A method and system for dynamic optimization of time-of-use pricing for virtual power plants

Abstract

This invention discloses a method and system for dynamic optimization of time-of-use pricing in virtual power plants. By acquiring distributed resource power time-series data and user response records, it identifies power fluctuation components and generates price sensitivity coefficients, constructing an elastic response space reflecting user response potential. Boundary scanning of the elastic response space generates a dispatchable capacity envelope; trigger thresholds are set along the envelope, and the timing of energy storage intervention is derived in reverse, forming a time-of-use scheduling strategy. The grid dispatch price is projected onto the elastic space and truncated based on power balance requirements to determine the price fluctuation range. Within this range, user response paths are searched, inflection points of response intensity changes are identified, and stability is evaluated to generate price anchor points. Time interval analysis is performed on the anchor points to obtain price ramp-up rates and change rates, extracting synchronization rate indicators of group response behavior. The synchronization rate is compared with the target value to generate an optimized price sequence, achieving dynamic adaptive adjustment of time-of-use pricing.

Description

Technical Field

[0001] This invention relates to the field of power system optimization and control technology, and in particular to a method and system for dynamic optimization of time-of-use electricity pricing for virtual power plants. Background Technology

[0002] A virtual power plant is a power system that uses advanced information and communication technologies and software systems to achieve coordinated optimization and centralized control of distributed energy resources (such as solar, wind, energy storage devices, and adjustable loads). However, the pricing mechanisms of existing virtual power plants mostly adopt fixed time-of-use pricing or simple peak-valley flat pricing, which makes it difficult to fully mobilize the response enthusiasm of users and cannot effectively adapt to the dynamic changes in the grid operation status.

[0003] The core challenges currently facing the operation of virtual power plants are: on the one hand, user response behavior is highly heterogeneous and time-varying, and different types of users have significantly different sensitivities to price signals, making it difficult for traditional uniform pricing strategies to stimulate differentiated response potential; on the other hand, grid dispatch demand changes in real time with load fluctuations and changes in renewable energy output, and static time-of-use pricing cannot flexibly match dynamic dispatch requirements, resulting in the virtual power plant's regulation capacity not being fully utilized, which affects the safe and economical operation of the power grid. Summary of the Invention

[0004] This invention provides a method and system for dynamic optimization of time-of-use pricing for virtual power plants. The aim is to characterize the differentiated response characteristics of users by constructing an elastic response space, setting multi-level trigger thresholds based on the dispatchable capacity envelope, generating time-of-use scheduling strategies through reverse derivation of energy storage intervention timing, identifying user response inflection points by combining path search within the price fluctuation range, determining price anchor points through stability assessment, and then dynamically correcting the price sequence based on feedback feedback of the group response synchronization rate, thereby achieving adaptive optimization of time-of-use pricing for virtual power plants.

[0005] The first aspect of this invention proposes a method for dynamic optimization of time-of-use pricing for virtual power plants, comprising the following steps:

[0006] Acquire power time-series data and user-side response records of distributed resources in a virtual power plant; identify fluctuation components based on the power time-series data; generate price sensitivity coefficients using the user-side response records; and construct an elastic response space based on the matching relationship between the fluctuation components and the price sensitivity coefficients.

[0007] A boundary scan is performed on the elastic response space to generate a schedulable capacity envelope. Trigger threshold points are set along the schedulable capacity envelope. The timing of energy storage intervention is deduced in reverse based on the trigger threshold points. A time-sharing scheduling strategy is generated based on the timing of energy storage intervention.

[0008] Obtain the power grid dispatch price sequence and power balance requirements, project the power grid dispatch price sequence onto the elastic response space to form an effective price range, and truncate the effective price range based on the power balance requirements to determine the price fluctuation range;

[0009] The time-sharing scheduling strategy is used to perform path search within the price fluctuation range to obtain changes in user response intensity. Based on the changes in user response intensity, inflection point positions are identified, and stability assessments are performed on the inflection point positions to generate price anchor points.

[0010] The price anchor point is analyzed over time intervals to generate a price ramp-up rate. The price ramp-up rate is used to form the price change rate. The group response behavior is obtained based on the price change rate. The synchronization rate index is extracted from the group response behavior.

[0011] The synchronization rate index is compared with the preset target value to form a deviation signal. Based on the deviation signal, the price anchor point is corrected to generate an optimized price sequence, thus completing the dynamic optimization of time-of-use electricity prices for virtual power plants.

[0012] A second aspect of this invention proposes a dynamic optimization system for time-of-use pricing in virtual power plants, comprising:

[0013] The data acquisition module is used to acquire power time-series data and user-side response records of distributed resources in the virtual power plant, identify fluctuation components based on the power time-series data, generate price sensitivity coefficients using the user-side response records, and construct an elastic response space based on the matching relationship between the fluctuation components and the price sensitivity coefficients.

[0014] The scheduling generation module is used to perform boundary scanning on the elastic response space to generate a schedulable capacity envelope, set trigger threshold points along the schedulable capacity envelope, deduce the energy storage intervention timing based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the energy storage intervention timing.

[0015] The price determination module is used to obtain the power grid dispatch price sequence and power balance requirements, project the power grid dispatch price sequence onto the elastic response space to form an effective price range, and truncate the effective price range based on the power balance requirements to determine the price fluctuation range.

[0016] Anchoring generation module is used to perform path search within the price fluctuation range using the time-sharing scheduling strategy to obtain changes in user response intensity, identify inflection point positions based on changes in user response intensity, and perform stability assessment on the inflection point positions to generate price anchoring points.

[0017] The synchronization analysis module is used to perform time interval analysis on the price anchor point to generate a price ramp rate, form a price change rate based on the price ramp rate, obtain group response behavior based on the price change rate, and extract the synchronization rate index from the group response behavior.

[0018] The price optimization module is used to compare the synchronization rate index with the preset target value to form a deviation signal, and to correct the price anchor point based on the deviation signal to generate an optimized price sequence, thereby completing the dynamic optimization of the time-of-use electricity price of the virtual power plant.

[0019] The beneficial effects of this invention are reflected in the following points: First, by constructing response potential difference and gradient field technologies, a three-dimensional characterization of user response potential and precise adaptation to grid demand are achieved. The peak-valley coupling analysis of positive and negative response regions is transformed into a potential energy field, and the elastic response space is determined along equipotential lines. Power balance requirements are ensured through price projection mapping and truncation optimization, transforming the originally discrete user response characteristics into a continuously adjustable three-dimensional scheduling domain, thus improving the precision and executability of price signal regulation. Second, predictive scheduling of energy storage resources is achieved using envelope scanning and threshold back-derivation methods. By setting multi-level trigger thresholds at the dispatchable capacity boundary, the power ramp-up trajectory is traced backward from the trigger point, and the intervention timing is determined by considering the forward shift of response delay, transforming energy storage from post-event compensation to pre-event prevention, improving the system's regulation timeliness. Finally, a price anchoring mechanism based on disturbance recovery characteristics and closed-loop optimization of synchronization rate indicators are established, ensuring the stability of electricity price adjustments and the coordination of group responses. By applying perturbation to the response inflection point and analyzing the recovery time series, a fast recovery point is selected as the price anchoring benchmark. Based on the closed-loop correction of price ramp-up rate analysis and synchronization rate quantification, the electricity price optimization can both quickly respond to system demand and maintain dispatch stability, achieving coordination and unification for differentiated users.

[0020] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0021] The accompanying drawings illustrate specific examples of the technical solutions described in this invention and, together with the detailed embodiments, form part of the specification, serving to explain the technical solutions, principles, and effects of this invention.

[0022] Unless otherwise specified, the same reference numerals in different figures represent the same or similar technical features, and different reference numerals may be used to represent the same or similar technical features.

[0023] Figure 1 This is a flowchart illustrating a method for dynamic optimization of time-of-use electricity pricing for virtual power plants according to the present invention.

[0024] Figure 2This is a structural block diagram of a virtual power plant time-of-use electricity price dynamic optimization system according to the present invention. Detailed Implementation

[0025] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0026] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0027] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0028] The technical solutions of the embodiments of this application will be described below.

[0029] like Figure 1 As shown, this embodiment of the invention provides a method for dynamic optimization of time-of-use electricity pricing for virtual power plants, including the following steps S110-S160:

[0030] Step S110: Obtain power time-series data and user-side response records of the distributed resources of the virtual power plant; identify fluctuation components based on the power time-series data; generate price sensitivity coefficients using the user-side response records; and construct an elastic response space based on the matching relationship between the fluctuation components and the price sensitivity coefficients.

[0031] Specifically, the system acquires power time-series data and user-side response records for distributed resources within the virtual power plant. Power time-series data acquisition covers all distributed resources within the virtual power plant, including real-time power data from distributed photovoltaic systems, energy storage systems, controllable loads, and electric vehicle charging stations. The data acquisition frequency is set to 5 minutes per acquisition to ensure the capture of rapid power changes. Each data point includes a timestamp, device identifier, active power, reactive power, and operating status. User-side response records collect historical user responses to electricity price signals, including response time, power changes before and after the response, response duration, and electricity price level. The response record time span covers nearly 6 months to ensure coverage of different seasons and electricity consumption patterns. Data preprocessing includes outlier removal, missing value imputation, and time alignment. Outliers are defined as data points exceeding the device's rated power range or whose rate of change exceeds physical limits. Data storage employs a time-series database architecture, supporting efficient time window queries and aggregation calculations. A device-user mapping table is established to associate distributed resources with corresponding user response behaviors.

