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energies Article A Multistage DC-DC Step-Up Self-Balanced and Magnetic Component-Free Converter for Photovoltaic Applications: Hardware Implementation Mahajan Sagar Bhaskar 1 , Sanjeevikumar Padmanaban 1, * and Frede Blaabjerg 2 1 2 * Department of Electrical and Electronics Engineering, University of Johannesburg, PO Box 524, Auckland Park, Johannesburg 2006, South Africa; [email protected] Centre for Reliable Power Electronics (CORPE), Department of Energy Technology, Aalborg University, 9000 Aalborg, Denmark; [email protected] Correspondence: [email protected]; Tel.: +27-79-219-9845 Academic Editor: Tapas Mallick Received: 24 December 2016; Accepted: 15 May 2017; Published: 18 May 2017 Abstract: This article presents a self-balanced multistage DC-DC step-up converter for photovoltaic applications. The proposed converter topology is designed for unidirectional power transfer and provides a doable solution for photovoltaic applications where voltage is required to be stepped up without magnetic components (transformer-less and inductor-less). The output voltage obtained from renewable sources will be low and must be stepped up by using a DC-DC converter for photovoltaic applications. 2 K diodes and 2 K capacitors along with two semiconductor control switch are used in the K-stage proposed converter to obtain an output voltage which is (K + 1) times the input voltage. The conspicuous features of proposed topology are: (i) magnetic component free (transformer-less and inductor-less); (ii) continuous input current; (iii) low voltage rating semiconductor devices and capacitors; (iv) modularity; (v) easy to add a higher number of levels to increase voltage gain; (vi) only two control switches with alternating operation and simple control. The proposed converter is compared with recently described existing transformer-less and inductor-less power converters in term of voltage gain, number of devices and cost. The application of the proposed circuit is discussed in detail. The proposed converter has been designed with a rated power of 60 W, input voltage is 24 V, output voltage is 100 V and switching frequency is 100 kHz. The performance of the converter is verified through experimental and simulation results. Keywords: DC-DC converter; self-biased; magnetic component free; multistage; step-up; photovoltaic application 1. Introduction Renewable energy resources are becoming popular and trendy with the increase in demand and cost of energy. The proper utilization of energy resources is one of the most important issues of the present century. There are various renewable energy resources, including solar, tidal, wind, bio, nuclear and geothermal, with zero pollution emissions. Solar energy is a free, inexhaustible source of energy and is increasingly competitive with other energy sources. This energy is utilized with the help of arrays, consisting of a number of solar panels, connected in series [1–3]. In the past, various PV system methods or structures were adopted to minimize the cost to efficiency ratio. In [4–8], a Photovoltaic Central Inverter Structure (PV-CIS) is employed to feed photovoltaic energy to the electric grid. In PV-CIS PV lines are arranged in parallel and connected to one central inverter as shown in Figure 1. The drawback of CIS are: (i) a large number of panels are required which increases the cost of system; (ii) more number of DC cables with high-voltage rating are needed; (iii) losses in Energies 2017, 10, 719; doi:10.3390/en10050719 www.mdpi.com/journal/energies Energies 2017, 10, 719 Energies 2017, 10, 719 Energies 2017, 10, 719 2 of 28 2 of 28 2 of 28 losses inloss the line; line; (iv) loss loss of power power due to to module mismatch; mismatch; (v) common common Maximum Power Point the line; (iv) of power due to module mismatch; (v) common Maximum PowerPower PointPoint Tracking losses in the (iv) of due module (v) Maximum Tracking (MPPT) is used; (vi) system reliability depends on the single inverter. (MPPT) is used; (vi) system the single inverter. Tracking (MPPT) is used;reliability (vi) systemdepends reliabilityon depends on the single inverter. Figure 1. Photovoltaic Central Inverter Structure (PV-CIS) forfor transfer Figure 1. Photovoltaic Central Inverter Structure (PV-CIS) transferofofPV PVenergy energytotoan anelectric electric grid. Figure 1. Photovoltaic Central Inverter Structure (PV-CIS) for transfer of PV energy to an electric grid. grid. In [4–8], a Photovoltaic String Inverter structure (PV-SIS) is employed to feed photovoltaic energy In [4–8], [4–8], Photovoltaic String Inverter structure (PV-SIS) is employed to feed feed seriesphotovoltaic In String structure (PV-SIS) employed to photovoltaic to the electric grid.aaInPhotovoltaic PV-SIS, several PVInverter lines are used, which are is made up of several connected energy to the electric grid. In PV-SIS, several PV lines are used, which are made up of several seriesenergy to the electric grid. In PV-SIS, several PV lines are used, which are made up of several seriesPV panels as shown in Figure 2. All the PV lines are connected to separate inverters via a DC-DC connected PV PV panels panels as as shown shown in in Figure Figure 2. 2. All All the the PV PV lines lines are are connected connected to to separate separate inverters inverters via via aa connected converter and the inverter outputs are connected in parallel and and feedfeed intointo thethe electric grid. The DC-DC converter and the inverter outputs are connected in parallel electric grid. DC-DCofconverter andsystem the inverter outputs are connected in parallel and feed into the aelectric grid. drawbacks the PV-SIS are: (i) it requires a large number of panels to design several PV line; The drawbacks drawbacks of of the the PV-SIS PV-SIS system system are: are: (i) (i) it it requires requires aa large large number number of of panels panels to to design design aa several several The (ii) a large number of converters are required to feed the grid;the (iii) the(iii) costthe is cost highisdue to thetoseparate PV line; (ii) a large number of converters are required to feed grid; high due the PV line; (ii) a large number of converters are required to feed the grid; (iii) the cost is high due to the MPPTseparate and complex control circuitry iscircuitry requiredisto synchronize all the inverters. MPPT and complex control required to synchronize all the inverters. separate MPPT and complex control circuitry is required to synchronize all the inverters. Figure 2. Photovoltaic String Inverter Structure (PV-SIS) for transfer of PV energy to the electric grid. Figure 2. Photovoltaic String InverterStructure Structure (PV-SIS) (PV-SIS) for ofof PVPV energy to the electric grid. grid. Figure 2. Photovoltaic String Inverter fortransfer transfer energy to the electric In [4–8], [4–8], Photovoltaic Photovoltaic AC AC Module Module Structure Structure (PV-ACMS) (PV-ACMS) is is discussed discussed to to fed fed photovoltaic photovoltaic energy energy In to [4–8], the electric electric grid and andAC it provides provides viable solution solution to overcome overcome the drawbacks drawbacks of PV-CIS PV-CIS and and In Photovoltaic ModuleaaStructure (PV-ACMS) is discussed to fed photovoltaic energy to the grid it viable to the of PV-SIS. Ingrid PV-ACMS a single photovoltaic panel is connected to the electric grid via an inverter as to thePV-SIS. electricIn and it provides a viable solution to overcome the drawbacks of PV-CIS and PV-SIS. PV-ACMS a single photovoltaic panel is connected to the electric grid via an inverter as shown in Figure 3a. The drawbacks of PV-ACMS are: (i) it requires several module inverters which In PV-ACMS single3a. photovoltaic panel is connected the electricseveral grid via an inverter shown in shown in aFigure The drawbacks of PV-ACMS are: to (i) it requires module invertersaswhich Figure 3a. The drawbacks of PV-ACMS are: (i) it requires several module inverters which increase the cost of the system; (ii) separate MPPT is needed for each panel; (iii) the overall efficiency is low. In [4–8], Photovoltaic Multi-String Inverter Structure (PV-MSIS) is discussed to overcome the drawback of 2017, 10, 719 EnergiesEnergies 2017, 10, 719 3 of 283 of 28 increase the cost of the system; (ii) separate MPPT is needed for each panel; (iii) the overall efficiency is low. In [4–8], Multi-String Inverterseveral Structure discussed totoovercome the PV-CIS, PV-SIS and Photovoltaic PV-SIS structures. In PV-MSIS PV(PV-MSIS) panels areisconnected a single inverter drawback of PV-CIS, PV-SISconverters and PV-SISas structures. PV-MSIS PV panelscombines are connected to a connected via several DC-DC shown inInFigure 3b.several This structure the features singleand inverter connected several DC-DC converters concept as shown 3b. This structure of PV-SIS PV-ACMS. Thevia drawback of the PV-MSIS is:in(i)Figure it required several DC-DC combines the features of PV-SIS and PV-ACMS. The drawback of the PV-MSIS concept is: (i) it converters to transfer energy to the inverter; (ii) high cost due to the greater number of converters and required several DC-DC converters to transfer energy to the inverter; (ii) high cost due to the greater separate MPPT. number of converters and separate MPPT. (a) (b) Figure 3. (a) Photovoltaic AC Module Structure (PV-ACMS); (b) Photovoltaic Multi-String Inverter Figure 3. (a) Photovoltaic AC Module Structure (PV-ACMS); (b) Photovoltaic Multi-String Inverter Structure (PV-MSIS) for transfer of PV energy to the electric grid. Structure (PV-MSIS) for transfer of PV energy to the electric grid. The output obtained from a photovoltaic cell/array is usually low, so before feeding this voltage to the inverter for practical purposes, it must is beusually stepped low, up using a conventional DC-DC The output obtained fromapplication a photovoltaic cell/array so before feeding this voltage converter [1–15]. application With the increase in the duty-cycle of switch and leakage resistanceDC-DC of to theboost inverter for practical purposes, it must be stepped up using a conventional inductors, the performance of the converter degrades. Due to these practical problems, conventional boost converter [1–15]. With the increase in the duty-cycle of switch and leakage resistance of inductors, DC-DC converters are unable to provide doable solutions for step-up voltage applications [15]. In the performance of the converter degrades. Due to these practical problems, conventional DC-DC theory, when a duty cycle approaches 100%, an infinite voltage conversion ratio is achieved with a converters are unable to provide doable solutions for step-up voltage applications [15]. In theory, when conventional boost converter, but in practice, the inductor leakage resistance of the inductor limits a duty approaches infinite[16], voltage ratio is achieved with conventional thecycle voltage conversion100%, of thean converter so theconversion traditional converters cannot be useda where the boostrequired converter, but in practice, the inductor leakage resistance of the inductor limits the voltage conversion ratio is four or more [16]. Furthermore, to achieve a high conversion ratio by conversion of the converter [16], so the converters cannot used where the required using large duty cycle compromises thetraditional utilization of high frequency forbe Pulse Width Modulation (PWM)ratio because of semiconductor control devices’ delay. Unluckily, a largelarge conversion is four or more [16]. Furthermore, to inherent achieve aswitching high conversion ratio by using reactive network follows the limited switching frequency which is employed to protect from the duty cycle compromises the utilization of high frequency for Pulse Width Modulation (PWM) because ripple condition of voltage and current [17]. The traditional buck-boost converter is not reliable due of semiconductor