# A Three-Phase Bidirectional Grid-Connected AC/DC Converter for V2G Applications

Authors: Jingang Han; Xiong Zhou; Song Lu; Pinxuan Zhao
Journal: Journal of Control Science and Engineering
 (2020)

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## 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.


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## Body

## 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. InSection 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 Figure1; 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.Figure 1
System configuration.


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

The topology of a three-phase voltage-source converter is shown in Figure2. An L filter is used to connect to the grid and converter. The ideal AC grid source is denoted as ea,eb,ec. And ia,ib,ic 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. udc and idc are the DC-side voltage and current. A resistance RL and eL in series are equivalent to the DC load.Figure 2
The circuit of bidirectional AC/DC converter.According to the KCL and KVL, the system model can be expressed as [22](1)ea=Ldiadt+Ria+uaN+uNO,eb=Ldibdt+Rib+ubN+uNO,ec=Ldicdt+Ric+ucN+uNO,Cdudcdt=idc−iL,where uaN,ubN,anducN are the voltage between the three converter legs midpoint and point N and uNO is the voltage between point N and O.When switchesSa1,Sb1,Sc1 are on and switches Sa2,Sb2,Sc2 are off, the switching function is Sk=1. When switches Sa2,Sb2,Sc2 are on and Sa1,Sb1,Sc1 are off, the function is Sk=0. Therefore, uk can be defined as [22](2)uk=ukN+uNO=Skudc+uNO,k=a,b,c.For a balanced three-phase system without the neutral line, the phase currents areia+ib+ic=0 and phase voltages are ea+eb+ec=0. Equation (1) can be described as [22](3)ea=Ldiadt+Ria+udcSa−13Sa+Sb+Sc,eb=Ldibdt+Rib+udcSb−13Sa+Sb+Sc,ec=Ldicdt+Ric+udcSc−13Sa+Sb+Sc,Cdudcdt=iaSa+ibSb+icSc−iL.Comparing to thea−b−c frame, it is convenient to control the system in stationary α−β frame. The transformation and inverse transformation of the stationary a−b−c frame to α−β frame used in this paper are defined as [23](4)xαxα=Mxaxbxc,M=231−12−1203232,(5)xaxbxc=32MTxαxβ,32MT=10−1232−1232,where xαandxβ are the stationary α−β frame quantities and xa,xb,andxc are the quantities of stationary a−b−c frame.Applying (5) to transform (3), the converter model in α−β frame can be described as [23](6)eα=Ldiαdt+Riα+Sαudc,eβ=Ldiβdt+Riβ+Sβudc,Cdudcdt=32iαSα+iβSβ−iL.It is no surprise that the grid voltage and current in stationaryα−β frame is sinusoidal time variable. In order to control the power flow conveniently, the synchronous d−q frame control is employed. The transformation and its inverse transformation of frame α−β to synchronous d−q frame is defined as [23](7)xdxq=Txαxβ,T=cosω0tsinω0t−sinω0tcosω0t,(8)xαxβ=T−1xdxq,T−1=cosω0t−sinω0tsinω0tcosω0t,where xα​andxβ are the stationary α−β frame quantities and xdandxq are the synchronous d−q frame quantities.Considering (7) and (6), the model can be described as [23](9)ed=Ldiddt+Rid−ω0Liq+Sdudc,eq=Ldiqdt+Riq+ω0Lid+Squdc,Cdudcdt=32idSd+iqSq−iL.According to (9), the mathematic model of three-phase voltage-source converter in synchronous d−q frame is shown in Figure 3.Figure 3
The model of three-phase converter in synchronousd−q frame.


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

The topology of the bidirectional DC/DC converter is shown in Figure4, 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 Vbus. The filter circuit consists of L1 and C0.Figure 4
The topology of bidirectional DC/DC converter.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](10)Gids=2VbussCo+1/RLoadL1Cos2+L1/RLoads+1.Similarly, the control transfer function for the converter in boost mode can be expressed as [24, 25](11)Gids=VbussCo+2/RLoadL1C0s2+L1/RLoads+2D′2,where D′ is a coefficient.


## 2.1. System Configuration

The configuration of V2G system is shown in Figure1; 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.Figure 1
System configuration.


