Modular Expandable Multi-Input Multi-Output (MIMO) High Step-Up Transformerless DC-DC Converter

In this paper, a Multi-Input Multi-Output (MIMO) high step-up transformerless DC-DC converter is proposed. The proposed converter can expand the number of ports from both input and output terminals. Also, it has a modular structure using voltage multiplier cells (a switch, two diodes, a capacitor, and an inductor). The proposed converter is useful for a wide range of applications and has the merit of interfacing multiple hybrid voltage sources with each other to supply different loads with various voltage levels. All the output voltages of the output ports can be regulated at the same time by tuning separate controlling parameters. Since digital control has the benefit of (1) enhancing efficiency, (2) higher flexibility than analog electronics, (3) ease of use, (4) improving reliability and stability in hybrid energy conversion applications, this method of controlling implementation is adopted. The key contributions of this article would be 1) expandable modular MIMO converter with high performance for all range of duty cycles; 2) integration of hybrid energy sources and delivering to multiple loads; 3) nonlinear digital controlling approach to achieve fast transient response under the variation of input voltage sources and output loads, and 4) high voltage gain with low normalized power stress on switches. To simplify the analysis, first, single-input, dual-output (SIDO) mother-module, dual-input, three-output (DITO) and three-input, four-output (TIFO) developed modules are carefully analyzed and then, the MIMO structure is explained. To verify the theoretical results, a prototype of SIDO operation of the proposed converter with a digital controlling scheme is implemented for 30V input voltage /150V, 250V output voltages with the total power of 450W. Furthermore, experimental results of DITO operation with 30V and 40V input voltages/150V, 250V, 405V output voltages with the total power of 800W are extracted.


I. INTRODUCTION
MULTIPORT DC-DC converters (MPCs) are applicable in versatile applications including photovoltaic (PV) energy systems [1]- [2], microgrids with multiple sources and integrated energy storage [3], battery systems [4], data centers [5], and electric traction [6]. Fig. 1(a) shows the general application of a DC-DC multiport converter. MPCs with the capability of increasing the voltage levels to the standard levels of different output loads are widely required [7]. Also, MPCs increase the reliability of using these sources by interfacing multiple sources together since the renewable energy sources are affected by the environmental changes [8]- [10].
Although several single-input single-output (SISO) DC-DC boost converters can be used to interface each of the sources to the loads as shown in Fig. 1(b), in that case, the number of components, power loss, selected duty cycles for the switches and costs will be considerably high. It is noteworthy that the voltage gains of the conventional SISO DC-DC boost converters are directly related to the duty cycle of their switches and by adopting extreme duty cycles when there is a voltage drop in the voltage source, the active switches would experience severe voltage spikes [11]. One DC-DC MIMO converter can be utilized instead of using several SISO converters to integrate multiple sources and multiple output loads to optimize the performance of system as shown in Fig.  1(c). Consequently, by using MIMO converters, the components' number and power conversion stages can be decreased, also the power density can be increased.
Multiport DC-DC converters can be generally divided into two main groups transformer-based and transformerless boost MPCs. In [12]- [18], MPCs based on transformers and coupled inductors are presented. The conversion ratios of these converters are increased by adding the turn ratio of the secondary windings of their utilized transformers or coupled inductors. However, converters with transformers suffer from the high volume, high voltage spikes on elements, and as much as the operating powers of these converters increase, the size of their transformers increases. Also, converters with coupled inductors experience high input current ripples which affect the life span of the renewable energy sources and cause high leakage inductances and conduction losses.
To avoid the drawbacks of the coupled-inductor or transformer-based DC-DC boost MPCs, simpler structures are presented in [19]- [23]. The main drawback of these converters is that their conversion ratios are directly dependent on the duty cycles of their switches. By selecting high duty cycles, the switches may experience voltage spikes, especially in high power applications. To reduce the voltage spikes on switches in transformerless DC-DC boost MPCs, interleaved converters are presented such as in [24]. In these converters by shifting phases between the switches, the voltage stress on active switches can be reduced. However, these converters have the constraint of providing different conversion ratios for different ranges of duty cycles. To achieve high voltage gains in transformerless DC-DC boost MPCs, converters with voltage multiplier (VM) cells have been presented such as in [25] and [26]. However, in these converters there is no specific switch for each output port, as a result, there is not enough controlling criterion to control each of the output ports, separately. In [27], there has been a DC-DC MIMO converter utilizing a single inductor presented. This converter has low voltage gain. Also, in this converter, the voltage sources and output loads are non-common grounded. As a result, when one of the switches in one of the modules is failed, the power cannot be delivered to other modules.
In [28], to improve transient responses in dc-dc converters, the idea of proximate time-optimal digital control is applied as a hybrid digital adaptive (HDA) controller. By HDA controller, the currents of the inductor and capacitor are estimated by an adaptive adjustment and are sent to HAD. This method achieves optimal transient responses for a wide range of step changes of the load with fixed input voltage. Due to the development of microprocessor boards in recent years, the implementation of these controlling schemes has become easier. In [29], a digital control strategy has been employed on a bidirectional fly-back converter. The presented digital control scheme in [29] leads to high efficiency and fast charge/discharge speed [30]. Implemented digital control in [31] has been increased flexibility compared to analog feedback systems.
In this paper, a transformerless MPC is presented. The number of input and output terminals of the proposed converter can be increased which makes the converter suitable for a wide range of applications. The active and passive components of the proposed converter would not experience voltage stress caused by leakage inductances. Comparing the four-input developed module of the proposed converter with other conventional ones, the proposed converter has higher voltage gain for ports with the least power stress on switches. Moreover, the voltage gain of the converter is increased by the utilized VM cell for each output port, therefore, extreme duty cycles would not be applied to active switches to achieve higher powers or compensating the output voltages. There is a specific switch for each output port that can regulate the output voltage to the desired demanded level by the load. The voltage gain of each of the output ports is increased and controlled by its own cell and the ports can be operated independent from each other. Considering that the input voltage sources might be different from each other with different generated voltage and current ratings and if they are renewable energy sources such as photovoltaic cells (PVs), they might not be available all the time and they might experience a sudden drop in energy generation due to their dependency to the environmental conditions, a nonlinear-based control that can compensate for the transient drop or raise of power by these sources is adopted.

