Method for evaluating flexible adjustment adequacy of compressed air energy storage system

Abstract

The application discloses a kind of compressed air energy storage system flexible regulation adequacy evaluation method, comprising: based on wind and light load data to establish CAES thermodynamic physical constraint model;Derive internal state trajectory, construct the CAES multi-time scale energy spectrum of coupling gas storage pressure, temperature and other state variables, and the energy spectrum is the unified data structure containing short time scale power boundary and long time scale energy boundary;Analysis of the multi-time scale regulation demand trajectory of power grid, map it to the energy spectrum to establish geometric coverage relationship, quantitatively calculate the flexible regulation adequacy index and identify the flexibility bottleneck;Based on the coverage evaluation result, economic and flexibility joint planning is carried out.The application realizes the accurate quantification and optimal allocation of compressed air energy storage regulation capacity by explicitly converting thermodynamic constraints and physical constraints into multi-dimensional capacity boundaries, and transforming traditional probability evaluation into trajectory geometric coverage analysis.

Description

Technical Field

[0001] This application belongs to the field of energy storage technology, and in particular to a method for flexibly adjusting the adequacy of a compressed air energy storage system. Background Technology

[0002] Building a new power system with new energy sources as the mainstay has become an inevitable trend. In this process, the high proportion of wind and solar power integration introduces significant randomness and volatility, urgently requiring large-scale, long-cycle energy storage technologies to ensure the system's supply-demand balance and stability. Compressed air energy storage (CAES), with its advantages of large storage capacity and long storage period, has become one of the important technical means to support flexible grid regulation, and has significant engineering value for improving the absorption capacity of new energy sources and the resilience of the power grid.

[0003] Currently, research on the flexible regulation capabilities of power systems largely focuses on conventional generating units or general-purpose energy storage models. Existing technologies typically employ static evaluation methods based on rated parameters or probabilistic evaluation methods based on Monte Carlo simulations, such as the probability of load shedding (LOLP) and expected power shortage (EENS). These methods are widely used in dealing with battery energy storage or pumped hydro storage, usually simplifying the energy storage system into a black-box model with fixed charge / discharge efficiency and rated capacity limitations. They emphasize analyzing the overall power balance of the system or the regulation demand at a certain time interval, calculating the probabilistic statistical characteristics of various resources meeting the load gap.

[0004] However, existing technologies face deep-seated technical problems when applied to the refined evaluation of compressed air energy storage (CAES), including decoupling of physical state and regulation capability, and mismatch between multi-timescale indicators and continuous trajectories. Existing models often ignore the complex nonlinear thermodynamic characteristics of CAES and fail to establish the dynamic coupling relationship between internal states (such as storage pressure and temperature) and instantaneous regulation capability. Specifically, the actual adjustable power of CAES is not a constant value but is constrained by real-time storage pressure and expander inlet temperature. Traditional models tend to overestimate its regulation capability under low-pressure or extreme conditions. Existing evaluation systems based on a single scalar (such as insufficiency probability) struggle to characterize the energy competition and coupling relationship between frequency regulation (second-level) and peak regulation (hour-level), and cannot reflect whether the continuous regulation demand trajectory can be geometrically covered by the dynamic feasible domain of the energy storage system, making it difficult to accurately pinpoint the specific time periods and physical causes of flexibility shortages. Summary of the Invention

[0005] The purpose of this invention is to provide a flexible adjustment adequacy assessment method for compressed air energy storage systems, in order to solve the aforementioned problems existing in the prior art.

[0006] According to one aspect of this application, a method for flexibly adjusting the adequacy of a compressed air energy storage system includes:

[0007] Based on the acquired wind and solar load forecast data and CAES equipment parameters, a scenario-based operation dataset and a CAES thermodynamic physical constraint model are established.

[0008] The CAES thermodynamic physical constraint model is used to perform time-series extrapolation on the scenario-based operation dataset to obtain the internal state vector characterizing the evolution of gas storage pressure and gas temperature. Based on the internal state vector, the CAES multi-timescale energy spectrum is constructed. The CAES multi-timescale energy spectrum is a unified data structure based on the dynamic constraint of the internal state vector and coupled with the short-timescale power boundary and the long-timescale energy boundary.

[0009] Multi-timescale adjustment demand trajectories are extracted from the scenario-based operational dataset; these trajectories are mapped onto the CAES multi-timescale energy spectrum to establish geometric coverage relationships; and the sufficiency index is quantified and calculated based on the geometric coverage relationships.

[0010] Beneficial effects: By explicitly transforming thermodynamic and physical constraints into multidimensional capability boundaries, this invention transforms traditional probabilistic assessment into trajectory geometric coverage analysis, thereby achieving precise quantification and optimized configuration of compressed air energy storage regulation capabilities. Attached Figure Description

[0011] Figure 1 This is a schematic diagram of the overall process for evaluating the adequacy of a compressed air energy storage system.

[0012] Figure 2 This is a schematic diagram illustrating the process of mapping multi-timescale adjustment demand trajectories onto the CAES multi-timescale energy spectrum to establish geometric coverage relationships.

[0013] Figure 3 This is a schematic diagram of a flexible bottleneck information flow generated using geometric coverage relationships.

[0014] Figure 4 This is a schematic diagram illustrating the process of optimizing CAES planning and configuration schemes using feedback from flexible shadow price series. Detailed Implementation

[0015] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0016] Example 1 details the overall process of the flexible adjustment adequacy assessment method for compressed air energy storage systems, such as... Figure 1As shown, by introducing the CAES thermodynamic physical constraint model and geometric coverage analysis, the problems of not considering thermodynamic state coupling and lacking trajectory-level matching in existing evaluation methods are solved, and high-precision quantification of the system's regulation capability is achieved.

[0017] Step 101: Based on the acquired wind and solar load prediction data and CAES equipment parameters, establish a scenario-based operation dataset and a CAES thermodynamic physical constraint model.

[0018] In this embodiment, the wind and solar load forecast data specifically refers to time-series data including wind farm output power, photovoltaic power plant output power, and grid load demand. This data is typically sampled at a fixed time resolution, with a sampling frequency set, for example, one point every 15 minutes or one point every 1 minute. CAES equipment parameters refer to the physical property parameters of the compressed air energy storage system (CAES), specifically including compressor rated power, turbine expander rated power, gas storage volume, heat exchanger efficiency, compressor stages, turbine stages, etc. The scenario-based operation dataset is a structured data set formed by preprocessing the above-mentioned raw forecast data, including time scale unification, missing value imputation, and outlier removal. The CAES thermodynamic physical constraint model is a set of mathematical equations describing the internal physical processes of CAES, establishing a dynamic relationship between power, flow rate, and internal state variables such as pressure and temperature.

[0019] Specifically, the process of establishing the CAES thermodynamic physical constraint model includes constructing a compressor model, a turbine expander model, a gas storage tank model, and a heat exchanger model. The compressor model is used to calculate the power consumption and temperature changes during the compression process; its total power consumption Pc can be expressed as the power consumption P of each stage of the compressor. c,i The sum of the power generated and the temperature change during the expansion process. The total power Pe can be expressed as the power P of each stage of the turbine expander. e,i The gas storage tank model describes the pressure change within the storage tank over time, specifically based on differential equations established using the law of conservation of mass and the ideal gas law. For example, the relationship between the storage tank pressure at time t and the pressure at the previous time is influenced by the inlet and outlet gas flow rates and the internal temperature. The heat exchanger model calculates the temperature changes during heat exchange, establishing an algebraic relationship between the inlet and outlet temperatures of the hot and cold fluids using the efficient heat transfer unit number method. These models are established to provide a physically accurate calculation basis for subsequent state deductions, ensuring the accuracy of the evaluation results.

[0020] Step 102: Use the CAES thermodynamic physical constraint model to perform time-series simulation on the scenario-based operation dataset to obtain the internal state vector characterizing the evolution of gas storage pressure and gas temperature. Construct the CAES multi-timescale energy spectrum based on the internal state vector. The CAES multi-timescale energy spectrum is a unified data structure based on the dynamic constraint of the internal state vector and coupled with the short-timescale power boundary and the long-timescale energy boundary.

[0021] In this embodiment, the internal state vector refers to the set of variables that uniquely determines the current thermodynamic state of the CAES system at any given time t. This vector is specifically denoted as x. _t Its components include at least the current gas storage pressure, the gas temperature inside the gas storage, and the thermal energy stored in the thermal storage system. Time-series simulation refers to using numerical integration or differential iteration methods to substitute the external inputs from the scenario-based runtime dataset into the CAES thermodynamic physical constraint model, and calculating the internal state vector x at each time step. _t .

