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Modified single‐carrier multilevel sinusoidal pulse width modulation for asymmetrical insulated gate bipolar transistor‐clamped grid‐connected inverter

2015; Institution of Engineering and Technology; Volume: 8; Issue: 8 Linguagem: Inglês

10.1049/iet-pel.2014.0519

1755-4543

Fengjiang Wu, Jiandong Duan, Fan Feng,

Microgrid Control and Optimization

IET Power ElectronicsVolume 8, Issue 8 p. 1531-1541 Research ArticlesFree Access Modified single-carrier multilevel sinusoidal pulse width modulation for asymmetrical insulated gate bipolar transistor-clamped grid-connected inverter Fengjiang Wu, Corresponding Author Fengjiang Wu shimeng@hit.edu.cn Department of Electrical Engineering, Harbin Institute of Technology, Harbin, 150001 People's Republic of ChinaSearch for more papers by this authorJiandong Duan, Jiandong Duan Department of Electrical Engineering, Harbin Institute of Technology, Harbin, 150001 People's Republic of ChinaSearch for more papers by this authorFan Feng, Fan Feng Department of Electrical Engineering, Harbin Institute of Technology, Harbin, 150001 People's Republic of ChinaSearch for more papers by this author Fengjiang Wu, Corresponding Author Fengjiang Wu shimeng@hit.edu.cn Department of Electrical Engineering, Harbin Institute of Technology, Harbin, 150001 People's Republic of ChinaSearch for more papers by this authorJiandong Duan, Jiandong Duan Department of Electrical Engineering, Harbin Institute of Technology, Harbin, 150001 People's Republic of ChinaSearch for more papers by this authorFan Feng, Fan Feng Department of Electrical Engineering, Harbin Institute of Technology, Harbin, 150001 People's Republic of ChinaSearch for more papers by this author First published: 01 August 2015 https://doi.org/10.1049/iet-pel.2014.0519Citations: 8AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Conventional sinusoidal pulse width modulation (SPWM) for single-phase asymmetrical seven-level insulated gate bipolar transistor (IGBT)-clamped grid-connected inverter (IC-GCI) needs an additional logic operation circuit and a dead zone generation circuit, which raises cost and complicates the implementation. In addition, both added circuitries decrease the reliability. In this study, a modified single-carrier multilevel SPWM (MSCM-SPWM) scheme suitable for IC-GCI is proposed. By setting one carrier, three digital signals to identify voltage zones and six equivalent modulation waves, the control signals of the switches in IC-GCI can be generated with only one digital signal processor controller and simple logic operation. It makes the implementation of the multilevel GCI easier. The detailed spectral character of the MSCM-SPWM is originally derived based on double-Fourier integral theory and then compared with the conventional scheme. It proves that they own the similar spectral character. Detailed simulation and experimental results verify the accuracy and feasibility of the MSCM-SPWM and the single-phase IC-GCI. Nomenclature uinv output voltage of inverter Udc DC source voltage Unom, ω amplitude and angle frequency of normal reference modulation wave M amplitude modulation ratio Utr amplitude of carrier θ1–θ8 critical phase angles of various voltage zones ur1–ur6 equivalent modulation waves of various voltage zones ωc carrier frequency x angle phase of carrier y angle phase of modulation wave Kp, KR proportional and resonant coefficients of quasi-proportional resonant (QPR) controller ω0, ωcut resonant frequency and cut-off frequency of QPR controller 1 Introduction Multilevel inverters have so many advantages over the two-level inverters, such as the higher equivalent switching frequency, lower total harmonics distortion (THD) and lower-voltage stress on the power switches. Just because of the former merits, in recent years, the multilevel inverters become more and more attractive and have obtained expansive foreground not only in the field of the high-voltage and huge-power system but also in the low-voltage and small-power system, such as the photovoltaic generation system [1-6]. Various multilevel topologies have been proposed over the recent years [7-12]. Common