Virtual power plant frequency modulation transaction optimization method and system based on fractional heavy-tailed noise modeling

Abstract

This invention provides a method and system for optimizing frequency regulation transactions in virtual power plants based on fractional heavy-tailed noise modeling, belonging to the field of power market technology. By systematically collecting and preprocessing grid frequency, market settlement, and generation data from virtual power plants, it achieves deep fusion and effective governance of multi-source data, providing high-quality, structured input for subsequent analysis and significantly improving data-driven decision-making capabilities. Using a voltage characteristic model, the energy and response time distribution required for dynamic and static frequency responses can be calculated separately, enabling quantitative and structured analysis of grid frequency regulation needs. This allows virtual power plants to more accurately assess the matching relationship between their own response potential and system requirements. This provides important technical support for the market-oriented and large-scale application of distributed resources under new power systems.

Description

Technical Field

[0001] This invention belongs to the field of electricity market technology, specifically relating to a virtual power plant frequency regulation trading optimization method and system based on fractional heavy-tailed noise modeling. Background Technology

[0002] Virtual power plants (VPPs) integrate distributed resources such as renewable energy, energy storage, and adjustable loads to achieve unified scheduling and optimized trading, making them "virtual power plants" that can provide stable power and services within the power grid. VPPs play an increasingly crucial role in improving grid reliability and promoting the consumption of new energy sources, especially in the field of frequency regulation ancillary services.

[0003] As the proportion of renewable energy increases, the inertia of the power system decreases, and frequency fluctuations intensify, making the need for rapid and precise frequency regulation increasingly urgent. Frequency regulation trading aims to maintain system frequency stability by adjusting the balance between power supply and demand, typically involving primary and secondary frequency regulation. Virtual power plants, with their aggregated distributed power sources, energy storage devices, and flexible loads, can participate in the frequency regulation market holistically, providing dynamic responses.

[0004] Currently, frequency regulation services have developed relatively mature technologies and market mechanisms, with energy storage systems (especially battery storage) playing a crucial supporting role due to their millisecond-level response capabilities. Smart grids optimize scheduling through real-time monitoring and automatic control, in collaboration with virtual power plants. Market operations typically employ auction mechanisms, with virtual power plants bidding and allocating resources based on price signals.

[0005] However, existing frequency regulation trading decisions are mostly based on traditional Gaussian processes or mean regression models, which are difficult to accurately describe the periodicity, long-range correlation and heavy-tailed characteristics in actual frequency data. This makes it easy for virtual power plants to underestimate the risk of extreme fluctuations when bidding, resulting in insufficient capacity allocation or overly conservative strategies, which affects returns and system stability.

[0006] Although some studies have attempted to improve tail fitting using fractional noise or Lévy stable distribution, they still lack an effective combination with market settlement cycles and frequency-related damping characteristics, and have not formed an optimization strategy that directly guides virtual power plant bidding.

[0007] Therefore, developing new modeling methods that can more realistically depict frequency dynamics and embed market mechanisms and scheduling constraints is of great significance for improving the economic efficiency and reliability of virtual power plants in the frequency regulation market. In the future, it is necessary to further combine data-driven approaches with physical laws to construct bidding and scheduling models suitable for high-frequency fluctuations and extreme scenarios, so as to fully leverage the supporting role of virtual power plants in new power systems. Summary of the Invention

[0008] The purpose of this invention is to overcome the aforementioned shortcomings and provide a virtual power plant frequency regulation trading optimization method and system based on fractional heavy-tailed noise modeling. Its core lies in establishing a compact statistical model that reflects market settlement periodicity, long-range frequency correlation, heavy-tailed characteristics of extreme fluctuations, and frequency-dependent damping effects. Based on this model, it provides capacity allocation and bidding decision support for virtual power plants. By solving this problem, the default risk of virtual power plants in market participation can be significantly reduced, profitability improved, and the overall robustness and flexibility of the power system enhanced.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, the present invention provides a virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling, comprising the following steps: Collect grid frequency data, market settlement data, and power generation data from the virtual power plant, and preprocess the collected virtual power plant data; The preprocessed virtual power plant data is input into a pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static power grid frequency response. Based on the energy demand and response time distribution of dynamic and static grid frequency response, combined with market revenue structure and risk constraints, the optimal bidding capacity of the virtual power plant is determined.

