Virtual power plant time-of-use electricity price dynamic optimization method and system

Abstract

The invention discloses a virtual power plant time-of-use electricity price dynamic optimization method and system, and the method comprises the steps: recognizing a power fluctuation component through obtaining distributed resource power time sequence data and a user response record, generating a price sensitivity coefficient, and constructing an elastic response space reflecting the user response potential; performing boundary scanning on the elastic response space to generate a schedulable capacity envelope, setting a trigger threshold along the envelope, and reversely deriving an energy storage intervention opportunity to form a time-sharing scheduling strategy; projecting the power grid dispatching price to an elastic space, cutting off based on a power balance requirement, and determining a price floating range; searching a user response path in the range, identifying a response intensity change inflection point, evaluating stability, and generating a price anchor point; performing time interval analysis on the anchor points to obtain a price ramp rate and a change speed, and extracting a synchronization rate index of group response behaviors; and comparing the synchronization rate with a target value to generate an optimized price sequence, thereby realizing dynamic adaptive adjustment of the time-of-use electricity price.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimization and control, and in particular to a method and system for dynamically optimizing time-of-use electricity prices in a virtual power plant. Background Art

[0002] A virtual power plant (VPP) is a power system that uses advanced information and communication technologies and software systems to coordinate, optimize, and centrally control distributed energy resources (such as solar and wind power, energy storage equipment, and adjustable loads). However, existing VPP pricing mechanisms often rely on fixed time-of-use electricity prices or simple peak-valley and flat-rate pricing, which struggles to fully mobilize user response and effectively adapt to dynamic changes in grid operation.

[0003] The core challenges currently facing virtual power plant operations are: on the one hand, user response behavior is highly heterogeneous and time-varying, and different types of users have significant differences in sensitivity to price signals. Traditional unified pricing strategies are difficult to stimulate differentiated response potential; on the other hand, grid dispatching needs change in real time with load fluctuations and changes in renewable energy output. Static time-of-use electricity prices cannot flexibly match dynamic dispatching requirements, resulting in the virtual power plant's regulation capabilities not being fully utilized, affecting the safe and economic operation of the power grid. Summary of the Invention

[0004] The present invention provides a method and system for dynamic optimization of time-of-use electricity prices in a virtual power plant. The method aims to characterize the differentiated response characteristics of users by constructing an elastic response space, set multi-level trigger thresholds based on the dispatchable capacity envelope, generate a time-of-use scheduling strategy by reverse deduction of the energy storage intervention opportunity, identify user response inflection points by combining path search within the price fluctuation range, determine the price anchor point by stability assessment, and then dynamically correct the price sequence based on the deviation feedback of the group response synchronization rate to achieve adaptive optimization of the time-of-use electricity price of the virtual power plant.

[0005] A first aspect of the present invention provides a method for dynamically optimizing time-of-use electricity prices in a virtual power plant, comprising the following steps: Obtaining power time series data and user-side response records of distributed resources of a virtual power plant, identifying fluctuation components based on the power time series data, generating price sensitivity coefficients using the user-side response records, and constructing an elastic response space based on a matching relationship between the fluctuation components and the price sensitivity coefficients; Performing boundary scanning on the elastic response space to generate a dispatchable capacity envelope, setting a trigger threshold point along the dispatchable capacity envelope, reversely deducing an energy storage intervention timing based on the trigger threshold point, and generating a time-sharing dispatch strategy based on the energy storage intervention timing; Obtaining a grid dispatch price sequence and a power balance requirement, projecting the grid dispatch price sequence into the elastic response space to form a valid price range, and truncating the valid price range based on the power balance requirement to determine a price floating range; Using the time-sharing scheduling strategy to perform a path search within the price fluctuation range to obtain changes in user response intensity, identifying an inflection point position based on the changes in user response intensity, and performing a stability assessment on the inflection point position to generate a price anchor point; Performing time interval analysis on the price anchor point to generate a price climbing rate, forming a price change speed based on the price climbing rate, obtaining a group response behavior based on the price change speed, and extracting a synchronization rate indicator from the group response behavior; The synchronization rate index is compared with the preset target value to form a deviation signal, and the price anchor point is corrected based on the deviation signal to generate an optimized price sequence, thereby completing the dynamic optimization of the virtual power plant time-of-use electricity price.

[0006] The second aspect of the present invention provides a virtual power plant time-of-use electricity price dynamic optimization system, comprising: a data acquisition module configured to acquire power time series data and user-side response records of distributed resources of 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 a matching relationship between the fluctuation components and the price sensitivity coefficients; a scheduling generation module, configured to perform boundary scanning on the elastic response space to generate a dispatchable capacity envelope, set trigger threshold points along the dispatchable capacity envelope, reversely deduce energy storage intervention timing based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the energy storage intervention timing; a price determination module, configured to obtain a grid dispatch price sequence and a power balance requirement, project the grid dispatch price sequence into the elastic response space to form a valid price range, and truncate the valid price range based on the power balance requirement to determine a price floating range; An anchor generation module, configured to use the time-sharing scheduling strategy to perform a path search within the price fluctuation range to obtain changes in user response intensity, identify an inflection point position based on the changes in user response intensity, and perform a stability assessment on the inflection point position to generate a price anchor point; a synchronization analysis module, configured to perform time interval analysis on the price anchor points to generate a price climbing rate, form a price change rate based on the price climbing rate, obtain a group response behavior based on the price change rate, and extract a synchronization rate indicator 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 based on the deviation signal, correct the price anchor point to generate an optimized price sequence to complete the dynamic optimization of the virtual power plant time-of-use electricity price.

[0007] The beneficial effects of the present invention are reflected in the following aspects: First, through the response potential difference and gradient field construction technology, a three-dimensional characterization of the user response potential and a precise adaptation of the power grid demand are achieved. The peak-valley coupling analysis of the positive and negative response areas is converted into a potential field, the elastic response space is determined along the equipotential line, and the power balance requirement is ensured through price projection mapping and truncation optimization, so that the originally discrete user response characteristics form a continuously adjustable three-dimensional scheduling domain, thereby improving the control accuracy and executability of the price signal. Secondly, the envelope scanning and threshold reverse derivation methods are adopted to achieve predictive scheduling of energy storage resources. By setting a multi-level trigger threshold at the dispatchable capacity boundary, tracing the power climbing trajectory back from the trigger point, considering the response delay to determine the intervention time, the energy storage is transformed from post-compensation to pre-prevention, thereby improving the timeliness of the system's regulation. Finally, a price anchoring mechanism based on the disturbance recovery characteristic and a closed-loop optimization of the synchronization rate index are established to ensure the stability of the electricity price adjustment and the coordination of the group response. By applying disturbances to the response inflection points and analyzing the recovery time series, screening the rapid recovery points as the price anchoring benchmark, and making closed-loop corrections based on price ramp-up rate analysis and synchronization rate quantification, electricity price optimization can both quickly respond to system demand and maintain scheduling stability, thereby achieving coordination and unification of differentiated users.

[0008] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The accompanying drawings herein illustrate specific examples of the technical solutions described in the present invention, and together with the specific implementation methods constitute a part of the specification, and are used to explain the technical solutions, principles and effects of the present invention.

[0010] Unless otherwise specified, the same reference numerals in different drawings represent the same or similar technical features, and the same or similar technical features may also be represented by different reference numerals.

[0011] Figure 1 It is a flow chart of a method for dynamically optimizing time-of-use electricity prices in a virtual power plant according to the present invention.

[0012] Figure 2 It is a structural block diagram of a virtual power plant time-of-use electricity price dynamic optimization system of the present invention. DETAILED DESCRIPTION

[0013] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0014] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0015] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in 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 "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0016] The technical solutions of the embodiments of this application are introduced below.

[0017] like Figure 1 As shown, an embodiment of the present invention provides a method for dynamically optimizing time-of-use electricity prices in a virtual power plant, comprising the following steps S110 to S160: Step S110: obtain the power time series data and user-side response records of the distributed resources of the virtual power plant, identify the fluctuation component based on the power time series data, generate the price sensitivity coefficient using the user-side response record, and construct an elastic response space based on the matching relationship between the fluctuation component and the price sensitivity coefficient.