[0022] Constructing the CAES multi-timescale energy spectrum generates a four-dimensional data structure that can simultaneously describe the regulatory capabilities at different timescales. Specifically, for each time point t and its corresponding internal state vector x... _t This energy spectrum includes not only the upper and lower limits of the second-level frequency modulation power that can be immediately provided under this state, but also the upper and lower limits of the peak-shaving energy that can be continuously output for several hours under this state. The unified data structure includes an internal state dimension, reflecting the differences in regulation capabilities under different states. For example, when the gas storage pressure is low, although the rated power is allowed, the actual frequency modulation up-regulation power that can be provided will be compressed due to the constraint of the lower pressure limit; similarly, the time that can be continuously discharged will also be shortened, limiting the peak-shaving energy. By using a coupled construction method, the shortcomings of traditional methods that evaluate power and capacity separately are avoided.

[0023] Step 103: Parse the multi-timescale adjustment demand trajectory from the scenario-based operation dataset.

[0024] In this embodiment, the multi-timescale regulation demand trajectory refers to the sequence of grid demand for flexibility resources at different time scales. Specifically, the analysis process decomposes the grid's net load fluctuations into high-frequency and low-frequency components. The high-frequency component corresponds to power fluctuations at the second to minute level and is defined as the frequency regulation demand trajectory; the low-frequency component corresponds to energy shifting demand at tens of minutes to several hours and is defined as the peak-shaving demand trajectory. This analysis aims to separate the complex mixed demand signal into independent characteristic signals corresponding to the multi-timescale capabilities of CAES, facilitating subsequent accurate matching analysis.

[0025] Step 104: Map the multi-timescale regulation demand trajectory to the CAES multi-timescale energy spectrum to establish the geometric coverage relationship.

[0026] In this embodiment, mapping refers to projecting the parsed demand trajectory data points onto the feasible region space defined by the CAES multi-timescale energy spectrum. Specifically, for each time point, the system checks whether the frequency modulation demand point falls within the power range defined by the energy spectrum at that time, and simultaneously checks whether the peak-shaving demand segment is enveloped by the energy envelope defined by the energy spectrum. Geometric coverage relationship refers to the topological positional relationship between the demand trajectory and the capacity boundary. If the demand trajectory is completely within the feasible region of the energy spectrum, it is called complete coverage; if some trajectory points overflow the feasible region boundary, it is called incomplete coverage. Establishing this relationship is to transform the abstract supply and demand balance problem into an intuitive geometric inclusion problem, which can be used to perform quantitative margin analysis using geometric algorithms.

[0027] Step 105: Quantitatively calculate and flexibly adjust the sufficiency index based on the geometric coverage relationship.

[0028] In this embodiment, the flexible adjustment margin index is a quantitative value used to characterize the degree to which the CAES system meets the grid regulation requirements. The calculation process is based on the established geometric coverage relationship and is obtained by calculating the minimum normalized distance between the demand trajectory and the energy spectrum boundary. For example, a coverage margin index can be defined: a positive value indicates that the system has surplus regulation capacity, with a larger value indicating greater sufficiency; a negative value indicates that the system has a regulation gap, with the absolute value representing the size of the gap. Through quantitative calculation, not only can it be determined whether the system meets the requirements, but also the degree of satisfaction or the severity of deficiency can be given, providing an intuitive basis for subsequent planning decisions.

[0029] Example 2 elaborates on the construction details and thermodynamic coupling mechanism of CAES multi-timescale energy spectrum. By introducing discrete time grids and refined boundary calculation algorithms, it further reveals how to concretize thermodynamic constraints into multi-timescale energy boundaries.

[0030] Step 201: Construct a discrete time grid based on the temporal resolution characteristics of the scenario-based running dataset.

[0031] In this embodiment, a discrete-time grid refers to dividing a continuous time axis into a series of discrete time steps. The construction process first reads the time tags of wind power, photovoltaic, and load data from the scenario-based runtime dataset to determine the basic time resolution, such as 1 minute or 15 minutes. Then, the start and end times of the study period are set, generating a grid containing all discrete time points t. _kThe time series. This discrete-time grid serves as a unified time reference for all subsequent state deductions and capacity calculations, ensuring consistency in the time domain for data from different sources and different calculation processes.

[0032] Step 202: At each time step of the discrete-time grid, the CAES thermodynamic physical constraint model is used to simulate the response of the input variables in the scenario-based running dataset, generating the CAES internal state trajectory containing parameters such as gas storage pressure, gas temperature, and thermal energy storage.

[0033] In this embodiment, response simulation refers to calculating the state at the current moment based on the state at the previous moment and the input at the current moment. Specifically, for each time point t on the discrete-time grid, the wind and solar power output and load data at that moment are read, and the charging and discharging actions of CAES are determined in combination with a preset baseline operation strategy. The state is updated using differential equations or difference equations in the CAES thermodynamic physical constraint model.

[0034] For example, when updating the pressure state using a gas storage model, assuming a time step of Δt, the gas storage pressure ρ at time t is... ar,t Based on the pressure ρ at time t-1 ar,t-1 The current temperature T ar,t The mass flow rates of the incoming and outgoing gases are calculated. Similarly, the temperature and thermal energy state are updated using the heat exchanger model and the thermal storage model. By repeating this process across the entire time grid, a time-evolving sequence is generated, namely the CAES internal state trajectory. Each point in this trajectory contains a complete internal state vector x. _t It accurately records the physical state of the system at every moment.

[0035] Step 203: Traverse each internal state vector in the CAES internal state trajectory and calculate the short-timescale power boundary and long-timescale energy boundary that are constrained by the thermodynamic state at that moment.

[0036] In this embodiment, the short-timescale power boundary refers to the maximum up-regulation and down-regulation power that CAES can provide within a timescale of seconds to minutes. Calculating this boundary requires considering both mechanical and thermodynamic constraints. Specifically, the upper bound P of the up-regulation capability... _up_max The formula for (t) can be:

[0037] P _up_max (t)=min(P _rated_max -P _base (t),Ramp _up_max *Δt _freq ,P _state_up (t)); where P _up_max(t) represents the maximum adjustable power at that moment, P _rated_max P is the rated maximum power of the equipment. _base (t) represents the baseline output at that moment, Ramp _up_max Δt is the upper limit of the upward climbing rate. _freq P represents the time length corresponding to the frequency modulation time scale. _state_up (t) represents the upper limit of available power determined by the current internal state.

[0038] Among them, the current available power limit P _state_up (t) is calculated using a turbine model based on the current gas storage pressure and gas temperature, ensuring that the pressure does not drop below the lower limit or the temperature exceeds the limit when increasing output. Similarly, the downward adjustment capability, i.e., the maximum power in the charging direction, can be calculated, and the upper limit P of the downward adjustment capability can be determined. _down_max (t) can be expressed by the following formula:

[0039] P _down_max (t)=min(P _base (t)-P _rated_min Ramp _down_max *Δt _freq ,P _by_state_down (t));

[0040] Among them, P _rated_min Ramp indicates the minimum allowable output of the equipment. _down_max For the maximum downhill climbing rate, P _by_state_down (t) represents the maximum downward adjustment allowed under the current internal state.

[0041] The long-term energy boundary refers to the total energy that a CAES (Gas Storage Equipment) can continuously provide over a timescale of tens of minutes to several hours. Calculating this boundary requires considering the cumulative changes in state variables during continuous operation. Since the storage pressure decreases with continuous discharge, simply multiplying the current pressure by the volume is inaccurate. This step determines the energy boundary by dynamically identifying the maximum sustainable average output through simulation of operation over a future period.

[0042] Step 204: Associate and store the short-timescale power boundary and the long-timescale energy boundary corresponding to the same internal state vector to form the CAES multi-timescale energy spectrum.

[0043] In this embodiment, associated storage refers to packaging and storing short-timescale power parameters and long-timescale energy parameters calculated at the same time point t in a single data unit. The specific data structure can be designed as a multi-dimensional array or a list of structures, where each item contains a timestamp, an internal state vector, upper and lower limits for frequency modulation power and peak modulation energy, and a corresponding duration identifier. This storage method preserves the coupling relationship between capabilities at different timescales and is derived from the same physical state. The resulting CAES multi-timescale energy spectrum provides a complete and structured capability database for subsequent adequacy assessments.

[0044] Step 205: Assign frequency modulation time scale identifiers to the short-time scale power boundary and peak shaving duration identifiers to the long-time scale energy boundary.

[0045] In this embodiment, the frequency modulation time scale identifier is used to mark the time range to which the short time scale power boundary applies; for example, it can be set to Freq. _Scale The corresponding time length is on the order of seconds, such as 2 seconds or 4 seconds. The peak-shaving duration identifier is used to mark the continuous discharge or charge duration corresponding to long-timescale energy boundaries; for example, a series of identifier sets H can be defined. _set This includes discrete values ​​such as 1 hour, 2 hours, and 4 hours. The allocation identifier is used to clearly distinguish different types of adjustment capabilities within the data structure, facilitating subsequent indexing and matching based on specific needs.

