Offshore wind plant adjustable capacity estimation method and system considering submarine cable line loss

Abstract

The invention provides an offshore wind plant adjustable capacity estimation method and system considering submarine cable line loss. According to the method, a wind power prediction model is constructed by adopting minimum positive Markov; constructing a nonlinear mapping relation between a load level and a line loss rate based on a wind power prediction result and submarine cable characteristics; carrying out optimization calculation by applying minimum positive Markov implementation in a random and deterministic environment, and generating an adjustable capacity estimation result; and quantizing uncertainty through an error propagation model, and providing a final result with a confidence interval. According to the method, the problem that the relation between wind power prediction and submarine cable line loss calculation cannot be effectively integrated in the prior art is solved, and the accuracy and reliability of the adjustable capacity estimation of the offshore wind plant are improved.

Description

Technical Field

[0001] This application relates to the field of wind power generation technology, and in particular to a method and system for estimating the adjustable capacity of offshore wind farms considering submarine cable losses. Background Technology

[0002] Offshore wind farms, as an important component of clean energy, have been widely used and developed globally. With the continuous increase in installed offshore wind power capacity, accurately estimating the adjustable capacity of wind farms to achieve efficient grid dispatch and economical operation has become a key focus for the industry.

[0003] Traditional wind farm capacity estimation techniques primarily rely on meteorological data and wind turbine characteristic curves for power prediction, such as short-term power prediction methods based on numerical weather prediction (NWP) models and historical data analysis methods based on statistical learning. These methods typically employ machine learning algorithms, such as support vector machines (SVM) or artificial neural networks (ANN), to establish a mapping relationship between wind speed and output power, thereby enabling the prediction of wind farm power generation.

[0004] Current advanced technologies employ multi-source data fusion, combining weather forecasts, historical operational data, and wind turbine status information to construct wind farm power prediction models. This technology simulates the power generation characteristics of wind farms by establishing complex mathematical models and uses real-time data for model correction to improve prediction accuracy. However, this technology has limitations in addressing the unique issue of submarine cable losses in offshore wind farms, failing to fully consider the impact of energy losses during submarine cable transmission on adjustable capacity estimation.

[0005] The main shortcomings of existing technologies are: on the one hand, they fail to effectively integrate the relationship between wind power prediction and submarine cable loss calculation, resulting in systematic errors in adjustable capacity estimation; on the other hand, under conditions of large random wind changes, existing deterministic models are unable to accurately reflect the actual adjustable capacity of offshore wind farms, lack an effective mechanism for handling uncertainties, and cannot meet the high-precision requirements of grid dispatch. Summary of the Invention

[0006] In view of this, this application provides a method and system for estimating the adjustable capacity of offshore wind farms that takes into account submarine cable losses, which solves the problem in the prior art that the relationship between wind power prediction and submarine cable loss calculation is not effectively integrated, resulting in systematic errors in the adjustable capacity estimation.

[0007] This application provides a method for estimating the adjustable capacity of offshore wind farms considering submarine cable losses, including: Historical operational and meteorological data of offshore wind farms are collected, and the state space of the wind farm is constructed using the least positive Markov model. The state transition probability matrix is ​​calculated to form a wind power prediction model. The prediction results of the wind power prediction model are received, and combined with the physical characteristic parameters of the submarine cable and environmental monitoring data, a nonlinear mapping relationship between load level and line loss rate is constructed to obtain the submarine cable line loss dataset. Based on the prediction results of the wind power prediction model and the submarine cable loss dataset, the minimum positive Markov implementation is used to perform optimization calculations in both stochastic and deterministic environments to generate adjustable capacity estimation results. The adjustable capacity estimation results are obtained, an error propagation model is established, confidence intervals are calculated and risk assessment is performed, and the final adjustable capacity estimation result with confidence intervals is output through an adaptive correction algorithm.

[0008] The construction of the wind farm state space using the aforementioned minimum positive Markov model includes: The historical operational data and meteorological data are received, and principal component analysis is used to perform dimensionality reduction processing to obtain the dimensionality-reduced feature data. Based on the reduced feature data and the slope change of the wind power curve, state quantization processing is performed to construct the wind farm state space.

[0009] Calculate the state transition probability matrix, including: Using the wind farm state space as input, the transition frequencies between each state are statistically analyzed to generate a state transition frequency matrix. The state transition frequency matrix is ​​normalized to ensure that the sum of probabilities is 1, and its positive definiteness is verified by matrix iteration to form the state transition probability matrix.

[0010] Constructing a nonlinear mapping relationship between load level and line loss rate includes: Input the physical characteristic parameters of the submarine cable and the rated voltage and rated current parameters, and use the equivalent circuit model to calculate the line loss characteristics under rated load to form the physical characteristic model of the submarine cable. By utilizing the line loss characteristics of the aforementioned submarine cable physical characteristic model and combining them with the environmental monitoring data, a correction coefficient calculation is performed to generate the submarine cable line loss dataset.

[0011] Using the line loss characteristics of the aforementioned submarine cable physical characteristic model, and combining the aforementioned environmental monitoring data, a correction factor calculation is performed, including: Receive the line loss characteristics of the submarine cable physical characteristic model, extract seawater temperature data, seawater salinity data and seabed topography data from the environmental monitoring data, and perform parameter correlation analysis; Using the results of the parameter correlation analysis, the line loss correction coefficient is calculated at one-hour intervals.

[0012] The least positive Markov implementation is used to perform optimization calculations in both stochastic and deterministic environments, including: Input the grid dispatch constraints and the prediction interval of the wind power prediction model, with the goal of maximizing the adjustable capacity of the wind farm and the rated capacity of the submarine cable as a constraint, and construct a mathematical model of the adjustable capacity of the wind farm considering line loss. Using the mathematical model and the least positive Markov implementation, iterative optimization is performed under two environments: deterministic power prediction and predictive power probability distribution, to form a deterministic optimal control strategy and a stochastic optimal control strategy.

[0013] Using the mathematical model and employing the least positive Markov implementation, iterative optimization is performed under two environments: predictive power determination and predictive power probability distribution. This includes: Input the deterministic optimal control strategy and the stochastic optimal control strategy, extract real-time load level data and reserve capacity data of the power grid, and calculate the fusion weight coefficient using the proportional allocation method; Based on the fusion weight coefficients, weighted calculations are performed on the deterministic optimal control strategy and the stochastic optimal control strategy respectively to generate the adjustable capacity estimation result.

[0014] Establish an error propagation model, including: Input the prediction results and measured power data of the wind power prediction model, the submarine cable loss dataset and measured line loss data, perform a comparison operation, and generate a power prediction error sequence and a line loss calculation error sequence; Using the power prediction error sequence and the line loss calculation error sequence, an error distribution function is constructed using probabilistic statistical simulation methods to form the error propagation model.

[0015] Obtaining the adjustable capacity estimation results, establishing an error propagation model, calculating the confidence interval, and conducting a risk assessment include: Input the sequence of differences between the adjustable capacity estimation results and the actual operating data, use the nearest neighbor clustering method to identify error features, and construct an error pattern feature library; Using the error pattern feature library, the current wind farm operating status feature vector is extracted, similarity matching is performed and coefficient correction is carried out to form the corrected adjustable capacity estimation result.

[0016] This application also provides an adjustable capacity estimation device for offshore wind farms that takes into account submarine cable losses, including: The prediction model building module is used to collect historical operation data and meteorological data of offshore wind farms, construct the wind farm state space using the least positive Markov implementation, calculate the state transition probability matrix, and form a wind power prediction model. The line loss calculation module is used to receive the prediction results of the wind power prediction model, combine the physical characteristic parameters of the submarine cable and environmental monitoring data, construct a nonlinear mapping relationship between the load level and the line loss rate, and obtain the submarine cable line loss dataset. The capacity estimation module is used to perform optimization calculations in stochastic and deterministic environments using the least positive Markov implementation based on the prediction results of the wind power prediction model and the submarine cable loss dataset, and generate adjustable capacity estimation results. The correction processing module is used to obtain the adjustable capacity estimation result, establish an error propagation model, calculate the confidence interval and perform risk assessment, and output the final adjustable capacity estimation result with confidence interval through an adaptive correction algorithm.

