Prediction of power generation output of compressed air energy storage tank based on temperature limitation

The pressure and temperature of the CAES system drop during the power generation process. This generation will be forced to stop when the temperature reaches the metal material limit. To avert the power generation process from stopping due to the temperature dropping too low, it is necessary to monitor and predict the power output of the CAES system in real time. By setting the relevant control operation logic, according to the temperature limit value of the gas canister, the minimum allowable temperature of the gas canister design, and the maximum value of the minimum allowable temperature of the pipe design between the gas canister and the heat exchanger, the minimum allowable temperature of the gas canister is obtained. the residual energy release energy and residual energy release time of the gas storage tank can be calculated by collecting relevant parameters in real time. It is verified by the simulation experiment of the 10 MW CAES system model. By monitoring the changes in parameters such as the temperature of the gas canister during the energy release process, the prediction model can calculate the compressed gas in the gas canister more accurately, and the power generation output can be predicted in the operation of the CASE system. Mastering the residual energy release energy and residual energy release time of the gas canister can arrange the operation mode in advance and improve the reliability of unit operation.


Research background and current situation
Under the "dual carbon" policy, China actively promotes the expansion of new renewable energy sources such as wind and solar energy.However, their inherent intermittency and instability pose challenges for grid integration [1].Energy storage technology offers a solution to the low stability of wind power generation, and large-scale power energy storage is considered one of the most effective methods for overcoming the difficulties of connecting new energy to the grid [2] [3].The Compressed Air Energy Storage System (CAES) is regarded as a proven, large-scale power energy storage technology with promising development prospects, offering advantages such as significant energy storage capacity, long storage cycles, and minimal environmental pollution [4] [5].
Germany began to build a CAES power station in Huntorf in 1975 and put it into commercial use in 1978 with an overall operating efficiency of 42%.
On September 30, 2021, a successful grid-connected test of the national demonstration project of CAES in Jintan salt cave in Jiangsu Province in which the first phase is the power generation and installation of 60 MW, which is the first non-supplementary combustion CAES power station in the world, which marks a breakthrough in the research and application of new energy storage technology in China.
On December 1, 2023, the demonstration project of the world's first 300 MW CAES power station in Yingcheng, Hubei Province, was successfully electrified once, the core technical indicators of energy conversion efficiency reached 70%.
On September 28, 2022, the world's largest 350 MW salt cave compressed air energy storage project of Shandong Taian 2 × 300 MW compressed air energy storage innovation demonstration project started.The project adopts the world's first high-temperature adiabatic compression technology of low melting point molten salt.After completion, it will achieve the world's largest single-machine power, conversion efficiency, and energy storage scale in the field of CAES [6].
At present, China Reserve National Energy has a complete 100-megawatt advanced CAES system with independent intellectual property rights.With 100-megawatt advanced CAES system research and development, design, core equipment manufacturing, and project implementation, as well as a full set of power plant investment and operation capacity, the R&D and industrialization process has been in an international leading position [7].
With the growth of CAES technology, it has developed from the traditional supplementary combustion large CAES power station to a new integrated energy storage system that integrates power generation, power storage, heat storage, heating, and cooling, which is combined with the distributed energy system to help realize the multi-energy Fed co-supply of the distributed integrated energy system.The future distributed adiabatic compressed air energy storage technology will become a significant solution for the coordination and integrated utilization of a variety of clean energy sources in the integrated energy system under double carbon targets [8].

Research significance
The gas storage system is an important part of the compressed air system.At present, CAES includes high-pressure gas tanks, low-temperature storage tanks, waste caves, new caves, salt caves, and other forms [9].Among them, the high-pressure gas tank has the characteristics of mature technology, no site restriction, and flexible layout, so it is very suitable for distributed energy systems.However, in the process of power generation and energy release, which is different from the conventional power generation technology, the temperature of the high-pressure compressed air stored in the gas tank decreases with the decrease of pressure in the process of doing work.It cannot generate electricity when it reaches the limit value of metal materials.The existing technology can only monitor the temperature and pressure parameters of the gas canister, but it cannot directly monitor the residual energy release amount and residual energy release time of the gas tank based on the temperature limit.At present, the corresponding research content has not been reported in the literature at home and abroad.Therefore, it is necessary to conduct relevant research to predict the residual energy release amount and time and improve the reliability of unit operation.

