An Adaptive Smart Grid Regulation Method and System

Abstract

The present invention provides an adaptive intelligent power grid regulation method and system, belonging to the field of power technology. First, historical operation data of the power grid is collected, including power grid frequency fluctuations, distributed energy output status, and external disturbance information. Then, a fractal chaotic attractor model is constructed, and the complex structure of the power grid dynamic behavior is deeply understood by calculating the fractal dimension and correlation coefficient of the power grid state variables. Based on this model, the system can predict the stability boundary of the power grid, design a fractal control signal with a self-similar structure, and inject it into the distributed energy control system to actively control power grid disturbances. By real-time monitoring the power grid operation status and external environment changes, the fractal control parameters are dynamically adjusted using reinforcement learning to ensure that the control strategy always matches the actual working conditions, thereby maximizing the system performance. The present invention significantly enhances the anti-disturbance performance and self-healing ability of the power grid, and improves the energy utilization rate and power supply quality.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric power, and particularly relates to an adaptive intelligent power grid regulation method and system. Background Art

[0002] Currently, the smart grid faces unprecedented challenges and opportunities. With the large-scale access of renewable energy and the popularization of distributed energy systems, the complexity of the power grid has increased significantly, making it difficult for traditional regulation strategies to meet the real-time changes of the power grid dynamically, precisely, and efficiently. Variable factors such as disturbance turbulence fluctuations in power grid operation, uncertainties in the external environment, and internal faults all require that the power grid regulation system must have a higher level of intelligence to ensure stability and self-healing ability. Traditional regulation methods are difficult to accurately predict power grid disturbances, and the control strategies are not proactive enough, resulting in slow response speed, inability to adapt to the dynamic changes of the power grid, and affecting the overall efficiency and safe operation stability of the power grid. Therefore, a more intelligent, dynamic, and adaptable regulation method is needed to improve the comprehensive performance of the power grid. Summary of the Invention

[0003] Based on the above technical problems, the present invention provides an adaptive intelligent power grid regulation method and system. By integrating the non-linear dynamics analysis of chaos theory and the self-similar characteristics of fractal geometry, high-precision prediction and active control of power grid disturbances are achieved, significantly improving the anti-disturbance performance and self-healing ability of the power grid.

[0004] The present invention provides an adaptive intelligent power grid regulation method, which includes:

[0005] Step S1: Collect historical operation data of the power grid;

[0006] Step S2: Construct a fractal chaos attractor model and calculate the fractal dimension of the power grid state variables;

[0007] Step S3: Predict the stability boundary of the power grid based on the fractal chaos attractor model;

[0008] Step S4: Design a fractal control signal to generate a control signal with a self-similar structure;

[0009] Step S5: Inject the fractal control signal into the distributed energy control system;

[0010] Step S6: Dynamically adjust the fractal control parameters according to the power grid operation state and external environment changes.

[0011] Optionally, the constructing of the fractal chaos attractor model and calculating the fractal dimension of the power grid state variables specifically includes:

[0012] Select key state variables and arrange the selected variables in sequence according to time;

[0013] Map a one-dimensional time series to a high-dimensional space to construct a sequence of state vectors, specifically including:

[0014] Select embedding parameters, where the embedding parameters include the embedding dimension m and the time delay τ ;

[0015] For each time point t, construct a state vector, denoted as:

[0016] X t = [f(t), f(t + τ),..., f(t + (m - 1)τ), V(t), V(t + τ),..., V(t + (m - 1)τ)]

[0017] For each time point t, based on the above m and τ, construct a state vector X that includes the states at the past m - 1 time points and the current moment; t ; Through m and τ, the original one-dimensional time series is converted into a set of points in a multi-dimensional state space, that is, each time point corresponds to an m-dimensional vector;

[0018] Calculate the correlation dimension D C , specifically including:

[0019] For any two state vectors X i , X j , calculate the distance between them, denoted as:

[0020]

[0021] In the formula, x ik and x jk are the elements of the state vectors X i and X j in the k-th dimension respectively;

[0022] Count the number of neighboring point pairs, set the neighborhood radius r, and count the number of point pairs N i (r) within the neighborhood of each point state vector X i ; that is, the number of state vectors within the sphere centered at X i with a radius of r;

[0023] Find the average number of neighboring point pairs for all points to obtain N(r), denoted as:

[0024]

[0025] In the formula, N is the total number of state vectors; N(r) describes the variation of the average distribution density of points in the state space with the radius;

[0026] Plot the correlation function graph and calculate the correlation dimension, denoted as:

[0027] Define the correlation function C(r) as the natural logarithm of the number of neighboring points, i.e., C(r) = ln[N(r)];

[0028] The slope D obtained by linear regression analysis C , expressed as:

[0029]

[0030] In the formula, D C is the correlation dimension.

[0031] Optionally, predicting the stability boundary of the power grid based on the fractal chaos attractor model specifically includes:

[0032] Perform local linearization on the system, approximated as the Jacobian matrix J(X t , t), where X is the state vector and t is time;

[0033] Perform iterative operations, specifically including:

[0034] Initial vector setting, select a small initial vector difference δX0;

[0035] Iterative update, at each time step t, through δX t+1 = J(X t , t)·δX t Update the vector difference;

[0036] Average growth rate calculation, calculate the average growth rate Λ I , expressed as:

[0037]

[0038] In the formula, T is the time length of the analysis;

[0039] Repeat the iterative process for different orthogonal directions of the system state space to obtain a series of Lyapunov exponents λ1, λ2,..., λ n , constituting the Lyapunov spectrum; if the largest Lyapunov exponent λ max > 0, it indicates that the system is in a chaotic state and has potential instability; if λ max < 0, the system tends to be stable; by continuously tracking the largest Lyapunov exponent λ max , find the region where λ max = 0, and identify the critical point from stable to chaotic, that is, the stability boundary.

[0040] Optionally, designing the fractal control signal to generate a control signal with a self-similar structure specifically includes:

[0041] Using the fBm fractal model, Hurst exponent, and time scale, a control signal is generated, expressed as:

[0042]

[0043] In the formula, B H (t) is the fBm value at time point t; t K = KΔt, where Δt is the time interval; σ K is the standard deviation of each step adjusted based on the Hurst exponent; Z K is a variable of the standard normal random distribution;

[0044] The generated control signal is fine-tuned by modifying the amplification factor of the generated control signal or using a filter.

