From Non-Modular to Modular Concept of Bidirectional Buck / Boost Converter for Microgrid Applications

: In this article, the practical comparison of the operational performance of the modular (or multiport) and non-modular bidirectional buck / boost (bi-BB) DC / DC converter is realized. The main contribution of the work is the evaluation of both concepts based on various aspects, considering the qualitative indicators of the systems relevant for microgrids. Here, we discuss e ﬃ ciency, electrical properties, costs, and component values. At the same time, critical comparisons are provided for converters based on SiC and GaN technology (non-modular high-voltage SiC-based dual-interleaved converter and modular low-voltage GaN-based). The concepts are speciﬁc with their operating frequency, whereby for each solution, the switching frequency is di ﬀ erent and directly inﬂuences relevant components. The e ﬃ ciency, overall system volume, output voltage ripple, and input current ripple are compared mutually between both concepts with a dependency on power delivery. These factors, together with overall volume and costs, are very important considering modern converters for microgrid systems. The summary of pros and cons is realized for each of the proposed converters, whereby the evaluation criterion is reﬂected within the electrical properties targeting microgrid application. electrolytic capacitors with MLCC capacitors and power inductors. The vertical board consists of GaN transistors with gate drivers, DC / DC isolated modules, optical isolators, and connector sockets. The vertical board is connected to the motherboard trough socket for better serviceability of measured parameters and more suitable electronic components maintenance.


Introduction
Electricity generation, transmission, and distribution are being revolutionized due to various economic, technical, and environmental reasons. A microgrid (MG) is among the new technologies that have attracted great attention recently. The existing centralized grid system is actively being replaced by distributed energy resources located closer to consumers to meet their requirements effectively and reliably. A microgrid is a modern distributed power system using local, sustainable power resources designed through the various smart grid in initiatives. Energy resources such as small capacity hydro units, wind turbines, and photovoltaic systems, in cooperation with energy storage systems, are within MG for electrification. Here, we discuss mainly households where grid electricity access is not simple due to poor access to remote areas or technical skills [1][2][3][4].
A DC-based microgrid is one of the proposed architectures for geographically remote users. The considered architecture can investigate the performance and feasibility of a DC-based microgrid for the small domestic area, as illustrated in Figure 1. In this model, several types of sources, such as solar energy, a wind power generator, or an energy storage system (ESS), are connected to the DC distribution node. Each energy source is connected to a common DC node through a relevant power converter. Bidirectional energy flow between the DC bus and ESS can be secured by a wide spectrum of power converter topologies, among which the buck/boost converter is mostly utilized due to definitions on input/output operational parameters [8][9][10][11]. Even bidirectional buck/boost (bi-BB) topology exhibits many variations (considering isolation, soft-switching, etc.); it is recommended to utilize the robust, reliable, redundant, and efficient solution. Simultaneously, such a solution shall not require high investments and cost for design and development [12][13][14][15][16].
Due to the mentioned fact, this paper focuses on the more detailed investigation and analyses of standard bidirectional buck/boost converter (two alternatives). At the same time, the main criterion of the evaluation is reflected within efficiency performance, costs, and input/output ripple of electrical variables. Here, an interleaved non-modular solution of a bi-BB converter equipped with SiC technology is compared to modular solution equipped by GaN transistors. Concepts differ in power semiconductor technology; thus, operating frequency and power level of individual modules comprising the whole converter system are specific for both types. For the evaluation of pros and cons, specifications on operational parameters have been defined considering DC microgrid subpart ESS-BiBB converter-DC bus. Due to purposes of laboratory testing, the converters are prototyped in a reduced power ratio, i.e., 1:10 related to power delivery and electric stress (reflected in power losses). A detailed evaluation of both technological concepts is provided, while key evaluation criteria are subjected to the main specifics of the microgrid systems (concept flexibility, complexity). The major contribution is focused on the mutual evaluation of SiC technology and GaN technology from the perspective of the application scope. In contrast, such evaluation concerning the functionality of the target application was not carried out in detail in already published studies [17][18][19][20][21].

Bi-BB Converter from Non-Modular to Modular Topology-Properties Analysis
For the purposes of the analyses related to the design of a microgrid's ESS power converter system, the focus is given on the determination of electrical properties of non-isolated bidirectional buck/boost alternative, whose principal diagram is shown on Figure 2 [4]. Since interleaved Bidirectional energy flow between the DC bus and ESS can be secured by a wide spectrum of power converter topologies, among which the buck/boost converter is mostly utilized due to definitions on input/output operational parameters [8][9][10][11]. Even bidirectional buck/boost (bi-BB) topology exhibits many variations (considering isolation, soft-switching, etc.); it is recommended to utilize the robust, reliable, redundant, and efficient solution. Simultaneously, such a solution shall not require high investments and cost for design and development [12][13][14][15][16].
Due to the mentioned fact, this paper focuses on the more detailed investigation and analyses of standard bidirectional buck/boost converter (two alternatives). At the same time, the main criterion of the evaluation is reflected within efficiency performance, costs, and input/output ripple of electrical variables. Here, an interleaved non-modular solution of a bi-BB converter equipped with SiC technology is compared to modular solution equipped by GaN transistors. Concepts differ in power semiconductor technology; thus, operating frequency and power level of individual modules comprising the whole converter system are specific for both types. For the evaluation of pros and cons, specifications on operational parameters have been defined considering DC microgrid subpart ESS-BiBB converter-DC bus. Due to purposes of laboratory testing, the converters are prototyped in a reduced power ratio, i.e., 1:10 related to power delivery and electric stress (reflected in power losses). A detailed evaluation of both technological concepts is provided, while key evaluation criteria are subjected to the main specifics of the microgrid systems (concept flexibility, complexity). The major contribution is focused on the mutual evaluation of SiC technology and GaN technology from the perspective of the application scope. In contrast, such evaluation concerning the functionality of the target application was not carried out in detail in already published studies [17][18][19][20][21].

