Modelling of a Power Converter with Multiple Operating Modes - MDPI

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Modelling of a Power Converter with Multiple Operating Modes Wang Feng

ID

and Luo Yutao *

School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China; [email protected] * Correspondence: [email protected]; Tel.: +86-020-87110191 Received: 7 May 2018; Accepted: 28 May 2018; Published: 5 June 2018







Abstract: In order to achieve DC voltage matching, on-board charging, and DC/AC power inversion, three independent power converters are often needed in traditional Distributed Power Converter (DPC) systems of electric vehicles (EVs): bidirectional DC/DC (Bi-DC/DC), AC/DC, and DC/AC. The requirement of electronic devices such as power switches, inductors, and capacitors make the converter costly and complicated in structure. In this paper, a power converter with multi-operating mode (PCMM) is presented. The proposed PCMM can work in Bi-DC/DC, AC/DC, and DC/AC modes. The state-space averaging model of PCMM considering resistance of Insulated Gate Bipolar Transistor (IGBT) and the inductor is presented. Based on this model, the transfer function of the system is derived and the controller is designed. The simulation and experimental results show that PCMM can meet the design target and verify the feasibility of the model. The measurement results show that the weight of PCMM proposed in this paper is reduced by 51.2% compared with the traditional structure. Keywords: power converter; bidirectional DC/DC; AC/DC; DC/AC

1. Introduction Carbon dioxide (CO2 ) from vehicle exhaust is one of the main causes of the greenhouse effect. Electric vehicles (EVs) are considered to be an important development direction of the future automobile industry because of their advantages in reducing CO2 emissions. In order to improve the performance of the energy storage system, a hybrid energy source can be used. [1]. In electric vehicles (EVs), lithium-ion batteries or fuel cells are often used as the primary power source, which is supplemented by a super-capacitor pack or battery pack as the auxiliary power source to constitute a hybrid energy storage system (HESS) [2]. As the primary and auxiliary power sources usually have different voltage levels, a DC/DC converter is needed to achieve voltage matching [3]. Meanwhile, in order to charge the battery pack, a charger with AC/DC function is needed [4], which converts the grid AC into DC. In addition, when AC power supply is required for cases like outdoor activities, a DC/AC inverter is needed to convert the battery DC into AC [5]. Simultaneously, a DC/AC inverter also needs to have the grid connection function, so that the battery power level of EVs can be fed back to the grid after inversion when the EVs sits idle in the garage, thereby playing a role in grid peak shifting and regulation. The DC/DC converter plays an important role in DC power level conversion of energy storage systems, including hybrid energy storage systems [6], PV systems [7,8], fuel cell systems [9], etc. Interleaved is one of the DC/DC topologies [9]. The advantages of this topology include low output current ripple and high power density [10]. The interleaved DC/DC can be composed of two phases [11], three phases [12], or multi-phase [13]. It has greatly reduced volume and weight compared to the traditional Bi-DC/DC. World Electric Vehicle Journal 2018, 9, 7; doi:10.3390/wevj9010007

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To improve the power factor in the process of AC/DC conversion, power factor correction (PFC) World Electric Vehicle Journal 2018, 9, x FOR PEER REVIEW 2 of 17 is needed with a special circuit. The traditional PFC method adds a boost converter behind the rectifier bridge [14]. a method requires a rectifier bridge and conversion, a boost circuit, which the disadvantage ToSuch improve the power factor in the process of AC/DC power factorhas correction (PFC) of lowis conversion To improve the conversion efficiency, researchers proposed a needed withefficiency. a special circuit. The traditional PFC method adds a boost converterhave behind the rectifier bridge [14]. Such a method requires a rectifier bridge and a [15]. boost One circuit, which is has bridgeless PFC circuit topology that does not require rectifier bridges solution tothe add two disadvantage conversion efficiency. To improve the conversion researchers have totem additional diodes of to low improve the EMI problem [16]. Another solutionefficiency, is bridgeless PFC with proposed a bridgeless PFC circuit topology that does not require rectifier bridges [15]. One solution pole topology [17]. This topology does not require additional power elements. It only needs to drive is to add two additional diodes to improve the EMI problem [16]. Another solution is bridgeless PFC two switches of the bridge independently. with totem pole topology [17]. This topology does not require additional power elements. It only There three main topologies for DC/AC inverters [18]. One is the push-pull configuration needs are to drive two switches of the bridge independently. inverter, which consists of few power devices and is easy [18]. to drive [19]. due to structural There are three main topologies for DC/AC inverters One is the However, push-pull configuration characteristics of theconsists circuitofitself, the push-pull circuit cannot output sinusoidal voltage inverter, which few power devices and is easytopology to drive [19]. However, due to structural characteristics the circuit the push-pull circuit topology sinusoidal voltage waveforms, which isofsuitable foritself, low-power applications. Anothercannot is the output half-bridge topology inverter, which is components suitable for low-power applications. Another is the half-bridge whichwaveforms, has few switching and a simple structure. Nevertheless, the ratedtopology current of its inverter, which has few switching components and a simple structure. Nevertheless, the rated current power switch is twice that of the power components in a full-bridge inverter circuit, with large current of its power switch is twice that of the power components in a full-bridge inverter circuit, with large stress. The third one is the full-bridge inverter, whose output current and current through switching current stress. The third one is the full-bridge inverter, whose output current and current through components arecomponents both half ofare theboth half-bridge circuit. The circuit. drive circuit of the full-bridge inverter switching half of theinverter half-bridge inverter The drive circuit of the fullis more complex than the two previous topologies due to the presence of four switching devices. bridge inverter is more complex than the two previous topologies due to the presence of four Inswitching EVs with hybrid energy storage systems, the traditional Distributed Power Converter (DPC) devices. In EVs energy storageBi-DC/DC, systems, the AC/DC, traditionaland Distributed Converter (DPC) scheme needs at with leasthybrid three independent DC/ACPower converters. When an EV is at least three independent Bi-DC/DC, AC/DC, and DC/AC converters. When an EV is the being scheme driven,needs the buck converter and boost converter are needed to convert the power between being driven, the buck converter and boost converterconverter are neededistoneeded convert to thecharge power between the pack. battery pack and the auxiliary energy. An AC/DC the battery battery pack and the auxiliary energy. An AC/DC converter is needed to charge the battery pack. A A DC/AC converter is needed to supply the AC power to the electric appliances. The topology of this DC/AC converter is needed to supply the AC power to the electric appliances. The topology of this systemsystem is shown in Figure 1. Each converter needs to be equipped with separate radiators, which are is shown in Figure 1. Each converter needs to be equipped with separate radiators, which are thus structurally complex andand costly. thus structurally complex costly.

Figure 1. Conventional distributed power converter (DPC) topology.

Figure 1. Conventional distributed power converter (DPC) topology. Some researchers have studied multifunctional power converters. The power converter system integrating a motorhave controller andmultifunctional battery charger proposed by JY Lee et al. power enabledconverter the AC/DCsystem Some researchers studied power converters. The conversion to share the power devices of a motor controller [20]. Serkan Dusmez et al. integrated integrating a motor controller and battery charger proposed by JY Lee et al. enabled the the AC/DC AC/DCtocharger battery on the basis a DC/DC converter[20]. by sharing power devices of a conversion share of thea power devices of aofmotor controller Serkanthe Dusmez et al. integrated boost DC/DC converter [21,22]. Ting-Chia Ou et al. proposed a multi-input power converter to the AC/DC charger of a battery on the basis of a DC/DC converter by sharing the power devices of achieve different operation modes [23]. a boost DC/DC converter [21,22]. Ting-Chiamainly Ou etfocuses al. proposed a multi-input converter to Previous research on power converters on their performance. Forpower the integration achieve differentthe operation modes [23]. converters, literature only mentioned DC/DC and AC/DC integration. Compared with the Previous research on power converters onmulti-function their performance. Forinclude the integration traditional converters, this paper presents mainly a novel focuses integrated converter BiDC/DC,the AC/DC, and DC/AC. Based on the topologyand of the Bi-DC/DC, the presented PCMM adds converters, literature only mentioned DC/DC AC/DC integration. Compared with the only one switch andthis an AC capacitor to achieve multifunction It shares converter the inductor, traditional converters, paper presents a novel integratedoperation. multi-function include capacitor, and IGBT modules and offers three conversions functions and reduced system weight. PCMM Bi-DC/DC, AC/DC, and DC/AC. Based on the topology of the Bi-DC/DC, the presented

adds only one switch and an AC capacitor to achieve multifunction operation. It shares the inductor, capacitor, and IGBT modules and offers three conversions functions and reduced system weight.

