A Novel Hybrid Control Strategy and Dynamic Performance Enhancement of a 3.3 kW GaN–HEMT-Based iL²C Resonant Full-Bridge DC–DC Power Converter Methodology for Electric Vehicle Charging Systems

Abstract

The conventional resonant inductor–inductor–capacitor (L²C) DC–DC converters have the major drawbacks of poor regulation, improper current sharing, load current ripples, conduction losses, and limiting the power levels to operate at higher loads for electric vehicle (EV) charging systems. To address the issues of the L²C converter, this paper proposes an interleaved inductor–inductor–capacitor (iL²C) full-bridge (FB) DC–DC converter as an EV charger with wide input voltage conditions. It comprises two L²C converters operating in parallel on the primary side with 8-GaN switches and maintains the single rectifier circuit on the secondary side as common. Further, it introduces the hybrid control strategy called variable frequency + phase shift modulation (VFPSM) technique for iL²C with a constant voltage charging mode operation. The design requirements, modeling, dynamic responses, and operation of an iL²C converter with a controller are discussed. The analysis of the proposed concept designed and simulated with an input voltage of 400 V_in at a load voltage of 48 V₀ presented at different load conditions, i.e., full load (3.3 kW), half load (1.65 kW), and light load (330 W). The dynamic performances of the converter during line and load regulations are presented at assorted input voltages. In addition, to analyze the controller and converter performance, the concept was validated experimentally for wide input voltage applications of 300–500 V_in with a desired output of 48 V₀ at full load condition, i.e., 3.3 kW and the practical efficiency of the iL²C converter was 98.2% at full load.

1. Introduction

These days, conventional internal combustion engines (ICEs) are becoming saturated due to a deficiency of fossil resources, and the environment is polluted with toxic gases, carbon emissions, and drastic climate changes. Considering this, there is a global call for implementing clean energy transportation to safeguard against climatic changes. Recently, EVs as an eco-friendly power source have gained significant popularity, with the promising objective of replacing ICEs and reducing CO₂ emissions [1]. Electrifying the transportation sector with battery electric vehicles (BEVs), fuel-cell electric vehicles (FCEVs), hybrid electric vehicles (HEVs), ultra-capacitor electric vehicles (UCEVs), supercapacitor electric vehicles (SCEVs), and plugin hybrid electric vehicles (PHEVs) can significantly reduce emission rates. The industry is advancing toward the adoption of electric vehicles achieve net-zero emissions by 2030 in Europe and 2050 in India. Due to the increasing demand for EVs, the development of charging topologies that are more reliable and efficient is essential. There are several charging topologies in terms of power electronics architectures for applications such as solar, EV, etc., with optimizing methods discussed in [2,3,4]. The typical block diagram of a charging architecture is shown in Figure 1.

During the past decade, much research has been conducted on a wide variety of DC–DC converters for various applications such as electric vehicles, photovoltaics, and fuel cell applications [5,6]. Many L²C resonant converters are gaining popularity due to their merits of zero voltage switching (ZVS) operation on the primary side at all load conditions and zero current switching (ZCS) operation on the secondary side with synchronous rectification, wide voltage gain, the ability to provide soft switching characteristics, and high power density with high switching frequency capability [7,8]. Additionally, the dv/dt at the primary side of the circuit is smaller due to the L²C converter’s lower turn-off current, resulting in lower electromagnetic interference (EMI) [9,10].

A typical L²C Resonant FB DC–DC converter is shown in Figure 2. It consists of a series resonant tank, which includes an inductor L_r and capacitor C_r in series with a high-frequency transformer to provide sufficient galvanic isolation, and a parallel inductance also available in the resonant tank, which is called magnetizing inductance L_m to form the resonant network [11]. For wide voltage gain applications, the switching frequency f_s must vary in a wide range, and the designer needs to take care of the ZVS function because it may be lost if the switching frequency is too low. The effect of the junction capacitance C_j, as discussed in [12], of secondary side rectifying diodes causes poor voltage control when f_s exceeds the resonant frequency f_r. The magnetic component size is constrained by the low switching frequency f_s. As a result, designing an L²C converter with a broad output voltage range poses considerable challenges, and performance degrades rapidly as f_s deviates from f_r [13,14]. In general, there are three different modes of operation in a L²C converter, including above resonance, below resonance, and at resonance. During all these modes of operation, the regulation control on the ZCS region is fully achieved, but in the case of the ZVS region, there is poor performance in regulation at different load conditions with variable input voltages. Additionally, to utilize the L²C converter as an EV charger, there are certain limitations such as increasing the load capacity to operate at higher power levels, current and voltage ripples at the output side causing damage to the product, and the efficiency at high power levels being low [15].

