# Virtual Synchronous Motor Based-Control of a Three-Phase Electric Vehicle Off-Board Charger for Providing Fast-Charging Service

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## Abstract

**:**

## 1. Introduction

## 2. Overview of System Configuration

- VSM control not only ensures inertia and damping emulation and frequency support as well as voltage control, but also make the off-board charger provide the constant-current fast charging service for the EV’s power battery.
- Double closed-loop control is in charge of stabilizing the DC bus voltage U
_{dc}.

## 3. Off-board Charger Control

#### 3.1. VSM Control

#### 3.1.1. Droop Control Based on Charging Mode

_{bat}-ω and Q-U curves is expressed in Figure 3b, in which Q-U curve remains invariable while the charging power P

_{bat}substitutes the active power of the rectifier P.

_{bat}represent the active power of the rectifier and charging power of the power battery, respectively. ω is the angular frequency. Q and U are the reactive power and the AC voltage amplitude of the rectifier. D

_{p}and D

_{q}are the frequency and voltage droop coefficients. Reference values for any given signal x are indicated by a superscript asterisk as x*.

_{bat}-ω and Q-U are given by

_{bat}* in Equation (3), as shown in Equation (5).

_{bat}is the feedback value of the real-time charging voltage of Battery, which changes with variation of state of charge (SOC) and charging current during the charging process. I

_{bat}* is the charging current reference value. The product of U

_{bat}and I

_{bat}* constitutes the charging power reference P

_{bat}*.

_{bat}* is greater than the value of the power battery capacity, i.e., ${I}_{\mathrm{bat}}^{*}\left|\mathrm{Capacity}\left(\mathrm{Ah}\right)\right|$.

_{g}. Integrating the relationships of Equation (4), Equation (6) and ω

_{g}, the new primary regulation features of the proposed VSM are shown by Equation (7).

- The rectifier is the capacity to take part in the primary regulation of the voltage and frequency in the case of steady state.
- The off-board charger feeds the power battery in the way of constant-current fast charging.

#### 3.1.2. Behaviors of the Inertia and Damping

_{e}is the electromagnetic power; P

_{m}is mechanical power; ω is electrical angular velocity of the VSM; ω* is the rated angular frequency; ω

_{g}is the grid angular frequency; θ is the power angle.

_{bat}-ω droop control (Equation (7)) to comprise a power-frequency controller, there are two setting forms depending on whether losses are considered. If the efficiency of the conversion circuit is extremely high, the losses can be ignored. The relations are defined by Equation (9).

_{bat}< I

_{bat}*. Thus, to strictly let I

_{bat}= I

_{bat}*, Equation (9) is amended as follows.

_{bat}/P. P is not only the rectifier power but also the input power of the off-board charger. P

_{bat}represents the charging power of the power battery as well as the output power of the off-board charger.

_{m}is represented by the P

_{bat}-ω droop control, and the electromagnetic power P

_{e}is denoted by real-time charging power P

_{bat}of the power battery.

_{m}of the rectifier. Electrical angle θ of the power controller and E of the excitation regulator synthesize the three-phase excitation electromotive force e

_{abc}through Equation (11).

#### 3.2. Double Closed-Loop Control

_{dc}. The post-stage DC/DC converter does not directly regulate the charging power P

_{bat}of the power battery, which is processed by pre-stage AC/DC converter.

_{ref}which is obtained by outer-loop voltage U

_{dc}control and the effective value I

_{r}of resonant current emit the PWM modulated signals D through PI control. When the battery is charged, the full-bridge resonant LLC converter is in the step-down mode. Under such circumstances, the direction of the current flowing into the battery is positive, i.e., I

_{bat}> 0, but U

_{dc-ref}− U

_{dc}< 0. Accordingly, the reference value of the inner-loop current is engendered by using U

_{dc}− U

_{dc-ref}for PI control.

## 4. Synchronous Grid Control

_{e}, Q

_{e}and ω

_{m}are output active power, output reactive power and rotor speed of the SG respectively. D

_{pg}and D

_{qg}are the droop coefficients of the synchronous grid. U

_{mg}is the SG actual output voltage u

_{gabc}amplitude.

## 5. Verification

#### 5.1. Simulation Parameters

#### 5.2. Verification Process

#### 5.2.1. Verification of the Basic Functionalities of the Proposed VSM Control

- ①
- Before 1.5 s, the power grid supplies power to 1 kVar reactive load, power battery I and power battery II.
- ②
- Off-board charger II is out of operation at 1.5 s and connects to the power grid again at 2.5 s.
- ③
- 1 kVar reactive load at the AC interface exits operation at 3.5 s.

#### 5.2.2. Comparison of Control Schemes

_{bat}* = 1.5 |Capacity| =150 A, so P

_{bat}* = I

_{bat}* × U

_{bat}= 150 U

_{bat}.

- ①
- The simulation time is 4.5 s. The grid quickly charged the power battery I with a charging current of 150 A through an off-board charger I before 1.5 s.
- ②
- Power battery II is connected to the grid through the off-board charger II at 1.5 s, but the battery II exits operation at 2.5 s. In this time range, the consumed active power of the off-board charger II is 60 kW.
- ③
- 2 kVar reactive load at the AC interface is connected to the grid at 3.5 s.

_{1}, x = a, b, c, …, h) and the blue line represents the proposed control (Denoted by x

_{2}, x = a, b, c, …, h).