Bi-BB Converter from Non-Modular to Modular Topology-Properties Analysis
For the purposes of the analyses related to the design of a microgrid's ESS power converter system, the focus is given on the determination of electrical properties of non-isolated bidirectional buck/boost alternative, whose principal diagram is shown on Figure 2 [4]. Since interleaved topologies are becoming increasingly utilized due to the number of positives, here we consider dual interleaved bi-BB converter as non-modular topology ( Figure 3). The modular concept of n-modules will be composed of standard bi-BB converter (Figure 3), while the means of the connection of input/output terminals is described later within text.
Energies 2020, 13, x FOR PEER REVIEW 3 of 23 topologies are becoming increasingly utilized due to the number of positives, here we consider dual interleaved bi-BB converter as non-modular topology ( Figure 3). The modular concept of n-modules will be composed of standard bi-BB converter (Figure 3), while the means of the connection of input/output terminals is described later within text. Investigation of the waveforms of voltages and currents might be considered for the output and input parts of the converter as well. Regarding current ripples, they influence the effective value of current of the output capacitor, what affects its lifetime. Therefore, analyses according to current ripples must be provided if the optimized operation of the converter is the target [22][23][24].

Current/Voltage Ripple Dependencies
One module of the modular converter and one two-phase non-modular converter is depicted in Figure 3. The difference in the modular and non-modular converter is that the modular converter has modules connected in series, i.e., outputs are connected in series, and input sources are independent of each other. On the other side, the connection of modules in a non-modular converter is in parallel.
The assumption is that the inductor current is continuous in cases where the converter works in a boost or a buck mode, as shown in Figure 2. In a steady state, the inductor current is the sum of the DC and AC parts. If the condition of minimal value of input capacitor Equation (1) is satisfied [25], the input current drawn from the battery is constant. In this case, the AC component is provided by  topologies are becoming increasingly utilized due to the number of positives, here we consider dual interleaved bi-BB converter as non-modular topology ( Figure 3). The modular concept of n-modules will be composed of standard bi-BB converter (Figure 3), while the means of the connection of input/output terminals is described later within text. Investigation of the waveforms of voltages and currents might be considered for the output and input parts of the converter as well. Regarding current ripples, they influence the effective value of current of the output capacitor, what affects its lifetime. Therefore, analyses according to current ripples must be provided if the optimized operation of the converter is the target [22][23][24].

Current/Voltage Ripple Dependencies
One module of the modular converter and one two-phase non-modular converter is depicted in Figure 3. The difference in the modular and non-modular converter is that the modular converter has modules connected in series, i.e., outputs are connected in series, and input sources are independent of each other. On the other side, the connection of modules in a non-modular converter is in parallel.
The assumption is that the inductor current is continuous in cases where the converter works in a boost or a buck mode, as shown in Figure 2. In a steady state, the inductor current is the sum of the DC and AC parts. If the condition of minimal value of input capacitor Equation (1) is satisfied [25], the input current drawn from the battery is constant. In this case, the AC component is provided by the capacitor current. Then, the AC component is equal to the ripple of the inductor current, Equations (2) and (3) [17], which are valid for the boost and a buck converter, respectively. Investigation of the waveforms of voltages and currents might be considered for the output and input parts of the converter as well. Regarding current ripples, they influence the effective value of current of the output capacitor, what affects its lifetime. Therefore, analyses according to current ripples must be provided if the optimized operation of the converter is the target [22][23][24].

