Cross-regional delivery and consumption water scenery collaborative scheduling method, system and program product

Abstract

This invention belongs to the field of power system optimization scheduling and intelligent optimization algorithms, and relates to a method, system, and program product for cross-regional hydropower, wind power, and solar power coordinated scheduling based on a clustering-guided algorithm. The method includes: initializing the population for the clustering-guided optimization algorithm; performing cluster analysis on the current population and dividing it into sub-populations; implementing differentiated guided updates based on the quality of the sub-populations; performing boundary control on all individuals in the updated population; dynamic tournament selection based on ε-relaxation; time-driven elite pool maintenance and termination judgment; and constructing and solving the cross-regional hydropower, wind power, and solar power coordinated scheduling model. This invention addresses the problems of traditional intelligent optimization algorithms ignoring population spatial structure and low search efficiency due to uniform update strategies. It provides an optimization method that can implement differentiated search based on population quality differences, achieving efficient coordinated scheduling of hydropower, wind power, and photovoltaic power in the context of cross-regional power transmission and consumption, and improving the stability and reliability of system operation.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization scheduling and intelligent optimization algorithm application, and relates to a cross-regional water-wind-solar coordinated scheduling method, system and program product for cross-regional power transmission and consumption. More specifically, it relates to a cross-regional water-wind-solar coordinated scheduling method, system and program product based on clustering guided algorithm, which is applicable to the coordinated operation optimization problem of multi-energy complementary systems under complex constraints. Background Technology

[0002] With the rapid growth of new energy installed capacity, the coordinated operation of hydropower, wind power, and photovoltaic power generation in new power systems has become an important research direction. Hydropower has good regulation capabilities, while wind and photovoltaic power generation have the advantages of being clean and low-carbon. However, their output is significantly affected by meteorological conditions, exhibiting strong randomness and volatility. In the context of cross-regional power transmission, the parallel operation of multiple transmission channels and significant differences in receiving-end loads make the coordinated scheduling problem of hydropower, wind power, and photovoltaic power generation exhibit complex characteristics of multi-timescale, multi-constraint, and multi-objective coupling.

[0003] Existing methods for coordinated scheduling of water, wind, and solar power mainly rely on mathematical programming or traditional intelligent optimization algorithms for solving problems. However, mathematical programming methods often suffer from problems such as the curse of dimensionality and low solution efficiency when facing nonlinear, nonconvex, and large-scale discrete constraints. Traditional intelligent optimization algorithms usually assume that individuals within the population are homogeneous and adopt a uniform update strategy, making it difficult to characterize the spatial structure of the population during the search process. This can easily lead to problems such as over-concentration of search directions, premature convergence, or insufficient adaptability to complex constraints.

[0004] Especially in cross-regional power transmission and consumption scenarios, the scheduling model not only includes strong physical constraints such as reservoir water balance, water level changes, and power output ramp-up, but also needs to take into account the capacity limitations of transmission channels and the principle of prioritizing wind and solar power consumption, making the feasible solution space highly non-convex. Existing algorithms lack a mechanism to identify the population search structure and implement differentiated search strategies accordingly, making it difficult to achieve efficient and stable local development while ensuring global exploration capabilities.

[0005] Therefore, there is an urgent need to propose an optimization method that can combine the spatial structure characteristics of the population and is applicable to the coordinated scheduling problem of water, wind and solar power under complex constraints, so as to improve the scheduling efficiency and solution quality in the context of cross-regional transmission and consumption. Summary of the Invention

[0006] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a method, system, and program product for cross-regional water, wind, and solar power coordinated scheduling based on a clustering-guided algorithm. The purpose is to solve the technical problems of low search efficiency caused by traditional intelligent optimization algorithms ignoring population spatial structure and using a unified update strategy.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for coordinated scheduling of cross-regional water, wind, and solar power transmission and consumption based on a clustering-guided algorithm is provided, comprising:

[0008] Clustering guidance steps:

[0009] S1: Initialize the population for the clustering-guided optimization algorithm; use the outflow from the reservoir of the cascade hydropower stations and the power generation ratio on the left bank of the hydropower stations in the cross-regional water-wind-solar coordinated scheduling system as the population individuals, and set the population size, maximum number of function evaluations, and elite pool size; within the upper and lower bounds of the decision variables, initialize the population individuals in a uniform random manner; evaluate the fitness of the initialized population, obtain the current global best individual, and add it to the elite pool;

[0010] S2: Using the current population in the elite pool as the parent population, perform cluster analysis on the parent population in the current iteration and divide it into sub-populations; in each generation of evolution, perform cluster analysis on the current population to characterize the distribution structure of the population in the decision space; divide the population into a preset number of sub-clusters; calculate the average fitness value of each sub-cluster, rank each sub-cluster according to the quality of the average fitness value, and divide them into high-quality clusters, medium-quality clusters, and low-quality clusters in sequence;

[0011] S3: For the high-quality clusters, medium-quality clusters, and low-quality clusters obtained in S2, different search strategies are used to guide individual differentiated updates;

[0012] S4: Apply a boundary control strategy combining reflection and truncation to all individuals in the population after differential guidance update to obtain individuals within the feasible domain or its neighborhood, which form the offspring population;

[0013] S5: Select new feasible solutions using a dynamic tournament based on ε-relaxation; merge the parent population with the offspring population obtained through differentiated guided updates to form a candidate population; adopt a dynamic tournament selection mechanism to adaptively adjust the tournament size according to the algorithm's evolution stage; adopt an ε-relaxation constraint handling mechanism to allow infeasible solutions to participate in the competition in the early stages of the algorithm, and gradually tighten the constraint tolerance as the iteration progresses, eventually obtaining new feasible solutions;

[0014] S6: Time-driven elite pool maintenance and termination judgment; set up an elite pool to store historical high-quality solutions, and introduce an elite pool update mechanism based on time decay score; when a new feasible solution is better than the historical high-quality solution currently stored in the elite pool in terms of score or fitness, update the elite pool; when the preset maximum number of function evaluations is reached or the convergence criterion is met, terminate the algorithm iteration.

