An Original Transformer and Switched-Capacitor (T & SC)-Based Extension for DC-DC Boost Converter for High-Voltage/Low-Current Renewable Energy Applications: Hardware Implementation of a New T & SC Boost Converter

: In this article a new Transformer and Switched Capacitor-based Boost Converter (T & SC-BC) is proposed for high-voltage/low-current renewable energy applications. The proposed T & SC-BC is an original extension for DC-DC boost converter which is designed by utilizing a transformer and switched capacitor (T & SC). Photovoltaic (PV) energy is a fast emergent segment among the renewable energy systems. The proposed T & SC-BC combines the features of the conventional boost converter and T & SC to achieve a high voltage conversion ratio. A Maximum Power Point Tracking (MPPT) controller is compulsory and necessary in a PV system to extract maximum power. Thus, a photovoltaic MPPT control mechanism also articulated for the proposed T & SC-BC. The voltage conversion ratio ( V o / V in ) of proposed converter is (1 + k )/(1 − D ) where, k is the turns ratio of the transformer and D is the duty cycle (thus, the converter provides 9.26, 13.88, 50/3 voltage conversion ratios at 78.4 duty cycle with k = 1, 2, 2.6, respectively). The conspicuous features of proposed T & SC-BC are: (i) a high voltage conversion ratio ( V o / V in ); (ii) continuous input current ( I in ); (iii) single switch topology; (iv) single input source; (v) low drain to source voltage ( V DS ) rating of control switch; (vi) a single inductor and a single untapped transformer are used. Moreover, the proposed T & SC-BC topology was compared with recently addressed DC-DC converters in terms of number of components, cost, voltage conversion ratio, ripples, efﬁciency and power range. Simulation and experimental results are provided which validate the functionality, design and concept of the proposed approach.


Introduction
In recent years the importance of using renewable energies has grown significantly due to the fact that the usage of fossil fuels such as oil, coal, and gas results in environmental pollution and serious greenhouse effects which have a huge influence on the world [1,2]. The demands for energy and power converters have been increasing for the last several decades, due to the greater industrialization, rising population and increased living standards of society [3][4][5][6][7][8][9]. The International Energy Agency (IEA) has anticipated that the developing nations are raising their energy utilization at a quicker pace than developed ones and will need to nearly the double their present installed generation facility by the year 2020 for fulfill their energy requirements. The total energy consumption of the world from 1980 to 2025 is depicted in Figure 1a [10][11][12]. The IEA has also details that more than 1.3 billion people in the developing nations are living with insufficient or without any access to electricity because of the unavailability of electric grid in these regions and other constraints [10][11][12]. Thus, there is a need for new sources of energy that are cheaper and sustainable with less carbon emissions [13,14]. Photovoltaic energy is considered as a reliable, promising and favorable source and it has various advantages such as being pollution free, long life, low maintenance, etc. [15][16][17][18]. In Figure 1b the global cumulated PV capacity (in Gigawatts) from 1996 to 2012, and an estimation (E) by 2020 is shown. It is observed that PV is a fast emergent segment among renewable energy systems [19]. To increase the effectiveness and efficiency of power conditioning to tracking Maximum Power Point (MPP) plays an important role in increasing the conversion efficiency. A PV system has non-linear P-V and I-V characteristics and the generated power depends on the environmental conditions such as solar irradiation and temperature [20][21][22]. The power of a PV system is higher at the knee point of the P-V characteristic curve, as the MPP keeps on changing according to the varying irradiation levels, a MPPT method is used to track the MPP of the system. The PV grid-connected power system in domestic applications is becoming a fast-rising segment in the PV market [23][24][25][26]. Unfortunately, the output voltage of the PV arrays or panels is relatively low. Thus, PV series-connected configurations are generally used in order to satisfy the demand and the high bus voltage requirements of the half and full-bridge, multilevel inverters (MLI) needed to transfer energy to electric grid. This type of system suffers from partial shading, reduced PV module efficiency, and mismatched MPPT control [27,28]. Thus boost converters with high voltage conversion ratio and inverters are required to feed energy to the electric grid. In practice DC-DC converters with high efficiency with low input voltage, high input current, high output voltage and high voltage conversion ratio provide a practicable solution for photovoltaic systems to transfer photovoltaic energy to the electric grid via inverters [29,30].