ones are cascaded H-bridge [7], flying capacitor [8] and diode-clamped [9]. Furthermore, in the single-phase system, the asymmetrical topologies consisted of two kinds of half-bridge legs with different level numbers are presented [10-12]. Specially, in [12], a single-phase asymmetrical seven-level insulated gate bipolar transistor (IGBT)-clamped grid-connected inverter (IC-GCI) is proposed. Shown as in Fig. 1a, the IC-GCI uses only six power switches to implement up to seven-level output voltage. The reduction of the number of the power switches reduces the cost and bulk obviously. Especially, when they are used in the lower-power and smaller-voltage grid-connected system, such as photovoltaic and wind generation system, the following benefit can be obtained, such as the lower electromagnetic interference, lower acoustic noise, lower core losses and smaller filter size. Fig. 1Open in figure viewerPowerPoint Diagrams of single-phase asymmetrical seven-level IC-GCI and proposed MSCM-SPWM a Seven-level IC-GCI b Proposed MSCM-SPWM with 1 ≥ M > 0.667 c Proposed MSCM-SPWM with 0.667 ≥ M > 0.333 d Proposed MSCM-SPWM with M ≤ 0.333 Among the single-phase multilevel sinusoidal pulse width modulation (SPWM) strategies, the most frequently used ones are the multi-carrier-based one [13] and the multi-modulation wave-based one [14, 15]. However, there are some problems when they are used in the IC-GCI as shown in Fig. 1a. (i) For the multi-carrier-based strategies, many timers are needed to generate carriers. It cannot be implemented with a single digital signal processor (DSP) controller only. Additional controller, such as field-programmable gate array (FPGA), is necessary. The addition of the FPGA increases the cost of the system and the development difficulty. (ii) For the multi-modulation wave-based strategies, the pulse width modulation (PWM) signals with up to seven levels can be implemented with a single DSP controller only. However, because of the asymmetric character of IC-GCI, during the positive- and negative-half cycles of the modulation wave, the comparison logics between the modulation wave and carrier are independent. In the SPWM strategy in [12], the comparison logics during the positive- and negative-half cycles are the same, thus a series of complex logic operation to distinct the comparison logic must be performed to achieve actual control signals. Attached logic operation circuit or special controller must be used, which increases the complication of the implementation platform. The main contribution of this paper is depicted as follows. To control the IC-GCI under a simpler way, a modified single-carrier multilevel (MSCM) SPWM suitable for implementing with DSP controller is proposed. The modification mainly includes the following aspects. (i) Within different voltage zones, the modulation wave is summed by different DC offsets and compared with the same carrier to generate PWM signals and (ii) three digital signals are set to identify the voltage zones. With these identification signals and the PWM signals, the control signals of various power switches can be obtained with only 'AND' and 'OR' operation. The proposed MSCM-SPWM has the following advantages. Only one carrier is used, the non-synchronous problem between the carriers in the conventional multi-carrier strategies does not exist. Only one timer and one PWM generation module in DSP is employed to implement the MSCM-SPWM. It makes that the PWM strategy and current control algorithm can be implemented in the same DSP controller, as a result the implementation platform of the multilevel GCI is simplified significantly. Moreover, because the number of used timer and PWM generation module in DSP for implementing the MSCM-SPWM is independent of the level number of the output voltage, theoretically, based on the MSCM-SPWM, the arbitrary level number of multilevel inverter can be controlled with a single DSP controller. This paper is organised as follows. Section 2 introduces the principle of IC-GCI. In Section 3, the proposed SPWM is depicted in detail. In Section 4, the current control strategy with a QPR controller and the system structure are analysed. In Section 5, the simulation and experimental results of the proposed SPWM and IC-GCI are represented. Finally, Section 6 gives the conclusion. 