To overcome the drawbacks of the L²C converter, this paper considered a two-stage interleaved L²C (iL²C) converter. Due to the resonant tank design of L²C, the load capacity is limited, which results in an increased circulating current and thereby lower efficiency. Using iL²C this problem can be solved by adding the L²C in parallel to double the load capacity [16]. Additionally, at high current applications, the major power loss component is the transformer, which has eddy current loss (AC loss) and winding losses of copper resistance (DC loss), and splitting the circuit transformer current reduces the losses of AC and DC. Using the interleaving technique reduces the current ripples [17].

To date, numerous control strategies have been defined to provide soft switching, tight regulation, and reduce the circulating current [18,19]. These methods are operated by adding the transformer current via injecting zero-voltage on the primary or secondary side, and this can also be obtained by changing the phase shifting method. Some papers suggested [18,19] that different control strategies can be used at different regions such as f_s < f_r, f_s = f_r and f_s > f_r but this affects the regulation. Rather than using the zero-voltage sequence method and other techniques mentioned to extend the soft switching region [20], this paper proposes a hybrid control strategy called the VFPSM technique for iL²C FB converter. It is based on switching at a predefined current value. The proposed scheme allows either a ZCS or ZVS depending on how the designer chooses the switching current level. In addition, it also minimizes the root mean square (RMS) current in the transformer by fixing the predefined value of reactive current [21,22]. Hence, it provides an additional advantage to the controller concerning conventional phase shift modulation between the primary and secondary of transformer [23,24]. Additionally, with this method, soft switching can be achieved with low conduction losses, and proper load and line regulations are conducted and increase the system’s efficiency. Meanwhile, there are certain limitations, such as its complicated design, which require proper tuning of control parameters [25,26].

Furthermore, this paper also sheds light on the GaN-HEMT-based technology’s implementation on the proposed system [27,28]. The superior characteristics of GaN technology compared to Si (silicon), such as a wideband gap, reliability, packaging, heating, efficiency, and operating at high power density with frequency, serve as major advantages of GaN technology [29]. To reduce the losses at high power operation, a lower R_dson is required to improve the efficiency of the entire system to confer more reliable operation at higher switching speeds [30].

The main research contributions of this paper are summarized below:

• Modeling of iL²C converter topology was carried out to enhance the load capacity, reduce the current ripples, and reduce the circulating current;
• A hybrid control strategy was introduced across all operating modes to improve the regulation, minimize switching losses, and enable soft switching;
• Theoretical and simulation analysis was performed for various load conditions of the converter, including full load, half load, and light load with load regulation of the voltage, and current was also described;
• To examine the controller performance, simulations were performed for variable input voltages with line regulation of load voltage, and current deviations were determined;
• An experimental prototype for a 3.3 kW electric vehicle charger was demonstrated using GaN-HEMT technology;
• Furthermore, the highlights of the entire theoretical, simulation, and experimental validations were discussed for steady-state and transient voltage and current ripples at the load side.

The organization of this paper is as follows. Section 1 presents the introduction and literature overview. Section 2 details the iL²C resonant FB converter topology with the working principle, followed by detailed analysis of the design parameters in Section 3. In Section 4, we discuss the proposed control strategy and present its detailed design. Section 5 provides the simulation results and various case studies, while experimental results and validation are detailed in Section 6. Section 7 presents the converter’s dynamic performance analysis under line and load regulations. Section 8 details the outcomes and conclusions of the proposed research work.

2. Interleaved L²C Resonant FB DC–DC Converter Topology and the Working Principle

A typical iL²C resonant FB DC–DC converter topology is shown in Figure 3 and key waveforms are presented in Figure 4. It consists of two resonant tanks, two switching circuits, and a single diode rectifier circuit [24]. The primary side employs two L²C resonant switching circuits called converter 1 and converter 2 connected in parallel, and secondary side is outfitted with two transformer secondary windings with a single rectifier network. The proposed technique provides operation in a phase shift angle of 180° of phase difference between the gate signals of converter 1 and converter 2, and the resonant frequency of he converter 1 is defined in Equation (1). Since the two converters’ operation is identical, all the equations and circuit operation are discussed for converter 1 with resonant network 1.

$$f_r=\frac{1}{2\pi \sqrt{L_r{\times C}_r}}$$

(1)

Mode 1: Before t₀, the switch S₂ and S₃ are turned ON with all the secondary side diodes in the OFF condition. At the point of t₀–t₁, the switches S₂ and S₃ are turned OFF, and the body diodes of S₁ and S₄ are ON with the negative resonant current of i_Lr1.