CAES system and its problems
CAES can be divided into two main phases: compression energy storage and power generation energy release.Electricity is used to initiate the process of air compression when there is surplus electricity on the power grid.The air is compressed into the compressor, which is powered by a motor, and the air pressure is increased to store it in a gas storage tank.The power generation and energy release phase involves initiating the process of air expansion and energy release when the power grid is experiencing a shortage of power.Expansion is started to release energy for power generation.High-pressure air enters the expansion machine from the gas canister, and the energy released through expansion drives a synchronous generator to produce electricity.The exhaust air is then released into the atmosphere [10].The system diagram is displayed in Figure 1.In the power generation system, the amount of available work medium (the remaining gas stored in the gas canister) during the energy release stage is limited, primarily determined by factors such as the volume, temperature, and pressure of the high-pressure gas canister.The outgassing process of the gas canister varies during the power generation process.By applying the mass and energy balance equation, the variation of the gas state parameters in the gas canister can be obtained as follows: Gas tank temperature Gas tank pressure ∋ ( Figure 2 illustrates the variation in gas state parameters within the gas canister.The volume of the gas canister remains constant, while the gas pressure and temperature decrease as the work air flows out of the gas canister.
. Figure 2. The curve of pressure and temperature of the gas storage tank changes with time.
When the power unit is consistently generating electricity, both the gas storage allowance and the temperature of the gas canister display a downward trend, indicating alignment.The temperature parameters of the gas canister reflect the level of gas storage capacity.However, if the gas temperature in the tank drops too low, it can pose a risk to the gas storage device and associated pipes, thus jeopardizing the safety of the unit's operation.To address this issue, the gas temperature in the gas canister is selected as the constraint parameter and a predictive method is proposed to monitor the remaining power generation capacity of the gas canister.

Simulation model of 10 MW CAES unit
In this article, a comprehensive simulation model has been developed for the expansion power generation system of a 10 MW advanced adiabatic CAES system.This model is visually represented in Figure 3, providing a clear and detailed representation of the system's components and processes.The model is simulated under rated operating conditions.Under the rated operating conditions of total mechanical power of 10.37 MW and generating power of 10 MW, the rated parameters of all levels of the expansion machine are displayed in Table 1.
The simulation results reveal that the deviation between the operational parameters of the model and the intended value falls within the permissible range, affirming the precision and dependability of the model.

Operation control logic and steps
During unit operation, the temperature limit of the gas canister, the minimum allowable temperature of the gas canister design, and the peak value of the minimum allowable temperature of the pipe design between the gas canister and the heat exchanger are chosen as the limiting conditions for monitoring parameters, for example, the temperature of the gas canister.Using a derived formula, the real-time calculation of residual energy release time for the expansion power generation system is constrained by the temperature of the gas storage tank.Subsequently, systemic residual energy is evaluated based on the current power generation output.The control logic is displayed in Figure 4.The steps are as follows: Step 1. Parameters are collected such as gas tank air pressure P, gas tank air temperature Tac, gas tank outlet air flow m, and current power generation value P; Step 2. The minimum allowable temperature of gas tank Ts is determined.
According to the temperature limit T1 of the gas tank, the minimum allowable temperature of the gas tank design T2 and the designed minimum allowable temperature of the pipe between the gas tank and the heat exchanger T3, the lowest allowable temperature of the gas tank Ts is obtained.
Among them, the method to determine the temperature limit T1 of the gas canister in the operation of the unit, the original state of the gas canister, and the heat storage tank are both in the designed full state.On this basis, the rated operating conditions are used.Finally, because the operating conditions of the unit are not satisfied, the temperature of the gas canister is T1 which is limited to the temperature of the gas canister in the operation of the unit.
Step 3. The compressed air quality in the gas tank is calculated.
According to the perfect air equation of state, the connection between the state parameters of the air tank in the energy release stage is as follows.
where V is the volume of the gas tank, Rg is the gas constant of the air and Mu is the compressed air quality at the current moment in the gas canister.The formula for calculating the pressurized air mass Mu in the gas canister is derived from (3).

