A method for configuring offshore wind storage considering wind power output uncertainty and sea cable transmission efficiency

Abstract

The application discloses a kind of offshore wind storage configuration methods considering wind power output uncertainty and sea cable transmission efficiency, it is related to the field of energy storage optimization configuration, this offshore wind storage configuration method includes: clustering offshore wind power output data set using the firefly forest clustering algorithm of pearson correlation coefficient, obtain the annual operating scenario of offshore wind power;Affine mathematical techniques are used to establish a line impedance complex affine model based on the uncertainty of sea cable line impedance;Convergence discrimination techniques are used to calculate power flow for the optimized line impedance complex affine model, and a sea cable transmission efficiency model with line parameter uncertainty is established based on the power flow calculation results;Based on the annual operating scenario of offshore wind power, a two-stage optimization configuration model is established, and the two-stage optimization configuration model is solved.The application solves the defect that voltage complex affine number cannot use traditional comparison complex module through power flow calculation and discrimination method of line impedance complex affine model.

Description

Technical Field

[0001] This invention relates to the field of energy storage optimization configuration, and more specifically, to an offshore wind and energy storage configuration method that takes into account the uncertainty of wind power output and submarine cable transmission efficiency. Background Technology

[0002] In recent years, with the deepening of the global energy transition, offshore wind power, as a clean and renewable energy source, has received widespread attention and rapid development. Due to the characteristics of strong output fluctuation and high uncertainty of offshore wind power, direct grid connection will have an adverse impact on the stability of the power grid and power quality. To alleviate this problem, energy storage technology has been widely used in wind power systems to improve the stability and economy of the system by peak shaving, valley filling and power output regulation.

[0003] However, in practical applications, the optimal configuration of offshore wind and energy storage systems still faces many challenges. First, the operation scenarios of offshore wind power are complex and varied. Traditional clustering algorithms require predefining the number of clusters or setting a fixed number of neighborhoods, which limits the accuracy and robustness of the clustering results. At the same time, these methods generally rely on computationally intensive iterative processes, resulting in low computational efficiency. In addition, submarine cables, as an important transmission channel for offshore wind and energy storage systems, are susceptible to environmental factors, exhibiting a certain degree of uncertainty. This adds additional complexity to the accurate calculation of transmission losses. If the uncertainty of submarine cable parameters is not fully considered, it may lead to deviations in system planning results, thereby affecting the overall economic efficiency and stability.

[0004] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0005] To address the problems in related technologies, this invention proposes an offshore wind power storage configuration method that considers the uncertainty of wind power output and the efficiency of submarine cable transmission, in order to overcome the aforementioned technical problems existing in the existing related technologies.

[0006] Therefore, the specific technical solution adopted by the present invention is as follows:

[0007] A method for configuring offshore wind power storage that considers the uncertainty of wind power output and the efficiency of submarine cable transmission, the method comprising:

[0008] S1. Obtain the offshore wind power output dataset and use the firefly forest clustering algorithm based on Pearson correlation coefficient to cluster the offshore wind power output dataset to obtain the annual operation scenario of offshore wind power.

[0009] S2. Establish a complex affine model of line impedance based on the uncertainty of submarine cable line impedance using affine mathematics techniques, and optimize the complex affine model of line impedance based on polynomial fitting techniques.

[0010] S3. Use convergence discrimination technology to perform power flow calculation on the optimized line impedance complex affine model, and establish a submarine cable transmission efficiency model with uncertain line parameters based on the power flow calculation results.

[0011] S4. Based on the annual operation scenario of offshore wind power, establish a two-stage optimization configuration model and solve the two-stage optimization configuration model to realize the offshore wind-storage configuration.

[0012] Preferably, an offshore wind power output dataset is obtained, and the dataset is clustered using a firefly forest clustering algorithm based on Pearson correlation coefficients to obtain annual operating scenarios for offshore wind power, including:

[0013] S11. Obtain an offshore wind power output dataset containing several independently distributed data points, and use the Pearson coefficient to characterize the dissimilarity between data points;

[0014] S12. Based on the dissimilarity between data points, iterate through each data point in the offshore wind power output dataset, and perform maximum likelihood estimation on the number of neighbors of the data point in each iteration to obtain the likelihood ratio of the comprehensive model.

[0015] S13. Determine whether the likelihood ratio of the integrated model meets the preset conditions. If it meets the preset conditions, update the number of neighbors of the current maximum likelihood estimate and execute step S14. Otherwise, repeat the iteration process of the data points until the likelihood ratio of the integrated model meets the preset conditions.

[0016] S14. Treat the data points as fireflies with adaptive brightness, cluster the fireflies to form a tree structure, merge the tree structures to generate a firefly forest, and obtain the annual operation scenario of offshore wind power.

[0017] Preferably, the data points are used as fireflies with adaptive brightness, and the fireflies are clustered to form a tree structure. The tree structures are then merged to generate a firefly forest, resulting in the following annual operation scenarios for offshore wind power:

[0018] S141. Treat the data points as fireflies, initialize the firefly parameters based on the distribution parameters of the predefined offshore wind power output dataset, and calculate the firefly brightness based on the firefly parameters.

[0019] S142. Arrange the fireflies in descending order based on their brightness. Each firefly selects the nearest brighter firefly as a guide to obtain preliminary clustering results. Then, use a tree structure to store the preliminary clustering results to form a firefly tree.

[0020] S143. Based on the luminescence interaction signals of firefly populations, firefly trees are merged to form a firefly forest, and the final clustering result is obtained. The final clustering result is used as the annual operation scenario for offshore wind power.

[0021] Preferably, the data points are used as fireflies, and the firefly parameters are initialized based on the distribution parameters of a predefined offshore wind power output dataset. The firefly brightness is then calculated based on the firefly parameters, including:

[0022] S1411. Treat the data points as fireflies with adaptive brightness, and initialize the firefly parameters according to the distribution parameters of the offshore wind power dataset. The firefly parameters include brightness and the number of neighbors estimated by maximum likelihood.

[0023] S1412. Calculate the interquartile range of the number of neighbors estimated by the maximum likelihood using the interquartile range formula, and calculate the upper and lower bounds of the number of neighbors based on the interquartile range of the number of neighbors.

[0024] S1413. Based on the upper and lower bounds of the number of neighbors, perform interquartile range testing on the number of neighbors estimated by maximum likelihood, identify outlier neighbors in the number of neighbors estimated by maximum likelihood, and obtain the error of the maximum likelihood estimation density.

[0025] S1414. Based on the error of the maximum likelihood estimation density, calculate the firefly brightness using the formula for calculating firefly brightness.

[0026] Preferably, the fireflies are sorted in descending order based on their brightness. Each firefly selects the nearest brighter firefly as a guide to obtain preliminary clustering results. The preliminary clustering results are then stored using a tree structure to form a firefly tree, including:

[0027] S1421. Sort the fireflies in descending order according to their brightness values, and iterate over each firefly and its maximum likelihood estimate neighbors.

[0028] S1422. Compare the brightness value of the neighboring fireflies with the brightness value of the current firefly. If the brightness value of the neighboring firefly is greater than that of the current firefly, then the neighboring firefly becomes the middle firefly of the current firefly, and the current firefly is added to the corresponding firefly tree.

[0029] S1423. If the brightness values ​​of all neighboring fireflies are less than that of the current firefly, it indicates that the current firefly is the root firefly, and the root firefly obtains a new cluster label and generates a new firefly tree, which is used as the local cluster center.

[0030] S1424. Traverse the remaining fireflies. If the root firefly becomes an intermediate firefly among the remaining fireflies, then assign its cluster label to the remaining fireflies to obtain the preliminary clustering results. Use a tree structure to store the preliminary clustering results to form a firefly tree.