Mode 2: During t₁–t₂, the switch S₁ and S₄ are turned ON and the voltage V_ab1 at transformer 1 T₁ is equal to input voltage V_in. The resonant inductor L_r1 starts resonating with resonant capacitor C_r1; meanwhile, filter capacitor C₀ is discharged through the secondary current of i_NS1. Additionally, diodes D₁ and D₄ are in the ON condition with the flow of current and voltage. The voltage at magnetizing inductance L_m1 is defined in the following Equation (2) and the current across the i_Lm1 increases linearly. At this period, the voltage at V_NS1 is equal to the output voltage, which is defined in Equation (3),

$$L_{m1}=\frac{V_0}{n}$$

(2)

$$V_{NS1}=V_0$$

(3)

The state space equation during stage 2 is defined in Equation (4) below:

$$\left\{\begin{array}{c}{i}_{Lr1}\left(t\right)=I_0\cos \left({\omega }_{r}t\right)+\frac{\left(n{V}_{in}-V_0-n{V}_0\right)}{n{Z}_r}\sin \left({\omega }_{r}t\right)\\ V_{Cr1}\left(t\right)=I_0{Z}_r\sin \left({\omega }_{r}t\right)+\left(V_0+\frac{V_0}{n}-V_{in}\right)\cos \left({\omega }_{r}t\right)\\ +V_{in}-\frac{V_0-V_{C0}}{n}\end{array}\right.$$

(4)

Mode 3: During the period t₂–t₃, the switches S₁ and S₄ are turned OFF; due to the positive flow of the current at i_Lr1, the switches S₂ and S₃ are turned ON with all the secondary side diodes in the OFF condition.

Mode 4: During the period t₃–t₄, the switches S₂ and S₃ are turned ON; because of negative current flow in i_NS1 the secondary side diodes, D₂ and D₄ are ON. Therefore, the voltage at the secondary side of the transformer is defined by −V_C0 with very low voltage, and hence the current i_Lm1 decreases linearly. The resonant inductor L_r1 starts resonating with resonant capacitor C_r1; meanwhile, filter capacitor C₀ is charged through the secondary current of i_NS1. At this period, the voltage V_NS1 is given as follows:

$$V_{NS1}=-V_0$$

(5)

The state space equation during stage 4 is defined in Equation (6) below:

$$\left\{\begin{array}{c}{i}_{Lr1}\left(t\right)=I_{Lr1}\left(t_2\right)\cos \left({\omega }_{r}t\right)+\frac{\left(n{V}_{in}-V_0-n{V}_{Cr1}(t_2\right)}{n{Z}_r}\sin \left({\omega }_{r}t\right)\\ V_{Cr1}\left(t\right)=I_{Lr1}\left(t_2\right)Z_r\sin \left({\omega }_{r}t\right)+\left(V_{Cr1}\left(t_2\right)-\frac{V_0}{n}-V_{in}\right)\cos \left({\omega }_{r}t\right)\\ +V_{in}+\frac{V_0}{n}\end{array}\right.$$

(6)

Mode 5: During the period t₄–t₅, D₂ and D₃ are in the ON state with the secondary side transformer current i_NS1 going to zero. The secondary side of the transformer voltage is denoted by Equation (7), and respective to that the magnetizing inductance decreases slowly. Furthermore, the resonant inductor L_r1 starts resonating with the resonant capacitor C_r1.

$$V_{NS1}=-V_0$$

(7)

The state space equation during stage 5 is defined in Equation (8) below:

$$\left\{\begin{array}{c}{i}_{Lr1}\left(t\right)=I_{Lr1}\left(t_4\right)\cos \left({\omega }_{r}t\right)+\frac{\left(n{V}_{in}+V_0-n{V}_{Cr1}(t_4\right)}{n{Z}_r}\sin \left({\omega }_{r}t\right)\\ V_{Cr1}\left(t\right)=I_{Lr1}\left(t_4\right)Z_r\sin \left({\omega }_{r}t\right)+\left(V_{Cr1}\left(t_4\right)-\frac{V_0}{n}-V_{in}\right)\cos \left({\omega }_{r}t\right)\\ +V_{in}+\frac{V_0}{n}\end{array}\right.$$

(8)

Mode 6: During the period t₅–t₆, the secondary side of the transformer current i_NS1 is completely zero with all the diodes in the OFF condition. At this period, the magnetizing inductance i_Lm1 starts resonating with resonant capacitor C_r1 and inductor L_r1.

After evaluating all the gains at peak values, we can define the ideal curve, as shown in Figure 5; if the frequency is 1, then the converter is operating at a resonance condition where f_s = f_r; likewise, if the frequency is less than 1, the converter is operating at below the resonance condition where f_s < f_r, and similarly, if the frequency is greater than 1, then the converter is operating above the resonance condition, where f_s > f_r [31].

3. Parameter Design

This section deals with the step-by-step design calculations of the iL²C converter for all the components and their associated critical values [32]. Since converter 1 and converter 2 are identical in operation, the parametric design was calculated for converter 1. The main system parameters are shown in

Table 1. Main parameters of an EV charger powered by an iL²C resonant DC–DC converter.

Parameter Description	Symbol	Electrical Value	Units
Minimum Input Voltage	Vin_min	300	Vdc
Maximum Input Voltage	Vin _max	500	Vdc
Rated Output Voltage	Vo	48	V
Rated Power	P	3300	W
Maximum Switching Frequency	fn_max	1.8 × 150 = 270	kHz
Maximum Switching Frequency	fn_min	120	kHz
Resonant Frequency	fr	150	kHz

and the AC equivalent circuit of LLC converter 1 is shown in Figure 6.

