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The AC loss of an HTS transformer by 2D and 3D numerical calculation
Physica C 469 (2009) 1736–1739
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
The AC loss of an HTS transformer by 2D and 3D numerical calculation S. Choi a, S.H. Park a, S.Y. Lee a, W. Kim b, C. Park b, J.B. Song c, H. Lee c, K. Choi a,*, S. Hahn b a b c
Graduate School of Energy, Korea Polytechnic University, 2121 Jeongwang-dong, Siheung-si, Gyeonggi-do 429-793, Republic of Korea Seoul National University, Gwanka_599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea Department of Materials Science and Engineering, Korea University, Anam-dong, Seongbuk-Gu, Seoul 136-701, Republic of Korea
a r t i c l e
i n f o
Article history: Available online 7 June 2009 PACS: 74.25.Ha 85.25.–j Keywords: AC loss HTS transformer Numerical analysis
a b s t r a c t For the design of a high temperature superconductor (HTS) power transformer the AC loss is a critical issue because the energy is dissipated as heat in the low temperature. It is necessary to study the AC losses theoretically and experimentally. For the analysis of AC losses in an HTS power transformer, two-dimensional numerical analysis has been carried out until now. However, AC losses which are calculated by using two-dimensional numerical analysis differ from those using three-dimensional numerical analysis because the geometry of the HTS transformer is not symmetric. AC losses of a 1 MVA-single-phase HTS transformer were calculated using both two-dimensional and three-dimensional numerical analysis. To prove the effectiveness of the calculations, the numerical results were compared with the measured results for a transformer fabricated using Bi2Sr2CaCu2O8+d tapes in 2004. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It is essential to establish the substation in residential area or to expand conventional substation because of increment and magnification of city center area of power demand. The substation of high voltage power transformers in metropolis such as Seoul in Korea is located at the basements of buildings. This brings insufficiency of the space, where the transformer is established newly or additionally. Therefore, more efficient transformer than the conventional transformer has been studied and a high temperature superconductor (HTS) transformer can be one of solutions. The fundamental structure of HTS transformer changes little compared with a conventional transformer. The HTS transformer can reduce a size and a weight greatly. Because a HTS wire is light and thin compared with a copper wire, and has a large capacity of current. The HTS transformer also has many advantages such as high efficiency, long lifetime, the potential fire and environmental friendly technology [1]. Several types of the HTS transformers have developed, especially in Korea. A single phase 1 MVA-HTS transformer was developed [2]. We also have studied on conceptual designs for single phase 154 kV class 5 MVA-HTS transformers to obtain the key technology for fabricating the three phase 100 MVA-HTS transformers [3]. HTS wires which compose a coil generate a magnetic field along various directions. These magnetic fields operate as external magnetic fields and gen-
* Corresponding author. Tel.: +82 31 8041 0332; fax: +82 31 8041 0349. E-mail address: [email protected] (K. Choi). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.05.254
erate magnetization loss in each part of the coil. This loss is one of the major issues of the HTS transformer, because large AC loss causes an increase of cooling factor and decreases of efficiency and economical feasibility. Therefore the estimation of the AC loss of the HTS transformer must be done before the manufacture of the HTS transformers. In this paper, we calculated the AC loss of 1 MVA-HTS transformer using the two-dimensional numerical analysis and the three-dimensional numerical analysis. 1 MVA-HTS transformer was fabricated and the magnetization loss was measured. The effectiveness of the calculation can be proven by the comparison between the numerical analysis result and the measured result. 2. 1 MVA-HTS transformer The capacity of the HTS transformer is 1 MVA and the rated primary and secondary voltages is 22.9 kV and 6.6 kV, respectively. The operating temperature is 65 K. The HTS transformer is composed of HTS windings, iron core and cryostats. The design parameters of 1 MVA-HTS transformer with arrangement winding are shown in Table 1. 2.1. HTS winding The Bi2Sr2CaCu2O8+d (BSCCO-2223) HTS tape double pancake winding is adopted in 1 MVA-HTS transformer. This HTS tape is manufactured by American Superconductor Company (AMSC) and reinforced by stainless steel tape in order to sustain mechani-
S. Choi et al. / Physica C 469 (2009) 1736–1739
2.2. Iron core
Table 1 Design parameters of 1 MVA-HTS transformer. Specification
Value
Unit
Rating Phase Capacity Voltage Current
1 1 22.9/6.6 44/152
MVA kV A
Cryostat Inner dia. Outer dia. Height
334 948 1200
mm mm mm
Iron core Material Cross-section area
Silicon steel plate 715.16
cm2
Table 2 Specification of BSCCO-2223 HTS tape. Quantity
Value
Unit
Thickness (avg) Width (avg) Critical current density, Je Min. critical current, Ic Critical stress (77 K) Critical strain (77 K) Min. bend dia
0.31 (±0.02) 4.1 (±0.2) >9.2 >115 265 0.4 70
mm mm kA/cm2 Aa MPab %b mm
a b
1737
The shell type iron core was composed of laminated silicon steel plates of which height and width is 1580 mm and 1340 mm, respectively. Fig. 2 shows the configuration of a laminated iron core. 3. The AC loss of 1 MVA-HTS transformer 3.1. The AC loss of the HTS transformer The magnetic field generates magnetization loss in each part of the coil. The AC losses by perpendicular magnetic fields are calculated by the strip model, and those by parallel field are calculated by the slab model [4]. But, the main property of the AC loss is the loss which is caused by the perpendicular component of the magnetic fields. Fig. 3 shows the magnetization losses of BSCCO-2223 tape according to the external magnetic fields. The magnetic field by the current which flows in the HTS coil operates as the external magnetic fields to each HTS coil and generates the magnetization loss of the HTS wire. It is important to analyze the AC losses in
At 77 K, self-field, 1 lV/cm2. With 95% Ic Retention.