Current/Voltage Ripple Dependencies
One module of the modular converter and one two-phase non-modular converter is depicted in Figure 3. The difference in the modular and non-modular converter is that the modular converter has modules connected in series, i.e., outputs are connected in series, and input sources are independent of each other. On the other side, the connection of modules in a non-modular converter is in parallel. The assumption is that the inductor current is continuous in cases where the converter works in a boost or a buck mode, as shown in Figure 2. In a steady state, the inductor current is the sum of the DC and AC parts. If the condition of minimal value of input capacitor Equation (1) is satisfied [25], the input current drawn from the battery is constant. In this case, the AC component is provided by the capacitor current. Then, the AC component is equal to the ripple of the inductor current, Equations (2) and (3) [17], which are valid for the boost and a buck converter, respectively.
where C min is the minimal value of input capacitance, f sw is the switching frequency, ∆V CIN is the voltage ripple on the input capacitor, ∆I IN , ∆I L, and ∆I CIN are the values of the ripple of the input current, the inductor and the input capacitor, respectively, V IN is the input supply voltage, D is the duty cycle, and V OUT is the value of the converter output voltage. The inductor current ripple, Equation (2), is dependent on the input voltage (battery voltage), duty cycle, inductor value, and the switching frequency. A modular converter, unlike a non-modular one, has separate input sources. A non-modular converter has one input source or input source connected in series (e.g., serially connected battery packs). It means that the input voltage is much lower in the case of a modular converter, and therefore the current ripple is much smaller. This fact significantly reduces the ripple of the input current. Therefore, an inductance with a much smaller value is enough to maintain the same input ripple in comparison to the non-modular solution. For example, the n-module modular converter is used, and n-series connected battery packs are used for the non-modular case, the inductor value should be n times lower for the maintenance of the same current ripple.
The character of the input capacitor current for both converters is triangular, not impulse. Therefore, the impact on a voltage ripple is smaller than in the case of the impulse current. The input voltage ripple is dependent on an AC component of the inductor current and ESR of the battery pack and input capacitor. However, due to DC current drawn from the battery, as was mentioned earlier, and the parallel-connected battery pack with high capacity to the input capacitor, the input voltage ripple is negligible.
The topology of the non-modular converter is classical interleaved bidirectional buck/boost converter. In the case of interleaved topology, it is possible to achieve a state when the input current ripple is zero due to current ripple cancelation between parallel-connected phases [26][27][28]. This situation is depicted in Figure 4, [29]. The ratio between the input current and the inductor current is shown. It is an advantageous property in cases where the operation of the converter is at or around the desired duty cycle. In the case of a four-phase converter, the desired duty cycle is 0.25, 0.5, and 0.75. Ideally, the input voltage ripple is also zero or almost zero. It can be seen from Figure 4 that the ripple of the input current is smaller over the entire range of the duty cycle (∆I L is also inductor current of the modular converter). This statement applies under the condition mentioned above, and the input voltage is the same for the modular and non-modular converter. A more detailed explanation of a current ripple for the interleaved topologies is given in Appendix A.  For a better image of the current and voltage ripple cancellation at the output of the modular converter, the simplification of the converter must be performed. If we simplify the given converter by the replacement of the output series-connected capacitor with one capacitor, then the current to this capacitor is continuous and does not have a pulse character (only triangular) during operation for up to 87.5% of the duty cycle. This operational mode is valid for modular concepts; thus, it meets this criterion. The value of the capacitor is then n times lower, and ESR is n times higher. The load current of the simplified converter (conventional bi-BB converter) is equal to the effective value of the capacitor current of the one module in the modular converter. The ripple of the output capacitor current is as follows: An explanation of the simplification and calculation of the output current ripple is given in Appendix B.
In the case of the non-modular converter, the output capacitor current is continuous when the value of the duty cycle is above 50%. Otherwise, the current has a pulse character, and the ripple is much higher. Therefore, the utilization of a modular converter is a better solution because the current ripple cancelation is within the wide operational range of the converter. The voltage ripple calculation is performed according to Equations (4) and (5), respectively [17].

Bi-BB Converter Design Guideline Considering Components Selection and Costs
Since the design of the bi-BB converter must be adjusted to the nominal parameters of the target application, the input specifications are exactly defined ( Table 1). The target application is considered as a low-power installation of a smart-grid node within the family house. The primary source of energy from renewable energy types is the photovoltaic block ( Figure 1), which supplies the MPPT converter, whose output supplies the DC bus with 600 V of nominal voltage, which represents the input side of the bi-BB converter. For the modular system, the input voltage is divided between the serial connection of the modular converter blocks ( Figure 5). Table 1. Operational parameters of target application reflecting the situation from Figure 1.

Parameter
Value Output voltage range from PV panels 500-560 V DC For a better image of the current and voltage ripple cancellation at the output of the modular converter, the simplification of the converter must be performed. If we simplify the given converter by the replacement of the output series-connected capacitor with one capacitor, then the current to this capacitor is continuous and does not have a pulse character (only triangular) during operation for up to 87.5% of the duty cycle. This operational mode is valid for modular concepts; thus, it meets this criterion. The value of the capacitor is then n times lower, and ESR is n times higher. The load current of the simplified converter (conventional bi-BB converter) is equal to the effective value of the capacitor current of the one module in the modular converter. The ripple of the output capacitor current is as follows: An explanation of the simplification and calculation of the output current ripple is given in Appendix B.
In the case of the non-modular converter, the output capacitor current is continuous when the value of the duty cycle is above 50%. Otherwise, the current has a pulse character, and the ripple is much higher. Therefore, the utilization of a modular converter is a better solution because the current ripple cancelation is within the wide operational range of the converter. The voltage ripple calculation is performed according to Equations (4) and (5), respectively [17].

Bi-BB Converter Design Guideline Considering Components Selection and Costs
Since the design of the bi-BB converter must be adjusted to the nominal parameters of the target application, the input specifications are exactly defined ( Table 1). The target application is considered as a low-power installation of a smart-grid node within the family house. The primary source of energy from renewable energy types is the photovoltaic block ( Figure 1), which supplies the MPPT converter, whose output supplies the DC bus with 600 V of nominal voltage, which represents the input side of the bi-BB converter. For the modular system, the input voltage is divided between the serial connection of the modular converter blocks ( Figure 5). Table 1. Operational parameters of target application reflecting the situation from Figure 1.