[0010] In the step of collecting grid frequency data, market settlement data, and power generation data of the virtual power plant and preprocessing the collected virtual power plant data, the collected grid frequency data includes real-time frequency measurements, frequency deviation, and rate of change; the market settlement data includes settlement cycle, clearing price, product type, and capacity price; and the power generation data includes the output of each distributed resource within the virtual power plant, the state of charge of energy storage, and adjustable capacity.

[0011] By establishing a unified data interface and time synchronization mechanism, the multi-source heterogeneous data of the collected virtual power plant can be accurately aligned in the time dimension.

[0012] The method for inputting the preprocessed data into a pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static frequency responses is as follows: Collect historical power grid frequency data, market settlement data, and power generation data; The collected historical power grid frequency data is cleaned and divided into non-random periodic components and random noise components. Periodic parameters are estimated for the periodic components to generate a time-sharing bidding strategy; noise characteristic parameters are estimated for the random noise components to obtain the continuous response demand and extreme event response capacity of the virtual power plant. The time-sharing bidding strategy generated by the periodic component, as well as the virtual power plant response demand and extreme event response capacity obtained from the analysis of the random noise component, are transferred to the damping modeling stage to construct a voltage characteristic model. A large-scale frequency data sample sequence was generated through Monte Carlo simulation, and the energy demand distribution and response duration distribution of the dynamic and static frequency responses were calculated using the constructed voltage characteristic model.

[0013] The method for estimating the periodic parameters of the periodic components and generating a time-sharing bidding strategy is as follows: For non-random periodic components, a time mapping relationship between power grid frequency data and settlement periods is established by dividing the data using market settlement data; Based on the established time mapping relationship between power grid frequency data and settlement periods, periodic parameters are estimated, and multi-scale periodic patterns of intraday, intraweek, and seasonality are fitted to obtain the periodic mean function. and scaling function ; Based on the obtained periodic mean function and scaling function Conduct periodic characteristic analysis and generate time-sharing bidding strategies; Based on the generated time-sharing bidding strategy, high-volatility and low-volatility periods are identified. By comparing and analyzing volatility, the differences in volatility across different periods are revealed and quantified. The driving effect of market settlement data on frequency volatility is obtained, and a time-sharing bidding strategy is generated.

[0014] The method for estimating the noise characteristic parameters of random noise components to obtain the continuous response demand and extreme event response capacity of the virtual power plant is as follows: The random noise components were estimated using a fractional heavy-tailed noise model to obtain the Hurst exponent h, which describes the long-range correlation of frequency deviations, and the Levy exponent, which describes the heavy-tailed characteristics of frequency data. ; The persistence of frequency deviation is analyzed based on the Hurst exponent h, and the long-term continuous response requirements and response duration of the virtual power plant are predicted. Based on the Levy index Analyze the probability distribution of extreme events and assess the emergency response capacity required by the virtual power plant to cope with extreme frequency shift events.

[0015] The method for analyzing the persistence of frequency deviation and predicting the long-term continuous response requirements and response duration of the virtual power plant based on the Hurst exponent h is as follows: When h > 0.5, the frequency deviation is determined to be persistent, and the system requires a longer response time to smooth it out; when h < 0.5, the frequency deviation is determined to be regressive, and the system requires a fast response but does not need to maintain continuous force for a long time; when h < 0.5, the frequency deviation is determined to be Brownian motion.

[0016] Based on the Levy index The method for analyzing the probability distribution of extreme events and assessing the emergency response capacity required by a virtual power plant to cope with extreme frequency shift events is as follows: when When <2, the frequency data distribution is judged to have fat-tailed characteristics; when When the value is ≥2, the virtual power plant is configured according to the conventional capacity.

[0017] In the step of transferring the time-sharing bidding strategy generated by the periodic components and the virtual power plant response demand and extreme event response capacity obtained from the analysis of random noise components to the damping modeling stage to construct the voltage characteristic model, the construction frequency of the voltage characteristic model depends on the damping function. This function takes different values ​​in different frequency deviation ranges to simulate the differences in controller triggering and response in actual power systems inside and outside the dead zone.

