# An Optimal Control Algorithm with Reduced DC-Bus Current Fluctuation for Multiple Charging Modes of Electric Vehicle Charging Station

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## Abstract

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## 1. Introduction

- The DC-side bus current is expressed and reconstructed in various modes by analyzing the charging power and EVs’ charging mode.
- The current sum of multiple MCMs converters is calculated by current amplitude and current phase offset, and an optimization algorithm is used to control the phase deviation of different EVs charging voltage to reduce the bus current fluctuation.

## 2. DC-Bus Current Analysis of MCMs

_{DC}, U

_{dc}

_{1}, and U

_{dc}

_{2}represent the DC-link voltages; i

_{dcA}, i

_{dcB}, and i

_{dcC}are the current flowing from the positive bus to the three-phase bridge arm, respectively; I

_{A}, I

_{B}, and I

_{C}are the output current of the three-phase AC side of the inverter, respectively; C

_{1}and C

_{2}are capacitors on DC link. Figure 1c shows the LC filter and switch position between the MCMs converter and EVs. L and C are filters; J1, J2, and J3 are isolating switches.

_{K}is assumed to be the switching function of the k (k∈{A, B, C}) phase of the three-level inverter and is defined as [18]

_{k}of the AC side bridge arm neutral point relative to the DC side neutral point O is given

#### 2.1. DC Charging Mode

_{out}), output current (I

_{L}), equivalent impedance of the load (Z), and input voltage (u

_{in}) are constant, respectively. The mathematical model of DC bus current I

_{dc-bus}is given

#### 2.2. Single-Phase AC Charging Mode

_{out}; the output voltage amplitudes and the phase are defined as U

_{out}and $\theta $ respectively; the output power factor angle is defined as $\phi $;

_{out}and current i

_{L}expression are defined as

_{in}is calculated as follows:

_{K}is contained in Equation (7). Obviously, the DC bus current I

_{dc-bus}flowing into the converter contains high-frequency components related to the switching frequency. Nevertheless, the bus capacitor can filter out high-frequency components, so it is not considered.

_{in}in Formula (1), when sinusoidal pulse width modulation (SPWM) strategy is adopted, the average value in switching period of S

_{k}can be approximately expressed as:

#### 2.3. Three-Phase AC Charging Mode

_{A−in}is calculated as follows:

_{K}is contained in Equation (15). Obviously, the DC bus current I

_{dc-bus}flowing into the converter contains high-frequency components related to the switching frequency. Nevertheless, the high-frequency components can be filtered out by the bus capacitor, so it is not considered.

_{n-k}in Formulas (13) and (14), when sinusoidal pulse width modulation (SPWM) strategy is adopted, the switching function S

_{K}can be approximately expressed as [19]:

## 3. Optimal Control Algorithm

_{e}and I

_{out-I}am also 0. Additionally, when j = 0, m

_{g}and I

_{out-j}are also 0.

**a**branch by single-phase charging mode, the sum of DC-bus current I

_{dc-sum}is calculated as:

Algorithm 1 An Optimization Control Algorithm Implementation |

/*ga is the Genetic Algorithm that has been Used to Solve Optimization Problems.input:$\left[{M}_{1},{M}_{2},\cdots {M}_{n}\right]$: matrix of n amplitudes; ${M}_{n+1}$: amplitude of n+1; k: change the number of parameter variables; output: $\left[{\delta}_{1},{\delta}_{2},\cdots {\delta}_{n}\right]$: initial phase matrix of n phases;${\delta}_{n+1}$: phase of n+1;${f}_{min}$: bus current fluctuation amplitudes; $M=sort\left(\left[{M}_{1},{M}_{2},\cdots {M}_{n}\right]\right)$; /*Sort by initial amplitude; $\left[\delta ,{f}_{min}\right]=\mathrm{g}a\left(f\left({\delta}_{1},{\delta}_{2},\cdots {\delta}_{n}\right),n\right)$; /*Calculate the minimum amplitude and the corresponding phase; ${\sigma}_{n}={\mathit{arctan}}^{-1}\left(\frac{{{\displaystyle \sum}}_{i=1}^{n}{m}_{n}\mathit{cos}\left({\delta}_{n}\right)}{-{{\displaystyle \sum}}_{i=1}^{n}{m}_{n}\mathit{sin}\left({\delta}_{n}\right)}\right)$; /* Calculate the second harmonic phase of bus current; When ${M}_{n+1}$ is added; /*A new EV with single-phase AC charging mode; for z from 0 to k if $\left({{\displaystyle \sum}}_{i=0}^{n-1}{M}_{n-1}\le {M}_{n}\right)\left|\right|\left({{\displaystyle \sum}}_{i=0}^{n-1}{M}_{n-1}\ge {M}_{n}\&\&{M}_{n+1}\le 2{M}_{n}\right)$ then $\left[\delta ,{f}_{min}\right]=ga\left(f\left({\sigma}_{n-1},{\delta}_{n},{\delta}_{n+1}\right),3\right)$; k = 1; break; end if ${{\displaystyle \sum}}_{i=0}^{n-1}{M}_{n-1}\ge {M}_{n}\&\&2{M}_{n}\le {M}_{n+1}$ then $\left[\delta ,{f}_{min}\right]=ga\left(f\left({\sigma}_{n-z},{\delta}_{n-z+1},\cdots ,{\delta}_{z},{\delta}_{z+1}\right),z+2\right)$; k=z; if ${f}_{min}\to 0$ then break; end end end return matrix $\delta $, numeric ${f}_{min}$, coefficient k |

