Figure
1.
The maximum fault current in CRAFT converters.
| Citation: |
Zhongma WANG, Chaoyi SHI, Xiuqing ZHANG, Wenwu LU, Sheng ZHANG, Xianhe GAO, Tao XU, Xingxing SHAO, Liansheng HUANG. Analysis and verification of electrodynamic force, thermal stress and current sharing for CRAFT converter structure design[J]. Plasma Science and Technology, 2024, 26(8): 085601. DOI: 10.1088/2058-6272/ad3c6c
|
In the design realm of fusion power supplies, structural components play a pivotal role in ensuring the safety of fusion devices. To verify the reliability of the converter structure design at the Comprehensive Research Facility for Fusion Technology (CRAFT), meticulous analysis of the converter’s dynamic impact is carefully performed based on the worst fault current (400 kA), firstly. Subsequently, the thermal stress analysis based on the maximum allowable steady-state temperature is finished, and the equivalent thermal stress, thermal deformation, maximum shear stress of a single bridge arm and the whole converter are studied. Furthermore, a simple research method involving the current-sharing characteristics of a bridge arm with multi-thyristor parallel connection is proposed using a combination of Simplorer with Q3D in ANSYS. The results show that the current-sharing characteristics are excellent. Finally, the structural design has been meticulously tailored to meet the established requirements.
Fusion energy has been widely studied in the world due to its cleanliness and high-energy output characteristics [1–3]. In a bid to advance the frontiers of fusion energy research, China has initiated a project known as the Comprehensive Research Facility for Fusion Technology (CRAFT) to build a great experimental conditions facility for future commercialization [4, 5]. The power supply of CRAFT is mainly composed of four sets of converter units, each rated at 0.25 kV/25 kA, which are designated for the performance evaluation of a superconducting magnet [6]. To guarantee that the CRAFT converter meets experimental demands, it is imperative to verify the reliability of the converter structure through meticulous topological design and fault analysis [7, 8]. This entails ensuring that the CRAFT converter can endure the maximum fault current without significant structural damage. The maximum transient impulse current is approximately 400 kA, as shown in figure 1, where the Idf is the instantaneous value and IRMSdf is its root mean square value [9].
The fault current is higher than those of all operational fusion devices, and whether the structure could be satisfied with the design needs to be verified. Consequently, a thorough analysis of the dynamic stability performance of the CRAFT converter is warranted. To ensure the structural design reliability, the fault current for analysis is set as 400 kA, which effectively incorporates a safety margin. If the converter structure could withstand this condition, it would undoubtedly fulfill the design specifications across various scenarios.
Excessive thermal stress poses a significant concern as it can lead to the accelerated accumulation of fatigue damage, the reduction of service life and the early generation of cracks [10–12]. The thermal stress caused by temperature is ignored in the previous analysis. However, as the output of fusion power gradually intensifies, the issue of local overheating has become increasingly pronounced, as shown in figure 2. Therefore, it is necessary to verify whether the converter could be damaged by thermal stress during rated operation.
To ensure that the CRAFT converter maintains its rated current output capacity of 25 kA, a configuration of multiple thyristors connected in parallel is employed. However, the variability in the conduction path parameters among individual thyristors can result in unequal current distribution across each parallel branch. The current-sharing characteristics of multi-parallel device branches are a critical objective in converter design. The previous theoretical calculation is too complex and time-intensive, and a method that could be used to quickly analyze the current-sharing effects during the design stage is needed [13–15]. Moreover, it is essential to validate that the current-sharing characteristics meet the specified requirements. Otherwise, it may cause certain overheating of some devices, which affects the safe operation of the converter [16–18].
The structure of this paper is as follows. Firstly, the electrodynamic analyses of the soft connector, AC busbar and converter are studied, respectively. Secondly, the thermal stress of a single bridge and converter is verified with/without supports. Thirdly, based on the inductance matrix, a co-simulation utilizing Q3D and Simplorer is developed to validate the current-sharing characteristics. Finally, a conclusion is given.
