The negative ion based neutral beam injector (NNBI) with a beam energy of 400 keV is one of the subsystems at the Comprehensive Research fAcility for Fusion Technology (CRAFT) in China. The distributed capacitance of the high-voltage components is an important basis for the design of surge suppression devices at CRAFT NNBI. This study conducted calculations of distributed capacitance for the key components, including the high-voltage deck, transmission line and isolation transformer in the power supply system using the finite element method. The relationship between the high-voltage deck (HVD) distributed capacitance and the distance from the wall is discussed. The differences in distributed capacitance and energy storage between non-coaxial and coaxial transmission lines are also debated. Finally, the capacitance between the primary and secondary windings of the −400 kV isolation transformer, as well as between the secondary winding and the oil tank casing, was calculated.
Neutral beam injectors (NBIs) are one of the most important ignition and auxiliary heating methods for magnetic confinement fusion [1–7]. A radio frequency (RF) negative ion based neutral beam injector (NNBI) was selected for the future tokamak fusion demonstration reactor because of its long lifespan and high neutralization efficiency at high beam energy [8–10]. As a result, a −400 kV NNBI validation device has been incorporated into Comprehensive Research fAcility for Fusion Technology (CRAFT) and is currently under construction, it is known as the CRAFT NNBI [11–16].
The power supply (PS) system of an NNBI is responsible for the task of energy provision [17–21]. The PS system consists of a two-stage acceleration grid (AG) PS, an extraction grid (EG) PS, RF PSs, auxiliary PSs, a high-voltage deck (HVD), a transmission line (TL) and an isolation transformer. The total area occupied by the power supply system exceeds 200 m2. The HVD, TL and isolation transformer are among the largest pieces of equipment in terms of volume. The aforementioned three devices are considered as key components in the NNBI power supply system and need to be independently designed due to their non-standard characteristics and significance. A significant number of conductors within the key components operate at a potential of −400 kV and are insulated from the ground. These conductors form capacitance with the ground or other conductors at different potentials, known as distributed capacitance. The value of distributed capacitance is an important design reference for surge suppression devices known as snubbers [22–25]. Generally, the electrostatic energy storage in high-voltage (HV) circuits is directly proportional to the distributed capacitance. The larger the distributed capacitance, the higher the requirements for surge suppression devices. Therefore, it is necessary to calculate and possibly optimize the distributed capacitance before the implementation of the HVD, TL and isolation transformer.
In this paper, the power supply system of the CRAFT NNBI is introduced first. Subsequently, the closest distance of the HVD from the wall is calculated using finite element analysis (FEA). Subsequently, the relationship between the distributed capacitance of single and double-layer HVDs and the distance from the wall is also calculated. Afterward, the characteristics of coaxial and non-coaxial TLs in terms of distributed capacitance are discussed. Finally, the distributed capacitance of the −400 kV isolation transformer is calculated. All of the calculations were conducted by the FEA method. The accuracy of the FEA method in calculating distributed capacitance has been verified in reference [26].
2.
The power supply system of the CRAFT NNBI
All of the PSs are numbered and their main parameters apart from RF PS are listed in table 1. Nos. 3–8 are the auxiliary PSs. The residual ion dump PS provides the highest 30 kV voltage to the ion dump to deflect the charged particles [14]. Two RF PSs are required for the CRAFT NNBI and each one provides 200 kW RF power to the source driver. The frequency range of the RF PS is designated as 0.9–1.1 MHz to realize frequency tuning [27].
Table
1.
The power supply parameters of the CRAFT NNBI.
An ITER NBI-like power supply system for the CRAFT NNBI is shown in figure 1 [28]. The RF PSs, EG PS and auxiliary PSs work at the potential of −416 kV. Hence, the Nos. 2–9 PSs are placed in the enclosed HVD and powered by an isolation transformer to realize insulation to ground, and their conductors are transmitted in the −400 kV HV conductor [29].
Figure
1.
Schematic diagram of the CRAFT NNBI power supply system.
The cooling and constant temperature water system provides cooling water to the drivers, expansion chamber, bias plate (BP), plasma grid (PG), EG and AG. High-impedance deionized water is used in the system to meet insulation requirements. To avoid surface creep and flashover breakdown of adjacent pipelines, water pipelines are transmitted from −400 kV and −200 kV HV conductors based on potential [29].
The HVD is scheduled to be placed in the HV hall. The height from the floor to the ceiling of the HV hall is 29 m. The jib of the crane is located below the ceiling. During operation of the NNBI, the crane is parked against the wall to avoid affecting the HV equipment. Meanwhile, the AG PS will also be installed inside the HV hall. The effective area in the HVD should be greater than 130 m2 to provide sufficient space for the placement of the PSs and auxiliary equipment. Silicone rubber insulators are used for the support of the HVD. The upper layer of the HVD is enclosed by an aluminum casing to isolate the internal and external electric fields. The total weight of the HVD is approximately 50 T.
