Design of a High Step-Up DC-DC Converter with Voltage Doubler and Tripler Circuits for Photovoltaic Systems

Department of Electrical Engineering, National University of Computer and Emerging Sciences, Islamabad, Pakistan Department of Electrical Engineering, University of Engineering & Technology Mardan, Pakistan School of Electronics and Information Engineering, Taizhou University, Taizhou, 318000 Zhejiang, China Department of Computer Software Engineering, University of Engineering & Technology Mardan, Pakistan Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad 44000, Pakistan


Introduction
Renewable energy generation becomes more popular during the last decade. Renewable energy sources, for example, solar, wind, and fuel cell systems, are most effective sources to reduce the power generation crisis all over the world [1]. Energy resources, for example, coal, natural gas, and oil, have various bad influences on nature, such as pollution and greenhouse impacts; also, there is a massive contradiction among the global energy need and the fossil fuel supply.
The key matters for human being development are lack of energy and environmental pollution. Renewable sources such as photovoltaic modules are a clean energy source, and their addition to the power system is constantly rising. It will contribute a huge amount of electricity among all the renewable energy sources [2,3]. The PV grid-connected power system turns into a fast emergent section in the PV market [4]. Power electronics circuits must be followed for using energy sources (wind cells, solar, and fuel) as a front end of the electrical system [5]. Bidirectional DC-DC converters are also needed in the energy storage systems (ESSs), to store the excess energy during production and release it when needed in peak demand or off peak hours; hence, boost converter is required to step up low voltage of storage system [6]. The full utilization of power is generated through PV module, and to satisfy safety requirements, the latest research trend is to make parallel arrangement of PV module instead of series. A high DC bus voltage is required for the half-bridge, fullbridge, and multilevel grid inverters. The power in series configuration drops off significantly due to partial shading, particularly in the urban regions and mismatch of modules [7]. In this case, the PV parallel arrangement is more effective than the PV series-connected arrangement due to the functioning of PV modules [8,9]. H-bridge multilevel inverters or other multilevel configurations are employed to enhance the PV modules output power in grid-connected PV power system [10,11], but for this, some other power devices are needed, and the cost is increased in these solutions. Renewable sources mostly generate electrical power with small DC voltage. Hence, the electrical power has been produced with low DC voltage, and we know that 1.414 times of AC voltage is needed on the DC side to convert it into the desirable AC voltage. The complete model is shown in Figure 1.
Therefore, DC/DC high step-up converters are required. The conventional boost converters can attain a high gain on a high duty cycle, which causes a reverse recovery problem and high-voltage stress across the switching devices, which decreases the efficiency [12]. A triangle modulation (TRM) scheme decreased circulating current with ZCS behavior for the whole operating range; however, the feasibility of TRM is limited for the operation to gain more than unity [13]. To minimize these issues, it is desirable to plan a DC-DC step-up converter that can attain a high-voltage gain exclusive of high duty cycle, less reverse recovery problem, and improved efficiency with low-voltage stress across the main transistors. Theoretically, boost converter can attain infinite gain, but because of various parasitic in experimental layout, the infinite gain cannot achieve practically. Therefore, to overcome the limitation of such type on gain, different types of solutions have been introduced in the literature. In recent years, switched capacitor voltage boost converter has got more attention because of its exceptional full monolithic integration applications and higher power density as compared with conventional inductor-based voltage boost converters. The multistage switched-capacitor voltage boost converter characteristics can be investigated with no involvement of magnetic components [14,15]. This particular property allows it to be used in analytical models and estimate the performance of voltage boost converter [16,17]. Moreover, conventional models by using simple   International Journal of Photoenergy switched-capacitor voltage boost converters have been reviewed in [18]; a small number of reports on a model using the modified switched-capacitor voltage boost converters can be discovered. Furthermore, even though the usual models practice a switching frequency FS and flying capacitance CF to design voltage boost converter, load capacitance CL and complementary switched-capacitor configuration are not taken into account. Hence, the accuracy of the model is not enough and cannot be used in real voltage boost converters. A switched-capacitor voltage boost converter has been used in the power range from monolithic integration to higher power application [19,20]. Several voltage boost converters have been proposed. Boost converters with switched capacitor are broadly used since they can achieve high-voltage gain by linking voltage boost converters in a cascade [21]. It can generate a high gain, but the overall system efficiency will be reduced because the resultant efficiency will be the product of the efficiencies of the linked converters. Theoretically coupled inductor-based converter increased DC gain, by increasing the turns ratio of the coupled inductor, though the leakage inductance drawback should be thoroughly controlled [22]. Hence, a new interleaved boost converter with voltage doubler and tripler circuit is proposed here which gives improved results in terms of gain and voltage stress across the switching devices on small duty cycle. The circuit diagram of the mentioned topology is presented in Figure 2.
The mentioned topology is a three-phase interleaved circuit which consists of three inductors, voltage doubler and tripler circuits and a basic boost converter circuit. Switching devices M 1 , M 2 , M 3 , M 4 , and M 5 are turned on and off by a PWM source with a 120-degree phase shift for switch M 1 , M 2 , and M 3 , while the switch M 4 will be on when the switch M 1 is off and vice versa. The same is the case for switches M 5 and M 2 , such as both the switches will not be on or off at the same time. The inductors will charge in the on time of the switch M 1 , M 2 , and M 3 and will discharge to the capacitors when the switch M 1 , M 2 , and M 3 are in off state. With the proposed topology, the voltage gain will increase, and voltage stress across the switches, such as voltage drop, will reduce; hence, the losses will decrease.