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Thispaper paperpresents presentsaaPCMM PCMMconverter converterand andbuilds buildsthe themodel modelof ofthe thesystem systemusing usingaastate-space state-space This This paper presents a PCMM converter and builds the model of the system using a state-space averaging modelling method [24]. Section 2 introduces the model of the converter in each operating averaging modelling modelling method method [24]. [24]. Section Section 22 introduces introduces the the model model of of the the converter converter in in each each operating operating averaging mode.Part Part 3performs performsthe theexperimental experimentalresults. results.Experimental Experimentalevaluation evaluation ofthe thePCMM PCMMisispresented presented mode. mode. Part 33performs the experimental results. Experimental evaluation of of the PCMM is presented in in Section 4. in Section Section 4. 4.

K K1 1

~~

C K C33 K22

~~

VV DCL DCL

L L11

K K33

+ +

-

+ +

C C22

L L2 2

C C11

-

VV DCH DCH

AC ACinin AC ACout out

Modellingand andControl Controlof ofthe theSystem System 2.2.Modelling Modelling 2. and Control of the System ThePCMM PCMMproposed proposedin inthis thispaper paperhas hasthree threeworking workingmodes. modes.The Thetopology topology isshown shown inFigure Figure The The PCMM proposed in this paper has three working modes. The topology is is shown in in Figure 2. Whenworking working inBi-DC/DC Bi-DC/DCmode, mode, the switchKK22isisturned turned onand andthe theswitch switchKK11isisturned turnedoff. off.The The 2.2.When When working ininBi-DC/DC mode, the switch switch K2 is turnedonon and the switch K1 is turned off. system works in buck mode or boost mode. In AC/DC mode, switch K 1 is turned on and the switch system works in buck mode or boost mode. In AC/DC mode,mode, switchswitch K1 is turned on andon theand switch The system works in buck mode or boost mode. In AC/DC K1 is turned the K 2 is turned off, the system works with bridgeless PFC topology, and the energy flows from the grid K2 is turned the off, system bridgeless PFC topology, and the and energy from thefrom grid switch K2 is off, turned the works systemwith works with bridgeless PFC topology, theflows energy flows to the the battery battery side. In In DC/AC mode, mode, switch switch KK11 isis turned turned on and and switch switch KK22isis turned turned off. The The energy energy to the grid to theside. batteryDC/AC side. In DC/AC mode, switch K1on is turned on and switch Koff. off. 2 is turned flows from the battery side to the AC side to achieve DC to AC conversion. flows from the battery side to the AC side to achieve DC to AC conversion. The energy flows from the battery side to the AC side to achieve DC to AC conversion.

-

-

Figure2. Proposedtopology. topology. Figure Figure 2.2.Proposed Proposed topology.

Asshown shown inFigure Figure 3,when when thevehicle vehicle is driving,the thePCMM PCMMworks worksin inthe theBi-DC/DC Bi-DC/DCmode. mode.The The As As shown in in Figure 3, 3, whenthe the vehicleisisdriving, driving, the PCMM works in the Bi-DC/DC mode. controller distributes distributes the the power power for for the the battery battery and and the auxiliary auxiliary energy source source according to to the the controller The controller distributes the power for the battery andthe the auxiliaryenergy energy source according according to the power demand of the inverter. The auxiliary energy source will provide energy when the PCMM power demand demand of of the the inverter. inverter. The The auxiliary auxiliary energy energy source source will will provide provide energy energy when when the the PCMM PCMM power operates in the boost mode. PCMM detects the DC bus voltage, calculates the reference current operates in in the the boost boost mode. mode. PCMM PCMM detects detects the the DC DC bus bus voltage, voltage, calculates calculates the the reference reference current current operates according to the power that the auxiliary energy needs to respond with. When the auxiliary energy according to to the the power power that that the the auxiliary auxiliary energy energy needs needs to to respond respond with. with. When When the the auxiliary auxiliary energy energy according source is needed for energy recovery, the PCMM operates in buck mode. The PCMM detects the source is is needed needed for for energy energy recovery, recovery, the thePCMM PCMMoperates operates in inbuck buckmode. mode. The The PCMM PCMM detects detects the the source voltageof ofthe theauxiliary auxiliaryenergy energyand andcalculates calculatesthe thetarget targetcurrent currentaccording accordingto tothe thepower powerrecovered recoveredby by voltage voltage of the auxiliary energy and calculates the target current according to the power recovered by the auxiliary energy. When the battery pack needs charging, the PCMM operates in the AC/DC mode. the auxiliary auxiliaryenergy. energy.When Whenthe thebattery batterypack packneeds needscharging, charging,the thePCMM PCMMoperates operatesin inthe theAC/DC AC/DC mode. the mode. In the constant current charging stage, the control objective of the PCMM is the output current.In Inthe the In the the constant constant current current charging chargingstage, stage,the thecontrol controlobjective objectiveof ofthe thePCMM PCMMisisthe theoutput outputcurrent. current. In In the constant voltage voltage charging charging stage, stage, the the control control objective objective of of PCMM PCMM isis the the output output voltage. voltage. The The PCMM PCMM constant constant voltage charging stage, the control objective of PCMM is the output voltage. The PCMM works in DC/AC mode when it is necessary to provide single-phase AC for the electrical equipment. worksin in DC/AC DC/AC mode works mode when when it it is is necessary necessary to to provide provide single-phase single-phase AC AC for for the the electrical electrical equipment. equipment. PCMM adopts double loop control; the current of the inductor is the inner loop, the the output output AC AC PCMMadopts adoptsdouble doubleloop loop control; current of inductor the inductor the loop, innerthe loop, PCMM control; thethe current of the is the is inner output AC voltage voltage is outer loop, and the control target is output voltage. voltage is outer and thetarget control output voltage. is outer loop, andloop, the control is target outputisvoltage. Start Start

Driving? Driving?

No No

Yes Yes

Recycle Recycle energy energy

Buck Buck

Auxiliary Auxiliary energy energy Supply Supply energy energy Boost Boost

Charging? Charging? Yes Yes AC/DC AC/DC

AC supply？ AC supply？ Yes Yes DC/AC DC/AC

Figure Flow Figure3. Flowchart chartof ofthe thefunction functionneeded neededin inEVs EVswith withhybrid hybridenergy energystorage storagesystems. systems. Figure 3.3.Flow chart of the function needed in EVs with hybrid energy storage systems.

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2.1. Bi-DC/DC Mode 2.1. Bi-DC/DC Mode In buck mode of the Bi-DC/DC converter, the equivalent circuit of the system is as show in Figure 4. In buck mode of the Bi-DC/DC converter, the equivalent circuit of the system is as show in Figure 4. rs +

L1

rL + Vo -

C1

rL

rs

C2

Vi RL

L2

rs

rs

-

Figure mode. Figure 4. 4. The The equivalent equivalent circuit circuit of of the the Bi-DC/DC Bi-DC/DC mode.

) , and t ) are The current of of thethe inductors i L1 (itL)1 ,(tand i L2 (itL)2 (are selected as the The voltage voltage of ofthe thecapacitor capacitorvcv(ct()t,)the , the current inductors selected as state variable of the system. The high side voltage vi (t)vis selected as the input variable, and the low ( t ) the state variable of the system. The high side voltage i is selected as the input variable, and the side voltage vo (t) is selected as the output variable. The state equations and output equations of the v ( t ) o low sidecan voltage is selected(1) as and the output variable. The state equations and output equations system be given as Equations (2). of the system can be given as Equations (1) and (2).  ·    i L1 (t )  i L1 (t)  · i L1 ( t)   (t )     (1) (t)  + B[vi (t)]  i L2 (t )  = A iLi1L2 · i L 2 (t )  A i v(ct()t) B  v (t )  (1)  i vc (t)  L2     vc (t )    vc (t )     i L1 (t)   vo (t) = C  i L2 (t)  + D [vi (t)] (2)  iL1 (t )  vc (t) vo (t )  C iL 2 (t )  D  vi (t ) (2) For the bi-DC/DC converter operating in an inductor continuous mode (CCM), the coefficient  vc (t )  matrix of the state space averaging equations is given as Equation (3).

