Single‐phase high‐voltage gain switched LC Z‐source inverters
2017; Institution of Engineering and Technology; Volume: 11; Issue: 5 Linguagem: Inglês
10.1049/iet-pel.2017.0634
ISSN1755-4543
AutoresVinod Kumar Bussa, Anish Ahmad, Rajeev Kumar Singh, Ranjit Mahanty,
Tópico(s)Silicon Carbide Semiconductor Technologies
ResumoIET Power ElectronicsVolume 11, Issue 5 p. 796-807 Research ArticleFree Access Single-phase high-voltage gain switched LC Z-source inverters Vinod Kumar Bussa, Corresponding Author Vinod Kumar Bussa vinod.rs.eee14@iitbhu.ac.in Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this authorAnish Ahmad, Anish Ahmad orcid.org/0000-0003-4899-0886 Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this authorRajeev Kumar Singh, Rajeev Kumar Singh Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this authorRanjit Mahanty, Ranjit Mahanty Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this author Vinod Kumar Bussa, Corresponding Author Vinod Kumar Bussa vinod.rs.eee14@iitbhu.ac.in Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this authorAnish Ahmad, Anish Ahmad orcid.org/0000-0003-4899-0886 Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this authorRajeev Kumar Singh, Rajeev Kumar Singh Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this authorRanjit Mahanty, Ranjit Mahanty Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 221005 IndiaSearch for more papers by this author First published: 01 May 2018 https://doi.org/10.1049/iet-pel.2017.0634Citations: 15AboutSectionsPDF 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 Recently, switched-inductor Z-source inverters (SL-ZSIs) have been reported to achieve high-voltage gain and good power inversion operation at low shoot-through duty ratio D as compared to conventional ZSI. As the SL-ZSIs have high passive component count, weight, volume and losses of the system increases that lead to reduction in efficiency. To address the issues of conventional ZSI and SL-ZSIs, two single-phase switched LC (SLC)-ZSIs (Type 1 SLC-ZSI and Type 2 SLC-ZSI) are proposed in this study to achieve high-voltage gains at low values of D with lower passive component count as compared to SL-ZSIs. At low values of D, modulation index M approaches to higher values which results into improved AC output at reduced harmonic distortion. Due to low passive component count in the proposed inverters, weight, volume and losses decreases resulting into increase in efficiency. The proposed inverters can be used in various DC–AC and DC–DC power conversions in renewable energy applications due to their high-voltage gain, better immunity to EMI noise and higher reliability. The detailed steady-state analysis of the two proposed SLC-ZSIs is given in this study. Scaled down experimentation has been carried out to verify the performance of the proposed inverters. 1 Introduction Conventional voltage-source inverter (VSI) and current-source inverters (CSIs) are commonly used in different applications such as UPS systems, distribution generation systems (nano-grid, micro-grid and smart-grids), motor drives, electric vehicles. However, when these are operated from renewable energy sources such as solar PV and fuel cells to match AC distribution system voltage levels, due to low-voltage gain of VSI and limitations of conventional inverters (VSIs and CSIs), they are not suitable for such systems [1]. To overcome the limitations of conventional inverters, a new topology called the Z-source inverter (ZSI) [2] was introduced. In recent times, many researchers have shown improvements in the ZSIs in different ways which includes new topologies, control strategies, modelling and applications [3-14]. The forbidden shoot-through state in the conventional VSI decides the required boost gain of the ZSI. The boost factor B of the conventional ZSI is given by (1)The shoot-through duty ratio (D) and modulation index (M) are interdependent in single-phase ZSI systems under the constraint of (). Thus, increase in the boost gain would reduce the modulation index. The inversion at low values of M will result into poor fundamental frequency component with increased harmonic distortion. To obtain high-voltage gain along with high modulation index; switched-inductor (SL), switched-capacitor (SC), hybrid SC/SL and voltage multiplier cells [15, 16] are integrated in ZSIs. Successful integration of SL cell with the ZSI [17-23] provides high boost inversion with reduced harmonic distortion at low output voltages of renewable sources as compared to conventional ZSI. Although, SL-ZSIs give high boost inversion, they have high passive component count which leads to reduction in efficiency and increase in weight