A Co-simulation Model for the Hydraulic Operating Mechanism of High-Voltage Circuit Breaker

doi:10.21203/rs.3.rs-1961241/v1

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A Co-simulation Model for the Hydraulic Operating Mechanism of High-Voltage Circuit Breaker

https://doi.org/10.21203/rs.3.rs-1961241/v1

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The dynamic characteristics of hydraulic operating mechanism is of great significance to the reliability of high-voltage circuit breaker (HVCB). Due to the lack of co-simulation models considering the coupling links of different physics, previous research works were limited to the analysis of some discrete parts. The purpose of this study is to propose a novel technique for the co-simulation of hydraulic operating mechanism (OM). For that aim, lumped parameter method is adopted for the modeling of hydraulic system and finite element analysis method is employed for that of transmission mechanism. Then, distributed parallel type co-simulation framework is applied, and the coupling links between different subsystems are achieved by input-output variables exchange with shared memory. Simulation and experimental validations are implemented in a 550KV HVCB. It proves that co-simulation model can accurately capture the dynamic responses of hydraulic OM, including predicting the dynamic responses under different operation parameters and quantifying important features like stress distribution and dynamic responses evolution.

Hydraulic operating mechanism

hydraulic system

transmission mechanism

co-simulation

As protection and control apparatus in electric power system, HVCB can accurately and timely complete opening and closing operations to cut or connect the circuit [1–2]. In general, its OM can be classified into spring, motor, electromagnetic and hydraulic types. Among them, hydraulic OM has the advantage of high-power density and much more stable dynamic performance, thus it is now widely applied [3]. Hydraulic OM can be further divided into two subsystems, namely hydraulic system and multi-link articulated transmission mechanism, employed for the movement and driving load transmission, just as outlined in Fig. 1. According to the international surveys, OM is critical for the operation reliability of HVCB, since approximately 59% of the major operation failure is of OM origin, which causes great economic loss [4]. In the past decades, the performances of hydraulic OM have captivated wide attention. Many scholars focused on mechanical fault diagnosis and health assessment based on all types of machine learning and online monitoring techniques [5–7], which significantly contributed to improving its service reliability. These studies improved the maintenance effectiveness of hydraulic OM but cannot reduce its machinery fault from design source. As the performance expectation rises, more effective simulation tools of hydraulic OM are needed.

With the development of computer-aided engineering (CAE) technology, some numerical simulation methodologies are gradually introduced to the dynamic analysis of multibody system dynamics, such as well-known finite element analysis (FEA) [8–9], and computational fluid dynamics (CFD) [10–11]. The CAE technology can greatly minimize the number of design reversions and test cycles, hence reducing cost and raising efficiency. However, independent simulation methods were mainly adopted in previous studies for some discrete parts of hydraulic OM. For instance, the performance optimization of switching, directional valve, and buffer head of cylinder in hydraulic system [12–14], as well as the design and dynamic simulation of a new electromagnetic motor for HVCB [15] were reported.

Due to the lack of coupling links between hydraulic system and transmission mechanism, system-level co-simulation studies were absent. Independent simulation methods can only focus on the performance of separate hydraulic system or transmission mechanism with given kinematic and load boundary conditions. However, without the accurate feedback of other coupled subsystems, the dynamic responses of hydraulic system or transmission mechanism are incomplete. For the hydraulic OM of HVCB, there generally exists strong coupling effects between fluid and mechanical structure [16]. The coupling effects of hydraulic-mechanical are of significance for accurate dynamic responses analysis, and its performance requires the overall evaluation of hydraulic system and transmission mechanism.

The analysis of hydraulic OM is a typical multi-physics issue including hydraulic system and transmission mechanism. Generally speaking, monolithic and co-simulation approaches are adopted for multi-physics problems [17–18]. In a monolithic simulation, an all-encompassing dynamic equation set that describes the behavior of every component needs to be defined and solved. For instance, through lumped parameter method (LM), an equation set that describes the responses of hydraulic system and transmission mechanism can be obtained [19], then the dynamic behavior of whole hydraulic OM system was solved together as a single matrix system. Monolithic method could be accurate but require modeling details of every subsystem which might be prohibitive for more complicated multi-physics cases.

