VOLTAGE REGULATION USING PHASE SHIFT MODULATION IN SINGLE-DC-SOURCE OR SOLAR VOLTAGE SOURCE USING CASCADED H-BRIDGE MULTILEVEL CONVERTERS

Transcription

1 VOLTAGE REGULATION USING PHASE SHIFT MODULATION IN SINGLE-DC-SOURCE OR SOLAR VOLTAGE SOURCE USING CASCADED H-BRIDGE MULTILEVEL CONVERTERS Mohd Mustafa Assistant Professor, Dept. of EEE, Aurora s Scientific, Technological & Research Academy (ASTRA), Hyderabad, India Abstract Cascaded H-bridge multilevel power electronic converters generally require several dc sources. An alternative option is to replace all the separate dc sources feeding the H-bridge cells with capacitors, leaving only one H-bridge cell with a real dc voltage source. This will yield a cost-effective converter. However, the required capacitor voltage balancing is challenging. In this paper, using the phase-shift modulation approach, a new control method for cascaded H-bridge multilevel converters fed with only one independent dc source is presented. The proposed method has a wide voltage regulation range for the replacement capacitors in the H-bridge cells. Experimental and simulation results support the proposed control method. Index Terms Capacitor voltage regulation, cascaded H-bridge converter, H-bridge cell, multilevel converter, DC source, solar voltage source. I. INTRODUCTION IN Multilevel power electronic converters, the desired output voltage is synthesized by combining several separate dc voltage sources [1] [3]. Solar panels, fuel cells, batteries, and ultra capacitors are the most common independent sources used [4], [5]. These converters have single- and three-phase applications. The main advantages of multilevel converters are low harmonic distortion of the generated output voltage, low electromagnetic emissions, high efficiency, the ability to operate at high voltages, and modularity [4], [6] [8]. In general, multilevel converters are categorized into diodeclamped [9] [11], flying capacitor [12] [14], and cascaded H-bridge multilevel topologies [1][15] [17]. Applications of diode clamped multilevel converters include high-power ac motor drives in conveyors, pumps, fans, and mills [3], [4], [15]. The flying capacitor multilevel converter has been used in high-bandwidth high-switching frequency applications such as mediumvoltage traction drives [6]. Finally, the cascaded H-bridge multilevel converter has been applied to high-power and high-quality applications [1], [17] such as static volt-ampere reactive generation [1], active filters, reactive power compensators, power photovoltaic power conversion [5], [8], [18], [19], uninterruptible supplies, and magnetic resonance imaging. Furthermore, one of the growing applications for multilevel power electronic converters is electricdrive vehicles in which the traction motor is driven by batteries [15], [20], [21]. The method used to switch cascaded H-bridge cells can be based either on the fundamental switching frequency, i.e., staircase modulation, or the pulse width modulation (PWM) technique [7], [22] [28]. In the fundamental switching frequency approach, the switching losses are less, but the harmonics in the output voltage waveform appear at lower frequencies. Several methods are proposed in the literature to selectively eliminate harmonics in the output waveforms of multilevel converters [7], [24], [29], [30]. In the PWM Switching method, the harmonics in the output waveform appear at higher frequencies, but due to a higher switching frequency, the switching losses are greater [7], [31]. Fig. 1 shows the block diagram of a cascaded H- bridge inverter system, which consists of main and auxiliary H-bridge cells. In early implementations [32], each H-bridge cell was supplied by an independent dc source. Later, research showed that only one cell needs to be supplied by a dc power source; the remaining cells can be fed by capacitors [7], [11], [31], [33] [35]. The method proposed in [7], [22], [31], and [36] uses the switching state redundancy for capacitor voltage regulation, where the voltage level of the auxiliary cell usually is selected to be half that of the main H-bridge 39