[0018] Specifically, power time series data and user-side response records for distributed resources in the virtual power plant are collected. Power time series data collection covers all distributed resources within the virtual power plant, including real-time power data from distributed photovoltaic (PV) equipment, energy storage systems, controllable loads, electric vehicle charging stations, and other devices. Data collection is performed every five minutes to capture rapidly changing power patterns. Each data point includes information such as timestamp, device identifier, active power, reactive power, and operating status. User-side response records capture historical user responses to electricity price signals, including parameters such as response time, power change before and after the response, response duration, and electricity price level. Response records span nearly six months to ensure coverage across different seasons and electricity usage patterns. Data preprocessing includes outlier removal, missing value interpolation, and time alignment. Outlier criteria are defined as data points exceeding the rated power range of the device or with a rate of change exceeding physical limits. Data storage utilizes a time series database architecture, supporting efficient time window queries and aggregate computations. A device-user mapping table is established to associate distributed resources with corresponding user responses.

[0019] Fluctuation components are identified based on power time series data. The empirical mode decomposition (EMD) method is used to decompose power time series data into multiple intrinsic mode function (IMF) components. The decomposition process extracts fluctuation characteristics at different time scales through iterative screening. Each IMF component represents power fluctuations within a specific frequency range. Fluctuation component identification focuses on medium- and high-frequency IMF components with time scales ranging from 15 minutes to 4 hours. These components reflect dispatchable power fluctuations. The 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 symbol, P_i(t) is the i-th IMF component, P_avg_i is its mean, and N is the number of data points. The fluctuation period is determined by Hilbert transform to extract the instantaneous frequency and identify the dominant periodic component. Fluctuation components are categorized into regular fluctuations (with obvious periodic characteristics), random fluctuations (without obvious pattern), and sudden fluctuations (with short-term large changes). The fluctuation intensity index is defined as the energy ratio of each IMF component. Components with higher intensity have a greater impact on system operation. A fluctuation feature vector is established, containing multi-dimensional features such as amplitude, period, phase, and energy, for subsequent matching analysis.

[0020] Price sensitivity coefficients are generated using user-side response records. The price sensitivity coefficient reflects 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-of-day differentiation analysis divides a day into peak, flat, and off-peak periods, and calculates the sensitivity coefficient for each period. Based on response characteristics, users are categorized as highly sensitive (K_p > 0.5), moderately sensitive (0.2 ≤ K_p ≤ 0.5), and lowly sensitive (K_p < 0.2). The time-varying nature of the sensitivity coefficient is captured using a sliding window approach, 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 coefficient and establishes a correction model. Response delay analysis identifies the time lag between price signal issuance and user response, with a typical delay ranging from 5 to 30 minutes. A sensitivity coefficient matrix is ​​constructed, with rows representing different user groups and columns representing different time periods. The matrix elements represent the corresponding sensitivity coefficient values. The confidence level of the coefficient is assessed by the number of responses and the consistency of the responses; coefficients with a large number of responses and high consistency have high confidence levels.

[0021] In some embodiments, constructing the elastic response space based on the matching relationship between the fluctuation component and the price sensitivity coefficient includes: identifying positive response areas and negative response areas through the matching relationship between the fluctuation component and the price sensitivity coefficient; coupling analysis of the peak value of the positive response area and the valley value of the negative response area 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.

[0022] Positive and negative response regions are identified by matching the fluctuation component with the price sensitivity coefficient. Differentiated matching is performed based on the fluctuation component type: a periodic matching algorithm is used for regular fluctuations, a statistical correlation method is used for random fluctuations, and a threshold trigger mechanism is used for sudden fluctuations. The matching calculation takes user sensitivity into account, with a weighting coefficient of 1.5 for highly sensitive users, 1.0 for moderately sensitive users, and 0.5 for low-sensitivity users. A correlation coefficient greater than 0.7 is considered a strong match. To account for response delay, the price signal is shifted forward by 5-30 minutes for matching to ensure accurate time series alignment. A sensitivity coefficient matrix is ​​used for time-of-day matching, with corresponding sensitivity coefficient values ​​used for peak, average, and valley periods. Positive response regions are defined as spatiotemporal regions where the fluctuation component rises and the price sensitivity coefficient is positive, indicating that power increases and price increases move in the same direction. Negative response regions are defined as spatiotemporal regions where the fluctuation component falls and the price sensitivity coefficient is negative, indicating that power decreases and price increases move in opposite directions. Region boundaries are determined using a clustering algorithm, and the DBSCAN method is used to identify clusters of response points with similar density. Spatiotemporal mapping projects the response region onto a two-dimensional time-power plane, with the time axis representing a 24-hour day and the power axis representing per-unit power levels. Regional area calculation quantifies the response potential, with larger areas having greater regulatory capacity. Boundary fuzzification takes into account the uncertainty of the actual response and uses fuzzy set methods to process regional boundaries.

[0023] The peaks of the positive response region and the valleys of the negative response region are coupled to generate a response potential difference. A local maximum search algorithm is used to identify the maximum response intensity within the positive response region. Valley identification uses a local minimum search algorithm to identify the minimum response intensity within the negative response region. Coupling analysis considers the temporal correlation between peaks and valleys; peak-valley pairs with a time interval of less than two 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 definition comprehensively considers the response intensity and duration, and is proportional to the product of the two. The coupling strength is assessed using the cross-correlation function of the peak-valley responses; a high cross-correlation coefficient indicates strong coupling. Time-shift analysis identifies the optimal coupling time difference for optimal peak-valley matching. Potential difference distribution statistics analyze the probability density function of the potential difference. The physical meaning of the potential difference characterizes the energy barrier required for a system to adjust from a valley state to a peak state.

[0024] The response potential difference is used to construct the response gradient field. 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 potential energy increase. 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. The gradient field is smoothed using a Gaussian filter with a kernel size of 3×3 to eliminate computational noise. The gradient amplitude reflects the severity of the response change, with regions of large amplitude corresponding to rapid 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 by integrating the gradient field. The divergence and curl analysis of the gradient field identifies the source-sink characteristics and vortex structure of the response. A positive divergence indicates a divergent response, while a negative divergence indicates a converging response.

[0025] The elastic response space is determined along the equipotential lines of the response gradient field. Equipotential lines are defined as lines connecting points of equal potential energy in the gradient field, reflecting areas of equal response potential. Equipotential lines are extracted 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, with different equipotential lines corresponding to different response margins. The spatial boundary is determined using the outermost equipotential lines, which represent the region with actual response capacity. Spatial capacity calculation quantifies the total response potential through volume integration. Response path optimization searches for the path with the minimum gradient within the elastic space to achieve smooth scheduling. Spatial dynamic characteristics analyze changes in the elastic space at different times, identifying expansion and contraction patterns. Multi-dimensional expansion combines price, power, and time into a three-dimensional elastic response space, providing more comprehensive support for scheduling decisions. 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.

[0026] Step S120 , performing boundary scanning on the elastic response space to generate a dispatchable capacity envelope, setting trigger threshold points along the dispatchable capacity envelope, reversely deducing energy storage intervention timing based on the trigger threshold points, and generating a time-sharing scheduling strategy based on the energy storage intervention timing.

[0027] Specifically, the elastic response space is boundary scanned to generate the dispatchable capacity envelope. Using the ray method, rays with equal angle intervals are emitted outward from the geometric center of the elastic response space. The angle step is set to 5 degrees, and a total of 72 rays cover the entire plane. The intersection of each ray and the boundary of the elastic space constitutes a boundary point set. The time coordinates and power coordinates of the intersection are recorded to form a boundary feature database. The dispatchable capacity is defined as the radial distance from the boundary point to the center, reflecting the maximum regulation ability in this direction. Envelope generation connects all boundary points through cubic spline interpolation to ensure the second-order continuity and smoothness of the curve. Time-varying characteristic analysis examines the morphological changes of the envelope at different times, identifies the periods of capacity expansion and contraction, and establishes a dynamic capacity prediction model. The envelope area calculation quantifies the total dispatchable capacity, A=∫∫ D dP·dt, where A is the area enclosed by the envelope, subscript D is the elastic response space domain, P is power, t is time, ∫∫ is the double integral symbol, dP is the power element, and dt is the time element. Morphological feature extraction includes geometric indicators such as the envelope's convexity, symmetry, compactness, and eccentricity, which are used to evaluate the distribution of scheduling potential.

