Reduced-order model parameter optimization method of self-evolution whale optimization algorithm based on environment feedback
By using a self-evolving whale optimization algorithm based on environmental feedback to adjust the search strategy and parameters in real time, the problem of insufficient environmental awareness in the reduction of complex power system models is solved, achieving high-precision and stable optimization of the reduced-order model and adapting to the needs of systems with different complexities.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ELECTRIC POWER RESEARCH INSTITUTE OF STATE GRID JIBEI ELECTRIC POWER CO LTD
- Filing Date
- 2025-12-12
- Publication Date
- 2026-05-15
AI Technical Summary
Existing whale optimization algorithms lack real-time perception and response capabilities for environmental feedback information during the order reduction process of complex power system models, resulting in rigid strategy switching, difficulty in achieving a balance between global exploration and local development, and insufficient convergence accuracy and stability.
A self-evolving whale optimization algorithm based on environmental feedback is adopted. The search state is adjusted in real time through multi-dimensional environmental feedback indicators. Combined with strategy updates in exploration, development and equilibrium states, as well as the self-evolution mechanism, the algorithm parameters and population structure are dynamically adjusted to optimize the parameters of the power system model.
It improves the accuracy and practicality of the reduced-order model, enhances the matching ability between the model and the dynamic response of the original system, strengthens the convergence stability and adaptability of the algorithm, and adapts to complex and ever-changing optimization environments.
Smart Images
Figure CN122047281A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of power system technology, specifically to a method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm with environmental feedback. Background Technology
[0002] As high-dimensional, nonlinear dynamic systems, complex power systems require accurate modeling and simulation analysis for system stability and control. However, full-order models suffer from low simulation and analysis efficiency due to their high dimensionality and strong nonlinearity. Employing model reduction techniques to construct lower-order equivalent models while preserving the dominant dynamic characteristics of the original system has become an effective way to improve analysis and control efficiency. The core of model reduction lies in optimizing parameters to make the reduced model approximate the dynamic response of the original system as closely as possible in the time or frequency domain.
[0003] Whale Optimization (WOA) is widely used for complex optimization problems due to its simple structure, fast convergence speed, and few parameters. Existing improved WOA algorithms mainly achieve performance enhancements by introducing strategies such as particle swarm optimization and differential evolution. These methods often use fixed rules or preset thresholds for strategy switching, which can easily lead to getting trapped in local optima in the later search stages. Summary of the Invention
[0004] To address at least some of the aforementioned technical problems, embodiments of this application provide a method for optimizing the parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback.
[0005] This application provides a method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback, comprising:
[0006] S1. Map the parameter set of the reduced-order model to be optimized in the power system to the individual position vector in the whale optimization algorithm, and initialize the whale population within the feasible region of the parameters, wherein the parameter set includes key time constant, gain coefficient and damping ratio;
[0007] S2. Repeat steps a to d until the preset iteration termination condition is met:
[0008] a. Based on the current whale population, calculate a multidimensional environmental feedback index that includes population diversity, convergence speed, and search distribution indicators.
[0009] b. Based on the multidimensional environmental feedback indicators, classify the current search state into exploratory state, development state, or equilibrium state;
[0010] c. Based on the current search status type, execute the corresponding parameter update strategy to update the individual whale's position;
[0011] d. During the iteration process, the search status is continuously monitored. When the search status meets the preset stagnation conditions, a self-evolution operation is performed. The self-evolution operation includes population recombination and adaptive adjustment of algorithm parameters.
[0012] S3. When the iteration termination condition is met, output the position vector corresponding to the current global best individual as the optimized reduced-order model parameter.
[0013] In some embodiments, the population diversity index, convergence rate index, and search distribution index are calculated according to the following formulas:
[0014]
[0015] in, For the diversity index of the t-th generation population, For population size, For the first The position vectors of individual whales The average position of the population;
[0016]
[0017] in, Let be the convergence rate index for generation t, where For the first Replace the optimal fitness value, For the first -1 generation optimal fitness value, It is a very small constant;
[0018]
[0019] in, Let t be the search distribution index for the t-th generation. This is the current globally optimal solution.
[0020] In some embodiments, the fitness value of each individual whale is calculated according to the following fitness function:
[0021]
[0022] in, For the i-th individual whale fitness value; This refers to the simulation duration. This is the output response of the original power system model; The parameters at time t are The time-domain response of the time-reduced order model.