The TL is divided into TL1, TL2 and TL3 based on its different contents. The conductors of AG PSs, −200 kV and −400 kV, enter the TL1, respectively. The lengths of TL1, TL2 and TL3 are 4 m, 29.6 m and 10 m, respectively. The conductors of the PSs in the HVD enter the −400 kV HV conductor from the starting section of TL2 and the water pipelines enter the −400 kV and −200 kV HV conductor from the starting section of TL3.
An isolation transformer with the insulation level of direct current 400 kV is used to power the PSs on the HVD. The isolation transformer achieves insulation using transformer oil and insulating paper. The above-mentioned HVD, TL and isolation transformer are the main devices with distributed capacitance. Their distributed capacitance will be discussed in the next section.
3.
The distributed capacitance of the key components
3.1
The HVD
The HVD is placed in the HV hall with the width × length × height of 30 m×41.1 m×29 m. The south wall, north wall and floor of the HV hall are smooth concrete structures. The remaining walls are cladded with aluminum alloy. There are two schemes for the primary design of HVD, namely single-layer and double-layer, respectively, and the basic parameters of the two kinds of HVD are shown in table 2. The vertical edges of the shell are rounded with a radius of 0.4 m. The horizontal edges of the HVD are wrapped by grading rings with a radius of 0.2 m to make the boundary electric field distribution more uniform. The mechanical structure of the HVD is shown in figure 2.
Table
2.
The power supply parameters of the CRAFT NNBI.
The effective area of the single-layer HVD is more concentrated. Meanwhile, the single-layer HVD is more stable due to its larger base area and lower center of gravity. The double-layer HVD can save precious floor area in the HV hall. In this part, the two schemes will be discussed from the aspects of distributed capacitance. The calculation is modeled and performed by the FEA method. All diagonal insulators and most of the main insulators are ignored to simplify the model.
The distributed capacitance of the HVD is primarily related to its position within the HV hall when the dimensions of the HVD and HV hall are fixed. The location of the HVD in the HV hall is represented in figure 3. Dx and Dy are used to represent the distance between the HVD and the wall. The distributed capacitance of the HVD is calculated by applying voltage, U, to the HVD and calculating the stored electrical energy, E. The conversion between electrical energy storage and capacitance is carried out through the following formula:
Figure
3.
The horizontal position of the HVD in the HV hall.
Dx and Dy are scanned with a step size of 0.5 m. The relationship between the distance of the HVD from the wall and the distributed capacitance is shown in figure 4. When the distance from the wall is small, the distributed capacitance of a single-layer HVD is lower than that of a double-layer HVD. However, when it is far away from the wall, the capacitance of the single-layer HVD distribution is higher than that of the double-layer HVD. The reason is that the side area of a single-layer HVD is smaller than that of a double-layer HVD. At this point, the dielectric effect between the HVD and the wall is more significant, and the distance between HVDs and the roof and ground does not change with Dx and Dy. Hence, the double-layer HVD with smaller upper and lower bottom areas has smaller distributed capacitance when it is far away from the wall. The distributed capacitance of two types of HVDs tends to stabilize after a distance of more than 8.5 m from the wall.
Figure
4.
The relationship between the distance from the wall and the distributed capacitance of the single-layer HVD (a) and the double-layer HVD (b).
Considering the stability and convenience of equipment installation within the HVD, the single-layer HVD is chosen. Meanwhile, the Dx and Dy are chosen as 5.4 m and 8.6 m to preserve the aisle space and maintain the HVD distributed capacitance at around 1.4 nF. Under the operating conditions of −400 kV, the energy storage of the HVD is 112 J.
3.2
The TL
TLs can be designed as non-coaxial and coaxial structures. The structures of the two kinds of TL are shown in figures 5 and 6, respectively. Their insulation situations have been discussed in [29–31]. Both types of TL include a −400 kV conductor, a −200 kV conductor and grounding shield. The distributed capacitances of the non-coaxial and coaxial TLs are calculated based on the FEA method.
Figure
5.
The structure of non-coaxial TL1 (left), TL2 (right) and TL3 (right).
The non-coaxial TL is a multi-conductor electrostatic independent system. The distributed capacitance of the non-coaxial TL consists of the capacitance between the −400 kV conductor and the grounding shield, C400−G, the capacitance between the −200 kV conductor and the grounding shield, C200−G, and the capacitance between the −400 kV conductor and the −200 kV conductor, C400−200, which is the so-called mutual capacitance. The charges on the −200 kV and −400 kV conductors can be represented as:
In the equation, q200 and q400 are the charges of −200 kV and −400 kV conductors, respectively. The U200−G, U200−400 and U400−G correspond to the voltage difference between −200 kV conductor and grounding shield, the −200 kV conductor and −400 kV conductor, and the −400 kV conductor and grounding shield, respectively. The mutual capacitance matrix:
C=[C200−GC400−200C400−200C400−G].
