1. Introduction

Isolated bidirectional DC/DC converters (BDCs) have become increasingly developing and widely used in uninterruptible power supplies (UPS), electric vehicles (EVs), and energy storage systems (ESS) in recent years. For their essential interfacing with energy storage systems, the bidirectional isolated DC/DC converter has become a popular research topic recently, and is widely used with DC power systems in low voltage such as batteries storage systems.

An LLC resonant converter is a typically isolated dc/dc converter that is widely used in energy storage systems due to its high efficiency, a wide range of zero voltage switching (ZVS), zero current switching (ZCS), and electrical isolation. When the power flows in forward mode, the LLC converter can achieve voltage gain greater than one or less than one which means can operate in both boost mode and buck mode by applying frequency conversion for the switches. However, when the power flows in backward mode, the magnetizing inductance of LLC is not involved in the resonant because it is paralleling with the voltage on the secondary side. Owing to the excitation inductance clamped by the voltage on the secondary side, the LLC resonant tank has become LC-type during backward mode ⁽¹⁾. The voltage gain of the backward mode is less than one, thus the converter cannot operate in boost mode to achieve the requirement of voltage gain at the high voltage side. That is why LLC resonant converter is usually used in the case of unidirectional voltage regulation or bidirectional without voltage regulation ⁽²⁾. However, in the ESS application, the bidirectional LLC resonant converter required a wide-rage voltage regulation during the backward mode.

To achieve the wide-range voltage regulation of a bidirectional LLC converter, many researchers generally modified the resonant tank of the circuit. By adding a resonant capacitor on the secondary side, the CLLC resonant converter can operate bidirectional power transmission but it has a complexity of parameter design and control strategy ⁽³⁾. In ⁽⁴⁾, the auxiliary LC resonant tank was added at the secondary side to equalize the primary LC component when operating in backward mode. The converter becomes a symmetrical CLLLC resonant converter. However, it required the accuracy of the resonant parameters and was not suitable for applications with different forward and backward voltage gain. In ⁽⁵⁾, a resonant tank with bidirectional symmetry can be built by paralleling the auxiliary inductor on the input side of the resonant tank, but the loss and volume of the auxiliary inductor are significant. In ⁽⁶⁾, the parallel configuration of switches in LLC resonant converter was proposed for battery charger. In ⁽⁷⁾, a three-level LLC resonant converter was proposed by adding more switches. This method can be used to modify the resonant tank and achieve bidirectional wide-range voltage regulation.

Through the topologies mentioned above, it is possible to achieve effective backward voltage regulation. However, the addition of components has an impact on the efficiency of the forward mode, and the difficulty of converter parameter design. Without modifying the basic structure of the LLC resonant converter as presented in ⁽⁸⁾, the step-up control technique was proposed to help the backward normalized voltage gain being greater than one. This step-up control technique turns on rectifier switches for recovery of the energy of resonant components to increase the normalized voltage gain value to two. However, since its backward normalized voltage gain is two at the resonant frequency, it is not appropriate for shifting between backward step-down and backward step-up modes. Simultaneously, when operating in light load, the switching frequency required to obtain normalized voltage gain is near to one that leads to generating large switching loss.

In summary, there has been a lot of research on bidirectional wide-range voltage regulation, which illustrates the significance of this study. However, the majority of this research relies on changing the topology, which increases the number of additional components, system loss, difficulty in designing parameters, and complexity of the control scheme. These implementations were only focused on the forward mode analysis due to the symmetrical operation of the converter after modifying the resonant tank. There has been a few research on achieving a bidirectional wide gain range without modifying the architecture. With only control methods cannot switch smoothly and the control effect is weak for light loads condition.

To solve the issue of wide-range voltage gain without changing the basic circuit of the LLC resonant tank, the two-stage structure is implemented in this paper as studied in ⁽⁹⁾. this paper proposed a two stages structure topology which is a simple topology in order to achieve natural bidirectional power flow, easy for control, wide-range voltage regulation, and capable for the variable load. Figure 1 shows the two-stage bidirectional converter scheme. The isolated LLC resonant converter operated near the resonant frequency to achieve high efficiency and without voltage regulation. Furthermore, it could be operated at a fixed frequency and fixed duty cycle and play a simple role in galvanic isolation. In terms of voltage regulation capability and dynamic performance, the non-isolated bidirectional DC-DC converter was provided the operation in buck/boost mode to achieve voltage gain adjustment. The non-isolated converter is operated to regulate voltage either high side voltage or low side voltage according to the demanded load power. And also directly control current or voltage for CC or CV mode for charging and discharging operation, respectively.