[0031] Preferably, the expression for the complex affine model of line impedance based on the impedance uncertainty of submarine cable lines is:

[0032]

[0033] In the formula, Let R represent the complex affine model of the line impedance from node i to node j; represent the affine form of the parameters; i-j and X i-j δ represents the line resistance and reactance from node i to node j, respectively; r,1 This refers to a parameter used to measure line resistance fluctuations.

[0034] Preferably, the optimized line impedance complex affine model is used to perform power flow calculations using convergence discrimination techniques, and a submarine cable transmission efficiency model with uncertain line parameters is established based on the power flow calculation results, including:

[0035] S31. Based on the known load and initial state of node j, obtain the current between node i and node j, and calculate the injected power of each node according to the complex affine model of current and line impedance.

[0036] S32. Based on the injected power of each node, calculate the current and voltage drop between each node and other nodes;

[0037] S33. Iteratively calculate the voltage difference of each node relative to the previous iteration, and use the affine number fluctuation domain overlap area comparison convergence discrimination technique to judge the similarity of the two iteration results, and obtain the power flow calculation results of the line impedance complex affine model.

[0038] S34. Based on the power flow calculation results of the line impedance complex affine model, analyze the relationship between energy storage output and submarine cable head voltage, and establish a submarine cable transmission efficiency model with uncertain line parameters based on the relationship between energy storage output and submarine cable head voltage.

[0039] Preferably, based on the annual operation scenario of offshore wind power, a two-stage optimization configuration model is established, and the two-stage optimization configuration model is solved to achieve the offshore wind-storage configuration including:

[0040] S41. With the optimization objectives of minimizing the annual comprehensive cost, net load fluctuation, and voltage fluctuation of offshore wind storage, construct an upper-level capacity configuration model for offshore wind storage.

[0041] S42. Using the upper-level capacity configuration model as input and minimizing the daily loss of submarine cable transmission lines as the optimization objective, construct the lower-level optimized operation model for offshore wind storage.

[0042] S43. The improved geyser algorithm is used to solve the upper-level capacity configuration model, and the solver is used to solve the lower-level optimization operation model.

[0043] Preferably, the improved geyser algorithm is used to solve the upper-level capacity configuration model, including:

[0044] Initialize the parent population P op Calculate the fitness function of the upper-level capacity configuration model and ensure that the fitness function of the upper-level capacity configuration model satisfies the constraints.

[0045] Generating offspring population R using eruption mechanisms T , the parent population P op and its offspring population R T Merging to form population S T And based on the cooling process, the population S T Sort and evaluate population S T The quality of each solution;

[0046] Based on the dominance level and reference distance of each solution, from the population S T Select the best solution and generate the next generation parent population P op,T+1 The repeated eruption mechanism and cooling process continue to generate a new generation of parent populations until the convergence condition is met.

[0047] The final parent population P op The Pareto optimal solution of the upper-level capacity configuration model is used, and the final solution of the upper-level capacity configuration model is selected by gray target decision based on entropy weight method.

[0048] Preferably, the expression for the lower-level optimized operation model is:

[0049]

[0050] In the formula, P bg,t η represents the active power injected into the head end of the submarine cable at time t; hl,t K represents the transmission efficiency of the submarine cable at time t, considering the uncertainty of the line parameters; d This indicates the number of annual operational scenarios for offshore wind power; T k This represents the number of days corresponding to the k-th scenario.

[0051] The beneficial effects of this invention are as follows:

[0052] 1. This invention presents a firefly forest clustering algorithm based on Pearson correlation coefficient. It achieves dynamic adjustment through adaptive neighborhood estimation. The brightness of each data point is calculated according to its distribution characteristics, eliminating the need to manually set the number of neighbors. This significantly simplifies parameter tuning and improves flexibility. It exhibits excellent scalability when processing large-scale datasets. Furthermore, it filters outliers using the interquartile range method, ensuring the stability of brightness calculation and the accuracy of clustering results. Thus, it has significant advantages when dealing with complex data distributions and large-scale data, and is particularly suitable for practical application scenarios that require high efficiency and high precision. In addition, this invention applies the improved firefly forest clustering algorithm to scene clustering, which has higher robustness and stability compared to common clustering algorithms.

[0053] 2. This invention uses affine mathematics to model the uncertainty of line impedance, obtaining a complex affine model of line impedance based on the uncertainty of submarine cable line impedance. It also uses a polynomial fitting method to improve the traditional affine division, so that the conservatism of the original affine number division can be overcome in subsequent affine calculations with a slight loss of realism. Furthermore, through the power flow calculation and discrimination method of the line impedance complex affine model, the defect that the voltage complex affine number cannot be compared with the traditional complex number model is solved.

[0054] 3. The present invention derives a formula for the transmission efficiency of submarine cable lines that takes into account the uncertainty of line parameters. Compared with the traditional derivation method that assumes the line impedance to be fixed, it has better conservatism and thus more accurately characterizes the transmission efficiency of submarine cable lines under actual conditions. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart of an offshore wind power storage configuration method that considers the uncertainty of wind power output and the efficiency of submarine cable transmission according to an embodiment of the present invention.

[0057] Figure 2 This is a flowchart of the firefly forest clustering algorithm in an offshore wind power storage configuration method that considers the uncertainty of wind power output and the efficiency of submarine cable transmission according to an embodiment of the present invention. Detailed Implementation

[0058] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention.

[0059] According to an embodiment of the present invention, an offshore wind power storage configuration method considering the uncertainty of wind power output and the efficiency of submarine cable transmission is provided.

[0060] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 1 As shown, according to an embodiment of the present invention, an offshore wind and energy storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency includes:

[0061] S1. Obtain the offshore wind power output dataset and use the firefly forest clustering algorithm based on Pearson correlation coefficient to cluster the offshore wind power output dataset to obtain the annual operation scenario of offshore wind power.

[0062] This involves acquiring a dataset of offshore wind power output and using a firefly forest clustering algorithm based on Pearson correlation coefficients to cluster the dataset, resulting in the following annual operating scenarios for offshore wind power:

[0063] S11. Obtain an offshore wind power output dataset containing several independently distributed data points, and use the Pearson coefficient to characterize the dissimilarity between data points;

[0064] S12. Based on the dissimilarity between data points, iterate through each data point in the offshore wind power output dataset, and perform maximum likelihood estimation on the number of neighbors of the data point in each iteration to obtain the likelihood ratio of the comprehensive model.

[0065] S13. Determine whether the likelihood ratio of the integrated model meets the preset conditions. If it meets the preset conditions, update the number of neighbors of the current maximum likelihood estimate and execute step S14. Otherwise, repeat the iteration process of the data points until the likelihood ratio of the integrated model meets the preset conditions.

[0066] S14. Treat the data points as fireflies with adaptive brightness, cluster the fireflies to form a tree structure, merge the tree structures to generate a firefly forest, and obtain the annual operation scenario of offshore wind power.

[0067] The data points are used as fireflies with adaptive brightness, and the fireflies are clustered to form a tree structure. The tree structures are then merged to generate a firefly forest, resulting in the following annual operation scenarios for offshore wind power:

[0068] S141. Treat the data points as fireflies, initialize the firefly parameters based on the distribution parameters of the predefined offshore wind power output dataset, and calculate the firefly brightness based on the firefly parameters.

[0069] The process involves treating data points as fireflies, initializing firefly parameters based on the distribution parameters of a predefined offshore wind power output dataset, and calculating firefly brightness based on these parameters.