## 2.2. Modeling of Bidirectional AC/DC Converters

The topology of a three-phase voltage-source converter is shown in Figure2. An L filter is used to connect to the grid and converter. The ideal AC grid source is denoted as ea,eb,ec. And ia,ib,ic 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. udc and idc are the DC-side voltage and current. A resistance RL and eL in series are equivalent to the DC load.Figure 2
The circuit of bidirectional AC/DC converter.According to the KCL and KVL, the system model can be expressed as [22](1)ea=Ldiadt+Ria+uaN+uNO,eb=Ldibdt+Rib+ubN+uNO,ec=Ldicdt+Ric+ucN+uNO,Cdudcdt=idc−iL,where uaN,ubN,anducN are the voltage between the three converter legs midpoint and point N and uNO is the voltage between point N and O.When switchesSa1,Sb1,Sc1 are on and switches Sa2,Sb2,Sc2 are off, the switching function is Sk=1. When switches Sa2,Sb2,Sc2 are on and Sa1,Sb1,Sc1 are off, the function is Sk=0. Therefore, uk can be defined as [22](2)uk=ukN+uNO=Skudc+uNO,k=a,b,c.For a balanced three-phase system without the neutral line, the phase currents areia+ib+ic=0 and phase voltages are ea+eb+ec=0. Equation (1) can be described as [22](3)ea=Ldiadt+Ria+udcSa−13Sa+Sb+Sc,eb=Ldibdt+Rib+udcSb−13Sa+Sb+Sc,ec=Ldicdt+Ric+udcSc−13Sa+Sb+Sc,Cdudcdt=iaSa+ibSb+icSc−iL.Comparing to thea−b−c frame, it is convenient to control the system in stationary α−β frame. The transformation and inverse transformation of the stationary a−b−c frame to α−β frame used in this paper are defined as [23](4)xαxα=Mxaxbxc,M=231−12−1203232,(5)xaxbxc=32MTxαxβ,32MT=10−1232−1232,where xαandxβ are the stationary α−β frame quantities and xa,xb,andxc are the quantities of stationary a−b−c frame.Applying (5) to transform (3), the converter model in α−β frame can be described as [23](6)eα=Ldiαdt+Riα+Sαudc,eβ=Ldiβdt+Riβ+Sβudc,Cdudcdt=32iαSα+iβSβ−iL.It is no surprise that the grid voltage and current in stationaryα−β frame is sinusoidal time variable. In order to control the power flow conveniently, the synchronous d−q frame control is employed. The transformation and its inverse transformation of frame α−β to synchronous d−q frame is defined as [23](7)xdxq=Txαxβ,T=cosω0tsinω0t−sinω0tcosω0t,(8)xαxβ=T−1xdxq,T−1=cosω0t−sinω0tsinω0tcosω0t,where xα​andxβ are the stationary α−β frame quantities and xdandxq are the synchronous d−q frame quantities.Considering (7) and (6), the model can be described as [23](9)ed=Ldiddt+Rid−ω0Liq+Sdudc,eq=Ldiqdt+Riq+ω0Lid+Squdc,Cdudcdt=32idSd+iqSq−iL.According to (9), the mathematic model of three-phase voltage-source converter in synchronous d−q frame is shown in Figure 3.Figure 3
The model of three-phase converter in synchronousd−q frame.


## 2.3. Modeling of Bidirectional DC/DC Converters

The topology of the bidirectional DC/DC converter is shown in Figure4, 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 Vbus. The filter circuit consists of L1 and C0.Figure 4
The topology of bidirectional DC/DC converter.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](10)Gids=2VbussCo+1/RLoadL1Cos2+L1/RLoads+1.Similarly, the control transfer function for the converter in boost mode can be expressed as [24, 25](11)Gids=VbussCo+2/RLoadL1C0s2+L1/RLoads+2D′2,where D′ is a coefficient.


