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

Abstract

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.

1. 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 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.

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):

$$\begin{array}{l}I=I_{ph}-I_d-I_{Sh},I_d=I_o(e^{\frac{V+I{R}_S}{n{V}_T}}-1),I_{Sh}=\frac{V+I{R}_S}{R_{Sh}}\\ V_T=\frac{kT}{q},V_T=0.0259VatT=25°\mathrm{C}\end{array}\}$$

(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]. The concept of the P & O MPPT algorithm is shown in Figure 4a–c with the P-V and I-V characteristics. To extract the maximum power, a P & O MPPT control mechanism is used to locate the MPP for the proposed T & SC-BC.

The conspicuous features of proposed T & SC-BC are:

(1)

High voltage conversion ratio (V_o/V_in),

(2)

Continuous input current (I_in),

(3)

Single switch topology,

(4)

Single input source,

(5)

Low Drain to Source voltage (V_DS) rating of switch,

(6)

Single inductor and single untapped transformer.

Simulation and experimental result are provided which validate the functionality, design and concept of the proposed approach.

2. 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. L_P 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. L_S 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 sub- modes 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.

2.1. 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.

$$\begin{array}{l}Loop-1\to V_{in}-V_{L1}-V{C}_{01}=0\\ Loop-2\to V_{in}-V_{L1}+V{C}_1-V_{LP}-V{C}_{01}=0\\ Loop-3\to V_{LS}+V{C}_2-V_{CO}+V{C}_{01}=0\end{array}\}$$

(2)

2.2. 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.

$$\begin{array}{l}Loop-1\to V_{in}-V_{L1}+V{C}_1=V_{LP}+V{C}_{01}\\ Loop-2\to V_{LS}+V{C}_2=V_{CO}-V{C}_{01}\end{array}\}$$

(3)

2.3. 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.

$$\begin{array}{l}Loop-1\to V_{in}-V_{L1}=0\\ Loop-2\to V{C}_1-V_{LP}-V{C}_{01}=0\\ Loop-2\to V_{LS}+V{C}_2+V{C}_{01}=V_{CO}\end{array}\}$$

(4)

2.4. 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.

$$\begin{array}{l}Loop-1\to V_{in}-V_{L1}=0\\ Loop-2\to V{C}_1-V_{LP}-V{C}_{01}=0\\ Loop-3\to V{C}_2=-V_{LS}\end{array}\}$$

(5)

2.5. 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.

$$\begin{array}{l}Loop-1\to V_{in}-V_{L1}=0\\ Loop-2\to V{C}_1=V_{LP}+V{C}_{01}\end{array}\}$$

(6)

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.

$$\begin{array}{l}\frac{V_o}{V_{in}}=\frac{2}{1-D}=\frac{2T}{T-t_{on}}\\ V_{DS}=\frac{1}{1-D}{V}_{in}=\frac{V_o}{2}=\frac{T}{T-t_{on}}{V}_{in}\end{array}\}$$

(7)

The voltage conversion ratio (V_o/V_in) and Drain to Source voltage of switch (V_DS) of the proposed T & SC-BC are calculated by Equation (8), where T is the total time of one switching cycle. The relation of V_DS/V_in with duty cycle (D) is graphically shown in Figure 9b. The relation of voltage conversion ratio (V_o/V_in), turns ratio (k), and duty cycle (D) of the proposed T & SC-BC is shown graphically in 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.

$$\begin{array}{l}\frac{V_o}{V_{in}}=\frac{1+k}{1-D}=\frac{(1+k)T}{T-t_{on}}\\ V_{DS}=\frac{1}{1-D}{V}_{in}=\frac{V_o}{1+k}=\frac{T}{T-t_{on}}{V}_{in}\\ k=\frac{\mathrm{Turns}\mathrm{of}\mathrm{Sec}\mathrm{ondary}\mathrm{winding}\mathrm{of}\mathrm{transformer}(N_{LS})}{\mathrm{Turns}\mathrm{of}\mathrm{Primary}\mathrm{winding}\mathrm{of}\mathrm{transformer}(N_{LP})}\end{array}\}$$

(8)

3. 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 D₁ semiconductor loss is V_D1; (iii) forward conduction loss of diode D₁ 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 L₁; (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 L₁, switch S and capacitor C₀₁ respectively. I_L1, Is and I_C01 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 V_in:

$$\begin{array}{l}{V}_{in}-v_{L1}-i_{in}{R}_{L1}-i_s{R}_s=0,i_{in}=i_s\\ v_{L1}=V_{in}-i_{in}(R_{L1}+R_s)\approx V_{in}-I_{in}(R_{L1}+R_s)\\ i_c(t)=-V_{c01}/R_{T\&SC}\end{array}\}$$