The transformer T₁ turning ratio and maximum and minimum values of the voltage gain of the iL²C converter at rated operating conditions are derived in Equations (9)–(11) [33,34].

$$n=\frac{V_{in\_min}}{V_{0\_min}}$$

(9)

$$M_{min}=\frac{n*V_{0\_min}}{V_{in\_max}}$$

(10)

$$M_{max}=\frac{n*V_{0\_max}}{V_{in\_min}}$$

(11)

where n is transformer turning ratio, V_{in_max} and V_{in_min} are maximum and minimum input voltages, V_{0_max} and V_{0_min} are maximum and minimum output voltages, and M_max and M_min are the maximum and minimum voltage gain.

The value of the inductor ratio L_actual is determined in the following Equation (12), where f_n represents the switching frequency. When the switching frequency is adjusted to the maximum value, the output from the previous step ensures that the converter enters the cut-off mode at the minimum output and maximum input [35].

$$L_{actual}=\left(\frac{1}{M_{min}}-1\right)\times \frac{8\times f_{n\_max}^2}{8\times f_{n\_max}^2-{\pi }^2}$$

(12)

At the next step, we consider the resonant tank design of resonant inductance L_r1, capacitance C_r1, impedance Z₀₁, and magnetizing inductance L_m1 with equivalent resistance R_ac1 in the following Equations (13)–(17). The resonant inductor is derived from Equation (12) and the magnetizing inductance of the converter. The equivalent resistance of the converter circuit is derived using Equation (13) followed by other critical equations.

$$R_{ac1}=\frac{8n^2}{{\pi }^2}\times R_L$$

(13)

$$L_{m1}=\frac{n^2}{f_r}\times \frac{V_{o\_crit}}{4*n*I_{sc}+\left[{\pi }^2*L*M_{crit}-4\right]*I_{o\_crit}}$$

(14)

$$L_{r1}=L_{actual}\times L_{m1}$$

(15)

$$C_{r1}=\frac{1}{L_{r1}\times {\left(2\pi f_r\right)}^2}$$

(16)

$$Z_{01}=\sqrt{\frac{L_{r1}}{C_{r1}}}$$

(17)

The critical operating values of conversion gain M_crit, maximum impedance Z₀, input current I_{in_crit}, output voltage V_{0_crit}, and current I_{0_crit} are determined in Equations (18)–(22), where P_{0_max} is the output power and η is the efficiency [36,37].

$$M_{crit}=\sqrt{1+\sqrt{\frac{L}{1+L}}}$$

(18)

$$Z_{0\_max}=\frac{8}{{\pi }^2}\times \frac{V_{in\_min}^2}{P_{0\_max}}\times [L+\sqrt{L\left(1+L\right)}]$$

(19)

$$V_{0\_crit}=\frac{M_{crit}\times V_{in\_min}}{n}$$

(20)

$$I_{0\_crit}=\frac{P_{0\_max}}{V_{0\_crit}}$$

(21)

$$I_{in\_crit}=\frac{P_{0\_max}}{{\eta *V}_{in\_min}}$$

(22)

The other important parametric Equations (23)–(27) are the quality factors of minimum Q_min and maximum Q_max, and the switching frequency of f_{n_max} and f_{n_min}, where R_{ac_max} and R_{ac_min} are the equivalent resistance of the maximum and minimum values, respectively, I_{in_max} is the input maximum current, and f_{n_max} and f_{n_min} are the switching frequency of the maximum and minimum values, respectively; further, f_{n_max} is 1.8 times the resonant frequency of f_r.

$$Q_{min}=\frac{Z_0}{R_{ac\_max}}$$

(23)

$$Q_{max}=\frac{Z_0}{R_{ac\_min}}$$

(24)

$$I_{in\_max}=\frac{n\times V_{0\_max}}{4\times L_{m1}\times f_{r1}}$$

(25)

$$f_{n\_min}=\left(1-\frac{N{I}_{i{n}_{crit}}-I_{0_{crit}}}{n*I_{s\_max}}\right)\times f_r$$

(26)

$$f_{n\_max}=1.8\times f_r$$

(27)

4. Hybrid Control Strategy

There are many control methods available currently in research on frequency modulation and phase shifting strategies, but in practice, they have their own drawbacks, namely, the converter has wide input and output voltage operations. In general, the phase shifting strategy is easy to design but complicated at wide input voltage ranges, and frequency modulation is an effective but complicated magnetic design. This paper proposes the combination of a hybrid control strategy named as the VFPSM technique for an iL²C converter, which operates at all conditions with the same control strategy, unlike those in [25,26].