[0070] S1411. Treat the data points as fireflies with adaptive brightness, and initialize the firefly parameters according to the distribution parameters of the offshore wind power dataset. The firefly parameters include brightness and the number of neighbors estimated by maximum likelihood.

[0071] S1412. Calculate the interquartile range of the number of neighbors estimated by the maximum likelihood using the interquartile range formula, and calculate the upper and lower bounds of the number of neighbors based on the interquartile range of the number of neighbors.

[0072] S1413. Based on the upper and lower bounds of the number of neighbors, perform interquartile range testing on the number of neighbors estimated by maximum likelihood, identify outlier neighbors in the number of neighbors estimated by maximum likelihood, and obtain the error of the maximum likelihood estimation density.

[0073] S1414. Based on the error of the maximum likelihood estimation density, calculate the firefly brightness using the formula for calculating firefly brightness.

[0074] S142. Arrange the fireflies in descending order based on their brightness. Each firefly selects the nearest brighter firefly as a guide to obtain preliminary clustering results. Then, use a tree structure to store the preliminary clustering results to form a firefly tree.

[0075] The fireflies are sorted in descending order based on their brightness. Each firefly selects the nearest brighter firefly as a guide to obtain preliminary clustering results. The preliminary clustering results are then stored in a tree structure to form a firefly tree, which includes:

[0076] S1421. Sort the fireflies in descending order according to their brightness values, and iterate over each firefly and its maximum likelihood estimate neighbors.

[0077] S1422. Compare the brightness value of the neighboring fireflies with the brightness value of the current firefly. If the brightness value of the neighboring firefly is greater than that of the current firefly, then the neighboring firefly becomes the middle firefly of the current firefly, and the current firefly is added to the corresponding firefly tree.

[0078] S1423. If the brightness values ​​of all neighboring fireflies are less than that of the current firefly, it indicates that the current firefly is the root firefly, and the root firefly obtains a new cluster label and generates a new firefly tree, which is used as the local cluster center.

[0079] S1424. Traverse the remaining fireflies. If the root firefly becomes an intermediate firefly among the remaining fireflies, then assign its cluster label to the remaining fireflies to obtain the preliminary clustering results. Use a tree structure to store the preliminary clustering results to form a firefly tree.

[0080] S143. Based on the luminescence interaction signals of firefly populations, firefly trees are merged to form a firefly forest, and the final clustering result is obtained. The final clustering result is used as the annual operation scenario for offshore wind power.

[0081] To facilitate understanding of the above technical solutions of the present invention, the following provides a detailed explanation of how the present invention obtains offshore wind power output datasets in practice and uses the Pearson correlation coefficient-based firefly forest clustering algorithm to cluster the offshore wind power output datasets to obtain the annual operation scenarios of offshore wind power:

[0082] Step 1: Similarity representation based on Pearson coefficient:

[0083] Given a wind power output dataset, there exists a series of independent and identically distributed data points {x1, ..., x...} n Each point can be considered as a firefly, and the Pearson coefficient is used to characterize the data point x. i and x j The dissimilarity between them is shown in equation (1):

[0084]

[0085] In the formula: r i,j Represents data point x i and x j The dissimilarity between them, a larger r i,j The value represents x i and x j The differences between them are greater; n represents the number of data points; x represents i The mean; x represents j The mean.

[0086] Step 2: Maximum likelihood estimation based on the integrated model:

[0087] The volume v of the hypersphere is defined as shown in equation (2):

[0088] v i,l =σ·r i,l -r i,l-1 (2)

[0089] In the formula: r i,l Representing point x i The dissimilarity between it and its l-th nearest neighbor; r i,l-1Representing point x i The dissimilarity between the hypersphere and its (l-1)th nearest neighbor; σ represents the scaling factor of the hypersphere.

[0090] The volume v of the hypersphere follows an exponential distribution with parameter ρ, as shown in equation (3):

[0091] f(v)=ρ·e -ρ·v (3)

[0092] In the formula: f(v) represents the volume v of the hypersphere following an exponential distribution with parameter ρ; e represents the exponential function (i.e., e^(-v / v)). x ).

[0093] Data point x i The density likelihood estimation function of the k nearest neighbors is shown in Equation (4):

[0094]

[0095] In the formula: L i (ρ i |{r i,l} i≤k ) represents data point x i The density likelihood estimation function of V and its k nearest neighbors; i,k Indicates data point x i The total volume of the hypersphere centered at its k nearest neighbors; ρ i L represents the likelihood density of the k nearest neighbors; i Represents data point x i The density likelihood estimation function, i.e., L i (x).

[0096] To obtain the maximum likelihood estimate, we need to adjust equation (4) with respect to the parameter ρ. i Differentiate:

[0097]

[0098] In the formula: L' is set i =0, calculate parameter ρ i Maximum likelihood estimation, where L' i This represents the derivative of the likelihood estimation function.

[0099] The comprehensive model D is obtained using the likelihood ratio method. k As shown in equation (6):

[0100] D k =-2k[log(V i,j )+log(V j,k )-2log(V i,k +V j,k)+log(4)]; (6)

[0101] In the formula: V i,k Indicates data point x i The total volume of the hypersphere centered at its k nearest neighbors; V j,k Indicates data point x j The total volume of the hypersphere centered at its k nearest neighbors; V i,j Indicates data point x i The total volume of the hypersphere centered at its j nearest neighbors, where the comprehensive model D k It follows a chi-square distribution with 1 degree of freedom. As k increases, a larger D... k The value indicates that the maximum likelihood estimate of k has a higher confidence level.

[0102] To adaptively obtain the maximum likelihood estimate of the number of neighbors k for each data point, a threshold D is set. thr This makes equation (6) satisfy:

[0103]

[0104] In the formula: the algorithm starts traversing from the first neighbor and updates the current maximum likelihood estimate of the number of neighbors to k. Assume there exists a value k ≤ k such that D k <D thr And D k+1 >D thr Therefore, it can be considered that, in relation to D thr At the corresponding confidence level, the nearest neighbors of the data point in the maximum likelihood estimate is k, and the density ρ of the point is defined by equation (8):

[0105]

[0106] At this point, the corresponding estimation error is defined as equation (9):

[0107]

[0108] Where: ε i ρ represents the error corresponding to the maximum likelihood estimate density; k represents the number of neighbors of the maximum likelihood estimate of density ρ. Represents data point x i The nearest neighbor number of the maximum likelihood estimate.

[0109] This invention avoids the need for preset parameters and reduces the time complexity typically associated with biomimetic algorithms by allowing the algorithm to dynamically adjust nearest neighbor relationships.

[0110] Step 3: Define the sub-modules of the Firefly Forest algorithm:

[0111] The Firefly Forest algorithm consists of three main modules: outlier filtering and brightness calculation, firefly tree generation, and merging firefly trees into a firefly forest. Initially, data points are treated as fireflies with adaptive brightness; these fireflies are then clustered based on brightness and proximity to form a tree structure; finally, the clusters are merged into a firefly forest, yielding the final clustering result.

[0112] 1) Outlier filtering brightness calculation:

[0113] Each data point is treated as a firefly, and its brightness and adaptive number of neighbors are initialized based on the distribution and defined parameters of the offshore wind power dataset.

[0114] 2) Firefly Tree Spawning:

[0115] Fireflies are arranged in descending order of brightness. Each firefly selects the nearest brighter firefly as its guide, thus joining the cluster of that guide. Fireflies that guide other fireflies but are not guided by other fireflies are called "root fireflies," while fireflies that both guide other fireflies and are guided by brighter fireflies are called "intermediate fireflies." This process completes the initial clustering, and these fireflies are stored using a tree data structure, with members of the same cluster residing on the same firefly tree.