Parameter Value
Output voltage range from PV panels 500-560 V DC Output power from PV panels 10 kW peak Output voltage (DC bus voltage) 600 V DC Output MPPT converter power 10 kW peak application, the input specifications are exactly defined ( Table 1). The target application is considered as a low-power installation of a smart-grid node within the family house. The primary source of energy from renewable energy types is the photovoltaic block ( Figure 1), which supplies the MPPT converter, whose output supplies the DC bus with 600 V of nominal voltage, which represents the input side of the bi-BB converter. For the modular system, the input voltage is divided between the serial connection of the modular converter blocks ( Figure 5). Table 1. Operational parameters of target application reflecting the situation from Figure 1.

Parameter
Value Output voltage range from PV panels 500-560 V DC Output power from PV panels 10 kW peak Output voltage (DC bus voltage) 600 V DC Output MPPT converter power 10 kW peak The input voltage for both concepts shall be 600 V, thus for the non-modular solution, the output is single. In contrast, the modular solution is characterized by the serial connection of the input terminals of the individual converters. The output of bi-BB supplies energy storage components (battery pack). At the same time, the non-modular concept is defined by 520 V of single output voltage, whereby the modular concept has an n-independent low-voltage output connected to ESS. The advantage of a modular concept is the possibility of active battery management provided by individual modules of the concept, as it has an independent output connected to batteries. It improves power management and prolongs life expectations, as discussed in [30,31]. The non-modular solution shall be equipped by additional active/passive balancing units if required.
Focusing on the circuit component selection, the modular system may be based on the GaN technology of the semiconductor components. Such a solution is suitable due to the division of the power and voltages to separate individual modules in reduced merit. It also enables us to increase switching frequency several times. Such an approach might reduce the dimensions of used components (magnetic components, capacitors, PCB). Thanks to lower dimensions, it is possible to design converters with smaller PCB, while the volume of a complex modular system would be smaller compared to the non-modular system. Operational parameters of the non-modular system predetermine SiC technology as the main switching component. The switching frequency for these components can be higher compared to standard Si transistors, whereby, considering high voltage and power levels, it is not recommended due to efficiency reduction. Next, Equations (6)-(8) were used for the determination of the values of the main circuit components (Figure 3) affecting the converter volume. Figure 6 shows the 3D dependency of the values of inductor L and filter capacitor C OUT received using (6)- (8) for the situation when the number of modules and switching frequency vary [17]. At the same time, input/output parameters are relevant for individual module count. where V in is the input converter voltage (V), V out is the output converter voltage (V), f sw is the switching frequency (Hz), ∆i L is the ripple of inductor current (%), and I out_max is the maximum output current (A).
where V in_min is the minimum input converter voltage (V), and V out is the output converter voltage (V).
where I out_max is the maximum output current (A), D is the duty cycle (%), f sw is the switching frequency (kHz), ∆V out is the ripple of the output voltage (%), and V out is the output voltage (V).
used for the determination of the values of the main circuit components (Figure 3) affecting the converter volume. Figure 6 shows the 3D dependency of the values of inductor L and filter capacitor COUT received using (6)- (8) for the situation when the number of modules and switching frequency vary [17]. At the same time, input/output parameters are relevant for individual module count.
where Vin is the input converter voltage (V), Vout is the output converter voltage (V), fsw is the switching frequency (Hz), ΔiL is the ripple of inductor current (%), and Iout_max is the maximum output current (A).
where Vin_min is the minimum input converter voltage (V), and Vout is the output converter voltage (V).
where Iout_max is the maximum output current (A), D is the duty cycle (%), fsw is the switching frequency (kHz), ΔVout is the ripple of the output voltage (%), and Vout is the output voltage (V). It must be noted that the interpretation considers one module situation. For the whole modular solution, the result must be multiplied by the relevant number of the considered modules. Table 2 shows input/output parameters that have been included within the calculation of the L and C OUT if real operational conditions are valid. At this point, the need for semiconductor devices is considered for various scenarios. It is seen that for the non-modular solution, a high voltage SiC transistor module is needed. For two and four modules, high-voltage GaN transistors (650 V) must be used, while for a higher number of modules, it is allowed us to utilize 100 V GaN transistors. At this place, the economic performance, together with efficiency and power density calculation, is given. Initially, Table 3 shows an expert estimation of the investments necessary for the design of proposed solutions of the bi-BB converter. The estimation considers with the whole bill of materials of electronic parts (power semiconductor components, drivers, magnetic components, passive components, and PCB), while the standard distribution network was considered. It is seen that Energies 2020, 13, 3287 8 of 21 the initial costs of the non-modular DC-DC interleaved converter based on the SiC technology are comparable to the initial costs that are relevant for up to a 16-stage modular DC-DC converter.  Figure 7 shows the graphical interpretation of the so-called qualitative parameters of power semiconductor converters with a dependency on switching frequency. Here, it was defined that these parameters are material costs, efficiency, and expected converter volume (concerning power delivery can be considered as power density). Initially, a non-modular solution is compared that has a dependency on switching frequency. It is seen that with the increase in the switching frequency, the costs together with volume decrease, which is related to the fact that smaller reactive components can be used within the converter's main circuit. Efficiency is almost similar for each of the operating frequencies, as SiC transistors are suitable for the investigated range of this parameter. Consequently, comparisons are provided between non-modular and modular concepts, while switching frequency is considered as 100 kHz. Considering the volume of the converter (power density), a non-modular solution exhibits performance that is most suitable regarding given switching frequency and input/output parameters that are limited due to power delivery and semiconductor performance (Figure 8). For high power levels, it is expected to operate at lower frequencies in order to prevent unwanted negative impacts (safety reasons, EMC, efficiency reduction, etc.). At the same time, robust semiconductors must be used (IGBT, SiC MOSFETS) [32][33][34].   Consequently, comparisons are provided between non-modular and modular concepts, while switching frequency is considered as 100 kHz. Considering the volume of the converter (power density), a non-modular solution exhibits performance that is most suitable regarding given switching frequency and input/output parameters that are limited due to power delivery and semiconductor performance (Figure 8). For high power levels, it is expected to operate at lower frequencies in order to prevent unwanted negative impacts (safety reasons, EMC, efficiency reduction, etc.). At the same time, robust semiconductors must be used (IGBT, SiC MOSFETS) [32][33][34]. density), a non-modular solution exhibits performance that is most suitable regarding given switching frequency and input/output parameters that are limited due to power delivery and semiconductor performance (Figure 8). For high power levels, it is expected to operate at lower frequencies in order to prevent unwanted negative impacts (safety reasons, EMC, efficiency reduction, etc.). At the same time, robust semiconductors must be used (IGBT, SiC MOSFETS) [32][33][34]. The modular solution is not attractive for low switching frequencies due to a power density point of view, which influences the cost of such a solution. On the other side, it is seen that this parameter is best for the case of an eight-module solution. It is related to cheaper power components   The modular solution is not attractive for low switching frequencies due to a power density point of view, which influences the cost of such a solution. On the other side, it is seen that this parameter is best for the case of an eight-module solution. It is related to cheaper power components when the input/output voltage is reduced. Thus, components with lower current/voltage loading can be utilized, and a reasonable number of modules shall be selected (for 20 modules, the cost is very high due to the high number of components). Therefore, the high-switching frequency operation is easy to utilize.
Evaluation of the impact of switching frequency increase is reported in Figures 9 and 10, where only modular solutions are compared for 500 kHz and 1 MHz. With this increase, the volume of the passive components can be visibly reduced. Moreover, when GaN technology is considered, the volume of the semiconductors also minimizes. A GaN-based converter system has a big advantage if a very small volume and weight are required. Typical examples are mobile systems, compact converter systems, or electromobility. From Figures 9 and 10, it is seen that with the increase in switching frequency, the total volume of the modular converter system can be reduced below the volume of the non-modular solution, whereby this is valid from 500 kHz of switching frequency and above four numbers of the modules. The positive impact of frequency increase is the opposite if efficiency is evaluated. For 1 MHz of switching frequency, the efficiency drops below 93% if more than eight modules are used.
Energies 2020, 13, x FOR PEER REVIEW 9 of 22 when the input/output voltage is reduced. Thus, components with lower current/voltage loading can be utilized, and a reasonable number of modules shall be selected (for 20 modules, the cost is very high due to the high number of components). Therefore, the high-switching frequency operation is easy to utilize. Evaluation of the impact of switching frequency increase is reported in Figures 9 and 10, where only modular solutions are compared for 500 kHz and 1 MHz. With this increase, the volume of the passive components can be visibly reduced. Moreover, when GaN technology is considered, the volume of the semiconductors also minimizes. A GaN-based converter system has a big advantage if a very small volume and weight are required. Typical examples are mobile systems, compact converter systems, or electromobility. From Figures 9 and 10, it is seen that with the increase in switching frequency, the total volume of the modular converter system can be reduced below the volume of the non-modular solution, whereby this is valid from 500 kHz of switching frequency and above four numbers of the modules. The positive impact of frequency increase is the opposite if efficiency is evaluated. For 1 MHz of switching frequency, the efficiency drops below 93% if more than eight modules are used.

