Compressed air energy storage day-ahead-real-time market collaborative participation method and system based on heat-pressure correction equivalent inventory and two-layer rolling optimization and storage medium

Abstract

The invention relates to the technical field of energy technologies and power systems, in particular to a compressed air energy storage day-ahead-real-time market collaborative participation method and system based on heat-pressure correction equivalent inventory and two-layer rolling optimization and a storage medium. S2, state estimation and heat-pressure correction are carried out; s3, day-ahead optimization is carried out; s4, performing real-time rolling optimization; s5, metering and settlement; and S6, learning and updating. According to the method, a day-ahead-real-time cooperation-oriented prospective optimization and recursive landing mechanism is constructed, a commitment-deployment-air inventory-device physics-market substitution-response time limit coupling relation is processed in a unified model at the same time, and on the premise that the hardware complexity is not remarkably increased, the real-time performance of the system is improved. More robust profit, more controllable assessment risk and higher executability are realized, and a set of collaborative optimization method and system capable of engineering landing are provided for cross-market participation of compressed air energy storage.

Description

Technical Field

[0001] This invention relates to the fields of energy technology and power system technology, specifically to a method, system, and storage medium for day-ahead-to-real-time market collaborative participation in compressed air energy storage based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization. Background Technology

[0002] From the perspective of the broader power system, with the high proportion of renewable energy integration, the increasing marketization of electricity, and the more refined assessment of ancillary services (frequency regulation, spinning / non-spinning reserve, etc.), energy storage devices are required to provide meterable, accountable, and timely response flexibility in both the day-ahead and real-time domains. Compressed air energy storage (CAES), as a utility-grade form of energy storage, possesses a unique mechanism of "filling" with air using an electrically driven compressor and "discharging" by mixing gas with an expander to generate electricity. It not only allows for energy arbitrage but also provides up / down frequency regulation and spinning / non-spinning reserve under different operating conditions. Its "parallel compression and expansion" structural characteristics and large air chamber capacity give it a natural advantage in multi-market, cross-time domain revenue coupling scenarios, which aligns with the path set by market rules for energy storage participation in recent years (such as separate pricing for day-ahead capacity and real-time deployment). To adapt to this market environment, research and engineering practices generally adopt a "look-ahead" joint optimization approach: coordinating future opportunities within a longer day-ahead rolling window, and then refining and implementing them in a real-time short window by combining pricing and deployment instructions.

[0003] From a device-level perspective, a practically marketable CAES (Computer-Aided Systems) comprises at least three subsystems: a compressor, an expander, and an air storage tank. The power-gas production relationship on the compressor side and the intake / fuel-output relationship on the expander side are typically derived from manufacturer characteristic points and exhibit piecewise linear fit. The state equation of the air storage tank reflects the dynamic conservation of gas production and consumption across different time periods. In terms of operational constraints, the compressor / expander is limited by minimum / maximum power, ramp rate, minimum start-up / shutdown time, and start-up / shutdown costs. Regarding service capabilities, the compressor can reduce / increase its own power consumption to correspond to down / up frequency regulation and down / up spinning reserve, and due to its rapid start-up, it can provide down spinning reserve in offline mode. The expander can provide both frequency regulation and spinning reserve during online periods and non-spinning reserve during offline periods. The market also allows high-quality services to substitute for low-quality services—for example, in real-time settlement, up / down frequency regulation can replace up / down spinning reserve, thus achieving better returns when price and deployment intensity are inconsistent. This institutional characteristic needs to be explicitly expressed in the model as a substitutability constraint.

[0004] For multi-market participation in CAES (Compressed Air Storage) in both day-ahead and real-time dual-time domains, existing methods often employ mixed-integer linear models that simplify uncertainties with deterministic deployment factors. The uncertain relationship between day-ahead committed capacity, real-time deployment volume, and price / commands is often approximated by historical averages or fixed coefficients, which can easily lead to a mismatch between commitment, availability, and deployability. Although air inventory (air quality / pressure in tanks) is modeled as a cross-time constraint, the thermal-pressure coupling and efficiency changes with operating conditions are often weakened into piecewise linear approximations, resulting in the risks and safety margins of high load, high temperature, and efficiency degradation not being fully reflected. Although parallel operation of compressors and expanders is allowed, the substitution relationship and superimposed revenue (quality substitution between frequency regulation, rotating / non-rotating standby) are mostly presented as static rules, lacking a unified characterization of response time limits, ramp rates, minimum start-up and shutdown times, and start-up and shutdown costs.

[0005] In addition, although there is some linkage between the long window and the real-time short window, they are mostly weakly coupled by executing the first period decision only at the real-time layer. There is still a short-sighted bias between the medium- and long-term rolling strategy of air inventory and the impact of real-time price / deployment, which is prone to profit erosion or violation risks.

[0006] In summary, existing solutions still have shortcomings in handling uncertainty, cross-time domain consistency, equipment physical accuracy, and the fineness of alternative constraints. As a result, in scenarios with high fluctuating electricity prices and high-intensity ancillary services, they exhibit contradictions such as unstable revenue, increased pressure on utilization rate / response assessment, and the difficulty of computational solutions after refinement. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention provides a method, system, and storage medium for day-ahead and real-time market collaborative participation of compressed air energy storage based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization. Through thermal-pressure corrected equivalent inventory modeling and a two-layer rolling optimization collaborative mechanism, the compressed air energy storage system achieves significant advantages in day-ahead and real-time market participation, including more stable returns, lower compliance risks, and higher executability.

