#### Abstract

The smart grid and electric vehicles (EVs) are widely used all over the world. As the key role, the Vehicle-to-Grid (V2G) has been attracting increasing attention. The bidirectional grid-connected AC/DC converter is one of the indispensable parts in the V2G system, which can realize bidirectional power flow and meet the power quality requirements for grid. A three-phase bidirectional grid-connected AC/DC converter is presented in this paper for V2G systems. It can be used to achieve the bidirectional power flow between EVs and grid, supply reactive power compensation, and smooth the power grid fluctuation. Firstly, the configuration of V2G systems is introduced, and the mathematical model of the AC/DC converter is built. Then, for bidirectional AC/DC converters, the grid voltage feedforward decoupling scheme is applied, and the analysis of PI control strategy is proposed and the controller is designed. The system simulation model is established based on MATLAB/Simulink, and the experiment platform of the bidirectional grid-connected converter for V2G is designed in lab. The simulation and experiment results are shown, and the results evaluate the effectiveness of the model and the performance of the applied control strategy.

#### 1. Introduction

Recently, with the environmental degradation, climate change, and the shortage of fossil energy, the traditional energy costs have risen a lot. Thus, it is urgent to use new and clean energy worldwide. Plug-in Electric Vehicles (PEVs) and Electric Vehicles (EVs) have attracted increasing attention worldwide [1–3], due to the representativeness of new energy vehicles. There are a lot of advantages about EVs and PEVs, such as peak power regulating, peak load shifting, environment protection, low cost, and so on. EVs and PEVs not only can be loads in grid-to-vehicle (G2V) charge mode but also can be generators in vehicle-to-grid (V2G) discharge mode [4]. Generally, both V2G and G2V applications are suitable for “V2G.”

The power converter is unidirectional for G2V in general, which includes conventional and fast charging system. Owing to the fact that the power of typical electrical vehicles is twice higher than the average household load, the grid network will be stressed by the fast charging [5]. If the G2V charger does not employ the state-of-the-art conversion, this may lead to disturbances in grid, such as undesirable peak loads, harmonics, and low power factor [6, 7]. Thus, it is essential to support energy injection back to the grid in V2G system. Bidirectional grid-connected AC/DC converter is one of the indispensable parts in the V2G system, which can realize the sinusoidal input current and bidirectional power flow. For V2G applications, improving power density, reducing input and output current ripple, and having reactive power compensation capability are the major research directions for bidirectional AC/DC converter [8–10].

In recent years, there are different kinds of AC/DC converter topologies used in the V2G system, including single-stage single-phase and three-phase, two-stage single-phase and three-phase, ZVS inverter, and so on [11, 12]. Reference [13] presents an electrical vehicle charger that used a single-phase interleaved AC/DC boost converter. In [14], a high-performance single-phase bridgeless interleaved PFC converter is proposed. Both [13, 14] have the same function, which can reduce the battery charge and discharge current ripple, however, neither of them could work with wide output voltage. In [15, 16], unidirectional buck-boost converters with wide output voltage are proposed, which can reduce the Total Harmonic Distortion (THD) of AC current. Because of the unidirectional switches, all these converters cannot feedback the battery energy to the grid. To realize the bidirectional power flow, the AC/DC matrix converters are proposed in [17]. However, the converter is known for its large amounts of semiconductor switches and high-frequency operation, which will lead to higher cost and larger losses including switching losses and conduction losses. In [18], a current-source rectifier is shown with an auxiliary switching network. The advantages of this converter are high efficiency and achieved the bidirectional power flow, but it will reduce the battery life owing to the input current ripple. The study in [19] proposed a current-source rectifier with PWM pulse signal trilogic control method. In [20, 21], the intelligence protection technique is proposed, which can be used in the high-power grid-connected converter. The authors of [22, 23] presented the maximum current control and grid voltage full-feedforward scheme for three-phase voltage-source rectifier.

There are several different disadvantages in the topologies mentioned above when used in V2G, such as the narrow output voltage range, large losses, and high input current ripple. As an effective alternative, a three-phase bidirectional grid-connected converter for V2G system is analyzed and designed in this paper, which realized bidirectional power flow, high efficiency, unity power factor, and wide battery pack voltage range. In Section 2, the system configuration is introduced, and the mathematical models of bidirectional AC/DC and DC/DC converter are built in detail. In Section 3, the control strategies, including the grid voltage feedforward decoupling scheme, and the double closed-loop control of AC/DC converter are analyzed and designed. In Section 4, the experimental prototype is built in lab; then, the simulation and experiment results are proposed and discussed. Finally, conclusions of this paper are in Section 5.