This paper analyzed the backward mode operation by applying a simple topology to achieve wide-range voltage regulation and soft switching. The operational characteristic for bidirectional LLC converter is analyzed in Section II. The analysis of the backward mode LLC converter operational characteristics was presented in Section III. The backward mode of LLC converter soft switching is verified by simulation and experiment presented in Section IV.

2. Analysis of bidirectional LLC converter operation characteristic

Figure 2 shows the LLC resonant converter schematic. The switch S$_{H1}$ – S$_{H4}$ are primary switches, S$_{L1}$ – S$_{L4}$ are secondary side switches. C$_{R}$ is the resonant capacitor, L$_{R}$ is the resonant inductor, L$_{m}$ is the transformer excitation inductor, the transformer turn ratio is 10:1, C$_{i}$ is the primary capacitor, and C$_{o}$ is the secondary capacitor. V$_{i}$ is the primary input voltage of the converter, V$_{BAT}$ is the secondary output voltage of the converter, and V$_{CR}$ is the voltage on the resonant capacitor.

When the converter is operating in forward mode, it means charging the batteries. The power flows from the higher voltage side to the lower voltage side of the battery. In contrast, the converter is operating in backward mode, which means discharging the batteries. The power flows back from the lower voltage of batteries to the higher voltage side.

The bidirectional LLC converter equivalent circuits are shown in Figure 3. In the charging case as shown in Figure 3 (a), LLC resonant converter provides isolation and helps to achieve a wide range of soft switching. In addition, the integrated resonant inductance in the transformer can achieve high power density. In the discharge case, the magnetizing inductance is in parallel with the battery voltage and not involved in the resonance illustrated in Figure 3 (b). But the reactive current via the magnetizing inductance can improve the soft switching and reduce the switching loss. Owing to the magnetizing inductance L$_{m}$ of the LLC converter is generally made with a large value, the $I_{Lm_max}$ value is small, and the turn-off losses of switches are small which helps to achieve soft switching. The turn-off losses are possibly neglected when the $I_{Lm_max}$ value is very small.

According to the equivalent circuit of Figure 3, a resonant frequency can determine by resonant tank L$_{R}$ and C$_{R}$ as shown in equation (1). The equivalent load resistance R$_{e}$ is shown in equation (2). The ratio of total primary inductance to resonant inductance m is expressed in equation (3) ⁽¹⁰⁾.

Where R$_{0}$ is the load resistance, V$_{0}$ is the output voltage, P$_{0}$ is the output power, N$_{P}$ is the primary turns number, and N$_{S}$ is the secondary turns number.

The voltage gain of the resonant converter was obtained by relating with equivalent load resistance R$_{e}$, quality factor Q$_{e}$, and normalized switching frequency F$_{x}$. The quality factor Q$_{e}$ value depends on the load current as shown in equation (4). Lighter load conditions operate at lower Q$_{e}$ values whereas heavy loads operate at high Q$_{e}$ values. The normalized switching frequency F$_{x}$ is expressed in equation (5) which is the result of the division between switching frequency f$_{s}$ and resonant frequency fr.

In the LLC condition mode, the ratio of total primary inductance to resonant inductance m is involved in voltage gain K(Q$_{e}$, m, F$_{x}$) as shown in equation (6) ⁽¹⁰⁾. Since the backward mode is different from the forward mode of the LLC resonant converter, the voltage gains of backward are not involved with magnetizing inductance L$_{m}$ due to the paralleling of L$_{m}$ and lower voltage side. Equation (7) expressed the voltage gain of the LLC converter in backward mode K(Q$_{e}$, F$_{x}$).

Figure 4 shows the operation mode of the LLC converter for discharging direction. Mode I, switches S$_{H1}$, S$_{H4}$, S$_{L1}$, S$_{L4}$ are turn-on and S$_{H2}$, S$_{H3}$, S$_{L2}$, S$_{L3}$ are turn-off. Power flows through the resonant tank (L$_{R}$, C$_{R}$) and also charges into the magnetizing inductance of transformer L$_{m}$ then supply to the load. In Mode II, all switches are turned off during dead time. The magnetizing inductance L$_{m}$ charge/discharge to the output capacitor of switches. During Mode III, the switches S$_{H1}$, S$_{H4}$, S$_{L1}$, S$_{L4}$ are turn-off and S$_{H2}$, S$_{H3}$, S$_{L2}$, S$_{L3}$ are turn-on. This operation mode is similar to Mode I. After Mode III the dead time and other half-switching period begin again.

