- Email: [email protected]
The transport current redistribution between the core layers on the models of HTS cables
Physica C 310 Ž1998. 367–371
The transport current redistribution between the core layers on the models of HTS cables P.I. Dolgosheev a , V.E. Sytnikov a
a,)
, G.G. Svalov a , N.V. Polyakova a , D.I. Belij
b
JSC ‘ VNIIKP’, 5, Shosse EntuziastoÕ, Moscow, 111024, Russian Federation b Cabix Consulting, Moscow, Russian Federation
Abstract The multilayer conductors with insulated and non-insulated layers are analyzed. The space–time current redistributions between the layers of the conductor are investigated for the next parameters: values of electric resistance at the current leads, transverse contact electric resistance between the layers, the model length, time, the conductor dimension, the current—its peak value, the change law and the ramp of the total current input. Most of the published test results for short Žfrom 1 to 10 m. conductor models do not reflect the true current distribution of the real long length cable conductors. The criterion of experimental model constructions and, in particular, the calculation of its minimum length are presented. The calculations demonstrate the electromagnetic processes in real cable conductors. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Superconducting cable; Multilayer core; Current distribution; Numerical analysis
1. Introduction It is known from last year’s papers that jump from testing the short models of HTSC cable cores to the fabrication and testing the long lengths of cables Ž; 50 m., its current carrying ability can sharply fall w1,2x. In short models, this is caused by the fact that current distribution between layers is determined mainly by electrical resistance of joints between layers and current leads, but in long models—by inductive connections between layers. In the work the influence of electrical and geometric characteristics of cable core on regularities of current distribution between layers is analyzed. In the analysis of results, the criterions are offered which allow us to
)
Corresponding author. Fax: q7-96-757-1259; E-mail: [email protected]
define minimum length modes under given conditions of current test, or choose parameters of current test, which provide reception of information on electrodynamics in long cable core models.
2. Analysis of behaviour of multilayer conductors in current tests The mathematical model for calculation of the current distribution in multilayer cable conductors is presented in our works w3–5,8x. The model was upgraded for two- to ten-layer cable cores w6x. The analysis was made for approximation of current– voltage dependence of the superconductor by power function with the electric intensity within 0.1 to 1.0 mVrcm. Figs. 1–4 display the results of analysis of influence of the different parameters for traditional conductors Žalternating twist direction from layer to
0921-4534r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 4 9 3 - 6
368
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
Fig. 1. Layer current distribution as a function of total current on insulated four layer cable core.
layer. with a twist pitch of 750 mm. The layers were assigned numbers from the inner layer to the outer one. Superconducting tape with linear density of critical current equal to 6 Armm was used in calculation. The diameter of the support element equals 40 mm. For the electrically insulated layer cores, a current distribution between the layers depends on the relationship between impedance values of the layers. It is determined by their electric and design parameters, core length and a rate of common current input to the core. In so doing, a relationship between the layer currents is constant throughout the core length. These cores are characterised by two limiting cases: R i 4 L i ld Iirdt and R i < L i ld Iird t, where lL i and R i are effective values of inductance and effective resistance of the ith layer of the core. The first case is characteristic of short models of the core and Žor. of a very slow current input. The second case is typical for long-length cable models, for fast input of direct current and for an alternating current. For electrically non-insulated layer cores current across the layers in a general case vary along the cable length depending on the number of parameters. To demonstrate these problems, we give below a brief analysis of current tests performed on two 50-m sections of cable cores of four insulated ŽFig. 1. and ten uninsulated ŽFig. 2. layers. Fig. 1 shows the results of current distribution calculation between the layers in time Žfrom 0 to 20 s. for four-layer insulated cable model at a linear law of current input at a speed of 100 Ars is taken equal to 10y9 V.
Contact specific resistance Ž s . between non-insulated layers depends on a number of factors and vary over a wide range. Fig. 2 demonstrates a distribution of currents between the layers in a 10-layer conductor along the cable length in linear current input at a speed of 100 Ars for time of 10 s for s s 10y5 V m Ža. and 10y3 V m Žb.. In experimental work w2x it was discovered that highly irregular current distribution between layers in vicinities of instrument shunts and the current distribution is similar to one that is presented by Fig. 2. As shown in Figs. 1 and 2, even at a moderate current input rate equal to 100 Ars, influence of inductive couplings between the layers is predominant on the current distribution. On testing at frequency 50–60 Hz, R i < v L i l in both cables and transport current flows in two outer layers. With the appearance of resistance in these layers, the current has no time to be redistributed, which leads to quenching. Thus, maximum current did not exceed the values of critical
Fig. 2. Layer current distribution on non-insulated ten layer cable core along cable length for ss10y5 V m Ža. and ss10y3 V m Žb..