2 cell. However, studies have shown that regulating the capacitor voltage is not as easy as initially predicted [7], [22], [37]. The existence of redundant switching states has been assumed to be adequate for capacitor voltage regulation. However, the output current of the inverter and the time duration of the redundant switching states greatly impact the charging or discharging patterns of the replacement capacitors [7], [31]. This paper proposes a control method applicable to single dc- source or solar voltage source cascaded H- bridge multilevel inverters to improve their capacitor voltage regulation. The proposed method, phase shift modulation, is robust and does not incur much computational burden. In this method, the main inverter switches at the fundamental frequency, and the auxiliary inverter switches nonlinear V I characteristic of a PV generator can be modeled using current source, diode, and resistors. The single-diode model shown in Fig. 1 (a) is widely used for the PV source modeling. This model provides a trade- off between accuracy and complexity. Thevenin s equivalent model with non constant voltages and resistances has been proposed in to closely approximate the characteristic of PV generator. The Thevenin s based model provides simpler prediction and computation for the maximum power point of PV array under different operating conditions. Thevenin s theorem is not valid for a nonlinear model, but the nonlinear model could be represented by a linear one with non constant parameters. In for example, the piecewise linearization is used to linearize the diode. The parameters in Fig. 1(a) can be estimated using the manufacturer s datasheet. As shown in Fig. 1(b), the ctual diode characteristic has been divided into three regions and the characteristic in each region is approximated as a straight line. Each line can be further represented by a set of voltage source Vx,n and resistance one of the boundary points such that the operation at this point has no approximation error. The single-diode model of the PV generator with linearize diode is shown in Fig. 1(c), where the diode is approximated by the voltage source Vx,n and resistance Rd. The values of Vx and Rd are dependent on the operation region of the PV generator. The Thevenin s equivalent model of Fig. 2(c) is shown in Fig. 1(d). From the derivation in, the Vpv_th,n and Rpv_ th,n can be calculated by Fig 1. Block diagram of a cascaded H-bridge inverter At the PWM frequency. The working theory of the cascaded H-bridge multilevel inverter is briefly introduced in Section II. Section III introduces the phase-shift modulation technique and describes its principles of operation. Simulation results and harmonic Analysis also are presented in this section. Section IV is dedicated to design guidelines on the selection of an appropriate voltage level for the auxiliary cell capacitor. The experimental results appear in Section V. Section VI offers concluding remarks and an overall evaluation of the proposed method. II SOLAR VOLTAGE SOURCE OR PV CELL VOLTAGE Solar voltage or PV generator as input source has significant effect on the converter dynamics. The 40

3 III. MULTILEVEL H-BRIDGE CONVERTER FUNDAMENTALS OF OPERATION The structures of the main and auxiliary cells are very similar to each other, the only difference being that the main inverter uses a dc voltage source or a battery while the auxiliary inverter uses a capacitor (see Fig. 1). H - bridge cells are connected in series; hence, the synthesized voltage waveform is the sum of all individual cell outputs. The output voltage of the inverter can be described as V out = v 1 + v 2. (1) In most applications, the desired output voltage waveform of the cascaded H-bridge multilevel inverter is a sinusoidal waveform that can be described as V out, ref (t) = V m sin(ωt) (2) Where V m is the desired amplitude of the output voltage. Fig. 2 describes how the desired output voltage waveform is synthesized using the main and auxiliary H- bridge cells. The main H-bridge cell, which is supplied by V dc, generates a rectangular waveform (v 1), the frequency of which equals that of the desired output voltage. Furthermore, the width of this rectangular waveform is chosen in such a way that the amplitude of its fundamental harmonic also equals that of the desired output voltage. In other words α = cos 1 (πv m/4v dc) (3) Fig. 2. Thevenin s equivalent circuit derived from the single-diode model. (a) Single-diode model of a PV generator. (b) V I characteristic of diode: actual and linear approximation. (c) Single-diode model with linearize diode. (d) Thevenin s equivalent circuit for a single-diode model with linearized diode. Fig 3. Desired output waveforms of the main and auxiliary cell v 2, ref (t) = v out, ref (t) v 1(t). (4) The PWM technique at a higher frequency will be applied to the auxiliary cell to construct v 2,ref (t). The 41

