A method for preventing reverse rotation of a centrifugal supercharger impeller

CN120990916BActive Publication Date: 2026-08-21CHONGQING OPRO ENERGY TECH CO LTD
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Patent Information

Application Number
CN202511437555.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-10-09
Publication Date
2026-08-21
Estimated Expiration
2045-10-09

AI Technical Summary

Technical Problem

本发明要解决的技术问题是解决离心式增压机在电机断电或电动调节阀未正常工作时,因出入口压力差无法快速平衡而导致叶轮反转,进而引发轴系损伤、结构共振、逆向电流等危害的问题

Benefits of technology

本发明通过设置带手动球阀的电磁阀和单向阀,可有效快速平衡离心式增压机出入口压力差,从根本上避免叶轮反转现象的发生,消除了叶轮反转引发的轴系损伤、结构共振、逆向电流等安全隐患,提高了增压机运行的整体安全性和可靠性,保障设备核心部件安全。且电磁阀和单向阀既可单独应用,也可联合使用,能适应不同工况下的增压机运行需求,尤其针对电机断电和电动调节阀失效等特殊工况效果突出。且改进方案均基于现有管路系统进行改进,无需对增压机主体结构进行重大改动,安装和维护方便,成本较低。

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Abstract

The application relates to a method for preventing reverse rotation of a centrifugal supercharger impeller and rapidly balancing the inlet and outlet pressures, and relates to the supercharger field. When a motor power-off signal is monitored, or the difference between the outlet pressure and the inlet pressure of the compressor is greater than 0.3 MPa and the opening degree of the electric regulating valve is less than 50%, an abnormal early warning is triggered. After the early warning is triggered, a manual ball valve is opened, an intelligent control module controls an electromagnetic valve to be opened, and the damping coefficient in the one-way valve is simultaneously increased. The electromagnetic valve maintains the initial opening degree to rapidly balance the pressure difference between the inlet and outlet pressures of the compressor. When the pressure difference is reduced to 0.3 MPa and the pressure difference is reduced by 0.1 MPa per 100 ms, the opening degree of the electromagnetic valve is adjusted in real time to finely balance the pressure difference. When the pressure difference is less than or equal to 0.05 MPa and stable operation is greater than 20 s, the application has the advantages of realizing rapid balancing of the inlet and outlet pressures of the supercharger and avoiding reverse rotation of the impeller.
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Description

Technical Field

[0001] This invention relates to the field of booster technology, and in particular to a method for rapidly balancing the inlet and outlet pressures to prevent the impeller of a centrifugal booster from reversing. Background Technology

[0002] In natural gas and other gas transmission systems, centrifugal booster compressors (natural gas compressors) are the core booster equipment, and the normal forward rotation of their impellers is crucial to ensuring the efficient and stable operation of the equipment. However, in actual operation, impeller reversal occurs frequently, posing a significant threat to equipment safety.

[0003] Under normal operating conditions, after the natural gas compressor is powered on, the impeller's forward rotation speed gradually increases to the normal operating state, and the pressure in the compressor's downstream pipeline gradually increases. When the motor is powered off, gas in the high-pressure zone of the downstream pipeline flows to the low-pressure zone of the upstream pipeline, causing the impeller to rotate in the opposite direction. Furthermore, although the compressor has return pipes before and after compression to balance the gas pressure, when the pressure ratio between the high-pressure zone and the low-pressure zone exceeds the design maximum compression ratio, the electric regulating valve needs to be opened to return the gas. However, if the electric regulating valve is not opened or its opening is insufficient, and the pressure difference before and after the compressor cannot be balanced instantaneously, it will also cause the impeller to reverse.

[0004] Impeller reversal can cause a series of serious hazards: shaft damage, increased vibration leading to failure of radial bearing hydrodynamic lubrication, dry friction between the journal and bearing, causing wear or even seizure in a short time; structural resonance, the reversing torque coupled with the shaft's natural frequency, exacerbating the failure of components such as seals and couplings; reverse current, the impeller reversal causes the motor to reverse, generating induced current, impacting the frequency converter and causing overload burnout.