Co-simulation is another increasingly important methodology, which enables the complicated multi-physics problem to be solved in parallel mode by several simulation units with data transformation between individual physics solvers [20]. Since it is based on a distributed framework, thus the advantages of different physics solvers can be fully utilized. In the past decades, co-simulation received much attention in which hydraulically actuated mechanism was a particularly interesting case. Considering the effectiveness and stability of numerical solution, a non-iterative co-simulation method was proposed for mechanical and hydraulic components of a manipulator [21]. In the non-iterative co-simulation model, information exchange between subsystems proceeds at selected discrete synchronization points. As the mechanical structure was simplified as a purely rigid subsystem, only the most representative dynamic behaviors can be preserved. Thus, it essentially belongs to a reduced-order co-simulation method. Nowadays, a variety of software is also considering the system-level multi-physics co-simulation problem. For instance, the ANSYS provides a collaborative environment for developing multi-physics solutions where the dynamic behavior of hydraulic system is solved by CFD and multi-body subsystem by FEA simulation [22]. It has a wide range of applications in the fields like heavy machinery [23], and automotive simulation [24].

However, for hydraulic OM, its hydraulic system contains a cylinder, multiple valves, and a group of pipelines and joints. Modeling them by CFD method can be painstaking and prohibitive in terms of computation time. As an alternative, hydraulic system can be built up in AMESim by LM for its high computation efficiency. It is also worth mentioning that AMESim provides the interface program for co-simulation with RecurDyn and Adams. For example, a seabed remotely operated vehicle is modeled in RecurDyn and then integrated into its hydraulic control system under the AMESim environment for co-simulation [25]. However, in that co-simulation case, the mechanical simulation model worked as the slave machine of hydraulic system, thus it needed to be compiled into an executable sub-model and then integrated into the AMESim environment. To achieve this, the mechanical part is generally simplified as a rigid body system. For hydraulic OM, the operation process is designed in the order of 10ms [26]. Under those circumstances, the flow in hydraulic system characterizes as high pressure and large rate, which eventually affect the non-linear dynamic responses of the transmission mechanism [27].

In the other side, under the high-speed condition, the flexibility characteristics could cause the vibration of transmission mechanism and further feedback to hydraulic system [28–29]. Result comparison of rigid mechanical structure by reduced-order method and its flexible counterparts by FEA can be found in previous studies [30–31]. It was reported that neglecting the flexibility of the transmission mechanism will bring large analysis errors to the dynamic response analysis of hydraulic OM, thus FEA method is suggested for the modeling of the transmission mechanism. As for the hydraulic system, the detailed flow distribution is not concerned in the co-simulation model of hydraulic OM, thus the fluid dynamics solver called AMESim is considered for its model building. To achieve the co-simulation, different subsystems running in individual physics solvers in different processes need to communicate with each other. As the individual solver cannot directly interact with each other, a computational co-simulation framework is designed to manage the simulation process.

The novel co-simulation method provides a useful and unique tool to analyze the performance of hydraulic OM in optimization and new product design. More specifically, the main contributions of this study are threefold.

Co-simulation approach is innovatively developed to build the coupling links between the hydraulic system and transmission mechanism of hydraulic OM.

Experimental results of displacement and stress evolution of a real HVCB verify the effectiveness of the co-simulation model.

In the application of co-simulation model, it captures the dynamic responses of the hydraulic OM, and obtains a system-level optimization scheme.

The remainder of the paper can be described as follows. Section 2 outlines the independent simulation model of the studied hydraulic OM at first, then describes the co-simulation framework. Experiment validation and model application are illustrated in section 3 and section 4. Finally, the conclusions of this study are drawn in section 5.

The schematic diagram of the hydraulic OM in the paper is shown in Fig. 1. It generally consists of hydraulic system (from components 1 to 7), and transmission mechanism (from components 8 to 16). Working as the executive component of hydraulic system, the valve-controlled cylinder 7 is connected with the pushing link 8 of transmission mechanism. In short, the operation of hydraulic OM of HVCB is the touching or separation movement between master and slave contact, which corresponds to the closing and opening operation of external circuit.

