*3.3. Inductor Selection*

The inductor current selection is significant since it is the primary variable in the entire control strategy. The input and output power must comply with the relationship *Pin*,max > *P<sup>o</sup>* in order for the proposed converter to function properly. The selection of inductor and change in inductor current can be represented as,

$$
\Delta \dot{\mathbf{u}}\_{La} = \frac{1}{L\_a} V\_{input1} D\_1 T \tag{11}
$$

$$L\_d = \frac{V\_{input1} D\_1 T}{\Delta I\_{Ld}} = \frac{V\_{input1} D\_1}{f \Delta I\_{Ld}} = \frac{5 \times 0.79}{25 \, 000 \times 7} = 0.225 \, \mu\text{H} \tag{12}$$

$$
\Delta \dot{\mathbf{u}}\_{Lb} = \frac{1}{L\_b} V\_{input2} \mathbf{D}\_2 \mathbf{T} \tag{13}
$$

$$L\_b = \frac{V\_{input2}D\_2T}{\Delta I\_{Lb}} = \frac{V\_{input2}D\_2}{f\Delta I\_{Lb}} = \frac{12 \times 0.67}{25,000 \times 7} = 0.8 \text{ }\mu\text{H} \tag{14}$$

The choice of the inductor is crucial to guaranteeing a constant source current for the output cells. The proposed arrangement operates in its worst possible condition when there is just a single source of power going to the output cells, and the switches for the two output cells are continuously off. The source with the fixed input cell is the source that consistently supplies power for the proposed control mechanism.

#### *3.4. Capacitor Selection*

The output voltage of the VSM unit should be constant in order to preserve the steadystate connection between the input and the current. The choice of the appropriate capacitor is determined by this criterion. The voltage drop of *C*<sup>1</sup> can be written as,

$$
\Delta V\_{c1} = \frac{I\_{La}}{f \times \mathcal{C}\_1} \tag{15}
$$

To guarantee a constant output voltage, the values of *C*<sup>1</sup> and *C*<sup>3</sup> must meet the inequality shown below:

$$C\_1 = \frac{I\_{01}}{f \times \Delta V\_\odot} = \frac{2.4}{25,000 \times 15} = 6.4 \text{ }\mu\text{F} \tag{16}$$

$$C\_3 = \frac{I\_{03}}{f \times \Delta V\_{\odot}} = \frac{1.5}{25,000 \times 15} = 4 \text{ }\mu\text{F} \tag{17}$$

#### *3.5. Stability Analysis*

To achieve system stability, the closed-loop poles of the characteristic polynomial should be within the unit circle [30]. Because it transfers the left half of the S-plane to the inside of the unit circle in the Z-plane it preserves compensator stability. The projected error variables must meet at zero from any non-zero beginning value, since the controller is primarily designed to check the robustness of the control rule. This validates that the system under consideration is stable with the appropriate pole positions. The transfer function of the proposed converter for *C*<sup>3</sup> = 4 µF is found as follows,

$$H(s) = \frac{6 \times 10^6 s^2 + 3 \times 10^7 s + 11 \times 10^{12}}{4s^4 + 5200s^3 + 7500s^2 - 4 \times 10^5 s + 750 \times 10^{11}}\tag{18}$$

*R*2 15 Ω

The converter remains steady even when the value of the capacitor *C*<sup>1</sup> is increased. The system poles, on the other hand, migrate to the right side of the axis, and their imaginary values are falling. As a result, by lowering the imaginary quantities of the poles, the frequency of the converter's dampening variations will be lowered.

#### **4. Results and Discussion** *Energies* **2022**, *15*, 5559 11 of 20

To assess its performance, the proposed converter was simulated under various circumstances. The proposed system was developed and modeled using MATLAB/Simulink software. The values of the parameters are shown in Table 1. Figure 7 shows the input voltage waveforms of the proposed converter. The matching input voltages 5 V and 12 V are kept at a constant state. Inductors *La* 0.225 μH *Lb* 0.8 μH *Lc* 0.8 μH


**Table 1.** Design parameters. Load Resistance *R*1 10 <sup>Ω</sup>

**Figure 7.** Simulation response of input voltage waveform. (**a**) **Figure 7.** Simulation response of input voltage waveform.

