IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 6, JUNE 2011 2435

Single-Phase Seven-Level Grid-Connected Inverterfor Photovoltaic System

Nasrudin A. Rahim, Senior Member, IEEE, Krismadinata Chaniago, Student Member, IEEE, and Jeyraj Selvaraj

Abstract—This paper proposes a single-phase seven-level in-verter for grid-connected photovoltaic systems, with a novelpulsewidth-modulated (PWM) control scheme. Three referencesignals that are identical to each other with an offset thatis equivalent to the amplitude of the triangular carrier sig-nal were used to generate the PWM signals. The inverteris capable of producing seven levels of output-voltage levels(Vdc, 2Vdc/3, Vdc/3, 0, −Vdc, −2Vdc/3, −Vdc/3) from thedc supply voltage. A digital proportional–integral current-controlalgorithm was implemented in a TMS320F2812 DSP to keep thecurrent injected into the grid sinusoidal. The proposed system wasverified through simulation and implemented in a prototype.

Index Terms—Grid connected, modulation index, multilevelinverter, photovoltaic (PV) system, pulsewidth-modulated (PWM),total harmonic distortion (THD).

I. INTRODUCTION

THE ever-increasing energy consumption, fossil fuels’soaring costs and exhaustible nature, and worsening

global environment have created a booming interest in renew-able energy generation systems, one of which is photovoltaic.Such a system generates electricity by converting the Sun’s en-ergy directly into electricity. Photovoltaic-generated energy canbe delivered to power system networks through grid-connectedinverters.

A single-phase grid-connected inverter is usually used forresidential or low-power applications of power ranges that areless than 10 kW [1]. Types of single-phase grid-connectedinverters have been investigated [2]. A common topology ofthis inverter is full-bridge three-level. The three-level invertercan satisfy specifications through its very high switching, butit could also unfortunately increase switching losses, acousticnoise, and level of interference to other equipment. Improvingits output waveform reduces its harmonic content and, hence,also the size of the filter used and the level of electromagneticinterference (EMI) generated by the inverter’s switching opera-tion [3].

Multilevel inverters are promising; they have nearly sinu-soidal output-voltage waveforms, output current with better

Manuscript received January 18, 2010; revised May 12, 2010; acceptedJune 23, 2010. Date of publication August 30, 2010; date of current versionMay 13, 2011.

The authors are with the Center of Research for Power Electronics,Drives, Automation and Control (UMPEDAC), Faculty of Engineering, Univer-sity Malaya, Kuala Lumpur 50603, Malaysia (e-mail: nasrudin@um.edu.my;krismadinata@um.edu.my; jeyraj95@um.edu.my).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2010.2064278

Fig. 1. Proposed single-phase seven-level grid-connected inverter for photo-voltaic systems.

harmonic profile, less stressing of electronic components owingto decreased voltages, switching losses that are lower than thoseof conventional two-level inverters, a smaller filter size, andlower EMI, all of which make them cheaper, lighter, and morecompact [3], [4].

Various topologies for multilevel inverters have been pro-posed over the years. Common ones are diode-clamped [5]–[10], flying capacitor or multicell [11]–[17], cascaded H-bridge[18]–[24], and modified H-bridge multilevel [25]–[29].

This paper recounts the development of a novel modi-fied H-bridge single-phase multilevel inverter that has twodiode embedded bidirectional switches and a novel pulsewidth-modulated (PWM) technique. The topology was applied to agrid-connected photovoltaic system with considerations for amaximum-power-point tracker (MPPT) and a current-controlalgorithm.

