# Experimental Study for the Assessment of the Measurement Uncertainty Associated with Electric Powertrain Efficiency Using the Back-to-Back Direct Method

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. General Description

#### 2.2. Experimental Setup

#### 2.3. Experimental Procedure

#### 2.4. Forward and Regenerative Mode Efficiency and Efficiency Uncertainty

_{i}) represents the standard uncertainty associated to the measurement of the quantity q

_{i}.

## 3. Results and Discussion

#### 3.1. Power Train Forward-Mode and Regenerative-Mode Efficiencies ${}^{b}\eta _{m}$ and ${}^{m}\eta _{b}$

#### 3.2. Forward-Mode Efficiencies of the Motor and Driver ${}^{d}\eta _{m}$ and ${}^{b}\eta _{d}$

#### 3.3. Regenerative-Mode Efficiencies of the Motor and Driver ${}^{m}\eta _{d}$ and ${}^{d}\eta _{b}$

#### 3.4. Efficiency Uncertainty

## 4. Simulation of an Urban Driving Cycle

_{i}is a random variable from a rectangular distribution, limited to the range of −1,1. This means that the efficiency map for the ith run was always over-estimated or under-estimated. As mentioned previously, we chose such a conservative hypothesis because of the absence of information on the characteristics of the error sources.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Graphical description of the five hybridization schemes from P0 to P5, considering the different positioning of the electrical machines in the powertrain of the vehicle.

**Figure 2.**Electric motors are the powertrain of the Hi-Quad quadricycle, and they are placed inside the rear wheels. The inverters are inside the metal box behind the two seats, the battery pack is divided into two parts, and they are inside the aluminum packages that are located underneath the seats.

**Figure 4.**From the top: current, speed, and torque signals related to the torque controlled motor during one of the tests. The figure shows the typical steady-state condition achieved by the electrical and mechanical signals during the measurement phase.

**Figure 5.**Voltage waveforms: the averaged signal and the Discrete Fourier Transform (DFT) signal are reported for each phase. One phase is red and the other one is blue, and the amplitudes are equal to 2% of accuracy, and the voltage profiles are 120° out of phase with the same accuracy.

**Figure 6.**Current waveforms: one phase is red and the other one is blue. The amplitudes are equal to 2% of accuracy, and the current profiles are 120° out of phase with the same accuracy.

**Figure 11.**Forward mode efficiency (expanded) uncertainty U$\left({}^{b}\eta _{m}\right)$ associated with driver 1 and motor 1.

**Figure 12.**Urban Driving Cycle (UDC) velocity profile, limited to 45 km/h: the driving cycle consists of three steps of acceleration and deceleration actions.

**Figure 13.**Block diagram of the UDC simulation: electrical/mechanical quantities reported inside the red boxes were evaluated experimentally.

Operating Condition | Voltage Range for Gen4 36/48V Controller |
---|---|

Conventional working voltage range | 25.2 V to 57.6 V |

Working voltage limits | 19.3 V to 69.6 V |

Non-operational overvoltage limits | 79.2 V |

Quantity | Device | Accuracy | Distribution |
---|---|---|---|

Torque | Torque meter | ±0.1% reading | 2 |

DS1104 | ±0.1% reading | 2 | |

Speed | Inverter | ±1 rpm reading | √3 |

DC voltage and DC current | DAQ NI 9206 | ±0.1% full scale | 2 |

Shunt resistor | ±0.25% reading | √3 | |

AC motor current | Oscilloscope | ±3% reading | √3 |

Clamp meter | ±3% reading ± 50 mA full scale | √3 | |

AC motor voltage | Oscilloscope | ±3% reading | √3 |

Differential probe | ± 2% full scale | √3 |

**Table 3.**Uncertainty associated with the measured and estimated efficiencies that are available in the literature. Only a few studies involving asynchronous motors, computed the uncertainty associated with the efficiency.

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**MDPI and ACS Style**

De Santis, M.; Agnelli, S.; Patanè, F.; Giannini, O.; Bella, G.
Experimental Study for the Assessment of the Measurement Uncertainty Associated with Electric Powertrain Efficiency Using the Back-to-Back Direct Method. *Energies* **2018**, *11*, 3536.
https://doi.org/10.3390/en11123536

**AMA Style**

De Santis M, Agnelli S, Patanè F, Giannini O, Bella G.
Experimental Study for the Assessment of the Measurement Uncertainty Associated with Electric Powertrain Efficiency Using the Back-to-Back Direct Method. *Energies*. 2018; 11(12):3536.
https://doi.org/10.3390/en11123536

**Chicago/Turabian Style**

De Santis, Michele, Sandro Agnelli, Fabrizio Patanè, Oliviero Giannini, and Gino Bella.
2018. "Experimental Study for the Assessment of the Measurement Uncertainty Associated with Electric Powertrain Efficiency Using the Back-to-Back Direct Method" *Energies* 11, no. 12: 3536.
https://doi.org/10.3390/en11123536