[0018] Secondly, the present invention provides a virtual power plant frequency regulation trading optimization system based on fractional heavy-tailed noise modeling, comprising: The data acquisition and preprocessing module is used to collect grid frequency data, market settlement data, and power generation data from the virtual power plant, and to preprocess the collected virtual power plant data. The calculation module is used to input the pre-processed virtual power plant data into the pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static power grid frequency response. The implementation module is used to determine the optimal bidding capacity of the virtual power plant based on the energy demand and response time distribution of the dynamic and static grid frequency response, combined with the market revenue structure and risk constraints.

[0019] Compared with the prior art, the present invention has the following beneficial effects: This invention provides a method and system for optimizing frequency regulation trading in virtual power plants based on fractional heavy-tailed noise modeling. By systematically collecting and preprocessing grid frequency, market settlement, and generation data from virtual power plants, it achieves deep fusion and effective governance of multi-source data, providing high-quality, structured input for subsequent analysis and significantly enhancing data-driven decision-making capabilities. Using a voltage characteristic model, the energy and response time distributions required for dynamic and static frequency responses can be calculated separately, enabling quantitative and structured analysis of grid frequency regulation demands. This allows virtual power plants to more accurately assess the matching relationship between their response potential and system requirements. Through multi-level data processing, refined modeling, and risk-reward balancing, it significantly improves the bidding competitiveness and operational efficiency of virtual power plants in the frequency regulation market, providing crucial technical support for the market-oriented and large-scale application of distributed resources under the new power system.

[0020] Furthermore, by decomposing historical frequency data into periodic components and random noise components, and estimating parameters separately, it is possible to simultaneously take into account the regular trends and uncertain fluctuations of power grid frequency changes, thereby generating a time-sharing bidding strategy that is more in line with actual operating scenarios, and reasonably reserving response capacity to cope with extreme events.

[0021] Furthermore, by generating a large-scale frequency sample sequence through Monte Carlo simulation and combining it with a voltage characteristic model to calculate the response energy and duration distribution, the effectiveness of the strategy was verified in a near-realistic random environment. This improved the robustness and adaptability of the bidding scheme and provided reliable simulation support for actual operation.

[0022] Furthermore, through frequency-dependent damping modeling, this invention can support virtual power plants in formulating differentiated response strategies in different frequency ranges, thereby improving overall flexibility. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a flowchart of the periodic modeling process in this invention; Figure 3 This is a timing diagram of the power grid frequency in Embodiment 2 of the present invention; Figure 4 This is a diagram showing the periodic modeling results of Embodiment 2 in this invention; Figure 5 This is a high and low fluctuation period diagram of Embodiment 2 of the present invention; Figure 6 This is a random noise distribution diagram of Embodiment 2 in this invention; Figure 7 This is a comparison chart of cumulative revenue in Example 2 of the present invention; Figure 8This is a comparison chart of bidding capacity strategies at different time periods in Embodiment 2 of the present invention. Detailed Implementation

[0024] To further understand the content of this invention, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0025] Example 1 like Figure 1 As shown, a virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling includes the following steps: S1: Collect grid frequency data, market settlement data, and power generation data from the virtual power plant, and preprocess the collected virtual power plant data; S2: Input the pre-processed virtual power plant data into the pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static power grid frequency response; S3: Based on the energy demand and response time distribution of dynamic and static grid frequency response, combined with market revenue structure and risk constraints, determine the optimal bidding capacity of the virtual power plant.

[0026] Specifically, in S1, grid frequency data, market settlement data, and power generation data of the virtual power plant are collected first. By establishing a unified data interface, the precise alignment of frequency data and market event data in the time dimension is ensured.

[0027] The data acquisition phase is the fundamental step for virtual power plants to participate in the grid frequency response market. It mainly collects three types of core data: grid frequency data (including real-time frequency measurements, frequency deviations and rates of change, sourced from SCADA systems and PMU devices), market settlement data (including settlement cycles, clearing prices, product types and capacity / energy prices, sourced from power trading platforms and ancillary service markets), and generation data (including output of each distributed resource within the virtual power plant, energy storage status of charge and adjustable capacity, sourced from the energy management system).

[0028] By establishing a unified data interface and time synchronization mechanism, precise alignment of multi-source heterogeneous data in the time dimension is achieved. After preprocessing steps such as anomaly detection, quality control, and data cleaning, the integrity and reliability of the data are ensured.