_{1},b

_{1}show that the off-board charger I system does not partake in the active and reactive power regulation no matter how the loads change. In this case, the whole variations of power are entirely borne by the grid. As a result, the active power sent by the grid increases from 115 kW to 175 kW (as shown in Figure 10c

_{1}), which results in the decrease of 0.32 Hz in grid frequency (as indicated from Figure 10e

_{1}). Furthermore, From Figure 10d

_{1},f

_{1}, after 3.5 s, the reactive power emitted by grid increases from 0 Var to 2000 Var, which causes the voltage amplitude to drop from 311.159 V to 306 V.

_{2},c

_{2}that the active power of the rectifier reduces from 100 kW to 75 kW, and the power transmitted from the grid increases from 115 kW to 145 kW. The sum of these two adjustments equals the consumed active power 60 kW of the off-board charger II. Compared with traditional control, the grid frequency only declines to 0.17 Hz in Figure 10e

_{2}. In addition, aiming at the access of 2 kVar reactive load at 3.5 s, Figure 10b

_{2},d

_{2}display that the rectifier reduces the reactive absorption of 1 kVar and the grid generates 1 kVar of reactive power. According to reactive droop coefficient, the voltage amplitude of the grid is a 3.15 V declines in Figure 10f

_{2}, whose drop degree is less than traditional control. Since VSM-controlled off-board charger I is involved in the regulation of the frequency and voltage, the charging current of the power battery I is lowered in Figure 10g

_{2}during the access period of the power battery II. However, the charging current remains constant at 150 A in the traditional control of Figure 10g

_{1}. Besides, it can be observed in Figure 10h

_{2}that the post-stage closed-loop control can stabilize the DC bus voltage at a reference value of 800 V.

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison chart of the droop curves (

**a**) Traditional droop curves; (

**b**) Droop curves based on charging mode.

**Figure 8.**The influence of different inertia and damping on the active power of the rectifier (

**a**) Different inertia J; (

**b**) Different damping D.

**Figure 9.**Primary regulation of VSM (

**a**) Active power of the rectifier; (

**b**) Frequency of VSM; (

**c**) Reactive power of the rectifier; (

**d**) Voltage amplitude of VSM.

**Figure 10.**Dynamic response waveforms of the grid and off-board charger I (

**a**,

_{1}**a**) Active power of the rectifier; (

_{2}**b**,

_{1}**b**) Reactive power of the rectifier; (

_{2}**c**,

_{1}**c**) Active power of the grid; (

_{2}**d**,

_{1}**d**) Reactive power of the grid; (

_{2}**e**,

_{1}**e**) Frequency of the grid; (

_{2}**f**,

_{1}**f**) Voltage amplitude of the grid; (

_{2}**g**,

_{1}**g**) Charging current of the power battery I; (

_{2}**h**,

_{1}**h**) DC bus voltage.

_{2}Parameters | Values | |
---|---|---|

Filter parameters | The series inductance of the filter, L | 3 mH |

The series resistance of the filter, R | 0.5 Ω | |

The parallel capacitance of the filter, C | 10 μF | |

LLC converter parameters | DC side capacitance, C | 1900 μF |

Resonant inductor, L_{r} | 0.06 nF | |

Resonant capacitor, C_{r} | 34 μF | |

Excitation inductance, L_{m} | 0.24 nH | |

Transformer ratio, T | 1.4 | |

Power battery parameters | Nominal voltage | 400 V |

Rated capacity | 100 Ah | |

System parameters | Reference value of DC voltage, U_{dc-ref} | 800 V |

Resonant frequency | 35 kHz | |

Rated frequency | 50 Hz | |

AC phase voltage effective value | 220 V | |

Rectifier switching frequency | 10 kHz |

Parameters | Values | |
---|---|---|

VSM control parameters | The charging power reference of the power battery I, P_{bat}* | 150 U_{bat} |

The reactive power reference of the rectifier, Q* | 0 Var | |

The active droop coefficient of the VSM, D_{p} | 0.00009 | |

The reactive droop coefficient of the VSM, D_{q} | 0.003 | |

The virtual Inertia of the VSM, J | 0.1 | |

The virtual damping of the VSM, D | 20 | |

Grid control parameters | The active power reference of the grid, P_{e}* | 200 × 10^{3} W |

The reactive power reference of the grid, Q_{e}* | 0 Var | |

The active droop coefficient of the grid, D_{pg} | 0.00002 | |

The reactive droop coefficient of the grid, D_{qg} | 0.003 | |

The virtual Inertia of the grid, J_{g} | 0.01 |

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## Share and Cite

**MDPI and ACS Style**

Yan, X.; Li, J.; Zhang, B.; Jia, Z.; Tian, Y.; Zeng, H.; Lv, Z.
Virtual Synchronous Motor Based-Control of a Three-Phase Electric Vehicle Off-Board Charger for Providing Fast-Charging Service. *Appl. Sci.* **2018**, *8*, 856.
https://doi.org/10.3390/app8060856

**AMA Style**

Yan X, Li J, Zhang B, Jia Z, Tian Y, Zeng H, Lv Z.
Virtual Synchronous Motor Based-Control of a Three-Phase Electric Vehicle Off-Board Charger for Providing Fast-Charging Service. *Applied Sciences*. 2018; 8(6):856.
https://doi.org/10.3390/app8060856

**Chicago/Turabian Style**

Yan, Xiangwu, Jiajia Li, Bo Zhang, Zhonghao Jia, Yang Tian, Hui Zeng, and Zhipeng Lv.
2018. "Virtual Synchronous Motor Based-Control of a Three-Phase Electric Vehicle Off-Board Charger for Providing Fast-Charging Service" *Applied Sciences* 8, no. 6: 856.
https://doi.org/10.3390/app8060856