II. THE PROPOSED CONVERTER
The basic power circuit of the proposed single-input, twooutput converter is shown in Fig. 2(a). The proposed converter has the components of the inductors 1 L , 2 L , The capacitors are large enough to be considered the constant DC voltages across In the proposed converter, by using the duty cycles of 1 D and 2 D , the first and second output voltages of 1 o V and 2 o V , respectively are regulated at the same time for any constant voltages under the input voltage or output loads variations. In this study, at first, the proposed SIDO mother-module is analyzed and then the results of the expanded form of the proposed converter to 2-input/3output, 3-input/4-output, 4-input/5-output and also ( ) 1 N −input/ N -output are given. The power circuit of expanded multi-input, multi-output converter is illustrated in Fig. 2(b). As an example, in Fig. 3 the switching pattern of switches for 12 DD  is shown.
Moreover, it includes two switches 1 S and 2 S with the operating duty cycles of 1 D and 2 D , respectively.
As a result, in the steady state, the voltage balance law for the inductor 1 L can be written as follows: By simplifying the above equation, it is obtained as follows: (3) Considering Figs. 4(b) and 4(c), during modes 2 and 3, the switch 1 S is OFF and the diodes 1a D and 2b D are ON. As a result, it can be written as follows: Considering Fig. 4(a), during mode 1, the switch 1 S and diode 1a D are conducting. The conversion ratio of first output voltage over the input voltage for the first port is obtained as follows: Considering Fig. 4, the voltage across the inductor 2 L during a switching period is calculated as follows:   As a result, in the steady-state, it can be written that:

DC-DC Converter
Consequently, the conversion ratio of second output voltage over the input voltage is obtained as follows: Considering Fig. 4, the voltage stresses on switches and diodes during the time interval that they are OFF is calculated as following equations: where considering Fig. 3 DT is equal to the time interval for mode 1. Considering Fig. 4, the average currents of switches and diodes during their conducting interval time are calculated as following equations: Considering power balance law, the average current of 1 L I would be obtained as follows: 12 DD  The equivalent circuits of the proposed converter during first and third modes for 12

