Soft Switched Current Fed Dual Active Bridge Isolated Bidirectional Series Resonant DC-DC Converter for Energy Storage Applications

Abstract

This paper proposes a high-frequency isolated current-fed dual active bridge bidirectional DC–DC series resonant converter with an inductive filter for energy storage applications, and a steady-state analysis of the converter is carried out. The performance of the proposed converter has been compared with a voltage-fed converter with a capacitive output filter. The proposed converter topology is operated in continuous conduction mode with zero circulation current (ZCC), less current stress and high efficiency. The conditions required for soft switching are determined, and it is found that the converter operates with soft switching of all switches for a wide variation in load and input voltage without loss of duty cycle. Current-fed converters are suitable for low-voltage renewable energy applications because of their inherent boosting capability. An inductive output filter is chosen to make the output current ideal for fast charging and high-power-density battery storage applications. Simple single-phase shift control is used to control the switches. The performance of the converter is studied using PSIM simulation software. These results are confirmed by an experiment on a 135 W converter on an OPAL-RT real-time simulator. The maximum efficiency obtained in simulation is 96.31%. Simulation and theoretical results are given in the comparison table for both forward and reverse modes of operation. A breakdown of the losses of this converter is also presented.

1. Introduction

With increasing pollution and an alarming climate situation, it has become imperative to switch from conventional energy sources to renewable energy sources. These renewable energy resources can produce cleaner energy than conventional energy resources. Renewable energy resources are abundant but intermittent in availability. Among the renewable energy resources, solar energy is the most abundant in nature. To utilize this energy, power electronics play a crucial role. In power electronics, DC-DC converters, in combination with photovoltaic systems, can convert solar energy into electrical energy. Due to the non-availability of solar energy at night and lack of sufficient technological advancements, this energy has been given less importance in previous decades. Due to the advances in photovoltaic technology, and pollution damaging the environment, it has become necessary for industry, policymakers and academia shift the focus to solar energy [1,2]. Policymakers are encouraging the use of renewable energy sources such as fuel cells, photovoltaics, wind, etc., for power generation. Currently, solar PVs are becoming more popular and are being installed on rooftops of individual houses. In this scenario, using DC-DC converters and recent advancements in energy storage systems, the drawback of the non-availability of solar energy during the night is no longer a severe problem and soon DC-DC converters will enable solar power to be stored in energy storage systems [3].

Isolated bidirectional dual active full-bridge converters (IBDC) have more advantages in terms of DC-DC converters. Galvanic isolation separates both bridges electrically. Dual active-bridge converters are symmetrical in structure and easy to analyze and control [4,5,6]. In isolated dual active-bridge converters, both voltage-fed non-resonant [7,8,9,10] and resonant [11,12,13,14,15] converters have been discussed. In voltage-fed converters [7,11], the output current has a negative component, which is circulating and incurs more losses. To avoid the circulating current, a discontinuous mode of operation has been chosen for these converters [8,9] in which no power is transferred to the load for a short time. A method has been discussed for a series-resonant DAB converter to reduce the current stress, increase the soft switching range and efficiency, and reduce the effect of dead-time on power transmission and soft switching [16]. A topology has been discussed without an isolation transformer to integrate the photovoltaic system and the grid. The absence of a transformer makes this converter compact but results in a lack of protection through isolation [17]. In [18], a hybrid bridge has been discussed to integrate the DC bus and energy storage system. This topology is a solution when the transformation ratio ‘n’ is away from unity and it has been operated with high efficiency and soft switching even when ‘n’ is not close to unity [18]. A controller has been discussed in [19] to regulate power transmission and reduce losses using a minimum-current-point-tracking technique. This controller is generic in design, as it does not depend on the circuit parameters and complicated circuit modeling [19].

In [20], a topology has been discussed to transfer more power than a conventional dual active-bridge (DAB) converter. This topology has twice the power transmission capacity of conventional DAB converters and has found application in electric-powered aircraft [20]. In a topology with a high step-down ratio, inverter bridges are stacked in series through a capacitor, and rectifier bridges are connected in parallel. Series-connected bridges lead to additions of voltage at the input. Parallel-connected bridges at the output lead to less voltage and more current. This converter uses GaN semiconductor switches and offers the highest efficiency of 99% and the least of 97.5% [21,22]. In [23], a scheme has been discussed to increase the dynamic response, especially for a wide range of load changes. Specifically, this topology is a good candidate for DES, solid-state transformers and energy storage applications [23]. A hybrid-switching scheme has been proposed to reduce the losses for a DAB converter with advanced switching devices like SiC; it has achieved 98.96% efficiency [24].

Voltage-current-fed isolated bidirectional DC-DC (IBDC) converters without a resonant network [25,26,27] have been discussed. The magnetizing current in these converters results in more current stress and losses. Voltage-current-fed IBDC converters with resonant networks [28,29,30] can offer a nearly sinusoidal current. This feature provides lower current stress and conduction losses. Voltage-current-fed converters are unsymmetrical structures due to extra inductors on one of the bidirectional operations. This structure leads to the uneven distribution of current on the switches. Current-fed isolated bidirectional DC-DC resonant converters (IBDC), in both the forward and reverse modes of operation, are symmetrical. These converters require less gate drive than voltage-fed converters, making them suitable for low-voltage applications due to their inherent boosting capability. A search of the literature shows that current-fed isolated bidirectional DC-DC series resonant converters with an inductive filter have not been studied in detail. In this work, a current-fed IBDC with an inductive filter has been studied. The important contributions of this paper are: (i). The converter is operated with an inductive output filter (ii). Continuous conduction mode without loss of duty cycle, (iii) The circulating current at the load is zero to avoid the current stress on the switches and corresponding losses. Due to their bidirectional power transfer capability and high gain, these converters have become an essential part of the conventional structure of plug-in hybrid electric vehicles [6,10]. Current-fed converters allow solar energy generation utilizing PV with a small voltage output, even for individual households. This article presents the operational performance of a high-frequency series-resonant IBDC with a current source for energy storage application. Section 2 describes the proposed circuit in forward and reverse modes of operation. Section 3 describes the steady-state analysis and soft switching boundary conditions for the current-fed IBDC converter. Simulation and experimental results are presented in Section 4; Section 5 gives a comparison of results, and Section 6 presents the conclusion.

