A New DC-DC Double Quadratic Boost Converter

A New DC-DC Double Quadratic Boost Converter Franciéli L. de Sá, Domingo Ruiz-Caballero, Samir A. Mussa Federal University of Santa Catarina, Department of Electrical Engineering, Power Electronics nstitute; Pontifícia Universidad Católica de Valparaíso. Florianópolis, Brazil; Valparaíso, Chile Phone: +55 (48) 371-94; +56 (3) 7-3695 Fax: +55 (48)334-54 Email: {francieli; samiramussa} @inep.ufsc.br; {domingo.ruiz} @ucv.cll URL: http://www.inep.sites.ufsc.br Acknowledgments The authors gratefully acknowledge to National Council for Scientific and Technological Development (CNPQ), the Federal University of Santa Catarina (Brazil), all for financial support and structure provided. The assistance is gratefully acknowledged for the Walbermark M. dos Santos, a graduate student at the Federal University of Santa Catarina, for their help and collaboration in the work. Keywords <<DC-DC Converter non-isolated high-gain>>, <<External characteristic of converter>>. Abstract This paper presents a study of a new dc-dc converter non-isolated high gain called Double Boost Quadratic Converter. The external characteristic curve is made analyzing the topological states and the waveforms of converter. n addition to the simulation results, experimental results are present, confirming the theoretical analysis and simulated results. ntroduction n the last years has been growing concern about the increased consumption and energy efficiency. n this context, the system of generation and supply of power has been optimized, by producing energy in a distributed manner. n cases where distributed generation is done in continuous current, as for example the photovoltaic and the fuel cells, and still it is need of a great increase in output voltage, it becomes eresting to use the DC-DC converters with high gain. The DC-DC converters with high gain have been studied in several works. n [1] was presented the switching cell of the DC-DC converters quadratics. After the analyse of converter was developed in continuous, critical and discontinuous conduction mode, []. The study of Converter Boost quadratic quasi-resonant, was exposed in [3]. A new DC-DC quadratic converter based on the works of [1] and [] was roduced in [4], this converter was also shown in the works [5] and [6]. nside this paper the study of a new DC-DC Converter non-isolated high-gain also called Double Boost Quadratic Converter is made. n the study of the converter is performed the analysis the operating stages, it is made the curve ideal characteristic of static transfer of the converter operating in continuous, critical and discontinuous conduction mode, as well as the drawing of the external characteristic curve of the converter. The experimental results confirm the theoretical analysis and simulation results. Converter Topology The Double Boost Quadratic Converter Proposed is characterized by average output voltage is higher than the input voltage, and the voltage on the ermediates capacitors also greater than the input voltage. n this structure the inductances L 1 and L are placed in series with the power supply V in and with the ermediate capacitor, respectively. Thus, both the power supply as the ermediate capacitor will behave

as a current source. The output capacitors should behave as a voltage source. An eresting question that simplifies the analysis of the topology of the converter is its symmetry, the lower components have the same behavior of the upper. The Figure 1 shows the topology Double Boost Quadratic Converter Proposed. n this structure the voltage across switches S 1 and S are equal to half of the output voltage total. L1 D1 L D D 3 S 1 C 1 C V 1 R1 in C S C R D 6 L 4 D 5 L 3 D 4 Figure 1: Topology of Double Boost Quadratic Converter Proposed. deal Characteristic of Static Transfer of the Converter Continuous Conduction Mode Analysis of the operating stages: First Stage: (t, t 1 ) At this stage the switches S 1 and S are closed. The diodes D and D 4 are inversely polarized, isolating the output of power supplies L1 and L, that during this stage are a short circuited. The current i S1 is equal to the sum of L1 with L, and the current i D1 is null. Second Stage: (t 1, t ) At this stage the switches S 1 and S are open. The diodes D and D 4 come o conduction and current sources L1 and L, begin to deliver energy to the output. n this stage, the current i S1 and i S are null, i D1 L1 and i D L. The topological states in continuous conduction mode, are presented in Figure, as well as the command to the switches S 1 and S. According to the operating stages described, the structure shows the waveforms in Figure 3, with their respective time ervals corresponding to each stage. Figure : Stages operating of Converter in Continuous Conduction: a) First Stage; b) Second Stage; c) Single command of the switches S 1 e S.