For the bi-DC/DC operating inan inductor continuous mode (CCM), the coefficient  rsconverter   rL 0 equations − L11 is given asLdEquation (3). − L+averaging h i matrix of the state space 1 1     0 − rs L+2r L − L12 ,B =  Ld , C = 0 0 1 , D = [0] A= (3) 02d  1 1   1 rs  rL 1 − C1 0 R L C1 L  C1  L1 L1    1  d  resistance of the IGBT, and d is the duty  rL rs inductor, where, r L is the internal resistance of r1s is the internal   A 0 (3)  , B    , C   0 0 1 , D   0  cycle of the PWM. L2 L2    L2   derivative   is0 zero,  In steady state, the of and the relation between the steady 1 1 each state 1 variable      state output voltage and can be1 expressed C1 input voltage C1 RL C  by Equation (4).  the rs is 2R L dthe internal resistance of the IGBT, and d is the where, r L is the internal resistance of inductor, Vo = V (4) 2R L + r L + rs i duty cycle of the PWM. In R steady state, the derivative of each state variable is zero, and the relation between the steady where, L is the load resistance. state The output voltage and of thethe input voltage canexpressed be expressed bysum Equation average vector system can be as the of the(4). steady-state value and the

small signal value, shown in Equation (5). 2 RL d Vo  V (4)    2 RL  rL rs i  ˆ hi L1 (t)iTs IL1 i L1 (t)     ˆ   where, RL is the load resistance. (5) (t)   hi L2 (t)i Ts  =  IL2  +  i L2 The average vector of the system can be expressed as the sum of the steady-state value and the Vc vˆc (t) hvc (t)iTs small signal value, shown in Equation (5).

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In the vicinity of the steady state, the small signal model of the system can be obtained by the partial derivative of the variable, and the Laplace transform can be used as Equation (6). 

  ˆ (s) i L1  ˆ   s i L2 (s)  = A vˆc (s)

  V  i ˆ (s) i L1 L1   V ˆ (s)  + Bvˆi (s) +  i  dˆ(s) i L2 L2  vˆc (s) 0

(6)

Make dˆ(s) = 0, the transfer function of the input voltage to each state variable can be determined via Equation (7). Gxvi = (SI − A)−1 B (7) Make vˆi (s) = 0, the transfer function of the duty cycle to each state variable can be calculated as Equation (8). h iT (8) Gxd = (SI − A)−1 LVi LV2i 0 1

The boost model and the buck model have dual symmetry, and the coefficient matrix of the average state space equation in the boost mode is given by Equation (9).

− rs L+1r L  0 A= 

1− d C2

0

− rs L+2r L 1− d C2

  1  − 1L−1d h i L   1  − 1L−2d ,B =  L1 , C = 0 0 1 , D = [0] 2 − R L1C2 0

(9)

The relation between the steady state output voltage and the input voltage can be expressed as Equation (10). 2R L (1 − d) Vo = Vi (10) (1 − d)2 2R L + r L + rs The transfer function of the input voltage to each state variable can be determined by Equation (11). Gxvi = (SI − A)−1 B

(11)

The transfer function of the duty cycle to each state variable can be calculated with Equation (12). Gxd = (SI − A)−1

h

Vc L1

Vc L2

− ICL12 −

IL2 C2

iT

(12)

The control structure of the Bi-DC/DC mode is shown in Figure 5. The controller consists of two inner loops and one outer loop. In buck mode, V ref is the reference voltage of the low voltage side, V out is the output voltage, dx1 is the duty cycle of Q1 , and dx2 is the duty cycle of Q2 . In boost mode, V ref is the reference voltage of the high voltage side, V out is the output voltage, dx1 is the duty cycle of Q3 , and dx2 is the duty cycle of Q4 . PIx1 , PIx2 , and PIx3 is the PI regulator of the system. Based on the model of the system illustrated in Equations (1)–(12), the parameters of the PI regulators in buck mode and boost mode can be obtained easily by the “sisotool” toolbox of MATLAB.

theoutput outputvoltage, voltage,ddx1x1isisthe theduty dutycycle cycleofofQQ1,1,and andddx2x2isisthe theduty dutycycle cycleofofQQ2.2.In Inboost boostmode, mode,VVrefrefisis isisthe the reference voltage of the high voltage side, V out is the output voltage, dx1 is the duty cycle of Q3, the reference voltage of the high voltage side, Vout is the output voltage, dx1 is the duty cycle of Q3, andddx2x2isisthe theduty dutycycle cycleofofQQ4.4.PI PIx1x1, ,PI PIx2x2, ,and andPI PIx3x3isisthe thePI PIregulator regulatorofofthe thesystem. system.Based Basedon onthe themodel model and of the system illustrated in Equations (1)–(12), the parameters of the PI regulators in buck mode and of theElectric system illustrated in 9, Equations (1)–(12), the parameters of the PI regulators in buck mode6 and World Vehicle Journal 2018, 7 of 17 boost mode can be obtained easily by the “sisotool” toolbox of MATLAB. boost mode can be obtained easily by the “sisotool” toolbox of MATLAB.

ACAC

Vac Vac

-

-

C3 C3

VVdcL dcL

++

---

Q1 Q1 K1 K1 K2 K2

L1 L1 L2 L2

C2 C2

Q4 Q4 Q3 Q3

C1 C1 + +

Vout Vout Vref++ Vref

++

Q2 Q2

VVdcH dcH

+ +

-

PI PIx1x1

-

d

+ +-

0.5 0.5

--

-

x1 PI dx1 PIx2x2

d

x2 PI dx2 PIx3x3

Figure 5. The control structure of the Bi-DC/DC mode. of the the Bi-DC/DC Bi-DC/DC mode. Figure 5. The control structure of mode.

2.2. AC/DCMode Mode 2.2. 2.2. AC/DC AC/DC Mode The equivalentcircuit circuitofofthe theAC/DC AC/DCmode mode is showininFigure Figure 6. The The equivalent equivalent circuit of the AC/DC mode isis show show in Figure 6. 6. r rs s

+ V+ Vacac -

L L1 1

r rL L r rL L

+ +

r rs s

L L2 2

r rs s

r rs s

C C2 2

Vo Vo RL RL

-

Figure 6. The equivalent circuit of the AC/DC mode. Figure 6. The equivalent circuit of the AC/DC mode. AC/DC mode.