4 conventional unipolar PWM switching method [38] is used in this work. IV. PHASE-SHIFT MODULATION Regulating the capacitor voltage in the auxiliary H- bridge cell is a challenging task [39], [40]. In the method proposed here, capacitor voltage regulation is achieved by adjusting the active power that the main H-bridge cell injects into the system. By shifting the voltage waveform generated by the main H-bridge cell (see Fig. 3) to the left or right, one can inject more (or less) active power, which can be used to charge (or discharge) the capacitor on the auxiliary cell. Some reasonable assumptions are made in order to simplify the analytical description of the principle of operation of phase shift modulation. Here, it is assumed that the output voltage of the auxiliary cell is equal to the commanded waveform for that cell, i.e., v 2(t) = v 2, ref (t). Because PWM switching is used for this H-bridge cell, this assumption is relatively accurate. The other assumption is that the output current is sinusoidal, as the load usually behaves like a low-pass filter. The Fourier series of the rectangular output voltage waveform of the main cell can be expressed as V 1(t)= Vmsin(ωt)+ n=3,5 [ansin(n t)+bncos(n t)] = Vm sin(ωt) + hn(nωt) (5) where h n(nωt) encompasses all of the harmonics in the output of the main cell except for the fundamental harmonic. Based on (3), the magnitude of the fundamental harmonic of the main cell s voltage is set to be equal to the magnitude of the output voltage. Consequently, the output voltage of the auxiliary cell is given by v 2(t) = h n(nωt). (6) For a general case, as shown in Fig. 3(a), in which the output current has a θ phase shift from the output voltage, i.e., Fig. 4. Impact of a phase shift in v1 on the power supplied by the auxiliary cell. (a) No phase shift ((p 2) = 0). (b) Shift to the right (p2) is negative, capacitor charging). (c) Shift to the left (p2) is positive, capacitor discharging). i Load(t) = I m sin(ωt θ), the average output power can be described as < p out >= 0.5V mi m cos(θ) (7) The average power that the harmonics send out during a cycle is zero, which therefore does not contribute to the output power of the cell. Thus, (p 1)= (p out), and (p 2)= 0. Now, if the voltage of the main cell is shifted to the right by Δα based on the operation principle of the converter, the output voltage and, consequently, the output current and output power do not change. In this case, the output voltage of the cells can be expressed as 42

5 v1=v m sin(ωt Δα)+h n (n(ωt Δα)) (8) v 2(t)=V msin(ωt) V msin(ωt Δα) h n(n(ωt Δα)) (9) As a result, the output power of each cell is given by (p1) =0.5V mi m cos(θ Δα) (10) (p2) =0.5V mi m [cos(θ) cos(θ Δα)] (11) Therefore, when both θ and Δα are positive, the generated active power in the main cell will be greater than the power transferred to the load, i.e., cos(θ Δα) > cos(θ). This causes the remaining power to be delivered to the auxiliary cell, consequently charging the capacitor of that cell. In other words, when Δα is positive, (p2) is negative, meaning that the capacitor is charging, and when Δα is negative, (p2) is positive, meaning that the capacitor is discharging. Therefore, controlling Δα makes it possible to charge or discharge the capacitor to regulate its voltage at the desired value. Note that, by using this method, capacitor voltage regulation is not possible for purely resistive load. Because, with resistive instance, when Δα is 10, using (10), the output power of the main cell is only 2084 W. The remaining 343 W must be supplied by the auxiliary cell, which causes the capacitor to discharge [see Fig. 