Optimum Design for Multilevel Boost Converter

Transcription

1 Proceedings of the 14th International Middle East Power Systems Conference (MEPCON 10), Cairo University, Egypt, December 19-21, 2010, Paper ID 2. Optimum Design for Multilevel Boost Converter Mostafa Mousa 1, IEEE student member, Mohamed Hilmy 1, IEEE student member, Mahrous Ahmed 1, IEEE Member, Mohamed Orabi 1, IEEE Senior Member, and Ahmed Alaa El-koussi 2 1 APEARC, South Valley University, Aswan City, Egypt 2 Cairo University, Cairo, Egypt Abstract - This paper gives a comprehensive study for the losses in DC-DC Multilevel Boost Converter MLBC. A closed formula for the currents in different branches and the of the system are calculated. Different switching frequencies will be considered. The equations given to calculate the power loss in each branch is used to give an indication of the individual power loss that facilitates component selection. The calculated of the system is compared to the simulation one to validate the analyses. A simple program is designed to find the optimum design for the components that should be used in this topology. Matlab/Simulink software is used to compare the simulation with the calculated. Index Terms Multilevel Boost Converter (MLBC), equivalent series resistance (ESR), losses in DC-DC converter I. INTRODUCTION Loss calculations in an electronic circuit have different methods. Switches, diodes, resistances, capacitances, and inductances all consume energy as losses. By looking in the literature, it can be found that the calculation of losses in an inductance is described in [1] [3], the switching losses are described in [4] [6] and the losses in the transformer are treated in [7] and[8]. The loss information combines the week points of operation and gives a clear way of how to design a high converter. It is worth noting that a good loss information give the life for some topologies through a good design for them. A multilevel boost converter is very attractive topology that has been introduced in [9] and [10]. In [10], they explain the operation and compare between this topology and other topologies. But they do not show the inductor and capacitor equations design for this topology. Besides that, no one has explained the for this topology and calculate the losses of it. Generally speaking, looking into its component number can give an indication that it should be used only at higher power applications. So to determine the best region of operation and its desired operating regions, one should understand first its feature through studying its loss analysis. Therefore, in this paper the loss calculations for multilevel boost converter is developed and their design feature has been made clear. This paper explains and analysis the inductor and capacitor design. Moreover, it shows the optimal design for inductor and capacitor that will use in this circuit. A new program is written to choose the better number of level, better switching frequency, Suitable duty cycle for the input and output voltage and optimal inductor and capacitor. This work is supported by STDF Fund, Egypt. The main application for the multilevel boost converter can be used ina photovoltaic (PV) and fuel cell generation systemsthis applications uses a multilevel inverter to inverse dc voltage to ac voltage so several controlled voltage levels are required with self balancing and unidirectional current flow, so this paper use multilevel boost converter(mbc) to be used as DC-link in this applications and to boost small dc voltage to large dc voltage without transformer. The main advantages for this topology against traditional topologies are low voltage stress, low EMI noise, large conversion ratio without extreme duty cycle and ability to operate without magnetic components. The large ratio of this topology without transformer gives the ability to use this topology in a lot of applications that require high gain. But the main disadvantage for this topology is that the of it is small. So to design this topology we should choose the correct components to operate this topology in a high. II. OPERATIONAL PRINCIPLES OF MULTILEVEL BOOST CONVERTER. The main advantage of the multilevel boost converter isitcan achieve high gain without increasing the duty cycle. This section illustrates the operational principles of this circuit. Fig. 1 illustrates the multilevel boost converter which combines the boost converter and the switched capacitor function to provide an output of several capacitors in series with the same voltage and self-balanced voltage. The major advantages of this topology are: (i) its input current is continuous, (ii) it has a very large conversion ratio with low duty cycle and without a transformer, its gain approximately three times compared to the conventional boost converter.its output voltage can be increased to any value by increasing the number of levels. It can be built in a modular way andmore levels canbe addedwithout changing themain circuit.it provides several self-balancedvoltage levels andonly one switch is necessary. The control of this topology is simple because there is only one switch in this converter unlike other topologies like switched capacitor converter with a boost stage [11].When the switch is ON, the inductor is connected to the voltage source. If C2 s voltage is smaller than C1 s voltage, C1 charges C2 through the diode D2 and the switch. Simultaneously, if the voltage across C2+C4 is smaller than the voltage across C1+C3, C1 and C3 charge C2 and C4 through the diode D4 as shown in Fig. 2. In the same time the capacitor voltage across C1+C3+C5 discharges in the load. Besides that, when the switch turns off, the diode D1 turns on because the inductor charges the capacitor C1 until the voltage 734