S,S 1 1 L1 L 1 _max L 1_md input L 1 _min L L _max L _md S1 L _min + S 1_max L 1_max L _max D1 D 1 _max D 1_md V V _ max V _ min V VS 1_max = V _max/ S 1,S t 1 st Stage t 1 nd Stage t T S Time(s) Figure 3: Waveforms Double Boost Quadratic Converter Proposed operating in continuous conduction mode. To survey the ideal curve of static gain, considers the source V in and the inductor L 1 a source of constant current L1. The energy supplied by the source ω in in one operating period is equal to (1). ω in = V in. L1. t 1 (1) The energy received by ermediate capacitor ω C1 for an operating period is given by (). ω C1 = V C1. L1. t () Considering the converter an ideal system, in a period of operating, all energy supplied by the source ω in is received by ermediate capacitor ω C1. Thus, equating the equations 1 and we obtain the gain static ideal equation for the first part of the converter, as shown in (3). V C1 = 1 V in 1 D (3) The same analysis is performed for the second part of the converter, considering the source of the input the ermediate capacitor V C1, and the inductor L a source of constant current L. Using the principle of superposition, for the first and second parts of converter analyzed, obtains the static gain total ideal of the Double Quadratic Boost Converter Proposed as a function of the output voltage for the input voltage, given in (4): V V in = 1 (1 D) (4) The Figure 4 presents the static gain curve as a function of duty cycle for Double Boost Quadratic Converter Proposed, for comparison purposes is also presented the static gain curve the Boost Converter Conventional.

1 8 Double Quadratic Boost Conventional Boost V/Vin 6 4.1..3.4.5.6.7.8.9 1 D Figure 4: deal Static Gain of the Double Boost Quadratic Converter compared with the deal Static Gain of Boost Converter Conventional. Critical Conduction Mode The stages of operation for the critical conduction mode are the same described for the continuous conduction mode. What distinguishes these two modes operation is that the current in the inductors have minimum value min equal to zero. Thus, during the first stage of operation, the currents in the inductors L 1 and L are initially zero and they are again canceled exactly at the end of the period of operation of the converter. The waveforms of the converter operating in critical conduction mode is showed in the Figure 5, with respective time ervals corresponding to each stage. S,S 1 1 L1 L S1 L 1 _max L _max L 1_md + S 1_max L 1_max L _max L _md input D1 D 1 _max D 1_md V V _ max V _ min V V 1 = V / S 1,S S _max _max t 1 st Stage t 1 nd Stage t T S Time(s) Figure 5: Waveforms Double Boost Quadratic Converter Proposed operating in Critical Conduction Mode. The calculation of the critical inductances L 1 and L is accomplished by analyzing the current ripple in the inductors, as shown in (5) and (6). L1 L1 max = V in L 1.t 1 = V in L 1. D f L L max = V C1 L.t 1 = V C1 L. D f (5) (6)

The average current ermediate shown in Equation (7) is given from the average current of the diode D 1 to the first part of the analysis of the converter, which will be the input voltage V in and output voltage V C = V C1 +V C. For the second part of the analysis of the converter, which is considered to V C input voltage and output voltage V = V C1 +V C, the output current is given by the average current in the diode D, as shown in Equation (8). = 1 T s = 1 T s T T ( L1 max + L1 min i D1 (t)dt = ( L max + L min i D (t)dt = ).(1 D) (7) ).(1 D) (8) Given the maximum and minimum values of the input current L1 max and L1 min as a function of the current ermediate capacitor for continuous conduction mode, the critical inductance is found canceling the current L1 min, and substituting Equation (5) in Equation (7), obtaining (9). (1 D) V in.d.l 1 CR. f (9) Thus, the critical inductance L 1 is given by (1). L 1 CR = V in. f..d.(1 D) (1) Repeating the same analysis for the inductor L, data the maximum and minimum values of the input current L max and L min as a function of current of the output capacitor for continuous conduction mode, the critical inductance is found canceling out the current L1 min, and substituting Equation (6) in Equation (8), obtaining (11). L CR = V C f..d.(1 D) (11) Discontinuous Conduction Mode The topological states for the discontinuous conduction mode are described below. The 1 st and nd stages of operation are identical to continuous conduction mode, therefore will not be described again in this section. Thrid Stage: (t, t 3 ) At this stage all the energy stored in L was transferred to the load. Therewith, the diode D blocks and the capacitors, C 1 and C, feeding the load. The inductor L 1 continues to provide energy to the capacitors C 1 and C. Fourth Stage: (t 3, t 4 ) n this last stage, all the energy stored in the inductor L 1 disappears and the diode D 1 blocks. n this step just the capacitors C 1 and C feed the load. The Figures 6 and 7 show the stages operating and waveforms of the converter, respectively. To analyze the static gain in the discontinuous conduction mode the ripple current in the inductor L 1 is considered again, as in (1). Since the inductor voltage is equal to the input voltage for the first stage of operation. L1 L1 max = V in.l 1 dis. D f Analyzing the currents of the inductor L 1 and of the diode D 1, to the first part of the converter as shown in Figure 7, it is possible obtain the Equation (13). (1) L1 md D1 md L1 max.d (13)