[0116] 3) The firefly trees are merged into a firefly forest:

[0117] Some firefly populations gather at night and flash synchronously, communicating through light signals and achieving collective synchronization by controlling the timing and frequency of their flashes. Fireflies that do not guide other fireflies are called "leaf fireflies." Each firefly cluster represents a tree, and interactions and merging between clusters occur through leaf fireflies. The merging of clusters is similar to the merging of trees, ultimately forming a unified firefly forest.

[0118] The outlier filtering brightness calculation includes:

[0119] The number of nearest neighbors estimated by maximum likelihood can be used to calculate the corresponding point density. The number of nearest neighbors obtained by maximum likelihood estimation is usually related to the confidence level. The higher the confidence level, the more accurate the result, but more neighbors will be obtained. This will lead to an overestimation of the actual number of neighbors, resulting in errors in subsequent density calculations. Therefore, the overestimated number of neighbors needs to be corrected.

[0120] After the current number of neighbors satisfies formula (7), the estimated number of neighbors is subjected to an interquartile range (IQR) test. Define data point x. i The list of hypersphere volumes is V i,list Store each neighboring v in ascending order. i,l The formula for calculating IQR is:

[0121]

[0122] In the formula: IQR represents the interquartile range; List of hypersphere volumes V i,list The third quartile in; List of volumes of hyperspherical shells V i,list The first quartile in the spectrum.

[0123] After obtaining the IQR, calculate the lower and upper bounds according to formulas (11) and (12):

[0124]

[0125] In the formula: L ower Bound and U pper Bound These represent the upper and lower bounds of the volume of the hypersphere, respectively; I thr This indicates the threshold for the IQR test; a higher IQR value indicates a lower threshold. thr The value represents a more lenient test, making it easier for the estimated number of neighbors to pass the test, thus resulting in a slightly larger estimate and a smaller I. thr The value represents a more stringent test, making it harder for the estimated number of neighbors to pass the test, resulting in a slightly smaller estimate.

[0126] After obtaining the lower and upper bounds, in order to identify outlier neighbors, the estimated number of neighbors is tested using the IQR method, as shown in equations (13)-(15):

[0127]

[0128] V i,final =V i,list -V i,koutliers (14)

[0129] k final =number(V i,final (15)

[0130] In the formula: List of volumes of hyperspherical shells V i,list The portion of V that is greater than the upper bound or less than the lower bound; i,final This means remove all. List of remaining hyperspherical shell volumes V i,list Part; k outliers Indicates the proximity of outliers; k final This represents the final estimated number of neighbors, whose value is equal to the set V. i,final The number of elements in the middle.

[0131] Considering the impact of prediction error, a larger prediction error indicates greater instability of the corresponding result. Therefore, the brightness of a firefly is inversely proportional to its prediction error, and the formula for calculating the brightness of a firefly is as shown in equation (16):

[0132]

[0133] In the formula: B right,i Indicates the brightness of a firefly; ε i k represents the error corresponding to the maximum likelihood estimation density; final Represents the maximum likelihood nearest neighbor; sum(V) i,final ) represents data point x i and its surrounding k final The sum of IQR check volumes of the hyperspherical shells between each neighbor.

[0134] Construct a KD-tree (K-Dimensional Tree, i.e., a partitioning structure for high-dimensional spatial data) to create the nearest neighbor matrix and distance matrix of the wind power output dataset; initialize the nearest neighbor and threshold judgment information for each point; iterate over each point in the dataset until all points have been traversed; during each iteration, perform maximum likelihood estimation on the corresponding ρ value according to equation (6) to obtain the comprehensive model D. k and D k+1 The likelihood ratio is determined, and the relationship between the comprehensive model and the threshold is determined. If the maximum likelihood nearest neighbor is reached, the algorithm will start IQR filtering and use formula (16) to calculate the brightness and save the relevant information.

[0135] The generation of firefly trees includes:

[0136] After obtaining the brightness and maximum likelihood estimate of the nearest neighbor for each point, the firefly tree generation module is executed, which performs preliminary clustering of the dataset according to the following definition:

[0137] 1) Definition 1:

[0138] If all k maximum likelihood estimates of the nearest neighboring brightness values ​​are lower than x i Brightness value B right,i Then we can consider x i The firefly x has a brightness peak i For the root firefly.

[0139] 2) Definition 2:

[0140] If we are surrounding Firefly X i Among the k maximum likelihood estimates of a neighborhood, there exists a brightness value B. right,j Greater than x i Brightness value B right,i Firefly x j Then firefly xi Firefly x j They were grouped into the same cluster, and it was assumed that fireflies x j It's the firefly in the middle.

[0141] 3) Definition 3:

[0142] If Fireflies X i If a firefly does not become an intermediate firefly or a root firefly, it is considered a leaf firefly.

[0143] like Figure 2 As shown, based on the above definition, the process of generating a firefly tree is as follows:

[0144] 1) Sort the fireflies in descending order based on their brightness values, iterate through each firefly, and iterate through the nearest neighbors of the maximum likelihood estimate for each firefly. For example, when iterating over the i-th firefly, denoted as firefly... i ;

[0145] 2) For each neighbor, compare its brightness value with the brightness value of the current firefly. If the brightness value of the neighboring firefly is greater than that of the current firefly, the neighboring firefly becomes the middle firefly of the current firefly, the cluster label of the current firefly is the same as that of the neighboring firefly, and the current firefly is added to the corresponding firefly tree.

[0146] 3) If the brightness values ​​of all neighboring fireflies are less than that of the current firefly, it means that the current firefly is the root firefly. At this time, the root firefly obtains a new cluster label and generates a new firefly tree, which can be regarded as the local cluster center.

[0147] 4) When traversing other fireflies in subsequent steps, the root firefly in step 3) may become an intermediate firefly for other fireflies and assign its cluster label to other fireflies, thereby achieving local clustering. This step provides the foundation for the initial clustering of the entire algorithm.

[0148] The merging of firefly trees into firefly forests includes:

[0149] The firefly tree generation module generates initial clusters and firefly trees. The firefly trees are then merged into a firefly forest module to obtain the final clusters. The process of merging firefly trees into a firefly forest is as follows:

[0150] 1) Identify the leaf nodes of each cluster and guide the fireflies to traverse each cluster. Since the data points of each cluster are stored in the firefly tree, the corresponding leaf nodes can be obtained through the tree structure. The construction of the firefly tree starts from the center of the cluster and propagates towards the data points with lower brightness. Therefore, the further away from the root node of the firefly tree, the lower the brightness of the corresponding node.

[0151] 2) Traverse the nearest neighbor of each leaf node and determine whether the label of the nearest neighbor is the same as its own label, and find the neighbors with different labels.

[0152] 3) Calculate the brightness difference between the firefly on the leaf and fireflies in different clusters, as shown in equation (17):

[0153]

[0154] In the formula: BG represents the brightness difference between the leaf firefly and fireflies in different clusters; B right,NC B represents the brightness value of neighboring clusters. right,leaf This represents the brightness value of the leaf node; NC represents the neighboring cluster.

[0155] In this module, the root firefly is first traversed to find the corresponding leaf firefly. Then, each leaf firefly is traversed. For each leaf firefly, its k nearest neighbors are traversed. It is determined whether the label of the neighboring fireflies is the same as its own label. If they are the same, no operation is performed. If they are different, the brightness difference is calculated and updated until all traversals are completed.

[0156] S2. Establish a complex affine model of line impedance based on the uncertainty of submarine cable line impedance using affine mathematics techniques, and optimize the complex affine model of line impedance based on polynomial fitting techniques.