[0032] Fluctuation components are identified based on power time-series data. The Empirical Mode Decomposition (EMD) method is used to decompose the power time-series data into multiple Intrinsic Mode Function (IMF) components. The decomposition process iteratively filters and extracts fluctuation features at different time scales, with each IMF component representing power fluctuations within a specific frequency range. Fluctuation component identification focuses on mid-to-high frequency IMF components, with time scales ranging from 15 minutes to 4 hours, reflecting schedulable power fluctuations. Fluctuation amplitude is calculated using the standard deviation method: σ_i = sqrt(Σ(P_i(t) - P_avg_i)² / N), where σ_i is the standard deviation of the i-th IMF component, sqrt(·) is the square root function, Σ is the summation sign, P_i(t) is the i-th IMF component, P_avg_i is its mean, and N is the number of data points. Fluctuation period is determined by extracting instantaneous frequencies using Hilbert transform to identify the dominant periodic component. Fluctuation components are classified as: regular fluctuations (with obvious periodic characteristics), random fluctuations (without obvious patterns), and sudden fluctuations (short-term, large changes). The volatility intensity index is defined as the energy proportion of each IMF component; components with higher intensity have a greater impact on system operation. A volatility feature vector is established, including multi-dimensional features such as amplitude, period, phase, and energy, for subsequent matching analysis.

[0033] Price sensitivity coefficients are generated using user-side response records. These coefficients reflect the relationship between user power adjustments and electricity price changes. The calculation formula is K_p = ΔP / ΔC, where K_p is the price sensitivity coefficient, ΔP is the power change, and ΔC is the electricity price change. Time-based differentiation analysis divides the day into peak, flat, and valley periods, calculating the sensitivity coefficient for each period. User classification is based on response characteristics, categorizing users into high-sensitivity (K_p > 0.5), medium-sensitivity (0.2 ≤ K_p ≤ 0.5), and low-sensitivity (K_p < 0.2). The time-varying characteristics of the sensitivity coefficients are captured using a sliding window method with a window length of 30 days and a step size of 1 day. Seasonal correction considers the impact of environmental factors such as temperature and humidity on the sensitivity coefficients, establishing a correction model. Response delay analysis identifies the time lag between price signal release and user response, typically ranging from 5 to 30 minutes. A sensitivity coefficient matrix is ​​constructed, with rows representing different user groups, columns representing different time periods, and matrix elements representing the corresponding sensitivity coefficient values. The confidence level of a coefficient is determined by the number of responses and the consistency of those responses; coefficients with a high number of responses and high consistency have high confidence.

[0034] In some embodiments, constructing the elastic response space based on the matching relationship between the volatility component and the price sensitivity coefficient includes: identifying positive and negative response regions through the matching relationship between the volatility component and the price sensitivity coefficient; performing coupling analysis on the peak value of the positive response region and the valley value of the negative response region to generate a response potential difference; constructing a response gradient field using the response potential difference; and determining the elastic response space along the equipotential lines of the response gradient field.

[0035] Positive and negative response regions are identified by matching the volatility components with price sensitivity coefficients. Differentiated matching is performed based on volatility component type: periodic matching algorithms are used for regular volatility, statistical correlation methods are used for random volatility, and threshold triggering mechanisms are used for sudden volatility. The correlation between volatility feature vectors and sensitivity coefficients is calculated, considering user sensitivity classification: a weight coefficient of 1.5 for highly sensitive users, 1.0 for moderately sensitive users, and 0.5 for low-sensitive users. A correlation coefficient greater than 0.7 is considered a strong match. The response delay effect is also considered, with price signals shifted forward by 5-30 minutes for matching to ensure accurate time alignment. Differentiated matching is performed using a sensitivity coefficient matrix, with corresponding sensitivity coefficient values ​​for peak, normal, and trough periods. A positive response region is defined as a spatiotemporal region where volatility components increase and price sensitivity coefficients are positive, indicating that power increases and price increases move in the same direction. A negative response region is defined as a spatiotemporal region where volatility components decrease and price sensitivity coefficients are negative, indicating that power decreases and price increases move in opposite directions. Region boundaries are determined using clustering algorithms, and the DBSCAN method is used to identify sets of response points with similar densities. Spatiotemporal mapping projects the response region onto a time-power two-dimensional plane, with the time axis representing a 24-hour day and the power axis representing the per-unit power level. The region area is used to quantify the response potential; larger regions have greater regulation capacity. Boundary fuzzing considers the uncertainty of the actual response and employs a fuzzy set method to handle the region boundaries.

[0036] The response potential difference is generated by coupling analysis of the peak value in the positive response region and the valley value in the negative response region. A local maximum search algorithm is used to find the maximum point of response intensity in the positive response region. A local minimum search algorithm is used to find the minimum point of response intensity in the negative response region. Coupling analysis considers the temporal correlation between peaks and valleys; peak-valley pairs with a time interval of less than 2 hours are considered coupled. The response potential difference is calculated as ΔΦ = Φ_peak - Φ_valley, where ΔΦ is the response potential difference, Φ_peak is the peak response potential energy, and Φ_valley is the valley response potential energy. The potential energy is defined as proportional to the product of response intensity and duration. Coupling strength is evaluated using the cross-correlation function of the peak and valley responses; a high cross-correlation coefficient indicates tight coupling. Time-shift analysis identifies the optimal coupling time difference to achieve the best peak-valley matching effect. The probability density function of the potential difference is statistically analyzed. The physical meaning of the potential difference characterizes the energy barrier that the system needs to overcome to adjust from a valley state to a peak state.

[0037] A response gradient field is constructed using the response potential difference. The gradient field represents the rate of change of the response potential energy in the spatiotemporal domain, with the gradient direction pointing in the direction of the fastest increase in potential energy. The gradient is calculated using the finite difference method, with a spatial step size of 15 minutes and a power step size of 5% of the rated power. The mathematical expression of the gradient vector field is ∇Φ=(∂Φ / ∂t,∂Φ / ∂P), where ∇Φ is the gradient vector, ∂Φ / ∂t is the partial derivative of the potential energy with respect to time, and ∂Φ / ∂P is the partial derivative of the potential energy with respect to power. A Gaussian filter with a kernel size of 3×3 is used for gradient field smoothing to eliminate computational noise. The gradient magnitude reflects the drastic change in response; regions with large magnitudes correspond to fast response zones. Statistical analysis of the gradient direction identifies the dominant response direction, providing guidance for scheduling strategies. Streamline plotting visualizes the dynamic evolution path of the response through gradient field integration. Divergence and curl analysis of the gradient field identifies the source and sink characteristics and vortex structure of the response. Positive divergence indicates that the response is divergent, while negative divergence indicates that the response is convergent.

[0038] The elastic response space is determined along equipotential lines in the response gradient field. Equipotential lines are defined as lines connecting points with equal potential energy in the gradient field, reflecting regions with similar response potential. Equipotential line extraction is performed using a contour tracing algorithm, with the potential energy interval set to 5% of the maximum potential difference. The elastic response space consists of a region enclosed by a set of closed equipotential lines; different equipotential lines correspond to different response margins. The spatial boundary is determined using the outermost equipotential line, within which the region possesses actual response capability. Spatial capacity is calculated through volume integration to quantify the total response potential. Response path optimization finds the path with the minimum gradient within the elastic space to achieve smooth scheduling. Spatial dynamic characteristics analysis identifies changes in the elastic space at different times, recognizing expansion and contraction modes. Multi-dimensional expansion constructs a three-dimensional elastic response space using price, power, and time, providing more comprehensive scheduling decision support. The elasticity coefficient is defined as η = V_elastic / V_total, where η is the elasticity coefficient, V_elastic is the elastic space capacity, and V_total is the total installed capacity, reflecting the overall elasticity level of the system.

[0039] Step S120: Perform boundary scanning on the elastic response space to generate a schedulable capacity envelope, set trigger threshold points along the schedulable capacity envelope, deduce the timing of energy storage intervention based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the timing of energy storage intervention.

[0040] Specifically, a boundary scan of the elastic response space is performed to generate a schedulable capacity envelope. Using the ray casting method, rays with equal angular intervals are emitted outward from the geometric center of the elastic response space, with an angular step size of 5 degrees, resulting in 72 rays covering the entire plane. The intersection points of each ray with the boundary of the elastic space form a boundary point set. The time and power coordinates of these intersection points are recorded to create a boundary feature database. Scheduling capacity is defined as the radial distance from a boundary point to the center, reflecting the maximum adjustment capability in that direction. Envelope generation connects all boundary points using cubic spline interpolation, ensuring the second-order continuity and smoothness of the curve. Time-varying characteristic analysis examines the morphological changes of the envelope at different times, identifying periods of capacity expansion and contraction, and establishing a dynamic capacity prediction model. The envelope area is calculated to quantify the total schedulable capacity: A = ∫∫ D dP·dt, where A is the area enclosed by the envelope, the subscript D is the elastic response spatial domain, P is the power, t is the time, ∫∫ is the double integral symbol, dP is the power infinitesimal element, and dt is the time infinitesimal element. Morphological feature extraction includes geometric indices such as the convexity, symmetry, compactness, and eccentricity of the envelope, used to evaluate the distribution of scheduling potential.