Introduction
In recent years the importance of using renewable energies has grown significantly due to the fact that the usage of fossil fuels such as oil, coal, and gas results in environmental pollution and serious greenhouse effects which have a huge influence on the world [1,2]. The demands for energy and power converters have been increasing for the last several decades, due to the greater industrialization, rising population and increased living standards of society [3][4][5][6][7][8][9]. The International Energy Agency (IEA) has anticipated that the developing nations are raising their energy utilization at a quicker pace than developed ones and will need to nearly the double their present installed generation facility by the year 2020 for fulfill their energy requirements. The total energy consumption of the world from 1980 to 2025 is depicted in Figure 1a [10][11][12]. The IEA has also details that more than 1.3 billion people in the developing nations are living with insufficient or without any access to electricity because of the unavailability of electric grid in these regions and other constraints [10][11][12]. Thus, there is a need for new sources of energy that are cheaper and sustainable with less carbon emissions [13,14]. Photovoltaic energy is considered as a reliable, promising and favorable source and it has various advantages such as being pollution free, long life, low maintenance, etc. [15][16][17][18]. In Figure 1b the global cumulated PV capacity (in Gigawatts) from 1996 to 2012, and an estimation (E) by 2020 is shown. It is observed that PV is a fast emergent segment among renewable energy systems [19]. To increase the effectiveness and efficiency of power conditioning to tracking Maximum Power Point (MPP) plays an important role in increasing the conversion efficiency. A PV system has non-linear P-V and I-V characteristics and the generated power depends on the environmental conditions such as solar irradiation and temperature [20][21][22]. The power of a PV system is higher at the knee point of the P-V characteristic curve, as the MPP keeps on changing according to the varying irradiation levels, a MPPT method is used to track the MPP of the system. The PV grid-connected power system in domestic applications is becoming a fast-rising segment in the PV market [23][24][25][26]. Unfortunately, the output voltage of the PV arrays or panels is relatively low. Thus, PV series-connected configurations are generally used in order to satisfy the demand and the high bus voltage requirements of the half and full-bridge, multilevel inverters (MLI) needed to transfer energy to electric grid. This type of system suffers from partial shading, reduced PV module efficiency, and mismatched MPPT control [27,28]. Thus boost converters with high voltage conversion ratio and inverters are required to feed energy to the electric grid. In practice DC-DC converters with high efficiency with low input voltage, high input current, high output voltage and high voltage conversion ratio provide a practicable solution for photovoltaic systems to transfer photovoltaic energy to the electric grid via inverters [29,30]. Additionally, traditional boost converters are not a practicable solution to achieve high conversion ratios due to the leakage resistance of the inductor, high switch stress and the performance of a boost converter is deteriorated by the high duty cycle of the power switch and thus, not able to Additionally, traditional boost converters are not a practicable solution to achieve high conversion ratios due to the leakage resistance of the inductor, high switch stress and the performance of a boost converter is deteriorated by the high duty cycle of the power switch and thus, not able to achieve conversion ratios of more than four. To operate the DC-DC converters for getting high output voltage without using high duty cycles for power semiconductor controlled switches, isolated converters can be employed which contain transformers, coupled inductors, etc. [29][30][31][32][33][34][35][36][37], but the usage of such a large number of magnetic components increases the size of the circuit as well as the leakage reactance of the converter and also produces electromagnetic interference which reduces the converter function ability and efficiency. Recently many boost converter topologies are addressed by extending the power circuit of the traditional boost converter. In [38], a single switch n-stage Cascaded Boost Converter (n-stage CBC) is discussed to achieve high voltage but it requires a large number of inductors, diodes and capacitors. Figure 2a depicts the power circuit of a single switch n-stage Cascaded Boost Converter (single switch n-stage CBC). In [38], a single switch boost converter with a voltage multiplier extension to achieve high voltage is discussed, but it requires a large number of diodes and capacitor circuitry. Figure 2b depicts the power circuit of a single switch boost converter with voltage multiplier. In [39], a new coupled inductor-based step-up converter is discussed with a large pump. The voltage can be easily achieved by modifying the turns-ratio of coupled inductors but the leakage energy induces high voltage stress and switching losses. The power circuit of coupled inductor based step-up converter is shown in Figure 2c. In [40], a new Quadratic Boost Converter (QBC) with coupled inductor in second boost converter is proposed and shown in Figure 2d. This QBC achieves high step-up voltage gain with an appropriate duty ratio and low voltage stress on the power switch.
Energies 2018, 11, x 3 of 23 achieve conversion ratios of more than four. To operate the DC-DC converters for getting high output voltage without using high duty cycles for power semiconductor controlled switches, isolated converters can be employed which contain transformers, coupled inductors, etc. [29][30][31][32][33][34][35][36][37], but the usage of such a large number of magnetic components increases the size of the circuit as well as the leakage reactance of the converter and also produces electromagnetic interference which reduces the converter function ability and efficiency. Recently many boost converter topologies are addressed by extending the power circuit of the traditional boost converter. In [38], a single switch n-stage Cascaded Boost Converter (n-stage CBC) is discussed to achieve high voltage but it requires a large number of inductors, diodes and capacitors. Figure 2a depicts the power circuit of a single switch nstage Cascaded Boost Converter (single switch n-stage CBC). In [38], a single switch boost converter with a voltage multiplier extension to achieve high voltage is discussed, but it requires a large number of diodes and capacitor circuitry. Figure 2b depicts the power circuit of a single switch boost converter with voltage multiplier. In [39], a new coupled inductor-based step-up converter is discussed with a large pump. The voltage can be easily achieved by modifying the turns-ratio of coupled inductors but the leakage energy induces high voltage stress and switching losses. The power circuit of coupled inductor based step-up converter is shown in Figure 2c. In [40], a new Quadratic Boost Converter (QBC) with coupled inductor in second boost converter is proposed and shown in Figure 2d. This QBC achieves high step-up voltage gain with an appropriate duty ratio and low voltage stress on the power switch.  In [41], a DC-DC non-inverting Nx Interleaved Multilevel Boost Converter (Nx IMBC) is proposed to achieve a high voltage conversion ratio (V o /V in ) and to reduce voltage/current ripple. Nx-IMBC provides N times more voltage conversion ratio compared to traditional boost converters but requires large number of diodes and capacitors. In [42,43], DC-DC non-inverting 2Nx and 4Nx Interleaved Boost converters (2Nx IMBC and 4Nx IMBC) are proposed to achieve high voltage conversion ratio (V o /V in ) and to reduce voltage/current ripple. 2Nx IMBC and 4Nx IMBC provide 2N and 4N times more voltage conversion ratio compared to traditional boost converters, but also require large numbers of diodes and capacitors. To achieve a high inverting voltage conversion ratio, a new inverting Nx and 2Nx Multilevel Boost Converter (MBC) was proposed for renewable energy applications [44]. In [45,46], a new family of DC-DC converters called "X-Y Converter Family" was proposed to achieve high conversion ratios for renewable applications. These converters are well suited to achieve high voltage, but need more number of devices, thus increasing the size and cost of the converter.
In this article, a new T & SC-BC is proposed for high-voltage/low-current renewable applications to overcome the drawback of recently addressed converters. The power circuit and block diagram of proposed converter scheme system is shown in Figure 3. The proposed T & SC-BC is an original extension for DC-DC boost converters which is based on T & SC. The proposed T & SC-BC converter combines the features of a conventional boost converter and T & SC [47] to achieve high voltage conversion ratios. In a PV cell model the current source is basically associated in parallel with the reversed diode and also has series and parallel resistance as shown in Figure 3. Resistance in series (R S ) is due to barrier in the pathway of flow of electrons from n to p junction and resistance in shunt (R Sh ) is due to the leakage current [48]. The relation between the currents of a PV cell is shown in Equation (1): where I ph is the photocurrent generated by the cell, I d is the current flowing through the diode of the solar cell, I Sh is the shunt current flowing through the shunt resistance (R Sh ), I is the output current or current flowing through the series resistance (R S ), V is the voltage at the output terminal of the cell, I o is the reverse saturation current, n is the diode ideal factor, V T is the thermal voltage, k is the Boltzmann constant and T is the absolute temperature. When irradiance strikes the flat surface of a PV module or cell, an electrical field is produced within the cell. In the presence of an electric field, these charges can create a current that can be used in a peripheral circuit. This current depends on the concentration and intensity of the incident solar radiation. The higher the level of the light intensity, the more electrons can be allowed to run free from the flat surface, and the more current is created. All the time it is necessary to track MPP due to deviation of hotness and irradiation of the array [49,50]. MPPT techniques to track MPP have been addressed and published over years of research [50][51][52][53]. Every MPPT method has its own merits and demerits like required sensors, complexity, cost, range of effectiveness, convergence speed, correct tracking when the irradiation and temperature change. The Perturb & Observe (P & O) algorithm and Incremental Conductance algorithm is the most popular and simple methods to track MPP. The P & O algorithm is depends on hill climbing concept hence also called "hill-climbing P & O Method". This is one of most used algorithms due to its simplicity and ease of implementation and low cost [49,53]. It operates with a cyclic perturbation (increase or decrease) of the array terminal voltage and by comparing the PV power of last perturbation. If the power increases the perturbation goes with the same direction otherwise it will goes with the reverse direction. In this method, the sign of the last perturbation and the sign of the last increment in the power are used to decide what the next perturbation should be [53]. require large numbers of diodes and capacitors. To achieve a high inverting voltage conversion ratio, a new inverting Nx and 2Nx Multilevel Boost Converter (MBC) was proposed for renewable energy applications [44]. In [45,46], a new family of DC-DC converters called "X-Y Converter Family" was proposed to achieve high conversion ratios for renewable applications. These converters are well suited to achieve high voltage, but need more number of devices, thus increasing the size and cost of the converter.  [47] to achieve high voltage conversion ratios. In a PV cell model the current source is basically associated in parallel with the reversed diode and also has series and parallel resistance as shown in Figure 3. Resistance in series (RS) is due to barrier in the pathway of flow of electrons from n to p junction and resistance in shunt (Rsh) is due to the leakage current [48]. The relation between the currents of a PV cell is shown in  where Iph is the photocurrent generated by the cell, Id is the current flowing through the diode of the solar cell, Ish is the shunt current flowing through the shunt resistance (Rsh), I is the output current or current flowing through the series resistance (RS), V is the voltage at the output terminal of the cell, Io is the reverse saturation current, n is the diode ideal factor, VT is the thermal voltage, k is the Boltzmann constant and T is the absolute temperature. When irradiance strikes the flat surface of a PV module or cell, an electrical field is produced within the cell. In the presence of an electric field, these charges can create a current that can be used in a peripheral circuit. This current depends on the concentration and intensity of the incident solar radiation. The higher the level of the light intensity, the more electrons can be allowed to run free from the flat surface, and the more current is created. All the time it is necessary to track MPP due to deviation of hotness and irradiation of the array [49,50]. MPPT techniques to track MPP have been addressed and published over years of research [50][51][52][53]. Every MPPT method has its own merits and demerits like required sensors, complexity, cost, range of effectiveness, convergence speed, correct tracking when the irradiation and temperature change. The Perturb & Observe (P & O) algorithm and Incremental Conductance algorithm is the most popular and simple methods to track MPP. The P & O algorithm is depends on hill climbing concept hence also called "hill-climbing P & O Method". This is one of most used algorithms due to its simplicity and ease of implementation and low cost [49,53]. It operates with a cyclic perturbation (increase or decrease) of the array terminal voltage and by comparing the PV power of last perturbation. If the power increases the perturbation goes with the same direction otherwise it will goes with the reverse direction. In this method, the sign of the last perturbation and the sign of the last increment in the power are used to decide what the next perturbation should be [53].   Simulation and experimental result are provided which validate the functionality, design and concept of the proposed approach.