## 3. Control Strategy

Based on the previously described model of the three-phase bidirectional grid-connected AC/DC converter withL 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 synchronousd−q 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 d−q frame can be described as the following equation, when ud=Sdudc and uq=Squdc [26]:(12)ud=ed−Ldiddt+ω0Liq−Rid,uq=eq−Ldiqdt−ω0Lid−Riq.It can be confirmed that adjustingid and iq can obtain the AC-side voltage ud and uq. Define the reference ud∗ and uq∗ as [26](13)ud∗=Ldiddt+Rid,uq∗=Ldiqdt+Riq.The injected grid current can be described as (14) according to (13). And ud and uq are obtained as (15), when the PI regulator is used [26]:(14)ids=1sL+Rud∗s,iqs=1sL+Ruq∗s,(15)ud=ed+ω0Liq−KP+KIsid∗−id,uq=eq+ω0Lid−KP+KIsiq∗−iq,where id∗ and iq∗ are the reference current of d-axis and q-axis, respectively. KP and KI are the proportional and integration coefficients. From (15), the control diagram of feedforward decoupling is shown in Figure 5 [26, 27].Figure 5
Control diagram of feedforward decoupling.Applying (15) to (12), the model in d−q frame is obtained as [26](16)diddt=−1LR+Kp+KIsid+1LKp+KIsid∗,diqdt=−1LR+Kp+KIsiq+1LKp+KIsiq∗.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.Figure 6
Current loop control diagram of grid voltage feedforward decoupling.In this paper,iq∗ and id∗ are set to control the system reactive power and active power. The system is operating at unit power factor, so iq∗ 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 theid and iq current loops are similar and symmetrical. Taking the id current loop as an example, the decoupling control diagram of d-axis current loop is shown in Figure 7. Ts is the sample period of current loop; KiP and KiI are the proportional and integration coefficients of PI regulator, respectively; and Kpwm is the equivalent gain of the three-phase pulse width modulated converter. In this paper, SVPWM modulation is applied, so Kpwm is 1. Ignoring the grid voltage effects, the simplified inner current loop diagram can be described as in Figure 8 [28].Figure 7
The control diagram of inner current loop.Figure 8
The simplified control diagram of inner current loop.τi can be expressed as [28](17)τi=KiPKiI.The current open-loop transfer function is [28](18)Gois=KiPKpwmRτis1.5Tss+1.Whenζ=0.707, it can be derived that [28](19)1.5TsKiPKpwmRτi=12.Considering (18) and (19), the parameter of current loop can be calculated as follows [28]:(20)KiP=Rτi3TsKpwm,KiI=KiPτi=R3TsKpwm.Similarly, the current closed-loop transfer function can be derived from open-loop transfer function, which can be expressed as(21)Gcis=11+Rτi/KiPKpwms+1.5TsRτi/KiPKpwms2.When the system switching frequency is high enough, it means thatTs is small enough. s2 can be omitted. Thus, the current closed-loop transfer function can be simplified as(22)Gcis≈11+Rτi/KiPKpwms.Comparing (20) and (22), Gcis can be simplified to(23)Gcis=11+3Tss.From (23), the current loop can be equivalent to a first-order inertial element, where 3Ts 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 Figure9. τv is the inertial time constant of voltage closed loop; Kv and Tv are the PI parameters of voltage loop; and Gcis is the current loop transfer function. K can be expressed as [28](24)0.75mcosθ≤1,where m is the PWM modulation ratio and θ is the initial phase.Figure 9
The control diagram of voltage closed loop.In Figure9, K is time variable, which is not convenient for system design. Because the max PWM modulation ratio is 1, it is obvious that the 0.75mcosθ≤1. 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.Figure 10
The simplified control diagram of voltage closed loop.The voltage open-loop transfer function can be expressed as [28](25)Govs=0.75KvTvs+1CTvs2Tevs+1,where Tev=τv+3Ts. Then, the voltage closed-loop transfer function can be expressed as(26)Gcv=11+CTvs2Tevs+1/0.75KvTvs+1.The intermediate-frequency bandwidth of the voltage loop is defined as [29](27)hv=TvTev.According to the principles of the typical II system [29, 30], it can be expressed as(28)0.75KvCTv=hv+12hv2Tev2.Considering the immunity and followability of the voltage loop,hv is generally set as 5. After substitution and calculation, the parameters of voltage loop are(29)Tv=5Tev=5τv+3Ts,Kv=4Cτv+3Ts.


