Design Consider ations, Modeling and Control of Dual Active Full … · Electric Vehicles Charging...

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Design Considerations, Modeling and Control of Dual Active Full Bridge for Electric Vehicles Charging Applications

Fatma Jarraya, Ahmad Khan, Adel Gastli, Lazhar Ben-Brahim, Ridha Hamila

Electrical Engineering Department, College of Engineering, Qatar University, P.O. Box 2713, Doha, Qatar *[email protected]

Abstract: The Dual Active Full Bridge (DAFB) is one of the promising isolated DC/DC converter topologies that will play a significant role in the future of Electric Vehicle (EV) integration in Smart Grids (SGs). This is due to its inherent soft switching and control simplicity. Therefore, this paper presents first the latest developments related to the design of DAFB converter in EV charging technology. It provides a brief discussion of the crucial recommendations regarding the reliability, efficiency, system configuration, EV charger control scheme, battery lifetime and system materials. Then, it presents a step-by-step modelling approach for a non-ideal DAFB for the purpose of designing its controller. In addition, the model provided by this paper includes all non-idealities due to the High Frequency (HF) transformer, semiconductor switches, passive components and digital system delays. Eventually, the proposed system design and analysis was validated by implementing a 6.1kW prototype on Simulink and Typhoon-HIL real-time simulator.

1 Introduction

1.1 Motivation and incitement

The environment and their increasing cost lead to

the accelerating growth in Electric Vehicles (EV) technology

[1]-[3]. The EVs importance in integration with Smart Grids

(SGs) is that they tackle the issues of inherent intermittence

and randomness in renewable energy sources by providing a

power management solution [4]. Even though, in systems

without renewable energy integrations the benefit of using

the vehicle battery as a temporary storage is non-existing;

still EV bidirectional chargers offer a promising solution to

support the power grid during peak demand and

contingencies through Vehicle-to-Grid (V2G) battery

discharging operation mode [5]-[8]. In SGs, bidirectional EV

battery charger is the key interface that controls the different

power-flow modes Grid-to-Vehicle (G2V) or/and V2G [9]-

[12].

1.2 Literature review

The general common structure of a bidirectional EV

battery charging system is shown in Fig. 1 [13].

Fig. 1. Overall block diagram of bidirectional EV charger.

The system is mainly composed of bidirectional DC/DC

converter cascaded with a bidirectional AC/DC converter

(PWM single-phase or three-phase converter). Generally, the

most appropriate bidirectional AC/DC converter topology

used in this application is the Full-Bridge inverter either

three-phase or single-phase topology as it does not require

any Power Factor Correction (PFC) circuitry and control

[13]. Thus, this paper focuses on the design and control

aspects of the bidirectional DC/DC converter that provides

the suitable interface between the utility grid and the EV

battery. Besides, in G2V and V2G applications, non-isolated

(transformerless) designs are not preferred due to the

following reasons:

▪ Leakage current circulation increases hazards risks which led the EV grid-integration standards to emphasize on isolation requirement for safety assurance [13]-[14].

▪ Large mismatch between the battery and grid nominal voltages. Therefore, matching the voltage levels without using transformers would require increasing the number of batteries connected in-series [15], [16]. However, this increases the probability of batteries State of Charge (SoC%) mismatch occurrences [17].

Therefore, his paper will focus only on the isolated

configuration of the Dual Active Full Bridge (DAFB)

utilizing a High-Frequency (HF) transformer.

1.3 Contribution and paper organization

This paper discusses the design considerations for the

DAFB used as a bidirectional EV battery charger. It also

presents a modeling approach applied to the DAFB topology

with its control techniques. The developed DAFB model and

its control techniques are implemented and validated under

both G2V and V2G operations using Matlab/Simulink and

Hardware in the Loop (HIL). The power flow dynamics and

the converter efficiency are also investigated under various

operating scenarios.

This paper is therefore structured as follows: section

2 presents an overview of the DAFB design considerations

and features in-light of G2V and V2G applications; section

3 elaborates on the DAFB converter modeling approach;

section 3 discusses key recommendations and design

considerations on using the DAFB in EV charging

applications; section 5 discusses the simulation and

experimental results; finally, section 5 concludes the paper.

Power Grid

Bidirectional AC-DC Converter

Bidirectional

DC-DC Converter

=

= =

EV Battery

DAFB V2G mode (Discharging

mode) G2V mode (Charging mode)

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2

2 Overview of DAFB Design Considerations

Fig. 2 shows the overall topology of a typical DAFB for

EV G2V and V2G applications.

Fig. 2. General DAFB topology

The use of this topology is proposed for applications

where automatic bidirectional power flow, power density,

reliability, efficiency and cost are the primary design

considerations. The system is mainly composed of

bidirectional PWM DC/AC inverter followed by a High

Frequency (HF) transformer feeding a bidirectional AC/DC

converter, which in turn charges the EV battery. The DAFB

system bidirectional power-flow between the grid and the

battery is controlled by adjusting the phase shift (φ) between

the two bridges’ PWM control signals.