Concepts Description
Due to initial validation purposes, the parameters listed in Table 1 were reduced by the power ratio 1:10. Considering similar conditions to the real system, voltage levels were also modified for experimental prototypes of converters ( Table 4). The block diagram ( Figure 11) indicates the voltage levels selected for practical experiments, while the values are reduced for power delivery of 1 kW full power (the real system operates at 10 kW).

Concepts Description
Due to initial validation purposes, the parameters listed in Table 1 were reduced by the power ratio 1:10. Considering similar conditions to the real system, voltage levels were also modified for experimental prototypes of converters ( Table 4). The block diagram ( Figure 11) indicates the voltage levels selected for practical experiments, while the values are reduced for power delivery of 1 kW full power (the real system operates at 10 kW). The converters in the modular solution are phase-shifted by 360/8° to achieve a low output voltage and current ripple. However, this power ratio emulation is also reflected within component design and selection of the converter's main circuit devices in order to provide us with the most realistic conditions as possible. The non-modular concept utilizes SiC transistors operating at lower switching frequencies (app. 100 kHz) and uses standard inductors. On the other hand, in order to  The converters in the modular solution are phase-shifted by 360/8 • to achieve a low output voltage and current ripple. However, this power ratio emulation is also reflected within component design and selection of the converter's main circuit devices in order to provide us with the most realistic conditions as possible. The non-modular concept utilizes SiC transistors operating at lower switching frequencies (app. 100 kHz) and uses standard inductors. On the other hand, in order to provide an increase in power density performance, the modular concept utilizes low voltage/high-speed GaN transistors (operating over 300 kHz) with planar inductors. This approach shall demonstrate the optimization possibilities of a bidirectional buck-boost converter using a modular converter concept.
The physical prototypes of the converters were designed based on parameters given in Table 4. Table 5 lists the main circuit components used within a non-modular and modular converter prototype.  Figure 12 shows a physical sample of proposed bi-BB converters. The non-modular concept uses inductors that are made on PQ40 N87 cores, while the winding is made of isolated copper foil in order to achieve low conduction losses. In order to secure the safe operation of the control system, the isolation on the side of gate drivers was used.  An experimental prototype of one module that is used for a modular concept, where eight converters with separate inputs and common output are connected to achieve the 200 V of the output voltage, is shown in Figure 12 as well. The proposed module consists of two boards. The horizontal motherboard is composed mostly of filtering components like electrolytic capacitors with MLCC capacitors and power inductors. The vertical board consists of GaN transistors with gate drivers, DC/DC isolated modules, optical isolators, and connector sockets. The vertical board is connected to the motherboard trough socket for better serviceability of measured parameters and more suitable electronic components maintenance.

Operation Properties Comparisons
The experimental measurements focused on the evaluation of main operational characteristics for both the buck and boost mode of designed bi-BB converter concepts. The evaluations were made separately for efficiency and voltage/current ripples. The laboratory equipment and experimental setup used within measurements are shown in Figure 13. An experimental prototype of one module that is used for a modular concept, where eight converters with separate inputs and common output are connected to achieve the 200 V of the output voltage, is shown in Figure 12 as well. The proposed module consists of two boards. The horizontal motherboard is composed mostly of filtering components like electrolytic capacitors with MLCC capacitors and power inductors. The vertical board consists of GaN transistors with gate drivers, DC/DC isolated modules, optical isolators, and connector sockets. The vertical board is connected to the motherboard trough socket for better serviceability of measured parameters and more suitable electronic components maintenance.