[0028] Trigger thresholds are set along the dispatchable capacity envelope. The threshold distribution strategy considers the envelope's morphological characteristics: Convex regions increase threshold density, symmetric regions adopt a symmetrical layout, and compact regions reduce threshold spacing. Based on the envelope's curvature analysis, threshold points are prioritized where curvature changes dramatically, ensuring a sensitive response to system state changes. The curvature calculation formula is κ=|d²P / dt²| / (1+(dP / dt)²)^(3 / 2), where κ is the curvature, P is power, t is time, |·| is the absolute value sign, d²P / dt² is the second-order derivative of power with respect to time, dP / dt is the first-order 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 based on system response speed and dispatch accuracy requirements. The threshold interval is 10 MW in fast-response regions and 20 MW in slow-response regions. 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). This 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 the threshold point records the corresponding time and validity period, which is used for time-series scheduling decisions and threshold update management. Threshold sensitivity analysis evaluates the impact of small changes in system state on threshold triggering and establishes a sensitivity matrix.

[0029] In some embodiments, the reverse derivation of the energy storage intervention timing based on the trigger threshold point includes: tracing back based on the trigger threshold point to generate a power climbing trajectory; identifying an acceleration starting point according to the power climbing trajectory; obtaining an energy storage response delay through the acceleration starting point; and moving the acceleration starting point forward based on the response delay to determine the energy storage intervention timing.

[0030] Differentiated reverse derivation strategies are employed for different trigger threshold levels. The warning threshold corresponds to the pre-preparation mode (retracing back 15 minutes), the action threshold corresponds to the rapid response mode (retracing back 30 minutes), and the extreme threshold corresponds to the emergency intervention mode (retracing back 45 minutes). Power ramp trajectories are generated by tracing back from the trigger threshold. The tracing time window is set based on the threshold level to ensure that the complete power change process and early warning signs are captured. Trajectory reconstruction uses the reverse 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, which is increased to 10 seconds through interpolation to ensure the temporal resolution and change details of the trajectory. A Kalman filter is used for trajectory smoothing, and the state equation considers the physical constraints of power change to eliminate the impact of measurement noise on the trajectory. Slope calculation identifies the power change rate, which is measured in MW / min. Trajectory segmentation is based on slope change and duration, dividing the complete trajectory into stable segments (rate of change less than 5 MW / min), slowly rising segments (rate of change 5-20 MW / min), and rapidly rising segments (rate of change greater than 20 MW / min). Feature point marking includes key locations such as starting points, turning points, acceleration points, and peak points, creating a feature point time series database. Multiple trajectories are compared and analyzed for climbing patterns associated with different triggering events, extracting common features and establishing a standard climbing template. Trajectory data storage includes multi-dimensional information such as time series, power series, slope series, and acceleration series.

[0031] The acceleration onset is identified based on the power ramp trajectory. Curvature characteristics are taken into account when identifying the acceleration onset. Acceleration thresholds are lowered in high-curvature regions, and identification parameters are adjusted using a sensitivity matrix. The acceleration onset is defined as the moment when the power rate of change first exceeds a set threshold and maintains an upward trend. The threshold is set to the greater of 1.5 times the average rate of change or 10 MW / min. Second-order derivative analysis identifies acceleration changes, with the power acceleration unit expressed in MW / min². Candidate acceleration points are identified when the acceleration is positive and continuously increases by more than 0.5 MW / min². Continuity checks ensure that the acceleration process lasts for more than 3 minutes, eliminating false acceleration points caused by transient disturbances and measurement noise. Multi-scale analysis identifies acceleration characteristics at different time scales, such as 1 minute, 5 minutes, and 10 minutes, to comprehensively assess the true acceleration behavior. Acceleration intensity assessment quantifies the average and peak accelerations of the acceleration segment and establishes an acceleration intensity classification standard. Temporal consistency analysis analyzes the temporal distribution patterns of multiple acceleration points to identify systematic acceleration patterns. Acceleration pattern classification identifies acceleration types such as linear, exponential, step, and oscillatory acceleration, and differentiated response strategies are developed for each pattern. Prioritization determines the main acceleration points based on the comprehensive scores of acceleration intensity, duration and stability.

[0032] The energy storage response delay is obtained by accelerating the starting point. Response delay consists of three main components: communication delay, decision delay, and execution delay, each of which is subject to uncertainty. Communication delay 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 delay involves the computation time of the scheduling algorithm and the multi-objective optimization solution, and ranges from 1-5 seconds depending on system complexity and optimization accuracy requirements. Execution delay is the time from when the energy storage system receives a command until its actual output power reaches 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 delay is calculated as T_delay = T_comm + T_dec + T_exec, where T_delay is the total response delay, T_comm is the communication delay, T_dec is the decision delay, and T_exec is the execution delay. The probability distribution analysis of delays takes into account random factors such as network congestion and computational load, and uses a gamma distribution to describe it.

[0033] Based on the response delay, the acceleration starting point is advanced to determine the timing of energy storage intervention. The advance equals the total response delay plus a safety margin: T_advance = T_delay + T_margin, where T_advance is the advance time and T_margin is the safety margin, typically 20% of the total delay. The intervention timing is calculated as the acceleration starting point minus the advance, ensuring that energy storage action is synchronized with demand. Timing validity verification examines system status at the time of intervention, including constraints such as available energy storage capacity, grid acceptance, and other resource scheduling. Multi-scenario adaptability analyzes intervention timing differences based on load patterns, seasonal characteristics, and weather conditions, establishing a scenario knowledge base. Intervention intensity presets determine the initial output power based on factors such as power shortfall 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 uses Monte Carlo simulation to analyze the impact of uncertainties on intervention timing. A coordination mechanism manages the timing of interventions for multiple energy storage systems to avoid power surges caused by simultaneous activation.

[0034] A time-of-use dispatch strategy is generated based on the timing of energy storage intervention. The dispatch strategy takes response delay characteristics into account, with energy storage devices with larger T_delay being started earlier. Power ramp-up trajectories are used to predict dispatch intensity requirements. Time-of-use scheduling comprehensively considers system load characteristics, electricity price levels, and user electricity consumption behavior, dividing the day into six dispatch periods: morning peak (7:00-9:00), morning flat period (9:00-11:00), afternoon peak (11:00-14:00), afternoon flat period (14:00-17:00), evening peak (17:00-21:00), and nighttime valley period (21:00-7:00). Dispatching targets are set differently for each period, with a focus on peak load reduction during peak periods, maintaining stable power during flat periods, and optimizing energy reserves during valley periods. Energy storage charging and discharging plans are developed based on power demand forecasts, electricity price signals, and energy storage status for each period, and are optimized using a dynamic programming algorithm. Charging priority is set based on a comprehensive consideration of factors such as electricity prices, energy storage state of charge (SOC), and expected discharge demand. Priority is given to charging when electricity prices are low and SOC is low. The power allocation strategy considers the power and capacity constraints of energy storage, with 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 that energy storage has sufficient energy reserves at critical moments, maintaining a healthy SOC range of 20%-80%, with an allowable range of 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.

[0035] Step S130, obtaining a grid dispatch price sequence and a power balance requirement, projecting the grid dispatch price sequence into the elastic response space to form a valid price range, and truncating the valid price range based on the power balance requirement to determine a price floating range.

[0036] Specifically, grid dispatch price series and power balance requirements are obtained. The grid dispatch price series is derived from day-ahead market clearing results and real-time market price signals. It contains time-of-use electricity price data for the next 24 hours. Each data point includes attributes such as timestamp, electricity value, and price type identifier. Price data covers various pricing mechanisms, including benchmark electricity prices, peak-valley time-of-use electricity prices, tiered electricity prices, and dynamic electricity prices. The time resolution is 15 minutes, consistent with the virtual power plant's dispatch cycle. The historical price data lookback window is set to 30 days, building 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 (using a boxplot method to identify outliers exceeding 1.5 times the interquartile range), missing value filling (using a weighted average of the preceding and following values), and noise filtering (applying a 5-point moving average filter). Power balance requirements are obtained in real time through a dedicated interface of the dispatch automation system. They include core parameters such as load forecast values ​​for each time period, upper and lower limits on dispatchable capacity, ramp rate constraints, and spinning reserve requirements. Balancing accuracy must be strictly controlled within ±2% of the total system load, and a graded response mechanism must be established to handle varying degrees of power deviation. System constraints comprehensively consider multiple dimensions, including transmission line thermal stability limits, transformer capacity limitations, busbar voltage deviation range, and system frequency deviation tolerances.