2 Principle of single-phase seven-level IC-GCI and proposed MSCM-SPWM The schematic diagram of single-phase asymmetrical seven-level IC-GCI is shown in Fig. 1a. It comprises a single-phase conventional H-bridge inverter, two bidirectional switches and three DC sources with identical output voltages: E1, E2 and E3. One filter inductor is connected in series between the H-bridge inverter and the grid. In the following, the operation principle of the IGBT-clamped inverter is analysed. With different combinations of on or off states of the power switches, the IGBT-clamped inverter can output seven different voltage levels. The detailed relationship is listed in Table 1. It can be seen from Table 1 that, if S2 and S4 are controlled by the synchronous signals of the tied grid, for any voltage level, only two power switches are in conducting state. When the level of output voltage changes between any adjacent two voltage levels, only two power switches change their switching states. It means that the IGBT-clamped inverter owns lower conducting and switching losses than the symmetrical diode-clamped multilevel inverter under the same output level number conditions. It can also be seen that, during the total period of the tied grid, each power switch must be controlled with a special PWM signal, which cannot be obtained by operating logic 'NOT' of the PWM signal of any other power switch. If any modification is not made, the conventional multilevel SPWM cannot be directly used to drive the IGBT-clamped inverter. Table 1. Output voltages corresponding to states of power switches uinv S1 S2 S3 S4 S5 S6 3Udc on off off on off off 2Udc off off off on on off Udc off off off on off on 0+ off off on on off off 0− on on off off off off −Udc off on off off on off −2Udc off on off off off on −3Udc off on on off off off The basic operation principle waveform of the proposed MSCM-SPWM for the IC-GCI is shown in Fig. 1b. The main idea is depicted as follows. For the right bridge arm, S2 and S4 are controlled by the synchronous signals of the tied grid. As for the left bridge arm, the MSCM-SPWM is utilised. One triangle carrier and one normal sinusoidal reference modulation wave are set. According to the relationship of the instantaneous value of the normal modulation wave and the amplitude of the carrier, the plane of the normal modulation wave is divided into six voltage zones. Within various voltage zones, different DC offsets related with the integer multiple of the carrier amplitude are biased on the normal modulation wave to limit the actual modulation wave not to exceed the carrier amplitude. Thus, the PWM signals of the six voltage zones can be obtained only through comparing the equivalent modulation waves with the carrier. To identify the various voltage zones, three digital signals are introduced. With the corresponding logic operation between the voltage zones identification signals and the PWM signals, the actual control signals of various power switches can be obtained. The shapes of the three digital signals are designed carefully to implement unified logic operation for the same power switch within various voltage zones. In the following, the switching phase angles and the actual equivalent modulation waves of various voltage zones are derived. Assuming that the amplitude of carrier is Utr and the normal reference modulation wave is (1)where Unom and ω are the amplitude and angle frequency of normal reference modulation wave, respectively. Around the boundary of any two adjacent voltage zones, the value of the modulation wave is equal to the amplitude of the carrier or its integer multiple, that is (2)Here, θ1−θ8 denote the switching phase angles of various voltage zones. According to (2), the actual expressions of the switching phase angles are derived as (3)Various DC offsets within these phase regions are added on the normal reference sinusoidal modulation wave to obtain the functions of the equivalent modulation wave within various phase regions. Within the positive-half cycle of the normal reference modulation