Operating Principle of Proposed Converter
A three-phase interleaved boost converter with voltage doubler and tripler circuit is proposed in this paper. The belowmentioned assumptions were made for the operation of the mentioned converter.
(1) Capacitor C 1 , C 2 , C 3 , and Co are of enough size that the voltage ripple is minor through them compared to their DC values The operating mode is continuous conduction mode; thus, the current I 1 through inductor L 1 , I 2 through inductor L 2 , and I 3 through inductor L 3 flow continuously (4) Inductors L 1 , L 2 , and L 3 have the same inductance L All switches are operated by PWM signals. Signals for switchs M 1 , M 2 , and M 3 are having a phase shift of 120 degrees. The PWM signal for switch M 4 is the inverse of switch M 3 , and the signal to switch M 5 is the inverse signal of the switch. V S is the input voltage, and V O is the output voltage. The proposed is converter operating with constant switching constant frequency F S , where T S = 1/F S . For the proposed converter, there are six switching states such as modes in one complete switching period as shown in Figure 3 and a few major waveforms defining the operating behavior of the mentioned converter. The six switching states are t o = 0 sec, t 1 = ðDTs − 2Ts/3Þ sec, t 2 = ðTs/3Þ sec, t 3 = ðDTs − Ts/3Þ sec,t 4 = ð2Ts/3Þ sec, t 5 = DTs sec, and t 6 = ðTsÞ sec All the six switching states are described as follows: States I, III, and V are the same for the proposed converter. It begins when switches M 1 , M 2 , and M 3 are set high at starting of time with PWM signals to V GS1 , V GS2 , and V GS3 . Diodes D 1 , D 2 , D 3 , and D 4 are off in these states. The circuit diagram for this state is shown in Figure 4. Inductors L 1 , L 2 , and L 3 are get charged by DC input voltage, and I 1 , I 2 , and I 3 through inductors L 1 , L 2 , and L 3 rise linearly with slopes VS/L1, VS/L2, and VS/L3, respectively. The capacitors C 1 , C 2 , and C 3 are neither charges nor discharges. In this state, the output capacitor C O discharges to load, and  This circuit diagram for this state is shown in Figure 5. The inductor L 1 discharge in this state to capacitors C 2 and C 3 , while L 2 and L 3 are still charging, and I 2 and I 3 through inductors L 2 and L 3 constantly rise with a slope of VS/L2 and VS/L3, respectively. So, in this state, the voltage across capacitors C 2 and C 3 increases because the capacitor is charging. Voltage across capacitor C 1 is still constant because current is not flowing through capacitor C 1 . In this state, the output capacitors C O discharge to load resistance, and hence, the voltage V O at output across C O falls linearly with a slope of −VO/ðRL * COÞ.
The circuit diagram for this state is presented in Figure 6. Inductor L 1 is charging, and I 1 and I 3 through inductors L 1 and L 3 increase linearly with a slope of VS/L1 and VS/L3, correspondingly, inductor L 2 and capacitors C 2 and C 3 are discharging to capacitor C 1 .So, in this state, the voltage across capacitors C 2 and C 3 decreases, and voltage across capacitor C 1 increases. In this state, the output capacitor C O discharges to load; hence, the voltage at the output V O through C O decreases linearly with a slope of −VO/ðRL * CoÞ.    The circuit diagram for this interval is presented in Figure 7. Inductors L 2 and L 3 are charging while L 1 is discharging. I 2 and I 3 rise linearly with a slope of VS/L2 and Vs/L3 correspondingly, and inductor L 1 and capacitor C 1 are discharging to capacitor Co and load Ro. The voltage across capacitor C 1 is decreasing and the output capacitor Co gets charging, and hence, the voltage at output such as V O across Co increases linearly.

Steady-State Analysis
To make an easy and simple assessment of the proposed circuit diagram, the time intervals for switching states put across in terms of switching period TS of duty cycle D as follows: t o = 0 sec, t 1 = ðDTs − 2Ts/3Þ sec, t 2 = ðTs/3Þ sec, t 3 = ðDTs − Ts/3Þ sec, t 4 = ð2Ts/3Þ sec, t 5 = DTs sec, and t 6 = ðTsÞ sec.