[0037] The grid dispatch price series is projected onto the elastic response space to form effective price intervals. The projection process takes into account differences in pricing mechanisms: linear mapping is used for base prices, segmented mapping is used for peak and valley time-of-use prices, step mapping is used for tiered prices, and nonlinear mapping is used for dynamic prices. The projection process transforms the one-dimensional price time series into a two-dimensional time-power response plane, establishing a quantitative relationship between price signals and the system's regulatory capacity. The mapping function is based on the price-power response model fitted with 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 baseline operating power, K_p is the price sensitivity matrix (accounting for differentiated responses by user type), C_ref is the reference price level, and ε is a random perturbation term. The effective interval identification algorithm determines whether each price projection point lies within the feasible region of the elastic response space. Computational geometry methods are used 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 within the response space. High-density areas represent the system's normal operating range.

[0038] In some embodiments, the truncation of the effective price range based on the power balance requirement to determine the price floating range includes: generating a supply and demand deviation threshold according to the power balance requirement; performing upper bound compression on the effective price range based on the supply and demand deviation threshold to produce a compressed range; performing a stability test on the compressed range to produce a stable sub-range; and selecting the longest continuous segment from the stable sub-range as the price floating range.

[0039] Supply-demand deviation thresholds are generated based on power balance requirements. These thresholds are set based on historical price fluctuation statistics and are adjusted to take into account system constraints such as transmission line thermal stability limits and transformer capacity limitations. Real-time supply-demand deviation calculations are based on a comprehensive analysis of load forecasts, renewable energy output forecasts, and dispatchable resource capacity. ΔP(t) = P_load(t) + P_loss(t) - P_gen(t) - P_res(t), where ΔP(t) represents the supply-demand deviation at time t, P_load(t) represents the load demand, P_loss(t) represents the network loss, P_gen(t) represents the output of conventional generators, and P_res(t) represents the output of renewable energy sources. The threshold system uses a dynamic, tiered setting. The deviation threshold for normal operation is ±50 MW, increasing to ±100 MW for warning status and ±150 MW for emergency status. In extreme cases, ±200 MW is permitted. Time-varying characteristics take into account system operating characteristics at different times of day. The threshold is tightened by 20% during peak hours in the morning and evening to improve control accuracy, and relaxed by 30% during off-peak hours in the middle of the night to reduce control costs. The statistical threshold is based on a probability distribution analysis of historical operating data. Kernel density estimation is used to fit the deviation distribution, and the quantile corresponding to a 90% confidence level is selected as the upper threshold limit. An adaptive adjustment mechanism dynamically adjusts the threshold based on factors such as the system's real-time status, weather changes, and major events. Intelligent adjustments are implemented through a rule-based expert system.

[0040] Based on the supply-demand deviation threshold, the upper bound of the effective price range is compressed to generate a compressed range. The compression strategy incorporates the projected density distribution characteristics, prioritizing high-density areas. The post-compression power response is predicted using the mapping function P(C). Starting from the upper bound of the price range, the compression strategy uses an iterative algorithm with an adaptive step size to gradually lower the upper bound until the predicted system response meets all deviation threshold constraints. The iterative algorithm combines the fast convergence characteristics of the Newton-Raphson method with the global convergence guarantee of the bisection method, dynamically switching algorithms based on convergence. 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. It inputs the compressed price upper bound and outputs the expected power response and deviation level. Convergence is determined using a dual criterion: a price change of less than 0.01 yuan / kWh and a deviation improvement rate of less than 1%, or if the number of iterations exceeds 50, forcing the system to terminate. The compression path optimization records the complete state of each iteration, including price value, prediction deviation, various user responses, and system stability indicators, to construct a state transition diagram for the compression process.

[0041] Stability testing is performed on the compressed interval to generate stable subintervals. Stability testing takes into account the projected density distribution, reducing testing intensity in high-density areas and strengthening verification in low-density areas. The stability test design comprehensively considers small-signal stability, transient stability, and voltage stability, building a comprehensive test case library. The disturbance signal generator produces standard test signals: step disturbances (amplitude 5% of the interval width, duration 30 seconds), ramp disturbances (rate of change 0.02 yuan / kWh / min), sinusoidal disturbances (frequency 0.1-1Hz, increasing amplitude), and white noise disturbances (power spectral density 0.001). Dynamic response evaluation utilizes standard stability metrics: overshoot, rise time, settling time, steady-state error, damping ratio, and other key parameters. Sensitivity analysis calculates the sensitivity matrix of the system output to price disturbances, identifying high-sensitivity areas and marking them as potentially unstable. Phase trajectory analysis plots the system trajectory in state space and determines the system's stability type (asymptotically stable, Lyapunov stable, or unstable) based on the trajectory shape. The stability margin is quantitatively assessed using gain margin and phase margin metrics, requiring a gain margin greater than 6dB and a phase margin greater than 45 degrees. The subinterval partitioning algorithm, based on stability test results, employs dynamic programming to identify the maximum continuous stable segment, allowing for multiple discontinuous stable subintervals.

[0042] The longest continuous segment within the stable sub-interval is selected as the price fluctuation range. The continuity criteria comprehensively consider temporal and numerical continuity: the time interval between adjacent price points must not exceed 30 minutes, the price jump must not exceed 0.02 yuan / kWh, and the rate of change must not exceed 0.05 yuan / kWh / h. A weighted approach is used to measure length, taking into account time span, stability, and coverage. The multi-objective optimization model considers objectives such as maximizing interval length, maximizing stability margins, including the current operating point, and covering key time periods. The NSGA-II algorithm is used to find the Pareto optimal solution set. Endpoint optimization fine-tunes the interval endpoints to maximize interval length while ensuring stability. The optimal endpoints are determined using a golden section search. Time period coverage requires that the selected interval cover at least 85% of key periods, such as the morning peak (7:00-9:00) and evening peak (18:00-20:00). If this requirement is not met, a multi-interval splicing solution 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. Decision support information includes the basis for interval selection, analysis of expected scheduling effects, potential risk warnings, and suggestions for alternative plans.

[0043] Step S140 , using the time-sharing scheduling strategy to perform a path search within the price floating range to obtain changes in user response intensity, identifying an inflection point position based on the changes in user response intensity, and performing a stability assessment on the inflection point position to generate a price anchor point.

[0044] Specifically, a time-sharing scheduling strategy is used to search for paths within the price fluctuation range to capture changes in user response intensity. A dynamic programming algorithm is used to discretize 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 price state, taking into account ramp rate constraints and price boundary limits. A 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 integration symbol, τ is the integration variable, ΔC(τ) is the price change at time τ, and dτ is the integral differential element. Response delay characteristics are described using a transfer function, taking into account the differences in response time for different user types: industrial users have a delay of 1-3 minutes, commercial users 3-5 minutes, and residential users 5-10 minutes. Response strength is quantified using a normalization method, using the ratio of actual response power to maximum adjustable power as the strength indicator. Path evaluation metrics include total cost, response volatility, execution difficulty, and other dimensions.

[0045] Inflection points are identified based on changes in user response intensity. Inflection point identification takes into account differences in user type. Industrial users with short delays use high-frequency detection (1-minute windows), while residential users with long delays use low-frequency detection (5-minute windows). An inflection point is defined as the spatiotemporal location where the response intensity trend significantly changes, including instances where the growth rate changes from positive to negative, from negative to positive, or a sudden change in the rate of change. The mathematical identification method uses the first- and second-order derivatives of the response intensity. The first-order derivative represents the rate of change of the response, while the second-order derivative represents the acceleration of change. Inflection point determination criteria are: the second-order derivative crosses zero, the absolute value of the first-order derivative exceeds a threshold of 0.05 / min, or the rate of change of the first-order derivative exceeds twice the average value. The sliding window detection method uses different window widths based on 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 inflection point (response trend reversal), and sudden inflection point (response changes abruptly). Inflection point strength is defined as the product of the absolute value of the curvature at the inflection point and the magnitude of the response change. A higher strength indicates a more significant inflection point. Temporal cluster analysis combines inflection points with similar time intervals (less than 10 minutes apart) into inflection point clusters, selecting the strongest inflection point within the cluster as a representative. Multi-scale detection identifies inflection points at different time scales, such as 5 minutes, 15 minutes, and 30 minutes, and integrates detection results from different scales to improve accuracy. The inflection point feature vector contains attributes such as temporal location, price level, response strength, inflection point type, and impact range.

[0046] In some embodiments, the stability assessment of the inflection point position to generate a price anchor point includes: constructing a disturbance test window based on the inflection point position; using the response data within the test window to generate a recovery time series; using the recovery time series to screen fast recovery inflection points; and determining a price anchor point by performing homogenization screening on the fast recovery inflection points.