[0041] Trigger threshold points are set along the schedulable capacity envelope. The threshold point distribution strategy considers the envelope morphology: threshold density is increased in areas with strong convexity, symmetrical arrangement is used in areas with good symmetry, and threshold intervals are reduced in areas with high compactness. Based on the curvature analysis of the envelope, threshold points are preferentially set at locations with drastic curvature changes to ensure sensitive response to changes in system state. The curvature calculation formula is κ=|d²P / dt²| / (1+(dP / dt)²)^(3 / 2), where κ is curvature, P is power, t is time, |·| is the absolute value sign, d²P / dt² is the second derivative of power with respect to time, dP / dt is the first derivative of power with respect to time, and ^(3 / 2) represents the power of 3 / 2. Locations with curvature greater than 0.01 are marked as candidate threshold points. The threshold density is determined according to the system response speed requirements and scheduling accuracy requirements: the threshold point interval is 10MW in fast response areas and 20MW in slow response areas. Threshold types are divided into three levels: warning threshold (80% of the envelope), action threshold (90% of the envelope), and extreme threshold (95% of the envelope). A multi-level threshold system establishes a progressive triggering mechanism, with different levels corresponding to different scheduling action intensities and response priorities. The time attribute of each threshold point records the corresponding time and validity period, used for time-series scheduling decisions and threshold update management. Threshold sensitivity analysis assesses the impact of minor changes in system state on threshold triggering, establishing a sensitivity matrix.

[0042] In some embodiments, the step of reversely deducing the timing of energy storage intervention based on the trigger threshold point includes: generating a power ramp-up trajectory by tracing back based on the trigger threshold point; identifying an acceleration start point based on the power ramp-up trajectory; obtaining the energy storage response delay through the acceleration start point; and determining the timing of energy storage intervention by moving the acceleration start point forward based on the response delay.

[0043] Differentiated reverse derivation strategies are employed for different trigger thresholds: the early warning threshold corresponds to the pre-preparation mode (tracing back 15 minutes), the action threshold corresponds to the rapid response mode (tracing back 30 minutes), and the extreme threshold corresponds to the emergency intervention mode (tracing back 45 minutes). Power ramp-up trajectories are generated by tracing back from the trigger thresholds. The tracing time window is set according to the threshold level to ensure the capture of the complete power change process and early signs. Trajectory reconstruction uses an inverse integration method, calculating the power path backward along the time axis from the trigger point, with a step size of 10 seconds. The data sampling interval is 1 minute, improved to the 10-second level through interpolation algorithms to ensure the temporal resolution and detail of the trajectory changes. A Kalman filter is used for trajectory smoothing, and the state equation considers the physical constraints of power changes to eliminate the influence of measurement noise on the trajectory. Slope calculation identifies the power change rate, with the unit of power change rate being MW / min. Trajectory segmentation divides the complete trajectory into a stable segment (change rate less than 5 MW / min), a gradually rising segment (change rate 5-20 MW / min), and a rapidly rising segment (change rate greater than 20 MW / min) based on slope changes and duration. Feature point marking includes key locations such as starting points, turning points, acceleration points, and peak points, establishing a feature point time-series database. Multi-track comparative analysis of climbing patterns under different triggering events extracts common features to establish standard climbing templates. Track data storage includes multi-dimensional information such as time series, power series, slope series, and acceleration series.

[0044] The acceleration initiation point is identified based on the power climb trajectory. Curvature characteristics are considered in this identification process; the acceleration threshold is lowered in high-curvature regions, and the identification parameters are adjusted using a sensitivity matrix. The acceleration initiation point is defined as the moment when the power change rate first exceeds a set threshold and maintains an upward trend. The threshold is set to the larger of 1.5 times the average change rate or 10 MW / min. Second-derivative analysis is used to identify acceleration changes, with power acceleration measured in MW / min². Initiation moments where acceleration is positive and continuously increases by more than 0.5 MW / min² are marked as candidate acceleration points. Continuity checks ensure the acceleration process lasts for more than 3 minutes, eliminating false acceleration points caused by instantaneous disturbances and measurement noise. Multi-scale analysis identifies acceleration characteristics at different time scales (1 minute, 5 minutes, 10 minutes, etc.) to comprehensively judge the true acceleration behavior. Acceleration intensity is assessed by quantifying the average and peak acceleration of the acceleration segment, establishing a grading standard for acceleration intensity. Time consistency analysis analyzes the temporal distribution patterns of multiple acceleration points to identify systematic acceleration patterns. Acceleration patterns are classified into linear acceleration, exponential acceleration, step acceleration, and oscillatory acceleration, and differentiated response strategies are developed for different patterns. Priority ranking determines the primary acceleration point based on a comprehensive score of acceleration intensity, duration, and stability.

[0045] The energy storage response latency is obtained by accelerating the starting point. Response latency comprises three main components: communication latency, decision latency, and execution latency, each with inherent uncertainties. Communication latency depends on the type and load of the data transmission network; typical values ​​are 100-300 milliseconds for fiber optic communication and 300-500 milliseconds for wireless communication. Decision latency involves scheduling algorithm computation time and multi-objective optimization solutions, ranging from 1-5 seconds depending on system complexity and optimization accuracy requirements. Execution latency is the time from receiving the command to the actual output power reaching the target value; typical values ​​are 200 milliseconds for battery energy storage, 50 milliseconds for flywheel energy storage, and 2-5 seconds for compressed air energy storage. The total latency is calculated using the formula T_delay = T_comm + T_dec + T_exec, where T_delay is the total response latency, T_comm is the communication latency, T_dec is the decision latency, and T_exec is the execution latency. The probability distribution analysis of latency considers the influence of random factors such as network congestion and computational load, and uses a gamma distribution to describe it.

[0046] The timing of energy storage intervention is determined by shifting the acceleration start point forward based on response delay. The forward shift equals the total response delay plus a safety margin: T_advance = T_delay + T_margin, where T_advance is the forward shift time and T_margin is the safety margin, typically 20% of the total delay. The intervention timing is calculated by subtracting the forward shift from the acceleration start point, ensuring that energy storage actions are synchronized with demand. Timing effectiveness verification checks the system state at the intervention time, including constraints such as available energy storage capacity, grid acceptance capacity, and other resource scheduling. Multi-scenario adaptive analysis examines the differences in intervention timing under different load patterns, seasonal characteristics, and weather conditions, establishing a scenario knowledge base. The intervention strength preset determines the initial output power based on factors such as power gap prediction, ramp-up rate, and duration. Intervention signal generation includes complete control parameters such as intervention time, initial power, power ramp-up rate, expected duration, and exit conditions. Timing stability assessment analyzes the impact of uncertainties on intervention timing through Monte Carlo simulation. A coordination mechanism handles the intervention sequence of multiple energy storage systems to avoid power surges caused by simultaneous actions.

[0047] A time-sharing scheduling strategy is generated based on the timing of energy storage intervention. The scheduling strategy considers response delay characteristics; energy storage devices with a longer T_delay are started earlier, and power ramp-up trajectories are used to predict scheduling intensity demand. The time-sharing division comprehensively considers system load characteristics, electricity price levels, and user electricity consumption behavior, dividing the day into six scheduling periods: morning peak (7:00-9:00), morning plateau (9:00-11:00), afternoon peak (11:00-14:00), afternoon plateau (14:00-17:00), evening peak (17:00-21:00), and nighttime off-peak (21:00-7:00). Scheduling objectives are differentiated for each period: peak shaving and valley filling are prioritized during peak periods, power stability is maintained during plateau periods, and energy reserves are optimized during off-peak periods. The energy storage charging and discharging plan is comprehensively formulated based on power demand forecasts, electricity price signals, and energy storage status for each period, and optimized using a dynamic programming algorithm. Charging priority settings comprehensively consider factors such as electricity price levels, energy storage SOC status, and expected discharge demand, prioritizing charging when electricity prices are low and SOC is low. The power allocation strategy considers the power and capacity constraints of energy storage: P_min ≤ P_storage(t) ≤ P_max, where P_storage(t) is the energy storage power at time t, and P_min and P_max are power limits, while also satisfying energy balance constraints. State of charge management ensures sufficient energy reserves for energy storage at critical moments, maintaining SOC within a healthy range of 20%-80%, with the possibility of extending to 10%-90% in extreme cases. Strategy switching conditions are dynamically determined based on real-time monitoring data and event triggering mechanisms, including sudden changes in electricity prices, load surges, and fluctuations in renewable energy.

[0048] Step S130: Obtain the power grid dispatch price sequence and power balance requirements, project the power grid dispatch price sequence onto the elastic response space to form an effective price range, and truncate the effective price range based on the power balance requirements to determine the price fluctuation range.

[0049] Specifically, the system acquires the grid dispatch price series and power balance requirements. The grid dispatch price series originates from day-ahead market clearing results and real-time market price signals, including time-of-use (TOU) price data for the next 24 hours. Each data point includes attributes such as timestamp, electricity value, and price type identifier. The price data covers various pricing mechanisms, including benchmark prices, peak-valley TOU prices, tiered pricing, and dynamic pricing, with a time resolution of 15 minutes, consistent with the dispatch cycle of virtual power plants. The historical price data backtracking window is set to 30 days, constructing a complete price time series database that supports trend analysis, periodic pattern mining, and predictive model training. The price data preprocessing process includes key steps such as outlier detection (identifying outliers exceeding 1.5 times the interquartile range based on box plot methods), missing value imputation (using a weighted average of adjacent values), and noise filtering (applying a 5-point moving average filter). Power balance requirements are acquired in real-time through a dedicated interface of the dispatch automation system, including core parameters such as load forecasts for each time period, upper and lower limits of dispatchable capacity, ramp rate constraints, and spinning reserve demand. The balancing accuracy must be strictly controlled within ±2% of the total system load, and a graded response mechanism must be established to handle power deviations of different degrees. System constraints comprehensively consider multiple dimensions of limitations, including transmission line thermal stability limits, transformer capacity limitations, bus voltage deviation range, and system frequency deviation tolerance.