The supply port P in hydraulic system is connected to high-pressure oil and port T to the oil tank. In the initial state, two pilot valves and secondary valves are closed. For closing operation, the high-speed solenoid 1.1 is first energized and the spool would be lifted, thus open pilot valve 2.1. Then, chamber Cs1 would connect with port T and decrease its pressure. As the decline of the oil pressure in chamber Cs1, the spool of secondary valve 3.1 would be raised by its inner spring to connect chamber A and chamber B. Secondly, the opening of secondary valve 3.1 makes the pressure in chamber Cm rise quickly and pushes the main spool leftward. Then, port P would connect to the cylinder to inject high-pressure oil to drive the closing operation.

On the other hand, for opening operation, once the high-speed solenoid is energized, pilot valve 2.2 would connect chamber Cs2 with port T to decrease its chamber pressure. Then, the secondary valve is raised to connect chamber A with chamber B. As secondary valve 3.2 opens, the pressure in chamber Cm decreases promptly due to the large flow into port T. Therefore, the main spool moves rightwards and the cylinder is connected to port T. As a result, the piston rod would perform back movement to complete the opening operation. The transmission mechanism is a set of multi-link articulated mechanical system. It should be noted that compression chamber 9, master contact 10, and nozzle 12 are fixedly connected. Nozzle 12 is articulated with two nozzle links, and arc-extinguish chamber 13 is articulated with two chamber links 15. Driven by the hydraulic system, the master and slave contact would keep moving in the opposite direction to complete the circuit closing or opening operation.

2.1 Modeling of hydraulic system

The hydraulic system mainly consists of two pilot valves with high-speed solenoids, two secondary valves, one main valve, one cylinder, and complicated pipelines, which introduce a large number of governing equations. It would be quite time-consuming and easily stuck in non-convergence problems to perform CFD analysis for hydraulic system. LM can produce more comprehensive results while ignoring the details of the flow field, thus it generally runs fast. Therefore, the dynamic simulation model of hydraulic system is established by LM under the AMESim software platform. For the cylinder, an inside multi-step cushion is applied for impact suppression which affects the motion of transmission mechanism greatly [20]. Since a multi-step structure is adopted in cushion plunger, it cannot be modeled by the standard hydraulic components in AMESim library. The cushion process in cylinder is phased whose dynamic equation changes with the displacement of rob in cylinder, and the related modeling of cushion process is given below.

Figure 2 describes the main structure of the cushion plunger of cylinder and its cushion process. It can be seen non-standard structure is adopted in cushion plunger, which makes the flow field of cushion process complex. In order to accurately express the flow dynamic in cushion process, the fluid dynamic equation can be divided into three stages [18], namely cylindrical throttling, cone throttling, and torus throttling. In cylindrical throttling, the plunger is far away from the inner convex surface of cylinder wall, in which, flow channel section suddenly shrinks, resulting in local pressure loss. The flow rate in this stage can be expressed as below:

$${Q_{c1}}={C_f}\frac{{\pi {d^2}}}{4}\sqrt {\frac{2}{{{\rho _o}}}({p_c} - {p_l})}$$

where C_f is the flow coefficient, d is the inner diameter of the cushion hole, p_c and p_l represent the pressure difference before and after the flow passage area reduction. ρ_o is the oil density. As plunger moves rightward and gets close to convex surface of cylinder wall, sharp-edged orifice restriction can be used to describe the fluid dynamics in cone throttling process:

$${Q_{c2}}={C_f}d\pi \sqrt {{{\left( {{l_0} - x} \right)}^2}+{\delta ^2}} \sqrt {\frac{2}{\rho }({p_c} - {p_l})}$$

where l₀ is the initial distance between the plunger and cushion hole at the beginning of cushion process, and x is the plunger displacement, δ demonstrates the plunger step annular gap. When plunger enters the cushion hole, torus throttling is formed, and the related flow rate equation is generally defined as:

$${Q_{c3}}=d\pi \left[ {\frac{{({p_c} - {p_l}){\delta ^3}}}{{12\mu \left( {x - {l_0}} \right)}}+\frac{{\delta v}}{2}} \right]$$

where µ is the dynamic viscosity of the oil, and v is the movement speed of the piston. The cylinder model is programmed to set up a sub-model with taking its inside cushion process into account. As for the other valves, they can be completed with the standard sub-model provided by hydraulic component library in AMESim and then connected by its pipelines.