3(c)]. Note that, in all three figures, the PWM modulation has not been applied yet. Based on the previous discussion, one can devise a control scheme that regulates the voltage across the auxiliary capacitor,as shown in Fig. 4. In order to include the effect of the PWM modulation scheme, a MATLAB/Simulink model has been developed. In this model, the load is assumed to consist of a resistor in series with an inductor. In order to verify these results, the system has been modeled using MATLAB/Simulink. The simulation results with a load comprising a 10-Ω resistor and load, θ is zero using (11), (p2) is always positive regardless of the value of Δα. Thus, charging the capacitor is not possible by changing Δα. For instance, when Vdc = 100 V, if the desired amplitude of the output voltage is 120 V, then, using (3), Fig. 5. Open-loop control diagram for auxiliary capacitor voltage conduction regulation. angle α should be set at In this case, if the load draws a sinusoidal current with 50 A of amplitude and 36 of phase lag, the waveforms would look like what appears in Fig. 3(a). In this figure, p2(t) denotes the instantaneous power delivered by the auxiliary H-bridge. The average value of this power is zero (_p2_ = 0); therefore, the auxiliary capacitor will neither charge nor discharge. The output power of the main H-bridge cell is 2427 W [based on (7)], which equates to the power that the load is consuming. Now, if the voltage waveform that the main H-bridge cell is generating is shifted to the right [denoted by Δα in Fig. 3(b)], as the phase difference between that and the output current decreases, the main H-bridge cell will provide some extra power. This extra power will be absorbed by the capacitor in the auxiliary cell. For our particular numerical example, the main cell will Fig.6. Simulation results of open-loop phase-shift modulation. generate, using (10), 2696 W if Δα is +10. The difference, 269 W, will be absorbed by the capacitor. This case is shown in Fig. 3(b). Similar to Fig. 3(a), p2(t) indicates the instantaneous power delivered by the auxiliary cell, which has a negative average value in this case. Similarly, when a left shift is applied to v1(t), the main cell will not supply as much power. Consequently, the capacitor in the auxiliary cell will be discharged. For 43

6 Fig. 7. Closed-loop control block diagram of the capacitor voltage regulation system. a 15.3-mH inductor [i.e., lagging power factor (PF)] connected in series, when Vdc is 100 V and Vdcx is selected to be 70 V, are shown in Fig. 5. This figure shows changes in the capacitor voltage for two different values of Δα. When Δα = +1, the capacitor voltage increases, which indicates a charging capacitor. When Δα = 1, the capacitor voltage decreases, which indicates a discharging capacitor. Based on the previous discussion, a closed-loop control system for capacitor voltage regulation can be designed. The proposed capacitor voltage regulation method is shown in Fig. 6. Δα is adjusted to regulate the capacitor voltage inthe auxiliary cell. The simulation results of the closed-loop phase-shift system with an inductive load are shown in Fig. 7, which indicates that the capacitor voltage regulation control has successfully regulated the capacitor by changing Δα. The frequency spectrum of the output voltage is presented in Fig. 8. In this figure, the amplitude of each harmonic is scaled based on the fundamental frequency (120 V here) and is shown as a percentage. Note that this figure presents only 0% to 5%. The figure reveals that the lowest harmonics are very small compared to the fundamental component. Fig. 9. Frequency spectrum of the output voltage (the chart is cut out at 5%). IV. CONSTRAINTS ON CAPACITOR VOLTAGE SELECTION OF AUXILIARY H-BRIDGE CELL In this section, constraints on the voltage level chosen for the auxiliary H-bridge are discussed. As shown in Fig. 2, the maximum value for the reference of the auxiliary H-bridge occurs at the switching instants of the main H-bridge, i.e., at ωt = α, π α, π + α, and 2π α. It is clear that the voltage source of the auxiliary H-bridge should be chosen to be greater than the peak of its reference voltage. Based on this limitation, it is possible to find the minimum value for the voltage level of the auxiliary H-bridge. Using (2) and (3), the output voltage at α can be calculated as follows: v α =v out ( ) = Vm sin(α) = V m (12) v α+ =V dc v out( ) = V dc V α. (13) For different values of the commanded minimum V dcx is given by Vm, the Min.V dcx = max(v α, v α+). (14) Fig. 8. Simulation results of the closed-loop phase-shift modulation. 44