3. Analysis of backward LLC converter operation characteristic

When the power flows in backward mode, the magnetizing inductance of LLC is not involved in the resonant tank but parallel with the secondary side voltage. Even though LLC resonant tank becomes the LC type during backward mode due to the excitation inductance clamped by the voltage on the secondary side, the backward LLC resonant converter is not the same as the series resonant converter (SRC).

As previously mentioned, the backward mode of the LLC converter has different soft switching conditions from the SRC converter even though their voltage gains are the same. SRC converter usually operates the switching frequency above the resonant to guarantee the soft switching ⁽¹⁾, but when the backward mode of the LLC converter operates the switching frequency above the resonant, the turn-off current would be larger. However, the freewheeling of field current helps the converter achieve soft switching while the switching frequency is slightly smaller than the resonant. Thus, the switching frequency of LLC backward mode is operated below the resonant frequency in the range $0.89\le f_{s}/f_{r}\le 0.92$ in order to achieve the soft switching, ZCS for secondary switches, and near ZCS for primary switches. Figure 5 shows the key waveforms of LLC backward mode operated in three different frequency ranges $0.65\le f_{s}/f_{r}<0.89$, $0.89\le f_{s}/f_{r}\le 0.92$, and $0.92<f_{s}/f_{r}\le 1.2$, respectively.

In this bidirectional LLC backward mode as shown in Figure 5, the waveform of current and voltage of secondary switches are expressed about ZCS. Figure 5 (a) condition, turn-on current is achieved ZCS but turn-off current has generated the losses. The turn-off current losses are larger when f$_{s}$/f$_{r}$ moves to a lower value. Figure 5 (b) condition, the turn-on and turn-off current are achieved ZCS. Figure 5 (c) condition, turn-on current generated the losses, and turn-off current is large. The turn-on current losses and turn-off current are larger when f$_{s}$/f$_{r}$ moves to a higher value.

Figure 6 shows the equivalent circuit of backward mode LLC that is derived from Figure 4. V$_{i}$ in here is the voltage terminal between leg1 and leg2 of primary side switches. nV$_{BAT}$ is the voltage at the primary side of the transformer. Figure 7 shows the key waveform of the operation principle for LLC backward mode.

Mode I (t$_{0}$~t$_{1}$): The equivalent circuit of this mode is shown in Figure 6 (a). Start at t$_{0}$, switches S$_{H1}$, S$_{H4}$, S$_{L1}$, S$_{L4}$ are turn-on and S$_{H2}$, S$_{H3}$, S$_{L2}$, S$_{L3}$ are turn-off. The secondary side switches are turn-on and turn-off ZCS. Based on the equivalent circuit we can drive the resonant current $i_{LR(t)}$ as following equation below:

The resonant current $i_{LR(t)}$ in Mode I is a sinusoidal waveform. Then it can be expressed as

Where $\omega_{R}$ is the angular resonant frequency, $Z_{R}$ is the impedance of the resonant tank, and $n$ is the turn ratio of the transformer.

Mode II (t$_{1}$~t2): The equivalent circuit of Mode II is shown in Figure 6 (b). All switches are turn-off at t$_{1}$ and resonant current $i_{LR(t1)}$, becomes equal to peak magnetizing current $i_{Lm_max}$ obtained in equation (14). During mode II the output capacitors of primary side switches are charged and discharged by the $i_{Lm_max}$.

Mode III (t2~t3): The equivalent circuit of Mode III is shown in Figure 6 (c) which opposite switches on-off with Mode I. the switches S$_{H1}$, S$_{H4}$, S$_{L1}$, S$_{L4}$ are turned off and S$_{H2}$, S$_{H3}$, S$_{L2}$, S$_{L3}$ are turned on. The operation mode and formula equations are similar to Mode I. The soft switching for the primary side is nearly ZCS and achieved ZCS for the secondary side. After Mode III the dead time and other half-switching period begin again.

4. Simulation and experiment

Table 1 shows the system parameters of the LLC resonant converter. Figure 8 shows the voltage gains of the LLC converter backward mode. The best point of normalized frequency FX is 0.9 which means the switching frequency is 50kHz. According to equations (2) and (4) the maximum quality factor Q$_{e}$ is 0.56 when the maximum power is 4kW. Thus, the voltage gain matched three curves as seen in Figure 8.

Figure 9 shows the simulation schematic for an isolated LLC resonant converter in backward mode. The system parameters in Table 1 are used in the simulation. Backward mode discharges the battery power to supply load at the primary side. The battery voltage is 24V and the load is used as resistance. The operated switching frequency for backward mode is 50kHz. The primary side switches are near soft switching ZCS, and the secondary side switches are achieved pure soft switching ZCS. Since the secondary side currents are high, the soft switching ZCS at the secondary side must be more concentrated due to the heating and efficiency effect. Figure 10 shows the simulation waveform of primary and secondary switches. Figure 11 shows the current and voltage simulation waveform of primary and secondary that express ZCS achievement. The current and voltage are met at

zero crossing which means the converter operated on soft switching ZCS.