[0050] The grid dispatch price series is projected onto the elastic response space to form an effective price range. The projection process considers differences in pricing mechanisms: a linear mapping is used for the benchmark price, a segmented mapping for peak-valley time-of-use pricing, a step mapping for tiered pricing, and a nonlinear mapping for dynamic pricing. The projection process achieves the mapping transformation from a one-dimensional price time series to a two-dimensional time-power response plane, establishing a quantitative relationship between price signals and system regulation capacity. The mapping function is based on a price-power response model fitted from historical operating data: P(C) = P_base + K_p × (C - C_ref) + ε, where P(C) is the expected power response corresponding to price C, P_base is the benchmark operating power, K_p is the price sensitivity coefficient matrix (considering the differentiated responses of different user types), C_ref is the reference price level, and ε is a random disturbance term. An effective range identification algorithm determines whether each projected price point is within the feasible region of the elastic response space, using computational geometry methods to quickly determine the positional relationship between the point and the polygon. The projection density distribution uses kernel density estimation to analyze the clustering characteristics of price points in the response space; high-density areas represent the normal operating range of the system.

[0051] In some embodiments, determining the price fluctuation range by truncating the effective price range based on the power balance requirement includes: generating a supply-demand deviation threshold according to the power balance requirement; compressing the effective price range at its upper bound based on the supply-demand deviation threshold to generate a compressed range; performing a stability test on the compressed range to generate a stable sub-range; and selecting the longest continuous segment from the stable sub-range as the price fluctuation range.

[0052] Supply-demand deviation thresholds are generated based on power balance requirements. Threshold settings reference historical price fluctuation statistics and are adjusted to account for system constraints such as transmission line thermal stability limits and transformer capacity limitations. Real-time supply-demand deviation calculation is based on a comprehensive analysis of load forecasting, renewable energy output forecasting, and dispatchable resource capacity: ΔP(t) = P_load(t) + P_loss(t) - P_gen(t) - P_res(t), where ΔP(t) is the supply-demand deviation at time t, P_load(t) is the load demand, P_loss(t) is the network loss, P_gen(t) is the output of conventional units, and P_res(t) is the output of renewable energy. The threshold system adopts a dynamic hierarchical setting: the deviation threshold is ±50MW under normal operating conditions, ±100MW under warning conditions, ±150MW under emergency conditions, and ±200MW is allowed in extreme cases. Time-varying characteristics consider the system operating characteristics at different times: the threshold is tightened by 20% during morning and evening peak hours to improve control accuracy, and relaxed by 30% during late-night off-peak hours to reduce regulation costs. The statistical threshold is based on probability distribution analysis of historical operational data. A kernel density estimation method is used to fit the deviation distribution, and the quantile corresponding to the 90% confidence level is selected as the upper limit of the statistical threshold. The adaptive adjustment mechanism dynamically corrects the threshold based on factors such as real-time system status, weather changes, and major events, establishing a rule-based expert system to achieve intelligent adjustment.

[0053] The effective price range is compressed based on a supply-demand deviation threshold to generate a compressed range. The compression strategy incorporates projection density distribution characteristics, prioritizing high-density regions, and uses a mapping function P(C) to predict the compressed power response. Starting from the upper bound of the price range, the compression strategy employs an iterative algorithm with adaptive step sizes to gradually reduce the upper limit until the predicted system response satisfies all deviation threshold constraints. The iterative algorithm combines the fast convergence of the Newton-Raphson method with the global convergence guarantee of the bisection method, dynamically switching algorithms based on convergence status. The compression effect is evaluated by comprehensively considering the price range compression ratio and the degree of deviation improvement. The response prediction model uses a Long Short-Term Memory (LSTM) network combined with physical constraints, taking the compressed upper price limit as input and outputting the expected power response and deviation level. Convergence is determined using a dual standard: a price change less than 0.01 yuan / kWh and a deviation improvement rate less than 1%, or more than 50 iterations, resulting in forced termination. The compression path optimization constructs a state transition diagram of the compression process by recording the complete state of each iteration, including price values, prediction deviations, various user response quantities, and system stability indicators.

[0054] Stability testing is performed on the compressed interval to generate stable sub-intervals. The stability test considers the projected density distribution, reducing test intensity in high-density areas and strengthening verification in low-density areas. The stability test scheme design comprehensively considers small-signal stability, transient stability, and voltage stability, constructing a comprehensive test case library. A disturbance signal generator produces standard test signals: step disturbance (amplitude 5% of the interval width, duration 30 seconds), ramp disturbance (rate of change 0.02 yuan / kWh / min), sinusoidal disturbance (frequency 0.1-1Hz, amplitude increasing), and white noise disturbance (power spectral density 0.001). Dynamic response evaluation uses standard stability indicators: overshoot, rise time, settling time, steady-state error, damping ratio, and other key parameters. Sensitivity analysis calculates the system output sensitivity matrix to price disturbances, identifying high-sensitivity areas and marking them as potentially unstable regions. Phase trajectory analysis plots the system trajectory in state space, and the stability type of the system (asymptotically stable, Lyapunov stable, unstable) is determined by the trajectory shape. The stability margin is quantitatively assessed using gain margin and phase margin indices, requiring a gain margin greater than 6 dB and a phase margin greater than 45 degrees. The sub-interval partitioning algorithm is based on stability test results and uses dynamic programming to identify the largest continuous stable segment, allowing for multiple discontinuous stable sub-intervals.

[0055] The longest continuous segment is selected from the stable sub-intervals as the price fluctuation range. The continuity criterion comprehensively considers temporal and numerical continuity, with the time interval between adjacent price points not exceeding 30 minutes, price jumps not exceeding 0.02 yuan / kWh, and the rate of change not exceeding 0.05 yuan / kWh / h. A weighted method is used for length measurement, comprehensively considering time span, stability weight, and coverage weight. A multi-objective optimization model considers objectives such as maximizing interval length, maximizing stability margin, including the current operating point, and covering key time periods, using the NSGA-II algorithm to solve for the Pareto optimal solution set. Endpoint optimization technology maximizes the interval length while ensuring stability by fine-tuning the interval endpoint positions, using the golden section search to determine the optimal endpoints. Time period coverage requires the selected interval to cover more than 85% of key time periods such as morning peak (7:00-9:00) and evening peak (18:00-20:00); if this is not met, a multi-interval splicing scheme is initiated. Interval feature extraction calculates statistical features such as mean price, price variance, trend, and peak-to-valley difference to form an interval feature vector. The decision support information includes the basis for interval selection, analysis of expected scheduling effects, potential risk warnings, and suggestions for alternative solutions.

[0056] Step S140: Use the time-sharing scheduling strategy to perform path search within the price fluctuation range to obtain changes in user response intensity, identify inflection point positions based on changes in user response intensity, and perform stability assessment on the inflection point positions to generate price anchor points.

[0057] Specifically, a time-sharing scheduling strategy is used to perform path search within the price fluctuation range to obtain changes in user response intensity. A dynamic programming algorithm is employed, discretizing the price fluctuation range into grid nodes, with a time step of 5 minutes and a price step of 0.01 yuan / kWh. The objective function comprehensively considers economic efficiency, stability, and user satisfaction. The state transition equation describes the feasible transition path from the current price state to the next time-sharing price state, considering ramp-up constraints and price boundary limitations. The user response model is established based on the time-sharing scheduling strategy and historical response data: R(t) = R_base × (1 + K_1 × ΔC(t) + K_2 × ∫ΔC(τ) dτ), where R(t) is the response intensity at time t, R_base is the baseline response level, ΔC(t) is the price change, K_1 is the immediate response coefficient, K_2 is the cumulative response coefficient, ∫ is the integral sign, τ is the integral variable, ΔC(τ) is the price change at time τ, and dτ is the integral infinitesimal element. Response latency characteristics are described using a transfer function, taking into account the response time differences among different user types: 1-3 minutes for industrial users, 3-5 minutes for commercial users, and 5-10 minutes for residential users. Response intensity is quantified using a normalization method, with the ratio of actual response power to maximum adjustable power used as the intensity index. Path evaluation metrics include multiple dimensions such as total cost, response volatility, and execution difficulty.

[0058] Inflection point location is identified based on changes in user response intensity. Inflection point identification considers user type differences: industrial users with short latency use high-frequency detection (1-minute window), while residential users with long latency use low-frequency detection (5-minute window). An inflection point is defined as the spatiotemporal location where the trend of response intensity change changes significantly, including situations such as the growth rate changing from positive to negative, from negative to positive, or abrupt changes in the rate of change. The mathematical identification method uses the first and second derivatives of the response intensity for analysis. The first derivative represents the rate of change of the response, and the second derivative represents the acceleration of change. The inflection point determination criteria are set as follows: the second derivative crosses zero and the absolute value of the first derivative is greater than the threshold of 0.05 / min, or the rate of change of the first derivative exceeds twice the average value. The sliding window detection method sets different window widths according to user type, fits the response curve within the window, and calculates the curvature change. Inflection point types include: peak inflection point (response reaches a local maximum), valley inflection point (response reaches a local minimum), turning point inflection point (response trend reverses), and abrupt change inflection point (response changes drastically). Inflection point strength is defined as the product of the absolute value of curvature at the inflection point and the magnitude of the response change; a higher strength indicates a more significant inflection point. Temporal clustering analysis merges inflection points with similar time intervals (less than 10 minutes) into inflection point clusters, selecting the strongest inflection point within each cluster as the representative. Multi-scale detection identifies inflection points at different time scales, such as 5 minutes, 15 minutes, and 30 minutes, combining detection results from different scales to improve accuracy. The inflection point feature vector includes attributes such as time location, price level, response strength, inflection point type, and scope of influence.

[0059] In some embodiments, the step of performing stability assessment on the inflection point to generate a price anchor point includes: constructing a disturbance test window based on the inflection point; generating a recovery time series using response data within the test window; filtering fast recovery inflection points using the recovery time series; and determining a price anchor point through homogenization filtering using the fast recovery inflection points.