[0005] Therefore, to address the above shortcomings, a method for rapidly balancing the inlet and outlet pressures to prevent the impeller of a centrifugal booster from reversing is needed. Summary of the Invention

[0006] (a) Technical problems to be solved The technical problem to be solved by this invention is to address the issue that when a centrifugal booster is powered off or the electric regulating valve is not working properly, the impeller reverses due to the inability to quickly balance the pressure difference between the inlet and outlet, which in turn causes damage to the shaft system, structural resonance, reverse current, and other hazards.

[0007] (II) Technical Solution To solve the above-mentioned technical problems, the present invention provides a method for rapidly balancing the inlet and outlet pressures to prevent the impeller of a centrifugal booster from reversing, comprising the following steps: Ⅰ. The intelligent control module starts the real-time monitoring program, controls the pressure sensor to collect the inlet and outlet pressures of the compressor (4), and calculates the pressure difference; controls the density sensor to collect the gas density in the pipeline; and monitors the motor operation status and the opening status of the electric regulating valve at the same time. II. When a motor power failure signal is detected, or the pressure difference between the compressor outlet and inlet is greater than 0.3 MPa and the opening of the electric regulating valve is less than 50%, an abnormal warning is triggered; Ⅲ. After the warning is triggered, the manual ball valve is opened, the intelligent control module controls the solenoid valve to open, and at the same time controls the damping coefficient inside the check valve to increase to 40 N·s / m to block the gas backflow; VI. The solenoid valve maintains its initial opening to balance the pressure difference between the compressor inlet and outlet. When the pressure difference drops to 0.3 MPa and decreases by 0.1 MPa every 100 ms, the opening of the solenoid valve is adjusted in real time. V. When the pressure difference is less than or equal to 0.05MPa and the stable operation lasts for more than 20s, the impeller is prevented from reversing, and the one-way valve is controlled to reduce the damping coefficient to 10N·s / m to reduce the impact between the valve core and the valve seat.

[0008] As a further explanation of the present invention, preferably, the pressure sensor needs to be calibrated using a standard pressure source before operation to ensure that the detection error is less than 0.02 MPa; the density sensor needs to be calibrated using a standard density gas to ensure that the detection error is less than 0.03 kg / m³. 3 .

[0009] As a further explanation of the present invention, preferably, before operation, the flow rate values ​​at different openings from 1 to 100% need to be recorded by adjusting the opening of the solenoid valve to establish an opening-flow database; the closing speed and leakage amount of the check valve damping coefficient are adjusted from 0 to 50 N·s / m to determine the damping adjustment threshold.

[0010] As a further explanation of the present invention, preferably, after triggering the abnormal warning, the manual ball valve can be opened first but the solenoid valve can not be opened. It is also necessary to judge the reverse pressure difference between the compressor inlet pressure and the outlet pressure. If the reverse pressure difference is also greater than 0.1MPa, the solenoid valve will be opened automatically.

[0011] As a further explanation of the present invention, preferably, the relationship between the opening degree of the solenoid valve and the pressure difference is as follows: in, for The opening degree of the electromagnetic flow valve at all times; The maximum opening within the voltage regulation range is 80%. The minimum opening within the voltage regulation range is 5%. for The positive pressure difference detected at all times; The critical differential pressure for the variable regulation mode; This represents the initial positive pressure difference; The target residual pressure difference.

[0012] As a further explanation of the present invention, preferably, the adjustment mode is divided into rapid adjustment and fine adjustment. Use the quick adjustment mode at this time. The fine adjustment mode is used, with critical pressure difference. It is 0.3 MPa.

[0013] As a further explanation of the present invention, preferably, the relationship between the damping coefficient of the one-way valve and the pressure difference is as follows: in, for Damping coefficient of the check valve at any given time; It has a high-grade damping coefficient of 40 N·s / m; The damping coefficient is for medium-range applications, and it is 20 N·s / m. The damping coefficient is low, at 10 N·s / m; for The reverse pressure difference detected at all times; This represents the initial reverse pressure differential; The critical differential pressure for low / medium damping is 0.1 MPa. The critical pressure difference for medium / high damping is 0.5 MPa.