Power Circuit and Operation Modes of Transformer and Switch Capacitor Based Boost Converter (T & SC-BC)
A conventional boost converter with SC or Voltage Doubler (VD) is shown in Figure 5a. A circuit connection of capacitor C 1 , C 0 and diode D 2 , D 0 forms a SC stage or VD stage. A transformer is employed in the SC stage to provide a T & SC stage for high voltage conversion. The power circuit of the proposed T & SC-BC is shown in Figure 5b. The proposed T & SC-BC is designed by using a conventional/traditional boost converter by employing a T & SC stage at the output side. In Figure 5, inductor L 1 , switch S, diode D 1 and capacitor C 01 form a conventional boost converter. The input supply is directly connected to the conventional boost converter. Capacitor C 1 , C 2 , diode D 0 , D 2 and transformer form the newly designed T & SC stage. L P is the primary winding of the transformer whose one terminal is connected via capacitor C 1 at the inductor of conventional boost converter or at the drain terminal of a switch and the other terminal is directly connected at the cathode of diode D 1 or at output capacitor C 01 of the conventional boost converter. L S is the secondary winding of the transformer whose one terminal is directly connected to the anode of diode D 2 and another terminal connected to capacitor C 2 . Simulation and experimental result are provided which validate the functionality, design and concept of the proposed approach.