DC Conversion Ratio.
Voltage gain can be derived by using volt-second balance principles. Inductor L 3 is charging in states I, III, IV, V, and VI and discharging in state II.
The volt second balance of inductor L 2 gives: Similarly, inductor L 2 is charging during the interval I, II, III, V, and VI and discharging in IV.
The volt second balance of inductor L 2 gives: Inductor L 1 gets charged during states I, II, III, IV, and V and discharged during interval VI.
The volt second balance of inductor L 2 gives: The gain of the proposed converter is obtained as: The voltage stress through switch M 2 can be obtained as  International Journal of Photoenergy The voltage stress across the switch M 3 can be obtained as 3.3. Ripple Current and Ripple Voltage. The Δi1 is the ripple current in current I 1 , Δi2 in current I 2 , and Δi3 in current I 3 .
The ripple current through inductors L 1 , L 2 , and L 3 can be expressed as follows: The ΔVco is the ripple voltage in V CO , ΔVc1 in V C1 , Δ Vc2 in V C2 , ΔVc3 in V C3 , and ΔVc4 in V C4 .
For finding ΔVco, the capacitor CO is discharging to the load. The ΔVco can be expressed as follows: For ΔVc1, capacitor C 1 is discharging to Co and load; ΔVc1 can be expressed as follows:

International Journal of Photoenergy
Here, I1 can be expressed as follows: For finding ΔVc2, capacitor C 2 is discharging to C 1 ; Δ Vc2 can be expressed as follows: For finding ΔVc3, capacitor C 3 is discharging to C 1 ; Δ

International Journal of Photoenergy
Vc2 can be expressed as follows: 3.4. Voltage Stress across the Switches. Voltage stress across the MOSFET M 1 can be expressed as follows: Voltage stress across the MOSFET M 2 can be expressed as follows:

Results
The simulation has been performed in Matlab Simulink to verify the performance of the proposed interleaved triphase boost converter and conventional DC-DC interleaved boost converter with parameters given in Table 1. The derived mathematical equations have been used up to obtain the theoretical results presented in Table 1.

Simulation Results.
Output voltage waveforms of the proposed boost converter with a 70% duty cycle is 200 V shown in Figure 8 The voltages stress across the MOSFET M 1 , M 2 , and M 3 is 50 V as shown in Figures 9(a)-9(c); the phase current through inductors L 1 , L 2 , and L 3 is shown in Figure 10.
The simulation results clearly show that there is no difference between simulation results and theoretical results.

4.2.
Comparison. Now, utilizing the parameters given in Table 1, the simulation results of the conventional DC-DC interleaved boost converter are also acquired. The output voltage waveform of the conventional boost converter is given in Figure 11, which is 50 volts with a 70% duty cycle. The conventional interleaved boost converter gives the output voltage 200 volts on a 92.5% duty cycle value such as D = 0:925 (as shown in Figure 12 It is clear from the simulation results that the presented converter topology has very good results as compared to the conventional interleaved DC-DC boost converter. As compared with a conventional converter, it is obvious that the proposed boost converter has a four times higher voltage conversion ratio, and the voltage stresses on main switches are approximately four times smaller than the conventional DC-DC interleaved boost converter. In the conventional IBC, the output voltage appears across the main switching devices, while the current is divided into all phases, due to which the inductor size is reduced in both conventional and proposed IBC. Simulation results are provided for the conventional interleaved DC-DC boost converter and proposed interleaved DC-DC boost converter, which indicates that the proposed converter yields better results as compared with a conventional interleaved boost converter at the expense of only two additional switches (proposed converter uses 5 MOSFETs while conventional uses 3). The comparisons between the gain of the conventional IBC and proposed IBC are shown in Figure 14.

Conclusion
Compared with the conventional IBC, the proposed IBC has several good extra characteristics, which comprise a high gain/conversion ratio, and across the main MOSFETs, the low-voltage stress. Voltage doubler plus voltage tripler circuits are used to gain these benefits. The steady-state analysis and working principle of the offered converter of each state are examined clearly with the proposed circuit diagram and mathematical equations. Simulation results in Matlab Simulink show that normal interleaved DC-DC boost converter is affected by operating on extreme value of D (duty cycle) and will be having reverse recovery problem for switching devices for boosting 15-volt input voltage to 200 volts, while it is clear from both the simulation and theoretical outcomes that the presented converter can simply achieve 200 V with the appropriate value of D, and the voltage stress across the switches will also reduce to one-fourth of output voltage. The above-mentioned qualities of high DC-DC conversion ratio and reduced voltage stress across switching devices make the mentioned boost converter an appropriate candidate in case of low voltage renewable sources with low DC output voltages and more other functions where a high step-up conversion ratio is wanted.

Data Availability
Data will be provided on request.