control devices’ inherent switching delay. Unluckily, a large reactive network follows to its discontinuous input current, results in utilization of ripple the input source [13,15]. By and the limited switching frequency whichwhich is employed to low protect from the condition of voltage increasing the switching frequency of the converter, the problem of leakage resistance for certain current [17]. The traditional buck-boost converter is not reliable due to its discontinuous input current, values of ripple can be overcome. The finite switching time in a normal power device limits the which results in low utilization of the input source [13,15]. By increasing the switching frequency of switching frequency if the duty ratio is either too high or too small, so in order to abolish the above the converter, of leakage resistance forhigh certain values of ripple can be overcome. The finite problemsthe andproblem simultaneously acquire essential voltage, isolated converters can be engaged. switching in aand normal power device limits the switching frequency the duty either Manytime isolated non-isolated converter topologies have proposed overiftime, whichratio makeisuse of too high or too small, so in inductors order to abolish the above[16–27]. problems acquire due essential inductors, coupled and transformers Theand highsimultaneously voltage stress occurring to the high transformer inductance to switching losses and electromagnetic (EMI) voltage, isolated leakage converters can be leads engaged. Many isolated and non-isolated interference converter topologies problems, resulting in the reduced efficiency of conventional converters. Hard switching converters have proposed over time, which make use of inductors, coupled inductors and transformers [16–27]. are inconvenient to occurring use for highdue voltage applications dueleakage to theirinductance circuit complexity, higher voltage The high voltage stress to the transformer leads to switching losses and electromagnetic interference (EMI) problems, resulting in the reduced efficiency of conventional converters. Hard switching converters are inconvenient to use for high voltage applications due to their circuit complexity, higher voltage stress across the switch and the increased cost of the converter. Hence, for isolated topologies the size, weight and losses of power transformers are Energies 2017, 10, 719 4 of 28 Energies 2017, 10, 719 4 of 28 limiting factors. Recently, various combinations of coupled inductors, voltage multipliers or switched stress across the switch and the increased cost of the converter. Hence, for isolated topologies the capacitor multipliers [23–35] along with a switched inductor (SI), switched capacitor (SC), voltage lift size, weight and losses of power transformers are limiting factors. Recently, various combinations of switched inductor (VLSI) and modified VLSI were used to accomplish thealong necessity coupled inductors, voltage multipliers or principles switched capacitor multipliers [23–35] with [15,26]. a Figure 4a–c shows the recent SI, VLSI and modified VLSI inductive networks. For acquiring a high switched inductor (SI), switched capacitor (SC), voltage lift switched inductor (VLSI) and modified boostVLSI ratio,principles a cascaded approach is introduced. To design a Cascaded Converter (CBC), a number were used to accomplish the necessity [15,26]. Figure Boost 4a–c shows the recent SI, VLSI of inductors are essential, which networks. is the most part. In addition, losses and increased and modified VLSI inductive Forcomplex acquiring a high boost ratio, a cascaded approachcurrent is introduced. Toadesign Cascaded (CBC), a and number of efficiency inductors are essential, ripple prove to be barriera to achieveBoost a highConverter conversion ratio better [36–38]. With an which the most complex part. In gain addition, and aincreased currentthe ripple prove toBoost be a barrier objective ofisacquiring a high voltage just losses by using single switch, Quadratic Converter to achieve a high conversion ratio and better efficiency [36–38]. With an objective of acquiring a high (QBC) was proposed, though, in a QBC, higher voltage rating switches are required with higher voltage gain just by using a single switch, the Quadratic Boost Converter (QBC) was proposed, RDS-ON , as voltage stress raised across the switch is equal to the output voltage [39–41]. Multilevel though, in a QBC, higher voltage rating switches are required with higher RDS-ON, as voltage stress converters provide a suitable solution for power conversion because of the low voltage stress across raised across the switch is equal to the output voltage [39–41]. Multilevel converters provide a each suitable device [42]. High is achieved by multilevel converters capacitors solution for voltage power conversion because of the lowDC-DC voltage stress acrossusing each device [42]. and diodeHigh circuitry at the output end and the output voltage level can be increased without voltage is achieved by multilevel DC-DC converters using capacitors and diode circuitry at actually the disturbing varying of output levels anddisturbing duty cycle, voltage output the end actual and thecircuit. output By voltage levelthe cannumber be increased without actually thethe actual gain circuit. of multilevel converters can beofvaried [43,44]. multilevel converters, designing By varying the number output levels For andconventional duty cycle, the voltage gain of multilevel converters can be like varied [43,44]. isFor conventional designing magnetic magnetic components inductors a complex task, multilevel which alsoconverters, induces electromagnetic emission components like inductors is a complex task, which also induces electromagnetic emission noise. Other than these issues the presence of inductors and transformers in the power circuitnoise. degrades Other than capability these issuesand the increases presence ofthe inductors and transformers theconverters. power circuit degrades the the integration cost, weight and size ofin the Switched Capacitor integration capability and increases the cost, weight and size of the converters. Switched Capacitor (SC) power circuits provide good integration ability due to their small volume and weight, since (SC) power circuits provide good integration ability due to their small volume and weight, since magnetic components like transformers and inductors is not needed to design a SC converter [33]. magnetic components like transformers and inductors is not needed to design a SC converter [33]. (a) (b) (c) Figure 4. Inductive networks: (a) Switched Inductor; (b) Voltage Lift switched Inductor cell; (c) Figure 4. Inductive (a) Switched Inductor; (b) Voltage Lift switched Inductor cell; modified voltage liftnetworks: switched inductive cell. (c) modified voltage lift switched inductive cell. In this article, a new magnetic component-free (transformer-less and inductor-less) DC-DC converter is proposed to magnetic overcome the drawbacks of PV-CIS, PV-SIS, PV-ACMS, PV-MSIS and the In this article, a new component-free (transformer-less and inductor-less) DC-DC above discussed converter topology. The proposed converter provides a viable solution for existing converter is proposed to overcome the drawbacks of PV-CIS, PV-SIS, PV-ACMS, PV-MSIS and the photovoltaic application systems where voltage must be stepped up without magnetic components above discussed converter topology. The proposed converter provides a viable solution for existing before transferring energy to a multilevel-inverter. The single proposed converter is sufficient to photovoltaic application systemsinverter where as voltage be stepped up without magnetic components transfer energy to a multilevel shownmust in Figure 5. before transferring energy to a multilevel-inverter. The single proposed is sufficient to The proposed photovoltaic system (PV System) consists of PV modules, converter the proposed DC-DC transfer energybattery to a multilevel inverter as shown(MLI) in Figure converter, and the multilevel inverter which5.converts the battery/proposed DC-DC The proposed photovoltaic (PV consists of PV modules, proposed DC-DC converter voltage to AC voltagesystem to power ACSystem) loads/feed in the electric grid. Somethe amount of power is lost during the conversion of photovoltaic energy to electric energy. The PV device maximum converter, battery and the multilevel inverter (MLI) which converts the battery/proposed DC-DC outputvoltage power to (product of voltage and current) is described by the Maximum Poweramount Point (MPP) converter AC voltage to power AC loads/feed in the electric grid. Some of power and it is also depends on the environmental conditions (generally on temperature andmaximum light is lost during the conversion of photovoltaic energy to electric energy. The PV device conditions). A Maximum Power Point Tracker is compulsory to ensure the maximum power output output power (product of voltage and current) is described by the Maximum Power Point (MPP) and (Pmax) of a solar PV device. The Maximum Power Point Tracker can be used to adjust its input it is also depends on the environmental conditions (generally on temperature and light conditions). voltage to utilize the maximum photovoltaic output power and then transform this power to supply A Maximum Power Point Tracker is compulsory ensureisthe maximum powerwill output (Pmax ) of a the varying voltage requirements. When the PVtovoltage increased the current ultimately solardecrease, PV device. The Maximum Power Point Tracker can be used to adjust its input voltage utilize and when the PV current is increased the voltage will ultimately decrease. Dependingtoon the maximum photovoltaic output power and then transform this power to supply the varying voltage parameters like irradiance and temperature the MPP of the I-V curve of a PV module changes requirements. When the PV voltage is increased the current will ultimately decrease, and when the PV current is increased the voltage will ultimately decrease. Depending on parameters like irradiance and temperature the MPP of the I-V curve of a PV module changes dynamically. Therefore, the MPP needs to be located by a tracking algorithm as it is not known beforehand. Energies 2017, 10, 719 5 of 28 Energies 2017, 10, 719 5 of 28 Energies 2017, 10, 719 Therefore, the MPP needs to be located by a tracking algorithm as it is not known5 of 28 dynamically. dynamically. beforehand. Therefore, the MPP needs to be located by a tracking algorithm as it is not known beforehand. Figure 5. Proposed multistage self-balanced and magnetic component-free DC-DC converter in a Figure 5. Proposed multistage self-balanced and magnetic component-free DC-DC converter in a Figure 5. Proposed self-balanced and magnetic converter in a photovoltaic systemmultistage for the transfer of photovoltaic energy tocomponent-free a DC load, gridDC-DC or motor. photovoltaic system for the transfer of photovoltaic energy to a DC load, grid or motor. photovoltaic system for the transfer of photovoltaic energy to a DC load, grid or motor. To achieve the maximum power transfer from the PV module to the load it is necessary to To achieve the maximum transfer from the module to the load it is necessary match the load resistance Rpower L topower thetransfer best possible output resistance the PV module RPV (Rmpp = To achieve the maximum from the PVPV module toof the load it is necessary totomatch match the load resistance R L to the bestand possible output resistance of the PV module R PV (R mpp = V mpp/Impp ). Characteristic power-voltage current-voltage graphs or curves are shown in Figure the load resistance RL to the best possible output resistance of the PV module RPV (Rmpp = Vmpp /Impp ). V mpp/Impp). Characteristic power-voltage and current-voltage graphs or curves are shown in Figure 6a. Characteristic power-voltage and current-voltage graphs or curves are shown in Figure 6a. 6a. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) (f) (f) Figure 6. (a) Power- voltage or current- voltage graphs of a photovoltaic system; (b) MPPT when ∆P = 0 and ∆V = 0; (c) MPPT when ∆P < 0 and ∆V < 0; (d) MPPT when ∆P > 0 and ∆V > 0; (e) MPPT when ∆P > 0 and ∆V < 0; (f) MPPT when ∆P < 0 and ∆V > 0. Energies 2017, 10, 719 6 of 28 Energies 2017, 10, 719 6 of 28 Figure 6. (a) Power- voltage or current- voltage graphs of a photovoltaic system; (b) MPPT when ∆P = 0 and ∆V = 0; (c) MPPT when ∆P < 0 and ∆V < 0; (d) MPPT when ∆P > 0 and ∆V > 0; (e) MPPT when The of PVwhen module ∆P >output 0 and ∆Vpower < 0; (f) MPPT ∆P < will 0 andbe ∆Vzero > 0. when the photovoltaic current (IPV ) is equal to the short circuit current (ISC ) or the photovoltaic voltage (VPV ) is equal to the open circuit voltage (VOC ). power of PVthe module will bepower zero when the(MPP) photovoltaic current (IPV) cell is equal to the Thus, The it is output possible to track maximum point of a photovoltaic by regulating the short circuit current SC) or the photovoltaic voltage (V PV ) is equal to the open circuit voltage (V OC). operating voltage of(IV . In [45] Maximum Power Point Tracking is discussed for a reconfigurable PV Thus, it is possible to track the and maximum point (MPP) of observation a photovoltaic(P&O) cell byalgorithm regulating is the switched-capacitor converter in [46]power a perturbation and discussed operating voltage of VPV. In [45] Maximum Power Point Tracking is discussed for a reconfigurable for DC-DC converters connected to photovoltaic generators. The concept to control power of a switched-capacitor converter and in [46] a perturbation and observation (P&O) algorithm is multistage magnetic component-free DC-DC converter is explained in Figure 6b–f. Thus, to regulate discussed for DC-DC converters connected to photovoltaic generators. The concept to control power the operating voltage V component-free , the ON timeDC-DC of the converter capacitorisand number of stages (if the structure is of a multistage magneticPV explained in Figure 6b–f. Thus, to reconfigurable) are two controlled parameters in the proposed therefore it forces the MPPT regulate the operating voltage VPV, the ON time of the capacitor system, and number of stages (if the charge controller to extract the maximum power PV module to operate at a voltage close structure is reconfigurable) are two controlled parameters in the proposed system, therefore it forces to the maximum point which causesthe it maximum to draw the maximum available power theclose PV module. the MPPT power charge controller to extract power PV module to operate at afrom voltage to the maximum power point which it tofor draw maximum available power from systems the PV where The proposed converter is alsocauses suitable thethe DC link application in DC-AC module. voltage balancing is the main challenge. The proposed converter also provides a viable capacitor Thefor proposed converter is also suitable for the DC and link transformers application in are DC-AC systems where solution low power applications, since inductors not required to design the capacitor voltage balancing is the main challenge. The proposed converter also provides a viable proposed converter. solution for low power applications, since inductors and transformers are not required to design the converter. 2.proposed Recent Transformer-Less and Inductor-Less DC-DC Converters 2. Recent and Inductor-Less Converters In thisTransformer-Less section recent transformer-less andDC-DC inductor-less DC-DC converter power circuit topologies and their drawbacks are discussed in detail. Various multilevel DC-DC converters and switched In this section recent transformer-less and inductor-less DC-DC converter power circuit capacitor topologies inductor were recently in the literature. topologies and their without drawbacks are discussed in detail.addressed Various multilevel DC-DC converters and switched capacitor topologies without inductor were recently addressed in the literature. 2.1. Series-Parallel Switched Capacitor (SC) Converter 2.1. Series-Parallel Switched Capacitor (SC) Converter In [47–49], a series-parallel switched capacitor (SPSC or series-parallel SC) converter using only Inswitching [47–49], a series-parallel switched capacitor (SPSC or series-parallel SC) converter using only control elements and capacitors was proposed. In Figure 7a three-level series-parallel SC control switching elements and capacitors was proposed. In Figure 7a three-level series-parallel SC converter is depicted. The operation of this topology is simple and divided into only two modes (two converter states is depicted. operation of this is in simple divided into two modes switching only). The All the switches are topology controlled such and a way that all theonly capacitors are charged (two switching states only). All the switches are controlled in such a way that all the capacitors are in series and discharged in parallel. The conversion ratio of an N-level series-parallel SC converter charged in series and discharged in parallel. The conversion ratio of an N-level series-parallel SC is 1/N (in step-down mode) and N times (in step-up mode). More than 90% efficiency is reported in converter is 1/N (in step-down mode) and N times (in step-up mode). More than 90% efficiency is the literature. reported in the literature. (a) (b) Figure 7. (a) Three–Level Series-Parallel Switched Capacitor (Series-Parallel SC) Converter; (b) Flying Capacitor Multilevel DC-DC Converter (FCMDC). Energies 2017, 10, 719 7 of 28 However the series-parallel SC converter has following drawbacks: 1. 2. 3. 4. 5. Difficult to change the switching state of the converter due to the several switching elements. Unequal voltage across switches, thus power switches of various ratings are required. Series-parallel SC is bidirectional, but it is not possible to control the power flow. It depends on the voltages at the input and output DC buses. If switching is not properly controlled, it may instigate a charge unbalance situation among the converter capacitors. Non-modularity, since a large number of switches, gate drivers and diodes are required and the number of devices increases with the number of levels. Due to this a series parallel converter is large in size and has high cost. 2.2. Flying Capacitor Multilevel DC-DC Converter (FCMDC) In [49–51], flying capacitor multilevel DC-DC converter (FCMDC) is proposed. Figure 7b depicts the power circuit of a three–level FCMDC. The conversion ratio of an N-level FCNDC is 1/N (in step-down mode) and N times (in step-up mode). FCMDC is a bidirectional converter with efficiency higher than 95%. The voltage stress of switches is also equal and thus requires same rating of the switching devices. Nevertheless FCMDC has the following drawbacks: 1. 2. 3. 4. 5. A large number of transistors and capacitors is required (2N the number of switches and N number of capacitors are required to design an N-level FCMDC), hence this converter is large in size and also has a high cost. Difficult to extend the power circuit to increase the number of stages to change the output conversion ratio since the converter does not have a modular structure. A complicated switching scheme is required to operate the converter. FCMDC is inefficient at high switching frequency when the ON time is comparable to the rise and fall time of the switches since; to transfer energy from the input source to the capacitors a very small time frame is allowed. Utilization of components is less. It is not possible to control the power circuit if any of the switches fails. 2.3. Magnetic-Less Multilevel DC-DC Converter (MMDC) In [52], a magnetic-less multilevel DC-DC converter (MMDC) is proposed by connecting two transistor and one capacitor switching cells (modular block) in a mesh pattern. Figure 8 depicts the power circuitry of the three-level MMDC. The conversion ratio of an N-Level MMDCC is 1/N (in step-down mode) and N times (in step-up mode). The voltage stress of each transistor of the switching cells is the same and equal to Vin and also it is independent of the duty cycle and conversion ratio of the converter. However, the following are the drawbacks of the MMDC: 1. 2. 3. A very large number of switching devices and capacitors are required to design an MMDC N (N + 1) switches, N (N + 1) diodes and 0.5N (N + 1) capacitors are required to design the N-Level MMDCC. It is difficult to manage direction of power flow of the converter due to the greater number of transistors present in the conducting path. The power flow of the converter is also depends on the voltages at the input and output DC buses, thus it is not a good option for the applications where the source voltage may vary. Energies 2017, 10, 719 8 of 28 Energies 2017, 10, 719 8 of 28 Energies 2017, 10, 719 8 of 28 Figure 8. Three-Level Magnetic-Less Multilevel DC-DC Converter (MMDC). Figure 8. Three-Level Magnetic-Less Multilevel DC-DC Converter (MMDC). 2.4. Fibonacci DC-DC Converter 2.4. Fibonacci DC-DC Converter In [53], a Fibonacci DC-DC converter is proposed using capacitors and switching device Figure 8. Three-Level Magnetic-Less Multilevel DC-DC Converter (MMDC). In [53], a Fibonacci DC-DC converter is proposed using capacitors and switching device circuitry. circuitry. The voltage conversion ratio of the converter follows the well-known Fibonacci series. Figure 9 depicts the power circuitry of the three stage-Fibonacci converter. High voltage is achieved The voltage conversion ratio of the converter follows the well-known Fibonacci series. Figure 9 depicts 2.4. Fibonacci DC-DC Converter but it circuitry still requires large stage-Fibonacci number of switching devices andvoltage capacitors. The following are requires the the power of thea three converter. High is achieved but it still In [53], Fibonacci DC-DC converter is proposed using capacitors and switching device drawbacks of athe Fibonacci DC-DCand converter: a large number of switching devices capacitors. The following are the drawbacks of the Fibonacci circuitry. The voltage conversion ratio of the converter follows the well-known Fibonacci series. DC-DC 1. converter: A large number of control switches are required to design the converter (3N + 1 number of 1. 2. 3. Figure 9 depicts the power circuitry of the three stage-Fibonacci converter. High voltage is achieved control switchesaare required to design an N-stage converter) but it still requires large number of switching devices and capacitors. The following are the A large number of DC-DC control switches are required to design series the converter + 1not number of control 2. The Fibonacci converter follows the Fibonacci and thus(3N it is possible to drawbacks of the Fibonacci DC-DC converter: switches arevoltage required to design an N-stage achieve conversion ratios like 2, 4…converter) (which are not present in the Fibonacci converter) 1. Fibonacci A islarge number control switches required to design the converter (3N possible + 1 number of 3. It not capable ofoftransferring powerare inthe both directions. The DC-DC converter follows Fibonacci series and thus it is not to achieve control switches are required to design an N-stage converter) voltage conversion ratios like 2, 4 . . . (which are not present in the Fibonacci converter) 2. The Fibonacci DC-DC converter follows the Fibonacci series and thus it is not possible to It is not capable of transferring power directions. achieve voltage conversion ratios likein 2, both 4… (which are not present in the Fibonacci converter) 3. It is not capable of transferring power in both directions. Figure 9. Three-Level Fibonacci DC-DC converter. 