Laddered Multilevel DC/AC Inverters used in Solar Panel Energy Systems

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1 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Laddered Multlevel DC/AC Inverters used n Solar Panel Energy Systems Fang Ln Luo, Senor Member IEEE Anhu Unversty, HeFe, Chna 3060 Tel: (86) , Fax: (86) , e-mal: [email protected] Abstract Multlevel DC/AC Inverters have varous structures. They have many advantages. Unfortunately, most exstng nverters content too many components (ndependent/floatng batteres/sources, dodes, Capactors and swtches). The author ntroduces the "Laddered Multlevel DC/AC Inverters n ths paper that s new approach of the development n ths area. Ther smple structure and clear operaton are obvously dfferent from the exstng nverters. Its applcaton n Solar Panel Energy Systems s successful. The smulaton and expermental results strongly support our desgn. We beleve that these nverters wll draw much attenton over the world, and be appled n other renewable energy systems. Keywords-component; Laddered Multlevel DC/AC Inverters, Toggle swtch, one-pole two-throw swtch, ndependent/floatng batteres, Lnear Ladder, Bnary Ladder, Luo-Progresson (Seres) Ladder, Trnary (Ternary) Ladder. Solar Panel Energy Systems, Renewable Energy Systems. I. INTRODUCTION Multlevel DC/AC Inverters have varous structures such as dode-clamped nverter (also called the neutral-pont clamped (NPC) nverter), flyng capactor nverters, H- Brdged nverter and so on []. Wth comparson to PWM DC/AC Inverters, multlevel DC/AC Inverters have the advantages () the swtchng flyng voltage s low (from one level to next level); () the d/dt and dv/dt s low; (3) The swtchng frequency s low; (4) THD s better. Unfortunately, most exstng nverters content too many components (ndependent/floatng batteres/sources, dodes, Capactors and swtches). For example, a NPC nverter has n = (b +) levels and needs the components are [ 3]: 4b swtches, b capactors. (4b - ) dodes Another, a lnear H-Brdged nverter has n = (b +) levels and needs the components are [4-8]: b floatng batteres, 4b swtches, 4b dodes, where n s the level that s always an odd, b s the stage (from the neutral pont to the top pont) or brdge. We ntroduce few new crcuts of multlevel DC/AC Inverters n ths paper that are dfferent from the exstng multlevel DC/AC Inverters. We call them Laddered Multlevel DC/AC Inverters. Ther structure s smple, and ts operaton s clear that s new approach of the development n the DC/AC nverter area. II. PROGRESSIONS (SERIES) In Mathematcs, a progresson s a seres of s or quanttes n whch there s always the same relaton between each quantty and the one succeedng t. We ntroduce several progressons n ths secton. We assume all progressons have the value of ther frst tem s, the value of the general tem s. A. Arthmetcal Progressons Arthmetcal progressons are general seres. We usually see them as: Unt progresson; Natural progresson; Odd progresson. All arthmetcal progressons have the same deference value between the adjacent two tems. We defne the value of the frst tem s, the value of the general tem s, and the deference s d. therefore, the value of the general tem s, = + ( ) d () The sum of the tems from the frst tem to th tem s S, ( ) S = + d () () The Unt progresson s lsted n Table. We assume the last tem s b, and the value s b. The general tem s tem, and the value s. Snce the d s 0, the sum of the tems from to the th tem s. Table. Unt progresson Item 3 4 b alue S 3 4 b () The Natural progresson s lsted n Table. Snce the deference d s, the sum of the tems from Publshed by Atlants Press, Pars, France. 3075