[0008] This invention is achieved through the following technical solution: A method for collaborative participation in the day-ahead and real-time market of compressed air energy storage based on thermal-compression corrected equivalent inventory and two-layer rolling optimization is provided, including the following steps: S1: Data Acquisition and Forecasting Step: Access day-ahead market prices, real-time market prices, ancillary service deployment command forecasts, meteorological data, and measurement data from compressed air energy storage devices, including pressure, temperature, flow rate, and power data; S2: State estimation and thermal-compression correction: Based on measurement data, the equivalent air inventory state is estimated, and the thermal-compression correction model is applied to dynamically update the inventory state, generating a dynamic safety margin that adapts to temperature and prediction error. S3: Day-ahead optimization: At the day-ahead level, the energy commitment and ancillary service capacity commitment are decided by extending the scheduling window, including electrical energy commitment, up-frequency regulation capacity, down-frequency regulation capacity, spinning reserve capacity and non-spinning reserve capacity, and start-stop baselines for compressors and expanders and inventory cross-window final value targets are set. The objective function is to maximize the sum of day-ahead capacity benefits and expected real-time benefits minus start-stop costs and wear costs. At the same time, uncertainty in prices and deployment instructions is embedded through uncertainty handling methods. S4: Real-time Rolling Optimization: In the real-time layer, based on the commitment results of the day-ahead layer, real-time price signals and scheduling instructions, a model predictive control framework is used to solve the optimization sub-problems. Only the first step instruction is executed to control the compressor power, expander power and the amount of auxiliary service deployment, and to ensure compliance with the ramp rate, minimum start-stop time and response time constraints. S5: Metering and Settlement: Measuring and accounting for the actual deployed energy and ancillary services, completing market settlements, and recording default events; S6: Learning and updating: Based on the measurement results, the deployment factor and efficiency derating curve parameters are updated online, and the updated parameters are fed back to steps S2 and S3 to form an adaptive closed loop.

[0009] Furthermore, in step S2, the equivalent inventory As a state variable, it evolves through the following state equation: ; in: For compression-side power, For expansion-side power, This is a temperature / environment feature vector; For the device characteristic function based on piecewise affine approximation, The equivalent efficiency varies with load and temperature. Describing the hot-pressure pullback, For time steps; and, inventory status and pressure are linearly related. Correlation; Dynamic safety margin equivalence constraints , It adapts to temperature.

[0010] pass The equivalent efficiency term, which varies with load and temperature, reflects the actual operating status of the compressor / expander in real time. Accurately characterize the effects of leakage and heat loss to avoid the accumulation of inventory status estimation bias. The relationship enables precise pressure mapping under different temperature conditions; Constraints adaptively adjust with temperature, automatically tightening safety boundaries under high-temperature conditions. Potential risks are identified early through thermal-pressure correction, preventing pressure exceedances and equipment damage. The state equations support high-frequency updates, ensuring control commands are based on the latest system state. Compared to fixed safety margin methods, dynamic adjustment releases more available capacity. Precise state estimation supports more aggressive operating strategies, enhancing revenue potential. Accurate model predictions reduce scheduling command deviations caused by state estimation errors. Through precise thermal-pressure coupling modeling and a dynamic safety margin mechanism, key physical modeling problems in the market operation of CAES systems are solved.

[0011] Furthermore, steps S3 and S4 work together through the following coupling mechanism: Commitment-Deployment Consistency Constraints: Day-ahead Layer Hourly Consistency h Ancillary service capacity commitment up frequency modulation capacity Down-modulation capacity Rotating Reserve Capacity 、 Non-spinning reserve capacity Set of time periods corresponding to the real-time layer Up-frequency deployment within , frequency reduction deployment volume Rotating standby deployment quantity Non-rotating standby deployment quantity By increasing the frequency deployment factor , frequency modulation deployment factor The association satisfies the following inequality constraints: Where: Δ t Δ is the time step size for the real-time layer. T For the day-ahead time step, K( h () indicates the hourly level before the day. h The corresponding real-time time period set; Inventory end value coupling across windows: The inventory end value target set in the day-ahead layer is used as the boundary condition for the real-time layer's rolling optimization; Start-stop baseline linkage: The start-stop status of the compressor and expander decided by the day-ahead layer is transmitted to the real-time layer through binary variables to ensure that the start-stop operation of the real-time layer is consistent with the day-ahead commitment.

[0012] Commitment-deployment consistency constraints achieve precise matching between day-ahead capacity commitments and real-time deployable quantities; inventory cross-window final value coupling ensures coordination and unity between medium- and long-term gas storage strategies and short-term market responses; start-stop baseline linkage ensures consistency of equipment start-stop operations at the day-ahead and real-time levels; a three-layer collaborative coupling mechanism is established, realizing deep collaboration between day-ahead and real-time optimization, generating a system effect of "1+1>2", solving the key problem of the disconnect between day-ahead commitments and real-time deployment in existing technologies, and providing a reusable technical framework for the large-scale application of energy storage technology in new power systems.

[0013] Furthermore, step S4 also includes handling the substitutability and mutual exclusion constraints across multiple service levels: Substitutability constraint: FM upscaling service In the quality coefficient Replacement rotation spare Frequency downgrade service In the quality coefficient Replacement non-rotating spare It satisfies the following inequality constraints: in, , These represent the real-time time periods. k Up-frequency modulation deployment quantity and down-frequency modulation deployment quantity , These represent the amount of spinning reserve deployed and the amount of non-spinning reserve deployed, respectively. , This is the quality coefficient, with a value range of (0, 1]. , The upper limit of dynamic available capacity is determined by online capacity, ramp-up capability, inventory status, temperature, and pressure. Mutual exclusion constraint: Prevents the same capacity from being measured repeatedly by coupling the upper bound to the binary variable; Response consistency: The response time limit and ramp rate are integrated into the calculation of the upper limit of available output, supporting interlocking limit when the compressor and expander are running in parallel.

[0014] Substitutability constraints enable flexible substitution and revenue optimization among ancillary services of different quality levels, through quality coefficients. Frequency modulation services can replace backup services when prices are favorable, breaking down service type barriers, fully tapping equipment potential, and adapting to dynamic changes in price signals across different markets. Mutual exclusion constraints completely resolve compliance risks caused by duplicate capacity metering, preventing the same capacity from being settled repeatedly in multiple markets through binary variable linkage, meeting the stringent requirements of regulatory agencies for capacity metering, and avoiding economic penalties and reputational losses due to duplicate metering. Response consistency ensures a perfect match between market response requirements and equipment physical characteristics, transforming response time limits into executable ramp rate constraints, maintaining responsiveness in rapidly changing markets, and balancing response speed with equipment lifespan. Through a multi-level service collaborative optimization mechanism, a unity of technical feasibility and economic optimality is achieved, resolving the revenue loss and compliance risks caused by independent optimization of various auxiliary services in existing technologies.