[0017] This application embodiment also provides a computer device, the computer device comprising: At least one processor; and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which enable the at least one processor to perform the above-described method for estimating the adjustable capacity of offshore wind farms that takes into account cable losses.

[0018] This application also provides a computer-readable storage medium storing computer instructions for causing a computer to execute the above-described method for estimating the adjustable capacity of an offshore wind farm, taking into account cable losses.

[0019] This application also provides a computer program product, including computer instructions, which, when executed by a processor, implement the steps of the above-described method for estimating the adjustable capacity of offshore wind farms considering cable losses.

[0020] This application has the following technical effects: By employing the least positive Markov realization technique to construct a wind power prediction model, the state space dimension can be effectively reduced while maintaining the model's prediction accuracy and improving the system's computational efficiency. By establishing a nonlinear mapping relationship between submarine cable loss and environmental factors and load levels, accurate calculation of submarine cable loss can be achieved, reducing systematic errors in traditional loss estimation. By applying the minimum positive Markov algorithm under both random and deterministic settings, and combining weight allocation and scenario analysis to achieve optimal fusion of results under the two settings, the adaptability and robustness of adjustable capacity estimation are improved. By using an error propagation model and an adaptive correction algorithm, the uncertainty of adjustable capacity estimation is quantified, and a final result with a confidence interval is provided, thus providing a more reliable basis for power grid dispatching. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings used in the embodiments will be briefly described below. These drawings are incorporated in and constitute a part of this specification. They illustrate embodiments conforming to this disclosure and, together with the specification, serve to explain the technical solutions of this disclosure. It should be understood that the following drawings only show some embodiments of this disclosure and should not be considered as limiting the scope. Those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of the method for estimating the adjustable capacity of offshore wind farms considering submarine cable losses, provided in the embodiments of this application; Figure 2 This is a flowchart illustrating the construction of the wind power prediction model in the embodiments of this application; Figure 3 This is a flowchart illustrating the precise calculation of submarine cable loss in the embodiments of this application; Figure 4 This is a flowchart of the adjustable capacity estimation based on the least positive Markov implementation in the embodiments of this application; Figure 5 This is a flowchart of the uncertainty quantification and correction process for adjustable capacity estimation results in the embodiments of this application; Figure 6 This is a system architecture diagram of an adjustable capacity estimation system for offshore wind farms that takes into account cable losses in the embodiments of this application. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. The components of the embodiments of this disclosure described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this disclosure provided in the accompanying drawings is not intended to limit the scope of the claimed disclosure, but merely represents selected embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the embodiments of this disclosure without inventive effort are within the scope of protection of this disclosure.

[0024] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0025] In this document, the term "and / or" merely describes a relationship, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0026] like Figure 1 As shown in the embodiment of this application, a method for estimating the adjustable capacity of an offshore wind farm considering submarine cable losses is provided, including: S1: Collect historical operation data and meteorological data of offshore wind farms, construct the wind farm state space using the least positive Markov model, calculate the state transition probability matrix, and form a wind power prediction model. The process of constructing the wind farm state space using the least positive Markov model includes: The historical operational data and meteorological data are received, and principal component analysis is used to perform dimensionality reduction processing to obtain the dimensionality-reduced feature data. Based on the reduced feature data and the slope change of the wind power curve, state quantization processing is performed to construct the wind farm state space.

[0027] S1.2: Calculate the state transition probability matrix, including: Using the wind farm state space as input, the transition frequencies between each state are statistically analyzed to generate a state transition frequency matrix. The state transition frequency matrix is ​​normalized to ensure that the sum of probabilities is 1, and its positive definiteness is verified by matrix iteration to form the state transition probability matrix.

[0028] S2: Receive the prediction results of the wind power prediction model, combine the physical characteristic parameters of the submarine cable and environmental monitoring data, construct a nonlinear mapping relationship between load level and line loss rate, and obtain the submarine cable line loss dataset. The nonlinear mapping relationship between load level and line loss rate is constructed, including: Input the physical characteristic parameters of the submarine cable and the rated voltage and rated current parameters, and use the equivalent circuit model to calculate the line loss characteristics under rated load to form the physical characteristic model of the submarine cable. By utilizing the line loss characteristics of the aforementioned submarine cable physical characteristic model and combining them with the environmental monitoring data, a correction coefficient calculation is performed to generate the submarine cable line loss dataset.

[0029] Using the line loss characteristics of the aforementioned submarine cable physical characteristic model, and combining the aforementioned environmental monitoring data, a correction factor calculation is performed, including: Receive the line loss characteristics of the submarine cable physical characteristic model, extract seawater temperature data, seawater salinity data and seabed topography data from the environmental monitoring data, and perform parameter correlation analysis; Using the results of the parameter correlation analysis, the line loss correction coefficient is calculated at one-hour intervals.

[0030] S3: Based on the prediction results of the wind power prediction model and the submarine cable loss dataset, the minimum positive Markov implementation is used to perform optimization calculations in both stochastic and deterministic environments to generate adjustable capacity estimation results. The least positive Markov implementation is used to perform optimization calculations in both stochastic and deterministic environments, including: Input the grid dispatch constraints and the prediction interval of the wind power prediction model, with the goal of maximizing the adjustable capacity of the wind farm and the rated capacity of the submarine cable as a constraint, and construct a mathematical model of the adjustable capacity of the wind farm considering line loss. Using the mathematical model and the least positive Markov implementation, iterative optimization is performed under two environments: deterministic power prediction and predictive power probability distribution, to form a deterministic optimal control strategy and a stochastic optimal control strategy.

[0031] Using the mathematical model and employing the least positive Markov implementation, iterative optimization is performed under two environments: predictive power determination and predictive power probability distribution. This includes: Input the deterministic optimal control strategy and the stochastic optimal control strategy, extract real-time load level data and reserve capacity data of the power grid, and calculate the fusion weight coefficient using the proportional allocation method; Based on the fusion weight coefficients, weighted calculations are performed on the deterministic optimal control strategy and the stochastic optimal control strategy respectively to generate the adjustable capacity estimation result.

[0032] S4: Obtain the adjustable capacity estimation result, establish an error propagation model, calculate the confidence interval and conduct a risk assessment, and output the final adjustable capacity estimation result with a confidence interval through an adaptive correction algorithm.

[0033] The establishment of an error propagation model includes: Input the prediction results and measured power data of the wind power prediction model, the submarine cable loss dataset and measured line loss data, perform a comparison operation, and generate a power prediction error sequence and a line loss calculation error sequence; Using the power prediction error sequence and the line loss calculation error sequence, an error distribution function is constructed using probabilistic statistical simulation methods to form the error propagation model.

[0034] Obtaining the adjustable capacity estimation results, establishing an error propagation model, calculating the confidence interval, and conducting a risk assessment include: Input the sequence of differences between the adjustable capacity estimation results and the actual operating data, use the nearest neighbor clustering method to identify error features, and construct an error pattern feature library; Using the error pattern feature library, the current wind farm operating status feature vector is extracted, similarity matching is performed and coefficient correction is carried out to form the corrected adjustable capacity estimation result.

[0035] like Figure 6 As shown in the embodiment of this application, an adjustable capacity estimation device for offshore wind farms that takes into account submarine cable losses is also provided, including: The prediction model building module is used to collect historical operation data and meteorological data of offshore wind farms, construct the wind farm state space using the least positive Markov implementation, calculate the state transition probability matrix, and form a wind power prediction model. The line loss calculation module is used to receive the prediction results of the wind power prediction model, combine the physical characteristic parameters of the submarine cable and environmental monitoring data, construct a nonlinear mapping relationship between the load level and the line loss rate, and obtain the submarine cable line loss dataset. The capacity estimation module is used to perform optimization calculations in stochastic and deterministic environments using the least positive Markov implementation based on the prediction results of the wind power prediction model and the submarine cable loss dataset, and generate adjustable capacity estimation results. The correction processing module is used to obtain the adjustable capacity estimation result, establish an error propagation model, calculate the confidence interval and perform risk assessment, and output the final adjustable capacity estimation result with confidence interval through an adaptive correction algorithm.