∋ (
where M is the molar mass of the gas.
Step 4. The remaining energy release time of the gas canister is calculated.
During the outgassing process of the gas canister, the gas state parameters in the gas canister  3) and (4).Ignoring the heat loss, Formula (4) can be simplified to ∋ ( where φ is an air-to-heat ratio, pv C /C φ < , which is generally 1.4.The formula for calculating the residual energy release time of the gas tank is obtained from the minimum allowable temperature Ts of the gas tank.
where tu is the remaining energy release time of the gas tank.
Step 5.The residual energy release energy of the gas canister is calculated according to the remaining energy release time of the gas tank and the power generation power of the expander.
In the formula, Apu is the residual energy released from the gas storage tank.

Emulation analysis
According to the calculation principle of the gas tank output prediction method, a correlation calculation module is added to the 10 MW CAES power generation system model to realize the real-time monitoring of residual energy release time and residual energy release.
The gas canister has a minimum allowable temperature of T1, which is set at 5℃.To validate the accuracy and feasibility of the prediction model's calculations, the simulation operation data from the power station's energy release power generation process are compared with the prediction model's calculated results.The simulation results are presented in Table 2 and Figure 5, providing a visual representation of the data.From Figure 5, it is evident that as the unit runs stably at rated power, the residual energy release time and residual energy release decrease linearly and monotonously with the temperature of the gas canister.Additionally, according to Table 2, the predicted results indicate that the gas storage in the gas storage tank is full at zero time with a temperature of 30℃.The prediction results further indicate that the gas storage in the gas canister can generate continuous power for 72 minutes with a residual energy release energy of 12 MW•h.As the energy release time increases, the temperature of the gas canister gradually decreases.Once the temperature of the gas canister reaches 5℃ (the minimum allowable temperature), the unit begins to shut down.At this point, both the residual energy release time and residual energy simultaneously reduce to zero.
In summary, by monitoring changes of parameters, for example, the temperature of the gas canister during the energy release process, the temperature limit value of the gas canister, the minimum allowable temperature limit value of the gas tank meter, and the highest value of the minimum allowable temperature limit value of the pipe design between the gas tank and the heat exchanger are selected as the calculated temperature limit value.It can accurately calculate the residual energy release time and residual energy under the condition of gas temperature limitation in the gas tank and realize the effective prediction of the output of the gas tank, thus arranging the operation mode in advance.The method is reasonable and reliable.

Conclusion
The pressure and temperature of the gas canister will decrease during the power generation of the CAES system, and due to the corresponding temperature restrictions, the expansion generator will be forced to stop operation.
According to the temperature limit T1 of the gas tank in the operation of the unit, the minimum allowable temperature in the gas tank design T2 and the designed minimum allowable temperature of the pipe between the gas tank and the heat exchanger T3, the lowest allowable temperature of the gas tank Ts is obtained.
The relevant parameters are collected in real-time during the operation of the CAES system.Through the set operation logic, the residual energy release energy and residual energy release time of the gas tank can be calculated, the power output can be predicted, and the reliability of the unit operation can be improved.

Figure 3 .
Figure 3. Simulation model of expansion power generation system for CAES system.

Figure 5 .
Figure 5. Compared with the simulation results: (a) Generating power; (b) Gas storage tank temperature; (c) Remaining release time; (d) Remaining power generation

Table 1 .
Rated condition parameters of each expander.

Table 2 .
Comparison of simulation results and prediction results of gas storage tank during energy release process.