The generation of switching frequency f_s was carried out based on the provided error voltage by taking the output voltage V_o and comparing it with the reference input voltage V_ref. The comparison of input and output voltage references can be completed by using the Voltage Control Oscillator (VCO), which also drives the gate signals. The controller will control the output voltage V_o and vary the current, which is called the CV mode of operation, and the control circuit is shown in Figure 7. The design of the outer feedback compensator is greatly aided by the third-order transfer function mentioned in Equation (28), where the sub equations in the transfer function are discussed in Equations (29)–(33).

$$Gvf(s)=\frac{{V\left(s\right)}_0}{{w\left(s\right)}_s}=G_{dc}\frac{X_{eq}^2+R_{eq}^2}{(s^2{L}_e^2+s{L}_e{R}_{eq}+X_{eq}^2)(1+s{R}_L{C}_f)+R_{eq}(s{L}_e+R_{eq})}$$

(28)

$$L_e=L_r+\frac{1}{C_r{\Omega }_s^2}=L_r(1+\frac{{\Omega }_0^2}{{\Omega }_s^2})$$

(29)

$$R_{eq}=\frac{8}{{\pi }^2}{n}^2{R}_L$$

(30)

$$X_{eq}={\Omega }_s{L}_r-\frac{1}{{\Omega }_s{C}_r}$$

(31)

$$L_n=\frac{L_m}{L_r}$$

(32)

$$Q=\frac{\sqrt{\frac{L_r}{C_r}}}{n^2{R}_L}$$

(33)

Generating the switching frequency from Figure 7 provides pulse generation to the switches. The phase shift of the 180° degree method was used to regulate the high input voltage over the broad range from 300–500 V_in and the VFPSM technique provided tight regulation of the line and load voltage and current. The switching operation of converter 1 and converter 2 is based on the phase shifting methodology termed as before 180° and after 180°, and the typical switching control circuit is shown in Figure 8.

5. Simulation Results and Analysis

The simulation analysis was carried out in MATLAB/Simulink to check the performance of the proposed iL²C converter with the VFPSM control technique. The actual design values of the converter were simulated and are tabulated in

Table 2. Modeling parameters of the iL²C Converter.

Parameter Description	Symbol	Electrical Value	Units
Maximum Characteristic Impedance	Zo_max	56.88	Ω
Characteristic Impedance	Zo	20.83	Ω
Critical Voltage Gain	M_critical	1.311	V
Magnetizing Inductance	Lm1	20.55	µH
Minimum Equivalent Resistance	Rac1_min	22.12	Ω
Maximum Equivalent Resistance	Rac1_max	55.81	Ω
Resonant Inductor	Lr1	22.11	µH
Resonant Capacitor	Cr1	50.94	nF
Transformer Turns	n1	8.82	-
Filter Capacitor	C0	100	µF

. The simulated analysis is presented for different case studies in the first case, and the nominal input and nominal output voltage at full load conditions were analyzed. In the next two cases, the converter was analyzed for half load and light load conditions at nominal voltage values; in addition to that, the load regulation of the voltage and current is presented. In the next step, two cases were performed to examine the hybrid controller: a variable step change in input voltages from 300–500 V_in and 500–300 V_in with a constant output voltage of 48 V₀ at full load condition, which is discussed in terms of the line regulation of the load voltage and current.

5.1. Case 1: Performance Analysis of the Converter for a Nominal Input Voltage (400 V_in) with a Fixed Output Voltage (48 V₀) at Full Load Condition, i.e., 3.3 kW

This section analyzes the performance of the iL²C converter at a full load condition, i.e., 3.3 kW. Figure 9 shows the nominal input voltage of 400 V_in as the constant. The converter simulated results were examined with a controlled nominal load voltage and current of 48 V₀ and 68.75 A at a full load condition, i.e., 3.3 kW, which is presented in Figure 10. The ripple voltage and currents were found with a voltage deviation of +0.5 V (+1.04%) at a rated output of 48 V₀ and the current deviation is around +0.65 A (+0.94%) at a full load current of 68.75 A.

5.2. Case 2: Performance Analysis of the Converter for a Nominal Input Voltage (400 V_in) with a Fixed Output Voltage (48 V₀) at a Half Load Condition, i.e., 1.65 kW

In this case, the converter operation was simulated at half of the load of the full load condition, which is at 1.65 kW. The nominal load voltage of 48 V₀ and load current of 38.375 A at a half load condition are presented in Figure 11. The ripple voltage and currents were found with a voltage deviation of +0.3 V (+0.62%) at a rated output of 48 V₀ and the current deviation was around +0.175 A (+0.5%) at a half load current of 38.375 A.

5.3. Case 3: Performance Analysis of the Converter for a Nominal Input Voltage (400 V_in) with a Fixed Output Voltage (48 V₀) at a Light Load Condition, i.e., 0.33 kW

In this case, the converter operation was simulated at a light load, which is 10% of the full load condition, i.e., 330 W. The nominal load voltage of 48 V₀ and the load current of 6.875 A at a light load condition are presented in Figure 12. The ripple voltage and currents were found with a voltage deviation of +0.15 V (+0.31%) at a rated output of 48 V₀ and the current deviation was around +0.017 A (+0.25%) at a light load current of 6.875 A.