[0060] A disturbance test window was constructed based on the inflection point location. The test window design considered the differences in inflection point types: the observation period was extended to 40 minutes for peak and trough inflection points, shortened to 25 minutes for transitional inflection points, and increased to ±8% for abrupt change inflection points. The test window was centered on the inflection point, extending forward by 10 minutes as a preparation period and backward by 30 minutes as an observation period, forming a total test period of 40 minutes. The disturbance signal design included both positive and negative price disturbances, with the disturbance amplitude set according to the inflection point type to ensure it remained within the system's linear response range. The disturbance injection timing was chosen to be 2 minutes after the inflection point, when the system had just completed its state transition and was most sensitive to the disturbance response. The disturbance duration was set to 5 minutes to stimulate the system's dynamic response without causing excessive interference. The data sampling frequency within the window was increased to 30 seconds / time to accurately capture rapid dynamic changes in the system. Environmental variable control ensured that other influencing factors remained stable during the test, isolating the single impact of price disturbances. A multiple-repetition testing strategy was used to perform 5 independent disturbance tests for each inflection point, eliminating the influence of random factors through statistical averaging. The test data record includes complete information such as the baseline state before the disturbance, the response trajectory during the disturbance, and the recovery process after the disturbance. Boundary condition handling adjusts the disturbance direction to avoid exceeding the limits, targeting inflection points near the price range boundaries.

[0061] Recovery time series are generated using response data within the test window. The recovery process is defined as the complete time period from the end of the disturbance to the system response recovering to the pre-disturbance steady-state level. The baseline is determined by the weighted average of the response intensity within the 5 minutes prior to the disturbance, with weights increasing over time to reflect the latest state. The recovery criterion is set as the response intensity returning to within ±2% of the baseline and remaining there for more than 2 minutes to avoid misjudgments caused by temporary crossovers. The time series is constructed by recording the response intensity values ​​during the recovery process at 1-minute intervals, forming a discrete time series. The recovery trajectory is fitted using an exponential decay model: R_rec(t) = R_base + (R_disturb - R_base) × exp(-t / τ), where R_base is the baseline response, R_disturb is the peak disturbance response, τ is the time constant, t is the time variable, exp(-t / τ) is the exponential decay function, where exp is an exponential function with the natural constant e as the base, and R_rec(t) is the recovery response intensity at time t. The time constant τ reflects the system's recovery speed characteristics; a smaller τ indicates faster recovery. Recovery quality indicators include key parameters such as recovery time, overshoot, number of oscillations, and steady-state deviation. Abnormal recovery mode identification includes oscillatory recovery, stepped recovery, and divergent recovery, with different modes reflecting different stability characteristics of the system.

[0062] We used recovery time series to screen for rapid recovery inflection points. Rapid recovery is defined as a recovery time of less than 10 minutes and a monotonic recovery process without oscillations. The screening index system adds a weight to inflection point strength, prioritizing inflection points with high strength. The screening index system is established, with the main indicators being recovery time (weight 0.3), recovery quality (weight 0.25), recovery stability (weight 0.25), and inflection point strength (weight 0.2). The recovery time score is calculated using an inverse proportional function. The recovery quality score comprehensively considers overshoot and steady-state error. The recovery stability score is based on the number of oscillations and the consistency of the time constant. The inflection point strength score is determined based on the absolute value of curvature and the magnitude of response change. The comprehensive score uses a weighted summation method, and inflection points with a score exceeding 0.7 are marked as rapid recovery inflection points. Statistical analysis is performed on the distribution characteristics of rapid recovery inflection points, including distribution density within price ranges and temporal distribution patterns. Recovery pattern clustering groups inflection points with similar recovery characteristics into one category to identify typical recovery patterns. Outlier handling removes abnormal inflection points with extremely short (<2 minutes) or extremely long (>20 minutes) recovery times. Priority ranking is based on the overall score, from highest to lowest.

[0063] For example, the step of determining the price anchor point through homogenization screening using the fast recovery inflection point includes: assessing the distribution density based on the fast recovery inflection point to determine the screening intensity, wherein the distribution density includes temporal concentration, spatial coverage, and distance between inflection points; setting retention rules according to the screening intensity; and using the retention rules to screen the fast recovery inflection point to generate a price anchor point.

[0064] The screening intensity is determined based on the distribution density assessment of rapid recovery inflection points. Temporal concentration is calculated using a sliding time window method with a window width of 2 hours, statistically analyzing the density of inflection points within the window. Spatial coverage assesses the uniformity of inflection point distribution along the price dimension, dividing the price range into 10 equal sub-ranges and calculating the Gini coefficient to reflect the degree of distribution unevenness. The distance between inflection points includes two dimensions: time distance and price distance, measured using normalized Euclidean distance: d_ij = sqrt((Δt_ij / T_range)² + (ΔC_ij / C_range)²), where d_ij is the normalized Euclidean distance, sqrt(·) is the square root function, ² represents the squaring operation, Δt_ij and ΔC_ij are the time and price differences respectively, and T_range and C_range are normalization parameters. Density levels are classified based on a comprehensive assessment of three indicators: high-density areas (requiring strong screening), medium-density areas (requiring moderate screening), and low-density areas (requiring weak screening). The screening intensity coefficient is determined based on density levels: 30% is retained in high-density areas, 50% in medium-density areas, and 70% in low-density areas. Spatial autocorrelation analysis uses the Moran index to assess the spatial clustering characteristics of inflection points; positive correlation indicates clustered distribution, requiring stronger screening. Hotspot analysis identifies spatiotemporal regions with highly concentrated inflection points; these regions require focused screening to improve distribution uniformity.

[0065] Retention rules are set based on screening intensity. Differentiated retention strategies are developed according to density levels: strict screening rules for high-density areas, moderate screening rules for medium-density areas, and lenient screening rules for low-density areas. The mandatory retention rule ensures that inflection points at key locations are not screened out: the first inflection point of the day (starting scheduling), the peak-to-valley transition inflection point (change in scheduling direction), and inflection points near price extremes (boundary control). The performance priority rule prioritizes retaining inflection points with higher recovery performance scores under equal conditions; the score is calculated by comprehensively considering recovery time, recovery quality, and stability. The uniform distribution rule requires that retained inflection points be distributed as evenly as possible along the time axis, using K-means clustering to determine ideal locations and selecting the inflection point closest to the cluster center. The complementarity rule considers the functional complementarity between inflection points, pairing peak and valley inflection points for retention, and balancing the selection of rising and falling inflection points. The time-segment balance rule ensures a relatively balanced number of anchor points across different time periods, avoiding excessive density or sparseness in certain periods. Rule priority settings: Mandatory retention rule > Time-segment balance > Performance priority > Uniform distribution > Complementarity.

[0066] Price anchor points are generated by filtering rapid recovery inflection points using retention rules. Anchor point scoring considers path evaluation metrics, with inflection points exhibiting lower total cost, lower volatility, and lower execution difficulty receiving bonus points. Multiple rounds of screening are strictly executed according to rule priorities: the first round applies the mandatory retention rule to identify key inflection points; the second round implements the time-segment balancing rule to ensure balance across time periods; the third round applies the performance-priority rule to select high-scoring inflection points; the fourth round implements the uniform distribution rule to optimize time distribution; and the fifth round considers the complementarity rule to achieve functional pairing. The scoring function comprehensively considers individual performance, overall distribution effect, and path evaluation metrics. Constraint satisfaction checks ensure the final solution meets all hard constraints: minimum interval, quantity limits, coverage requirements, etc. Anchor strength is assigned different weight coefficients based on the inflection point's influence range and responsiveness, with strong anchor points having a weight of 1.5 and ordinary anchor points having a weight of 1.0. Timeliness is marked with an expiration period for each anchor point, generally 24 hours for general anchor points, and determined based on the duration of special event anchor points. Relationships are established, recording successor-successor relationships, mutual exclusion relationships, and reinforcing relationships between anchor points, forming an anchor point relationship network.

[0067] Step S150: Perform time interval analysis on the price anchor point to generate a price ramp rate, form a price change rate based on the price ramp rate, obtain the group response behavior based on the price change rate, and extract the synchronization rate index from the group response behavior.

[0068] Specifically, a time interval analysis is performed on price anchor points to generate the price ramp-up rate. The time interval calculation involves extracting the timestamp information for each pair of adjacent price anchor points: Δt_i = t_{i+1} - t_i, where Δt_i is the i-th time interval and t_i is the time position of the i-th anchor point. The price change calculation involves the price difference between adjacent anchor points: ΔC_i = C_{i+1} - C_i, where ΔC_i is the price change and C_i is the price value of the i-th anchor point. The ramp-up rate is defined as the price change per unit time: r_i = ΔC_i / Δt_i, in yuan / (kWh·h), where r_i is the ramp-up rate, reflecting the speed of price adjustment, ΔC_i is the price change, and Δt_i is the time interval. The ramp rate is classified according to its magnitude and direction: slow ramp (|r|<0.1) is suitable for stable system operation, normal ramp (0.1≤|r|<0.3) is used for routine adjustments, and rapid ramp (|r|≥0.3) is used to deal with emergencies. Directional analysis distinguishes between ascending ramp (r>0) used to suppress load or promote energy storage discharge, and descending ramp (r<0) used to stimulate power consumption or energy storage charging. Ramp duration assessment identifies a sequence of anchor points for continuous ramps in the same direction; ramps lasting more than 2 hours are defined as trend ramps. The ramp rate sequence forms a complete time series {r_1,r_2,...,r_n}.