2 on the capacitor C1 equal to the summation voltage on the voltage source and the inductor voltage. After that, the diode D3 turns on so the voltage source, the inductor and capacitor C2 charging the capacitor C1+C3 through it. Besides that, when the voltage on the C1+C3 is equal to the summation voltage on the voltage source, the voltage on the inductor and the voltage on the capacitor C2, the diode D3 turns off and the diode D5 turns on so the voltage source, inductor and capacitors C2 and C4 will charging capacitors C5, C3, C1 until the voltage on it equal to the summation of the voltage on the voltage source, inductor and capacitors C2+C4 as shown in Fig. 3. III. MULTILEVEL BOOST CONVERTER DESIGN. The transfer function of the conventional boost converter is: V = () But in the multilevel converter the transfer function can be calculated as: V = () It is shown from last two equations that the MLBC has a big conversion ratio without extreme duty cycle.the differencebetween two equations is the number of level of the multilevelboost converter. The inductor sizes are decided such that the change in inductor currents is no more than 5% of the average inductor current. The following equations give the value of the inductor which is selected in MLBC to make the MLBC work in continuous conduction mode (CCM).From equation (4) the inductor size is smaller than the inductor size that is used in the conventional boost converter but the problem of this topology is that the current in the inductor is higher than the current in the conventional boost converter. (1) (2) I = () (3) L = () DT (4) Where: Vc is the input voltage, D is the duty cycle, Rout is the output load, Ts is the switching period and N is the number of stage of the multilevel converter.the design criterion for capacitors is that the ripple voltage across them should be less than 5%.The following equation gives the value of the capacitor which is selected in MLBC. As shown from this equation, the capacitor size is like the capacitor size of the conventional boost converter. C = V (5) Inductor C4 C2 Switch D5 D4 D3 D2 D1 C5 C3 C1 Figure1: Multi-level boost converter Load Figure 2: ON state. 735

3 Figure 3:OFF state. IV. DERIVATION OF THE INPUT CURRENT EQUATION I () = 0.5I I B e (16) When the MLBC boost converter compared to the conventional converter, one can notice that its gain ratio is very large and in the same time it has many components.so it is very important to study to study the losses and the of it. In this section, a closed formula for the input current will be derived. By applying Kirchhoff s current law on the MLBC ON/OFF circuits as shown in Fig. 2 and 3, the capacitor currents can be found and thus the input current equation can be derived. Accordingly, equations (6), (7), (8), (9) and (10) give the capacitor currents during the ON state, and thus the input current at the on state is given by equation (11). Where: A = I () B = I () I () B = I () 1.03I () C = I e C = (I I )e I is the switch current at on state.from equation (11) and (17) the input current is mentioned in equation (18). I () = I I I I () = I I (6) (7) I () = 0.5I + A e (8) I () = 0.5I A e (9) I () = I (10) I () = Ae (11) Likewise, the input current at the OFF state can be derived by applying Kirchhoff s current law at different nodes of the OFF state circuit shown in Fig. 3 to find the capacitors currentsequations, then the input current can calculated. Equations (12),(13),(14),(15) and (16) give the capacitors currents and equation (17) gives the input current. I () = I I (12) I () = 0.5I B e (13) I () = 0.5I + B e (14) I () = I 1.5I + B e (15) Figure 4: Efficiency vs. switching frequency using arbitrary choices for the values of loss and power. Switching loss causes the to decrease rapidly at high frequency..i () = I + C e cos DT + C e sin I = Ae D + I + C e cos t + C e sin DT (17) t D (18) 736