[0157] To facilitate understanding of the above technical solutions of the present invention, the following provides a detailed explanation of how the present invention utilizes affine mathematics to establish a complex affine model of line impedance based on the uncertainty of submarine cable line impedance in practical applications, and optimizes the complex affine model of line impedance based on polynomial fitting techniques:

[0158] A complex affine model of line impedance based on the impedance uncertainty of submarine cable lines is established using affine mathematics:

[0159] Assume that the line resistance and reactance each have fluctuation ranges. in, R , These represent the lower and upper bounds of the line resistance fluctuation, respectively. X , These represent the lower and upper bounds of the line reactance fluctuation, respectively. The line impedance complex affine model is described as follows:

[0160]

[0161] R i-j =R0+R1δ r,1 (19)

[0162] X i-j =X0+X1δ x,1(20)

[0163]

[0164] In the formula: R0 and X0 represent the theoretical values ​​of line resistance and reactance, respectively, δ r,1 and δ x,1 R1 and X1 are used to measure the fluctuations in line resistance and reactance, respectively, with values ​​ranging from [-1, 1]; R1 and X1 represent the fluctuation amplitudes of uncertain variables; R i-j and X i-j These represent the line resistance and reactance values ​​from node i to node j (where a node represents a node in the power flow calculation of the power system), respectively. Represents the complex affine model of the line impedance from node i to node j; represents the affine form of the parameters.

[0165] Line impedance typically fluctuates by 25% to 30%, therefore, the upper and lower limits of line impedance are:

[0166]

[0167] In summary, the complex affine model of the line impedance from node i to node j can be obtained as follows:

[0168]

[0169] Suppose we have two related variables, α and β, whose affine forms are as follows:

[0170] α = 4 + 3θ1; (25)

[0171] β=2+θ1; (26)

[0172] In the formula: θ1 represents the noise element, and its value ranges from [-1, 1].

[0173] Affine numbers are essentially linear functions of noise elements. The quotient of an affine number does not possess the linear characteristic of an affine number; therefore, it is not an affine form and cannot participate in subsequent affine operations. By using curve polynomial fitting to transform the result of affine number division into a polynomial function containing only existing noise elements, setting the number of terms to 9 yields:

[0174]

[0175] In the formula: α and β represent the affine forms of the two related variables; p represents the coefficient of the i-th term.

[0176] S3. Utilize convergence discrimination technology to perform power flow calculations on the optimized line impedance complex affine model, and establish a submarine cable transmission efficiency model with uncertain line parameters based on the power flow calculation results.

[0177] Among these methods, the optimized line impedance complex affine model is used to perform power flow calculations using convergence discrimination techniques, and a submarine cable transmission efficiency model with uncertain line parameters is established based on the power flow calculation results, including:

[0178] S31. Based on the known load and initial state of node j, obtain the current between node i and node j, and calculate the injected power of each node according to the complex affine model of current and line impedance.

[0179] S32. Based on the injected power of each node, calculate the current and voltage drop between each node and other nodes;

[0180] S33. Iteratively calculate the voltage difference of each node relative to the previous iteration, and use the affine number fluctuation domain overlap area comparison convergence discrimination technique to judge the similarity of the two iteration results, and obtain the power flow calculation results of the line impedance complex affine model.

[0181] S34. Based on the power flow calculation results of the line impedance complex affine model, analyze the relationship between energy storage output and submarine cable head voltage, and establish a submarine cable transmission efficiency model with uncertain line parameters based on the relationship between energy storage output and submarine cable head voltage.

[0182] To facilitate understanding of the above technical solutions of the present invention, the following provides a detailed explanation of how the present invention utilizes convergence discrimination technology to perform power flow calculations on the optimized line impedance complex affine model in practical applications, and establishes a submarine cable transmission efficiency model with uncertain line parameters based on the power flow calculation results:

[0183] The power flow calculation based on the traditional forward and reverse power flow calculation using a complex affine model of line impedance mainly includes the following three steps:

[0184] 1) Back-substitution:

[0185] Using the affine load S at node j j,l And the initial state, and assume it is equal to the rated voltage U. j ; obtain the current between nodes i and j:

[0186]

[0187] Based on the composite affine model of current and line impedance, the power loss of this segment and the injected power at node i are calculated as follows:

[0188]

[0189] In the formula: S j,l S represents the affine load of node j; i,l U represents the affine load of node i; j Indicates the rated voltage; R i-j and Xi-j These represent the line resistance and reactance values ​​from node i to node j, respectively. Represents the complex affine model of the line impedance from node i to node j; This represents the current between nodes i and j.

[0190] 2) Push forward:

[0191] Using the injected power and first-segment voltage obtained from the back-substitution process for each node, the current and voltage drop between each node and other nodes are calculated. The calculation process is as follows:

[0192]

[0193] U j =U i -ΔU i-j (32)

[0194] In the formula: and U i-j These represent the current and voltage between node i and node j, respectively. U represents the load of node i; j U represents the voltage at node j; i This represents the voltage at node i; This represents the complex power of node i.

[0195] 3) Convergence judgment:

[0196] The traditional power flow algorithm terminates its iterations when the voltage deviation of each node relative to the previous iteration is less than an allowable value. However, for line loss calculations considering line impedance uncertainties, the voltage difference between two iterations is:

[0197]

[0198] In the formula: Both represent complex affine numbers; The reference term representing the voltage during iteration; This indicates an additional term for the voltage during iteration; This represents the voltage correction factor.

[0199] It should be noted that the voltage difference is not only a complex number, but also an affine number with a fluctuating range, and cannot be simply judged based on the amplitude of the voltage difference between successive iterations. To address the limitation of traditional comparison of complex affine numbers in voltage complex numbers, this invention proposes a convergence discrimination method based on the overlapping area of ​​the fluctuation domain of complex affine numbers.

[0200] Assume that the rectangular regions S and S' are complex affine numbers. and The area of ​​the overlapping region in the fluctuation domain of complex affine numbers represents the convergence of the iterative process; the larger the overlapping area, the better the convergence. The convergence criterion for comparing the overlapping regions of the complex affine number fluctuation domain is to determine whether the ratio of the area of ​​the overlapping region S to the sum of the areas of regions S1 and S2 is less than a set threshold δ. The calculation formula is as follows:

[0201] S / (S1+S2)<δ; (34)

[0202] By comparing overlapping areas, the similarity between the results of two iterations can be determined, thus indicating whether the iteration termination condition has been met.

[0203] Derivation of the formula for submarine cable transmission efficiency based on uncertainties in line parameters:

[0204] This invention specifies that the offshore wind storage is located at the initial section of the submarine cable, and the grid-connected side is the end of the submarine cable. The voltage at the beginning of the submarine cable can be adjusted through energy storage. The relationship between the energy storage output and the voltage at the beginning of the submarine cable is as follows:

[0205]

[0206] In the formula: U1 represents the voltage at the beginning of the submarine cable; P1 and Q1 represent the active power and reactive power of the beginning segment of the submarine cable, respectively; Y 1-j U represents the admittance between the cable head and other nodes; j P represents the voltage at node j; BESS,t P represents the output power of the stored energy at time t; ref and Q ref This indicates the power at the beginning of the submarine cable that is not connected to wind power or energy storage and does not account for transmission losses; P WT,t and Q WT,t P represents the active and reactive power output of offshore wind power at time t, respectively. bg Q represents the active power at the beginning of the submarine cable; bg This indicates the reactive power at the beginning of the submarine cable.