ReferringtotoFigure Figure6,6,assume assumethat thatthe theparameters parametersofofthe thefour fourpower powerswitches switchesare arethe thesame. same.The The Referring Referring to Figure 6, assumehalf that the and parameters of the four power switches are the same. equivalent circuits of the negative cycle the positive half cycle of the sine wave are the same. equivalent circuits of theofnegative half cycle and the positive half cycle the of sine theare same. The equivalent circuits the negative half cycle and the positive half of cycle thewave sine are wave C 2 vcthe (t ) , Therefore, only the positive half cycle needs to be analyzed. The voltage of the capacitor C ), 2 vc (tC Therefore, only the positive half cycle be analyzed. The voltage of the capacitor same. Therefore, only the positive halfneeds cycle to needs to be analyzed. The voltage of the capacitor 2 i ( t ) i ( t ) L(1t ) , and i L( 2t ) are selected as the state variables of the system. The AC the current of the inductor i v ( t ) , the current of the inductor i ( t ) , and i ( t ) are selected as the state variables of the system. L 1 L 2 c L2 L1 , and are selected as the state variables of the system. The AC the current of the inductor vac (t ) isv ac v (t ) voselected The AC side voltage (t) is selected as thevariable, input variable, theside high side voltage (t) is selected selected as the input andthe theand high voltage asthe the side voltage v ( t ) vo o(t ) isis is selected as the input variable, and high side voltage selected as side voltage ac as the output variable. The state space equation of the system andthe theoutput outputequation equation are are expressed in output variable. The state space equation of the system and expressed output variable. The state space equation of the system and the output equation are expressed inin Equations (1) and (2). The coefficient matrix of the average state space average equation of the system Equations(1) (1)and and(2). (2).The Thecoefficient coefficientmatrix matrixofofthe theaverage averagestate statespace spaceaverage averageequation equationofofthe thesystem system Equations isisexpressed by Equation (13). expressed by Equation (13). is expressed by Equation (13).  2rs +2r    1− d 1 1 L 2r  2r   −   L21 r+s Ls2 2 rL L 0 0 − L1 +L12 1dd   L1 + L12   h i   1L1  L2   2r0L 1 −d L1   ,B L2= A =    0LL1 1LL2 2− 2rLs + ,C = 0 0 1 , D = [0] (13) −      L L  L L  + L L + L L + L 1 2 1 2 2 2 1 1    1 21   1− d 1  2 2 r r  1 d L  02 rs s 2 rL− 0 A  R L C21  d   B  0 1 (13)  L A    C2 0  L2  L1  L2  B    L1  L2  (13) 1  L1  L2 L1  L2   L L 1 2   voltage  In steady state, between the steady and the input voltage can be 1 relation 1 state output d   the 1 d 00    1  0   0    expressed as Equation (14).    C   0 0 1 D   0  C RL C 2  C2 2 RL C ,   0 0 1 , ,D   0   ,  ,C  R2L (1 ,− d) Vo = V (14) i (1 − d)2 R L + 2r L + 2rs

small signal value, as shown in Equation (15).

 ^   iL1 (t )   iL1 (t )  Ts    I L1   ^   iL 2 (t )    I L 2   iL 2 (t )  Ts      ^   vc (t ) T   Vc   v (t )  c s    

World Electric Vehicle Journal 2018, 9, 7

(15) 7 of 17

The average vector ofsteady the system expressed the sum of system the steady-state value and In the vicinity of the state,can thebe small signal as model of the can be obtained by the the small signal value, as shown in Equation (15). partial derivative of the variable, and the Laplace transform is carried out with Equation (16).       ˆc (t)  iVL1 h^ i L1 (t)iTs ^ IL1    ˆ     =   (15) s )(t)i Ts  i  iLh1i(L2 L2L(2t )  L1 ( s )   IL2  + L1i  V  ^hvc (t)i Ts  ^  Vc ^ vˆcc (t) ^ s iL 2 ( s )   A iL 2 ( s )   B vi ( s )    d (s) (16)  L1  L2   ^   ^  In the vicinity of the steady  Iof the  system can be obtained by the vc ( s )  signal model ( s )  the small  vcstate, L1    out with Equation (16).     partial derivative of the variable, and the Laplace transform is carried  C2       Vc  ^ ˆ (s) ˆ (s) i L1 i L1 L + L2 d (s)  0 , thetransfer   ˆthe input   1Vcstate  variable ˆ ˆ (s) function Make can be determined s i L2 Bvˆi (s) +toeach (16) i L2 (s)  + voltage  = A of L1 + L2  d ( s ) I as Equation (17). vˆc (s) vˆc (s) − CL12 1 G xvi   S I  A  B (17) ˆ Make d(s) = 0, the transfer function of the input voltage to each state variable can be determined ^ as Equation v(17). (s)  0 , the transfer function of the duty cycle to each state variable can be calculated as Make i Gxvi = (SI − A)−1 B (17) Equation (18). Make vˆi (s) = 0, the transfer function of the duty cycle to each state variable can be calculated as T Vc Vc I L1  1  Equation (18).   iT Gxd   SI  A h (18) −1 L1 VL  L C IL1 Vc L2 c2  1 2 − C2 (18) Gxd = (SI − A) L1 + L2 L1 + L2

The control control structure structure of of the the AC/DC AC/DC mode 7. The mode is is shown shown in in Figure Figure 7. + es

Vac

Q1

C3

-

+

Q2

K1

VdcL

--

L2

K2

VdcH

L1

+

C2

Q4 Q3

C1

Vac d

PI2

-

-

+

PI1

+

Vr ef

1/V2rms RMS

Figure 7. The control structure of the AC/DC mode. Figure 7. The control structure of the AC/DC mode.

The The loop loop is is composed composed of of an an inner inner current current loop loop and and an an outer outer loop. loop. The The output output of of the the regulator regulator PI PI11 v in the outer loop and the input voltage v are multiplied, so that the output current is proportional to in the outer loop and the input voltage acac are multiplied, so that the output current is proportional the input voltage. In order to keeptothe output the input is disturbance, to the input voltage. In order keep the power outputconstant power when constant whenvoltage the input voltage is the RMS value of the input voltage is added as the feed forward. The signal calculated by the multiplier is used as a reference of the current loop, and the current loop is adjusted by regulator PI2 to obtain the duty cycle of the PWM. 2.3. DC/AC Mode The wave form of the output in DC/AC mode is a sinusoidal form, and there is no DC steady state operation point. It is a typical large signal nonlinear system, and the equivalent circuit in the DC/AC mode is shown in Figure 8.

2.3. DC/AC Mode The wave form of the output in DC/AC mode is a sinusoidal form, and there is no DC steady state operation point. It is a typical large signal nonlinear system, and the equivalent circuit in the World Electric Vehicle Journal 2018, 9, 7 8 of 17 DC/AC mode is shown in Figure 8. rs +

Vac

Z0

C1

rL

L1

rL

L2

a

rs b

rs

rs

Vdc

-

Figure8.8.The Theequivalent equivalentcircuit circuitininDC/AC DC/ACmode. mode. Figure

i (t ) i (t ) of the inductors ( L 1 , L 2 ) 1 and Thevoltage voltagevcv(ct()t )ofof the capacitorC1 Cand current The the capacitor the the current (i L1((tL)1, i L2, (tL)2) of) the inductors (L1 , L2 ) are v ( t ) selected as the variables of theofsystem. The voltage v ab (t) between the two points ‘a’ and‘a’ ‘b’and is ab are selected asstate the state variables the system. The voltage between the two points taken as the input variable, and the output voltage v ac (t)vis taken as the output variable. Because of ‘b’ is taken as the input variable, and the output voltage ac (t ) is taken as the output variable. Because i L1 (t) = i L2 (t), the equation of the circuit can be expressed as Equations (19)–(22). of iL1 ( t )  iL 2 ( t ) , the equation of the circuit can be expressed as Equations (19)–(22). di (t) (19) ( L1 + L2 ) L1 diL1 (= t ) −2r L i L1 (t) − vc (t) + v ab (t)  2rL iL1 (t )  vc (t )  vab (t ) (19)  L1  L2dt dt di L1 (t) = −2r L i L2 (t) − vc (t) + v ab (t) (20) ( L1 + L2 ) dtdiL1 (t )  2rL iL 2 (t )  vc (t )  vab (t )  L1  L2  (20) vc (t) dvcdt(t) C2 = i L1 (t) − (21) dt Z0 dv (t ) v (t ) (22) C 2 v acc (t) =iLv1 c((t )t) c (21) dt Z0 The coefficient matrix of the state space equation is shown in Equation (23). (22)   v ac( t )  v c ( t )  0 − L1 +1 L2 − L12r+LL2 1/( L1 + L2 ) h i    coefficient matrix the equation is shownin Equation (23). 1 space (23) AThe = 0 − L12r+LLof − Lstate ,B =  1/( L1 + L2 ) , C = 0 0 1 , D = [0] 2 1 + L2 1 1 0 0 − 2rL 1  C2  0 Z0 C2      L L L L2  2 1  1 The voltage v ab signal, which can be averaged over a switching period to  (t) is a discontinuous 2rL 1 0For unipolar A state.   obtain its average modulation, the modulation wave is vre f (t) = Vre f sin((23) ωt)   when 1/  ( L1  L2 )  L1  L2 L  L2   and the carrier amplitude is Vt , the average 1value of the voltage v ab(t) in one period can be expressed  1 1  B  1/ ( L1  L2 )  as Equation (24).  0   Z 0 C2  V  sin(0ωt)  C   0 0 1 D   0  C2 re f , , , (24) hv ab (t)iTs = Vdc Vt v ( t ) ab is(24) a discontinuous which can be averaged overcharacteristics a switching period The voltageEquation Substituting into the state signal, equation of the system, the related can beto vref (t )  Vref sin ( t ) derived. The internal resistance of the two inductorswhen is defined as r L , then the transfer function of the obtain its average state. For unipolar modulation, the modulation wave is Vt vab (t ) system can be expressed by Equation (25). and the carrier amplitude is , the average value of the voltage in one period can be expressed as Equation (24). Gxvi = (SI − A)−1 B (25) Vref sin(t ) shown Vdc (24) ab (t ) Tsis The control structure of the DC/ACvmode in Vt Figure 9. The control system is composed of an inner loop and an outer loop. The reference voltage (Vre f ) of the output voltage is a sinusoidal wave with required frequency. Regulating by the regulator (PI1 ), the reference of the current loop is obtained, and the duty cycle of the PWM is output by the regulator (PI2 ).