Power Circuit and Operation Modes of Transformer and Switch Capacitor Based Boost Converter (T & SC-BC)
A conventional boost converter with SC or Voltage Doubler (VD) is shown in Figure 5a. A circuit connection of capacitor C1, C0 and diode D2, D0 forms a SC stage or VD stage. A transformer is employed in the SC stage to provide a T & SC stage for high voltage conversion. The power circuit of the proposed T & SC-BC is shown in Figure 5b. The proposed T & SC-BC is designed by using a conventional/traditional boost converter by employing a T & SC stage at the output side. In Figure 5, inductor L1, switch S, diode D1 and capacitor C01 form a conventional boost converter. The input supply is directly connected to the conventional boost converter. Capacitor C1, C2, diode D0, D2 and transformer form the newly designed T & SC stage. LP is the primary winding of the transformer whose one terminal is connected via capacitor C1 at the inductor of conventional boost converter or at the drain terminal of a switch and the other terminal is directly connected at the cathode of diode D1 or at output capacitor C01 of the conventional boost converter. LS is the secondary winding of the transformer whose one terminal is directly connected to the anode of diode D2 and another terminal connected to capacitor C2. The operation of the proposed T & SC-BC is divided into two main modes; one when switch S is turned ON and another when switch S is turned OFF. These two modes are divided into five submodes to explain the CCM operation of the proposed T & SC-BC in detail. The CCM characteristic waveforms with the five sub-modes are shown in Figure 6. The operation of the proposed T & SC-BC is divided into two main modes; one when switch S is turned ON and another when switch S is turned OFF. These two modes are divided into five submodes to explain the CCM operation of the proposed T & SC-BC in detail. The CCM characteristic waveforms with the five sub-modes are shown in Figure 6.

Mode-1 (Time ta-tb)
In Mode-1, switch S is turned OFF and inductor L1 is demagnetized. Thus, the energy stored in the inductor L1 is transferred to capacitor C01 through diode D1. The energy of capacitor C1, C2, transformer windings is also transferred through diode D0 to the output capacitor C0. The equivalent circuit of the proposed converter for this mode is shown in Figure 7a. In this mode diode D1, D0 are operated in forward biased condition whereas diode D2 are operated in reverse biased condition.

Mode-1 (Time ta-tb)
In Mode-1, switch S is turned OFF and inductor L 1 is demagnetized. Thus, the energy stored in the inductor L 1 is transferred to capacitor C 01 through diode D 1 . The energy of capacitor C 1 , C 2 , transformer windings is also transferred through diode D 0 to the output capacitor C 0 . The equivalent circuit of the proposed converter for this mode is shown in Figure 7a. In this mode diode D 1 , D 0 are operated in forward biased condition whereas diode D 2 are operated in reverse biased condition.

Mode-1 (Time ta-tb)
In Mode-1, switch S is turned OFF and inductor L1 is demagnetized. Thus, the energy stored in the inductor L1 is transferred to capacitor C01 through diode D1. The energy of capacitor C1, C2, transformer windings is also transferred through diode D0 to the output capacitor C0. The equivalent circuit of the proposed converter for this mode is shown in Figure 7a. In this mode diode D1, D0 are operated in forward biased condition whereas diode D2 are operated in reverse biased condition.

Mode-2 (Time tb-tc)
In Mode-2, switch S is turned OFF and inductor L 1 is still demagnetized but the energy stored in the inductor L 1 is not directly transferred to capacitor C 01 through diode D 1 (diode D 1 is acting as an open circuit) but rather transferred through the windings. The energy of capacitor C 1 , C 2 , transformer windings is also transferred through diode D 0 to output capacitor C 0 . The equivalent circuit of proposed converter for this mode is shown in Figure 7b. In this mode diode D 0 are operated in forward biased condition whereas diode D 1 , D 2 are operated in reverse biased condition.

Mode-3 (Time tc-td)
In Mode-3, switch S is turned ON and inductor L 1 is magnetized through switch S. The energy of capacitor C 1 , C 2 , transformer windings is transferred through diode D 0 to output capacitor C 0 but the diode D 0 current start decreasing and current slope (di/dt) is limited by the transformer. Hence, the diode reverse current recovery problem is decreased. The equivalent circuit of the proposed converter in this mode is shown in Figure 8a. In this mode diode D 0 are operated in forward biased condition whereas diodes D 1 , D 2 are reverse biased.

Mode-2 (Time tb-tc)
In Mode-2, switch S is turned OFF and inductor L1 is still demagnetized but the energy stored in the inductor L1 is not directly transferred to capacitor C01 through diode D1 (diode D1 is acting as an open circuit) but rather transferred through the windings. The energy of capacitor C1, C2, transformer windings is also transferred through diode D0 to output capacitor C0. The equivalent circuit of proposed converter for this mode is shown in Figure 7b. In this mode diode D0 are operated in forward biased condition whereas diode D1, D2 are operated in reverse biased condition.

Mode-3 (Time tc-td)
In Mode-3, switch S is turned ON and inductor L1 is magnetized through switch S. The energy of capacitor C1, C2, transformer windings is transferred through diode D0 to output capacitor C0 but the diode D0 current start decreasing and current slope (di/dt) is limited by the transformer. Hence, the diode reverse current recovery problem is decreased. The equivalent circuit of the proposed converter in this mode is shown in Figure 8a. In this mode diode D0 are operated in forward biased condition whereas diodes D1, D2 are reverse biased.