2. Proposed Circuit: Current-Fed Isolated Dual Active Bridge Bidirectional DC-DC Series Resonant Converter

Renewable energy resources require power electronics to make use of the energy that they generate. The importance of power electronics in distributed energy systems is shown in Figure 1. Different types of low-voltage DC DES, which are in operation across the globe, are discussed along with their power and voltage ratings [31]. The voltage-fed DAB and proposed current-fed isolated DAB (CFIBDC) converters are shown in Figure 2a and Figure 2b, respectively. These converters are very useful in charging the battery during daylight hours and discharge the same power from the battery whenever necessary [5]. The CFIBDC shown in Figure 2b consists of a boost stage with ‘V_pv’ as the input voltage, and inductor ‘L_b’, capacitor ‘C_b’, and inductor ‘L_dc’ are used for maintaining a constant current. The switches Q₁ to Q₄ are on the primary bridge, and Q₅ to Q₈ are on the second bridge. Diodes D₁ to D₈ are the anti-parallel body diodes of the switches Q₁ to Q₈, as shown in Figure 2b. The high-frequency transformer has a turns ratio of 1: n. The elements L_r and C_r are part of the series-resonant circuit. Circuit element C_r aids in avoiding transformer saturation [13,14,15,32]. An inductor Lo can reduce ripples in the load current [28].

The model operating waveforms of the voltage-fed converter and current-fed converter for both forward and reverse operation modes are shown in Figure 3a,b and Figure 3c,d, respectively. These features can be avoided in the current-fed IBDC converter. Figure 3c,d shows a DC current without any negative component at the output of the second bridge in both modes of operation. This means no circulating current or stress on the switches due to the circulating current. This feature enhances the efficiency of the converter [9]. Due to technological advancements in power semiconductor switches, a high-frequency current-fed isolated bidirectional DC-DC converter (CFIBDC) can offer low input-current ripples, built-in short circuit protection, no duty cycle loss, higher gain, easy-to-control current and high-power density. The merits of these CFIBDC converters, which are given in [27], make them suitable for various applications, such as electric vehicles, battery storage power quality improvement and fuel cell EVs [27].

For the CFIBDC converter, a single-phase shift control (SPS) control technique is applied. This technique is the simplest and most-preferred technique for isolated bidirectional dual active-bridge converters. In this technique, diagonal switch pairs in two bridges are turned ON to produce square waveforms having a 50% duty cycle for the respective switches. The square waveforms on either side of the isolation transformer have a phase difference; the leading voltage-side bridge delivers the power to the lagging voltage-bridge side of the transformer. Only a phase-shift ratio (or angle) ‘φ’ is chosen as the freedom of control; adjusting ‘φ’ allows power between the bridges to be controlled [33]. The various operation intervals in the converter’s forward and reverse modes of operation are described in the following subsections. The equivalent circuits during the forward and reverse modes of operation are shown in Figure 4.

2.1. Forward Mode of Operation

Mode-1 (t₀–t₁): for t ≥ t₀, Q₁ and Q₂ are given the pulses, and since the primary current i_p is negative, Q₁ and Q₂ remain off. Primary current flows through the anti-parallel diodes D₁ and D₂ on the primary side. Q₅ and Q₆ are triggered and are reverse-biased; negative current on the secondary side flows through diodes D₅ and D₆ through the load till t = t₁. V_ab = $V_{\mathrm{o}}^{\prime }$, V_cd = −V_o, v_cr(t_o⁺) is zero and i_p(t_o) = (−nI_o).

Mode-2 (t₁–t₂): At t ≥ t₁, primary current continues to flow through the anti-parallel body diodes D₁ and D₂ till t = t₂. On the secondary side, switches Q₇ and Q₈ are triggered and a secondary current starts flowing through Q₇ and Q₈; the current reaches zero at t = t₂. V_ab = $V_{\mathrm{o}}^{\prime }$, V_cd = V_o, v_cr(t₂) = −V_cp and i_p(t₂) = 0.

$$i_{\mathrm{p}}(t_2)=C_{\mathrm{r}} \frac{d{v}_{\mathrm{cr}}}{dt} \mathrm{and} L_{\mathrm{r}} \frac{d{i}_{\mathrm{p}}}{dt}+v_{\mathrm{cr}}(t_2)=\frac{-V_{\mathrm{o}}}{n}$$

(1)

$$i_{\mathrm{p}}(t)=I_{\mathrm{Lr}}\cos \left({\omega }_{r}t\right)+\frac{\left(v_{\mathrm{ab}}-n{v}_{\mathrm{cr}}-V_{\mathrm{o}}\right)}{n{Z}_c}\sin \left({\omega }_{r}t\right)$$

(2)

$$v_{\mathrm{cr}}(t)=\frac{-V_{\mathrm{o}}}{n}+I_{\mathrm{Lr}}{z}_c\sin \left({\omega }_{r}t\right)+(v_{cr}+\frac{V_{\mathrm{o}}}{n}-V_{\mathrm{ab}})\cos \left({\omega }_{r}t\right)+V_{\mathrm{ab}}$$

(3)

Mode-3 (t₂–t₃): At t₂, i_P ≥ 0, switches Q₁ and Q₂ conduct on the primary side, and the primary current increases till the end of this mode. Q₇ and Q₈ didn’t conduct; increasing i_p makes Q₇ and Q₈ reverse-biased. D₇ and D₈ conduct on the secondary side. At t₂, the end of this mode, Q₁ and Q₂ turn off. At t₃, I_P reaches a maximum and then decreases for t > t₃. V_ab = $V_{\mathrm{o}}^{\prime }$, V_cd = V_o,

$$i_{\mathrm{p}}(t)=i_{\mathrm{p}}(t_2)\cos {\omega }_r\left(t-t_2\right)+\frac{n\left(v_{\mathrm{ab}}-n{v}_{\mathrm{cr}}\right)-V_{\mathrm{o}}}{n{Z}_c}\sin {\omega }_r\left(t-t_2\right)$$