[0015] Furthermore, in step S6, uncertainty is addressed through any one of the following: scenario set, opportunity constraint, and split-bar optimization. The probability of violation and the reserve realization rate are incorporated into the optimization constraints. The learning update uses a data assimilation algorithm to update the deployment factor online. , and efficiency parameters And write back to the state estimation model and the day-ahead optimization model.

[0016] The scenario set method can capture the distribution characteristics of price and deployment instructions through multi-scenario simulation. Opportunity constraints can directly incorporate the probability of violation into the optimization constraints, enabling risk-controlled optimization decisions. Distributed robust optimization can seek the optimal solution in the worst case under distribution uncertainty. Advanced uncertainty modeling methods significantly improve system robustness. The online learning mechanism realizes a dynamic optimization system with adaptive parameters. The system can autonomously evolve with changes in market rules and equipment status, establish a data-driven parameter update mechanism, introduce advanced uncertainty handling methods, and form a complete closed loop of "run-learn-optimization".

[0017] A compressed air energy storage system for implementing a day-ahead-real-time market collaborative participation method for compressed air energy storage based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization, comprising: Unit layer: includes compressor, motor drive, cooler, check valve, air chamber, pressure regulating valve group, expander, generator and grid connection switch. The compressor outlet is connected to the air chamber inlet via the cooler and check valve, and the expander inlet is connected to the air chamber outlet via the pressure regulating valve group. Sensing layer: including pressure sensors, temperature sensors, flow meters and energy meters, deployed on the compressor side, expander side and air chamber, used to execute step S1; The optimization layer includes a state estimator, a hot-press corrector, a day-ahead optimizer, and a real-time optimizer, corresponding to steps S2, S3, and S4, respectively. Execution layer: Policy executor, used to execute real-time instructions; Market Interfaces: Price Clearing Interface and Deployment Settlement Interface, used to support step S5; Learning and updating module: used to implement step S6.

[0018] Furthermore, at the unit level: the compressor outlet is connected to the air chamber inlet via a check valve and cooler; the expander inlet is supplied with air from the air chamber via a pressure regulating valve group; the pressure regulating valve group has an interlocking limiting function, rejecting out-of-bounds commands when inventory, pressure, and temperature rise are limited; pressure sensors, temperature sensors, and flow meters are deployed on the compressor side and the expander side respectively, and the signals are sent to the state estimator; the grid connection side of the two units is metered by an energy meter, and the data is uniformly aggregated to the real-time optimizer and settlement interface.

[0019] Furthermore, the state estimator in the optimization layer calculates the equivalent air inventory state based on measurement data. Furthermore, a temperature-adaptive safety margin is introduced through a hot-press corrector; the day-ahead optimizer and the real-time optimizer employ a mixed-integer linear programming framework.

[0020] Furthermore, it includes a safety and constraint manager for managing inventory safety domains, unit power limits, ramp constraints, minimum start-up and shutdown times, and start-up and shutdown cost constraints, and applies soft default penalties at the real-time layer.

[0021] A storage medium storing a computer program that, when executed by a processor, implements a method for day-ahead-real-time market collaborative participation in compressed air energy storage based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization.

[0022] The beneficial effects of this invention are: I. Significantly improved model accuracy and security This invention achieves an accurate characterization of the operating state of compressed air energy storage systems through equivalent inventory modeling with thermal-pressure correction. Compared to the simplified linear approximation in existing technologies, the dynamic safety margin mechanism of this invention can adaptively adjust the pressure boundary with temperature changes, reducing inventory prediction errors by 30-40% and pressure exceedance events by more than 40%. The accurate modeling of the thermal-pressure coupling effect avoids the risk of efficiency degradation under high-load, high-temperature conditions, ensuring the safety of system operation.

[0023] II. Achieving Breakthroughs Through Optimized Collaboration The two-layer rolling optimization architecture designed in this invention solves the disconnect between day-ahead commitments and real-time deployments. Through a triple mechanism of commitment-deployment consistency constraints, inventory cross-window final value coupling, and start / stop baseline linkage, it achieves an organic unity between medium- to long-term strategies and short-term responses. Practical applications show that the feasibility rate of day-ahead commitments at the real-time layer is increased to over 95%, effectively avoiding profit erosion caused by short-sighted behavior in traditional methods.

[0024] Third, through a multi-service-level substitutable optimization mechanism, this invention can increase the revenue share of ancillary services by 20-30% in market environments with significant price differences. The quality substitution coefficient between frequency modulation services and standby services allows the system to flexibly adjust the service combination based on real-time price signals, achieving a better risk-reward ratio for the same equipment capacity; start-up and shutdown costs are reduced by 15-20%, and default penalties are reduced by more than 40%. The system's adaptive learning capability can optimize deployment factors and efficiency parameters based on historical operating data, avoiding additional costs caused by unreasonable parameter settings. The mutual exclusion constraint mechanism completely solves the problem of duplicate capacity metering, eliminating related compliance risks and economic losses.

[0025] In addition, this invention transforms response time requirements into executable ramp rate constraints, ensuring that all market commitments are physically achievable. In grid environments with high renewable energy volatility, the system can respond quickly to dispatch commands, significantly improving the reliability of compressed air energy storage as a flexible resource.

[0026] A mixed-integer linear programming (MILP) framework, combined with piecewise affine approximation, ensures that the weekly-scale optimization problem can be solved within 4 hours, meeting the timeliness requirements of engineering practice. The real-time layer model predictive control (MPC) adopts a "first step only" strategy, balancing optimization accuracy and computational burden.

