is revealed, and the area of ​​the security domain is quantified to be reduced by about 65% under extremely weak grids.

[0055] 2. The performance fault phenomenon dominated by the frequency change rate constraint was identified and defined, and a multi-dimensional frequency modulation capability boundary covering instantaneous power, dynamic energy and recovery trajectory monotonicity was constructed.

[0056] 3. With the goal of minimizing the annualized total cost over the entire life cycle, an improved particle swarm optimization algorithm based on boundary sensitivity operators was used to achieve accurate optimization of heterogeneous resources within the safe domain.

[0057] Simulation results show that, under the premise of satisfying the safety constraints of extremely weak grids, the proposed heterogeneous scheme reduces the annualized total cost by 18.78% and the lithium battery degradation cost by 45.03% compared with the single lithium battery scheme, and exhibits strong robustness under the scenario of drastic fluctuations in grid short-circuit ratio.

[0058] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0059] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for collaborative allocation of heterogeneous wind and energy storage resources based on frequency regulation capability boundary driving, characterized in that, include: S1: Establish a linearized state-space model of the system based on the incremental deviation of the output power of conventional units, wind turbines, flywheel batteries, and lithium batteries in the power grid; The trajectory evolution of system eigenvalues ​​based on the linearized state-space model describes the variation characteristics of grid strength and system frequency security domain in parameter space. S2: Based on the aforementioned change characteristics, construct a multi-dimensional frequency modulation capability boundary from the supply side, including instantaneous power domain boundary, dynamic energy domain boundary, and recovery trajectory boundary; S3: Based on the instantaneous power domain boundary, dynamic energy domain boundary, recovery trajectory boundary and grid strength, a boundary sensitivity operator is constructed, and an objective function to minimize the annualized total cost over the entire life cycle is constructed. Based on the objective function and an improved particle swarm algorithm guided by the boundary sensitivity operator, the optimization is performed in the multidimensional frequency regulation capability boundary to obtain a heterogeneous capacity configuration scheme.

2. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 1, characterized in that, The linearized state-space model of the system includes: The dynamic evolution equation of the system's state vector is expressed as: ； ； in, The dynamic evolution of the state vector is represented by A(·), where A(·) represents the state matrix and SCR represents the grid strength. Let B represent the state vector, and let B represent the input matrix, which includes the frequency deviation rate of change, the output power increment deviation rate of the conventional generator speed governor, the output power increment deviation rate of the wind turbine generator, the output power increment deviation rate of the flywheel energy storage system, the output power increment deviation rate of the lithium battery energy storage system, and the rotor angular velocity deviation rate of the wind turbine generator. This indicates the per-unit value of the disturbance power. Indicates frequency deviation. This indicates the deviation in the incremental output power of conventional generating units. This indicates the deviation in the incremental output power of the fan. This indicates the deviation in the output power increment of the flywheel battery. This indicates the deviation in the incremental output power of the lithium battery. This indicates the angular velocity deviation of the fan rotor, where T represents transpose; The frequency deviation evolves dynamically with the state vector, and the evolution equation is as follows: ； in, This represents the dynamic evolution of frequency deviation. This represents the equivalent moment of inertia dependent on the strength of the power grid. This represents the load damping coefficient that depends on the strength of the power grid.

3. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 2, characterized in that, The expression for the state matrix is: ； in, This represents the droop characteristic coefficient of a conventional generator set speed governor. This represents the equivalent time constant between the governor and the prime mover of a conventional generator set. This represents the virtual inertia of the wind turbine's primary frequency control. This represents the equivalent response time constant of the active frequency regulation control loop of the wind turbine. This indicates the frequency modulation power gain of the flywheel energy storage system. This represents the equivalent control response time constant of the flywheel energy storage system. Indicates the frequency modulation power gain of a lithium battery energy storage system. This represents the equivalent control response time constant of a lithium battery energy storage system. This represents the dynamic damping coefficient of the wind turbine generator. This represents the rotor inertia constant of a wind turbine generator set.

4. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 1, characterized in that, The expression for the system's eigenvalues ​​is: ； in, Indicates the equivalent damping ratio. Indicates the undamped natural frequency. Representing the system's characteristic roots, Represents the imaginary unit; The equivalent damping ratio is directly proportional to the change in grid strength. The system frequency security domain is represented as: ； in, Represents the system frequency security domain. Indicates the rate of change of frequency. Indicates the frequency deviation limit. This represents the limit value of the rate of change of frequency.

5. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 4, characterized in that, The trajectory evolution of system eigenvalues ​​based on the linearized state-space model describes the variation characteristics of grid strength and system frequency security domain in parameter space, including: In a strong power grid environment, the equivalent damping ratio increases and the system characteristic root is far away from the imaginary axis. The manifold envelope of the system frequency safety domain far exceeds the limit, and the stability is dominated by the recovery time. For medium-intensity power grid environments, a decrease in the equivalent damping ratio leads to an increase in frequency deviation, and the system frequency safety domain collapses laterally toward the origin, making the maximum frequency deviation a constraint. In extremely weak power grid environments, the inertia dilution effect causes the system's eigenvalues ​​to approach the imaginary axis, and the system's frequency security domain to... When the shaft collapses vertically along its axial direction, the instantaneous rate of change of frequency exceeds the limit, and the system fails dynamically.

6. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 5, characterized in that, S2 include: The instantaneous rate of change of frequency under disturbance is strongly constrained by the equivalent rotational inertia dependent on grid strength, the equivalent time delay of the wind-storage control system, and the output power of the flywheel energy storage system. Therefore, the instantaneous power domain boundary is defined as follows: ； ； ； in, This indicates the per-unit value of the disturbance power. Indicates the equivalent delay of the flywheel energy storage system 'output power' This represents the equivalent moment of inertia dependent on the strength of the power grid. This represents the output power of the flywheel energy storage system at time t. Indicates that the flywheel energy storage system is in Maximum output power at any given time This represents the equivalent response time constant of the flywheel system; The frequency deviation limit depends on the energy difference of the disturbance process, and the dynamic energy domain boundary is defined as follows: ； in, t nadir The time point representing the quasi-steady-state equilibrium point. This indicates the per-unit value of the disturbance power. This represents the deviation of the output power increment of a conventional unit at time t. This represents the incremental deviation of the fan's output power at time t when the fan load reduction rate is a. This indicates the deviation in the output power increment of the flywheel battery. This represents the deviation in the incremental output power of the lithium battery at time t. Represents the equivalent moment of inertia. f 0 indicates the initial nominal frequency of the system; The monotonicity guarantee criterion for the frequency recovery stage is derived using the convergence region analysis method, and the disturbance power is guaranteed. If the lower time-domain frequency trajectory is greater than 0, then the recovered trajectory boundary is defined as: ； in, This indicates the output power of the lithium battery. Indicates partial derivative, The angular velocity of the fan rotor is... The output power of the fan This indicates the ramp-up rate of conventional generating units, which depends on the strength of the power grid.

7. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 6, characterized in that, Disturbance power The lower time-domain frequency trajectory is represented as: ； in, f ( t () indicates the disturbance power The time-domain frequency trajectory at time t. Indicates the load damping coefficient. This represents the initial phase angle.

8. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 7, characterized in that, Boundary sensitivity operators are constructed based on instantaneous power domain boundaries, dynamic energy domain boundaries, recovery trajectory boundaries, and grid strength, including: ； in, S SCR Represents the boundary sensitivity operator. B R Indicates the instantaneous power domain boundary. B f Represents the boundary of the dynamic energy domain. B rec The boundary of the recovered trajectory is represented by SCR, the power grid strength is represented by T, and the transpose is represented by T.

9. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 8, characterized in that, The expression for the objective function is: ； ； ； ； ； ； in, C total This represents the annualized total cost over the entire life cycle. C cap This indicates annualized capital expenditure. C opex Indicates operation and maintenance costs. C curt This indicates the cost of wind curtailment compensation. C deg Indicates the cost of energy storage degradation. C pen This represents adaptive default penalty, r represents the discount rate, L represents the total lifespan, F represents the flywheel, and B represents the lithium battery. This indicates the unit power of the flywheel or lithium battery. This indicates the capacity cost of the flywheel or lithium battery. μ k This represents the annual maintenance coefficient. This represents the price compensation coefficient per unit of wind curtailment energy. This represents the rated total installed capacity of the wind farm, and 'a' represents the wind turbine derating rate. C B,repl This represents the benchmark for battery replacement costs. This represents the magnitude of the change in state of charge caused by the t-th charge-discharge cycle. N cycle (DoD) indicates the maximum number of cycles under DoD. γ (SCR) represents the dynamic weight mapping coefficient, and SCR represents the grid strength. Vio (·) represents the default function. This represents the default weight corresponding to the instantaneous power domain boundary. This represents the default weight corresponding to the boundary of the dynamic energy domain. This represents the default weight corresponding to the recovery trajectory boundary, where T represents the number of years in the entire lifecycle. P k Indicates the first k Configuration power of energy storage resources E k Indicates the first k The capacity of energy storage resources; DoD represents the depth of discharge. The constraints include: Instantaneous inertia safety constraints are expressed as: ； Dynamic energy balance constraints are expressed as: ； in, This indicates the maximum frequency deviation. The second-order drop constraint is represented as: ； in, E BESS Indicates the capacity of the lithium battery. This represents the maximum ramp rate of conventional generating units, dependent on grid strength. t rec Indicates the target time point for frequency transient recovery. This represents the equivalent power deficit function caused by the rotor kinetic energy withdrawal during the transient recovery phase of a wind turbine generator, expressed by the wind turbine load factor. α angular velocity of the fan rotor ω t And time t together determine it.

10. The wind-storage heterogeneous resource collaborative allocation method based on frequency regulation capability boundary driving according to claim 9, characterized in that, The process of obtaining a heterogeneous capacity configuration scheme includes: Step 1; Define the position vector of the particle and the search space. The position vector of the i-th particle is denoted as: , This indicates the output power of the flywheel energy storage system. This indicates the output power of the lithium battery. E BESS The capacity of the lithium battery is represented by 'a', the derating rate of the wind turbine is represented by 'T', and the transposition is represented by 'T'. The search space is dynamically limited by the boundary of the multi-dimensional frequency modulation capability. Step 2: Obtain the grid strength, system equivalent inertia, system equivalent damping, and per-unit disturbance power of the power grid; Step 3: Population initialization, using Gaussian distribution to force 70% of the particles to be distributed on the multidimensional tuning capability boundary; Step 4: Calculate the fitness of each particle based on the objective function and boundary sensitivity operator. The calculation formula is as follows: ； in, F ( X i ) represents the fitness of the i-th particle. ，B j This represents the boundary of the instantaneous power domain, the boundary of the dynamic energy domain, or the boundary of the recovered trajectory. This represents the set of indices for the instantaneous power domain boundary, dynamic energy domain boundary, and recovered trajectory boundary; exp(·) represents the adaptive penalty term; and Dist(·) represents the Euclidean distance. Represents the coordinates of the i-th particle; Step 5: Update the velocity and position of each particle using inertial weights; Step 6: Update the archive for all particles based on the Pareto dominance criterion; Step 7: Repeat steps 4-6 until the archive size reaches the upper limit or the Pareto front stops moving in a set number of consecutive iterations. The algorithm terminates and outputs a heterogeneous capacity configuration scheme. The heterogeneous capacity configuration scheme includes the optimal output power of the flywheel energy storage system, the output power of the lithium battery, the capacity of the lithium battery, and the wind turbine load factor.

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