To facilitate the simulation process, the model in the structure and thermal stress analysis is simplified based on the design experience and principles of International Thermonuclear Experimental Reactor (ITER) converters. The detailed simplifications applied to the model are outlined as follows. (1) The thyristor and fast fuse are replaced by aluminum blocks that match their respective dimensions. This is also the same as the structure verification experiment of the ITER converter. (2) In addition, to reduce the mesh numbers and improve the simulation speed, small links, such as the internal water-cooled pipeline and the chamfer of the converter edge are ignored. An electrical schematic and structural diagram of the converter are given in figure 3. In figure 3(a), the co-phase counter parallel connection topology is adopted in the CRAFT converter. The primary structure is crafted from aluminum, which is more prone to deformation; therefore, the aluminum segment is mainly analyzed. Due to the high stiffness of the clamp, it is not easy to deform. Therefore, it is disregarded during the structural model simplification, which is aligned with the design and analysis methodologies utilized for the ITER converter [19, 20]. The three-phase AC current is divided into 12 distinct current paths, which are ultimately rectified to form the positive and negative poles of the DC current. Each current path is composed of multiple parallel branches, which contain a thyristor and a fast fuse. The wires between different branches and devices are soft connectors in the actual structure. The structure of the half bridge in A-phase is given in figure 3(b). The current conduction path is indicated by the blue and red dashed lines. The busbar used to connect the thyristor to AC+ and AC− is called the thyristor busbar, and the busbar used to connect the fast fuse to DC+ and DC− is called the fast-fuse busbar. The thyristors and the fast fuses are also connected by busbars, which are called long busbars and short busbars, depending on their length.
The procedure for the electrical dynamic verification of the CRAFT converter is methodically structured as follows: firstly, the fault impulse current is imported into the 3D structure; then, the body stress density, total deformation and equivalent stress distribution are analyzed by ANSYS; finally, it is verified whether the structure is satisfied with the requirements.
In accordance with the design specifications, the short-circuit fault current, which is 400 kA at the front end of the converter reactor, is utilized as input conditions for structural verification with an added safety margin. With this premise, a series of electrodynamic analyses are conducted on the soft connector, AC busbar and whole converter with/without supports and are verified, respectively. The verification of the converter structure’s reliability during fault-current scenarios is achieved by comparing the simulated stress results against the yield strength of the materials used. For the convenience of evaluation, the material properties are given as shown in table 1. The requirement of the structural design is that the equivalent converter stress should not be higher than the yield strength and there is no significant deformation.
| Material | Yield strength | Poisson’s ratio | Specific components |
| No. 45 steel | 355 MPa | 0.3 | Bolt parts |
| No. 6061 aluminium | 276 MPa | 0.33 | Gasket clamp |
| No. 6063 aluminium | 214 MPa | 0.33 | Thyristor radiator |
| No. 6106 aluminium | 193 MPa | 0.33 | Busbars |
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The soft connector is crafted via the welding of multiple aluminum sheets to compensate for installation errors and reduce electric-power impact. It is not directly forged by the mold with a rigid component; thus, we used the term ‘soft’ when naming it. To simulate the most extreme scenario, it is hypothesized that during a fault, a single branch with two paralleled thyristors is operational, meaning the substantial 400 kA current is distributed between two soft connectors. To prevent a substantial increase in mesh divisions and consequently avoid prolonging the simulation time, this study opts to analyze these elements individually, rather than employing multiple slices. Due to the same phase reverse parallel structure of the CRAFT converter, the currents in two soft connectors are opposite, which in turn mitigates the electrodynamic forces arising from electromagnetic induction between them. The results of separate analyses are higher than the actual force, which is equivalent to retaining a safety margin. Recognizing that soft connectors are inherently composed of multiple thin sheets, the task of mesh subdivision becomes intricate, and the simulation process becomes significantly time-consuming. To address this, scenarios with 5, 10, and 20 pieces are compared and analyzed to simulate their deformation under the influence of fault currents. In figure 4, it can be seen that the deformation variables of long and short soft connectors have no significant increase with the change in the number of thin films. Therefore, the soft connectors of the CRAFT converter could withstand fault currents without damage. The maximum deformation position of two soft connectors is located at arc positions.