[0069] In some embodiments, the step of forming the price change rate based on the price ramp rate includes: extracting abrupt change points from the price ramp rate; dividing the ramp segments according to the abrupt change points; setting a buffer duration for the ramp segments based on the user-side response records; and reconstructing the ramp segments using the buffer duration to form the price change rate.

[0070] The price ramp-up rate is used to extract abrupt change points. Abrupt change point identification considers differences in ramp-up rate classification: for rapid ramp-up segments, the abrupt change threshold is lowered to 70% of the original value; for slow ramp-up segments, the threshold is raised to 150% of the original value. Different threshold coefficients are used for ascending and descending ramp-up segments. An abrupt change point is defined as the position where the ramp-up rate change exceeds a set threshold, indicating a turning point in the price adjustment strategy. The rate of change is calculated using the difference between adjacent ramp-up rates, with statistical thresholds determined based on historical data analysis. Abrupt change types are classified as follows: positive abrupt change indicates an accelerating upward trend, negative abrupt change indicates an accelerating downward trend, and bidirectional abrupt change indicates a reversal of the adjustment direction. Abrupt change intensity is quantified as the ratio of the actual rate of change to the threshold; an intensity greater than 2 is defined as a strong abrupt change. Time stamping precisely records the occurrence time of each abrupt change point for subsequent time-series analysis. Continuous abrupt change processing merges multiple abrupt change points with an interval of less than 10 minutes into a single abrupt change event to avoid over-segmentation. Abrupt change cause analysis is correlated with the system's operating status to identify whether the abrupt change is due to load fluctuations, new energy fluctuations, or scheduling strategy adjustments.

[0071] Climbing segments are defined based on abrupt changes in price. A climbing segment is defined as a continuous interval between two adjacent abrupt changes, exhibiting relatively consistent climbing characteristics. Segment boundaries are determined using the abrupt change point as a natural boundary, while also considering minimum segment length constraints (not less than 15 minutes) and maximum segment length limits (not exceeding 2 hours). Segment type identification is based on the climbing rate characteristics within the segment: starting segment (climbing from zero), acceleration segment (increasing climbing rate), constant speed segment (stable climbing rate), deceleration segment (decreasing climbing rate), and stopping segment (climbing rate approaching zero). Statistical features extracted within segments include: average climbing rate, climbing rate variance, cumulative price change, and duration. Transition segments identify buffer zones between two main climbing segments, typically with smaller and more gradual climbing rates, serving as a smooth transition. Abnormal segments are marked as segments with frequently alternating positive and negative climbing rates or values ​​exceeding a reasonable range, requiring special handling strategies. Segment merging rules merge short segments with similar characteristics and adjacent times. Segment correlation analysis identifies causal relationships and temporal dependencies between different climbing segments, constructing an inter-segment transition probability matrix.

[0072] Buffer durations are set for ramp-up periods based on user-side response records. Buffer duration reflects the reaction time required from user perception of price changes to actual adjustment of electricity consumption behavior. Historical response analysis extracts actual response delays under different ramp rates from user-side response records, establishing a ramp rate-response time mapping relationship. The response time model is established using a nonlinear fitting method. Differential settings are applied based on user classification: shorter buffer durations for large industrial users (faster response), moderate for commercial users (moderate response), and longer for residential users (slower response). Time-of-use factors consider user responsiveness at different times: shorter buffer durations during peak hours, normal during off-peak hours, and longer during low-peak hours. Buffer duration constraints are set with an upper limit of 15 minutes to prevent excessive delays and a lower limit of 3 minutes to ensure users have basic reaction time. A dynamic adjustment mechanism updates model parameters online based on real-time response feedback.

[0073] The price change rate is reconstructed by utilizing a buffer period. The reconstruction goal is to transform the original step-like climb into a smooth change process that considers user response characteristics. The speed curve is designed using an S-shaped function model: v(t) = v_max / (1 + exp(-k(t-t_c))), where v(t) is the price change rate at time t, v_max is the maximum change rate of this segment (equal to the original climb rate), k is the curve steepness parameter, t_c is the inflection point time (set at the midpoint of the buffer period), and exp(·) is an exponential function. Curve parameters are determined as follows: the value of k is calculated based on the buffer period to ensure that the main transition is completed within the buffer period. A speed limiting mechanism ensures that the maximum speed after reconstruction does not exceed the user's acceptable limit; if it does, peak reduction is performed. Cubic spline interpolation is used for segment transitions to ensure the continuity of the first derivative of the speed curves of adjacent segments and avoid abrupt speed changes. Cumulative price verification ensures that the total price change remains consistent before and after reconstruction. Time axis mapping maps the reconstructed speed curve onto the actual time axis, considering the specific time of the anchor point.

[0074] In some embodiments, obtaining the group response behavior based on the price change rate includes: broadcasting the price change rate in a tiered manner to generate a fast response group and a delayed response group; using the fast response group to synchronously guide the delayed response group to form an overall response; generating a behavior pattern from the overall response through cluster analysis; and performing feature extraction based on the behavior pattern to generate the group response behavior.

[0075] The price change rate is broadcast in tiers, creating fast response and delayed response groups. The tiered broadcast strategy considers the type of ramp-up phase: the initiation and acceleration phases prioritize notification to the fast response group, while the steady and deceleration phases focus on covering the delayed response group. The tiering criteria are determined based on a comprehensive assessment of the user's technical equipment level, historical response performance, and contract type. The fast response group includes industrial users equipped with automated demand response systems, large commercial users with real-time electricity price contracts, and energy storage power stations participating in ancillary services; these users can respond to price signals within one minute. The delayed response group includes small and medium-sized enterprises (SMEs), ordinary commercial users, and residential users who rely on manual adjustments; their response time is typically 5-15 minutes. The broadcast strategy employs differentiated information delivery: the fast group receives the raw real-time price change rate signal, updated every 30 seconds; the delayed group receives a smoothed signal, updated every 5 minutes. The signal encoding format includes fields such as timestamp, target group identifier, price rate value, expected response direction, and incentive coefficient. Communication priority settings ensure that the fast response group's signal is transmitted first, and a dedicated channel is used to reduce latency. The group dynamic adjustment mechanism evaluates users' actual response performance weekly, and users in the delay group with a response time rate of over 90% can be upgraded to the fast group.

[0076] A rapid response group is used to synchronize and guide the delayed response group, forming an overall response. A traction mechanism is designed based on the bandwagon and demonstration effects of behavioral economics. An information sharing platform displays the rapid response group's status in real time: the current number of responding users, average response level, and expected cost savings, such as displaying "15 companies in the industrial park have responded to the price signal, with an average load reduction of 20%, and an expected electricity cost saving of 80,000 yuan," thus motivating the delayed group to respond. A traction strength model describes the relationship between the traction effect and the difference in response between the two groups. A time window is set, with the traction effect lasting for 10 minutes; beyond this time window, the traction effect rapidly decays. The social network effect leverages business connections and geographical proximity among users, with related users' response behaviors influencing each other. The response synchronicity is measured using the Pearson correlation coefficient to assess the similarity of the two response curves, with a target value greater than 0.8. An incentive transmission mechanism automatically triggers additional incentive signals for the delayed group when the rapid group's response reaches a certain scale. Feedback enhancement uses methods such as app push notifications and SMS notifications to provide real-time feedback to users in the delayed group on the overall response effect and individual contributions.

[0077] Behavioral patterns are generated from the overall response through cluster analysis. The cluster feature vector construction includes multi-dimensional response features: response initiation time, response peak time, response amplitude, response duration, and recovery time. Data standardization uses the Z-score method to eliminate the influence of different feature dimensions. The clustering algorithm chosen is a hybrid method combining K-means and hierarchical clustering; K-means provides initial partitioning, while hierarchical clustering optimizes category boundaries. The optimal number of clusters is determined using a combination of the elbow rule and silhouette coefficient; analysis shows that the optimal number of clusters is 4-6. Typical behavioral patterns are identified: proactive response (rapid initiation, high amplitude, long duration) accounts for 25%, follower response (medium delay, medium amplitude) accounts for 40%, passive response (large delay, small amplitude) accounts for 25%, and no response accounts for 10%. A pattern transition matrix is ​​constructed to analyze the probability of user behavior pattern transitions under different price signals, identifying stable and volatile patterns. Temporal evolution analysis reveals the distribution and variation patterns of user behavior patterns in different time periods (morning, noon, evening) and different seasons (summer and winter). Abnormal behavior detection identifies unusual response behaviors that deviate from all normal patterns, which may be caused by equipment malfunction or special events.

[0078] Feature extraction is performed based on behavioral patterns to generate group response behavior. The feature extraction dimensions cover four aspects: time characteristics, amplitude characteristics, stability, and coordination of the response. Response speed features include: average response latency, response speed standard deviation, and the proportion of users with a fast response (the percentage of users with a latency of less than 2 minutes). Response depth features include: average response rate, response sufficiency (the percentage of users achieving more than 80% of the expected response), and peak response coefficient. Response consistency features are obtained by calculating the cross-correlation matrix of all user response curves, extracting the average correlation coefficient and consistency index. Response persistence features include: average duration, decay time constant, and rebound rate (the degree of load rebound after the response ends). A Gaussian mixture model is used to fit the group response curve. Feature time-varying analysis establishes the evolution equation of features over time to predict group response characteristics in future periods. Principal component analysis reduces the dimensionality of all features, extracting 3-5 principal components that explain more than 80% of the differences in response behavior.