7 logic device. The control signals were sent to insulated gate bipolar transistors (IGBTs) through optical fiber cables V/75-A Powerex CM75DU-24F IGBTs were used in the hardware setup. Furthermore, a sensor board was used to measure the voltage of the capacitor, and then, it was fed back to the DSP through a signal conditioning board. Fig. 10(b) shows the actual experimental setup. A 2.1-mF capacitor was used for the auxiliary cell. The fundamental frequency of the output voltage has been chosen to be 60 Hz, and the PWM switching frequency is 10 khz. In the following experimental results, the voltage source for the main H- bridge Fig.10. Minimum voltage of V dcx for different commanded Vm. Also, the modulation index is defined as m =V m/v dc = (4/ π)cos(α). (15) Based on (14), the minimum Vdcx for different values of the modulation index (m), along with their corresponding α, are graphed in Fig. 9. As shown, the lowest value for Min.V dcx/v dc is 0.5, which occurs when m is or The area in which operation without over modulation is possible is filled in the figure. According to this figure, for an inverter that is intended to operate in the entire range of possible modulation indices without over modulating the auxiliary H-bridge cell, V dcx should be equal to V dc. By selecting equal voltage sources for both H-bridge cells, the maximum number of voltage levels in the output waveform will be only five. However, by selecting unequal voltage sources, more voltage levels can be generated. Note that regulating the capacitor voltage for the auxiliary H-bridge is possible regardless of the selected voltage level, i.e., V dcx. In capacitor voltage regulation, a small Δα is added to α; therefore, a slightly higher V dcx than the minimum Vdcx provided in Fig. 9 must be selected to avoid over modulation and voltage distortion in the output. V. EXPERIMENTAL RESULTS In order to verify the proposed method, a hardware prototype of a single-dc-source cascaded H-bridge multilevel converter was developed in the laboratory. Fig. 10(a) shows the block diagram of the hardware prototype. The control schemewas programmed with a fixed-point TI-TMS digital signal processor (DSP) and a CY37128P84 complex programmable Fig. 11. Block diagram of the hardware prototype Fig. 12. Normal operation of the converter with V m = 120 V and V dcx =100 V. is selected to be 100 V. The load is composed of a variable resistor placed in series with a constant mh inductor. Fig. 11 shows the output waveforms of the cascaded converter when the commanded Vm is 120 V and Vdcx is selected to be 100 V, while the resistor connected in series with the inductor is 18 Ω, i.e., PF = 0.9. This figure shows, from top to bottom, the output voltage of the converter, the main H-bridge cell, the auxiliary H-bridge cell, and the output current. Due to the selected voltage level for the auxiliary H- bridge, i.e., 100 V, which is equal to the voltage source 45

8 of the main H-bridge cell, five voltage levels are generated in the output voltage. to the higher current, the capacitor s voltage ripple increases, but its voltage level is maintained by the control system. The extra visible small steps in the output voltage levels are caused by a voltage drop of the switches in the converter. These extra steps occur when the output current changes its direction. In practice, the operating voltage of the multilevel converter is high enough that these steps are negligible in the output waveform. The next experimental test demonstrates the dynamic operation of the converter when the commanded voltage of the capacitor of the auxiliary H- bridge cell, i.e., V dcx, changes suddenly. In Fig. 14, the waveforms of the converter are shown Fig. 13. Start-up operation of the converter with Vm = 120 V and Vdcx =100 V. The almost constant peak voltage of