[0027] The methodological framework of this invention is adaptable to different electricity market rules and equipment types, and has good potential for widespread application. Through modular design, the system can flexibly respond to changes in market rules, providing technical support for the large-scale application of compressed air energy storage in new power systems.

[0028] This invention, for the first time, integrates thermo-compression physical characteristics, market substitution rules, and cross-time-domain optimization systems, solving key technical bottlenecks in the market-oriented operation of CAES (Compressed Air Storage Systems). Its innovative constraint handling mechanism and learning algorithm provide a complete technical path for energy storage participation in the electricity market. By improving the economics and reliability of energy storage systems, it helps promote the consumption of a high proportion of renewable energy and supports the clean and low-carbon transformation of the power grid. Its standardized framework can provide technical reference for the industry, driving technological progress and commercial application in the energy storage industry. Through systematic technological innovation, it brings significant benefits in terms of technical effectiveness, economic benefits, system performance, and engineering practicality, providing a comprehensive solution for the efficient market-oriented operation of compressed air energy storage systems. Attached Figure Description

[0029] Figure 1 This is a structural block diagram of the system of the present invention.

[0030] Figure 2 This is a flowchart of the present invention.

[0031] Figure 3 This is a schematic diagram of the feasible region of air storage-pressure-temperature and heat-pressure correction in this invention.

[0032] Figure 4 This is a schematic diagram of the two-layer optimization structure and coupling variables (commitment-deployment-inventory cross-window) in this invention.

[0033] Figure 5 This is a schematic diagram illustrating the auxiliary service hierarchy and the substitutable / mutually exclusive relationships in this invention.

[0034] Figure 6 This is a schematic diagram illustrating the operation of the present invention.

[0035] As shown in the figure: 101. Compressor; 102. Variable frequency drive motor; 103. Cooler; 104. Check valve; 105. Air chamber; 106. Pressure regulating valve assembly; 107. Expander; 108. Generator and grid connection; 201. Pressure sensor; 202. Temperature sensor; 203. Flow meter; 204. Energy meter; 301. State Estimator; 302. Hot-Pressure Corrector; 303. Day-ahead Optimizer; 304. Real-Time Optimizer (MPC); 305. Safety and Constraint Manager; 306. Policy Executor; 401. Price Clearing Interface; 402. Deployment and Settlement Interface; 403. Price Weather Forecasting Service. Detailed Implementation

[0036] To clearly illustrate the technical features of this solution, the following detailed implementation method will be used to explain the solution.

[0037] Example 1: A method for day-ahead and real-time market collaborative participation in compressed air energy storage based on thermal-compression corrected equivalent inventory and two-layer rolling optimization includes the following steps: S1: Data Acquisition and Forecasting Step: Access day-ahead market prices, real-time market prices, ancillary service deployment command forecasts, meteorological data, and measurement data from compressed air energy storage devices, including pressure, temperature, flow rate, and power data.

[0038] S2: State estimation and thermo-compression correction: Based on measurement data, the equivalent air inventory state is estimated, and the thermo-compression correction model is applied to dynamically update the inventory state, generating a dynamic safety margin that adapts to temperature and prediction error.

[0039] Equivalent Inventory As a state variable, it evolves through the following state equation: ; in: For compression-side power, For expansion-side power, This is a temperature / environment feature vector; For the device characteristic function based on piecewise affine approximation, The equivalent efficiency varies with load and temperature. Describing the hot-pressure pullback, For time steps; and, inventory status and pressure are linearly related. Correlation; Dynamic safety margin equivalence constraints , It adapts to temperature.

[0040] S3: Day-ahead optimization: At the day-ahead level, the energy commitment and ancillary service capacity commitment are decided by extending the scheduling window, including electrical energy commitment, up-frequency capacity, down-frequency capacity, spinning reserve capacity and non-spinning reserve capacity, and start-stop baselines for compressors and expanders and inventory cross-window final value targets are set. The objective function is to maximize the sum of day-ahead capacity benefits and expected real-time benefits minus start-stop costs and wear costs. At the same time, uncertainty in prices and deployment instructions is embedded through uncertainty handling methods.

[0041] S4: Real-time Rolling Optimization: In the real-time layer, based on the commitment results of the day-ahead layer, real-time price signals and scheduling instructions, a model predictive control framework is used to solve the optimization sub-problems. Only the first step instruction is executed to control the compressor power, expander power and the amount of auxiliary service deployment, and to ensure compliance with ramp rate, minimum start-up and shutdown time and response time constraints.

[0042] It also includes handling substitutability and mutual exclusion constraints across multiple service tiers: Substitutability constraint: FM upscaling service In the quality coefficient Replacement rotation spare Frequency downgrade service In the quality coefficient Replacement non-rotating spare It satisfies the following inequality constraints: in, , These represent the real-time time periods. k Up-frequency modulation deployment quantity and down-frequency modulation deployment quantity , These represent the amount of spinning reserve deployed and the amount of non-spinning reserve deployed, respectively. , This is the quality coefficient, with a value range of (0, 1]. , The upper limit of the dynamic available capacity is determined by online capacity, ramp-up capability, inventory status, temperature, and pressure.

[0043] The performance is determined by a combination of factors including online capacity, ramp-up, inventory, temperature, and pressure; if parallel limitations exist, interlocking can be implemented. Mutual exclusion (such as the same capacity not being repeatable) is achieved by coupling an upper bound with binary linkage.

[0044] Mutual exclusion constraint: Prevents the same capacity from being measured repeatedly by coupling the upper bound to the binary variable; Response consistency: The response time limit and ramp rate are integrated into the calculation of the upper limit of available output, supporting interlocking limit when the compressor and expander are running in parallel.

[0045] S5: Metering and Settlement: Measuring and accounting for the actual deployed energy and ancillary services, completing market settlements, and recording default events.

[0046] S6: Learning and updating: Based on the measurement results, the deployment factor and efficiency derating curve parameters are updated online, and the updated parameters are fed back to steps S2 and S3 to form an adaptive closed loop.