[0047] A perturbation test window is constructed based on the inflection point location. The test window design takes into account the differences in inflection point types. The observation period is extended to 40 minutes for peak and trough inflection points, shortened to 25 minutes for turning inflection points, and increased to ±8% for sudden inflection points. The test window, centered at the inflection point, extends 10 minutes forward as a preparation period and 30 minutes backward as an observation period, for a total test period of 40 minutes. The perturbation signal design includes both positive and negative price perturbations, with the perturbation amplitude tailored to the inflection point type to ensure it falls within the system's linear response range. Perturbation injection is selected two minutes after the inflection point occurs, when the system has just completed its state transition and is most sensitive to perturbations. The perturbation duration is set to five minutes, stimulating the system's dynamic response without causing excessive disturbances. The data sampling frequency within the window is increased to 30 seconds per test to accurately capture rapid system dynamics. Environmental variable control ensures that other influencing factors remain stable during testing, isolating the impact of the price perturbation. A repeated testing strategy performs five independent perturbation tests for each inflection point, with statistical averaging used to eliminate the influence of random factors. The test data records include 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 processing targets inflection points near the boundaries of the price range and adjusts the disturbance direction to avoid crossing the boundary.

[0048] Recovery time series are generated using response data within the test window. The recovery process is defined as the complete period from the end of the disturbance to the point at which the system response returns to its pre-disturbance steady-state level. The baseline is determined by taking the weighted average of the response strength within the 5 minutes before the disturbance, with weights increasing over time to reflect the latest state. The recovery criterion is set as the response strength returning to within ±2% of the baseline and remaining within this range for at least 2 minutes to avoid misjudgments caused by temporary crossovers. Time series construction records the response strength 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, and exp(-t / τ) is the exponential decay function. Exp is an exponential function with the natural constant e as its base, and R_rec(t) is the recovery response strength at time t. The time constant τ reflects the system's recovery speed; 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 oscillation recovery, step recovery, and divergent recovery. Different modes reflect different stability characteristics of the system.

[0049] Recovery time series are used to screen for fast-recovery inflection points. A fast recovery is defined as a recovery time of less than 10 minutes with a monotonic, non-oscillatory recovery process. The screening index system increases the weight of inflection point strength, prioritizing those with high strength. A screening index system was established, with key indicators including 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 time constant consistency. The inflection point strength score is determined based on the absolute value of the curvature and the amplitude of the response change. A weighted summation method is used to calculate the overall score, with inflection points with a score exceeding 0.7 being labeled fast-recovery inflection points. Statistical analysis is conducted on the distribution characteristics of fast-recovery inflection points, including their density within the price range and their temporal distribution patterns. Recovery pattern clustering groups inflection points with similar recovery characteristics to identify typical recovery patterns. Outlier processing eliminates abnormal inflection points with extremely short (<2 minutes) or extremely long (>20 minutes) recovery times. Priority is ranked from high to low based on the overall score.

[0050] Exemplarily, the method of determining a price anchor point by performing homogenized screening on the rapid recovery inflection point includes: determining the screening intensity based on evaluating the distribution density of the rapid recovery inflection point, wherein the distribution density includes time concentration, spatial coverage, and distance between inflection points; setting a retention rule according to the screening intensity; and using the retention rule to screen the rapid recovery inflection point to generate a price anchor point.

[0051] Screening intensity is determined based on the distribution density of rapid recovery inflection points. Temporal concentration is calculated using a sliding time window with a 2-hour window width, and the number and density of inflection points within the window are counted. Spatial coverage assesses the uniformity of the distribution of inflection points in the price dimension. The price range is divided into 10 equal subranges, and the Gini coefficient is calculated to reflect the degree of distribution inequality. The distance between inflection points includes both temporal and price distances, measured using the normalized Euclidean distance metric: 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, and ² represents the square operation. Δt_ij and ΔC_ij are the time and price differences, respectively, and T_range and C_range are normalization parameters. Density grading is based on a comprehensive assessment of three indicators, with three levels: high-density (requiring strong screening), medium-density (moderate screening), and low-density (weak screening). The screening intensity coefficient is determined based on density level, with 30% 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 of inflection points. A positive correlation indicates a clustered distribution, necessitating enhanced screening. Hotspot analysis identifies spatiotemporal regions with a high concentration of inflection points; these areas require targeted screening to improve distribution uniformity.

[0052] Retention rules are set based on screening intensity. Differentiated retention strategies are developed based on density levels, with strict screening rules applied to high-density areas, moderate screening rules applied to medium-density areas, and loose screening rules applied to low-density areas. The mandatory rule ensures that inflection points in key locations are not excluded: the first inflection point of the day (initiating scheduling), peak-to-valley transition inflection points (changing scheduling direction), and inflection points near price extremes (boundary control). The performance priority rule prioritizes inflection points with high recovery performance scores under the same conditions. The score is calculated based on a comprehensive analysis of recovery time, recovery quality, and stability. The uniform distribution rule requires that retained inflection points be distributed as evenly as possible along the timeline. K-means clustering is used to determine the ideal location, 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 rising and falling inflection points for selection. The time period balance rule ensures a relatively balanced number of anchor points across different time periods, avoiding overcrowding or sparseness in some time periods. Rule priority setting: mandatory rule > time period balance > performance priority > uniform distribution > complementarity.

[0053] Retention rules are used to screen for fast-recovery inflection points to generate price anchor points. Anchor point scoring takes into account path evaluation metrics, with bonus points awarded for low total cost, low volatility, and low execution difficulty. Multiple rounds of screening are conducted strictly according to rule priority: the first round applies the mandatory rule to identify key inflection points; the second round applies the time period balance rule to ensure balance across time periods; the third round applies the performance priority rule to select high-scoring inflection points; the fourth round applies 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 effects, and path evaluation metrics. Constraint satisfaction checks ensure that the final solution meets all hard constraints, such as minimum interval, quantity restrictions, and coverage requirements. Anchor strength is assigned different weights based on the inflection point's impact and responsiveness, with strong anchor points receiving a weight of 1.5 and standard anchor points receiving a weight of 1.0. Timeliness annotation sets a validity period for each anchor point: general anchor points are valid for 24 hours, while special event anchor points are determined based on the duration of the event. Associations are established to record successive, mutually exclusive, and reinforcing relationships between anchor points, forming an anchor point relationship network.

[0054] Step S150 , performing time interval analysis on the price anchor point to generate a price climbing rate, forming a price change speed based on the price climbing rate, obtaining a group response behavior according to the price change speed, and extracting a synchronization rate indicator from the group response behavior.

[0055] Specifically, the price anchor points are analyzed for time intervals to generate the price ramp rate. The time interval calculation is for adjacent price anchor points, extracting the timestamp information of each pair of 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 calculates 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 rate is defined as the price change per unit time, r_i=ΔC_i / Δt_i, in units of yuan / (kWh·h), where r_i is the ramp rate, reflecting the speed of price adjustment, ΔC_i is the price change, and Δt_i is the time interval. Ramp rates are categorized by magnitude and direction: slow ramping (|r| < 0.1) is suitable for stable system operation, normal ramping (0.1 ≤ |r| < 0.3) is used for routine regulation, and rapid ramping (|r| ≥ 0.3) is used for emergency situations. Directional analysis distinguishes between increasing ramps (r > 0) for load suppression or energy storage discharge, and decreasing ramps (r < 0) for incentivizing power consumption or energy storage charging. Ramp persistence assessment identifies sequences of anchor points for continuous, unidirectional ramping. Ramp durations exceeding two hours are defined as trending. The ramp rate sequence forms a complete time series {r_1, r_2, ..., r_n}.

[0056] In some embodiments, forming the price change speed based on the price climbing rate includes: extracting the change sudden increase point from the price climbing rate; dividing the climbing segments according to the change sudden increase point; setting a buffer time for the climbing segments based on the user-side response record; and using the buffer time to reconstruct the climbing segments to form the price change speed.

[0057] Sudden changes are extracted from the price ramp rate. Sudden change point identification takes into account the differences in ramp rate classification. The sudden change threshold is lowered to 70% of the original value for fast ramping segments and increased to 150% for slow ramping segments. Different threshold coefficients are used for rising and falling ramps. A sudden change point is defined as the point where the ramp rate exceeds the set threshold, indicating a turning point in the price adjustment strategy. The rate of change is calculated by taking the difference between adjacent ramp rates, with a statistical threshold determined based on historical data analysis. Sudden change types are categorized as follows: a positive sudden change indicates an accelerating upward trend, a negative sudden change indicates an accelerating downward trend, and a bidirectional sudden change indicates a reversal of adjustment direction. Sudden change intensity is quantified as the ratio of the actual rate of change to the threshold, with an intensity greater than 2 being defined as a strong sudden change. A time stamp precisely records the occurrence of each sudden change point for subsequent time series analysis. Continuous sudden change processing combines multiple sudden changes with an interval of less than 10 minutes into a single sudden change event to avoid over-segmentation. Sudden change cause analysis correlates with system operating status to identify whether the cause is a sudden load change, fluctuations in renewable energy resources, or adjustments to the dispatch strategy.