[0036] The specific implementation of the above method will be explained in detail below: like Figure 2 As shown, S1 specifically includes: S1.1: Multi-source data acquisition and preprocessing Based on the SCADA system and meteorological monitoring station of offshore wind farm, meteorological data including historical wind speed, wind direction, air pressure, temperature, humidity and wind turbine operating status data are collected. Through preprocessing techniques such as data cleaning, outlier detection and missing value imputation, a standardized multi-source dataset is output.

[0037] S1.2: Construction of the Minimal Positive Markov State Space Based on the standardized multi-source dataset preprocessed in step 1.1, the wind farm state space is constructed using principal component analysis (PCA) dimensionality reduction and state quantization techniques. The minimum positive Markov realization (MPPI) principle is then applied to determine the minimum dimensional set of state variables, and the Markov state transition model of the wind farm is output.

[0038] Based on the standardized multi-source dataset preprocessed in step S1.1, dimensionality reduction of the high-dimensional data is required to extract the core features of the wind farm's operating status. Specifically, through principal component analysis (PCA), the system extracts features from multivariate meteorological data including wind speed, wind direction, air pressure, and temperature, retaining the principal components with the largest explained variance, thereby reducing the data dimensionality. This process is similar to compressing complex weather conditions into a few key indicators, making subsequent modeling more efficient.

[0039] The dimensionality-reduced data undergoes state quantization. A non-uniform quantization method is employed, using finer quantization intervals in regions with steep slopes in the wind power curve (such as near the cut-in wind speed and rated wind speed), while employing larger quantization intervals in flatter regions. This ensures the accuracy of the state representation while controlling the size of the state space. This quantization strategy better captures the nonlinear characteristics of the wind farm power curve.

[0040] Next, the minimum positive Markov realization (MPPI) principle is applied to determine the minimum dimension of the state space. The core idea of ​​MPPI is to find the minimum set of state variables that can fully describe the dynamic characteristics of the system while maintaining its observability and controllability. This process involves constructing the Hankel matrix and singular value decomposition. By analyzing the singular value distribution, the minimum state dimension that can cover the main dynamic characteristics of the system is determined.

[0041] Based on a defined state dimension and quantization strategy, a Markov state transition model for wind farms is constructed. This model describes the dynamic behavior of a wind farm as a stochastic transition process from one state to another, where the state transition depends only on the current state and not on historical paths, conforming to the Markov property. Such a model can capture the stochastic characteristics of wind farm operation while maintaining controllable computational complexity.

[0042] S1.3: Calculation of the state transition probability matrix Based on the Markov state transition model constructed in step 1.2, the state transition probability matrix is ​​calculated by statistically analyzing the transition frequency between states in historical data, and its positive definiteness is verified. The calibrated state transition probability matrix is ​​then output.

[0043] Based on the Markov state transition model constructed in step S1.2, it is necessary to calculate the transition probabilities between each state. Specifically, this involves statistically analyzing historical data to calculate the frequency of the system transitioning from state i to state j, forming an initial state transition frequency matrix. This process is similar to statistically analyzing the frequency with which a wind farm transitions to various possible states in the next moment when it is in a specific state over a past period.

[0044] The initial frequency matrix is ​​normalized to ensure that the sum of all possible transition probabilities from any state is 1, forming a standard state transition probability matrix P. Each element P(i,j) of this matrix represents the conditional probability of the system transitioning from state i to state j, and is a core component of the Markov prediction model.

[0045] Verifying the positive definiteness of the transition matrix is ​​crucial for ensuring the effectiveness of the MPPI method. A positive Markov process requires its state transition matrix to be strictly positive definite, meaning that for any non-zero vector x, x^T·P·x>0. If the matrix is ​​found to be non-positive definite, it needs to be adjusted using regularization methods. Common methods include adding small diagonal elements or using Cholesky decomposition to reconstruct the matrix.

[0046] The accuracy of the adjusted state transition probability matrix is ​​validated using historical data. An initial state over a period of time is input into the model, and subsequent state changes are predicted based on the transition probability matrix. The prediction accuracy is then calculated by comparing this prediction with the actual state sequence. Based on the validation results, further fine-tuning of the transition probability parameters may be necessary. The final output is a calibrated state transition probability matrix, laying the foundation for subsequent power prediction.

[0047] S1.4: Wind Power Prediction Model Training and Validation Based on the state transition probability matrix calculated in step S1.3, and combined with meteorological forecast data, a stochastic Markov prediction model is trained. The accuracy of the model is evaluated through cross-validation and backtesting with historical data, and the validated wind power prediction model and its prediction results are output.

[0048] Based on the state transition probability matrix calculated in step S1.3, and combined with the latest weather forecast data, a stochastic Markov prediction model for wind power is established. Specifically, the weather forecast data is converted into an initial state probability distribution through the mapping relationship determined in step S1.2. Then, using the state transition probability matrix, the state probability distribution at different future times is predicted through matrix iteration, and the state probability distribution is converted into power prediction values ​​and their probability distributions.

[0049] Cross-validation was used to evaluate the model's predictive performance. Historical data was divided into training and test sets. The model was built using the training set data, and its performance was validated on the test set. Evaluation metrics included mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). By adjusting model parameters, such as state space partitioning and transition probability smoothing coefficients, the model was continuously optimized until satisfactory predictive accuracy was achieved.

[0050] Conduct backtesting using historical data to verify the model's predictive stability under different wind conditions and seasons. Pay particular attention to the model's performance under extreme weather conditions and sudden changes in wind farm power to assess its adaptability to anomalies. Based on the backtesting results, it may be necessary to make targeted adjustments to the prediction strategy under specific conditions, such as using a specialized prediction model during typhoon weather.

[0051] Based on the validation and backtesting results, the final wind power prediction model and its parameter settings were determined, and the latest meteorological forecast data were used to generate wind power prediction results for a future period. These prediction results include not only point prediction values ​​but also probability distribution information, fully reflecting the uncertainty of the prediction and providing basic data for subsequent submarine cable loss calculation and adjustable capacity estimation.

[0052] In one embodiment, the wind power prediction model is trained based on a state transition probability matrix, combined with meteorological forecast data to construct a stochastic Markov prediction model. The training process first converts the meteorological forecast data into an initial state probability distribution through a predetermined mapping relationship, then uses the state transition probability matrix to perform matrix iterative calculations to predict the state probability distribution at different future times, and finally converts these state probability distributions into power prediction values ​​and their probability distributions.

[0053] The setting of model parameters mainly involves several key aspects. First is the state space partitioning, which determines the level of detail in the Markov model. According to the patent description, the system employs a non-uniform quantization method, using a finer quantization interval in regions with steeper wind curve slopes (such as near the cut-in wind speed and rated wind speed), while using a larger quantization interval in flatter regions. This parameter setting can control the size of the state space while maintaining accuracy, thus improving computational efficiency.

[0054] Secondly, the smoothing coefficient for the transition probabilities needs to be set. Since real-world data may contain noise or outliers, the initially calculated transition probabilities need to be smoothed. The smoothing coefficient is usually determined through cross-validation to reduce the risk of overfitting while ensuring the positive definiteness of the matrix.

[0055] Model validation employs cross-validation, dividing historical data into training and test sets. Evaluation metrics include mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). By continuously adjusting these parameters, the system optimizes the model until satisfactory prediction accuracy is achieved.

[0056] Of particular note is the backtesting of the model using historical data to examine its predictive stability under different wind conditions and seasons. This step focuses specifically on the model's performance under extreme weather conditions and sudden changes in wind farm power, assessing its adaptability to anomalies. Based on the backtesting results, the system may employ specific prediction parameter settings for particular conditions (such as typhoon weather).

[0057] The final wind power prediction model not only outputs point prediction values ​​but also includes the probability distribution information of the predictions, fully reflecting the uncertainty of the predictions and providing basic data for subsequent submarine cable loss calculations and adjustable capacity estimations. This parameter setting that considers probability distribution enables the model to more comprehensively characterize the randomness of wind farm power generation characteristics, improving the reliability of the overall prediction system.

[0058] like Figure 3 As shown, S2 specifically includes: S2.1: Acquisition of Physical Characteristic Parameters and Model Construction of Submarine Cables Based on the technical specifications and measured data of submarine cables, physical characteristic parameters such as resistivity, inductance, capacitance, and insulation level are collected to establish an equivalent circuit model of the submarine cable and output the physical characteristic model of the submarine cable.