cal stresses during winding process and electromagnetic stress in operation. The critical current of this HTS tape is more than 150 A in self-field at 65 K. Table 2 shows the specifications of BSCCO-2223 HTS tape. The windings in HTS transformer consists of the primary and secondary windings. The primary and secondary windings consist of five modules which are made of four double pancake windings. The total number of turns of each winding is 832 turns and 240 turns, respectively. The secondary windings are wound by four parallel HTS tapes without any transposition because the rated secondary current exceeds the critical current of the single HTS tape. Fig. 1 shows the arranged HTS windings using the double pancake windings. Fig. 2. The configurations of laminated iron core.
Fig. 1. The arranged HTS windings.
Fig. 3. The magnetization losses of BSCCO-2223 tape according to the external magnetic fields.
1738
S. Choi et al. / Physica C 469 (2009) 1736–1739
Fig. 4. 2D numerical analysis of 1 MVA-HTS transformer. (a) The Axi-symmetric model and (b) the magnetic field distribution.
the HTS windings because the AC losses due to the external magnetic fields cause a falling off the stability of the HTS winding such as reducing efficiency and increasing temperature and so on. The AC losses generated in 1 MVA-HTS transformer were calculated from the static magnetic field analysis by using MagNetÒ. 3.2. 2D numerical analysis of 1 MVA-HTS transformer The two-dimensional numerical analysis of 1 MVA-HTS transformer was carried out in order to calculate the AC loss. The twodimensional numerical analysis can be classified into two ways, the Cartesian (XY) model and the Axi-symmetric (RZ) model. A Cartesian model represents a cross-section of a device that extends infinitely in the line direction and an Axi-symmetric model represents a cross-section of a device that is revolved by 360° around the axis of symmetry (the z-axis). In this paper, the analysis model of 1 MVA-HTS transformer is set by the RZ model. Fig. 4a shows the RZ model of 1 MVA-HTS
transformer. The HTS coil was located in the lower part of the iron core because the HTS transformer cooled down using liquid nitrogen. Fig. 4b shows the distribution of the magnetic fields in the HTS coil when the rated current applied. The AC loss in the high voltage winding and the low voltage winding is 179.1 W and 342.22 W, respectively. We could know that the AC loss of the low voltage winding is larger than that of the high voltage winding. 3.3. 3D numerical analysis of 1 MVA-HTS transformer In order to calculate the magnetic fields in the HTS coil more accurately, 1 MVA-HTS transformer was modeled and analyzed using the three-dimensional numerical analysis because the designed shape of the iron core was not symmetric. Fig. 5a and b show the three-dimensional numerical analysis model and the magnetic field distribution of 1 MVA-HTS transformer when the rated current is applied. The maximum value of the magnetic field was calculated at 0.088 T. The result is shown in Fig. 5b. The result
Fig. 5. 3D numerical analysis of 1 MVA-HTS transformer. (a) 3D analysis model and (b) the magnetic field distribution.