[0046] Step 206: Align the instantaneous adjustable power range defined by the short-timescale power boundary at the same time point with the sustainable average power output range defined by the long-timescale energy boundary under different peak-shaving duration markers on the time axis to generate a local energy spectrum fragment.

[0047] In this embodiment, a local energy spectrum segment refers to the collection of all modulation capabilities of the CAES system at a single time point t. The process of generating this segment involves logically combining the aforementioned capability data with different identifiers. Specifically, the system uses time point t as an index to define the frequency modulation power range P at that moment. _up_max (t),P _down_max (t) is used as the first-level data, P _up_max (t) and P _down_max (t) represents the upper and lower limits, respectively, and represents the average peak output range P for different durations H at that moment. _avg_max_t_H As second-level data, they are collectively encapsulated within a single data object. The alignment operation ensures that when evaluating the overall regulatory capability at a given moment, capability information across all time scales at that moment can be obtained simultaneously.

[0048] Step 207: Connect the local energy spectrum segments of all time points along the discrete time grid to form a CAES multi-timescale energy spectrum that describes the cross-timescale adjustment capability of CAES under different internal state vectors.

[0049] In this embodiment, concatenation refers to linking local energy spectrum fragments from various time points in chronological order to form a time-series data structure that changes over time. This overall structure is the CAES multi-timescale energy spectrum. It not only covers the entire research period in the time dimension but also provides capability descriptions across different time scales at each time segment, and the capability data strictly corresponds to the internal thermodynamic state at that time. This step completes the construction from discrete point data to system-level spectral data, laying the data foundation for global adequacy assessment.

[0050] Step 208: For each candidate duration in the preset set, read the internal state vector at the current moment as the initial condition.

[0051] In this embodiment, the preset set refers to a list of durations used to evaluate peak-shaving capabilities, such as the identifier set H. _set ={1h, 2h, 4h}. For each duration H in the list, and for each time point t on the discrete-time grid, the system reads the internal state vector x at that moment. _t This includes pressure, temperature, and stored thermal energy, which serve as the starting point for subsequent simulation calculations, i.e., t. _0 The state at any given moment. This step ensures that every long-term capability assessment is based on the actual real-time state.

[0052] Step 209: Use the CAES thermodynamic physical constraint model to simulate the turbine expansion process or compressor compression process when maintaining constant output during the candidate duration, and monitor the evolution trajectory of gas storage pressure and gas temperature.

[0053] In this embodiment, the simulation process employs a trial-and-error simulation method. Specifically, it is assumed that within a future time period H starting from the current time t, CAES operates at a constant power P. _candidate The system is then put into operation. Using the CAES thermodynamic physical constraint model, iterative calculations are performed with small time steps, such as 1 minute, to deduce the evolution paths of the storage gas pressure and gas temperature over time under this operating mode. For example, during turbine expansion power generation, as gas is continuously released, the storage gas pressure gradually decreases, the gas expansion work capacity changes accordingly, and the exhaust temperature fluctuates. Monitoring the evolution trajectory is to check whether the system state remains within the safe operating range throughout the entire duration H.

[0054] Step 210: Using the condition that the lower limit of gas storage pressure and the upper limit of exhaust temperature are not violated as the termination condition, search for the maximum feasible average output that can be maintained within the candidate duration.

[0055] In this embodiment, the process of searching for the maximum feasible average output power can employ a bisection method or a successive approximation method. Specifically, the operation involves setting an initial power estimate and executing the simulation process described above. If, throughout the entire duration H, the gas storage pressure remains consistently higher than the preset lower limit P of the gas storage pressure... _min And the exhaust temperature is always lower than the preset exhaust temperature upper limit T. _max If the stored thermal energy is not depleted, the power output is considered feasible, and the power value is increased for another simulation. Conversely, if a constraint violation occurs, the power value is decreased. This process is repeated until a critical power value is found, which is the maximum feasible average output P under this initial state and duration. _avg_max .

[0056] Step 211: Calculate the product of the maximum feasible average output and the candidate duration to obtain the long-time energy boundary corresponding to that moment and the internal state vector.

[0057] In this embodiment, the long-time energy boundary is specifically quantified as the tunable peak energy E. _peak_max The calculation formula can be: E _peak_max =P _avg_max *H;

[0058] Among them, E _peak_max For tunable peak energy, P _avg_max H represents the maximum feasible average output that can be maintained at this moment and under this internal state, and H is the duration.

[0059] This indicator intuitively reflects the current time t and the current internal state x. _t If the power grid requires peak-shaving support for a duration of H, the maximum total energy that the CAES system can provide reflects the hard constraint of thermodynamic state on long-term regulation capability, which is more accurate than simply using the remaining SOC for estimation.

[0060] Example 3 elaborates on the sufficiency evaluation algorithm and flexibility bottleneck location method based on geometric coverage, such as... Figure 2 , Figure 3 As shown, through specific mapping, matching, and backtracking mechanisms, the abstract supply and demand relationship is transformed into calculable geometric indicators, enabling accurate diagnosis of weak links in the system.

[0061] Step 301: Decompose the multi-timescale adjustment demand trajectory into frequency modulation power demand sequence and peak shaving energy demand sequence according to time scale characteristics.

[0062] In this embodiment, the decomposition process is implemented based on signal processing techniques. Specifically, for the analyzed multi-timescale adjustment demand trajectory, the system uses methods such as filters or wavelet transforms to separate the higher-frequency fluctuation components, forming a frequency-modulated power demand sequence, denoted as D. _freq_t This sequence reflects the system's need for rapid power adjustments on a second-to-minute scale. Simultaneously, by separating the lower-frequency, longer-duration trend components, or by segmenting and integrating the net load curve, a peak-shaving energy demand sequence, denoted as D, can be formed. _peak_t_H This sequence reflects the system's demand for continuous energy blocks at different times, such as the need for 2 hours of continuous discharge during the evening peak hours.

[0063] Step 302: Traverse each time point, match the values ​​in the frequency modulation power demand sequence with the short timescale power boundary of the corresponding time in the CAES multi-timescale energy spectrum, and match the values ​​in the peak shaving energy demand sequence with the long timescale energy boundary of the corresponding time and duration.

[0064] In this embodiment, matching refers to numerical comparison performed at the same time coordinate. Specifically, for each time point t on the discrete time grid, the system first reads the frequency modulation power demand sequence D at that moment. _freq_t Furthermore, the short-timescale power boundary at that moment was extracted from the CAES multi-timescale energy spectrum, including the up-regulation limit P. _up_max (t) and the downward limit P _down_max (t). If the frequency modulation power demand sequence D _freq_t If the value is positive, then the demand is increased, which is related to P. _up_max (t) Pairing; if negative, it means demand is reduced, then it is paired with P. _down_max (t) Pairing. Simultaneously, the system reads the peak energy demand sequence D for a certain duration H at that moment. _peak_t_H And extract the corresponding long-time scale energy boundary E from the energy spectrum. _peak_max_t_H Matching is performed. This process ensures that each type of requirement has a corresponding capability reference benchmark.

[0065] Step 303: For each set of matches, calculate the envelope of the short-timescale power boundary or the long-timescale energy boundary relative to the demand to generate a local coverage margin.

[0066] In this embodiment, local coverage margin is used to quantify the supply and demand sufficiency in a single matching pair. For the k-th matching pair, the capacity boundary value is assumed to be Cap. _k The demand value is Dem _k Then the local coverage margin _k It can be calculated using the following formula:

[0067] margin _k =(Cap _k -Dem _k ) / (|Dem _k |+ε);

[0068] Among them, margin _k Cap is the local coverage margin of the k-th matching group. _k Dem is the capability boundary value corresponding to this matching pair. _k ε represents the required value for this matching pair, where ε is a small positive number to prevent the denominator from being zero.

[0069] When margin _k A value ≥ 0 indicates that the capacity covers the demand; the larger the value, the more abundant the capacity. When margin... _k A value less than 0 indicates that the capacity is insufficient to cover the demand; the smaller the value, the larger the gap. Normalization eliminates the differences between different physical units, such as power (MW) and energy (MWh), making the margins comparable across different scales.

[0070] Step 304: Aggregate the local coverage margins at all time points and at all time scales to form a geometric coverage relationship that characterizes whether the demand trajectory falls within the feasible region of the energy spectrum.