Figure 6: Stages operating of Converter in discontinuous conduction mode: a) First Stage; b) Second Stage; c) Third Stage; d) Fourth Stage; e) Command of switches S 1, S. S,S 1 1 L1 L S1 L 1 _max L _max L 1_md + input S 1_max L 1_max L _max L _md D1 D 1 _max D 1_md V V _ max V _ min V V S 1,S S 1_max = V _max/ V VS1 = VD+ t t 1 t t 3 t4 3 rd 1 st Stage nd Stage T S 4 th Stage Time(s) _max Figure 7: Waveforms in discontinuous conduction mode.

Assuming that the power at the input of the converter is equal to the sum of the powers in the ermediate capacitors V C1 and V C, and still substituting in (13) L1 max given in Equation (1), results in the Equation (14): ( ) D. VC 1 = V in. D V in.l 1 dis f (14) Rearranging Equation (14), is found (15) relative the first part of the ideal static gain of the converter operating in discontinuous conduction mode: V C = 1 + V in.d V in. C.L 1 Dis. f (15) Repeating the analysis of L 1 to the inductor L obtains (16), referring to the second part of the gain equation: V = 1 + V C.D V C..L Dis. f (16) To obtain the static gain total ideal of the converter operating in discontinuous conduction mode uses the principle of superposition of (15) and (16), getting (17). V = (1 + V in.d ) (17) V in..l Dis. f t is observed in (17), the duty cycle D must be able to compensate both variations of the input voltage V in, as the load variations. External Characteristic of Converter Analyzing the equation of static gain in Continuous Conduction Mode (4), in Discontinuous Conduction Mode (17), and making a = V /V in and γ =..L. f /V in, is obtained the equations of static gain for continuous and discontinuous conduction mode in a simplified manner. Making the necessary substitutions the equation (18) is obtained, which represents the boundary between the continuous conduction mode and discontinuous conduction mode. The Figure 8 shows the curve that represents the external characteristic of converter. a 1 γ = a (18) 5 D = 5. D = 5. D = 75. 15 V a= V in 1 5 1.. 3. 4. 5. γ=.l..fs Figure 8: External characteristic of the Proposed Converter. V in

Simulation Results n this section are presented the simulation results of the Double Boost Quadratic Converter Proposed. The Table shows the values used in the simulation of the converter. The modulation used in the simulation was the conventional PWM, just the comparison of the modulating of reference with triangular carrier. The simulation of the converter was performed in software PSM. Table : Data of converter. nput Voltage V in = 1V ntermediate Capacitor C 1,C = 5uF Output Capacitor C 1,C = 1.5uF Resistance R = 16Ω Switching Frequency f = 5Hz Duty Cycle Switches S 1,S D =.5 nput nductance - CCM L 1,L 4 =.5mH ntermediate nductance - CCM L,L 3 = mh nput nductance - CRCM L 1,L 4 = 5uH ntermediate nductance - CRCM L,L 3 =.1mH nput nductance - DCM L 1,L 4 = 1.5uH ntermediate nductance - DCM L,L 3 = 5uH *CCM - Continuous Conduction Mode; CRCM - Critical Conduction Mode; DCM - Discontinuous Conduction Mode. The Figure 9 a) shows the comparison between the input voltage with the output voltage, the voltage on the output capacitors and on the switches voltage S 1 and S, for the continuous conduction mode. The ripple voltage at the output is designed to be 1% of the total voltage. This result shows that the voltage on the switch is half the full voltage of the bus regulated in 4V. The inductor current is an important parameter for determining the mode of operation of the converter. Thus, for purposes of comparison are presented in Figure 9 b) the curves of currents of the inductors in continuous conduction modes, critical and discontinuous. The ripple current in the inductors is designed for 1% of the total current. 4 3 1 V C1 1 5. 1995. 199 1985. V C VS1V S 5 15 1 Vin V 5 199. 199. 1994. 1996. 1998. 1991. Time(s) (a) Voltages on the switches V S1 and V S. 1 8 6 4 15 1 5 4 3 1 L1 L L1 L L1 L 199. 199. 1994. 1996. 1998. 1991. Time(s) (b) Currents in the inductors L1 and L. Figure 9: Simulation Results

Experimental Results The Smartfusion AFM3F-FG484 was chosen to perform experimental tests, [7]. To egration of the FPGA with the Cortex-M3 microcontroller 3 bits is used analog to digital converters as well as 1 ADC channels, as shown in the Figure 1. To do experimental the tests it was necessary to develop a PWM (Pulse Width Modulator), which consists in a comparison between a reference signal and a triangular wave, with a frequency of 5 khz. The Figure 11 a) represents the implementation of signal obtained. Figure 1: Actel s SmartFusion Evaluation Kit. (a) Command signal to the drive switches (b) nput voltage V in in comparison with the total output voltage V of the converter. Figure 11: Experimentals Results To test the simulation results, the experimental results are obtained. The Figure 11 b) presents the input and output voltages. Although the simulation result of the waveform of the output voltage be presented through of the comparison between output voltage and input voltage and in function of output voltage in the capacitors V C1 and V C, its experimental waveform is given just as a function total output voltage V and compared to the total input voltage V in, proving their high static gain. n Figure 1 a) is shown the tensions in the switches, one can verify that the voltage at the switches is reduced compared with converters of the literature. These results are similar to the waveforms obtained in the simulation. The current in the inductors has great relevance in the analysis of the driving mode of the converter. However, in order to future applications in renewable energy, experimental tests were performed only in continuous driving. The currents in the inductors L 1 and L are shown in Figure 1 b).

(a) Voltages on the switches V S1 and V S. (b) Currents in the inductors L1 and L. Figure 1: Experimentals Results Conclusion This work presents the study of the converter non-isolated DC-DC high-gain. The topological states and the waveforms of the converter are shown for the modes of the conduction continuous, critical and discontinuous. With the making of the external characteristic curve of the converter, it was possible to determine the threshold value for which the conduction is continuous or discontinuous. Relevant simulation results are presented for the continuous conduction mode. However, as the inductors are key factors in conduction mode converter, these currents are presented for the three situations, continuous, critical and discontinuous. The experimental results show the output voltage, the switches voltage and the inductor currents in the continuous conduction mode. These results are similar to the simulation results, confirming the theoretical analysis. Thus, it was possible to experimentally verify the high static gain and the low voltage switches of the proposed converter compared to converters of the literature. References [1] Maksimovic, D. and Cuk, S., General properties and synthesis of PWM DC-to-DC converters, Power Electronics Specialists Conference, PESC, 1989. [] Maksimovic, D. and Cuk, S., Switching converters with wide DC conversion range, Power Electronics, EEE Transactions on, vol. 6, NO.1, Jan 1991. [3] Barreto, L. H. S. C.; Coelho, E. A. A.; Farias, V. J.; Oliveira, J. C.; Freitas, L. C. and Vieira Jr., J. B., A quasi-resonant quadratic boost converter using a single resonant network, EEE Transactions on ndustrial Electronics, vol. 5, NO., June 5. [4] Novaes, Y. R., Contribution Processing Systems Energy Fuel Cell,Federal University of Santa Catarina, Doctoral Thesis, 6. [5] Bottarelli, M. G., DC-DC Converters Basic Not solated Quadratic Three Levels, Federal University of Santa Catarina, Dissertation, 6. [6] Novaes, Y. R.; Barbi,.; Rufer, A., A New Three-Level Quadratic (T-LQ) DC-DC Converter Suitable for Fuel Cell Applications, EEJ Trans. A, vol. 18, NO.4, 8. [7] Actel Products and Hardware. Kits FPGA Smart Fusion.