[0045] Optionally, according to the grid operation state and external environment changes, the fractal control parameters are dynamically adjusted, specifically including:

[0046] Define the reinforcement learning parameters, specifically including:

[0047] State s t ∈ S, representing the state of the power grid at time step t;

[0048] Action a t ∈ A, the control action taken by the agent in state s t , that is, adjusting the control parameters;

[0049] Reward r t , the feedback immediately obtained by the agent after executing the action;

[0050] Maximize the cumulative reward through the learning process, that is, find the optimal policy, expressed as:

[0051]

[0052] In the formula, π*(s) is the optimal policy π* in the given state s; argmax π is to find the policy among all policies π that makes the expression in the parentheses reach the maximum value; is the expected value under policy π, which is the average or expected sum of future rewards when executed according to policy π; t is the time step; r t is the immediate reward obtained at time step t; γ is the discount factor;

[0053] The execution process specifically includes:

[0054] Initialize the parameters, set the initial policy π0, define the state space S, action space A, reward function R(s, a), and discount factor γ;

[0055] At each time step t, the agent observes the current state s of the power grid t ;

[0056] The agent selects an action a according to the current policy π t and applies it to the power grid, observing the next state s t = π t (s t ) and observes the immediate reward r t+1 ; t ;

[0057] The Q - learning algorithm is used to update the policy π according to s t , a t , r t , s t+1 to optimize the long - term reward; t ;

[0058] The learned policy is directly transformed into dynamic adjustment of the fractal control parameters.

[0059] The present invention also provides an adaptive intelligent power grid regulation system, which includes:

[0060] A data collection module for collecting historical operation data of the power grid;

[0061] A model construction module for constructing a fractal chaotic attractor model and calculating the fractal dimension of the power grid state variables;

[0062] A boundary prediction module for predicting the stability boundary of the power grid based on the fractal chaotic attractor model;

[0063] A signal generation module for designing a fractal control signal and generating a control signal with a self - similar structure;

[0064] A system control module for injecting the fractal control signal into the distributed energy control system;

[0065] A parameter optimization module for dynamically adjusting the fractal control parameters according to the power grid operation state and external environment changes.

[0066] Optionally, the model construction module specifically includes:

[0067] Selecting key state variables and arranging the selected variables in chronological order to form a sequence;

[0068] Mapping the one - dimensional time series to a high - dimensional space to construct a state vector sequence, specifically including:

[0069] Selecting embedding parameters, where the embedding parameters include the embedding dimension m and the time delay τ ;

[0070] For each time point \(t\), construct a state vector, denoted as:

[0071] X t = [f(t), f(t + τ),..., f(t + (m - 1)τ), V(t), V(t + τ),..., V(t + (m - 1)τ)]

[0072] For each time point \(t\), based on the above \(m\) and \(τ\), construct a state vector \(X\) that includes the states at the past \(m - 1\) time points and the current moment; t ; Through \(m\) and \(τ\), the original one - dimensional time series is converted into a set of points in a multi - dimensional state space, that is, each time point corresponds to an \(m\) - dimensional vector;

[0073] Calculate the correlation dimension \(D\) C , specifically including:

[0074] For any two state vectors \(X\) i , \(X\) j , calculate the distance between them, denoted as:

[0075]

[0076] where \(x\) ik and \(x\) jk are the elements of the state vectors \(X\) i and \(X\) j in the \(k\) - th dimension respectively;

[0077] Count the number of pairs of neighboring points. Set the neighborhood radius \(r\) and count the number of pairs of points \(N\) i (r) within the neighborhood of each point state vector \(X\) i ; that is, the number of state vectors within the sphere centered at \(X\) i with a radius of \(r\);

[0078] Find the average number of neighboring - point pairs for all points to obtain \(N(r)\), denoted as:

[0079]

[0080] where \(N\) is the total number of state vectors; \(N(r)\) describes how the average distribution density of points in the state space changes with the radius;

[0081] Plot the correlation - function graph and calculate the correlation dimension, denoted as:

[0082] Define the correlation function \(C(r)\) as the natural logarithm of the number of neighboring - point pairs, that is, \(C(r)=\ln[N(r)]\);

[0083] The slope \(D\) C obtained through linear regression analysis is denoted as:

[0084]

[0085] where D C is the correlation dimension.

[0086] Optionally, the boundary prediction module specifically includes:

[0087] Perform local linearization on the system, approximated as the Jacobian matrix J(X t , t), where X is the state vector and t is the time;

[0088] Perform iterative operations, specifically including:

[0089] Initial vector setting, select a small initial vector difference δX0;

[0090] Iterative update, at each time step t, through δX t+1 = J(X t , t)·δX t Update the vector difference;

[0091] Average growth rate calculation, calculate the average growth rate Λ I , expressed as:

[0092]

[0093] where T is the time length of the analysis;

[0094] Repeat the iterative process for different orthogonal directions of the system state space to obtain a series of Lyapunov exponents λ1, λ2,..., λ n , constituting the Lyapunov spectrum; if the largest Lyapunov exponent λ mmax > 0, it indicates that the system is in a chaotic state and has potential instability; if λ max < 0, the system tends to be stable; by continuously tracking the largest Lyapunov exponent λ max , find the region where λ max = 0, and identify the critical point from stability to chaos, i.e., the stability boundary.

[0095] Optionally, the signal generation module specifically includes:

[0096] Generate a control signal using the fBm fractal model, Hurst exponent, and time scale, expressed as:

[0097]

[0098] where B H (t) is the fBm value at time point t; t K=KΔt, Δt is the time interval; σ K is the standard deviation of each step based on the Hurst exponent adjustment; Z K is a variable with standard normal random distribution;

[0099] The generated control signal is fine-tuned by modifying its amplification factor or using a filter.

[0100] Optionally, the parameter optimization module specifically includes:

[0101] Define reinforcement learning parameters, including:

[0102] Status t ∈S, represents the state of the power grid at time step t;

[0103] Action a t ∈A, the agent is in state s t The control action taken under the above conditions is to adjust the control parameters;

[0104] Reward t , the feedback the agent gets immediately after performing an action;

[0105] Maximizing the cumulative reward through the learning process, that is, finding the optimal strategy, is expressed as:

[0106]

[0107] Where π*(s) is the optimal strategy π* in a given state s; argmax π To find the strategy that maximizes the expression in brackets among all strategies π; is the expected value under strategy π, which is the average or expected sum of future rewards when strategy π is executed; t is the time step; r t is the immediate reward obtained at time step t; γ is the discount factor;

[0108] The implementation process includes:

[0109] Initialize parameters, set initial strategy π0, define state space S, action space A, reward function R(s, a) and discount factor y;

[0110] At each time step t, the agent observes the current state of the grid s t ;

[0111] The agent follows the current policy π t , select action a t =π t (s t ), and apply it to the power grid, observing the next state s t+1 and instant rewardst ;

[0112] Use the Q - learning algorithm to update the policy π t according to s t , a t , r t+1 , s t , and optimize the long - term reward;

[0113] Directly convert the learned policy into the dynamic adjustment of the fractal control parameters.