2 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) to the th tem s S Ite m alu e ( ) = +. Table. Natural Number Progresson 3 4 b 3 4 b S ( ) + bb ( ) b + (3) The odd- progresson s lsted n Table 3. Snce the deference d s, the sum of the tems from to the th tem s S =. Table 3. The odd- progresson Item 3 4 b alue b- S b B: Geometrc Progressons Geometrc progressons are general seres. We usually see them as: Bnary progresson; Trnary progresson (sometmes called Ternary progresson). All geometrc progressons have the same proporton between the adjacent two tems. We defne the proporton s p. therefore, the value of the general tem s, = p (3) The sum of the tems from the frst tem to th tem s S, S p = p (4) () The Bnary progresson s lsted n Table 4. Snce the proporton p s, the sum of the tems from to the th tem s S =. Table 4. Bnary progresson Item 3 4 b alue b- S b - () The Trnary progresson s lsted n Table 5. Snce the proporton p s 3, the sum of the tems 3 from to the th tem s S =. Table 5. Trnary Progresson Item 3 4 b alue b- S C: Specal progressons Specal progressons are desgned for laddered multlevel nverters. We have: Luo-Progresson; Ye-Progresson. () Luo-Progresson s a new progresson that s deferent from any exstng progresson such as arthmetcal progressons, geometrc progressons and so on. The value of each tem s the twce of the sum of the all prevous tems plus From the 3 rd tem: = (5) The sum of the tems from the frst tem to th tem s S, 3 S = k = k = Luo-Progresson s lsted n Table 6. The sum of the tems 3 S from to the th = wth tem S s. Table 6. Luo-progresson Item 3 4 ( 3) b alue, b Sum, b 3 S (6) () Ye-Progresson s a new progresson that s deferent Publshed by Atlants Press, Pars, France. 3076

3 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) from any exstng progresson such as arthmetcal progressons, geometrc progressons and so on. The value of each tem s the twce of the sum of the all prevous tems plus From the 4th tem: u = ( ) (7) (a) (b) (c) (d) where u(-) s the unt-step functon. It s, 0 = u ( ) = (8) The sum of the tems from the frst tem to th tem s S, S = k = 3 k = Ye-Progresson s lsted n Table 7. The sum of the tems S 3 from to the th = wth tem S s. (9) Fgure. The Toggle-swtch and Change-over Swtch: (a) Toggle-swtch (b) Toggle-swtch off wth a battery dc (c) Swtched on (d) Change-over Swtch A two-pole two-throw (PT) swtch s shown n Fgure (d). It can reverse the output voltage from the nput voltage. We defne that the nput voltage s ww and the output voltage s NN. out = NN = WW WW swtch s on swtch s off B: General Crcut of Ladder Inverters (0) Item alu e, Sum, S Table 7. Ye-progresson ( 4) b b 4 b General Crcut of Ladder Inverters s shown n Fgure. It s a symmetrcal crcut refers to the neutral pont N,.e. there are two wngs: postve wng and negatve wng. Each wng has b sets of the toggle-swtch wth a swtch S and battery dc [where = -b, -(b-), -, -,,, b- and b]. b s the Ladder stage ; n s the total level. The postve wng contents the b sets; s the th set. The negatve wng contents the same sets (symmetrcally). Therefore, we have, III. Laddered Multlevel DC/AC Inverters A: Toggle Swtch and Change-over Swtch dc =,, b, b dc = () To smplfy the analyss, we assume the load s a purely resstve load R. We use Toggle-swtch as shown n Fgure (a), t s also called one-pole two-throw (PT) swtch. The swtch has one wper pole (W) and two contact poston a and b. We defne the swtch s on meanng the wper pole lnked to poston a ; otherwse the swtch s off meanng the wper pole lnked to poston b. The termnal voltage of WN s equal to dc durng swtch-on as shown n Fgure (c), and 0 durng swtch-off as shown n Fgure (b). Publshed by Atlants Press, Pars, France. 3077

4 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) We obtan n = b+ levels. For example, f b = 3, we have the total level n = 7 levels. The output voltage waveform s shown n Fgure 3 (a). (a) 7-levels (b) 5-levels Fgure 3. Mult-level output voltage waveform D: Natural Number Ladder Inverters (NNLI) Fgure. The General Crcut of Ladder Inverters C: Lnear Ladder Inverters (LLI) If we choose all DC voltages dc to be same voltage E n Fgure, we obtan the Lnear Ladder Inverters (LLI). Ths ladder was constructed as a Unt progresson. The output voltage out has n levels, n = b +. E = dc = b,,, b () The operaton status s shown below: out = be: All postve wng swtches on (others are out = (b -)E: Swtches S S b- are on (others are out = E: Swtches S S are on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; out = -E: only Swtch S - s on (others are out = -E: Swtches S - S - are on (others are out = - (b -)E: Swtches S - S -(b-) are on (others are out = - be: All negatve wng swtches on (others are If we choose all DC voltages dc to be the voltage E n Fgure, we obtan the Natural Number Ladder Inverters (NNLI). Ths ladder was constructed as a Natural Number progresson. The output voltage out has n levels, n= b + b+ (refer to Table ). E = dc = b,,, b (3) The operaton status s shown below: out = ne: All postve wng swtches on (others are out = (n -)E: Swtches S S b are on (others are out = E: only Swtch S s on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; out = -E: only Swtch S - s on (others are out = -E: only Swtch S - s on (others are out = - (n -)E: Swtches S - S -b are on (others are out = - ne: All negatve wng swtches on (others are We obtan n = b +b+ levels. For example, f b = 3, we have the total level n = 3 levels. Publshed by Atlants Press, Pars, France. 3078