Figure 8 shows the equivalent switching pulse waveforms. The corresponding input voltages 5 V and 12 V are maintained as a steady-state. The corresponding switching pulse waveforms are illustrated in Figure 8. By switching the inductor at a frequency of 25 kHz, the inductor waveform is produced. Figure 9 shows the input inductance currents (*ILa* and *ILb*) and the output capacitance (*Voutput*2). The current in the circuit tries to increase, while the coil stores energy when the switch is turned on, and the input voltages are given to the inductor circuit. The output capacitor provides the load current during this time. The proposed converter has a characteristic that minimizes switching fatigue and capacitive turn-on loss since there is no voltage spike across the switch because the energy stored in the leakage current is released through the diodes in the switch turn-off time. Figure 10 shows the simulation response of the output voltages. The output voltages can produce up to 24 V and 36 V. As a result, it was determined that combining a MIMO converter with a PV system produces 3 to 4 times the amount of input voltages. **Figure 7.** Simulation response of input voltage waveform.

*Energies* **2022**, *15*, 5559 11 of 20

Load Resistance *R*1 10 <sup>Ω</sup>

Duty Cycle *D*1 0.79

Switching Frequency *Fs* 25,000 Hz

with a PV system produces 3 to 4 times the amount of input voltages.

*La* 0.225 μH *Lb* 0.8 μH *Lc* 0.8 μH

*R*2 15 Ω

*D*2 0.67

Figure 8 shows the equivalent switching pulse waveforms. The corresponding input voltages 5 V and 12 V are maintained as a steady-state. The corresponding switching pulse waveforms are illustrated in Figure 8. By switching the inductor at a frequency of 25 kHz, the inductor waveform is produced. Figure 9 shows the input inductance currents (*ILa* and *ILb*) and the output capacitance (*Voutput*2). The current in the circuit tries to increase, while the coil stores energy when the switch is turned on, and the input voltages are given to the inductor circuit. The output capacitor provides the load current during this time. The proposed converter has a characteristic that minimizes switching fatigue and capacitive turn-on loss since there is no voltage spike across the switch because the energy stored in the leakage current is released through the diodes in the switch turn-off time. Figure 10 shows the simulation response of the output voltages. The output voltages can produce up to 24 V and 36 V. As a result, it was determined that combining a MIMO converter

Inductors

**Figure 8.** Simulation response of gate pulses (**a**) *Vds*1 and (**b**) *Vds*2**. Figure 8.** Simulation response of gate pulses (**a**) *Vds*<sup>1</sup> and (**b**) *Vds*<sup>2</sup> .

## *Experimental Results*

To show off the effectiveness of the proposed converter, a lab prototype was designed and is represented in Figure 11. The switching gate pulses are produced using a dsPIC 30F4013 micro controller. The proposed converter was tested under a constant load, step change in load, and variable load change conditions.

To show off the effectiveness of the proposed converter, a lab prototype was designed and is represented in Figure 11. The switching gate pulses are produced using a dsPIC

.

**Figure 10.** Simulation response of output voltages.

*Experimental Results* 

**Figure 9.** Simulation response of input inductor currents and capacitance voltage.

(**b**)

**Figure 8.** Simulation response of gate pulses (**a**) *Vds*1 and (**b**) *Vds*2**.**

(**b**)

*Energies* **2022**, *15*, 5559 12 of 20

**Figure 8.** Simulation response of gate pulses (**a**) *Vds*1 and (**b**) *Vds*2**.**

**Figure 9.** Simulation response of input inductor currents and capacitance voltage. **Figure 9.** Simulation response of input inductor currents and capacitance voltage. **Figure 9.** Simulation response of input inductor currents and capacitance voltage.

**Figure 10.** Simulation response of output voltages. **Figure 10.** Simulation response of output voltages. **Figure 10.** Simulation response of output voltages. change in load, and variable load change conditions.

When the fixed current control is the supplied input, the appropriate waveform is seen in Figure 12. To assess the converter's ability to balance the voltage, this input voltage (5 V) was recorded during steady-state execution (1 Div. = 5 V). The experimental wave-

.

**Figure 11.** Experimental setup. **Figure 11.** Experimental setup.

**Figure 12.** Input voltage 1 waveform.

under CCM while operating with both stable and unstable loads.