5.4. Case 4: Performance Analysis of the Converter for a Variable Input Voltage (300–500 V_in) at a Fixed Output Voltage (48 V₀) at a Full Load Condition

This section analyzes the performance of the iL²C converter for a variable input voltage of 300–500 V_in at a constant output voltage of 48 V₀ under a full load condition. Figure 13 shows that at 0.05 s, the voltage suddenly rose from 300 to 500 V_in; the load voltage and load current waveforms are presented in Figure 14. During the transition of 300–500 V_in, the load voltage and current disturbances occurred at 0.05 s, and magnified figures are also presented. For the steady state voltage and current deviation of +0.4 V (+0.83%) and +0.59 A (+0.85%), a transient voltage and a current dip of +5.2 V (+10.83%) and +7.25 A (+10.54%) were found, respectively, and attained a load voltage of 48 V₀ within 1.1 ms.

5.5. Case 5: Performance Analysis of the Converter for a Variable Input Voltage (500–300V_in) at a Fixed Output Voltage (48 V₀) at a Full Load Condition

This section analyzes the performance of the iL²C converter for a variable input voltage of 500–300 V_in at a constant output voltage of 48 V₀ under a full load condition. Figure 15 shows that at 0.05 the voltage suddenly dropped from 500 to 300 V_in; load voltage and load current waveforms are presented in Figure 16. During the transition of 500–300 V_in, the load voltage and current disturbances occurred at 0.05 s, and magnified figures are also presented. For the steady state voltage and current deviation of +0.42 V (+0.875%) and +0.64 A (+0.93%), a transient voltage and current dip of −3.5 V (−7.29%) and −4.75 A (−6.9%) were found, respectively, and attained a load voltage of 48 V₀ within 1.2 ms.

6. Experimental Analysis

This section describes the experimental validation of the iL²C converter using GaN-HEMT technology at a full load condition of 3.3 kW with a variable input voltage of 300–500 V_in at a load voltage of 48 V₀. Eight GaN-HEMT switches were utilized to operate the switching circuit; the parameters of the GaN switch GS66508T are presented in

Table 3. GaN GS66508T parameters (manufactured by GaN Systems).

Parameter Description	Symbol	Electrical Value	Units
Drain Source Voltage	Vds	650	V
Continuous Drain Current	IDs(ON)	30	A
Drain Source Resistance	RDs(ON)	50	mΩ
Reverse Recovery Charge	QRR	0	nC
Total Gate Charge	QG	5.8	nC
Gate Drain Charge	QGD	1.8	nC
Gate Source Charge	QGS	2.2	nC
Turn ON Delay Time @125 °C	td(ON)	4.3	ns
Turn OFF Delay Time @125 °C	td(OFF)	8.2	ns
Internal Gate Resistance	RG	1.1	Ω

and the manufacturer is GaN systems [38,39]. Its features include cooled technology with a lower-junction thermal case resistance at high power applications, lower on-state drain resistance, reverse recovery current, zero reverse recovery losses, well designed gate charge characteristics, and its enhancement mode (E-mode) transistor with better packaging capabilities, among others [40]. TMS320F28335 was used as a digital signal processor as the main controller for the iL²C converter, and the prototype was built as per the modeling parameters discussed in

Table 4. Practical prototype values of the iL²C resonant FB DC–DC converter.

Parameter Description	Symbol	Electrical Value	Units
Variable Input Voltage	Vin	300–500	V
Rated Output Voltage	Vo	48	V
Rated Power	P	3300	W
Magnetizing Inductance	Lm1 and Lm2	23	µH
Resonant Inductors	Lr1 and Lr1	21	µH
Resonant Capacitors	Cr1 and Cr1	56	nF
Transformer Turning Ratio	n1 and n2	8.82	-
Filter Capacitor	Co	100	µF

.

The hardware representation and experimental setup are presented in Figure 17. From Figure 18, the iL²C converter was validated for 3.3 kW (load voltage 48 V₀, load current 68.75 A) at variable load conditions.

The results were analyzed at T = 100 ms/div, load voltage = 20 V/div, denoted using a blue line, load current = 50 A/div, denoted using a pink line, and the input source voltage = 300 V/div, denoted using a red line. To perform the dynamic responses at the line side, the sudden change in input voltage occurred at 0.05 s (500 ms) with a small change in load voltage and the current was observed and marked, as shown in Figure 18. It is evident that the converter and controller performed as per the theoretical and simulation analysis. For the steady state voltage and current deviation of +0.76 V (+1.58%) and +1.38 A (+2.0%), a transient voltage and current dip of +6.17 V (+12.85%) and +8.29 A (+12.05%) were found, respectively, and attained a load voltage of 48 V₀ within 18 ms.

The efficiency was measured during eight variable load conditions from full load to light load as summarized in

Table 5. Efficiency vs. power at 400 V_in with a 48 V₀.

