# Research on an Electromagnetic Interference Test Method Based on Fast Fourier Transform and Dot Frequency Scanning for New Energy Vehicles under Dynamic Conditions

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## Abstract

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## 1. Introduction

## 2. Framework of the Electromagnetic Interference (EMI) Test Based on Fast Fourier Transform (FFT) and Dot Frequency Scanning (DFS) for New Energy Vehicles under Dynamic Conditions

## 3. Identification Method for Accelerating, Sliding, and Braking Conditions

_{observe}. Then, we have the measured values of speed, ${V}_{\mathrm{measured}}=\left[{v}_{1},{v}_{2},\dots ,{v}_{i},\dots ,{v}_{n}\right]$, and the calculated values of acceleration, ${A}_{\mathrm{calculated}}=$$\left[{a}_{1},{a}_{2},\dots ,{a}_{i},\dots \right]$. The minimum speed in ${t}_{\mathrm{observe}}$ is ${v}_{\mathrm{min}}$, ${v}_{\mathrm{min}}=\mathrm{min}\left\{{V}_{\mathrm{measured}}\right\}$. The minimum acceleration is ${a}_{\mathrm{min}}$, ${a}_{\mathrm{min}}=\mathrm{min}\left\{{A}_{\mathrm{calculated}}\right\}$. The maximum acceleration is ${a}_{\mathrm{max}}$, ${a}_{\mathrm{max}}=\mathrm{max}\left\{{A}_{\mathrm{calculated}}\right\}$. Features of different dynamic conditions of new energy vehicles are shown in Table 1. The physical significance is as follows:

- (1)
- When the new energy vehicle is accelerating, ${a}_{i}>0$, and then ${a}_{\mathrm{min}}>0$. To avoid misjudgments, a small, positive threshold, ${a}_{\mathrm{T}\_\mathrm{acc}}$, is introduced. Therefore, ${a}_{i}\ge {a}_{\mathrm{min}}>{a}_{\mathrm{T}\_\mathrm{acc}}>0$. On the other hand, if the situation when ${a}_{\mathrm{min}}>{a}_{\mathrm{T}\_\mathrm{acc}}$ is detected, it indicates that the new energy vehicle is accelerating.
- (2)
- When the new energy vehicle is sliding, ${v}_{\mathrm{idling}}<{v}_{i}$ and ${a}_{i}<0$, then ${v}_{\mathrm{idling}}<{v}_{\mathrm{min}}\le {v}_{i}$ and ${a}_{\mathrm{max}}<0$. To avoid misjudgments, a small, negative threshold, $-{a}_{\mathrm{T}\_\mathrm{slide}}$, is introduced. Therefore, ${v}_{\mathrm{idling}}<{v}_{\mathrm{min}}\le {v}_{i}$ and ${a}_{\mathrm{max}}<-{a}_{\mathrm{T}\_\mathrm{slide}}$. On the other hand, if the situation when ${v}_{i}\ge {v}_{\mathrm{min}}>{v}_{\mathrm{idling}}$ and ${a}_{\mathrm{max}}<-{a}_{\mathrm{T}\_\mathrm{slide}}$ is detected, it indicates that the new energy vehicle is sliding.
- (3)
- When the new energy vehicle is braking, ${a}_{i}<{a}_{\mathrm{slide}}<0$, then ${a}_{i}\le {a}_{\mathrm{max}}<{a}_{\mathrm{slide}}<0$. To avoid misjudgments, a small, negative threshold, $-{a}_{\mathrm{T}\_\mathrm{brake}}$, is introduced. Therefore, ${a}_{i}\le {a}_{\mathrm{max}}<{a}_{\mathrm{slide}}-{a}_{\mathrm{T}\_\mathrm{brake}}<0$. On the other hand, if the situation when ${a}_{i}\le {a}_{\mathrm{max}}<{a}_{\mathrm{slide}}-{a}_{\mathrm{T}\_\mathrm{brake}}$ is detected, it indicates that the new energy vehicle is braking.

^{2}). According to the features of speed and acceleration, the dynamic conditions of the vehicle during the period from 0 to 43.5 s can be identified, which consist of 0~5.6 s (accelerating), 5.6~8.0 s (sliding), 8.0~9.2 s (braking), 9.2~12.3 s (sliding), 12.3~20.8 s (accelerating), 20.8~25.3 s (sliding), 25.3~27.0 s (braking), 27.3~30.5 s (sliding), 30.5~40.2 s (accelerating), and 40.2~43.5 s (sliding). Based on the features of speed and acceleration, different dynamic conditions can be identified from any group of speed and acceleration curves. In steady conditions, there is no dynamic accelerating, sliding, and braking conditions but only idling, cruising, and steady braking conditions. EMI is more in line with actual driving conditions under dynamic conditions for changing speed.