and volume of the system. In this paper, two single-phase switched LC ZSIs (SLC-ZSIs) are proposed to address the issues associated with SL-ZSIs. The proposed inverters have higher voltage gains which can be achieved at low values of D with lesser number of passive components as compared to the SL-ZSIs [17-21]. Due to low values of D, modulation index can be increased which gives power inversion at reduced harmonic distortion [17]. Due to lesser number of passive components, the SLC-ZSIs are more efficient and reduced in volume and weight as compared to SL-ZSIs. The proposed SLC-ZSIs can be applied to various DC–AC and DC–DC power conversions in renewable energy applications. Moreover, the voltage stress on capacitors, shoot-through current through the inverter switches and current stress on diodes and inductors in the proposed inverters are lower than the SL-ZSIs for the same input and output voltages. 2 Review of SL-ZSIs Switched-inductor (SL) ZSI reported in [17] to achieve high-voltage gain at low values of D is shown in Fig. 1a. Although it gives high boost inversion at low shoot-through duty ratio, it has more passive component count which leads to increase in weight and volume resulting into decrease in efficiency of the system. It also suffers from drawbacks such as discontinuous input current, high start-up inrush current and different DC and AC grounds. The boost factor B of the SL-ZSI topology is given as (2) Fig. 1Open in figure viewerPowerPoint Switched-inductor (SL) ZSI topologies (a) SL-ZSI, (b) SL-qZSI,(c) rSL-qZSI and cSL-qZSI,(d) L-ZSI SL-qZSI reported in [18] to address the challenges of SL-ZSI and quasi-ZSI (qZSI), is shown in Fig. 1b. Although it overcomes the drawbacks of SL-ZSI and qZSI [18], it has less boost inversion ability compared to SL-ZSI at low shoot-through duty ratio. The boost factor B of the SL-qZSI topology is given as (3)Two modified SL-qZSIs, namely ripple current SL-qZSI (rSL-qZSI) and continuous current SL-qZSI (cSL-qZSI), are reported in [19] to achieve high-voltage gain at low values of D, are shown in Fig. 1c. Even though they give high-voltage gains, they have more passive component count such as SL-ZSI. The boost factor B of the rSL-qZSI topology is given as (4)The boost factor B of the cSL-qZSI topology is given as (5)L-ZSI is reported in [20] to improve the boosting capability without capacitors, is shown in Fig. 1d. Although it has less passive component count, it has less boosting capability as compared to conventional ZSI and SL-ZSIs. Moreover, due to the absence of capacitor, it is not suitable for inductive load operation as discussed in [21]. The boost factor B of the L-ZSI topology is given as (6)To overcome the above issues of SL-ZSI topologies and to achieve high-voltage gain at low shoot-through duty ratio with less passive component count, two single-phase SLC-ZSIs (Type 1 and Type 2) are proposed in this paper and as shown in Fig. 2. Fig. 2Open in figure viewerPowerPoint Proposed SLC- ZSIs (a) Type 1 SLC-ZSI, (b) Type 2SLC-ZSI 3 Proposed SLC- ZSIs In order to obtain higher voltage gain with lesser number of passive components as compared to the existing SL-ZSIs, Type 1 SLC-ZSI has been proposed which is derived from L-ZSI by adding a capacitor, a diode and two switches as shown in Fig. 2a. Further, it has been observed that if the diode is replaced by a capacitor in the SL cell of the proposed Type 1 SLC-ZSI, the voltage gain can further be improved which results into proposed Type 2 SLC-ZSI as shown in Fig. 2b. These circuit arrangements help the proposed inverters to give high boost inversion at low shoot-through duty ratio (i.e. high modulation index) using lesser number of passive components as compared to SL-ZSIs, discussed in Section 2. Moreover, the proposed inverters give continuous input current, common DC ground and limit the start-up inrush current as compared to the SL-ZSIs. The comparative analysis of number components of various ZSIs is given in Table 1 along with the total cost of the elements. The applications of the both the proposed SLC-ZSIs are identical and can be used in various DC–AC and DC–DC power conversions in renewable energy applications. Table 1. Comparative analysis of the number of components with their cost among the ZSIs Parameter Part number Unit price, USD SL-ZSI SL-qZSI rSL/cSL-qZSI Type 1 SLC-ZSI Type 2 SLC-ZSI inductors — 13.45 4 3 4 2 2 capacitors — 3.64 2 2 2 1 2 diodes 40EPF06 5.51 7 4 7 4 3 inverter switches FGH40T65UPD 4.63 4 4 4 4 4 other switches IRG7PH42UPBF 5.21 — — — 2 2 gate drivers FOD3184 2.06 4 4 4 6 6 total number of components — — 17 13 17 13 13 total cost, USD — — 126.41 96.43 126.41 93.88 92.01 3.1 Operation of the Type 1 SLC-ZSI For easy analysis, the H-bridge inverter circuit is replaced by a single switch, S. The operation of the Type 1 SLC-ZSI is explained for shoot-through and non-shoot through intervals. 