II. PROPOSED MULTILEVEL INVERTER TOPOLOGY

The proposed single-phase seven-level inverter was devel-oped from the five-level inverter in [25]–[29]. It comprises asingle-phase conventional H-bridge inverter, two bidirectionalswitches, and a capacitor voltage divider formed by C1, C2,and C3, as shown in Fig. 1. The modified H-bridge topologyis significantly advantageous over other topologies, i.e., lesspower switch, power diodes, and less capacitors for invertersof the same number of levels.

photovoltaic (PV) arrays were connected to the inverter via adc–dc boost converter. The power generated by the inverter isto be delivered to the power network, so the utility grid, ratherthan a load, was used. The dc–dc boost converter was required

0278-0046/$26.00 © 2010 IEEE

2436 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 6, JUNE 2011

because the PV arrays had a voltage that was lower than the gridvoltage. High dc bus voltages are necessary to ensure that powerflows from the PV arrays to the grid. A filtering inductanceLf was used to filter the current injected into the grid. Properswitching of the inverter can produce seven output-voltage lev-els (Vdc, 2Vdc/3, Vdc/3, 0,−Vdc,−2Vdc/3,−Vdc/3) from thedc supply voltage.

The proposed inverter’s operation can be divided into sevenswitching states, as shown in Fig. 2(a)–(g). Fig. 2(a), (d),and (g) shows a conventional inverter’s operational states insequence, while Fig. 2(b), (c), (e), and (f) shows additionalstates in the proposed inverter synthesizing one- and two-thirdlevels of the dc-bus voltage.

The required seven levels of output voltage were generatedas follows.

1) Maximum positive output (Vdc): S1 is ON, connectingthe load positive terminal to Vdc, and S4 is ON, con-necting the load negative terminal to ground. All othercontrolled switches are OFF; the voltage applied to theload terminals is Vdc. Fig. 2(a) shows the current pathsthat are active at this stage.

2) Two-third positive output (2Vdc/3): The bidirectionalswitch S5 is ON, connecting the load positive terminal,and S4 is ON, connecting the load negative terminalto ground. All other controlled switches are OFF; thevoltage applied to the load terminals is 2Vdc/3. Fig. 2(b)shows the current paths that are active at this stage.

3) One-third positive output (Vdc/3): The bidirectionalswitch S6 is ON, connecting the load positive terminal,and S4 is ON, connecting the load negative terminalto ground. All other controlled switches are OFF; thevoltage applied to the load terminals is Vdc/3. Fig. 2(c)shows the current paths that are active at this stage.

4) Zero output: This level can be produced by two switchingcombinations; switches S3 and S4 are ON, or S1 andS2 are ON, and all other controlled switches are OFF;terminal ab is a short circuit, and the voltage applied tothe load terminals is zero. Fig. 2(d) shows the currentpaths that are active at this stage.

5) One-third negative output (−Vdc/3): The bidirectionalswitch S5 is ON, connecting the load positive terminal,and S2 is ON, connecting the load negative terminal toVdc. All other controlled switches are OFF; the voltageapplied to the load terminals is −Vdc/3. Fig. 2(e) showsthe current paths that are active at this stage.

6) Two-third negative output (−2Vdc/3): The bidirectionalswitch S6 is ON, connecting the load positive terminal,and S2 is ON, connecting the load negative terminalto ground. All other controlled switches are OFF; thevoltage applied to the load terminals is −2Vdc/3. Fig. 2(f)shows the current paths that are active at this stage.

7) Maximum negative output (−Vdc): S2 is ON, connectingthe load negative terminal to Vdc, and S3 is ON, con-necting the load positive terminal to ground. All othercontrolled switches are OFF; the voltage applied to theload terminals is −Vdc. Fig. 2(g) shows the current pathsthat are active at this stage.

Fig. 2. Switching combination required to generate the output voltage (Vab).(a) Vab = Vdc. (b) Vab = 2Vdc/3. (c) Vab = Vdc/3. (d) Vab = 0.

RAHIM et al.: SINGLE-PHASE SEVEN-LEVEL GRID-CONNECTED INVERTER FOR PHOTOVOLTAIC SYSTEM 2437

Fig. 2. (Continued.) Switching combination required to generate the outputvoltage (Vab). (e) Vab = −Vdc/3. (f) Vab = −2Vdc/3. (g) Vab = −Vdc.

TABLE IOUTPUT VOLTAGE ACCORDING TO THE SWITCHES’ ON–OFF CONDITION

Table I shows the switching combinations that gen-erated the seven output-voltage levels (0,−Vdc,−2Vdc/3,−Vdc/3, Vdc, 2Vdc/3, Vdc/3).