[0058] Ramp-up segments are divided based on the sudden change points. A ramp-up segment is defined as a continuous interval between two adjacent sudden change points, exhibiting relatively consistent ramp-up characteristics. Segment boundaries are determined using the sudden change points as natural demarcations, while also considering minimum segment length constraints (no less than 15 minutes) and maximum segment length limits (no more than 2 hours). Segment type identification is based on intra-segment ramp-up rate characteristics: start-up segment (ramp-up from zero), acceleration segment (increasing ramp-up rate), constant speed segment (stable ramp-up rate), deceleration segment (decreasing ramp-up rate), and stop segment (ramp-up rate approaching zero). Segment statistical features extracted include average ramp-up rate, ramp-up rate variance, cumulative price change, and duration. Transition segments identify buffer zones between two major ramp-up segments. These typically have low ramp-up rates and gradual changes, providing a smooth transition. Abnormal segments are segments where the ramp-up rate frequently alternates between positive and negative, or where the value exceeds the reasonable range, requiring special handling strategies. Segment merging rules merge short segments with similar characteristics and adjacent time periods. Segment correlation analysis identifies causal relationships and temporal dependencies between different ramp-up segments and constructs an inter-segment transition probability matrix.

[0059] A buffer period is set for ramp-up periods based on user-side response records. This buffer period reflects the time it takes for users to react from perceiving a price change to actually adjusting their electricity usage. Historical response analysis extracts actual response delays at different ramp-up rates from user-side response records and establishes a ramp-rate-response time mapping. A response time model is constructed using a nonlinear fitting method. Differentiated settings are implemented for user categories: large industrial users have shorter buffer periods (fast response), commercial users have moderate buffer periods (moderate response), and residential users have longer buffer periods (slow response). The time-of-day influencing factor considers user response enthusiasm during different time periods, shortening the buffer period during peak hours, maintaining a normal buffer period during off-peak hours, and extending the buffer period during off-peak hours. The buffer period constraint is set with an upper limit of 15 minutes to prevent excessive delays and a lower limit of 3 minutes to ensure users have sufficient response time. A dynamic adjustment mechanism updates model parameters online based on real-time response feedback.

[0060] The buffer duration is used to reconstruct the ramping segments to generate the price change rate. The reconstruction goal is to transform the original step-like ramping into a smooth process that takes into account user response characteristics. The speed curve is modeled using the S-shaped function: 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 for that segment (equal to the original ramp rate), k is the curve steepness parameter, t_c is the inflection point time (set at the midpoint of the buffer duration), and exp(·) is an exponential function. Curve parameter determination: The k value is calculated based on the buffer duration to ensure that the main transition is completed within the buffer duration. A speed limit mechanism ensures that the reconstructed maximum speed does not exceed the user-acceptable limit; if it exceeds, peak shaving is implemented. Cubic spline interpolation is used to connect segments, ensuring the continuity of the first-order derivatives of the speed curves of adjacent segments and avoiding sudden speed changes. Cumulative price verification ensures that the total price change before and after reconstruction is consistent. Timeline mapping maps the reconstructed speed curve to the actual timeline, taking into account the specific time of the anchor points.

[0061] In some embodiments, obtaining group response behavior based on the price change speed includes: hierarchically broadcasting the price change speed to generate a quick response group and a delayed response group; synchronously pulling the delayed response group with the help of the quick response group to form an overall response; generating a behavior pattern for the overall response through cluster analysis; and performing feature extraction according to the behavior pattern to generate group response behavior.

[0062] A tiered broadcast strategy based on the speed of price changes creates a fast-response group and a delayed-response group. This tiered broadcast strategy takes into account the ramp-up phase, prioritizing the fast-response group during startup and acceleration phases, while focusing on the delayed-response group during steady-state and deceleration phases. The tiering criteria are determined based on 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 pricing contracts, and energy storage power plants 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), general commercial users, and residential users who rely on manual adjustments, with a typical response time of 5-15 minutes. The broadcast strategy utilizes differentiated information push: the fast group receives the raw, real-time price change speed signal, updated every 30 seconds; the delayed group receives the smoothed signal, updated every 5 minutes. The signal encoding format includes fields such as timestamp, target group identifier, price speed value, expected response direction, and incentive coefficient. Communication priority settings ensure that signals from the fast-response group are transmitted first, using dedicated channels to minimize latency. The dynamic group adjustment mechanism evaluates users' actual response performance once a week. Users in the delayed group with a timely response rate exceeding 90% can be upgraded to the fast group.

[0063] The fast-responding group leverages the delayed-responding group to synchronize and leverage their response, leading to a coordinated response. A traction mechanism is designed based on the herd effect and demonstration effect of behavioral economics. The information sharing platform displays the fast-responding group's response status in real time: the current number of responding users, average response rate, and projected cost savings. For example, a display such as "15 enterprises in the industrial park have responded to the price signal, reducing their load by an average of 20%, resulting in an estimated electricity bill savings of 80,000 yuan" motivates the delayed-responding group. A traction intensity model describes the relationship between the traction effect and the difference in response between the two groups. The traction effect is valid for 10 minutes, after which the effect rapidly decays. The social network effect leverages the business connections and geographic proximity between users, allowing the response behaviors of related users to influence each other. The response synchronization metric uses the Pearson correlation coefficient to assess the similarity of the response curves of the two groups, with a target value greater than 0.8. The incentive transmission mechanism automatically triggers additional incentive signals for the delayed group when the fast-responding group reaches a certain scale. Feedback enhancement provides real-time feedback on the overall response effect and individual contributions to users in the delayed group through app push notifications and SMS notifications.

[0064] Cluster analysis was used to identify behavioral patterns in overall responses. Cluster feature vectors were constructed, encompassing multidimensional response features: response onset time, response peak time, response amplitude, response duration, and recovery time. Data normalization employed the Z-score method to eliminate dimensionality effects among different features. A hybrid clustering algorithm, combining K-means and hierarchical clustering, was selected. K-means provided preliminary segmentation, while hierarchical clustering optimized cluster boundaries. The optimal number of clusters was determined using a combination of the elbow rule and the silhouette coefficient. Analysis indicated that the optimal number of clusters was 4-6. Typical behavioral patterns identified included active responses (fast onset, high amplitude, and long duration) accounting for 25%, follower responses (medium delay and medium amplitude) accounting for 40%, passive responses (large delay and small amplitude) accounting for 25%, and non-responsiveness accounting for 10%. A pattern transition matrix was constructed to analyze the probability of user behavior pattern transitions under different price signals, identifying stable and volatile patterns. Time series evolution analysis was performed to analyze the distribution and evolution of user behavior patterns across different time periods (morning, noon, and evening) and seasons (summer and winter). Abnormal behavior detection identifies unusual response behaviors that deviate from all normal patterns and may be caused by equipment failures or special events.

[0065] Feature extraction is performed based on behavioral patterns to generate group response behavior. Feature extraction dimensions cover four aspects of response: temporal characteristics, amplitude characteristics, stability, and coordination. Response speed features include: average response delay, response speed standard deviation, and rapid response ratio (percentage of users with a delay of less than 2 minutes). Response depth features include: average response rate, response adequacy (percentage of users achieving at least 80% of the expected response), and peak response coefficient. Response consistency features are characterized by calculating the cross-correlation matrix of all user response curves to extract 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). A Gaussian mixture model is used to fit group response curves. Feature time-varying analysis establishes equations for the time-varying evolution of features to predict group response characteristics in future time periods. Principal component analysis reduces the dimensionality of all features, extracting 3-5 principal components that explain at least 80% of the variance in response behavior.