## 4. Method to Determine Characteristic Points

#### 4.1. Distribution Diagram of Characteristic Points

#### 4.2. EMI Evaluation Indexes for New Energy Vehicles under Dynamic Conditions

#### 4.3. Method to Determine Characteristic Points Based on EMI Evaluation Indexes

- (1)
- ${p}_{\mathrm{max}}\left({U}_{\mathrm{max}},{f}_{\mathrm{U}\_\mathrm{max}}\right)$, where ${U}_{\mathrm{max}}=\mathrm{max}\left\{{\mathbf{U}}_{\mathrm{suspect}}\right\}$. ${f}_{\mathrm{U}\_\mathrm{max}}$ is a frequency concerned by the EMI test for new energy vehicles under dynamic conditions.
- (2)
- When ${U}_{\mathrm{down}}$ (${U}_{\mathrm{down}}={U}_{\mathrm{T}}$) and w are constant, the larger ρ is, the more EMI that is generated by new energy vehicles. Therefore, the frequencies in the area whose ρ is larger than the threshold (especially the area whose ρ is maximum) should be included in the EMI test for new energy vehicles under dynamic conditions.

## 5. Implementations and Experiments

#### 5.1. Implementation Flow

#### 5.2. Construction of the Experimental System

#### 5.3. Experimental Process and Results

#### 5.3.1. Experiments of GA5 PHEV

#### 5.3.2. Test Results of Other Test Vehicles

#### 5.4. Comparison Among Different EMI Test Methods

## 6. Conclusions and Prospects

**Π**, ratio η, and density coefficient ρ of high-amplitude characteristic points. ${U}_{\mathrm{max}}$ is an index to evaluate extreme values. η is a comprehensive index to evaluate the overall region. And ρ is an index to evaluate the local region. The calculation formula of each index is deduced, while the physical significance of each index is expounded.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The framework of the electromagnetic interference (EMI) test based on fast Fourier transform (FFT) and dot frequency scanning (DFS) for new energy vehicles under dynamic conditions. ADC, analog to digital converter; IPC, industrial personal computer.

**Figure 2.**The schematic of the EMI test based on FFT and DFS for new energy vehicles under dynamic conditions. (

**a**) The rough sweep with FFT spectrum analysis; (

**b**) The precise sweep with FFT and DFS.

**Figure 4.**Schematic of EMI test results based on FFT for new energy vehicles under dynamic conditions.

**Figure 7.**Flow chart of the EMI test based on FFT and DFS for new energy vehicles under dynamic conditions.

**Figure 8.**The experimental system of the EMI test based on FFT and DFS for new energy vehicles under dynamic conditions.

**Figure 9.**A group of EMI test results based on FFT for new energy vehicles under dynamic conditions.

**Figure 10.**Distribution diagram of different dynamic conditions of characteristic points. (

**a**) Distribution diagram of characteristic points under accelerating conditions; (

**b**) distribution diagram of characteristic points under sliding conditions; and (

**c**) distribution diagram of characteristic points under braking conditions.

**Figure 11.**The relationship between ${U}_{\mathrm{T}}$ and ${\rho}_{\mathrm{max}}$ when $w=0.9\text{}\mathrm{MHz}$. (

**a**) The relationship between ${U}_{\mathrm{T}}$ and ${\rho}_{\mathrm{max}}$ under accelerating conditions; (

**b**) the relationship between ${U}_{\mathrm{T}}$ and ${\rho}_{\mathrm{max}}$ under sliding conditions; and (

**c**) the relationship between ${U}_{\mathrm{T}}$ and ${\rho}_{\mathrm{max}}$ under braking condition.

**Figure 12.**The relationship between w and ${\rho}_{\mathrm{max}}$ when ${U}_{\mathrm{T}}=-41.6\mathrm{dB}\mathsf{\mu}\mathrm{V}$. (

