Applying a Current Sharing Method Based on Partial Energy Processing to Multiphase LLC Resonant Converters

Abstract

In this paper, partial energy processing is applied to the current sharing technique for multiphase LLC resonant converters. The proposed circuit consists of an LLC resonant converter and a flyback converter, where the flyback converter is only used for partial energy processing. The input voltage of the LLC resonant converter is fine-tuned by the flyback converter to solve the problem of a voltage gain difference between the two phases of the LLC resonant converter caused by the error of the resonant tank components, which prevents the output current from being nonequalized. Since the compensation power is much smaller than the output power, and only one phase will be during circuit operation, the impact on the overall efficiency is minimal. Due to the low dependence between the LLC resonant converter and the flyback converter, they are operated at different switching frequencies. In addition, due to the low dependence between each phase, the circuit can be expanded using odd and even phases.

1. Introduction

The increase in network traffic has raised the importance of data centers to meet and properly manage these growing demands. The data center is one of the most energy-intensive building types, consuming 10 to 50 times more energy per floor of space than a typical commercial office building, and these values are growing every year. As shown in Figure 1, where VRM is the abbreviation for the voltage-regulated module, in a traditional structure, major processor/memory devices are powered by 12 V, and the uninterruptible power system (UPS) is placed on the high voltage side. As shown in Figure 2, compared with the traditional 12 V structure, the 48 V structure can reduce the copper loss and bus loss by 16 times. In addition, the UPS can be placed on the low-voltage side, so it has the advantages of high efficiency, low cost, and small size [1,2]. The 48 V structure complies with the international electrotechnical commission (IEC) 60335-1 safety extra low voltage (SELV) standard [3]. Because of these advantages, Google has started using the 48 V structure in its data centers [4], and this structure has been widely used in LED panels, power tools, automobiles, and telecommunication systems [5].

Distributed power systems (DPSs), widely used in data centers and telecommunication systems, have the advantages of thermal management, reliability, maintainability, high flexibility, and high efficiency [6]. Therefore, LLC resonant converters are widely used as front-end isolation converters in DPS systems. The DC transformer (DCX) has many advantages. For example, the switches of the half-bridge LLC resonant converter switch near the resonant frequency with a duty cycle close to 50%. There is no voltage control loop, so the best efficiency can be obtained. At the same time, the zero-voltage switching (ZVS) turn-on for the primary side switches and the zero-current switching (ZCS) turn-off for the secondary side diodes function over all the load ranges. Due to the discontinuous output current of an LLC resonant converter, it is necessary to parallel multiple capacitors to suppress excessive ripple and heat generation, especially in high output current applications.

Multiphase power converters distribute the load current to each phase, thus effectively minimizing current ripple and spreading component losses and thermal stress [7]. Compared with the traditional single power converter, parallel power supplies can realize high efficiency in high power applications. However, in practice, due to a difference in the resonant tank components of each phase, the impedance of the resonant tanks varies from phase to phase, resulting in the current supplied by each phase being inconsistent. Therefore, how to balance the currents between the phases of an LLC resonant converter is an important issue in today’s research [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. As shown in Figure 3, the general current sharing strategies for multiphase resonant converters can be classified into the circuit topology method [8,9,10,11,12,13,14,15,16,17], the switch regulation method [19,20,21,22,23,24,25], and the auxiliary circuit method [25,26,27,28,29,30,31].

The circuit topology method belongs to the passive current sharing method and is mainly used to change the connection of the circuit or to insert additional passive components into the circuit, so as to achieve the purpose of equalizing the current of each phase without additional control. The advantage of this method is that it does not need to additional complex control; however, when one of the converters is damaged, it will not work properly. The literature [8] proposes a way to parallelize the resonant capacitors of the two phases so that the resonant capacitors of the two phases of the LLC resonant converter can be regarded as the same one in the equivalent circuit; hence, the current sharing can be achieved. Based on a similar concept, the literature [9] proposes a way to parallelize the resonant inductors of the two phases so that the resonant inductors of the two phases of the LLC resonant converter can be considered as the same one in the equivalent circuit. Thus, the current sharing can be realized, but it is not applicable to the circuit in which the leakage inductance of the main transformer is used as the resonant inductor. The two-phase LLC resonant converter of the literature [10] uses the same resonant inductor and half-bridge circuit, so the circuit size can be effectively reduced. However, when the leakage inductances of the main transformers of the two-phase LLC resonant converter are different, the current sharing performance will be influenced. The literature [11] proposes a secondary winding integration method to achieve output current sharing by connecting the secondary windings of the two-phase LLC resonant converter in series. The literature [12] proposes a primary side resonant tank integration method to achieve equalization of the secondary current by connecting the resonant tanks in series. The literature [13] proposes a common-mode transformer added to the resonant tank between two phases of the LLC resonant converter to utilize the characteristics of the transformer for current sharing. The literature [14] presents a current sharing method using the ampere-second balance of a capacitor. Due to the characteristics of the capacitor, this circuit can only be applied to two phases of the LLC resonant converter, but it is not possible to expand the phase count. The above-mentioned technique realizes current sharing by means of the circuit topology or the passive element, so there is no need for additional switch control; thus, it has the advantage of simple control. However, due to the limitation of the connection between the passive element and the circuit, the main switch of each phase circuit has to be switched synchronously. Therefore, the studies in the literature [8,9,10,11,12,13,14] do not have the advantage of reducing the current ripple. Compared with the above-mentioned circuits, although the passive current sharing method is also adopted in the literature [15,16,17], the main switch of each phase circuit does not need to be switched synchronously, so it has the function of reducing the output ripple. The literature [15] proposes a method to balance the current based on the output filter. The literature [16] adopts common-mode chokes to achieve current sharing in a three-phase LLC resonant converter. The literature [17] uses the input capacitors connected in series to automatically adjust the input capacitor voltages of the two phases when there is an error in the resonant tank element to realize the purpose of balancing the currents in a two-phase LLC resonant converter.