(4)

$${ }_{\mathrm{cr}}(t_2)= V_{\mathrm{ab}}-\frac{V_{\mathrm{o}}}{n}+i_{\mathrm{p}}\left(t_2\right)z_c\sin {\omega }_r\left(t-t_2\right)+(v_{\mathrm{Cr}}\left(t_2\right)+\frac{V_{\mathrm{o}}}{n}-V_{\mathrm{ab}})\cos {\omega }_r\left(t-t_2\right)$$

(5)

Mode-4 (t₃–t₄): Since Q₁ and Q₂ turn off at t₃, Switches Q₃ and Q₄ are triggered but reverse-biased by the I_P. I_P decreases linearly till t₄ and discharges through D₃ and D₄ on the primary side; its voltage remains zero during this interval. The anti-parallel diodes D₇ and D₈ still conduct on the secondary side, Q₇ and Q₈ are still reverse-biased by the I_p and the current starts decreasing from its peak value from t₃ onward.

$$V_{\mathrm{ab}}=-V_{\mathrm{o}}^{\prime }, V_{\mathrm{cd}}=+V_{\mathrm{o}}, i_{\mathrm{p}}(t_3)=I_{\mathrm{p(peak)}}$$

(6)

$$i_{\mathrm{p}}(t)=i_{\mathrm{p}}(t_3)\cos {\omega }_r\left(t-t_3\right)+\frac{n\left(v_{\mathrm{ab}}-n{v}_{\mathrm{cr}}\right)-V_{\mathrm{o}}}{n{Z}_c}\sin {\omega }_r\left(t-t_3\right)$$

(7)

Mode-5 (t₄–t₅): At t₄, Q₃ and Q₄ are still reverse-biased. I_P is positive and continues to freewheel through D₃ and D₄, linearly decreasing to zero at t₅. On the secondary side, switches Q₅ and Q₆ are triggered, and current flow through the load in the opposite direction, making the net current reach zero at t = t₅. During this interval V_ab = −$V_{\mathrm{o}}^{\prime }$, V_cd = −V_o, i_p(t₅) = 0.

Mode-6 (t₅–t₆): For t ≥ t₅, the primary current is negative and starts increasing linearly; Q₃ and Q₄ are already triggered. These switches start to conduct and the −I_p reaches a maximum at t = t₆. At t ≥ t₅, Q₅ and Q₆ are reverse-biased, and the secondary current gets discharged through the anti-parallel diodes D₅ and D₆. Switches Q₃ and Q₄ are turned off at t = t₆. V_ab = −$V_{\mathrm{o}}^{\prime }$, V_cd = −V_o, i_p(t) is negative.

$$i_{\mathrm{p}}(t)=-i_{\mathrm{p}}(t_4)\cos {\omega }_r\left(t-t_4\right)+\frac{n\left(-v_{\mathrm{ab}}-v_{\mathrm{cr}}\left(t_4\right)+V_{\mathrm{cd}}\right)}{n{Z}_c}\sin {\omega }_r\left(t-t_4\right)$$

(8)

$$v_{\mathrm{cr}}(t)=\frac{V_{\mathrm{cd}}}{n}-V_{\mathrm{ab}}+i_{\mathrm{p}}\left(t_4\right)z_c\sin {\omega }_r\left(t-t_4\right)+(v_{\mathrm{Cr}}\left(t_4\right)-\frac{V_{\mathrm{cd}}}{n}+V_{\mathrm{ab}})\cos {\omega }_r\left(t-t_4\right)$$

(9)

2.2. Reverse Mode of Operation

Mode-1 (t₀–t₁): At t₀, Q₇ and Q₈ are turned on; since the secondary current i_s discharging and is negative, these switches (Q₇ and Q₈) are forward biased, and the voltage (v_cd & v_ab) across the secondary and primary is positive. Current on the primary flows through the anti-parallel body diodes D₁ and D₂ in this reverse mode of operation.

$$V_{\mathrm{ab}}=V_{\mathrm{o}}^{\prime }, V_{\mathrm{cd}}=V_{\mathrm{Battery}}, v_{\mathrm{cr}}(t_1)\mathrm{is} V_{\mathrm{cp}} (\mathrm{peak}) \mathrm{and} i_{\mathrm{p}}(t_{\mathrm{o}})=(-n{I}_{\mathrm{o}}).$$

$$i_{\mathrm{p}}(t)=C_{\mathrm{r}} \frac{d{v}_{\mathrm{cr}}}{dt}, \mathrm{and} L_{\mathrm{r}} \frac{d{i}_{\mathrm{p}}}{dt}+v_{\mathrm{cr}}\left(t_1\right)=-n{V}_{\mathrm{o}}$$

(10)

$$v_{\mathrm{cr}}(t)=\frac{V_{\mathrm{o}}}{n}+I_{\mathrm{Lr}}{z}_c\sin \left({\omega }_{r}t\right)+(v_{\mathrm{cr}}+\frac{V_{\mathrm{o}}}{n}-V_{\mathrm{ab}})\cos \left({\omega }_{r}t\right)-V_{\mathrm{ab}}$$

(11)

Mode-2 (t₁–t₂): At t₁, i_p ≥ 0, switches Q₇ and Q₈ are triggered, and the positive i_p makes these switches reverse-biased. Current conducts through the anti-parallel diodes D₇ and D₈ on the secondary side. On the primary, this change in the direction of the current makes Q₁ and Q₂ forward-biased and current flows through Q₂ and Q₁. The current increases linearly till the end of the following mode. V_ab = $V_{\mathrm{o}}^{\prime }$, V_cd = V_Battery, v_cr(t₁) is −V_cp (peak value); for t = t₁⁺ voltage across the resonant capacitor starts decreasing towards zero, and i_p(t₂) = 0, i_p(t) reaches a maximum by the end of this mode.

$$I_{\mathrm{p}}(t)=i_{\mathrm{p}}(t_1)\cos {\omega }_r\left(t-t_1\right)+\frac{n\left(v_{\mathrm{ab}}-n{v}_{\mathrm{cr}}\right)+V_{\mathrm{o}}}{n{Z}_c}\sin {\omega }_r\left(t-t_1\right)$$