[0047] Uncertainty is addressed by applying any one of the following: scenario set, opportunity constraint, and split bar optimization. The probability of violation and the reserve realization rate are incorporated into the optimization constraints. The learning update uses a data assimilation algorithm to update the deployment factor and efficiency parameters online and writes them back to the state estimation model and the day-ahead optimization model.

[0048] Wherein, steps S3 and S4 work together through the following coupling mechanism: Commitment-Deployment-Consistency Constraints: Day-ahead Layer Hourly h Ancillary service capacity commitment up frequency modulation capacity Down-modulation capacity Rotating Reserve Capacity 、 Non-spinning reserve capacity Set of time periods corresponding to the real-time layer Up-frequency deployment within , frequency reduction deployment volume Rotating standby deployment quantity Non-rotating standby deployment quantity By increasing the frequency deployment factor , frequency modulation deployment factor The association satisfies the following inequality constraints: Where: Δ t Δ is the time step size for the real-time layer.T For the day-ahead time step, K( h () indicates the hourly level before the day. h The corresponding real-time time period set; Inventory end value coupling across windows: The inventory end value target set in the day-ahead layer is used as the boundary condition for the real-time layer's rolling optimization; Start-stop baseline linkage: The start-stop status of the compressor and expander decided by the day-ahead layer is transmitted to the real-time layer through binary variables to ensure that the start-stop operation of the real-time layer is consistent with the day-ahead commitment.

[0049] Feasible domain: inventory / pressure safety domain, unit power limit and ramp constraints , The minimum start / stop time and start / stop cost are implemented using binary variables. To ensure the scalability of the MILP solution, all nonlinear relationships are implemented using piecewise affine transformations combined with segment / order constraints.

[0050] The real-time layer in each small step Read: Day-ahead commitments, inventory / stress estimates, dispatch instructions, and real-time prices; solve the MPC subproblem that only implements the first step. ; Constrained by inventory dynamics, safety margins, committed reserves, and response time / ramp-up conditions. Soft default is permitted. Penalty control. The execution layer only issues the first power command. With deployment volume The metering is then updated and the next rolling step begins. To enhance robustness, the real-time layer can apply a conservative coefficient (operational strategy) to the upper bound of available output.

[0051] The implementation process of this embodiment is as follows: Data Acquisition and Forecasting Phase (S1) Data source access includes: Market data: Day-ahead / real-time electricity price forecasts are obtained via API interface, with data update frequency of 15 minutes; Meteorological data: Accessed from the meteorological bureau's numerical weather prediction system; temperature forecast accuracy ±1.5℃. Device data: Sensor data is uploaded via Modbus TCP protocol, with a sampling period of 1 second; Prediction algorithm: Electricity price forecasts are generated using an ARIMA-LSTM hybrid model, providing forecasts 24 hours in advance. Load forecasting takes into account weekday / holiday patterns and updates forecast results on a rolling basis.

[0052] Optimize the decision-making and execution phases (S3-S4) Day-ahead optimization execution process: Start day-ahead optimization at 08:00 every day, input the forecast data for the next 7 days; solve the MILP problem to generate energy and ancillary service capacity commitments; submit day-ahead bid combinations through market interface 401; output start-stop plan baseline to the real-time optimizer.

[0053] Real-time rolling optimization process: MPC optimization is started every 5 minutes, with a rolling time domain of 4 hours (48 time periods); only the first time period decision is implemented to ensure the executability of instructions; the safety constraint manager 305 verifies the operation boundary in real time; the policy executor 306 issues power instructions to the device controller.

[0054] Learning and updating phase (S6) Parameter adaptive mechanism: Deployment factors are updated every 24 hours using an exponential smoothing algorithm; efficiency parameters are calibrated every 8 hours based on least squares regression; safety margin coefficients are assessed and adjusted monthly, taking into account equipment aging factors.

[0055] Example 2: A compressed air energy storage system for implementing a day-ahead-real-time market collaborative participation method for compressed air energy storage based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization, comprising: Unit layer: includes compressor, motor drive, cooler, check valve, air chamber, pressure regulating valve group, expander, generator and grid connection switch. The compressor outlet is connected to the air chamber inlet via the cooler and check valve, and the expander inlet is connected to the air chamber outlet via the pressure regulating valve group. Sensing layer: including pressure sensors, temperature sensors, flow meters and energy meters, deployed on the compressor side, expander side and air chamber, used to execute step S1; The optimization layer includes a state estimator, a hot-press corrector, a day-ahead optimizer, and a real-time optimizer, corresponding to steps S2, S3, and S4, respectively. Execution layer: Policy executor, used to execute real-time instructions; Market Interfaces: Price Clearing Interface and Deployment Settlement Interface, used to support step S5; Learning and updating module: used to implement step S6.

[0056] In the unit layer: the compressor outlet is connected to the air chamber inlet via a check valve and cooler; the expander inlet is supplied with air from the air chamber via a pressure regulating valve group; the pressure regulating valve group has an interlocking limiting function, which rejects out-of-bounds commands when inventory, pressure and temperature rise are limited; pressure sensors, temperature sensors and flow meters are deployed on the compressor side and the expander side respectively, and the signals are sent to the state estimator; the grid connection side of the two units is metered by an energy meter, and the data is uniformly aggregated to the real-time optimizer and settlement interface.

[0057] The state estimator in the optimization layer calculates the equivalent air inventory state based on measurement data. Furthermore, a temperature-adaptive safety margin is introduced through a hot-press corrector; the day-ahead optimizer and the real-time optimizer employ a mixed-integer linear programming framework.

[0058] It also includes a safety and constraint manager for managing inventory safety domains, unit power limits, ramp constraints, minimum start-stop times, and start-stop cost constraints, and applies soft default penalties at the real-time layer.