2.1 Reliability

Reliability studies of power electronics converters

focus on the weakest element in the system. Particularly,

capacitors are considered as the most fragile part of the

system [18]-[21]. In fact, failures due to capacitors have the

highest cost/failure ratio since they are difficult to detect and

hence require a special attention [21]. Particularly, when the

capacitance requirement is large, it is inevitable to avoid

using unreliable electrolytic capacitors because it is difficult

to find commercial reliable non-polarized film capacitors

with high capacitance values [22]. Moreover, the high

capacitance requirement is due to the low inertia of the

system that causes second order voltage harmonics to appear

on the DC-Link [23]. Even though, this phenomena is severe

with single-phase systems; yet, any system with an

instantaneous power that is not constant would possess high

input capacitance requirement to match this power mismatch.

Consequently, the lifespan of the system is highly

deteriorated in case the charger is constructed with single-

phase topology.

However, the input capacitance could be reduced

with single-phase systems by using an appropriate power-

decoupling scheme [24]. Authors in [25] reviewed the

power decoupling methods that require extra switches and

energy storage devices and [26] provides a switchless power

decoupling method. Yet, adopting a power-decoupling

control scheme would increase the complexity of overall

battery charger [27]. Consequently, it is recommended to

use the DAFB in a three-phase topology to minimize the

DC-Link capacitance requirement that would reflect

positively on the system reliability [10], [28]-[30].

2.2 Battery Lifetime Considerations

To assure the safe operation of the system and avoid

damaging the battery due to over-charge or over-discharge,

the system should monitor the SoC% of the battery to select

the appropriate operation mode [10]. Fig. 3 depicts the

different SoC% level and the suitable V2G or G2V

operation modes. Note that, in the range of (15%-80%) the

priority of the operation is set by the user. Meaning that, in

normal operation, V2G mode would be set by a command

that is provided by the SG; unless, the EV user predefined

G2V priority for EV charging.

Fig. 3. Operation modes based on battery SoC%.

2.3 ZVS, ZCS and Efficiency Considerations

It is well known that the DAFB has inherent Zero

Voltage Switching (ZVS) capabilities in case the ratio of the

voltages applied on the HF transformer sides is equal to the

transformer ratio [31]. ZVS condition means that the turn-on

losses are negligible and therefore efficiency is high.

Nevertheless, many of the recent literatures on the DAFB

configuration are focused on increasing the ZVS region. For

instance, [31] investigates the ZVS boundaries if a 3-level

modulation is adopted. Besides, [32] provides a summary of

different modulation schemes – Extended-Phase-Shift (EPS)

[33], Dual-Phase-Shift (DPS) [34], and Triple-Phase-Shift

(TPS) [35] – that are often used with the DAFB to reduce

the switching loss and extend the ZVS region. In addition,

[36] proposed a new modulation technique that is based on

online optimization algorithm called Half-bridge-Pulse-

width-modulation-plus-Phase-Shift (HPPS) that is similar to

TPS of [35]. Also, there are some other control schemes that

are based on online frequency modulation control to

optimize the AC-Link reactance such as the control

proposed by [37]-[39]. Nevertheless, simply controlling the

DC-Link voltage to assure that the voltage applied on the

HF transformer sides is equal to the transformer ratio would

be sufficient to accomplish ZVS conditions [32].

Unlike the turn-on losses, turn-off losses are non-

negligible due to the existence of a significant LV-Side

leakage inductance [28]. In fact, to further increase the

efficiency, a turn-off RC snubber circuit must be considered;

especially with the LV-Side bridge MOSFETs to attain Zero

Current Switching (ZCS) conditions [28].

On the other hand, MOSFET’s characteristics make

them attractive to use in EV applications. Specifically, the

type of the modulation used either on the DAFB or on the

bidirectional inverter allows harnessing the intrinsic body

diode of the MOSFET instead of using actual antiparallel

diodes [40], [41]. As a result, reducing the components

counts and cost and increasing the reliability. Additionally,

the nature of the ZVS of the DAFB permits high switching

frequency operation, which makes the MOSFETs an

attractive option over IGBTs. However, the drawback of the

Silicon MOSFETs is the significant on-state loss.

Consequently, Silicon Carbide (SiC) MOSFETs can be

adopted in the design to reduce the conduction losses [42].

Phase shift ()

C1

+

_

S11

S12

S13

S14

i1

HF Filter

Capacitors

leg11 leg

12

Active Bridge 1

(Full Bridge)

Positive Power Flow

IAC1

v

HF1 VHF2

IAC2

n:1

Primary Side/Grid Side Secondary Side/Battery

Side

S21

S22

S23

S24

leg21 leg

22

HF Isolation

Transformer

C2

i2

HF Filter

Capacitors Active Bridge 2

(Full Bridge)

Iout I

in

Vin V

2

+

_

V1

0% 15%

80

% 100

% G2

V V2G or G2V V2

G

SoC%

→ Operation

→




3

2.4 HF Transformer Core Materials

The HF transformer is required for both isolation and

voltage matching between the primary and the secondary

sides of the DAFB. Usually, iron-based nanocrystalline soft-

magnetic cores are preferred over ferrite cores because they

have greater saturation magnetic flux density, higher

magnetic permeability, higher Curie temperature and lesser

iron loss [15], [32]. Hence, an efficient utilization of the HF

transformer and pushing the power density further can be

achieved by designing the core with nanocrystalline

materials [43].