the auxiliary H- bridge,i.e., v 2, shows that the voltage of the capacitor is regulated at 100 V. In Fig. 12, the start-up operation of the converter is shown for a case in which V m = 120 V, V dcx = 100 V, and the output resistance is 9 Ω, i.e., PF = As shown, the capacitor is charged from 0 V to the commanded voltage, i.e., 100 V, and is regulated around this value afterward. In the control system, a discrete ant windup proportional-integral controller is implemented in the experiment to avoid excessive integration of the error when the output of the controller, i.e. Δα, is saturated. It is interesting to note that the magnitude of the output current is constant regardless of the voltage of the capacitor in the auxiliary H-bridge. This clearly indicates that only the main H-bridge is involved in generating the fundamental harmonic of the output voltage, while the auxiliary cell does not contribute to this process; it only handles other harmonics and improves the quality of the output power. In order to highlight the operation of the converter and the capacitor voltage regulation system during the load change, the output resistance is suddenly changed from 36 to 9 Ω, i.e., from PF = 0.97 to 0.77, at s, as shown in Fig. 13. In this experiment, V m = 120 V and Vdcx = 70 V are commanded. As the figure shows, with this voltage level combination of the H-bridges, the output waveform has nine voltage levels. According to Fig. 13, after initiating a sudden load increase, due Fig. 14. Converter s waveforms during sudden load change when V m =120 V and V dcx = 70 V at s. Fig. 15. Step change in commanded capacitor voltage from 70 to 100 V and vice versa. 46

9 for a case in which the commanded V dcx is changed from 70 to 100 V at 0.1 s and returned to 70 V at 0.5 s, while the commanded peak of the output voltage is kept constant at 120 V. In this test, the output resistor is 9 Ω, i.e., PF = As shown, the output current is only slightly affected at 0.1 s but returns to its steady-state value after two cycles. This phenomenon occurs due to a sudden load change in the dc power supply of the main H-bridge. In fact, when the commanded voltage of the capacitor changes, the extra power required to charge the capacitor is provided by the dc power supply of the main H-bridge. This causes a sudden decrease in the output voltage of the power supply and consequently causes a slight change in the output current of the converter. The converter s operation during a low commanded output voltage is shown in Fig. 15, in which V m = 40 V, V dcx = 70 V, and the output resistor is set at 36 Ω. In this case, due to a lower modulation index, the number of output voltage levels is reduced to seven compared to Fig. 13, which has nine voltage levels.. Fig. 17. The effect of over modulation of auxiliary H-bridge when Vm = V and Vdcx = 50 V. Fig. 16. Converter s waveforms for low commanded output voltage when Vm = 40 V and Vdcx = 70 The last laboratory test shows the effect of capacitor voltage level selection, i.e., Vdcx, and over modulation. Based on Fig. 9, for m = , the minimum voltage of Vdcx is half that of V dc. Therefore, for V dc = 100 V, the commanded Vm = V only requires Vdcx = 50 V to avoid over modulation. According to the discussion in Section IV, the selected voltage level of the capacitor should be higher than the minimum required value to allow some room for changes initiated by Δα. Therefore, if a marginal value of Vdcx is selected, over modulation occurs because of Δα. In Fig. 16, the converter waveforms are illustrated for this case. In this figure, the effect of over modulation is clearly visible. Two instances of over modulation have been denoted with dashed circles. In these conditions, the commanded voltage for the auxiliary H-bridge is greater than 50 V, which leads to a constant output voltage. This error can be eliminated, as shown in the previous experiments, by selecting a capacitor voltage level that is greater than the minimum required value. VI. CONCLUSION A single-dc-source cascaded H-bridge multilevel converter has been analyzed. A new control method, phase-shift modulation is used to regulate the voltage of the capacitors replacing the independent dc source in the auxiliary H-bridge cell. The main H-bridge cell operates at the fundamental frequency, while the auxiliary cell 47