[0023] In some embodiments, classifying the current search state into an exploratory state, an exploration state, or a balanced state based on the multidimensional environmental feedback indicators includes:
[0024] like and The current search state is then classified as the exploratory state, where... The maximum threshold for population diversity, This is the minimum threshold for convergence speed;
[0025] like and The current search state is then classified as the "development state". The minimum threshold for population diversity, The maximum threshold for convergence speed;
[0026] If the current search state is neither in the exploratory state nor the development state, then the current search state is classified as the equilibrium state.
[0027] In some embodiments, executing a corresponding parameter update strategy based on the type of the current search state to update the individual whale's location includes:
[0028] If the current search state is exploratory, then an enhanced random search is used to update the individual whale's position:
[0029]
[0030] in, Let be the position vector of the (t+1)th generation whale individual. Let be the position vector of the t-th generation whale individual. To explore the strength coefficient, It is a random direction vector;
[0031] If the current search state is open, a locally refined search based on singular perturbation theory is used to update the individual whale's position:
[0032]
[0033] in, Let be a standard normally distributed random perturbation vector. The adaptive weight matrix based on sensitivity is expressed as follows:
[0034]
[0035] in, This represents the normalized sensitivity of the j-th parameter. To prevent tiny positive numbers with a denominator of zero; The calculation formula is a difference approximation:
[0036]
[0037] If a parameter The large value indicates that the direction is extremely steep, requiring a reduction in the search step size. If the step size decreases, it indicates that the direction is flat, and the step size needs to be increased to accelerate convergence.
[0038] If the current search state is in equilibrium, the standard WOA search strategy is used to update the individual whale positions:
[0039]
[0040] in, The distance between an individual and the optimal solution; Let this be the position of the individual whale in the current t-th iteration; It is the constant that defines the shape of the logarithmic spiral; It is a random number between [-1, 1].
[0041] In some embodiments, population recombination includes:
[0042] Retaining the current top E% of elite whale individuals, perform Cauchy mutation on the remaining F% of whale individuals using the following formula to obtain a new whale population:
[0043]
[0044] in, Let be the position vector of the (t+1)th generation whale individual. It is a standard Cauchy distribution random number generator.
[0045] In some embodiments, the algorithm parameter adaptive adjustment operation includes:
[0046] Adjust the WOA convergence factor according to the following formula. :
[0047]
[0048] in, This represents the current iteration number. The maximum number of iterations, It is a non-linear adjustment index; when stagnation is detected, it decreases. make Maintaining a large value forces the algorithm to re-explore.
[0049] In some embodiments, the iteration termination condition is as follows:
[0050]
[0051] in To improve convergence accuracy, This represents the maximum number of iterations.
[0052] In some embodiments, the method further includes:
[0053] Based on the optimized reduced-order model parameters, a reduced-order model is established;
[0054] The effectiveness and accuracy of the reduced-order model are verified by comparing the output response of the reduced-order model with that of the original power system model through multi-condition time-domain simulation.
[0055] This application also provides a device for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback, comprising:
[0056] An initialization module is used to map the parameter set of the reduced-order model to be optimized in the power system to the individual position vector in the whale optimization algorithm, and to initialize the whale population within the feasible domain of the parameters. The parameter set includes key time constants, gain coefficients and damping ratios.
[0057] The iteration module is used to repeatedly execute the following steps a to d until a preset iteration termination condition is met:
[0058] a. Based on the current whale population, calculate a multidimensional environmental feedback index that includes population diversity, convergence speed, and search distribution indicators.
[0059] b. Based on the multidimensional environmental feedback indicators, classify the current search state into exploratory state, development state, or equilibrium state;
[0060] c. Based on the current search status type, execute the corresponding parameter update strategy to update the individual whale's position;
[0061] d. During the iteration process, the search status is continuously monitored. When the search status meets the preset stagnation conditions, a self-evolution operation is performed. The self-evolution operation includes population recombination and adaptive adjustment of algorithm parameters.
[0062] The output module is used to output the position vector corresponding to the current global best individual as the optimized reduced-order model parameters when the iteration termination condition is met.
[0063] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the methods described in any of the above embodiments.
[0064] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described in any of the above embodiments.
[0065] This application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the methods described in any of the above embodiments.