2.5. Modified Step-Up DC-DC Converter (Switch Mode DC-DC Converter) In [54], a modified step-up DC-DC converter (switch mode DC-DC converter) is proposed Figure 9. Three-Level Fibonacci DC-DC converter. Figure 9. Three-Level converter. which has continuous input current capability. Fibonacci Figure 10 DC-DC depicts the switch mode DC-DC converter. Its power circuitry is divided into two parallel parts. A detailed study 2.5. Modified Step-Up DC-DC Converter (Switch Mode DC-DC Converter) about the mode of operation and capacitor state is given in Table(Switch 1. The operation of theConverter) proposed converter is simple and the 2.5. Modified Step-Up DC-DC Converter Mode DC-DC In [54],ratio a modified step-up isDC-DC converter (switch modecycle. DC-DC converter) proposed conversion of the converter adjusted by varying the duty In addition, theiscontinuous which has continuous input current capability. Figure 10 depicts the switch mode DC-DC converter. In [54],current a modified step-up DC-DC converter (switch mode DC-DC converter) is proposed which input from low voltage input sources reduces the EMI problem. Its power circuitry is divided into twoFigure parallel A detailed study about the mode of operation has continuous input current capability. 10parts. depicts the switch mode DC-DC converter. Its power andiscapacitor given in Table 1. The operation of the proposed converter is simpleand andcapacitor the circuitry dividedstate into is two parallel parts. A detailed study about the mode of operation conversion ratio of the converter is adjusted by varying the duty cycle. In addition, the continuous state is given in Table 1. The operation of the proposed converter is simple and the conversion ratio of input current from low voltage input sources reduces the EMI problem. the converter is adjusted by varying the duty cycle. In addition, the continuous input current from low voltage input sources reduces the EMI problem. Energies 2017, 10, 719 9 of 28 Energies 2017, 10, 719 9 of 28 Energies 2017, 10, 719 9 of 28 Figure 10. Modified Step-up DC-DC Converter (Switch Mode DC-DC Converter). Figure 10. Modified Step-up DC-DC Converter (Switch Mode DC-DC Converter). Table 1. Mode of operation and state of capacitors of Modified Step-up DC-DC Converter. Table 1. Mode of operation and state of capacitors of Modified Step-up DC-DC Converter. Operation Mode Switches State Capacitors of Capacitors of Figure 10. Modified Step-up DC-DC Converter (Switch Mode DC-DC LeftConverter). Part Right Part S1 S2 S3 S4 S5 S6 S7 S8 Switches State (Section-I) (Section-II) Capacitors of Left Capacitors of Right Operation Mode-I Table OFF ONstate ONcapacitors ON PartOFF Discharging 1. Mode ofS3operation Step-up Charging DC-DC Converter. (Section-I) Part (Section-II) Mode S1OFF S2 ON S4 and S5 S6of S7 OFFS8of Modified Mode-II Mode-I Mode-III Operation Mode-II Mode-III Mode Mode-III Mode-III Mode-I OFF OFF OFFON ON OFF OFF OFFON OFF OFF OFF S1 S2 ON OFF ON ONOFFOFF ON ON OFF OFF ON OFF ON Switches ON State ON OFF OFF OFF ON ONOFF OFF ON OFF ONOFFOFF ON OFF OFF S3 S4 S5 S6 OFF OFF ON OFF ON ON OFF OFF S7 OFF OFF OFF ON OFF ON OFFOFFOFF ON HoweverOFF this converter has theOFF following drawbacks: Mode-II OFF OFF ON OFF ON Mode-III ON OFF ON OFF OFF ON OFF 1. A large number of switching devices is required. Mode-III thisON OFF has ON OFF OFFdrawbacks: OFF OFF However converter the following OFF No action OFF ON OFF No action Discharging Discharging Charging Capacitors of ON Discharging Left Part No actionDischarging OFF S8 Discharging(Section-I) Discharging OFF Charging Discharging Discharging Capacitors Chargingof Right Part Discharging No Action (Section-II) Charging NoDischarging Action Discharging Charging No Action 2. It introduces high switching losses and thus the efficiency of the converter is less. 3. Moreover, there is no extension of the circuit to increase the voltage conversion ratio. However thisof converter hasdevices the following drawbacks: 1. A large number switching is required. 4. This converter is not suitable for high power high voltage applications due to the lower voltage 2. It introduces high switching losses andisthus the efficiency of the converter is less. 1. A large number of switching devices required. conversion ratio. 2. It introduces and thus the efficiencythe of the converter is less. ratio. 3. Moreover, there high is noswitching extensionlosses of the circuit to increase voltage conversion 3. Moreover, there is no extension of the circuit to increase the voltage conversion 2.6. Switched Capacitor DC-DC Converter 4. This converter is not suitable for high power high voltage applications due toratio. the lower voltage 4. This converter is not suitable for high power high voltage applications due to the lower voltage conversion In [55], aratio. new switched capacitor DC-DC converter with low ripple input current is proposed. conversion ratio. Figure 11 depicts the power circuit of the converter. The low ripple and continuous input current 2.6. Switched Capacitor DC-DC help to reduce EMI of the Converter circuit. However this circuit has no provision to increase the voltage 2.6. Switched Capacitor DC-DC Converter conversion ratio. In [55], a new switched capacitor DC-DC converter with low ripple input current is proposed. In [55], a new switched capacitor DC-DC converter with low ripple input current is proposed. Figure 11 depicts the the power circuit The low lowripple rippleand and continuous input current Figure 11 depicts power circuitofofthe theconverter. converter. The continuous input current help help to reduce EMIEMI of the circuit. circuithas hasnonoprovision provision increase voltage to reduce of the circuit.However However this this circuit to to increase the the voltage conversion ratio.ratio. conversion Figure 11. Switched Capacitor DC-DC Converter. 2.7. Multilevel Modular Capacitor Clamped DC-DC Converter (MMCCC) Figure 11. Switched Capacitor DC-DC Converter. Figure 11. Switched Capacitor DC-DC Converter. 2.7. Multilevel Modular Capacitor Clamped DC-DC Converter (MMCCC) Energies 2017, 10, 719 10 of 28 2.7. Multilevel Modular Capacitor Clamped DC-DC Converter (MMCCC) Energies 2017, 10, 719 10 of 28 In [56], a multilevel modular capacitor clamped DC-DC converter (MMCCC) is proposed. 2017, 10, 719 10 of 28 of Figure Energies 12 In depicts power circuit of the MMCCC for five levels.converter The following are the drawbacks [56], athe multilevel modular capacitor clamped DC-DC (MMCCC) is proposed. Figure 12 depicts the power circuit of the MMCCC for five levels. The following are the drawbacks the MMCCC: 1. 2. In [56], a multilevel modular capacitor clamped DC-DC converter (MMCCC) is proposed. of the MMCCC: Figurethis 12 depicts theapower circuit ofconversion the MMCCC for is five levels. The areathe drawbacks Using topology high voltage ratio achieved, butfollowing it requires large number of 1.of the Using this topology a high voltage conversion ratio is achieved, but it requires a large number MMCCC: switching devices and capacitors. of switching devices and capacitors. 1. Using this topology a switches high voltage conversion ratio is achieved, but itlevel requires a large number The voltage stress across ofofthe high. For N MMCCC the voltage 2. The voltage stress across switches the converter converter isishigh. For anan N level MMCCC the voltage of switching devices and capacitors. stress of N-2 devices is equal to 2V and thethe remaining switches have VinVinvoltage stress of switching N-2 switching devices is equal toin2V in and remaining switches have voltagestress. 2. stress. The voltage stress across switches of the converter is high. For an N level MMCCC the voltage stress of N-2 switching devices is equal to 2Vin and the remaining switches have Vin voltage stress. Figure 12. Multilevel Modular Capacitor Clamped DC-DC Converter (MMCCC). Figure 12. Multilevel Modular Capacitor Clamped DC-DC Converter (MMCCC). Figure 12. Multilevel ModularComponent-Free Capacitor ClampedMultistage DC-DC Converter (MMCCC). 3. Proposed Self-Balanced and Magnetic DC-DC Converter 3. Proposed Self-Balanced and Magnetic Component-Free Multistage DC-DC Converter 3. Proposed Self-Balanced and Magnetic Component-Free Multistage DC-DC Converter 3.1. Mode of Operation 3.1. Mode of Operation power circuit of the proposed self balanced and magnetic component-free (transformer-less 3.1.The Mode of Operation The circuit of the proposed selfconverter balanced for andKmagnetic (transformer-less and power inductor-less) multistage DC-DC stages iscomponent-free depicted in Figure 13. The The power circuit of the proposed self balanced and magnetic component-free (transformer-less conspicuous features of theDC-DC proposed topologyfor are:K(i)stages it is magnetic components free; continuous and inductor-less) multistage converter is depicted in Figure 13.(ii) The conspicuous and current; inductor-less) multistage DC-DC converterdevices for K and stages is depictedmodularity; in Figure (v) 13.easy The input (iii) lowtopology voltage rating semiconductor capacitors; features of the proposed are: (i) it is magnetic components free; (ii)(iv) continuous input current; conspicuous features of the proposed topology are: (i) it is magnetic components free; (ii) continuous to add a higher number of levels to increase (vi) only control switches aretoused (iii) low voltage rating semiconductor devicesthe andvoltage; capacitors; (iv)two modularity; (v) easy addwith a higher input current; (iii) low voltage rating control. semiconductor devicesDC-DC and capacitors; modularity; easy alternating operation; and (vii) simple The proposed converter(iv) topology is free(v) from number of levels to increase the voltage; (vi) only two control switches are used with alternating to add a higher number of levels to increase the voltage; (vi) only two control switches are used with magnetic components like inductors and it is designed for unidirectional power transfer operation; and (vii) simpleand control. The proposed DC-DC converter topologytopology is free from magnetic alternating operation; (vii) simple control. The DC-DC converter is free from applications. The proposed topology provides an proposed output voltage higher than the input voltage components like inductors and it is designed for unidirectional power transfer applications. The magnetic components like inductors and it is designed for unidirectional power transfer without any magnetic components. The operation at high frequency permits a reduction in the size proposed topology provides an output voltage higher than the input voltage without any magnetic applications. The proposed topology provides an output voltage higher than the input voltage of capacitors thus enabling a reduced size of the circuit without external components. In this withoutThe anyoperation magneticofcomponents. The operation at high frequency permits reduction in theenabling size components. atcontrol high frequency permits a reduction in the size of topology the number switches does not depend on the number of acapacitors levels. The thus required of capacitors thus enabling a reduced size of the circuit without external components. In this a reduced size the circuit withoutdepends externaloncomponents. this topology thediodes number control number of of diodes and capacitors the number ofInoutput levels. Two andoftwo topology the number of control switches does not depend on the number of levels. The required capacitors are required to increase the level of the The proposed converter by one. Thus, to design a switches does not depend on the number of levels. required number of diodes and capacitors number of diodesstep-up and capacitors depends on the number of output levels. Two diodes and two 4-stage proposed DC-DC converter topology, two control switches, eight uncontrolled depends on the number of output levels. Two diodes and two capacitors are required to increase the capacitors are and required to increaseare therequired. level of the proposed converter by one. Thus, to design a diodes) eight capacitors level (power of the proposed converter by one. Thus, to design a 4-stage proposed step-up DC-DC converter 4-stage proposed step-up DC-DC converter topology, two control switches, eight uncontrolled topology, two control switches, eight uncontrolled (power diodes) and eight capacitors are required.