wave, during [0, θ1) and [θ4, π), the function of ur1 has the same format with the normal one. No DC offset is biased. During [θ1, θ2) and [θ3, θ4), the function of ur2 is (4)During [θ2, θ3), the function of ur3 is (5)As for the negative-half cycle, a series positive DC offsets are biased on the normal reference modulation wave. During [π, θ5) and [θ8, 2π), the function of ur4 is (6)During [θ5, θ6) and [θ7, θ8), the function of ur5 is (7)During [θ6, θ7), the function of ur6 is (8)The amplitude modulation ratio is (9)Additionally, considering that the power switches under working state are different within various voltage zones, three digital signals are introduced to identify the various voltage zones, which are denoted as GZ1, GZ2 and GZ3. It can be known from Fig. 1b that the control signals of various power switches are not symmetrical around the zero-cross axis of the normal reference modulation wave. Therefore the shapes of GZ1, GZ2 and GZ3 will be different in the positive- and negative-half cycles of the normal reference modulation wave. Shown as in Fig. 1b, the shapes of GZ1, GZ2 and GZ3 are modified to simplify the logic operation between GZ1, GZ2, GZ3 and PWM signals. The actual relationships among the control signals of various power switches: GZ1, GZ2, GZ3 and PWM signals are (10)Seen as (10), with only 'AND' and 'OR' logic operations, the control signals of various power switches can be obtained. In the following, the level number of the output voltage with the change of the amplitude modulation ratio is analysed. It can be known from (9) that when Unom > 2Utr, namely, 1 ≥ M > 0.667, θ2 is less than π/2, it means that the inverter can output seven-level voltage waveform. Although, when 2Utr ≥ Unom > Utr, namely, 0.667 ≥ M > 0.333, θ2, θ3, θ6, θ7 already cannot be solved with a true result. Under this condition, only the equivalent modulation waves: ur1, ur2, ur4 and ur5 remain. The output voltage degrades into five-level waveform and the operation principle sketch is shown in Fig. 1c. To maintain the integrity of the PWM algorithm, θ2 and θ3 are defined as π/2 and θ6 = θ7 = 3π/2. As for Unom ≤ Utr, namely, M ≤ 0.333, only the modulation waves: ur1 and ur4 remain, the operation principle sketch is shown in Fig. 1d. Under this condition, θ1 = θ2 = θ3 = θ4 = π/2, θ5 = θ6 = θ7 = θ8 = 3π/2. Since the spectral character of the multi-level PWM strategy determines the THD of the output voltage directly, the detailed theoretical derivation of the spectral character of the proposed MSCM-SPWM is performed. In this paper, the double-Fourier integral theory is used to derive the spectral distribution. The phase angle of the carrier wave, x, and the phase angle modulation, y, are defined as (11)where ωc is the angular frequency of the carrier. Since the modulation wave and carrier are both periodic, the output voltage (per unit) is defined as double-Fourier series [16] (12) (13)The key point of calculating Cmn is to determine the integral limits of x and y. The integral limits of y are determined first. The integral limit of y is mainly determined by the various switching phase angles, shown as (3). In the following, the integral limits of x with respect to different level numbers of the output voltage are analysed. According to the amplitude relationships of the modulation wave and the carrier, the ranges of the phase angle within one carrier cycle corresponding to different level numbers of the output voltages are derived; the results of the PWM strategies are represented in Table 2. Table 2. Integral limits of x and y of the proposed SPWM uinv, pu y x 1 0 ≤ y < θ1 −3πM sin y ≤ x ≤ 3πM sin y 2 θ1 ≤ y < θ2 π−3πM sin y ≤ x ≤ −π+3πM sin y 3 θ2 ≤ y < θ3 2π−3πM sin y ≤ x ≤ −2π + 3πM sin y 2 θ3 ≤ y < θ4 π−3πM sin y ≤ x ≤ −π + 3πM sin y 1 θ4 ≤ y < π −3πM sin y ≤ x ≤ 3πM sin y −1 π ≤ y < θ5 π + 3πM sin y ≤ x ≤ π−3πM sin y −2 θ5 ≤ y < θ6 2π + 3πM sin y ≤ x ≤ −3πM sin y −3 θ6 ≤ y < θ7 3π + 3πM sin y ≤ x ≤ −π−3πM sin y −2 θ7 ≤ y < θ8 2π + 3πM sin y ≤ x ≤ −3πM sin y −1 θ8 ≤ y < 2π π + 3πM sin y ≤ x ≤ π−3πM sin y The contour curves are plotted in Fig. 2. Each curve defines a transition in voltage. Utilising the superposition principle, the