No of Loads	Power (kW)	Efficiency (%)
1 (light load)	0.33	99.10
2	0.55	99.02
3	1.00	98.83
4 (half load)	1.65	98.72
5	2.00	98.59
6	2.50	98.50
7	3.00	98.32
8 (full load)	3.30	98.20

, i.e., 3.3 kW, 3.0 kW, 2.5 kW, 2.0 kW, 1.65 kW, 1.0 kW, 0.5 kW, and 0.33 kW, respectively, when the input and output voltages were 400 V_in and 48 V₀. The measured efficiency was 98.2%, 98.7%, and 99.1% at a full load of 3.3 kW, half load of 1.65 kW, and light load of 0.33 kW, respectively. Figure 19 shows the efficiency curve with regard to power.

7. Converter Analysis Tables

This section describes the steady state and transient deviations of the voltage and current in various simulated and experimentally analyzed case studies. The values were recorded in tabular format, and

Table 6. Steady state analysis of the load voltage regulation at different load conditions.

Various Load Cases	Load Voltage	Voltage Ripple		Max. Load Voltage Deviation	Avg. %Load Voltage Ripple
		Minimum	Maximum
Case 1: 3.30 kW	48 V	47.70 V	48.50 V	+0.50 V	+1.04%
Case 2: 1.65 kW	48 V	47.80 V	48.30 V	+0.30 V	+0.62%
Case 3: 0.33 kW	48 V	47.94 V	48.15 V	+0.15 V	+0.31%

and

Table 7. Steady state analysis of load current regulation at different load conditions.

Various Load Cases	Load Current	Current Ripple		Max. Load Current Deviation	Avg. %Load Current Ripple
		Minimum	Maximum
Case 1: 3.30 kW	68.75 A	68.30 A	69.40 A	+0.650 A	+0.94%
Case 2: 1.65 kW	34.375 A	34.20 A	34.55 A	+0.175 A	+0.50%
Case 3: 0.33 kW	6.875 A	6.865 A	6.892 A	+0.017 A	+0.25%

describe the voltage and current ripple in terms of full load (3.3 kW), half load (1.65 kW), and light load (0.33 kW).

Table 8. Steady state and transient analysis of load voltage during line regulation.

Variable Input Voltage	Steady State Voltage Ripple		Max. Load VoltageDeviation	Avg. %Load Voltage Ripple	Transient Analysis
	Min	Max			Voltage Dip	Avg% of Dip	Settling Time
Case 4: 300–500 V	47.60 V	48.40 V	+0.40 V	+0.830%	+5.2 V	+10.83%	1.1 ms
Case 5: 500–300 V	47.70 V	48.42 V	+0.42 V	+0.875%	−3.5 V	−07.29%	1.2 ms

and

Table 9. Steady state and transient analysis of load current during line regulation.

Variable Input Voltage	Steady State Current Ripple		Max. Load Current Deviation	Avg. %Load Current Ripple	Transient Analysis
	Min	Max			Current Dip	Avg% of Dip	Settling Time
Case 4: 300–500 V	68.2 A	69.34 A	+0.59 A	+0.85%	+7.25 A	+10.54%	1.1 ms
Case 5: 500–300 V	68.3 A	69.39 A	+0.64 A	+0.93%	−4.75 A	+06.90%	1.2 ms

show the steady state and transient dip and ripples of the voltage and current during variable input voltages from 300 to 500 V_in and 500 to 300 V_in.

From Table 6, the simulations were performed at different load conditions at a rated load voltage of 48 V₀ and a source of 400 V_in for examining the load voltage regulation. In case 1, with a minimum voltage ripple of 47.70 V and a maximum voltage ripple of 48.50 V with a load deviation of +0.50 V, the average percentage load voltage ripple was found to be +1.04%. In the next two cases, the minimum voltage ripple and maximum voltage ripple were generated at 47.80 V, 47.94 V and 48.30 V, 48.15 V, respectively. The load deviations occurred at +0.30 V and +0.15 V with an average percentage load voltage ripple of +0.62% and +0.31%, respectively.

Similarly, from Table 7, simulations were performed at different load conditions by maintaining the constant voltages of load 48 V₀ and source 400 V_in to examine the load current regulation. In case 1, for a minimum current ripple of 68.30 A and maximum current ripple of 69.40 A with a load deviation of +0.65 A, the average percentage of the load current ripple was found to be +0.94%. In the next two cases, the minimum current ripple and the maximum current ripple were generated at 34.20 A, 6.865 A and 34.55 A, 6.892 A, respectively. The load deviations occurred at +0.175 A and +0.017 A with an average percentage load current ripple of +0.50% and +0.25%, respectively.