(9)

when switch is in OFF state, diode D₁ is conduct and inductor is discharged to charge capacitor C₀₁:

$$\begin{array}{l}{V}_{in}-v_{L1}-i_{in}{R}_{L1}-i_{D1}{R}_{D1}-V_{D1}-V_{c01}=0,i_{in}=i_{D1}\\ v_{L1}=V_{in}-i_{in}(R_{L1}+R_{D1})-V_{D1}-V_{c01}\approx V_{in}-I_{in}(R_{L1}+R_{D1})-V_{D1}-V_{c01}\\ i_c(t)=i_{in}-V_{c01}/R_{T\&SC}\end{array}\}$$

(10)

Inductor volt second balance method and capacitor charge method is used to calculate the voltage conversion ratio equation:

$$\begin{array}{l}{V}_{c01}=(\frac{1}{1-D})(V_{in}-(1-D)V_{D1})(\frac{{(1-D)}^2{R}_{T\&SC}}{{(1-D)}^2{R}_{T\&SC}+R_{L1}+D{R}_s+(1-D)R_{D1}})\\ \frac{V_{c01}}{V_{in}}=(\frac{1}{1-D})(1-\frac{(1-D)V_{D1}}{V_{in}})(\frac{1}{1+\frac{R_{L1}+D{R}_s+(1-D)R_{D1}}{{(1-D)}^2{R}_{T\&SC}}})\end{array}\}$$

(11)

$$V_o=V_{c01}(1+k)-losses\mathrm{of}\mathrm{transformer}$$

(12)

$$\begin{array}{l}{V}_o=(1+k)(\frac{1}{1-D})(V_{in}-(1-D)V_{D1})(\frac{{(1-D)}^2{R}_{T\&SC}}{{(1-D)}^2{R}_{T\&SC}+R_{L1}+D{R}_s+(1-D)R_{D1}})\\ \frac{V_o}{V_{in}}=(1+k)(\frac{1}{1-D})(1-\frac{(1-D)V_{D1}}{V_{in}})(\frac{1}{1+\frac{R_{L1}+D{R}_s+(1-D)R_{D1}}{{(1-D)}^2{R}_{T\&SC}}})\end{array}\}$$

(13)

$$ConversionLosses=(\frac{1+k}{1-D})\frac{(1-D)V_{D1}}{V_{in}}(\frac{1}{1+\frac{R_{L1}+D{R}_s+(1-D)R_{D1}}{{(1-D)}^2{R}_{T\&SC}}})$$

(14)

$$\eta ,efficiency=\frac{(1-\frac{(1-D)V_{D1}}{V_{in}})}{1+\frac{R_{L1}+D{R}_s+(1-D)R_{D1}}{{(1-D)}^2{R}_{T\&SC}}}\}$$

(15)

If all the components efficiency is 100% (ideal components) then:

$$Losses=0,\eta =100\%and\frac{V_o}{V_{in}}=(1+k)(\frac{1}{1-D})$$

(16)

The ideal voltage conversion ratio of T & SC-BC is given in Equation (16).

4. 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. Comparison summary of the proposed T & SC-BC with recently addressed DC-DC converters.

DC-DC Converter	Voltage Conversion Ratio (Vo/Vin)	Number of Switches	Number of Inductors	Number of Capacitors	Number of Diodes
Single switch n-stage CBC [38]	$\frac{1}{{(1-D)}^n}$	1	n	n	2n − 1
Single switch boost converter with voltage multiplier [38]	$\begin{array}{l}\frac{n+D}{1-D},n=1,3\dots \\ \frac{n+1+D}{1-D},n=2,4\dots \end{array}$	1	2	2n + 1	2n
Coupled inductor based step-up converter [39]	$\frac{1+(1+k)D}{1-D},k=\frac{n_2}{n_1}$	1	3 (2 Inductor are Coupled)	3	3
Quadratic Boost Converter (QBC) with coupled inductor [40]	$\frac{1+kD}{{(1-D)}^2},k=\frac{n_2}{n_1}$	1	3 (2 Inductor are Coupled)	3	4
Boost converter with voltage doubler (Figure 5a)	$\frac{2}{1-D}$	1	1	3	3
Proposed converter	$\frac{1+k}{1-D},k=\frac{n_{LS}}{n_{LP}}$	1	1 Inductor with 1 transformer	4	3

n = Number of stages and k = Turns ratio.

