 Open Access
 Total Downloads : 549
 Authors : Vu Tran, Mufeed Mahd
 Paper ID : IJERTV3IS060890
 Volume & Issue : Volume 03, Issue 06 (June 2014)
 Published (First Online): 15072014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Analysis and Modeling of Transformerless High Gain BuckBoost DCDC Converters
Vu Tran
Department of Electrical and Computer Engineering, University of Massachusetts
Lowell, USA
Mufeed Mahd
Department of Electrical and Computer Engineering, University of Massachusetts
Lowell, USA
AbstractThis paper proposes a transfomerless switched capacitor buck boost converter that is based on a traditional buck boost topology. The proposed converter achieves high voltage gain and higher efciency when compared to the conventional buck boost converter. The average model based on statespace description is analyzed in the paper. The simulation results are presented to conrm the capability of the converter to generate highvoltage ratios. The proposed converter is suitable for applications which require high stepup DCDC converters such as DC microgrids and solar electrical energy.
Keywordsbuckboost converter; statespace description; averagedmodel; simulation.

INTRODUCTION
In recent years, extensive use of electrical equipment has increased rapidly. As the demand for power is signicantly increasing, renewable energy sources have received a lot of attention as an alternatives way of generating directly electricity. Using renewable energy system can eliminate harmful emissions from polluting the environment while also offering inexhaustible resources of primary energy. There are many sources of renewable energy, such as solar energy, wind turbines, and fuel cells. However, fuel cells and solar cells have low output voltage [1], [2], [3]. Thus, a high efciency and stepup DCDC converter is desired in the power conversion systems to increase the voltage supplied to the grid or be compatible in other applications.
Theoretically, the conventional boost DCDC converter can provide a very high voltage gain by using an extremely high duty cycle. However in actual application, for a very high duty cycle, the voltage gain is reduced because of the non ideal elements in circuits such as inductors, capacitors, switches, diodes, etc. Moreover, extremely high duty cycle can create electromagnetic interference [4] [5], which might diminish the efciency of the operation of circuits.
Several researchers have designed models that can achieve high voltage gain. Stepup converter using transformer is presented in [6] [7] [8]. They can control the voltage gain by creating a conversion ratio function of the duty ratio and the transformer turns ratio. However, its efciency will dramatically degrade by losses associated with the leakage inductance, and may cause power losses and heat dissipation problems [9] [10]. Another disadvantage is the size and weight of the transformer, which is often desired to be as
compact as possible. In [4] [9] [11] [12] [13] [14] [15], high step up converters using coupledinductor technique is introduced. Coupled inductors were modeled to provide a high step up voltage and reduce the switch voltage stress, and the reverse recovery problem of the diode was reduced. However, the electromagnetic interference and efciency is reduced due to the leakage inductance [16] [14], and the designing of the converter is relatively complex [17].
High gain can also be achieved by cascading two or more stepup converter stages [16] [17] [18] [19]. Extreme duty cycle can be avoided by setting an intermediate voltage between the two stages. However, additional components are required, the control circuit is more sophisticated and the total efciency is reduced [5] [20].
An integration of a switchedcapacitor (SC) circuit with a boost converter is proposed in [1] [14] [21] [22]. The voltage gain can be improved by increasing number of charge pumps. However, the voltage gain will be reduced signicantly if the input voltage is as small as the voltage dropping on two diodes [23]. The other limitation is charge pump itself, if the switching frequency is not sufciently fast, the capacitors will block the DC current, making the system less efciency.
In order to deal with lowvoltage photovoltaic (PV) arrays and the required higher voltage of the grid, a novel buck boost converter is proposed based on the traditional buck boost converter. The model is simple, which includes only one inductor, two capacitors and four power switches and two diodes, and thus, it is very easy to implement. With this model, we are able to save the wasted energy in the OFF state of the switches used in the circuit. Therefore, the proposed converter can not only provide with high voltage gain, but also reduce the extremely high duty cycles of power switches, and increase the efciency of the converter.
The paper is organized as follow. The new circuit schematic is described in Section II. Its steadystate topologies are analyzed by using statespace approach in Section III. Section IV presents the simulation results for averaged model and pulse width modulation (PWM) model. Conclusion is presented in Section V.