Fig. 3. Switching pattern for the single-phase seven-level inverter.

III. PWM MODULATION

A novel PWM modulation technique was introduced togenerate the PWM switching signals. Three reference signals(Vref1, Vref2, and Vref3) were compared with a carrier signal(Vcarrier). The reference signals had the same frequency andamplitude and were in phase with an offset value that wasequivalent to the amplitude of the carrier signal. The referencesignals were each compared with the carrier signal. If Vref1

had exceeded the peak amplitude of Vcarrier, Vref2 was com-pared with Vcarrier until it had exceeded the peak amplitudeof Vcarrier. Then, onward, Vref3 would take charge and wouldbe compared with Vcarrier until it reached zero. Once Vref3 hadreached zero, Vref2 would be compared until it reached zero.Then, onward, Vref1 would be compared with Vcarrier. Fig. 3shows the resulting switching pattern. Switches S1, S3, S5,and S6 would be switching at the rate of the carrier signalfrequency, whereas S2 and S4 would operate at a frequency thatwas equivalent to the fundamental frequency.

For one cycle of the fundamental frequency, the proposedinverter operated through six modes. Fig. 4 shows the per-unit output-voltage signal for one cycle. The six modes aredescribed as follows:

Mode 1 : 0 < ωt < θ1 and θ4 < ωt < π

Mode 2 : θ1 < ωt < θ2 and θ3 < ωt < θ4

Mode 3 : θ2 < ωt < θ3

Mode 4 : π < ωt < θ5 and θ8 < ωt < 2π

Mode 5 : θ5 < ωt < θ6 and θ7 < ωt < θ8

Mode 6 : θ6 < ωt < θ7. (1)

2438 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 6, JUNE 2011

Fig. 4. Seven-level output voltage (Vab) and switching angles.

The phase angle depends on modulation index Ma. Theoreti-cally, for a single reference signal and a single carrier signal,the modulation index is defined to be

Ma =Am

Ac(2)

while for a single-reference signal and a dual carrier signal, themodulation index is defined to be [26]–[29]

Ma =Am

2Ac. (3)

Since the proposed seven-level PWM inverter utilizes threecarrier signals, the modulation index is defined to be

Ma =Am

3Ac(4)

where Ac is the peak-to-peak value of the carrier signal and Am

is the peak value of the voltage reference signal Vref .When the modulation index is less than 0.33, the phase angle

displacement is

θ1 = θ2 = θ3 = θ4 =π

2(5)

θ5 = θ6 = θ7 = θ8 =3π

2. (6)

On the other hand, when the modulation index is more than0.33 and less than 0.66, the phase angle displacement isdetermined by

θ1 = sin−1

(Ac

Am

)(7)

θ2 = θ3 =π

2(8)

θ4 = π − θ1 (9)

θ5 = π + θ1 (10)

θ6 = θ7 =3π

2(11)

θ8 = 2π − θ1. (12)

If the modulation index is more than 0.66, the phase angledisplacement is determined by

θ1 = sin−1

(Ac

Am

)(13)

θ2 = sin−1

(2Ac

Am

)(14)

θ3 = π − θ2 (15)

θ4 = π − θ1 (16)

θ5 = π + θ1 (17)

θ6 = π + θ2 (18)

θ7 = 2π − θ2 (19)

θ8 = 2π − θ1. (20)

For Ma that is equal to, or less than, 0.33, only the lowerreference wave (Vref3) is compared with the triangular car-rier signal. The inverter’s behavior is similar to that of aconventional full-bridge three-level PWM inverter. However,if Ma is more than 0.33 and less than 0.66, only Vref2 andVref3 reference signals are compared with the triangular carrierwave. The output voltage consists of five dc-voltage levels. Themodulation index is set to be more than 0.66 for seven levelsof output voltage to be produced. Three reference signals haveto be compared with the triangular carrier signal to produceswitching signals for the switches.

IV. CONTROL SYSTEM

As Fig. 5 shows, the control system comprises a MPPT algo-rithm, a dc-bus voltage controller, reference-current generation,and a current controller. The two main tasks of the controlsystem are maximization of the energy transferred from the PVarrays to the grid, and generation of a sinusoidal current withminimum harmonic distortion, also under the presence of gridvoltage harmonics.