Figure 12 shows the expanded voltage waveform of secondary side that generated the parasitic resonant oscillation during deadtime. This parasitic resonant oscillation is generated on the secondary side of the converter due to parasitic impedance, such as the stray capacitance of switches and stray inductances. The equivalent stray capacitance is about 2800pF, and the equivalent stray inductance of the secondary side is transformed from the primary side, which equals 0.185uH. By using the formula (1), the parasitic resonant waveform during dead time is calculated to be 7MHz.

Figure 13 shows the simulation results of load resistance variation to demonstrate ZCS operation. The simulation compares the secondary voltage and current for power levels ranging from 1kW to 4kW.

Figure 14 shows the experimental setup for a bidirectional LLC resonant battery charger. The system parameter values used in the experimental setup are shown in Table 1. The main parts of this experimental setup are the DSP board for control of the system, the filter inductor of the non-isolated converter, transformer,

non-isolated converter parts for buck/boost voltage gain requirement, the primary side of isolated converter parts, the secondary side of isolated converter parts. The bidirectional LLC resonant converter can operate in forward and backward modes. In the forward mode, the switching frequency is fixed and operated at the resonant point. The power flow from the high-voltage side (DC-link) to the low-voltage side (batteries). The non-isolated DC-DC converter is operated for voltage regulation in buck/boost mode to achieve voltage gain adjustment and directly control current or voltage for CC or CV mode in charge/discharge operation. In backward mode, the switching frequency is fixed 50kHz and operated slightly smaller than the resonant point is 0.9 of normalized switching frequency. The voltage of the primary side is lower than the DC-link voltage. Then the non-isolated converter regulates voltage to meet the required value. Operated in this point of frequency for backward mode, the LLC resonant converter achieved the soft switching.

Figure 15 shows the backward mode experiment waveform of the LLC resonant converter expressing the soft switching ZCS. Figure 15 (a) is the soft switching ZCS of comparison between primary voltage V$_{Pri}$ and secondary current $I_{Sec}$. Figure 15 (b) is the soft switching ZCS of comparison between secondary voltage V$_{Sec}$ and secondary current $I_{Sec}$. Figure 15 (c) compares waveform of primary current $I_{L_R}$ and secondary current $I_{Sec}$. The experimental result showing for soft switching characteristic ZCS for the secondary side of converter. These waveforms were generated in a 2 kW, where the higher voltage side is the DC-link voltage of the PV system at 370V. A non-isolated DC-DC converter, controlled by a DSP control board using current and voltage control methods, was used for buck/boost voltage connected with V$_{i}$ voltage in the range of 210V to 270V.

The resonant frequency of the resonant circuit is designed to be close to the switching frequency of the converter. This ensures that the switching transitions occur at zero voltage or zero current points, which minimizes switching losses and reduces electromagnetic interference. This is achieved by controlling the switching timing and frequency of the converter.

During the on-time of the switching device, energy is transferred from the input voltage source to the resonant tank. The resonant inductor stores the energy in the form of a magnetic field, while the resonant capacitor stores the energy in the form of an electric field. The resonant tank continues to accumulate energy until the voltage across the resonant capacitor reaches the voltage of the input source.

At the beginning of each switching cycle, the current through the resonant circuit is zero, and the voltage across the switching device is also zero. As the switch turns on, the voltage across the primary winding of the transformer begins to increase, and the resonant circuit begins to oscillate. The voltage across the switch then rises gradually until it reaches the resonant voltage of the resonant circuit. This means that the switch is turned on at a zero-current point, which results in soft switching. Similarly, during turn-off, the resonant circuit discharges through the switch,

and the switch is turned off at a zero-voltage point, which also results in soft switching.

5. Conclusion

This paper presented the backward mode analysis of the bidirectional LLC resonant converter without changing the basic topology of the LLC resonant tank. In forward mode, the converter operates at the fixed frequency at the resonant point which has kept voltage gain constant at 1 with load variation and achieved soft switching. In backward mode, the converter also operated in fixed frequency but below the resonant point which is 0.9 of normalized frequency in order to achieve soft switching. The fixed frequency operation is an easy control method for isolated LLC resonant converter. The complement of voltage gain requirement for DC-link voltage during backward mode is achieved by the non-isolated converter.