As a critical component, the three-phase AC busbar is the focus of analysis in this section. The CRAFT busbar is a closed structure, which features a shielding layer that envelops the current-carrying busbar. Its two sides are fixed; one side is connected to a transformer, and the other side is connected to a converter. For the purposes of this study, our attention is concentrated solely on the electrical connection segment with the converter considered in this study. The segment connected to the converter has been included in the subsequent overall structural analysis, and the analysis results are given in figure 5 and table 2.
| Fault current | FXb (N) | FYb (N) | FZb (N) | Ftotalb (N) | |
| A1 | +200 kA | −30343.7 | 402.9 | 0 | 30346.4 |
| A2 | −200 kA | 29954.8 | −370.7 | 0 | 29957.1 |
| B1 | +200 kA | −30526.2 | 41.8 | 0 | 30526.2 |
| B2 | −200 kA | 30643.9 | −272.2 | 0 | 30645.1 |
| C1 | +200 kA | −30787.3 | 16.2 | 0 | 30787.3 |
| C2 | −200 kA | 30629.5 | −275.1 | 0 | 30630.7 |
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The simulation assumes that the fault current, specified at 400 kA, is fully absorbed by the A-phase, while the B-phase and C-phase each handle half of the fault current, which are 200 kA, respectively. When it is taken as the input condition, only the busbar segment is considered, and the influence of other front and rear stages is ignored, and the AC busbar stress is analyzed. As shown in figure 5, the identification method used here is consistent with the previous approach, and 6 busbars are named A1, A2, B1, B2, C1, and C2 from left to right. It can be seen that the maximum physical density is 0.003 N/mm3 (figure 5(a)), the maximum deformation is nearly 0.01 mm (figure 5(b)), and the maximum stress is 1.34 MPa (figure 5(c)). In another scenario, there is a current flowing into the A-phase and out of another phase (either the B-phase or C-phase). From simulation, we found that the maximum deformation and equivalent stress in this situation are not significantly different from the previous conditions.
For a comprehensive comparison of various scenarios, the force results of each phase busbar under the maximum fault current are summarized in table 2. In table 2, FXb, FYb and FZb represent the force of AC busbars in three directions, and Ftotalb is the total value. The reason for the polarity difference in the soft connectors in table 2 is because the AC currents are divided into positive and negative poles. It could be inferred that the overall stress experienced by adjacent busbars in the A-phase, B-phase and C-phase is fundamentally similar. Among them, the maximum force is located in the A-phase, as its passing current is double that of the other two phases. Because the B-phase is closer to the A-phase, which is more affected by the A-phase than the B-phase, the force of the B-phase is slightly higher than that of the C-phase. At the same time, the force on each phase busbar in the Z direction is 0. This is because the current directions of the six busbars are parallel in space; only the X and Y directions are stressed. It is important to note that the aforementioned analysis is predicated on the assumption that the total fault current simultaneously flows into the A-phase together. In reality, any phase’s busbar is capable of withstanding the total fault current. Therefore, the conclusion of this analysis is applicable to the maximum stress condition of the three-phase AC busbar, indicating that each busbar is capable of fulfilling the design requirements. After analysis, when the converter is short circuited at the front end of the reactor, the stress of the AC busbar is less than the material yield strength, which meets the design requirements.
The simulation results of the converter with supports are shown in figure 6. As previously discussed in this paper, the three-phase AC currents flow from the bottom of the converter, and the DC current flows from the top of the converter to other equipment after rectification by the thyristor. Additionally, the current of each phase is transmitted through both the long and short soft connectors. The total deformation is nearly 0.15 mm, as shown in figure 6(a). The maximum equivalent stress is 12.2 MPa, as shown in figure 6(b). The maximum stress point is located at the A-phase support of the three-phase AC busbars. The maximum stress of the converter is nearly 5.0 MPa, as shown in figure 6(c). Therefore, when the converter is operated under the worst current conditions, the stress is less than the material yield strength, which meets the structure design requirements.
The process for verifying the thermal stress in the CRAFT converter is methodically structured as follows: firstly, the maximum steady-state operating temperatures of various components of the converter are determined according to the allowable limits and incorporated into a 3D structure for the simulation under the worst conditions; then, the results of equivalent thermal stress, equivalent thermal strain and maximum shear stress are analyzed using ANSYS; finally, it is compared with the design requirements to verify whether the structure could be satisfied.