Operation Properties Comparisons
The experimental measurements focused on the evaluation of main operational characteristics for both the buck and boost mode of designed bi-BB converter concepts. The evaluations were made separately for efficiency and voltage/current ripples. The laboratory equipment and experimental set-up used within measurements are shown in Figure 13.
Energies 2020, 13  For buck and boost mode, three input voltages were applied, while the investigated variables were analyzed for the whole output power range. Figure 14 shows the efficiency dependency for the boost mode, while the input voltage varied within 90 V and 110 V. Both tested solutions offer almost 97% efficiency, whereby the difference between analyzed converter types is visible in dependency on output power. The input voltage of the modular system is created by a sum of eight voltages on the inputs of individual modules. The efficiency decreases with the increase in output power, while on the other side, the non-modular system has increasing character. These facts are caused due to operational character, for example, due to the three times higher switching frequency of modular concept. Even for the buck mode of operation, the modular system has a decreasing character of efficiency (Figure 15), which is also a cause of the higher number of switching transistors that are used. More transistors cause more hard switching losses and lower efficiency for higher output loads. If both For buck and boost mode, three input voltages were applied, while the investigated variables were analyzed for the whole output power range. Figure 14 shows the efficiency dependency for the boost mode, while the input voltage varied within 90 V and 110 V. Both tested solutions offer almost 97% efficiency, whereby the difference between analyzed converter types is visible in dependency on output power. The input voltage of the modular system is created by a sum of eight voltages on the inputs of individual modules. The efficiency decreases with the increase in output power, while on the other side, the non-modular system has increasing character. These facts are caused due to operational character, for example, due to the three times higher switching frequency of modular concept.  For buck and boost mode, three input voltages were applied, while the investigated variables were analyzed for the whole output power range. Figure 14 shows the efficiency dependency for the boost mode, while the input voltage varied within 90 V and 110 V. Both tested solutions offer almost 97% efficiency, whereby the difference between analyzed converter types is visible in dependency on output power. The input voltage of the modular system is created by a sum of eight voltages on the inputs of individual modules. The efficiency decreases with the increase in output power, while on the other side, the non-modular system has increasing character. These facts are caused due to operational character, for example, due to the three times higher switching frequency of modular concept. Even for the buck mode of operation, the modular system has a decreasing character of efficiency (Figure 15), which is also a cause of the higher number of switching transistors that are used. More transistors cause more hard switching losses and lower efficiency for higher output loads. If both efficiency characteristics for boost and buck mode are analyzed, the modular solution exhibits an  Even for the buck mode of operation, the modular system has a decreasing character of efficiency (Figure 15), which is also a cause of the higher number of switching transistors that are used. More transistors cause more hard switching losses and lower efficiency for higher output loads. If both efficiency characteristics for boost and buck mode are analyzed, the modular solution exhibits an advantage below 60% of the nominal power. In contrast, above this point, non-modular solutions become more effective.
Energies 2020, 13, x FOR PEER REVIEW 13 of 22 Figure 16 shows the output current ripple of the systems in boost mode of operation. The modular system has a current ripple of around 1% and a non-modular system around 3% if nominal power is considered. From the diagram, it is seen that the modular concept has a lower ripple than a non-modular system within the whole power range. This fact is caused by the higher switching frequency in a modular system and interleaved operation given by the 360/8° ratio of control signals.   Figure 17 shows the output current ripple of the systems in the buck mode of operation. The modular system again reaches much lower values compared to the non-modular system, while the values of the ripple are below 0.5% if the output power is higher than 30% of the nominal converter's power. During the change in the input voltage, a modular solution exhibits visible independence, while the non-modular system is visibly dependent if the ripple vs. input voltage is analyzed. The lowest ripple for the non-modular solution is achieved at a high output power, which is related to the extension of the duty cycle if the output power is increased. boost non-mod. 90V boost non-mod. 100V boost non-mod. 110V boost mod. 90V boost mod. 100V boost mod. 110V Figure 15. The dependency of efficiency on output power and input voltage for proposed bi-BB converters for buck mode. Figure 16 shows the output current ripple of the systems in boost mode of operation. The modular system has a current ripple of around 1% and a non-modular system around 3% if nominal power is considered. From the diagram, it is seen that the modular concept has a lower ripple than a non-modular system within the whole power range. This fact is caused by the higher switching frequency in a modular system and interleaved operation given by the 360/8 • ratio of control signals.
Energies 2020, 13, x FOR PEER REVIEW 13 of 22 Figure 16 shows the output current ripple of the systems in boost mode of operation. The modular system has a current ripple of around 1% and a non-modular system around 3% if nominal power is considered. From the diagram, it is seen that the modular concept has a lower ripple than a non-modular system within the whole power range. This fact is caused by the higher switching frequency in a modular system and interleaved operation given by the 360/8° ratio of control signals.   Figure 17 shows the output current ripple of the systems in the buck mode of operation. The modular system again reaches much lower values compared to the non-modular system, while the values of the ripple are below 0.5% if the output power is higher than 30% of the nominal converter's power. During the change in the input voltage, a modular solution exhibits visible independence, while the non-modular system is visibly dependent if the ripple vs. input voltage is analyzed. The lowest ripple for the non-modular solution is achieved at a high output power, which is related to the extension of the duty cycle if the output power is increased.   