#### 2. System Configuration and Model

##### 2.1. System Configuration

The configuration of V2G system is shown in Figure 1; the system consists of three parts, AC grid, converters, and loads. AC grid supplies original AC voltage to converters through a transformer, of which the ratio is 380:480. Converters consist of AC/DC converter and DC/DC converter. The AC/DC converters transform AC energy to DC energy. The bidirectional DC/DC converter connects the battery to the DC bus. In this paper, charging the battery is defined as positive; on the contrary, discharging is defined as negative.

##### 2.2. Modeling of Bidirectional AC/DC Converters

The topology of a three-phase voltage-source converter is shown in Figure 2. An *L* filter is used to connect to the grid and converter. The ideal AC grid source is denoted as . And denote the source current. *L* is the inductance filter, and *R* is the resistance of series *R*-*L* circuit. *C* is the DC-side capacitor. and are the DC-side voltage and current. A resistance and in series are equivalent to the DC load.

According to the KCL and KVL, the system model can be expressed as [22]where are the voltage between the three converter legs midpoint and point *N* and is the voltage between point *N* and *O*.

When switches are on and switches are off, the switching function is . When switches are on and are off, the function is . Therefore, can be defined as [22]

For a balanced three-phase system without the neutral line, the phase currents are and phase voltages are . Equation (1) can be described as [22]

Comparing to the frame, it is convenient to control the system in stationary frame. The transformation and inverse transformation of the stationary frame to frame used in this paper are defined as [23]where are the stationary frame quantities and are the quantities of stationary frame.

Applying (5) to transform (3), the converter model in frame can be described as [23]

It is no surprise that the grid voltage and current in stationary frame is sinusoidal time variable. In order to control the power flow conveniently, the synchronous frame control is employed. The transformation and its inverse transformation of frame to synchronous frame is defined as [23]where are the stationary frame quantities and are the synchronous frame quantities.

Considering (7) and (6), the model can be described as [23]

According to (9), the mathematic model of three-phase voltage-source converter in synchronous frame is shown in Figure 3.

##### 2.3. Modeling of Bidirectional DC/DC Converters

The topology of the bidirectional DC/DC converter is shown in Figure 4, which connects DC bus to battery pack. And the bidirectional H-bridge DC/DC converter will meet the wide voltage requirement of battery. The DC bus voltage of DC/DC converter is denoted as . The filter circuit consists of and .

The converter works in buck mode for charging the battery. On the contrary, the converter works in boost mode. Taking the buck mode as example, the control transfer function for the converter can be expressed as [24, 25]

Similarly, the control transfer function for the converter in boost mode can be expressed as [24, 25]where is a coefficient.

#### 3. Control Strategy

Based on the previously described model of the three-phase bidirectional grid-connected AC/DC converter with *L* filter, this section has introduced the converter control strategy. The DC bus voltage of the V2G system is the main control object. Therefore, the most widely used control strategy, the voltage outer-loop, and current inner-loop double PI control are applied in this paper. So as to improve the stability of the system, the grid voltage feedforward decoupling scheme is used.

##### 3.1. Grid Voltage Feedforward Decoupling Scheme

Obviously, cross-coupling term is in synchronous frame from the previously described model. In order to control the *d*-axis and *q*-axis current independently, decoupling method is used frequently. And the output also will be turbulent by the grid voltage. So, the grid voltage feedforward decoupling scheme is applied to the converter.

From (9), the model of synchronous frame can be described as the following equation, when and [26]:

It can be confirmed that adjusting and can obtain the AC-side voltage and . Define the reference and as [26]

The injected grid current can be described as (14) according to (13). And and are obtained as (15), when the PI regulator is used [26]:where and are the reference current of *d*-axis and *q*-axis, respectively. and are the proportional and integration coefficients. From (15), the control diagram of feedforward decoupling is shown in Figure 5 [26, 27].

Applying (15) to (12), the model in frame is obtained as [26]

From (16), there are no cross-coupling terms and grid voltage effects. Figure 6 shows the current loop control diagram of grid voltage feedforward decoupling.

In this paper, and are set to control the system reactive power and active power. The system is operating at unit power factor, so is set to 0.

##### 3.2. Current Closed-Loop Design

The inner current closed loop is used to keep the sinusoidal current input for system. It is obvious that the and current loops are similar and symmetrical. Taking the current loop as an example, the decoupling control diagram of *d*-axis current loop is shown in Figure 7. is the sample period of current loop; and are the proportional and integration coefficients of PI regulator, respectively; and is the equivalent gain of the three-phase pulse width modulated converter. In this paper, SVPWM modulation is applied, so is 1. Ignoring the grid voltage effects, the simplified inner current loop diagram can be described as in Figure 8 [28].

can be expressed as [28]

The current open-loop transfer function is [28]

When , it can be derived that [28]

Considering (18) and (19), the parameter of current loop can be calculated as follows [28]:

Similarly, the current closed-loop transfer function can be derived from open-loop transfer function, which can be expressed as

When the system switching frequency is high enough, it means that is small enough. can be omitted. Thus, the current closed-loop transfer function can be simplified as

Comparing (20) and (22), can be simplified to

From (23), the current loop can be equivalent to a first-order inertial element, where is inertial time constant. It can be concluded that the system current loop has fast dynamic response in high switch frequency.