While the converter is indeed cooled by deionized water in actual operation, it would still undergo a certain temperature rise. Thermal stress is caused by the change of material properties with temperature variation. When there is no external constraint, the material will be expanded freely under temperature influence. The thermal stress fluctuations of a single bridge arm and the whole converter with/without supports are analyzed below. To ensure the converter’s long-term operational efficiency, its temperature is generally not higher than 40 °C at CRAFT. On this basis, to prevent excessive heating of the soft connector, the temperature difference between it and the converter is not allowed to surpass 40 °C; the maximum temperature of the soft connector is set as 70 °C. Of course, it should be noted that in certain projects, this value could be adjusted to align with the designer’s needs. The maximum temperatures at various positions are adopted as the foundation for the analysis, representing the threshold limit values. The premise is that if the converter can endure the worst-case scenario, it can also be capable of withstanding less severe scenarios. In practical terms, if the temperature exceeds the allowable value, the rate of temperature increase can be mitigated by enhancing the flow of cooling water. The thermal stress analysis results for a single bridge arm are shown in figure 7.
The maximum equivalent stress of a single bridge arm without supports is 65.3 MPa in figure 7(a), and the maximum equivalent stress with supports is 88 MPa in figure 7(d). The maximum equivalent deformation of a single bridge arm is 1.3 mm without supports and 0.75 mm with supports, as shown in figures 7(b) and (e), respectively. The maximum shear stress of a single bridge arm without supports is 35.1 MPa in figure 7(c), and the maximum equivalent shear stress with supports is 50.6 MPa in figure 7(f).
Similarly, the thermal stress of the converter with/without supports is analyzed, as shown in figure 8. When the device is equipped with supports, the entire converter structure is underpinned by epoxy resin.
As shown in figures 8(a) and (c), the maximum equivalent stress of the converter is 67.2 MPa without supports and 168.0 MPa with supports. The maximum deformation of the converter without supports is 1.8 mm in figure 8(b), and the maximum equivalent stress with supports is 0.83 mm in figure 8(d). The maximum equivalent shear stress of the converter without supports is 36.3 MPa in figure 8(c), and the effect is equal when the converter is supported. The maximum shear stress is 91.5 MPa in figure 8(f). The thermal stress of the CRAFT converter is less than the yield strength of aluminum, which meets the design requirements.
It can be found from the analysis results that the thermal stress of a single bridge arm is increased when it is supported. The integral thermal stress is less than the material yield strength, which meets the design requirements. In this paper, only the steady-state temperature rise is discussed. However, it is acknowledged that further research will be dedicated to examining the transient temperature rise resulting from the 400 kA fault current in future studies.
To rapidly analyze the current-sharing characteristics, a stray parameter extraction idea based on current path module segmentation is adopted in this study. This approach has been validated for its correctness and accuracy in the analysis of similar types of multi-parallel devices, as evidenced by [21–24]. The current-sharing analysis process of the CRAFT converter is shown in figure 9. Firstly, the converter bridge arm is divided into three segments based on the flow of current: thyristor busbars, soft connectors and fuse busbars. Then, the Q3D is utilized to extract the inductance matrix for each distinct branch and to construct the corresponding sub-circuits. Finally, the converter working circuit model is established to verify whether the current-sharing coefficient could meet the design requirements.
Among these inductance matrices in figure 9, Th1–Th6 represent thyristors 1–6, Fuse1–Fuse6 represent fast fuses 1–6, Sh1–Sh3 represent three short busbars and Lo4–Lo6 represent three long busbars. The three tables in figure 9 represent the inductance matrices for different segments of the structure, with each unit clearly marked in the top-left cell of the respective table. The values along the diagonal represent self-inductance, whereas the off-diagonal entries signify mutual inductance. The difference between the diagonal terms Sh2 and other terms is mainly due to the accuracy of the mesh division. In fact, in the entire circuit, the current-sharing characteristics of the system are determined by the three divided segments. Although there are certain differences here, this has little impact on the overall analysis conclusion. This is because the current-sharing analysis circuit considers not only inductance but also resistance, and the discrepancies mentioned are relatively insignificant compared to the total inductance value. Furthermore, in the tables, the off-diagonal terms bear the same value. This uniformity arises because the mutual inductance between two branches is influenced solely by their individual structures and spatial configuration, rather than their sequential arrangement. Therefore, they are symmetrically distributed diagonally.
The converter bridge arm is intricately assembled from a multitude of thyristors connected in parallel. Each thyristor is connected in series with a fast fuse through a soft connector, and then it is converged to the fast-fuse busbar. During steady-state operation, the varying impedance present in each thyristor branch leads to a divergence in the currents flowing through them. Therefore, it is necessary to verify the current-sharing effects of all the branches. The current-sharing effect is determined by the current-sharing coefficient (kunb), which is defined as:
| kunb=Imax | (1) |
Here, Imax is the maximum branch current, Np is the number of branches in parallel, and Itotal is the total output current. When kunb is less than 1.2, it is considered to be within the acceptable parameters for engineering applications.