[0029] Specifically, in S2, the preprocessed data is input into a pre-built voltage characteristic model to calculate the energy demand and response duration distribution of dynamic and static frequency responses. This reflects the driving effect of the market settlement mechanism on frequency fluctuations. This process can reveal the differences between high-fluctuation and low-fluctuation periods, providing a reference for the time-of-use bidding strategy of virtual power plants. The specific method is as follows: S21: Collect historical power grid frequency data, market settlement data, and power generation data.

[0030] These high-quality data play three key roles in subsequent processes: First, they provide a foundation for periodic modeling by identifying the regular impact of market mechanisms on frequency fluctuations through the correspondence between historical frequency data and market settlement periods; second, they provide samples for random noise modeling by estimating long-range correlations and extreme event characteristic parameters through statistical analysis of frequency sequences; and third, they provide constraints for bidding optimization decisions. The technical parameters and responsiveness in the power generation data directly determine the range of available bidding capacity and performance capabilities of the virtual power plant, while market price data is the core input for constructing the revenue function, thus supporting the entire closed loop from data-driven modeling to market decision optimization.

[0031] S22: Clean the collected historical power grid frequency data, divide the cleaned data into non-random periodic components and random noise components, estimate the periodic parameters of the periodic components to generate a time-sharing bidding strategy, and estimate the noise characteristic parameters of the random noise components to obtain the continuous response demand and extreme event response capacity of the virtual power plant.

[0032] 1) The method for estimating the periodic parameters of periodic components is as follows: For non-random periodic components, a time mapping relationship between power grid frequency data and settlement periods is established by dividing the data using market settlement data; Based on the established time mapping relationship between power grid frequency data and settlement periods, periodic parameters are estimated, and multi-scale periodic patterns of intraday, intraweek, and seasonality are fitted to obtain the periodic mean function. and scaling function ; Based on the obtained periodic mean function and scaling function Conduct periodic characteristic analysis and generate time-sharing bidding strategies; Based on the generated time-of-use bidding strategy, high-fluctuation periods (such as peak load, renewable energy output fluctuations, and market settlement thresholds) and low-fluctuation periods (such as low nighttime loads, stable output periods, and the middle of the settlement cycle) are identified. By comparing fluctuations and revealing mechanisms, the differences in fluctuations across different periods are quantified, and the driving effect of the market settlement mechanism on frequency fluctuations is obtained. Finally, a time-of-use bidding strategy reference is generated, suggesting increasing bidding capacity and risk premiums for high-fluctuation periods and optimizing capacity configuration to reduce costs for low-fluctuation periods. The periodic model parameters, time period division results, and bidding strategy suggestions are output to the subsequent modeling stage, providing key basis for the accurate response and revenue optimization of virtual power plants.

[0033] 2) The method for modeling random noise components is as follows: The random noise components were estimated using a fractional Levy noise model to obtain the Hurst exponent h, which describes the long-range correlation of frequency deviations, and the Levy exponent, which describes the heavy-tailed characteristics of the frequency data. ; Based on the Hurst exponent h, the persistence of frequency deviation is analyzed, and the long-term continuous response demand and response duration required by the virtual power plant are predicted accordingly. When h > 0.5, the frequency deviation is considered persistent, meaning that past increments are positively correlated with future increments. If the frequency deviation continues to deviate, it tends to continue to deviate, and the system needs a longer response time to smooth it out. When h < 0.5, the frequency deviation is considered regressive, meaning that the system tends to correct in the opposite direction. The frequency deviation fluctuates sharply but will not deviate unidirectionally for a long time. The system needs a fast response but does not need long-term continuous output. When h = 0.5, the frequency deviation is considered to be Brownian motion, without long-term memory. Past increments have no impact on the future, meaning there is neither persistence nor anti-persistence. The next change cannot be predicted using historical trends.

[0034] Based on the Levy index Analyze the probability distribution of extreme events and assess the emergency response capacity required by the virtual power plant to cope with extreme frequency drift events; when When <2, the frequency data distribution is judged to have fat-tailed characteristics, and the probability of extreme events is greater than that of a Gaussian distribution; when At time 2, the frequency data distribution is close to a Gaussian distribution, and the probability of extreme events can be predicted using traditional statistical methods. The virtual power plant can be configured according to conventional capacity.