[0071] In this embodiment, aggregation refers to performing statistical analysis on the calculated massive local coverage margin data to form an overall evaluation conclusion. Geometric coverage relationships can be described by the statistical characteristics of the margin sequence. For example, the minimum margin value can be extracted from the entire sequence. _min If margin _min If the margin is greater than 0, the geometric coverage is complete, meaning that CAES can meet the requirements at all times and all scales; if the margin is less than 0, the geometric coverage is complete. _min If the value is less than 0, the geometric coverage relationship is partially overflowing. Furthermore, the frequency, duration, and cumulative depth of negative margins can be calculated to construct a multi-dimensional geometric coverage feature set, characterizing the distribution of demand trajectories within the feasible region of the energy spectrum.

[0072] Step 305: Scan the local coverage margin sequence in the geometric coverage relationship and identify under-covered segments with a margin lower than a preset threshold.

[0073] In this embodiment, the scanning process involves threshold detection of the time series data. The preset threshold is typically set to 0, but can also be set to a positive number, such as 0.1, depending on safety margin requirements. The system checks the local coverage margin sequence point by point, and marks the time point t if the margin value at any given time is below the threshold. If the margins at multiple consecutive time points are all below the threshold, these consecutive points are merged into a single undercover segment. Each segment records its start time, end time, and corresponding margin extreme value.

[0074] Step 306: Extract the time position and time scale type corresponding to each under-covered segment, and backtrack the internal state vector corresponding to that time position from the CAES multi-time scale energy spectrum.

[0075] In this embodiment, extraction and backtracking are used to explore the underlying causes of insufficient flexibility. For each identified coverage gap, the system first records the time period in which it occurs, such as 18:00 to 19:00, and the type of demand causing the gap, such as frequency regulation demand or 4-hour peak shaving demand. The system then uses a time index to query the underlying data upon which the energy spectrum was constructed, i.e., backtracking to the internal state trajectory of the CAES within that time period. Specifically, the system extracts physical parameters such as the gas storage pressure sequence and temperature sequence within that time period. For example, it may be found that although it is in a frequency regulation gap, the gas storage pressure is currently close to the preset lower limit of the gas storage pressure.

[0076] Step 307: Combine the extracted time location, time scale type and internal state vector to generate flexibility bottleneck information, so as to locate the specific physical working conditions and state ranges that lead to insufficient flexible adjustment capability.

[0077] In this embodiment, the flexibility bottleneck information is a structured diagnostic report that links the extracted elements to form a complete description of the system's weaknesses. For example, a typical bottleneck might be described as: at time position T... _conflict At a certain moment, insufficient flexibility in the frequency regulation scale was observed, and the associated internal state vector indicated that the gas storage pressure was below 40 bar. This information suggests that the physical condition of excessively low gas storage pressure prevented the system from providing sufficient frequency regulation power at that time. Generating such information not only informs the user of the insufficiency but also explains its cause, providing a direct basis for subsequent targeted adjustments to operating strategies or planning parameters.

[0078] Example 4 details the construction, solution, and closed-loop optimization mechanism of the joint planning model of economy and flexibility based on shadow prices. On the basis of the energy spectrum evaluation system constructed in the previous examples, it further solves the problem of how to transform the flexibility evaluation results into planning decision signals. By introducing the flexibility shadow price, it achieves an optimal configuration that takes into account both the whole life cycle cost and the multi-time scale adjustment capability.

[0079] Step 401: Read the cost parameters from the scenario-based running dataset and establish an economic objective function with the goal of minimizing the total life cycle cost.

[0080] In this embodiment, the cost parameters in the scenario-based operation dataset specifically include the unit power investment cost, unit capacity investment cost, operation and maintenance cost coefficient, wind and solar curtailment penalty unit price, standby capacity call-up unit price, and grid frequency and voltage deviation penalty coefficient for the compressed air energy storage system. The economic objective function is established to find a planning scheme that minimizes the total expenditure of the system throughout its entire lifecycle. This overall objective function C... _total It can be represented as:

[0081] C _total =C _inv +C _om +C _cur +C _res +C _pun ;

[0082] Among them, C _total C represents the total objective function value. _inv For the investment cost of compressed air energy storage, C _om For operation and maintenance costs, C _cur To mitigate the penalties for curtailing wind and solar power, C _res For backup costs, C _pun The cost of penalizing grid stability.

[0083] Step 402: Using surrogate modeling or piecewise linearization, the flexible adjustment adequacy index is mapped to a function of decision variables to construct adequacy constraints, ensuring that the system meets the preset minimum coverage margin requirement.

[0084] In this embodiment, since the flexible adjustment adequacy index calculated in the previous embodiments is based on a complex geometric coverage algorithm, directly introducing it as a constraint into the optimization model would lead to a nonlinear or even nonconvex problem, making it difficult to solve efficiently. This step uses a piecewise linearization method to transform the index into an algebraic constraint that the optimizer can recognize. Specifically, the system pre-trains a surrogate model that describes the mapping relationship between CAES configuration parameters, namely compressor power, turbine power, gas storage volume, and coverage margin index R.

[0085] As a specific implementation method, the sensitivity coefficient method can be used to construct linear constraints. That is, the constraint condition is set as: R _0 +S T ΔCap≥R _min Among them, R _0 S is the initial coverage margin, S is the sensitivity vector reflecting the improvement in coverage margin per unit increase in capacity, and ΔCap is the configuration increment vector. T ΔCap represents the dot product of the sensitivity vector and the configuration increment vector, R _min This is the preset minimum coverage margin.

[0086] In some implementations, sufficiency constraints can also be directly manifested as mandatory requirements on the energy spectrum boundary, such as requiring the planned CAES system to meet the critical bottleneck period t. _bottleneck It must have a value of not less than P _req Frequency modulation capability reserves, P _req This constraint is designed to meet minimum frequency modulation power reserve requirements. This constraint construction method reduces the solution complexity of the optimization model while ensuring computational accuracy.

[0087] Step 403: Integrate the economic objective function, adequacy constraints, and CAES thermodynamic physical constraint model to generate an economic-flexibility joint programming model.

[0088] In this embodiment, the integration process refers to integrating the aforementioned objective function and all constraints into a unified mathematical programming framework. In addition to the aforementioned adequacy constraints, the model must also include the operational constraints corresponding to the CAES thermodynamic physical constraint model, specifically including power balance constraints, CAES equipment ramp-up constraints, gas storage state of charge (SOC) constraints, and thermal storage system energy balance constraints.

[0089] Specifically, the power balance constraint requires that at any time t, the sum of wind power output, photovoltaic power output, and CAES discharge power must equal the sum of load demand, CAES charging power, and the amount of wind and solar curtailment. The CAES equipment constraint requires turbine output P... _exp (t) and compressor power consumption P _com (t) must be between its minimum technical output and rated capacity, and is subject to the ramp rate constraint. The gas storage facility constraint requires that the gas storage volume at time t must equal the gas storage volume at the previous time plus the filling flow rate minus the venting flow rate, and the gas storage volume must always be between the minimum and maximum volumes. By combining physical constraints with economic objectives and flexibility constraints, a mixed-integer linear programming (MILP) model or a nonlinear programming (NLP) model is generated, i.e., an economic-flexibility joint programming model.

[0090] Step 404: Numerically solve the economic-flexibility joint programming model to obtain the optimized solution results including the solutions of the original variables and the solutions of the dual variables.

[0091] In this embodiment, numerical solution refers to using commercial mathematical optimization solvers such as CPLEX, Gurobi, or open-source solvers to compute the generated planning model. The solution process can employ branch and bound, interior-point methods, or Lagrange relaxation algorithms. The original variable solution refers to the specific numerical values ​​of the decision variables obtained after optimization, including planning variables such as optimal compressor capacity, turbine capacity, and gas storage volume, as well as operational variables such as equipment output at each moment in each scenario. The dual variable solution refers to the shadow price or Lagrange multiplier corresponding to each constraint. The dual variable reflects the rate of change of the objective function value when the right-hand side of the constraint undergoes a small change. For example, the dual variable of power balance constraints is usually interpreted as the nodal marginal electricity price; this invention focuses on the dual variables related to energy spectrum boundary constraints.

[0092] Step 405: Extract the Lagrange multiplier sequence corresponding to the short-timescale power boundary constraint and the long-timescale energy boundary constraint in the CAES multi-timescale energy spectrum from the dual variable solution of the optimization solution.

[0093] In this embodiment, the extraction operation is performed under certain constraints. In the joint programming model, to meet flexibility requirements, a constraint is introduced that limits the output of the CAES to not exceeding its energy spectrum boundary, for example, P. _exp (t)≤P _up_max (t). When the constraint is under tension at a certain moment, i.e., equality holds, the solver will produce a non-zero Lagrange multiplier λ. _t The multiplier λ _t This characterizes the short-timescale power boundary up-adjustment limit P of CAES at that moment. _up_max (t) represents the amount by which the total system cost will decrease when one unit is added. The system iterates through all time steps and time scales, extracting these multipliers to form time series data.

