# The Sensitivity in Consumption of Different Vehicle Drivetrain Concepts Under Varying Operating Conditions: A Simulative Data Driven Approach

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## Abstract

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## 1. Introduction

## 2. State of the Art

#### 2.1. Vehicle Consumption Modelling

^{TM}[3,4], AVL-Cruise

^{TM}[3,4] or MATLAB/Simulink

^{TM}[5,6]. Models based on the driving resistances can be either forwards facing or backwards facing. Forwards facing models use a driver model, for example a simple PID-Controller, to follow the given driving cycle by calculating a traction demand based on the error between the set velocity and actual velocity. Backwards facing models assume that the vehicle is following the given driving cycle at each time and thus only calculate the required traction demand for this without the need of a driver model. In Reference [2], the consumption calculation based on a backwards facing powertrain model is introduced. Velocity and acceleration data in time domain is used to calculate the requested tractive torque on the side shaft by considering air drag, rolling resistance, road slope and acceleration force. An operating strategy is used to decide on the torque and energy management for a specific operating point. The operating strategy determines gear choices and the power distribution to the traction machines and thus determines requested torques and speeds at the crank shaft of the internal combustion engine and the output shaft of the electric machines. Efficiency maps are used to evaluate the losses in the traction machines and hence estimate the energy consumption in the operating points.

#### 2.2. Secondary Demand Model

#### 2.3. Studies Concerning Range/Consumption

_{2}emissions through electric energy production in the U.S., considering battery efficiency and cabin climate control. They found that at low temperatures, electric cabin heating consumes significantly more power compared to cooling down the cabin at high temperatures. At low temperatures, batteries have a lower performance resulting in a range decrease of up to 36% in cold climates.

## 3. Data Basis for the Evaluation of Vehicle’s Consumption

- The mean velocity:$${\theta}_{1}\text{}=\text{}\frac{1}{{t}_{\mathrm{end}}}{{\displaystyle \int}}_{0}^{{t}_{\mathrm{end}}}v\left(t\right)dt$$
- The variance of the velocity signal:$${\theta}_{2}\text{}=\text{}\frac{1}{{t}_{\mathrm{end}}}{{\displaystyle \int}}_{0}^{{t}_{\mathrm{end}}}{\left(v\left(t\right)\text{}-\text{}{\theta}_{1}\right)}^{2}dt$$
- The variance of the longitudinal acceleration:$${\theta}_{3}\text{}=\text{}\frac{1}{{t}_{\mathrm{end}}}{{\displaystyle \int}}_{0}^{{t}_{\mathrm{end}}}{\left(a\left(t\right)\text{}-\text{}\overline{a}\right)}^{2}dt$$
- The normalized energy demand for the air drag over the evaluation time:$${\theta}_{4}\text{}=\text{}\frac{1}{{s}_{\mathrm{tot}}}{{\displaystyle \int}}_{t\in {\tau}_{\mathrm{acc}}}^{{t}_{\mathrm{end}}}v{\left(t\right)}^{3}dt$$
- The normalized energy demand for the rolling resistance over the evaluation time:$${\theta}_{5}\text{}=\text{}\frac{1}{{s}_{\mathrm{tot}}}{{\displaystyle \int}}_{t\in {\tau}_{\mathrm{acc}}}^{{t}_{\mathrm{end}}}v\left(t\right)\text{}dt$$
- The normalized energy demand for the acceleration resistance over the evaluation time:$${\theta}_{6}\text{}=\text{}\frac{1}{{s}_{\mathrm{tot}}}{{\displaystyle \int}}_{t\in {\tau}_{\mathrm{acc}}}^{{t}_{\mathrm{end}}}a\left(t\right)\text{}v\left(t\right)\text{}mdt$$

## 4. Vehicle Model

#### 4.1. Primary Consumption Model

^{TM}. The lateral and vertical dynamics of the vehicle are not considered, assuming that they have a neglectable effect on the vehicle consumption. Using a backwards facing model, as stated in Section 2.1, avoids the necessity of having a driver model. A driving resistance equation is used to calculate the required torque and rotational speed at the wheels for a given driving cycle and vehicle parameters. An efficiency map based modelling of the drivetrain is then applied to allow for an accurate estimation of the required energy demand. A brake specific fuel consumption (BSFC) map and an efficiency map taken from literature are used for the internal combustion engine (ICE) and electrical traction machine (EM), respectively, to model the losses in the machines as a function of torque and speed. The BSFC map is taken from ADVISOR model data [18], the efficiency map of the EM is based on measurements of a real machine [19,20]. For the multiple speed transmissions (ICEV and PHEV) and the single speed transmission (BEV), constant efficiencies are defined. The battery is likewise modelled with a constant charging and discharging efficiency. This approach yields a good trade-off between consumption estimation accuracy and computational effort.

#### 4.2. Secondary Consumption Model

## 5. Results

#### 5.1. Internal Combustion Engine Vehicle

#### 5.2. Battery Electric Vehicle

#### 5.3. Plug-In Hybrid Electric Vehicle

_{2}reduction having the increasing percentage of renewable energies on the energy mix in mind.

## 6. Summary

_{2}-emissions, it is mandatory to assess the vehicles CO

_{2}-emissions in an analysis with extended system boundaries that depict the real world usage. By doing so, it is assured that efforts to reduce greenhouse gas emissions are effective. That is why the dependency of the consumption on external parameters needs to be analysed. In this contribution, the authors present a method to analyse the consumption of different drivetrain concept vehicles, namely a BEV, a PHEV and an ICEV, under extended system boundaries.

_{2}-emissions, fleet representative driving conditions including the real driving behaviour and external operating conditions have to be considered. From the authors view, this should be done by defining an approach to generate a more realistic procedure for the consumption evaluation of different drivetrain concepts by simultaneously investigating the energy demand of drivetrain concepts under all operating conditions and their frequency of occurrence. In this way, the sensitivity of the drivetrain concepts would be incorporated. For doing so, the approach within this contribution should be further extended to enable a quantitative comparison of the consumption of different drivetrain concepts under equal but realistic operating conditions. This can be done by using larger datasets for the cycle generation and considering the trip distances of the GPS tracks. Additionally, the HVAC and thermodynamic cabin models should be further developed and validated experimentally. For a quantitative comparison, the main drivetrain parameters chosen for the investigation of the different vehicle concepts have to be optimized to yield minimal total CO

_{2}emissions while still fulfilling all of the requirements on the vehicle.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Database of driving data used for this study as an input for the cycle synthesis procedure [16]. In (

**a**), the considered tracks from the region around the cities of Darmstadt and Frankfurt in Germany are illustrated. In (

**b**), the occurrence frequency of driving states in the velocity-acceleration plane is plotted.

**Figure 3.**On the

**left**, the error distributions regarding the criteria set θ of the 10,000 synthesized cycles are displayed for each trip distance. There is a bigger variation in cycle quality for shorter trips because it is more difficult to satisfy all evaluation criteria in this case. On the

**right**, the best cycles for each trip distance and the corresponding errors are displayed, which correspond to the best value of the error distribution on the left from the same row.

**Figure 4.**Exemplary outputs of the primary consumption model for the plug-in hybrid electric vehicle (PHEV) on a representative driving cycle with a trip distance of 100 km. In (

**a**), the time-resolved graphs of vehicle velocity, gear, internal combustion engine (ICE) and electrical traction machine (EM) torques, state of charge (SOC) are shown. In (

**b**) and (

**c**), the chosen operating points of ICE and EM, with the corresponding operation conditions including boosting and shifting, are shown in the brake specific fuel consumption (BSFC) and efficiency maps, respectively.

**Figure 5.**The figure shows the fuel consumption in dependency of ambient temperature and trip distance for an ICEV. It shows that the overall dependency in temperature is small at a maximum derivation of 5.5% whilst the dependency in trip distance of 1.9% is even lower. The WLTP consumption without secondary energy demands is simulated at 4.17 l/100 km and is thus at least 20.6% lower.

**Figure 6.**The figure shows the electricity consumption in dependency of ambient temperature and trip distance for a BEV. It shows that the overall dependency in trip distance is higher than in case of an ICEV at a maximum derivation of 11.0% whilst the dependency in ambient temperature is even higher at a maximum of 22.7%. The WLTP electricity consumption without secondary energy demands is simulated at 12.9 kWh/100 km and is thus at least 35.5% lower.

**Figure 7.**The figure shows the electricity (

**a**) as well as the fuel (

**b**) consumption as a function of ambient temperature and trip distance for the PHEV. Since the operating strategy tries to fully deplete the battery, the electrical energy consumption is highly sensitive to trip distance. Below the electrical range of the vehicle, the electric consumption is much higher and shows a strong dependency on ambient temperature, similar to the BEV. Above the electrical range, the electric consumption is almost constant with respect to ambient temperature but decreases with higher trip distances because of the increasing use of fuel.

**Table 1.**Exemplary calculation of the overall error of the best synthesized cycle at a trip distance of 80 km for all single criteria ${\theta}_{i}$ and the criteria set θ. The results of all error calculations are presented in Figure 3.

Criteria | Profile | Single Cycle | Error |
---|---|---|---|

${\theta}_{1}$ | 23.067 | 22.987 | 0.3% |

${\theta}_{2}$ | 150.481 | 150.233 | 0.1% |

${\theta}_{3}$ | 0.2084 | 0.2105 | 1.0% |

${\theta}_{4}$ | 577.369 | 582.641 | 0.9% |

${\theta}_{5}$ | 0.584 | 0.587 | 0.5% |

${\theta}_{6}$ | 0.1223 | 0.1236 | 0.1% |

θ | 0.66% |

Main Parameters | ICEV | BEV | PHEV |
---|---|---|---|

ICE power in kW | 96 | ~ | 85 |

EM power in kW | ~ | 300 | 120 |

Battery capacity in kWh | ~ | 60 | 20 |

Number of gears | 7 | 1 | 7 |

Total mass in kg | 1109 | 1635 | 1358 |

Necessary starting torque in Nm | 1656 | 2442 | 2028 |

Typical electrical power rating of HVAC system in W [24] | 400–2000 | 6000 | 3500 |

**Table 3.**Heating ventilation and air conditioning (HVAC) technology depending on vehicle concepts where hooks in brackets (✓) are not considered within this work.

HVAC Technology | ICEV | BEV | PHEV |
---|---|---|---|

Heat exchanger heating | ✓ | ✕ | ✓ |

PTC element heating | (✓) | ✓ | ✓ |

Heat pump heating | ✕ | (✓) | ✕ |

Heat pump cooling | ✓ | ✓ | ✓ |

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**MDPI and ACS Style**

Jardin, P.; Esser, A.; Givone, S.; Eichenlaub, T.; Schleiffer, J.-E.; Rinderknecht, S.
The Sensitivity in Consumption of Different Vehicle Drivetrain Concepts Under Varying Operating Conditions: A Simulative Data Driven Approach. *Vehicles* **2019**, *1*, 69-87.
https://doi.org/10.3390/vehicles1010005

**AMA Style**

Jardin P, Esser A, Givone S, Eichenlaub T, Schleiffer J-E, Rinderknecht S.
The Sensitivity in Consumption of Different Vehicle Drivetrain Concepts Under Varying Operating Conditions: A Simulative Data Driven Approach. *Vehicles*. 2019; 1(1):69-87.
https://doi.org/10.3390/vehicles1010005

**Chicago/Turabian Style**

Jardin, Philippe, Arved Esser, Stefano Givone, Tobias Eichenlaub, Jean-Eric Schleiffer, and Stephan Rinderknecht.
2019. "The Sensitivity in Consumption of Different Vehicle Drivetrain Concepts Under Varying Operating Conditions: A Simulative Data Driven Approach" *Vehicles* 1, no. 1: 69-87.
https://doi.org/10.3390/vehicles1010005