Figure 17 shows the output current ripple of the systems in the buck mode of operation. The modular system again reaches much lower values compared to the non-modular system, while the values of the ripple are below 0.5% if the output power is higher than 30% of the nominal converter's power. During the change in the input voltage, a modular solution exhibits visible independence, while the non-modular system is visibly dependent if the ripple vs. input voltage is analyzed. The lowest ripple for the non-modular solution is achieved at a high output power, which is related to the extension of the duty cycle if the output power is increased.  Figures 18 and 19 show the dependency of the output voltage ripple of both concepts in the boost and buck modes of operation. The modular system has a voltage ripple around 0.8% and a nonmodular system around 1.6% at the nominal point of operation if buck mode is considered. For boost mode, the modular system has voltage ripple around 1% and the non-modular system around 1.8% at full power. If both operational modes are analyzed (buck and boost), the modular system has a better voltage ripple performance than a non-modular system for any voltage level applied at the input terminals of converters.     Figures 18 and 19 show the dependency of the output voltage ripple of both concepts in the boost and buck modes of operation. The modular system has a voltage ripple around 0.8% and a non-modular system around 1.6% at the nominal point of operation if buck mode is considered. For boost mode, the modular system has voltage ripple around 1% and the non-modular system around 1.8% at full power. If both operational modes are analyzed (buck and boost), the modular system has a better voltage ripple performance than a non-modular system for any voltage level applied at the input terminals of converters.  Figures 18 and 19 show the dependency of the output voltage ripple of both concepts in the boost and buck modes of operation. The modular system has a voltage ripple around 0.8% and a nonmodular system around 1.6% at the nominal point of operation if buck mode is considered. For boost mode, the modular system has voltage ripple around 1% and the non-modular system around 1.8% at full power. If both operational modes are analyzed (buck and boost), the modular system has a better voltage ripple performance than a non-modular system for any voltage level applied at the input terminals of converters.    Previous analyses showed the advantages and disadvantages of the operational characteristics of designed bi-BB converters. Both have pros and cons related to costs, power density, efficiency performance, as well as the character of electrical variables. Related to the mentioned facts, it is further valuable to investigate the impact of previous research within the target application (i.e.,   The inductor current ripples and input current ripple for boost interleaved non-modular converter is seen in Figure A1. During the state, as mentioned earlier (T1 is on, and T3 is off), the voltage across the inductor L 1 is equal to V in . From Faraday's law, it is known that the voltage across an inductor is equal to the inductance L times the rate of the current change V L = Ldi/dt, and therefore for di L1 and di L2 : and in this state dt = DT S . Therefore, the values of ripples for D < 1/2 are expressed in Equations (A3)-(A5) Then, the solution for input ripple current is as follows: The solution of input current ripple for the duty ratio within a range of 1/2 ≤ D < 1 is shown in Figure A2.
valid for the input current of a boost converter.
The same manner can be used for a buck mode within the investigation of output current ripple. It must be stated that the output current of a buck converter is an input current of the non-modular converter as well.
The inductor current ripples and input current ripple for boost interleaved non-modular converter is seen in Figure A1. During the state, as mentioned earlier (T1 is on, and T3 is off), the voltage across the inductor L1 is equal to Vin. From Faraday's law, it is known that the voltage across an inductor is equal to the inductance L times the rate of the current change VL = Ldi/dt, and therefore for diL1 and diL2: and in this state dt = DTS. Therefore, the values of ripples for D < 1/2 are expressed in Equations (A3)-(A5) Then, the solution for input ripple current is as follows: The solution of input current ripple for the duty ratio within a range of 1/2 ≤ D < 1 is shown in Figure A2.    Figure A2. Input and inductor currents for 1/2 ≤ D < 1.
The inductor current ripples are given in Equations (A6) and (A7). The procedure for obtaining Equations (A6) and (A7) is the same as in the previous case. The difference is that the dt = dTS. The new parameter d is involved in the calculation because the input current ripple occurs within the interval dTS. The parameter d is expressed in Equation (A8). The procedure for obtaining an equation is Then, the solution for the input current ripple is a sum of the inductor current ripples, Equation (A9).
These solutions for D ≤ ½ and 1/2 ≤ D < 1 are also shown in Table A1. The number of phases is two, and interval I and interval II are considered. It must be stated that with an increase in the number of phases, the number of intervals also increases. This is due to the greater number of operating modes of the converter. Therefore, the n-phase converter is divided into n intervals.
The same assumption is valid for the converter in a buck mode. The difference is only in output Vout and input voltage Vin. It should be noted that the output voltage of the boost converter is the input voltage of the buck converter. Therefore, for a non-modular converter, the equations are the same. Then, the input current ripples for the two-, three-, four-and n-phase non-modular converters in a boost and buck mode are shown in a Table A1 and Table A2, respectively. The inductor current ripples are given in Equations (A6) and (A7). The procedure for obtaining Equations (A6) and (A7) is the same as in the previous case. The difference is that the dt = dT S . The new parameter d is involved in the calculation because the input current ripple occurs within the interval dT S . The parameter d is expressed in Equation (A8). The procedure for obtaining an equation is Then, the solution for the input current ripple is a sum of the inductor current ripples, Equation (A9).
These solutions for D ≤ 1 2 and 1/2 ≤ D < 1 are also shown in Table A1. The number of phases is two, and interval I and interval II are considered. It must be stated that with an increase in the number of phases, the number of intervals also increases. This is due to the greater number of operating modes of the converter. Therefore, the n-phase converter is divided into n intervals.
The same assumption is valid for the converter in a buck mode. The difference is only in output V out and input voltage V in . It should be noted that the output voltage of the boost converter is the input voltage of the buck converter. Therefore, for a non-modular converter, the equations are the same. Then, the input current ripples for the two-, three-, four-and n-phase non-modular converters in a boost and buck mode are shown in a Tables A1 and A2, respectively. Table A1. The equations of output current ripples for the 2-,3-, 4-and n-phase non-modular boost converter.