1739
S. Choi et al. / Physica C 469 (2009) 1736–1739 Table 3 The comparison between the calculated and measurement results. Contents
Value
The calculated result using 2D analysis
Prim. 1 Prim. 2 Sec Total
74.97 104.13 342.22 521.32
The calculated result using 3D analysis
Prim. 1 Prim. 2 Sec Total
91.84 120.19 368.0 580.03
The experimental result
Total
231.65
was not yet established. We could not divide to the enough number of meshes because of the memory space. These reasons make a difference between the calculated and measurement results. 4. Conclusions
Fig. 6. The experiment setup of 1 MVA-HTS transformer.
of the AC losses calculated by using the magnetic fields in the high and low voltage windings is 212.03 W and 368 W, respectively. 3.4. Comparison between calculation and measurement of the AC loss To prove the effectiveness of the calculations, the numerical results were compared with measured results. The experiment for manufactured 1 MVA-HTS transformer was done at 65 K. Fig. 6 shows the experiment setup of 1 MVA-HTS transformer. The AC loss at the rated current was measured by the calorimetric method. Table 3 shows the comparison between the calculated result and the measurement results. The total of calculated AC loss is about 2.5 times larger than the measured one; they were different because of several reasons. The AC losses by perpendicular magnetic fields are calculated by the strip model, and those by parallel field are calculated by the slab model. But these models are used for analyzing a single tape model. The secondary windings in HTS transformer are wound by four HTS tapes in parallel. And we estimated that our analysis method
In this paper, the magnetic field calculation is carried out to analyze the AC loss of 1 MVA-HTS transformer. The AC losses of HTS transformer was calculated by the electromagnetic analysis. The calculated AC loss and measured AC loss of 1 MVA-HTS transformer are compared. The calculated value is higher than the measurement result. To improve the analysis technique, we will carry out research on the model which composed of multiple HTS tapes and analysis method. Acknowledgement This research was supported by a grant from Center for Applied Superconductivity Technology of the 21st Century Frontier R&D Program funded by the Ministry of Education, Science and Technology, Republic of Korea. References [1] S.P. Metha, N. Aversa, M.S. Walker, IEEE Spectrum 34 (1997) 34. [2] W.S. Kim, J. H Han, S.H. Kim, IEEE Trans. Appl. Supercond. 14 (2004) 904. [3] J. Choi, S. Lee, M. Park, W. Kim, S. Kim, J. Han, H. Lee, K. Choi, Physica C 463–465 (2007) 223. [4] J.K. Lee, S.W. Lee, M. Park, G. Cha, IEEE Trans. Appl. Supercond. 14 (2004) 630.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
The AC loss of an HTS transformer by 2D and 3D numerical calculation S. Choi a, S.H. Park a, S.Y. Lee a, W. Kim b, C. Park b, J.B. Song c, H. Lee c, K. Choi a,*, S. Hahn b a b c
Graduate School of Energy, Korea Polytechnic University, 2121 Jeongwang-dong, Siheung-si, Gyeonggi-do 429-793, Republic of Korea Seoul National University, Gwanka_599 Gwanak-ro, Gwanak-gu, Seoul 151-742, Republic of Korea Department of Materials Science and Engineering, Korea University, Anam-dong, Seongbuk-Gu, Seoul 136-701, Republic of Korea
a r t i c l e
i n f o
Article history: Available online 7 June 2009 PACS: 74.25.Ha 85.25.–j Keywords: AC loss HTS transformer Numerical analysis
a b s t r a c t For the design of a high temperature superconductor (HTS) power transformer the AC loss is a critical issue because the energy is dissipated as heat in the low temperature. It is necessary to study the AC losses theoretically and experimentally. For the analysis of AC losses in an HTS power transformer, two-dimensional numerical analysis has been carried out until now. However, AC losses which are calculated by using two-dimensional numerical analysis differ from those using three-dimensional numerical analysis because the geometry of the HTS transformer is not symmetric. AC losses of a 1 MVA-single-phase HTS transformer were calculated using both two-dimensional and three-dimensional numerical analysis. To prove the effectiveness of the calculations, the numerical results were compared with the measured results for a transformer fabricated using Bi2Sr2CaCu2O8+d tapes in 2004. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It is essential to establish the substation in residential area or to expand conventional substation because of increment and magnification of city center area of power demand. The substation of high voltage power transformers in metropolis such as Seoul in Korea is located at the basements of buildings. This brings insufficiency of the space, where the transformer is established newly or additionally. Therefore, more efficient transformer than the conventional transformer has been studied and a high temperature superconductor (HTS) transformer can be one of solutions. The fundamental structure of HTS transformer changes little compared with a conventional transformer. The HTS transformer can reduce a size and a weight greatly. Because a HTS wire is light and thin compared with a copper wire, and has a large capacity of current. The HTS transformer also has many advantages such as high efficiency, long lifetime, the potential fire and environmental friendly technology [1]. Several types of the HTS transformers have developed, especially in Korea. A single phase 1 MVA-HTS transformer was developed [2]. We also have studied on conceptual designs for single phase 154 kV class 5 MVA-HTS transformers to obtain the key technology for fabricating the three phase 100 MVA-HTS transformers [3]. HTS wires which compose a coil generate a magnetic field along various directions. These magnetic fields operate as external magnetic fields and gen-
* Corresponding author. Tel.: +82 31 8041 0332; fax: +82 31 8041 0349. E-mail address: [email protected] (K. Choi). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.05.254
erate magnetization loss in each part of the coil. This loss is one of the major issues of the HTS transformer, because large AC loss causes an increase of cooling factor and decreases of efficiency and economical feasibility. Therefore the estimation of the AC loss of the HTS transformer must be done before the manufacture of the HTS transformers. In this paper, we calculated the AC loss of 1 MVA-HTS transformer using the two-dimensional numerical analysis and the three-dimensional numerical analysis. 1 MVA-HTS transformer was fabricated and the magnetization loss was measured. The effectiveness of the calculation can be proven by the comparison between the numerical analysis result and the measured result. 2. 1 MVA-HTS transformer The capacity of the HTS transformer is 1 MVA and the rated primary and secondary voltages is 22.9 kV and 6.6 kV, respectively. The operating temperature is 65 K. The HTS transformer is composed of HTS windings, iron core and cryostats. The design parameters of 1 MVA-HTS transformer with arrangement winding are shown in Table 1. 2.1. HTS winding The Bi2Sr2CaCu2O8+d (BSCCO-2223) HTS tape double pancake winding is adopted in 1 MVA-HTS transformer. This HTS tape is manufactured by American Superconductor Company (AMSC) and reinforced by stainless steel tape in order to sustain mechani-
S. Choi et al. / Physica C 469 (2009) 1736–1739
2.2. Iron core
Table 1 Design parameters of 1 MVA-HTS transformer. Specification
Value
Unit
Rating Phase Capacity Voltage Current
1 1 22.9/6.6 44/152
MVA kV A
Cryostat Inner dia. Outer dia. Height
334 948 1200
mm mm mm
Iron core Material Cross-section area
Silicon steel plate 715.16
cm2
Table 2 Specification of BSCCO-2223 HTS tape. Quantity
Value
Unit
Thickness (avg) Width (avg) Critical current density, Je Min. critical current, Ic Critical stress (77 K) Critical strain (77 K) Min. bend dia
0.31 (±0.02) 4.1 (±0.2) >9.2 >115 265 0.4 70
mm mm kA/cm2 Aa MPab %b mm
a b
1737
The shell type iron core was composed of laminated silicon steel plates of which height and width is 1580 mm and 1340 mm, respectively. Fig. 2 shows the configuration of a laminated iron core. 3. The AC loss of 1 MVA-HTS transformer 3.1. The AC loss of the HTS transformer The magnetic field generates magnetization loss in each part of the coil. The AC losses by perpendicular magnetic fields are calculated by the strip model, and those by parallel field are calculated by the slab model [4]. But, the main property of the AC loss is the loss which is caused by the perpendicular component of the magnetic fields. Fig. 3 shows the magnetization losses of BSCCO-2223 tape according to the external magnetic fields. The magnetic field by the current which flows in the HTS coil operates as the external magnetic fields to each HTS coil and generates the magnetization loss of the HTS wire. It is important to analyze the AC losses in
At 77 K, self-field, 1 lV/cm2. With 95% Ic Retention.
cal stresses during winding process and electromagnetic stress in operation. The critical current of this HTS tape is more than 150 A in self-field at 65 K. Table 2 shows the specifications of BSCCO-2223 HTS tape. The windings in HTS transformer consists of the primary and secondary windings. The primary and secondary windings consist of five modules which are made of four double pancake windings. The total number of turns of each winding is 832 turns and 240 turns, respectively. The secondary windings are wound by four parallel HTS tapes without any transposition because the rated secondary current exceeds the critical current of the single HTS tape. Fig. 1 shows the arranged HTS windings using the double pancake windings. Fig. 2. The configurations of laminated iron core.
Fig. 1. The arranged HTS windings.
Fig. 3. The magnetization losses of BSCCO-2223 tape according to the external magnetic fields.