[0207] Assuming the voltage at the submarine cable's grid connection point is the reference voltage, then:

[0208]

[0209] Assume the voltage relationship between the beginning and end of the submarine cable and the grid connection point satisfies:

[0210]

[0211] In the formula: θ represents the ratio of the voltage amplitude at the beginning of the submarine cable to that at the grid connection end; τ represents the voltage phase angle difference between the beginning of the submarine cable and that at the grid connection end; τ represents the discount rate. Indicates the voltage at the submarine cable's grid connection end; This indicates the voltage at the beginning of the submarine cable.

[0212] The following is an affine model of submarine cable impedance and admittance considering the uncertainties of line parameters:

[0213] Z = R + jωL; (39)

[0214] Y = G + jωC; (40)

[0215] In the formula: represents the affine form of the parameters; Z and Y represent the impedance and admittance of the submarine cable, respectively; R and G represent the resistance and conductance of the submarine cable, respectively; L and C represent the inductance and capacitance of the submarine cable, respectively; ω represents the angular frequency; j represents a complex number.

[0216] The affine model for the characteristic impedance and propagation coefficient of the submarine cable is thus obtained as follows:

[0217]

[0218] In the formula: Z c γ represents the characteristic impedance of the submarine cable; γ represents the propagation coefficient of the submarine cable.

[0219] The voltage-current relationship between the beginning and end terminals of the equivalent circuit of a long line, considering the uncertainty of line parameters, is as follows:

[0220]

[0221] Therefore, a submarine cable Y-parameter matrix that takes into account the uncertainty of line parameters can be constructed:

[0222]

[0223] In the formula: and These represent the current at the beginning and end of the submarine cable, respectively. and These represent the voltage at the beginning and end of the submarine cable, respectively.

[0224] Thus, the admittance matrix Y is obtained. hl :

[0225]

[0226] In the formula: Y hl Y represents the admittance matrix; L and Y R These represent the parameters of the admittance matrix.

[0227] Based on the admittance matrix considering the uncertainties of line parameters, a calculation model for the complex affine transmission loss of submarine cables is obtained:

[0228]

[0229] In the formula: P lossIndicates the transmission loss of the submarine cable; P bg and P grid These represent the power at the beginning and end (i.e., the grid connection end) of the submarine cable, respectively; * indicates conjugate; Re indicates taking the real part.

[0230] Based on the above affine transmission loss calculation model, the formula for calculating submarine cable transmission efficiency is obtained:

[0231]

[0232] In the formula: η hl This indicates the transmission efficiency of the submarine cable.

[0233] Based on the voltage relationship between the beginning and end of the submarine cable considering energy storage output, we can obtain:

[0234]

[0235] In summary, the formula for submarine cable transmission efficiency considering uncertainties in line parameters can be obtained as follows:

[0236]

[0237] S4. Based on the annual operation scenario of offshore wind power, establish a two-stage optimization configuration model and solve the two-stage optimization configuration model to realize the offshore wind-storage configuration.

[0238] Specifically, based on the annual operation scenario of offshore wind power, a two-stage optimization configuration model is established and solved to achieve the following offshore wind-storage configuration:

[0239] S41. With the optimization objectives of minimizing the annual comprehensive cost of offshore wind storage, minimizing net load fluctuation, and minimizing voltage fluctuation, a capacity configuration model for the upper layer of offshore wind storage is constructed.

[0240] S42. Using the upper-level capacity configuration model as input and minimizing the daily loss of submarine cable transmission lines as the optimization objective, construct the lower-level optimized operation model for offshore wind storage.

[0241] S43. The improved geyser algorithm is used to solve the upper-level capacity configuration model, and the solver is used to solve the lower-level optimization operation model.

[0242] Among them, the improved geyser algorithm is used to solve the upper-level capacity configuration model, including:

[0243] Initialize the parent population P op Calculate the fitness function of the upper-level capacity configuration model and ensure that the fitness function of the upper-level capacity configuration model satisfies the constraints.

[0244] Generating offspring population R using eruption mechanisms T , the parent population Pop and its offspring population R T Merging to form population S T And based on the cooling process, the population S T Sort and evaluate population S T The quality of each solution;

[0245] Based on the dominance level and reference distance of each solution, from the population S T Select the best solution and generate the next generation parent population P op,T+1 The repeated eruption mechanism and cooling process continue to generate a new generation of parent populations until the convergence condition is met.

[0246] The final parent population P op The Pareto optimal solution of the upper-level capacity configuration model is used, and the final solution of the upper-level capacity configuration model is selected by gray target decision based on entropy weight method.

[0247] To facilitate understanding of the above technical solutions of the present invention, the following describes the establishment of a two-stage optimization configuration model (based on the impedance uncertainty of submarine cables and the transmission efficiency of submarine cables) in the annual operation scenario of offshore wind power in actual practice. The two-stage optimization configuration model is then solved to achieve offshore wind-storage configuration in detail.

[0248] To achieve optimal economic efficiency, system stability, and minimum submarine cable transmission loss for offshore wind power storage, this invention constructs a two-layer optimization configuration model for offshore wind power storage capacity allocation. The upper-layer capacity configuration model aims to minimize the annual comprehensive cost of offshore wind power storage, net load fluctuation, and voltage fluctuation, determining the configured capacity of the offshore wind power storage system and serving as input for the second-stage optimization operation model. The lower-layer optimization operation model aims to minimize the daily loss of submarine cable transmission lines.

[0249] minF1=C inv +C OM -B FLC -B loss -B cur (51)

[0250] Upper-layer capacity configuration model for offshore wind storage:

[0251] minF1=C inv,WT +C inv,BESS +C OM,WT +C OM,BESS -I I-P -I WT (52)

[0252] In the formula: C inv,WT and C inv,BESSC represents the investment costs of wind power and energy storage, respectively; OM,WT and C OM,BESS These represent the operation and maintenance costs of wind power and energy storage, respectively; I I-P Indicates the benefits of energy storage; I WT This indicates the revenue from selling wind power.

[0253] The expression for the investment cost of energy storage is:

[0254]

[0255] In the formula: τ represents the discount rate; y BESS Indicates the lifespan of energy storage; F P and F E These represent the unit power and unit capacity cost of energy storage, respectively; P BAT and E BAT These represent the configured power and configured capacity of the energy storage, respectively.

[0256] The expression for the investment cost of wind power is:

[0257]

[0258] In the formula: y WT Indicates the investment period for wind power; F WT P represents the unit investment cost of wind power; WT This indicates the configured capacity of wind power.

[0259] The expression for the operation and maintenance cost of energy storage is:

[0260]

[0261] In the formula: ρ OM,P and ρ OM,E P represents the operation and maintenance factor per unit power and per unit capacity, respectively; BESS and E BESS These represent the configured power and configured capacity of the energy storage, respectively.

[0262] The expression for the investment cost of wind power is:

[0263]

[0264] In the formula: ρ OM,WT This represents the operation and maintenance coefficient of wind power.

[0265] The expression for the benefits of energy storage is:

[0266]

[0267] In the formula: ω sell,t and ω pur,t K represents the electricity sales price and the electricity purchase price at time t, respectively;d This indicates the number of annual operational scenarios for offshore wind power; T k P represents the number of days corresponding to the k-th scenario; dis,t and P cha,t Let represent the discharge power and charging power of the energy storage at time t, respectively, where:

[0268]

[0269] In the formula: ω WT,t P represents the electricity price of offshore wind power at time t; WT,t This represents the configured capacity of wind power at time t.

[0270]

[0271] In the formula: L(t) represents the net load at time t; L(t-1) represents the net load at time t-1.