[0066] The synchronization rate metric is extracted from group response behavior. Synchronization rate calculations take into account user grouping differences, with a time window of 3 minutes for the fast-responding group and 10 minutes for the delayed-responding group. The synchronization rate is then calculated for each group. The synchronization rate, defined as the proportion of users who successfully respond to the price signal within the specified time window, is a key indicator for measuring demand response effectiveness. 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 who respond synchronously (response delays are within the specified window and the response amplitude exceeds 50% of the expected value), and N_total is the target total number of users. Segmented synchronization rate statistics divide the entire day into 96 15-minute time periods, calculating the synchronization rate for each period and identifying the temporal distribution of the synchronization rate. Synchronization rates are calculated based on differentiated behavioral patterns, with targets of over 90% for active responses, over 75% for follow-up responses, and over 60% for passive responses. The response quality-weighted synchronization rate considers not only the number of responses but also the quality of responses. Influencing factor analysis uses multivariate regression to analyze the influence of factors such as price change magnitude, change speed, incentive level, and time period characteristics on the synchronization rate. The synchronization rate target grading is set as follows: excellent (S_rate ≥ 85%), good (70% ≤ S_rate < 85%), qualified (60% ≤ S_rate < 70%), and needs improvement (S_rate < 60%).

[0067] Step S160: Compare the synchronization rate index with a preset target value to form a deviation signal, and based on the deviation signal, correct the price anchor point to generate an optimized price sequence, thereby completing the dynamic optimization of the virtual power plant time-of-use electricity price.

[0068] Specifically, the synchronization rate indicator is compared with the preset target value to form a deviation signal. Deviation analysis takes into account differences in user grouping, 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 differentiated based on the virtual power plant's operating requirements and grid dispatch needs. The target synchronization rate during peak hours is 85% to ensure peak shaving, 75% during normal hours to balance economy and reliability, and 70% during valley hours to moderately guide valley filling. The deviation calculation uses 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 categorizes deviation severity into four levels: minor deviations (|e| < 5%) for which the system can self-correct; moderate deviations (5% ≤ |e| < 10%) requiring appropriate intervention; severe deviations (10% ≤ |e| < 15%) requiring immediate adjustments; and extreme deviations (|e| ≥ 15%) triggering emergency response mechanisms. Time-series deviation analysis uses a sliding window approach with a 30-minute window width to calculate the moving average and trend of deviations, identifying systematic deviations and random fluctuations. Deviation persistence assessment measures the duration of continuous deviations. Deviations lasting more than one hour are considered persistent and require in-depth policy adjustments. Deviation distribution characteristics analyze the frequency and magnitude of positive deviations (targets exceeding actual values) and negative deviations (actual values ​​exceeding targets). Frequent positive deviations indicate insufficient incentives, while frequent negative deviations may indicate overreaction. Weighted deviation calculations take into account the importance of different time periods, with a weight of 1.5 for peak periods, 1.0 for flat periods, and 0.8 for trough periods. The deviation integral metric reflects long-term control effectiveness, with a 24-hour integral window. The deviation change rate analyzes the dynamic characteristics of the deviation, reflects the improvement or deterioration trend of the deviation, and provides a basis for predictive control.

[0069] In some embodiments, the method of correcting the price anchor point based on the deviation signal to generate an optimized price sequence includes: evaluating the correction requirement based on the deviation signal to determine the adjustment range, the correction requirement including the deviation direction, duration and impact range; repositioning the price anchor point according to the adjustment range to form a new anchoring layout; formulating a price transition path according to the new anchoring layout; and generating an optimized price sequence through the price transition path.

[0070] Based on the deviation signal, the need for correction is assessed and the magnitude of the adjustment is determined. The magnitude of the adjustment is differentiated based on the deviation level: minor deviations are subject to fine-tuning (coefficient × 0.5), moderate deviations are subject to normal adjustments, severe deviations are subject to intensive adjustments (coefficient × 1.5), and extreme deviations trigger emergency adjustment mode. The direction of the deviation is identified by its sign. A positive deviation (e>0) indicates insufficient synchronization and requires increased price incentives, while a negative deviation (e<0) indicates an overreaction and requires a moderated price signal. Duration statistics are timed from the first time the deviation exceeds the threshold, recording the cumulative duration of consecutive deviations. Short-term deviations (<30 minutes) are subject to fine-tuning, while long-term deviations (>1 hour) require structural adjustments. Impact assessments analyze the size of the user group affected by the deviation and the total load. Correlation analysis identifies the distribution of affected user types. Industrial users are particularly affected and require special attention. The need for correction assessment combines weighted deviations and integral indicators. The weighted deviation reflects the importance of the time period, while the integral indicator assesses 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 represents the price adjustment, K_p = 0.02 yuan / (kWh·%) is the proportional coefficient, K_i = 0.005 yuan / (kWh·%·h) is the integral coefficient, and K_d = 0.001 yuan / (kWh·% / h) is the differential coefficient. e(t) represents the deviation signal at time t, dt represents the time element, ∫ represents the integral sign, and de / dt represents the time derivative of the deviation. A range limit mechanism sets an upper limit for single adjustments to prevent system oscillations caused by excessive adjustments. The maximum adjustment range does not exceed the smaller of 10% of the current price or 0.1 yuan / kWh. A sensitivity analysis assesses the elasticity of the impact of different adjustment ranges on the synchronization rate. An adjustment range-synchronization rate improvement curve is established to identify the optimal adjustment range.

[0071] The price anchor points are repositioned according to the adjustment magnitude to form a new anchoring layout. Anchor point adjustments take into account behavioral differences: moderate adjustments are made in areas with proactive users, larger adjustments are made in areas with reactive users, and a standard adjustment strategy is applied to areas with responsive users. The anchor point displacement calculation is based on the original position and the adjustment magnitude: 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 that accounts for deviation characteristics and time factors, and ΔC is the price adjustment amount. The correction function uses a nonlinear mapping design: small deviations are adjusted linearly, while large deviations are compressed using a logarithmic function to prevent overreaction. Displacement direction rules: Positive deviations increase prices to enhance incentives, while negative deviations decrease prices to reduce incentives. The direction is opposite to the deviation, forming negative feedback control. Displacement constraints ensure that the adjusted anchor point remains within the price fluctuation range. If it exceeds the range, it is automatically corrected to the nearest boundary, and the number of constraint activations is recorded. Adjacent anchor points are coordinated to avoid excessively dense or sparse anchor points after adjustment, maintaining a minimum spacing of 0.03 yuan / kWh and a 30-minute interval. When a specific anchor point undergoes a significant adjustment, adjacent anchor points will be moderately linked, with the linkage coefficient decaying with distance. Layout optimization uses a genetic algorithm to globally search for the optimal anchor point configuration. The fitness function comprehensively considers factors such as expected synchronization rate improvement, price smoothness, and execution difficulty.

[0072] A price transition path is developed based on the new anchoring layout. The path planning goal is to achieve a smooth transition from the current price state to the new anchoring point layout, minimizing system disturbances during the transition. Trajectory generation uses cubic spline interpolation to connect the new anchoring points, ensuring second-order continuity of the price curve and avoiding sudden changes in the rate of change. The time allocation strategy determines the total transition period (generally 2-4 hours) and the allocation ratio for each segment based on the urgency of the adjustment and the system's tolerance. Transition rate control ensures that the price change rate does not exceed user adaptability, with a maximum rate limit of 0.4 yuan / (kWh·h). Key constraints include monotonicity (to prevent price fluctuations), boundedness (to maintain within a floating range), and ramp rate (to meet physical constraints). Intermediate node optimization inserts auxiliary control points between anchoring points, adjusting their positions to optimize the curve shape and reduce overshoot and oscillation. Path smoothing uses Bezier curves or B-spline techniques to improve curve smoothness while maintaining the path through the anchoring points. Feasibility testing verifies point by point that the transition path meets all technical constraints and scheduling requirements, and makes local adjustments if not. Prepare 2-3 alternative paths for possible execution deviations and switch based on real-time feedback.

[0073] An optimized price sequence is generated based on the price transition path. The price transition path is discretely sampled with a 5-minute sampling interval, in accordance with the time resolution requirements of the virtual power plant dispatch system, to ensure the real-time and enforceable nature of the price signal. Timestamps are used to precisely mark the execution moment for each price point, using a standard time format to ensure inter-system clock synchronization and avoid scheduling confusion caused by time deviations. Price accuracy is maintained to 0.001 yuan / kWh, meeting the accuracy requirements of the billing system while avoiding execution difficulties caused by excessive accuracy. A sequence integrity check ensures that the generated price sequence covers the entire dispatch cycle (24 hours) with no missing or duplicated periods, ensuring dispatch continuity. Outlier filtering detects and corrects anomalous price points in the sequence, such as negative prices, over-limit prices, and trip points, to ensure the rationality of the price signal. Trend preservation ensures that the overall trend of the optimized sequence matches the system load forecast, with distinct peak-valley characteristics, achieving the dispatch objective of peak shaving and valley filling. Quality metrics calculated include sequence smoothness, peak-valley difference, average rate of change, and maximum rate of change, to comprehensively evaluate the optimization results and complete the dynamic optimization of the virtual power plant's time-of-use electricity price.