[0059] Based on the submarine cable technical specifications, basic physical parameters of the submarine cable are collected, including structural parameters such as conductor material, cross-sectional area, insulation material and thickness, and armor type, as well as electrical parameters such as rated voltage, rated current, and rated power. These parameters are the basic data for constructing the physical model of the submarine cable and can usually be obtained from the technical documents provided by the submarine cable manufacturer.

[0060] Through on-site testing or monitoring systems, actual measurement data of the submarine cable during operation is collected, including resistance, inductance, and capacitance values ​​under different load conditions, as well as the relationship between temperature and resistance. This measured data reflects the physical characteristics of the submarine cable in the actual marine environment and is more meaningful than the nominal values ​​in the specifications. Measurement methods include the four-terminal method for measuring resistance, an LCR meter for measuring inductance and capacitance, and an infrared thermal imager for monitoring temperature distribution.

[0061] Based on the collected parameters, an equivalent circuit model of the submarine cable is established. For submarine cables, a π-type equivalent circuit model is typically used, considering the cable's distributed resistance R, distributed inductance L, distributed capacitance C, and distributed conductance G. The π-type model treats the submarine cable as multiple cascaded π-type networks, each representing a small segment of the cable. This modeling approach can effectively describe the transmission characteristics of the submarine cable. Specifically, the relationship between the model parameters and the physical characteristics of the submarine cable is as follows: the distributed resistance R is related to the conductor material, cross-sectional area, and temperature; the distributed inductance L is related to the conductor geometry and permeability; the distributed capacitance C is related to the dielectric constant and geometric dimensions of the insulation material; and the distributed conductance G is related to the leakage characteristics of the insulation material.

[0062] The equivalent circuit model was calibrated and verified using measured data. The calculated electrical characteristics of the model were compared with the measured data, and the model parameters were adjusted using optimization algorithms such as the least squares method to minimize the error between the model's predicted values ​​and the measured values. The calibrated submarine cable physical characteristic model accurately reflects the electrical characteristics of the submarine cable under different operating conditions, laying the foundation for subsequent line loss calculations.

[0063] S2.2: Modeling the impact of environmental factors on submarine cable loss Based on the physical characteristic model of the submarine cable in step S2.1, combined with environmental monitoring data such as seawater temperature, salinity, and seabed topography, the influence of environmental factors on the cable loss is analyzed, an environment-loss relationship model is established, and an environmental correction coefficient is output.

[0064] Based on the physical characteristic model of the submarine cable in step S2.1, the influence mechanism of various environmental factors on the cable loss is analyzed. The main influencing factors of the marine environment include seawater temperature, seawater salinity, seabed topography, and ocean current velocity. These factors indirectly affect the electrical characteristics and loss level of the submarine cable by influencing its heat dissipation conditions, grounding resistance, and external mechanical stress. In particular, seawater temperature has a significant impact on conductor resistance. Based on the temperature coefficient of copper conductors being approximately 0.00393 / ℃, the resistance increases by approximately 0.393% for every 1℃ increase in temperature, thus leading to an increase in line loss.

[0065] Collect environmental monitoring data around offshore wind farms, including seasonal and diurnal variations in seawater temperature, salinity distribution, seabed topography, and ocean current velocity and direction. This data can be acquired through marine environmental monitoring stations, marine meteorological buoys, underwater robotic surveys, or satellite remote sensing. The temporal and spatial resolution of the data should meet the requirements for accurate modeling, typically requiring at least one year of continuous monitoring data to cover the complete seasonal variation cycle.

[0066] Based on collected environmental data and submarine cable physical characteristic models, relationship models between environmental factors and line loss parameters are established. For example, a temperature-resistance relationship model R(T)=R0[1+α(T-T0)] can be established, where R0 is the resistance value at a reference temperature T0 and α is the temperature coefficient; a seawater salinity-grounding resistance relationship model can be established; and a seabed topography-mechanical stress-resistance relationship model can be established, etc. These sub-models can be directly modeled using physical equations or learned from historical data through data-driven methods.

[0067] By integrating the effects of each sub-model, line loss correction coefficients are calculated for different environmental conditions. These correction coefficients reflect the proportion of line loss variation due to environmental factors relative to standard conditions. For example, line loss during high summer temperatures may be 15-20% higher than during low winter temperatures. The correction coefficients can be expressed as a function of environmental parameters K=f(T,S,G,...), where T represents temperature, S represents salinity, G represents topographic factors, etc. These environmental correction coefficients will play a crucial role in subsequent load-line loss mapping, ensuring accurate estimation of line loss under various environmental conditions.

[0068] S2.3: Nonlinear mapping of the relationship between load level and line loss Based on the wind power prediction results in step S1.4 and the environmental correction coefficient in step S2.2, a nonlinear mapping relationship between load level and line loss rate is established. The line loss rate under different loads is quantified by piecewise linear or polynomial fitting method, and the load-line loss mapping function is output.

[0069] Based on the wind power prediction results in step S1.4, the potential load range that the submarine cable can withstand is determined. Wind farm output fluctuates, and the submarine cable load can range from no load to full load; therefore, it is necessary to establish a line loss mapping relationship across the entire load range. Line loss issues are particularly prominent during peak wind farm output periods, when load levels are high and require close monitoring.

[0070] Considering the environmental correction coefficient obtained in step S2.2, the relationship between submarine cable load and line loss is analyzed under different environmental conditions. According to the principle of power transmission, line loss power is proportional to the square of the current (P=I²R), therefore, there is a nonlinear relationship between line loss and load level. However, in actual submarine cable systems, this relationship is more complex due to factors such as temperature effect, skin effect, and proximity effect. An accurate mapping relationship needs to be established through theoretical analysis combined with measured data.

[0071] Piecewise linear or polynomial fitting methods are used to quantify the line loss rate under different load ranges. For ranges with lower loads (e.g., <30% of rated capacity), the line loss rate changes relatively smoothly, and linear fitting can be used. For ranges with higher loads (e.g., >70% of rated capacity), the line loss rate increases more rapidly due to the increased resistance caused by temperature effects, and quadratic or cubic polynomial fitting can be used. The fitting function for each segment must ensure a smooth transition at the segmentation points to avoid abrupt changes in the line loss calculation. The mathematical expression for the fitting can be expressed as line loss rate η=f(P,K), where P is the load power and K is the environmental correction factor.

[0072] The established load-line loss mapping function was verified and fine-tuned. The actual load and measured line loss from historical operational data were compared and analyzed to calculate the prediction error of the mapping function. Based on the error characteristics, the function parameters were optimized and adjusted. Furthermore, the impact of cable aging on line loss needs to be considered; a time factor can be introduced to correct the line loss rate, reflecting the performance degradation of the cable over time. The verified and adjusted load-line loss mapping function will become the core tool for subsequent line loss calculations.

[0073] S2.4: Comprehensive Calculation and Verification of Submarine Cable Losses Based on the load-line loss mapping function in step S2.3, and combined with the actual operating data of the wind farm, the parameters of the line loss calculation model are optimized and the accuracy is verified. By comparing and analyzing the error between the theoretical calculation value and the measured value, the calibrated submarine cable line loss dataset is output.

[0074] Based on the load-line loss mapping function established in step S2.3, line loss calculations are performed for typical wind farm operating scenarios. Typical scenarios include full-load operation, partial-load operation, and low-wind-speed operation, covering the annual operating status of wind farms. For each scenario, considering seasonal environmental changes, line loss levels are calculated for different seasons such as summer and winter, forming a preliminary line loss dataset.

[0075] Collect actual operating data from the wind farm, including measured values ​​of active power, reactive power, voltage, and current at both ends of the submarine cable. Actual line loss data can be obtained by calculating the power difference between the cable's inlet and outlet. To ensure data reliability, data from stable operating periods needs to be selected to avoid measurement errors caused by rapid power changes. Simultaneously, record the environmental conditions during measurement, including seawater temperature, cable load level, and other relevant parameters.

[0076] The theoretically calculated line loss values ​​are compared and analyzed with the measured line loss values ​​to calculate the statistical characteristics of the error, including indicators such as mean error, standard deviation, and maximum error. Through error analysis, shortcomings in the line loss calculation model are identified, such as the recurring problem of large errors under certain specific conditions. To address these issues, the parameters of the load-line loss mapping function are optimized and adjusted using optimization algorithms such as least squares and gradient descent to make the theoretically calculated values ​​closer to the measured values.