be derived. The internal resistance of the two inductors is defined as the system can be expressed by Equation (25).

rL

, then the transfer function of

1

G xvi   SI  A  B

(25)

World Electric Vehicle Journal 2018, 9, 7

9 of 17

The control structure of the DC/AC mode is shown in Figure 9. + C3

-

Q1

+

Q2

K1 L1

+

VdcL --

L2

K2

Q4

C2

VdcH

AC

Vac

Q3

C1

Vac Vref

+

PI1

+-

PI2

d

Figure9.9.The Thecontrol controlstructure structureofofthe theDC/AC DC/ACmode. mode. Figure

V 2.4. Limitations of Proposed The control system isModel composed of an inner loop and an outer loop. The reference voltage ( ref ) of the output voltage is a sinusoidal wave with required frequency. Regulating by the regulator (PI1), The PCMM model established in this paper has the following limitations. the reference of the current loop is obtained, and the duty cycle of the PWM is output by the regulator Firstly, the model is based on the average state variable established by the average state space (PI2). model. The state variable of the model reflects the average value of variables in a switching cycle. This model cannot effectively reflect the description of switch details. 2.4. Limitations of Proposed Model Secondly, the model is a small signal model, which reflects the small signal disturbance The PCMM model established in this paper has the following limitations. characteristic of the system near steady state. When the system is disturbed by a large signal, such as Firstly, the model is based on the average state variable established by the average state space start-up, short circuit, or sudden break, the system characteristics cannot be accurately described. model. The state of the model reflects the average value of variables a switching cycle. To reflect the variable system characteristics more accurately, a nonlinear modelinginmethod is needed. This model effectively reflect the of switch details. However, thecannot system model obtained by description the nonlinear modeling method is rather complex, which Secondly, the model is a small design. signal This model, which reflects the control small signal will bring difficulties to the controller’s model can use classical theory disturbance to design a characteristic of the system near steady state. When thethat system is the disturbed by a large signal, such as controller for PCMM. It can quickly design a controller meets engineering requirements. start-up, short circuit, or sudden break, the system characteristics cannot be accurately described. 3. Simulation thesystem PCMMcharacteristics more accurately, a nonlinear modeling method is needed. To reflectofthe However, the system model requirements obtained by the modeling method is ratherneeds complex, which According to the design of anonlinear certain vehicle model, the PCMM to achieve will bring difficulties to the controller’s design. This model can use classical control theory to design DC conversion between the super capacitor bank and the lithium-ion battery pack, conversion from a controller for It can quickly design a controller that meets single-phase ACPCMM. to the lithium-ion battery pack, and conversion fromthe theengineering lithium-ion requirements. battery pack to

single-phase AC. The performance requirements of the PCMM are shown in Table 1. 3. Simulation of the PCMM Table 1.toDesign parameters of the power multi-operating (PCMM). According the design requirements of converter a certain with vehicle model, the mode PCMM needs to achieve DC conversion between the super capacitor bank and the lithium-ion battery pack, conversion from Parameter Value single-phase AC to the lithium-ion battery pack, and conversion from the lithium-ion battery pack to High side requirements voltage range of the PCMM 350–420 V single-phase AC. The performance are shown in Table 1.

Low side voltage range 110–230 V Voltage of AC input or output Rms 180–240 V Table 1. Design parameters of the power converter with multi-operating mode (PCMM). AC frequency 50 Hz Output power of AC 3 kW Value Parameter Rated inductor current 250 A High side voltage range 350–420 V Low side voltage range 110–230 V Voltage of AC inputof or current output ripple and voltage Rms 180–240 In order to meet the requirements rippleVin different modes, AC frequency 50 Hz capacitance and inductance need to be matched with PCMM design parameters [25]. The results Output power of AC 3 kW obtained by the parameter matching show that the inductance of L1 and L2 is 690 uH, the AC filter Rated inductor current 250 A

capacitor C3 is 3 µF, the high side filter capacitor C2 is 9400 F, and the low side capacitor C1 is 2200 F. Matlab/Simulink was used for simulation and the main circuit of the simulation model is shown in Figure 10.

capacitance and inductance need to be matched with PCMM design parameters [25]. The results L L obtained by the parameter matching show that the inductance of L1 and L2 is 690 uH, the AC filter obtained by of 1 and 2 is 690 uH, the ACCfilter C the parameter matching show that the inductance C capacitor C3 is 3 μF, the high side filter capacitor C2 is 9400 F, and the low side capacitor C1 is 3 is 3 μF, the high side filter capacitor 2 is 9400 F, and the low side capacitor 1 is capacitor 2200 F. Matlab/Simulink was used for simulation and the main circuit of the simulation model is 2200 Electric F.inMatlab/Simulink is World Vehicle 10. Journal 2018,was 9, 7 used for simulation and the main circuit of the simulation model 10 of 17 shown Figure shown in Figure 10.

Figure 10. Main circuit of the simulation model. Figure 10. 10. Main circuit of of the the simulation simulation model. model. Figure Main circuit

Inductor current(A) Inductor current(A)

150 150

IL IL PWM1 IL1 PWM1 IL2 IL1 IL2

100 100

PWM2 PWM2

50 50 0 0.06000 0 0.06000

0.06005 0.06005

0.06010 0.06010

t(s) t(s)

1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0

PWM PWM

3.1. Bidirectional DC/DC Mode 3.1. Bidirectional DC/DC Mode Mode 3.1. Bidirectional DC/DC In buck mode, as shown in Figure 11, the inductor current and drive signals are obtained for an In buck mode, mode, as shown involtage Figureof 11,220 theV, inductor current and of drive signals are obtained obtained forthe an inputIn voltage of 350as V,shown outputin and output power 30 kW. During operation, buck Figure 11, the inductor current and drive signals are for an input voltage of 350 V, output voltage of 220 V, and output power of 30 kW. During operation, the two IGBTs turnofon alternately each phase by 180 degrees to reduce the During output current ripple. input voltage 350 V, outputand voltage of 220lags V, and output power of 30 kW. operation, the two IGBTs turn on alternately alternately and each eachwaveform phase lags 180 degrees to the output ripple. In Figure 11, IL1 and IL2 are the and current the two inductors. IL is the of Icurrent L1 and IL2 . The two IGBTs turn on phase lagsofby by 180 degrees to reduce reduce thesum output current ripple. In Figure Figure 11, IIL1 areA. the current waveform ofof the two inductors. IL is sum ofILIof L1 and IL2. The current ripple ofand IL1 isIIL255.0 Because of the interleaved structure, the output is reduced In 11, and the current waveform the two inductors. ILthe iscurrent the sum IL1 and Ito L1 L2 are L2 . current ripple of I L1 is 55.0 A. Because of the interleaved structure, the output current IL is reduced to 23.8 A. The current ripple of IL1 is 55.0 A. Because of the interleaved structure, the output current IL is reduced 23.8 A.A. to 23.8

Figure DC/DC mode. Figure 11. 11. Inductor Inductor current current waveform waveform in in bi-directional bi-directional DC/DC mode. Figure 11. Inductor current waveform in bi-directional DC/DC mode.