(12)

$$v_{\mathrm{cr}}(t_2)=\frac{V_{\mathrm{o}}}{n}-V_{\mathrm{ab}}+i_{\mathrm{p}}\left(t_1\right)z_c\sin {\omega }_r\left(t-t_1\right)+(v_{\mathrm{Cr}}\left(t_1\right)-\frac{V_{\mathrm{o}}}{n}+V_{\mathrm{ab}})\cos {\omega }_r\left(t-t_1\right)$$

(13)

Mode-3 (t₂–t₃): For t = t₂, the Q₅ and Q₆ switches are turned on. For t > t₂, the secondary current i_s increases linearly and passes through Q₅ and Q₆ on the HV-bridge side. Switches Q₁ and Q₂ continue to conduct on the primary side of the converter. The current reaches its peak value at t = t₃, the end of this mode. Switches Q₁ and Q₂ on the primary side are turned off at the end of this mode. V_ab = $V_{\mathrm{o}}^{\prime }$, V_cd = −V_Battery, v_cr(t₃) is zero; and i_p(t₂) = I_p (peak). i_p(t) starts decreasing from t = t₂.

Mode-4 (t₃–t₄): For t > t₃, the Q₅ and Q₆ switches continue to conduct on the secondary side. The current i_s starts decreasing linearly from its peak value. The current starts flowing through the anti-parallel body diodes D₃ and D₄ on the primary side. The current reaches zero at t = t₄, the end of this mode. V_ab = −$V_{\mathrm{o}}^{\prime }$, V_cd = −V_Battery, v_cr increases with a positive slope and reaches a maximum V_cp at t = t₄; i_p(t) starts decreasing from t = t₃ and reaches zero at t = t₄, i_p(t₄) = 0.

$$V_{\mathrm{ab}}=-V_{\mathrm{o}}^{\prime }, V_{\mathrm{cd}}=+V_{\mathrm{o}}, i_{\mathrm{p}}(t_3)=I_{\mathrm{p(peak)}}$$

(14)

$$i_{\mathrm{p}}(t)=i_{\mathrm{p}}(t_3)\cos {\omega }_r\left(t-t_2\right)+\frac{n\left(v_{\mathrm{ab}}-n{v}_{\mathrm{cr}}\right)-V_{\mathrm{o}}}{n{Z}_c}\sin {\omega }_r\left(t-t_2\right)$$

(15)

Mode-5 (t₄–t₅): For t ≥ t₄, the current changes its direction, and switches Q₅ and Q₆ are reverse-biased. Now, the current i_s starts flowing through the anti-parallel diodes D₅ and D₆ during this interval on the secondary side. This change in the direction of the current makes the switches Q₃ and Q₄ forward-biased on the primary side. So, the current starts linearly increasing for t ≥ t₄. V_ab = −$V_{\mathrm{o}}^{\prime }$, V_cd = −V_Battery, v_cr decreases with a negative slope and reaches zero t = t₅⁺; and. i_p(t) starts increasing negatively from t = t₄ and reaches -I_p (peak).

$$I_{\mathrm{p}}(t)=-i_{\mathrm{p}}(t_4)\cos {\omega }_r\left(t-t_4\right)+\frac{n\left(-v_{\mathrm{ab}}-v_{\mathrm{cr}}\left(t_4\right)+V_{\mathrm{cd}}\right)}{n{Z}_c}\sin {\omega }_r\left(t-t_4\right)$$

(16)

$$v_{\mathrm{cr}}(t)= \frac{V_{\mathrm{cd}}}{n}-V_{\mathrm{ab}}+i_{\mathrm{p}}\left(t_4\right)z_c\sin {\omega }_r\left(t-t_4\right)+(v_{\mathrm{Cr}}\left(t_4\right)-\frac{V_{\mathrm{cd}}}{n}+V_{\mathrm{ab}})\cos {\omega }_r\left(t-t_4\right)$$

(17)

Mode-6 (t₅–t₆): For t > t₅, switches Q₇ and Q₈ are forward-biased and start conducting on the secondary side. Switches Q₃ and Q₄ continue to conduct on the primary side till the end of this mode. i_s reaches its peak value at t = t₅. V_ab = −$V_{\mathrm{o}}^{\prime }$, V_cd = V_Battery, v_cr decreases with a negative slope and reaches zero at t = t₅⁺; and. i_p(t) starts increasing negatively from t = t₄ and reaches −I_p (peak).

To summarise, a current-fed isolated bidirectional DC-DC series resonant converter has been analyzed for different operating intervals. Next, a 135 W converter with the specification given in

Table 1. Specifications of the converter.

Parameter	Specification
Output power (Po)	135 W
Output voltage (Vo)	48 V
Switching frequency (fs)	100 kHz
DC Input supply (VPV)	12–18 V

is studied through PSIM simulation and experiment, and the results are presented in Section 4.

3. Steady-State Analysis of the Current-Source IBDC Converter

The current-fed isolated DAB bidirectional DC-DC converter transfers power by a phase shift between the gating signal between the primary and secondary sides on either side of the isolation transformer. To carry this analysis to the proposed topology using approximate analysis, the exceptions are given in [12,34,35,36]. The circuit shown in Figure 2b can be implemented in the forward mode of operation for PV and FC applications; the input is controlled by using the switch Q_b1 to maintain a constant voltage, as shown in Figure 5a. Figure 5b shows input-voltage control by turning off the switch Q_b1. Voltage v_cd is taken as ‘V_rt’ in Figure 6a [11]. The phasor equivalent circuit of the proposed topology is shown in Figure 6b. The equivalent circuit of the proposed topology with fundamental voltages ‘v_ab’ and ‘v_cd’ is shown in Figure 6c. The expression for the fundamental components of the voltages shown in Figure 6c is given as

$$v_{\mathrm{ab}1}=V_{\mathrm{ab}} \sin \left(\mathsf{\omega }\mathrm{t}\right)$$

(18)

$$v_{\mathrm{cd}1}=v_{\mathrm{cd}} \cos \left(\mathsf{\omega }\mathrm{t}-\phi \right)$$

(19)