(3)
The FEA method cannot directly calculate the mutual capacitor. Therefore, it is necessary to solve the Maxwell capacitance matrix to indirectly obtain the mutual capacitances. First, the grounding shield is set to ground potential. The following equation is used to describe the relationship between the charges on the −200 kV conductor and the −400 kV conductor and their voltages:
The U200 and U400 represent the −200 kV and −400 kV conductors’ voltages. The U200 and U400 conductors are set to 0 V successively, and the CM can be solved using the FEA method. The relationship between the mutual capacitance matrix and the Maxwell capacitance matrix is:
For coaxial TL, the distributed capacitance consists of the capacitance between the −400 kV conductor and the −200 kV conductor, C400−200, and the capacitance between the −200 kV conductor and grounding shield, C200−G. Due to the shielding effect of the −200 kV conductor, there is no dielectric relationship between the −400 kV conductor and the grounding shield. Hence, it is not necessary to introduce the Maxwell capacitance matrix into the calculation of the distributed capacitance of the coaxial TL. The distributed capacitance calculation results of the coaxial TL are shown in table 4.
Table
4.
Distributed capacitance of the coaxial TL.
Considering the lengths of each section of the TL, the total distributed capacitance and stored energy of the non-coaxial TL are 4.466 nF and 259.14 J, respectively. The total distributed capacitance and stored energy of the coaxial TL are 11.424 nF and 228.64 J, respectively. According to equation (1), the energy stored in a capacitor is directly proportional to the square of the voltage applied across it. The distributed capacitance voltage of the coaxial TL is 200 kV throughout, while a substantial part of the distributed capacitance in the non-coaxial TL is the capacitance between the −400 kV conductor and the grounding shield. Therefore, even though the total distributed capacitance of the coaxial TL is greater than that of the non-coaxial TL, the total energy storage of the coaxial TL is less than that of the non-coaxial TL.
It is commonly known that the capacitance is directly proportional to the area of the plates facing each other and inversely proportional to the distance between the plates. Therefore, the TL1 section of the two types of TL exhibits a lower capacitance value due to the smaller conductor radius, and the distributed capacitance of the coaxial TL is more than double that of the non-coaxial TL.
In table 3, C400−200 in TL1 is smaller than the C400−200 in TL2 and TL3 and C200−G in TL1 is greater than the C200−G in TL2 and TL3. In the non-coaxial TL, the position and radius of the −200 kV conductor remain unchanged after the transition from TL1 to TL2. However, the increase in the radius of the −400 kV conductor leads to more electric field lines connecting with the −400 kV conductor, which are connected to the −200 kV conductor, and reduces the connections with the grounding shield. This explains the aforementioned changes in C400−200 and C200−G.
3.3
The isolation transformer
The isolation transformer is a three-phase transformer with a capacity of 3 MVA. The parameters of the isolation transformer are listed in table 5. The simplified model of the isolation transformer used for calculations is shown in figure 7. The dimensions of the isolation transformer tank casing are 4.682 m×2.174 m×3.518 m. The primary winding is located on the inside of the secondary winding and operates at ground potential. The secondary winding operates at the potential of −400 kV. The primary insulation between the primary and secondary windings is composed of insulating paper, so does the outer insulation between the secondary winding and oil tank wall. The relative dielectric constants of oil-impregnated insulating paper and transformer oil are 4.5 and 2.1 in the calculation, respectively [32]. The characteristic of the high relative dielectric constant of the insulating paper can provide better insulating performance.
One pole of the distributed capacitance of the isolation transformer is the secondary winding for Phases A, B, and C operating at −400 kV. The other pole of the distributed capacitance is the primary winding, core, and the oil tank casing which are operating at ground potential. Then the total capacitance of the three-phase secondary windings to ground is 3.6 nF.
Figure
7.
The mechanical structure of the −400 kV isolation transformer.
Calculations revealed that under conditions of greater distance from the wall, the distributed capacitance of the double-layer HVD is less than that of single-layer HVD. After considering stability and ease of installation, the single-layer HVD is chosen and placed at Dx = 5.4 m and Dy = 8.6 m. Under these circumstances, the distributed capacitance of the single-layer HVD is approximately 1.4 nF. Furthermore, calculations revealed that the non-coaxial TL has an advantage over coaxial TL in terms of numerical values of distributed capacitance. In fact, the energy stored in the coaxial TL is less than that in the non-coaxial TL, because there is no capacitance formed between the −400 kV conductor and the grounding shield in the coaxial TL. The total distributed capacitance of the isolation transformer is 3.6 nF.
In summary, the total distributed capacitance provided by the single-layer HVD, coaxial TL, and isolation transformer is approximately 16.4 nF. Distributed capacitance is an important basis for the surge protection design of the CRAFT NNBI HV circuit.
Acknowledgments
This work was supported by the Comprehensive Research Facility for Fusion Technology Program of China (No. 2018-000052-73-01-001228), National Natural Science Foundation of China (No. 11975263) and Postgraduate Research and Practice Innovation Program of NUAA (No. xcxjh20231501). The authors express their gratitude to Shengmin Pan, Xueshan Li and Wei Lu from the Institute of Plasma Physics, Hefei Institutes of Physical Science, Chinese Academy of Science for their support in the research.
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