[0077] Based on the optimized line loss calculation model, line loss data under various operating scenarios and environmental conditions are recalculated to form a calibrated submarine cable line loss dataset. This dataset includes not only point estimates but also the range of uncertainty in the estimates, reflecting the reliability of the line loss calculation. This dataset will serve as an important input for subsequent adjustable capacity estimation, ensuring accurate assessment of the available capacity of offshore wind farms while considering line losses. Furthermore, a line loss monitoring and model self-calibration mechanism is established. By continuously comparing measured and calculated values, the line loss model parameters are dynamically updated to maintain the long-term stability of the model's accuracy.

[0078] like Figure 4 As shown, S3 specifically includes: S3.1: Problem Modeling and Optimization Goal Setting Based on the wind power prediction results from step S1.4 and the submarine cable loss dataset from step S2.4, a mathematical model of the adjustable capacity of the wind farm considering line loss is established, the optimization objective function and constraints are set, and a formalized description of the optimization problem is output.

[0079] Based on the wind power prediction results from step S1.4 and the submarine cable loss dataset from step S2.4, a mathematical model is constructed to describe the adjustable capacity estimation problem of offshore wind farms considering line losses. This model needs to accurately characterize the relationship between wind power output, submarine cable loss, and adjustable capacity. Specifically, if the predicted wind farm output is P_pred(t) and the submarine cable loss rate is η(P,K), then the actual transmitted power... P_out(t) = P_pred(t)×(1-η(P_pred(t),K)) Where K is the environmental correction factor. This expression clearly demonstrates the impact of line loss on adjustable output capacity, laying the foundation for subsequent optimization calculations.

[0080] An optimization objective function needs to be defined. In grid dispatching, it is generally desirable for the adjustable capacity of offshore wind farms to both ensure the safe and stable operation of the grid and maximize the absorption of wind power. Therefore, the objective function can be set as maximizing the adjustable capacity of the wind farm while ensuring that it does not exceed the rated capacity of the submarine cable and meets the grid dispatching requirements. Mathematically, this can be expressed as: maximizing ∫P_adj(t)dt, where P_adj(t) is the adjustable capacity of the wind farm at time t, and is subject to the constraints P_adj(t)≤ P_out(t) and P_adj(t)≤ P_cap, where P_cap is the maximum adjustable capacity required by the grid. This objective setting considers both maximizing wind power utilization and grid security constraints.

[0081] Various constraints need to be clearly defined. In addition to the basic constraints mentioned above, the dynamic thermal capacity limit, voltage stability constraint, and power ramp-up rate limit of the submarine cable also need to be considered. The dynamic thermal capacity of the submarine cable depends on the ambient temperature and load history, and can be expressed as P_thermal(t) = f(T_env, P_history); the voltage stability constraint requires that the transmitted power cannot cause the voltage at the end of the submarine cable to exceed the limit; the power ramp-up rate constraint requires that |P_adj(t)-P_adj(t-1)| ≤ R_max, where R_max is the maximum allowable ramp-up rate. These constraints together constitute a complex optimization problem with multiple objectives and constraints.

[0082] The objective function and constraints described above are formalized into a standard optimization problem description, facilitating subsequent application of the MPPI control algorithm for solution. The optimization problem can be expressed as: given the predicted wind power output P_pred(t), the line loss model η(P,K), and various constraints, solve for the time series P_adj(t) such that: Maximize ∫P_adj(t)dt. This formal description clearly defines the variables, objective, and constraints of the optimization, providing a clear mathematical framework for subsequent algorithm design and implementation.

[0083] S3.2: Deterministic Implementation of the MPPI Control Algorithm Based on the optimization problem description in step S3.1, the MPPI control algorithm is applied under deterministic conditions. The optimal control strategy is calculated iteratively to solve the wind farm adjustable capacity optimization problem and output the adjustable capacity estimation results under deterministic conditions.

[0084] Based on the optimization problem description in step S3.1, the MPPI control algorithm is implemented in a deterministic environment. A deterministic environment assumes that the wind farm's output changes exactly as predicted, without considering prediction errors or random fluctuations. In this case, the problem can be simplified to a deterministic optimal control problem. The core idea of ​​the MPPI control algorithm is to sample multiple possible control trajectories and generate a probability-weighted optimal control strategy based on the performance score of each trajectory. Under deterministic settings, this process is more stable and efficient.

[0085] Construct the system state transition equations and control strategy space. The state transition equations describe the dynamic characteristics of the system state as a function of the control input. For the adjustable capacity problem of a wind farm, the state can include the current wind power output, submarine cable temperature, grid load, etc. The control strategy space defines the range and rate of change of the adjustable capacity. In practice, the control time domain can be discretized into several time intervals, with the adjustable capacity in each time interval serving as a control variable to form a control vector. U = [P_adj(1), P_adj(2), ..., P_adj(N)] Under the premise of satisfying various constraints, sampling is performed in the control vector space to generate multiple candidate control trajectories.

[0086] Performance evaluation is performed on each candidate trajectory. Evaluation metrics include wind power utilization, line loss level, and control stability. A comprehensive scoring function can be designed. J(U) = w1∫P_adj(t)dt-w2∫η(P_adj(t))dt-w3∫(P_adj(t)-P_adj(t-1))²dt Here, w1, w2, and w3 are weighting coefficients, reflecting the degree of importance attached to wind power utilization, line loss control, and stability, respectively. By calculating the score for each trajectory, the optimal control strategy can be identified. Furthermore, a penalty mechanism needs to be designed to reduce the weight of trajectories that violate constraints, ensuring that the final selected control strategy satisfies all constraints.

[0087] The optimal control policy is solved through an iterative optimization method. The MPPI algorithm employs a gradient-based iterative optimization process. In each iteration, the current policy is slightly perturbed to generate multiple candidate policies, and their performance is evaluated before updating the current policy.

[0088] S3.3: Random Setting Implementation of MPPI Control Algorithm Based on the optimization problem description in step S3.1 and the state transition probability matrix in step S1.3, the MPPI control algorithm is applied in a stochastic environment. Considering the uncertainty of wind speed and power prediction, the stochastic optimal control strategy is calculated, and the adjustable capacity estimation result under stochastic conditions is output.

[0089] Based on the optimization problem description in step S3.1 and the state transition probability matrix in step S1.3, the MPPI control algorithm is implemented under a stochastic environment. The stochastic environment considers the uncertainty of wind power prediction, which is more consistent with the actual operating characteristics of wind farms. Under the stochastic setting, wind power output is no longer a deterministic predicted value, but a probability distribution, which can be represented as P_pred(t) ~ N(μ(t), σ²(t)), where μ(t) is the predicted average, and σ²(t) is the predicted variance, reflecting the level of uncertainty in the prediction.

[0090] A stochastic state transition model is constructed. Unlike deterministic settings, state transitions under stochastic settings need to consider the impact of random disturbances. Based on the state transition probability matrix calculated in step S1.3, the stochastic transition characteristics of the system under different wind conditions can be described. In specific implementation, for each initial state, multiple possible state sequences are generated according to the transition probabilities, forming a probability tree that covers the possible future power output scenarios of the wind farm. This probability-based state prediction method can more comprehensively consider the randomness and volatility of wind power output.

[0091] Designing control strategies under stochastic environments is crucial. Unlike deterministic settings, control strategies under stochastic settings need to adapt to uncertainty. Here, a scenario-based stochastic optimal control method is adopted, where a control strategy is designed for each possible wind power output scenario, and the final control decision is obtained through probability weighting. The control strategy can be expressed as a conditional function P_adj(t) = f(P_pred(t), θ(t)), where θ(t) is the strategy parameter, which needs to be solved through optimization. For performance evaluation, the expected performance index E[J(U)] needs to be calculated, which is a probability-weighted average of the performance across all possible scenarios.

[0092] The control strategy parameters are optimized using the stochastic gradient descent method. The core of the stochastic MPPI algorithm is to progressively improve the control strategy through multiple sampling and evaluation. Each iteration first generates multiple wind power output scenarios, designs a control strategy for each scenario, evaluates its performance, and then updates the strategy parameters based on the performance score. After multiple iterations, the algorithm converges to a robust control strategy that can adapt to various wind power output scenarios, outputting an adjustable capacity estimate under stochastic conditions. This result takes into account the uncertainty of wind power forecasting, better reflects actual operational needs, and can maximize the utilization of wind power while ensuring grid security.