The current transferred from one source to another, as shown in Figure 6b, is given as

$$\overline{I_{\mathrm{Lr}}}=\frac{v_{\mathrm{ab}1}-v_{\mathrm{cd}1}}{j\left(\omega L_{\mathrm{r}}-\frac{1}{\omega C_{\mathrm{r}}}\right)}$$

(20)

The power transferred to load in forward mode P_cd(t) is given as p_cd(t) = v_cd(t)i(t), and the resultant power then becomes the average power over one full cycle as

$${\mathrm{p}}_{\mathrm{cd}}\left(t\right)=\frac{v_{\mathrm{ab}} v_{\mathrm{cd}}}{\left(\omega L_{\mathrm{r}}-\frac{1}{\omega C_{\mathrm{r}}}\right)}\sin \left(\mathsf{\omega }\mathrm{t}\right)\cos \left(\omega t-\phi \right)$$

(21)

3.1. R_ac for the Inductive Output Filter

The output current (i_o) referred to the primary side, as shown in Figure 6a, is given by the following equation

$$i_{\mathrm{o}}^{\prime }=\frac{2}{T_s}{{\displaystyle \int }}_0^{T_s/2}\frac{I_{\mathrm{Lr}}}{n}\sin \left(\omega t\right)d\left(\omega t\right)$$

(22)

so the peak current of the $i_{\mathrm{o}}^{\prime }$ is given as $I_{\mathrm{o}}^{\prime }$ = $\frac{2I_{\mathrm{Lr}}}{n\pi }$; The series-resonant tank current in terms of $I_{\mathrm{o}}^{\prime }$ is given as i_Lr(t) = $\frac{n\pi }{2}{I}_{\mathrm{o}}^{\prime }\sin \left(\omega t\right).$ By using Fourier-series analysis, the peak and fundamental component of the voltage input to the rectifier bridge (at the ‘c’ and ‘d’ terminals) in terms of $V_{\mathrm{o}}^{\prime }$(output voltage referred to primary side) is

$$V_b=\frac{4V_{\mathrm{o}}^{\prime }}{n\pi }; v_{\mathrm{b}}(\mathrm{t})=\frac{4}{n\pi }{V}_{\mathrm{o}}^{\prime }\sin \left(\omega t\right)$$

(23)

$$R_{\mathrm{ac}}=\frac{v_{\mathrm{b}}\left(t\right)}{i_{\mathrm{Lr}}\left(t\right)}=\frac{8}{{\pi }^2}{R}_L^{\prime }$$

(24)

The sinusoidal current flowing in the series-resonant components is expressed as

i_Lr(t) = I_LrSin(ωt − ϕ)

(25)

The peak current stress is the same for the resonant elements and switches, and it is expressed as

$$I_{\mathrm{Lr}}=\frac{V_{\mathrm{ab}1\left(\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}\right)}}{\left|Z_{\mathrm{ab}}\right|}$$

(26)

The impedance (Z_ab) offered by the circuit across the terminals ‘a’ and ‘b’ is given as;

Z_ab = R_ac + j X_ab

(27)

From Z_ab, the expression for ϕ is given as

ϕ = tan⁻¹(X_ab/R_ac)

(28)

The sign of the magnitude of the resonant current i_Lr(t) at ωt = 0 decides the kind of soft switching (either zero-voltage switching (ZVS)/zero-current switching (ZCS)). If i_Lr(0) is negative then switches are turned-on with ZVS.

i_Lr(0) = I_Lr Sin(−ϕ)

(29)

When i_Lr(0) is positive, this indicates that the switches are turned off with ZCS. The ZVS/ZCS schemes minimize switching losses. The maximum voltage across C_r is V_CP is given as V_Cp = I_Csp · |X_Cr|.

3.2. Soft Switching

The performance of the current-fed DAB converter can be analyzed by determining the soft-switching range and conditions of the converter. These boundary conditions of the converter are the critical factors that define the soft switching of the converter [33]. This converter is operated under the above resonance method to achieve ZVS for the switches; the corresponding switching pulses, voltage and current waveforms are shown in Figure 7. The two expressions given in (30) are derived by using simple trigonometry for the current waveshapes shown in Figure 7a. The corresponding equivalent circuit, which depicts the waveforms of Figure 7a during the turn-on transient time in the forward mode, is shown in Figure 8a,b, where C_stray,_Qz (z = 1~8) represents stray capacitance in parallel with the switches (Q₁ to Q₈).

$$\begin{array}{c}{I}_{t2}=\frac{\pi n{V}_b-\left(\pi -2\varnothing \right)n^2{V}_{\mathrm{o}}}{2\pi L_{\mathrm{r}}{f}_s}\\ I_{t1}=\frac{\pi n^2{V}_{\mathrm{o}}-\left(\pi -2\varnothing \right)n{V}_b}{4\pi L_{\mathrm{r}}{f}_s}\end{array}\}$$

(30)

The bridges are symmetrical, so events belonging to Q₄ on the input and Q₇ on the output bridge are considered. The dynamic expressions (31) belong to the capacitor C_stray,Q4 and the series inductor are shown in Figure 8a,b.

$$\begin{array}{c}{L}_{\mathrm{r}}\frac{d{i}_{\mathrm{p}}\left(t\right)}{dt}=v_{Cstray,Q4}\left(t\right)-\left[V_b-v_{Cstary,Q3}\left(t\right)\right]-V_{\mathrm{o}}^{\prime }\\ =2v_{Cstray,Q4}\left(t\right)-V_{\mathrm{o}}^{\prime }-V_b\\ C_{stray,Q4}\frac{d{v}_{Cstray,Q4}\left(t\right)}{dt}=-\frac{1}{2}{i}_{\mathrm{p}}\left(t\right)\\ i_{\mathrm{p}}\left(0\right)=-n{I}_{t2}\\ v_{Cstray,Q4}\left(0\right)=V_b\end{array}\}$$

(31)

The expression for the capacitor voltage can be given with a frequency ${\omega }_1$

$$v_{Cstray,Q4}\left(t\right)=\frac{V_b-V_{\mathrm{o}}^{\prime }}{2}\cos \left({\omega }_{1}t\right)-\frac{n{I}_{t2}{\omega }_1{L}_{\mathrm{r}}}{2}\sin \left({\omega }_{1}t\right)+\frac{V_b+V_{\mathrm{o}}^{\prime }}{2}$$

(32)

where ${\omega }_1=\frac{1}{\sqrt{L_{\mathrm{r}}{C}_{stray,Q4}}}$. By reorganizing (32), the expression for ${\theta }_1$ is expressed in (33).

