# An Approach to the Design and the Interactions of a Fully Superconducting Synchronous Generator and Its Power Converter

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## Abstract

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## 1. Introduction

## 2. Dependencies and System Design Conflicts

_{c}= 52 A. This tape width is currently the most narrow one available.

_{1}on the number of parallel branches a, because ${U}_{1}\propto \frac{1}{a}$. For a power rating in the MW range and a coil current of I

_{coil}≈ I

_{c}= 52 A, large phase voltages U

_{1}have to be expected even without a series connection of the coils inside the armature winding. Although a suitable PEC could theoretically be designed, practical issues such as component properties and device costs usually aim for a more balanced distribution of voltage and current load for a PEC, which in this case requires the parallel connection of the FSSG coils.

## 3. Design of a Fully Superconducting Synchronous Generator (FSSG)

#### 3.1. Basic Design Constraints of a 10 MW FSSG for Wind Power Plants

#### 3.2. Armature Winding

#### 3.3. Field Winding

## 4. Parameter Studies for an FSSG

#### 4.1. Parameter Study 1: Variation of the Number of Pole Pairs

#### 4.2. Parameter Study 2: Variation of the Pole Pitch

#### 4.3. Summary of Parameter Studies

## 5. Design Options for the Rectifier–Machine Interface

_{1}of a synchronous generator can be calculated according to (7). Depending on the topology of the PEC, either the peak phase voltage or the peak phase-to-phase voltage define the maximum voltage that power semiconductors inside a power rectifier are exposed to. Ignoring overvoltage events and observing (8) for the investigated FSSG concept, these peak values calculate according to (9) and (10), respectively.

#### 5.1. Rectifier-Side Possibilities

#### 5.2. Machine-Side Possibilities

## 6. Rectifier Concepts and Topologies for FSSGs

- Conventional converters that are designed for a specific conversion task and usually try to minimise the number of functional components;
- Modular or cell-based converters that combine multiple copies of a basic converter “cell” to address various conversion tasks and/or to enable a more flexible system.

#### 6.1. Conventional Converter Concepts

#### 6.1.1. Two-Level Active Rectifiers

#### 6.1.2. Three-Level Active Rectifiers

#### 6.2. Cell-Based Multi-Level Converters

#### 6.2.1. Flying Capacitor Converter

#### 6.2.2. Stacked-Multi-Cell Converter

#### 6.2.3. Modular Multi-Level Converter

#### 6.2.4. Cascaded Power Cells

#### 6.2.5. Cascaded H-Bridge Concept for the FSSG

#### 6.2.6. Realising an AC Grid Connection

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

CHB | Cascaded H-bridge | MF | Medium Frequency |

DAB | Dual Active Bridge | MMC | Modular Multilevel Converter |

FC | Flying Capacitor | MV | Medium Voltage |

HTS | High Temperature Superconductor | PEC | Power Electronic Converter |

HVDC | High-Voltage Direct Current | SMC | Stacked-Multicell Converter |

## Nomenclature

a | Number of parallel branches | ${P}_{1}$ | Real power of the generator |

${a}_{\mathrm{max}}$ | Maximum number of parallel branches | ${P}_{\mathrm{AC}}$ | AC losses in HTS tapes |

${B}_{\mathrm{t}}$ | Tangential flux density | ${P}_{\mathrm{N}}$ | Rated output power of the generator |

d | Width of the HTS tape | q | Number of slots per pole and per phase |

${f}_{1}$ | Electric frequency in the stator winding | ${S}_{1}$ | Apparent power of the generator |

${f}_{\mathrm{grid}}$ | AC grid frequency | ${s}_{\mathrm{Gen}}$ | Number of independent three-phase systems |

${I}_{1}$ | RMS phase current of the generator | ${s}_{\mathrm{PEC}}$ | Number of parallel three-phase systems per PEC |

${I}_{\mathrm{coil}}$ | Coil current | ${T}_{\mathrm{N}}$ | Rated input torque of the generator |