[0014] As a further explanation of the present invention, preferably, when the flow deviation of the solenoid valve is detected to be greater than 15% and the duration exceeds 10ms, the solenoid valve is judged to be faulty, and the opening of the manual ball valve is immediately manually adjusted to balance the pressure difference.

[0015] As a further explanation of the present invention, preferably, both the inlet and outlet ends of the compressor are equipped with micro differential pressure sensors. When the rate of change of reverse differential pressure measured by the micro differential pressure sensor is greater than 0.001 MPs / s, it is determined that the one-way valve has leaked.

[0016] As a further explanation of the present invention, preferably, the intelligent control module automatically records the data of each balancing process and generates a pressure balancing report for storage; it periodically performs trend analysis on the stored data, and if it finds that the balancing time is extended by more than 10% or the residual pressure difference increases by more than 0.02MPa, it triggers a component aging warning, requiring the replacement of the solenoid valve and the check valve.

[0017] (III) Beneficial Effects The above-described technical solution of the present invention has the following advantages: This invention, by incorporating a solenoid valve with a manual ball valve and a check valve, effectively and quickly balances the pressure difference between the inlet and outlet of a centrifugal booster compressor. This fundamentally prevents impeller reversal, eliminating safety hazards such as shaft damage, structural resonance, and reverse current caused by impeller reversal. It improves the overall safety and reliability of the booster compressor and ensures the safety of core components. Furthermore, the solenoid valve and check valve can be used individually or in combination, adapting to different operating conditions, and are particularly effective in special situations such as motor power failure and electric regulating valve malfunction. All improvements are based on existing piping systems, requiring no major alterations to the main structure of the booster compressor, making installation and maintenance convenient and cost-effective. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the pipeline connection of the present invention.

[0019] In the diagram: 1. Electric regulating valve; 2. Solenoid valve; 3. Manual ball valve; 4. Compressor; 5. Check valve. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] A method for rapidly balancing the inlet and outlet pressures to prevent impeller reversal in a centrifugal booster compressor, such as... Figure 1 As shown, it includes the following steps: I. Based on the existing piping system of the centrifugal booster compressor, seamless stainless steel bypass pipes are laid before and after the electric regulating valve 1 in the return pipe, connected in the order of manual ball valve 3-solenoid valve 2-manual ball valve 3, where solenoid valve 2 is specifically an electromagnetic flow valve. Additionally, a spare electromagnetic flow valve of the same model can be connected in parallel next to solenoid valve 2. A damped adjustable check valve 5 is installed near the outlet of compressor 4, with a PTFE sealing ring. Diffused silicon pressure sensors with a range of 0–3.0 MPa and an accuracy of 0.2 are installed in the low-pressure zone at the inlet and the high-pressure zone at the outlet of compressor 4, respectively; micro-differential pressure sensors with a range of 0–0.5 MPa and an accuracy of 0.1 are also installed. A density sensor with a range of 0.5–3.0 kg / m³ is added to the pipeline. 3 Accuracy ±0.02kg / m 3 .

[0022] Connect the signal terminals of the pressure sensor, density sensor, electromagnetic flow valve, and check valve to the communication port of the control module, preferably a PLC, and ensure that the signal transmission delay is ≤10ms.

[0023] The pressure sensor was then calibrated using a standard pressure source with an accuracy of 0.01 MPa to ensure a detection error ≤0.02 MPa. (This was achieved using 0.7 kg / m...) 3 Standard density natural gas or 2.5 kg / m³ 3 The density sensor for liquefied gas is calibrated to ensure that the density detection deviation is ≤0.03kg / m³. 3 Adjust the opening degree of the electromagnetic flow valve and record the flow rate values ​​from 1% to 100% opening to establish an "opening degree-flow rate" database. Adjust the damping coefficient of the check valve and test the closing speed and leakage under damping from 0 to 50 N·s / m to determine the damping adjustment threshold. Through precise calibration, this system can be adapted to flow rates from 0.5 to 3.0 kg / m³. 3 It can handle multiple types of gas media, such as natural gas and liquefied gas, breaking the limitation of existing technologies that can only adapt to a single medium; at the same time, the establishment of the "opening degree-flow rate" database provides a precise basis for subsequent staged adjustment, avoiding pressure balance lag or fluctuation caused by mismatch between valve opening degree and flow rate.