[0272]

[0273] In the formula: minF1, minF2, and minF3 represent the minimum optimization objectives of the upper-level capacity configuration model, namely, annual comprehensive cost, net load fluctuation, and voltage fluctuation, respectively; U i,j,t This represents the per-unit voltage value of the i-th node on the k-th typical day; N represents the average voltage at the i-th node on the k-th typical day; nodes Indicates the number of nodes.

[0274] Constraints:

[0275] Node voltage constraints:

[0276] U i,min ≤U i,t ≤U i,max (61)

[0277] In the formula: U i,max and U i,min These are the upper and lower limits of the voltage at node i, respectively; U i,t Let t represent the voltage at node i at time t.

[0278] Energy storage power and capacity constraints:

[0279]

[0280] In the formula: E BESS,max E BESS,min P BESS,max P BESS,min These represent the upper and lower limits of the energy storage configuration capacity and the upper and lower limits of the configuration power, respectively.

[0281] Node power balance constraints:

[0282]

[0283] In the formula: U j,t θ represents the voltage at node j at time t; ij,t G represents the voltage phase difference between node i and node j at time t; ij and B ij P represents the equivalent conductance and susceptance of the line between node i and node j; i (t) represents the active power of node i at time t; Q i (t) represents the reactive power of node i at time t.

[0284] Offshore wind power resource endowment constraints:

[0285] 0≤P WT ≤P WT,max (64)

[0286] In the formula: P WT,max This indicates the upper limit of physical resources for offshore wind power.

[0287] Lower-level optimized operation model:

[0288]

[0289] In the formula: P bg,t η represents the active power injected into the head end of the submarine cable at time t; hl,t K represents the transmission efficiency of the submarine cable at time t, considering the uncertainty of the line parameters; d This indicates the number of annual operating scenarios for offshore wind power.

[0290] Constraints:

[0291] Energy storage charge and discharge constraints:

[0292]

[0293] In the formula: γ cha and γ dis These represent the charging efficiency and discharging efficiency of energy storage, respectively; P BESS Indicates the configured power of energy storage; P cha,t and P dis,t Let t represent the charging power and discharging power of the stored energy at time t, respectively.

[0294] SOC constraints:

[0295] SOC min ≤SOC i (t)≤SOC max (67)

[0296] Where: SOC max and SOC min These represent the upper and lower limits of the State of Charge (SOC) for energy storage; SOC i (t) represents the SOC of the stored energy at time t.

[0297] SOC at time t:

[0298]

[0299] In the formula: Δt represents the charging and discharging time; SOC i (t-1) represents the SOC of the stored energy at time t-1.

[0300] Solving the two-stage optimal configuration model:

[0301] An improved Multi-Objective Geyser Algorithm (MOGA) is used to solve the upper-level model (upper-level capacity configuration model), and a solver is used to solve the lower-level model (lower-level optimization operation model), which specifically includes:

[0302] Input raw data such as load and branch parameters of each node, and offshore wind power parameters;

[0303] Set MOGA parameters and variable constraints;

[0304] Initialize a parent population P of size m. op Calculate the fitness functions of equations (52), (59), and (60), and ensure that the constraints of equations (61)-(64) are satisfied;

[0305] The offspring population R is generated using an eruption mechanism. T ;

[0306] Population P op and R T Merge into a population S of size 2m T And sort them using a cooling process;

[0307] Based on the dominance level and reference distance, select the m best solutions from 2m solutions to generate the next generation parent population P. op,T+1 ;

[0308] Continue the eruption and cooling process until the convergence condition is met, then return to the final parent population P. op As the Pareto solution of the upper-level model, the final solution is selected using gray target decision-making based on the entropy weight method.

[0309] The process of inputting the results from the upper-level model into the lower-level model and solving the lower-level model using a solver includes:

[0310] The process of passing the results of the upper-level model as input to the lower-level model typically refers to hierarchical optimization problems. The solver of the lower-level model (such as the CPLEX solver, Gurobi solver, etc.) is the mathematical tool used to solve this hierarchical optimization problem. The solver solves the lower-level model, and the results are fed back to the upper-level model. The upper-level model then makes corrections based on the results of the lower-level model, and the process is iterated repeatedly until convergence.

[0311] This invention uses a firefly forest clustering algorithm based on Pearson correlation coefficient to cluster annual operation scenarios of offshore wind power. To address the uncertainty of submarine cable impedance and ensure that the calculation results do not fluctuate excessively, an improved affine division method is used to propose a submarine cable transmission loss model that considers the uncertainty of submarine cable parameters. A two-stage optimization configuration model for offshore wind and energy storage is established. The first stage comprehensively considers the economics of energy storage, the net load fluctuation of the system, and voltage fluctuation; the second stage considers the transmission loss of the submarine cable. An improved geyser algorithm is used to solve this model.

[0312] The firefly forest algorithm based on Pearson correlation coefficient proposed in this invention solves the problems of traditional clustering techniques, such as the need to set a fixed number of neighbors, predefined number of clusters, and reliance on computationally intensive group iteration processes. It improves the accuracy and robustness of clustering results, eliminates the dependence on predefined number of clusters, and reduces computational complexity. It not only ensures the economy of offshore wind storage and the power quality of the system, but also makes the calculation of submarine cable transmission efficiency more accurate by considering the uncertainty of line parameters. At the same time, it uses submarine cable transmission loss as the objective function of the lower-level model, which can ensure the economy of offshore wind storage and the stability of the system while taking into account the transmission loss of submarine cables, and further ensures the economy of the planning scheme.

[0313] In summary, by utilizing the above-mentioned technical solution of this invention, the firefly forest clustering algorithm based on Pearson correlation coefficient achieves dynamic adjustment through adaptive neighborhood estimation. Each data point calculates its brightness according to its distribution characteristics, eliminating the need for manually setting the number of neighbors. This significantly simplifies parameter tuning and improves flexibility. It exhibits excellent scalability when processing large-scale datasets. Furthermore, it filters outliers using the interquartile range method, ensuring the stability of brightness calculation and the accuracy of clustering results. Therefore, it has significant advantages in handling complex data distributions and large-scale data, and is particularly suitable for practical applications requiring high efficiency and high precision. Moreover, this invention applies the improved firefly forest clustering algorithm to scene clustering, achieving higher performance compared to common clustering algorithms. The invention improves the robustness and stability of submarine cable lines. It employs affine mathematics to model the uncertainty of line impedance, resulting in a complex affine model of line impedance based on the uncertainty of submarine cable line impedance. Furthermore, it utilizes polynomial fitting to improve upon traditional affine division, overcoming the conservatism of the original affine division method with a slight loss of realism in subsequent affine calculations. Finally, it addresses the limitation of voltage complex affine numbers not being able to use traditional comparative complex moduli through power flow calculation and discrimination methods based on the complex affine model of line impedance. The invention derives a formula for the transmission efficiency of submarine cable lines considering the uncertainty of line parameters, which is more conservative than traditional derivation methods that assume fixed line impedance, thus more accurately characterizing the transmission efficiency of submarine cable lines under actual conditions.