When the fixed current control is the supplied input, the appropriate waveform is seen in Figure 12. To assess the converter's ability to balance the voltage, this input voltage (5 V) was recorded during steady-state execution (1 Div. = 5 V). The experimental waveform of input voltage 2 is represented as Figure 13 under a fixed current control state. It demonstrates that the proposed MIMO converter can maintain a steady DC voltage level under CCM while operating with both stable and unstable loads. When the fixed current control is the supplied input, the appropriate waveform is seen in Figure 12. To assess the converter's ability to balance the voltage, this input voltage (5 V) was recorded during steady-state execution (1 Div. = 5 V). The experimental waveform of input voltage 2 is represented as Figure 13 under a fixed current control state. It demonstrates that the proposed MIMO converter can maintain a steady DC voltage level under CCM while operating with both stable and unstable loads.

30F4013 micro controller. The proposed converter was tested under a constant load, step

*Energies* **2022**, *15*, 5559 13 of 20

change in load, and variable load change conditions.

**Figure 12.** Input voltage 1 waveform. **Figure 12.** Input voltage 1 waveform.

**Figure 11.** Experimental setup.

**Figure 13.** Input voltage 2 waveform. **Figure 13.** Input voltage 2 waveform.

Figure 14 shows the output voltage 1, the inductance voltage VLa, and the drain-tosource voltage of switch 1. The driving signal for the two input units is identical in this scenario since it is produced through closed-loop regulation. The inductive voltage (VLb) Figure 14 shows the output voltage 1, the inductance voltage VLa, and the drain-tosource voltage of switch 1. The driving signal for the two input units is identical in this scenario since it is produced through closed-loop regulation. The inductive voltage (VLb)

waveform is shown in Figure 15 (1 Div. = 2 V). It displays how the converter can function in two modes when the frequency is pulse-width-modulated. It is important to observe

confirmed. Figure 16 exhibits the output voltage 1 and the drain-to-source voltages of switch 2. Figure 17 depicts the output voltage 2 experiment waveform (1 Div. = 10 V). The proposed converter could deliver many outputs at once, according to the experimental findings. It is clear that duty cycles and switching periods of the two input cells varied. It

demonstrates that the input voltage is triple the output voltage.

**Figure 14.** Switching voltage 1, inductor voltage *VLa*, and output voltage 1 waveform.

waveform is shown in Figure 15 (1 Div. = 2 V). It displays how the converter can function in two modes when the frequency is pulse-width-modulated. It is important to observe that at the conclusion of each switching cycle, the current flowing through the inductor La,b becomes continuous. As a result, the proposed converter's operation in the CCM is confirmed. Figure 16 exhibits the output voltage 1 and the drain-to-source voltages of switch 2. Figure 17 depicts the output voltage 2 experiment waveform (1 Div. = 10 V). The proposed converter could deliver many outputs at once, according to the experimental findings. It is clear that duty cycles and switching periods of the two input cells varied. It demonstrates that the input voltage is triple the output voltage. scenario since it is produced through closed-loop regulation. The inductive voltage (VLb) waveform is shown in Figure 15 (1 Div. = 2 V). It displays how the converter can function in two modes when the frequency is pulse-width-modulated. It is important to observe that at the conclusion of each switching cycle, the current flowing through the inductor La,b becomes continuous. As a result, the proposed converter's operation in the CCM is confirmed. Figure 16 exhibits the output voltage 1 and the drain-to-source voltages of switch 2. Figure 17 depicts the output voltage 2 experiment waveform (1 Div. = 10 V). The proposed converter could deliver many outputs at once, according to the experimental findings. It is clear that duty cycles and switching periods of the two input cells varied. It demonstrates that the input voltage is triple the output voltage.

Figure 14 shows the output voltage 1, the inductance voltage VLa, and the drain-tosource voltage of switch 1. The driving signal for the two input units is identical in this

*Energies* **2022**, *15*, 5559 15 of 20

**Figure 13.** Input voltage 2 waveform.

*Energies* **2022**, *15*, 5559 14 of 20

**Figure 14.** Switching voltage 1, inductor voltage *VLa*, and output voltage 1 waveform. **Figure 14.** Switching voltage 1, inductor voltage *VLa*, and output voltage 1 waveform.

**Figure 15.** Inductance voltage *VLb* waveform. **Figure 15.** Inductance voltage *VLb* waveform.

**Figure 16.** Switching voltage 2 waveform.

**Figure 16.** Switching voltage 2 waveform. **Figure 16.** Switching voltage 2 waveform.

**Figure 15.** Inductance voltage *VLb* waveform.

**Figure 17.** Output voltage 2 waveform. **Figure 17.** Output voltage 2 waveform.

fluctuating irradiance and load.

