Independent Double-Boost Interleaved Converter with Three-Level Output

This paper introduces a novel converter topology based on an independent controlled double-boost configuration. The structure was achieved by combining two independent classic boost converters connected in parallel at the input and in series at the output. Through proper control of the two boost converters, an interleaved topology was obtained, which presents a low ripple for the input current. Being connected in series at the output, a three-level structure was attained with twice the voltage gain of classic boost and interleaved topologies. A significant feature of the proposed converter is the possibility of independent operation of the two integrated boost converters, in both symmetrical and asymmetrical modes. This feature may be particularly useful in voltage balancing or interconnection with bipolar DC grids/applications. The operation principle, simulations, mathematical analysis, and laboratory prototype experimental results are presented.


Introduction
The need for high-gain boost topology converters with a low ripple of the input current can be justified in various applications, such as bidirectional chargers for electric vehicles in smart homes [1], development of energy storage for renewable power systems [2][3][4], and DC microgrid and mobility-related concepts [5][6][7][8]. The present work focuses on the power conversion stage of low voltage DC renewable sources, such as photovoltaic panels with power optimizers and/or micro-inverter applications in AC or DC distribution microgrids [9].
The classic interleaved boost converter is recognized for its high efficiency and low ripple input current. On the other hand, this type of converter exhibits a limited voltage gain. High-gain interleaved DC-DC voltage converters in transformerless structures have been explored in various studies [10][11][12][13]. A floating, high-gain voltage interleaved converter widely employed in research studies was analyzed in [14,15]. This structure is based on the principle of the intercalated operation of two classic boost converters. However, the output circuit for this application does not have purely capacitive filtering, thus it requires a more complex scheme for the output voltage control. Numerous studies commonly use the three-level boost converter [16], but since the input source and inductor currents are the same, there is no interleaved characteristic, and the voltage gain is limited. The same limitations were found in the research of [17], where a three-level DC-DC boost converter with dual output was presented. An interleaved step-up DC-DC converter topology composed of two boost converters was introduced in [18]. During operation, the converter stages are indirectly connected in a series, which ensures a high voltage gain of the output. Since the output consists of two series capacitors, a three-level output is achieved. The individual voltage drop across each capacitor is balanced according to the operating state of the converter, but a fully independent control is not achieved for

Converter Topology, Switching States, and Presumptive Waveforms
The proposed converter topology, named an independent double-boost interleaved converter and henceforth referred to as IDBIC, is based on a patent application [33] developed especially for PV/wind energy harvesting and battery energy conversion systems. The basic converter topology is represented in Figure 1, while the main operating stages of the converter are presented in Figure 2, in which nine independent switching states (S1-S9) are underlined. Appl. Sci. 2021, 11,   The characteristic waveforms during operation are introduced in Figure 3, in which the continuous conduction mode (CCM) and discontinuous conduction mode (DCM)   Figure 1. The electronic schematic of the proposed converter-IDBIC.
S8-Charging L1. S9-Charging L2. The characteristic waveforms during operation are introduced in Figure 3, in which the continuous conduction mode (CCM) and discontinuous conduction mode (DCM) The characteristic waveforms during operation are introduced in Figure 3, in which the continuous conduction mode (CCM) and discontinuous conduction mode (DCM) operations are exemplified in conjunction with the S1-S9 switching states. These four presumptive switching patterns are mainly triggered by the duty cycle values of the T1 and T2 transistor command signals. In view of this, for a duty cycle smaller than 0.5, the inductor currents have steeper falling slopes during the S2 and S3 switching stages. For a duty cycle larger than 0.5, inductor current waveforms and behavior similar to the regular boost interleaved converter can be observed. operations are exemplified in conjunction with the S1-S9 switching states. These four presumptive switching patterns are mainly triggered by the duty cycle values of the T1 and T2 transistor command signals. In view of this, for a duty cycle smaller than 0.5, the inductor currents have steeper falling slopes during the S2 and S3 switching stages. For a duty cycle larger than 0.5, inductor current waveforms and behavior similar to the regular boost interleaved converter can be observed. As documented in these switching stages and presumptive functioning patterns, the two integrated boost converters work independently from each other, with the inputs connected in parallel and the outputs in series. From this observation, one of the key characteristics of the proposed double-boost converter is defined. S1 S4 S5 S4 S1 S4