When multiple devices and branches are connected in parallel, each branch encompasses not only its inherent resistance and inductance but also the resistance and inductance parameters that arise from the coupling effects of adjacent branches. Therefore, when the electrical parameters of the bridge arm could be equivalent to a circuit model, it will be very complex. In this study, co-simulation of Q3D and Simplorer in ANSYS is used for current-sharing analysis of the converter.
Because the CRAFT converter is a three-phase six pulses bridge structure in which each bridge arm structure is exactly the same, one arm is selected for analysis in this study. The connection mode of the bridge arms is an in-phase inverse parallel structure, and each bridge arm is divided into upper and lower segments. During each operational cycle, only half of these thyristors will be conducted. To simplify the analysis, only half of the bridge arm is chosen for computational purposes. It is divided into three segments, as shown in figure 10, segment 1 (figure 10(a)): contact surfaces between AC busbars and thyristors; segment 2 (figure 10(b)): soft connectors; segment 3 (figure 10(c)): contact surfaces between fast fuses and DC busbars, and all the thyristors are installed in the front and back sides. For the convenience of explanation, the imprinted surface of the front-stage device and busbar is set as a red solid line, and the imprinted surface of the rear-stage device and busbar is set as a black dotted line. It is important to note that these distinctions are made solely for ease of identification and visualization. In actual practice and simulation, the marking surfaces of the black dotted lines’ identification are taken on the other side of each branch.
Based on the stray inductance parameters of each divided branch extracted by Q3D, a circuit model of the bridge arm is established using Simplorer in ANSYS. This advanced setup enables each partition module to be seamlessly encapsulated into a sub-circuit, complete with defined input and output ports. The model is used to analyze the current-sharing effect of the parallel branch in the bridge arm. The results are shown in figure 11, where B1–B6 represent branches 1–6. The simulation results confirm that the current-sharing characteristics of six branches are highly efficient (kunb = 1.05 < 1.2), and thus adhere to the design requirements. The steady-state currents of each branch are slightly different. This is because the distances between each branch and input current are different and the branch resistors will be increased in turn, caused by connected busbars. Moreover, the triggering times and closing times of different branches are not exactly the same, which is due to the different stray parameters of each branch. The maximum error time is less than 200 μs, which is acceptable for practical application.
To validate the structural reliability of the CRAFT converter, a comprehensive investigation of electrodynamic impact analysis and thermal stress analysis are studied in this work. It is verified that the converter could withstand the worst fault current and maximum steady-state temperature without structural damage. Concurrently, the inductance of the bridge arm is extracted by Q3D and integrated into a co-simulation with Simplorer in ANSYS. The results indicate that the current-sharing coefficient of the bridge arm is 1.05: a value that aligns perfectly with the design requirements. This method could be used to quickly analyze the current-sharing characteristics of multiple parallel power devices.
The authors express their gratitude to the Institute of Plasma Physics Chinese Academy of Sciences (ASIPP), for their invaluable assistance in the design process of the fusion power converter. This work was supported by the Talent Research Fund of Hefei University (No. 21-22RC09), and National Natural Science Foundation of China (No. U22A20225).
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Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Material | Yield strength | Poisson’s ratio | Specific components |
| No. 45 steel | 355 MPa | 0.3 | Bolt parts |
| No. 6061 aluminium | 276 MPa | 0.33 | Gasket clamp |
| No. 6063 aluminium | 214 MPa | 0.33 | Thyristor radiator |
| No. 6106 aluminium | 193 MPa | 0.33 | Busbars |
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| Fault current | FXb (N) | FYb (N) | FZb (N) | Ftotalb (N) | |
| A1 | +200 kA | −30343.7 | 402.9 | 0 | 30346.4 |
| A2 | −200 kA | 29954.8 | −370.7 | 0 | 29957.1 |
| B1 | +200 kA | −30526.2 | 41.8 | 0 | 30526.2 |
| B2 | −200 kA | 30643.9 | −272.2 | 0 | 30645.1 |
| C1 | +200 kA | −30787.3 | 16.2 | 0 | 30787.3 |
| C2 | −200 kA | 30629.5 | −275.1 | 0 | 30630.7 |
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