[0094] Step 406: Classify the Lagrange multiplier sequences according to the time scale of frequency modulation and peak modulation, and construct a flexibility shadow price sequence that represents the marginal value of adjustment capability at different times and under different states.

[0095] In this embodiment, the flexibility shadow price series is the result of interpreting the physical meaning of the extracted Lagrange multipliers and structuring them. Specifically, for the frequency modulation time scale, a frequency modulation flexibility shadow price series Price is constructed. _freqIts value is equal to the multiplier value of the short-time power boundary constraint at the corresponding moment; for the peak-shaving time scale, a peak-shaving flexibility shadow price series Price is constructed. _peak Its value is equal to the multiplier value of the energy boundary constraint at the corresponding time and duration. This price series visually shows the moment when the system is least flexible. For example, if the frequency regulation flexibility shadow price is high at 19:00 during the evening peak, it indicates that the system's frequency regulation capacity is severely insufficient at this time, and each additional 1MW of frequency regulation capacity has high economic value. This series provides planners with a more refined economic signal than simply indicating insufficient capacity.

[0096] Step 407: Analyze the temporal distribution characteristics of the flexibility shadow price series, identify periods of scarce flexibility resources based on price levels, and adjust the power capacity parameters, gas storage capacity parameters, and thermal storage capacity parameters of the compressed air energy storage system based on these periods of scarce flexibility resources to generate an updated CAES planning and configuration scheme.

[0097] In this embodiment, analyzing the temporal distribution characteristics refers to statistically analyzing the time periods and frequencies during which shadow prices peak. The logic for identifying scarce periods is: the higher the price, the higher the scarcity. The parameter adjustment strategy is based on the bottleneck elimination principle. If the shadow price for frequency regulation flexibility is found to be persistently high, it indicates that the turbine or compressor's ramp-up capability or rated power is the bottleneck. Therefore, the power capacity parameter, compressor power P, is added to the update scheme. _exp_cap Or turbine power P _com_cap If the shadow price for peak-shaving flexibility over a long timescale is found to be too high, it indicates insufficient energy storage duration, and the gas storage capacity parameter, gas storage volume V, should be increased. _air_cap .

[0098] For example, a specific adjustment algorithm can employ the idea of ​​gradient descent, calculating the gradient direction and step size for capacity adjustment based on the shadow price. For instance:

[0099] T new =T old +α·Π shadow Among them, T new For the updated turbine capacity, T old α represents the current (or existing) turbine capacity; α represents the learning rate; Π shadow This represents the cumulative shadow price return corresponding to this capacity.

[0100] By making quantitative adjustments, an updated CAES planning and configuration scheme is generated, which in theory can solve the flexibility bottleneck problem identified in the previous round more economically.

[0101] Step 408: The updated CAES planning configuration scheme is fed back as a boundary condition to the economic-flexibility joint planning model for iterative solution until the volatility characteristics of the flexibility shadow price series meet the preset convergence criteria.

[0102] In this embodiment, iterative solution refers to fixing the updated hardware parameters to known constants and running steps 404 to 407 again. The preset convergence criterion can be set as follows: the rate of change of the total cost between two adjacent iterations is less than a set threshold, such as 0.1%, or the maximum value of the flexibility shadow price is lower than a certain acceptable marginal cost upper limit. The iterative process simulates the balance between planning and operation, ensuring that the final solution not only statically meets capacity requirements but also can cope with various flexibility challenges at a reasonable economic cost during dynamic operation.

[0103] Step 409: Output the final CAES planning and configuration scheme that meets the convergence criteria, as the basis for project construction decisions, such as... Figure 4 As shown.

[0104] In this embodiment, the final CAES planning configuration scheme output is a complete set of engineering parameters, specifically including the compressor's rated power, the turbine expander's rated power, the gas storage tank's design volume, the thermal storage tank's design capacity, and the corresponding heat exchanger parameters. Furthermore, the output may also include typical daily operating strategy curves and a flexibility assessment report based on this configuration scheme. This scheme, serving as the basis for engineering construction decisions, has undergone refined evaluation based on the energy spectrum and closed-loop optimization based on shadow prices. Compared to traditional schemes that configure only based on the maximum load gap, it can reduce redundant investment while improving the system's operational safety under extreme conditions.

[0105] Example 5 provides a system-level implementation and verification supplement to the above method, detailing the computer system architecture and scheme verification process used to execute the above evaluation and planning methods, providing hardware carrier and effect verification support for the practical application of the method of the present invention.

[0106] In a preferred embodiment, the apparatus for executing the method of the present invention can be embodied in a high-performance computing workstation or a cloud server cluster. At the hardware level, the system mainly includes a processor, memory, input / output interfaces, and a communication bus. The processor can be a central processing unit (CPU) or a graphics processing unit (GPU) for performing complex numerical integration, optimization solutions, and matrix operations. The memory stores massive amounts of scenario-based operational data, a library of thermodynamic and physical models, and generated energy spectrum data. The input / output interfaces receive external meteorological data and power grid dispatch instructions and output planning reports.

[0107] To verify the effectiveness of the method of the present invention, this embodiment also includes a verification process. The specific operations are as follows: A high-precision multiphysics simulation model is established using the final CAES planning and configuration scheme. Extreme cycles in history where wind and solar power curtailment or load shedding has occurred are selected as test scenarios. These scenarios are replayed in the simulation model, and the system is forced to execute according to the operating strategy planned in this invention. The actual gas storage pressure, temperature changes, and grid frequency fluctuations are monitored during the simulation process.

[0108] Verification results show that, compared to traditional capacity planning methods that do not consider thermodynamic coupling, the CAES system configured using the method of this invention exhibits a significant reduction in frequency regulation failures under extreme operating conditions. For example, in a sudden wind power drop event, the traditional method failed to anticipate the power limitation caused by low pressure in the gas storage facility, resulting in actual output falling below the commanded value and causing a frequency drop. In contrast, the method of this invention identifies the low-pressure bottleneck in advance through energy spectrum analysis and increases the gas storage capacity margin or optimizes the pre-planning gas storage strategy, thus supporting frequency stability and improving the safety and stability of the new power system.

[0109] In some alternative implementations, the flexibility assessment system of the present invention can also be integrated into the power grid energy management system (EMS) as an online dispatching auxiliary tool. In this mode, the system no longer outputs planning parameters, but instead calculates the energy spectrum coverage margin for the next few hours in real time and displays it on the dispatcher's workbench in the form of a heat map, providing intuitive early warning of flexibility risks and further expanding the scope of application of the present invention.

[0110] Example 6 details the specific calculation process for establishing the CAES thermodynamic physical constraint model and the economic objective function.

[0111] Step 601: Based on the acquired wind and solar load prediction data and CAES equipment parameters, establish a scenario-based operation dataset and a CAES thermodynamic physical constraint model.

[0112] In this embodiment, the CAES thermodynamic physical constraint model is described by specific energy and mass conservation equations. Specifically, for the compressor model, the formula for the total power consumption of the compressor is:

[0113] Pc=∑P c,i Where Pc is the total power consumption of the compressor, P c,i Let be the power consumption of the i-th stage compressor.

[0114] The power consumption P of the i-th stage compressor c,i It can be calculated using the following formula:

[0115] P c,i =(1 / η m,i )c p mac *(T out,c,i -T in,c,i ); where η m,i Let c be the efficiency of the i-th compressor. p For the specific heat capacity at constant pressure, m ac T is the air mass flow rate of the compressor. in,c,i Let T be the intake temperature of the i-th stage compressor. out,c,i Let be the outlet temperature of the i-th compressor.

[0116] For the turbine expander model, the formula for the total power of the turbine expander is: Pe = ∑P e,i Where Pe is the total power of the turbine expander, and P e,i Let be the power of the i-th stage turboexpander.

[0117] Among them, the power P of the i-th stage turboexpander e,i It can be calculated using the following formula:

[0118] P e,i =η e,i c p m ad *(T in,e,i -T out,e,i ); where η e,i Let c be the efficiency of the i-th turbine expander. p For the specific heat capacity at constant pressure, m ad T is the air mass flow rate of the turbine expander. in,e,i T represents the inlet temperature of the i-th stage turboexpander. out,e,i Let be the outlet temperature of the i-th turbine expander.

[0119] For the gas storage model, its pressure evolution follows mass balance and the gas state equation. Specifically, the formula for the pressure evolution of the gas storage is:

[0120] ρ ar,t =ρ ar,t-1 +(R g T ar,t / V ar (m) in,t -m out,t )*Δt;

[0121] Where, ρ ar,t Let ρ be the pressure in the gas storage tank at time t. ar,t-1 R is the gas storage pressure at time t-1. g T is the universal gas constant. ar,t Let V be the temperature in the gas storage tank at time t. ar Let be the volume of the gas storage tank, and Δt be the duration of the time interval, in meters. in,t For inflation mass flow rate, mout,t Let be the venting mass flow rate. This relationship describes the integral change in pressure due to the injection or outflow of air mass over a duration of time interval Δt.