DD 
are same as them for 12 DD  , which are illustrated in Fig. 4(a) and 4(c), respectively. The equivalent power circuit for second mode of 12 DD  is shown in Fig. 5. Accordingly, the equations (1)- during a switching period is: Consequently, applying the voltage balance law for the inductor 2 L results that the conversion ratio of second output voltage over the input voltage This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
The voltage stresses on switches and diodes during the time interval that they are OFF is calculated as follows: Also, in this operation, same as the operation of 12 DD  , the equations (9)- (11) and (13) (20). Considering power balance law, the average current of 1 L I would be obtained as follows:

A3. Design Considerations
In continuous conduction mode (CCM) operation of the proposed converter, the average values of the currents passing through the inductances 1 L and 2 L have to be higher than half of their current ripples [ ( / 2)] LL II  . Consequently, the following inequalities have to be verified; The inductors' currents ripple is calculated as Therefore, it can be written that: For both conditions of 12 DD  and 12 DD  , the average currents of the capacitors are calculated as follows; As a result, the minimum values of the capacitors can be calculated as given in Table I.

A4.1. Continues PI Controlling System
According to Fig. 4, it is assumed that the inductor currents should be regulated. Accordingly, the state matrixes as follows: The state matrix and matrixes , are obtained as (36) and (37).
As a result, the transfer functions of the output voltages This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2022.3175876, IEEE Access Author Name: Preparation of Papers for IEEE Access (February 2017) 6 VOLUME XX, 2017 (41) Therefore, by adjusting the PI parameters Kp and Ki of the voltage loop controllers, the closed-loop system of the proposed converter which is shown in Fig. 6, can achieve a better stability performance.
In order to generate the drive signals for S1 and S2 in Fig. 6 the PWM technique is used and D1 and D2 are respectively compared with the saw tooth wave Vt. When D1 is higher than Vt, S1 is in on-state. Moreover, S2 is in on-state when D2 is larger than Vt.

A4.2. Digital Nonlinear Controlling System Design for the Proposed SIDO Mother-Module
The proposed nonlinear control for the proposed converter is written as following form: Where, Consequently, the state equations for error dynamics can be concluded as equation (52).
The equilibrium point of error Matrix in (53) is obtained by setting error matrix equal to 0 as follows;

B. Analysis of the Proposed Dual-input, Three-output DITO Developed Module
The power circuit of the proposed dual input, thee output converter is illustrated as Fig. 9. The proposed converter has six conditions of duty cycles for 2 input, 3 output topology as shown in the left column of Table II. As a result, the calculated equations for the output voltage of 3 o V in six conditions of duty cycle are illustrated in second column of Table II.
According to the third row of Table II,  during a switching period is shown in Fig. 10. Considering Fig. 10, the voltage stress on switch and diodes in the third stage of DITO converter, during the time interval that they are OFF is calculated as following equations :   2  3  3  1  2  3  1  3   3  3  3  2  3  2  1 3 2 The voltage stress on switches and diodes in the first and second stages of the proposed DITO converter during their conducting interval time are calculated as (9)-(14) for SIDO converter. Considering Fig. 10, the average currents of switch and diodes in the third stage of the proposed converter during their conducting interval time are calculated as following equations: On the other hand, considering that the diodes D3b and D2a are turning ON in the same time interval. As a result, it can be written that:  I  I  I  I  I  during  D  T The average value of inductor current in the third stage is obtained as follows: (63) By simplifying (62), it can be resulted that

/ (1 )
Considering above equation, the average value of inductor current , would be obtained as follows:

C. Analysis of proposed Three-input, Four-output (TIFO) developed module
The proposed converter has twenty forth conditions of duty cycles for 3-input, 4-output topology as shown in the left column of Table III. As a result, the calculated equations for the output voltages in each condition of duty cycles are illustrated in second column of Table III.  (1

N − Input, N Output Converter
In the proposed converter, the number of input ports and output ports can be increased. As a result, considering Tables II and III, the output voltages of the proposed 1 N − input, N output converter in Fig. 2