Fourier integrals of the proposed SPWM yield from Table 2 as (14) Fig. 2Open in figure viewerPowerPoint Contour curves within 2π phase wraparound The expansion formula of the Jacobi-angle series is [16] (15)Setting ξ = 3mMπ, the Fourier series of the output voltage of the proposed SPWM are derived as (16)where (17) (18)As for 0.667 ≥ M > 0.333, according to Fig. 2a, the Fourier series of the output voltage are solved as (19)where (20) (21)Similarly, as for M ≤ 0.333, according to Fig. 2b, the Fourier series of the output voltage are solved as (22)where (23) (24)Similarly, the Fourier series of the output voltage of the conventional strategy in [12] with 1 ≥ M > 0.667 yields (25)where (26)It can be known from (16) to (26) that there is no harmonics at the integer multiple of the frequency of the modulation wave. There are harmonics at the integer multiple of the frequency of the carrier and sideband harmonics. Around the points with the even-time frequencies of the carrier, there are only the sideband harmonics at the odd-time frequencies of the modulation wave, vice versa. The distribution outline of the spectral character of the output voltage is independent of the level number. When the level number changes, the only difference is that the amplitudes of the various-order harmonics are unequal. As for the SPWM in [12], there is also no harmonics at the integer multiple of the frequency of the modulation wave. There are harmonics at the integer multiple of the frequency of the carrier and sideband harmonics. The difference from the proposed one is that, around the points of the integer-time frequencies of the carrier, there are only the bandside harmonics at the odd-times frequencies of the modulation wave. 3 Current control and system structure In the single-phase multilevel GCI, the grid current needs to be controlled online. The conventional proportional–integral controller is frequently used in the DC-type closed-loop control system; however, when it is used to control the sinusoidal wave, it is very difficult to obtain zero-steady state error performance. In this paper, a QPR controller is combined with the proposed MSCM-SPWM to control the grid current. The basic idea of the proportional resonant (PR) controller is to introduce an infinite gain at a selected resonant frequency for eliminating steady-state error at certain frequency. The transfer function of PR controller is [17] (27)where KP and KR are the proportional and resonant coefficients, respectively, ω0 is the resonant frequency (set as grid frequency in a grid-connected system). However, the bandwidth of traditional PR controller is low, when the actual frequency of grid voltage is deviated from the preset one, ω0, the actual control performance of PR controller will be deteriorated. In [18], a QPR controller is presented to extend the bandwidth of PR controller. The transfer function of QPR controller is (28)where ωcut is the cut-off frequency. The bode plots of PR and QPR controllers are shown in Fig. 3 to compare their performance. The control parameters are set as follows. KP = 5, KR = 50, ω0 = 314 rad/s (equal to the normal frequency of china grid), ωcut = 12.56 rad/s, namely, with the allowable frequency ripple of ±2 Hz. Seen as from Fig. 3, the bandwidth of QPR controller is larger than PR controller, which is helpful to eliminate the effect of the error existed between the actual frequency of tied grid and ω0 on the control performance of the grid current. The frequency error may be caused by the frequency ripple of the grid or by the steady-state estimation error of the phase-locked loop algorithm. With the same control parameters, the amplitude gain of the PR controller is much larger than the one of QPR controller. Fig. 3Open in figure viewerPowerPoint Bode plots of PR and QPR controllers Furthermore, the overall implementation platform of IC-GCI with DSP controller and combining the MSCM-SPWM with QPR controller is achieved and shown in Fig. 4. The entire algorithm is operated in the DSP controller. The sine value of the phase angle of tied grid is estimated by the enhanced phase-locked loop [19]. The output of the QPR controller inputs the MSCM-SPWM to