[0114] Compared with the prior art, the present invention has the following beneficial effects:

[0115] Through the high - precision prediction of power grid disturbances, the present invention realizes the transformation from passive response to active control, can take measures before the stability of the power grid is threatened, and prevent accidents; by integrating chaos theory and fractal geometric characteristics, the power grid shows higher stability and resilience in the face of internal and external disturbances; through the adaptive adjustment of the control strategy, the power grid can quickly return to the normal operation state after a fault, realizing self - repair; by using reinforcement learning to automatically optimize the fractal control parameters, the scheduling strategy is made intelligent and dynamic, improving the operation efficiency of the power grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] Figure 1 is a flowchart of an adaptive intelligent power grid regulation method of the present invention;

[0117] Figure 2 is a structural diagram of an adaptive intelligent power grid regulation system of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0118] The present invention will be further described below in conjunction with specific implementation cases and the drawings, but the present invention is not limited to these embodiments.

[0119] Embodiment 1

[0120] As Figure 1 shown, the present invention discloses an adaptive intelligent power grid regulation method, and the method includes:

[0121] Step S1: Collect the historical operation data of the power grid.

[0122] Step S2: Construct a fractal - chaotic attractor model and calculate the fractal dimension of the power grid state variables.

[0123] Step S3: Predict the stability boundary of the power grid based on the fractal - chaotic attractor model.

[0124] Step S4: Design a fractal control signal to generate a control signal with a self - similar structure.

[0125] Step S5: Inject the fractal control signal into the distributed energy control system.

[0126] Step S6: Dynamically adjust the fractal control parameters according to the grid operating status and external environment changes.

[0127] The following is a detailed discussion of each step:

[0128] Step S1: Collect historical grid operation data, including but not limited to grid frequency fluctuation records, distributed energy output status, and external disturbance information.

[0129] Step S1 specifically includes:

[0130] Data types, specifically including:

[0131] Grid frequency fluctuation records, the grid frequency (usually referring to the frequency of alternating current, such as 50Hz or 60Hz) is a key indicator to measure the stability of the power system; the frequency fluctuation records include time series data, showing the changes in grid frequency at different time periods; these changes may be caused by factors such as supply-demand imbalance, large load mutations, generator failures, etc.; recording these fluctuations helps analyze the response characteristics of the grid, detect abnormal events, and evaluate the regulation ability of the system.

[0132] Distributed energy output status, with the development of renewable energy and distributed generation technologies, it becomes particularly important to record the output power and start-stop status of each distributed energy source (such as solar photovoltaic, wind power generation, micro hydropower stations, etc.); it not only reflects the contribution degree of distributed energy to the grid, but also is an important basis for evaluating the flexibility of the grid, planning and dispatching, and balancing supply and demand.

[0133] External disturbance information, the grid operation is affected by various external factors, such as weather conditions (affecting the output of renewable energy), large-scale user behavior patterns (such as peak electricity consumption during holidays), natural disasters (causing damage to transmission lines), load mutations (such as the start-up or shutdown of large factories), grid fault records, and any external events that may affect the grid operation; it helps predict possible grid stress situations and take countermeasures in advance.

[0134] Data sources, specifically including:

[0135] Sensor network, sensors (such as voltage, current, and frequency sensors) deployed at key nodes of the grid continuously monitor the grid status and transmit the data to the data center or cloud platform in real time.

[0136] Smart meters, smart meters installed at the user end can collect detailed electricity consumption information, reflecting the user's electricity consumption pattern, which is crucial for demand-side management.

[0137] Meteorological station and environmental monitoring system, used to collect environmental data affecting the output of distributed energy, such as wind speed, light intensity, temperature, etc.

[0138] SCADA system (Supervisory Control and Data Acquisition system), widely used in modern power grids, centrally monitors and controls power grid equipment, and collects a large amount of real-time operation data.

[0139] Data collection and integration, specifically including:

[0140] Timed collection, set the data collection frequency to ensure the continuity and integrity of the data; for key parameters (such as power grid frequency), collection at second-level or shorter time intervals may be required.

[0141] The collected raw data needs to be preprocessed (such as cleaning, verification, standardization) for analysis.

[0142] Data cleaning, remove invalid, incorrect or abnormal data records, such as abnormal readings caused by sensor failures.

[0143] Standardization and formatting, uniformly convert data from different sources and formats into a standard format suitable for analysis, facilitating subsequent processing.

[0144] Data application, specifically including:

[0145] Historical data analysis, by analyzing historical data, the operation rules of the power grid can be discovered, potential risk points can be identified, and operation strategies can be optimized.

[0146] Model establishment and prediction, as the basis for constructing a power grid model (such as the fractal chaotic attractor model in step S2), used to simulate and predict the behavior of the power grid.

[0147] Control strategy formulation, based on data insights, formulate more accurate control strategies and scheduling plans to improve the stability and efficiency of the power grid.

[0148] Step S2: Construct a fractal chaotic attractor model, and calculate the fractal dimension and correlation coefficient of the power grid state variables.

[0149] Step S2 specifically includes:

[0150] Data preprocessing, specifically including:

[0151] Ensure that the historical operation data of the power grid (frequency fluctuations, energy output, external disturbances, etc.) obtained from S1 is clean and continuous; remove outliers through data cleaning, and smooth the data to reduce random noise to ensure data quality; this means converting all measured power grid variables to the same scale, such as through standardization (dividing by the standard deviation after subtracting the mean) or normalization (adjusting to a specific interval such as 0 to 1); the purpose is to eliminate the differences in magnitude between different variables and make the comparison meaningful.

[0152] Select key state variables, such as the grid frequency f(t), the voltage V(t) of key nodes, etc., to construct a time series. The operating state of the power grid can be described by multiple variables, but not all of them are equally important for analyzing chaotic characteristics. Selecting the grid frequency f(t) and the voltage V(t) of key nodes as representatives is directly related to the stability and efficiency of the power grid.

[0153] Construct a time series by arranging the selected variables in chronological order to form a sequence, which provides basic data for subsequent dynamic analysis.