CIRCUIT DESCRIPTION
The traditional buck boost converter is presented in Fig. 1. When the switch is ON, the energy from the power supply (PV panel) Vg is stored in the inductor. When the switch is
OFF, it is easy to see that this energy is wasted. For example, if the duty cycle is 60%, at least 100% – 60% = 40% of power is wasted. The new model of buck boost converter is proposed to save that wasted energy, which is illustrated in Fig. 2.
Fig. 1. Traditional buck boost converter
Fig. 2. Switchedcapacitor buckboost converter with high voltage gain
In the OFF state, energy from power source is stored in capacitors C, then, in the ON state, it is pushed back to the circuit. Hence, the energy is saved and the efficiency is improved when compared with that of the traditional buck boost converter.
Fig. 3. One stage switchedcapacitor buckboost converter
The model can be extended to increase the voltage gain by simply increasing the stage, which includes the capacitor C, diode D1, switch Sb, and two switches Sr. For simplicity, we consider the case of one stage as in Fig. 3. Adding more stages can be treated similarly.
In OFF state, the circuit is modeled in Fig. 4. Two switches Q1 and Q2 are OFF, Q3 and Q4 are ON, the current
flows through Q3 and Q4, energy from power source Vgis charged for the capacitor C. Diode D0 is forward biased, which allows the current to go through the inductor to charge for capacitor C0 and provide for the output simultaneously.
Fig. 4. Switching topology of proposed circuit in OFF state
Fig. 5. Switching topology of proposed circuit in ON state
Fig. 5 describes the circuit in the ON state. Two switches Q1 and Q2 are ON, Q3 and Q4 are OFF. Voltage source Vg combined with the voltage on C create a higher voltage, which will be pushed to the inductor L. More energy will be stored in the inductor compared with the traditional buckboost converter. Diode D1 acts as a freewheeling diode.

STATESPACE MODEL OF THE SWITCHED CAPACITOR BUCKBOOST CONVERTER
In this section, the equivalent circuits of traditional model and proposed model are analyzed for ON and OFF states. In both models, when the diode operates in forward bias region, it is replaced by a voltage source VD. When it is in reverse biasregion, it blocks thecurrent, hence it is replaced by an open circuit. MOSFET switches are controlled by PWM signals. When MOSFET is OFF, it works like an open circuit. When it is ON, it works like a resistor with the resistance RON.
Let the duty cycle of the PWM signal be D and the DC voltage supply be Vg.The input is u = [VgVD]T.

Statespace description of the traditional model
Let the state of the traditional buckboost converter be
XT= [ILV0]T.
In ON state, the equivalent circuit is described in Fig. 6 Apply the KVL equations for this circuit, we have
= +
0 = 0 1
0
=
02 1 1
and
0
0
0 1
02 =
Fig. 6. Traditional buck boost converters equivalent circuit in ON state
The statespace description of the circuit can be
0 0
Under the assumption of high frequency and ideal switching, the average model can be described as
XT = DXT(ON) + (1 – D)XT(OFF)
XT = (DA01+(1D)A02)XT +(DB01+(1D)B02)u (1)
At steady state, the state of the circuits can be consideredstable, or X(t) = 0. Solve the equations (1) with the conditionof steady state XT = 0, we have the state of the circuit XT .
represented as XT(ON)=A
In which,
01XT + B01u
XT = (DA01+(1D)A02)1(DB01+(1D)B02)u (2)
From equation (1) we have the output voltage V0.
+ 0
0
= 1 ( 1 )
+ + 1 2
(3)
And
01 = 1
0
0
1
We will not consider the full range [0,1] of duty cycle due to the nonidealities. For very large or very small duty cycle, the averaged model does not reflect precisely the real circuit. Since there is no benefit in increasing the duty cycle beyond the value where the minimal output voltage is reached, we
01 = 0
0 0
In OFF state, the equivalent circuit is described in Fig. 7
would prefer to limit the duty cycle in a smaller range. For the above example, we may limit D [0.1, 0.85].
Assumed that the resistors RON and RL are much smallerthan R, and VD is much smaller compared to Vg. The equation(3) can be simplified as
0
V D
1D
Vg (4)
Fig. 7. Traditional buck boost converters equivalent circuit in OFF state
Similarly, applying the KVL equations for this circuit yields