[0074] In order to implement the virtual power plant time-of-use electricity price dynamic optimization method corresponding to the above method embodiment, to achieve the corresponding functions and technical effects. Figure 2 , Figure 2 The following is a block diagram of a virtual power plant time-of-use electricity price dynamic optimization system 200 provided in an embodiment of the present application. For ease of explanation, only the parts related to this embodiment are shown. The virtual power plant time-of-use electricity price dynamic optimization system 200 provided in an embodiment of the present application includes: The data acquisition module 201 is configured to obtain power time series data and user-side response records of 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; a scheduling generation module 202 configured to perform boundary scanning on the elastic response space to generate a dispatchable capacity envelope, set trigger threshold points along the dispatchable capacity envelope, reversely deduce energy storage intervention timing based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the energy storage intervention timing; A price determination module 203 is configured to obtain a grid dispatch price sequence and a power balance requirement, project the grid dispatch price sequence into the elastic response space to form a valid price range, and truncate the valid price range based on the power balance requirement to determine a price fluctuation range; Anchor generation module 204, configured to use the time-sharing scheduling strategy to perform a path search within the price fluctuation range to obtain changes in user response intensity, identify an inflection point based on the changes in user response intensity, and perform a stability assessment on the inflection point to generate a price anchor point; A synchronization analysis module 205 is configured to perform time interval analysis on the price anchor points to generate a price climbing rate, form a price change rate based on the price climbing rate, obtain a group response behavior based on the price change rate, and extract a synchronization rate indicator from the group response behavior; 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 virtual power plant time-of-use electricity price.

[0075] The virtual power plant time-of-use electricity price dynamic optimization system 200 can implement the virtual power plant time-of-use electricity price dynamic optimization method of the above-mentioned method embodiment. The optional options in the above-mentioned method embodiment also apply to this embodiment and are not described in detail here. The remaining contents of the embodiment of this application can refer to the contents of the above-mentioned method embodiment and are not repeated in this embodiment.

[0076] The purpose of the above embodiments is to exemplify and deduce the technical solution of the present invention, and to fully describe the technical solution, purpose and effect of the present invention. Its purpose is to enable the public to have a more thorough and comprehensive understanding of the disclosed content of the present invention, and it does not limit the scope of protection of the present invention.

[0077] The above embodiments are not exhaustive and may include many other embodiments not listed above. Any replacements and improvements made without violating the concept of the present invention are within the scope of protection of the present invention.

Claims

1. A method for dynamic optimization of time-of-use electricity prices in a virtual power plant, characterized in that: include: Obtaining power time series data and user-side response records of distributed resources of a virtual power plant, identifying fluctuation components based on the power time series data, generating price sensitivity coefficients using the user-side response records, and constructing an elastic response space based on a matching relationship between the fluctuation components and the price sensitivity coefficients; Performing boundary scanning on the elastic response space to generate a dispatchable capacity envelope, setting a trigger threshold point along the dispatchable capacity envelope, reversely deducing an energy storage intervention timing based on the trigger threshold point, and generating a time-sharing dispatch strategy based on the energy storage intervention timing; Obtaining a grid dispatch price sequence and a power balance requirement, projecting the grid dispatch price sequence into the elastic response space to form a valid price range, and truncating the valid price range based on the power balance requirement to determine a price floating range; Using the time-sharing scheduling strategy to perform a path search within the price fluctuation range to obtain changes in user response intensity, identifying an inflection point position based on the changes in user response intensity, and performing a stability assessment on the inflection point position to generate a price anchor point; Performing time interval analysis on the price anchor point to generate a price climbing rate, forming a price change speed based on the price climbing rate, obtaining a group response behavior based on the price change speed, and extracting a synchronization rate indicator from the group response behavior; The synchronization rate index is compared with the preset target value to form a deviation signal, and the price anchor point is corrected based on the deviation signal to generate an optimized price sequence, thereby completing the dynamic optimization of the virtual power plant time-of-use electricity price.

2. The method according to claim 1, characterized in that The constructing of the elastic response space based on the matching relationship between the fluctuation component and the price sensitivity coefficient includes: Identifying a positive response region and a negative response region through a matching relationship between the fluctuation component and the price sensitivity coefficient; Couple 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; An elastic response space is determined along equipotential lines of the response gradient field.

3. The method according to claim 1, characterized in that The reverse deducing of the energy storage intervention timing based on the trigger threshold point includes: Generate a power ramp trajectory based on the trigger threshold point; identifying an acceleration starting point according to the power ramp-up trajectory; Obtaining energy storage response delay through the acceleration starting point; The acceleration starting point is moved forward based on the response time delay to determine an energy storage intervention timing.

4. The method according to claim 1, wherein The determining of the price floating range by truncating the valid price interval based on the power balance requirement includes: generating a supply-demand deviation threshold according to the power balance requirement; Compressing the upper bound of the effective price range based on the supply and demand deviation threshold to generate a compressed range; Performing a stability test on the compression interval to generate a stable subinterval; The longest continuous segment is selected from the stable sub-interval as the price fluctuation range.

5. The method according to claim 1, wherein The step of performing stability assessment on the inflection point position to generate a price anchor point includes: Constructing a disturbance test window based on the inflection point position; generating a recovery time series using the response data within the test window; Using the recovery time series to screen a rapid recovery inflection point; The price anchor point is determined by performing homogenization screening through the rapid recovery inflection point.

6. The method according to claim 1, characterized in that The forming of the price change speed based on the price climbing rate includes: Extracting a sudden change point from the price climbing rate; Dividing the climbing section according to the sudden increase point of the change; Setting a buffer time for the climbing section based on the user-side response record; The buffer duration is used to reconstruct the ramp segment to form a price change speed.

7. The method according to claim 1, characterized in that The obtaining of group response behavior according to the price change speed includes: Broadcasting the price change speed in a graded manner to generate a quick response group and a delayed response group; Using the fast response group to synchronously pull the delayed response group to form an overall response; generating a behavioral pattern for the overall response through cluster analysis; Feature extraction is performed according to the behavior pattern to generate group response behavior.

8. The method according to claim 1, characterized in that The step of modifying the price anchor point based on the deviation signal to generate an optimized price sequence includes: Evaluate the correction requirement based on the deviation signal and determine the adjustment range, wherein the correction requirement includes the deviation direction, duration and impact range; Reposition the price anchor point according to the adjustment range to form a new anchor layout; Develop a price transition path based on the new anchor layout; An optimized price sequence is generated through the price transition path.

9. The method according to claim 5, characterized in that The determining of the price anchor point by performing homogenization screening based on the rapid recovery inflection point includes: Determining screening intensity based on the rapid recovery inflection point evaluation distribution density, wherein the distribution density includes temporal concentration, spatial coverage, and distance between inflection points; setting retention rules based on the screening intensity; The retention rule is used to screen the rapid recovery inflection point to generate a price anchor point.

10. A virtual power plant time-of-use electricity price dynamic optimization system, characterized in that: include: a data acquisition module configured to acquire power time series data and user-side response records of distributed resources of 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 a matching relationship between the fluctuation components and the price sensitivity coefficients; a scheduling generation module, configured to perform boundary scanning on the elastic response space to generate a dispatchable capacity envelope, set trigger threshold points along the dispatchable capacity envelope, reversely deduce energy storage intervention timing based on the trigger threshold points, and generate a time-sharing scheduling strategy based on the energy storage intervention timing; a price determination module, configured to obtain a grid dispatch price sequence and a power balance requirement, project the grid dispatch price sequence into the elastic response space to form a valid price range, and truncate the valid price range based on the power balance requirement to determine a price floating range; An anchor generation module, configured to use the time-sharing scheduling strategy to perform a path search within the price fluctuation range to obtain changes in user response intensity, identify an inflection point position based on the changes in user response intensity, and perform a stability assessment on the inflection point position to generate a price anchor point; a synchronization analysis module, configured to perform time interval analysis on the price anchor points to generate a price climbing rate, form a price change rate based on the price climbing rate, obtain a group response behavior based on the price change rate, and extract a synchronization rate indicator 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 based on the deviation signal, correct the price anchor point to generate an optimized price sequence to complete the dynamic optimization of the virtual power plant time-of-use electricity price.

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