CCM Operation of the Proposed Converter
Considering the CCM operation, Figure 4 shows the steady-state waveforms for the inductor voltage and current at a duty cycle D larger and smaller than 0.5. For a duty cycle D larger than 0.5, the voltage ratio of the proposed converter can easily be deduced by the classic boost converter analysis approach [34], where the average inductor voltage equation is: where the capacitors C1 and C2 voltages are: The deduced voltage gain is given as: Working at a duty cycle D smaller than 0.5, the average inductor voltage equation is: As documented in these switching stages and presumptive functioning patterns, the two integrated boost converters work independently from each other, with the inputs connected in parallel and the outputs in series. From this observation, one of the key characteristics of the proposed double-boost converter is defined.

CCM Operation of the Proposed Converter
Considering the CCM operation, Figure 4 shows the steady-state waveforms for the inductor voltage and current at a duty cycle D larger and smaller than 0.5. For a duty cycle D larger than 0.5, the voltage ratio of the proposed converter can easily be deduced by the classic boost converter analysis approach [34], where the average inductor voltage equation is: where the capacitors C 1 and C 2 voltages are: The deduced voltage gain is given as: Working at a duty cycle D smaller than 0.5, the average inductor voltage equation is: Thus, for this condition, the voltage gain can be expressed as: Considering (3) and (5), Figure 5 shows the DC conversion ratio M(D), of the proposed IDBIC converter for CCM operation in conjunction with the regular boost converter gain. Thus, for this condition, the voltage gain can be expressed as: Considering (3) and (5), Figure 5 shows the DC conversion ratio M(D), of the proposed IDBIC converter for CCM operation in conjunction with the regular boost converter gain.

DCM Operation of the Proposed Converter
2.3.1. Case 1 Figure 6 shows the steady-state waveforms of inductor voltage and current for DCM operation in Case 1, where three different time intervals (D, D1, and D2) can be observed in a switching period. These waveforms are specific to the regular DCM boost converter [34].
From the average inductor voltage equation, the time interval defined by the time D1 in Figure 6 can be expressed as: Considering the output C1 capacitor charge balance, the converter load resistance R, the current area A from Figure 6, and the peak current ipk, the diode D1 average current equation can be described as: Thus, for this condition, the voltage gain can be expressed as: Considering (3) and (5), Figure 5 shows the DC conversion ratio M(D), of the proposed IDBIC converter for CCM operation in conjunction with the regular boost converter gain.

DCM Operation of the Proposed Converter
2.3.1. Case 1 Figure 6 shows the steady-state waveforms of inductor voltage and current for DCM operation in Case 1, where three different time intervals (D, D1, and D2) can be observed in a switching period. These waveforms are specific to the regular DCM boost converter [34].
From the average inductor voltage equation, the time interval defined by the time D1 in Figure 6 can be expressed as: Considering the output C1 capacitor charge balance, the converter load resistance R, the current area A from Figure 6, and the peak current ipk, the diode D1 average current equation can be described as:   Figure 6 shows the steady-state waveforms of inductor voltage and current for DCM operation in Case 1, where three different time intervals (D, D 1 , and D 2 ) can be observed in a switching period. These waveforms are specific to the regular DCM boost converter [34].
From the average inductor voltage equation, the time interval defined by the time D 1 in Figure 6 can be expressed as: Considering the output C1 capacitor charge balance, the converter load resistance R, the current area A from Figure 6, and the peak current i pk , the diode D1 average current equation can be described as: By substituting the time interval D 1 into (7), the voltage gain in DCM Case 1 becomes: where: Using (8) and different values of the parameter K, Figure 7 shows the DC conversion ratio, M(D,K), of the IDBIC boost converter for DCM Case 1.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 6 of 14 By substituting the time interval D1 into (7), the voltage gain in DCM Case 1 becomes: where: Using (8) and different values of the parameter K, Figure 7 shows the DC conversion ratio, M(D,K), of the IDBIC boost converter for DCM Case 1.  This DCM working case is illustrated in Figure 8, in which the converter is working at a duty cycle smaller than 0.5, where four different time intervals (D, D1, D2, and D3) can be observed, and the inductor current has two falling slopes. For this operation mode, the average current of the diode D1 can be expressed using the current represented by the area A and the output capacitor C1 charge balance.
By substituting the time interval D1 into (7), the voltage gain in DCM Case 1 becomes: where: Using (8) and different values of the parameter K, Figure 7 shows the DC conversion ratio, M(D,K), of the IDBIC boost converter for DCM Case 1.  This DCM working case is illustrated in Figure 8, in which the converter is working at a duty cycle smaller than 0.5, where four different time intervals (D, D1, D2, and D3) can be observed, and the inductor current has two falling slopes. For this operation mode, the average current of the diode D1 can be expressed using the current represented by the area A and the output capacitor C1 charge balance.