5 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) E: Odd Ladder Inverters (ONLI) If we choose all DC voltages dc to be the voltage ( -)E (n postve wng) n Fgure, we obtan the Odd Ladder Inverters (ONLI). Ths ladder was constructed as an Odd progresson. The output voltage out has n levels, n= b + (refer to Table 3). dc ( ) E = (+ ) E (4) The operaton status s shown below: out = b E: All postve wng swtches on (others are out = (b -)E: Swtches S S b are on (others are out = 3E: only Swtch S s on (others are out = E: Swtch S and S - are on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; out = -E: only Swtch S - s on (others are out = -E: Swtch S - and S are on (others are out = -3E: only Swtch S - s on (others are out = - (b -)E: Swtches S - S -b are on (others are out = - b E: All negatve wng swtches on (others are We obtan n = b + levels. For example, f b = 3, we have the total level n = 9 levels. F: Bnary Ladder Inverters (BLI) We obtan the Bnary Ladder Inverters (BLI). The output voltage out has n levels, n = b+ -. The operaton status s shown below: out = ( b- -)E: All postve wng swtches on (others are out = 3E: Swtches S S are on (others are out = E: only Swtch S s on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; out = -E: only Swtch S - s on (others are out = -E: only Swtch S - s on (others are out = - 3E: Swtches S - S - are on (others are out = - ( b- -)E: All negatve wng swtches on (others are We obtan n = b+ - levels. For example, f b = 3, we have an n = 5 levels output voltage waveform as shown n Fgure 3 (b). G: Modfed Bnary Ladder Inverters (MBLI) The Modfed Bnary Ladder Inverters (MBLI) s shown n Fgure 4. We used a two-pole two-throw swtch, and save a half of the batteres and swtches. S b dcb S b- If we choose all DC voltages dc to be the voltage (-)E n Fgure, we obtan the Bnary Ladder Inverters (BLI). Ths ladder was constructed as an Bnary progresson. The output voltage out has n levels, Table 4). n b+ = (refer to dc(b-) S R out If we choose the DC voltages dc to be bnary voltage n Fgure. dc S dc = E E (5) dc N Fgure 4. The Modfed Bnary Ladder Inverters Publshed by Atlants Press, Pars, France. 3079

6 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) We use a PT swtch exchange the output voltage polarty, and can save half of the total PT swtches and batteres n the negatve wng. The operaton status and output voltage waveform can refer to the Secton F (also Fgure 3 (b)). The output voltage out has n levels, n = b+ -. H: Luo-Progresson (Seres) Ladder Inverters (LPLI) In the research process we defned a new progresson (seres), and called t Luo-Progresson (Seres). It s dfferent from all exstng progressons such as the arthmetcal progresson, geometrc progresson and so on. We stll use the symbols as b s the progresson stage : s the th tem; s the th tem value; n s the total value (sum). We defne: = (5) The total level s n s b b ( ) 7 3 = (6) n= + = b Table 8: Luo-Progresson (contnued) stage th ( 3) b Item alue Sum, S total levels b 3 b 3 3 b From Table 8 f we construct a ladder wth 4 stages (b = 4) n each wng, we can obtan 63 levels (n = 63). We stll assume the level unt s E. The operaton status s shown below: out = 3E: All postve wng swtches on (others are out = 4E: Swtches S 3, S - S - are on (others are out = 3E: Swtches S S are on (others are out = E: only Swtch S s on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; out = -E: only Swtch S - s on (others are out = - 3E: Swtches S - S - are on (others are out = - 4E: Swtches, S -3, S S are on (others are out = - 3E: All negatve wng swtches on (others are I: Ye-Progresson Ladder Inverters (YPLI) In our research process we nvent and defned another new progresson, and called t Ye-Progresson. It s dfferent from all exstng progressons such as the arthmetcal progresson, geometrc progresson and so on. We stll use the symbols as b s the progresson stage : s the th tem; s the th tem value; S s the sum value; n s the level. We defne: = u( ) (7) The total levels, n s b b 3 ( ) (7) = n= + = b Table 9. Ye-Progresson (contnued) stage th ( 4) b Item alu e Sum, S total level s b 4 b b 3 From Table 9, f we construct a ladder wth 4 stages (b = 4) n both wng, we can obtan 75 levels (n = 75). We stll assume the level unt s E. The operaton status s shown below: out = 37E: All postve wng swtches on (others are out = 4E: Swtches S and S3 are on (others are out = 3E: only Swtch S s on (others are out = E: Swtches S and S- are on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; Publshed by Atlants Press, Pars, France. 3080