[0059] The compressed air energy storage system of this invention adopts a modular design in its hardware, including the following core components: Compressor unit module: adopts multi-stage centrifugal compressor 101, with a single unit power range of 5-20MW; equipped with variable frequency drive motor 102 to achieve stepless load adjustment from 10% to 100%; each compressor outlet is equipped with check valve 104 and cooler 103, and the cooling medium is a closed-loop circulating water system; Gas storage system module: Air chamber 105 adopts underground salt cavern or pressure vessel structure, with a working pressure range of 4-8 MPa; Pressure regulating valve group 106 is equipped with intelligent positioner, with a response time of <100ms; Safety valve is equipped with double protection, with a burst pressure of 1.5 times the working pressure; Expander power generation module: Multi-stage axial flow expander 107 is directly connected to synchronous generator 108; the generator grid connection switch adopts vacuum circuit breaker with closing time <60ms; the fuel system supports natural gas blending with a calorific value adjustment range of 30-45MJ / kg.

[0060] The system has a well-configured monitoring network, and the specific implementation parameters are as follows: Pressure monitoring points: Compressor inlet and outlet pressure sensors 201, range 0-10MPa, accuracy 0.1%FS; air chamber pressure monitoring points are evenly arranged along the height direction, with a total of 8 measuring points; expander inlet pressure sensor, temperature resistance 300℃, explosion-proof rating ExdIICT4; Temperature monitoring network: Thermocouples 202 are arranged on key heat exchange surfaces with a sampling frequency of 1Hz; temperature measuring points in the air chamber are arranged in layers to monitor the thermal stratification effect; the inlet and outlet temperatures of the cooler are monitored with a control accuracy of ±0.5℃; Flow metering system: Gas flow meter 203 adopts vortex flow meter with an accuracy of 1.0 class; Electricity meter 204 adopts 0.2S class smart meter and supports DL / T645 protocol.

[0061] The core algorithm of the state estimator 301 is implemented using a mix of C++ and Python programming. class StateEstimator: def update_state(self, c_k, t_k, theta_k, delta_t): # Equivalent Inventory Status Update xi_next = self.xi_current + \ self.eta_in self.G_in(c_k, theta_k) delta_t - \ (1 / self.eta_out) self.G_out(t_k, theta_k) delta_t -\ self.v_function(self.xi_current, theta_k) delta_t return xi_next.

[0062] Hot-press corrector 302 parameter settings: Efficiency curve , Cubic spline interpolation was used for fitting. The safety margin changes linearly with temperature; for every 10°C increase in temperature, the margin decreases by 3%. The pressure-inventory relationship coefficient was obtained through regression analysis of experimental data.

[0063] The optimization layer algorithm is implemented using the Gurobi solver to perform mixed-integer linear programming.

[0064] The current optimizer 303 configuration is as follows: optimization period: 7 days (168 time periods); variable size: approximately 5000 continuous variables + 2000 integer variables; solution time limit: 4 hours, optimal gap setting: 0.1%.

[0065] Real-time optimizer 304MPC implementation: class MPCController: def solve_mpc(self, current_state, price_forecast): # Building a Scrolling Optimization Problem prob = Model("real_time_mpc") # Objective function: Maximizing profit obj = quicksum(price_forecast[t] power[t] for t in range(self.horizon)) prob.setObjective(obj, GRB.MAXIMIZE) # Constraints: Inventory dynamics, ramp-up limits, etc. self.add_constraints(prob, current_state) prob.optimize() return prob.getSolution().

[0066] Price Clearing Interface 401: Communication Protocol: IEC 61850, IEEE 1815 (DNP3); Data Format: XML Schema compliant with market rules; Employs two-way digital certificate authentication.

[0067] Deploy settlement interface 402: Receives scheduling instructions in real time with a response time of <2 seconds; automatically generates settlement vouchers and supports blockchain notarization; automatically records and generates reports of abnormal events.

[0068] The data bus design adopts the ROS2 distributed communication framework, with a data transmission latency of <100ms, and supports disconnection reconnection and data caching.

[0069] The human-computer interaction interface is a web-based monitoring interface that supports access from multiple terminals, displays system status and economic benefit indicators in real time, provides a manual intervention interface, and allows for hierarchical management of permissions.

[0070] Example 3: A storage medium storing a computer program that, when executed by a processor, implements a method for day-ahead-real-time market collaborative participation in compressed air energy storage based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization.

[0071] The following are application examples of this invention in actual production: This case study selects a power grid in a province in my country with a high proportion of renewable energy. This power grid has the following characteristics: Wind power and photovoltaic power account for more than 40% of installed capacity, and the maximum daily power fluctuation reaches 30% of the installed capacity; the electricity market has opened the day-ahead energy market, the real-time balance market and the frequency regulation ancillary service market; the ancillary service assessment is strict, with frequency regulation response required to be ≤5 minutes and standby capacity required to be available within 15 minutes.

[0072] Basic information about compressed air energy storage power stations: Installed capacity: 2×60MW compressor units + 1×110MW expansion generator unit; Gas storage capacity: underground salt cavern gas storage, with an effective volume of 200,000 cubic meters; Service life: newly commissioned power station, which needs to adapt to the market environment quickly; Geographical location: adjacent to wind farm clusters and load centers.

[0073] Hardware system specific configuration Compression subsystem: It adopts two 60MW three-stage centrifugal compressors, each equipped with an ABB ACS6080 frequency converter; the cooling system adopts closed-loop water cooling, with a designed inlet water temperature of 25℃ and an outlet water temperature of 45℃; the check valve response time is <80ms to prevent gas backflow.

[0074] Gas storage system: The underground salt cavern has a working pressure range of 4-8MPa, and the temperature monitoring is arranged in 3 layers with 12 measuring points; the pressure regulating valve group adopts the Fisher DVC6000 series intelligent positioner; the safety valve is equipped with dual protection, with the mechanical safety valve and the electromagnetic relief valve connected in parallel.

[0075] Expanding power generation system: a single 110MW multi-stage axial flow expander, equipped with a Siemens SGen5-100A generator; natural gas blending system, with a calorific value adjustment range of 35-42MJ / kg; grid connection switch adopts ABB VD4 vacuum circuit breaker, with a closing time of 50ms.

[0076] Software system parameter settings State estimation module: Equivalent inventory state Update cycle: 5 minutes; Temperature correction factor α(T) range: 0.85-1.15; Efficiency parameters Initial value: 0.72 Initial value: 0.68.

[0077] Optimized algorithm parameters: Day-to-day optimization window: 7 days (168 hours); Real-time MPC rolling time domain: 4 hours (48 5-minute time intervals); Solver optimal gap setting: 0.1%, time limit 4 hours.

[0078] The current optimization phase (08:00 on day T-1) Input data: Day-ahead electricity price forecast: peak period (08-11, 14-17, 19-21) price 0.8-1.2 yuan / kWh; ancillary service demand forecast: frequency regulation capacity demand 200MW, spinning reserve 150MW; weather forecast: daytime high temperature 28℃, nighttime low 18℃.

[0079] Optimization results: Energy Market: The declared discharge capacity is 80MW (peak hours) and the charging capacity is 60MW (valley hours). Frequency regulation market: 40MW of up-frequency regulation capacity and 35MW of down-frequency regulation capacity have been declared; Standby market: 30MW of rotating standby and 25MW of non-rotating standby are declared.

[0080] Real-time rolling execution (running days) Operating hours: 05:00-08:00 (off-peak hours) Actual electricity price was 0.35 yuan / kWh, lower than the forecast; MPC decision: charge at 50MW power while providing down-frequency regulation service; inventory status. From 0.25 to 0.45 Morning rush hour operation: 08:00-11:00 Real-time electricity prices surged to 1.35 yuan / kWh, and frequency regulation prices rose accordingly; MPC optimization results: discharge power 90MW, full capacity participation of frequency regulation up-regulation; service substitution adopted: 10MW of spinning reserve was converted to frequency regulation up-regulation service.

[0081] Special event handling 11:30 Sudden frequency fluctuation event in the power grid: If the frequency deviation exceeds 0.2Hz, the dispatch center issues an emergency frequency adjustment command; system response: based on the 90MW discharge, increase the frequency adjustment output by 20MW within 5 minutes; the thermal-pressure correction model dynamically adjusts the safety margin to ensure that the gas storage pressure is within the safe range of 6.5MPa.

[0082] Wind power output drops sharply from 14:00 to 16:00: Wind power output decreased by 800MW, and the real-time electricity price rose to 1.5 yuan / kWh; MPC optimization adjustment: discharge power increased to 105MW (close to the limit); deployment factors were dynamically adjusted through a learning mechanism. It increased from 0.85 to 0.92.

[0083] I. Economic Benefit Analysis Composition of daily revenue: Energy market revenue: Discharge revenue of RMB 382,000, charging cost of RMB 156,000, net profit of RMB 226,000; Ancillary service revenue: Frequency regulation service revenue of RMB 183,000, standby capacity revenue of RMB 72,000; Total revenue: RMB 481,000, of which ancillary services accounted for 53%.

[0084] Compared with traditional methods: Improved returns: 26.5% higher than the fixed-parameter method; Number of violations: No violations recorded throughout the day; traditional methods average 2-3 minor violations. Equipment utilization rate: The average load rate of compressors / expanders was 85%, an increase of 15 percentage points.

[0085] II. Technical Performance Index Analysis: State estimation accuracy: Inventory forecast error: maximum deviation 3.2%, average deviation 1.5%; Pressure estimation accuracy: deviation from measured value < 0.15 MPa; Temperature correction effect: Efficiency estimation error during high-temperature periods is <2%.

[0086] Optimize computational performance: The current optimized solution time is 3.2 hours (7-day window). Real-time MPC single-run solution time: average 45 seconds, maximum 78 seconds; Learning update cycle: Deployment factors are automatically updated every 24 hours.

[0087] The actual operational data from this case study verifies the technical advantages of this invention in multiple aspects: Model accuracy: The thermal-compression correction model effectively addresses temperature changes, and the safety margin is dynamically adjusted reasonably; Collaborative optimization: Two-layer rolling optimization achieves a perfect connection between day-ahead commitments and real-time execution; Adaptive capability: The learning mechanism enables the system to quickly adapt to market changes.

[0088] In this case study, the investment payback period is estimated at 5.2 years, 1.8 years shorter than traditional operating methods; operational reliability is 98.7% annual availability, meeting grid performance requirements; and the system architecture supports subsequent capacity expansion and changes in market rules. This case study provides a complete technical path and engineering practice experience for the market operation of similar compressed air energy storage power stations. Especially in grid environments with a high proportion of renewable energy, the technical advantages of this invention are more significant, and it has good industry promotion value.

[0089] Of course, the above description is not limited to the examples above. Technical features not described in this invention can be implemented by or using existing technology, and will not be repeated here. The above embodiments and drawings are only used to illustrate the technical solutions of this invention and are not intended to limit this invention. This invention has been described in detail with reference to preferred embodiments. Those skilled in the art should understand that any changes, modifications, additions or substitutions made by those skilled in the art within the scope of this invention do not depart from the spirit of this invention and should also fall within the scope of protection of the claims of this invention.

Claims

1. A method for coordinated participation of compressed air energy storage in day-ahead and real-time markets based on thermal-pressure corrected equivalent inventory and two-layer rolling optimization, characterized in that, Comprising the following steps: S1: Data collection and prediction: access day-ahead market price, real-time market price, ancillary service deployment instruction prediction, meteorological data, and measured data of compressed air energy storage device, including pressure, temperature, flow rate, and electric power data; S2: State estimation and thermal-pressure correction: based on the measured data, estimate the equivalent air inventory state, and apply a thermal-pressure correction model to dynamically update the inventory state, generating a dynamic safety margin that is adaptive to temperature and prediction error; S3: Day-ahead optimization: in the day-ahead layer, decide energy commitment and ancillary service capacity commitment, including electric energy commitment, upward frequency regulation capacity, downward frequency regulation capacity, spinning reserve capacity, and non-spinning reserve capacity, and set the start-stop baseline of the compressor and expander, and the inventory cross-window terminal value target, the objective function is to maximize the sum of day-ahead capacity revenue and expected real-time revenue minus start-stop cost and wear cost, while embedding the uncertainty of price and deployment instruction through an uncertainty processing method; S4: Real-time rolling optimization: in the real-time layer, based on the commitment results of the day-ahead layer, real-time price signal and dispatching instruction, solve the optimization sub-problem using model predictive control framework, only execute the first instruction, control the power of compressor, expander and ancillary service deployment amount, and ensure to comply with the ramp rate, minimum start-stop time and response time limit constraints; S5: Measurement and settlement: measure and account for the actual deployed energy and ancillary services, complete market settlement, and record default events; S6: Learning and updating: based on the measured results, update the deployment factor and efficiency reduction curve parameters online, and feed back the updated parameters to steps S2 and S3, forming an adaptive closed loop.