[0066] The method for optimizing parameters of a reduced-order model based on an environmental feedback-driven self-evolving whale optimization algorithm provided in this application's embodiments maps the parameter set of the reduced-order model to be optimized in the power system to an individual position vector in the whale optimization algorithm, and initializes the whale population within the feasible region of the parameters. The parameter set includes key time constants, gain coefficients, and damping ratios. The following steps a to d are repeated until a preset iteration termination condition is met: a) Calculate a multi-dimensional environmental feedback index, including population diversity, convergence speed, and search distribution indicators, based on the current whale population; b) Classify the current search state into exploratory, development, or equilibrium states based on the multi-dimensional environmental feedback index; c) Execute the corresponding parameter update strategy according to the type of the current search state to update the individual whale positions; d) Continuously monitor the search state during the iteration process. When the search state meets a preset stagnation condition, a self-evolutionary operation is performed, including population recombination and adaptive adjustment of algorithm parameters; When the iteration termination condition is met, the position vector corresponding to the current globally optimal individual is output as the optimized reduced-order model parameters. It has the ability to dynamically adjust strategies according to the search environment. The environmental feedback mechanism provides a basis for dynamic adjustment of the algorithm by monitoring the search status in real time, while the self-evolutionary characteristic enables the algorithm to autonomously adjust its search behavior according to environmental changes. Introducing environmental feedback and self-evolutionary mechanism into WOA can significantly improve the optimization effect of parameters of the reduced-order model. Attached Figure Description
[0067] 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. In the drawings:
[0068] Figure 1 This is a flowchart illustrating a method for optimizing the parameters of a reduced-order model based on an environmental feedback-based self-evolving whale optimization algorithm, as provided in an embodiment of this application.
[0069] Figure 2This is a partial flowchart illustrating a method for optimizing the parameters of a reduced-order model based on an environmental feedback-based self-evolving whale optimization algorithm, as provided in an embodiment of this application.
[0070] Figure 3 This is a flowchart illustrating a method for optimizing the parameters of a reduced-order model based on an environmental feedback-based self-evolving whale optimization algorithm, as provided in an embodiment of this application.
[0071] Figure 4 This is a schematic diagram of the structure of a parameter optimization device for a reduced-order model based on an environmental feedback-based self-evolving whale optimization algorithm, provided in an embodiment of this application.
[0072] Figure 5 This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of this application. Detailed Implementation
[0073] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the embodiments of this application will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments and their descriptions are used to explain this application, but are not intended to limit this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily arranged.
[0074] The terms “first,” “second,” etc., used in this document are not intended to specifically refer to order or sequence, nor are they used to limit this application; they are merely used to distinguish elements or operations described using the same technical terms.
[0075] The terms “include,” “including,” “have,” “contain,” etc., used in this article are all open-ended terms, meaning that they include but are not limited to.
[0076] The term "and / or" as used in this document includes any or all of the items mentioned.
[0077] Currently, improved WOA algorithms, while traditional model reduction methods based on singular perturbation theory and factor analysis can maintain the system structure, have limited effect on parameter optimization of the reduced model and lack real-time perception and response capabilities to environmental conditions. Specifically, current improved WOA algorithms have the following drawbacks in the field of model reduction:
[0078] The rigid strategy switching mechanism cannot dynamically adjust and optimize strategies according to changes in the search environment, resulting in an imbalance between global exploration and local development.
[0079] Without effectively utilizing environmental feedback information, the algorithm struggles to adapt to complex and ever-changing optimization environments.
[0080] When faced with parameter optimization of high-dimensional, highly nonlinear models, the convergence accuracy and stability of existing methods need to be improved.
[0081] Traditional methods for optimizing parameters in reduced-order models often neglect environmental feedback information, making it difficult to achieve a high degree of matching between the reduced-order model and the dynamic response of the original system.
[0082] To address the aforementioned technical problems, this application proposes a method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback. This method overcomes the shortcomings of existing technologies in optimizing parameters of reduced-order power system models, specifically including:
[0083] At the algorithm level, it addresses the issues of standard WOA lacking environmental awareness and being unable to adaptively adjust strategies based on search status, as well as the shortcomings of existing hybrid algorithms such as rigid strategy switching and complex parameter settings.
[0084] At the application level of the reduced-order model, it addresses issues such as low accuracy in parameter optimization, poor convergence stability, and insufficient ability to fit the dynamic response of the system caused by algorithm defects, thereby improving the accuracy and practicality of the reduced-order model.
[0085] Figure 1 This is a flowchart illustrating a method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback, as provided in an embodiment of this application. Figure 1 As shown in the embodiment of this application, a method for optimizing the parameters of a reduced-order model based on an environmental feedback-driven self-evolving whale optimization algorithm is provided, comprising:
[0086] S1. Map the parameter set of the reduced-order model to be optimized in the power system to the individual position vector in the whale optimization algorithm, and initialize the whale population within the feasible region of the parameters, wherein the parameter set includes key time constant, gain coefficient and damping ratio;
[0087] Step S1 is used to construct the search space for the reduced-order model parameters and initialize the population. Specifically, the high-order mathematical model of the original power system is obtained, and the set of parameters for the reduced-order model to be optimized is determined based on model characteristics (such as singular perturbation characteristics) or a preset reduced-order structure. The reduced-order model parameter set is mapped to the individual whale position vectors in the whale optimization algorithm. The whale population is initialized within the feasible region of the parameters, where each individual represents a set of potential reduced-order model parameter configurations.