[0015] Model building steps:

[0016] S7: Construct a cross-regional hydropower, wind power and solar power coordinated dispatch model; within a given dispatch cycle, construct a coordinated dispatch model including hydropower, wind power and photovoltaic power generation, with the stability of the remaining load of the receiving end power grid as the optimization objective, and under the principle of prioritizing wind and solar power consumption, use the regulation capacity of hydropower to smooth the remaining load;

[0017] Solution steps: The cross-regional water, wind and solar coordinated scheduling model described in S7 is solved using the methods in steps S1-S6.

[0018] Further, S1 includes:

[0019] S11: At the beginning of the evolutionary phase, the population is uniformly and randomly initialized within a given boundary; for each individual in the population... The initialization rules are as follows:

[0020] ,

[0021] In the formula, individual This refers to the outflow from the reservoir of a cascade hydropower station and the ratio of power generation on the left bank of the hydropower station in a cross-regional water-wind-solar coordinated dispatch system for power transmission and consumption. Represents an individual The d dimension, N The total number of individuals. D The total number of dimensions. , ; and These represent the decision variables at the th... d Upper and lower bounds of a dimension; A uniformly random number on [0, 1];

[0022] S12: The fitness evaluation is to calculate the target that needs to be optimized for cross-regional water, wind and solar coordinated scheduling. For the minimization problem, the individual with the smallest objective function is the global optimal individual.

[0023] Further, S2 includes:

[0024] S21: In each generation of evolution, the current population Perform clustering; the number of clusters is set to... k This divides the population into k Non-overlapping subclusters:

[0025] ,

[0026] in, Indicates the original population P The division k Non-overlapping subclusters;

[0027] S22: Calculate the average objective function value for each cluster:

[0028] ,

[0029] in, This represents the average objective function value. Indicates the first c Subclusters, Subclusters C c The objective function values ​​of each individual entity. x ∈ C 1 C 2 C 3;

[0030] For minimization optimization problems, according to Sort the subclusters from smallest to largest to obtain three types of subgroups: high-quality clusters. medium cluster and inferior clusters .

[0031] Further, S3 includes:

[0032] Introducing a uniform time perturbation factor into the search strategy , , U () indicates a uniform distribution;

[0033] ,

[0034] In the formula, The amplitude of the disturbance; FE With max FE These represent the current number of evaluations and the maximum number of evaluations, respectively; time disturbance factor. It is uniformly invoked during population renewal;

[0035] For individuals belonging to the superior cluster Two development strategies were constructed and randomly selected:

[0036] (a) Multi-source guided search

[0037] This strategy simultaneously incorporates globally optimal individuals, cluster structure centers, and cross-generational accumulated elite knowledge, and considers time perturbation factors. Multiple candidate search directions are generated under the adjustment, and then a comprehensive update is performed;

[0038] (b) Simplex Local Search

[0039] The simplex method includes four aspects: reflection, expansion, compression, and regression; the steps are as follows:

[0040] Step 1: perturbation solution The initial point is randomly generated in the search space. D 10 different vertices together constitute D A simplex with +1 vertex For disturbance factor;

[0041] Step 2: Calculate the fitness value of each point F (·) Sort them according to their advantages and disadvantages, and determine the optimal point. X l , worst X h and second difference X s At the same time, calculate the remaining values ​​except for the worst point. D The centroid of each vertex ;

[0042] Step 3: Reflection operation; calculate the reflection point. X r If fitness Then proceed to Step 4; if fitness If yes, proceed to Step 5; otherwise, let... Proceed to Step 7;

[0043] Step 4: Expanding operation; Calculate the expansion point X e If fitness ,make Otherwise Jump to Step 7;

[0044] Step 5: Compression operation; for fitness Then, before starting the compression operation, set... Regarding fitness Then calculate the compression point. X c If fitness ,make If yes, proceed to Step 7; otherwise, proceed to Step 6.

[0045] Step 6: Rollback operation; if the compression operation is ineffective, keep the optimal position unchanged, calculate the rollback point for the remaining points, and jump to Step 7;

[0046] Step 7: If the preset stopping condition is met, i.e., the value is less than the preset tolerance. Then stop the iteration process; otherwise, go to Step 2.

[0047] ,

[0048] ,

[0049] in, This indicates an updated individual obtained through multi-source guidance. For the updated individual ;

[0050] For individuals belonging to the intermediate cluster A balanced update operator is constructed with the cluster center as the anchor point and elite information as the offset reference, and its form is as follows:

[0051] ,

[0052] In the formula, For random perturbation quantities, ; It serves as the cluster center for medium-sized clusters; The historical best individual randomly sampled from the elite pool;

[0053] For individuals belonging to inferior clusters Two exploration strategies were constructed and randomly selected:

[0054] (i) The elite jump individual update formula combined with Lévy flight is:

[0055] ,

[0056] In the formula, For random perturbation quantities, ; It serves as the cluster center for inferior clusters; B Let Lévy be the step size vector;

[0057] (ii) Double random jump

[0058] ,

[0059] In the formula, For random perturbation vectors, ; These are two different individuals randomly selected from the population.

[0060] Further, S4 includes:

[0061] For all updated descendant individuals, if they exceed the upper and lower boundaries, they are handled according to the following formula:

[0062] ,

[0063] In the formula, Indicates the individual after the update The d dimension.

[0064] Further, S5 includes:

[0065] Tournament size K Defined as a linear function that changes with iteration:

[0066] ,

[0067] In the formula, the scale of the tournament K This indicates the number of individuals selected from the population each time using the tournament selection method; , These represent the maximum and minimum number of individuals that can be retrieved, respectively.