4 Once current in different branches of the circuit have been calculated, the of the circuit can be found. The common method to calculate the considers only the inductor losses and diode losses in the calculation only [12].But in this paper, the capacitors losses have been considered due to the large number of capacitor that are included in the circuit and their effects cannot be neglected. The previous derivation equations give the capacitor currents in ON and OFF states and knowing the effective series resistance of capacitor (SER), the power losses on each capacitor can be calculated as follows: P () = DP () + D P () (19) P () = I () R (20) P () = I () R (21) Where n is the capacitor number. Thus the total losses of the converter will be as shown in equation (22). Switching frequency is very important factor in component losses as shown in equation (22). Optimum operation of the circuit can be described by finding the critical frequency [12]. It defines the limit of the operation beyond it the losses of the circuit will not be acceptable and thus the will be severely affected. The critical frequency is defined in equation (23).Equation (24) determines the value of the fixed power losses and equation (25) determines the value of the conduction power losses. f = (23) 2DI P = 4DI I + 2DI I + 2.5I +D (2B + B )e + 1.5D I + 2I + D I 2I I 4D I I + (2I + 2D I 4I D I B I + D B )e + 2A De + (A I + A D)e R (22) P = {2DI 4DI I + 2DI I + 2.5I + 1.5D I + 2I + D I 2I I 4D I I } R (24) P = D (2B + B )e + (2I + 2D I 4I D I B I + D B )e + 2A De + (A I + A D)e R (25) W = W + W + W (26) η = (27) Where P fixed is frequency- independent power loss, P cond. is frequency- dependant power loss or conduction loss, W tot is total energy loss due to switching, W on is the energy loss due to switching at on state, W off is the energy loss due to switching at off-state and W c is the energy loss in the capacitors. V. OPTIMAL CIRCUIT PARAMETERSCALCULATION This section explains the proposed program that calculates optimal circuit parameters(capacitance, inductance, switching frequency, duty cycles and number of stages). First this programe reads input voltage, output voltage, swichingfrequancy and the load, thenit calculates the duty cycles and the number of stages that made the duty cycle not larger than % and not less than 10%, then calculate C opt and L opt as shown in Fig. 5. To calculate optimal frequancy the program compare the designed frequancy with critical frequancy that is calculated from equation (23) then calculate the at this frequency. VI. COMPARISON AMONGSIMULATION AND CALCULATION RESULTS In this section, a comparison among the calculation and the simulation results will be executed. Matlab/simulinksoftware is used to do the simulation results. Making use of equations (4) and (5) at different switching frequencies,values of the inductor and capacitors of the multilevel boost converter can be found. The switching frequencies that are used are 10 khz, 100 khz, 300 khz and 0 khz. From the datasheet of component used, the equivalent series resistance(esr) for capacitorsand the DC resistance (DCR) for the inductor can be found. Table 1 shows values of the capacitors and inductor at variable switching frequencies. Fig. 6 (a), (b), (c) and (d) show the comparing results among calculation and simulation results of the at different frequencies.it can be noticed here that the calculation results are very close to the simulation. Thus it can be confirmed that the derivation of the above equations is acceptable. Fig. 7 (a) and (b) shows calculated and simulated results for the chosen frequencies. The is at 100 khz switching frequency has the highest values with flat cure. It is identical results between simulation and calculation so it is proves that the derivative equation is right equation for this topology. 737