generate the control signals of various power switches. Fig. 4Open in figure viewerPowerPoint DSP-based implementation platform sketch of IC-GCI 4 Simulation and experimental results To verify the feasibility of the IC-GCI based on MSCM-SPWM and QPR controller, the simulation model based on MATLAB/SIMULINK is made. The parameters of the simulation model are shown in Table 3. Table 3. Parameters of seven-level IC-GCI Parameters Values grid side inductor 5 mH carrier frequency 5 kHz single-phase grid voltage 220 V total DC supply voltage 450 V DC capacitor 2200 µF First, the performance of MSCM-SPWM is simulated. The simulation is performed under the condition of load free and without dead time between various PWM signals. Fig. 5 shows the simulation results with M = 0.8, 0.5, 0.3 including the equivalent modulation waves, identification signals of voltage zones, the output voltage of the inverter and its spectral distribution waveforms. The simulated waveforms are the same as Fig. 1 even under different amplitude modulation ratio conditions. Fig. 5Open in figure viewerPowerPoint Simulation results of MSCM-SPWM with different amplitude modulation ratio a M = 0.8 b M = 0.5 c M = 0.3 Furthermore, the spectral characters of the proposed MSCM-SPWM and the one applied in [12] are also shown in Fig. 5 with M = 0.8, 0.5, 0.3. Seen as from Fig. 5, around the point of carrier frequency, for the proposed SPWM, there are the harmonics at the carrier frequency and sideband harmonics at the odd-time frequencies of the modulation wave. As for the one in [12], there are also the harmonics at the carrier frequency while there are only sideband harmonics at the even-time frequencies of the modulation wave. Under various M conditions, the differences of the THDs of the two SPWMs are all very tiny. It means that the simulation results are similar with the theoretical analysis in the former section. As a result, the conventional SPWM in [12] can be replaced by the proposed one to simplify the implementation. It can be known from the spectral distribution waveforms that the shapes are similar when M changes. The difference is that the amplitudes of the harmonics increase when M decreases. The THDs are also increased. Furthermore, the single-phase IC-GCI is simulated. Figs. 6a and b show the steady-state simulated results with the current amplitudes of 10 and 20 A, respectively, including the grid voltage, the reference and actual grid currents and their error and the THDs of the actual grid currents. Seen as from Fig. 6, with different current amplitudes, both the current errors are very small, the actual current waveforms are sinusoidal and the THDs are smaller than 5%. Fig. 6Open in figure viewerPowerPoint Simulation results of IC-GCI a b c Current amplitude stepping up d Current amplitude stepping down At last, the dynamic response with current amplitude stepping change is simulated. Figs. 6c and d show the results of current amplitudes stepping from 10 up to 20 A and from 20 back to 10 A. When the current amplitude jumps, the actual current tracks the reference one well, and the settling time is about 0.4 ms. On the basis of Fig. 4, the digital implementation prototype of the IC-GCI is set up. The system parameters and test conditions are the same with the simulations. Three DC sources are achieved by the following way. The grid voltage inputs the isolation transformer with three independent output to obtain three AC voltages with the same amplitude. The obtained three AC voltages are rectified by diode-based rectifiers and filtered by the larger DC capacitors to obtain three identical DC voltages. It must indicate that, because there is periodic ripple in the DC output current, a relatively larger DC capacitor is introduced to eliminate the influence of the current ripple on the DC voltage. Fig. 7 shows the experimental results of the proposed MSCM-SPWM with different amplitude modulation ratios. The results are obtained under the condition of load free and without dead time between various PWM signals. Compared with Fig. 5, it can be known that, the correct waveforms, including the equivalent modulation waves, identification signals of voltage zones and