3 DAFB Modeling

The DAFB-based bidirectional EV battery charging

system configuration is shown in Fig. 4. The system is

mainly composed of bidirectional PWM DC/AC inverter

followed by a HF transformer feeding a bidirectional

AC/DC converter, which in turn charges the EV battery. The

DAFB system bidirectional power-flow between the grid

and the battery is controlled by adjusting the phase shift (φ)

between the two bridges’ PWM control signals. Notice that

an outer control loop uses a Proportional-Integral (PI)

controller to regulate the SoC% of the EV battery.

Fig. 4. DAFB-based bidirectional EV battery charger

system

It is important to model the DAFB system in order to

derive an appropriate transfer function between the DAFB

output current and the phase shift ratio to design a proper

controller for the battery charging and discharging operation.

However, the challenge in modeling the DAFB is that the

system is highly non-linear due to its HF transformer current

shape. Even though, there are various types of models in the

literature, the most used models neglect the magnetization

inductance and the core losses of the HF transformer [44]-

[47]. Recently, authors in [48] proposed a better modelling

methodology that requires less complexity and includes the

core losses and the effect of the magnetization inductance.

Therefore, similar modeling approach is used hereafter. This

approach is based on averaging the input current of the HV-

side Bridge (iAC1) and output current of LV-side Bridge (iAC2)

over half of the switching cycle (denoted here by T=1/2fs).

In other words, these currents can be represented by

dependent current sources, with the assumption that the

other variables are constant over the averaging period as

depicted in Fig. 5. Note that this model is for the

conventional SPS control scheme. Nevertheless, before

going to the small-signal model, the large-signal model is

first derived.

3.1 Large-Signal Model

The dynamics of the large-signal model are

expressed as follows:

𝐶1𝑑𝑣1𝑑𝑡

= 𝑖𝑖𝑛 − 𝑖𝐴𝐶1 (1)

𝐿𝑖𝑑𝑖𝑖𝑛𝑑𝑡

+ 𝑅𝑖𝑖𝑖𝑛 = 𝑣𝑖𝑛 − 𝑣1 (2)

𝐶2𝑑𝑣2𝑑𝑡

= 𝑖𝐴𝐶2 − 𝑖𝑜𝑢𝑡 (3)

𝐿𝑜𝑑𝑖𝑜𝑢𝑡𝑑𝑡

+ 𝑅𝑜𝑖𝑜𝑢𝑡 = 𝑣2 − 𝑣𝑜𝑢𝑡 (4)

where all parameters are shown in Fig. 5. The current

waveforms for iAC1 and iAC2 are obtained by a piecewise

solution of linear ordinary differential equations (5) and (6).

𝑣1 + 𝑛𝑣2

𝐿=𝑑𝑖𝐴𝐶1(𝑡)

𝑑𝑡+𝑅

𝐿𝑖𝐴𝐶1(𝑡) ∀ 𝑡 ∈ [0, 𝑑𝑇)

(5) 𝑣1 − 𝑛𝑣2𝐿

=𝑑𝑖𝐴𝐶1(𝑡)

𝑑𝑡+𝑅

𝐿𝑖𝐴𝐶1(𝑡) ∀ 𝑡 ∈ [𝑑𝑇, 𝑇)

−𝑛𝑣1 + 𝑛

2𝑣2𝐿

=𝑑𝑖𝐴𝐶2(𝑡)

𝑑𝑡+𝑅

𝐿𝑖𝐴𝐶2(𝑡) ∀ 𝑡 ∈ [0, 𝑑𝑇)

(6) 𝑛𝑣1 − 𝑛2𝑣2

𝐿=𝑑𝑖𝐴𝐶2(𝑡)

𝑑𝑡+𝑅

𝐿𝑖𝐴𝐶2(𝑡) ∀ 𝑡 ∈ [𝑑𝑇, 𝑇)

The current waveforms are therefore following exponential

patterns as shown in (7) and (8).

𝑖𝐴𝐶1(𝑡) = {

𝑣1 + 𝑛𝑣2𝑅

+ (−𝐼1 −𝑣1 + 𝑛𝑣2

𝑅) 𝑒−

𝑅𝐿 𝑡 ∀ 𝑡 ∈ [0, 𝑑𝑇)

𝑣1 − 𝑛𝑣2𝑅

+ (𝐼2 −𝑣1 + 𝑛𝑣2

𝑅) 𝑒−

𝑅𝐿( 𝑡−𝑑𝑇) ∀ 𝑡 ∈ [𝑑𝑇, 𝑇)

(7)

𝑖𝐴𝐶2(𝑡) =

{

−

𝑛𝑣1 + 𝑛2𝑣2

𝑅+ (𝑛𝐼1 +


𝑅) 𝑒−

𝑅𝐿 𝑡 ∀ 𝑡 ∈ [0, 𝑑𝑇)

𝑛𝑣1 − 𝑛2𝑣2

𝑅+ (𝑛𝐼2 −

𝑛𝑣1 − 𝑛2𝑣2

𝑅) 𝑒−

𝑅𝐿( 𝑡−𝑑𝑇) ∀ 𝑡 ∈ [𝑑𝑇, 𝑇)

(8)

Note that R is the equivalent resistance of the HF transformer

and the two bridges that can be approximated by (9), L is the

equivalent inductance of the HF transformer and expressed

as in (10), where n is the transformer ratio and d is the phase

shift ratio (𝑑 =𝜑

𝜋 ).