(power diodes) and eight capacitors are required. Figure 13. Self-balanced and magnetic component-free multistage converter for K stages. 13. Self-balanced magnetic component-freemultistage multistage converter KK stages. FigureFigure 13. Self-balanced andand magnetic component-free converterfor for stages. Energies 2017, 10, 719 11 of 28 ToEnergies explain operation modes of the proposed magnetic component-free K-stages converter 2017,the 10, 719 11 of 28 circuit the following is considered. The mode of operation of the converter is divided into two modes: Energies 10, 719 11 of 28 To2017, explain modes the proposed magneticON) component-free converter Mode 1 when switchtheSboperation and Sa act as aofshort circuit (turned and open K-stages circuit (turned OFF) circuit the following is considered. The mode of operation of the converter is divided into two respectively, Mode when switch Sb act as amagnetic short circuit (turned ON) and converter open circuit Toand explain the 2operation modesSaofand the proposed component-free K-stages modes: Mode 1 when switch Sb and Sa act as a short circuit (turned ON) and open circuit (turned (turnedcircuit OFF),the respectively. switch switch S are in operation. following is Hence, considered. The Smode of operation of complementary the converter is divided into twoThe a and OFF) respectively, and Mode 2 when switch Sa and Sb act bas a short circuit (turned ON) and open modes: Mode 1 when switch Sb andand Sa actoperated as a shortat circuit (turned ON) open (turned proposed topology simple control fixed cycleand of 0.5 tocircuit provide voltage circuit (turned has OFF), respectively. Hence,isswitch Sa and aswitch Sduty b are complementary in operation. OFF) respectively, and Mode 2 when switch Sis a and Sbnot act required as a short to circuit (turned ON) and open an to photovoltaic devices. A complex gate driver also drive the switch; instead The proposed topology has simple control and is operated at a fixed duty cycle of 0.5 to provide circuit (turned OFF), respectively. Hence, switch Sa and switch Sb are complementary in operation. oscillator is sufficient to provide a gated signal. voltage to photovoltaic devices. A complex gate driver is also not required to drive the switch; The proposed topology has simple control and is operated at a fixed duty cycle of 0.5 to provide is sufficient a gated Ininstead Modean 1 oscillator (Figure 14), switch to Sbprovide is turned ONsignal. and switch Sa is turned OFF, capacitor C12 is voltage to photovoltaic devices. A complex gate driver is also not required to drive the switch; Modevoltage 1 (Figure 14), switch Sb D is11turned ON and a is voltage turned OFF, capacitor C12 C is12 is charged byIninput through diode and switch S switch when Sthe across capacitor instead an oscillator is sufficient to provide a gated signal.b charged by input voltage through diode D 11 and switch Sb when the voltage across capacitor C12 is smaller than input voltage.14), When theSvoltage across capacitors C a is+ turned C22 is smaller than theCvoltage Inthe Mode 1 (Figure switch b is turned ON and switch S12 OFF, capacitor 12 is than the input stored voltage. When the voltage across capacitors C 12 + C22 is smaller than the VC11 +smaller V , then the energy in the capacitor C is transferred to capacitor C through D1221isand in 11 22capacitor C charged by input voltage through diode D11 and switch Sb when the voltage across voltage VC11 + Vin, then the energy stored in the capacitor C11 is transferred to capacitor C22 through switch smaller S . Similarly capacitor C(k-1)1 transfers energyacross to C capacitors when the capacitors than the input voltage. When theits voltage C12voltage + C22 isacross smaller than the C D21b and switch Sb. Similarly capacitor C(k-1)1 transfers its K2 energy to CK2 when the voltage across 12 voltage C11is + smaller Vin, then than the energy stored the to capacitor C22D through + C22 +capacitors . . . + CVK2 voltage Vin +inV +C +C.11. is . +transferred VC(K-1)1 through diode C11capacitor K1 . In this C12 + C22 +… + CK2 is smaller than voltage VC21 in + VC11 + CC21 +… + VC(K-1)1 through diode DK1. D21 output and switch Sb. Similarly capacitor C(k-1)1 transfers its energy to C K2 when the voltage across mode the voltage is equal to the input voltage (V ) + V +V + . . . + V . in C21 CK1 In this mode the output voltage is equal to the input voltage (VC11 in) + VC11 +VC21 +…+VCK1 . capacitors C12 + C22 +… + CK2 is smaller than voltage Vin + VC11 + CC21 +… + VC(K-1)1 through diode DK1. In this mode the output voltage is equal to the input voltage (Vin) + VC11+VC21 +…+VCK1. 14. Switch b of proposed magnetic component free multistage DC-DC converter is ON. FigureFigure 14. Switch Sb ofSproposed magnetic component free multistage DC-DC converter is ON. Switch S15), b of proposed magnetic component free multistage DC-DC converter is ON. In Figure Mode 14. 2 (Figure control switch Sa is turned ON and switch Sb is turned OFF, when the Involtage Modeacross 2 (Figure 15), control switch Sa capacitor is turnedCON and switch Sb is is charged turned OFF, when the capacitor C11 is smaller than 12, then capacitor C11 by capacitor In Mode 2 (Figure 15), control switch S a is turned ON and switch S bCis turned OFF, when the voltageC12across capacitor C is smaller than capacitor C , then capacitor is charged by capacitor through diode D1211 and switch Sa. When the voltage12across capacitor C11 11 + C21 is smaller than the voltage across capacitor C 11 is smaller than capacitor C12, then capacitor C11 is charged by capacitor C12 through Sa22., When the voltage across capacitor C11 C21 is smaller than the voltagediode acrossDcapacitor C12 + C then capacitor C22 transfers its energy to +capacitor C21 through 12 and switch C12 through diode D12 and switch Sa. When the voltage across capacitor C11 + C21 is smaller than the and switch Sa. +Similarly capacitor CK2 C transfers its energy to capacitor CK1 through DK2 diode D22capacitor voltage across C12 C22 , then capacitor its energy to capacitor C21 through 22 transfers voltage across capacitor C12 + C22, then capacitor C22 transfers its energy to capacitor C21 through the switch voltage S across capacitor C 11 + C21+…+ C k1 is smaller than the voltage C 12 +CC 22 + C K2. In thisD diode when D22 and . Similarly capacitor C transfers its energy to capacitor through a Sa. Similarly capacitor K2 CK2 transfers its energy to capacitor CK1K1 through DK2 K2 diode D22 and switch mode the output voltage is equal to+the input voltage (Vsmaller in) + VC12 + VC22 + …+ VCK2. when the voltage across capacitor C C + . . . + C is than the voltage C + CK222. In +C 11 21 12 K2 . In k1 when the voltage across capacitor C11 + C21+…+ Ck1 is smaller than the voltage C12 +C22 + C this this mode the output voltage is equal to the input voltage (V ) + V + V + . . . + V . in C12 C22 CK2 mode the output voltage is equal to the input voltage (Vin) + VC12 + VC22 + …+ VCK2. Figure 15. Switch Sa of proposed magnetic component free multistage DC-DC converter is ON. Figure 15.Analysis Switch a of proposed magnetic component free multistage DC-DC converter is ON. Figure 15. Gain Switch Sa ofSproposed magnetic component multistage DC-DC converter is ON. 3.2. Voltage of a Multistage Converter withoutfree Diode and Switches Loss When the voltage drop across diodes and switches are not considered, all capacitors are subjected to the same voltage Vin. The voltage conversion ratio or voltage gain is equal to the (K + 1) When the voltage drop across diodes and switches are not considered, all capacitors are i.e., number of stages +1 across and also depends number of Figure 16a,b depict theare graphs of When the voltage drop diodes andonswitches arecapacitors. not considered, all capacitors subjected subjected to the same voltage Vin. The voltage conversion ratio or voltage gain is equal to the (K + 1) the required number of devices/components versus the number of stages in 2-dimensional and in to the same voltage or voltage gain Figure is equal to the (K +the 1) graphs i.e., number in . The i.e., number ofV stages +1 voltage and alsoconversion depends on ratio number of capacitors. 16a,b depict of 3-dimensional view, respectively. From Figure 16a,b it is observed that the number of of stages and also depends on number of capacitors. Figure 16a,b graphs of theand required the+1 required number of devices/components versus the number of depict stages the in 2-dimensional in devices/components linearly increases as the number of stages is increased. Thus, with each stage number of devices/components versus the number stagesitin is 2-dimensional andthe in 3-dimensional 3-dimensional view, respectively. From Figureof 16a,b observed that number of devices/components linearly16a,b increases as the number is increased. Thus, with each stage view, respectively. From Figure it is observed that of thestages number of devices/components linearly 3.2. Voltage Gain Analysis of a Multistage Converter without Diode and Switches Loss 3.2. Voltage Gain Analysis of a Multistage Converter without Diode and Switches Loss Energies 2017, 10, 719 12 of 28 increases as2017, the 10, number of stages is increased. Thus, with each stage increase two more diodes Energies 719 12 of 28 and capacitors are needed. It is also observed that the number of diodes is equal to the number of capacitors. increase two more diodes and capacitors are needed. It is also observed that the number of diodes is equal to the number of capacitors. VC11 = VC12 = VC21 = VC22 = VCK2 = Vin (1) Vo = (K + 1) × Vin (2) KC + 2 × Vin 2 K +2 = D × Vin 2 Vo = (3) Vo (4) KC = KD = 0.5 K (5) where, KC and KD number of capacitor and diode used to design the proposed circuit. The graph of voltage gain versus number of stages is shown in Figure 17a. It is observed that the proposed converter with K stages provides a K + 1 voltage conversion ratio. The graph of the number of stage (a) (b) devices/components versus voltage gain is shown in Figure 17b. It is observed thatview; the (b) number of Figure 16. Number of devices/components versus the number of stages (a) 2-dimensional Energies 2017, 10, 719 12 of 28 devices/components increases as the voltage gain requirement is increased. Thus, two diodes 3-dimensionallinearly view. and two capacitors need to be connected to increase voltage gain by a factor of 1. It is also observed increase two more diodes and capacitors are needed. It is also observed that the number of diodes is that 2equal K diodes 2 K of capacitors are to attain to the and number capacitors. V required =V =V = V a=voltage V = Vgain K + 1. C11 C12 C21 C22 CK2 in Vo = (K + 1) × Vin KC + 2 × Vin 2 KD + 2 Vo = × Vin 2 Vo = KC = KD = 0.5 K (1) (2) (3) (4) (5) where, KC and KD number of capacitor and diode used to design the proposed circuit. The graph of voltage gain versus number of stages is shown in Figure 17a. It is observed that the proposed converter with K stages provides a K + 1 voltage conversion ratio. The graph of the number of stage (a) (b) devices/components versus voltage gain is shown in Figure 17b. It is observed that the number of Figure 16. Number linearly of devices/components the number stages (a) 2-dimensional view; (b) two devices/components increases as versus the voltage gain ofrequirement is increased. Thus, Figure 16. Number of devices/components versus the number of stages (a) 2-dimensional view; 3-dimensional view. diodes and two capacitors need to be connected to increase voltage gain by a factor of 1. It is also (b) 3-dimensional view. observed that 2 K diodes and 2 K capacitors are required to attain