${I}_{\mathrm{c}}$ | Critical current of the HTS tape | ${U}_{\mathrm{Cell},\mathrm{DC},\mathrm{max}}$ | Maximum DC voltage of one power cell |

${I}_{\mathrm{PEC}}$ | Phase current of the PEC | ${U}_{\mathrm{Cell},\mathrm{DC}}$ | DC voltage of one power cell |

${l}_{\mathrm{tape}}$ | Effective length of the HTS tape | ${U}_{\mathrm{Cell},\mathrm{ph}}$ | RMS phase voltage of one power cell |

m | Number of phases | ${U}_{\mathrm{Grid},\mathrm{DC},\mathrm{max}}$ | Maximum total DC voltage with series power cell concept |

n | Rotational speed | ${U}_{\mathrm{PEC},\mathrm{DC}}$ | DC voltage of one three-phase rectifier |

${n}_{\mathrm{Cell},\mathrm{ph},\mathrm{min}}$ | Minimum number of power cells per phase | ${U}_{1}$ | RMS phase voltage of the generator |

${n}_{\mathrm{Cell},\mathrm{ph}}$ | Number of power cells per phase | ${Z}_{1}$ | Number of stator slots |

${n}_{\mathrm{Cell},\mathrm{tot}}$ | Total number of power cells | $cos\phi $ | Power factor |

${n}_{\mathrm{N}}$ | Rated rotor speed of the generator | ${\widehat{u}}_{1}$ | Amplitude of the generator phase voltage |

${n}_{\mathrm{PEC}}$ | Number of PEC | ${\widehat{u}}_{\mathrm{phase}-\mathrm{phase}}$ | Amplitude of the generator phase-to-phase voltage |

p | Number of pole pairs | ${\widehat{u}}_{\mathrm{Cell},\mathrm{ph},\mathrm{max}}$ | Maximum possible AC voltage amplitude of one power cell |

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**Figure 2.**Dependency of the AC losses, the iron mass, the inner diameter, the axial length and the total HTS tape length on the number of pole pairs.

**Figure 3.**Dependency of the phase voltage, the power factor and the inductance on the number of pole pairs.

**Figure 4.**Dependency of the AC losses, the iron mass, the inner diameter, the axial length and the total HTS tape length on the pole pitch.

**Figure 6.**Interdependencies between the power electronic rectifier and the generator design.

**Top**: Non-complete survey of available power IGBT modules (

**left**) and their working voltage capabilities (

**right**) with an assumed safety margin of 40%.

**Bottom**: Peak phase-to-phase voltages for the investigated generator concepts (

**left**) and the possible segmentation options for each concept (

**right**). A combination of these investigations, marked by the solid, dashed and dotted lines in the bottom-right graph allows the identification of technically and economically feasible generator/rectifier combination candidates.

**Figure 7.**Example topologies for active rectifiers. (

**a**) Standard B6, (

**b**) 3-Level ANPC as an example of multi-level topologies.

**Figure 8.**Proposed converter concept with a common DC voltage link for a superconducting generator with ${s}_{\mathrm{Gen}}$ three-phase systems. For the AC grid connection, a galvanic isolation is also to be ensured, which can be realised, e.g., with a grid-side transformer on system-level or, depending on the topology, by several medium frequency (MF) transformers on cell level.

**Figure 9.**(

**a**) 5-Level Flying Capacitor (FC) Converter. (

**b**) 5-Level Stacked-Multi-Cell Converter (SMC).

**Figure 10.**Topology of the Modular Multi-Level Converter (MMC) and the exemplary circuit diagram of one cell, configured as full bridge circuit.

**Figure 12.**Possible design for a single power cell, consisting of an H-bridge rectifier and an isolated DAB.

**Figure 13.**Two possible rectifier concepts. (

**a**) Each branch is connected to one three-phase rectifier; therefore, 50 A modules can be used. (

**b**) Direct parallelisation of five generator branches leads to a lower number of three-phase rectifiers but reduces the possibilities in the independent branch control. Here, 250 A modules can be used.