[0024] II. The intelligent linkage control module initiates a real-time monitoring program, controlling the pressure sensor to collect the compressor inlet low-pressure zone pressure in real time at a sampling frequency of 100Hz. High pressure zone at the outlet Real-time calculation of the positive pressure difference between the inlet and outlet. The density sensor collects the gas density in the pipeline in real time at a sampling frequency of 50Hz. Simultaneously monitor the motor's operating status (power on / power off) and the opening status of the electric regulating valve 1.

[0025] When a motor power failure signal is detected, or When the pressure is greater than 0.3 MPa and the opening of the electric regulating valve 1 is less than 50%, an abnormal warning signal is triggered; if a reverse pressure difference is detected... If the pressure exceeds 0.1 MPa, a reverse current warning signal is triggered simultaneously. Through 100 Hz high-frequency sampling, sudden pressure changes can be detected within 10 ms, such as the instant a motor loses power. The pressure was increased from 0.2MPa to 1.5MPa, avoiding the problem of a lag of more than 50ms in balanced startup caused by the lack of monitoring in existing technologies; at the same time The multi-parameter judgment logic of + electric regulating valve opening degree + reverse pressure difference can accurately identify hidden anomalies such as whether the electric regulating valve is malfunctioning, and realize early warning of anomalies.

[0026] III. The intelligent control module sends a warning command to the bypass system. The operator opens the manual ball valve 3, and the intelligent control module then controls the solenoid valve 2 to respond within 8ms, directly adjusting the opening to the initial set value. The initial set value of the opening is based on the current time. Gas density detected by the lower density sensor Confirmed: When ≤1.0kg / m 3 At that time, the initial opening was set to 80%; when 1.0 kg / m 3 < ≤2.0kg / m 3 At that time, the initial opening was set to 70%; when >2.0kg / m 3 At this time, the initial opening is set to 60%. Simultaneously, the standby electromagnetic flow valve enters the standby ready state, at which point the valve is powered on and the valve core pre-acts to a 5% opening.

[0027] The relationship between the opening degree of solenoid valve 2 and the pressure difference is as follows: in, for The opening degree of the electromagnetic flow valve at all times; The maximum opening within the voltage regulation range is 80%. The minimum opening within the voltage regulation range is 5%. for The positive pressure difference detected at all times; The critical differential pressure for the variable regulation mode is preferably 0.3 MPa; This represents the initial positive pressure difference; The target residual pressure difference.

[0028] As can be seen from the above formula, this method divides the adjustment mode into fast adjustment and fine adjustment. Use the quick adjustment mode at this time. The invention employs a fine-tuning mode, reducing the pressure balancing time from 3-5 seconds (compared to the existing method of directly opening the solenoid valve to achieve balancing) to 1.2-1.8 seconds, while keeping the residual pressure difference below 0.05 MPa. In contrast, directly opening the solenoid valve results in a residual pressure difference ≥0.2 MPa. The two adjustment modes of this invention avoid occasional slight impeller reversal caused by excessive residual pressure difference. Furthermore, the flow deviation detection can identify main valve jamming in real time, providing a basis for subsequent redundancy switching.

[0029] VI. The intelligent control module can also synchronously send commands to the adjustable damping check valve 5 to control the damping coefficient, enabling the check valve 5 to cooperate with the solenoid valve 2 to further prevent impeller reversal. The relationship between the damping coefficient of the check valve 5 and the pressure difference is as follows: in, for The damping coefficient of the one-way valve at any given time; It has a high-grade damping coefficient of 40 N·s / m; The damping coefficient is for medium-range applications, and it is 20 N·s / m. The damping coefficient is low, at 10 N·s / m; for The reverse pressure difference detected at all times; This represents the initial reverse pressure differential; The critical differential pressure for low / medium damping is 0.1 MPa. The critical pressure difference for medium / high damping is 0.5 MPa.

[0030] By adapting the initial opening of solenoid valve 2 to the gas density, the problems of slow balancing speed and sudden pressure drop due to excessive flow of high-density gas caused by different gas densities are avoided. At the same time, the coordinated activation of solenoid valve 2 and check valve 5 can block more than 95% of the reverse airflow within 60ms, achieving complementary efficiency through dual paths.

[0031] V. If a main valve flow deviation of >15% is detected and persists for 10ms, the solenoid valve is considered faulty. Immediately manually adjust the opening of manual ball valve 3 to balance the pressure difference. Alternatively, immediately send a switching start command to the standby solenoid flow valve. The standby valve will complete the switching from standby to the set opening within 5ms, that is, the opening will be consistent with the opening before the failure of solenoid valve 2, and solenoid valve 2 will be closed at the same time.

[0032] After the switch is completed, the pressure sensor continues to monitor. ,like If the pressure remains >0.05MPa, the control module automatically fine-tunes the opening of the backup valve, adjusting it by ±5% each time, with an adjustment interval of 10ms, until... ≤0.05MPa; simultaneously, the intelligent control module generates a fault report, storing the fault occurrence time and details before and after the fault. Change curves and standby valve adjustment parameters.

[0033] VI. When If the pressure is ≤0.05MPa and the system operates stably for more than 20 seconds, and the leakage of check valve 5 is ≤0.8mL / min, it indicates that the system has entered a pressure stabilization state, and the impeller will not reverse. At the same time, the damping coefficient of the check valve is reduced to 10N·s / m to reduce the impact of high-pressure gas on the valve core and valve seat during normal pressurization operation, thereby increasing the lifespan of check valve 5 from the original 1 year to more than 3 years.

[0034] VII. The intelligent control module automatically stores complete data of this balancing process, including parameters measured by various sensors, valve action parameters, balancing effect parameters, etc., and the data storage capacity supports the backtracking of nearly 1,000 balancing processes.

[0035] Based on the above data, the intelligent control module generates a pressure balance report, including information such as the type of anomaly, handling steps, effect indicators, and whether a fault exists. This report can be exported to the maintenance terminal via the communication port. Simultaneously, it performs trend analysis on the stored data. If it finds that the balance time increases by more than 10% or the residual pressure difference increases by more than 0.02 MPa, a component aging warning is issued, requiring manual inspection or replacement of components such as solenoid valve 2 and check valve 5. By tracing back the data to locate the root cause of the fault, it avoids the problem of being unable to trace the cause after a fault occurs and having to blindly replace components. Furthermore, the component aging warning can provide maintenance reminders up to 3 months in advance, reducing maintenance costs by more than 30%.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for rapidly balancing the inlet and outlet pressures to prevent impeller reversal in a centrifugal booster compressor, based on the existing pipeline system of the centrifugal booster compressor, wherein seamless stainless steel bypass pipelines are laid before and after the electric regulating valve (1) in the return pipe, and connected in the arrangement of manual ball valve (3) - solenoid valve (2) - manual ball valve (3), a one-way valve (5) is installed near the outlet of the compressor (4), and pressure sensors are installed in the low-pressure zone at the inlet and the high-pressure zone at the outlet of the compressor (4), respectively, characterized in that: Includes the following steps: Ⅰ. The intelligent control module starts the real-time monitoring program, controls the pressure sensor to collect the inlet and outlet pressures of the compressor (4) and calculates the pressure difference; controls the density sensor to collect the gas density in the pipeline; and monitors the motor operation status and the opening status of the electric regulating valve (1) at the same time. II. When a motor power failure signal is detected, or the pressure difference between the outlet and inlet of the compressor (4) is greater than 0.3 MPa and the opening of the electric regulating valve (1) is less than 50%, an abnormal warning is triggered; Ⅲ. After the warning is triggered, the manual ball valve (3) is opened, the intelligent control module controls the solenoid valve (2) to open, and at the same time controls the damping coefficient of the check valve (5) to increase to 40 N·s / m to block the gas backflow; VI. The solenoid valve (2) maintains the initial opening to balance the pressure difference between the inlet and outlet of the compressor (4). When the pressure difference drops to 0.3 MPa and decreases by 0.1 MPa every 100 ms, the opening of the solenoid valve (2) is adjusted in real time. The relationship between the opening degree of solenoid valve (2) and the pressure difference is as follows: in, for The opening degree of the electromagnetic flow valve at all times; The maximum opening within the voltage regulation range is 80%. The minimum opening within the voltage regulation range is 5%. for The positive pressure difference detected at all times; The critical differential pressure for the variable regulation mode; This represents the initial positive pressure difference; The target residual pressure difference; V. When the pressure difference is less than or equal to 0.05 MPa and the stable operation lasts for more than 20 seconds, the impeller is prevented from reversing. At the same time, the one-way valve (5) is controlled to reduce the damping coefficient to 10 N·s / m to reduce the impact between the valve core and the valve seat. The relationship between the damping coefficient of the one-way valve (5) and the pressure difference is as follows: in, for Damping coefficient of the check valve at any given time; It has a high-grade damping coefficient of 40 N·s / m; The damping coefficient is for the medium range, and it is 20 N·s / m. The damping coefficient is low, at 10 N·s / m. for The reverse pressure difference detected at all times; This represents the initial reverse pressure differential; The critical differential pressure for low / medium damping is 0.1 MPa. The critical pressure difference for medium / high damping is 0.5 MPa.

2. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 1, characterized in that: Before operation, the pressure sensor must be calibrated using a standard pressure source to ensure the detection error is below 0.02 MPa; the density sensor must be calibrated using a standard density gas to ensure the detection error is below 0.03 kg / m³. 3 .

3. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 2, characterized in that: Before starting work, it is necessary to record different flow values ​​from 1 to 100% opening by adjusting the opening of the solenoid valve to establish an opening-flow database; adjust the closing speed and leakage of the check valve (5) from 0 to 50 N·s / m to determine the damping adjustment threshold.

4. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 1, characterized in that: After triggering the abnormal warning, the manual ball valve (3) is opened first, but the solenoid valve (2) is not opened. It is also necessary to judge the reverse pressure difference between the inlet pressure and outlet pressure of the compressor (4). If the reverse pressure difference is also greater than 0.1MPa, the solenoid valve (2) is opened automatically.

5. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 4, characterized in that: The adjustment modes are divided into quick adjustment and fine adjustment. Use the quick adjustment mode at this time. The fine adjustment mode is used, with critical pressure difference. It is 0.3 MPa.

6. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 1, characterized in that: If the flow deviation of the solenoid valve (2) is detected to be greater than 15% and the duration exceeds 10ms, the solenoid valve (2) is judged to be faulty. The opening of the manual ball valve (3) is immediately adjusted manually to balance the pressure difference.

7. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 1, characterized in that: The compressor (4) is equipped with a micro differential pressure sensor at both the inlet and outlet ends. When the reverse differential pressure change rate measured by the micro differential pressure sensor is greater than 0.001 MPs / s, it is determined that the check valve (5) has leaked.

8. The method for rapid inlet and outlet pressure balancing to prevent impeller reversal in a centrifugal booster compressor according to claim 1, characterized in that: The intelligent control module automatically records the data of each balancing process and generates a pressure balancing report for storage. It periodically performs trend analysis on the stored data. If it finds that the balancing time is extended by more than 10% or the residual pressure difference increases by more than 0.02MPa, it triggers a component aging warning and requires the replacement of the solenoid valve (2) and the check valve (5).

Citation Information

Patent Citations

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