[0088] Let the state-space expression of the original power system (higher-order model) be:
[0089]
[0090] in, It is an n-order higher-order state vector. For the input vector, For the output vector, , , , It is a coefficient matrix; for The first-order partial derivative.
[0091] Let the order of the reduced-order model be... Its parameterized state-space equation is:
[0092]
[0093] in, The set of parameters to be optimized for order reduction has a dimension of d and includes key physical parameters such as time constant, gain coefficient, and damping ratio in the reduced-order system matrix.
[0094] Then, population initialization is performed. The parameter set is then... Mapped to individual position vectors in the whale optimization algorithm Initialize a population of N individuals in a d-dimensional search space. .
[0095] For the j-th dimension parameter of the i-th individual Its initialization formula can be:
[0096]
[0097] in, , , Let these be the physical lower and upper bounds for the j-th parameter to be optimized; It is a random number uniformly distributed between [0,1].
[0098] During initialization, the fitness function can also be pre-built. fitness function It can be configured to calculate the dynamic response error between the reduced-order model and the original system under the same time-domain excitation. The smaller the error, the better the fitness, and the higher the accuracy of the reduced-order model in approximating the original system. The fitness function is defined as the integral of the output error between the original system and the reduced-order model under typical operating conditions (such as step response):
[0099]
[0100] in, For the i-th individual whale fitness value; This refers to the simulation duration. This is the output response of the original power system model; The parameters at time t are The time-domain response of the time-reduced order model.
[0101] S2. Repeat steps a to d until the preset iteration termination condition is met:
[0102] a. Based on the current whale population, calculate a multidimensional environmental feedback index that includes population diversity, convergence speed, and search distribution indicators.
[0103] In step a, during each iteration of the algorithm, multidimensional environmental feedback indicators of the population are calculated in real time to provide a basis for decision-making in subsequent adaptive optimization. These indicators include:
[0104] Population diversity index: used to quantify the dispersion of a population distribution in a reduced-order parameter space;
[0105] Convergence rate metric: used to quantify the rate of change of the optimal fitness value of a population;
[0106] Search distribution metrics: used to quantify the clustering trend of individuals in a specific region of the parameter space.
[0107] Population diversity is used to assess the distribution of a population in the search space, and its mathematical expression is:
[0108]
[0109] in, As an indicator of population diversity, For population size, For the first The position vectors of individual whales This represents the average location of the population. This indicator reflects the degree of dispersion of the population distribution in the search space. The larger the value of this indicator, the more dispersed the population distribution and the stronger the global exploration capability.
[0110] The convergence rate metric is used to monitor the convergence progress of an algorithm and is defined as follows:
[0111]
[0112] in, The convergence speed index is denoted by , where For the first Replace the optimal fitness value, To prevent division by zero for extremely small constants. This metric reflects the degree of improvement of the algorithm between adjacent iterations.
[0113] The search distribution index is used to quantify the clustering state of the population around the optimal solution, and its expression is:
[0114]
[0115] in, For search distribution indicators, This represents the current globally optimal solution. This metric describes the degree to which the population clusters around the optimal solution. The larger the value of this metric, the more uneven the population distribution.
[0116] b. Based on the multidimensional environmental feedback indicators, classify the current search state into exploratory state, development state, or equilibrium state;
[0117] In step b, based on the environmental feedback indicators established in step a, the search status is classified in real time. The search status classification is achieved through the following criteria:
[0118]
[0119] in, The maximum threshold for population diversity, The minimum threshold for population diversity, This is the minimum threshold for convergence speed; The threshold values represent the maximum convergence speed, and can be adjusted appropriately based on the specific problem. For example, , , , .
