A Bidirectional Isolated DC-to-DC Converter with Hybrid Control of Pulse Width Modulation and Pulse Frequency Modulation

Abstract

This paper proposes a modified bidirectional isolated DC/DC converter with hybrid control, which can be applied to bidirectional power transfer between energy storage systems and DC microgrids. Batteries are usually applied to energy storage systems. The battery lifespan may be shortened if the converter has large current ripple during the battery charging process. The proposed topology consists of a CLLC converter and an interleaved buck converter. The first stage is an isolated full bridge CLLC converter, and the second stage is an interleaved buck converter with hybrid control of pulse width modulation (PWM) and pulse frequency modulation (PFM). Additionally, the proposed topology achieves zero voltage switching (ZVS) for all switches and reduces the output current ripple. The operational principles of bidirectional power flow in both directions are described in detail. Finally, a 1.5 kW experimental prototype, rated with a high side voltage of 380 V and low side voltage range of 40–58 V, was constructed and tested to investigate the system performance. The measured highest efficiency for the proposed converter is 90% in charging mode, and 94% in discharging mode.

1. Introduction

With the advancement of technology and the increasing demand for energy, it is important to recognize the need for efficient energy utilization. Excessive reliance on non-renewable energy sources has led to serious environmental pollution. The growing awareness of environmental protection has driven the development of renewable energy sources worldwide. As renewable energy usage increases, the role of DC power systems and DC microgrids [1,2] with energy storage systems (ESSs) becomes essential for enhancing power quality, conversion efficiency, and the reliability of power generation. Therefore, energy conservation is a primary concern in this industry. Improving the efficiency of power converters is a key objective to achieve this goal. ESSs typically consist of a battery operating at a lower voltage than the DC bus. A bidirectional DC/DC converter is used to charge and discharge the battery set of an ESS. Enhancing the efficiency and power density of bidirectional DC/DC converters is crucial for enabling residential energy storage systems. Additionally, galvanic isolation is necessary to guarantee converter safety, usually achieved through the implementation of an isolated converter topology such as dual-active-bridge (DAB) converters, LLC converters, and CLLC converters.

The DAB converters [3,4,5,6] use the leakage inductance of the high-frequency transformer as the power transfer element thereby increasing power density with simple control requirements. However, DC sources such as energy storage systems, Li-Ion Battery, or renewable energy sources have wide voltage variations, leading to a limited zero voltage switching range and high circulating current, especially at light loads. Ensuring soft switching across the entire load range was proposed through complex modulation involving three or more control variables [7,8]. However, this approach complicates the controller implementation and necessitates an offline optimization to select the optimal combination of variables.

The isolated bidirectional LLC [9,10,11] and CLLC resonant DC/DC converters [12,13,14,15,16,17] consist of dual bridges and resonant tanks. Compared to the DAB converter, resonant converters have a wider zero voltage switching (ZVS) load range, which leads to higher efficiency. Nevertheless, resonant converters may suffer the problem of reduced efficiency when the switching frequency is deviated from the resonant frequency. Therefore, resonant converters may not operate in optimal condition at the entire load range if the converter is designed as a single-stage structure.

In [9], the proposed topology can overcome the problem of circulating current when the LLC converter operates at its resonant frequency. However, this topology incorporates two sets of LLC resonant tanks, which increases the number of switches and could potentially reduce the overall efficiency of the converter. Ref. [14] presents a detailed design procedure for a CLLC-type resonant converter for battery charging, ensuring soft-switching in all switches and enabling high-frequency operation. The design methodology includes determining transformer turns ratio, magnetizing inductance design, and calculating resonant inductance and capacitance.

In [17], a hybrid control strategy is proposed. This innovative control strategy combines pulse frequency modulation (PFM) and phase-shift modulation (PSM) to achieve high efficiency and stable operation. The proposed control can be easily implemented using a digital signal processor, making it a practical solution for power electronics applications. These circuit topologies offer several advantages such as soft switching, wide voltage gains, and minimized circulating currents. However, CLLC converters have a large output ripple, which may reduce battery life.

To deal with the issue of output ripple, a two-stage circuit was implemented, in which the second stage circuit adjusts the output voltage [18,19,20,21]. Ref. [22] introduces a digital adaptive control for a bidirectional DC/DC charger/discharger; this method achieves ZVS [23,24,25,26,27,28] without the need for an auxiliary zero-crossing detection (ZCD) circuit. It determines the appropriate switching frequency through digital calculation to satisfy ZVS conditions, allowing for soft switching over a wide range of input and output voltages. Although using a two-stage circuit increases the number of components, which may slightly decrease overall efficiency, it allows for an extension of the output voltage range and a reduction in output ripple.

This paper proposes a modified bidirectional isolated DC/DC converter with hybrid control, as illustrated in Figure 1. The first stage circuit is a full bridge CLLC converter that functions as a transformer to achieve galvanic isolation and uses an open-loop fixed frequency control to reduce electromagnetic interference. This topology facilitates the achievement of ZVS and zero current switching (ZCS) thereby improving the overall efficiency of the converter. The second stage circuit is an interleaved buck converter that employs pulse width modulation (PWM) and PFM controls to extend the output voltage range and enhance converter efficiency under light load conditions. The proposed approach allows for an expanded output voltage range and reduced output current ripple. The article is organized as follows: In Section 2, the operational principles and hybrid control strategy are described in detail. In Section 3, the circuit parameters are designed, and an experimental prototype is built and tested to verify the theoretical analysis. Finally, the conclusion is presented in Section 4.

2. Proposed Bidirectional Converter and Operation Principle

The proposed bidirectional isolated DC/DC converter with hybrid control is shown in Figure 1. The power flow is transferred from V_high to V_bat when the converter is operating in charging mode. In the discharging mode, the converter operation is reversed. Since the operation principles of the converter are similar in both charging and discharging modes, only the analysis of the operation principle for the proposed converter in the charging mode will be presented. In this article, the analysis of the first stage circuit and the second stage circuit will be provided.

2.1. CLLC Resonant Converter

The CLLC resonant converter, as illustrated in Figure 1b, is capable of bidirectional power transfer. In charging mode, the direction of power flow is transferred from the V_high to the V_bus, and vice versa in discharging mode. The CLLC converter comprises two full bridge circuits and the resonant tank including L_r1, C_r1, L_m, L_r2, and C_r2. The primary side bridge functions as a high-frequency inverter, while the secondary side bridge performs rectification in charging mode. In discharging mode, the roles of these two full bridges are reversed.

Therefore, the resonant frequency f_r, the quality factor Q, and the inductance ratio k, are obtained as follows:

$$f_r={\displaystyle \frac{1}{2\pi \sqrt{L_{r1}{C}_{r1}}}}$$

(1)

$$Q={\displaystyle \frac{Z_r}{R_{o,e}}}$$

(2)

$$k={\displaystyle \frac{L_{r1}}{L_m}}$$

(3)

where the characteristic impedance Z_r and equivalent resistance of resonant network R_o,e are given by

$$Z_r=\sqrt{{\displaystyle \frac{L_{r1}}{C_{r1}}}}$$

(4)

$$R_{o,e}={\displaystyle \frac{8n^2}{{\pi }^2}}{R}_o$$

(5)

As shown in Figure 2, the operation of the CLLC resonant converter can be divided into four stages. The operations of Stages 1–4 are presented as follows:

Stage 1 [t₀–t₁, Figure 3a]: In Stage 1, S₁, S₄, S₆, and S₇ are turned on, and S₂, S₃, S₅, and S₈ are turned off. The inductor current flows through the secondary resonant inductor and capacitor to the V_bus. In this mode, the resonant current i_p flows through the resonant inductor and capacitor, changing its direction from negative to positive.

Stage 2 [t₁–t₂, Figure 3b]: S₁, S₄, S₆, and S₇ are turned off and the CLLC converter enters into the duration of dead time. The voltage of parasitic capacitors C_oss1 and C_oss4 are charging from zero to V_high. Meanwhile, the voltage of parasitic capacitors C_oss2 and C_oss3 are discharging from V_high to zero. At this stage, the primary side current i_p decreases, and the primary current commutation is completed. The stage ends when S₂, S₃, S₅, and S₈ are turned on.

Stage 3 [t₂–t₃, Figure 3c]: In Stage 3, S₂ and S₃ are turned on under ZVS condition. Energy is transmitted to the secondary side through the transformer. During this stage, the primary side current i_p flows through the resonant inductor and capacitor, reversing the direction from positive to negative.

Stage 4 [t₃–t₄, Figure 3d]: In this stage, the operation principle is similar to Stage 2. The difference between Stage 4 and Stage 2 is that the voltage of C_oss1 and C_oss4 discharges to zero and the voltage of C_oss2 and C_oss3 charges to V_high. When S₁, S₄, S₆, and S₇ are turned on, this stage ends.

2.2. Interleaved Buck Converter

The interleaved buck converter, as illustrated in Figure 1c, is capable of bidirectional power transfer between V_bus and V_bat. The proposed converter is operated in boundary conduction mode (BCM) using hybrid control to reduce inductor current ripple, enabling S₉ to S₁₂ achieve ZVS. The operation of the main structure can be divided into eight stages. The operations of Stages 1–4, as shown in Figure 4, are similar to that of Stages 5–8 thus only Stages 1–4 are presented.

As shown in Figure 4, S₉ and S₁₀ are complementary, as are S₁₁ and S₁₂. The two sets of signals are driven with a phase-shift of 180 degree. The inductor currents are interleaved to reduce output current ripple.

In this circuit, the average current of each phase can be obtained by

$$I_{L,avg}={\displaystyle \frac{I_{bat}}{N_{phase}}}$$

(6)

The peak inductor current I_L,peak can be expressed as follows:

$$I_{L,peak}=2\cdot (I_{L,avg}+I_R)$$

(7)

Using the inductor volt-second balance, the equations for calculating the duty cycle D_buck, and switching frequency f_sw,buck of the interleaved buck converter can be obtained as follows:

$$D_{buck}={\displaystyle \frac{V_{bat}}{V_{bus}}}$$

(8)

$$f_{sw,buck}={\displaystyle \frac{V_{bat}(V_{bus}-V_{bat})}{L\cdot V_{bus}\cdot I_{L,peak}}}$$

(9)

By substituting I_L,peak into Equation (10), the required inductor value for the circuit can be obtained from Equation (10).

$${L=L}_1=L_2={\displaystyle \frac{V_{bat}(V_{bus}-V_{bat})}{f_{sw,min}\cdot V_{bus}\cdot (I_{L,peak}+I_R)}}$$

(10)

Stage 1 [t₀–t₁, Figure 5a]: In Stage 1, S₉ and S₁₁ are turned on, and S₁₀ and S₁₂ are turned off. The inductor current i_L1 and i_L2 will increase to the maximum value.

Stage 2 [t₁–t₂, Figure 5b]: This stage is the dead time between S₁₁ and S₁₂. S₁₁ is turned off, and the inductor L₂ changes from stored energy to release energy. The inductor L₁ still stores energy.

Stage 3 [t₂–t₃, Figure 5c]: S₁₂ turns on under ZVS condition. The inductor L₂ releases energy. The inductor current i_L2 decreases linearly to the minimum value.

Stage 4 [t₃–t₄, Figure 5d]: This stage is similar to Stage 2. S₁₂ turns off, the inductor L₂ changes from released energy to stored energy.

2.3. Proposed Digital Hybrid Control

A flowchart of the hybrid control is illustrated in Figure 6. The proposed digital hybrid control combines PWM with PFM and is implemented using the digital signal processor (DSP) TMS320F28335. An analog-digital-converter (ADC) module is used to detect the V_bat, I_bat, and V_bus.

When the circuit parameters and operating conditions are defined, the switching frequency primarily dictates the operating mode of the converter. If the switching frequency is too high, the interleaved buck converter operates in continuous conduction mode (CCM), resulting in the loss of ZVS for the switches. It is less efficient due to increased switching losses. Conversely, if the switching frequency is too low, the converter generates a higher circulating current, leading to increased conduction losses, which also adversely affects the converter efficiency. Therefore, selecting an appropriate switching frequency based on the specific operating conditions is crucial to ensure that the converter can operate under various load conditions efficiently and increase the proposed converter performance and reduce power losses.

For balancing the trade-offs between switching losses and conduction losses to achieve possible maximum efficiency, the interleaved buck converter can operate in BCM. According to Equation (9), the inductance value and battery voltage are used to calculate the maximum and minimum values of f_sw,buck. The maximum and minimum values of f_sw,buck are set as the upper and lower boundary of the switching frequency. If the calculated result is over the boundary, f_sw,buck will be limited at the maximum or minimum value and the modulation will be changed from PFM to PWM. Conversely, the PFM is used continually.

3. Experimental Results

Based on the design conditions described in Section 2, a 1.5 kW experimental prototype incorporating the proposed digital hybrid control was constructed to verify the converter performance. The high side voltage of the converter ranges from 380 to 400 V, and the battery voltage ranges from 40 to 58 V. The switching frequency of the first stage CLLC converter is 130 kHz, while the switching frequency of the second stage interleaved buck converter is between 40 kHz and 110 kHz. The parameters of the proposed converter are listed in

Table 1. The parameters of the proposed converter.

High side voltage Vhigh	380–400 V
Bus voltage Vbus	100 V
Battery voltage Vbat	40–58 V
Rated power Po	1.5 kW
Switching frequency fsw,CLLC	130 kHz
Switching frequency fsw,buck	40~110 kHz
Magnetizing inductor Lm	208 μH
Resonant inductor Lr1	77 μH
Resonant inductor Lr2	5.5 μH
Resonant capacitor Cr1	18.56 nF
Resonant capacitor Cr2	291.3 nF
Transformer turn ratio n:1	4:1
Inductor L1, L2	20 μH

.

Figure 7, Figure 8, Figure 9 and Figure 10 show the experimental waveforms for the proposed converter with output power 150 W (10% of full load) and 1.5 kW (full load) in charging mode. Figure 7 and Figure 8 show that the CLLC converter can achieve ZVS when operating under a light load and full load conditions. Figure 9 and Figure 10 show that the interleaved buck converter can operate at different switching frequencies with different loads. Figure 10 shows the current waveforms of the inductors L₁ and L₂. The two-phase interleaving operation of the proposed converter can be achieved effectively, which significantly reduces output current ripples, thus enhancing system overall performance and stability.

The efficiency curves of the proposed converter are shown in Figure 11. The blue line represents the efficiency of the proposed converter, the orange line shows the efficiency of the first stage CLLC converter, and the green line indicates the efficiency of the second stage interleaved buck converter. Because the proposed converter is a two-stage topology, the efficiency equation of the converter in both modes can be expressed as follows:

$${\eta }_{overall}={\eta }_{CLLC}\ast {\eta }_{buck}$$

(11)

It was found that the proposed interleaved buck converter is more efficient than the traditional converter under light load conditions. This efficiency improvement in both charging and discharging modes enhances the overall performance for the proposed converter. The maximum efficiency of the proposed converter is 90% in charging mode and 94% in discharging mode.

The proposed converter was compared to different converters with similar voltage gain in [3,29,30] and the converter of two-stage topology was compared in [31], as shown in

Table 2. Comparison of proposed converter with different converters.

Condition	Proposed Converter	[3]	[10]	[17]	[29]	[30]	[31]
Rated Power (W)	1500	1000	1000	2000	1000	500	500
Number of Switches	12	8	8	8	6	8	10
Output Current Ripple	low	high	high	high	low	high	high
Implementation Complexity	medium	medium	simple	medium	medium	simple	medium
Peak Efficiency (%)	94	97	97	97	96	97	94

. Although the proposed converter uses more components than the converter in [3,10,29,30,31], the output power of proposed one is higher. Compared with [3,10,17,30], although they have higher efficiency, the higher output current ripple will lead to a reduced lifespan of the ESS.

4. Conclusions

This paper has presented a modified bidirectional isolated DC/DC converter with hybrid control to enhance power conversion efficiency and performance. The proposed converter integrates a CLLC resonant converter in the first stage and an interleaved buck converter in the second stage, resulting in significant efficiency improvements and high operational stability. The hybrid control combining PWM and PFM techniques enhances light load efficiency for the converter by balancing switching and conduction losses. The CLLC converter achieves ZVS under light load and full load conditions, while the interleaved buck converter reduces output current ripples at different switching frequencies and various loads. Efficiency curves show the proposed converter achieved a maximum efficiency of 90% in charging mode and 94% in discharging mode. Even though the proposed converter used more components, the efficiency of the converter in both charging and discharging modes make it ideal for bidirectional power transfer in the applications of energy storage systems and DC microgrids.