2. The method of claim 1, wherein the method is characterized by: In step S2, the equivalent inventory As a state quantity, evolves by the following state equation: ； wherein: Pcomp is the compression-side power, Pexp is the expansion-side power, Tenv is the temperature / environment feature vector; Pdev is a device characteristic function based on piecewise affine approximation, ηeq is the equivalent efficiency as a function of load and temperature, φ describes the thermal-pressure hysteresis, t is the time step; and, the inventory state and pressure are related through a linear relationship dynamic safety margin equivalent constraint temperature-adaptive adjustment.​ 3. The method of claim 1, wherein the method is characterized by: Steps S3 and S4 are coupled through the following mechanism: Commitment-Deployment Consistency Constraints: Day-ahead Layer Hourly Consistency h Ancillary service capacity commitment up-frequency modulation capacity Down-modulation capacity Rotating Reserve Capacity 、 Non-spinning reserve capacity Set of time periods corresponding to the real-time layer Up-frequency deployment within , frequency reduction deployment volume Rotating standby deployment quantity Non-rotating standby deployment quantity By increasing the frequency deployment factor , frequency reduction deployment factor The association satisfies the following inequality constraints: where: Δ t is the real-time layer time step, Δ T is the day-ahead layer time step, K( h ) denotes the day-ahead layer hour h corresponding real-time layer period set; Inventory cross-window terminal value coupling: the inventory terminal value target set in the day-ahead layer is used as the boundary condition for the real-time layer rolling optimization; Start-stop baseline linkage: the start-stop state of the compressor and expander decided by the day-ahead layer is passed to the real-time layer through binary variables, ensuring that the real-time layer start-stop operation is consistent with the day-ahead commitment.

4. The method of claim 1, wherein the method is characterized by: In step S4, it also includes multi-service level alternative and mutual exclusion constraint processing: Alternative constraint: FM up service Quality factor Alternative non-rotating standby down , FM down service Quality factor Alternative non-rotating standby down , satisfying the following inequality constraint: wherein, , denote the up- and down-regulation deployment amount of real-time tier period k , , denote the rotational and non-rotational backup deployment amount, respectively; , is a quality coefficient, whose value range is (0, 1]; , is the upper bound of dynamic available capacity, which is determined by online capacity, ramping capability, inventory status, temperature and pressure. Mutual exclusion constraint: prevent the same capacity from being counted repeatedly by coupling the upper bound and binary variables; Response consistency: integrate the response time limit and ramp rate into the available output upper bound calculation, supporting interlocking limiting when the compressor and expander run in parallel.

5. The method of claim 1, wherein the method is characterized by: In step S6, the uncertainty is incorporated into the optimization constraints by any one of the scenario set, chance constraint, distributionally robust optimization, and the violation probability is incorporated with the backup redemption rate, and the learning updates the deployment factors online through the data assimilation algorithm 、 and the efficiency parameters , and back to the state estimation model and day-ahead optimization model.

6. A compressed air energy storage system for implementing the compressed air energy storage day-ahead-real-time market coordinated participation method based on thermal-pressure correction equivalent inventory and two-layer rolling optimization according to any one of claims 1-5, characterized in that: Comprising: Device layer: including compressor, motor drive, cooler, check valve, air tank, pressure regulating valve group, expander, generator and grid-connected switch, the compressor outlet is connected to the air tank inlet through the cooler and check valve, and the expander inlet is connected to the air tank outlet through the pressure regulating valve group; Sensing layer: including pressure sensor, temperature sensor, flow meter and electric energy meter, deployed on the compressor side, expander side and air tank, for executing step S1; Optimization layer: including state estimator, thermal-pressure corrector, day-ahead optimizer and real-time optimizer, corresponding to steps S2, S3 and S4 respectively; Execution layer: strategy executor, for executing real-time instructions; Market interface: offer clearing interface and deployment settlement interface, for supporting step S5; Learning update module: for implementing step S6.

7. The compressed air energy storage system of claim 6, wherein: In the device layer: the compressor outlet is connected to the air tank inlet through a check valve and a cooler; the expander inlet is supplied with air from the air tank through a pressure regulating valve group; the pressure regulating valve group has an interlocking limiting function, which refuses to exceed the boundary when the inventory, pressure and temperature rise are limited; pressure sensors, temperature sensors and flow meters are respectively arranged on the compressor side and the expander side, and signals are sent to the state estimator; the grid-connected side of the two units is metered by an electric energy meter, and is uniformly gathered to a real-time optimizer and a settlement interface.

8. The compressed air energy storage system of claim 6, wherein: The state estimator in the optimization layer calculates an equivalent air inventory state based on measurement data and introduces temperature-adaptive safety margins through a thermal press corrector; the day-ahead optimizer and the real-time optimizer employ a mixed-integer linear programming framework.

9. The compressed air energy storage system of claim 6, wherein: A safety and constraint manager is further included for managing the inventory safety domain, the upper limit of unit power, the ramping constraint, the minimum start-stop time and the start-stop cost constraint, and imposing a soft violation penalty term in the real-time layer.

10. A storage medium having a computer program stored thereon, the program being executed by a processor to implement the method of any one of claims 1-5.

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