[0122] For the heat exchanger model, the heat exchange process is calculated based on the efficiency number of heat transfer units (NTU). The outlet temperatures of the heat and cold fluids in the heat exchanger depend on the inlet temperature of the hot fluid, the inlet temperature of the cold fluid, the heat exchanger efficiency ε, the number of heat transfer units (NTU), and the heat exchanger coefficient.

[0123] The specific mathematical expressions constitute the calculation process of the CAES thermodynamic physical constraint model, ensuring the physical accuracy of state deduction in the subsequent energy spectrum construction process.

[0124] Step 602: Read the cost parameters from the scenario-based running dataset and establish an economic objective function with the goal of minimizing the total life cycle cost.

[0125] In this embodiment, the economic objective function is the total life-cycle cost C. _total The cost is broken down into five specific components, and the calculation formula can be:

[0126] C _total =C _inv +C _om +C _cur +C _res +C _pun ;

[0127] Among them, C _total C represents the total objective function value. _inv For the investment cost of compressed air energy storage, C _om For operation and maintenance costs, C _cur To mitigate the penalties for curtailing wind and solar power, C _res For backup costs, C _pun The cost of penalizing grid stability.

[0128] Specifically, investment cost C _inv The calculation formula can be:

[0129] C _inv =(r*((1+r) L ) / (((1+r) L )-1))(c _inv_com P _com_cap +c _inv_exp P _exp_cap +c _inv_ air V _air_cap +c _inv_th *Q _th_cap );

[0130] Where r is the discount rate, L is the operating life, and c _inv_com c _inv_exp c _inv_air c _inv_th These represent the investment costs per unit compression power, per unit turbine power, per unit volume of gas storage chamber, and per unit of heat storage, respectively. _com_cap P _exp_cap V _air_cap Q _th_cap These are compressor power, turbine power, gas storage volume, and heat storage capacity, respectively.

[0131] Operation and maintenance costs C _om The calculation formula can be:

[0132] C _om =C _inv *k _om ; where k _om This is a fixed maintenance coefficient.

[0133] The cost of curtailing wind and solar power (C) _cur The calculation formula can be:

[0134] C _cur =c _cur *(P _cur_w +P _cur_pv ); where P _cur_w For wind curtailment power, P _cur_pv This refers to the power of abandoned light.

[0135] Backup cost C _res The calculation formula can be: C _res =c _res *P _res Among them, P _res This refers to the backup power that is being called up.

[0136] Power grid stability penalty cost C _pun The calculation formula can be:

[0137] C _pun =w f (Δf) 2 +w U (ΔU) 2 Where Δf is the frequency deviation, ΔU is the voltage deviation, and w f and w U These are the weighting coefficients for frequency and voltage deviation, respectively.

[0138] By using sophisticated mathematical modeling, the abstract economic optimization objective is transformed into a concrete algebraic equation that can be processed by numerical optimization algorithms, thus ensuring the credibility of the planning results in terms of engineering economics.

[0139] According to one aspect of this application, in the process of constructing a CAES multi-timescale adjustable energy spectrum, a discrete-time grid is constructed and internal state trajectory data of the CAES is generated, specifically as follows:

[0140] The temporal resolution of wind power output, photovoltaic power output, and load, as well as the grid dispatch cycle, are obtained from the scenario-based operational dataset. This information is then unified into a basic time step, such as in minutes, to generate a unified time grid covering the entire research period.

[0141] At the initial moment, by combining the CAES structural parameters and CAES operational constraint parameters, initial values ​​such as initial gas storage pressure, initial gas temperature, and initial thermal energy are set. Initialization calculations are performed through the basic physics and constraint model to obtain the initial internal state data of the CAES at the initial moment.

[0142] Along a unified time grid, wind power, photovoltaic and load data are acquired at each time step. Combined with the assumed baseline operation strategy, internal variables such as gas storage pressure, gas temperature and thermal energy are gradually updated through the basic physics and constraint model to obtain CAES internal state trajectory data covering the entire time grid. This data contains the internal state vector at each time point.

[0143] CAES internal state trajectory data will be used as input for calculating short- and long-term timescale regulation capabilities.

[0144] According to one aspect of this application, during the construction of a CAES multi-timescale tunable energy spectrum, the calculation of short-timescale frequency-modulated tunable power capability data is specifically as follows:

[0145] At each time point, the internal states such as gas storage pressure, gas temperature, and thermal energy are obtained from the internal state trajectory data of CAES. At the same time, the maximum power, minimum power, maximum ramp rate, and minimum ramp rate in the CAES operation constraint parameters are also obtained.

[0146] Based on fundamental physics and constraint models, a calculation relationship for the power feasible interval on a short timescale is constructed for each time point.

[0147] By traversing a unified time grid, the upward and downward adjustable power limits are calculated at each time point, and the upward adjustment limit P at each time point is... _up_max (t) and the downward limit P _down_max (t) is recorded as the instantaneous adjustment capability on the frequency modulation time scale at that moment, and the summation yields the frequency modulation adjustable power capability data covering the entire study period.

[0148] Frequency-modulated adjustable power capability data will be used as part of the construction of a unified energy spectrum data structure.

[0149] According to one aspect of this application, during the construction of a CAES multi-timescale adjustable energy spectrum, the available energy capacity for long-timescale peak shaving is calculated, specifically as follows:

[0150] At each point in time, the current gas storage pressure, gas temperature, and thermal energy are obtained from the CAES internal state trajectory data. Combined with parameters such as the upper and lower limits of gas storage pressure, the allowable exhaust temperature range, and turbine efficiency in the CAES operation constraints, an estimation relationship for the total available energy is established.

[0151] For each candidate duration window, for example, by setting multiple sets of duration lengths, a set of feasible output trajectories for each duration starting from the current moment is constructed. Using a fundamental physics and constraint model, the changes in internal pressure and temperature during continuous turbine power generation are simulated for each duration length. The upper limit of the average output allowed within that duration window is calculated without violating the lower limit of gas storage pressure, the upper limit of exhaust temperature, and the capacity constraints of the thermal storage system. Multiplying this upper limit by the duration yields the corresponding scalable peak energy.

[0152] The average peak output limit and peak energy corresponding to each time point and each duration are recorded as structured data, forming peak-shaving adjustable energy capability data covering the entire study period and multiple long-term scales. This data includes time coordinates, duration length, and corresponding sustainable output range, reflecting the load tracking and peak-shaving capabilities that CAES can undertake on long-term scales.

[0153] Peak-shaving adjustable energy capability data and frequency-modulated adjustable power capability data will be integrated into a unified multi-timescale energy spectrum.

[0154] According to one aspect of this application, in the process of constructing a CAES multi-timescale adjustable energy spectrum, a unified CAES multi-timescale energy spectrum data is constructed, specifically as follows:

[0155] Acquire frequency-modulated adjustable power capacity data and peak-shaving adjustable energy capacity data, align the time and duration labels used in the two datasets, and map the power range of short time scale and the energy range of long time scale to the same time scale labeling system.

[0156] For each time point, a set of multi-timescale capability entries is generated. Each entry contains the maximum upward regulation power, the maximum downward regulation power, the average output power that can be provided sustainably for each peak shaving duration, and the corresponding shaving energy. These entries are organized into a hierarchical structure to form a local energy spectrum segment for that time point.

[0157] Along the entire timeline, local energy spectrum fragments at all time points are concatenated and compressed as needed, such as aggregating fragments with similar capabilities at adjacent time points and downsampling the capability limits to reduce the data size while ensuring accurate characterization of key constraint boundaries, thus forming CAES multi-timescale energy spectrum data covering the entire study period.

[0158] CAES multi-timescale energy spectrum data will be directly used as input for the assessment of flexible adjustment adequacy and as the basis for constructing the capacity boundary of joint planning constraints.

[0159] According to one aspect of this application, in the assessment of flexible regulation adequacy based on energy spectrum, multi-timescale regulation demand trajectory data is extracted, specifically:

[0160] Based on the deviation between the predicted output of wind and solar power and the actual operating scenarios, and combined with load changes and grid safety and stability requirements, the active power imbalance at each time point in each scenario is calculated from the scenario-based operation data set. The imbalance is statistically analyzed on a time scale from seconds to minutes to obtain the frequency regulation demand trajectory of each scenario on a short time scale.

[0161] For characteristic periods such as morning and evening peaks and large-scale increases or decreases in wind power in the daily load curve, the net load change on a time scale of tens of minutes to several hours is calculated from the scenario-based operation data according to the system planning objectives and reserve capacity settings, so as to obtain the peak-shaving demand trajectory of each scenario on a long time scale.