[0068] In each update, the parent and offspring populations are merged to form a population of size 2. N Candidate populations were selected and screened through a tournament. N The winning individuals constitute the next generation;

[0069] The ε-relaxation constraint handling mechanism refers to setting a threshold ε that decreases as the number of algorithm iterations increases, following the principles below:

[0070] ① When the constraints of two solutions are violated to a certain degree If the values ​​are equal to or both are less than the threshold ε, then the individual fitness level is considered. Compare;

[0071] ② Otherwise, based on the degree of constraint violation Comparison, Smaller individual solutions are better.

[0072] Further, S6 includes:

[0073] Time decay score The calculation formula is as follows:

[0074] ,

[0075] In the formula, For the first i The target value for an elite individual; For the first i The number of FE function evaluations when an elite individual is added to the elite pool. ρ These are empirical parameters;

[0076] The method for maintaining the elite pool is as follows: if the elite pool is not yet full, the current new global optimal feasible solution is added to the elite pool; otherwise, for the minimization problem, if the elite individual with the highest score in the elite pool is added to the new global optimal feasible solution... Beyond, that is If so, the elite individual is replaced.

[0077] Furthermore, in S7:

[0078] The cross-regional water, wind and solar power coordinated scheduling model includes an objective function and constraints.

[0079] The objective function is the mean square error of the average residual load of the receiving-end power grid. F The smallest is represented as:

[0080] ,

[0081] ,

[0082] In the formula, T For the total scheduling period, S The number of power transmission channels for the complementary system. s =1~ S ; , and They represent power transmission channels. s During the period t The corresponding remaining load of the receiving-end power grid, the load of the receiving-end power grid, and the transmission power; For power transmission channels s The corresponding average remaining load of the receiving-end power grid;

[0083] The constraints include at least one of the following: water balance constraints, water level constraints, water level fluctuation constraints, reservoir characteristic constraints, outflow constraints, head calculation formula, hydropower output constraints, dispatch boundary constraints, channel capacity constraints, complementary system operation mode constraints, hydropower station left and right bank output constraints, and hydropower output ramping constraints.

[0084] According to another aspect of the present invention, a computer system is provided, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the cross-regional water, wind and solar coordinated scheduling method based on clustering guidance algorithm as described in any of the preceding claims.

[0085] According to another aspect of the present invention, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the cross-regional water, wind and solar coordinated scheduling method based on a clustering-guided algorithm as described in any of the preceding claims.

[0086] In summary, the technical solutions conceived in this invention, compared with the prior art, can achieve the following beneficial effects:

[0087] 1. This invention introduces a clustering analysis mechanism to explicitly characterize the spatial structure features of the population during the search process, realizing a differentiated search strategy based on quality differences. This avoids the efficiency bottleneck caused by the uniform update strategy of traditional algorithms, enabling efficient coordinated scheduling of hydropower, wind power, and photovoltaic power in the context of cross-regional transmission and consumption, and improving the stability and reliability of system operation.

[0088] 2. This invention combines multi-source guidance information with time perturbation factors to maintain necessary global exploration capabilities while ensuring local search accuracy, effectively reducing the risk of getting trapped in local optima.

[0089] 3. The method described in this invention has good adaptability to complex physical and operational constraints and can stably solve the water-wind-solar coordinated scheduling problem under the background of cross-regional power transmission and consumption.

[0090] 4. The algorithm of this invention has a clear structure and well-defined parameter meanings, and has good versatility and scalability. It can be extended to various optimization scheduling scenarios of multi-energy complementary systems. Attached Figure Description

[0091] Picture 1 This is a flowchart illustrating a preferred embodiment of the present invention. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0093] like Picture 1As shown, the cross-regional water, wind, and solar power coordinated scheduling method of the present invention mainly includes: first, parameter initialization settings, then population initialization and population fitness evaluation, adding the globally optimal individual obtained from the population fitness evaluation to the elite pool; then, in each generation of evolution, K-means++ clustering analysis is performed to obtain high-quality clusters, medium-quality clusters, and low-quality clusters; a time perturbation factor is introduced, and for high-quality clusters, multi-source guided search and simplex method search are performed; for medium-quality clusters, a balance update operator is constructed; for low-quality clusters, elite jumps combined with Lévy flight and double random jumps are performed; thus forming an updated offspring population, then a boundary control strategy combining reflection and truncation is executed, and then the parent population and offspring population are merged to form a candidate population; the candidate population is subjected to dynamic tournament selection based on ε-relaxation to obtain the population fitness evaluation, and at the same time, an elite pool update mechanism based on time decay scoring is used to update the elite pool by taking the globally optimal individual; finally, it is determined whether the termination condition is met, if so, the final population is output, otherwise, the population K-means++ clustering analysis is returned.

[0094] More specifically, this invention provides a cross-regional coordinated scheduling method for water, wind, and solar power transmission and consumption based on a cluster-guided optimization (CGO) algorithm, comprising the following steps:

[0095] S1: Initialize the population for the clustering-guided optimization algorithm. Set the population size, maximum number of function evaluations, and elite pool size. Initialize the population individuals using a uniform random method within the upper and lower bounds of the decision variables. Evaluate the fitness of the initialized population, obtain the current globally optimal individual, and add it to the elite pool.

[0096] S2: Using the current population in the elite pool as the parent population, perform cluster analysis on the parent population in the current iteration and divide it into subpopulations. During each generation of evolution, use K-means++ cluster analysis on the current population to characterize its distribution structure in the decision space. Divide the population into a predetermined number of subclusters; calculate the average fitness value of each subcluster; rank the subclusters according to their fitness level, and classify them into high-quality clusters, medium-quality clusters, and low-quality clusters.

[0097] S3: Implement differentiated guided updates based on subpopulation quality. Different search strategies are used for differentiated guided updates of individuals for subpopulations of different quality levels (high-quality clusters, medium-quality clusters, and low-quality clusters).