[0154] Map the one-dimensional time series to a high-dimensional space to construct a state vector sequence, specifically including:

[0155] Select embedding parameters, where the embedding parameters include the embedding dimension m and the time delay τ 。

[0156] The embedding dimension m determines how many consecutive states (for example, the values of the grid frequency and voltage at different time points) are used to construct a state vector. It is usually determined using the false nearest neighbor method criterion to ensure that the topological structure between data points in the high-dimensional space can be correctly reflected.

[0157] The time delay τ refers to the time interval between adjacent state variables when constructing the state vector. By calculating the autocorrelation function to find the first minimum point where it decays to zero, this is used as the estimated value of τ to ensure that there is both correlation and not excessive overlap between state variables.

[0158] In this embodiment, it determines how many consecutive time points are needed to describe the state of the system (for example, selecting the information of the past four time points to predict the state of the fifth point, and at this time the embedding dimension m is 4), and the time interval (time delay τ) between these points.

[0159] For each time point t, construct a state vector, expressed as:

[0160] X t =[f(t), f(t + τ),..., f(t + (m - 1)τ), V(t), V(t + τ),..., V(t + (m - 1)τ)]

[0161] For each time point t, based on the above m and τ, construct a state vector X that includes the states of the past m - 1 time points and the current moment, t so as to reflect the dynamic behavior of the system; based on the selected parameters, construct a vector containing multiple variables for each time point; if considering the grid frequency and voltage, and m = 2, τ = 1, then a state vector may be [f(t), V(t + 1)].

[0162] Through \(m\) and \(\tau\), the original one-dimensional time series is transformed into a set of points in a multi-dimensional state space, that is, each time point corresponds to an \(m -\)dimensional vector.

[0163] Calculate the correlation dimension \(D\) C , specifically including:

[0164] For any two state vectors \(X\) i , \(X\) j , calculate the distance between them, denoted as:

[0165]

[0166] In the formula, \(x\) ik and \(x\) jk are the elements of the state vectors \(X\) t and \(X\) j in the \(k -\)th dimension respectively. The distance measures the proximity of two points in the state space and is the basis for subsequent calculations.

[0167] Count the number of pairs of neighboring points. Set the neighborhood radius \(r\) and count the number of pairs of points \(N\) i within the neighborhood of each point state vector \(X\) ij (that is, all points with a distance \(d\) i less than \(r\)); that is, the number of state vectors within the sphere centered at \(X\) i with a radius of \(r\).

[0168] Find the average number of neighboring point pairs for all points to obtain \(N(r)\), denoted as:

[0169]

[0170] In the formula, \(N\) is the total number of state vectors; \(N(r)\) describes how the average distribution density of points in the state space changes with the radius.

[0171] Plot the correlation function graph and calculate the correlation dimension, denoted as:

[0172] Define the correlation function \(C(r)\) as the natural logarithm of the number of neighboring point pairs, that is, \(C(r)=\ln[N(r)]\).

[0173] Depict the relationship between \(C(r)\) and \(\ln[r]\) through a scatter plot. If the system exhibits a certain self - similarity, when \(r\) is small, \(C(r)\) shows a linear relationship with \(\ln[r]\).

[0174] If there is a linear region, the slope \(D\) C obtained through linear regression analysis

[0175]

[0176] In this embodiment, when choosing the neighborhood radius r, if the points are very dense, a smaller r may be more appropriate because it can more finely distinguish the points within the neighborhood; conversely, if the points are sparse, a larger r may be needed to ensure that each neighborhood has enough points for statistical analysis; if the system exhibits self-similarity, then the structures at different scales should be similar. When choosing r, it is necessary to ensure that it can span at least several self-similar intervals so that a clear linear region can be observed on the correlation function graph, thereby accurately estimating the correlation dimension; in a finite dataset, an overly large r will cause boundary effects, that is, when the state vector is close to the dataset boundary, its neighborhood is truncated and cannot truly reflect the global characteristics.

[0177] In this embodiment, the method for calculating the fractal dimension adopts the correlation dimension method or the maximum Lyapunov exponent estimation because they are applicable to the analysis of chaotic systems.

[0178] For two state vectors X i , X j , calculate their correlation coefficient C ij , to understand the interaction and dependence relationships between each state variable, which helps to identify the coupling mechanism within the system.

[0179] In this embodiment, the above content has obtained a set of points in a high-dimensional state space (representing the dynamic behavior of the power grid), and also understood the complex structure of these point sets through the fractal dimension, revealed the unpredictability of the system through the analysis of chaotic characteristics, and explored the internal interactions of the system through the correlation coefficient matrix. All these combined constitute a "fractal chaotic attractor model", which is not only a high-level abstraction of the power grid's dynamic behavior but also the theoretical basis for predicting future states and formulating control strategies.

[0180] Step S3: Predict the stability boundary of the power grid based on the fractal chaotic attractor model.

[0181] Step S3 specifically includes:

[0182] Starting from the state space reconstruction result obtained in S2, select a sufficiently long stationary state sequence to ensure the reliability of the analysis; the state space reconstruction obtains a multi-dimensional representation of the power grid's dynamic behavior, that is, a series of m-dimensional state vectors.

[0183] Perform local linearization processing on the system, approximated as the Jacobian matrix J(X t , t), where X is the state vector and t is the time; the Jacobian matrix describes the small-range linear behavior of the system at this point and is the basis for calculating the Lyapunov exponent.

[0184] Perform iterative operations, specifically including:

[0185] Initial vector setting: Select a small initial vector difference δX0, usually a unit vector, as the starting point for divergence measurement.

[0186] Iterative update: At each time step t, through δX t+1 = J(X t , t)·δX t Update the vector difference to simulate the divergence or convergence process of adjacent orbits.

[0187] Calculation of average growth rate: Calculate the average growth rate Λ I , expressed as:

[0188]

[0189] In the formula, T is the time length of analysis. This step is obtained by calculating the natural logarithm of the growth rate of the vector difference compared to the initial value and taking the average.

[0190] Repeat the above iterative process for different orthogonal directions in the system state space. Finally, obtain a series of Lyapunov exponents λ1, λ2,..., λ n , which constitute the Lyapunov spectrum; the largest Lyapunov exponent is particularly crucial because it is directly related to the chaotic characteristics of the system.

[0191] If the largest Lyapunov exponent λ max > 0, it indicates that the system is in a chaotic state and has potential instability; if λ max < 0, the system tends to be stable.

[0192] By continuously tracking the change of the largest Lyapunov exponent λ max with system parameters or external conditions, find the region where λ max = 0. This is the boundary where the system changes from stable to unstable, and identify the critical point from stable to chaotic, that is, the stability boundary.