[0162] The frequency regulation demand trajectory and peak shaving demand trajectory under each scenario are unified and organized to form a unified format of regulation demand trajectory data, which includes scenario identifier, time index, time scale identifier and corresponding demand power or demand energy value, as the demand-side input for subsequent coverage analysis.

[0163] The adjustment demand trajectory data will be matched and calculated with CAES multi-timescale energy spectrum data.

[0164] According to one aspect of this application, in the assessment of flexible adjustment adequacy based on energy spectrum, a set of energy spectrum and demand matching divided by scenario is constructed, specifically:

[0165] The time-series demand information for each scenario is obtained from the demand trajectory data. At the same time, the energy spectrum fragments at the corresponding time points are obtained from the CAES multi-timescale energy spectrum data. The time index is matched one by one, and the demand items at each time point are packaged with the capacity items at the same time point to form a local matching record for that scenario.

[0166] For frequency regulation demand, at each time point, the demand power on a short time scale is paired with the maximum upward adjustment power and the maximum downward adjustment power at that time point in the frequency regulation adjustable power capability data; for peak shaving demand, at each representative start-up time point, the demand energy or average demand output on a long time scale is paired with the sustainable output range in the peak shaving adjustable energy capability data.

[0167] The capability and requirement items at all time points and time scales in each scenario are combined to form the scenario energy spectrum matching data corresponding to that scenario, which is used to calculate the coverage margin of a single scenario.

[0168] According to one aspect of this application, in the flexible adjustment adequacy assessment based on energy spectrum, the coverage margin sequence of a single scenario across multiple time scales is calculated, specifically as follows:

[0169] For each scenario, at each point in time and at each time scale, obtain the corresponding capability items and requirement items. If the requirement is to be adjusted upward, compare the required power or required energy with the capability upper limit; if the requirement is to be adjusted downward, compare the required power or required energy with the capability downward adjustment space.

[0170] For each matching entry, calculate the local coverage margin. _k The calculation process is a formula, which has been shown in the previous embodiments and will not be described in detail here.

[0171] Within each scene, margins at all points in time and at all time scales. _k Aggregation is performed, for example, taking the minimum value or a certain low quantile as the overall coverage margin of the scenario to obtain the total margin value of the scenario, while retaining the local margin sequence at each time point to form the scenario coverage margin sequence data.

[0172] Scene coverage margin sequence data is used to statistically analyze the overall system's flexibility in adjusting sufficiency and to locate bottleneck segments.

[0173] According to one aspect of this application, in the assessment of sufficiency based on energy spectrum flexibility, the statistical system flexibly adjusts the sufficiency index, specifically as follows:

[0174] Extract the summary value representing the overall margin level of each scenario from the scenario coverage margin sequence data of each scenario. For example, the minimum margin value or low quantile margin value of each scenario constitutes the margin sample of the system under the multi-scenario set.

[0175] Statistical analysis of margin samples can be performed using quantiles, for example, by selecting a margin value at a certain probability level as the adequacy for flexible system adjustment, or by subtracting variance weights from the expected value to form a adequacy index that takes into account both average level and risk.

[0176] The statistically obtained index values ​​and their corresponding probability levels or weight parameters are recorded as flexible adjustment sufficiency indicators, which serve as the lower limit of constraints or target references in subsequent joint planning models.

[0177] According to one aspect of this application, in the assessment of the adequacy of flexible regulation based on energy spectrum, information data on flexibility bottlenecks is extracted, specifically as follows:

[0178] Scan the scene coverage margin sequence data for each scenario to find time points and time scale entries where the local margin value is less than or close to zero. These entries represent insufficient regulation capacity at the corresponding time point and time scale.

[0179] For each identified bottleneck item, record its associated scenario, time location, time scale type, demand size, capacity limit, and related CAES internal state range to form a bottleneck item record.

[0180] The bottleneck items in all scenarios are aggregated and clustered according to time period, time scale, or internal state region. For example, long-term bottlenecks concentrated during the evening peak period or frequency regulation bottlenecks concentrated in a certain gas storage pressure range are formed to create structured flexible bottleneck information data, which is used to guide the constraint strengthening and capacity configuration adjustment of the joint planning model.

[0181] According to one aspect of this application, in the joint planning optimization of economic efficiency and flexibility, an economic objective function and basic constraints are constructed, specifically as follows:

[0182] The investment cost coefficient, operation and maintenance cost coefficient, wind and solar curtailment penalty coefficient, reserve capacity cost coefficient, and frequency and voltage deviation penalty coefficient are obtained from economic parameters, and electricity price, load, and wind and solar output scenario data are obtained from scenario-based operation datasets.

[0183] By combining fundamental physics and constraint models, power balance constraints are constructed for each time point and each scenario, incorporating CAES output, other unit output, wind and solar power output, and load demand into the constraints, and adding grid voltage and frequency limits as well as upper and lower limits for unit output constraints.

[0184] Based on the above constraints, a calculation structure for the whole life cycle cost is defined. For example, the investment cost is converted into the equivalent annual cost, and the operation and maintenance cost, wind and solar curtailment cost, reserve capacity cost and frequency and voltage deviation penalty are summed according to time and scenario to form an economic objective function data structure that can be called by the optimization solver.

[0185] The economic objective function data structure and basic constraints will be combined with flexibility constraints to form a complete joint optimization model.

[0186] According to one aspect of this application, in the joint planning optimization of economic efficiency and flexibility, flexibility constraints based on energy spectrum and sufficiency are injected, specifically as follows:

[0187] Acquire CAES energy spectrum data at multiple time scales, and transform the capacity boundary at each time point and time scale into a constraint relationship on CAES output and gas storage. For example, limit the output variation at the frequency regulation time scale, and limit the cumulative output within a given duration to not exceed the upper limit given by the energy spectrum at the peak regulation time scale.

[0188] Based on the flexible adjustment sufficiency index, an overall flexibility constraint lower limit is set. For example, it is required that after joint optimization, the system's flexible adjustment sufficiency should not be lower than a certain planning target value. This requirement is transformed into nonlinear or piecewise linear constraints on decision variables, forming a macroscopic sufficiency constraint.

[0189] By utilizing flexibility bottleneck information data, constraints on specific time periods and time scales can be strengthened. For example, stricter energy spectrum coverage conditions can be imposed on time periods where bottlenecks are concentrated. The local strengthening rules can be organized into a set of additional constraint items to form a comprehensive flexibility constraint data structure.

[0190] According to one aspect of this application, in the joint planning optimization of economic efficiency and flexibility, a joint optimization model of economic efficiency and flexibility is constructed, specifically as follows:

[0191] Define a set of optimization decision variables, including planning and configuration variables such as CAES installed power capacity, gas storage capacity, and thermal storage capacity, as well as operation strategy variables such as CAES output, charging and discharging status, and gas storage trajectory at each time point and in each scenario, to form a unified decision vector.

[0192] By using an economic objective function data structure as the objective function of the optimization model, the solution process is dedicated to minimizing the total life cycle cost.

[0193] The basic operational constraints and flexibility constraints data structures are added to the model to form a complete constraint system. The energy spectrum capacity boundary, the overall adequacy lower limit, and the bottleneck period reinforcement requirements are embedded into the optimization problem, generating economic-flexibility joint optimization model data that can be called by numerical optimization algorithms.

[0194] According to one aspect of this application, in the joint optimization of economic efficiency and flexibility, solving the joint optimization model and constructing the flexibility shadow price series are specifically as follows:

[0195] Choose a solution strategy suitable for the model structure, such as using a decomposition coordination algorithm, a two-layer optimization framework, or a Lagrange relaxation method, to solve the capacity planning variables and the running strategy variables in layers to improve computational efficiency.

[0196] During the solution process, the Lagrange multipliers applied to the flexibility-related constraints are tracked, and the multiplier values ​​corresponding to each time period and each time scale are interpreted as the flexibility shadow price for that time period, reflecting the opportunity cost of unit adjustment capacity under the condition of satisfying energy spectrum coverage.

[0197] After the solution converges, the configuration results such as CAES installed capacity, gas storage capacity and thermal storage capacity are extracted from the optimization results to form a CAES planning and configuration scheme; at the same time, the optimal output and gas storage trajectory at each time point are extracted to form CAES operation strategy data; the Lagrange multipliers of flexibility constraints obtained in the solution process are arranged in chronological order to form a flexibility shadow price series.

[0198] CAES planning and configuration schemes, CAES operation strategy data, and flexible shadow price series will serve as the basis for verification and result output.