2.2 Modeling of transmission mechanism

Featuring high speed and heavy load, the dynamic responses of transmission mechanism are affected greatly by its parts’ flexibility. Alternate elastic deformation and recovery occur in transmission mechanism, which damages the movement accuracy and causes the reduced service life of hydraulic OM. Compared with rigid model, the synthesis of FEA into co-simulation permits the detailed stress distribution analysis of transmission mechanism, which is useful in the design process of hydraulic OM. Therefore, the effect of mechanical flexibility is essential in the co-simulation modeling process.

In that case, FEA method is employed for the modeling of transmission mechanism. Meanwhile, considering the structural complexity of transmission mechanism, related meshing work is carried out in HyperMesh, in which three key steps are mainly involved, including geometry preparation, attribute setting, and mesh generation. More specifically, in geometry preparation process, the three-dimensional components are first imported into HyperMesh software, then perform model scale selection, necessary geometric simplification, topology repairment, and structure segmentation. Afterward, material properties, boundary conditions, simulation parameters setting, and data interaction surface creation are completed in attribute setting steps. Finally, mesh type selection and division method are determined in mesh generation step, and the simulation solution file is exported to LS-DYNA.

It is worth noting that structure meshing is of significance for simulation accuracy and efficiency while performing the analysis of the dynamic of transmission mechanism by FEA method. In general, smaller elements mean higher simulation calculation accuracy but longer computer running time. Besides, high-quality structured mesh type likes hexahedron can achieve better convergence and computational efficiency than its unstructured counterpart likes tetrahedron, but also increase the difficulty of structure meshing process. Therefore, structure mesh generation step is critical and a multi-objective tradeoff process. The final FEA model under LS-DYNA R8.0 of transmission mechanism is shown in Fig. 3.

According to Fig. 3, for the sake of the aforementioned accuracy and efficiency, enough hexahedral element is firstly utilized to discretize the components of transmission mechanism. It should be ensured that there are at least three layers of elements in the thickness direction of rod parts. Meanwhile, for most complicated parts like the middle link in Fig. 1, a hybrid selection of tetrahedral and hexahedral meshes is considered for meshing. After the element size independence verification, the whole transmission mechanism is divided into a total of 1.2 million elements.

2.3 Coupling and co-simulation

As outlined in Fig. 4, the co-simulation framework in the work is based on shared memory and distributed parallel, which ensures the efficiency and stability of simulation process without compromising the overall simulation performance [22]. In the co-simulation framework, there exist three input–output variables between different simulation models and shared memory. A total of four shared memory areas are developed for data interaction and identifier conversion.

As the co-simulation is executed in distributed parallel mode with two spawned solver processes, communication for the different simulation process control and coupling data transfers between different subsystem solvers is indispensable. To achieve the communication between shared memory and hydraulic system, TCP/IP-based client-server infrastructure is adopted. In that case, TCP/IP communication module is developed and added to the simulation model of hydraulic system, then set as a server. In one co-simulation step, the identifier value in shared memory is initially set as a positive state, and the hydraulic system model is first activated. When one simulation step of hydraulic system is completed, the TCP module would access the preset shared memory to write the obtained hydraulic force and read the displacement and velocity of master contact. Then switch the identifier to a negative state, and suspend the hydraulic system simulation. It is worth mentioning that in this process, the dynamic solver of transmission mechanism is suspended but keeps accessing the identifier.