[0193] Predict the instability trend: If it is observed that λ in some regions max gradually increases over time, this may indicate that the system is approaching instability; by analyzing these trends, measures can be taken in advance to prevent potential failures.

[0194] In actual power grid operation, continuously monitor the largest Lyapunov exponent. Once it approaches or exceeds the threshold, an early warning signal is sent, indicating that the system may be about to enter an unstable state; according to the early warning information, preventive measures are taken, such as adjusting the output of generator sets, changing load distribution and other control strategies, to slow down or avoid the system from entering an unstable state. Lyapunov exponent analysis not only provides early warning but also guides how to optimize system performance and stability through parameter adjustment.

[0195] In this embodiment, the Lyapunov exponent is an index that measures the divergence or convergence rate of adjacent orbits in the state space of a system and is a core tool for analyzing chaotic systems. For an n-dimensional dynamical system, there are n Lyapunov exponents. A positive value of the largest Lyapunov exponent indicates that the system has chaotic behavior, while a negative value means that the system tends to a stable fixed point or periodic motion.

[0196] Step S4: Design a fractal control signal to generate a control signal with a self-similar structure.

[0197] Step S4 specifically includes:

[0198] Fractal theory is a discipline that studies the geometric forms with non-integer dimensions commonly existing in nature, and it reveals characteristics such as self-similarity and scale invariance in complex systems; in the power system, phenomena such as load changes and voltage fluctuations in the power grid often exhibit fractal characteristics, which provides a theoretical basis for designing control signals that match the natural fluctuation patterns of the power grid.

[0199] Common fractal generation models include fractional Brownian motion fB m , the Hurst exponent model, the Mandelbrot set, etc.; in this scenario, fBm is particularly suitable for generating control signals that match the dynamics of the power grid because it can well simulate a random process with long-term memory; the mathematical definition of fB m can be characterized by the Hurst exponent H to represent its statistical properties, where H ∈ (0, 1) corresponds to different types of self-similarity.

[0200] Based on the fractal feature analysis of the power grid in step S2, determine the Hurst exponent of the power grid fluctuations, which reflects the long-term memory or anti-memory of the signal, and identify and quantify the fractal characteristics of the data sequence in the power grid, involving statistical analysis of historical monitoring data to capture its self-similarity and scale invariance characteristics.

[0201] Use statistical means such as R / S analysis (rescaled range analysis), Hurst exponent calculation methods, etc. to estimate the Hurst exponent of the power grid dynamics; the value range of the Hurst exponent is from 0 to 1. H < 0.5 indicates that the signal has anti-persistence or negative correlation, H = 0.5 represents a random walk, and H > 0.5 means that the signal has long-term memory or positive correlation.

[0202] According to the actual frequency of power grid operation and the instability trend identified in step S3, determine the time scale of the control signal to ensure that the signal can effectively act on the key dynamic processes of the system.

[0203] By analyzing real-time monitoring data and historical data of the power grid, identify any trends that may indicate system instability; including changes in indicators such as increased power fluctuations, abnormal frequencies, and increased voltage fluctuations. Use time series analysis, machine learning algorithms, or signal processing techniques to detect abnormal patterns and periodic changes in the data, thereby predicting future instability.

[0204] Based on the instability trends identified in S3, for example, if it is found that certain instability events tend to occur within specific time periods (such as daily cycles, weekly cycles, or seasonal variations), then the time scale of the control signal should match; this means that the design of the control signal should take into account these critical time windows to ensure that the frequency and duration of the signal can respond in a timely manner and intervene in these instability trends, thereby maximizing its effectiveness when the system most needs control intervention.

[0205] Using the selected fractal model (fBm), combined with the determined Hurst exponent and time scale, generate a control signal, expressed as:

[0206]

[0207] where B H (t) is the fBm value at time point t; t K = KΔt, where Δt is the time interval; σ K is the standard deviation of each step adjusted based on the Hurst exponent; Z K is a variable of the standard normal random distribution.

[0208] Implement this process using a computer program (such as the fractionalBrownianMotion function in MATLAB), and generate a signal sequence with specified self-similar characteristics by inputting the Hurst exponent H and the required length of the time series.

[0209] Fine-tune the signal by modifying the amplification factor of the signal or using a filter to ensure that the signal is more in line with the details of the power grid fluctuations; by adjusting the local intensity or frequency components of the signal, the generated control signal not only matches the power grid fluctuations in terms of statistical characteristics, but also exhibits a self-similar structure similar to the natural fluctuations of the power grid in terms of waveform.

[0210] Step S5: Inject the fractal control signal into the distributed energy control system to achieve multi-scale fractal synchronization between different nodes through communication protocols and algorithms.

[0211] Step S5 specifically includes:

[0212] First, the distributed energy control system can be regarded as consisting of multiple subsystems or nodes, and each node is responsible for monitoring and controlling the energy distribution and consumption in a specific area. Suppose the system contains Num nodes, and the dynamic behavior of each node can be described by a non-linear dynamics equation, which contains chaotic characteristics. Taking the typical chaotic Lorenz system as an example, the dynamics equation of the J-th node can be expressed as:

[0213]

[0214] In the formula, where x J , y J , z J are the state variables of node J, and σ, ρ are system parameters; u J (t) is the optimized fractal control signal in step S4, which aims to guide the chaotic behavior of each node into a synchronous state, and this signal needs to have the characteristics self-similar to the natural fluctuation mode of the system.

[0215] To achieve multi-scale fractal synchronization, the master-slave synchronization or mutual synchronization strategy is adopted, and combined with the distributed control theory, the differential synchronization method is adopted in this application, which is that each node tries to reduce the difference from the state of neighboring nodes; it is assumed that the nodes are connected through a network, and the information exchange follows a specific communication protocol, such as Zigbee or a customized wireless sensor network protocol, to achieve real-time sharing of state information. The differential synchronization equation is expressed as:

[0216] Δx J =q(x J+1 -x J ), J = 1,..., Num - 1

[0217] In the formula, Δx J is the state difference between node J and J + 1, and q is the synchronization gain; by adjusting q, the system can be promoted to reach the global synchronization state.

[0218] Distributed fractal chaos synchronization not only improves the system response speed but also significantly enhances its anti-disturbance ability. When the system suffers from external interference or internal faults, the synchronization mechanism prompts each node to quickly correct each other, and through local interaction, the global state can be quickly restored, reflecting the self-repairing characteristics. This is because the introduction of the fractal control signal enhances the non-linear dynamic stability of the system, enabling the system to maintain or quickly return to the synchronous state when facing disturbances, effectively preventing the propagation and amplification of disturbances.