In boost mode, for the input voltage of 220 V, output voltage of 350 V, and load power of 30 kW, In boost mode, for the input voltage of 220 V, output voltage of 350 V, and load power of 30 kW, the output voltage response is shown in Figure 12a. is as asvoltage shown of in 350 Figure 12a. voltage of 220 V, and load power of 30 kW, In buck mode, response for the input V, output In buck mode, for the input voltage of 350 V, output the output voltage response process is as shown in Figurevoltage 12b. of 220 V, and load power of 30 kW, 360 the output voltage response process is as shown Figure 12b.80 ms in boost mode and buck mode, The output voltage reached a steady state inin100 ms and 220 80 ms in boost mode and buck mode, The output voltage reached a steady state in 100 ms and 340 respectively. The error of output voltage is less than 1%. The controller designed based on the respectively. Theiserror of output voltage is less than 1%. The controller designed based on the presented model accurate. 320 presented model is accurate. 218 VdcL(V)

VdcH(V)

In Electric boost mode,response for the input voltage of 220 V, 12a. output voltage of 350 V, and load power of 30 kW, Vehicle Journal 2018, x FOR PEER REVIEW 11 of 17 theWorld output voltage is9,as shown in Figure

300 280

216

260 0.00

0.02

0.04

0.06

t(s)

(a)

0.08

0.10

0.12

214 0.00

0.02

0.04

0.06

0.08

0.10

t(s)

(b)

Figure Output voltage waveform: boost mode; buck mode. Figure 12.12. Output voltage waveform: (a)(a) boost mode; (b)(b) buck mode.

3.2. AC/DC Mode In AC/DC mode, simulation studies were carried out for the input voltages of 180 V and 240 V, respectively. For the output voltage of DC 400 V, load resistance of 60 ohms, and output power of 2.667 kW at steady state, the input voltage and current are as shown in Figure 13. In this mode, the

220

340

VdcL(V)

VdcH(V)

320 300

World Electric Vehicle Journal 2018, 9, 7 280

218

11 of 17

216

260

In buck mode, for the input voltage of 350 V, output214 voltage of 220 V, and load power of 30 kW, 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.00 0.02 0.04 0.06 0.08 0.10 the output voltage response process is as shown in Figure 12b. t(s) t(s) The output voltage(a) reached a steady state in 100 ms and 80 ms in boost (b) mode and buck mode, respectively. The error of output voltage is less than 1%. The controller designed based on the presented model is accurate. Figure 12. Output voltage waveform: (a) boost mode; (b) buck mode. 3.2. AC/DC Mode

AC/DC mode, In AC/DC mode,simulation simulationstudies studieswere werecarried carriedout outfor forthe theinput inputvoltages voltagesof of180 180VVand and240 240V, V, respectively. For the output voltage of DC 400 V, load load resistance of 60 ohms, and output power of 2.667 kW at are asas shown in in Figure 13.13. In this mode, the at steady steadystate, state,the theinput inputvoltage voltageand andcurrent current are shown Figure In this mode, PCMM rectified the the AC AC power supply andand realized power factor correction. the PCMM rectified power supply realized power factor correction. 60

Vac1

Vac2 Iac1

Iac_rec

200

40

Iac2 Iac_rec

Iac1

100

Vac(V)

Vac1

Vac2

20

Iac2

0

0

-100

Iac(A)

300

-20

-200 -40 -300 0.70

0.72

-60 0.76

0.74

t(s)

Figure 13. Output voltage and current waveform.

V 1 I ac1 is the the waveform for the input As shown in Figure Figure 13, 13, Vac input voltage voltage RMS RMSvalue valueof of180 180V, V,and and Iac1 ac1 is Vacac2 is waveform. V RMS value value of of 240 240 V, V, and 2 is is the the waveform waveform for for the the input input voltage voltage RMS and is the the input input current current waveform. the Iac2 is the corresponding input current waveform. In contrast, I is the input current without ac_rec I ac _ rec I 2 is the corresponding input current In contrast, is the proportionally input current the acfactor power correction. With the power factorwaveform. correction, the input current changes without power factor correction. With the power factor correction, the input current with the input voltage, and the circuit shows a resistive load characteristic. The power factor ischanges greater proportionally with the input voltage, and the circuit shows a resistive load characteristic. The power than 0.996. factorThe is greater than 0.996. spectrum of input current is analyzed, and different order harmonics are shown in Table 2. The spectrum input current is analyzed, and different order harmonics are shown in Table 2. The total harmonicofdistortion (THD) of the input current (I h1 ) is 6.62% for AC 180 V. For AC The total harmonic distortion (THD) of the input current (I h1) is 6.62% for AC 180 V. For AC 240 V, 240 V, the THD of the input current (Ih2 ) is 8.22%, which meets the requirements of the Class A the THD ofinthe current (I h2) is 8.22%, which meets the requirements of the Class A equipment equipment theinput IEC6000-3-2 standard (Ihs ). Ih_rec is the harmonic of the input current without power in the IEC6000-3-2 standard (I hs). Ih_rec is the harmonic of the input current without power factor factor correction. correction. Table 2. Harmonics of input current. Harmonic Order

Ih_rec (A)

Ih2 (A)

Ih1 (A)

0 1 2 3 4 5 6 7 8 9 10

0.0000 10.2426 0.0000 8.4349 0.0000 5.4647 0.0000 2.6145 0.0000 1.0190 0.0000

0.0193 15.6923 0.0130 0.4684 0.0052 0.2243 0.0025 0.1856 0.0030 0.1600 0.0106

0.0544 20.0396 0.0367 0.2735 0.0034 0.1358 0.0054 0.1163 0.0031 0.1143 0.0119

Ihs (A)

1.0800 2.3000 0.4300 1.1400 0.3000 0.7700 0.2300 0.4000 0.1840

Harmonic Order

Ih_rec (A)

Ih2 (A)

Ih1 (A)

His (A)

11 12 13 14 15 16 17 18 19 20

0.8765 0.0000 0.6629 0.0000 0.3919 0.0000 0.3624 0.0000 0.2929 0.0000

0.1371 0.0079 0.1198 0.0157 0.1187 0.0086 0.0706 0.0055 0.0623 0.0110

0.0942 0.0060 0.0861 0.0030 0.0911 0.0148 0.1022 0.0142 0.0682 0.0145

0.3300 0.1533 0.2900 0.1314 0.2570 0.1150 0.2265 0.1022 0.2026 0.0836

In an independent inverter mode, the output AC voltage and current phase do not need to track the phase of the grid voltage. A voltage controller is used to regulate the output voltage. For the DC voltage of 400 V and output voltage RMS value of 220 V, the output voltage and current are shown in Figure 14. World Electric Vehicle Journal 2018, 9, 7 12 of 17 V For the output voltage of RMS 220 V with loads of 500 W, 3 kW, and 1.5 kW, the voltage ac1 , Vac 2 , and Vac 3 are shown in Figure 14. Iac1, Iac2, and Iac3 are the current waveforms for 500 W, 3 kW, 3.3. DC/AC Mode and 1.5 kW operation. In an independent inverter mode, the outputspectrum, AC voltage and current do not need tointrack The output current is analyzed by frequency and each orderphase harmonic is shown the the phase grid voltage. A voltageofcontroller is used to regulate the voltage. Forcurrent the DC Table 3. Ih1,of Ih2the , and Ih3 are the harmonics Iac1, Iac2, and Iac3, respectively. Theoutput THD of the input output value of 220 V, the current are shown in isvoltage 9.12% of in 400 500 V W,and 1.53% in 3 voltage kW (220RMS V), and 2.28% in 1.5 kWoutput (110 V)voltage mode, and respectively. It can meet Figure 14. the requirements of Class A equipment according to the IEC6000-3-2 standard.