## 3.1. Grid Voltage Feedforward Decoupling Scheme

Obviously, cross-coupling term is in synchronousd−q 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 d−q frame can be described as the following equation, when ud=Sdudc and uq=Squdc [26]:(12)ud=ed−Ldiddt+ω0Liq−Rid,uq=eq−Ldiqdt−ω0Lid−Riq.It can be confirmed that adjustingid and iq can obtain the AC-side voltage ud and uq. Define the reference ud∗ and uq∗ as [26](13)ud∗=Ldiddt+Rid,uq∗=Ldiqdt+Riq.The injected grid current can be described as (14) according to (13). And ud and uq are obtained as (15), when the PI regulator is used [26]:(14)ids=1sL+Rud∗s,iqs=1sL+Ruq∗s,(15)ud=ed+ω0Liq−KP+KIsid∗−id,uq=eq+ω0Lid−KP+KIsiq∗−iq,where id∗ and iq∗ are the reference current of d-axis and q-axis, respectively. KP and KI are the proportional and integration coefficients. From (15), the control diagram of feedforward decoupling is shown in Figure 5 [26, 27].Figure 5
Control diagram of feedforward decoupling.Applying (15) to (12), the model in d−q frame is obtained as [26](16)diddt=−1LR+Kp+KIsid+1LKp+KIsid∗,diqdt=−1LR+Kp+KIsiq+1LKp+KIsiq∗.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.Figure 6
Current loop control diagram of grid voltage feedforward decoupling.In this paper,iq∗ and id∗ are set to control the system reactive power and active power. The system is operating at unit power factor, so iq∗ 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 theid and iq current loops are similar and symmetrical. Taking the id current loop as an example, the decoupling control diagram of d-axis current loop is shown in Figure 7. Ts is the sample period of current loop; KiP and KiI are the proportional and integration coefficients of PI regulator, respectively; and Kpwm is the equivalent gain of the three-phase pulse width modulated converter. In this paper, SVPWM modulation is applied, so Kpwm is 1. Ignoring the grid voltage effects, the simplified inner current loop diagram can be described as in Figure 8 [28].Figure 7
The control diagram of inner current loop.Figure 8
The simplified control diagram of inner current loop.τi can be expressed as [28](17)τi=KiPKiI.The current open-loop transfer function is [28](18)Gois=KiPKpwmRτis1.5Tss+1.Whenζ=0.707, it can be derived that [28](19)1.5TsKiPKpwmRτi=12.Considering (18) and (19), the parameter of current loop can be calculated as follows [28]:(20)KiP=Rτi3TsKpwm,KiI=KiPτi=R3TsKpwm.Similarly, the current closed-loop transfer function can be derived from open-loop transfer function, which can be expressed as(21)Gcis=11+Rτi/KiPKpwms+1.5TsRτi/KiPKpwms2.When the system switching frequency is high enough, it means thatTs is small enough. s2 can be omitted. Thus, the current closed-loop transfer function can be simplified as(22)Gcis≈11+Rτi/KiPKpwms.Comparing (20) and (22), Gcis can be simplified to(23)Gcis=11+3Tss.From (23), the current loop can be equivalent to a first-order inertial element, where 3Ts 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 Figure9. τv is the inertial time constant of voltage closed loop; Kv and Tv are the PI parameters of voltage loop; and Gcis is the current loop transfer function. K can be expressed as [28](24)0.75mcosθ≤1,where m is the PWM modulation ratio and θ is the initial phase.Figure 9
The control diagram of voltage closed loop.In Figure9, K is time variable, which is not convenient for system design. Because the max PWM modulation ratio is 1, it is obvious that the 0.75mcosθ≤1. 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.Figure 10
The simplified control diagram of voltage closed loop.The voltage open-loop transfer function can be expressed as [28](25)Govs=0.75KvTvs+1CTvs2Tevs+1,where Tev=τv+3Ts. Then, the voltage closed-loop transfer function can be expressed as(26)Gcv=11+CTvs2Tevs+1/0.75KvTvs+1.The intermediate-frequency bandwidth of the voltage loop is defined as [29](27)hv=TvTev.According to the principles of the typical II system [29, 30], it can be expressed as(28)0.75KvCTv=hv+12hv2Tev2.Considering the immunity and followability of the voltage loop,hv is generally set as 5. After substitution and calculation, the parameters of voltage loop are(29)Tv=5Tev=5τv+3Ts,Kv=4Cτv+3Ts.


