# Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency

^{*}

## Abstract

**:**

## 1. Introduction

- “wheel-to-distance” optimization
- “tank-to-distance” optimization
- minimization of ${a}^{2}$

- To formulate an online capable optimization of vehicle speed and powertrain operation for different electric powertrain topologies, taking realistic motor efficiency into account.
- To compare the optimization to a quadratic representation of the electrical power and to the minimization of acceleration, which are widely used in literature.
- To verify the optimization by a DP algorithm.

## 2. Methods

#### 2.1. Eco-Driving-Algorithm

#### 2.2. Algorithm in Car-Following

#### 2.3. Dynamic Programming

#### 2.4. Case Studies

## 3. Results

#### 3.1. Comparison of Fits

#### 3.2. Comparison of Algorithms

#### 3.3. Comparison of Powertrain Topologies

#### 3.4. Sensitivity Analysis: Energy-Efficiency vs. Jerk

#### 3.5. Car-Following

## 4. Discussion

#### 4.1. Discussion of Results

#### 4.2. Numerical Proof of Global Optimality

#### 4.3. Limitations and Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

1M1G | Topology with one motor and single-speed transmission |

1M2G | Topology with one motor and two-speed transmission |

2M1G | Topology with one motor and single-speed transmission at each axle |

C2C | City-to-city scenario |

CAV | Connected autonomous vehicle |

CVT | Continuously variable transmission |

DP | Dynamic Programming |

HEV | Hybrid electric vehicle |

IM | Induction motor |

LUT | Look-up table |

MPC | Model Predictive Control |

NLP | Nonlinear programming |

OCP | Optimal Control Problem |

P&G | Pulse and Glide |

PMSM | Permanent magnetic synchronous motor |

WLTP | Worldwide harmonized light-vehicles test procedure |

## Appendix A

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**Figure 2.**Comparison of different optimization methods for a 1M1G topology (

**a**) speed profiles (

**b**) energy savings to ${a}^{2}$ minimization.

**Figure 3.**Comparison of different topologies with Poly 6 × 6 (

**a**) speed profiles (

**b**) energy consumption.

**Figure 4.**Comparison of different topologies with Poly 1 × 2 (

**a**) speed profiles (

**b**) energy consumption.

**Figure 7.**Optimized speed profiles for different topologies and original worldwide harmonized light vehicles test procedure (WLTP).

**Figure 8.**Comparison of Dynamic Programming (DP) and nonlinear programming (NLP) for city to city (C2C) scenario.

Parameter | C2C | Car-Following |
---|---|---|

Initial acceleration | 0 m/s^{2} | 0 m/s^{2} |

Final acceleration | 0 m/s^{2} | 0 m/s^{2} |

Initial velocity | 50 m/s | 0 m/s |

Final velocity | 50 m/s | 0 m/s |

Final time | 100 s | - |

Final distance | 2500 m | - |

Minimal velocity | 40 km/h | v${}_{\mathrm{lv}}$ − 18 km/h |

Maximal velocity | 120 km/h | v${}_{\mathrm{lv}}$ + 18 km/h |

Min./max. jerk | ±0.9 m/s^{3} | ±0.9 m/s^{3} |

Min. acceleration | −3.5 m/s^{2} | −3.5 m/s^{2} |

Max. acceleration | 2 m/s^{2} | 2 m/s^{2} |

Minimal time gap | - | 1.5 s |

Maximal time gap | - | 3.5 s |

Reference time gap | - | 2.5 s |

Max. distance at stand still | - | 5 m |

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

m | 1320 | kg | [35] |

$\lambda $ | 1.05 | - | Estimated |

r | 0.35 | m | [35] |

${A}_{\mathrm{a}}$ | 2.8 | m^{2} | - |

${c}_{\mathrm{a}}$ | 0.29 | - | [35] |

${f}_{\mathrm{r}}$ | 0.01 | - | Estimated |

${P}_{1,\mathrm{max}}$ | 125 (PMSM) | kW | [35] |

${T}_{\mathrm{T}1}=-{T}_{\mathrm{B}1}$ | 250 | Nm | [35] |

${i}_{\mathrm{gb}11}$ | 9.665 | - | [35] |

${\eta}_{\mathrm{gb}11}$ | 0.95 | - | Estimated |

${i}_{\mathrm{gb}12}$ | 3 | - | - |

${\eta}_{\mathrm{gb}12}$ | 0.96 | - | Estimated |

${m}_{2.\mathrm{gear}}$ | 20 | kg | Estimated |

${P}_{2,\mathrm{max}}$ | 36 (IM) | kW | - |

${T}_{\mathrm{T}2}=-{T}_{\mathrm{B}2}$ | 110 | Nm | - |

${i}_{\mathrm{gb}21}$ | 5 | - | - |

${\eta}_{\mathrm{gb}21}$ | 0.96 | - | Estimated |

${m}_{2.\mathrm{motor}}$ | 80 | kg | Estimated |

Experiment (Section) | Algorithm | ${\mathit{w}}_{\mathbf{j}}$ | ${\mathit{w}}_{\mathbf{a}}$ | ${\mathit{w}}_{\mathbf{E}}$ | ${\mathit{w}}_{\mathbf{r}}$ | ${\mathit{w}}_{\mathbf{scm}}$ | ${\mathit{w}}_{\mathbf{scg}}$ | ${\mathit{w}}_{\mathbf{s}}$ | ${\mathit{w}}_{\mathbf{vEnd}}$ | ${\mathit{g}}_{\mathbf{j},\mathbf{g}}$$\mathbf{Active}?$ |
---|---|---|---|---|---|---|---|---|---|---|

C2C (3.2–3.4) | ${a}^{2}$ | 4 | 1 | 0 | 0 | 0.1 | 0.2 | - | - | Reference |

Poly 6 × 6/Poly 1 × 2 | 0 | 0 | ${10}^{-3}$ | 0 | 0.1 | 0.2 | - | - | Yes | |

[l]C2C-DP Comparison (4.2) | DP | 250 | 0 | ${10}^{-3}$ | 0 | 0 | 0 | - | - | No |

Poly 6 × 6 | 250 | 0 | ${10}^{-3}$ | 0 | 0.1 | 0.2 | - | - | No | |

Car-following (3.5) | Poly 6 × 6/Poly 1 × 2 | 0.15 | 0 | ${10}^{-3}$ | $5\times {10}^{-4}$ | 0.1 | 0.2 | $5\times {10}^{-3}$ | 0.1 | No |

Algorithm | 1M1G | 1M2G | 2M1G | |
---|---|---|---|---|

${a}^{2}$ | Abs. in Wh | 424.0 | 379.9 | 377.1 |

Poly 1 × 2 | Abs. in Wh | 420.2 | 421.6 | 429.2 |

Rel. difference to ${a}^{2}$ in % | −0.9 | +11 | +13.8 | |

Presented Poly 6 × 6 | Abs. in Wh | 408.8 | 377.1 | 372.8 |

Rel. difference to ${a}^{2}$ in % | −3.6 | −0.7 | −1.1 | |

Rel. difference to Poly 1 × 2 in % | −2.8 | −11.8 | −15.1 |

Algorithm/Cycle | 1M1G | 1M2G | 2M1G | |
---|---|---|---|---|

WLTP | Abs. in kWh | 3.24 | 2.95 | 3.0 |

Poly 1 × 2 | Abs. in kWh | 3.17 | 3.16 | 3.29 |

Rel. difference to WLTP in % | −2.4 | +7.2 | +9.7 | |

Presented Poly 6 × 6 | Abs. in kWh | 3.12 | 2.82 | 2.85 |

Rel. difference to WLTP in % | −3.7 | −4.5 | −5 | |

Rel. difference to Poly 1 × 2 in % | −1.4 | −10.9 | −13.4 |

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**MDPI and ACS Style**

Koch, A.; Bürchner, T.; Herrmann, T.; Lienkamp, M.
Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency. *World Electr. Veh. J.* **2021**, *12*, 6.
https://doi.org/10.3390/wevj12010006

**AMA Style**

Koch A, Bürchner T, Herrmann T, Lienkamp M.
Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency. *World Electric Vehicle Journal*. 2021; 12(1):6.
https://doi.org/10.3390/wevj12010006

**Chicago/Turabian Style**

Koch, Alexander, Tim Bürchner, Thomas Herrmann, and Markus Lienkamp.
2021. "Eco-Driving for Different Electric Powertrain Topologies Considering Motor Efficiency" *World Electric Vehicle Journal* 12, no. 1: 6.
https://doi.org/10.3390/wevj12010006