[0120] c. Based on the current search status type, execute the corresponding parameter update strategy to update the individual whale's position;
[0121] In step c, based on the current search state type, the corresponding optimization strategy is selected and executed to achieve real-time optimization of algorithm performance. When in the exploration state, an enhanced stochastic search strategy is executed. By increasing the stochastic perturbation step size of position updates, the population is driven to perform a divergent search across the global scope of the reduced-order parameter space, preventing the algorithm from prematurely converging to locally suboptimal reduced-order parameter solutions. When in the development state, a local fine-tuning search strategy based on singular perturbation theory is executed. Utilizing the separation characteristics of the original system's fast and slow time scales, key time constant parameters or gain parameters are fine-tuned with small steps to achieve in-depth mining of the local accuracy of the reduced-order model. When in the equilibrium state, a standard whale optimization spiral encirclement strategy is executed. While maintaining a certain level of population diversity, the population is guided to shrink towards the currently discovered optimal reduced-order parameter region.
[0122] Specifically, when in the exploratory state, an enhanced random search is employed:
[0123]
[0124] in, For randomly selected individual locations, To explore the intensity coefficient (with a value of 1.5), It is a random direction vector.
[0125] When in the development phase, a local fine-grained search based on singular perturbation theory is employed. Due to the strong nonlinearity and multi-timescale characteristics of the original power system, the parameter space of the constructed reduced-order model typically exhibits a "canyon"-shaped ill-conditioned distribution. That is, some parameters are extremely sensitive to the fitness function, while others are relatively insensitive.
[0126] Traditional random search is prone to oscillations at the bottom of the "canyon". A local gradient field can be constructed using parameter sensitivity information to fine-tune the optimal solution with a non-uniform step size, thus matching the terrain features of the parameter space.
[0127]
[0128] in, This represents the globally optimal reduction parameter individual in the current iteration. This is the learning rate.
[0129] To reduce computational complexity, in practical engineering implementations, the pseudo-inverse of the first-order sensitivity matrix is often used to approximate the inverse of the Hessian matrix H. The simplified engineering formula is as follows:
[0130]
[0131] in It provides the driving force for local search for a standard normally distributed random perturbation vector. The adaptive weight matrix based on sensitivity is expressed as follows:
[0132]
[0133] in, This represents the normalized sensitivity of the j-th parameter. To prevent tiny positive numbers with a denominator of zero. The calculation formula is a difference approximation:
[0134]
[0135] If a parameter The large value indicates that the direction is extremely steep, requiring a reduction in the search step size. If the step size increases, it indicates that the direction is flat, and the step size needs to be increased to accelerate convergence.
[0136] When the system is in equilibrium, the standard WOA search strategy is used to maintain search stability:
[0137]
[0138] in, The distance between an individual and the optimal solution; It is the constant that defines the shape of the logarithmic spiral; It is a random number between [-1, 1].
[0139] d. During the iteration process, the search status is continuously monitored. When the search status meets the preset stagnation conditions, a self-evolution operation is performed. The self-evolution operation includes population recombination and adaptive adjustment of algorithm parameters.
[0140] In step d, to further improve algorithm performance, a self-evolution mechanism was designed. During the iteration process, the search state is continuously monitored, and the self-evolution mechanism is triggered when the search state meets a preset stagnation condition.
[0141] Population recombination: retain the current elite individuals (i.e., the parameter set corresponding to the minimum order reduction error), and reinitialize or Gaussian mutate the inferior individuals with lower rankings;
[0142] Parameter adaptation: Based on the environmental feedback data from historical iterations, the convergence factor and weight coefficients within the algorithm are dynamically adjusted;
[0143] Strategy Update: Based on the success rate of different search strategies in historical iterations, update the probability model of strategy selection in step c online.
[0144] The triggering conditions for the self-evolution mechanism can be:
[0145]
[0146] in, For a stall counter, For tolerance. If If the error exceeds the preset threshold, it indicates that the algorithm has not significantly reduced the optimal error found over multiple generations, suggesting that the algorithm has stagnated and triggering the self-evolution mechanism.
[0147] After self-evolution is triggered, the population recombination operation is performed first:
[0148]
[0149] As a standard Cauchy distribution random number generator, it can retain the top 10% of elite individuals and perform Cauchy mutation on the remaining 90% of individuals, thereby increasing population diversity by utilizing the long tail characteristic of the Cauchy distribution.
[0150] At the same time, dynamically adjust the WOA convergence factor. This prevents it from decreasing linearly, but instead adapts to the speed of historical evolution:
[0151]
[0152] in This represents the current iteration number. This represents the maximum number of iterations. This is a non-linear adjustment index. When stagnation is detected, it decreases. make Maintaining a large value forces the algorithm to re-explore.
[0153] S3. When the iteration termination condition is met, output the position vector corresponding to the current global best individual as the optimized reduced-order model parameter.
[0154] In step S3, the decision to terminate the optimization process is made based on the iteration termination condition:
[0155]
[0156] in For convergence accuracy, This represents the maximum number of iterations. When any condition is met, the position vector corresponding to the current globally optimal individual is output as the parameters of the optimized reduced-order model, thus completing the entire optimization process.