[0079] Synchronization rate is extracted from group response behavior. The synchronization rate calculation considers differences in user grouping: a 3-minute time window for the rapid response group and a 10-minute time window for the delayed response group, with synchronization rates calculated separately for each group. Synchronization rate is defined as the proportion of users who successfully respond to price signals within the specified time window, and is a key indicator for measuring the effectiveness of demand response. The calculation formula is S_rate = N_sync / N_total × 100%, where S_rate is the synchronization rate, N_sync is the number of users responding synchronously (response delay less than the set window and response magnitude reaching more than 50% of the expected value), and N_total is the total number of target users. Segmented synchronization rate statistics divide the entire day into 96 15-minute time slots, calculating the synchronization rate for each time slot to identify the temporal distribution pattern of the synchronization rate. Synchronization rates are calculated based on behavioral pattern differences: over 90% for proactive responses, over 75% for follower responses, and over 60% for passive responses. Response quality-weighted synchronization rate considers both the quantity and quality of responses. Influencing factor analysis uses multiple regression analysis to analyze the impact coefficients of factors such as price change magnitude, change rate, incentive level, and time period characteristics on the synchronization rate. Synchronization rate target grading is set as follows: Excellent (S_rate≥85%), Good (70%≤S_rate<85%), Satisfactory (60%≤S_rate<70%), and Needs Improvement (S_rate<60%).

[0080] Step S160: Compare the synchronization rate index with the preset target value to form a deviation signal, and correct the price anchor point based on the deviation signal to generate an optimized price sequence, thereby completing the dynamic optimization of the time-of-use electricity price of the virtual power plant.

[0081] Specifically, the synchronization rate index is compared with a preset target value to form a deviation signal. Deviation analysis considers differences in user groups, with target values ​​set for the fast response group and the delayed response group: 90% for industrial users, 80% for commercial users, and 70% for residential users. The preset target values ​​are set differently based on the virtual power plant operation requirements and grid dispatch needs: 85% synchronization rate during peak hours to ensure peak shaving, 75% during normal hours to balance economy and reliability, and 70% during off-peak hours to moderately guide valley filling. Deviation is calculated using the difference between the actual synchronization rate and the target value: e(t) = S_target(t) - S_actual(t), where e(t) is the deviation signal at time t, S_target(t) is the target synchronization rate, and S_actual(t) is the actual measured synchronization rate. Deviation grading assessment classifies deviation severity into four levels: minor deviation (|e|<5%) allows the system to self-adjust; moderate deviation (5%≤|e|<10%) requires moderate intervention; severe deviation (10%≤|e|<15%) requires immediate adjustment; and extreme deviation (|e|≥15%) triggers an emergency response mechanism. Time-series deviation analysis uses a sliding window method with a 30-minute window width to calculate the moving average and trend of deviations, identifying systematic deviations and random fluctuations. Deviation persistence assessment statistically analyzes the duration of continuous deviations; deviations lasting more than one hour are defined as persistent deviations, requiring in-depth strategy adjustments. Deviation distribution characteristic analysis analyzes the frequency and amplitude distribution of positive deviations (target higher than actual) and negative deviations (actual higher than target); positive deviations often indicate insufficient incentives, while negative deviations may indicate over-response. Weighted deviation calculation considers the differences in importance across different time periods: peak periods have a weight of 1.5, average periods 1.0, and trough periods 0.8. The deviation integral index reflects long-term control effectiveness, with an integration time window of 24 hours. Deviation change rate analysis reveals the dynamic characteristics of deviations, reflecting the trend of improvement or deterioration of deviations, and providing a basis for predictive control.

[0082] In some embodiments, the step of generating an optimized price sequence by correcting the price anchor point based on the deviation signal includes: assessing the correction requirement based on the deviation signal and determining the adjustment range, wherein the correction requirement includes the deviation direction, duration, and scope of influence; repositioning the price anchor point according to the adjustment range to form a new anchoring layout; formulating a price transition path based on the new anchoring layout; and generating an optimized price sequence through the price transition path.

[0083] The adjustment range is determined based on the assessment of deviation signals to determine the correction requirements. The adjustment range is determined according to the deviation classification: minor deviations use a fine-tuning strategy (coefficient × 0.5), moderate deviations require normal adjustment, severe deviations require stronger adjustment (coefficient × 1.5), and extreme deviations trigger an emergency adjustment mode. Deviation direction is identified by sign: positive deviation (e>0) indicates insufficient synchronization rate requiring stronger price incentives, while negative deviation (e<0) indicates over-response requiring a moderate price signal. Duration statistics start counting from the first time the deviation exceeds the threshold, recording the cumulative time of continuous deviations. Short-term deviations (<30 minutes) use a fine-tuning strategy, while long-term deviations (>1 hour) require structural adjustments. The impact scope assessment analyzes the scale of the user groups affected by the deviation and the total load, identifying the distribution of affected user types through correlation analysis; industrial users are significantly affected and require special attention. The correction requirement assessment comprehensively considers weighted deviation and integral indicators. Weighted deviation reflects the importance of the time period, while integral indicators assess the cumulative effect. The adjustment range is calculated using a proportional-integral-derivative (PID) control strategy: ΔC = K_p × e(t) + K_i × ∫e(t)dt + K_d × de / dt, where ΔC is the price adjustment amount, K_p = 0.02 yuan / (kWh·%) is the proportional coefficient, K_i = 0.005 yuan / (kWh·%·h) is the integral coefficient, K_d = 0.001 yuan / (kWh·% / h) is the derivative coefficient, e(t) is the deviation signal at time t, dt is the time infinitesimal, ∫ is the integral sign, and de / dt is the derivative of the deviation with respect to time. An amplitude limiting mechanism sets an upper limit for a single adjustment to prevent overly aggressive adjustments from causing system oscillations; the maximum adjustment range does not exceed the smaller of 10% of the current price or 0.1 yuan / kWh. Sensitivity analysis assesses the elasticity of the impact of different adjustment ranges on the synchronization rate, establishes an adjustment range-synchronization rate improvement curve, and identifies the optimal adjustment range.

[0084] The price anchor points are repositioned according to the adjustment range to form a new anchoring layout. Anchor point adjustments consider behavioral patterns: moderate adjustments are made for areas with proactively responsive users, larger adjustments are made for areas with passively responsive users, and a standard adjustment strategy is adopted for areas with follower-responsive users. Anchor point displacement calculation is based on the original position and adjustment range: C_new = C_old + ΔC × f(e,t), where C_new is the adjusted anchor point price, C_old is the original price, f(e,t) is a correction function considering deviation characteristics and time factors, and ΔC is the price adjustment amount. The correction function design uses a non-linear mapping; small deviations are adjusted linearly, while large deviations are compressed using a logarithmic function to prevent overreaction. Displacement direction rules: positive deviations increase the price to enhance incentives, negative deviations decrease the price to reduce incentives, and the direction is opposite to the deviation to form negative feedback control. Displacement constraints ensure that the adjusted anchor points remain within the price fluctuation range; when exceeding the limit, it automatically corrects to the nearest boundary and records the number of constraint activations. Coordination between adjacent anchor points avoids excessively dense or sparse anchor points after adjustment, maintaining a minimum spacing of 0.03 yuan / kWh and a 30-minute time interval. The linkage adjustment mechanism allows for moderate linkage between adjacent anchor points when a significant adjustment is made to a particular anchor point, with the linkage coefficient decreasing with distance. Layout optimization employs a genetic algorithm to globally search for the optimal anchor point configuration, and the fitness function comprehensively considers factors such as expected synchronization rate improvement, price smoothness, and execution difficulty.

[0085] A price transition path is formulated based on the new anchor point layout. The goal of path planning is to achieve a smooth transition from the current price state to the new anchor point layout, minimizing system disturbances during the transition. Trajectory generation uses cubic spline interpolation to connect the new anchor points, ensuring the second-order continuity of the price curve and avoiding abrupt changes in the rate of change. The time allocation strategy determines the total transition period (generally 2-4 hours) and the allocation ratio of each segment based on the urgency of the adjustment and the system's capacity. Transition rate control ensures that the price change rate does not exceed the user's adaptability, with a maximum rate limit of 0.4 yuan / (kWh·h). Key constraints are addressed, including: monotonicity constraints (to avoid repeated price fluctuations), boundedness constraints (to keep prices within the floating range), and ramp rate constraints (to meet physical limitations). Intermediate node optimization involves inserting auxiliary control points between anchor points, optimizing the curve shape by adjusting the control point positions, and reducing overshoot and oscillations. Path smoothing uses Bézier curves or B-splines to improve curve smoothness while maintaining the passage through anchor points. Feasibility verification checks each point to ensure the transition path meets all technical constraints and scheduling requirements; if not, local adjustments are made. Prepare 2-3 alternative paths to address potential execution deviations, and switch between them based on real-time feedback.

[0086] Optimized price sequences are generated through price transition paths. Following the time resolution requirements of the virtual power plant dispatch system, the price transition paths are discretely sampled at 5-minute intervals to ensure the real-time nature and executability of price signals. Timestamps are used to precisely mark the execution time for each price point, employing a standard time format to ensure clock synchronization between systems and avoid dispatching chaos caused by time deviations. Price precision is set to 0.001 yuan / kWh, meeting the accuracy requirements of the billing system while avoiding execution difficulties caused by excessive precision. Sequence integrity checks ensure that the generated price sequences cover the entire dispatching cycle (24 hours), with no missing or overlapping periods, guaranteeing dispatching continuity. Outlier filtering detects and corrects abnormal price points in the sequence, such as negative prices, over-limit prices, and jump points, ensuring the rationality of price signals. Trend maintenance ensures that the overall trend of the optimized sequence matches the system load forecast, with clear peak-valley characteristics, achieving the dispatching goal of peak shaving and valley filling. Quality index calculations include sequence smoothness, peak-valley difference, average rate of change, and maximum rate of change, comprehensively evaluating the optimization effect and completing the dynamic optimization of time-of-use pricing for the virtual power plant.