Compared to the passive current sharing method mentioned above, the switch regulation method and the auxiliary circuit method are active current sharing methods. For the switch regulation method to be considered, it needs to realize the purpose of current balance by modulating the switching frequency or duty cycle of the switch, which has relative advantages in design and cost since it does not require the use of an additional auxiliary circuit. The literature [18] presents an LLC resonant converter to adjust the voltage gain by varying the switching frequency to achieve current sharing. Although this is easier to realize, it will produce a larger output current ripple. The literature [19] proposes a phase shift control strategy to adjust the phase difference between the input voltages of the resonant tanks to realize current sharing, but the design needs to consider the phase of the resonant current so as to avoid loss of the ZVS feature. The literature [20] presents a way to control the width of the duty cycle to realize current balancing. The literature [21,22,23,24] presents a way to replace the secondary side rectifier diode with an active switch or to use an additional active switch and then to adjust the on-time of the switch to change the equivalent resistance mapped back to the primary side to achieve the purpose of current equalization.

In contrast to the switch regulation method, the auxiliary circuit method utilizes an applied circuit for current balancing. The literature [25,26] presents a variable capacitor composed of an active switch and a capacitor to achieve current equalization by adjusting the on-time of the active switch and changing the capacitance of the resonant capacitor to compensate for the difference in impedance of the resonant tanks between phases. The literature [27] proposes a variable inductor by applying the phenomenon that the relative permeability of ferromagnetic materials decreases with the increase of magnetic field strength. Due to the presence of an auxiliary winding and a controllable current source, the Inductance is changed by controlling the auxiliary winding current to establish the corresponding bias magnetic field strength during circuit operation; however, the additional iron losses increase the losses. The literature [28] presents a method of adding a pre or post converter to each phase of the LLC resonant converter and then adjusting the voltage gain of each phase through the pre or post converter to achieve current equalization; however, this method needs to be considered in terms of cost and efficiency. In order to solve the problem of efficiency degradation caused by the two-stage structure, the literature [29,30,31] propose a low-power circuit with partial power processing. In [29], an isolated low-power auxiliary DC-DC converter is added to the resonant tank of each phase of the LLC resonant converter, and the purpose of equalizing the current is realized by adjusting the duty cycle of the switch of the DC-DC converter. Similar to [29], the auxiliary circuit in [30] is a phase shift full bridge (PSFB) circuit where the transformer of the auxiliary circuit is integrated with the main transformer of the LLC resonant converter. The auxiliary circuit in [31] utilizes a buck-type converter, but it has the disadvantage that the primary and secondary sides are not isolated. Since the phase current balancing is achieved by the auxiliary circuit, the auxiliary and main circuits can usually be operated independently of each other, which provides a simpler control strategy as compared to the switch regulation method. The current sharing approach based on partial energy processing offers several advantages in such scenarios by managing the nonlinear characteristics of inductors [32,33,34], ensuring stable and precise current control, and reducing the electromagnetic interference (EMI). In addition, a three-phase LCL filter is designed for grid-connected PWM inverters using hybrid bacteria foraging and particle swarm optimization [35].

Based on that mentioned above, this paper presents the partial energy applied to the current equalization of the two-phase LLC resonant converter, which is realized by fine-tuning of the input voltage of the resonant tank through the flyback converter to change each phase voltage gain so that each phase impedance can be as identical as possible so as to achieve current equalization between the two phases. The limitations of this circuit are relatively high cost and relatively complex control method. However, the proposed circuit is suitable for driving LED strings. In addition, the proposed methodology is different from those reported in the literature [11,14,22,29,30]. Consequently, the following are the advantages and objectives of the proposed circuit:

(1)

Dependent voltage source circuits provide only part of the input voltage in steady state, so the power required is very low;

(2)

Dependent voltage source circuits have quite low dependence on the main circuits and can be operated and regulated independently of each other;

(3)

The two-phase main circuits can reduce output current ripple due to interleave operation;

(4)

As the output power required by the load has to be increased, the overall power can be increased by increasing the number of phases.

2. Main Power Stage

Figure 4 shows the structure of the single-phase circuit proposed in this paper, which consists of an LLC resonant converter combined with a flyback converter. In addition, the multiphase system can be expanded by this circuit, and each phase can operate independently of each other with the same mode of operation. Figure 5 displays the two-phase LLC resonant converter with partial energy processing proposed in this paper. The first phase consists of four switches S₁, S₂, S₃, and S₄; a resonant inductor L_r1; a resonant capacitor C_r1; an output capacitor C_o1; and a transformer T_r1, which consists of a magnetizing inductor L_m1 combined with an ideal transformer. The primary and secondary coils of the transformer are denoted by N_p1 and N_s1, respectively. The corresponding flyback converter is composed of a switch S₅, a diode D₁, an output capacitor C_o2, and a transformer T_r2, which consists of a magnetizing inductor L_m2 combined with an ideal transformer. The primary and secondary coils of the transformer are signified by N_p2 and by N_s2, respectively. The second phase consists of four switches S₆, S₇, S₈, and S₉; a resonant inductor L_r2; a resonant capacitor C_r2; an output capacitor C_o3; and a transformer T_r3, which is composed of a magnetizing inductor L_m3 combined with an ideal transformer. The primary and secondary coils of the transformer are denoted by N_p3 and N_s3, respectively. The corresponding flyback converter contains a switch S₁₀, a diode D₂, an output capacitor C_o4, and a transformer T_r4, which is composed of a magnetizing inductor L_m4 combined with an ideal transformer. The primary and secondary coils of the transformer are signified by N_p4 and N_s4, respectively. Also, the input voltage is V_dc, the output voltage is V_o, and the dependent voltages V_ctrl1 and V_ctrl2 come from the individual flyback converters. Moreover, in Figure 4 and Figure 5, the symbols of voltages and currents correspond to the individual components.

3. Current Sharing Technique Analysis of the Proposed Circuit

In this section, partial energy processing is applied to current sharing for the multiphase LLC resonant converter, where the input voltage to the resonant tank is fine-tuned by the flyback converter to compensate for the difference in voltage gain due to component tolerance of the multiphase LLC resonant converter. Accordingly, how the flyback converter works with the LLC multiphase resonant converter to realize current sharing is described in detail herein.

3.1. LLC Voltage Gain

The voltage gain of the LLC resonant converter is analyzed in this section. The half-bridge LLC resonant converter is designed to switch the two switches at a high frequency to change the impedance of the resonant tank so as to transfer the energy to the rear stage. At the same time, it adopts a constant frequency and drives the two switches with complementary driving signals having a duty cycle of about 50%. In addition, the quality factor Q of the circuit, the ratio K of the magnetizing inductance L_m1 to the resonance inductance L_r1, the resonant radian frequency ω_r1, and the switching radian frequency ω_s1 need to be considered. Since the voltage across the switch S₂, called v_ds2, is located between zero and the input voltage V_dc, this square wave voltage is analyzed using the first harmonic approximation (FHA) method. Specifically, only the fundamental wave component is considered, which is denoted by v_in. Afterwards, the voltage gain of the LLC resonant converter will be analyzed. Figure 6 shows the equivalent circuit containing the resonant inductor L_r1, the resonant capacitor C_r1, the magnetizing inductance L_m1, and the equivalent resistance R_ac, which is reflected from the load resistance R_o on the secondary side to the primary side, where the turns ratio n₁ is equal to N_p1 divided by N_s1, namely, n₁ = N_p1/N_s1. Therefore, R_ac can be expressed as follows:

$$R_{ac}={n_1}^2\times {\displaystyle \frac{8}{{\pi }^2}}\times {\displaystyle \frac{V_o}{I_{o1}}}$$

(1)

where I_o1 is the output current.

$$Q={\displaystyle \frac{Z_{r1}}{R_{ac}}}={\displaystyle \frac{\sqrt{\frac{L_{r1}}{C_{r1}}}}{R_{ac}}}={\displaystyle \frac{{\omega }_{r1}\times L_{r1}}{R_{ac}}}$$

(2)

$$K={\displaystyle \frac{L_{m1}}{L_{r1}}}$$

(3)

Eventually, the voltage gain M_LLC1(s) is derived from the equivalent circuit in Figure 7 and is expressed as follows:

$$\begin{array}{l}{M}_{LLC1}(s)={\displaystyle \frac{n_1{V}_o\left(s\right)}{0.5V_{dc}\left(s\right)}}={\displaystyle \frac{s{L}_{m1}//R_{ac}}{s{L}_{r1}+\frac{1}{s{C}_{r1}}+\left(s{L}_{m1}//R_{ac}\right)}}\\ ={\displaystyle \frac{s^2\times \frac{L_{m1}}{L_{r1}}\times {\left(\frac{1}{{\omega }_{r1}}\right)}^2}{s^3\times \frac{L_{m1}}{L_{r1}}\times \frac{L_{r1}{\omega }_{r1}}{R_{ac}}\times {\left(\frac{1}{{\omega }_{r1}}\right)}^3+s^2\times {\left(\frac{1}{{\omega }_{r1}}\right)}^2\times \left(1+\frac{L_{m1}}{L_{r1}}\right)+\frac{s}{{\omega }_{r1}}\times \frac{{\omega }_{r1}{L}_{r1}}{R_{ac}}\times \frac{L_{m1}}{L_{r1}}+1}}\end{array}$$

(4)

Equation (4) can be simplified as follows:

$$M_{LLC1}(s)={\displaystyle \frac{{\left(\frac{s}{{\omega }_{r1}}\right)}^2\times K}{{\left(\frac{s}{{\omega }_{r1}}\right)}^3\times K\times Q+{\left(\frac{s}{{\omega }_{r1}}\right)}^2\times \left(1+K\right)+\frac{s}{{\omega }_{r1}}\times Q\times K+1}}$$

(5)

Let s = jω_s1 = j2πf_s1 and ω_r1 = 2πf_r1. By substituting these expressions into (5), the corresponding magnitude M_LLC1 can be obtained as follows:

$$M_{LLC1}={\displaystyle \frac{n_1{V}_o}{0.5V_{dc}}}=\left|M_{LLC1}(j2\pi f_{s1})\right|={\displaystyle \frac{K\times {\left(\frac{f_{s1}}{f_{r1}}\right)}^2}{\sqrt{{\left[\left(K+1\right)\times {\left(\frac{f_{s1}}{f_{r1}}\right)}^2-1\right]}^2+{\left\{\left[{\left(\frac{f_{s1}}{f_{r1}}\right)}^3-1\right]\times \frac{f_{s1}}{f_{r1}}\times Q\times K\right\}}^2}}}$$

(6)

From (6), it can be seen that the voltage gain M_LLC1 is affected by the parameters of Q and K.

Assume that the resonant inductance L_r2 and the magnetizing inductance L_m3 of the second phase are 1.2 times that of the resonant inductance L_r1 and the magnetizing inductance L_m1 of the first phase, and the capacitances of the resonant capacitors C_r1 and C_r2 of the two phases are the same. The parameters of the two phases are brought into (6), and then the two voltage gain curves can be plotted, namely M_LLC1 and M_LLC2, as shown in Figure 8. As can be seen from this figure, the voltage gains are different at the same operating frequency due to errors in the passive component values in the resonant tanks, and this makes the output current provided by the two phases inconsistent.

3.2. Voltage Gain of the Proposed Circuit

In order to solve the problem that the output currents cannot be equalized due to the difference in impedance of the resonance tanks, a method of connecting a dependent voltage source in series with the input voltage is proposed, so that the voltage gain can be compensated by adjusting the voltage of the dependent voltage source. In addition, the voltage of the dependent voltage source in steady state is much smaller than the input voltage, so it is only necessary to use an isolated low-power DC converter to realize voltage gain compensation.

From Figure 4, the equivalent circuit of Figure 9 can be derived, and the difference between Figure 9 and Figure 6 is that the operating voltage of the resonant tank is composed of the dependent voltage V_ctrl1 in series with the input voltage V_dc, where the dependent voltage V_ctrl1 comes from the voltage-dependent source, named the flyback converter, as shown in Figure 10.

The voltage gain of the proposed circuit can be rewritten from (6) as follows:

$$0.5\left(V_{dc}+V_{ctrl1}\right)\times M_{LLC1}=n_1{V}_o$$

(7)

Also, the voltage gain of the flyback converter is expressed as follows:

$$M_{flyback}={\displaystyle \frac{V_{ctrl1}}{V_o}}={\displaystyle \frac{D}{n_2\left(1-D\right)}}$$

(8)

where D is the duty cycle.

By substituting (8) into (7), the voltage gain M₁(D) can be expressed as a function of the duty cycle D as below:

$$M_1\left(D\right)={\displaystyle \frac{V_o}{V_{dc}}}={\displaystyle \frac{0.5M_{LLC1}}{n_1-0.5n_2\times \frac{D}{1-D}}}$$

(9)

The resonant inductance L_r2 and magnetizing inductance L_m3 of the second phase are 1.2 times of the resonant inductance L_r1 and magnetizing inductance L_m1 of the first phase, respectively, and the capacitance of the resonant capacitors C_r1 and C_r2 of the two phases are the same. By substituting the required parameter values of the two phases into (9), the two voltage gain curves M₁ and M₂ can be drawn, where the horizontal axis is the duty cycle D for the flyback converter, as shown in Figure 11. As can be seen from this figure, under the same operating frequency, when the switches of both of the flyback converters are turned off (D₁ = D₂ = 0), the voltage gain of the phase 1 circuit (M₁(0) = 0.1187) will be larger than that of the phase 2 circuit (M₂(0) = 0.1176). This is due to the errors of the passive elements of the two resonant tanks, making the two phases not provide the same output current. Accordingly, the switch of the phase 1 circuit’s flyback converter (D₁ = 0) is turned off, and the switch of the phase 2 circuit’s flyback converter is regulated (D₂ = 0.255) to make the voltage gains of the two phases as close to the same as possible, so as to compensate for the failure of equalizing the output currents.

3.3. Extension of the Phase Account

As shown in Figure 12, the proposed circuit can upgrade the overall power by increasing the phase account. Its operating principle and component design will not be redesigned, so it is quite convenient in practical applications.

4. Design Considerations

4.1. Parameter Design

The system circuit consists of an LLC resonant converter as well as a flyback converter, so that the power is expressed as follows:

$$P_T=P_o+P_{Flyback}$$

(10)

The total output power P_T is the output power P_o plus the consumption power P_Flyback of the flyback converter. As shown in

Table 1. Specifications of the single-phase LLC resonant converter.

Specification	Value
Rated input voltage (Vdc)	400 V
Rated output voltage (Vo)	48 V
Rated output current (Io1,rated)	21 A
Switching frequency (fs1)	110 kHz
Resonant frequency (fr1)	120 kHz
Ratio of magnetizing inductance to resonant inductance (K)	20
Quality factor (Q)	0.2

and

Table 2. Specifications of the flyback converter.

Specification	Value
Rated input voltage (Vo)	48 V
Maximum dependent voltage (Vctrl,max)	10 V
Output maximum current (Iin1,max)	2.7 A
Output minimum current (Iin1,min)	1 A
Switching frequency (fs2)	100 kHz

, P_Flyback is much smaller than P_o, so the effect of the flyback converter on the voltage gain of the LLC resonant converter can be ignored. Since the designs of two-phase LLC components are the same, the following is assumed: two LLC transformers T_r1 = T_r3 = T_r,LLC, two flyback transformers T_r2 = T_r4 = T_r,Flyback, two LLC turns ratios n₁ = n₃ = n_LLC, two flyback turns ratios n₂ = n₄ = n_Flyback, two LLC magnetizing inductances L_m1 = L_m3 = L_m,LLC, two flyback magnetizing inductances L_m2 = L_m4 = L_m,Flyback, two LLC resonant inductors L_r1 = L_r2 = L_r, two LLC primary side windings N_p1,LLC1 = N_p2,LLC2 = N_p,LLC, two LLC secondary side windings N_s1,LLC1 = N_s2,LLC2 = N_s,LLC, two LLC resonant capacitors C_r1 = C_r2 = C_r, two LLC output capacitors C_o1 = C_o3 = C_o,LLC, two flyback output capacitors C_o2 = C_o4 = C_o,Flyback, and two flyback currents i_ds5 = i_ds10 = i_ds,Flyback. In order to obtain the error in the two-phase resonant inductances, this can be achieved by adjusting the air gap of the iron core.

4.1.1. Design of the Resonant Tank Parameter

The switching frequency of the two-phase LLC resonant converter is initially set at 110 kHz. In order to make the two-phase resonant inductances different from each other, namely, L_r2 = 1.2L_r1, the resonance frequency of the first-phase circuit is about 120 kHz, and the resonance frequency of the second-phase circuit is about 110 kHz, as shown in Table 1.

Selection of Turns Ratio n_LLC of T_r,LLC

In this paper, the switching frequency of the LLC resonant converter is close to the first resonant frequency, so the voltage gain M_LLC is approximated to be 1, which can be expressed as follows:

$$M_{LLC}=2\times {\displaystyle \frac{n_{LLC}{V}_o}{V_{dc}}}$$

(11)

By rearranging (11), the turns ratio n_LLC (=N_p,LLC/N_s,LLC) is shown below:

$$n_{LLC}=M_{LLC}\times {\displaystyle \frac{1}{2}}\times {\displaystyle \frac{V_{dc}}{V_o}}=1\times {\displaystyle \frac{1}{2}}\times {\displaystyle \frac{400}{48}}=4.17$$

(12)

Based on the calculation in (12), the turns ratio of n_LLC is selected to be 4.25.

Determination of Output Equivalent Resistance R_ac

The output load resistance R_o at rated load is shown below:

$$R_o={\displaystyle \frac{V_o}{I_{o1,rated}}}={\displaystyle \frac{48}{21}}=2.286 \mathsf{\Omega }$$

(13)

where I_o1,rated is the rated output current.

Since the voltage gain will be affected by the load, the output resistance R_o should be equivalent to the primary side of the transformer T_r,LLC to facilitate the design and analysis of parameters of the resonant tank. By substituting the result of (13) into (1), the output equivalent resistance R_ac is given as follows:

$$R_{ac}=n_{LLC}^2\times {\displaystyle \frac{8}{{\pi }^2}}\times R_o={4.25}^2\times {\displaystyle \frac{8}{{\pi }^2}}\times 2.286=33.465 \mathsf{\Omega }$$

(14)

Determination of the Values of K and Q

From (2), when the load and switching frequency are fixed, the smaller the value of L_r is, the smaller the value of Q, and the smaller the value of L_r is, the smaller the parasitic resistance of the winding is. Thus, the value of Q is set at 0.2. In addition, with a fixed value of L_r, the larger the value of K is, the smaller the effect of load on voltage gain, and the circulating current generated by L_m,LLC will be reduced to improve the efficiency. However, if the value of K is too large, the primary side half-bridge switches will not be able to achieve ZVS turn-on. Consequently, based on the simulation software PSIM 9.11, the ZVS condition can be satisfied by setting the value of K at 20.

Determination of the Values of L_r, C_r and L_m,LLC

Since the value of Q is 0.2, and the resonance frequency f_r is 120 kHz, the resonant capacitance C_r is calculated as 198.161 nF, as shown in (15):

$$\begin{array}{l}Q=\sqrt{{\displaystyle \frac{L_r}{C_r}}}\times {\displaystyle \frac{1}{R_{ac}}}={\displaystyle \frac{1}{2\pi \times f_r\times R_{ac}\times C_r}}\\ \Rightarrow C_r={\displaystyle \frac{1}{2\pi \times Q\times f_r\times R_{ac}}}\\ \Rightarrow C_r={\displaystyle \frac{1}{2\pi \times 0.2\times 120\times {10}^3\times 33.465}}=198.161\mathrm{nF}\end{array}$$

(15)

Therefore, the selected resonant capacitance C_r is 220 nF, and the resonant inductance L_r can be determined using the resonant capacitance C_r and the resonant frequency f_r.

$$\begin{array}{l}{f}_r={\displaystyle \frac{1}{2\pi \sqrt{L_r\times C_r}}}\\ \Rightarrow L_r={\displaystyle \frac{1}{{\left(2\pi \times f_r\right)}^2\times C_r}}\\ \Rightarrow L_r={\displaystyle \frac{1}{{\left(2\pi \times 120\times {10}^3\right)}^2\times 220\times {10}^{-9}}}=7.996 \mathsf{\mu }\mathrm{H}\end{array}$$

(16)

Based on (16), the required magnetizing inductance L_m,LLC can be obtained as follows:

$$L_{m,LLC}=K\times L_r=20\times 7.996\times {10}^{-6}=159.913 \mathsf{\mu }\mathrm{H}$$

(17)

4.1.2. Design of Flyback Converter Parameter

The magnetizing inductance of the flyback converter will be figured out as below.

Selection of Turns Ratio n_Flyback of T_r,Flyback

According to [36], D_max is set at 0.45, and the turns ratio n_Flyback (=N_p,Flyback/N_s,Flyback) is expressed as follows:

$$n_{Flyback}={\displaystyle \frac{V_o\times D_{max}}{V_{ctrl,max}\times \left(1-D_{max}\right)}}={\displaystyle \frac{48\times 0.45}{10\times \left(1-0.45\right)}}=3.927$$

(18)

Based on (18), the turns ratio of n_Flyback is chosen as 3.667.

Determination of the Value of L_m,Flyback

In order to ensure that the flyback converter can operate in the continuous conduction mode (CCM) when the output current I_in1 is above the minimum current of 1 A, Equation (19) is obtained as follows:

$$L_{m,Flyback,BCM}={\displaystyle \frac{{\left(V_o\times D_{max}\right)}^2}{2I_{in1,min}\times V_{ctrl1}\times f_{s2}}}={\displaystyle \frac{{\left(48\times 0.45\right)}^2}{2\times 1\times 10\times 100\times {10}^3}}=233.28 \mathsf{\mu }\mathrm{H}$$

(19)

where L_{m,Flyback,BCM} means the magnetizing inductance L_m,Flyback for the flyback converter operating in the boundary conduction mode (BCM). L_m,Flyback should satisfy the condition of L_m,Flyback > L_{m,Flyback,BCM}.

5. System Control Strategy

Figure 13 shows the main program flow chart, which consists of two analog-to-digital converters (ADCs) for sampling and data calculation, a proportional-integral (PI) module with 12-bit ADCs, and a pulse-width modulation (PWM) module with a 16-bit PWM. It is noted that the system functions required will be accomplished within one PWM cycle. Afterwards, the associated signals will be sent to the PI module and then to the PWM module to generate suitable control forces to drive the switches.

5.1. ADC Sampling Triggering and Data Calculation

Figure 14 shows the program flowchart of ADC sampling triggering and data calculation. As PWM1 triggers sampling and calculation of ADC1 and ADC2, the former is responsible for the phase 1 output current, whereas the latter is responsible for the phase 2 output current. After this, the resulting digital current signal I_o2 is subtracted from the resulting digital current signal I_o1, namely, I_o1 − I_o2, to obtain an error signal, called Error, which will be sent to the PI module.

5.2. PI Module

Figure 15 shows the PI module. Multiplying the signal Error by the coefficient k_p obtains the proportional control force P, and multiplying the signal Error by the coefficient k_i as well as adding this value with the previous integral control force yields the integral control force I. Finally, the control force CF is obtained by summing P and I. When I_o1 < I_o2, the control force CF will be less than zero, this value is multiplied by −1 to obtain the signal Flyback1_Duty, and the first phase flyback converter will operate. When I_o1 > I_o2, the control force CF will be greater than zero, the signal Flyback2_Duty is equal to CF, and the second phase flyback converter will operate. After this, a duty limiter is used to limit the maximum duty cycle to 0.45, proceeding to the PWM module. The values of k_p and k_i are 0.1 and 0.01, respectively.

5.3. PWM Module

In the PWM module, the PWM control will be realized by setting PWM-related registers, which include frequency, duty cycle, phase, blanking time, complementary signal, etc. Therefore, the value of the control force CF is directly fed into the duty cycle-related registers. The half-bridge gate driving signal of the first phase, called v_gs1, is generated by PWM1, whereas the half-bridge gate driving signal of the second phase 2, called v_gs6, is generated by PWM2. The frequencies of PWM1 and PWM2 are set at 110 kHz, the duty cycle is set to 45% with the prescribed blanking time of 200 ns, and the phase difference between v_gs1 and v_gs6 is set to 90°. The gate driving signal of phase 1’s flyback converter, called v_gs5, is created by PWM3, whereas the gate driving signal of phase 2’s flyback converter, called v_gs10, is created by PWM4. The frequencies of PWM3 and PWM4 are set at 100 kHz.

As shown in Figure 16, the flyback converters of the two phases will not operate simultaneously. Only the phase with insufficient voltage gain will operate, causing the efficiency to be improved to some extent.

6. Experimental Results

Experimental results contain measured waveforms and measured data, which are used to validate the effectiveness of the proposed circuit.

6.1. Measured Waveforms

The following associated experimental waveforms at rated load are shown from Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25, Figure 26, Figure 27, Figure 28 and Figure 29.

As can be seen in Figure 17, when the switches S₁ and S₂ are turned off, the voltages across them are equal to the input voltage V_in.

As can be seen in Figure 18, Figure 19, Figure 20 and Figure 21, the duty cycle of the gate driving signal v_gs1 for the switch S₁ and the gate driving signal v_gs2 for the switch S₂ are about 45%, and they are complementary signals. The duty cycle of the gate driving signal v_gs6 of the switch S₆ and the gate driving signal v_gs7 of the switch S₇ are about 45%, and they are also complementary signals. In addition, the phase difference between v_gs1 and v_gs6 is 90°. Therefore, the phase difference between the phase 1 resonant inductor current i_Lr1 and the phase 2 resonant inductor current i_Lr2 is 90°. According to [34], it can be known that the gate driving signals of v_gs3, v_gs4, v_gs8, and v_gs9 will be reduced from 10.9 V to 5 V in order to speed up the switching turn-off time.

In Figure 22, the output currents of both phases can be equalized. In Figure 23, before the switch S₁ is turned on, the voltage across S₁ drops to zero, so S₁ is turned on with ZVS. In Figure 24, before the switch S₂ is turned on, the voltage across S₂ drops to zero, so S₂ is turned on with ZVS. In Figure 25, before the switch S₆ is turned on, the voltage across S₆ drops to zero, so S₆ is turned on with ZVS. In Figure 26, before the switch S₇ is turned on, the voltage across S₇ drops to zero, so S₇ is turned on with ZVS.

As shown in Figure 27, when the switch S₅ is turned off, the voltage across S₅ is equal to the input voltage V_in plus the secondary side voltage reflected to the primary side voltage, called n_flybackV_ctrl1. When the switch S₁₀ is turned off, the voltage across S₁₀ is equal to the input voltage V_in plus the secondary side voltage reflected to the primary side voltage, called n_flybackV_ctrl2.

From Figure 28, it can be seen that the switch S₅ is turned off, so the current i_ds5 is equal to zero. However, when the switch S₁₀ is turned on, the current i_ds10 is not zero, implying that phase 2’s flyback converter is operated in CCM. That is, the two flyback converters do not need to be operated simultaneously. From Figure 29, the negative part of V_ctrl1 is due to the forward-biased voltage of the diode, and V_ctrl2 is the compensation voltage.

6.2. Measured Data

For efficiency measurement to be considered, one current-sensing resistor is connected in series with the input current path and the other output current-sensing resistor is connected in series with the output current path. Then, the voltage across the current-sensing resistor is measured with a digital meter to obtain the input and output currents, and the input and output voltages are also measured with a digital meter, so as to obtain the input and output power. Finally, the resulting input and output powers are used to calculate the overall efficiency. In addition, the absolute value of the percentage error of the two-phase output currents, called ΔI_o, can be defined as follows:

$$\Delta I_o=\left|{\displaystyle \frac{I_{o1}-I_{o2}}{I_{o1}+I_{o2}}}\right|\times 100\%$$

(20)

where I_o1 is the output current of the first phase, and I_o2 is the output current of the second phase.

From Figure 30, it can be seen that the efficiency of the two-phase circuit proposed in this paper can be maintained above 96.24% at 10% of the rated power, and the maximum efficiency can reach 98.26%. The maximum efficiency of the single-phase circuit proposed in this paper can reach 98.27%. That is to say, in order to improve the efficiency of the two-phase circuit at the light load, the system can be operated in single-phase circuit by shutting down one of the two phases of the circuit to improve the efficiency at light load. As shown in Figure 31, the light-load efficiency of the two-phase circuit with current sharing control is lower than that without current sharing control because of the increase in the loss caused by the compensation voltage. As shown in Figure 32 and Figure 33, without current sharing control, the output current error percentage is higher than 45% at 10% of the rated power, while with current sharing control, the output current error percentage can be maintained within 3% all over the load range.

6.3. Experimental Setup

Figure 34 shows the photo prototype.

7. Literature Comparison

As shown in

Table 3. Comparison of the proposed current equalization strategy with the related literature.

	Reference	[11]	[14]	[23]	[30]	[31]	Proposed
Item
Phase Shift Capability		No	No	Yes	Yes	Yes	Yes
Phase Expansion Capability		No	No	Yes	Yes	Yes	Yes
Additional Auxiliary Circuit		No	No	No	Yes	Yes	Yes
Additional Passive Component		No	Yes	No	No	No	No
Peak Efficiency		97.5%	97.3%	None	96.8%	97.1%	98.26%
Current Sharing Error Percentage (at rated load)		0.5%	0.55%	None	4.8%	1%	1.27%

, literature comparison contains seven items: (i) phase shift capability; (ii) phase expansion capability; (iii) additional auxiliary circuit; (iv) additional passive component; (iv) peak efficiency; and (v) current sharing error percentage at rated load.

The circuit in [11] has an output power of 960 W at rated load. The input voltage is 340 V to 400 V, and the output voltage is 48 V. The circuit in [14] has an output power of 600 W at rated load, an input voltage of 400 V, and an output voltage of 12 V. The circuit in [23] has an output power of 1 kW at rated load, an input voltage of 390 V to 410 V, and an output voltage of 54 V. The circuit in [30] has an output power of 1.5 kW at rated load, an input voltage of 350 V to 370 V, and an output voltage of 40 V. The circuit in [31] has an output power of 200 W at rated load, an input voltage of 48 V to 60 V and an output voltage of 5 V. The proposed circuit has an output power of 2 kW at rated load, an input voltage of 400 V, and an output voltage of 48 V.

Table 3 shows that the two-phase circuits in [11,14] must work simultaneously and cannot operate under interleave control, resulting in an inability to minimize the output current ripple. This makes it impossible to improve the efficiency of the system by shutting down one phase of the circuit during light load operation. In [30,31], the current equalization control is carried out by additional auxiliary circuits. The literature [11] achieves current equalization by changing the secondary winding connection, so there is no need for any additional auxiliary circuit and passive component. The literature [14] achieves current equalization by inserting an additional capacitor to the two-phase circuit and using the ampere-second balance of the capacitor. The literature [23] achieves current equalization by controlling the secondary rectifier switch, so there is no need to use any additional auxiliary circuit and passive component to the circuit. Compared to [11,14,23,30,31], the proposed circuit has a relatively high peak efficiency of 98.26%.

8. Discussion

In the following, there are two items to be discussed:

• In this paper, LLC converter has been designed based on the constant duty cycle and switching frequency near the resonant frequency to obtain better efficiency. At the same time, the value of the K factor is designed to be relatively large to achieve better efficiency, thereby making the voltage gain hard to control.
• The auxiliary flyback converters are designed only to compensate for the resonant tank component deviation between different phases. If the voltage gain needs to be compensated, the relatively high powers coming from these auxiliary circuits should be afforded.

9. Conclusions

In this paper, a flyback converter is added to an LLC resonant converter, and the input voltage of the LLC resonant converter can be adjusted by controlling the flyback converter in order to balance the output currents of the two phases. Above all, since the required power of the flyback converter is very small compared to the output power and only one phase operates at the same time, the flyback converter has very little effect on the overall efficiency. Since the LLC resonant converter is operated at constant frequency and close to the first resonant frequency, high efficiency can be achieved during circuit operation. Furthermore, the low dependency between the two phases makes it possible to expand the circuit according to the output power required. Without equalization control, the error of the output current of the two phases is more than 45% at 30% of the rated power. However, by adding the proposed equalization control strategy, the output current error between the two phases can be reduced to less than 1% at 30% of rated power, and the efficiency is higher than 97.5% or above at 30% of rated power, with a peak efficiency of 98.26%.

Regarding future work, the following are the potential challenges:

• How to apply this proposed methodology to the series, parallel, and series-parallel resonant converters.
• How to reduce magnetic component by integrating the magnetic component of the LLC converter and that of the flyback converter so as to increase the power density.