1738
S. Choi et al. / Physica C 469 (2009) 1736–1739
Fig. 4. 2D numerical analysis of 1 MVA-HTS transformer. (a) The Axi-symmetric model and (b) the magnetic field distribution.
the HTS windings because the AC losses due to the external magnetic fields cause a falling off the stability of the HTS winding such as reducing efficiency and increasing temperature and so on. The AC losses generated in 1 MVA-HTS transformer were calculated from the static magnetic field analysis by using MagNetÒ. 3.2. 2D numerical analysis of 1 MVA-HTS transformer The two-dimensional numerical analysis of 1 MVA-HTS transformer was carried out in order to calculate the AC loss. The twodimensional numerical analysis can be classified into two ways, the Cartesian (XY) model and the Axi-symmetric (RZ) model. A Cartesian model represents a cross-section of a device that extends infinitely in the line direction and an Axi-symmetric model represents a cross-section of a device that is revolved by 360° around the axis of symmetry (the z-axis). In this paper, the analysis model of 1 MVA-HTS transformer is set by the RZ model. Fig. 4a shows the RZ model of 1 MVA-HTS
transformer. The HTS coil was located in the lower part of the iron core because the HTS transformer cooled down using liquid nitrogen. Fig. 4b shows the distribution of the magnetic fields in the HTS coil when the rated current applied. The AC loss in the high voltage winding and the low voltage winding is 179.1 W and 342.22 W, respectively. We could know that the AC loss of the low voltage winding is larger than that of the high voltage winding. 3.3. 3D numerical analysis of 1 MVA-HTS transformer In order to calculate the magnetic fields in the HTS coil more accurately, 1 MVA-HTS transformer was modeled and analyzed using the three-dimensional numerical analysis because the designed shape of the iron core was not symmetric. Fig. 5a and b show the three-dimensional numerical analysis model and the magnetic field distribution of 1 MVA-HTS transformer when the rated current is applied. The maximum value of the magnetic field was calculated at 0.088 T. The result is shown in Fig. 5b. The result
Fig. 5. 3D numerical analysis of 1 MVA-HTS transformer. (a) 3D analysis model and (b) the magnetic field distribution.
1739
S. Choi et al. / Physica C 469 (2009) 1736–1739 Table 3 The comparison between the calculated and measurement results. Contents
Value
The calculated result using 2D analysis
Prim. 1 Prim. 2 Sec Total
74.97 104.13 342.22 521.32
The calculated result using 3D analysis
Prim. 1 Prim. 2 Sec Total
91.84 120.19 368.0 580.03
The experimental result
Total
231.65
was not yet established. We could not divide to the enough number of meshes because of the memory space. These reasons make a difference between the calculated and measurement results. 4. Conclusions
Fig. 6. The experiment setup of 1 MVA-HTS transformer.
of the AC losses calculated by using the magnetic fields in the high and low voltage windings is 212.03 W and 368 W, respectively. 3.4. Comparison between calculation and measurement of the AC loss To prove the effectiveness of the calculations, the numerical results were compared with measured results. The experiment for manufactured 1 MVA-HTS transformer was done at 65 K. Fig. 6 shows the experiment setup of 1 MVA-HTS transformer. The AC loss at the rated current was measured by the calorimetric method. Table 3 shows the comparison between the calculated result and the measurement results. The total of calculated AC loss is about 2.5 times larger than the measured one; they were different because of several reasons. The AC losses by perpendicular magnetic fields are calculated by the strip model, and those by parallel field are calculated by the slab model. But these models are used for analyzing a single tape model. The secondary windings in HTS transformer are wound by four HTS tapes in parallel. And we estimated that our analysis method
In this paper, the magnetic field calculation is carried out to analyze the AC loss of 1 MVA-HTS transformer. The AC losses of HTS transformer was calculated by the electromagnetic analysis. The calculated AC loss and measured AC loss of 1 MVA-HTS transformer are compared. The calculated value is higher than the measurement result. To improve the analysis technique, we will carry out research on the model which composed of multiple HTS tapes and analysis method. Acknowledgement This research was supported by a grant from Center for Applied Superconductivity Technology of the 21st Century Frontier R&D Program funded by the Ministry of Education, Science and Technology, Republic of Korea. References [1] S.P. Metha, N. Aversa, M.S. Walker, IEEE Spectrum 34 (1997) 34. [2] W.S. Kim, J. H Han, S.H. Kim, IEEE Trans. Appl. Supercond. 14 (2004) 904. [3] J. Choi, S. Lee, M. Park, W. Kim, S. Kim, J. Han, H. Lee, K. Choi, Physica C 463–465 (2007) 223. [4] J.K. Lee, S.W. Lee, M. Park, G. Cha, IEEE Trans. Appl. Supercond. 14 (2004) 630.