the output voltage of the inverter are all obtained. Fig. 7Open in figure viewerPowerPoint Experimental results of MSCM-SPWM with different amplitude modulation ratios a M = 0.8 b M = 0.5 c M = 0.3 Then, the IC-GCI is experimented including the steady-state and dynamic response performance with the experimental results shown in Fig. 8. It can be seen that, under steady-state conditions, the actual current tracks the reference one well, and is almost in phase with the tied grid. Fig. 8Open in figure viewerPowerPoint Experimental results of IC-GCI with different current amplitudes a b It is worthy noting that, the output voltage of the inverter is no more perfect multilevel waveform, while with some voltage pulse disturbances. It is caused by the dead time between various control signals of power switches. In the following, the reason of generating the voltage pulse disturbance is analysed. The case of grid current under its positive-half cycle is considered. According to the principle of the IC-GCI as shown in Fig. 1, during the duration of the dead time, none of power switch in the left bridge arm is under on state. The grid current can only flow through the anti-parallel diode of S3; it results in the output of the inverter clamped at zero level. It is regarded as 'voltage pulse disturbance'. However, because it is caused by the current freewheeling state, it is essentially a 'fake pulse'. On the other hand, because the dead time is very small (it is set as 1 µs in this paper), the 'voltage pulse disturbance' has no obvious effect on the actual grid current. The spectral characters of the actual grid currents with different amplitudes are shown in Fig. 8. Furthermore, the experimental waveforms of the output voltage of the inverter and the grid current and the fast Fourier transform (FFT) curves of the grid current with different dead times are tested and shown in Fig. 9 to reveal the effect of the dead time on the grid current. It can be seen from Figs. 8 and 9 that, with the increase of the dead time, the number of the 'fake pulse' in output voltage of the inverter increases as well. However, the FFT curves of the grid current are similar. It means that the THDs of grid current are similar despite the differences of the dead time. The effect of the 'fake pulse' caused by the dead time is very tiny. Fig. 9Open in figure viewerPowerPoint Experimental results of IC-GCI with different dead times a 2 µs b 3 µs c 4 µs At last, the dynamic performance of the IC-GCI is tested with the current amplitude step change and the experimental results are shown in Fig. 10. During the dynamic process, the actual grid current tracks the reference one well and the settling time is about 3 ms. Fig. 10Open in figure viewerPowerPoint Dynamic experimental results of IC-GCI a Current amplitude stepping up b Current amplitude stepping down 5 Conclusion An MSCM-SPWM suitable for the single-phase asymmetrical seven-level IC-GCI is proposed. The theoretical analysis results of the spectral characters of the proposed MSCM-SPWM and conventional one prove that its performance is similar with the existing multilevel SPWM schemes. The simulation and experimental results of the IC-GCI with the proposed MSCM-SPWM indicate that high control performance of grid current is obtained. It means that in the actual IC-GCI, the conventional SPWM strategy can be absolutely replaced by the proposed one. As a result, the implementation of the IC-GCI is more compact and the excellent performance is still guaranteed. The cost and complication of the multilevel IC-GCI is reduced, and the integration level and reliability are both increased. 6 Acknowledgment This work was supported by the National Natural Science Foundation of China (grant no. 51107018). 