## 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 Figure1, and the detailed parameters of the converter are shown in Table 1.Table 1
System parameters.
SymbolParametersValue (V)ea,eb,ecGrid voltage (RMS)220LGrid-side filter inductance0.9RResistor0.1CDC-bus filter capacitor12000L1DC inductance0.2CoDC capacitor2000udcDC-bus voltage800ubatBattery voltage500fsSwitching frequency10flineGrid frequency50The system Bode diagrams are shown in Figure11. 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 Kv=4, Kv/Tv=45 have been selected for voltage PI regulator shown in Figure 11(b).Figure 11
The Bode diagram of system. (a) Bode diagram of current closed loop in the case of different values for the proportional and integration coefficients (21). (b) Bode diagram of voltage closed loop in the case of different values for the proportional and integration coefficients (26).
(a)(b)Figure12 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 12
The DC bus voltage waveform of AC/DC converter without load.Figure13 shows the dynamic performance of three-phase bidirectional grid-connected converter. The load steps from 0 to full load, when time = 0.01s.Figure 13
Step response of converter. (a) The step response of AC/DC converter DC bus voltage. (b) The step response of AC/DC converter grid-connected current.
(a)(b)From Figure13(a), udc 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 ia,ib,ic 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 comparingudc and ia,ib,ic 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.Figure14 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.Figure 14
The waveforms of V2G system in different conditions. (a) The DC bus voltage of bidirectional AC/DC converter. (b) The state of charge (SOC) of battery. (c) The gird-connected current curve of phase A. (d) The grid voltage curve of phase A.
(a)(b)(c)(d)From Figure14(a), udc increases from 800 V to 837.6 V at the beginning of discharging. After about 175.37 ms, udc restored to original output and the ripple is about 2 V. udc 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 ia and ea are the same frequency but opposite phase, when time <0.25 s. And ia and ea 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 Figure15. 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 15
The photo of experiment platform.Figure16 shows the converter waveforms in different conditions. The DC bus voltage udc and grid-connected current ia are shown in Figure 16(a) when the converter output with full load in charging. The udc is 800 V and the ripple is about 3 V. Fourier analysis is made for ia; 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.Figure 16
The waveforms of bidirectional AC/DC converters. (a) The grid-connected current and DC bus voltage of converter in full load condition. (b) The DC voltage and grid-connected current of converter in step response. (c) The DC bus voltage and grid-connected current of converter in power flow reverse condition. (d) The grid voltage and grid-connected current of converter in power flow reverse condition.
(a)(b)(c)(d)From Figure16(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, ia and ea 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 Figure17(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.Figure 17
The curve of converter under different load conditions. (a) The efficiency curve. (b) The power factor curve. (c) THD curve.
(a)(b)(c)Figure17(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.Figure17(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.


## 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 Figure1, and the detailed parameters of the converter are shown in Table 1.Table 1
System parameters.
SymbolParametersValue (V)ea,eb,ecGrid voltage (RMS)220LGrid-side filter inductance0.9RResistor0.1CDC-bus filter capacitor12000L1DC inductance0.2CoDC capacitor2000udcDC-bus voltage800ubatBattery voltage500fsSwitching frequency10flineGrid frequency50The system Bode diagrams are shown in Figure11. 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 Kv=4, Kv/Tv=45 have been selected for voltage PI regulator shown in Figure 11(b).Figure 11
The Bode diagram of system. (a) Bode diagram of current closed loop in the case of different values for the proportional and integration coefficients (21). (b) Bode diagram of voltage closed loop in the case of different values for the proportional and integration coefficients (26).
(a)(b)Figure12 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 12
The DC bus voltage waveform of AC/DC converter without load.Figure13 shows the dynamic performance of three-phase bidirectional grid-connected converter. The load steps from 0 to full load, when time = 0.01s.Figure 13
Step response of converter. (a) The step response of AC/DC converter DC bus voltage. (b) The step response of AC/DC converter grid-connected current.
(a)(b)From Figure13(a), udc 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 ia,ib,ic 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 comparingudc and ia,ib,ic 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.Figure14 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.Figure 14
The waveforms of V2G system in different conditions. (a) The DC bus voltage of bidirectional AC/DC converter. (b) The state of charge (SOC) of battery. (c) The gird-connected current curve of phase A. (d) The grid voltage curve of phase A.
(a)(b)(c)(d)From Figure14(a), udc increases from 800 V to 837.6 V at the beginning of discharging. After about 175.37 ms, udc restored to original output and the ripple is about 2 V. udc 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 ia and ea are the same frequency but opposite phase, when time <0.25 s. And ia and ea 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 Figure15. 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 15
The photo of experiment platform.Figure16 shows the converter waveforms in different conditions. The DC bus voltage udc and grid-connected current ia are shown in Figure 16(a) when the converter output with full load in charging. The udc is 800 V and the ripple is about 3 V. Fourier analysis is made for ia; 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.Figure 16
The waveforms of bidirectional AC/DC converters. (a) The grid-connected current and DC bus voltage of converter in full load condition. (b) The DC voltage and grid-connected current of converter in step response. (c) The DC bus voltage and grid-connected current of converter in power flow reverse condition. (d) The grid voltage and grid-connected current of converter in power flow reverse condition.
(a)(b)(c)(d)From Figure16(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, ia and ea 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 Figure17(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.Figure 17
The curve of converter under different load conditions. (a) The efficiency curve. (b) The power factor curve. (c) THD curve.
(a)(b)(c)Figure17(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.Figure17(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 synchronousd−q 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 d−q 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.



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*Source: 8844073-2020-09-07.xml*