a voltage gain K + 1. VC11 = VC12 = VC21 = VC22 = VCK2 = Vin (1) Vo = (K + 1) × Vin (2) KC + 2 × Vin 2 KD + 2 Vo = × Vin 2 Vo = KC = KD = 0.5 K (3) (4) (5) where, KC and KD number of capacitor and diode used to design the proposed circuit. The graph of voltage gain versus number that the proposed (a) of stages is shown in Figure 17a. It is observed (b) converter with K stages provides a K + 1 voltage conversion ratio. The graph of the number of stage devices/components versus voltage gain isFigure shown Figure 17b. It is observed that the number of 17.inCont. devices/components linearly increases as the voltage gain requirement is increased. Thus, two diodes and two capacitors need to be connected to increase voltage gain by a factor of 1. It is also observed that 2 K diodes and 2 K capacitors are required to attain a voltage gain K + 1. Energies 2017, 10, 719 13 of 28 Energies 2017, 10, 719 13 of 28 (c) (d) Figure 17. Relations of converter parameters: (a) graph of voltage gain versus number of stages; (b) Figure 17. Relations of converter parameters: (a) graph of voltage gain versus number of stages; graph of the number of devices/component versus voltage gain; (c) graph of the voltage gain (Vo/Vin), (b) graph of the number of devices/component versus voltage gain; (c) graph of the voltage gain number of stages (K) and duty cycle (D); (d) output voltage for stage 1 to 9 for 25 V input voltage. (Vo /Vin ), number of stages (K) and duty cycle (D); (d) output voltage for stage 1 to 9 for 25 V inputThe voltage. graph of voltage gain (Vo/Vin), number of stages (K) and duty cycle (D) is shown in Figure 17c. It is observed that two capacitors and two diodes are required to design one stage of the proposed graph of output voltage for stages 1 to 9 by considering an input voltage of The graphconverter. of voltageThe gain (Vo /V in ), number of stages (K) and duty cycle (D) is shown in Figure 17c. 25 V is shown in Figure 17d. It is observed that the output voltage is increased as the number of It is observed that two capacitors and two diodes are required to design one stage of the proposed stages increases, and each stage contributes a voltage equal to the input voltage (25 V) to an output converter. The graph of output voltage for stages 1 to 9 by considering an input voltage of 25 V is voltage of the proposed converter. shown in Figure 17d. It is observed that the output voltage is increased as the number of stages increases, and each contributes a voltage equalwith to the input 3.3. Voltage Gainstage Analysis of the Multistage Converter Diode andvoltage Switches(25 LossV) to an output voltage of the proposed converter. The voltage drop across power diodes and switches is ignored in medium and high power applications, but in low power applications it is considered. The analysis of the circuit is done with 3.3. Voltage Gain Analysis of the Multistage Converter with Diode and Switches Loss consideration of the voltage drop across diodes and switches. For simplicity, the voltage drop across diodes and switches is assumed to bediodes equal toand Vd. switches is ignored in medium and high power The voltage drop across power applications, but in low power applications it is considered. The analysis of the circuit is done with consideration of the voltage drop across For simplicity, the voltage drop (6) across VC11diodes = VC12 −and VD12 switches. − VSa diodes and switches is assumed to be equal to Vd . VC11 = Vin − 4Vd VC11V ==VV VD12 − VSa C12− − 2V C12 in (7) (8) d Vin − −V4V=dV − 4V VC21 = VC12 + VC22V−C11 VC11=− V D22 Sa in d V = V − 2V in C12 d V = V + V − V − V − V = V − 4V (9) (6) (7) (10) (8) VC21 = VC12 + VC22 V −=VVC11 −− 4VVD22 − VSa = Vin − 4Vd (11) (9) VC22 = Vin + VC11 − =VV Vd D21 − VSb = Vin − 4Vd VCK2 −−4V C12 in (12) (10) C22 in C11 C12 CK1 D21 in Sb in d d Vin − 4Vd is equal to Vin − 4Vd except for the (11) CK1 =each It is investigated that the voltageVacross capacitor voltage across capacitor C12. The voltage across capacitor C12 is equal to Vin − 2Vd. Thus, the proposed VCK2 = Vin − 4V (12) topology is self-balanced and magnetic component-free. dThe output voltage of the converter is by the devices’ forward voltage andeach number of devices. Itlimited is investigated that the voltage across capacitor is equal to Vin − 4Vd except for the voltage The graph output voltage of 2V stages with a practical across capacitor C12of. the Theproposed voltage converter across capacitor C12 is versus equal number to Vin − d . Thus, the proposed diode (Vd = 1) and ideal diode is shown in Figure 18a. The graph of the proposed converter output topology is self-balanced and magnetic component-free. The output voltage of the converter is limited voltage versus number of diodes or capacitors with a practical diode (Vd = 1) and an ideal diode is by the devices’ forward voltage and number of devices. shown in Figure 18b. From Figure 18a,b it is observed that the difference between the ideal and The graph of the proposed converter output voltage versus number of stages with a practical practical output voltage increases as the number of stages, diodes and capacitor requirement is diodeincreased. (Vd = 1) The anddifference ideal diode is shown in Figure 18a. The graph of thedepends proposed converter between the ideal and practical output voltage on the number output of voltage versus number of diodes or capacitors with a practical diode (V = 1) and an ideal diode is d (15). stages of the proposed converter and it is equal to 4KVd as given in Equation shown in Figure 18b. From Figure 18a,b it is observed that the difference between the ideal and practical output voltage increases as the number of stages, diodes and capacitor requirement is increased. The Energies 2017, 10, 719 14 of 28 difference between the ideal and practical output voltage depends on the number of stages of the Energiesconverter 2017, 10, 719and it is equal to 4KV as given in Equation (15). 14 of 28 proposed d Energies 2017, 10, 719 VC11V= V = V=CK1 VCK1 = Vin − 4Vd = C21 V = = VVC22 =V V == V − 4V C11 C21 C22 CK1 CK1 in d VVC12C12 = V= −Vin 2V− 2Vd VC11 = VC21 = VC22 = VCK1 in= VCK1 =d Vin − 4Vd V0==(K(+ K1)V + 1)−V4KV in − 4KVd V 0 in d V = Vin − 2V C12 d (13) (14) (13) (15) (14) V0 = (K +1)Vin − 4KVd (a) 14 of 28 (13) (14) (15) (15) (b) Figure 18. Comparison graph considering Vin = 24 V. (a) Graph of converter output voltage versus Figure 18. Comparison graph converter output voltage versus (a) considering V = 24 V. (a) Graph of(b) number of stages (practical and ideal diode);in (b) graph of converter output voltage versus number of number of stages (practical and ideal diode); (b) graph of converter output voltage versus number of diodes capacitors (practical and ideal diode). Figure 18.or Comparison graph considering Vin = 24 V. (a) Graph of converter output voltage versus diodes or capacitors (practical and ideal diode). number of stages (practical and ideal diode); (b) graph of converter output voltage versus number of 4. Design of the Capacitors of the Proposed Converter diodes orCalculation capacitors (practical and ideal diode). 4. DesignTo Calculation the Capacitors Converter explain the of designed calculationofofthe theProposed proposed converter a 1-stage proposed converter is 4. Design Calculation of the Capacitors of the Proposed Converter considered. The designed power circuit of the 1-stage converter is shown in Figure 19a. The ON To explain the calculation of theproposed proposed converter a 1-stage proposed converter is state and OFF state equivalent circuit of the 1-stage proposed converter is depicted in Figure 19b,c To explain the designed calculation of the proposed converter a 1-stage proposed converter is considered. The power circuit of the 1-stage proposed converter is shown in Figure 19a. The ON respectively, D is the resistance of the diode, is RSshown is the forward of the considered. Thewhere powerRcircuit offorward the 1-stage proposed converter in Figureresistance 19a. The ON state and OFF state equivalent circuit of the 1-stage proposed converter is depicted in Figure 19b,c switch, ISb is state the current through theof switch Sb and proposed ISa is the current through switch in Sa.Figure 19b,c state and OFF equivalent circuit the 1-stage converter is depicted respectively, where RD is the forward resistance of the diode, RS is the forward resistance of the switch, respectively, where RD is the forward resistance of the diode, RS is the forward resistance of the ISb switch, is the current the switch Sb andSbISa isIthe current through switch S S.a. ISb is thethrough current through the switch and Sa is the current through switch a (a) (a) (b) (c) Figure 19. (a) Power circuit of the 1-stage proposed converter; (b) equivalent circuit of 1-stage (b) (c) proposed converter when Sb is ON; (c) equivalent circuit of 1-stage proposed converter when Sa is ON. 19. (a) Power circuit of the 1-stage proposed converter; (b) equivalent circuit of 1-stage Figure Figure 19. (a) Power circuit of the 1-stage proposed converter; (b) equivalent circuit of 1-stage proposed proposed converter when Sb is ON; (c) equivalent circuit of 1-stage proposed converter when Sa is converter when Sb is ON; (c) equivalent circuit of 1-stage proposed converter when Sa is ON. ON. Energies 2017, 10, 719 15 of 28 Initially the voltage across capacitor C12 and C11 is zero. Capacitor C12 is charged through a resistance RD and RS from a supply voltage Vin when switch Sb is closed. The voltage across C12 does not increase to Vin instantaneously, but builds up exponentially and not linearly. C12 d(vC12 ) (RD + RS ) + vC12 dt d(vC12 ) dt Vin −vC12 = (RD +RS )C12 ) Vin = R d(vC12 ) Vin −vC12 = dt (RD +RS )C12 R t log(Vin − VC12 ) = − (R VC12 = Vin (1 − iC12 = (16) −t eT D +RS )C12 + K, K = log Vin (17) ), T = (RD + RS )C12 C d(vC12 ) d(C12 vC12 ) = 12 dt dt (18) Vin = iC12 (RD + RS ) + vC12 (19) Similarly: iSb = −t Vin eT (RD + RS ) (20) Capacitor C11 is charged through a resistance RD and RS from a capacitor C12 voltage when switch Sa is closed. Thus, when switch Sa is closed capacitors C11 and C12 is charging and discharging, respectively. ) VC12 = iC11 (RD + RS ) + vC1 (21) VC12 = iC12 (RD + RS ) + vC11 C11 d(vC11 ) (RD + RS ) + vC11 dt d(vC11 ) dt VC12 −vC11 = (RD +RS )C11 ) VC12 = R d(vC11 ) VC12 −vC11 = (22) dt (RD +RS )C11 R t log(VC12 − VC11 ) = − (R VC11 = VC12 (1 − −t eT D +RS )C11 + K, K = log VC12 ), T = (RD + RS )C11 (23) Similarly: iSa = −t VC12 eT (RD + RS ) (24) In steady state and at high switching frequency, the voltage across capacitor C11 and C12 at any instant during charging is cycled as given in Equations (25) and (26) where, VC0 and VC0 is the initial 11 12 voltage of capacitor C11 and C12 . If the initial storage voltage of C11 and C12 is positive: −t ) VC12 = (Vin − VC0 )(1 − e T ) + VC0 12 −t (25) 12 VC11 = (VC12 − VC0 )(1 − e T ) + VC0 11 11 If the initial storage voltage of C11 and C12 is negative: −t ) VC12 = (Vin + VC0 )(1 − e T ) − VC0 12 −t 12 VC11 = (VC12 + VC0 )(1 − e T ) − VC0 11 (26) 11 The time required for the capacitor C12 to attain any value of VC12 during the charging cycle is given in Equations (27) and (28). Energies 2017, 10, 719 16 of 28 When the initial voltage across the capacitor is positive: t = T log( Vin − VC0 12 Vin − VC12 ) = (RD + RS )C12 log( Vin − VC0 12 Vin − VC12 ) (27) ) (28) When the initial voltage across the capacitor is negative: t = T log( Vin + VC0 12 Vin − VC12 ) = (RD + RS )C12 log( Vin + VC0 12 Vin − VC12 The time required for the capacitor C11 to attain any value of VC11 during the charging cycle is given in Equations (29) and (30). When the initial voltage across the capacitor is positive: t = T log( VC12 − VC0 11 VC12 − VC11 ) = (RD + RS )C11 log( VC12 − VC0 11 VC12 − VC11 ) (29) ) (30) When the initial voltage across the capacitor is negative: t = T log( VC12 + VC0 11 VC12 − VC11 C12 = ) = (RD + RS )C11 log( 1 = 2πfsXC12 C11 == 1 2πfsXC11 VC12 + VC0 11 VC12 − VC11 1 IC12 = VC12 2πfsVC12 2πfs IC12 1 IC11 = = V 2πfsVC11 2πfs C11 IC11 (31) Voltage and current of all the capacitors are the same during the complete switching cycle. Thus the equal rating of all capacitors is suitable to design the proposed converter whose voltage rating is greater than the input voltage. 