7 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) out = -E: only Swtch S- s on (others are out = - E: Swtches S- and S are on (others out = -3E: only Swtch S- s on (others are out = - 4E: Swtches S- and S- are on (others are out = - 37E: All negatve wng swtches on (others are J: Trnary Ladder Inverters (TLI) If we choose the DC voltages dc to be trnary voltage n Fgure 4. dc 3 = E =, b, b (8) We have got the Trnary Ladder Inverters (TLI). The total level n = 3. The operaton status s shown below: out = (3 b- -)E: All postve wng swtches on (others are out = 3E: only Swtch S s on (others are out = E: Swtches S and S - are on (others are out = E: only Swtch S s on (others are out = 0: All Swtches are off; out = -E: only Swtch S - s on (others are out = -E: Swtches S and S - are on (others are out = - 3E: only Swtch S - s on (others are out = - ( b- -)E: All negatve wng swtches on (others are We obtan n = 3 b+ levels. For example, f b = 3, we have an n = 8 levels. I. COMPARISON WITH ALL LADDER INERTERS We ntroduce 8 types of Ladder Inverters n Secton III. In order to catch the clue of all Ladder Inverters and some other nverters, LLI - Lnear Ladder Inverters NNLI - Natural Number Ladder Inverters ONLI - Odd Ladder Inverters BLI - Bnary Ladder Inverters MBLI - Modfed Bnary Ladder Inverters LPLI - Luo-Progresson (Seres) Ladder Inverters YPLI - Ye-Progresson (Seres) Ladder Inverters TLI - Trnary Ladder Inverters NPCI - Neutral-Pont Clamped Inverters LHBI - lnear H-Brdged Inverters We compare wth them n the table 0.. SOLAR PANEL ENERGY SYSTEMS The sun s a star n the unverse; the earth s a planet surroundng the sun. The earth fles n an oval orbt surroundng the sun, the sun s locates n a focus of the oval orbt. The average dstance between sun and earth s about 50 Mkm (50,000,000 klometers). The sun radates the power 3.8 X 0 0 MW nto the space. Our Earth receves 74 X 0 9 MW from the Sun. The solar panel s constructed by the solar cell (or photovoltac cell), whch belongs to a wde multdscplnary area. It converts solar energy nto electrcty by the photovoltac effect. Brefly to sort the solar cells nto two groups: monocrystallne and multcrystallne slcon wafer. Fgure 5(a) shows a solar cell made from a monocrystallne slcon wafer n olts (a) (b) (c) Fgure 5. Solar panel: (a) A solar cell, (b) An approach of solar panel, (c) The theoretcal power/current curves The overall approach s shown n Fgure 5(b), whch s assembled by few solar cells. The theoretcal solar panel system (a certan solar panel) power/current curves are shown n Fgure 5(c). The current (from the solar panel) s nearly constant n the low voltage (from the solar panel) regan. When the nput voltage reaches 6., the nput current sharply reduces to zero. The blue curve s the output power wth ts maxmum power pont (MPP) at 3 W. We set the voltage unt E = 6.. It s easy to construct the batteres for a BLI: dc = dc- = E = 6. dc = dc- = E = 3.4 dc3 = dc-3 = 4E = 64.8 I. SIMULATION AND EXPERIMENTAL RESULTS We use a BLI wth b = 3 to do the smulaton. The output voltage has 5 levels. The smulaton result s shown n Fgure 6 (a). The correspondng expermental result s shown n Fgure 6 (b). Publshed by Atlants Press, Pars, France. 308

8 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) solar panels are naturally dependent/floatng DC sources (lkely batteres). Authors use a BLI and LPLI to a solar panel energy system, and obtan the satsfed smulaton and expermental results. It s strongly support our crcut desgn. We beleve these Laddered Multlevel Inverters wll be used n other renewable energy systems and other ndustral applcatons soon. (a) Fgure 6. A 5 level BLI: (a) The smulaton result, (b) The expermental result We use a LPLI wth b = 3 to do the smulaton agan. The output voltage has levels. The smulaton result s shown n Fgure 7 (a). The correspondng expermental result s shown n Fgure 7 (b). (a) Fgure 7. A level LPLI: (a) The smulaton result, (b) The expermental result II. CONCLUSION Ths paper ntroduces 8 Laddered Multlevel Inverters. All Laddered Multlevel nverters have smple structure, clear operaton procedure, easy control and more output voltage levels. We can use less components to construct more level output voltage, therefore the cost s lower. The (b) (b) References:. Luo F. L. and Ye H. Power Electroncs: Advanced Converson Technologes Taylor and Francs Group LLC, Boca Raton, Florda 07030, USA, 00. ISBN: Nabae, A., Takahash, I. and Akag, H. A Neutral- Pont Clamped PWM Inverter, Proceedngs of IEEE APEC 80 Conference, 980, pp Nabae, A., Takahash, I. and Akag, H. A Neutral- Pont Clamped PWM Inverter IEEE Transactons on Industry Applcatons, 98, pp Luo F. L. and Ye H. Advanced DC/DC Converters CRC Press LLC, Boca Raton, Florda 07030, USA, 004. ISBN: Peng, F. Z. A generalzed multlevel nverter topology wth self voltage balancng, IEEE Transactons on Industry Applcatons, 00, pp Lu Y. and Luo F. L. Trnary Hybrd 8-level Multlevel Inverter for Motor Drve wth Zero Common-Mode oltage IEEE-Transactons on Industral Electroncs, ol. 55, 3, March 008, pp Lu Y. and Luo F. L. Multlevel Inverter wth the Ablty of Self oltage Balancng IEE- Proceedngs on Electrc Power Applcatons, ol. 53,, January 006, pp Lu Y. and Luo F. L. Trnary Hybrd Multlevel Inverter Used n STATCOM wth Unbalanced oltages IEE- Proceedngs on Electrc Power Applcatons, ol. 5, 5, September 005, pp Table 0. Comparson wth all Ladder Inverters and some other nverters Inverter LL NN ON B MB L YPL T NP L s I LI LI LI LI P LI I LI CI H BI b, stage b b b b b b b b b b Battery b b b b b b b b / b Swtch b b b b b+ b b b 4b 4b Capacto r b 0 Publshed by Atlants Press, Pars, France. 308

9 Proceedngs of the nd Internatonal Conference on Computer Scence and Electroncs Engneerng (ICCSEE 03) Dode n, total levels b- 4b b + b +b + b + b+ - b+ - 7 x 5x 3 b b+ b 3 b- 3 b-3 + For example, f b = 3, we obtan the level s for each Inverter as shown n Table. Table. Comparson wth the Inverters (f b = 3) Inverter L NN ON B MB L Y T NP LH s LI LI LI LI LI P P LI CI BI LI LI stage Battery / 3 Swtch Capacto r Dode n, total levels For example, f b = 5, we obtan the level s for each Inverter as shown n Table. Table. Comparson wth the Inverters (f b = 5) Inverter LL NNON B MB LPL YP T NP LH s I LI LI LI LI I LI LI CI BI stage Battery / 5 Swtch Capacto r Dode n, total levels From Tables 0, t can obvously be seen that the Trnary Ladder Inverter (TLI), Ye-Progresson Ladder Inverter (LPLI) and Luo-Progresson Ladder Inverter (LPLI) use fewer components and yeld hgher of levels. For example, f we choose b = 5 we obtan 43 levels by usng TLI, 5 levels by usng YPLI and 89 levels by usng LPLI wth only 0 batteres and 0 swtches. Publshed by Atlants Press, Pars, France. 3083