300

Vac1 Vac2

200

Vac3

Vac(V)

100

60

40

Iac2

20

Iac3 Iac1

0

Iac(a)

400

0

-100

-20

-200 -40

-300 -400 0.00

0.01

0.02

0.03

-60 0.04

t(s)

Figure 14. Output voltage and current waveform. Figure 14. Output voltage and current waveform. Table 3. Harmonics of output current.

For the output voltage of RMS 220 V with loads of 500 W, 3 kW, and 1.5 kW, the voltage Vac1 , Vac2 , Harmonic order Ih1 (A) Ih2 (A) Ih3 (A) His (A) Harmonic order Ih1 (A) Ih2 (A) Ih3 (A) His (A) and Vac3 are shown in Figure 14. Iac1 , Iac2 , and Iac3 are the current waveforms for 500 W, 3 kW, and 0 0.0000 0.0000 0.0003 11 0.0006 0.0355 0.0186 0.3300 1.5 kW operation. 1 3.2150 19.0148 9.6702 12 0.0036 0.0018 0.0031 0.1533 2 0.0004 0.0004 0.0001 1.0800 spectrum, 13 and each 0.0025 0.0268 0.0185 is shown 0.2900 in the The output current is analyzed by frequency order harmonic 3 0.0066 0.1150 0.0627 2.3000 14 0.0028 0.0047 0.0004 0.1314 Table 3. Ih1 , Ih2 , and Ih3 are the harmonics of Iac1 , Iac2 , and Iac3 , respectively. The THD of the input 4 0.0007 0.0019 0.0024 0.4300 15 0.0023 0.0326 0.0168 0.2570 current is 9.12% in 5000.0194 W, 1.53% in 3 kW (2201.1400 V), and 2.28% (110 V) mode, respectively. 5 0.0660 0.0244 16in 1.5 kW 0.0014 0.0094 0.0044 0.1150 It can 6 0.0019 0.0007 0.0010 0.3000 0.0024 0.0233 0.0151 0.2265 meet the requirements of Class A equipment according to17the IEC6000-3-2 standard. 7 8 9 10

0.0114 0.0020 0.0024 0.0015

0.0398 0.0168 0.7700 18 0.0011 0.0008 0.0034 0.2300 19 0.0011 Table 3. Harmonics of output current. 0.0317 0.0132 0.4000 20 0.0010 0.0030 0.0051 0.1840

Harmonic Order

Ih1 (A)

Ih2 (A)

Ih3 (A)

0 1 2 3 4 5 6 7 8 9 10

0.0000 3.2150 0.0004 0.0066 0.0007 0.0194 0.0019 0.0114 0.0020 0.0024 0.0015

0.0000 19.0148 0.0004 0.1150 0.0019 0.0660 0.0007 0.0398 0.0008 0.0317 0.0030

0.0003 9.6702 0.0001 0.0627 0.0024 0.0244 0.0010 0.0168 0.0034 0.0132 0.0051

His (A)

1.0800 2.3000 0.4300 1.1400 0.3000 0.7700 0.2300 0.4000 0.1840

0.0007 0.0247 0.0059

0.0048 0.0141 0.0019

0.1022 0.2026 0.0836

Harmonic Order

Ih1 (A)

Ih2 (A)

Ih3 (A)

His (A)

11 12 13 14 15 16 17 18 19 20

0.0006 0.0036 0.0025 0.0028 0.0023 0.0014 0.0024 0.0011 0.0011 0.0010

0.0355 0.0018 0.0268 0.0047 0.0326 0.0094 0.0233 0.0007 0.0247 0.0059

0.0186 0.0031 0.0185 0.0004 0.0168 0.0044 0.0151 0.0048 0.0141 0.0019

0.3300 0.1533 0.2900 0.1314 0.2570 0.1150 0.2265 0.1022 0.2026 0.0836

4. Experimental In order to reduce the inductor volume, the L1 , L2 is 69 uH/150 A. In AC/DC and DC/AC modes, L1 and L2 are connected in series with an inductor for the values of 1.2 mH/20 A. Filter capacitor C3 employs a 3 uF/600 V capacitor, filter capacitor C2 employs two 4700 F/500 V aluminum electrolytic capacitors, and filter capacitor C1 employs a 2200 F/400 V aluminum electrolytic capacitor. The four switch tubes are made up of two MITSUBISHI PM200DV1A120 IPM modules. The current is sampled by a HAS-200-s LEM current sensor. The voltage sensor uses LEM’s LV25-P voltage sensor to isolate the samples. The experimental test bench is shown in Figure 15.

Lswitch 1 and L 2 are are connected inofseries with an inductor for the values of modules. 1.2 mH/20The A. current Filter capacitor C3 tubes made up two MITSUBISHI PM200DV1A120 IPM is sampled employs a 3 uF/600 capacitor, filterThe capacitor 2 employs 4700LV25-P F/500 Vvoltage aluminum electrolytic by a HAS-200-s LEMVcurrent sensor. voltageCsensor usestwo LEM’s sensor to isolate capacitors, and filter capacitor C 1 employs 2200 F/400 V aluminum electrolytic capacitor. The four the samples. The experimental test bench isashown in Figure 15. switch tubes are made up of two MITSUBISHI PM200DV1A120 IPM modules. The current is sampled by a HAS-200-s LEM current sensor. The voltage sensor uses LEM’s LV25-P voltage sensor to isolate World Electric Vehicle Journal 2018, 9, 7 13 of 17 the samples. The experimental test bench is shown in Figure 15.

Figure 15. Experimental test bench.

According to actual measurements of the experimental prototype, the electronic components Figure Experimental test weigh 8.7 kg, while accessories, such as15. the enclosure and wires, weigh 7.4 kg, resulting in a total Figure 15. Experimental testbench. bench. prototype weight of 16.1 kg. If the Bi-DC/DC, DC/AC, and AC/DC converters are installed According to toactual actual measurements of the experimentalPCMM prototype, theelectronic electronic components independently, the total weight will be 33of kg. Comparatively, can the reduce the weight by 51.2%. According measurements the experimental prototype, components weigh 8.7 kg, while accessories, such as the enclosure and wires, weigh 7.4 kg, resulting in a in total weigh 8.7 kg, while accessories, such as the enclosure and wires, weigh 7.4 kg, resulting a 4.1. Bi-DC/DC Mode prototype weight of 16.1 kg. If the Bi-DC/DC, DC/AC, and AC/DC converters are installed total prototype weight of 16.1 kg. If the Bi-DC/DC, DC/AC, and AC/DC converters are installed independently,the thetotal totalweight weight willbe be 33kg. kg. Comparatively, Comparatively,PCMM PCMMcan canreduce reduce theweight weightby by 51.2%. 51.2%. independently, The input voltage and thewill output33 voltage in Bi-DC/DC model are shown inthe Figure 16a,b. In the figures, the pink curves are the high side voltage. The blue curves are the low side voltage. 4.1. 4.1.Bi-DC/DC Bi-DC/DCMode Mode In boost mode, for an input voltage of 220 V, output voltage of 350 V, and load resistance of 30 The input voltage ininBi-DC/DC model shown in Figure In Theinput inputvoltage voltageand the output voltage Bi-DC/DC model are shown induring Figure16a,b. 16a,b. Inthe the Ω, the voltage andthe theoutput output voltage are as shown in are Figure 16a initiation of figures, the pink curves are the high side voltage. The blue curves are the low side voltage. figures, the pink curves are the high side voltage. The blue curves are the low side voltage. conversion. The conversion efficiency reaches 96.4%. In boost mode, for an input voltage of 220 V, output voltage of 350 V, and load resistance of 30 Ω, the input voltage and the output voltage are as shown in Figure 16a during initiation of conversion. The conversion efficiency reaches 96.4%.