[0314] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for configuring offshore wind power storage considering the uncertainty of wind power output and the efficiency of submarine cable transmission, characterized in that, The offshore wind storage configuration method includes: S1. Obtain the offshore wind power output dataset and use the firefly forest clustering algorithm based on Pearson correlation coefficient to cluster the offshore wind power output dataset to obtain the annual operation scenario of offshore wind power. S2. Establish a complex affine model of line impedance based on the uncertainty of submarine cable line impedance using affine mathematics techniques, and optimize the complex affine model of line impedance based on polynomial fitting techniques. S3. Use convergence discrimination technology to perform power flow calculation on the optimized line impedance complex affine model, and establish a submarine cable transmission efficiency model with uncertain line parameters based on the power flow calculation results. S4. Based on the annual operation scenario of offshore wind power, establish a two-stage optimization configuration model and solve the two-stage optimization configuration model to realize the offshore wind-storage configuration. Based on the annual operation scenario of offshore wind power, a two-stage optimization configuration model is established and solved to achieve the following offshore wind-storage configuration: S41. With the optimization objectives of minimizing the annual comprehensive cost, net load fluctuation, and voltage fluctuation of offshore wind storage, construct an upper-level capacity configuration model for offshore wind storage. S42. Using the upper-level capacity configuration model as input and minimizing the daily loss of submarine cable transmission lines as the optimization objective, construct the lower-level optimized operation model for offshore wind storage. S43. The improved geyser algorithm is used to solve the upper-level capacity configuration model, and the solver is used to solve the lower-level optimization operation model.

2. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 1, characterized in that, The process of acquiring offshore wind power output datasets and using the Pearson correlation coefficient-based firefly forest clustering algorithm to cluster these datasets to obtain annual operating scenarios for offshore wind power includes: S11. Obtain an offshore wind power output dataset containing several independently distributed data points, and use the Pearson coefficient to characterize the dissimilarity between data points; S12. Based on the dissimilarity between data points, iterate through each data point in the offshore wind power output dataset, and perform maximum likelihood estimation on the number of neighbors of the data point in each iteration to obtain the likelihood ratio of the comprehensive model. S13. Determine whether the likelihood ratio of the integrated model meets the preset conditions. If it meets the preset conditions, update the number of neighbors of the current maximum likelihood estimate and execute step S14. Otherwise, repeat the iteration process of the data points until the likelihood ratio of the integrated model meets the preset conditions. S14. Treat the data points as fireflies with adaptive brightness, cluster the fireflies to form a tree structure, merge the tree structures to generate a firefly forest, and obtain the annual operation scenario of offshore wind power.

3. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 2, characterized in that, The process of using data points as fireflies with adaptive brightness, clustering the fireflies to form a tree structure, and merging the tree structures to generate a firefly forest, yields the annual operation scenario for offshore wind power, including: S141. Treat the data points as fireflies, initialize the firefly parameters based on the distribution parameters of the predefined offshore wind power output dataset, and calculate the firefly brightness based on the firefly parameters. S142. Arrange the fireflies in descending order based on their brightness. Each firefly selects the nearest brighter firefly as a guide to obtain preliminary clustering results. Then, use a tree structure to store the preliminary clustering results to form a firefly tree. S143. Based on the luminescence interaction signals of firefly populations, firefly trees are merged to form a firefly forest, and the final clustering result is obtained. The final clustering result is used as the annual operation scenario for offshore wind power.

4. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 3, characterized in that, The step of treating data points as fireflies, initializing firefly parameters based on the distribution parameters of a predefined offshore wind power output dataset, and calculating firefly brightness based on the firefly parameters includes: S1411. Treat the data points as fireflies with adaptive brightness, and initialize the firefly parameters according to the distribution parameters of the offshore wind power dataset. The firefly parameters include brightness and the number of neighbors estimated by maximum likelihood. S1412. Calculate the interquartile range of the number of neighbors estimated by the maximum likelihood using the interquartile range formula, and calculate the upper and lower bounds of the number of neighbors based on the interquartile range of the number of neighbors. S1413. Based on the upper and lower bounds of the number of neighbors, perform interquartile range testing on the number of neighbors estimated by maximum likelihood, identify outlier neighbors in the number of neighbors estimated by maximum likelihood, and obtain the error of the maximum likelihood estimation density. S1414. Based on the error of the maximum likelihood estimation density, calculate the firefly brightness using the formula for calculating firefly brightness.

5. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 4, characterized in that, The process of sorting fireflies in descending order based on their brightness, with each firefly selecting the nearest brighter firefly as a guide to obtain preliminary clustering results, and storing these results in a tree structure to form a firefly tree includes: S1421. Sort the fireflies in descending order according to their brightness values, and iterate over each firefly and its maximum likelihood estimate neighbors. S1422. Compare the brightness value of the neighboring fireflies with the brightness value of the current firefly. If the brightness value of the neighboring firefly is greater than that of the current firefly, then the neighboring firefly becomes the middle firefly of the current firefly, and the current firefly is added to the corresponding firefly tree. S1423. If the brightness values ​​of all neighboring fireflies are less than that of the current firefly, it indicates that the current firefly is the root firefly, and the root firefly obtains a new cluster label and generates a new firefly tree, which is used as the local cluster center. S1424. Traverse the remaining fireflies. If the root firefly becomes an intermediate firefly among the remaining fireflies, then assign its cluster label to the remaining fireflies to obtain the preliminary clustering results. Use a tree structure to store the preliminary clustering results to form a firefly tree.

6. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 5, characterized in that, The expression for the complex affine model of line impedance based on the impedance uncertainty of submarine cable lines is as follows: In the formula, Let represent the complex affine model of the line impedance from node i to node j; ^ represents the affine form of the parameters; R i-j and X i-j These represent the line resistance and reactance values ​​from node i to node j, respectively. δ r,1 This refers to a parameter used to measure line resistance fluctuations.

7. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 6, characterized in that, The process of using convergence discrimination techniques to perform power flow calculations on the optimized line impedance complex affine model, and establishing a submarine cable transmission efficiency model with uncertain line parameters based on the power flow calculation results, includes: S31. Based on the known load and initial state of node j, obtain the current between node i and node j, and calculate the injected power of each node according to the complex affine model of current and line impedance. S32. Based on the injected power of each node, calculate the current and voltage drop between each node and other nodes; S33. Iteratively calculate the voltage difference of each node relative to the previous iteration, and use the affine number fluctuation domain overlap area comparison convergence discrimination technique to judge the similarity of the two iteration results, and obtain the power flow calculation results of the line impedance complex affine model. S34. Based on the power flow calculation results of the line impedance complex affine model, analyze the relationship between energy storage output and submarine cable head voltage, and establish a submarine cable transmission efficiency model with uncertain line parameters based on the relationship between energy storage output and submarine cable head voltage.

8. The offshore wind power storage configuration method considering wind power output uncertainty and submarine cable transmission efficiency according to claim 1, characterized in that, The method of using the improved geyser algorithm to solve the upper-level capacity allocation model includes: Initialize the parent population P op Calculate the fitness function of the upper-level capacity configuration model and ensure that the fitness function of the upper-level capacity configuration model satisfies the constraints. Generating offspring population R using eruption mechanisms T , the parent population P op and their descendants R T Merging to form population S T And based on the cooling process, the population S T Sort and evaluate population S T The quality of each solution; Based on the dominance level and reference distance of each solution, from the population S T Select the best solution and generate the next generation parent population P op,T+1 The repeated eruption mechanism and cooling process continue to generate a new generation of parent populations until the convergence condition is met. The final parent population P op The Pareto optimal solution of the upper-level capacity configuration model is used, and the final solution of the upper-level capacity configuration model is selected by gray target decision based on entropy weight method.

9. A method for configuring offshore wind power storage considering the uncertainty of wind power output and the efficiency of submarine cable transmission, as described in claim 8, is characterized in that... The expression for the lower-level optimized operation model is: In the formula, P bg,t This represents the active power injected into the head end of the submarine cable at time t; η hl,t K represents the transmission efficiency of the submarine cable at time t, considering the uncertainty of the line parameters; d This indicates the number of annual operational scenarios for offshore wind power; T k This represents the number of days corresponding to the k-th scenario.

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