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
369
Fig. 3. Current input rate dependence of layer current distribution at d Irdt s 10 4 Ars Ža. and 10 5 Ars Žb..
current at two outer layers and, as a result, in all the experiments with long-length cable cores Žabout 50 m. a current of 2.0 kA was not attained w1,2x. The nature of the current distribution between layers is defined by the correlation of active and inductive parts of layer impedance. Voltage on each layer is described by known correlation: Ui s R i Ii q L i Ž d Iirdt . l. Ž 1. For cables of real length the second summand is practically always more and the current distribution occurs inversely proportional to layer inductance. Obviously that during the experiments on short samples the next correlation should be kept: IirL i < l Ž d Iirdt . rR i . Ž 2. The right part of the last correlation—the three parameters can be varied during preparing and conducting an experiment. Typical value of this complex Ž10 12 –10 13 . mrV s. In experiments on short samples with non-insulated layers it is necessary to
watch the condition that time of the test cycle should be less than a constant time of own field axial diffusion. Real values of R i are within 10y7 to 10y1 0 V, while at Pi s 500–750 mm, L i values are within Ž10y9 –10y10 . Hrm. It means that for 1-m long model at d Irdt - 5 P 10 5 Ars or for AC with 50 Hz and current up to 10 3 A, a distribution of currents is determined by the R i value. Thus, a combination of values R i s 10y7 V, and L i s 10y1 0 Hrm gives an extreme value of complex Žd Irdt . l s 10y6 ŽArs. m. With 50-m long cable the extreme value of d Ird t amounts to 2 P 10 4 Ars. When a resistive section appears at least in one of the layers with the voltage range from 0.1 to 1.0 mVrcm, an effective value of electric resistance of layer ri Ž Ii . amounts to over 10y8 and 10y7 Vrm, respectively. By virtue of this fact, at R i below 10y8 V, their effect on a current realised in the experiment can be neglected. Redistribution of currents
370
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
non-uniform, and a voltage drop equal to 1.0 mVrcm occurs in the fourth layer even at a current amplitude equal to 1000 A ŽFig. 4.. It is easy to see that voltages in the third and fourth layers exceed critical values and a superconductor is in a resistive state. The currents have no time to be redistributed between the layers. In these designs, a maximum available current will be determined by a level of stabilisation and by cooling conditions. Herewith the forms of current and voltage curves are distorted, energy quality grows worse. Fig. 5 shows the results of calculation of current distributions and voltage for optimized four-layer model of conductor, type TDT Žtwo directions twisted conductor. w7x 50 m long for R i s 10y9 V at different current input laws. At rates ; 10 5 Ars for DC and also, at rates ; 10 6 Ars for AC, a superconductor in the layers is loaded by current almost uniformly. Realised value of critical
Fig. 4. Characteristics of traditional four layer cable core ŽTradvariant. as a function of time for AC Ž50 Hz. with current amplitude 2000 A.
between layers occurs at the voltage vastly smaller than widespread criterion E s 1 mVrcm. In this case Ž Ll .Žd Ird t . - ri Ž Ii . and the currents have a chance to be redistributed between the layers. However, with the further increase of the current input rate, a reduction of cable critical current Žat 1 mVrcm. is observed: at 10 4 Ars up to 2625 A and at 10 5 Ars up to 1000 A ŽFig. 3.. The foregoing holds good for ideal superconductor with Jc constant in length. However, in practice Jc value may vary along the cable length at least within "10%. Irregularity of superconductor properties may have a pronounced effect on the character of current redistribution between the layers and lead to a reduction of critical current being measured. Moreover for designs with traditional twisting a reduction of total current can exceed a degree of irregularity in the percentage ratio. During AC tests of four-layer conductors a current distribution between the layers is drastically
Fig. 5. Characteristics of optimized four layer cable core ŽTradvariant. as a function of time for AC Ž50 Hz. with current amplitude of 3000 A Ža. and a function of total current for DC Žb..
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
current equals 3000 A at a criterion of 1.0 mVrcm and ; 2700 A at a criterion of 0.1 mVrcm.
3. Conclusions Ž1. The accounting base for the analysis of experimental study results of the multilayer conductor behaviour is created. Ž2. From a diversity of possible designs of multilayer conductors Žfrom 2 to 10 layers., only ODT and TDT w7x variants provide a means of optimisation and close to 100% use of the superconductor in practical length cables. Ž3. For correct analyses of behaviour of practical cable cores the condition Ž2. must be met under current testing of short length model. Ž4. Irregularity of Jc on tape length lead to decline of current carrying ability and to decreasing a quality of sending electric power.
371
References w1x Jun Fujikami, Nobuhiro Saga, Kazuya Ohmatsu, Toshizaku Shibata, Michihiko Watanabe, Chizuru Suzawa, Shigeki Isojima, Ken-ichi Sato, Hideo Ishii, Shoichi Honjo, Tsukushi Hara, ICEC 16rICMC, Part 2, Kitakyushu, Japan, 1996, p. 975. w2x S. Mukoyama, K. Miyoshi, H. Tsubouti, M. Mimura, N. Uno, Y. Tanaka, N. Ichiyanagi, H. Ishii, S. Honjo, T. Hara, ICEC16rICMC, Part 2, Kitakyushu, Japan, 1996, p. 979. w3x V.E. Sytnikov, G.G. Svalov, G.I. Meshchanov, P.I. Dolgosheev, Cryogenics 23 Ž2. Ž1983. 77. w4x V.E. Sytnikov, G.G. Svalov, I.B. Peshkov, Cryogenics 29 Ž10. Ž1989. 971. w5x V.E. Sytnikov, G.G. Svalov, P.I. Dolgosheev, Electrotechnique Ž8. Ž1983. 50. w6x P.I. Dolgosheev, V.E. Sytnikov, G.G. Svalov, N.V. Polyakova, D.I. Belij, Applied Superconductivity 2 Ž1997. 1199. w7x P.I. Dolgosheev, V.E. Sytnikov, G.G. Svalov, N.V. Polyakova, D.I. Belij, ICMC ’98 AC Loss and Stability, May, 1998 ŽPC 2.. w8x V.E. Sytnikov, P.I. Dolgosheev, G.G. Svalov, N.V. Polyakova, D.I. Belij, Cryogenics Žin press..
The transport current redistribution between the core layers on the models of HTS cables P.I. Dolgosheev a , V.E. Sytnikov a
a,)
, G.G. Svalov a , N.V. Polyakova a , D.I. Belij
b
JSC ‘ VNIIKP’, 5, Shosse EntuziastoÕ, Moscow, 111024, Russian Federation b Cabix Consulting, Moscow, Russian Federation
Abstract The multilayer conductors with insulated and non-insulated layers are analyzed. The space–time current redistributions between the layers of the conductor are investigated for the next parameters: values of electric resistance at the current leads, transverse contact electric resistance between the layers, the model length, time, the conductor dimension, the current—its peak value, the change law and the ramp of the total current input. Most of the published test results for short Žfrom 1 to 10 m. conductor models do not reflect the true current distribution of the real long length cable conductors. The criterion of experimental model constructions and, in particular, the calculation of its minimum length are presented. The calculations demonstrate the electromagnetic processes in real cable conductors. q 1998 Elsevier Science B.V. All rights reserved. Keywords: Superconducting cable; Multilayer core; Current distribution; Numerical analysis
1. Introduction It is known from last year’s papers that jump from testing the short models of HTSC cable cores to the fabrication and testing the long lengths of cables Ž; 50 m., its current carrying ability can sharply fall w1,2x. In short models, this is caused by the fact that current distribution between layers is determined mainly by electrical resistance of joints between layers and current leads, but in long models—by inductive connections between layers. In the work the influence of electrical and geometric characteristics of cable core on regularities of current distribution between layers is analyzed. In the analysis of results, the criterions are offered which allow us to
)
Corresponding author. Fax: q7-96-757-1259; E-mail: [email protected]
define minimum length modes under given conditions of current test, or choose parameters of current test, which provide reception of information on electrodynamics in long cable core models.
2. Analysis of behaviour of multilayer conductors in current tests The mathematical model for calculation of the current distribution in multilayer cable conductors is presented in our works w3–5,8x. The model was upgraded for two- to ten-layer cable cores w6x. The analysis was made for approximation of current– voltage dependence of the superconductor by power function with the electric intensity within 0.1 to 1.0 mVrcm. Figs. 1–4 display the results of analysis of influence of the different parameters for traditional conductors Žalternating twist direction from layer to
0921-4534r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 9 8 . 0 0 4 9 3 - 6
368
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
Fig. 1. Layer current distribution as a function of total current on insulated four layer cable core.
layer. with a twist pitch of 750 mm. The layers were assigned numbers from the inner layer to the outer one. Superconducting tape with linear density of critical current equal to 6 Armm was used in calculation. The diameter of the support element equals 40 mm. For the electrically insulated layer cores, a current distribution between the layers depends on the relationship between impedance values of the layers. It is determined by their electric and design parameters, core length and a rate of common current input to the core. In so doing, a relationship between the layer currents is constant throughout the core length. These cores are characterised by two limiting cases: R i 4 L i ld Iirdt and R i < L i ld Iird t, where lL i and R i are effective values of inductance and effective resistance of the ith layer of the core. The first case is characteristic of short models of the core and Žor. of a very slow current input. The second case is typical for long-length cable models, for fast input of direct current and for an alternating current. For electrically non-insulated layer cores current across the layers in a general case vary along the cable length depending on the number of parameters. To demonstrate these problems, we give below a brief analysis of current tests performed on two 50-m sections of cable cores of four insulated ŽFig. 1. and ten uninsulated ŽFig. 2. layers. Fig. 1 shows the results of current distribution calculation between the layers in time Žfrom 0 to 20 s. for four-layer insulated cable model at a linear law of current input at a speed of 100 Ars is taken equal to 10y9 V.
Contact specific resistance Ž s . between non-insulated layers depends on a number of factors and vary over a wide range. Fig. 2 demonstrates a distribution of currents between the layers in a 10-layer conductor along the cable length in linear current input at a speed of 100 Ars for time of 10 s for s s 10y5 V m Ža. and 10y3 V m Žb.. In experimental work w2x it was discovered that highly irregular current distribution between layers in vicinities of instrument shunts and the current distribution is similar to one that is presented by Fig. 2. As shown in Figs. 1 and 2, even at a moderate current input rate equal to 100 Ars, influence of inductive couplings between the layers is predominant on the current distribution. On testing at frequency 50–60 Hz, R i < v L i l in both cables and transport current flows in two outer layers. With the appearance of resistance in these layers, the current has no time to be redistributed, which leads to quenching. Thus, maximum current did not exceed the values of critical
Fig. 2. Layer current distribution on non-insulated ten layer cable core along cable length for ss10y5 V m Ža. and ss10y3 V m Žb..
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
369
Fig. 3. Current input rate dependence of layer current distribution at d Irdt s 10 4 Ars Ža. and 10 5 Ars Žb..
current at two outer layers and, as a result, in all the experiments with long-length cable cores Žabout 50 m. a current of 2.0 kA was not attained w1,2x. The nature of the current distribution between layers is defined by the correlation of active and inductive parts of layer impedance. Voltage on each layer is described by known correlation: Ui s R i Ii q L i Ž d Iirdt . l. Ž 1. For cables of real length the second summand is practically always more and the current distribution occurs inversely proportional to layer inductance. Obviously that during the experiments on short samples the next correlation should be kept: IirL i < l Ž d Iirdt . rR i . Ž 2. The right part of the last correlation—the three parameters can be varied during preparing and conducting an experiment. Typical value of this complex Ž10 12 –10 13 . mrV s. In experiments on short samples with non-insulated layers it is necessary to
watch the condition that time of the test cycle should be less than a constant time of own field axial diffusion. Real values of R i are within 10y7 to 10y1 0 V, while at Pi s 500–750 mm, L i values are within Ž10y9 –10y10 . Hrm. It means that for 1-m long model at d Irdt - 5 P 10 5 Ars or for AC with 50 Hz and current up to 10 3 A, a distribution of currents is determined by the R i value. Thus, a combination of values R i s 10y7 V, and L i s 10y1 0 Hrm gives an extreme value of complex Žd Irdt . l s 10y6 ŽArs. m. With 50-m long cable the extreme value of d Ird t amounts to 2 P 10 4 Ars. When a resistive section appears at least in one of the layers with the voltage range from 0.1 to 1.0 mVrcm, an effective value of electric resistance of layer ri Ž Ii . amounts to over 10y8 and 10y7 Vrm, respectively. By virtue of this fact, at R i below 10y8 V, their effect on a current realised in the experiment can be neglected. Redistribution of currents
370
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
non-uniform, and a voltage drop equal to 1.0 mVrcm occurs in the fourth layer even at a current amplitude equal to 1000 A ŽFig. 4.. It is easy to see that voltages in the third and fourth layers exceed critical values and a superconductor is in a resistive state. The currents have no time to be redistributed between the layers. In these designs, a maximum available current will be determined by a level of stabilisation and by cooling conditions. Herewith the forms of current and voltage curves are distorted, energy quality grows worse. Fig. 5 shows the results of calculation of current distributions and voltage for optimized four-layer model of conductor, type TDT Žtwo directions twisted conductor. w7x 50 m long for R i s 10y9 V at different current input laws. At rates ; 10 5 Ars for DC and also, at rates ; 10 6 Ars for AC, a superconductor in the layers is loaded by current almost uniformly. Realised value of critical
Fig. 4. Characteristics of traditional four layer cable core ŽTradvariant. as a function of time for AC Ž50 Hz. with current amplitude 2000 A.
between layers occurs at the voltage vastly smaller than widespread criterion E s 1 mVrcm. In this case Ž Ll .Žd Ird t . - ri Ž Ii . and the currents have a chance to be redistributed between the layers. However, with the further increase of the current input rate, a reduction of cable critical current Žat 1 mVrcm. is observed: at 10 4 Ars up to 2625 A and at 10 5 Ars up to 1000 A ŽFig. 3.. The foregoing holds good for ideal superconductor with Jc constant in length. However, in practice Jc value may vary along the cable length at least within "10%. Irregularity of superconductor properties may have a pronounced effect on the character of current redistribution between the layers and lead to a reduction of critical current being measured. Moreover for designs with traditional twisting a reduction of total current can exceed a degree of irregularity in the percentage ratio. During AC tests of four-layer conductors a current distribution between the layers is drastically
Fig. 5. Characteristics of optimized four layer cable core ŽTradvariant. as a function of time for AC Ž50 Hz. with current amplitude of 3000 A Ža. and a function of total current for DC Žb..
P.I. DolgosheeÕ et al.r Physica C 310 (1998) 367–371
current equals 3000 A at a criterion of 1.0 mVrcm and ; 2700 A at a criterion of 0.1 mVrcm.
3. Conclusions Ž1. The accounting base for the analysis of experimental study results of the multilayer conductor behaviour is created. Ž2. From a diversity of possible designs of multilayer conductors Žfrom 2 to 10 layers., only ODT and TDT w7x variants provide a means of optimisation and close to 100% use of the superconductor in practical length cables. Ž3. For correct analyses of behaviour of practical cable cores the condition Ž2. must be met under current testing of short length model. Ž4. Irregularity of Jc on tape length lead to decline of current carrying ability and to decreasing a quality of sending electric power.
371
References w1x Jun Fujikami, Nobuhiro Saga, Kazuya Ohmatsu, Toshizaku Shibata, Michihiko Watanabe, Chizuru Suzawa, Shigeki Isojima, Ken-ichi Sato, Hideo Ishii, Shoichi Honjo, Tsukushi Hara, ICEC 16rICMC, Part 2, Kitakyushu, Japan, 1996, p. 975. w2x S. Mukoyama, K. Miyoshi, H. Tsubouti, M. Mimura, N. Uno, Y. Tanaka, N. Ichiyanagi, H. Ishii, S. Honjo, T. Hara, ICEC16rICMC, Part 2, Kitakyushu, Japan, 1996, p. 979. w3x V.E. Sytnikov, G.G. Svalov, G.I. Meshchanov, P.I. Dolgosheev, Cryogenics 23 Ž2. Ž1983. 77. w4x V.E. Sytnikov, G.G. Svalov, I.B. Peshkov, Cryogenics 29 Ž10. Ž1989. 971. w5x V.E. Sytnikov, G.G. Svalov, P.I. Dolgosheev, Electrotechnique Ž8. Ž1983. 50. w6x P.I. Dolgosheev, V.E. Sytnikov, G.G. Svalov, N.V. Polyakova, D.I. Belij, Applied Superconductivity 2 Ž1997. 1199. w7x P.I. Dolgosheev, V.E. Sytnikov, G.G. Svalov, N.V. Polyakova, D.I. Belij, ICMC ’98 AC Loss and Stability, May, 1998 ŽPC 2.. w8x V.E. Sytnikov, P.I. Dolgosheev, G.G. Svalov, N.V. Polyakova, D.I. Belij, Cryogenics Žin press..