3.1.1 Shoot-through interval The equivalent circuit of Type 1 SLC-ZSI is shown in Fig. 3a. When switches and are triggered ON and is triggered OFF, diodes and are forward biased and and are reverse biased. The capacitor C is discharged and the inductors ( and ) store energy from the DC source and capacitor through S and . From Fig. 3a, corresponding mathematical expressions can be written as (7) Fig. 3Open in figure viewerPowerPoint Circuit diagrams of proposed inverters during operating intervals (a) Shoot-through interval of Type 1 SLC-ZSI, (b) Non-shoot-through interval of Type 1 SLC-ZSI, (c) Shoot-through interval of Type 2 SLC-ZSI, (d) Non-shoot-through interval of Type 2 SLC-ZSI 3.1.2 Non-shoot-through interval The equivalent circuit of Type 1 SLC-ZSI is shown in Fig. 3b. When and are triggered OFF and is triggered ON, and are reverse biased and and are forward biased. In such a case, and are connected in series and the combined energy of DC source and stored magnetic energy is supplied to the inverter circuit. Also, the capacitor C is charged subsequently. From Fig. 3b, corresponding mathematical expressions can be written as (8)Applying the volt-second balance principle to and over a switching period , the capacitor voltage can be obtained as (9)Similarly, applying charge-second balance principle to C and assuming , the inductor current can be obtained as (10)The peak DC voltage across the inverter bridge is same as and can be rewritten as (11)where B is the boost factor of the proposed Type 1 SLC-ZSI. The boost factor B can be written as (12)The peak fundamental AC output voltage can be written as (13)The voltage gain factor G of the inverter circuit can be written as (14) 3.2 Operation of the Type 2 SLC-ZSI For easy analysis, the H-bridge inverter circuit of proposed Type 2 SLC-ZSI is also replaced by a single switch, S. The operation of the Type 2 SLC-ZSI is explained for shoot-through and non-shoot through intervals. 3.2.1 Shoot-through interval The equivalent circuit of the Type 2 SLC-ZSI is shown in Fig. 3c. When switches and are triggered ON an is triggered OFF, diodes and are reverse biased and is forward biased. The capacitors ( and ) are discharged and the inductors ( and ) store energy from the DC source and capacitors through and . From Fig. 3c, corresponding mathematical expressions can be written as (15) 3.2.2 Non-shoot-through interval The equivalent circuit of the Type 2 SLC-ZSI is shown in Fig. 3d. When and are triggered OFF and is triggered ON, is reverse biased and and are forward biased. The combined energy of DC source and stored magnetic energy of the inductors are supplied to the inverter. Also, the capacitors ( and ) are charged subsequently. From Fig. 3d, corresponding mathematical expressions can be written as (16)Applying the volt-second balance principle to over a switching period Ts, the following is obtained: (17)Similarly, applying volt-second balance principle to (18)Solving (17) and (18), can be obtained as (19)From (18) and (19), can be obtained as (20)Applying the charge-second balance principle to over a switching period (21)Similarly, applying charge-second balance principle to (22)Solving (21) and (22), can be obtained as (23)From (22) and (23), can be obtained as (24)The peak DC voltage across the inverter bridge is same as and can be rewritten as follows: (25)where B is the boost factor of the proposed Type 2 SLC-ZSI. The boost factor B can be written as (26)The peak fundamental AC output voltage can be written as (27)The voltage gain factor G of the inverter circuit can be written as (28)The correlation among voltage gain factors (G), modulation index (M) and shoot-through duty ratio (D) of proposed inverters are plotted and as shown in Fig. 4a for Type 1 SLC-ZSI and Fig. 4b for Type 2 SLC-ZSI. The M and D are interdependent on each other in shoot-through unipolar PWM technique used in proposed inverters. From (12) and (26), it can be stated that the Type 1 SLC-ZSI can be operated at maximum D up to 0.3333 and the Type 2 SLC-ZSI can be operated at maximum D up to 0.2929 theoretically. Fig. 4c shows the variation of boost factors B with shoot-through duty ratio D for different ZSI topologies. It can be noticed from Fig. 4c that the boost ability of the proposed Type 2 SLC-ZSI is higher than that of the Type 1 SLC ZSI and the other SL-ZSIs at low shoot-through duty ratio. Although SL-ZSI and rsL-qZSI have same boost factor as that of proposed Type 1 SLC-ZSI but they have higher number