From Table 8, simulations were performed to examine the load voltage deviation for variable input voltages, i.e., 300–500 V_in and 500–300 V_in, by maintaining the load voltage at 48 V₀ and the load current at 68.75 A, respectively, at full load. In case 4 (300–500 V_in), for a minimum voltage ripple of 47.60 V and maximum voltage ripple of 48.40 V with a load deviation of +0.40 V, the average percentage of load voltage ripple was found to be +0.83%. The transient voltage dip was found to be +5.2 V and its average percentage dip was +10.83%, respectively, with a settling time of 1.1 ms. During case 5 (500–300 V_in), for a minimum voltage ripple of 47.70 V and a maximum voltage ripple of 48.42 V with a load deviation of +0.42 V, the average percentage of the load voltage ripple was found to be +0.875%. The transient voltage dip was found to be −3.5 V and its average percentage dip was −7.29%, respectively, with a settling time of 1.2 ms.

From Table 9, simulations were performed to examine the load current deviation for variable input voltages, i.e., 300–500 V_in and 500–300 V_in, by maintaining the load voltage at 48 V₀ and load current at 68.75 A, respectively, at full load. In case 4 (300–500 V_in), for a minimum current ripple of 68.2 A and a maximum current ripple of 69.34 A with a load deviation of +0.59, A the average percentage of load current ripple was found to be +0.85%. The transient current dip was found to be +7.25 A and its average percentage dip was +10.54%, respectively, with a settling time of 1.1 ms. During case 5 (500–300 V_in), for a minimum current ripple of 68.3 A and maximum current ripple of 69.39 A with a load deviation of +0.64 A, the average percentage of the load current ripple was found to be +0.93%. The transient current dip was found to be −4.75 A and its average percentage dip was −6.90%, respectively, with a settling time of 1.2 ms.

Finally, after experimental validation of the iL²C converter’s topology and the VFPSM control technique with a variable input voltage of 300 V_in–500 V_in at a full load of 3.3 kW (V₀ = 48 V & I₀ = 68.75 A), its use was verified and a comparative table is presented in

Table 10. Simulation vs. experimental analysis of load voltage deviations during line regulation from (300–500 V_in).

Conditions	Steady State Voltage Ripple		Max. Load Voltage Deviation	Avg. %Load Voltage Ripple	Transient Analysis
	Min	Max			Voltage Dip	Avg% of Dip	Settling Time
Simulations	47.60 V	48.40 V	+0.40 V	+0.83%	+5.20 V	+10.83%	1.1 ms
Experimental	46.50 V	48.76 V	+0.76 V	+1.58%	+6.17 V	+12.85%	18 ms

and

Table 11. Simulation vs. experimental analysis of load current deviations during line regulation from (300–500 V_in).

Conditions	Steady State Current Ripple		Max. Load Current Deviation	Avg. %Load Current Ripple	Transient Analysis
	Min	Max			Current Dip	Avg% of Dip	Settling Time
Simulations	68.2 A	69.34 A	+0.59 A	+0.85%	+7.25 A	+10.54%	1.1 ms
Experimental	68.5 A	70.13 A	+1.38 A	+2.00%	+8.29 A	+12.05%	18 ms

in terms of line regulation for voltage and current at steady state and transient conditions respective to the simulations.

From Table 10, in the case of experimental analysis, for a minimum voltage ripple of 46.50 V and maximum voltage ripple of 48.76 V with a load deviation of +0.76 V, the average percentage of load voltage ripple was found to be +1.58%. The transient voltage dip was found to be +6.17 V and its average percentage dip was +12.85%, respectively, with a settling time of 18 ms.

From Table 11, in the case of experimental analysis, for a minimum current ripple of 68.5 A and maximum voltage ripple of 70.13 A with a load deviation of +1.38 A, the average percentage of the load voltage ripple was found to be +2.00%. The transient voltage dip was found to be +8.29 A and its average percentage dip was +12.05%, respectively, with a settling time of 18 ms.

8. Conclusions

An iL²C Resonant FB DC–DC converter with a hybrid control strategy called the VFPSM technique with a wide input voltage for EV charging systems was investigated.

Firstly, the iL²C converter was modeled and its working principle was demonstrated with the two-converter strategy, which increased the load capacity with a reduction in current ripples. To adapt the wide input voltage, tight regulation, and soft switching, a hybrid control strategy was proposed for the entire operating region, and its control loop design was discussed.

Simulations were conducted using MATLAB/Simulink for the entire proposed design. The converter performance was shifted in different case studies; during case 1, case 2, and case 3, the converter operated at different load conditions, i.e., full load (3.3 kW), half load (1.65 kW), and light load (10% of full load) with a constant input and load voltage of 400–48 V₀. The steady-state analysis of load voltage and current regulation was determined with average percentage ripples. The converter’s performance was also examined under assorted input voltage conditions from 300 to 500 V_in in case 4 and 500 to 300 V_in in case 5 at a full load condition. The load voltage and current deviations during line regulation were determined in terms of steady state and transient analysis.

Furthermore, to validate the converter and controller feasibility design, an experimental prototype was built for a 48 V₀ charging system with a variable input voltage of 300–500 V_in and implemented by using GaN-HEMT technology with an efficiency of 98.2% at full load. The steady-state and transient analysis of the proposed concept for voltage and current ripples at the load side was discussed.