## 4. Simulation and Results

#### 4.1. DC-Bus Current Error Analysis

_{dc-bus-re}is the current by the model; i

_{dc-bus}is the current by simulation

#### 4.2. Verification of Optimal Control Algorithm

#### 4.2.1. Single-Phase Charging Mode

_{out}is 311 V; the output current amplitudes matrix I

_{out}are $\left[100,90,80,70,60\right]$ A.

_{dc-bus}are $\left[41.8,37.2,32.6,28.2,24\right]$ A. The total current amplitude without the algorithm is 163.8 A by theoretical calculation. The total current amplitude is 162 A by simulation. By comparing theoretical calculation and simulation, the error of the average current is less than 2%, as shown in Figure 5a. According to the algorithm’s calculation results, the DC-bus current phase $\delta $ and output voltage phase $\theta $ are calculated as $\left[0,4.3689,3.0258,2.2538,6.1375\right]$ and $\left[-0.1189,2.0467,1.3567,0.9526,2.8768\right]$, respectively. Additionally, DC-bus current fluctuation amplitudes f

_{min}is lower, as shown in region 1 of Figure 5b.

#### 4.2.2. Three-Phase Charging Mode

_{A}, U

_{B}and U

_{C}is 311 V, and the phase difference is $120\xb0$ in turn; the output current amplitudes matrix I

_{out}are $\left[60,50,40,30,20\right]$ A.

_{dc-bus}is $\left[46.4,38.67,30.93,23.2,15.5\right]$ A. The total current amplitude without the algorithm is 155.7 A by theoretical calculation. The total current amplitude is 157 A by simulation. The average current error is less than 2% by comparing theoretical calculation and simulation, as shown in Figure 6a. According to the calculation results of the algorithm, DC-bus current phase $\delta $ and output voltage $\theta $ are calculated as $\left[0,2.3629,4.1835,5.0910,1.5205\right]$ and $\left[0.0745,0.8498,1.4445,1.7348,0.5326\right]$, respectively.

## 5. Conclusions

- According to the high-frequency mathematical model of NPC three-level PWM converter, the method of current reconstruction of DC-bus is established in different charging mode. By comparing theoretical calculation and simulation, the average current error is less than 2% in one cycle.
- An optimization algorithm is proposed to reduce the second harmonics current of DC-bus current in single-phase charging mode and reduce the third harmonics current of DC-bus current in three-phase charging mode. When multiple vehicles are charged simultaneously, the harmonic content is reduced by superimposing multiple second and third harmonics so that the bus current is DC by theoretical calculation and simulation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Simulation Parameters | Numerical Values |
---|---|

DC bus voltage (V_{dc}) | 800 V |

output DC voltage | 600 V |

RMS of output single-phase voltage (V_{out}) | 220 V |

RMS of output three-phase voltage (V_{A}/V_{B}/V_{C}) | 220 V |

Output current (I_{out}) | <100 A |

neutral clamp capacitor (C_{1}, C_{2}) | 500 uF |

the filter inductance (L) | 2 mH |

the filter capacitance (C) | 50 uF |

the working frequency of IGBT | 5 kHz |

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**MDPI and ACS Style**

Chen, T.; Fu, P.; Chen, X.; Dou, S.; Huang, L.; He, S.; Wang, Z.
An Optimal Control Algorithm with Reduced DC-Bus Current Fluctuation for Multiple Charging Modes of Electric Vehicle Charging Station. *World Electr. Veh. J.* **2021**, *12*, 107.
https://doi.org/10.3390/wevj12030107

**AMA Style**

Chen T, Fu P, Chen X, Dou S, Huang L, He S, Wang Z.
An Optimal Control Algorithm with Reduced DC-Bus Current Fluctuation for Multiple Charging Modes of Electric Vehicle Charging Station. *World Electric Vehicle Journal*. 2021; 12(3):107.
https://doi.org/10.3390/wevj12030107

**Chicago/Turabian Style**

Chen, Tao, Peng Fu, Xiaojiao Chen, Sheng Dou, Liansheng Huang, Shiying He, and Zhengshang Wang.
2021. "An Optimal Control Algorithm with Reduced DC-Bus Current Fluctuation for Multiple Charging Modes of Electric Vehicle Charging Station" *World Electric Vehicle Journal* 12, no. 3: 107.
https://doi.org/10.3390/wevj12030107