Figure 18 illustrates the relevant functioning waveforms of variable loads under the CCM. The output status is also unchanged as before. We confirm that the two output streams are separate of one another without needing any additional control obtained from the experiments. Therefore, regardless of the quantity of outputs, the control strategy can be the same straightforward constant current regulation. A step voltage command response is shown to demonstrate the proposed multi-objective control. An acceptable overshoot and a disturbance were seen as presented. The proposed converter is integrated into the PV system during fluctuating load under the CCM as shown in Figure 19 (1 Div. = 10 Figure 18 illustrates the relevant functioning waveforms of variable loads under the CCM. The output status is also unchanged as before. We confirm that the two output streams are separate of one another without needing any additional control obtained from the experiments. Therefore, regardless of the quantity of outputs, the control strategy can be the same straightforward constant current regulation. A step voltage command response is shown to demonstrate the proposed multi-objective control. An acceptable overshoot and a disturbance were seen as presented. The proposed converter is integrated into the PVsystem during fluctuating load under the CCM as shown in Figure <sup>19</sup> (1 Div. = 10 V). This

V). This result implies that the proposed converter can operate with ease in conditions of

**Figure 18.** Variable voltages waveform when step change in load.

**Figure 17.** Output voltage 2 waveform.

*Energies* **2022**, *15*, 5559 16 of 20

result implies that the proposed converter can operate with ease in conditions of fluctuating irradiance and load. the PV system during fluctuating load under the CCM as shown in Figure 19 (1 Div. = 10 V). This result implies that the proposed converter can operate with ease in conditions of fluctuating irradiance and load.

Figure 18 illustrates the relevant functioning waveforms of variable loads under the CCM. The output status is also unchanged as before. We confirm that the two output streams are separate of one another without needing any additional control obtained from the experiments. Therefore, regardless of the quantity of outputs, the control strategy can be the same straightforward constant current regulation. A step voltage command response is shown to demonstrate the proposed multi-objective control. An acceptable overshoot and a disturbance were seen as presented. The proposed converter is integrated into

**Figure 18.** Variable voltages waveform when step change in load. **Figure 18.** Variable voltages waveform when step change in load.

**Figure 19.** The output voltage (*Voutput*2) under variable changes in the load conditions. **Figure 19.** The output voltage (*Voutput*<sup>2</sup> ) under variable changes in the load conditions.

#### **5. Discussion 5. Discussion**

predicted to be 94.3%.

4 3 4 1 2 30 V, 20

1 5 2 2 2 34 V, 48

3 5 4 1 2 25 V, 20

MIMO converter 4 3 4 2 1 24 V, 20

[1]

[8]

[12]

MIMO high step-up transformerless converter

Switching boosting action-based MIMO

Step-up boost converter with CLD

cell

converter

[16] Single-inductor

**Table 2.** Comparison with existing works.

A detailed comparative analysis of a proposed converter with existing published converters is provided in Table 2 to further highlight the essential characteristics of the proposed converter. These converters are primarily contrasted in terms of converter type, quantity of switches, inputs, outputs, efficiency, and capacity for expansion and inferences. The proposed converter has a fewer number of switches as compared to the previous converters. Since, cross-regulation is not an issue, the appropriate control is simple and very effective. Furthermore, the stability study finds a high power density, which A detailed comparative analysis of a proposed converter with existing published converters is provided in Table 2 to further highlight the essential characteristics of the pro-posed converter. These converters are primarily contrasted in terms of converter type, quantity of switches, inputs, outputs, efficiency, and capacity for expansion and inferences. The proposed converter has a fewer number of switches as compared to the previous converters. Since, cross-regulation is not an issue, the appropriate control is simple and very effective. Furthermore, the stability study finds a high power density,

results in a high extended capacity. Figure 20 compares the proposed converter's power losses to that of a typical converter, with an anticipated total loss difference of 28.5 W.

conventional converter. Reduced conduction losses for switches and diodes as a consequence account for most of the efficiency gap between the two converters. The experimental results of the proposed converter's maximum efficiency under various load conditions are shown in Figure 21. At maximum loading power, the converter efficiency is