The proposed inverter utilizes the perturb-and-observe(P&O) algorithm for its wide usage in MPPT owing to itssimple structure and requirement of only a few measured pa-rameters. It periodically perturbs (i.e., increment or decrement)the array terminal voltage and compares the PV output powerwith that of the previous perturbation cycle. If the powerwas increasing, the perturbation would continue in the samedirection in the next cycle; otherwise, the direction would bereversed. This means that the array terminal voltage is perturbedevery MPPT cycle; therefore, when the MPP is reached, theP&O algorithm will oscillate around it.

The P&O algorithm was implemented in the dc–dc boostconverter. The output of the MPPT is the duty-cycle function.As the dc-link voltage Vdc was controlled in the dc–ac seven-level PWM inverter, the change of the duty cycle changes thevoltage at the output of the PV panels. A PID controller wasimplemented to keep the output voltage of the dc–dc boostconverter (Vdc) constant by comparing Vdc and Vdc ref andfeeding the error into the PID controller, which subsequentlytries to reduce the error. In this way, the Vdc can be maintained

RAHIM et al.: SINGLE-PHASE SEVEN-LEVEL GRID-CONNECTED INVERTER FOR PHOTOVOLTAIC SYSTEM 2439

Fig. 5. Seven-level inverter with closed-loop control algorithm.

at a constant value and at more than√

2 of Vgrid to inject powerinto the grid.

To deliver energy to the grid, the frequency and phase ofthe PV inverter must equal those of the grid; therefore, a gridsynchronization method is needed. The sine lookup table thatgenerates reference current must be brought into phase with thegrid voltage (Vgrid). For this, the grid period and phase must bedetected.

The proposed inverter provides an analog zero-crossing de-tection circuit on one of its input ports where the grid voltageis to be connected. The zero-crossing circuit then produces anin-phase square-wave output that is fed into the digital I/O porton eZdsp board TMS320F2812.

A PI algorithm was used as the feedback current controllerfor the application. The current injected into the grid, alsoknown as grid current Igrid, was sensed and fed back to acomparator that compared it with the reference current Igridref .Igridref is the result of the MPPT algorithm. The error fromthe comparison process of Igrid and Igridref was fed into the PIcontroller. The output of the PI controller, also known as Vref ,goes through an antiwindup process before being comparedwith the triangular wave to produce the switching signals forS1–S6. Eventually, Vref becomes Vref1; Vref2 and Vref3 can bederived from Vref1 by shifting the offset value, which was equiv-alent to the amplitude of the triangular wave. The mathematicalformulation of the PI algorithm and its implementation in theDSP are discussed in detail in [28].

Fig. 6. PWM switching signal generation.

V. SIMULATION AND EXPERIMENTAL RESULTS

A. Simulation Results

MATLAB SIMULINK simulated the proposed configurationbefore it was physically implemented in a prototype. ThePWM switching patterns were generated by comparing threereference signals (Vref1, Vref2, and Vref3) against a triangu-lar carrier signal (see Fig. 6). Subsequently, the comparing

2440 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 6, JUNE 2011

Fig. 7. PWM signals for S1 and S3.

Fig. 8. PWM signals for S2 and S4.

Fig. 9. PWM signals for S5 and S6.

process produced PWM switching signals for switches S1–S6,as Figs. 7–9 show.

One leg of the inverter operated at a high switching rate thatwas equivalent to the frequency of the carrier signal, while theother leg operated at the rate of the fundamental frequency(i.e., 50 Hz). Switches S5 and S6 also operated at the rate

Fig. 10. Inverter output voltage (Vinv).