𝑅 = 2𝑅𝐷𝑆 + 𝑅𝐴𝐶−𝐿𝑖𝑛𝑘 + 𝑅1 + 𝑛2𝑅2 + +2𝑛

2𝑅𝐷𝑆 (9) 𝐿 = 𝐿𝐴𝐶−𝐿𝑖𝑛𝑘 + 𝐿1 + 𝑛

2𝐿2 (10)

Note that the RC and LM are very large and they draw an

insignificant current; thus, their contributions to the

equivalent resistance and inductance in (9) and (10) are

neglected. In addition, since the magnetization and the

demagnetization of the shunt magnetization inductance is

synchronous during one switching ( 2𝑇 =1

𝑓𝑠) cycle; the

average of the current flowing in LM is zero.

iAC1

iAC2

n:1

Battery

PWM Generator (50% Duty Cycle)

Sampling

Frequency

fs

Battery Current PI

Controller

Phase Shift

State of charge

control

IBref

iout

IB=iout + -

SoC

SoC%

C1 C

2

v1 v

2

iin

Full Bridge 1

Full Bridge 2




4

Vin VoutC1

iin iAC1

R1 n2R2n

2L2L1

LM RC

Lo

C2

+v1-

+v2-

iAC2 iout

T3 T1

T4 T2

T5

T6

T7

T8

2RDS 2n2RDS n:1

RiLi Ro

LAC-Link RAC-Link

(a)

iin

iAC1 iAC2/n

n:1 iAC2 iout

vin vout

Ri Li Lo Ro

C1 C2

iAC1 iAC2/n

(b)

Fig. 5. DAFB Model: (a) Large-signal model and (b) Small-signal model

Moreover, an expression for the two initial current

conditions I1 and I2 can be found by harnessing the fact that

the piecewise current waveforms are continuous.

Furthermore, these two initial conditions represent the

transformer peak currents. Therefore, using the following

conditions (11)-(13); I1 and I2 are as determined by (14) and

(15), respectively.

−𝑛𝑖𝐴𝐶1(𝑡 = 0) = 𝑖𝐴𝐶2(𝑡 = 0) = −𝐼1 (11) 𝑛𝑖𝐴𝐶1(𝑡 = 𝑇) = 𝑖𝐴𝐶2(𝑡 = 𝑇) = 𝐼1 (12) 𝑛𝑖𝐴𝐶1(𝑡 = 𝑑𝑇) = 𝑖𝐴𝐶2(𝑡 = 𝑑𝑇) = 𝐼2 (13)

𝐼1 =𝑣1 − 𝑛𝑣2 + 2𝑛𝑣2𝑒

−𝑅𝐿(𝑇−𝑑𝑇) − (𝑣1 + 𝑛𝑣2)𝑒

−𝑅𝐿𝑇

𝑅 (1 + 𝑒−𝑅𝐿𝑇)

(14)

𝐼2 =𝑣1 + 𝑛𝑣2 − 2𝑣1𝑒

−𝑅𝐿𝑑𝑇 + (𝑣1 − 𝑛𝑣2)𝑒

−𝑅𝐿𝑇

𝑅 (1 + 𝑒−𝑅𝐿𝑇)

(15)

Now averaging (7) and (8) over half the switching

cycle – 𝑖̇ ̅ =1

𝑇∫ 𝑖(𝑡)𝑑𝑡 𝑇

0– yields (16) and (17).

�̇�𝐴𝐶1̅̅ ̅̅ ̅̅ =𝑣1 + 𝑛𝑣2

𝑅𝑑 +

𝑣1 − 𝑛𝑣2𝑅

(1 − 𝑑)

+𝐿

𝑅 𝑇(𝐼1 +

𝑣1 + 𝑛𝑣2𝑅

) (𝑒−𝑅𝐿𝑑𝑇 − 1)

+𝐿

𝑅 𝑇(𝑣1 − 𝑛𝑣2

𝑅− 𝐼2) (𝑒

−𝑅𝐿(𝑇−𝑑𝑇) − 1)

(16)

�̇�𝐴𝐶2̅̅ ̅̅ ̅̅ = −𝑛𝑣1 + 𝑛

2𝑣2𝑅

𝑑 +𝑛𝑣1 − 𝑛

2𝑣2𝑅

(1 − 𝑑)

−𝐿

𝑅 𝑇(𝑛𝐼1 +


𝑅) (𝑒−

𝑅𝐿𝑑𝑇 − 1)

+𝐿

𝑅 𝑇(𝑛𝑣1 − 𝑛

2𝑣2𝑅

− 𝑛𝐼2) (𝑒−𝑅𝐿(𝑇−𝑑𝑇) − 1)

(17)

To include the core losses in the model, the averaged current

�̇�𝐴𝐶2̅̅ ̅̅ ̅̅ in (17) must subtract the averaged current

�̇�𝑐𝑜𝑟𝑒̅̅ ̅̅ ̅̅ in the shunt core resistance Rc given by:

𝑖̇𝑐𝑜𝑟𝑒̅̅ ̅̅ ̅̅ ̅ =𝑛2𝑣2𝑅𝐶

(18)

Thus, (17) and (18) yield:

�̇�𝐴𝐶2̅̅ ̅̅ ̅̅ = −𝑛𝑣1 + 𝑛

2𝑣2𝑅

𝑑 +𝑛𝑣1 − 𝑛

2𝑣2𝑛𝑅

(1 − 𝑑)

−𝐿

𝑅 𝑇(𝑛𝐼1 +


𝑅) (𝑒−

𝑅𝐿𝑑𝑇 − 1)

+𝐿

𝑅 𝑇(𝑛𝑣1 − 𝑛

2𝑣2𝑅

− 𝑛𝐼2) (𝑒−𝑅𝐿(𝑇−𝑑𝑇) − 1)

−𝑛2𝑣2𝑅𝐶

(19)

3.2 Small-Signal Model

After deriving the average current expressions in (16) and

(19), the small-signal model can be developed by inserting

the equivalent average and perturbed values (20)-(26) in (1)-

(4).

𝑑 = 𝐷 + �̂� (20) 𝑣𝑖𝑛 = 𝑉𝑖𝑛 + �̂�𝑖𝑛 (21)

𝑣𝑜𝑢𝑡 = 𝑉𝑜𝑢𝑡 + �̂�𝑜𝑢𝑡 (22) 𝑣1 = 𝑉1 + �̂�1 (23) 𝑣2 = 𝑉2 + �̂�2 (24)

𝑖𝑖𝑛 = 𝐼𝑖𝑛 + 𝑖̇̂𝑖𝑛 (25)

𝑖𝑜𝑢𝑡 = 𝐼𝑜𝑢𝑡 + 𝑖̇̂𝑜𝑢𝑡 (26)

As a result, expressions (27)-(30) are yield.

𝐶1𝑑�̂�1𝑑𝑡

= 𝑖̇̂𝑖𝑛 − 𝑖̇̂𝐴𝐶1 (27)

𝐿𝑖𝑑𝑖̇̂𝑖𝑛𝑑𝑡

+ 𝑅𝑖𝑖̇̂𝑖𝑛 = �̂�𝑖𝑛 − �̂�1 (28)

𝐶2𝑑�̂�2𝑑𝑡

= 𝑖̇̂𝐴𝐶2 − 𝑖̇̂𝑜𝑢𝑡 (29)

𝐿𝑜𝑑𝑖̇̂𝑜𝑢𝑡𝑑𝑡

+ 𝑅𝑜𝑖̇̂𝑜𝑢𝑡 = �̂�2 − �̂�𝑜𝑢𝑡 (30)

However, the only difficulty left is to find the equivalent

small-signal approximation for the currents �̇̂�𝐴𝐶1 and �̇̂�𝐴𝐶2. For

that the first order Maclaurin series given by (31) is used,

which is valid because �̂� is very small.

𝑒±𝑅𝐿𝑑𝑇 = 𝑒±

𝑅𝐿(𝐷+�̂�)𝑇 ≈ 𝑒±

𝑅𝐿𝐷𝑇 (1 ±

𝑅𝑇

𝐿�̂�) (31)

Thus, the currents 𝑖̇̂𝐴𝐶1 and 𝑖̇̂𝐴𝐶2 can be derived as:

𝑖̇̂𝐴𝐶1 = 𝛼�̂� + 𝛽�̂�1 + 𝛾�̂�2 (32)

𝑖̇̂𝐴𝐶2 = 𝜀�̂� + 𝜓�̂�1 + 𝜇�̂�2 (33) where the coefficients 𝛼 , 𝛽 , 𝛾 , 𝜀 , 𝜓 and 𝜇 are as given in (34)-(39).

𝛼 =2𝑛𝑉2𝑅

−4𝑛𝑉2𝑒

−𝑅𝐿(1−𝐷)𝑇

𝑅 (𝑒−𝑅𝐿𝑇 + 1)

(34)

𝛽 =1

𝑅+2𝐿 (𝑒−

𝑅𝐿𝑇 + 1)

𝑇𝑅2 (𝑒−𝑅𝐿𝑇 + 1)

(35)

𝛾 =𝑛(2𝐷 − 1)

𝑅+2𝑛𝐿 (𝑒−

𝑅𝐿𝑇 − 2𝑒−

𝑅𝐿(1−𝐷)𝑇 + 1)


(36)




5

𝜀 = −2𝑛𝑉1𝑅

+4𝑛𝑉1𝑒

−𝑅𝐿𝐷𝑇

𝑅 (𝑒−𝑅𝐿𝑇 + 1)

(37)

𝜓 =𝑛(1 − 2𝐷)

𝑅+2𝑛𝐿 (𝑒−

𝑅𝐿𝑇 − 2𝑒−

𝑅𝐿𝐷𝑇 + 1)


(38)

𝜇 = −𝑛2

𝑅+2𝑛2𝐿 (1 − 𝑒−

𝑅𝐿𝑇)

𝑇𝑅2 (1 + 𝑒−𝑅𝐿𝑇)

−𝑛2

𝑅𝐶 (39)

Therefore, (27)-(30) and (32)-(33) represent the small-signal

model of the DAFB.