[0157] like Figure 2 As shown, in some embodiments, the method further includes:
[0158] S4. Based on the optimized reduced-order model parameters, establish a reduced-order model;
[0159] S5. By comparing the output response of the reduced-order model with that of the original power system model through multi-condition time-domain simulation, the effectiveness and accuracy of the reduced-order model are verified.
[0160] Specifically, a reduced-order model is constructed using the optimized reduced-order model parameters, and the root mean square error of the time-domain response is calculated to evaluate the performance of the reduced-order model:
[0161]
[0162] in, Output the full-order model (original power system model). For the output of the reduced-order model, The number of sampling points. For the current number One sampling point.
[0163] By establishing the error mapping relationship between the original power system model and the reduced-order model, the improved whale optimization algorithm is used to perform optimization in the parameter space, and a multi-dimensional environmental feedback mechanism is introduced to dynamically adjust the search strategy, ultimately obtaining a reduced-order model that can accurately approximate the dynamic characteristics of the original system.
[0164] This application proposes a method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm with environmental feedback. The environmental feedback mechanism enables the algorithm to acquire context awareness and intelligently switch search strategies, achieving simultaneous improvement in accuracy and convergence speed during reduced-order model parameter optimization. The self-evolutionary mechanism ensures that the algorithm autonomously adjusts according to the optimization process, adapting to the reduced-order requirements of systems with varying complexities. By combining advanced optimization algorithms with traditional reduced-order theory, the optimization performance of the reduced-order model is significantly improved while maintaining a simple algorithm structure. Compared with traditional methods, this method exhibits better convergence performance and stability in reduced-order model parameter optimization, effectively addressing the reduced-order requirements under large disturbance scenarios in power systems, and providing a more reliable model foundation for system analysis and control.
[0165] Furthermore, fuzzy logic systems can be used to replace hard threshold classification for environmental state assessment, or reinforcement learning can be used to replace rule bases for policy selection. Regarding order reduction methods, intrinsic orthogonal decomposition (POD) or balanced truncation can be used to replace singular perturbation theory, achieving the same inventive objective.
[0166] To better understand this application, the following specific embodiment will be used to describe in detail the method for optimizing the reduced-order model parameters of the self-evolving whale optimization algorithm based on environmental feedback provided in this application.
[0167] Figure 3 This is a flowchart illustrating a method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback, as provided in an embodiment of this application. Figure 3 As shown, the method includes:
[0168] Step 1: Construct the parameter search space and population initialization for the reduced-order model. Obtain the high-order mathematical model of the original system. Based on model characteristics (such as singular perturbation characteristics) or a preset reduced-order structure, determine the parameter set of the reduced-order model to be optimized. Map the reduced-order model parameter set to individual position vectors in the whale optimization algorithm. Initialize the whale population within the feasible region of the parameters, where each individual represents a set of potential reduced-order model parameter configurations. Set the fitness function to calculate the dynamic response error between the reduced-order model and the original system under the same time-domain excitation; the smaller the error, the better the fitness.
[0169] Step 2: Establish a multi-dimensional environmental feedback indicator system and state determination
[0170] In each iteration of the algorithm, a multidimensional environmental feedback index of the population is calculated in real time, including:
[0171] Population diversity index: used to quantify the dispersion of a population distribution in a reduced-order parameter space;
[0172] Convergence rate metric: used to quantify the rate of change of the optimal fitness value of a population;
[0173] Search distribution metrics: used to quantify the clustering trend of individuals in a specific region of the parameter space.
[0174] Based on the aforementioned multidimensional environmental feedback indicators, the current optimization search state is divided into three types: exploration state, development state, and equilibrium state.
[0175] Step 3: Execute an adaptive search strategy based on environment state.
[0176] Based on the search status determined in step 2, dynamically select and execute the corresponding parameter update strategy:
[0177] When in the exploration state, an enhanced stochastic search strategy is implemented. By increasing the stochastic perturbation step size of position updates, the population is driven to perform a divergent search in the global scope of the reduced-order parameter space, preventing the algorithm from prematurely converging to a locally suboptimal reduced-order parameter solution.
[0178] When in development mode, a local fine-tuning search strategy based on singular perturbation theory is executed. Utilizing the separation of fast and slow time scales of the original system, small-step directional fine-tuning is performed on key time constant parameters or gain parameters to achieve in-depth mining of the local accuracy of the reduced-order model.