State space description of the proposed model
Let the state of the traditional buckboost converter be
XN = [IL V0 VC]T .
In ON state, the equivalent circuit is described in Fig. 8
=
0
0 = 0
0
The statespace description of the circuit can be represented as XT(OFF)=A02XT + B02u
In which,
Fig. 8. Switched capacitor buck boost converters equivalent circuit in ON
state
KVL equations for this circuit is as follows
= 2
+
+
0 1
0
0
11 =
0
0
0 =
1 0
2
=
Under the assumption of high frequency and ideal switching, the average model can be described as
The state space description is XN(ON) = A11XN + B11u
X = DX (ON) + (1 – D)X (OFF)
In which,
2 +
0 1
and
N
X = (DA
N
+(1D)A
)X +(DB
N
+(1D)B
)u (5)
N 11
12 N 11 12
11 =
0 1 0
0
1 0 0
Under the same above assumption, the state of the circuit is represented in (6).
XN = (DA11+(1D)A12)1(DB11+(1D)B12)u (6)
From (1), the output voltage V0 is calculated in (7)
and
11
1 0
=
0 0
0 0
= 1 (2 1 ) (7)
0 2 2
2 + +2 + 1
V0 can be approximated as
0 g
V 2D V (8)
1D
In OFF state, the equivalent circuit is described in Fig. 9
Fig. 9. Switched capacitor buck boost converters equivalent circuit in OFF
state
Apply the KVL equations for this circuit
Hence, with the proposed switched capacitor buck boost circuit, the expected gain is doubled when compared with traditional buck boost converter. Generally, when we have n stages, by similarly calculation, the output gain is n times than the traditional one. The following part will demonstrate how the simulated circuit is working.


SIMULATION RESULTS
In this section, we constructed two simulation models, one is a statespace model based on the averaged circuit, which is called the averaged model. The other is a simulated circuit using SimPower in MatLab, which is called the PWM model. We will use this two circuits to demonstrate the theoretically results we obtain from section III. The parameters for the circuit are given as follow: L=0.1mH, RL=0.3, C0=0.33mF, C=0.047mH, R=48, RON=0.018, Vg=3V, VD=0.3V.
=
0
0 = 0
0
=
2
The circuit can be described as XN(OFF) = A12XN +B12u
In which,
1 0
Fig. 10. Output of averaged model
= 1 1 0
12 0
0
1
Fig. 10 shows results for the averaged model based on the averaged equations (3) and (7). In not a very high duty cycle
and
0 0
2
region, energy from power source is stored in capacitor C, the voltage VC is equal to Vg. When it is pushed back to the circuit, the input becomes Vg +VC = 2Vg. The output voltage of the proposed circuit is almost doubled compared with that of traditional buckboost converter.
Fig. 11 shows the simulation result. In this figure, the output voltage of traditional buckboost converter is plotted as the red curve; and the output of the proposed converter is represented as the blue curve. Four difference sub figures associated with the duty cycles being 30%, 50%, 70%, and 80% are plotted.We can see that the output voltages of the proposed model are almost doubled compared with the traditional one. This empirical result confirms the feasibility of the proposed model.
Fig. 11. Output voltage of simulink model compared with traditional buck boost circuit with D=30%, 50%, 70%, and 80%

CONCLUSION
A novel buck boost converter with a switched capacitor for high stepup converter is presented in this paper. Adding one more stage of switched capacitor significantly improves the voltage gain compared to the traditional one. Efficiency is also improved through the process of storing energy in the capacitor and then pushing it back to the circuit. The simulation results validate the theoretical results. The proposed converter is applicable in many applications in which high efficiency model is required.
REFERENCES

L. Zhigang, A.Q. Huang, G. Rong, High efficiency switched capacitor buckboost converter for PV application, Applied Power Electronics Conference and Exposition (APEC), 2012 TwentySeventh Annual IEEE, pp. 19511958, Feb. 2012.

G.R. Walker and P.C. Sernia, Cascaded DCDC converter connection of photovoltaic modules, IEEE Trans. Power Electronics, vol. 19, no. 4, pp. 1130 – 1139, July 2004.

J.Wang,F.Z. Peng, J. Anderson, A. Joseph, and R. Buffenbarger, Low cost fuel cell converter system for residential power generation, IEEE Trans. Power Electronics, vol. 19, no. 5, pp. 1315 1322, Sep. 2004.

Y. Hsieh, J. Chen,T. Liang, and L.Yang Novel High StepUp DCDC ConverterWith CoupledInductor and SwitchedCapacitorTechniques, IEEE Trans. Industrial Electronics, vol. 59, no. 2, pp. 998 1007, Feb. 2012.

G. Rong, L. Zhigang, Q.H. Alex A High Efciency Transformerless Stepup DCDC Converter with High Voltage Gain for LED Back lighting Applications IEEE Applied Power Electronics Conference

W.Y. Choi, J.S. Yoo, J.Y. Choi, M.K. Yang, and H.S. Cho, High efficiency stepup DCDC converter for lowDCrenewable energy sources, Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM), 2012 International Symposium on, pp. 1417 – 1421, 2012.