<sup>V</sup>21 V, 8 V Medium Medium NR 93.98

<sup>V</sup>80 V, 40 V Medium Medium NR 93.4

<sup>V</sup>22 V, 11 V High Low NR 92.1

<sup>V</sup>12 V, 8 V Medium Low NR 89.7

Hybrid energy sources integration

high voltage gain without maximum value of duty cycle

Improve the power density in various load applications

Integration of various loads with minimum number of components

and MO

**Ref. Converter Type Number of Switches IV OV PD EC Stability Efficiency Observations D C S L Outputs** 

which results in a high extended capacity. Figure 20 compares the proposed converter's power losses to that of a typical converter, with an anticipated total loss difference of 28.5 W. With conduction losses (S<sup>1</sup> and S2), inductor core losses, induction winding losses, diode conduction losses, and capacitor losses, the proposed converter has lower losses than the conventional converter. Reduced conduction losses for switches and diodes as a consequence account for most of the efficiency gap between the two converters. The experimental results of the proposed converter's maximum efficiency under various load conditions are shown in Figure 21. At maximum loading power, the converter efficiency is predicted to be 94.3%.


**Table 2.** Comparison with existing works.

D—Diode, C—Capacitors, S—Switch, L—Inductors, IV—Input Voltage, OV—Output voltage, PD—Power Density, EC—Extension capability, and NR—Not Reported. D—Diode, C—Capacitors, S—Switch, L—Inductors, IV—Input Voltage, OV—Output voltage, PD— Power Density, EC—Extension capability, and NR—Not Reported.

**Figure 20.** Power loss comparison of proposed converter with traditional converter. **Figure 20.** Power loss comparison of proposed converter with traditional converter.

**Figure 21.** Power versus efficiency graph.

This work developed a transformerless and non-isolated rapid step-up MIMO DC– DC power converter with low power losses. The proposed converter is suitable for energy storage applications since it simply has two switches. Because the proposed converter runs in just two operational modes throughout each duty cycle, the converter's control technique is simple. The performance concepts, theoretical voltage or current assessments, and steady-state analysis have been described. Furthermore, the proposed converter has two voltage gains for the first and second outputs. To ensure that the proposed converter works properly, it was compared to several different topologies. According to the

**6. Conclusions**

[28]

Proposed Work

Single-inductor– multi-input–multioutput DC–DC con-

High step-up MIMO Converter with low power

4 3 4 1 3 18 V, 22

<sup>V</sup>12 V, 8 V Low Medium NR 91.5

D—Diode, C—Capacitors, S—Switch, L—Inductors, IV—Input Voltage, OV—Output voltage, PD—

2 3 2 3 2 5 V, 12 V 24 V, 36 V High High Reported 94.3

Power Density, EC—Extension capability, and NR—Not Reported.

Integration of multiple loads with fixed current control

Tarnsformerless MIMO converter with fewer number of switches

verter

losses

**Figure 20.** Power loss comparison of proposed converter with traditional converter.

**Figure 21.** Power versus efficiency graph. **Figure 21.** Power versus efficiency graph.

#### **6. Conclusions 6. Conclusions**

This work developed a transformerless and non-isolated rapid step-up MIMO DC– DC power converter with low power losses. The proposed converter is suitable for energy storage applications since it simply has two switches. Because the proposed converter runs in just two operational modes throughout each duty cycle, the converter's control technique is simple. The performance concepts, theoretical voltage or current assessments, and steady-state analysis have been described. Furthermore, the proposed converter has two voltage gains for the first and second outputs. To ensure that the proposed converter works properly, it was compared to several different topologies. According to the This work developed a transformerless and non-isolated rapid step-up MIMO DC–DC power converter with low power losses. The proposed converter is suitable for energy storage applications since it simply has two switches. Because the proposed converter runs in just two operational modes throughout each duty cycle, the converter's control technique is simple. The performance concepts, theoretical voltage or current assessments, and steadystate analysis have been described. Furthermore, the proposed converter has two voltage gains for the first and second outputs. To ensure that the proposed converter works properly, it was compared to several different topologies. According to the comparative results, the proposed converter has a greater output voltage, fewer components, and minimal power dissipation. To that objective, a simulation and laboratory prototype was built for testing purposes, and experimental findings have been presented.

**Author Contributions:** Conceptualization, S.K.R.; methodology, S.K.R.; investigation, I.V.; writing original draft preparation, S.K.R. and I.V.; writing—review and editing, G.D.; resources, B.A.; visualization and administration, S.K.R. and I.V.; funding acquisition, B.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Research Groups Funding program grant code (NU/RG/ SERC/11/6).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are thankful to the Deanship of Scientific Research at Najran University for funding this work under the Research Groups funding program grant code (NU/RG/SERC/11/6).

**Conflicts of Interest:** There are no conflict of interest declared by the authors.

#### **References**