[0093] S3.4: Fusion of Deterministic and Randomized Results Based on the deterministic estimation results of step S3.2 and the stochastic estimation results of step S3.3, the optimal fusion of the results under the two settings is achieved through weight allocation and scenario analysis, and the estimated result of the adjustable capacity of the offshore wind farm that comprehensively considers line loss is output.

[0094] Based on the deterministic estimation results from step S3.2 and the stochastic estimation results from step S3.3, a systematic comparison and analysis are required. The estimation results under the deterministic setting are typically more aggressive, allowing for higher adjustable capacity, but facing the risk of wind power output falling short of expectations; the estimation results under the stochastic setting are more conservative, reserving more safety margins, but may lead to a waste of wind power resources. Comparing the differences between the two results and analyzing the advantages and disadvantages of the two methods under different wind conditions and time periods lays the foundation for subsequent result fusion.

[0095] A weight allocation strategy is designed based on the actual needs and risk tolerance of the power grid operation. Different power grid environments and dispatch objectives have different requirements for adjustable capacity. For example, during off-peak periods when the grid load is low, a more aggressive deterministic outcome can be adopted; while during peak periods when the grid is under pressure, a more conservative stochastic outcome is needed to ensure safety. The weight allocation can be expressed as... w_det(t) = f(load(t), reserve(t), risk_tolerance) Where load(t) is the grid load level, reserve(t) is the reserve capacity, and risk_tolerance is the risk tolerance. Through this dynamic weight allocation, an optimal balance between wind power utilization and system security can be achieved at different times.

[0096] Scenario analysis is conducted to evaluate system performance under different weight combinations. For various typical operating scenarios, such as high-wind-speed stability, low-wind-speed fluctuation, and extreme weather conditions, the system's operating state under different weights is simulated, and various indicators such as wind power utilization, submarine cable loss rate, and system reserve capacity are evaluated. Scenario analysis can identify the optimal weight combination that maximizes wind power utilization while ensuring system safety margins. This process can employ Monte Carlo simulation methods to generate a large number of random scenarios and statistically analyze performance indicators, yielding more comprehensive and objective evaluation results.

[0097] Based on a defined weighting strategy, the estimation results from deterministic and stochastic settings are fused to output a comprehensive estimate of the adjustable capacity of offshore wind farms, taking line losses into account. The fusion formula can be expressed as follows: P_adj(t) = w_det(t)×P_adj_det(t) + (1-w_det(t))×P_adj_rand(t) Where P_adj_det(t) is the estimation result under deterministic settings, and P_adj_rand(t) is the estimation result under stochastic settings. This fusion method considers both the efficient use of deterministic methods and the risk control of stochastic methods, enabling optimal estimation of wind farm adjustable capacity in dynamically changing environments. Furthermore, the fusion result should also include uncertainty assessments for dispatching departments to reference, such as providing confidence intervals for adjustable capacity, like the minimum adjustable capacity at a 90% confidence level, to help dispatchers make more informed decisions.

[0098] like Figure 5 As shown, S4 specifically includes: S4.1: Error Source Analysis and Uncertainty Propagation Based on the adjustable capacity estimation results in step S3.4, the error sources in wind power prediction and submarine cable loss calculation are analyzed. The error propagation law is studied by Monte Carlo simulation method, and the error propagation model is output.

[0099] Based on the adjustable capacity estimation results from step S3.4, various error sources affecting the estimation accuracy are systematically analyzed. The main error sources include wind power prediction errors, submarine cable loss calculation errors, and environmental parameter measurement errors. Wind power prediction errors are typically proportional to the prediction duration; the error rate for short-term predictions (1-4 hours) is between 5-15%, while the error rate for medium- and long-term predictions (4-24 hours) can reach 15-30%. Submarine cable loss calculation errors mainly stem from model simplification and parameter uncertainties, with typical errors between 3-8%. Environmental parameter measurement errors, such as seawater temperature measurement errors (around ±0.5℃), can lead to systematic biases in cable loss calculations. Quantifying the statistical characteristics of various error sources provides fundamental data for subsequent uncertainty propagation analysis.

[0100] An error propagation model is constructed to investigate how various error sources affect the final adjustable capacity estimation result. Monte Carlo simulation is employed, using extensive random sampling to simulate the error propagation process. Specifically, firstly, a large number of random error samples are generated based on the statistical characteristics of each error source; then, these error samples are substituted into the adjustable capacity estimation model to calculate the estimation result with errors; finally, the distribution characteristics of these results, such as mean, variance, and skewness, are statistically analyzed. This method can intuitively reflect the nonlinear characteristics of error propagation and is particularly suitable for handling uncertainty analysis in complex systems.

[0101] Analyze the sensitivity of different error sources to the final result. Sensitivity analysis can be performed using the controlled variable method, that is, considering only the influence of one error source at a time, keeping other error sources zero, and calculating the degree of influence of that error source on the final result. The sensitivity index can be defined as follows: S_i = (∂P_adj / ∂e_i)×(e_i / P_adj) Where e_i is the i-th error source, and S_i represents the change in the adjustable capacity estimation result by S_i% due to a 1% change in this error source. Through sensitivity analysis, the key error sources that have the greatest impact on the final result can be identified, providing targeted guidance for subsequent accuracy improvements.

[0102] Based on the error propagation analysis results, an error propagation model for adjustable capacity estimation is established. This model can predict the uncertainty range of the final estimation result according to the uncertainties of various input parameters. The model form can be an analytical expression, such as... P_adj_err = ∑(S_i×e_i)² This represents the square root of the weighted sum of squares of all error sources; it can also be an empirical model based on data, such as establishing a mapping relationship between error sources and the final error through regression analysis. This error propagation model will provide a theoretical basis for subsequent confidence interval calculations, help quantify the reliability of adjustable capacity estimation, and provide a risk assessment basis for power grid dispatching decisions.

[0103] S4.2: Confidence Interval Calculation and Risk Assessment Based on the error propagation model in step S4.1, the confidence interval of the adjustable capacity estimation result is calculated, and the scheduling risk is assessed according to different confidence levels, and the adjustable capacity estimation result with confidence interval is output.

[0104] Based on the error propagation model established in step S4.1, the probability distribution of the adjustable capacity estimation result is calculated. For each time point, the adjustable capacity estimate is no longer a fixed value, but a probability distribution, which can be described by the mean μ_adj(t) and the standard deviation σ_adj(t). According to the central limit theorem, when there are many independent error sources, the distribution of the final result usually approximates a normal distribution, i.e., P_adj(t) ~ N(μ_adj(t), σ_adj²(t)). If the error source distribution deviates significantly from normality, or if the system exhibits strong nonlinearity, other more suitable distribution forms need to be considered, such as the log-normal distribution, the Weibull distribution, etc. By fitting historical data, the most suitable distribution type and its parameters can be determined.

[0105] Based on the probability distribution, calculate the confidence intervals at different confidence levels. A confidence interval represents the range within which the true value will fall given a certain probability. For example, a 90% confidence interval means there is a 90% probability that the actual adjustable capacity will fall within this interval. For a normal distribution, the confidence interval at the α confidence level can be expressed as: [μ_adj(t) - z_(α / 2)×σ_adj(t), μ_adj(t) + z_(α / 2)×σ_adj(t)] Where z_(α / 2) is the quantile of the standard normal distribution. Commonly used confidence levels include 68% (±1σ), 90% (±1.645σ), 95% (±1.96σ), and 99% (±2.576σ). By calculating the confidence intervals at different time points and confidence levels, the uncertainty characteristics of adjustable capacity estimation can be comprehensively described.

[0106] Assessing dispatch risk based on confidence intervals. The main risk in power grid dispatch stems from actual available capacity falling below the dispatch plan, threatening power balance. Risk assessment first requires determining the risk acceptance criterion, such as the maximum acceptable probability of supply-demand imbalance for the power grid, typically between 1-5%. An appropriate confidence level is then selected based on the risk acceptance criterion; for example, if the risk acceptance criterion is 5%, then the lower limit of the 95% confidence level should be chosen as the dispatch basis. Furthermore, the severity of the risk's consequences must be considered. For instance, a higher risk is acceptable when reserve capacity is sufficient, while a more conservative risk strategy is needed when reserve capacity is tight. Through risk assessment, it can be determined which confidence level estimate should be used as the dispatch basis under different operating conditions.