5 Switching frequency TABLE I: Designed components values Capacitor Capacitor resistance Inductor Inductor resistance 10 khz 47 uf 330 mω 1 uh 7 mω 100 khz 3.3 uf 6 mω 25 uh 14 mω 300 khz 2.7 uf 6 mω 6 uh 20 mω 0 khz 1.8 uf 6 mω 4.5 uh 2.7 mω VII. CONCLUSION The multilevel boost converter (MLBC) is the topology that is used in the application which requires high voltage gain. But the main disadvantage of this topology is the. So this paper derives the equation to find the best components value and the optimal switching frequency to increase the of it. and calculation results are compared and derived that it is identical. ACKNOWLEDGMENT The authors gratefully thank the ministry of Science, Egyptian science and technology development funds (STDF project No 346), for supporting this project. Figure 5: flow chart of the program that calculate the optimal value of inductor and capacitor, switching frequency, number of level of the MLBC and the best value of the duty cycle (a) (b) (c) (d) Figure 6: and simulation of the at frequencies (a) 10 khz (b) 100 khz (c) 300 khz (d) 0 khz. 738

6 Efficiency at F=0 KHz Efficiency at F=100 KHz Efficiency at F=10 KHz Efficiency at F=300 KHz (a) Efficiency at F=10 KHz Efficiency at F=100 KHz Efficiency at F=300 KHz Efficiency at F=0 KHz (b) Figure 7:The (a) calculated (b) simulated. REFERENCES [1] L. Helle and S.Munk-Nielsen, Comparison of converter in large variable speed wind turbines, IEEE Proc. in APEC 01, vol. 1, 2001, pp [2] W. Dong, J.-Y. Choi, Y. Li, H. Yu, J. Lai, D. Boroyevich, and F. C. Lee, Efficiency considerations of load side soft-switching inverters for electric vehicle applications, IEEE Proc. in APEC 00, vol. 2, 2000, pp [3] J. S. Lai, R. W. Young, and J. W. McKeever, Efficiency consideration of DC link soft-switching inverters for motor drive applications, IEEE Proc. in PESC 94, vol. 2, 1994, pp [4] R. L. Steigerwald, R. W. De Doncker, and H. Kheraluwala, A comparison of high-power DC-DC soft switched converter topologies, IEEE Trans. on Industry Applications, vol. 32, no. 5, pp , September/October [5] E. R. C. da Silva, M. C. Cavalcanti, and C. B. Jacobina, Comparative study of pulsed DC-link voltage converters, IEEE Trans. on Power Electronics, vol. 18, no. 4, pp , July [6] S. Munk-Nielsen,M.M. Bech, R. Teodorescu, and J. K. Pedersen, Simulink model of a three level converter leg including device losses, IEEE Proc. in PCC 00, vol. 2, 2002, pp [7] M. H. Kheraluwala, R. W. Gasgoigne, D. M. Divan, and E. Bauman, Performance characterization of a high power dual active bridge DC/DC converter, IEEE Proc. in IAC, vol. 1, 19, pp [8] R. Asensi, J. A. Cobos, O. Garcia, R. Prieto, and J. Uceda, A full procedure to model high frequency transformer windings, IEEE Proc. in PESC 94, vol. 2, 1994,pp [9] Julio C. Rosas-Caro, Juan M. Ramírez, Pedro Martín García-Vite "Novel DC-DC Multilevel Boost Converter." IEEE Proc. on Power Electronics Specialists Conference, [10] J.C. Rosas-Caro, J.M. Ramirez, F.Z. Peng, A. Valderrabano A DC DC multilevel boost converter. IET Power Electron., 2010, Vol. 3, Iss. 1, pp [11]Abutbul, O.; Gherlitz, A.; Berkovich, Y.; Ioinovici, A.; Step-up switching-mode converter with high voltage gain using a switchedcapacitor circuit ; IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Volume, Issue 8, Aug Page(s): [12] Robert W. Erickson &Dragan, Fundamental of power electronics. Colorado:Kluwer Academic Publishers