Case 2
This DCM working case is illustrated in Figure 8, in which the converter is working at a duty cycle smaller than 0.5, where four different time intervals (D, D 1 , D 2 , and D 3 ) can be observed, and the inductor current has two falling slopes. For this operation mode, the average current of the diode D1 can be expressed using the current represented by the area A and the output capacitor C 1 charge balance.
Using the average inductor voltage equation, the expression of the time interval D 2 defined in Figure 8 is obtained: Appl. Sci. 2021, 11, 5993 7 of 14 Using the output C 1 capacitor charge balance, the converter load resistance R, and the current area A from Figure 8, the diode D 1 average current equation can be expressed as: By substituting the time interval defined by D 2 into the capacitor C 1 charge balance (11), the result is: Knowing that the time interval D 1 is 0.5, the voltage ratio of the converter becomes: Using (13) and different values of the parameter K, Figure 9 shows the DC conversion ratio, M(D, K), of the IDBIC boost converter for DCM Case 2. Using the average inductor voltage equation, the expression of the time interval D2 defined in Figure 8 is obtained: Using the output C1 capacitor charge balance, the converter load resistance R, and the current area A from Figure 8, the diode D1 average current equation can be expressed as: By substituting the time interval defined by D2 into the capacitor C1 charge balance (11), the result is: Knowing that the time interval D1 is 0.5, the voltage ratio of the converter becomes: Using (13) and different values of the parameter K, Figure 9 shows the DC conversion ratio, M(D, K), of the IDBIC boost converter for DCM Case 2.   Using the average inductor voltage equation, the expression of the time interval D2 defined in Figure 8 is obtained: Using the output C1 capacitor charge balance, the converter load resistance R, and the current area A from Figure 8, the diode D1 average current equation can be expressed as: By substituting the time interval defined by D2 into the capacitor C1 charge balance (11), the result is: Knowing that the time interval D1 is 0.5, the voltage ratio of the converter becomes: Using (13) and different values of the parameter K, Figure 9 shows the DC conversion ratio, M(D, K), of the IDBIC boost converter for DCM Case 2.

DCM-CCM Boudary Limit
In Figure 10, the DCM-CCM boundary limit is presented. Using the voltage gain Equations (3) and (8), the plot was obtained for D larger than 0.5, which complies with (14). For D smaller than 0.5, Equations (5) and (13) were used, and the evolution of the parameter K crt is defined by (15).

DCM-CCM Boudary Limit
In Figure 10, the DCM-CCM boundary limit is presented. Using the voltage gain Equations (3) and (8), the plot was obtained for D larger than 0.5, which complies with (14). For D smaller than 0.5, Equations (5) and (13) were used, and the evolution of the parameter Kcrt is defined by (15).   To operate the integrated boost converters in an independent manner, a three-voltage level system with two loads is needed at the output, as one can notice in Figure 13, where the generic voltage control loops and the PWM signal generator are highlighted. This schematic is suitable for an asymmetric control of the converter in which the reference voltages V ref 1 and V ref 2 can have different values; thus, each integrated boost converter needs to operate independently. the generic voltage control loops and the PWM signal generator are highlighted. This schematic is suitable for an asymmetric control of the converter in which the reference voltages Vref 1 and Vref 2 can have different values; thus, each integrated boost converter needs to operate independently.