Number of Phases
Interval

Appendix B
The inductor and output capacitor currents i L1 , i L2 , i C1 , and i C2 are depicted in Figure A3 for two modules of the modular converter. It is seen that the inductor current ripple ∆I L1 in one-phase is equal to capacitor current ripple ∆I Coff during the period that the transistor of the relevant phase is switched off. Therefore, according to the previous procedure, the following equation is valid: In the modular converter, the topology simplification can be used. The output capacitor is connected in series; then, the final value of the output capacitor is eight times lower. If we consider one output capacitor, the waveform of the output capacitor current is displayed in Figure A3 with a blue line. It is seen that the modified period of the output capacitor ripple current is one eighth of the switching period. This is due to the equal phase-shifting of the eight-module converter. Then, the output capacitor current ripple ∆I Cout is dependent on a slope of the inductor/capacitor current and the modified period.

Appendix B
The inductor and output capacitor currents iL1, iL2, iC1, and iC2 are depicted in Figure A3 for two modules of the modular converter. It is seen that the inductor current ripple ΔIL1 in one-phase is equal to capacitor current ripple ΔICoff during the period that the transistor of the relevant phase is switched off. Therefore, according to the previous procedure, the following equation is valid: In the modular converter, the topology simplification can be used. The output capacitor is connected in series; then, the final value of the output capacitor is eight times lower. If we consider one output capacitor, the waveform of the output capacitor current is displayed in Figure A3 with a blue line. It is seen that the modified period of the output capacitor ripple current is one eighth of the switching period. This is due to the equal phase-shifting of the eight-module converter. Then, the output capacitor current ripple ΔICout is dependent on a slope of the inductor/capacitor current and the modified period. The duration of the slope of the inductor current is (1 − D) TS, and the ripple is as follows.
The duration of the output capacitor current is 1/8 TS. Then we can write: The duration of the slope of the inductor current is (1 − D) TS, and the ripple is as follows.
Energies 2020, 13, 3287 20 of 21 The duration of the output capacitor current is 1/8 T S . Then we can write: