**Giuseppe Aiello 1, Mario Cacciato 2, Francesco Gennaro 1, Santi Agatino Rizzo 2,\*, Giuseppe Scarcella <sup>2</sup> and Giacomo Scelba <sup>2</sup>**


Received: 5 November 2020; Accepted: 14 December 2020; Published: 20 December 2020

**Abstract:** In this paper, a procedure to simulate an electronic power converter for control design and optimization purposes is proposed. For the addressed application, the converter uses SiC-MOSFET technology in bidirectional battery chargers composed of two power stages. The first stage consists of a single-phase AC/DC power factor correction synchronous rectifier. The following stage is a DC/DC dual active bridge. The converter has been modulated using a phase-shift technique which is able to manage bidirectional power flows. The development of a model-based simulation approach is essential to simplify the different design phases. Moreover, it is also important for the final validation of the control algorithm. A suitable tool consisting of a system-level simulation environment has been adopted. The tool is based on a block diagram design method accomplished using the Simulink toolbox in MATLAB™.

**Keywords:** automotive; battery charger; circuit modelling; power electronics; SiC MOSFET

#### **1. Introduction**

Powertrain electrification of electric vehicles (EVs) and plug-in hybrid vehicles (PHVs) has gained the attention of governments, media and the public as a possible alternative mode of supplying power to transport vehicles due to its inherent efficiency advantages, e.g., less CO2 emissions, in comparison with internal combustion engine vehicles [1,2]. EVs are key elements for the worldwide upgrade to sustainable energy systems. On the one hand, they directly affect the transition to environmentally friendly transportation. On the other, they are useful for compensating for the effects of dispersed generation based on renewable energy resources [3]. In more detail, when the power available from these generators surpasses the local load, it may be necessary to cut the exceeding power to avoid misoperation conditions, or worse yet, service continuity reductions. This limitation in green energy utilization can be overcome with EVs, since they involve an increment in the local load. Moreover, they can be used as energy storage systems which are able to mitigate fluctuations in primary energy resources and, more generally, are useful when coping with optimal power flow [4].

As a consequence of the diffusion of EVs and PHVs, an increasing number of connections to the public electrical grid of smart on- and off- board battery chargers has occurred [5]. These components are of fundamental importance for managing the energy flows between vehicles and the AC grid. Recently, a new EV operating mode, called Vehicle to Grid (V2G), was proposed [6]. V2G enables the use of the EVs as distributed large energy storage systems connected to the grid when parked [7]. The reward for providing ancillary services makes V2G economically convenient which, in turn,

enables a wider diffusion of EVs, leading to environmental benefits [8]. On the other hand, the control strategy must take battery degradation into account [9].

Several bidirectional battery chargers (BBCs) for V2G have been already treated in the literature to investigate viable methods to achieve a compact, efficient and inexpensive solution. In [10,11], two designs of single-phase on-board BBCs were proposed, aiming to show the feasibility of reactive power support to the utility grid. In particular, [11] deals with the advantage of using wide band-gap semiconductor devices at high frequencies to reduce the current ripple by implementing both hardware and control solutions, similar to those adopted in converters for fuel cell power units [12]. In [13], a simple and functional BBC topology for stationary application was introduced. This topology was specifically designed to enhance the capabilities of a joint operation with an energy management system exploiting a storage stage in a residential environment. A literature analysis highlighted the fact that a key issue is to design and test a suitable control strategy. More specifically, the evaluation of the modulation, as well as of some features (e.g., current ripple and load step response), requires proper testing of the control strategy in dynamic conditions on small-time scales. On the other hand, appropriate long-timescale tests to evaluate the energy management capabilities of BBCs must be also be performed. In some works [10–14], the development of a feasible converter model was needed to fulfil the specifications through a proper system design, optimizing the structure of the control strategy as well as the correct setting of the parameters for the controllers.

As in many physical system designs, the use of advanced computer-aided design (CAD) systems is important at different project stages [15]. At the beginning, they enable component sizing verification; subsequently, they are useful for offline control validation with uP-based simulators [16], where they are very helpful when applying a user-friendly GUI based simulation interface [17]. Other solutions which are increasingly being adopted in the industry are powerful real-time emulation systems based on FPGA, that are widely used both in power converters [18] and electrical drives applications [19,20], and are particularly useful for the study and testing of dangerous situations, such as systems faults [21].

In this framework, a proper design using an advanced simulator model is proposed in this paper. It enables the evaluation of the feasibility and the performance of the converter using CAD. This approach makes it possible to validate the operation of the BBC in both V2G and Grid to Vehicle (G2V) operating modes. The main contribution of this paper is to propose a tool with which to optimize the BBC design before constructing the converter prototype. Additionally, the model of SiC MOSFET power devices was integrated to exploit their advantages in BBCs. Indeed, such an approach can useful for the optimal design of other converters in automotive applications. Finally, a mock-up was realized and tested, obtaining valuable results. In detail, the converter investigated was a 5-kW, single-phase BBC with two conversion stages: an active front end (AFE) PWM rectifier and a cascade-connected dual active bridge (DAB) with high-frequency isolation. Such an architecture was adopted for its bidirectional power flow, galvanic isolation, high efficiency in a wide operating range and reduced size and weight. The last features are due to the high switching frequency reached thanks to the use of SiC MOSFET power devices [22]. Every apparatus connected to the grid has to meet the power quality standards; therefore, the converter first stage also included power factor correction (PFC) capability. Figure 1 shows a flowchart of the overall tool.

**Figure 1.** Overall picture of the evaluation tool.

#### **2. Modelling the Bidirectional Battery Charger**

For the application of a single-phase BBC, the proposed converter consists of two stages exploiting three H-bridges with modularity in the power board arrangement. Power devices with the same voltage breakdown should be used since the input and output voltage levels are similar. In this case, the three H-bridges can be identical, thus simplifying the converter design for the proposed converter that exploits identical SiC devices. As shown in Figure 2, the first stage is an AFE connected to the grid through an LCL filter which is useful to ensure both the power quality and the control of the power exchanged with the grid, while the second stage consists of a DAB converter.

The control strategy of the AC/DC converter is composed of a hierarchic control. On the one hand, it regulates the bidirectional power exchange with the grid. On the other, it shapes the current in a sinusoidal waveform. Hence, it consists of an inner loop current control in continuous conduction mode (CCM). The control is implemented on the dq rotating reference frame and is synchronous with the grid voltage. There is an outer loop to maintain constant the DC voltage, VDC, using linear regulators, i.e., standard industrial proportional-integral (PI) control. As usual, the DAB is modulated in phase-shift. In this way, the control algorithm sets a suitable phase-shift for application between the switching signals of the two active bridges while maintaining the duty cycle of every switching pattern at 50%. Such a strategy makes it possible to achieve zero voltage switching (ZVS) upon turning on all of the DAB power switches, thereby increasing the converter efficiency. The phase-shift value sets the energy flow: in G2V mode, the energy flows towards the battery, while in V2G mode, the energy flow is directed from the battery to the AC grid.

**Figure 2.** Converter topology. The first stage is the Active Front-End Rectifier; the second stage is the Dual Active Bridge.

#### *2.1. Active Front-End Rectifier*

The AFE, or synchronous rectifier, is connected via a filter to the utility grid where it performs AC/DC conversion and PFC [23,24]. Figure 3 shows the circuit test-bench emulator implementation using the Simulink Simscape Electrical Toolbox, a typical AFE control strategy based on the voltage oriented control algorithm. Park transformation is considered to obtain the best performance, e.g., zero error in steady-state and high control dynamics [25].

Park transformation is used to convert the two-phase stationary frame (α–β\*) (1) into the two-phase rotating frame (d–q) which is synchronous with the grid voltage phase θ (2). The two-phase voltages in reference to the dq reference frame are converted in stationary quantities α–β using the inverse matrix of the reference frame transformation [26]:

$$\begin{cases} L\frac{di\_a}{dt} + Ri\_\alpha = V\_{ta} - V\_{s\alpha} \\ L\frac{di\_\beta}{dt} + Ri\_\beta = V\_{t\beta} - V\_{s\beta} \end{cases} \tag{1}$$

$$\begin{cases} L\frac{di\_d}{dt} + Ri\_d - \omega(t)Li\_q = V\_{td} - V\_{sd} \\ L\frac{di\_q}{dt} + Ri\_q + \omega(t)Li\_d = V\_{tq} - V\_{sq} \\ \frac{d\rho}{dt} = \omega(t) \end{cases} \tag{2}$$

**Figure 3.** AC Stage—Implementation of the Active Rectifier in Simscape electrical Simulink.

The terms *id*, *iq* and ρ are state variables, while *Vtd*, *Vtq* and ω(*t*) are control variables. In particular, ω represents the control variable referring to the synchronous reference frame.

This model shows the nonlinearities related with the terms ω(*t*)*Lid* and the sinusoidal components of the AC system: *Vsd* = *V*ˆ *Scos*(ω0*<sup>t</sup>* + <sup>θ</sup><sup>0</sup> <sup>−</sup> <sup>ρ</sup>), *Vsq* = *<sup>V</sup>*<sup>ˆ</sup> *Ssin*(ω0*t* + θ<sup>0</sup> − ρ).

Using this modelling approach, the purpose of the control is the cancellation of the sinusoidal terms; a phase locked loop "PLL" algorithm is used for this purpose. Applying the AC voltage as the input, the PLL output is ρ(*t*) = ω0*t* + θ0, and Equation (2) turns to Equation (3), which contains only DC quantities in steady-state.

$$\begin{cases} L\frac{di\_d}{dt} = \omega\_0 L i\_q - R i\_d + V\_{td} - \vec{V}\_S\\ L\frac{di\_q}{dt} = -\omega\_0 L i\_d - R i\_q + V\_{tq} \end{cases} \tag{3}$$

$$\begin{cases} P\_S(t) = \frac{3}{2} \Big[ V\_{sd}(t)i\_d(t) + V\_{sq}(t)i\_q(t) \Big] \\ Q\_S(t) = \frac{3}{2} \Big[ -V\_{sd}(t)i\_q(t) + V\_{sq}(t)i\_d(t) \Big] \end{cases} \tag{4}$$

$$\begin{aligned} P\_S(t) &= \frac{3}{2} [V\_{sd}(t)i\_d(t)] \\ Q\_S(t) &= -\frac{3}{2} [V\_{sd}(t)i\_q(t)] \end{aligned} \tag{5}$$

In V2G applications, the goal is to suitably manage the flow of active and reactive powers, according to Equation (4). By estimating the phase angle of the AC system through the PLL and imposing *Vsq* = 0, it follows that it is possible to rewrite the power relationships given in Equation (4) according to Equation (5), where the coupling terms have been cancelled.

Since in dq-axis, the component *Vsd* is constant, from Equation (5), it is evident that it is possible to obtain the power control *PQre f* = *PQf eed* through the direct control of the current *idq re f* = *idq f eed*.

Finally, considering the general model, Equation (6), the command variables are obtained from the dq current control, Equation (7).

$$\begin{aligned} L\frac{di\_d}{dt} &= \alpha\_0 L i\_l - R i\_d + V\_{td} - V\_{sd} \\ L\frac{di\_q}{dt} &= -\alpha\_0 L i\_d - R i\_q + V\_{tq} - V\_{sq} \end{aligned} \tag{6}$$

$$\begin{aligned} V\_{td} &= \mu\_d - \alpha\_0 L i\_q + V\_{sd} \\\\ V\_{tq} &= \mu\_q + \alpha\_0 L i\_d + V\_{sq} \end{aligned} \tag{7}$$

Simple and robust PI current regulators can be used to track references since the dq-axis signals in steady-state are constants (Equation (8)). The result is the controlled model given by Equations (9) and (10), as shown in Figure 4.

$$\begin{aligned} u\_d &= \left( k\_p + \frac{k\_i}{s} \right) \left( i\_{d\_{ref}} - i\_{d\_{fad}} \right) \\ u\_q &= \left( k\_p + \frac{k\_i}{s} \right) \left( i\_{q\_{ref}} - i\_{q\_{fad}} \right) \end{aligned} \tag{8}$$

$$\begin{cases} \begin{aligned} V\_{td} &= \left( k\_p + \frac{k\_i}{s} \right) (i\_{d\_{ref}} - i\_{d\_{fad}}) - \alpha\_0 L i\_q + V\_{sd} \\\ V\_{tq} &= \left( k\_p + \frac{k\_i}{s} \right) (i\_{q\_{ref}} - i\_{q\_{fad}}) + \alpha\_0 L i\_q + V\_{sq} \end{aligned} \tag{9}$$

$$\begin{cases} L\frac{di\_d}{dt} + Ri\_d - \omega Li\_q = \left(k\_p + \frac{k\_i}{s}\right) \times \left(i\_d^\* - i\_d\right) - \omega Li\_q\\ L\frac{di\_q}{dt} + Ri\_q + \omega Li\_d = \left(k\_p + \frac{k\_i}{s}\right) \times \left(i\_q^\* - i\_q\right) + \omega Li\_q \end{cases} \tag{10}$$

**Figure 4.** Current control diagram. *idqre f* current references, *edq* current errors, *vdq* compensator terms, *Ddq* decoupling terms, *Vtdq* control voltages, *mdq* modulation index.

## *2.2. Dual Active Bridge*

The DAB is the DC/DC isolated bidirectional converter of the BBC (Figure 5). The DAB topology was chosen because of its high efficiency in a wide operating range [27]. It features a symmetrical structure, characterized by two full bridges connected via a high-frequency transformer which also provides galvanic isolation [28]. In Figure 6, a simplified equivalent circuit of the DAB converter is shown. The model of the transformer consists of two elements: the leakage inductor and an ideal transformer that models the voltage ratio. In Figure 7, a simplified circuit where the transformer has been represented on the secondary side to obtain a simple equivalent circuit is shown. The operating states of the converter switches are described in Equation (11).

*Energies* **2020**, *13*, 6733

$$\begin{aligned} v\_{\text{DAB1}}(t) &= \begin{cases} +V\_1 & I & T\_5, T\_8 \text{ on } \&\text{ }T\_6, T\_7 \text{ of } f\\ 0 & II & T\_5, T\_7 \text{ on } \&\text{ }T\_6, T\_8 \text{ of } f\\ -V\_1 & IV & T\_6, T\_7 \text{ on } \&\text{ }T\_5, T\_8 \text{ of } f\\ +V\_2 & I & T\_9, T\_{12} \text{ on } \&\text{ }T\_{10}, T\_{11} \text{ of } f\\ 0 & II & T\_9, T\_{11} \text{ on } \&\text{ }T\_{10}, T\_{12} \text{ of } f\\ 0 & III & T\_9, T\_{11} \text{ of } f \text{ } T\_{10}, T\_{12} \text{ on }\\ -V\_2 & IV & T\_{10}, T\_{11} \text{ on } \&\text{ }T\_9, T\_{12} \text{ of } f \end{cases} \tag{11}$$

**Figure 5.** DC/DC stage Dual Active Bridge.

**Figure 6.** DAB equivalent circuit W/ transformer.

**Figure 7.** DAB equivalent circuit W/O transformer.

The H-Bridge on the left produces a square-wave voltage with a 50% of duty cycle on the primary side of the transformer. The right-side H-Bridge performs the AC to DC conversion and implements the current control loop used to shape the current charging profile of the battery. The leakage inductance, *Llk*, plays a key role in the performance of the power conversion. Among the various modulation strategies suggested in the literature, single phase-shift modulation was used to control the power exchange between the BBC and the main grid.

The phase-shift (φ) is positive when the power flows from the grid to the battery and negative when the it flows in the opposite direction. The relation between the phase-shift and the delivered power is given by Equation (12):

$$P = P\_{\rm DAB1} = P\_{\rm DAB2} = \frac{nV\_1 V\_2 \phi(\pi - |\phi|)}{2\pi^2 f\_s L\_{\rm lk}}, \ -\pi < \phi < \pi \tag{12}$$

where −180◦ < φ < 180◦, *V*<sup>1</sup> and *V*<sup>2</sup> are the input and output voltages of the DAB (Figure 8); *n* is the transformer turn ratio; *fs* is the switching frequency and *Llk* is the leakage inductance when considering a lossless DAB model.

*P* > 0 denotes a power transfer from DAB1 to DAB2 and *P* < 0 denotes a power transfer from DAB1 to DAB2. The power transfer as a function of the phase-shift is depicted in Figure 8. The related absolute presents two maxima at two different phase-shift angles. The maximum power occurs for ∂*P*/∂φ = 0 is:

$$|P|P\_{\text{max}}| = \frac{n}{8} \frac{V\_1 \ V\_2}{f\_s L\_{lk}}, \ \phi = \pm \frac{\pi}{2} \tag{13}$$

Hence, for a specific active power *P*, the phase-shift φ that must be imposed between the input-output voltages is:

⎤

⎡

**Figure 8.** Power transfer vs. Phase-shift.

#### *2.3. High-Frequency Transformer*

The high-frequency transformer is responsible for the power transfer and permits to obtain the galvanic isolation [29]. Different core geometries and materials are widespread and the selection of the most appropriate solution mainly depends on the specific application. It is well known that the use of high switching frequency reduces the core size for a given power, while using suitable ferrite materials effectively eliminates eddy currents losses.

The design method is based on the "core geometry method" [30,31].

#### *2.4. Matlab—Simulink Implementation*

The model of the BBC and the model of its control were implemented in Matlab-Simulink to simulate the BBC behavior and to evaluate its performance considering different working conditions. The converter model included parasitic elements that affect each power conversion stage. The MOSFETs parameters were considered, as well as the dead-time set in the driving circuit. The closed-loop control block diagram for the AC/DC PFC converter is shown in Figure 9.

Using the Park's transformation, the regulation was implemented using the id and iq current components to control, respectively, the active and reactive power. This control structure makes it possible to regulate both the DC voltage value and the PF. During G2V mode, the AFE with the PF correction works as an AC to DC converter, and charges the battery while maintaining constant the DC voltage and unitary the PF.

**Figure 9.** AFE PFC closed-loop control block diagram.

In V2G mode, the battery is discharged and the bridge acts in inverter mode (DC/AC). The control strategy consists of maintaining constant the voltage value on the bus-dc and managing the PF to compensate the amount of reactive power required by the grid. The control loop block diagram for the DAB is shown in Figure 10.

**Figure 10.** Phase-shift control loop block diagram.