(a)

(b)

Figure16. 16.Input Inputvoltage voltageand andoutput outputvoltage voltageinin(a) (a)boost boostmode, mode,(b) (b)buck buckmode. mode. Figure

(a) (b) In buck mode, for an input voltage of 350 V, output voltage of 220 V, and load resistance of 30 In boost mode, for an input voltage of 220 V, output voltage of 350 V, and load resistance of 30 Ω, Ω, the input voltage output voltage as shown in (a) Figure during initiation Figure and 16. Input voltage and are output voltage in boost16b mode, (b) buck mode. of conversion. the input voltage and the output voltage are as shown in Figure 16a during initiation of conversion. The conversion efficiency is 96.1%. The conversion efficiency 96.4%. of 350 V, output voltage of 220 V, and load resistance of 30 In buck mode, for anreaches input voltage In input buck mode, anoutput input voltage voltage are of 350 V, output voltage 220 V, initiation and loadof resistance of Ω, the voltagefor and as shown in Figure 16bofduring conversion. 30 Ω, the input voltage and output voltage are as shown in Figure 16b during initiation of conversion. The conversion efficiency is 96.1%. The conversion efficiency is 96.1%. 4.2. AC/DC Mode The AC voltage connects a 3 kVA transformer to adjust the grid voltage for input of PCMM. The DC output is connected to a resistance load. In the absence of power factor correction, the four reverse diodes form a rectifier bridge, and the circuit operates in the uncontrolled rectifier state. The input voltage and current of the AC side are shown in Figure 17a. The power factor is 0.57, and the output voltage is uncontrollable.

4.2. AC/DC Mode voltage is uncontrollable. WithACpower factor correction, an output voltage DC 350 V, input current is The voltage connects a 3 kVA for transformer to adjust theof grid voltage forthe input of PCMM. The proportional to the input voltage. The input voltage, input current, and output DC voltage are shown DC output is connected to a resistance load. In the absence of power factor correction, the four reverse in Figure 17b. By power factorand correction, the power in factor is increased to 0.988. state. The conversion diodes form a rectifier bridge, the circuit operates the uncontrolled rectifier The input I voltage andis current of thethd AC are shown Figurevoltage 17a. Theispower 0.57, and the output efficiency 96.4%, the2018, 5.68%, and theinoutput stablefactor underisthe regulation ofofthe World Electric Vehicle Journal 9, 7isside 14 17 voltage is uncontrollable. regulator. With power factor correction, for an output voltage of DC 350 V, the input current is proportional to the input voltage. The input voltage, input current, and output DC voltage are shown in Figure 17b. By power factor correction, the power factor is increased to 0.988. The conversion I efficiency is 96.4%, the thd is 5.68%, and the output voltage is stable under the regulation of the regulator.

(a)

(b)

Figure 17. 17. Voltage Voltageand andcurrent currentin inAC/DC AC/DC mode: mode: (a) (a) without without power power factor factor correction; correction; (b) (b) with with power power Figure factor correction. factor correction.

4.3. DC/AC Mode With power factor correction, for an output voltage of DC 350 V, the input current is proportional (a) (b) DC/AC mode, forinput an input voltage of current, DC 350 V, of RMS V, load resistance to theIninput voltage. The voltage, input andoutput outputvoltage DC voltage are220 shown in Figure 17b. Figure 17. Voltage and current in AC/DC mode: (a) without power factor correction; (b) with power of 54 Ω, and frequency of 50 Hz, the wave form of the output voltage, input current, and DC side By power factor correction, the power factor is increased to 0.988. The conversion efficiency is 96.4%, factor correction. voltage as shown in Figure The is pink curve is the high side the blue curve is the the Ithd isare 5.68%, and the output18a. voltage stable under theDC regulation ofvoltage, the regulator. output voltage, and the yellow curve is the output current. The THD of the output current is 5.893% 4.3. Mode is 96.7%. andDC/AC the efficiency In DC/AC DC/ACmode, mode,for foran aninput inputvoltage voltageof ofDC DC350 350V, V, output output voltage voltage of of RMS RMS 220 220 V, V, load resistance of 54 Ω, Ω, and frequency of 50 Hz, the wave form of the output voltage, input current, and DC side voltage are as shown in Figure 18a. The pink curve is the DC high side voltage, the blue curve is the output voltage, and the yellow curve is the output current. The The THD THD of of the the output output current current is 5.893% 5.893% and the efficiency is 96.7%.

(a)

(b)

Figure 18. (a) Output voltage, output current, and output voltage of the DC/AC converter. (b) Waveform with motor load.

In order to verify the performance of the inverter with a motor load, a 900 W AC motor load was (a) load. The resulting waveform is(b) suddenly applied to the resistance shown in Figure 18b. During the Figure 18. (a) current, and and output output voltage voltage of of the the DC/AC DC/AC converter. converter. (b) Figure 18. (a) Output Output voltage, voltage, output output current, (b) Waveform with motor load. Waveform with motor load.

In order to verify the performance of the inverter with a motor load, a 900 W AC motor load was In order to verify the performance of the inverter with a motor load, a 900 W AC motor load suddenly applied to the resistance load. The resulting waveform is shown in Figure 18b. During the was suddenly applied to the resistance load. The resulting waveform is shown in Figure 18b. During the load change, the output power is 1800 W with a conversion efficiency of 96.7%, and the output is asymptotically stable. 5. Conclusions This paper presents a PCMM power converter with three different working modes for EV application. The proposed PCMM can work in Bi-DC/DC, AC/DC, and DC/AC modes. In super-capacitor & battery

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hybrid energy storage systems for EV applications, the Bi-DC/DC mode converts the power between the battery and the super-capacitor; the AC/DC mode charges the battery, and the DC/AC mode provides an AC source to electrical equipment. Mathematical representation of the state-space averaging model of the PCMM considering the resistance of IGBT and inductor is presented. Based on this model, the relationship between the steady state of the output voltage and the input voltage is given. In order to describe the system characteristics under small signal perturbations, the small signal model of the PCMM and the transfer function of the system are derived. Using the established PCMM model, the controller was designed. The simulation and experimental results show that the PCMM can meet the design target and the feasibility of the model is verified. The PCMM converter reduces costs and lightens the system weight by sharing inductors, IGBT, capacitors, and other components. The measured results show that, compared with a traditional vehicle power conversion system, the PCMM structure proposed in this paper reduces the weight by 51.2%. The model presented in this paper reflects the characteristics of the system under small signal disturbances. In future research, the response characteristics of the system under state switching will be studied based on nonlinear modeling. Author Contributions: Luo Yutao conceived the study. Wang Feng planned the experiments. Luo Yutao and Wang Feng wrote the manuscript. All authors submitted comments, read and approved the final manuscript. Funding: This research was funded by the Major Research and Development Project of Guangdong Science and Technology Department, grant number 2016B010132001. Conflicts of Interest: The authors declare no conflicts of interest.

Nomenclature EV PFC VDCL VDCH K1 K2 K3 Q1 ,Q2 Q3 ,Q4 L1 ,L2 C1 C2 C3 vc (t) vo (t) ˆ (t) i L1 ˆ (t) i L2 ˆ vc (t) PCMM THD v ac (t) i L1 (t) i L2 (t) RL Vo

Electric vehicle Power factor correction Low side voltage (V) High side voltage (V) Switch of DC/AC Switch of AC/DC Switch of DC/DC IGBT of the first phase IGBT of the second phase Inductor (H) Capacitor of the low side (F) Capacitor of the high side (F) Capacitor of the AC side (F) Voltage of the capacitor (V) Output voltage (V) Current small signal of L1 (A) Current small signal of L2 (A) Small signal of capacitor (V) Power converter with multi-operating mode Total harmonic distortion Voltage of AC side (V) Current of inductor L1 (A) Current of inductor L2 (A) The load resistance (Ω) Average output voltage in steady state (V)

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Vi Vc IL1 ,IL2 rL rs vi ( t ) d vre f (t) hvc (t)iTs hi L1 (t)iTs hi L2 (t)iTs

16 of 17

Average input voltage in steady state (V) Average capacitor voltage in steady state (V) Average current of inductor in steady state (A) Inductor resistance (Ω) IGBT resistance (Ω) Input voltage (V) Duty cycle The reference voltage (V) Average voltage of capacitor in one cycle (V) Average current of L1 in one cycle (A) Average current of L2 in one cycle (A)

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