[0107] By integrating the confidence interval with the risk assessment results, the adjustable capacity estimate with a confidence interval is output. This result representation provides both the best estimate (mean or median) and the uncertainty range (confidence interval), helping dispatchers to fully understand the reliability of the wind farm's adjustable capacity. Specifically, the format could be: the adjustable capacity estimate at time t is μ_adj(t) MW, with a 90% confidence interval of... [μ_adj(t) - 1.645×σ_adj(t), μ_adj(t) + 1.645×σ_adj(t)] MW The recommended dispatch value is μ_adj(t) - 1.645×σ_adj(t) MW (corresponding to a 10% risk level). This representation is both scientific and practical, effectively supporting grid dispatch decisions and balancing wind power utilization with system security.

[0108] S4.3: Construction of Historical Error Database and Pattern Recognition Based on the comparison between the confidence interval results of step S4.2 and the actual operating data, a historical error database is established, error patterns are identified through cluster analysis, and an error pattern feature library is output.

[0109] Based on the confidence interval results calculated in step S4.2 and the actual operating data, a historical error database is established. After each wind farm operation, the actual adjustable capacity data is collected and compared with the previous estimation results to calculate the error value e(t) = P_adj_real(t) - P_adj_est(t). Simultaneously, the operating environment at that time is recorded, such as wind speed range, wind direction stability, sea surface temperature, and grid load level. This data forms a structured historical error database, with each record containing a timestamp, predicted value, actual value, error value, confidence interval, and contextual characteristics. The database's time span should cover at least one full year to capture the impact of seasonal variations.

[0110] Statistical analysis of historical error data is crucial for identifying the fundamental characteristics of the errors. Statistical indicators include mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and maximum error. These indicators allow for the evaluation of the overall accuracy and stability of the estimation method. In particular, it is necessary to analyze the time-series characteristics of the errors, such as the presence of systematic bias, periodic fluctuations, or autocorrelation. For example, if the estimation results are found to be systematically low during specific time periods (such as early morning or evening), it may be necessary to adjust the prediction model for those periods. Furthermore, the validity of confidence intervals must be evaluated by calculating the frequency with which actual values ​​fall within different confidence intervals and verifying whether they match the theoretical probability.

[0111] Cluster analysis is used to identify error patterns. Historical error data is clustered according to contextual characteristics to identify specific conditions under which estimation errors are large or small. Commonly used clustering algorithms include K-means, hierarchical clustering, and DBSCAN. The purpose of cluster analysis is to identify key combinations of factors affecting estimation accuracy; for example, "high wind speed + rapid change + low temperature" may be a typical pattern leading to large errors. For each identified pattern, its error distribution characteristics are analyzed, including error magnitude, direction (positive / negative), and variability. This pattern recognition helps to understand the underlying causes of errors and provides guidance for targeted corrections.

[0112] Based on clustering analysis results, an error pattern feature library is constructed. Each pattern in the feature library includes a contextual feature description, error statistics, and a recommended correction strategy. For example, for the "high wind speed + rapid change + low temperature" pattern, the estimated value might be systematically overestimated by 20%. The recommended correction strategy under this condition is to multiply the estimated value by 0.8. The feature library should be self-updating, continuously optimizing and refining itself with the accumulation of new data. Furthermore, machine learning methods, such as random forests or support vector machines, can be used to establish a mapping model from contextual features to error correction coefficients, achieving more refined and automated error correction. This pattern recognition-based correction method can differentiate between different operating conditions, significantly improving the accuracy and reliability of the estimation.

[0113] S4.4: Adaptive Correction and Final Result Output Based on the error mode feature library in step S4.3, and combined with the current wind farm operating status, the adjustable capacity estimation results are dynamically corrected through an adaptive correction algorithm, and the final adjustable capacity estimation result with a confidence interval is output.

[0114] Based on the error pattern feature library obtained in step S4.3, an adaptive correction algorithm is designed. The core idea of ​​this algorithm is to identify the best-matching error pattern according to the current operating state of the wind farm and apply the corresponding correction strategy. Pattern matching can employ a nearest neighbor algorithm, which calculates the similarity between the current operating state and each pattern in the feature library, selecting the pattern with the highest similarity as a reference. The similarity can be based on the weighted Euclidean distance definition, such as sim(x,y) = ∑w_i(x_i-y_i)², where w_i is the weight of the i-th feature, reflecting the degree of influence of that feature on the error. After matching an appropriate pattern, the corresponding correction coefficients or correction functions are applied to adjust the preliminary estimation results.

[0115] Implement an adaptive learning mechanism for the correction algorithm. As new data accumulates, the error pattern feature library needs to be dynamically updated to adapt to the long-term changes in wind farm operating characteristics. Adaptive learning can be achieved through incremental learning, i.e., updating the statistical characteristics and correction strategy of the corresponding pattern each time new actual data is obtained. The update formula can be an exponentially weighted average, such as: s_new = α×s_actual + (1-α)×s_old Here, α is the learning rate, which controls the influence of new data. Through this adaptive learning, the system can gradually adapt to the effects of long-term factors such as equipment aging and seasonal changes, maintaining the long-term effectiveness of the correction.

[0116] The uncertainty of the corrected result needs to be reassessed. The correction process itself introduces new uncertainties, requiring a recalculation of the confidence interval. Here, the uncertainty of the original estimate and the uncertainty of the correction model can be combined using the uncertainty synthesis principle to calculate the overall uncertainty of the final result. The synthesis formula can be σ_final² = σ_original² + σ_correction², where σ_original is the standard deviation of the original estimate and σ_correction is the standard deviation of the correction model. This approach provides a more accurate uncertainty assessment, avoiding overconfidence or overconservatism. Furthermore, the validity of the corrected confidence interval needs to be evaluated to ensure that the probability of the actual value falling within the confidence interval matches the theoretical value.

[0117] Integrate all information to output the final adjustable capacity estimate with confidence intervals. The final result should include the following elements: (1) the best estimate at each time point, i.e., the point estimate after adaptive correction; (2) confidence intervals at different confidence levels (e.g., 68%, 90%, 95%), reflecting the range of uncertainty of the result; (3) recommended dispatch values ​​based on risk assessment, usually selecting the lower limit of an appropriate confidence level; and (4) pattern classification and reliability assessment of the current operating status to help dispatchers understand the credibility of the estimation results. This information should be presented in a clear and intuitive way, such as displaying the estimated values ​​and confidence intervals of the time series through charts, or displaying key indicators and risk levels using dashboards. This comprehensive and detailed representation of the results can maximize support for grid dispatch decisions and achieve scientific estimation and efficient utilization of the adjustable capacity of offshore wind farms.

[0118] This application also provides an adjustable capacity estimation device for offshore wind farms that takes into account submarine cable losses, including: The prediction model building module is used to collect historical operation data and meteorological data of offshore wind farms, construct the wind farm state space using the least positive Markov implementation, calculate the state transition probability matrix, and form a wind power prediction model. The line loss calculation module is used to receive the prediction results of the wind power prediction model, combine the physical characteristic parameters of the submarine cable and environmental monitoring data, construct a nonlinear mapping relationship between the load level and the line loss rate, and obtain the submarine cable line loss dataset. The capacity estimation module is used to perform optimization calculations in stochastic and deterministic environments using the least positive Markov implementation based on the prediction results of the wind power prediction model and the submarine cable loss dataset, and generate adjustable capacity estimation results. The correction processing module is used to obtain the adjustable capacity estimation result, establish an error propagation model, calculate the confidence interval and perform risk assessment, and output the final adjustable capacity estimation result with confidence interval through an adaptive correction algorithm.

[0119] This application embodiment also provides a computer device, the computer device comprising: At least one processor; and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which enable the at least one processor to perform the above-described method for estimating the adjustable capacity of offshore wind farms that takes into account cable losses.

[0120] This application also provides a computer-readable storage medium storing computer instructions for causing a computer to execute the above-described method for estimating the adjustable capacity of an offshore wind farm, taking into account cable losses.

[0121] This application also provides a computer program product, including computer instructions, which, when executed by a processor, implement the steps of the above-described method for estimating the adjustable capacity of offshore wind farms considering cable losses.

[0122] This application has the following technical effects: By employing the least positive Markov realization technique to construct a wind power prediction model, the state space dimension can be effectively reduced while maintaining the model's prediction accuracy and improving the system's computational efficiency. By establishing a nonlinear mapping relationship between submarine cable loss and environmental factors and load levels, accurate calculation of submarine cable loss can be achieved, reducing systematic errors in traditional loss estimation. By applying the minimum positive Markov algorithm under both random and deterministic settings, and combining weight allocation and scenario analysis to achieve optimal fusion of results under the two settings, the adaptability and robustness of adjustable capacity estimation are improved. By using an error propagation model and an adaptive correction algorithm, the uncertainty of adjustable capacity estimation is quantified, and a final result with a confidence interval is provided, thus providing a more reliable basis for power grid dispatching.

[0123] In some embodiments of this application, the prediction model construction module, line loss calculation module, capacity estimation module and correction processing module described above can be implemented as software modules running on a server or computer, or they can be implemented as hardware modules. The hardware modules can be implemented as application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), central processing units (CPUs), etc., which are not limited here.

[0124] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the following claims.

[0125] It should be understood that the present invention is not limited to the methods described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

[0126] This disclosure also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program performs the steps of the method and system for estimating the adjustable capacity of offshore wind farms considering cable losses, as described in the above-described method embodiments. The storage medium can be volatile or non-volatile computer-readable storage.

[0127] In addition, this disclosure also provides a computer program product, which stores a computer program. When the computer program is run by a processor, it executes the steps of the method and system for estimating the adjustable capacity of offshore wind farms considering submarine cable losses provided in any of the above embodiments of this disclosure. For details, please refer to the above method embodiments, which will not be repeated here.

[0128] The aforementioned computer program product can be implemented through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied in a computer storage medium, which can be a volatile or non-volatile computer-readable storage medium. In another optional embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0129] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices and apparatuses described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this disclosure, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. The apparatus embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interfaces; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0130] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0131] In addition, the functional units in the various embodiments of this disclosure can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0132] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this disclosure, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this disclosure. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0133] Finally, it should be noted that the above-described embodiments are merely specific implementations of this disclosure, used to illustrate the technical solutions of this disclosure, and not to limit it. The protection scope of this disclosure is not limited thereto. Although this disclosure has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this disclosure; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this disclosure, and should all be covered within the protection scope of this disclosure. Therefore, the protection scope of this disclosure should be determined by the protection scope of the claims.

Claims

1. A method for estimating the adjustable capacity of an offshore wind farm considering submarine cable losses, characterized in that, include: Historical operational and meteorological data of offshore wind farms are collected, and the state space of the wind farm is constructed using the least positive Markov model. The state transition probability matrix is ​​calculated to form a wind power prediction model. The prediction results of the wind power prediction model are received, and combined with the physical characteristic parameters of the submarine cable and environmental monitoring data, a nonlinear mapping relationship between load level and line loss rate is constructed to obtain the submarine cable line loss dataset. Based on the prediction results of the wind power prediction model and the submarine cable loss dataset, the minimum positive Markov implementation is used to perform optimization calculations in both stochastic and deterministic environments to generate adjustable capacity estimation results. The adjustable capacity estimation results are obtained, an error propagation model is established, confidence intervals are calculated and risk assessment is performed, and the final adjustable capacity estimation result with confidence intervals is output through an adaptive correction algorithm.

2. The method according to claim 1, characterized in that, The construction of the wind farm state space using the aforementioned minimum positive Markov model includes: The historical operational data and meteorological data are received, and principal component analysis is used to perform dimensionality reduction processing to obtain the dimensionality-reduced feature data. Based on the reduced feature data and the slope change of the wind power curve, state quantization processing is performed to construct the wind farm state space.

3. The method according to claim 1, characterized in that, Calculate the state transition probability matrix, including: Using the wind farm state space as input, the transition frequencies between each state are statistically analyzed to generate a state transition frequency matrix. The state transition frequency matrix is ​​normalized to ensure that the sum of probabilities is 1, and its positive definiteness is verified by matrix iteration to form the state transition probability matrix.

4. The method according to claim 1, characterized in that, Constructing a nonlinear mapping relationship between load level and line loss rate includes: Input the physical characteristic parameters of the submarine cable and the rated voltage and rated current parameters, and use the equivalent circuit model to calculate the line loss characteristics under rated load to form the physical characteristic model of the submarine cable. By utilizing the line loss characteristics of the aforementioned submarine cable physical characteristic model and combining them with the environmental monitoring data, a correction coefficient calculation is performed to generate the submarine cable line loss dataset.

5. The method according to claim 4, characterized in that, Using the line loss characteristics of the aforementioned submarine cable physical characteristic model, and combining the aforementioned environmental monitoring data, a correction factor calculation is performed, including: Receive the line loss characteristics of the submarine cable physical characteristic model, extract seawater temperature data, seawater salinity data and seabed topography data from the environmental monitoring data, and perform parameter correlation analysis; Using the results of the parameter correlation analysis, the line loss correction coefficient is calculated at one-hour intervals.

6. The method according to claim 1, characterized in that, The least positive Markov implementation is used to perform optimization calculations in both stochastic and deterministic environments, including: Input the grid dispatch constraints and the prediction interval of the wind power prediction model, with the goal of maximizing the adjustable capacity of the wind farm and the rated capacity of the submarine cable as a constraint, and construct a mathematical model of the adjustable capacity of the wind farm considering line loss. Using the mathematical model and the least positive Markov implementation, iterative optimization is performed under two environments: deterministic power prediction and predictive power probability distribution, to form a deterministic optimal control strategy and a stochastic optimal control strategy.

7. The method according to claim 6, characterized in that, Using the mathematical model and employing the least positive Markov implementation, iterative optimization is performed under two environments: predictive power determination and predictive power probability distribution. This includes: Input the deterministic optimal control strategy and the stochastic optimal control strategy, extract real-time load level data and reserve capacity data of the power grid, and calculate the fusion weight coefficient using the proportional allocation method; Based on the fusion weight coefficients, weighted calculations are performed on the deterministic optimal control strategy and the stochastic optimal control strategy respectively to generate the adjustable capacity estimation result.

8. The method according to claim 1, characterized in that, Establish an error propagation model, including: Input the prediction results and measured power data of the wind power prediction model, the submarine cable loss dataset and measured line loss data, perform a comparison operation, and generate a power prediction error sequence and a line loss calculation error sequence; Using the power prediction error sequence and the line loss calculation error sequence, an error distribution function is constructed using probabilistic statistical simulation methods to form the error propagation model.

9. The method according to claim 1, characterized in that, Obtaining the adjustable capacity estimation results, establishing an error propagation model, calculating the confidence interval, and conducting a risk assessment include: Input the sequence of differences between the adjustable capacity estimation results and the actual operating data, use the nearest neighbor clustering method to identify error features, and construct an error pattern feature library; Using the error pattern feature library, the current wind farm operating status feature vector is extracted, similarity matching is performed and coefficient correction is carried out to form the corrected adjustable capacity estimation result.

10. A device for estimating the adjustable capacity of an offshore wind farm considering submarine cable losses, characterized in that, include: The prediction model building module is used to collect historical operation data and meteorological data of offshore wind farms, construct the wind farm state space using the least positive Markov implementation, calculate the state transition probability matrix, and form a wind power prediction model. The line loss calculation module is used to receive the prediction results of the wind power prediction model, combine the physical characteristic parameters of the submarine cable and environmental monitoring data, construct a nonlinear mapping relationship between the load level and the line loss rate, and obtain the submarine cable line loss dataset. The capacity estimation module is used to perform optimization calculations in stochastic and deterministic environments using the least positive Markov implementation based on the prediction results of the wind power prediction model and the submarine cable loss dataset, and generate adjustable capacity estimation results. The correction processing module is used to obtain the adjustable capacity estimation result, establish an error propagation model, calculate the confidence interval and perform risk assessment, and output the final adjustable capacity estimation result with confidence interval through an adaptive correction algorithm.

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