From (32), ZVS of Q₄ can occur when its capacitance-voltage reaches zero by resonance. The ZVS condition for the input bridge is given in (34).

$${\theta }_1={\sin }^{-1}\left[\frac{\raisebox{1ex}{$n{I}_{t2}{\omega }_1{L}_{\mathrm{r}}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\sqrt{{\left(\frac{V_b-V_{\mathrm{o}}^{\prime }}{2}\right)}^2+{\left(\frac{n{I}_{t2}{\omega }_1{L}_{\mathrm{r}}}{2}\right)}^2}}\right]$$

(33)

$$I_{t2}\ge \frac{2}{n}\sqrt{\frac{V_b{V}_{\mathrm{o}}^{\prime }{C}_{stray,Q4}}{L_{\mathrm{r}}}}$$

(34)

The dead-time is essential and must be controlled so that switch turns on when the capacitor voltage of the respective switch discharges to a minimum value, and this will reduce the turn-on loss. The dead-time for the input bridge in the forward mode is derived [33] by substituting ${\omega }_1$ and (33) into (35) and is given as (36)

$$T_{\mathrm{dead},\mathrm{ab}}=\{\begin{array}{c}\raisebox{1ex}{${\theta }_1$}\!\left/ \!\raisebox{-1ex}{${\omega }_1$}\right. ;\left(V_b<V_{\mathrm{o}}^{\prime }\right)\\ \raisebox{1ex}{$\left(\pi -{\theta }_1\right)$}\!\left/ \!\raisebox{-1ex}{${\omega }_1$}\right. ;\left(V_b\ge V_{\mathrm{o}}^{\prime }\right)\end{array}$$

(35)

$$T_{\mathrm{dead},\mathrm{ab}}=\{\begin{array}{c}\sqrt{L_{\mathrm{r}}{C}_{stray,Q4}} {\sin }^{-1}\left[\sqrt{\frac{I_{t2}^2{L}_{\mathrm{r}}}{n^2{C}_{stray,Q4}{\left(V_b-n{V}_{\mathrm{o}}\right)}^2+I_{t2}^2{L}_{\mathrm{r}}}}\right];\\ \left(V_b<V_{\mathrm{o}}^{\prime }\right)\\ \sqrt{L_{\mathrm{r}}{C}_{stray,Q4}}\left\{\pi -{\sin }^{-1}\left[\sqrt{\frac{I_{t2}^2{L}_{\mathrm{r}}}{n^2{C}_{stray,Q4}{\left(V_b-n{V}_{\mathrm{o}}\right)}^2+I_{t2}^2{L}_{\mathrm{r}}}}\right]\right\};\\ \left(V_b\ge V_{\mathrm{o}}^{\prime }\right)\end{array}$$

(36)

For the bridge on the secondary, its ZVS analysis is simple, after t = t₁, i_p has a relatively small di/dt. It is assumed constant as I₁ over a short duration. During the transient time of the switch Q₇, its capacitor C_stray,_Q7 discharges by a current I_t1/2, instead of resonance between L_r and C_stray,_Q7. The voltage across the switch Q₇ capacitor (C_stray,_Q7) drops from V_o to zero and is supposed to satisfy the condition given in equation (37). This equation provides the condition for achieving ZVS for the output bridge given in (38)

$$\frac{I_{t1}}{2}{T}_{dead,l,c}\ge C_{stray,Q7}{V}_{\mathrm{o}}$$

(37)

$$I_{t1}\ge \frac{2C_{stray,Q7}{V}_{\mathrm{o}}}{T_{dead,l,c}}$$

(38)

The switches (Q₁ to Q₈) for the input and output bridges are shown in Figure 8c,d. The expression for ${\theta }_2,$ I_t1 and, during this mode, the charging and discharging of the capacitor across the switches, are shown in Figure 7b. The corresponding equivalent circuits of the input and output full bridges are shown in Figure 8b, I_t2 and I_t1 are still aligned with the turn-off of Q₁ at t₂ and Q₈ at t₁. The soft-switching conditions are evaluated for the single-phase shift control scheme, and it is as follows.

$$\frac{n{I}_{t2}}{2}{T}_{dead,h,d}\ge C_{stray,Q4}{V}_b$$

(39)

$$I_{t2}\ge \frac{2n{C}_{stray,Q4}{V}_b}{T_{dead,l,c}}$$

(40)

Using regular trigonometry, the expression for I_t2 and I_t1 in the discharging or reverse modes are the same as the expressions (30) derived in forward mode. The voltage and current waveforms for the reverse mode are shown in Figure 7b. Equivalent circuits representing the capacitors of the switches (Q₁ to Q₈) for the input and output bridges are shown in Figure 8c,d. The expression for ${\theta }_2,$ I_t1 and dead-time (T_dead,cd) for reverse operation are derived just as in the forward mode of operation. These expressions are given in (41) to (44)

$${\theta }_2={\sin }^{-1}\left[\frac{\raisebox{1ex}{$n^2{I}_{t1}{\omega }_2{L}_{\mathrm{r}}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\sqrt{{\left(\frac{n{V}_{\mathrm{o}}-V_b}{2n}\right)}^2+{\left(\frac{n^2{I}_{t1}{\omega }_2{L}_{\mathrm{r}}}{2}\right)}^2}}\right]$$

(41)

$$I_{t1}\ge 2\sqrt{\frac{n{V}_b{V}_{\mathrm{o}}{C}_{stray,Q1}}{L_{\mathrm{r}}}}$$

(42)

$$T_{\mathrm{dead},\mathrm{cd}}=\{\begin{array}{c}\raisebox{1ex}{$\left(\pi -{\theta }_2\right)$}\!\left/ \!\raisebox{-1ex}{${\omega }_2$}\right. ;\left(V_b<n{V}_{\mathrm{o}}\right)\\ \raisebox{1ex}{${\theta }_2$}\!\left/ \!\raisebox{-1ex}{${\omega }_2$}\right. ;\left(V_b\ge n{V}_{\mathrm{o}}\right)\end{array}$$