3.3 Output Current to Phase-Shift Ratio Transfer Function

The purpose of constructing the small-signal model is to

derive the transfer function of the DAFB output current to

the phase shift (𝐺𝑜𝑢𝑡(𝑠) =�̂̇�𝑜𝑢𝑡(𝑠)

�̂�(𝑠) ). Hence, (27)-(30) and (32)-

(33) are converted into Laplace domain as in (41)-(45).

𝑠𝐶1�̂�1(𝑠) = 𝑖̇̂𝑖𝑛(𝑠) − 𝑖̇̂𝐴𝐶1(𝑠) (40)

𝑠𝐿𝑖𝑖̇̂𝑖𝑛(𝑠) + 𝑅𝑖𝑖̇̂𝑖𝑛(𝑠) = �̂�𝑖𝑛(𝑠) − �̂�1(𝑠) (41)

𝑠𝐶2�̂�2(𝑠) = 𝑖̇̂𝐴𝐶2(𝑠) − 𝑖̇̂𝑜𝑢𝑡(𝑠) (42)

𝑠𝐿𝑜𝑖̇̂𝑜𝑢𝑡(𝑠) + 𝑅𝑜𝑖̇̂𝑜𝑢𝑡(𝑠) = �̂�2(𝑠) − �̂�𝑜𝑢𝑡(𝑠) (43)

𝑖̇̂𝐴𝐶1(𝑠) = 𝛼�̂�(𝑠) + 𝛽�̂�1(𝑠) + 𝛾�̂�2(𝑠) (44)

𝑖̇̂𝐴𝐶2(𝑠) = 𝜀�̂�(𝑠) + 𝜓�̂�1(𝑠) + 𝜇�̂�2(𝑠) (45) Combining (42), (43) and (45), it is possible to obtain (46).

𝑖̇̂𝑜𝑢𝑡(𝑠)

=𝜀�̂�(𝑠)

𝑠2𝐿𝑜𝐶2 + 𝑠(𝑅𝑜𝐶2 − 𝐿𝑜𝜇) − 𝜇𝑅𝑜 + 1

+𝜓�̂�1(𝑠)


−(𝑠𝐶2 − 𝜇)�̂�𝑜𝑢𝑡(𝑠)


(46)

From (46), the output current 𝑖̇̂𝑜𝑢𝑡(𝑠) is a function of

�̂�(𝑠) , �̂�1(𝑠) and �̂�𝑜𝑢𝑡(𝑠) . Nonetheless, since the control

parameter is the phase-shift ratio ( �̂�(𝑠)), thus, �̂�1(𝑠) and �̂�𝑜𝑢𝑡(𝑠) in (46) are considered as disturbances and can be eliminated by feedforward control. In addition, these

disturbances originate from power ripples (in case a single-

phase topology is adopted), unbalanced 3-phase system (if a

3-phase topology is adopted), or variations in battery voltage

caused by its charging and discharging processes. As a

result, the output current relation with the phase-shift ratio is:

𝐺𝑜𝑢𝑡(𝑠) =𝑖̇̂𝑜𝑢𝑡(𝑠)

�̂�(𝑠)|�̂�1(𝑠)=�̂�𝑜𝑢𝑡(𝑠)=0

=𝜀

𝑠2𝐿𝑜𝐶2 + 𝑠(𝑅𝑜𝐶2 − 𝜇𝐿𝑜) − 𝜇𝑅𝑜 + 1

(47)

Note that the poles of the transfer function of (47) show that

the system is always stable. Even though, there is a negative

term multiplied by µRo and µLo that might be negative.

Nevertheless, the factor µ is always negative. Making only

LHP poles existence in (47)..

Using (47), the appropriate PI controller gains in

Fig. 6 can be calculated with the feedforward considerations that were indicated in (46). However,

practically delays will exist in the system and (47) does not

accurately represent the plant. The possible causes of these

delays are: (i) PWM transport, (ii) Zero-Order-Hold (ZOH)

sampling and (iii) digital controller’s calculations. Each

introduces a delay of 0.5Ts; therefore, the total delay in the

system is considered as 1.5Ts. However, this delay can be

approximated using the second order Padé [49] as in (48).

𝐺𝑑𝑒𝑙𝑎𝑦(𝑠) =12 − 9𝑇𝑠𝑠 + 2.25𝑇𝑠

2𝑠2

12 + 9𝑇𝑠𝑠 + 2.25𝑇𝑠2𝑠2

()

Consequently, Fig. 6 shows the overall controller and plant

model that includes a realistic delay block inserted after the

PI controller.

Fig. 6. DAFB output current-to-phase shift ratio plant

model with the controller

Therefore, the closed loop system transfer function (𝐺𝐶𝐿(𝑠)) is

derived from Fig. 6, as:

𝐺𝐶𝐿(𝑠) =𝑃𝐼(𝑠)𝐺𝑑𝑒𝑙𝑎𝑦(𝑠)𝐺𝑜𝑢𝑡(𝑠)

1 + 𝑃𝐼(𝑠)𝐺𝑑𝑒𝑙𝑎𝑦(𝑠)𝐺𝑜𝑢𝑡(𝑠) (49)

Hence, (49) can be used to design the controller. Note that,

the delay effects on the feedforwarded signals is not

significant and can be neglected. In fact, these disturbances

can be considered constants during the delay duration.

Besides, the delay will only introduce very far RHP that are

not dominant; hence, no non-minimum phase response will

be observed and the system remains stable.

