# Multi-Inverter Linear Motor Based Vehicle Propulsion System for a Small Cargo Transportation

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## Abstract

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## 1. Introduction

## 2. Transportation System with Long Stator Linear Motor

- Stationary system—the track infrastructure;
- Mobile system—the vehicle and its appliance.

- Increased requirement for stator insulation breakdown voltage;
- Worse availability of high voltage semiconductor elements;
- Increased requirement for power converter output voltage;
- Complicated construction;
- Decreased power factor;
- Decreased efficiency;
- Increased drive system cost.

- Increased coverage factor understood as the ratio of mover length to the length of the supplied stator;
- Cost reduction by decreasing the required converter power.

#### 2.1. Single Inverter System

#### 2.2. Multi-Inverter System

## 3. Multi-Level Multi-Inverter System

## 4. Simulation Study

## 5. Experimental Study

## 6. Conclusions

## 7. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Theoretical characteristic of the linear motor power factor in relation to segment length.

**Figure 5.**Characteristics of ${k}_{F}$ in relation to ${L}_{\mathrm{seg}}$ for various (

**a**) ${v}_{\mathrm{veh}}$ and (

**b**) ${T}_{\mathrm{off}}$.

**Figure 13.**Example operation of the transportation system—simulation results. (

**a**) commanded and vehicle speed, (

**b**) thrust and resistant force, (

**c**) inverter 1 output current components in the $dq$ frame, (

**d**) inverter 2 output current components in the $dq$ frame.

**Figure 14.**Thrust genereation during vehicle movement at the stator segment-to-segment connection—simulation results. (

**a**) thrust generated by the stator fed by inverter 1, (

**b**) thrust generated by the stator fed by inverter 2, (

**c**) phase current of inverter 1, (

**d**) phase current of inverter 2.

**Figure 18.**Experimental results for single-inverter configuration, left column—acceleration, right column—deceleration.

**Figure 19.**Experimental results for dual-inverter configuration, left column—acceleration, right column—deceleration.

**Figure 20.**DC circuit analysis in single-inverter configuration—experimental results, (

**a**) inverter 1 output current, (

**b**) inverter 2 output current, (

**c**) inverter 1 DC voltages, (

**d**) inverter 2 DC voltages.

**Figure 21.**DC circuit analysis in dual-inverter configuration—experimental results, (

**a**) inverter 1 output current, (

**b**) inverter 2 output current, (

**c**) common DC circuit voltages, (

**d**) current between mid-points of DC circuits.

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

Max. speed | ${v}_{\mathrm{max}}$ | 100 | $\mathrm{m}$/$\mathrm{s}$ |

Vehicle weight | ${m}_{\mathrm{veh}}$ | 1500 | $\mathrm{k}$$\mathrm{g}$ |

Friction coefficient (viscous) | ${c}_{\mathrm{f}}$ | 2 | $\mathrm{N}$$\mathrm{s}$/$\mathrm{m}$ |

Rolling friction coefficient | ${c}_{\mathrm{rr}}$ | 0.005 | — |

Frontal area | ${A}_{\mathrm{F}}$ | 2 | $\mathrm{m}$ |

Drag coefficient | ${c}_{\mathrm{x}}$ | 0.35 | — |

Max. thrust | ${F}_{\mathrm{max}}$ | 10 | $\mathrm{k}$$\mathrm{N}$ |

Mover length | ${L}_{\mathrm{veh}}$ | 2.5 | $\mathrm{m}$ |

Motor type | — | PMLSM | — |

Stator resistance per meter | ${R}_{\mathrm{spu}}$ | 20 | $\mathrm{m}$$\Omega $/$\mathrm{m}$ |

Stator inductance per meter | ${L}_{\mathrm{spu}}$ | 112 | $\mathsf{\mu}$$\mathrm{H}$/$\mathrm{m}$ |

Parameter | Value | Unit |
---|---|---|

Number of inverters | 2 | — |

Inverter topology | 3-level NPC | — |

Recitfier topology | 6-pulse | — |

Switching frequency | 5 | $\mathrm{k}$$\mathrm{Hz}$ |

Max. DC voltage topology | 600 | $\mathrm{V}$ |

Max. phase current (RMS) | 70 | $\mathrm{A}$ |

Output frequency | 0–100 | $\mathrm{k}$$\mathrm{Hz}$ |

Output filter inductance | 500 | $\mathsf{\mu}$$\mathrm{H}$ |

Output filter capacitance | 50 | $\mathsf{\mu}$$\mathrm{F}$ |

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**MDPI and ACS Style**

Michalczuk, M.; Nikoniuk, M.; Radziszewski, P.
Multi-Inverter Linear Motor Based Vehicle Propulsion System for a Small Cargo Transportation. *Energies* **2021**, *14*, 4459.
https://doi.org/10.3390/en14154459

**AMA Style**

Michalczuk M, Nikoniuk M, Radziszewski P.
Multi-Inverter Linear Motor Based Vehicle Propulsion System for a Small Cargo Transportation. *Energies*. 2021; 14(15):4459.
https://doi.org/10.3390/en14154459

**Chicago/Turabian Style**

Michalczuk, Marek, Marcin Nikoniuk, and Paweł Radziszewski.
2021. "Multi-Inverter Linear Motor Based Vehicle Propulsion System for a Small Cargo Transportation" *Energies* 14, no. 15: 4459.
https://doi.org/10.3390/en14154459