(43)

$$T_{\mathrm{dead},\mathrm{cd}}=\{\begin{array}{c}\frac{\sqrt{L_{\mathrm{r}}{C}_{stray,Q7}}}{n} {\sin }^{-1}\left[\sqrt{\frac{I_{t1}^2{L}_{\mathrm{r}}}{C_{stray,Q7}{\left(n{V}_{\mathrm{o}}-V_b\right)}^2+I_{t1}^2{L}_{\mathrm{r}}}}\right];\\ \left(V_b\ge n{V}_{\mathrm{o}}\right)\\ \frac{\sqrt{L_{\mathrm{r}}{C}_{stray,Q7}}}{n}\left\{\pi -{\sin }^{-1}\left[\sqrt{\frac{I_{t1}^2{L}_{\mathrm{r}}}{C_{stray,Q7}{\left(n{V}_{\mathrm{o}}-V_b\right)}^2+I_{t1}^2{L}_{\mathrm{r}}}}\right]\right\};\\ \left(V_b<n{V}_{\mathrm{o}}\right)\end{array}$$

(44)

4. Simulation and Experimental Results

This section presents the simulation and experimental results of the proposed current-fed isolated DAB bidirectional DC-DC series resonant converter (CFIBDC) in Section 4.1 and Section 4.2, respectively.

4.1. Simulation Results

The specifications and design values for the proposed converter are shown in Table 1 and

Table 2. Designed values of the converter.

Parameter	Specification
Frequency ratio (F)	1.1
Gain (M)	0.95
Vo reflected to the primary side ($V_{\mathrm{o}}^{\prime }$)	42.75 V
Transformer turns ratio (1:n)	1.12
Load resistance (RL)	13.6 Ω
Resonant Inductor (Lr)	23.8 µH
Resonant Capacitor (Cr)	0.128 µF
Impedance (Zab)	11.02 + j2.52 Ω
Peak current (ILr)	4.71 A
Peak voltage (Vcp)	65.5 V
Filter inductance (Lo)	≤403.4 µH
Filter capacitance (Co)	≥1405 µF

. Results are presented for three cases with an output power of 135 Watts. Case 1: In forward mode with an input voltage V_in(min) = 12 Volts, V_o = 48 Volts at 100% and 10% of full load. Case 2: In forward mode with a V_in(max) = 18 Volts, V_o = 48 Volts at 100% and 10% of full load. If the load starts transferring back power to the input, then it is a reverse mode of operation. Case 3: In reverse mode, V_battery = 48 Volts, $V_{\mathrm{o}}^{\prime }$ = 42.5 Volts at 100% and 10% of full load. The comparison values of the theoretical and simulation values are given in

Table 3. Comparison of theoretical and simulation values in forward mode with an input voltage V_in = 12V_(min) & 18V_(max). and reverse mode with an input voltage V₂ or V_o = 48 V.

Parameter			Forward Mode									Reverse Mode
		Vin(min) = 12 V					Vin(max) = 18 V					V2 = 48 V
	100% Load			10% Load			Full Load		10% Load		Full Load			10% Load
	Cal.	Sim.	Expt.	Cal.	Sim.	Expt.	Cal.	Sim.	Cal.	Sim.	Cal.	Sim.	Expt.	Cal.	Sim.	Expt.
Vload(V)	48	44	48	48	49	50	48	44.8	48	49	42.7	39.8	50	42.7	43	50
Iload(A)	2.81	2.57	2.5	0.28	0.3	0.6	2.81	2.62	0.28	0.29	3.1	4.38	2.8	0.31	0.46	0.6
Isr,peak	3.92	4.4	5	1.09	1.23	0.5	3.93	4.41	1.29	1.45	3.9	4.38	5	0.41	0.46	0.5
Vcp	62.9	56.8	52	5.7	12.9	14	62.9	57.1	5.7	15	62.9	58	55	5.7	6.29	16
δ (o)	180		180	170		170	180		170		179		179	165		165
ZVS/ZCS	All		All	All		All	All		All		All		All	All		All

.

The voltage at the inverter output terminal voltage (v_ab), rectifier bridge input (v_cd), primary current (i_p) and the voltage across the resonant capacitor (v_cr) are shown in waveforms. The HV-side terminal current i_load, load voltage v_load, load current i_Load and current input to the IBDC converter i_b from the boost stage and the switches Q₁ to Q₈ voltages and currents are shown in Figure 9, Figure 10 and Figure 11. Simulation waveforms of the CFIBDC for Case 1 are shown in Figure 9, and for Case 2 are shown in Figure 10. Case 3, with the current input to the IBDC converter i_discharge from stored energy in a forward mode, which is fed back, is also shown in Figure 11. Soft switching is achieved for the switches Q₁ to Q₈ at full load; the corresponding voltage and current waveforms are offered for both forward and reverse modes of operations. Various losses of the converter are used for the simulation of the losses and efficiency of the converter. The simulation results and theoretical calculations are compared and found to be approximately equal, as can be seen in Table 3.