As for the communication between shared memory and the FEA solver of transmission mechanism, it involves the secondary development of the application programming interfaces of the software, mainly related to the modification of LS_DYNA communication files. At first, rewrite the subroutine program to add the functions of accessing shared memory, reading, and resetting the boundary conditions of coupling surface. Then recompile the amended communication files for a co-simulation. While the identifier value is converted to a negative state, the LS_DYNA solver would be activated via remote procedure calls. Similar with the simulation of hydraulic system, the obtained displacement and velocity after one simulation step is written to the shared memory, and the solver would read the hydraulic force for the next simulation step. Afterward, the identifier in shared memory is reset to a positive state, and one co-simulation step is completed. This cycle keeps repeating until the end of the whole co-simulation.

Based on the developed dynamic simulation model of each subsystem and the proposed coupling method, a system-level co-simulation model of hydraulic OM is established. The co-simulation model is executed on a windows 10 machine with a 64-bit operating system and Intel Xeon CPU 3.2 GHz (16 cores) that has 256 GB RAM. The total co-simulation time is 40ms, which takes approximately 32 hours of absolute wall-clock time to run, and the communication interval between different subsystems is 8.5e-08. Besides, the displacement and dynamic stress characteristics are measured from the operating experiment and compared with numerical results to verify the co-simulation model. The experimental setup and schematic of a 550KV HVCB prototype for co-simulation model validation are described in Fig. 5. Due to the transient characteristic of the HVCB operation, the sampling frequency of data acquisition is set 10KHz per channel.

3.1 Displacement validation

In general, high voltage and overheated electric arc would form between the two main contacts of HVCB during its opening process. A longer completion time of opening operation would prolong the pre-breakdown of the filling medium, and eventually increase the risk of contact welding. Therefore, the opening of HVCB needs to be completed in order of 10ms. On the other hand, overly fast opening operation movement also leads to a great challenge for structural strength, and promotes machinery fault of transmission mechanism. Therefore, the displacement curve of hydraulic system side (pushing link in Fig. 1), and the final execution side (slave contact in Fig. 1) during the opening operation is critical and must obey very strict timing standards. In this section, the measured displacements and their co-simulated counterparts are displayed in Fig. 6.

“s1” denotes the displacement-time curve of master contact, and “s2” is that of slave contact. It can be easily seen that both the travel curves of pushing link and slave contact from the co-simulation model agree well with the experimental data. The movement time of the two contacts obtained from co-simulation and experiment is 36.4ms and 37.9ms, only with the error of 1.5ms, which effectively verifies the accuracy of co-simulation model. The simulated opening completion time is slightly shorter than that of test, which can be explained by the time-varying oil viscosity and insufficient lubrication of mechanism system in experimental conditions.

3.2 Stress validation

The movement of OM belongs to a transient and heavy load process, usually accompanied by severe shocks and local stress concentration, which is the main reason for the structural failure of HVCB. The co-simulation in this paper also provides a new analysis tool for stress prediction, since the transmission mechanism is built by FEA method. In this section, the dynamic stress of the pushing link and middle link (refer to Fig. 1) during the movement of HVCB is extracted from co-simulation model. Related comparative analysis with experimental results is illustrated in Fig. 7.

It can be seen from Fig. 7, the experimental results show obvious oscillation characteristics, and the error between experiment and co-simulation can be explained from the following two aspects. At first, the hydraulic system is modeled by LM, thus the actual pressure fluctuations from hydraulic system are reduced in co-simulation. Secondly, the inevitable environmental interference also contributes to the stress oscillation of experimental results. All in all, the dynamic stress from simulation and experiment have comparable stress peak values and similar evolution laws, thus co-simulation model can be utilized to predict dynamic stress evolution during the HVCB’s operation.

The aim of the co-simulation of hydraulic OM is to shorten product development cycles and reduce the costs associated with testing, validation, and re-design of OM prototype. Consequently, the established co-simulation model should permit quantifying important features of system operation. In this section, based on the co-simulation model, the stress distribution of some key parts of transmission mechanism, and the operation prediction under different main parameters are analyzed to illustrate its capabilities.

4.1 Stress distribution analysis

Compared with the lumped multibody system, the modeling of transmission mechanism in our co-simulation model is based on FEA. Thus, it allows detailed stress analysis which is useful in structure optimization and intensity check of mechanical system. For instance, Fig. 8 shows the corresponding stress results of nozzle link, chamber link, and middle link in the transmission mechanism obtained from co-simulation under opening operation.