On the other hand, the dead-time has a considerable

effect on the power-flow dynamics of the DAFB due to the

significant error between the effective phase-shift-ratio and

the commanded phase-shift-ratio as discussed in [50]-[52].

However, this model does not include the dead-time

compensation techniques, since dead-time compensation

methods are only necessary with loads that are rapidly

changing. In fact, a battery bank as a load possesses a small-

time constant. Moreover, [53] introduced a methodology to

effectively reduce the error in the power-flow dynamics by

compensating the additional phase-shift due to the dead-time

for applications with rapidly varying loads.

4 Overall Control Scheme

The cascaded dual loop control methodology is

considered as a proper control approach. Specifically, an

outer voltage regulation loop is used to derive the reference

current for the inner current regulation loop. This control

methodology is used on both the bidirectional inverter and

on the DAFB as shown in Fig. 7 and Fig. 8, respectively.




6

Fig. 7. Bidirectional inverter controller

Fig. 8. DAFB controller

Nevertheless, further modification on the DAFB

converter control is to consider the SoC% as an extra degree

of freedom as depicted in Fig. 3. In other words, there will be

two reference currents for the inner current loop that will be

selected by using a data selector –Multiplexer– according to

the predefined priority whether G2V or V2G preference.

Since the outer voltage loops on both converters –the

bidirectional inverter and the DAFB– regulate DC

parameters, the suitable controller type is a simple single PI

controller for each loop. Similarly, the inner current loop of

the battery bank current control also uses a PI controller.

However, the inner grid current control uses a Proportional

Resonance (PR) controllers when stationary frame is used. Note that, the power-factor is controlled only in V2G

operation through adjusting the grid d-current component

(𝑖𝑑(𝐺2𝑉)𝑟𝑒𝑓 ).

5 Implementation

5.1 DAFB Testing Prototype

A 6.1 kW DAFB Hardware prototype is implemented

using a Typhoon HIL 602 device and STM32

microcontroller, as shown in Fig. 9. The DAFB ratings are

depicted in Table 1. The control of the DAFB is based on

the SPS control scheme. The experiments focus on the

following: (i) open-loop step response, (ii) power-flow

dynamics, (iii) closed-loop waveforms observation and (iv)

converter efficiency.

5.2 Open-Loop Step Response

The feasibility of the theoretical analysis in designing the PI

controller is based on testing the open-loop overall system

step response.

(a)

(b)

Fig. 9. Laboratory Typhoon HIL experimental setup:

(a) schematic (b) actual.

Table 1: DAFB Components values Parameter Symbol Value

Input voltage (HV-Side) [The HV-Side is adjusted to keep the voltage applied on the HF transformer sides equal to the transformer ratio]

Vin 317.10 V – 342.8 V

Output voltage (LV-Side) [Two series connected Li-ion Batteries with 26.6 V nominal voltage and 40 Ah capacity]

Vout 52.85 V – 57.3 V

Power rating Po 6.1 kW

Switching frequency fs 20 kHz

Dead-time Dt 1.25µs

Transformer turn ratio N 6:1

HF transformer inductance L 93.30 µH

HF transformer resistance R 338.50 mΩ

Magnetizing inductance Lm 1.76 mH

Core resistance RC 10 MΩ

HV-Side capacitor C1 7 mF

LV-Side capacitor C2 22 mF

LV-Side snubber capacitor Cs 141 nF

LV-Side snubber resistance Rs 1.67 mΩ

HV-Side source resistance Ri 1 mΩ

HV-Side source inductance Li 1 µH

LV-Side source resistance Ro 1µΩ

LV-Side source inductance Lo 1 µH

This was carried out using both Simulink software and

the HIL experimental prototyping. In Fig. 10, the step

response of the battery current was obtained by applying a

phase-shift-ratio step from 0 to 0.272 at time t=0.8 ms.

Notice that the battery current varied rapidly from 0 to 100A

with a very short time constant of 706 µs. Comparing the

open-loop system step responses in Fig. 10 indicates that the

Simulink model and the HIL model are consistent.

DC-Link

Voltage

Control

dq

to

+ _

+ _

PLL

abc

to

Grid

Current

Control

to abc

𝑣𝐷𝐶𝑟𝑒𝑓

𝑣𝐷𝐶

𝑣𝑔

𝑖𝑔

𝑖𝑑𝑟𝑒𝑓

𝑖𝑞𝑟𝑒𝑓

PF

Control

Mux

S=0

S=1

𝑖𝑑(𝑉2𝐺)𝑟𝑒𝑓

abc to

𝑣𝑔 Vg calculation

𝑉𝑔𝑟𝑒𝑓

𝑖𝑑(𝐺2𝑉)𝑟𝑒𝑓

𝑀𝑖

S=0 for G2V

S=1 for V2G

𝑉𝑔

+ _

+ _

Battery Voltage

Control 𝑣𝐵𝑟𝑒𝑓

Mux

S=0

S=1 S=0 for G2V S=1 for V2G

+ _

Battery Current

Control 𝑖𝐵(𝑉2𝐺)𝑟𝑒𝑓

𝑖𝐵(𝐺2𝑉)𝑟𝑒𝑓

SoC%

SoC

Observer

𝑣𝐵 𝑖𝐵

d 𝑖𝐵𝑟𝑒𝑓

Waveform

s

Display &

Analysis

HIL Model upload

&

data monitoring link

Controller code upload

& data monitoring link

STM32F

4

I/O

Control

Signals

Exchang

e Oscilloscop

e

Oscilloscope

Typhoon HIL 602

STM32F4 Controller

Card Laptop




7

Fig. 10. DAFB step response: HIL vs. Simulink

5.3 Power-flow Dynamics

Another validation tool of the HIL implementation was

performed by comparing the HIL system power-flow

dynamics with the theoretical ideal DAFB power-flow

equation (50) [54][55].