[0179] When in equilibrium, the standard whale-optimized spiral encirclement strategy is implemented. While maintaining a certain level of population diversity, the population is guided to shrink towards the currently discovered optimal reduction parameter region.
[0180] Step 4: Implement self-evolution mechanism and exception handling
[0181] The search status is continuously monitored during the iteration process, and a self-evolution mechanism is triggered when a preset stagnation condition is detected:
[0182] Population recombination: retain the current elite individuals (i.e., the parameter set corresponding to the minimum order reduction error), and reinitialize or Gaussian mutate the inferior individuals with lower rankings;
[0183] Parameter adaptation: Based on the environmental feedback data from historical iterations, the convergence factor and weight coefficients within the algorithm are dynamically adjusted;
[0184] Strategy update: Based on the success rate of different search strategies in historical iterations, update the probability model of strategy selection in step 3 online.
[0185] Step 5: Construction and Validation of the Reduced-Order Model
[0186] Repeat steps 2 to 4 until the preset termination condition is met (such as reaching the maximum number of iterations or the fitness function value being less than the preset accuracy threshold).
[0187] The position vector of the globally optimal individual is output as the final reduced-order model parameter. The target reduced-order model is constructed using these parameters, and the effectiveness and accuracy of the model are verified by comparing the output response of the reduced-order model with that of the original system through multi-condition time-domain simulations.
[0188] Based on the same inventive concept, this application also provides a device for optimizing the parameters of a reduced-order model using a self-evolving whale optimization algorithm based on environmental feedback.
[0189] Figure 4 This is a schematic diagram of a device for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm using environmental feedback, as provided in an embodiment of this application. Figure 4 As shown, the device includes:
[0190] Initialization module 21 is used to map the parameter set of the reduced-order model to be optimized in the power system to the individual position vector in the whale optimization algorithm, and initialize the whale population within the feasible domain of the parameters, wherein the parameter set includes key time constant, gain coefficient and damping ratio;
[0191] Iteration module 22 is used to repeatedly execute steps a to d until a preset iteration termination condition is met:
[0192] a. Based on the current whale population, calculate a multidimensional environmental feedback index that includes population diversity, convergence speed, and search distribution indicators.
[0193] b. Based on the multidimensional environmental feedback indicators, classify the current search state into exploratory state, development state, or equilibrium state;
[0194] c. Based on the current search status type, execute the corresponding parameter update strategy to update the individual whale's position;
[0195] d. During the iteration process, the search status is continuously monitored. When the search status meets the preset stagnation conditions, a self-evolution operation is performed. The self-evolution operation includes population recombination and adaptive adjustment of algorithm parameters.
[0196] Output module 23 is used to output the position vector corresponding to the current global best individual as the optimized reduced-order model parameters when the iteration termination condition is met.
[0197] This application proposes a parameter optimization device for a reduced-order model based on a self-evolving whale optimization algorithm with environmental feedback. Through an environmental feedback mechanism, the algorithm acquires context awareness, enabling intelligent switching of search strategies and achieving simultaneous improvement in accuracy and convergence speed during reduced-order model parameter optimization. The self-evolution mechanism ensures that the algorithm autonomously adjusts according to the optimization process, adapting to the reduced-order requirements of systems with varying complexity. By combining advanced optimization algorithms with traditional reduced-order theory, the optimization performance of the reduced-order model is significantly improved while maintaining a simple algorithm structure. Compared with traditional methods, this method exhibits better convergence performance and stability in reduced-order model parameter optimization, effectively addressing the reduced-order requirements under large disturbance scenarios in power systems, and providing a more reliable model foundation for system analysis and control.
[0198] The embodiments of the apparatus provided in this application can be used to execute the processing flow of the above method embodiments, and will not be repeated here. Please refer to the detailed description of the above method embodiments.
[0199] Figure 5 This is a schematic diagram of the physical structure of an electronic device provided in an embodiment of this application, as shown below. Figure 5 As shown, the electronic device may include a processor 301, a communications interface 302, a memory 303, and a communication bus 304, wherein the processor 301, the communications interface 302, and the memory 303 communicate with each other via the communication bus 304. The processor 301 may call logical instructions in the memory 303 to execute the methods described in any of the above embodiments.
[0200] Furthermore, the logical instructions in the aforementioned memory 303 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0201] This embodiment discloses a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by a computer, the computer can perform the methods provided in the above-described method embodiments.
[0202] This embodiment provides a computer-readable storage medium storing a computer program that causes the computer to perform the methods provided in the above-described method embodiments.
[0203] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0204] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0205] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0206] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.