**Figure 14.**Total number of power cells ${n}_{\mathrm{Cell},\mathrm{tot}}$ necessary for the 10 MW FSSG depending on the number of pole pairs p and the semiconductor voltage and current rating. A current rating of 50 A corresponds to ${s}_{\mathrm{PEC}}=1$ (one three-phase rectifier for each branch), 200 A to ${s}_{\mathrm{PEC}}=4$ (one three-phase rectifier for four parallelised branches) and 250 A to ${s}_{\mathrm{PEC}}=5$ (one three-phase rectifier for five parallelised branches). A power factor of $\mathrm{cos}\left(\phi \right)=0.85$ and a HTS current of ${I}_{\mathrm{coil}}=52$ A are assumed as well as a semiconductor voltage utilisation of 60% and a current utilisation of 105% to handle the HTS current.

**Figure 15.**Proposed topology for a direct MV AC grid connection. Each power cell is extended by another H-bridge single-phase AC inverter.

**Table 1.**Exemplary options for the electric segmentation of a machine with $p=20$, ${s}_{\mathrm{Gen}}=10$ and ${I}_{\mathrm{coil}}=52$ A.

No. of PECs n_{PEC} | Parallel Three-Phase Systems per PEC S_{PEC} | PEC Phase Current I_{PEC} |
---|---|---|

1 | 10 | 520 A |

2 | 5 | 260 A |

5 | 2 | 104 A |

10 | 1 | 52 A |

**Table 2.**Total number of required power cells and corresponding maximum reachable DC link voltages for a 10 MW FSSG depending on the used semiconductor voltage class and the number of parallel connected branches. The maximum reachable voltages for the options without parallel branches, marked with ∗, are purely theoretical. In practice, several DC cells or DC three-phase rectifier outputs would be paralleled for these options.

Semiconductor Voltage Class U _{CES} | 1200 V | 1700 V | 1200 V | 1700 V |
---|---|---|---|---|

Parallel branches ${s}_{\mathrm{PEC}}$ | 1 | 1 | 5 | 5 |

Number of 3ph-rectifier ${n}_{\mathrm{PEC}}$ | 10 | 10 | 2 | 2 |

Converter RMS phase current ${I}_{\mathrm{PEC}}$ | 52 A | 52 A | 260 A | 260 A |

Min. no. of required power cells ${n}_{\mathrm{Cell},\mathrm{tot}}$ | 450 | 330 | 90 | 66 |

Max. total DC voltage ${U}_{\mathrm{Grid},\mathrm{DC},\mathrm{max}}$ | 324 kV * | 336.6 kV * | 64.8 kV | 67.32 kV |

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## Share and Cite

**MDPI and ACS Style**

Lengsfeld, S.; Sprunck, S.; Frank, S.R.; Jung, M.; Hiller, M.; Ponick, B.; Mersche, S.
An Approach to the Design and the Interactions of a Fully Superconducting Synchronous Generator and Its Power Converter. *Energies* **2022**, *15*, 3751.
https://doi.org/10.3390/en15103751

**AMA Style**

Lengsfeld S, Sprunck S, Frank SR, Jung M, Hiller M, Ponick B, Mersche S.
An Approach to the Design and the Interactions of a Fully Superconducting Synchronous Generator and Its Power Converter. *Energies*. 2022; 15(10):3751.
https://doi.org/10.3390/en15103751

**Chicago/Turabian Style**

Lengsfeld, Sebastian, Sebastian Sprunck, Simon Robin Frank, Marco Jung, Marc Hiller, Bernd Ponick, and Stefan Mersche.
2022. "An Approach to the Design and the Interactions of a Fully Superconducting Synchronous Generator and Its Power Converter" *Energies* 15, no. 10: 3751.
https://doi.org/10.3390/en15103751