Mode-4 (Time td-te)
In Mode-4, switch S is turned ON and inductor L 1 is continuously magnetized through switch S. The energy of the transformer windings Ls is transferred to capacitor C 2 through diode D 2 . The energy conversion takes place in a resonant approach and the leakage inductance confines the current. The output capacitor C 0 provides energy to load. At the end of the mode capacitor C 2 is fully charged and diode D 2 is blocked. The equivalent circuit of proposed converter for this mode is shown in Figure 8b. In this mode diode D 2 are operated in forward biased condition whereas diode D 1 , D 0 are operated in reverse biased.

Mode-5 (Time te-tf)
In Mode-5, switch S is turned ON and inductor L 1 is continuously magnetized through switch S. The energy of transformer windings Ls is not transferred to capacitor C 2 due to diode D 2 is in reverse biased. The output capacitor C 0 provides energy to load. The equivalent circuit of proposed converter for this mode is shown in Figure 8c. In this mode no diodes are operated in forward biased condition whereas diodes D 0 , D 1 , D 2 are in reverse biased condition.
The voltage conversion ratio (V o /V in ) and Drain to Source voltage of switch (V DS ) of conventional boost converter with VD (power circuit of converter shown in Figure 5a) is calculated by Equation (7), where T is the total time of one switching cycle. The voltage conversion ratio (V o /V in ) and (V DS /V in ) of conventional boost converter with VD is shown graphically in Figure 9a. From graph it is observed that drain to source switch voltage is exactly half of the output voltage (for example at D = 0.75, V o /V in = 8 and V DS /V in = 4). Hence the drain to source voltage rating of the switch must be above four times of input to operate converter at 75% duty cycle.

Mode-4 (Time td-te)
In Mode-4, switch S is turned ON and inductor L1 is continuously magnetized through switch S. The energy of the transformer windings Ls is transferred to capacitor C2 through diode D2. The energy conversion takes place in a resonant approach and the leakage inductance confines the current. The output capacitor C0 provides energy to load. At the end of the mode capacitor C2 is fully charged and diode D2 is blocked. The equivalent circuit of proposed converter for this mode is shown in Figure 8b. In this mode diode D2 are operated in forward biased condition whereas diode D1, D0 are operated in reverse biased.

Mode-5 (Time te-tf)
In Mode-5, switch S is turned ON and inductor L1 is continuously magnetized through switch S. The energy of transformer windings Ls is not transferred to capacitor C2 due to diode D2 is in reverse biased. The output capacitor C0 provides energy to load. The equivalent circuit of proposed converter for this mode is shown in Figure 8c. In this mode no diodes are operated in forward biased condition whereas diodes D0, D1, D2 are in reverse biased condition.
The voltage conversion ratio (Vo/Vin) and Drain to Source voltage of switch (VDS) of conventional boost converter with VD (power circuit of converter shown in Figure 5a) is calculated by Equation (7), where T is the total time of one switching cycle. The voltage conversion ratio (Vo/Vin) and (VDS/Vin) of conventional boost converter with VD is shown graphically in Figure 9a. From graph it is observed that drain to source switch voltage is exactly half of the output voltage (for example at D = 0.75, Vo/Vin = 8 and VDS/Vin = 4). Hence the drain to source voltage rating of the switch must be above four times of input to operate converter at 75% duty cycle.
(a) (b)  Figure 9c. From the graphs it is observed that voltage conversion ratio is linearly increased with duty cycle and turns ratio. It is observed that the voltage conversion ratio is 16.67 at D = 0.784 when k = 2.6. The voltage conversion ratio is 60 at D = 0.9 when k = 5. It is also investigated that the drain to source switch voltage is exactly equal to the drain to source of a traditional boost converter with VD.

Turns of Secondary winding of transformer
Turns of Primary winding of transformer 1 ( 1 ) 1--

Steady State Analysis of Transformer and Switch Capacitor Based Boost Converter (T & SC-BC)
In this section a steady state analysis of the proposed T & SC-BC is explained and the conversion losses, efficiency and voltage conversion ratio are calculated. In order to analyze the T & SC-BC, we consider the T & SC is working in steady state and the following assumptions are considered throughout the switching: (i) ripple free DC Source (Vin) (ii) diode D1 semiconductor loss is VD1; (iii) forward conduction loss of diode D1 is modelled by ON-state resistance RD1 (efficiency of diode is 100% if VD1 and RD1 = 0); (iv) RS is ON-state resistance of controlled switch.   Figure 9c. From the graphs it is observed that voltage conversion ratio is linearly increased with duty cycle and turns ratio. It is observed that the voltage conversion ratio is 16.67 at D = 0.784 when k = 2.6. The voltage conversion ratio is 60 at D = 0.9 when k = 5. It is also investigated that the drain to source switch voltage is exactly equal to the drain to source of a traditional boost converter with VD.