10 runs at PWM frequency. The proposed method offers a robust regulation of the capacitor voltage when the inverter s load is inductive. Consequently, at the cost of adding some minor computational burden, it leads to a more simple and cost-effective single-dc-source multilevel converter. Constraints involved in selecting the voltage source level of the auxiliary H-bridge cell also have been discussed in this paper. The experimental results show the effectiveness of this method of regulating the capacitor in the auxiliary H-bridge cell. REFERENCES [1] J. Rodriguez, L. Jih-Sheng, and P. Fang Zheng, Multilevel inverters: A survey of topologies, controls, and applications, IEEE Trans. Ind. Electron., vol. 49, no. 4, pp , Aug [2] L. G. Franquelo, J. Rodriguez, J. I. Leon, S. Kouro, R. Portillo, and M. A. M. Prats, The age of multilevel converters arrives, IEEE Ind. Electron. Mag., vol. 2, no. 2, pp , Jun [3] J. S. Lai and F. Z. Peng, Multilevel converters A new breed of power converters, IEEE Trans. Ind. Appl., vol. 32, no. 3, pp , May [4] C. Cecati, A. Dell Aquila, M. Liserre, and V. G. Monopoli, Design of H-bridge multilevel active rectifier for traction systems, IEEE Trans. Ind. Appl., vol. 39, no. 5, pp , Sep [5] C. Cecati, F. Ciancetta, and P. Siano, A multilevel inverter for photovoltaic systems with fuzzy logic control, IEEE Trans. Ind. Electron., vol. 57, no. 12, pp , Dec [6] E. Ozdemir, S. Ozdemir, and L. M. Tolbert, Fundamentalfrequencymodulated six-level diode-clamped multilevel inverter for three-phase stand-alone photovoltaic system, IEEE Trans. Ind. Electron., vol. 56, no. 11, pp , Nov [7] H. Sepahvand, M. Khazraei, M. Ferdowsi, and K. A. Corzine, Feasibility of capacitor voltage regulation and output voltage harmonic minimization in cascaded H-bridge converters, in Proc. IEEE Appl. Power Electron.Conf. Expo., 2010, pp [8] E. Villanueva, P. Correa, and J. Rodriguez, Control of a single phase H-bridge multilevel inverter for grid-connected PV applications, in Proc.Power Electron. Motion Control Conf., 2008, pp [10] K. A. Corzine and J. R. Baker, Multilevel voltage-source duty-cycle modulation: Analysis and implementation, IEEE Trans. Ind. Electron., vol. 49, no. 5, pp , Oct [11] H. Sepahvand, M. Ferdowsi, and K. A. Corzine, Fault recovery strategy for hybrid cascaded H-bridge multi-level inverters, in Proc. IEEE Appl. Power Electron. Conf. Expo., 2011, pp [12] H. Sepahvand, M. Khazraei, M. Ferdowsi, and K. A. Corzine, Startup procedure and switching losses reduction for a single-phase flying capacitor active rectifier, IEEE Trans. Ind. Electron., to be published. [13] M. Khazraei, H. Sepahvand, K. A. Corzine, and M. Ferdowsi, Active capacitor voltage balancing in single-phase flying capacitor multilevel power converters, IEEE Trans. Ind. Electron., vol. 59, no. 2, pp , Feb [14] M. Khazraei, H. Sepahvand, M. Ferdowsi, and K. A. Corzine, Hysteresisbased control of a single-phase multilevel flying capacitor active rectifier, IEEE Trans. Power Electron., vol. 28, no. 1, pp , Jan [15] J. Dixon, J. Pereda, C. Castillo, and S. Bosch, Asymmetrical multilevel inverter for traction drives using only one dc supply, IEEE Trans. Veh. Technol., vol. 59, no. 8, pp , Oct [16] J. Dixon, L. Moran, J. Rodriguez, and R. Domke, Reactive power compensation technologies: State-of-the-art review, Proc. IEEE, vol. 93, no. 12, pp , Dec [17] E. Villanueva, P. Correa, J. Rodriguez, andm. Pacas, Control of a single-phase cascaded H-bridge multilevel inverter for grid-connected photovoltaic systems, IEEE Trans. Ind. Electron., vol. 56, no. 11, pp , Nov [18] S. Lu, K. A. Corzine, andm. Ferdowsi, A unique ultracapacitor direct integration scheme in multilevel motor drives for large vehicle propulsion, IEEE Trans. Veh. Technol., vol. 56, no. 4, pp , Jul [19] Z. Du, L. M. Tolbert, J. N. Chiasson, and B. Ozpineci, A cascade multilevel inverter using a single dc source, in Proc. IEEE Appl. Power Electron. Conf. Expo., 2006, pp [9] Y. Cheng and M. L. Crow, A diode-clamped multi-level inverter for the StatCom/BESS, in Proc. IEEE Power Eng. Soc. Winter Meeting, 2002, vol. 1, pp