[0035] By combining the aforementioned long-term continuous response requirements with the aforementioned emergency response capacity, a decision-making basis is provided for the capacity bidding, risk management, and performance guarantee of virtual power plants. This ensures that virtual power plants can both grasp normal fluctuation patterns and cope with extreme scenario challenges when facing uncertainties.

[0036] S23: The time-sharing bidding strategy generated by the periodic component, as well as the virtual power plant response demand and extreme event response capacity obtained from the analysis of the random noise component, are transferred to the damping modeling stage to construct a voltage characteristic model. Construction of voltage characteristic model using frequency-dependent damping function This function takes different values ​​in different frequency deviation ranges to simulate the differences in controller triggering and response in real power systems within and outside the dead zone. This method can more accurately reflect the dynamic characteristics of power systems under different deviation amplitudes, providing theoretical support for setting segmented response strategies for virtual power plants during bidding.

[0037] S24: A large-scale frequency data sample sequence is generated through Monte Carlo simulation. The energy demand distribution and response time distribution of the dynamic and static frequency responses are calculated using the constructed voltage characteristic model. This distribution information can provide a quantitative basis for the participation strategy of virtual power plants in different market products.

[0038] Specifically, in S3, the optimal bidding capacity of the virtual power plant is determined based on the energy demand and response duration distribution of dynamic and static frequency responses, combined with the market revenue structure and risk constraints.

[0039] By combining the market's revenue structure and default penalty mechanism, a bidding optimization model is established with the goal of maximizing expected profits. By setting risk tolerance constraints, the optimal bidding capacity, energy commitment value, and required margin are automatically calculated to ensure that the virtual power plant maximizes its profits within an acceptable risk range.

[0040] Example 2 Based on the above process, a scenario for optimizing bidding decisions in the regional power grid frequency response market using a virtual power plant was constructed: First, in the data acquisition phase, 30 days of power grid frequency time-series data were simulated and generated (sampling frequency 10 seconds, including intraday / weekly periodic characteristics and long-range correlated random noise), such as... Figure 3 As shown, the power grid frequency time series data for the previous seven days is presented, demonstrating the original acquisition results of some power grid frequency data. This verifies that the frequency fluctuations have obvious periodic characteristics (intra-day repetition pattern), with a fluctuation range between 49.96-50.06Hz, which is consistent with the actual operation characteristics of the power grid. The frequent crossing of dead zone boundaries indicates that frequent responses from the virtual power plant are required.

[0041] The blue waveform in the figure represents the measured grid frequency data (Hz), sampled every 10 seconds. The red dashed line represents the standard frequency baseline of 50Hz. The orange dashed line represents the dead zone boundary (±0.015Hz), i.e., 49.985Hz and 50.015Hz. Market settlement data (capacity and energy prices within a 15-minute settlement cycle) and virtual power plant resource data (5MW photovoltaic + 2MW / 2MWh energy storage + 3MW controllable load) are used, and time alignment ensures accurate matching of multi-source data within the settlement window.

[0042] In the periodic modeling phase, pandas was used for data grouping and statistical analysis to estimate the periodic mean function μ(t) and scaling function σ(t) for 24 hours within the day. High volatility periods (such as the morning and evening load peaks of 8-10 am and 18-22 pm) and low volatility periods (such as 1-5 am at night) were successfully identified, revealing the mechanism characteristics of increased volatility at the boundary of the market settlement window.

[0043] Figure 4The core results of the periodic modeling phase are showcased, namely the two-parameter characterization of intraday periodic patterns. The purple curve μ(t) in the figure represents the periodic mean function, ranging from -0.012 to +0.026 Hz, exhibiting sinusoidal characteristics and reflecting the systematic variation of frequency deviation. It reaches negative peaks at dawn and midnight (lower frequency, corresponding to load troughs), while positive peaks occur during morning and evening peaks (higher frequency, corresponding to rapid load increases), directly corresponding to the intraday characteristics of the power load curve. The green curve σ(t) in the figure represents the scaling function, ranging from 0.003 to 0.006 Hz, characterizing the time-varying characteristics of frequency fluctuation amplitude. It can be seen that the standard deviation increases significantly during periods of intense load transition (morning and evening peaks), indicating more severe and unpredictable frequency fluctuations, while the standard deviation decreases to its lowest point during periods of stable load (nighttime troughs and afternoon stability). The program uses a two-level statistical aggregation method to first group the 30-day data by hour (forming 24 time groups, each with approximately 120 samples), and then perform a second average on the mean and standard deviation within each group. This eliminates the influence of intraday random fluctuations, extracts stable intraday periodic patterns, and effectively compresses massive amounts of raw data into 24 concise periodic parameters.