Simulation and Practical Implementation
The most common usage of the asymmetrical control is related to the energy balancing/interconnections in bipolar DC grids/applications. Thus, in this case, the voltage references Vref 1 and Vref 2 are equal. Considering different values for the R1 and R2 loads in the asymmetric mode, indicating different inductor currents, the independent operation of the two integrated boost converters is demonstrated. For an application in which the overall output voltage Vout must be regulated, a symmetrical control loop approach is sufficient, meaning that only one PI controller and one voltage reference Vref are needed.  Figure 13. The generic output voltage control loop and PWM generator. Figure 14 presents the practical measurements for the symmetric and asymmetric control of the converter considering the control schematics presented in Figure 13. For this situation, the output voltage Vout is set at 400 V, and the voltages VR1 and VR2 are equal to 200 V. During CCM operation, the command signals are almost identical, while the inductor currents are equal for the symmetric control and have different values for the asymmetrical control.

PI Controller
Moreover, based on an application with 50 V and 100 V input voltages and a 400 V output DC voltage in symmetric operation mode, the efficiency measurements carried out with the Tektronix PA3000 power analyzer are illustrated in Figure 15. The laboratory test setup is presented in Figure 16. For the prototype, the components and some general test specifications are presented in Table 1. In addition, Table 2 comprises the generalized information regarding the main characteristics of the proposed converter, directly Considering different values for the R 1 and R 2 loads in the asymmetric mode, indicating different inductor currents, the independent operation of the two integrated boost converters is demonstrated. For an application in which the overall output voltage V out must be regulated, a symmetrical control loop approach is sufficient, meaning that only one PI controller and one voltage reference V ref are needed. Figure 14 presents the practical measurements for the symmetric and asymmetric control of the converter considering the control schematics presented in Figure 13. For this situation, the output voltage V out is set at 400 V, and the voltages V R1 and V R2 are equal to 200 V. During CCM operation, the command signals are almost identical, while the inductor currents are equal for the symmetric control and have different values for the asymmetrical control.
Moreover, based on an application with 50 V and 100 V input voltages and a 400 V output DC voltage in symmetric operation mode, the efficiency measurements carried out with the Tektronix PA3000 power analyzer are illustrated in Figure 15. The laboratory test setup is presented in Figure 16. For the prototype, the components and some general test specifications are presented in Table 1. In addition, Table 2 comprises the generalized information regarding the main characteristics of the proposed converter, directly compared with actual non-isolated topologies usually found targeting the same applications.   For analyses in wide voltage range applications, the laboratory prototype testing setup from Figure 16 was developed using high-voltage transistors, which exhibit quite high internal resistances (0.23 Ω). As one can see in Figure 15, at a 50 V input voltage, the     For analyses in wide voltage range applications, the laboratory prototype testing setup from Figure 16 was developed using high-voltage transistors, which exhibit quite high internal resistances (0.23 Ω). As one can see in Figure 15, at a 50 V input voltage, the efficiency decreases at high powers because of the transistors' conduction losses that become predominant.

Conclusions
This work emphasizes the development and analysis of an interleaved converter with independent operation of the two integrated boost converter stages, attaining at the output a three-level voltage structure. The symmetric and asymmetric operations were demonstrated, together with all possible CCM and DCM operations.
Although the prototype design is not fully optimized, the results are encouraging, and future improvements can be aimed at the selection of the electronic switching devices, analog components, and PCB design. The converter features good energy efficiency with twice the voltage gain of regular boost and interleaved topologies.
The proposed converter has no specific feature with outstanding performance, and in certain applications, a shortcoming of the converter could be that the output and input do not share a common ground. Moreover, the complexity of the proposed structure can be considered a drawback, but by increasing the number of power electronics applications and particularities, alternative approaches will increase as well (Table 2). Compared with these solutions, the general number of components in the proposed converter is not very high. Nevertheless, considering all the combined characteristics, namely the interleaved property, high gain, good efficiency, low voltage stress, output with three-voltage levels, and especially the independent control of the integrated electronic structures, this converter is an engaging solution for PV optimizers/microinverters and battery energy management systems. Hence, thorough analytical and experimental studies are foreseen in future work to validate the proposed structure in DC grid interconnections and other applications by finding the best performance and optimal command/control strategies.