[0219] In this embodiment, the above steps implement distributed fractal chaos synchronization control by integrating the optimized fractal control signal into each node of the distributed energy control system and realizing real-time state information exchange and synchronization through specific communication protocols and algorithms, thereby enhancing the overall anti-disturbance ability and self-repair function of the system; making full use of the complex dynamic characteristics of the chaotic system and the self-similarity of the fractal signal at multiple scales, providing a new and efficient regulation means for the field of distributed energy control.

[0220] Step S6: Dynamically adjust the fractal control parameters according to the current operating state of the power grid and changes in the external environment, optimize the control strategy, and achieve adaptive optimization of the control parameters.

[0221] Step S6 specifically includes:

[0222] Define the reinforcement learning parameters, specifically including:

[0223] Environment, the power grid and its external environment, including but not limited to load changes, renewable energy fluctuations, equipment failures, etc.; the state of the power grid can be represented by a series of observable variables, such as the voltage, current, frequency, etc. of each node.

[0224] Agent, the implementer of the control strategy, whose goal is to optimize the performance indicators of the power grid, such as stability, efficiency, cost, etc. by dynamically adjusting the fractal control parameters.

[0225] State s t ∈S, representing the state of the power grid at time step t, including all necessary observable variables, such as V t 、P t 、Q t 、f t representing voltage, active power, reactive power, and frequency respectively.

[0226] Action a t ∈A, the control action taken by the agent in state s t i.e., adjusting the control parameters, such as adjusting the tap position of the substation transformer, generator output, etc.

[0227] Reward r t , the feedback immediately obtained by the agent after executing the action, reflecting the immediate impact of this action on the performance of the power grid; the design of the reward function needs to consider long-term stability and efficiency, and may combine multiple performance indicators, such as reducing power loss, improving frequency stability, etc.

[0228] Objective, to maximize the cumulative reward through the learning process, that is, to find the optimal strategy, expressed as:

[0229]

[0230] Where, π*(s) is the optimal policy π* in the given state s; the optimal policy refers to the policy that can maximize the expected cumulative reward in any state; argmax π is to find the policy among all policies π that makes the expression in the brackets reach the maximum value; is the expected value under the policy π, which is the average or expected sum of future rewards when executing according to the policy π, considering all possible behavior sequences and their corresponding reward distributions during the policy execution process; t is the time step, starting from 0 until infinity; r t is the immediate reward obtained at the time step t; γ is the discount factor, whose value is between 0 and 1, used to reduce the importance of future rewards; when γ is close to 1, future rewards are almost equivalent to immediate rewards; when γ is close to 0, more importance is attached to immediate rewards and long-term effects are ignored.

[0231] The execution process specifically includes:

[0232] Initialize the parameters, set the initial policy π0, and define the state space S, action space A, reward function R(s, a), and discount factor γ.

[0233] At each time step t, the agent observes the current state s of the power grid t .

[0234] The agent selects an action a according to the current policy π t , and applies it to the power grid, observes the next state s t = π t (s t ), and observes the immediate reward r t+1 and t .

[0235] Use the Q-learning algorithm to update the policy π according to s t , a t , r t , s t+1 to optimize the long-term reward. t

[0236] Directly transform the learned policy into the dynamic adjustment of the fractal control parameters. This process continues during the operation of the power grid. The agent continuously learns and adapts to new states and environmental changes, thereby realizing the adaptive optimization of the control parameters.

[0237] In this embodiment, first collect the historical operation data of the power grid to provide data support for all subsequent analysis and control strategies. By obtaining the actual operation conditions of the power grid, such as frequency fluctuations, output of distributed energy, and external disturbance information, provide empirical basis for model construction and prediction.

[0238] Construct a fractal chaotic attractor model based on the data collected in S1, calculate the fractal dimension and correlation coefficient of the power grid state variables, which is a high-level abstraction of the dynamic characteristics of the power grid, identify the self-similarity and complexity characteristics in the dynamic behavior of the power grid, and lay a theoretical foundation for understanding and predicting the behavior of the power grid.

[0239] Apply the Lyapunov exponent analysis method to quantify the stability of the system, predict the stability boundary of the power grid, and identify the key to the potential instability trend of the system, enabling the control strategy to intervene before problems occur.

[0240] According to the instability trend identified in S3 and the fractal characteristics of the power grid in S2, the designed control signal has a self-similar structure that matches the natural fluctuation mode of the power grid, enhancing the compatibility between the control measures and the power grid dynamics and improving the control efficiency.

[0241] The control signal designed in S4 is injected into the distributed energy control system in this step, and synchronization between different nodes is achieved through specific communication protocols and algorithms, improving the overall response ability of the system and enhancing its resistance to disturbances and self-repair function.

[0242] The control strategy implemented in S5 is optimized in S6. According to the real-time state of the power grid and changes in the external environment, the fractal control parameters are dynamically adjusted to ensure that the control strategy always matches the actual situation, realizing the self-adaptability of the control strategy.

[0243] Embodiment 2

[0244] As Figure 2 shown, the present invention discloses an adaptive intelligent power grid regulation system, which includes:

[0245] A data collection module 10 for collecting historical operation data of the power grid.

[0246] A model construction module 20 for constructing a fractal chaotic attractor model and calculating the fractal dimension of the power grid state variables.

[0247] A boundary prediction module 30 for predicting the stability boundary of the power grid based on the fractal chaotic attractor model.

[0248] A signal generation module 40 for designing a fractal control signal and generating a control signal with a self-similar structure.

[0249] A system control module 50 for injecting the fractal control signal into the distributed energy control system.

[0250] A parameter optimization module 60 for dynamically adjusting the fractal control parameters according to the operation state of the power grid and changes in the external environment.

[0251] As an alternative implementation, the model construction module 20 of the present invention specifically includes:

[0252] Select key state variables and arrange the selected variables in chronological order to form a sequence.

[0253] Map the one-dimensional time series to a high-dimensional space to construct a state vector sequence, specifically including:

[0254] Select embedding parameters, where the embedding parameters include an embedding dimension m and a time delay τ.

[0255] For each time point t, construct a state vector, expressed as:

[0256] X t = [f(t), f(t + τ),..., f(t + (m - 1)τ), V(t), V(t + τ),..., V(t + (m - 1)τ)]

[0257] For each time point t, based on the above m and τ, construct a state vector X that includes the states of the past m - 1 time points and the current moment t ; through m and τ, the original one-dimensional time series is converted into a set of points in a multi-dimensional state space, that is, each time point corresponds to an m-dimensional vector.