7 References 1Juárez-Abad J.A., Linares-Flores J., and Guzmán-Ramírez E. et al.: 'Generalized proportional integral tracking controller for a single-phase multilevel cascade inverter: an FPGA implementation', IEEE Trans. Ind. Inf., 2014, 10, (1), pp. 256– 266 (doi: http://doi.org/10.1109/TII.2013.2242085) 2Wu J., Wu K., and Jou H. et al.: 'Small-capacity grid-connected solar power generation system', IET Power Electron., 2014, 7, (11), pp. 2717– 2725 (doi: http://doi.org/10.1049/iet-pel.2014.0015) 3Liu Y., Ge B., and Abu-Rub H. et al.: 'An effective control method for quasi-Z-source cascade multilevel inverter-based grid-tie single-phase photovoltaic power system', IEEE Trans. Ind. Inf., 2014, 10, (1), pp. 399– 407 (doi: http://doi.org/10.1109/TII.2013.2280083) 4Chavarria J., Biel D., and Guinjoan F. et al.: 'Energy-balance control of PV cascaded multilevel grid-connected inverters under level-shifted and phase-shifted PWMs', IEEE Trans. Ind. Electron., 2013, 60, (1), pp. 98– 111 (doi: http://doi.org/10.1109/TIE.2012.2186108) 5Rajesh M., and Singh B.: 'Analysis, design and control of single-phase three-level power factor correction rectifier fed switched reluctance motor drive', IET Power Electron., 2014, 7, (6), pp. 1499– 1508 (doi: http://doi.org/10.1049/iet-pel.2013.0621) 6Young C., Chu N., and Chen L. et al.: 'A single-phase multilevel inverter with battery balancing', IEEE Trans. Ind. Electron., 2013, 60, (5), pp. 1972– 1978 (doi: http://doi.org/10.1109/TIE.2012.2207656) 7Malinowski M., Gopakumar K., Rodriguez J., and Pérez M.A.: 'A survey on cascaded multilevel inverters', IEEE Trans. Ind. Electron., 2010, 57, (7), pp. 2197– 2206 (doi: http://doi.org/10.1109/TIE.2009.2030767) 8Alishah R.S., Nazarpour D., and Hosseini S.H. et al.: 'Switched-diode structure for multilevel converter with reduced number of power electronic devices', IET Power Electron., 2014, 7, (3), pp. 648– 656 (doi: http://doi.org/10.1049/iet-pel.2013.0208) 9Rodriguez J., Bernet S., Steimer P.K., and Lizama I.E.: 'A survey on neutral-point-clamped inverters', IEEE Trans. Ind. Electron., 2010, 57, (7), pp. 2219– 2230 (doi: http://doi.org/10.1109/TIE.2009.2032430) 10Zambra D.A.B., Rech C., and Pinheiro J.R.: 'Comparison of neutral-point-clamped, symmetrical and hybrid asymmetrical multilevel inverters', IEEE Trans. Ind. Electron., 2010, 57, (7), pp. 2297– 2306 (doi: http://doi.org/10.1109/TIE.2010.2040561) 11Perantzakis G.S., Christodoulou C.A., and Anagnostou K.E. et al.: 'Comparison of power losses, current and voltage stresses of semiconductors in voltage source transformerless multilevel inverters', IET Power Electron., 2014, 7, (11), pp. 2743– 2757 (doi: http://doi.org/10.1049/iet-pel.2013.0748) 12Nasrudin A.R., Krismadinata C., and Jeyraj S.: 'Single-phase seven-level grid-connected inverter for photovoltaic system', IEEE Trans. Ind. Electron., 2011, 58, (6), pp. 2435– 2443 (doi: http://doi.org/10.1109/TIE.2010.2064278) 13Liu Y., Ge1 B., and Abu-Rub H. et al.: 'Phase-shifted pulse-width-amplitude modulation for quasi-Z-source cascade multilevel inverter-based photovoltaic power system', IET Power Electron., 2014, 7, (6), pp. 1444– 1456 (doi: http://doi.org/10.1049/iet-pel.2013.0637) 14Govindaraju C., and Baskaran K.: 'Analysis and implementation of multiphase multilevel hybrid single carrier sinusoidal modulation', J. Power Electron., 2010, 10, (4), pp. 365– 373 (doi: http://doi.org/10.6113/JPE.2010.10.4.365) 15Wu F.J., Sun B., and Peng H.R.: 'Single-phase three-level SPWM scheme suitable for implementation with DSP', IET Electron. Lett., 2011, 47, (17), pp. 994– 996 (doi: http://doi.org/10.1049/el.2011.1969) 16McGrath B.P., and Holmes D.G.: 'An analytical technique for the determination of spectral components of multilevel carrier-based PWM methods', IEEE Trans. Ind. Electron., 2002, 49, (4), pp. 847– 857 (doi: http://doi.org/10.1109/TIE.2002.801071) 17Guo X.Q., Zhao Q.L., and Wu W.Y.: ' A single-phase grid-connected inverter system with zero steady-state error'. Proc. of the IEEE Power Electronics and Motion Control Conf., 2006, pp. 1– 5 18Teodorescu R., Blaabjerg F., Liserre M., and Loh P.C.: 'Proportional resonant controllers and filters for grid-connected voltage-source converters', IEE Proc. Electr. Power Appl., 2009, 153, (5), pp. 750– 762 (doi: http://doi.org/10.1049/ip-epa:20060008) 19Karimi-Ghartemani M.: 'Linear and pseudolinear enhanced phased-locked loop (EPLL) structures', IEEE Trans. Ind. Electron., 2014, 61, (3), pp. 1464– 1474 (doi: http://doi.org/10.1109/TIE.2013.2261035) Citing Literature Volume8, Issue8August 2015Pages 1531-1541 FiguresReferencesRelatedInformation