[0207] In the description of this specification, the references to terms such as "an embodiment," "a specific embodiment," "some embodiments," "for example," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.
[0208] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. A method for optimizing parameters of a reduced-order model based on a self-evolving whale optimization algorithm with environmental feedback, characterized in that, include: S1. Map the parameter set of the reduced-order model to be optimized in the power system to the individual position vector in the whale optimization algorithm, and initialize the whale population within the feasible region of the parameters, wherein the parameter set includes key time constant, gain coefficient and damping ratio; S2. Repeat steps a to d until the preset iteration termination condition is met: a. Based on the current whale population, calculate a multidimensional environmental feedback index that includes population diversity, convergence speed, and search distribution indicators. b. Based on the multidimensional environmental feedback indicators, classify the current search state into exploratory state, development state, or equilibrium state; c. Based on the current search status type, execute the corresponding parameter update strategy to update the individual whale's position; d. During the iteration process, the search status is continuously monitored. When the search status meets the preset stagnation conditions, a self-evolution operation is performed. The self-evolution operation includes population recombination and adaptive adjustment of algorithm parameters. S3. When the iteration termination condition is met, output the position vector corresponding to the current global best individual as the optimized reduced-order model parameter.
2. The method according to claim 1, characterized in that, The population diversity index, convergence rate index, and search distribution index are calculated using the following formulas: in, For the diversity index of the t-th generation population, For population size, For the first The position vectors of individual whales The average position of the population; in, Let be the convergence rate index for generation t, where For the first Replace the optimal fitness value, For the first -1 generation optimal fitness value, It is a very small constant; in, Let t be the search distribution index for the t-th generation. This is the current globally optimal solution.
3. The method according to claim 2, characterized in that, The fitness value of each individual whale is calculated using the following fitness function: in, For the i-th individual whale fitness value; This refers to the simulation duration. This is the output response of the original power system model; The parameters at time t are The time-domain response of the time-reduced order model.
4. The method according to claim 3, characterized in that, The current search state is classified into exploratory, development, or equilibrium states based on the multidimensional environmental feedback indicators, including: like and The current search state is then classified as the exploratory state, where... The maximum threshold for population diversity, This is the minimum threshold for convergence speed; like and The current search state is then classified as the "development state". The minimum threshold for population diversity, The maximum threshold for convergence speed; If the current search state is neither in the exploratory state nor the development state, then the current search state is classified as the equilibrium state.
5. The method according to claim 4, characterized in that, The step of executing the corresponding parameter update strategy based on the current search state type to update the individual whale's position includes: If the current search state is exploratory, then an enhanced random search is used to update the individual whale's position: in, Let be the position vector of the (t+1)th generation whale individual. Let be the position vector of the t-th generation whale individual. To explore the strength coefficient, It is a random direction vector; If the current search state is open, a locally refined search based on singular perturbation theory is used to update the individual whale's position: in, Let be a standard normally distributed random perturbation vector. The adaptive weight matrix based on sensitivity is expressed as follows: in, This represents the normalized sensitivity of the j-th parameter. To prevent tiny positive numbers with a denominator of zero; The calculation formula is a difference approximation: If a parameter The large value indicates that the direction is extremely steep, requiring a reduction in the search step size. If the step size decreases, it indicates that the direction is flat, and the step size needs to be increased to accelerate convergence. If the current search state is in equilibrium, the standard WOA search strategy is used to update the individual whale positions: in, The distance between an individual and the optimal solution; Let this be the position of the individual whale in the t-th iteration; It is the constant that defines the shape of the logarithmic spiral; It is a random number between [-1, 1].
6. The method according to claim 5, characterized in that, Population recombination operations include: Retaining the current top E% of elite whale individuals, perform Cauchy mutation on the remaining F% of whale individuals using the following formula to obtain a new whale population: in, Let be the position vector of the (t+1)th generation whale individual. It is a standard Cauchy distribution random number generator.
7. The method according to claim 6, characterized in that, Perform adaptive adjustment of algorithm parameters, including: Adjust the WOA convergence factor according to the following formula. : in, This represents the current iteration number. The maximum number of iterations, It is a non-linear adjustment index.
8. The method according to claim 7, characterized in that, The iteration termination condition is as follows: in To improve convergence accuracy, This represents the maximum number of iterations.
9. The method according to claim 8, characterized in that, The method further includes: Based on the optimized reduced-order model parameters, a reduced-order model is established; The effectiveness and accuracy of the reduced-order model are verified by comparing the output response of the reduced-order model with that of the original power system model through multi-condition time-domain simulation.
10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 9.