[0258] Calculate the correlation dimension D C , specifically including:

[0259] For any two state vectors X i , X j , calculate the distance between them, expressed as:

[0260]

[0261] In the formula, x ik and x jk are respectively the elements of the state vectors X i and X j on the kth dimension.

[0262] Count the number of neighborhood point pairs, set a neighborhood radius r, and count the number of point pairs N i (r) within the neighborhood of each point state vector X i ; that is, the number of state vectors within the sphere centered at X i with a radius of r.

[0263] Find the average number of neighborhood point pairs of all points to obtain N(r), expressed as:

[0264]

[0265] Wherein, N is the total number of state vectors; N(r) describes the variation of the average distribution density of points in the state space with the radius.

[0266] Plot the correlation function graph and calculate the correlation dimension, expressed as:

[0267] Define the correlation function C(r) as the natural logarithm of the number of neighbor point pairs, that is, C(r) = ln[N(r)].

[0268] The slope D obtained through linear regression analysis c , expressed as:

[0269]

[0270] Wherein, D c is the correlation dimension.

[0271] As an optional implementation manner, the boundary prediction module 30 of the present invention specifically includes:

[0272] Perform local linearization processing on the system, approximated as the Jacobian matrix J(X t , t), where X is the state vector and t is the time.

[0273] Perform iterative operations, specifically including:

[0274] Initial vector setting, select a small initial vector difference δX0.

[0275] Iterative update, at each time step t, update the vector difference through δX t+1 = J(X t , t)·δX t Update the vector difference.

[0276] Average growth rate calculation, calculate the average growth rate Λ I , expressed as:

[0277]

[0278] Wherein, T is the time length of the analysis.

[0279] Repeat the iterative process for different orthogonal directions of the system state space to obtain a series of Lyapunov exponents λ1, λ2,..., λ n , constituting the Lyapunov spectrum; if the largest Lyapunov exponent λ max > 0, it indicates that the system is in a chaotic state and has potential instability; if λ max < 0, the system tends to be stable; by continuously tracking the largest Lyapunov exponent λ max , find λ maxIn the region where it is equal to 0, the critical point from stability to chaos, i.e., the stability boundary, is identified.

[0280] As an optional implementation manner, the signal generation module 40 of the present invention specifically includes:

[0281] Using the fBm fractal model, Hurst exponent, and time scale to generate a control signal, expressed as:

[0282]

[0283] In the formula, B H (t) is the fBm value at time point t; t K = KΔt, where Δt is the time interval; σ K is the standard deviation of each step adjusted based on the Hurst exponent; Z K is a variable of standard normal random distribution.

[0284] Fine-tune the generated control signal by modifying the amplification factor of the generated control signal or using a filter.

[0285] As an optional implementation manner, the parameter optimization module 60 of the present invention specifically includes:

[0286] Define reinforcement learning parameters, specifically including:

[0287] State s t ∈S, representing the state of the power grid at time step t; action a t ∈A, the control action taken by the agent in state s t , that is, adjusting the control parameters; reward r t , the feedback immediately obtained by the agent after executing the action.

[0288] Maximize the cumulative reward through the learning process, that is, find the optimal policy, expressed as:

[0289]

[0290] In the formula, π*(s) is the optimal policy π* in the given state s; argmax π is to find the policy in all policies π that makes the expression in the brackets reach the maximum value; is the expected value under policy π, which is the average or expected sum of future rewards when executed according to policy π; t is the time step; r t is the immediate reward obtained at time step t; γ is the discount factor.

[0291] The execution process specifically includes:

[0292] Initialize the parameters, set the initial policy π0, and define the state space S, action space A, reward function R(s, a), and discount factor γ.

[0293] At each time step t, the agent observes the current state s of the power grid t .

[0294] The agent selects an action a according to the current policy π t , t = π t (s t ), and applies it to the power grid, observing the next state s t+1 and the immediate reward r t .

[0295] Use the Q - learning algorithm to update the policy π t , a t , r t , s t+1 , optimizing the long - term reward. t

[0296] Directly transform the learned policy into the dynamic adjustment of the fractal control parameters.

[0297] The above are only the preferred embodiments of the present invention and are not used to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.​

Claims

1. An adaptive intelligent power grid regulation method, characterized in that, The method includes: Step S1: Collect historical operation data of the power grid; Step S2: Construct a fractal chaotic attractor model and calculate the fractal dimension of the power grid state variables; Step S3: Predict the stability boundary of the power grid based on the fractal chaotic attractor model; Step S4: Design a fractal control signal to generate a control signal with a self-similar structure; The design of the fractal control signal to generate a control signal with a self-similar structure includes: Using the fBm fractal model, Hurst exponent and time scale to generate a control signal, expressed as: ； Wherein, is the fBm value at time point ; , is the time interval; is the standard deviation of each step adjusted based on the Hurst exponent; is the variable of the standard normal random distribution; Fine-tune the generated control signal by modifying the amplification coefficient of the generated control signal or using a filter; Step S5: Inject the fractal control signal into the distributed energy control system; Step S6: Dynamically adjust the fractal control parameters according to the operating state of the power grid and changes in the external environment.

2. The adaptive intelligent power grid regulation method according to claim 1, characterized in that The construction of the fractal chaotic attractor model and the calculation of the fractal dimension of the power grid state variables specifically include: Select key state variables and arrange the selected variables in chronological order to form a sequence; Map the one-dimensional time series to a high-dimensional space to construct a state vector sequence, specifically including: Select embedding parameters, the embedding parameters including an embedding dimension and a time delay ; For each time point , construct a state vector, denoted as: ； wherein, is the grid frequency, is the voltage of the key node; for each time point , based on the above and , a state vector containing the states of the past time points and the current moment is constructed; through and , the original one-dimensional time series is converted into a set of points in a multi-dimensional state space, that is, each time point corresponds to a -dimensional vector; Calculating the correlation dimension , specifically including: For any two state vectors , , calculate the distance between them, denoted as: ； In the formula, and are the elements of the state vectors and at the -th dimension, respectively; Count the number of neighboring points and set the neighborhood radius , and count the state vector of each point The number of points within the neighborhood ; that is, with as the center and a radius of The number of state vectors within the sphere Find the average number of neighboring points for all points to obtain , which is expressed as: ； In the formula, is the total number of state vectors; describes the variation of the average distribution density of points in the state space with the radius; Plot the correlation function graph and calculate the correlation dimension, expressed as: Define the correlation function is the natural logarithm of the number of neighboring points, that is ; The slope obtained by linear regression analysis , is expressed as: ； In the formula, is the correlation dimension.