, 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 = n₂/n₁) 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 = n₂/n₁) 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.

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. Comparison of the proposed T & SC-BC with recent DC-DC converters in terms of cost.

DC-DC Converter	Cost of Converter
Single switch n-stage CBC [38]	CS + [n × CL] + [n × CC] + [(2n − 1) × CD]
Single switch boost converter with voltage multiplier [38]	CS + [2 × CL] + [(2n + 1) × CC] + [(2n) × CD]
Coupled inductor based step-up converter [39]	CS + [(1 × CcL) + (1 × CL)] + [3 × CC] + [3 × CD]
QBC with coupled inductor [40]	CS + [(1 × CcL) + (1 × CL)] + [3 × CC] + [4 × CD]
Boost converter with voltage doubler (Figure 5a)	Cs + CL + [3 × CC] + [3 × CD]
Proposed T & SC-BC	CS + [(1 × CcL) + (1 × CT)] + [4 × CC] + [3 × CD]

C_s = Cost of single switch, C_L = Cost of single inductor, C_C = Cost of single capacitor, C_D = Cost of single diode, C_T = Cost of Transformer, C_CL = Cost of two inductor with couple effect.

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.

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 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 VC₂/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 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 cycle (D). In Figure 12e the plot of VC₀₁/V_in (ratio of capacitor C₀₁ 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. Comparison of the proposed T & SC-BC with recently addressed DC-DC converters in terms of switch drain to source voltage.

DC-DC Converter	Switch Drain to Source Voltage (VDS)	Efficiency	Applications	Output Ripple
Single switch n-stage CBC [38] (Figure 2a)	$\frac{V_{in}}{{(1-D)}^n},n=1,2,3\dots$	moderate (85–90%)	low/medium power	high
Single switch boost converter with voltage multiplier [38], (Figure 2b)	$\frac{V_{in}}{1-D}$	moderate (85–90%)	low/medium power	high
Coupled inductor based step-up converter [39], (Figure 2c)	$\frac{V_{in}}{1-D}$	high (90–95%)	medium/high power	low
Quadratic Boost Converter (QBC) with coupled inductor [40], (Figure 2d)	$\frac{V_O}{1+kD},k=\frac{n_2}{n_1}=1,2,3\dots$	high (90–95%)	medium/high power	low
Conventional boost converter with voltage doubler (Figure 5a)	$\frac{V_{in}}{1-D}$	high (90–95%)	low/medium power	high
Proposed converter (Figure 5b)	$\frac{V_{in}}{1-D}$	high (90–95%)	medium/high power	low

. 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.

5. 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. Simulation parameters of the proposed T & SC-BC.

Parameter	Value
Input voltage (Vin), Output voltage (Vo)	15 V, 250 V
Input current (Iin), Output current (I o)	3.34 A, 0.2 A
Power (P)	50 W
Duty cycle (D)	0.784
Switching frequency (fs)	20 kHz
Switch Drain to Source voltage (VDS)	70 V (Minimum Voltage)
Inductor (L1)	117.6 µH
Transformer windings	LP = 117.6 µH, LS = 794.97 µHTurns ratio, k = 2.6
Capacitors (C1, C2)	2.5 µF, 250 V
Capacitor C0 and C01	100 µF, 400 V

. The components are chosen and designed according to Equations (17)–(24).

$$Dutycycle,D=\frac{V_O-V_{in}(1+k)}{V_O}=\frac{250-15(1+2.6)}{250}=0.784or78.4\%$$

(17)

$$SwitchVoltage,V_{DS}=\frac{V_{in}}{1-\frac{T_{ON}}{T}}=\frac{V_{in}}{1-f{T}_{ON}}=\frac{V_{in}}{1-D}=\frac{15}{1-0.784}=69.44V\approx 70V$$

(18)

$$\begin{array}{l}Diode{D}_{0}Voltage,V_{D0}=\frac{n_{LS}}{n_{LP}}\times \frac{V_{in}}{1-\frac{T_{ON}}{T}}\\ =\frac{k{V}_{in}}{1-f{T}_{ON}}=\frac{k{V}_{in}}{1-D}=\frac{2.6\times 15}{1-0.784}=180.5V\approx 181V\end{array}\}$$