[0199] According to one aspect of this application, in the joint planning optimization of economic efficiency and flexibility, the collation and transmission of joint planning results specifically includes:

[0200] The CAES planning and configuration scheme is organized into a standardized configuration list according to equipment type and capacity parameters, including installed capacity, basic parameters of gas storage and thermal storage system capacity, etc., which is convenient for engineering designers to use directly.

[0201] The CAES operation strategy data is grouped according to time and scenario to form a scheduling sequence for simulation playback, which is used for physical constraint re-verification and flexibility index recalculation.

[0202] The flexibility shadow price series is plotted as a price curve or discrete series data along the time axis, allowing planners to analyze which periods are most scarce in flexibility, so that planning objectives can be adjusted or other flexibility resources can be introduced in subsequent versions.

[0203] This application constructs a CAES multi-timescale energy spectrum based on internal state vectors. By introducing a refined CAES thermodynamic physical constraint model, such as compressor, turbine, gas storage tank and heat exchanger models, the evolution of gas storage pressure and temperature is deduced step by step on a discrete time grid. Based on this, the power and energy boundaries constrained by thermodynamics are dynamically calculated. This solves the defect of the traditional model that simplifies CAES to a constant power battery. It realizes real-time strong coupling between regulation capability and physical conditions, ensures the authenticity of the evaluation results under extreme conditions such as low pressure, and solves the problem of overestimation of capability caused by decoupling of physical state and regulation capability.

[0204] This application employs a sufficiency assessment method based on geometric coverage relationships. It decomposes grid demand into frequency regulation and peak shaving trajectories and embeds them into the feasible region defined by a multi-timescale energy spectrum, calculating the envelope margin of the trajectory relative to the boundary. This solves the problem of traditional probabilistic indicators such as the Loss of Load Probability (LOLP) losing temporal and scale coupling information, quantifies the sufficiency level, and can accurately locate bottlenecks causing insufficient flexibility by tracing back the state vector (e.g., the specific moment when low-voltage conditions caused frequency regulation failure). This improves the interpretability of the assessment and solves the problem that a single scalar indicator cannot reflect multi-scale coupling and continuous trajectory characteristics.

[0205] By employing a closed-loop feedback mechanism based on flexibility shadow prices, and extracting Lagrange multipliers from the energy spectrum boundary constraints, a shadow price series reflecting the adjustment value at different times is constructed to guide capacity parameter adjustments. This achieves synergistic optimization of economy and flexibility, avoiding the redundancy or shortage of flexibility that may exist in traditional planning schemes. It also solves the problem of the disconnect between assessment and planning.

[0206] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for evaluating flexibility regulation adequacy of compressed air energy storage system, characterized in that, The method comprises the following steps: Based on the obtained wind and light load prediction data and CAES device parameters, a scenario operation data set and a CAES thermodynamic physical constraint model are established; The CAES thermodynamic physical constraint model is used to perform time sequence deduction on the scenario operation data set, to obtain an internal state vector representing the evolution of the gas storage pressure and the gas temperature, and to construct a CAES multi-time scale energy spectrum based on the internal state vector, which is a unified data structure based on dynamic constraints and coupling of short-time scale power boundaries and long-time scale energy boundaries; The multi-time scale adjustment demand trajectory is parsed from the scenario operation data set; The multi-time scale adjustment demand trajectory is mapped into the CAES multi-time scale energy spectrum to establish a geometric coverage relationship; The flexible adjustment adequacy index is quantitatively calculated according to the geometric coverage relationship; The method comprises the following steps: The multi-time scale adjustment demand trajectory is decomposed into a frequency modulation power demand sequence and a peak regulation energy demand sequence according to the time scale characteristics; At each time point, the values in the frequency modulation power demand sequence are matched with the short-time scale power boundaries at the corresponding time in the CAES multi-time scale energy spectrum, and the values in the peak regulation energy demand sequence are matched with the long-time scale energy boundaries at the corresponding time and duration; For each group of matches, the envelope degree of the short-time scale power boundary or the long-time scale energy boundary relative to the demand is calculated to generate a local coverage margin; All time points and local coverage margins under all time scales are aggregated to form a geometric coverage relationship representing whether the demand trajectory falls within the feasible region of the energy spectrum; The flexibility bottleneck information is generated using the geometric coverage relationship: The local coverage margin sequence in the geometric coverage relationship is scanned to identify insufficient coverage segments with a margin lower than a preset threshold; The time position and time scale type corresponding to each insufficient coverage segment are extracted, and the internal state vector corresponding to the time position is retrieved from the CAES multi-time scale energy spectrum; The extracted time position, time scale type and internal state vector are combined to generate flexibility bottleneck information to locate the specific physical working conditions and state intervals that cause insufficient flexible adjustment capacity.

2. The method of claim 1, wherein, The CAES thermodynamic physical constraint model is used to perform time sequence deduction on the scenario operation data set, to obtain an internal state vector representing the evolution of the gas storage pressure and the gas temperature, and to construct a CAES multi-time scale energy spectrum, comprising: A discrete time grid is constructed according to the time resolution characteristics of the scenario operation data set; At each time step of the discrete time grid, the input variables in the scenario operation data set are simulated using the CAES thermodynamic physical constraint model to generate a CAES internal state trajectory containing gas storage pressure, gas temperature and heat storage energy parameters; Each internal state vector in the CAES internal state trajectory is traversed to calculate the short-time scale power boundary and the long-time scale energy boundary limited by the thermodynamic state at that time. The short-time scale power boundary corresponding to the same internal state vector is stored in association with the long-time scale energy boundary to form a CAES multi-time scale energy spectrum.

3. The method of claim 2, wherein, The short-time scale power boundary corresponding to the same internal state vector is stored in association with the long-time scale energy boundary to form a CAES multi-time scale energy spectrum includes: The short-time scale power boundary is assigned a frequency modulation time scale identifier, and the long-time scale energy boundary is assigned a peak duration time scale identifier; The instantaneous adjustable power interval defined by the short-time scale power boundary at the same time point is time-axis aligned with the sustainable average output interval defined by the long-time scale energy boundary at different peak duration time scale identifiers to generate a local energy spectrum segment; All local energy spectrum segments of different time points are concatenated along a discrete time grid to form a CAES multi-time scale energy spectrum describing the cross-time scale adjustment capability of the CAES at different internal state vectors.

4. The method of claim 2, wherein, The long-time scale energy boundary limited by the thermodynamic state at the moment includes: For each candidate duration in the preset set, read the internal state vector at the current moment as the initial condition; Use the CAES thermodynamic physical constraint model to simulate the turbine expansion process or compressor compression process under the condition of maintaining constant output for the candidate duration, and monitor the evolution trajectory of the gas storage pressure and gas temperature; Take the lower limit of the gas storage pressure and the upper limit of the exhaust temperature as the termination condition, search for the maximum feasible average output maintained in the candidate duration; Calculate the product of the maximum feasible average output and the candidate duration to obtain the corresponding long-time scale energy boundary at the moment and the internal state vector.

5. The method of claim 1, wherein, Further comprising constructing an economic-flexibility joint planning model: Read the cost parameters in the scenario operation data set to establish an economic objective function with the optimization objective of minimizing the life cycle cost; Use the surrogate model technology or piecewise linearization method to map the flexible adjustment adequacy index to the function of the decision variable, construct the adequacy constraint condition to ensure that the system meets the preset minimum coverage margin requirement; Integrate the economic objective function, the adequacy constraint condition and the CAES thermodynamic physical constraint model to generate an economic-flexibility joint planning model.

6. The method of claim 5, wherein, Further comprising extracting a flexibility shadow price sequence based on the economic-flexibility joint planning model: Numerically solve the economic-flexibility joint planning model to obtain the optimization solution result containing the original variable solution and the dual variable solution; From the dual variable solution of the optimization solution result, extract the Lagrange multiplier sequence corresponding to the short-time scale power boundary constraint and the long-time scale energy boundary constraint in the CAES multi-time scale energy spectrum; Classify the Lagrange multiplier sequence according to the time scales of frequency modulation and peak modulation to construct a flexibility shadow price sequence representing the marginal value of adjustment capability at different moments and in different states.

7. The method of claim 6, wherein, Further comprising using the flexibility shadow price sequence to feedback and optimize the CAES planning configuration scheme: The time sequence distribution characteristics of the flexible shadow price sequence are analyzed, a period of flexible resource scarcity is identified according to the price level, and the power capacity parameter, the gas storage capacity parameter and the heat storage capacity parameter of the compressed air energy storage system are adjusted accordingly to generate an updated CAES planning configuration scheme; The updated CAES planning configuration scheme is fed back to the economic-flexibility joint planning model as a boundary condition for iterative solution until the fluctuation characteristics of the flexible shadow price sequence meet the preset convergence standard; The final CAES planning configuration scheme corresponding to the convergence standard is output as a decision basis for engineering construction.

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