Steady State Analysis of Transformer and Switch Capacitor Based Boost Converter (T & SC-BC)
In this section a steady state analysis of the proposed T & SC-BC is explained and the conversion losses, efficiency and voltage conversion ratio are calculated. In order to analyze the T & SC-BC, we consider the T & SC is working in steady state and the following assumptions are considered throughout the switching: (i) ripple free DC Source (V in ) (ii) diode D 1 semiconductor loss is V D1 ; (iii) forward conduction loss of diode D 1 is modelled by ON-state resistance R D1 (efficiency of diode is 100% if V D1 and R D1 = 0); (iv) R S is ON-state resistance of controlled switch. R L1 is internal resistance of winding of inductor L 1 ; (v) f s is switching frequency (vi) ripple across capacitor is very small (vii) T & SC cell losses include copper loss, iron loss and diode conduction loss (viii) R T&SC is the equivalent resistance of the T & SC cell. The steady state equivalent circuits of the T & SC-BC ON and OFF state are shown in Figure 10a,b respectively.
Consider i L1 , is and i c01 current is flowing through inductor L 1 , switch S and capacitor C 01 respectively. I L1 , Is and I C01 average current is flowing through inductor L 1 , switch S and capacitor C 01 respectively. Consider iL1, is and ic01 current is flowing through inductor L1, switch S and capacitor C01 respectively. IL1, Is and IC01 average current is flowing through inductor L1, switch S and capacitor C01 respectively.
When switch is in ON state, diode D1 is in reversed biased and inductor is charged by input supply Vin: when switch is in OFF state, diode D1 is conduct and inductor is discharged to charge capacitor C01: Inductor volt second balance method and capacitor charge method is used to calculate the voltage conversion ratio equation: If all the components efficiency is 100% (ideal components) then: When switch is in ON state, diode D 1 is in reversed biased and inductor is charged by input supply V in : when switch is in OFF state, diode D 1 is conduct and inductor is discharged to charge capacitor C 01 : Inductor volt second balance method and capacitor charge method is used to calculate the voltage conversion ratio equation: η, e f f iciency = If all the components efficiency is 100% (ideal components) then: The ideal voltage conversion ratio of T & SC-BC is given in Equation (16).

Comparison of Proposed Transformer and Switch Capacitor Based Boost Converter (T & SC-BC) with Newly Addressed DC-DC Converters
In this section the proposed T & SC-BC is compared with recently addressed DC-DC converters. Recently addressed converters are discussed in Section 1 of the article. In Table 1, the converter comparison is summarized in terms of voltage conversion ratio, number of inductors, number of switches, and number of diodes. First, it is observed that voltage conversion ratio of single switch n-stage CBC is depends on the number of cascaded stages (n) and duty cycle. To design single switch n-stage CBC [30], n-number of inductors, n-number of capacitors and 2n − 1 number of diodes along with single switch is required. Second, it is observed that voltage conversion ratio of single switch boost converter with voltage multiplier is depends on the odd and even number of voltage multiplier stage and duty cycle. To design single switch boost converter with voltage multiplier, 2 inductors, 2n + 1 number of capacitors and 2n number of diodes along with single switch is required. Third, it is observed that voltage conversion ratio of coupled inductor based step-up converter is depends on the coupling coefficient of coupled inductor (k = n 2 /n 1 ) and duty cycle. To design coupled inductor based step-up converter, 3 inductors (1 without coupling and 2 with coupled), 3 capacitors and 3 diodes along with single switch is required. Fourth, it is observed that voltage conversion ratio of Quadratic Boost Converter (QBC) with coupled inductor is depends on the coupling coefficient of coupled inductor (k = n 2 /n 1 ) and duty cycle. To design Quadratic Boost Converter (QBC) with coupled inductor, 3 inductors (1 without coupling and 2 with coupled), 3 capacitors and 4 diodes along with single switch is required. Fifth, it is observed that to design conventional boost converter with VD 1 inductor, 3 capacitors, 1 switch and 3 diodes are required. Sixth, it is observed that voltage conversion ratio of proposed converter (T & SC-BC) is depends on the transformer turns ratio (k) and duty cycle. To design proposed converter (T & SC-BC), 1 inductor, 1 transformer, 4 capacitors and 3 diodes along with single switch is required.

Number of Diodes
Single switch n-stage CBC [38] 1 Single switch boost converter with voltage multiplier [38] n+D 1−D , n = 1, 3 . . . Thus from Table 1 it is seen that the proposed converter required less components and has a higher voltage conversion ratio compared to the other discussed converters. In Table 2 the cost of the power circuit of the proposed T & SC-BC and recently addressed converters (discussed in Section 1) is tabulated and it is observed that the proposed converter requires less cost.