of passive components. Fig. 4d shows the variation of voltage gain factors, G with modulation index, M for different ZSI topologies under the constraint . It can be noticed from Fig. 4d that the voltage gain of the proposed SLC-ZSIs is higher than that of the SL-ZSIs at higher values of M. Fig. 4Open in figure viewerPowerPoint Correlation plots among G, D and M (a) Correlation among G, D and M for Type 1 SLC-ZSI, (b) Correlation among G, D and M for Type 2 SLC-ZSI, (c) Correlation between B and D for different ZSIs, (d) Correlation between G and M for different ZSIs For continuous conduction mode of operation, percentage inductor current ripples () and capacitor voltage ripples (, and ) can be calculated as follows: (29)where is voltage across the inductors, is current flowing through the inductors, are voltage across the capacitors, and are current flowing through the capacitors of the proposed inverters during shoot-through interval. The expressions of maximum voltage stresses of the devices in different topologies are given in Table 2 and the maximum current stresses are given in Table 3 based on the assumption that all the inverters are working at the same D and . It is clear from Table 3 that the current stresses of the switches of the proposed inverters (Type 1 SLC-ZSI and Type 2 SCL-ZSI) are lower as compared to conventional SL-ZSIs. Table 2. Comparative analysis of voltage stresses of elements Elements SL-ZSI SL-qZSI rSL-qZSI cSL-qZSI Type 1 SLC-ZSI Type 2 SLC-ZSI — — — — — — — — — — — — Table 3. Comparative analysis of current stresses of elements Element SL-ZSI SL-qZSI rSL-qZSI cSL-qZSI Type 1 SLC-ZSI Type 2 SLC-ZSI — — — — — — — — — — — 4 Shoot-through unipolar PWM technique The shoot-through unipolar PWM technique has been derived from the conventional unipolar PWM technique [24] to control the switches of proposed SLC-ZSIs. The control logic of proposed inverters is implemented in field programmable gate array based digital domain and its schematic is shown in Fig. 5a. The shoot-through interval is generated by comparing a constant reference signal with the carrier signal . For ensuring shoot-through state not to disturb the active state, it is placed within the zero state in each switching cycle. The PWM signals of proposed the SLC-ZSIs are shown in Fig. 5b for modulating signal, and , respectively. The voltage gain factor G depends on the amplitude of and the modulating signal . In this control technique, shoot-through duty ratio D and modulation index M are interdependent. The relationship between D, , and M, , are as follows: (30) Fig. 5Open in figure viewerPowerPoint Shoot-through unipolar PWM technique (a) Schematic of the PWM technique, (b) Switching pulses of proposed inverters for modulating signal and 5 Experimental verification of proposed SLC-ZSIs The steady-state performance of the proposed SLC-ZSIs (Type 1 and Type 2) is verified through experimentation on a scaled down laboratory prototype. The photograph of the laboratory prototype is shown in Fig. 6. The experimental PWM signals for the proposed SLC-ZSIs (at and ) are given in Figs. 7a and b for modulating signal, and , respectively. The proposed inverters have following specifications: input DC voltage , output AC LC filter , , switching frequency and line frequency . The various elements used in the proposed inverters for the experimental verification are listed in Table 1. Fig. 6Open in figure viewerPowerPoint Photograph of experimental prototype Fig. 7Open in figure viewerPowerPoint Experimental PWM signals of the proposed inverters at and (a) For modulating signal , (b) For modulating signal The steady-state experimental results of the Type 1 SLC-ZSI are shown in Fig. 8. The inductor and capacitor values used for the experimental verification of Type 1 SLC-ZSI are , and . It can be observed from Fig. 8a that voltage across C, ; fundamental AC output voltage, and output AC current, for input voltage, . It can be observed from Fig. 8b that the voltage appearing across the inverter switches, and shoot-through current flowing through inverter switches, . It can be noticed from Fig. 8c that the voltage stresses of diodes are , , and . Similarly, from Fig. 8d, voltage stresses of the switches are , and for . Fig. 8Open in figure viewerPowerPoint Steady-state experimental results of Type 1 SLC-ZSI for R load at and The steady-state experimental results of the Type 2 SLC-ZSI are shown in Fig. 9. The inductor and capacitor values used for the experimental verification of Type 2 SLC-ZSI are , , and . It can be observed from Fig. 9a that voltage across , ; fundamental AC output voltage and output AC current for input voltage . It can be observed from Fig. 9b that the voltage appearing across the inverter switches and shoot-through current flowing through inverter switches . It can be noticed from Fig. 9c that the voltage stresses of diodes are , and . Similarly, from Fig. 9d, voltage stresses of the switches are , and for . Fig. 9Open in figure viewerPowerPoint Steady-state experimental results of Type 2 SLC-ZSI for R load at and Harmonic spectrum of the proposed inverters for resistive load at and is carried out and is shown in Fig. 10a. The total harmonic distortion (THD) of AC output voltage as 2.4% for the Type 1 SLC-ZSI and for the Type 2 SLC-ZSI as 2.22%. The THD can be further reduced by proper tuning of output LC filter. The performance of proposed SLC-ZSIs is also verified for RL load , at and and is shown in Fig. 10b. Steady-state experimental results of the proposed SLC-ZSIs are also given at other values of D to match AC distribution system voltage levels, Fig. 10c shows experimental results of Type 1 SLC-ZSI at and and Fig. 10d shows experimental results of Type 2 SLC-ZSI at and . It can be observed from Fig. 10c that voltage across capacitor C, , inverter output voltage , fundamental AC output voltage and voltage appearing across the switch , along with gate pulse, of and the input voltage . It can be observed from Fig. 10d that voltage across capacitor , , inverter output voltage , fundamental AC output voltage and voltage appearing across the switch , along with gate pulse of and the input voltage . The ON time of switch is the shoot-through duty ratio D. Fig. 10Open in figure viewerPowerPoint Verification of proposed SLC-ZSIs under different conditions (a) Harmonic spectrum of AC output voltage in proposed SLC-ZSIs for R load at and , (b) Verification of proposed SLC-ZSIs for RL load at and , (c) Verification of Type 1 SLC-ZSI for R load at and , (d) Verification of Type 2 SLC-ZSI for R load at and The comparative efficiency analysis among the proposed inverters and some of the existing SL-ZSIs is carried out through simulation using PSIM 11.1 at the boost factor by considering non-idealities of all the elements and is shown in Fig. 11a. To achieve , the inverters have to be operated at different duty ratios. The required duty ratios and modulation indices of the inverters for obtaining are given in Table 4 under the constraint . The non-ideal parameters (assuming the same parameters for all the inverters) of the elements are: (i) DC resistance of inductor , (ii) equivalent series resistance of the capacitor , (iii) forward voltage drop of switches , (iv) ON state resistance of switches , (v) forward voltage drop of diodes , and (vi) ON state resistance of diodes . It can be noticed from Fig. 11a that the efficiency of the proposed SLC-ZSIs is higher than the other existing SL-ZSI topologies at . Table 4. Selection of D and M for different topologies to get SL-ZSI SL-qZSI rSL-qZSI cSL-qZSI Type 1 SLC-ZSI Type 2 SLC-ZSI B 6.07 6.05 6.07 6.02 6.07 6.08 D 0.264 0.334 0.264 0.278 0.264 0.237 M 0.736 0.666 0.736 0.722 0.736 0.763 Fig. 11Open in figure viewerPowerPoint Power loss distribution and efficiency analysis (a) Comparative efficiency analysis of ZSI topologies, (b) Experimental efficiency variation with load power along with power loss distribution of Type 1 SLC-ZSI, (c) Experimental efficiency variation with load power along with power loss distribution of Type 2 SLC-ZSI The power loss distribution among the elements of the proposed inverters is calculated as discussed in [25]. This is carried out by measuring the non-idealities, voltages and currents of the elements of the proposed inverters. Figs. 11b and c show power loss distribution and experimental efficiency variation of Type 1 SLC-ZSI and Type 2 SLC-ZSI, respectively. It can be observed from Fig. 11b that the maximum efficiency of Type 1 SLC-ZSI is 89.64% at a load power of 81.6 W. Further, it can be observed from Fig. 11c that the maximum efficiency of Type 2 SLC-ZSI is 90.34% at a load power of 79.96 W. 6 Conclusions In this paper, two single-phase SLC-ZSIs are proposed. The proposed SLC-ZSIs (Type 1 and Type 2) give higher voltage gains at low shoot-through duty ratio, D with lesser number of passive components as compared to the existing SL-ZSIs. Due to low values of D, modulation index can be increased which gives high AC output voltages at permissible THD. Further, use of less number of passive components makes the proposed inverters more efficient and also reduces its volume and weight as compared to the existing SL-ZSIs. The proposed SLC-ZSIs are applicable to various DC–AC and DC–DC power conversions in renewable energy applications. 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