5. Comparison of Proposed Converter with Recent DC-DC Inductor-less Converters In this section the proposed circuit is compared with recent transformer-less and inductor-less DC-DC converters (discussed in Section 2 of this article) in terms of number of controlled switches, diodes, capacitors, and voltage gain. The requirement of the number of switches to design DC-DC converters is tabulated in Table 2. Table 2. Number of switches required to design different DC-DC converters. Number of Levels/Stages Converter Type 1 2 3 4 5 6 7 8 N SPSC FCMDC MMDC Fibonacci Switch Mode MMCCC Proposed 1 2 2 4 4 1 2 4 4 6 7 8 4 2 7 6 12 10 12 7 2 10 8 20 13 16 10 2 13 10 30 16 20 13 2 16 12 42 19 24 16 2 19 14 56 22 28 19 2 22 16 72 25 32 22 2 3N − 2 2N N(N + 1) 3N + 1 4N 3N − 2 2 It is observed that proposed converter requires less switches compared to other recent transformer-less and inductor-less converters. It is also observed that the requirement of switches is independent of the number of levels of the converter (only two switches are required to design the Energies 2017, 10, 719 17 of 28 proposed converter). It is also observed that the requirement of the number of switches to design and MMCCC is the same. The requirement of the number of diodes and number of capacitors to design DC-DC converters is tabulated in Tables 3 and 4, respectively. It is observed that the proposed converter requires less diodes compared to recently proposed transformer-less and inductor-less DC-DC converters. The maximum number of diodes is required to design the Fibonacci converter. To design SPSC and MMCCC the number of diodes requirement is the same. It is observed that the proposed converter requires less capacitors compared to MMDCC and the switch mode converter. The proposed converter also requires fewer components in total compared to the other converters. In Table 5 voltage conversion ratio of recent inductor-less DC-DC converter is tabulated. Table 3. Number of diodes required to design the DC-DC converters. Number of Levels Converter Type 1 2 3 4 5 6 7 8 N SPSC FCMDC MMDC Fibonacci Switch Mode MMCCC Proposed 1 2 2 4 4 1 2 4 4 6 7 6 4 4 7 6 12 10 8 7 6 10 8 20 13 10 10 8 13 10 30 16 12 13 10 16 12 42 19 14 16 12 19 14 56 22 16 19 14 22 16 72 25 18 22 16 3N − 2 2N N(N + 1) 3N + 1 2N + 2 3N − 2 2N Table 4. Number of capacitors required to design the DC-DC converters. Number of Levels Converter Type 1 2 3 4 5 6 7 8 N SPSC FCMDC MMDC Fibonacci Switch Mode MMCCC Proposed 1 1 1 1 3 1 2 2 2 3 2 5 2 4 3 3 6 3 7 3 6 4 4 10 4 9 4 8 5 5 15 5 11 5 10 6 6 21 6 13 6 12 7 7 28 7 15 7 14 8 8 36 8 17 8 16 N N N(N + 1)/2 N 2N + 1 N 2N Table 5. Voltage conversion ratio of the DC-DC converters. Number of Levels Converter Type 1 2 3 4 5 SPSC FCMDC MMDC Fibonacci Switch Mode MMCCC Proposed 1 1 1 1 2 1 2 2 2 2 3 3 2 3 3 3 3 5 4 3 4 4 4 4 8 5 4 5 5 6 7 8 N 5 6 7 8 N 5 6 7 8 N Not feasible to design for higher levels 6 7 8 9 N+1 5 6 7 8 N 6 7 8 9 N+1 6 7 8 N In Figure 20a–d the proposed converter is compared with DC-DC converters (discussed in Section 2) in terms of number of switches, diodes, capacitors and voltage gain. Graphically it is also observed that the proposed converter provides a viable solution in terms of number of components. In Table 6 the proposed converter is compared in terms of cost. It is calculated that the proposed converter required less cost compared to other DC-DC converters. Only two switches are required to design an N-stage proposed converter hence it requires a simple control circuit. In Figure 20a–d the proposed converter is compared with DC-DC converters (discussed in Section 2) in terms of number of switches, diodes, capacitors and voltage gain. Graphically it is also observed that the proposed converter provides a viable solution in terms of number of components. In Table 6 the proposed converter is compared in terms of cost. It is calculated that the proposed Energies 2017, 10, 719 18 of 28 converter required less cost compared to other DC-DC converters. Only two switches are required to design an N-stage proposed converter hence it requires a simple control circuit. (a) (b) (c) (d) Figure 20. Comparison of the proposed converter with recent transformer-less and inductor-less Figure 20. Comparison proposed recent transformer-less andnumber inductor-less converters (Discussedofinthe Section 2) (a)converter Graph ofwith the number of switches versus of levels/stages; (b) graph of the number of diodes versus number of levels/stages; (c) graph of the converters (Discussed in Section 2) (a) Graph of the number of switches versus number of levels/stages; number capacitors versus numberversus of levels/stages; of the voltage versus of (b) graph of ofthe number of diodes number (d) of graph levels/stages; (c) conversion graph of ratio the number number of levels/stages. (A: SPSC, B: FCMDC, C: MMDC, D: Fibonacci, E: switch mode, F: MMCCC, capacitors versus number of levels/stages; (d) graph of the voltage conversion ratio versus number of G: proposed converter). levels/stages. (A: SPSC, B: FCMDC, C: MMDC, D: Fibonacci, E: switch mode, F: MMCCC, G: proposed converter). Table 6. Cost of the proposed and recent DC-DC converters (discussed in Section 2). Converter Table 6. SPSC FCMDC Converter MMDCC Fibonacci SPSC Switch Mode FCMDC MMCCC MMDCC Proposed Fibonacci Switch Mode MMCCC Proposed Cost of the Converter Cost of the proposed and recent DC-DC converters (discussed in Section 2). (3N − 2) (Cost of each switch + cost of each diode) + N (cost of each capacitor) 2N (Cost of each switch + cost of each diode) + N (cost of each capacitor) Cost ofofthe Converter N(N + 1){(Cost of each switch + cost each diode) + 0.5 (cost of each capacitor)} (3N + 1) (Cost of each switch + cost of each diode) +N (cost of each capacitor) (3N4N−(Cost 2) (Cost of each switch + cost of each diode) + N (cost of each capacitor) of each switch) + 2(N + 1)(cost of each diode) + (2N + 1) (cost of each capacitor) 2N (Cost of(Cost eachofswitch + cost ofofeach (cost of each capacitor) (3N − 2) each switch + cost eachdiode) diode) + + NN (cost of each capacitor) N(N + 1){(Cost switch+2N + cost eachdiode diode) + of 0.5each (cost of each capacitor)} 2 (Costofofeach each switch) (costof of each + cost capacitor) (3N + 1) (Cost of each switch + cost of each diode) +N (cost of each capacitor) 4N (Cost of each switch) + 2(N + 1)(cost of each diode) + (2N + 1) (cost of each capacitor) (3N − 2) (Cost of each switch + cost of each diode) + N (cost of each capacitor) 2 (Cost of each switch) +2N (cost of each diode + cost of each capacitor) 6. Experimental and Simulation Results of the Proposed Self-Balanced and Magnetic Component-Free Multistage DC-DC Converter The proposed self-balanced and magnetic component-free multistage DC-DC converter simulation and experimental results are discussed in this section. The proposed multistage converter has been designed for four stages with rated power 60 W, switching frequency 100 kHz, output voltage is 100 V and the supply voltage is 24 V. Switches Sa (here S1 ) and Sb (here S2 ) are operated complementarily with a 50% duty cycle. High switching frequency is used to reduce the rating of the capacitor. Component-Free Multistage DC-DC Converter 6. Experimental and Simulation Results of the Proposed Self-Balanced and Magnetic Component-Free Multistage DC-DC Converter The proposed self-balanced and magnetic component-free multistage DC-DC converter simulation and experimental results are in this section. The proposed multistage The proposed self-balanced anddiscussed magnetic component-free multistage DC-DC converter converter has been designed for four stages with rated power 60 W, switching frequency 100 kHz,converter output simulation and experimental results are discussed in this section. The proposed multistage voltage is 100 V and for the four supply voltage 24 V.power Switches Sa (here S1) and Sb (here S100 2) are operated has been designed stages withisrated 60 W, switching frequency kHz, output Energies 2017, 10, 719 19 of 28 complementarily a 50% duty voltage cycle. High frequency to Sreduce of the voltage is 100 V with and the supply is 24switching V. Switches Sa (hereisSused 1) and b (herethe S2) rating are operated capacitor. complementarily with a 50% duty cycle. High switching frequency is used to reduce the rating of the The output voltage and current waveform with ideal components (voltage drop across the capacitor. The output voltage and current waveform with ideal components (voltage drop across the switch switchThe andoutput the diode is zero) shownwaveform in Figure with 21a. Itideal is observed that the settling time for the voltage and iscurrent components (voltage drop across the and the diode is zero) is shown in Figure 21a. It is observed that the settling time for the output voltage output the proposed ideal 21a. components (forward of the diode is switchvoltage and theofdiode is zero) converter is shown with in Figure It is observed thatresistance the settling time for the of the0)proposed converter with ideal components (forward resistance of the diode 0)ofisthe less than 2 ms. is lessvoltage than 2 ms. The effect ofconverter voltage drop the diode is analyzed in the is previous section. output of the proposed withacross ideal components (forward resistance diode is The effect of voltage across the diode is drop analyzed previous section. The output The voltage current waveform (assuming 1 the Vthe voltage drop acrossin the switch andvoltage diode) 0) isoutput less than 2 drop ms.and The effect of voltage acrossin diode is analyzed the previous section.and current waveform (assuming 1 V voltage drop across the switch and diode) are shown in Figure are shown involtage Figure 21b. The output and current waveform (assuming 1 V voltage drop across the switch and diode)21b. are shown in Figure 21b. (a) (b) (a) (b) Figure 21. Simulation results (a) Output voltage and current waveform with ideal components and Figure 21. Simulation results (a) Output voltage and current waveform with ideal components and Vin VFigure in = 24 V; Output voltage with practical components and V in = 24 V. 21.