# A Simplified Model of Coaxial, Multilayer High-Temperature Superconducting Power Cables with Cu Formers for Transient Studies

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## Abstract

**:**

## 1. Introduction

## 2. Cable Modeling in PSCAD/EMTDC

_{HTS}) and the Cu-former (R

_{Cu}) layer were equal to the resistance in the normal state. Otherwise, the resistance of the HTS layer was set to the maximal value that was obtained from experimental measurements, while the resistance of the Cu-former layer was calculated by the subprocess in Figure 4b. The process in Figure 4 was executed in every time-step. The rapid rise in the former current caused a change in energy dissipation ($\Delta {J}_{i}$), resulting in an increased temperature ($\Delta T$). The resistively of the former (${\rho}_{Cu,i}$) was changed according to the increase of the temperature, which led to an increase in former resistance (${r}_{AC,i}$).

_{i}is the temperature of layer i in Kelvin; ${A}_{FE,i}$ is the former effective area; l is the cable length in meters; and ${\rho}_{Cu,i}$ is in Ωm.

^{3}; ${\mu}_{Cu}$ is the atomic mass of copper; volumetric heat capacity is in J/(Km

^{3}); and the coefficients ${a}_{n}$ are given by Table 1.

## 3. Simulation Results

#### 3.1. Validation of the High-Temperature Superconducting (HTS) Cable Model

#### 3.2. Performance of the Coaxial Multilayer HTS Cable Model

_{1}was highest. The resistance and temperature rise of the former in phase A were the smallest because the cross-section of former phase A was relatively large compared to other former layers. The resistances of formers in phase B and C were similar because they had similar geometries. However, the fault current in phase C was much larger than phase B, which resulted in a higher temperature of former phase C compared to former phase B.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Configuration of the coaxial, multilayer high-temperature superconducting (HTS) power cable; phase A consists of two HTS layers and one Cu-former layer; phase B consists of two Cu-former layers and one HTS layer; and phase C consists of one HTS layer and one Cu-former layer. The shield layer is based on copper.

**Figure 2.**Operation characteristics of the HTS cable: (

**a**) current flow into each phase in the normal state; and (

**b**) current flow into each phase in the transient state.

**Figure 4.**Calculation of the resistance and temperature of the Cu-former layer i in each simulation step: (

**a**) calculation process of the proposed model; and (

**b**) subprocess calculates ${R}_{Cu}$.

**Figure 5.**Compared results between the uses of the eighth-order interpolating polynomial and quadratic form.

**Figure 10.**Current distribution in each phase of the HTS cable: (

**a**) current in phase A that consists of one former layer (Af) and two HTS tape layers (At

_{1}and At

_{2}); (

**b**) current in phase B that consists of two former layers (Bf

_{1}and Bf

_{2}) and one HTS tape layer (Bt); (

**c**) current in phase C that consists of one former layer (Cf) and one HTS tape layer (Ct); and (

**d**) current in the shield layer.

**Figure 11.**The temperature of the Cu-former layers and the equivalent AC resistances of each phase in the HTS cable: (

**a**) temperature of the Cu-former layers; (

**b**) resistance of the former Af; (

**c**) resistances of the former Bf

_{1}and Bf

_{2}; and (

**d**) resistance of the former Cf.

**Figure 12.**AC resistances of the HTS tape layers and the equivalent resistance of each phase: (

**a**) resistance of the HTS tape layers; and (

**b**) equivalent resistance of each phase.

Coefficient | Value | Coefficient | Value |
---|---|---|---|

${a}_{0}$ | 4.89287 | ${a}_{5}$ | −132.5425 |

${a}_{1}$ | −57.51701 | ${a}_{6}$ | 38.17399 |

${a}_{2}$ | 238.2039 | ${a}_{7}$ | −6.07962 |

${a}_{3}$ | −345.4283 | ${a}_{8}$ | 0.4118687 |

${a}_{4}$ | 275.8975 |

Parameter | Symbol | Value |
---|---|---|

Cable length | l | 3 km |

Critical current | I_{c} | 3 kA |

Resistance of HTS layer at normal state | R_{HTS_norm} | 0.00000063 Ω/m |

Resistance of HTS layer at transient state | R_{HTS_max} | 2.5 mΩ/m |

Winding pitches | L_{p} | 280 mm |

Layer thickness | t | 1 mm |

Former effective coefficient | k | 0.76 |

Density of copper | D_{Cu} | 8900 kg/m^{3} |

Relative permeability of copper | µ_{r} | 1 |

Atomic mass of copper | µ_{Cu} | 0.0635 kg/mol |

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**MDPI and ACS Style**

Nguyen, T.-T.; Lee, W.-G.; Lee, S.-J.; Park, M.; Kim, H.-M.; Won, D.; Yoo, J.; Yang, H.S.
A Simplified Model of Coaxial, Multilayer High-Temperature Superconducting Power Cables with Cu Formers for Transient Studies. *Energies* **2019**, *12*, 1514.
https://doi.org/10.3390/en12081514

**AMA Style**

Nguyen T-T, Lee W-G, Lee S-J, Park M, Kim H-M, Won D, Yoo J, Yang HS.
A Simplified Model of Coaxial, Multilayer High-Temperature Superconducting Power Cables with Cu Formers for Transient Studies. *Energies*. 2019; 12(8):1514.
https://doi.org/10.3390/en12081514

**Chicago/Turabian Style**

Nguyen, Thai-Thanh, Woon-Gyu Lee, Seok-Ju Lee, Minwon Park, Hak-Man Kim, DuYean Won, Jaeun Yoo, and Hyung Suk Yang.
2019. "A Simplified Model of Coaxial, Multilayer High-Temperature Superconducting Power Cables with Cu Formers for Transient Studies" *Energies* 12, no. 8: 1514.
https://doi.org/10.3390/en12081514