DC-DC Converter Cost of Converter
Single switch n-stage CBC [38] C S + [n × C L ] + [n × C C ] + [(2n − 1) × C D ] Single switch boost converter with voltage multiplier [38] C S + [2 × C L ] + [(2n + 1) × C C ] + [(2n) × C D ] Coupled inductor based step-up converter [39] C Boost converter with voltage doubler (Figure 5a)  Figure 11a,b respectively. It is observed that the voltage conversion ratio increases with the increase in the number of cascaded stages, but the quasi-linear region of the converter decreases. The plot of the voltage conversion ratio of the coupled inductor based step-up converter and QBC with coupled inductor versus duty cycle considering coupling coefficients, k = 1 to 5 is depicted in Figure 11c,d respectively. It is observed that the voltage conversion ratio is greatly increased with the increase in coupling coefficient (k), but the quasi-linear region of the converter decreases.
Coupled inductor based step-up converter [39] CS The plots of the voltage conversion ratio of a single switch CBC and single switch boost converter with voltage multiplier versus duty cycle considering the number of stages, n = 1 to 5 is depicted in Figure 11a,b respectively. It is observed that the voltage conversion ratio increases with the increase in the number of cascaded stages, but the quasi-linear region of the converter decreases. The plot of the voltage conversion ratio of the coupled inductor based step-up converter and QBC with coupled inductor versus duty cycle considering coupling coefficients, k = 1 to 5 is depicted in Figure 11c,d respectively. It is observed that the voltage conversion ratio is greatly increased with the increase in coupling coefficient (k), but the quasi-linear region of the converter decreases. The voltage conversion ratio and capacitor voltage plot of a conventional boost converter with or without SC or VD stage is depicted in Figure 11e. It is observed that the conversion ratio is double with the voltage doubler compared to without the voltage doubler but the quasi-linear region is slightly reduced. The voltage conversion ratio plot of the proposed T & SC-BC versus duty cycle considering transformer ratio, k = 1 to 5 is depicted in Figure 11f. It is observed that the voltage conversion ratio is greatly increased with the increase in number of the transformer ratio (k) but the The voltage conversion ratio and capacitor voltage plot of a conventional boost converter with or without SC or VD stage is depicted in Figure 11e. It is observed that the conversion ratio is double with the voltage doubler compared to without the voltage doubler but the quasi-linear region is slightly reduced. The voltage conversion ratio plot of the proposed T & SC-BC versus duty cycle considering transformer ratio, k = 1 to 5 is depicted in Figure 11f. It is observed that the voltage conversion ratio is greatly increased with the increase in number of the transformer ratio (k) but the quasi-linear region of the converter is decreased.
In Figure 12a, the plot of VC n /V in (ratio of capacitor voltage to input voltage) versus duty cycle for a single switch n-stage CBC is shown considering stages n = 1 to 5. It is observed that the capacitor rating increases with the increase in stages and duty cycle. Thus, a single switch n-stage CBC requires more rated capacitors compared to a single switch n − 1 stage CBC. In Figure 12b the plot of VC n1 /V in and VC n2 /V in (ratio of capacitor voltage to input voltage) versus duty cycle for a single switch boost converter with voltage multiplier is shown considering stage n = 1 to 5. It is observed that the rating of the capacitor increases with the increase in voltage multiplier stages and duty cycle. In Figure 12c the plot of VC 2 /V in (ratio of capacitor voltage to input voltage) versus duty cycle for a coupled inductor-based step-up converter is shown with coupling coefficients k = 1 to 5. It is observed that the capacitor voltage is independent of the coupling coefficient but depends upon the duty cycle.
In Figure 12d the plot of VC 02 /VC 01 (ratio of capacitor C 02 voltage to capacitor C 01 voltage) versus duty cycle for the QBC with coupled inductor is shown with coupled coefficients k = 1 to 5. It is observed that the capacitor voltage depends on the coupling coefficient and also on the duty cycle. Thus, the rating of the capacitor is increased with an increase in coupling coefficient (k) and duty cycle (D). In Figure 12e the plot of VC 01 /V in (ratio of capacitor C 01 voltage to input voltage (V in )) versus duty cycle for the proposed T & SC-BC with transformer turn ratio k = 1 to 5. It is observed that the capacitor voltage is independent of the transformer ratio but depends upon the duty cycle. T & SC-BC is compared with recently addressed DC-DC converters (discussed in Section 1) in terms of the voltage conversion ratio (V o /V in ) and the comparison plot is shown in Figure 12f. It is observed that the proposed T & SC-BC provides higher voltage conversion ratios compared to other DC-DC converters. T & SC-BC is compared with recently addressed DC-DC converters in term of V DS /V in (ratio of Drain to source voltage and input voltage) and the comparison plot is shown in Figure 12g and also tabulated in Table 3. It is observed that the proposed converter has a smaller V DS /V in ratio (ratio of Drain to Source voltage with respect input voltage), hence low rating components are suitable to design the T & SC-BC compared to recently proposed DC-DC converters (discussed in Section 1). Also in Table 3, T & SC-BC is compared in terms of efficiency; power range and output ripple with recent DC-DC converters. The voltage conversion ratio and capacitor voltage plot of a conventional boost converter with or without SC or VD stage is depicted in Figure 11e. It is observed that the conversion ratio is double with the voltage doubler compared to without the voltage doubler but the quasi-linear region is slightly reduced. The voltage conversion ratio plot of the proposed T & SC-BC versus duty cycle considering transformer ratio, k = 1 to 5 is depicted in Figure 11f. It is observed that the voltage conversion ratio is greatly increased with the increase in number of the transformer ratio (k) but the quasi-linear region of the converter is decreased.
In Figure 12a, the plot of VCn/Vin (ratio of capacitor voltage to input voltage) versus duty cycle for a single switch n-stage CBC is shown considering stages n = 1 to 5. It is observed that the capacitor rating increases with the increase in stages and duty cycle. Thus, a single switch n-stage CBC requires more rated capacitors compared to a single switch n − 1 stage CBC. In Figure 12b the plot of VCn1/Vin and VCn2/Vin (ratio of capacitor voltage to input voltage) versus duty cycle for a single switch boost converter with voltage multiplier is shown considering stage n = 1 to 5. It is observed that the rating of the capacitor increases with the increase in voltage multiplier stages and duty cycle. In Figure 12c the plot of VC2/Vin (ratio of capacitor voltage to input voltage) versus duty cycle for a coupled inductor-based step-up converter is shown with coupling coefficients k = 1 to 5. It is observed that the capacitor voltage is independent of the coupling coefficient but depends upon the duty cycle. In Figure 12d the plot of VC02/VC01 (ratio of capacitor C02 voltage to capacitor C01 voltage) versus duty cycle for the QBC with coupled inductor is shown with coupled coefficients k = 1 to 5. It is observed that the capacitor voltage depends on the coupling coefficient and also on the duty cycle. Thus, the rating of the capacitor is increased with an increase in coupling coefficient (k) and duty