Firstly, as Fig. 8 shows, the average stress of nozzle link is the highest among the three components. Besides, visible local stress concentration appears in the revolute joint. The local stress on the journal can be as high as 389MPa where severe wear would generate and develop during the service of HVCB. Based on the aforementioned stress analysis by co-simulation, further structure optimization suggestions can be put forward. For example, shape topology optimization research focused on vibration reduction should be applied to transmission mechanism. Meanwhile, the stress concentration in revolute joint is sensitive to bearing hole diameter, shaft length, and joint clearance size. Therefore, Taguchi method is also recommended for the multi-factor optimization design aimed at weakening stress concentration.

4.2 Operation prediction

The input high-pressure oil provides the mechanical energy required for the closing and opening operation of HVCB, thus initial oil pressure greatly affects the dynamic outputs of transmission mechanism. Higher pressure oil speeds up the two main contacts’ movement to reduce operation time, but also means greater dynamic load to transmission mechanism and would inevitably increase the pressure fluctuations in hydraulic system. Additionally, oil leakage and severe vibration responses always appear in high-pressure operation conditions. A balance needs to be stroke between fast operation and performance stability. Therefore, the operation prediction under different initial oil pressure of accumulator is meaningful, especially in the new prototype design of hydraulic OM, since it can guide the structure optimization and operation test of hydraulic OM. The kinematic outputs of opening operation under different oil pressure are given in Fig. 9 and Fig. 10.

It can be seen from Fig. 9, within the studied oil pressure range, stable displacement outputs can be obtained, and the displacement stroke of hydraulic OM remains constant. After the opening operation, the total relative displacement between the two contacts is 0.32m, of which 0.18m is contributed by master contact, and 0.14m by slave contact. As expected, the opening time would be shortened as the initial oil pressure increases.

On the one hand, obvious fluctuation can be detected in the input velocity curve of the pushing link, and the fluctuation amplitude versus oil pressure are positively correlated. It suggests unstable hydraulic force from hydraulic system and non-linear axial vibration output of hydraulic OM. For the improvement of operation stability, the current cushion structure inside the cylinder needs further optimization. On the other hand, the velocity responses of slave contact are more stable, indicating that the flexible transmission mechanism has a buffering effect to suppress vibration. It is worth mentioning that 0.7ms delay appears in the startup of slave contact, which can be attributed to the elastic deformation accumulation process of flexible parts. Last but not the least, a good compromise between fast responses and stable performance output seems to be achieved in the oil pressure improved from 44MPa to 48 MPa, since obvious time shortening can be obtained with a slight increase of velocity fluctuation while oil pressure rises. Further investigation of the multi-objective parameters optimization of the hydraulic OM will be conducted through co-simulation in the future.

Availability of data and materials

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare that they have no competing interests.

Funding

This work was supported by the National Key Research and Development Program of China [2021YFF0500903], and the National Natural Science Foundation of China [52178271].

Acknowledgments

Not applicable.

Authors’ contributions

Xiaofeng Li performed the simulations and wrote the manuscript. Deng Zhao provided the numerical model and program. Zhou Wu provided idea for this paper. Tao Zhang and Li Yu modified the manuscript to improve the presentation. All authors read and approved the final manuscript.

Availability of data and materials

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare that they have no competing interests.

Funding

This work was supported by the National Key Research and Development Program of China [2021YFF0500903], and the National Natural Science Foundation of China [52178271].

Acknowledgments

Not applicable.

Authors’ contributions

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A Co-simulation Model for the Hydraulic Operating Mechanism of High-Voltage Circuit Breaker

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Abstract

Figures

1 Introduction

2 Co-simulation Model Building Of Hydraulic Om

2.1 Modeling of hydraulic system

2.2 Modeling of transmission mechanism

2.3 Coupling and co-simulation

3 Experiment Validation

3.1 Displacement validation

3.2 Stress validation

4 Model Application

4.1 Stress distribution analysis

4.2 Operation prediction

5 Conclusion

Declarations

References

Status:

Version 1