K.I. Hwu and W.Z. Jiang, Applying Coupled Inductor to Step UpConverter Constructed by KY and BuckBoost Converters, Industrial Electronics (ISIE), 2013 IEEE International Symposium on, vol. 20, no. 5, pp. 16, May 2013.

K.C. Tseng, and T.J. Liang, Novel highefficiency stepup converter, IEE Proc. Electr. Power Appl., vol 151, No. 2, pp. 182190, March 2004.

R.J. Wai and R.Y. Duan, High stepup converter with coupled inductor,IEEE Trans. Power Electronics, vol. 20, no. 5, pp. 1025 1035, Sep. 2005.

Y. Zhao, W. Li, Y. Deng, X. He, S. Lambert, V. Pickert, High stepup boost converter with coupled inductor and switched capacitor, Power Electronics, Machines and Drives (PEMD 2010), 5th IET International Conference on, pp. 16, Feb. 2010.

Y. Berkovich and B. Axelrod, High stepup DCDC converter with coupled inductor and reduced switchvoltage stress, IECON 2012 –
Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTICON), 2012 , pp. 14, May 2012.
and Exposition (APEC), 2011 TwentySixth Annual, pp. 1350 1356, March 2011. 
38thAnnual Conference on IEEE Industrial Electronics Society, pp. 453 – 458, Oct. 2012. 

[6] 
W.Y. Choi, J.S. Yoo, J.Y. Choi, High efficiency dcdc converter with high stepup gain for low PV voltage sources, Power Electronics and ECCE Asia (ICPE & ECCE), 2011 IEEE 8th International Conference on, pp. 1161 – 1163, June 2011. 
[16] 
M.C. Tanca and I. Barbi, A high stepup gain DCDC converter basedon the stacking of three conventional buck boost DCDC converters, IEEE Power Electronics Conference (COBEP), 2011 Brazilian, pp. 196 200, Sep. 2011. 
[7] [8] 
D.D.C. Lu, G.M.L. Chu, V.G. Agelidis, A High Stepup, Nonisolated DCDC Converter with Reduced Repeated Power Processing, IEEE Power Electronics Conference (IPEC), 2010 International, pp. 2897 – 2904, June 2010. D.M. Van de Sype, K. De Gusseme, W.R. Ryckaert, A.P. Van de 
[17] 
C.M. Young, M.H. Chen, T.A. Chang, C.C. Ko, and K.K. Jen, Cascade CockcroftWalton Voltage Multiplier Applied to Transformerless High StepUp DCDC Converter, Industrial Electronics, IEEE Transactions on, vol. 60, no. 2, pp. 523 – 537, Feb. 2005. 
[9] 
Bossche, J.A.i Melkebeek, A Single Switch BuckBoost Converter with a High Conversion Ratio, IEEE Power Electronics and Applications, 2005 European Conference on, pp. P.1P.10, Sep. 2005. X. Hu and C. Gong, A High Voltage Gain DCDC Converter 
[18] 
S.M. Chen, T.J. Liang, L.S. Yang, and J.F. Chen, A Cascaded High StepUp DCDC Converter With Single Switch for Microsource Applications, IEEE Trans. Power Electronics, vol. 26, no. 4, pp. 1146 – 1153, April 2011. 
Integrating CoupledInductor and DiodeCapacitor Techniques, IEEE Trans. Power Electronics, vol. 29, no. 2, pp. 789 – 800, Feb. 2014. 
[19] 
M. Delshad, S. Mohammadi, S. Moosavi, A New Cascaded High Stepup DCDC Converter, 9th International Conference on Electrical 

L.S. Yang, T.J. Liang, H.C. Lee, and J.F. Chen, Novel High StepUp DCDC converter With CoupledInductor and VoltageDoubler Circuits, Industrial Electronics, IEEE Transactions on, vol. 58, no. 9, pp. 4196 – 4206, Sep. 2011.

K. Eguchi, S. Pongswatd, T. Sugimura, T. Thepmanee, K. Tirasesth, H. Sasaki, Design of a switchedcapacitorbased serial DCDC converter using clean energy power supplies, Electrical Engineering/Electronics Computer Telecommunications and Information Technology (ECTICON), 2010 International Conference on, pp. 1226 – 1230, May 2010.

S. Pongswatd, K. Smerpituk, P. Julsereewong, K. Eguchi, and H. Sasaki, Design of fractional conversion ratio SC DCDC converters, Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTICON), 2013 10th International Conference on, pp. 1 – 4, 2013.

O. Abutbul, A. Gherlitz, Y. Berkovich, and A. Ioinovici, Boost converter with high voltage gain using a switched capacitor circuit, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS 03., pp. 296299, 2003.