[0044] The cross-analysis of these two curves reveals the dual driving effect of market settlement mechanisms and load curves on frequency fluctuations, among which... Reflecting predictable systematic shifts, Reflecting the intensity of unpredictable random fluctuations, the accurate identification of this periodic pattern provides a scientific basis for virtual power plants to formulate time-of-use differentiated bidding strategies. During periods of high volatility, a conservative strategy can be adopted to reduce the bidding capacity, while during periods of low volatility, an aggressive strategy can be adopted to increase the bidding capacity, thereby maximizing profits under controllable risks.

[0045] Figure 5 The results of identifying high and low fluctuation periods were presented, demonstrating the results based on... Intelligent classification of functions, and Figure 4 Similarly, the results of periodic modeling are also demonstrated. The height of the bars in the figure represents the standard deviation of the frequency deviation for each time period (i.e., Figure TwoThe green curve represents the value of σ(t). Red bars indicate high-fluctuation periods, mainly concentrated between 0-1 AM, 8-11 AM, and 6-11 PM. The standard deviation of these periods exceeds the threshold of 0.0062 Hz, corresponding to periods of drastic load changes (sudden load drops at night, rapid morning peak increases, and sustained high evening peaks) and market settlement thresholds, characterized by drastic and unpredictable frequency fluctuations. Green bars represent low-fluctuation periods, mainly distributed between 1-7 AM and 12-5 PM. The standard deviation of these periods is below the threshold, corresponding to stable load periods (stable operation during nighttime lows and afternoon load plateaus), with smaller and more predictable frequency fluctuations. The technical solution uses the 70th percentile of the standard deviation distribution as an adaptive classification threshold (black dashed line in the figure). All periods with standard deviations exceeding this threshold are marked as high-fluctuation (red), and those below are marked as low-fluctuation (green). This statistical thresholding method ensures the objectivity and robustness of the classification, avoiding bias from subjective human judgment.

[0046] Figure 5 and Figure 4 The periodic modeling results have a corresponding relationship. First, Figure 5 yes Figure 4 Green curve The binary classification results transform the continuous volatility function into discrete high and low volatility labels, facilitating subsequent bidding decisions. Secondly, Figure 5 The classification threshold is directly based on Figure 4 middle The statistical distribution characteristics are determined, and the data sources of both are consistent and mutually corroborative.

[0047] Figure 6 This paper showcases the core results of the random noise modeling phase and verifies the heavy-tailed characteristic of the noise distribution. The blue histogram in the figure represents the removal of periodic components. The actual probability distribution of the extracted random noise is shown on the horizontal axis, which represents the noise value range (-0.03 to +0.02 Hz), and the vertical axis represents the frequency statistics. The red smooth curve represents the theoretical normal distribution curve fitted based on the same mean and standard deviation parameters.

[0048] A comparison clearly reveals a significant difference between the actual distribution (blue) and the normal distribution (red): In the central region of the distribution (-0.01 to +0.01 Hz), the peak height of the blue histogram is significantly higher than that of the red curve, indicating a higher frequency of small fluctuations. However, in the tail region of the distribution (|noise value|>0.015 Hz), the blue histogram maintains a high frequency at both ends, while the red normal curve rapidly decays to near zero. This "sharp in the middle, thick at both ends" shape is a typical characteristic of a heavy-tailed distribution. The kurtosis of 0.33 is marked as positive in the figure, but more importantly, the probability at the tail is significantly higher than the normal assumption. The actual probability of extreme events (exceeding ±3 standard deviations) is approximately 0.85%, far exceeding the theoretical value of 0.27% for the normal distribution, more than three times the latter. The technical solution successfully separated this random noise component by subtracting the estimated periodic mean function μ(t) from the original frequency deviation. Then, statistical analysis was performed on approximately 260,000 noise sample points to draw this probability density distribution map, which was then compared and verified with a normal distribution with the same parameters.