##### 3.3. Voltage Closed-Loop Design

The voltage closed loop can keep the DC bus voltage stable and provide reference values for the current closed loop. Considering the simplified currentclose-loop transfer function, the voltage closed-loop diagram is shown in Figure 9. is the inertial time constant of voltage closed loop; and are the PI parameters of voltage loop; and is the current loop transfer function. can be expressed as [28]where is the PWM modulation ratio and is the initial phase.

In Figure 9, is time variable, which is not convenient for system design. Because the max PWM modulation ratio is 1, it is obvious that the . So, it can be replaced by a constant 0.75. At the same time, substituting the current loop transfer function, the simplified diagram of voltage closed loop is shown in Figure 10.

The voltage open-loop transfer function can be expressed as [28]where . Then, the voltage closed-loop transfer function can be expressed as

The intermediate-frequency bandwidth of the voltage loop is defined as [29]

According to the principles of the typical II system [29, 30], it can be expressed as

Considering the immunity and followability of the voltage loop, is generally set as 5. After substitution and calculation, the parameters of voltage loop are

#### 4. Simulation and Experiment Results

##### 4.1. Simulation Results

An 80 kW V2G system simulation model is established in MATLAB/Simulink. The control schemes mentioned above are applied to the AC/DC converter. And the single current closed loop is used in bidirectional DC/DC converter. System configuration is shown in Figure 1, and the detailed parameters of the converter are shown in Table 1.

The system Bode diagrams are shown in Figure 11. The proportional and integration coefficients of current PI regulator have been obtained as 2, 200, respectively, as shown in Figure 11(a). And the values of , have been selected for voltage PI regulator shown in Figure 11(b).

**(a)**

**(b)**

Figure 12 shows the converter output DC voltage waveforms with zero load. The initial voltage of converter is 570 V, and the output reference voltage is 800 V. After about 0.1 s, the output voltage is 800 V. The overshoot voltage of system is about 20 V, and the output ripple voltage is about 1 V.

Figure 13 shows the dynamic performance of three-phase bidirectional grid-connected converter. The load steps from 0 to full load, when time = 0.01s.

**(a)**

**(b)**

From Figure 13(a), drops from 800V to 747.1 V at time = 0.01 s. Then, the voltage returns to original output, which takes about 140.2 ms, and the ripple is about 1.8 V. Grid-connected currents are shown in Figure 13(b).The currents increase at time = 0.01 s and eventually stabilize at 99.77 A RMS. The Fourier analysis of grid-connected current shows that THD of the grid current is about 2.3%.

Through comparing and in Figure 13, it can be concluded that the proposed AC/DC converter works with a balanced and low THD three-phase grid-connected current, and it performs fast DC voltage regulation under full load disturbances.

Figure 14 shows the simulation results of the V2G system in charging and discharging. From time = 0 s to time = 0.25 s, the power flow of the system is negative, which indicates that the battery is discharging. From time = 0.25 s to time = 0.5 s, the power flow is positive, which indicates that the battery is charging. And the power of charge and discharge is 80 kW.

**(a)**

**(b)**

**(c)**

**(d)**

From Figure 14(a), increases from 800 V to 837.6 V at the beginning of discharging. After about 175.37 ms, restored to original output and the ripple is about 2 V. drops from 800 V to 722.5 V, when the power flow changes at time = 0.25 s. After about 200.25 ms, the voltage restored to original output. Figure 14(b) shows the battery State of Charge (SOC). From time = 0 s to time = 0.25 s, the battery is discharging. After time = 0.25 s, the battery is charging. Figures 14(c) and 14(d) depict the phase A grid-connected current and voltage. It can be observed that and are the same frequency but opposite phase, when time <0.25 s. And and are the same frequency and phase, when time >0.25 s. The current THD is 3.5%, while the battery is discharging. And the current THD is 2.23%, while the battery is charging.

The simulation results show the correctness of design in terms of high-power factor, low current harmonic distortion, and constant output voltage.

##### 4.2. Experiment Results

An 80 kW prototype is built and tested in lab, as shown in Figure 15. The AC/DC converter and DC/DC converter are both evaluated. The battery is replaced by a grid-connected converter. Table 1 shows the key parameters of system. The controller is DSP (TMS320F28335) and FPGA (XC6SLX9). The IGBT is Infineon FF450R12KT4, and the driver of IGBT is CONCEPT 2SC0435.