Simulation and Experimental Results
To verify the proposed converter functionality, the proposed converter is simulated in Matrix Laboratory (MATLAB) and the parameters are tabulated in Table 4. The components are chosen and designed according to Equations (17)- (24).
Trans f ormer Primary Winding, Trans f ormer Secondary Winding, The capacitors value of the proposed converter is calculated with the help of parameters voltage ripple through capacitors, switching frequency (f s ), current through capacitor and turn ratio of transformer (k). In Figure 13a the output voltage and input voltage waveform is depicted. It is observed that a constant 250 V is achieved with an input voltage of 15 V, hence the conversion ratio is 16.67.
The transient period analysis is investigated and it is observed that the time constant (τ) of output and input voltage waveforms is 0.006 s. The output and input voltage at 0.006 s is 157.5 V (63% of 250 V) and 9.45 V (63% of 15 V), respectively. It is observed that a constant 250 V is achieved at 0.035 s (approximately). In Figure 13b the output voltage and current waveform are depicted. It is observed that the time constant (τ) of output voltage and current waveform is 0.006 s. The output voltage and current at 0.006 s is 157.5 V and 0.126 A (63% of 0.2 A), respectively. It is observed that a constant 0.2 A is achieved at 0.035 s (approximately). In Figure 13c the output power waveform is depicted and it is observed that the output power at 0.006 s is 19.84 W. It is observed that a constant 50 W power is achieved at 0.035 s (approximately). In Figure 13d, the inductor (L 1 ) current waveform is depicted with gate pulse of the switch and slope of the waveforms is calculated by Equation (17). It is observed that the inductor (L 1 ) current slope is positive when switch S is in ON state and slope is negative when switch S is in OFF state. In Figure 13e, the switch drain to source voltage (V DS ) waveform is shown and nearly 70 V appears across the switch when it is in OFF state. A fluctuation is observed in the switch voltage due to the voltage across diode D 1 in the sub-modes. The voltage across capacitor C 1 , C 2 and C 01 is depicted in Figure 13f and it is observed that the voltage across capacitor C 01 is 70 V (approximately). The voltage across diode D 0 , D 1 and D 2 is depicted in Figure 13g and it is observed that diode D 0 is in forward biased when switch S is in OFF state. It is also that the voltage across D 1 is less than the voltage across diode D 0 and D 2 . The proposed T & SC boost converter is implemented and the details of parameters or components are provided in Table 5. The experimental setup of the proposed converter is shown in Figure 14. The output voltage and input voltage waveforms are shown in Figure 15a,b. It is observed that 249.6 V is achieved from 15.1 V input supply.
The capacitors value of the proposed converter is calculated with the help of parameters voltage ripple through capacitors, switching frequency (fs), current through capacitor and turn ratio of transformer (k). In Figure 13a the output voltage and input voltage waveform is depicted. It is observed that a constant 250 V is achieved with an input voltage of 15 V, hence the conversion ratio is 16.67. The transient period analysis is investigated and it is observed that the time constant (τ ) of output and input voltage waveforms is 0.006 s. The output and input voltage at 0.006 s is 157.5 V (63% of 250 V) and 9.45 V (63% of 15 V), respectively. It is observed that a constant 250 V is achieved at 0.035 s (approximately). In Figure 13b the output voltage and current waveform are depicted. It is observed that the time constant (τ ) of output voltage and current waveform is 0.006 s.
The output voltage and current at 0.006 s is 157.5 V and 0.126 A (63% of 0.2 A), respectively. It is observed that a constant 0.2 A is achieved at 0.035 s (approximately). In Figure 13c the output power

Future Extension and Combination of the Proposed T & SC-BC Topology with a Voltage Multiplier
To obtain a high voltage, the proposed T & SC-BC also provides a suitable solution by combining the features of a voltage multiplier. The power circuit of the proposed T & SC-BC with voltage multiplier is depicted in Figure 16. The voltage conversion ratio is analyzed and provided in Equation (26). The voltage across a switch is not affected by the voltage multiplier. The voltage multiplier level can be increased without disturbing the main power circuit of the T & SC to raise the voltage conversion ratio more.

Future Extension and Combination of the Proposed T & SC-BC Topology with a Voltage Multiplier
To obtain a high voltage, the proposed T & SC-BC also provides a suitable solution by combining the features of a voltage multiplier. The power circuit of the proposed T & SC-BC with voltage multiplier is depicted in Figure 16. The voltage conversion ratio is analyzed and provided in Equation (26). The voltage across a switch is not affected by the voltage multiplier. The voltage Energies 2018, 11, 783 20 of 23 multiplier level can be increased without disturbing the main power circuit of the T & SC to raise the voltage conversion ratio more.

Future Extension and Combination of the Proposed T & SC-BC Topology with a Voltage Multiplier
To obtain a high voltage, the proposed T & SC-BC also provides a suitable solution by combining the features of a voltage multiplier. The power circuit of the proposed T & SC-BC with voltage multiplier is depicted in Figure 16. The voltage conversion ratio is analyzed and provided in Equation (26). The voltage across a switch is not affected by the voltage multiplier. The voltage multiplier level can be increased without disturbing the main power circuit of the T & SC to raise the voltage conversion ratio more.

Conclusions
A new Transformer and Switch Capacitor-Based Boost Converter (T & SC-BC) is articulated for high-voltage/low-current renewable energy source applications. Conventional boost converter, transformer and switched capacitors functions are combined to design the proposed T & SC-BC for high voltage conversion ratio. A (1 + k)/(1 − D) voltage conversion ratio (V o /V in ) is achieved from the proposed converter where, k is the turns ratio of the transformer and D is the duty cycle. Conspicuous features of the proposed T & SC-BC are: (i) high voltage conversion ratio (V o /V in ); (ii) continuous input current (I in ); (iii) single switch topology; (iv) single input source; (v) low Drain to Source voltage (V DS ) rating of the switch; and (vi) single inductor and single untapped transformer. The proposed T & SC-BC topology has low drain to source switch voltage, low stress on output diodes and requires less components to achieve high voltage compared to recently addressed DC-DC converters. Moreover the cost of the proposed T & SC-BC topology is less and it is also suitable for combination with a voltage multiplier to achieve more voltage at the output. The proposed converter is designed for 50/3 voltage conversion ratio at 78.4% duty cycle and the turns ratio is 2.6. Simulation and experimental results are provided which validate the functionality, design and concept of the proposed approach.