[0098] S4: Apply a boundary control strategy combining reflection and truncation to all individuals in the differentiated population to ensure that individuals are always within the feasible domain or its neighborhood, thus obtaining the offspring population.

[0099] S5: Dynamic tournament selection based on ε-relaxation to choose new feasible solutions. The parent population is merged with the offspring population obtained through differentiated guided updates to form a candidate population. A dynamic tournament selection mechanism is employed, adaptively adjusting the tournament size according to the algorithm's evolutionary stage. An ε-relaxation constraint handling mechanism is used, allowing a certain degree of infeasible solutions to participate in the competition in the early stages of the algorithm. As iterations progress, the constraint tolerance is gradually tightened, thereby maintaining population diversity while ensuring feasibility, ultimately yielding new feasible solutions.

[0100] S6: Time-Driven Elite Pool Maintenance and Termination Judgment. An elite pool is set up to store historical high-quality solutions, and an elite pool update mechanism based on "time decay scoring" is introduced to dynamically measure the effectiveness of solutions in the elite pool. When a new feasible solution outperforms the currently stored historical high-quality solutions in the elite pool in terms of score or fitness, the elite pool is updated. The algorithm iteration terminates when the preset maximum number of function evaluations is reached or the convergence criterion is met.

[0101] S7: Construct a cross-regional hydropower, wind power, and solar power coordinated dispatch model. Within a given dispatch period, construct a coordinated dispatch model that includes hydropower, wind power, and solar power generation. With the stability of the remaining load of the receiving-end power grid as the optimization objective, and under the principle of prioritizing the consumption of wind and solar power, utilize the regulation capacity of hydropower to smooth the remaining load.

[0102] S8: Construct a solution to the cross-regional water, wind and solar coordinated scheduling model described in S6 using the clustering-guided algorithm.

[0103] Furthermore, S1 includes:

[0104] S11: At the beginning of the evolutionary phase, CGO performs a uniform random initialization of the population within a given boundary. For each individual in the population... , With dimension The initialization rules are as follows:

[0105] (1),

[0106] In the formula, individual This refers to the outflow from the reservoir of a cascade hydropower station and the ratio of power generation on the left bank of the hydropower station in a cross-regional water-wind-solar coordinated dispatch system for power transmission and consumption. Represents an individual The d dimension, N The total number of individuals. D This represents the total number of dimensions; and These represent the decision variables at the th... d The upper and lower limits of a dimension. It is a uniform random number on [0, 1].

[0107] S12: The fitness evaluation is the objective function calculation, specifically the objective that needs to be optimized for cross-regional water, wind and solar power coordinated scheduling. For a minimization problem, the individual with the smallest objective function is the globally optimal individual.

[0108] Furthermore, S2 includes:

[0109] S21: In each generation of evolution, the K-means++ method is used to analyze the current population. Perform clustering. The number of clusters is set to... k= 3. This divides the population into three non-overlapping subclusters:

[0110] (2),

[0111] in, Indicates the original population P The division k A number of non-overlapping sub-clusters, preferably, in this embodiment k =3.

[0112] S22: To measure the overall quality of each sub-cluster, the average objective function value of each cluster is further calculated:

[0113] (3),

[0114] in, This represents the average objective function value. Indicates the first c Subclusters, Subclusters C c The objective function values ​​of each individual entity. x ∈C1, C2, C3.

[0115] For minimization optimization problems, according to The subclusters are sorted from smallest to largest and then divided into three subgroups: high-quality clusters. The region with the smallest average target value represents a high-potential area, with the highest probability of containing the global optimum, and requires careful development; the medium-sized cluster... Clusters in the transition region, representing individuals with intermediate levels of the objective function, require appropriate guidance; low-quality clusters... The average target value is the largest, and it needs to be explored in depth.

[0116] Furthermore, S3 includes:

[0117] S31: In order to achieve adaptive adjustment of search step size and search intensity at different stages, CGO introduces a uniform time perturbation factor into the search strategy. . It is a scalar parameter. , U () indicates a uniform distribution.

[0118] (4),

[0119] In the formula, The amplitude of the disturbance; FE With max FE These represent the current number of evaluations and the maximum number of evaluations for the algorithm, respectively. Time perturbation factor. It will be uniformly invoked during the population update process, which coordinates the search intensity of different subpopulations globally, making the overall search transformation process of the algorithm smoother and more consistent.

[0120] S32: For individuals belonging to the superior cluster Two development strategies were constructed and randomly selected:

[0121] (a) Multi-source guided search

[0122] This strategy simultaneously introduces guiding reference points from different levels (i.e., globally optimal individuals, cluster structure centers, and cross-generational accumulated elite knowledge), and incorporates time perturbation factors. Multiple candidate search directions are generated under adjustment, and then they are comprehensively updated:

[0123] (5),

[0124] (6),

[0125] (7),

[0126] (8),

[0127] In the formula, ~ This indicates an updated individual obtained through multi-source guidance. For the updated individual ; This is the globally optimal feasible solution; The historical best individual randomly sampled from the elite pool; It serves as the cluster center for high-quality clusters; For random perturbation quantities, .

[0128] (b) Simplex Local Search

[0129] The simplex method focuses on four key aspects: reflection, expansion, compression, and regression. The main steps are as follows:

[0130] Step 1: Define the calculation parameters, including the reflection coefficient. Coefficient of expansion Shrinkage coefficient Shrinkage coefficient and preset tolerance .by perturbation solution The initial point is randomly generated in the search space. D 10 different vertices together constitute D A simplex with +1 vertices.

[0131] Step 2: Calculate the fitness value of each point F (·) Sort them according to their advantages and disadvantages, and determine the optimal point. X l , worst X h and second difference X s At the same time, calculate the remaining values ​​except for the worst point. D The centroid of each vertex :

[0132] (9).

[0133] Step 3: Reflection operation. Calculate the reflection point. X r If fitness Then proceed to Step 4; if fitness If yes, proceed to Step 5; otherwise, let... Proceed to Step 7:

[0134] (10).

[0135] Step 4: Expanding operation. Calculate the expansion point. X e If fitness ,make Otherwise Proceed to Step 7:

[0136] (11).

[0137] Step 5: Compression operation. (Regarding fitness...) Then, before starting the compression operation, set... Regarding fitness Then calculate the compression point. X c If fitness ,make If yes, proceed to Step 7; otherwise, proceed to Step 6.

[0138] (12).

[0139] Step 6: Rollback Operation. If the compression operation is ineffective, keep the optimal position unchanged, calculate the rollback points for the remaining points, and proceed to Step 7:

[0140] (13).

[0141] Step 7: If the stopping condition is met, stop the iteration process; otherwise, go to Step 2.

[0142] (14),

[0143] (15).

[0144] S33: For individuals belonging to the intermediate cluster A balanced update operator is constructed, which uses the cluster center as the anchor point and elite information as the offset reference. Its form is as follows:

[0145] (16),

[0146] In the formula, For random perturbation quantities, ; It serves as the cluster center for medium-sized clusters.

[0147] S34: For individuals belonging to inferior clusters Two exploration strategies were constructed and randomly selected:

[0148] (i) Elite jumps combined with Lévy flight

[0149] Lévy step size vector The update format is as follows:

[0150] (17),

[0151] (18),

[0152] in, This represents the gamma function, a parameter that is dynamically adjusted during Lévy flight. This value allows the step size distribution to adapt to different optimization stages, thus achieving a more reasonable balance between exploration and development.

[0153] (19),

[0154] Where FE and max FE These represent the current number of evaluations and the maximum number of evaluations for the algorithm, respectively.

[0155] The elite jump individual update formula combined with Lévy flight is as follows:

[0156] (20),

[0157] In the formula, For random perturbation quantities, ; It serves as the cluster center for inferior clusters; u and v These are two normally distributed variables with standard deviations of . and .

[0158] (ii) Double random jump

[0159] To further enhance the ability to explore the search space across domains, CGO proposes a globally aggressive "double random jump" strategy in inferior clusters to construct high-amplitude nonlocal perturbations and achieve proactive escape from the current region.

[0160] (twenty one),

[0161] In the formula, For random perturbation vectors, ; These are two different individuals randomly selected from the population.

[0162] Furthermore, S4 includes:

[0163] S41: The boundary control strategy combining reflection and truncation, for all updated descendant individuals, if they exceed the upper and lower boundaries, shall be processed according to the following formula:

[0164] (twenty two),

[0165] In the formula, Indicates the individual after the update The d dimension.

[0166] Furthermore, S5 includes:

[0167] S51: The tournament selection described is a commonly used individual selection mechanism in evolutionary algorithms. Its basic idea is to randomly select a number of individuals from the population to form a "small-scale tournament," and select the best performers from this tournament to advance to the next generation, thereby preserving and propagating high-quality solutions. Tournament size K This directly determines the strength of the selection pressure. To enable the selection pressure to adaptively adjust with the evolutionary stage, the CGO algorithm scales the tournament...K Defined as a linear function that changes with iteration:

[0168] (twenty three),

[0169] In the formula, K The number of individuals to be removed from the population each time for selecting a tournament method; , These represent the maximum and minimum number of individuals that can be retrieved, respectively. This study uses... , .

[0170] In each update, CGO merges the parent and child generations to form a size of 2. N Candidate populations were selected and screened through a tournament. N The winning individuals constitute the next generation. Introducing dynamic tournament scale. K Later, the algorithm used a smaller [size] in the early stages. K To maintain diversity, and gradually increase it in the later stages. K This strengthens the selection pressure, thereby enabling a natural transition from extensive exploration to rapid convergence.

[0171] S52: The ε-Constraint Method (EC) is a strategy that allows the algorithm to maintain diversity in the early stages, permitting a certain degree of competition from infeasible solutions, while gradually strengthening the preference for feasible solutions in the later stages. Its core idea is:

[0172] By setting a threshold ε, the algorithm relaxes the constraint tolerance in the early stages and gradually tightens it in the later stages. The threshold ε decreases as the number of algorithm iterations increases. Dynamic tournament selection based on ε-relaxation should follow these principles: ① When the degree of constraint violation between two solutions... If the values ​​are equal to or both are less than the threshold ε, then the individual fitness level is considered. ① Compare; ② Otherwise, base decisions on the degree of constraint violation. Comparison, Smaller individual solutions are better. For minimization problems, in EC, an individual solution is better when any of the following conditions are met. Superior to individuals :

[0173] (twenty four),

[0174] In the formula, , Representing individual x i and x j The objective function value.

[0175] The process by which the threshold ε decreases with the number of iterations in the EC strategy is as follows:

[0176] (25),

[0177] (26),

[0178] In the formula, The degree of initial constraint violation; Individuals in the initial population The degree of violation of the constraints.

[0179] Furthermore, S6 includes:

[0180] S61: The elite pool update mechanism based on "time decay score" has a time decay score. The calculation formula is as follows:

[0181] (27),

[0182] In the formula, For the first i The target value for an elite individual; The number of FE function evaluations when this individual is added to the elite pool. ρ This is an empirical parameter, preferably 0.3.

[0183] S62: Elite pool maintenance: If the elite pool is not yet full, the current globally optimal individual is added to it; otherwise, for the minimization problem, if the elite individual with the highest score is added to the new globally optimal feasible solution... Beyond, that is If so, the elite individual is replaced.

[0184] Furthermore, S7 includes:

[0185] S71: The cross-regional water, wind and solar power coordinated scheduling model includes its objective function and constraints.

[0186] S72: The objective function of the model described in S71 is to minimize the mean square error of the average residual load of the receiving-end power grid, which can be expressed as:

[0187] (28),

[0188] (29),

[0189] In the formula, F The objective function is the mean square error of the average residual load of the receiving-end power grid. T For the total scheduling period, S The number of power transmission channels for the complementary system. s =1~ S ; , and They represent power transmission channels. s During the period t The corresponding remaining load of the receiving-end power grid, the load of the receiving-end power grid, and the transmission power; For power transmission channels s The corresponding average remaining load of the receiving-end power grid.

[0190] S73: The model constraints described in S71 include:

[0191] (1) Water balance constraint

[0192] (30),

[0193] (31),

[0194] In the formula, and Hydropower stations m During the period t The initial and final storage capacities; For hydroelectric power station m During the period t Inbound traffic, This is water coming from the interval; , and Hydropower stations m During the period t The outflow from the reservoir, the power generation flow, and the power generation wastewater flow.

[0195] (2) Water level constraints

[0196] (32),

[0197] In the formula, , and Hydropower stations m During the period t The water level in front of the dam and its upper and lower limits.

[0198] (3) Water level fluctuation constraints

[0199] (33),

[0200] In the formula, and Hydropower stations m During the period t The upper and lower limits of water level fluctuations For hydroelectric power station m During the period t+1 water level in front of the dam.

[0201] (4) Reservoir characteristic constraints

[0202] (34),

[0203] (35),

[0204] In the formula, For hydroelectric power station m During the period t The tailwater level; , Indicates hydroelectric power station m Water level-reservoir capacity relationship, Indicates hydroelectric power station m The relationship between the discharge flow rate and the tailwater level.

[0205] (5) Outbound flow constraints

[0206] (36),

[0207] In the formula, and Hydropower stations m During the period t The upper and lower limits of the outbound flow rate.

[0208] (6) Head Calculation Formula

[0209] (37),

[0210] In the formula, This represents the head of the hydropower station m during time period t.

[0211] (7) Hydropower output constraints

[0212] (38),

[0213] In the formula, Indicates hydroelectric power station m At the water head Maximum expected output at that time; For the corresponding minimum output constraint, Indicates hydroelectric power station m At the water head The effort put in at that time.

[0214] (8) Scheduling boundary constraints

[0215] (39),

[0216] In the formula, and These are the water levels at the beginning and end of the time period, respectively. and These are the designated hydroelectric power stations. m The initial and final water levels during the scheduling period.

[0217] (9) Channel capacity constraints

[0218] (40),

[0219] In the formula, and These represent the maximum and minimum transmission power of the power transmission channel, respectively.

[0220] (10) Constraints on the operation mode of complementary systems

[0221] (41),

[0222] In the formula, For power transmission channels s During the period t The load that hydropower needs to bear; and Wind power and solar power, respectively, during the time period t Send into the power transmission channel s of effort.

[0223] (11) Output constraints on the left and right banks of the hydropower station

[0224] (42),

[0225] In the formula, and Hydropower stations m During the period t The power output from the left and right banks. (If the hydroelectric power station...) m Left bank via power transmission channel s If power is supplied to the receiving end of the power grid, then If the hydroelectric power station m Right bank via power transmission channel s If power is supplied to the receiving end of the power grid, then .

[0226] (12) Hydropower output ramping constraints

[0227] (43),

[0228] In the formula, and Hydropower stations m During the period t The output is limited when climbing uphill and downhill. Indicates hydroelectric power stationm The output during time period t-1.

[0229] Furthermore, S8 includes:

[0230] S81: For the cross-regional hydropower-wind-solar coordinated scheduling model for power transmission and consumption described in S7, the outflow from the hydropower station and the power generation ratio on the left bank of the hydropower station are used as population decision variables for encoding. An individual... This refers to the combination of the outflow from the reservoir of each hydropower station at each time period and the proportion of power generation on the left bank:

[0231] (44),

[0232] In the formula, For hydroelectric power station During the period t Outbound flow For hydroelectric power station During the period t The proportion of electricity generated on the left bank; M represents the number of hydropower stations. The number of hydroelectric power stations that transmit power separately on the left and right banks needs to be considered.

[0233] S82: The clustering-guided algorithm is used to solve the cross-regional water, wind and solar coordinated scheduling model described in S7, that is, S1-S6 are executed with the decision variables described in S71.

[0234] Taking a clean energy demonstration base as the research object, this study involves the cascade hydropower stations at the base and the supporting wind and photovoltaic power stations in the surrounding area, as well as the power grids corresponding to each hydropower station. This embodiment selects February 5, 2023 as a typical day for cross-regional power transmission and consumption hydropower-wind-solar coordinated scheduling calculations. During implementation, the superiority of the clustering-guided algorithm described in this invention is evaluated using objective function statistical indicators (optimal value, average value, and standard deviation), population feasibility indicators (the proportion of feasible solutions for individuals within the population), and residual load indicators (standard deviation, peak-valley difference, and load factor) under the average state of each power transmission channel.

[0235] This embodiment selects several popular evolutionary algorithms for comparison, including Arithmetic Optimization Algorithm (AOA), Chimpanzee Optimization Algorithm (CHOA), Differential Evolutionary Algorithm (DE), Harris Eagle Optimization Algorithm (HHO), Particle Swarm Optimization Algorithm (PSO), Sine and Cosine Algorithm (SCA), and Whale Optimization Algorithm (WOA).

[0236]

[0237]

[0238] Tables 1 and 2 respectively present the solution results of the proposed method and seven comparative algorithms for solving the cross-regional water-wind-solar coordinated dispatch model for power transmission and consumption. Table 1 compares the statistical results of the objective function after 10 independent runs of each algorithm; Table 2 compares the remaining load evaluation results of the optimal solution in 10 independent runs of each algorithm under the average state of each receiving-end power grid. The optimal results in the tables are highlighted in bold.

[0239] First, based on the statistical indicators of the objective function shown in Table 1, the method of this invention outperforms or significantly outperforms the other comparative algorithms in all three indicators: optimal value, average value, and standard deviation. Specifically, the method of this invention obtains the lowest optimal value of the objective function, and its average value is significantly lower than that of the comparative algorithms, indicating that it can stably search for a better scheduling scheme in multiple independent runs. Simultaneously, the standard deviation of the method of this invention is among the lowest of all algorithms, indicating that its search process has less fluctuation and stronger solution stability. Furthermore, the proportion of feasible solutions within the population for the method of this invention reaches 100%, significantly higher than some of the comparative algorithms, demonstrating its stronger ability to handle complex constraints.

[0240] Secondly, judging from the remaining load index results of each transmission channel under average conditions shown in Table 2, the method of the present invention achieved the best performance in key indicators such as remaining load standard deviation, peak-valley difference, and load factor. In particular, the method of the present invention is significantly lower than most comparative algorithms in terms of remaining load standard deviation and peak-valley difference, indicating that it can effectively utilize the hydropower regulation capacity to smooth out wind and solar power fluctuations, thereby reducing the operational fluctuation amplitude of cross-regional transmission channels and improving the stability of the receiving-end power grid.

[0241] The results from Tables 1 and 2 show that by introducing clustering guidance and differentiated search mechanisms, this invention enhances local development efficiency while ensuring global exploration capabilities. This not only improves the solution quality and stability of the scheduling model, but also significantly improves the coordinated operation of water, wind and solar power in cross-regional power transmission and consumption scenarios, fully verifying the effectiveness and superiority of the method in complex multi-energy complementary scheduling problems.

[0242] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for coordinated scheduling of cross-regional water, wind, and solar power transmission and consumption based on a clustering-guided algorithm, characterized in that, include: Clustering guidance steps: S1: Initialize the population for the clustering-guided optimization algorithm; use the outflow of the cascade hydropower stations and the power generation ratio on the left bank of the hydropower stations in the cross-regional water-wind-solar coordinated scheduling system as the population individuals, and set the population size, maximum number of function evaluations, and elite pool size; Within the upper and lower bounds of the decision variables, the population individuals are initialized using a uniform random method; the fitness of the initialized population is evaluated, the current global best individual is obtained, and added to the elite pool; S2: Using the current population in the elite pool as the parent population, perform cluster analysis on the parent population in the current iteration and divide it into sub-populations; in each generation of evolution, perform cluster analysis on the current population to characterize the distribution structure of the population in the decision space; divide the population into a preset number of sub-clusters; calculate the average fitness value of each sub-cluster, rank each sub-cluster according to the quality of the average fitness value, and divide them into high-quality clusters, medium-quality clusters, and low-quality clusters in sequence; S3: For the high-quality clusters, medium-quality clusters, and low-quality clusters obtained in S2, different search strategies are used to guide individual differentiated updates; S4: Apply a boundary control strategy combining reflection and truncation to all individuals in the population after differential guidance update to obtain individuals within the feasible domain or its neighborhood, which form the offspring population; S5: Select new feasible solutions using a dynamic tournament based on ε-relaxation; merge the parent population with the offspring population obtained through differentiated guided updates to form a candidate population; adopt a dynamic tournament selection mechanism to adaptively adjust the tournament size according to the algorithm's evolution stage; adopt an ε-relaxation constraint handling mechanism to allow infeasible solutions to participate in the competition in the early stages of the algorithm, and gradually tighten the constraint tolerance as the iteration progresses, eventually obtaining new feasible solutions; S6: Time-driven elite pool maintenance and termination judgment; set up an elite pool to store historical high-quality solutions, and introduce an elite pool update mechanism based on time decay score; when a new feasible solution is better than the historical high-quality solution currently stored in the elite pool in terms of score or fitness, update the elite pool; when the preset maximum number of function evaluations is reached or the convergence criterion is met, terminate the algorithm iteration. Model building steps: S7: Construct a cross-regional hydropower, wind power and solar power coordinated dispatch model; within a given dispatch cycle, construct a coordinated dispatch model including hydropower, wind power and photovoltaic power generation, with the stability of the remaining load of the receiving end power grid as the optimization objective, and under the principle of prioritizing wind and solar power consumption, use the regulation capacity of hydropower to smooth the remaining load; Solution steps: The cross-regional water, wind and solar coordinated scheduling model described in S7 is solved using the methods in steps S1-S6.

2. The method for cross-regional water, wind, and solar coordinated scheduling based on clustering guidance algorithm according to claim 1, characterized in that, S1 includes: S11: At the beginning of the evolutionary phase, the population is uniformly and randomly initialized within a given boundary; for each individual in the population... The initialization rules are as follows: In the formula, individual This refers to the outflow from the reservoir of a cascade hydropower station and the ratio of power generation on the left bank of the hydropower station in a cross-regional water-wind-solar coordinated dispatch system for power transmission and consumption. Represents an individual The d dimension, N The total number of individuals. D The total number of dimensions. , ; and These represent the decision variables at the th... d Upper and lower bounds of a dimension; A uniformly random number on [0, 1]; S12: The fitness evaluation is to calculate the target that needs to be optimized for cross-regional water, wind and solar coordinated scheduling. For the minimization problem, the individual with the smallest objective function is the global optimal individual.

3. The method for cross-regional water, wind, and solar coordinated scheduling based on clustering guidance algorithm according to claim 2, characterized in that, S2 includes: S21: In each generation of evolution, the current population Perform clustering; the number of clusters is set to... k This divides the population into k Non-overlapping subclusters: in, Indicates the original population P The division k Non-overlapping subclusters; S22: Calculate the average objective function value for each cluster: in, This represents the average objective function value. Indicates the first c Subclusters, Subclusters C c The objective function values ​​of each individual entity. x ∈ C 1, C 2,……, C k ; For minimization optimization problems, according to Sort the subclusters from smallest to largest to obtain three types of subgroups: high-quality clusters. medium cluster and inferior clusters .

4. The method for cross-regional water, wind, and solar coordinated scheduling based on clustering guidance algorithm according to claim 3, characterized in that, S3 includes: Introducing a uniform time perturbation factor into the search strategy , , U () indicates a uniform distribution; In the formula, The amplitude of the disturbance; FE With max FE These represent the current number of evaluations and the maximum number of evaluations, respectively; time disturbance factor. It is uniformly invoked during population renewal; For individuals belonging to the superior cluster Two development strategies were constructed and randomly selected: (a) Multi-source guided search This strategy simultaneously incorporates globally optimal individuals, cluster structure centers, and cross-generational accumulated elite knowledge, and considers time perturbation factors. Multiple candidate search directions are generated under the adjustment, and then a comprehensive update is performed; (b) Simplex Local Search The simplex method includes four aspects: reflection, expansion, compression, and regression; the steps are as follows: Step 1: perturbation solution The initial point is randomly generated in the search space. D A number of different vertices, together forming D A simplex with +1 vertex For disturbance factor; Step 2: Calculate the fitness value of each point F (·) Sort them according to their advantages and disadvantages, and determine the optimal point. X l , worst X h and second difference X s At the same time, calculate the remaining values ​​except for the worst point. D The centroid of each vertex ; Step 3: Reflection operation; calculate the reflection point. X r If fitness Then proceed to Step 4; if fitness If yes, proceed to Step 5; otherwise, let... Proceed to Step 7; Step 4: Expanding operation; Calculate the expansion point X e If fitness ,make Otherwise Jump to Step 7; Step 5: Compression operation; for fitness Then, before starting the compression operation, set... Regarding fitness Then calculate the compression point. X c If fitness ,make If yes, proceed to Step 7; otherwise, proceed to Step 6. Step 6: Rollback operation; if the compression operation is ineffective, keep the optimal position unchanged, calculate the rollback point for the remaining points, and jump to Step 7; Step 7: If the preset stopping condition is met, i.e., the value is less than the preset tolerance. If the iteration process stops, proceed to Step 2; otherwise, go to Step 2. in, This indicates an updated individual obtained through multi-source guidance. For the updated individual ; For individuals belonging to the intermediate cluster A balanced update operator is constructed with the cluster center as the anchor point and elite information as the offset reference, and its form is as follows: In the formula, For random perturbation quantities, ; It serves as the cluster center for medium-sized clusters; The historical best individual randomly sampled from the elite pool; For individuals belonging to inferior clusters Two exploration strategies were constructed and randomly selected: (i) The elite jump individual update formula combined with Lévy flight is: In the formula, For random perturbation quantities, ; It serves as the cluster center for inferior clusters; B Let Lévy be the step size vector; (ii) Double random jump In the formula, For random perturbation vectors, ; These are two different individuals randomly selected from the population.

5. A method for coordinated scheduling of cross-regional water, wind, and solar power transmission based on a clustering-guided algorithm according to claim 4, characterized in that, S4 includes: For all updated descendant individuals, if they exceed the upper and lower boundaries, they are handled according to the following formula: In the formula, Indicates the individual after the update The d dimension.

6. A method for cross-regional water, wind, and solar coordinated scheduling based on a clustering-guided algorithm according to claim 5, characterized in that, S5 includes: Tournament size K Defined as a linear function that changes with iteration: In the formula, the scale of the tournament K This indicates the number of individuals selected from the population each time using the tournament selection method; , These represent the maximum and minimum number of individuals that can be retrieved, respectively. In each update, the parent and offspring populations are merged to form a population of size 2. N Candidate populations were selected and screened through a tournament. N The winning individuals constitute the next generation; The ε-relaxation constraint handling mechanism refers to setting a threshold ε that decreases as the number of algorithm iterations increases, following the principles below: ① When the constraints of two solutions are violated to a certain degree If the values ​​are equal to or less than the threshold ε, the individual fitness level will be considered. Compare; ② Otherwise, based on the degree of constraint violation Comparison, Smaller individual solutions are better.

7. A method for coordinated scheduling of cross-regional water, wind, and solar power transmission based on a clustering-guided algorithm according to claim 1, characterized in that, S6 includes: Time decay score The calculation formula is as follows: In the formula, For the first i The target value for an elite individual; For the first i The number of FE function evaluations when an elite individual is added to the elite pool. ρ These are empirical parameters; FE With max FE These represent the current number of assessments and the maximum number of assessments, respectively. The method for maintaining the elite pool is as follows: if the elite pool is not yet full, the current new global optimal feasible solution is added to the elite pool; otherwise, for the minimization problem, if the elite individual with the highest score in the elite pool is added to the new global optimal feasible solution... Beyond, that is If so, the elite individual is replaced.

8. A method for coordinated scheduling of cross-regional water, wind, and solar power transmission based on a clustering-guided algorithm according to claim 1, characterized in that, In S7: The cross-regional water, wind and solar power coordinated scheduling model includes an objective function and constraints. The objective function is the mean square error of the average residual load of the receiving-end power grid. F The smallest is represented as: In the formula, T For the total scheduling period, S The number of power transmission channels for the complementary system. s =1~ S ; , and They represent power transmission channels. s During the period t The corresponding remaining load of the receiving-end power grid, the load of the receiving-end power grid, and the transmission power; For power transmission channels s The corresponding average remaining load of the receiving-end power grid; The constraints include at least one of the following: water balance constraints, water level constraints, water level fluctuation constraints, reservoir characteristic constraints, outflow constraints, head calculation formula, hydropower output constraints, dispatch boundary constraints, channel capacity constraints, complementary system operation mode constraints, hydropower station left and right bank output constraints, and hydropower output ramping constraints.

9. A computer system comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the cross-regional water, wind and solar coordinated scheduling method based on clustering guidance algorithm as described in any one of claims 1 to 8.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the cross-regional water, wind and solar coordinated scheduling method based on clustering guidance algorithm as described in any one of claims 1 to 8.

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