[0049] This discovery has significant practical implications. If virtual power plants make bidding decisions based on the traditional normal distribution assumption, the probability of extreme frequency deviation events will be severely underestimated. For example, when the frequency deviation exceeds 0.02Hz, an emergency response needs to be initiated. The normal distribution assumption considers this situation extremely rare and negligible, but actual data shows that the probability of such extreme events is several times higher than the normal distribution assumption. If the reserved capacity in the bidding is insufficient, the plant will face hefty penalties for default. Therefore, the technical solution uses the Lévy stable distribution or other heavy-tailed distribution models to characterize noise characteristics, which can more accurately reproduce the true probability of extreme deviation events. This provides a scientific basis for virtual power plants to reserve sufficient response margin (70% of energy storage capacity) and set a reasonable risk premium (+30%) during periods of high volatility. This is the core advantage of random noise modeling compared to the traditional normal distribution assumption.

[0050] Figure 7 and Figure 8 Together, they demonstrated the rationality verification and economic value quantification of the bidding strategy optimization, proving from different dimensions the significant advantages of the time-sharing bidding strategy based on periodic modeling and random noise modeling compared to the traditional fixed strategy.

[0051] Figure 7 A comparison chart of cumulative returns is shown, revealing that the optimized strategy consistently outperforms the benchmark strategy, with the gap widening over time. This validates the correctness of the chosen bidding strategy. Figure 8It can be seen that the strategy becomes very aggressive during periods of high volatility, bidding for almost all capacity and preparing a large amount of energy storage to respond to market demand and earn energy revenue, while avoiding defaults due to insufficient capacity. During periods of low volatility, the strategy becomes relatively conservative, bidding for less capacity because market demand is expected to be low, thus reducing unnecessary standby liabilities and conserving resources. Therefore, penalties are almost nonexistent during periods of high volatility, and unnecessary standby is reduced during periods of low volatility, resulting in a net return significantly exceeding the benchmark strategy. Specific revenue data and the number of defaults are shown in Table 1.

[0052] Table 1 Data Comparison Table

[0053] The final results show that the optimized strategy achieved a revenue increase of approximately 19.21% and a decrease in the number of defaults of 10.97% compared to the benchmark strategy. The above six visualization charts (frequency time series, periodic pattern, time period identification, noise distribution, capacity comparison, and cumulative revenue) comprehensively demonstrate the effectiveness of the modeling and verify that the technical process can provide a scientific basis for virtual power plants to formulate time-of-use bidding strategies with controllable risks and optimal returns by accurately depicting the deterministic laws and random characteristics of frequency fluctuations.

[0054] Example 3 A virtual power plant frequency regulation trading optimization system based on fractional heavy-tailed noise modeling includes: The data acquisition and preprocessing module is used to collect grid frequency data, market settlement data, and power generation data from the virtual power plant, and to preprocess the collected virtual power plant data. The calculation module is used to input the pre-processed virtual power plant data into the pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static power grid frequency response. The implementation module is used to determine the optimal bidding capacity of the virtual power plant based on the energy demand and response time distribution of the dynamic and static grid frequency response, combined with the market revenue structure and risk constraints.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling, characterized in that, Includes the following steps: Collect grid frequency data, market settlement data, and power generation data from the virtual power plant, and preprocess the collected virtual power plant data; The preprocessed virtual power plant data is input into a pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static power grid frequency response. Based on the energy demand and response time distribution of dynamic and static grid frequency response, combined with market revenue structure and risk constraints, the optimal bidding capacity of the virtual power plant is determined.

2. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 1, characterized in that, In the step of collecting grid frequency data, market settlement data, and power generation data of the virtual power plant and preprocessing the collected virtual power plant data, the collected grid frequency data includes real-time frequency measurements, frequency deviation, and rate of change; the market settlement data includes settlement cycle, clearing price, product type, and capacity price; and the power generation data includes the output of each distributed resource within the virtual power plant, the state of charge of energy storage, and adjustable capacity.

3. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 2, characterized in that, By establishing a unified data interface and time synchronization mechanism, the multi-source heterogeneous data of the collected virtual power plant can be accurately aligned in the time dimension.

4. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 1, characterized in that, The method for inputting the preprocessed data into a pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static frequency responses is as follows: Collect historical power grid frequency data, market settlement data, and power generation data; The collected historical power grid frequency data is cleaned, and the cleaned data is divided into non-random periodic components and random noise components. Periodic parameters are estimated for the periodic components to generate time-sharing bidding strategies. Noise characteristic parameters are estimated for random noise components to obtain the continuous response requirements and extreme event response capacity of the virtual power plant. The time-sharing bidding strategy generated by the periodic component, as well as the virtual power plant response demand and extreme event response capacity obtained from the analysis of the random noise component, are transferred to the damping modeling stage to construct a voltage characteristic model. A large-scale frequency data sample sequence was generated through Monte Carlo simulation, and the energy demand distribution and response duration distribution of the dynamic and static frequency responses were calculated using the constructed voltage characteristic model.

5. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 4, characterized in that, The method for estimating the periodic parameters of the periodic components and generating a time-sharing bidding strategy is as follows: For non-random periodic components, a time mapping relationship between power grid frequency data and settlement periods is established by dividing the data using market settlement data; Based on the established time mapping relationship between power grid frequency data and settlement periods, periodic parameters are estimated, and multi-scale periodic patterns of intraday, intraweek, and seasonality are fitted to obtain the periodic mean function. and scaling function ; Based on the obtained periodic mean function and scaling function Conduct periodic characteristic analysis and generate time-sharing bidding strategies; Based on the generated time-sharing bidding strategy, high-volatility and low-volatility periods are identified. By comparing and analyzing volatility, the differences in volatility across different periods are revealed and quantified. The driving effect of market settlement data on frequency volatility is obtained, and a time-sharing bidding strategy is generated.

6. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 4, characterized in that, The method for estimating the noise characteristic parameters of random noise components to obtain the continuous response demand and extreme event response capacity of the virtual power plant is as follows: The random noise components were estimated using a fractional heavy-tailed noise model to obtain the Hurst exponent h, which describes the long-range correlation of frequency deviations, and the Levy exponent, which describes the heavy-tailed characteristics of frequency data. ; The persistence of frequency deviation is analyzed based on the Hurst exponent h, and the long-term continuous response requirements and response duration of the virtual power plant are predicted. Based on the Levy index Analyze the probability distribution of extreme events and assess the emergency response capacity required by the virtual power plant to cope with extreme frequency shift events.

7. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 6, characterized in that, The method for analyzing the persistence of frequency deviation and predicting the long-term continuous response requirements and response duration of the virtual power plant based on the Hurst exponent h is as follows: When h > 0.5, the frequency deviation is determined to be persistent, and the system requires a longer response time to smooth it out; when h < 0.5, the frequency deviation is determined to be regressive, and the system requires a fast response but does not need to maintain continuous force for a long time; when h < 0.5, the frequency deviation is determined to be Brownian motion.

8. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 6, characterized in that, Based on the Levy index The method for analyzing the probability distribution of extreme events and assessing the emergency response capacity required by a virtual power plant to cope with extreme frequency shift events is as follows: when When <2, the frequency data distribution is judged to have fat-tailed characteristics; when When the value is ≥2, the virtual power plant is configured according to the conventional capacity.

9. The virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling according to claim 4, characterized in that, In the step of transferring the time-sharing bidding strategy generated by the periodic components and the virtual power plant response demand and extreme event response capacity obtained from the analysis of random noise components to the damping modeling stage to construct the voltage characteristic model, the construction frequency of the voltage characteristic model depends on the damping function. This function takes different values ​​in different frequency deviation ranges to simulate the differences in controller triggering and response in actual power systems inside and outside the dead zone.

10. A virtual power plant frequency regulation trading optimization system based on fractional heavy-tailed noise modeling, based on the virtual power plant frequency regulation trading optimization method based on fractional heavy-tailed noise modeling as described in any one of claims 1 to 9, characterized in that, include: The data acquisition and preprocessing module is used to collect grid frequency data, market settlement data, and power generation data from the virtual power plant, and to preprocess the collected virtual power plant data. The calculation module is used to input the pre-processed virtual power plant data into the pre-built voltage characteristic model to calculate the energy demand and response time distribution of the dynamic and static power grid frequency response. The implementation module is used to determine the optimal bidding capacity of the virtual power plant based on the energy demand and response time distribution of the dynamic and static grid frequency response, combined with the market revenue structure and risk constraints.

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