[0087] To implement the virtual power plant time-of-use pricing dynamic optimization method corresponding to the above method embodiments, and to achieve the corresponding functions and technical effects. See [link / reference]. Figure 2 , Figure 2 This diagram illustrates a structural block diagram of a virtual power plant time-of-use pricing dynamic optimization system 200 provided in an embodiment of this application. For ease of explanation, only the parts relevant to this embodiment are shown. The virtual power plant time-of-use pricing dynamic optimization system 200 provided in this embodiment includes:

[0088] The data acquisition module 201 is used to acquire power time-series data and user-side response records of the distributed resources of the virtual power plant, identify fluctuation components based on the power time-series data, generate price sensitivity coefficients using the user-side response records, and construct an elastic response space based on the matching relationship between the fluctuation components and the price sensitivity coefficients.

[0089] The scheduling generation module 202 is used to perform boundary scanning on the elastic response space to generate a schedulable capacity envelope, set trigger threshold points along the schedulable capacity envelope, deduce the energy storage intervention timing based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the energy storage intervention timing.

[0090] The price determination module 203 is used to obtain the power grid dispatch price sequence and power balance requirements, project the power grid dispatch price sequence onto the elastic response space to form an effective price range, and truncate the effective price range based on the power balance requirements to determine the price fluctuation range.

[0091] Anchoring generation module 204 is used to perform path search within the price fluctuation range using the time-sharing scheduling strategy to obtain changes in user response intensity, identify inflection point positions based on changes in user response intensity, and perform stability assessment on the inflection point positions to generate price anchoring points.

[0092] Synchronization analysis module 205 is used to perform time interval analysis on the price anchor point to generate a price ramp rate, form a price change rate based on the price ramp rate, obtain group response behavior based on the price change rate, and extract a synchronization rate index from the group response behavior.

[0093] The price optimization module 206 is used to compare the synchronization rate index with the preset target value to form a deviation signal, and to correct the price anchor point based on the deviation signal to generate an optimized price sequence, thereby completing the dynamic optimization of the time-of-use electricity price of the virtual power plant.

[0094] The aforementioned virtual power plant time-of-use pricing dynamic optimization system 200 can implement the virtual power plant time-of-use pricing dynamic optimization method described in the above method embodiments. The options in the above method embodiments are also applicable to this embodiment, and will not be detailed here. The remaining content of this application embodiment can be referred to the content of the above method embodiments, and will not be repeated in this embodiment.

[0095] The purpose of the above embodiments is to reproduce and derive the technical solution of the present invention by way of example, and to fully describe the technical solution, purpose and effect of the present invention. The purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosure of the present invention, and not to limit the scope of protection of the present invention.

[0096] The above embodiments are not an exhaustive list based on the present invention, and there may be many other embodiments not listed. Any substitutions and improvements made without departing from the concept of the present invention are within the protection scope of the present invention.

Claims

1. A method for dynamic optimization of time-of-use pricing for virtual power plants, characterized in that, include: The process involves acquiring power time-series data and user-side response records of distributed resources in a virtual power plant, identifying fluctuation components based on the power time-series data, generating a price sensitivity coefficient using the user-side response records, and constructing an elastic response space based on the matching relationship between the fluctuation components and the price sensitivity coefficient. This includes: identifying positive and negative response regions through the matching relationship between the fluctuation components and the price sensitivity coefficient; coupling the peak values ​​of the positive response regions with the valley values ​​of the negative response regions to generate a response potential difference; constructing a response gradient field using the response potential difference; and determining the elastic response space along the equipotential lines of the response gradient field. A boundary scan is performed on the elastic response space to generate a schedulable capacity envelope. Trigger threshold points are set along the schedulable capacity envelope. The timing of energy storage intervention is deduced backward from the trigger threshold points, and a time-sharing scheduling strategy is generated based on the energy storage intervention timing. The step of deducing the timing of energy storage intervention backward from the trigger threshold points includes: generating a power ramp-up trajectory by tracing back from the trigger threshold points; identifying an acceleration start point based on the power ramp-up trajectory; obtaining the energy storage response delay through the acceleration start point; and determining the energy storage intervention timing by shifting the acceleration start point forward based on the response delay. Obtain the power grid dispatch price sequence and power balance requirements, project the power grid dispatch price sequence onto the elastic response space to form an effective price range, and truncate the effective price range based on the power balance requirements to determine the price fluctuation range; The time-sharing scheduling strategy is used to perform path search within the price fluctuation range to obtain changes in user response intensity. Based on the changes in user response intensity, inflection point positions are identified, and stability assessments are performed on the inflection point positions to generate price anchor points. The price anchor point is analyzed over time intervals to generate a price ramp-up rate. The price ramp-up rate is used to form the price change rate. The group response behavior is obtained based on the price change rate. The synchronization rate index is extracted from the group response behavior. The synchronization rate index is compared with the preset target value to form a deviation signal. Based on the deviation signal, the price anchor point is corrected to generate an optimized price sequence, thus completing the dynamic optimization of the time-of-use electricity price of the virtual power plant.

2. The method according to claim 1, characterized in that, The step of determining the price fluctuation range by truncating the effective price range based on the power balance requirement includes: A supply-demand deviation threshold is generated according to the power balance requirements; Based on the supply-demand deviation threshold, the effective price range is compressed by applying an upper bound to generate a compressed range. Stability tests are performed on the compressed interval to generate stable sub-intervals; The longest continuous segment is selected from the stable sub-interval as the price fluctuation range.

3. The method according to claim 1, characterized in that, The process of performing a stability assessment on the inflection point to generate a price anchor point includes: A disturbance test window is constructed based on the inflection point location; The response data within the test window is used to generate a recovery time series; Use the recovery time series to screen for rapid recovery inflection points; The price anchor point is determined by homogenization screening using the aforementioned rapid recovery inflection point.

4. The method according to claim 1, characterized in that, The method of determining the rate of price change based on the price ramp-up rate includes: Extract the points of sudden increase in price rate; The climbing sections are divided based on the points of sudden increase in change; The buffer duration is set for the uphill section based on the user-side response records; The price change rate is formed by reconstructing the climbing section using the buffer period.

5. The method according to claim 1, characterized in that, The process of obtaining the group response behavior based on the rate of price change includes: The rate of price change is broadcast in a tiered manner to generate fast response groups and delayed response groups; The fast response group is used to synchronously guide the delayed response group to form an overall response; Behavioral patterns are generated from the overall response through cluster analysis; Feature extraction is performed according to the described behavioral pattern to generate group response behavior.

6. The method according to claim 1, characterized in that, The step of correcting the price anchor point and generating an optimized price sequence based on the deviation signal includes: The adjustment range is determined based on the assessment of the correction requirements according to the deviation signal, and the correction requirements include the deviation direction, duration, and scope of influence. The price anchor point will be repositioned according to the aforementioned adjustment range to form a new anchoring layout; A price transition path is determined based on the new anchoring layout; An optimized price sequence is generated through the price transition path.

7. The method according to claim 3, characterized in that, The process of determining the price anchor point through homogenization screening based on the rapid recovery inflection point includes: The screening intensity is determined based on the distribution density of the rapid recovery inflection point assessment, whereby the distribution density includes temporal concentration, spatial coverage, and distance between inflection points. The retention rules are set according to the screening intensity; The price anchor point is generated by optimizing the fast recovery inflection point using the retention rules.

8. A dynamic optimization system for time-of-use pricing in virtual power plants, characterized in that, include: The data acquisition module is used to acquire power time-series data and user-side response records of distributed resources in a virtual power plant. Based on the power time-series data, it identifies fluctuation components; using the user-side response records, it generates a price sensitivity coefficient; and based on the matching relationship between the fluctuation components and the price sensitivity coefficient, it constructs an elastic response space. This includes: identifying positive and negative response regions through the matching relationship between the fluctuation components and the price sensitivity coefficient; coupling the peak values ​​of the positive response regions with the valley values ​​of the negative response regions to generate a response potential difference; using the response potential difference to construct a response gradient field; and determining the elastic response space along the equipotential lines of the response gradient field. The scheduling generation module is used to perform boundary scanning on the elastic response space to generate a schedulable capacity envelope, set trigger threshold points along the schedulable capacity envelope, deduce the energy storage intervention timing based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the energy storage intervention timing. The deduce of the energy storage intervention timing based on the trigger threshold points includes: generating a power ramp-up trajectory by tracing back from the trigger threshold points; identifying an acceleration start point based on the power ramp-up trajectory; obtaining the energy storage response delay through the acceleration start point; and determining the energy storage intervention timing by shifting the acceleration start point forward based on the response delay. The price determination module is used to obtain the power grid dispatch price sequence and power balance requirements, project the power grid dispatch price sequence onto the elastic response space to form an effective price range, and truncate the effective price range based on the power balance requirements to determine the price fluctuation range. Anchoring generation module is used to perform path search within the price fluctuation range using the time-sharing scheduling strategy to obtain changes in user response intensity, identify inflection point positions based on changes in user response intensity, and perform stability assessment on the inflection point positions to generate price anchoring points. The synchronization analysis module is used to perform time interval analysis on the price anchor point to generate a price ramp rate, form a price change rate based on the price ramp rate, obtain group response behavior based on the price change rate, and extract the synchronization rate index from the group response behavior. The price optimization module is used to compare the synchronization rate index with the preset target value to form a deviation signal, and to correct the price anchor point based on the deviation signal to generate an optimized price sequence, thereby completing the dynamic optimization of the time-of-use electricity price of the virtual power plant.

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