3. An adaptive intelligent power grid regulation method according to claim 1, characterized in that The prediction of the stability boundary of the power grid based on the fractal chaotic attractor model specifically includes: Perform local linearization on the system, approximated as the Jacobian matrix , where is the state vector, is the time; Perform iterative operations, specifically including: Initial vector setting, select a tiny initial vector difference ; Iterative update, at each time step , through Update the vector difference; Average growth rate calculation, calculating the average growth rate over a period of time , expressed as: ； In the formula, is the time length for analysis; Repeat the iterative process for different orthogonal directions of the system state space to obtain a series of Lyapunov exponents , which constitute the Lyapunov spectrum; if the largest Lyapunov exponent , it indicates that the system is in a chaotic state and has potential instability; if , the system tends to be stable; by continuously tracking the largest Lyapunov exponent , find the region where the system changes from stable to chaotic, and identify the critical point from stability to chaos, namely the stability boundary.

4. An adaptive intelligent power grid regulation method according to claim 1, characterized in that Dynamically adjust the fractal control parameters according to the operating state of the power grid and changes in the external environment, specifically including: Define reinforcement learning parameters, specifically including: Status , indicating the status of the power grid at time step . Action , the control action taken by the agent in the state is to adjust the control parameters; Reward which is the feedback immediately obtained after the agent executes an action; Maximize the cumulative reward through the learning process, that is, find the optimal strategy, expressed as: ； Wherein, is the optimal strategy under a given state ; is to find the strategy that maximizes the expression in the brackets among all strategies ; is the expected value under the strategy , which is the average or expected total of future rewards when executed according to the strategy ; is the time step; is the immediate reward obtained at the time step ; is the discount factor; The execution process, specifically including: Initialize parameters and set the initial strategy , define the state space , the action space , the reward function and the discount factor ; At each time step , the agent observes the current state of the power grid ; The agent selects an action according to the current policy and applies it to the power grid, observing the next state and the immediate reward ; ; Use the Q-learning algorithm to update the policy , , , and optimize the long-term reward; ​ Directly convert the learned strategy into the dynamic adjustment of the fractal control parameters.

5. An adaptive intelligent power grid regulation system, characterized in that, The system includes: A data collection module for collecting historical operation data of the power grid; A model construction module for constructing a fractal chaotic attractor model and calculating the fractal dimension of the power grid state variables; A boundary prediction module for predicting the stability boundary of the power grid based on the fractal chaotic attractor model; A signal generation module for designing a fractal control signal to generate a control signal with a self-similar structure; The signal generation module includes: Using the fBm fractal model, the Hurst exponent and the time scale to generate a control signal, expressed as: ； Wherein, is the fBm value at the time point ; , is the time interval; is the standard deviation of each step adjusted based on the Hurst exponent; is the variable of the standard normal random distribution; Fine-tune the generated control signal by modifying the amplification coefficient of the generated control signal or using a filter; A system control module for injecting the fractal control signal into the distributed energy control system; A parameter optimization module for dynamically adjusting the fractal control parameters according to the operating state of the power grid and changes in the external environment.

6. An adaptive intelligent power grid regulation system according to claim 5, characterized in that, The model construction module specifically includes: Select key state variables and arrange the selected variables in chronological order to form a sequence; Map the one-dimensional time series to a high-dimensional space to construct a state vector sequence, specifically including: Select embedding parameters, where the embedding parameters include an embedding dimension and a time delay ; For each time point , a state vector is constructed, denoted as: ； wherein, is the power grid frequency, is the voltage of the key node; for each time point , based on the above and , construct a state vector containing the states of the past time points and the current moment; through and , the original one-dimensional time series is converted into a set of points in a multi-dimensional state space, that is, each time point corresponds to a -dimensional vector; Calculating the correlation dimension , specifically including: For any two state vectors , , calculate the distance between them, denoted as: ； Wherein, and are respectively the elements of the state vectors and in the th dimension; Count the number of neighboring points and set the neighborhood radius and count the state vector of each point in the neighborhood ; that is, taking as the center, the number of state vectors within the sphere with a radius of ; Find the average number of neighboring points for all points to obtain , which is expressed as: ； In the formula, is the total number of state vectors; describes the variation of the average distribution density of points in the state space with the radius; Plot the correlation function graph and calculate the correlation dimension, expressed as: Define the correlation function is the natural logarithm of the number of neighboring points, that is ; The slope obtained by linear regression analysis , is expressed as: ； In the formula, is the correlation dimension.

7. An adaptive intelligent power grid regulation system according to claim 5, characterized in that, The boundary prediction module specifically includes: Perform local linearization on the system and approximate it as the Jacobian matrix , where is the state vector, is the time; Perform iterative operations, specifically including: Initial vector setting, select a small initial vector difference ; Iteratively update at each time step , through Update the vector difference; Average growth rate calculation, calculating the average growth rate over a period of time , expressed as: ； In the formula, is the time length of the analysis; Repeat the iterative process for different orthogonal directions of the system state space to obtain a series of Lyapunov exponents , which constitute the Lyapunov spectrum; if the largest Lyapunov exponent , it indicates that the system is in a chaotic state and has potential instability; if , the system tends to be stable; by continuously tracking the largest Lyapunov exponent , find region, and identify the critical point from stable to chaotic, that is, the stability boundary.

8. An adaptive intelligent power grid regulation system according to claim 5, characterized in that, The parameter optimization module specifically includes: Define reinforcement learning parameters, specifically including: State , representing the state of the power grid at time step ; Action , the control action taken by the agent in state , i.e., adjusting the control parameters; Reward , the feedback immediately obtained by the agent after executing the action; Maximize the cumulative reward through the learning process, that is, find the optimal strategy, expressed as: ； wherein, is the optimal strategy under a given state ; is to find the strategy among all strategies that maximizes the expression within the parentheses; is the expected value under the strategy , which is the average or expected sum of future rewards when executed according to the strategy ; is the time step; is the immediate reward obtained at the time step ; is the discount factor; The execution process, specifically including: Initialize parameters and set the initial strategy , define the state space , the action space , the reward function and the discount factor ; At each time step the agent observes the current state of the power grid ; The agent selects an action according to the current policy and applies it to the power grid, observing the next state and the immediate reward ; ; Use the Q-learning algorithm to update the policy , , , and optimize the long-term reward; ​ Directly convert the learned strategy into the dynamic adjustment of the fractal control parameters.

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