𝑃 =𝑛𝑉𝑖𝑛𝑉𝑜𝑢𝑡2𝑓𝑠𝐿𝐴𝐶−𝐿𝑖𝑛𝑘

𝑑 (1 − |𝑑|) (50)

Fig. 11 shows that there is a good matching between the

theoretical power-flow and the power-flow dynamics of the

experimental HIL prototype. However, the curve is not an

odd function. In other words, the data points for the charging

portion are not a reflection in the origin for their counter data

points in the discharging portion. Yet, this small asymmetry

appears above the intended power ratings (±6.1 kW). In

addition, the small discrepancy between the theoretical and

experimental power-flow curves is because (50) does not

include non-idealities such as the converter deadtime. This

mismatch is more noticeable around the origin point.

Fig. 11. 6.1Kw DAFB power-flow dynamics: HIL vs.

theoretical

Fig. 12 shows the power-flow dynamics near the origin

point and considering diverse operating scenarios.

Different SoC% levels (60% & 90%) with or without

adjusting the ratio of the applied voltage on the two ports

of the HF transformer, are presented in Fig. 12.

Fig. 12. Power-flow dynamics near the origin point with

and without adjusting the ratio of the voltage applied on the

two sides of the HF transformer (VD1=Vin)

Notice that the curves’ transitions between the charging

and discharging modes are smoother for the adjusted HV-

Side voltage scenarios and are crossing the origin point. This

is because the circulating reactive current is reduced with

adjusted HV-Side voltage. In addition, the minor mismatch

in the curves with adjusted voltages is due to finite dead-time

effect. This could be improved further by applying deadtime

compensation techniques such those presented in [56]-[59].

5.4 Closed Loop Waveforms

Fig. 13 and Fig. 14 show the HF transformer voltage

and current waveforms obtained by Simulink simulation and

HIL, which are observed in both G2V and V2G modes,

experiments, respectively. During these tests, the reference

current 𝑖𝑜𝑢𝑡𝑅𝑒𝑓

is set to 100A and -100A in G2V and V2G

modes, respectively.

Notice that, both Simulink and HIL results are very

consistent. Note that, when the HV-side voltage (𝑣𝑝) is

lagging the LV-Side voltage (𝑣𝑠), a voltage drop appears on the AC-Link inductance in the region of the phase shift

resulting in power injected in the battery bank (G2V). On

the contrary, when the HV-Side voltage is leading the LV-

Side voltage, the battery is discharged in V2G operation

mode.

5.5 Converter Efficiency

Fig. 15 shows the variation of the DAFB converter

efficiency in both G2V and V2G operating conditions as a

function of the battery charging/discharging power. Notice

that the peak efficiency in G2V mode is around 96.6% at Po

= 3.1 kW. Similarly, the highest efficiency achieved in V2G

mode is approximately 92.7% at PO = 3.4 kW. The

difference between V2G and G2V efficiency plots is due to

the LV-Side capacitor C2 that absorbs higher current during

the battery discharging (V2G) mode.

Moreover, it can be observed that the optimal

operating condition is in the range of 2 kW to 6 kW in the

G2V mode. As well as, in the V2G mode the preferred

operation range is 2 kW to 6 kW. This is because the

converter operates around its peak efficiency in these

specified ranges.




8

Fig. 13. Simulink DAFB HF Transformer closed-loop

waveforms

(a) during charging (G2V) operation mode and (b) during

discharging (V2G) operation mode

6 Conclusion

In conclusion, this paper emphasized on the benefits

of the DAFB topology in applications related to SGs and EV

charging. The benefits of the DAFB topology were reviewed

and compared to those of the existing bidirectional DC/DC

converter topologies. In addition, brief discussions of the

reliability, efficiency, system configuration, EV charger

control scheme, battery lifetime and system materials, were

presented.

Furthermore, a non-ideal DAFB small-signal model

was derived to accurately designing the DAFB controller.

Finally, a 6.1 kW DAFB prototype was implemented on

Simulink and Typhoon HIL 602 device. Obtained results

validate the effectiveness of the DAFB topology for both

G2V and V2G operations.

7 Acknowledgment

This publication was made possible by the National

Priorities Research Program (NPRP) award [NPRP8-627-2-

260] from the Qatar National Research Fund (QNRF); a

member of the Qatar Foundation. Its contents are solely the

responsibility of the authors and do not necessarily represent

the official views of QNRF.

Fig. 14. HIL DAFB HF Transformer closed-loop waveforms:

(a) during charging (G2V) operation mode and (b) during

discharging (V2G) operation mode

Fig. 15. DAFB efficiency: (a) G2V mode and (b) V2G mode

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