III. COMPARATIVE RESULTS
The proposed converter with SIDO structure and the other conventional two-output converters are compared in Table IV and their DC characteristics including voltage conversion ratio of first output port Considering Fig. 12(a) the proposed SIDO mother-module has higher voltage gain than the other conventional SIDO converters. T G in the presented converters in Table IV can be considered as 12 Fig. 12(b) shows the ratio of , which the proposed SIDO mother-module has the medium value comparing to other compared converters. The ratio of total voltage gain over total components number ( / ) would be a fair factor to be compared as Fig. 12(c). Considering Fig. 12(c), the proposed SIDO mother-module has almost higher value of / TT GN than the other converters, which verifies the proposed SIDO mothermodule has better performance comparing to other converters in Table IV. The proposed converter with four input structure and the other conventional four input converters are compared in Table  V Fig. 13  (a). Considering Fig. 13 (a) the proposed four-input converter has the highest voltage gain comparing to two other conventional four-input converters. T G in the presented converters in Table V can be considered as By considering that, the voltage gain would be increased by using more components. As a result, the criteria of total voltage gain over total components number ( / ) TT GN would be a fair factor to be compared as Fig. 13 (b). Considering Fig. 13 (b), the proposed four-input converter has highest value of / TT GN which verifies the proposed converter has better performance comparing to two other converters. The presented converters in Table V have different voltage conversion ratios for the output ports (for the proposed four-input converter the voltage gain of five output ports are as , , port port port port port in which, in one port the voltage gain is higher than that for other ports of the converter and it can be named as max G . Consequently, in Fig. 13(c), the maximum reachable voltage gain of the presented converters in Table V is compared. It is resulted that the proposed four-input converter has the highest value of max G comparing to two other conventional four-input converters in Table V. Fig. 13 (d) shows the normalized maximum power stress on switch, in which the proposed fourinput converter has the minimum value comparing to other compared four-input converters in [22] and [28]. Consequently, the high cost related to selecting the switches with high power avoided for the proposed converter. Fig. 14 shows the twoinput, three-output version of the proposed multiport DC-DC converter and its equivalent three single-input, single-output DC-DC converters. From Table VI, one can see that the proposed converter can provide much higher conversion ratio with the same voltage stress on switches in comparison with the usage of three SISO DC-DC converters with the same structures as the ones used in the proposed converter.

IV. EXPERIMENTAL RESULTS
The proposed converter is implemented in Laboratory and the experimental results which are shown in Figs. 15-17 and 21-22 verify the accuracy performance of the proposed converter and the calculated theoretical results for SIDO and DITO operations, respectively. The used experimental parameters are given in Table VII.

A. Experimental Results of the Proposed SIDO Mother-Module
The input voltages and output voltages are considered as  A comparison between measured results in Figs. 15 and 16 and the theoretical results shows that they verify each other to a great extent. Both two output voltages can be controlled simultaneously as shown in Fig. 17. For controlling the output voltages, the microcontroller STM32F4DISCOVERY is used. The output voltage regulations of the proposed converter under variation of the input voltage, increasing suddenly from 30 V to 40 V and dropping to 20 V are extracted to demonstrate this capability of the circuit.      Fig. 19(a) where, in this figure the output powers ratio is as 12  oT P W = respectively. As a result, the power loss distribution among the different components is shown in Fig. 19(b). The implemented prototype of the proposed converter in Laboratory is shown in Fig. 20.

B. Experimental results of the proposed DITO developed module
The used experimental parameters are given in Table IX. The input voltages and output voltages are considered as       , from 225W to 112W and increasing to 225W at t=0.7[sec]. Moreover, in Fig. 23 Fig. 23(c). The values of used controlling parameters are as kp1=0.002, ki1=0.3, kp2=0.00000002 and ki2=0.08, kp3=0.001 and ki3=0.08. Considering Fig. (21), it can be seen that even by changing the out put load of each of three output ports at different moments, the three output voltages are remained at the stable value and the variations of output voltages under the variation of three output loads are negligible.

VI. CONCLUSION
In this paper, a transformerless multiport converter is presented. The number of input and output ports of the proposed converter can be increased which makes the converter suitable for a wide range of applications. The proposed converter has higher voltage gain for ports with the low power stress on switches. Moreover, high duty cycles would not be applied to the switches to obtain higher powers or stabilizing the output voltages. The voltage gain of each of the output ports is increased and controlled by its own cell and the ports can be operated independent from each other. Also, a nonlinear-based control that can compensate for the transient drop or raise of power by these sources is adopted. 3