(19)

$$Diode{D}_{1}Voltage,V_{D1}=\frac{V_{in}}{1-\frac{T_{ON}}{T}}=\frac{V_{in}}{1-f{T}_{ON}}=\frac{V_{in}}{1-D}=\frac{15}{1-0.784}=69.44V\approx 70V$$

(20)

$$\begin{array}{l}Diode{D}_{2}Voltage,V_{D2}=\frac{n_{LS}}{n_{LP}}\times \frac{V_{in}}{1-\frac{T_{ON}}{T}}\\ =\frac{k{V}_{in}}{1-f{T}_{ON}}=\frac{k{V}_{in}}{1-D}=\frac{2.6\times 15}{1-0.784}=180.5V\approx 181V\end{array}\}$$

(21)

$$Inductor,L_1=\frac{V_{in}\times \frac{T_{ON}}{T}}{\Delta i{L}_1\times f}=\frac{V_{in}\times DT}{\Delta i{L}_1}=\frac{15\times 0.784}{5\times 20000}=117.6\mu H$$

(22)

$$TransformerPrimaryWinding,L_P=\frac{V_{in}\times \frac{T_{ON}}{T}}{\Delta i{L}_1\times \frac{1}{T}}=\frac{V_{in}\times DT}{\Delta i{L}_1}=\frac{15\times 0.784}{5\times 20000}=117.6\mu H$$

(23)

$$TransformerSecondaryWinding,L_S=k^2\times \frac{V_{in}\times \frac{T_{ON}}{T}}{\Delta i{L}_1\times \frac{1}{T}}=k^2\times \frac{V_{in}\times DT}{\Delta i{L}_1}=794.97\mu H$$

(24)

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 ($\tau$) 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 ($\tau$) 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 (L₁) 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 (L₁) 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 D₁ in the sub-modes. The voltage across capacitor C₁, C₂ and C₀₁ is depicted in Figure 13f and it is observed that the voltage across capacitor C₀₁ is 70 V (approximately). The voltage across diode D₀, D₁ and D₂ is depicted in Figure 13g and it is observed that diode D₀ is in forward biased when switch S is in OFF state. It is also that the voltage across D₁ is less than the voltage across diode D₀ and D₂. The proposed T & SC boost converter is implemented and the details of parameters or components are provided in

Table 5. Parameters and component details of the prototype of the proposed T & SC-BC.

Parameter	Value
PV Panel	3 PV Panels (each of 18 V)
Input Voltage (Vin), Output Voltage (Vo)	15 V, 250 V
Input Current (Iin), Output Current (Io)	3.34 A, 0.2 A
Power (P)	50 W
Duty Cycle (D)	0.784
Switching frequency (fs)	20 kHz
Switch Drain to Source Voltage (VDS)	70 V (Minimum Voltage)
Inductor (L1)	120 µH
Transformer Windings	LP = 120 µH, LS = 800 µH Turns ratio = 2.6
Capacitors (C1 and C2)	3.3 µF, 250 V
Capacitor C0 and C01	100 µF, 400 V
Diode (D1, D2, D0)	MUR 860
Control Switch	IRF 540

. 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.

$$\begin{array}{l}\frac{d{i}_{L1}}{dt}=\frac{V{L}_{1ON}}{L_1}=PositiveSlope\\ \frac{d{i}_{L1}}{dt}=\frac{V{L}_{1OFF}}{L_1}=NegativeSlope\end{array}\}$$

(25)

6. 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.

$$\begin{array}{l}\frac{V_{C01}}{V_{in}}=\frac{1+k}{1-D}=\frac{(1+k)T}{T-t_{on}},\frac{V_{C03}}{V_{in}}=2\times \frac{1+k}{1-D}=2\times \frac{(1+k)T}{T-t_{on}}\\ \frac{V_{C05}}{V_{in}}=3\times \frac{1+k}{1-D}=3\times \frac{(1+k)T}{T-t_{on}},\\ \frac{V_{C02N-1}}{V_{in}}=\frac{V_o}{V_{in}}=N(\frac{1+k}{1-D})=N\frac{(1+k)T}{T-t_{on}}\\ V_{DS}=\frac{1}{1-D}{V}_{in}=\frac{V_{Co1}}{1+k}=\frac{V_o}{N(1+k)}=\frac{T}{T-t_{on}}{V}_{in}\\ k=\frac{TurnsofSecondarywindingoftransformer(N_{LS})}{Turnsofprimarywindingoftransformer(N_{LP})}\\ N=numberofvoltagemultiplierstage\end{array}\}$$

(26)

7. 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.