(b) Simulation resultsand (a) current Output waveform voltage and current waveform with ideal components and = 24 V; (b) Output voltage and current waveform with practical components and Vin = 24 V. Vin = 24 V; (b) Output voltage and current waveform with practical components and Vin = 24 V. It is observed that the settling time for the output voltage of the proposed converter with issettling approximately 4 the msfor due to output the forward resistance of the diode and switch. It iscomponents observed that the settling time the voltage of the proposed converter with Itpractical is observed that the time for output voltage of the proposed converter with practical Thus, theispractical waveform from because theof time (RDswitch. + RS)Thus, practical components is approximately 4 the ms due towaveform the forward resistance theconstant diode components approximately 4differs ms due to theideal forward resistance ofofthe diode and and switch. CThus, as explained in waveform Section 4. differs The output power and switch are shown the practical ideal waveform because thevoltage time constant + in RS) the practical waveform differs from thefrom idealthe waveform because of theoftime constant (RD(R+D R S ) C as Figure respectively. The4.output voltagepower and input voltage and waveform idealare components C as 22a,b, explained in Section The output waveform switchwith voltage shown in explained in Section 4. The output power waveform and switch voltage are shown in Figure 22a,b, (voltage drop across the switch the voltage diode isand zero) are voltage shown in Figure 22c. The output voltage Figure 22a,b, respectively. The and output input waveform with ideal components respectively. The output voltage and input voltage waveform with ideal components (voltage drop and input drop voltage waveform (assuming a 1diode V voltage drop theinswitch are shown in (voltage across the switch and the is zero) areacross shown Figureand 22c.diode) The output voltage acrossFigure the switch and the diode is zero) are shown in Figure 22c. The output voltage and input voltage 22d. voltage waveform (assuming a 1 V voltage drop across the switch and diode) are shown in and input waveform (assuming a 1 V voltage drop across the switch and diode) are shown in Figure 22d. Figure 22d. (a) (b) (a) (b) Figure 22. Cont. Energies 2017, 10, 719 20 of 28 Energies 2017, 10, 719 20 of 28 (c) (d) (e) (f) Figure 22. Simulation results (a) Output power of proposed converter; (b) Gate pulses to control Figure 22. Simulation resultsand (a) drain Output power of converter; proposed(c)converter; (b) Gate pulses to control switches of the converter to source of the Output voltage and input voltage switcheswaveform of the converter and drain to source of the converter; (c) Output voltage and input with ideal components; (d) Output voltage and input voltage waveform with practicalvoltage waveform with ideal components; (d) Output waveform practical D31 and Dand 41; (f) input Voltagevoltage across diode D12, D22,with D32 and components; (e) Voltage across diode D11, D21, voltage D42. (e) Voltage across diode D11 , D21 , D31 and D41 ; (f) Voltage across diode D12 , D22 , D32 components; and D42 . It is observed that 120 V output voltage is achieved from a 24 V input supply. Thus, ideally the voltage gain of the proposed converter is 5, which is equal to the number of stages +1. When the voltage drop across the diode is considered, an output voltage of 100 V is achieved from a 24 V supply. The voltage across the switch is equal to the input supply voltage (24 V). The voltage across all capacitors is same, which is equal to the input supply voltage (24 V) if the voltage drop across the diode Energies 2017, 10, 719 21 of 28 It is observed that 120 V output voltage is achieved from a 24 V input supply. Thus, ideally the Energies 2017, 10, 719 voltage gain of the proposed converter is 5, which is equal to the number of stages +1. When the 21 of 28 voltage drop across the diode is considered, an output voltage of 100 V is achieved from a 24 V supply. The voltage across the switch is equal to the input supply voltage (24 V). The voltage across all capacitors is same, which is equal the input supply voltage (24 V)the if the voltage drop across the The is not considered. The voltage across all to diodes is same (24 V) when diode is reversebiased. diode is not considered. voltage22e–f. acrossThe all diodes is across same (24 when the diode is reversevoltage across diodes is shown The in Figure voltage theV)capacitors is shown in Figure 23. biased.4-stage The voltage across diodes shown inDC-DC Figure 22e–f. The voltage across theexperimentally capacitors is and The proposed self-balanced and is magnetic converter is investigated shown in 719 Figure 23. The proposed 4-stage self-balanced and magnetic DC-DC converter is28 Energies 2017, 10, 21 of the result shows a good match with the simulation results. The hardware components are listed in investigated experimentally and the result shows a good match with the simulation results. The Table 7. hardware components are listed in Table 7. It is observed that 120 V output voltage is achieved from a 24 V input supply. Thus, ideally the voltage gain of the proposed converter is 5, which is equal to the number of stages +1. When the voltage drop across the diode is considered, an output voltage of 100 V is achieved from a 24 V supply. The voltage across the switch is equal to the input supply voltage (24 V). The voltage across all capacitors is same, which is equal to the input supply voltage (24 V) if the voltage drop across the diode is not considered. The voltage across all diodes is same (24 V) when the diode is reversebiased. The voltage across diodes is shown in Figure 22e–f. The voltage across the capacitors is shown in Figure 23. The proposed 4-stage self-balanced and magnetic DC-DC converter is investigated experimentally and the result shows a good match with the simulation results. The hardware components are listed in Table 7. 23. across Voltagecapacitor across capacitor C41, ,CC 31, C21 C11, C42, C32, C22 and C12 (Top to bottom in figure). Figure 23.Figure Voltage C41 , C 31 21 C11 , C42 , C32 , C22 and C12 (Top to bottom in figure). PIC18F45K20 is used to generate pulses and TLP250 is used as driver IC. The hardware Table 7. Hardware prototype of the proposed convertercomponent is shown indetails Figureof 24.the proposed converter. Sr/No Components Value No. of Components 1 2 3 4 5 Switch (S1 and S2 ) Diodes Capacitors Load Gate Driver IC IRF250 (0.085 ON sate resistance) BYQ28E 220 µF, 50 V 168 Ω, 60 W TLP250 2 8 8 1 2 Figure 23. Voltage across capacitor C41, C31, C21 C11, C42, C32, C22 and C12 (Top to bottom in figure). PIC18F45K20 is used to generate pulses and TLP250 is used as driver IC. The hardware prototype PIC18F45K20 is used to generate pulses and TLP250 is used as driver IC. The hardware of theprototype proposed converter is shown in Figure 24. of the proposed converter is shown in Figure 24. Figure 24. Hardware prototype of the proposed DC-DC converter. Figure Hardwareprototype prototype of the converter. Figure 24.24. Hardware theproposed proposedDC-DC DC-DC converter. Energies 2017, 10, 719 22 of 28 Energies 2017, 10, 719 22 of 28 Pulses are generated from a PIC controller and the gate driver output is shown in Figure 25a,b, Pulses are generated from a PIC controller and the gate driver output is shown in Figure 25a,b, respectively. Output voltage and input voltage waveform are shown in Figure 25c. It is observed that respectively. Output voltage and input voltage waveform are shown in Figure 25c. It is observed 100 Vthat output achieved from a from 24 V ainput supply. 100 Visoutput is achieved 24 V input supply. (a) (b) (c) (d) Figure 25. (a) PIC controller output; (b) TLP 250 gate driver output; (c) Output voltage and input Figure 25. (a) PIC controller output; (b) TLP 250 gate driver output; (c) Output voltage and input voltage waveform; (d) Output current waveforms. voltage waveform; (d) Output current waveforms. Table 7. Hardware component details of the proposed converter. The output waveform is shown in FigureValue 25d and it is observedNo. that the output current is Sr/No current Components of Components 0.619 A. The 1voltageSwitch across is shown in Figure 26a–h. It is observed (S1each and S2capacitor ) IRF250 (0.085 ON sate resistance) 2 that the voltage 2 Diodes the same and slightlyBYQ28E across each capacitor is nearly less than the input voltage 248V (an effect of the 3 Capacitors 220 μF, 50 V 8 diode). Voltage stress across each diode is shown in Figure 27a–h. It is observed that the voltage stress 4 Load 168 Ω, 60 W 1 across the diode is approximately voltage across the diode is 5 Gate Driver IC the same and the peak TLP250 2 slightly less than the input voltage (24 V) (an effect of the voltage drop). The voltages of all capacitors and all diodes The output waveform is shownofinthe Figure 25dand and switch. it is observed that thestages output(source current side) differ slightly due tocurrent the forward resistance diode The lower is 0.619are A. charged The voltage across the eachpath capacitor is shown in less Figure 26a–h.whereas It is observed the voltage capacitors through which contain diodes as thethat number of stages across each capacitor is nearly the same and slightly less than the input voltage 24 V (an effect of increases the path followed for the charging of higher stage (moving towards load) capacitors the contain stress acrossa each is shown in Figure in 27a–h. It is observed the voltage morediode). diodes.Voltage Thus, practically slightdiode difference is observed the voltage of thethat capacitors. stress across the diode is approximately the same and the peak voltage across the diode is slightly less than the input voltage (24 V) (an effect of the voltage drop). The voltages of all capacitors and all diodes differ slightly due to the forward resistance of the diode and switch. The lower stages (source side) capacitors are charged through the path which contain less diodes whereas as the number of stages increases the path followed for the charging of higher stage (moving towards load) capacitors contain more diodes. Thus, practically a slight difference is observed in the voltage of the capacitors. Energies 2017, 10, 719 23 of 28 Energies 2017, 10, 719 23 of 28 (a) VC11 = 21.0 V (b) VC12 = 22.3 V (c) VC21 = 19.4 V (d) VC22 = 20.3 V (e) VC31 = 18.6 V (f) VC32 = 18.8 V (g) VC41 = 18.4 V (h) VC42 = 18.8 V Figure 26. Capacitors voltage (a) C11 (b) C12 (c) C21 (d) C22 (e) C31 (f) C32 (g) C41 (h) C42. Figure 26. Capacitors voltage (a) C11 (b) C12 (c) C21 (d) C22 (e) C31 (f) C32 (g) C41 (h) C42 . Energies 2017, 10, 719 24 of 28 Energies 2017, 10, 719 24 of 28 (a) Mean VD11 = −11.8 V (b) Mean VD12 = −10.5 V (c) Mean VD21 = −10.5 V (d) Mean VD22 = −10 V (e) Mean VD31 = −9.23 V (f) Mean VD32 = −9.69 V (g) Mean VD41 = −8.85 V (h) Mean VD42 = −9.24 V Figure 27. Voltage across diodes (a) D11 (b) D12 (c) D21 (d) D22 (e) D31 (f) D32 (g) D41 (h) D42. Figure 27. Voltage across diodes (a) D11 (b) D12 (c) D21 (d) D22 (e) D31 (f) D32 (g) D41 (h) D42 . 7. Conclusions 7. Conclusions The self-biased and magnetic-free multistage step-up converter is articulated and designed for unidirectional renewable photovoltaic multistage applications.step-up The proposed converter is well suited for The self-biased and magnetic-free converter is articulated and designed for unidirectional renewable photovoltaic applications. The proposed converter is well suited for renewable photovoltaic applications where the voltage needs to be stepped up without using magnetic components. The proposed converter also provides a viable solution to improve the photovoltaic Energies 2017, 10, 719 25 of 28 systems in term of modularity, cost and control. The proposed converter is suitable for the DC link applications in DC-AC systems where capacitor voltage balancing is the main challenge. The proposed converter also provides a viable solution for low power applications, since the inductor and transformer are not required to design the proposed converter. Also Maximum Power Point Tracking (MPPT) can be easily implemented to improve the efficiency of the converter. The voltage across the switch is less; hence low voltage switches are used for designing high voltage converters. The conspicuous features of the proposed topology are: (i) (ii) (iii) (iv) (v) (vi) Magnetic component-free (transformer-less and inductor-less) Continuous input current Low voltage rating semiconductor devices and capacitors Modularity Easy to add a higher number of levels to increase the voltage Only two control switches with alternating operation and simple control are needed. The proposed converter has been designed with a rated power of 60 W, the input voltage is 24 V, the output voltage is 100 V and the switching frequency is 100 kHz. High switching frequency has been used to decrease the component size. The performance of the proposed converter is verified through simulation and experimental results. Author Contributions: M.S.B. and S.P. developed the proposed research concept with the complete theoretical background study. Further hardware prototype implementation tasks are carried out the same authors. 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