**a**) The relationship between w and ${\rho}_{\mathrm{max}}$ under accelerating conditions; (

**b**) the relationship between w and ${\rho}_{\mathrm{max}}$ under sliding conditions; and (

**c**) the relationship between w and ${\rho}_{\mathrm{max}}$ under braking conditions.

**Figure 14.**A group of EMI intensity graphs in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude. (

**a**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under accelerating conditions; (

**b**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under sliding conditions; and (

**c**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under braking conditions.

**Figure 18.**A group of EMI test results based on FFT for test vehicles under dynamic conditions. (

**a**) Test vehicle #1; (

**b**) Test vehicle #2.

**Figure 19.**A group of EMI test results based on FFT and DFS for test vehicle #1 under dynamic conditions. (

**a**) Identification results of the EMI test based on FFT and DFS; (

**b**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under accelerating conditions; (

**c**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under sliding conditions; and (

**d**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under braking conditions.

**Figure 20.**A group of EMI test results based on FFT and DFS for test vehicle #2 under dynamic conditions. (

**a**) Condition identification result of the EMI test based on FFT and DFS; (

**b**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under accelerating conditions; (

**c**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under sliding conditions; and (

**d**) EMI intensity graph in ${\rho}_{\mathrm{max}}$ area and ${f}_{\mathrm{U}\_\mathrm{max}}$ amplitude under braking conditions.

Acceleration | Sliding | Braking | |
---|---|---|---|

Features of speed and acceleration | ${a}_{i}\ge {a}_{\mathrm{min}}>{a}_{\mathrm{T}\_\mathrm{acc}}>0$ | ${v}_{\mathrm{idling}}<{v}_{\mathrm{min}}\le {v}_{i}$, ${a}_{\mathrm{max}}<-{a}_{\mathrm{T}\_\mathrm{slide}}$ | ${a}_{i}\le {a}_{\mathrm{max}}<{a}_{\mathrm{slide}}-{a}_{\mathrm{T}\_\mathrm{brake}}<0$ |

**Table 2.**The ${\rho}_{\mathrm{max}}$ and the frequency range when ${U}_{\mathrm{T}}=-41.6\text{}\mathrm{dB}\mathsf{\mu}\mathrm{V}$ and $w=0.9\text{}\mathrm{MHz}$.

Parameter | Acceleration | Sliding | Braking |
---|---|---|---|

${\rho}_{\mathrm{max}}$ (pt/MHz/dBμV) | 18.9 | 22.3 | 5.1 |

The frequency range of the area with ${\rho}_{\mathrm{max}}$ (MHz) | 20.0~20.9 | 21.0~21.9 | 21.4~22.3 |

**Table 3.**EMI evaluation indexes for different conditions of the test vehicles (The numerical value in the boxes is emphasized).

Parameter | Test Vehicle #1 | Test Vehicle #2 | ||||
---|---|---|---|---|---|---|

Accelerating (0~9.3 s) | Sliding (17.7~33.7 s) | Braking (12.5~17.7 s) | Accelerating (0s~35 s) | Sliding (35~62 s) | Braking (90~97 s) | |

${f}_{\mathrm{U}\_\mathrm{max}}$ (MHz) | 29.59 | 20.10 | 29.51 | 16.66 | 16.85 | 16.78 |

${U}_{\mathrm{max}}$ (dBμV) | −32.54 | −32.94 | −30.51 | −2.72 | −7.82 | −6.86 |

η | 0.78 | 0.67 | 0.90 | 0.94 | 0.87 | 0.87 |

The frequency range of the area with ${\rho}_{\mathrm{max}}$ (MHz) | 29.0~30.0 | 20.1~21.1 | 29.0~30.0 | 19.8~20.8 | 20.0~21.0 | 16.5~17.5 |

${\rho}_{\mathrm{max}}$/t (pt/MHz/dBμV/min) | 91.6 | 30.8 | 132.7 | 32.1 | 27.8 | 48.9 |

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**MDPI and ACS Style**

Liu, G.; Zhong, S.
Research on an Electromagnetic Interference Test Method Based on Fast Fourier Transform and Dot Frequency Scanning for New Energy Vehicles under Dynamic Conditions. *Symmetry* **2019**, *11*, 1092.
https://doi.org/10.3390/sym11091092

**AMA Style**

Liu G, Zhong S.
Research on an Electromagnetic Interference Test Method Based on Fast Fourier Transform and Dot Frequency Scanning for New Energy Vehicles under Dynamic Conditions. *Symmetry*. 2019; 11(9):1092.
https://doi.org/10.3390/sym11091092

**Chicago/Turabian Style**

Liu, Guixiong, and Senming Zhong.
2019. "Research on an Electromagnetic Interference Test Method Based on Fast Fourier Transform and Dot Frequency Scanning for New Energy Vehicles under Dynamic Conditions" *Symmetry* 11, no. 9: 1092.
https://doi.org/10.3390/sym11091092