Figure 16 shows the converter waveforms in different conditions. The DC bus voltage and grid-connected current are shown in Figure 16(a) when the converter output with full load in charging. The is 800 V and the ripple is about 3 V. Fourier analysis is made for ; the THD of current is 1.1%. The step response waveforms are shown in Figure 16(b). It can be observed that the reference steps from 0 to full load, when time = 0.0 s. DC bus voltage drops from 800 V to 769.8 V and returns to original output, after about 178.8 ms. The system performs well in step response and full load with designed control schemes and parameters.

**(a)**

**(b)**

**(c)**

**(d)**

From Figure 16(c), before power flow reverse, the battery is charging, which means that the bidirectional AC/DC converter works under rectifier state, and the phase current THD is 1.1%. After power flow reverse, the battery is discharging, which represents that the bidirectional AC/DC converter works in inverter state.And the phase current THD is 2.1%. Before the power flow changes, the DC-bus voltage is 800V. When the power flow changes, the voltage increased about 65 V and restored to the original output voltage after 260.5 ms. From Figure 16(d), in charging, and are at the same frequency and phase. On the contrary, in discharging, the current and voltage are at the same frequency but opposite phase. As a result, the converter is stable and works well in the power flow reverse condition.

The experiment results presented here further demonstrate the effectiveness of the converter proposed in this paper.

As shown in Figure 17(a), the lowest efficiency is 86.73% with 10 kW load, and the highest efficiency is 95.98% in charge mode; the lowest and highest efficiency are, respectively, 87.71% and 95.55% in discharge mode.

**(a)**

**(b)**

**(c)**

Figure 17(b) gives the converter power factor curve in charge state and discharge state. In charging, the lowest and highest power factors are 0.986 and 0.999, respectively. In discharging, the lowest and highest power factors are 0.984 and 0.999, respectively. Form Figure 17(b), it can be shown that the converter has a unit power factor.

Figure 17(c) shows the THD of the converter. Obviously, in charging, the THD is less than 5% when the converter output power is more than 20 kW. And the lowest THD is 1.1% with full load. In discharging, the THD is less than 5% when the battery output power is more than 23 kW. And the lowest THD is 1.9% with full load. Therefore, the converter grid-connected current is low THD.

Unfortunately, both in charge and discharge modes, the efficiency, and current THD of the converter are not very good with less than 20 kW. But, under other power condition, the converter works well. It also can be concluded that the AC/DC converter and control method can be applied to the V2G system.

#### 5. Conclusions

A three-phase bidirectional grid-connected AC/DC converter for V2G system is presented in this paper. And the mathematic model of three-phase AC/DC converter in the synchronous frame is built. Since the grid current will be affected by the grid voltage distortion and the cross-coupling terms, the feedforward scheme of grid voltage is applied to the bidirectional AC/DC converter in the synchronous frame. And the PI controllers of voltage and current closed loop for the converter are designed. Finally, the model is established in MATLAB/Simulink, and the experimental prototype is built in lab. Simulation and experiment results show that the converter works well for V2G application with unity power factor, low voltage ripple, high efficiency, and low current THD.

#### Abbreviations

, : | DC voltage and current of AC/DC converter |

: | Reference value of AC/DC converter DC voltage |

, : | Battery voltage and current |

: | Reference value of battery current |

: | Grid phase voltage |

: | Grid phase current |

: | Grid inductance filter and its equivalent resistor |

: | DC-bus filter capacitor |

: | Load current of AC/DC converter |

, : | DC load and DC electromotive force |

: | Switching function of IGBT switches |

, : | Stationary frame quantities |

: | Transformation matrix of to . |

, : | Frame components of voltage |

, : | Frame current |

, : | Rotation angular velocity of frame and angular velocity of grid |

, : | Synchronous frame quantities |

: | Transformation matrix of to |

, : | Frame components of voltage |

, : | Frame current |

: | Input voltage of DC/DC converter |

: | Output capacitor of DC/DC converter |

: | Output inductor of DC/DC converter |

: | Load of DC/DC converter |

: | Coefficient of DC/DC converter |

, : | Reference value of and |

, : | Proportional and integration coefficient of PI regulator |

: | Sample period of system |

, : | PI parameters of current controller |

: | Equivalent gain of the three-phase pulse width modulated converter |

, : | Inertial time constant of voltage and current closed loop |

, : | PI parameters of voltage loop |

: | PWM modulation ratio |

: | Initial phase of grid |

: | Intermediate-frequency bandwidth of the voltage loop. |

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant no. 61673260.