4.2. Experimental Results

To study the proposed converter’s performance, an experiment has been conducted. Experimental results are taken at V_in(min) and V_o for a variation in load from 100% to 10% in both forward and reverse modes of operation. The specifications and designed values are shown in Table 1 and Table 2. The experimental waveforms are presented in forward and reverse modes. The forward mode has two cases, Case 1 (Full load): square-wave voltages (v_ab & v_cd) across the terminals ‘a’, ’b’ and ‘c’, ’d’ are shown in Figure 12a along with the primary current and voltage across the resonant capacitor. The voltages v_ab & v_cd are the resultant of a single-phase shift control technique. The current flowing through the cross-connected switches such as Q₁, Q₂ & Q₃ and Q₄, in a bridge, is the same. The waveforms showing the ZVS for the four switches on the primary side through the complementary switches Q₁ and Q₃ are shown in Figure 12b. Similarly, the currents flowing through the switches Q₅, Q₆ & Q₇ and Q₈ are also the same. The corresponding ZCS for the four switches is shown in Figure 12c through switches Q₅ and Q₇. The load voltage, load current and input current are shown in Figure 12d, along with the voltage at the boost stage of the converter at 100% load. Case 2 (Full Load): The waveforms, as mentioned above, are shown in Figure 12e–h in the same order at 10% of full load. The reverse mode of operation waveforms are shown in Figure 13. Case 1 (10% of full load): Square waveforms v_ab & v_cd with an input voltage V₂ = 48 V and an output voltage V_o = 42.5 V are shown in Figure 13a along with the primary current i_p and resonant capacitor voltage v_cr. The waveforms showing ZVS for the switches (Q₅ to Q₈) on the primary side in the reverse mode of operation through complementary switches are shown in Figure 13b. The ZCS for the secondary side switches (Q₁ to Q₄) is shown in Figure 13c through the voltage and current waveforms of switches Q₁ and Q₄. The output voltage, load current and input current or discharge current in the reverse mode of operation are shown in Figure 13d. Case 2 (10% of full load): As mentioned above in the reverse mode of operation, the waveforms are shown in Figure 13e–h in the same order for 10% of the full load.

5. Comparison of Results

The performance of the proposed current fed series resonant dual active bridge converter with inductive output filter is analysed by comparing various losses as shown in Figure 14. The efficiecny of proposed converter at various loads is shown in Figure 15, and efficiency comparison of various topologies [7,8,10,11] is shown in Figure 16. The current stress of the proposed converter with the existing dual active bridge (DAB) converters of different topologies [7,8,10,11] is shown in Figure 17. The conventional DAB converter [7] without resonance achieved 93.5% efficiency at full load and 81% efficiency at 10% of full load. However, the converter is operated in discontinuous conduction mode to avoid the circulating current. The voltage-fed dual active-bridge converter with series resonance [11] has been operated with a single-phase shift control technique, and an efficiency of 95% at full load and 77% at 10% of full load is obtained. It has a circulating current at both full load and light load conditions. The non-resonant voltage-fed dual active-bridge (DAB) converter given in [8] has been operated with a zero circulating current modulation scheme. The proposed converter has achieved 94.5% efficiency at full load and 88% efficiency at 10% of full load. This modulation scheme results in low efficiency at light load as the converter is operated in discontinuous mode. The proposed current-fed series-resonant DAB converter has achieved 94.6% efficiency at full load and 83.02% efficiency at 10% of full load. In addition, this converter has achieved 96.31% efficiency at 50% of full load with an input voltage V_in(max) = 18 V and V_o = 48 V. The efficiency comparison of various topologies with the proposed current-fed isolated bidirectional DC-DC converter (CFIBDC) is given in

Table 4. Comparison of efficiencies of different topologies with proposed current-fed isolated bidirectional DC-DC converter (CFIBDC) (Percentage of output power (% of P_o) Vs. Efficiency of Topologies given with reference number).

% of Po	[7]	[8]	[10]	CFIBDC
10	84.5	77.5	69	83.02
20	86.5	79.5	74	86.5
30	88	83.5	89.5	90
40	90.5	89	82	94.5
50	91	92.5	83.5	95.19
60	91.5	92.5	84	94.3
70	92	93	86	94
80	93	93.5	87	94.2
90	93.2	94	88	94.3
100	93.5	95	89	94.6

. The proposed converter operated with soft switching for a wide range of loads; the reduced loading conditions are generally due to the peak switch currents (current stress) not reducing with the load.

The current stress of various topologies compared to that of the proposed CFIBDC converter is shown in

Table 5. Comparison of current stress in different topologies with current stress of proposed converter CFIBDC (Percentage of output power (% P_o) Vs. Current of Topologies given with reference number).

% of Po	[7] (Amp)	[8] (Amp)	[10] (Amp)	CFIBDC (Amp)
10	2.2	0.83	0.8	1.23
20	2.7	1	1.5	1.42
30	3.7	1.3	2.3	1.6
40	-	1.45	3	2
50	-	1.67	3.4	2.33
60	-	1.82	3.8	2.5
70	-	2.1	5	2.8
80	-	2.5	5.2	3.2
90	-	2.75	5.8	3.7
100	-	2.83	6	4.4

. High current stress on the switching devices leads to more conduction losses of the switches, which in turn reduces the efficiency of the converter and requires a more oversized heat sink. The current stress for a conventional dual active-bridge (DAB) converter is less during the light load condition, but it increases gradually. The conventional DAB [7] has been operated with two inductors, L₁ and L₂, to increase the light load efficiency of the DAB converter. If this converter uses only one inductor, L₁, it will have higher current stresses, but with two inductors, L₁ + L₂, it offers less current stress, giving higher efficiency at light load conditions. The voltage-fed series resonant DAB [11] converter offers less current stress, as shown in Figure 17. As per the percentage of full load current, the proposed current-fed series resonant converter with an inductive output filter offers lower current stresses from light load to full load compared to any other dual active-bridge converter topologies as can be seen in Figure 17.

6. Conclusions

A current-fed series resonant dual active-bridge isolated bidirectional DC-DC converter with an inductive output filter has been proposed, and its steady-state analysis has been carried out. The performance of the proposed converter has been compared with voltage-fed non-resonant and series-resonant isolated bidirectional DC-DC converters with a capacitive filter, and the results are presented. The proposed converter has been operated in continuous conduction mode without loss of duty cycle. It has shown better efficiency and less current stress and zero circulating current at the load than the voltage-fed non-resonant and series resonant dual-active bridge converters. The condition required for soft switching in both forward and reverse modes of operation for both bridges is derived. Simulation and experimental results for a load variation of 100% to 10% of full load are presented. A maximum efficiency of 96.31%, along with the breakdown of losses for the converter, are presented for a 135 W converter.

Strategies can be designed to overcome the disadvantages of current-fed isolated bidirectional converters, such as charging the inductor at the instant of turn-on and the occurrence of voltage spikes across the switches during the turn-off mode. The latter appears due to the mismatch in current flowing through the boost inductor at the input and leakage inductor of the HF isolation transformer. These current-fed IBDC converters can aid in building hybrid microgrid systems by using renewable energy resources with low voltage capacities such as fuel cells, PV systems and wind energy.