Fig. 11. Grid voltage (Vgrid) and grid current (Igrid).

of the carrier signal. Fig. 10 shows the simulation result ofinverter output voltage Vinv. The dc-bus voltage was set at300 V (>

√2Vgrid; in this case, Vgrid was 120 V). The dc-bus

voltage must always be higher than√

2 of Vgrid to inject currentinto the grid, or current will be injected from the grid into theinverter. Therefore, operation is recommended to be betweenMa = 0.66 and Ma = 1.0. Vinv comprises seven voltage levels,namely, Vdc, 2Vdc/3, Vdc/3, 0, −Vdc, −2Vdc/3, and −Vdc/3.The current flowing into the grid was filtered to resemble a puresinewave in phase with the grid voltage (see Fig. 11). As Igrid isalmost a pure sinewave at unity power factor, the total harmonicdistortion (THD) can be reduced compared with the THDin [28].

B. Experimental Results

A TMS320F2812 DSP was used to verify the simulationresults. PV arrays of 750 W were used as the inverter’s inputsource. Table II shows the characteristics of the PV modules

RAHIM et al.: SINGLE-PHASE SEVEN-LEVEL GRID-CONNECTED INVERTER FOR PHOTOVOLTAIC SYSTEM 2441

TABLE IIPV MODULE CHARACTERISTICS

Fig. 12. Experimental setup for the prototype single-phase seven-level PWMinverter.

Fig. 13. PWM switching for S1 and S3.

used in this paper. Ten modules of SIEMENS SP75 wereconnected in series to produce 750 W of peak power. Fig. 12shows the prototype of the seven-level PWM inverter. Bycomparing the three reference signals with the triangular carriersignal in the DSP, the switching patterns of Figs. 13–15 wereobtained. Fig. 16 shows the experimental result for Vinv andIgrid. Vinv consists of seven levels of output voltage, and Igrid

had been filtered to resemble a pure sinewave. At this instant,the modulation index Ma was above 0.66. The dc-bus voltagewas set at 300 V to inject current into the grid. Fig. 17 showsthe experimental result for Vgrid and Igrid, which illustrates thatboth the voltage and the current are in phase. The waveformswhen Ma was reduced are shown in Figs. 18 and 19 anddiscussed in [28].

Fig. 18 corresponds to Ma between 0.33 and 0.66. In thiscase, only Vref1 and Vref2 were compared with the triangular

Fig. 14. PWM switching for S5 and S6.

Fig. 15. PWM switching for S2 and S4.

Fig. 16. Experimental result for seven levels of output voltage.

carrier signal. Five levels of output voltage were produced. ForMa that was less than 0.33, only Vref1 was compared with thetriangular carrier signal, so only three levels of output voltagewere obtained, as Fig. 19 shows. For the case of Ma beingmore than 1.0, the results are not shown because the PV systemwas designed to operate at the condition of Ma being less thanone. This was done by calculating the input current and voltagecorresponding to the output voltage and current. Ma was thenvaried accordingly for the inverter to operate at minimumand maximum power conditions. Below the minimum powercondition (for example, during heavy clouds or nighttime) orabove the maximum power condition (for example, over rating

2442 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 58, NO. 6, JUNE 2011

Fig. 17. Experimental result for grid voltage and grid current that are in phase.

Fig. 18. Experimental result for five levels of output voltage.

Fig. 19. Experimental result for three levels of output voltage.

of the PV arrays, in which the inverter’s rating is exceeded),the inverter should not operate to ensure the safety of the PVsystem and the environment.

A FLUKE 43B power quality analyzer measured the THDand the power factor. The THD measurement of Fig. 20 cor-responds to the waveform of Fig. 16, while the THD mea-surements of Figs. 21 and 22 correspond to the waveformsof Figs. 18 and 19, respectively. Comparing all three THDmeasurements, the seven-level inverter produced the lowestTHD compared with the five- and three-level ones. This proves

Fig. 20. THD result for seven levels of output voltage of Fig. 16.

Fig. 21. THD result for five levels of output voltage of Fig. 18.

Fig. 22. THD result for three levels of output voltage of Fig. 19.

that, as the level increases, the THD reduces, which is anessential criterion for grid-connected PV systems.

VI. CONCLUSION

Multilevel inverters offer improved output waveforms andlower THD. This paper has presented a novel PWM switchingscheme for the proposed multilevel inverter. It utilizes three ref-erence signals and a triangular carrier signal to generate PWMswitching signals. The behavior of the proposed multilevelinverter was analyzed in detail. By controlling the modulationindex, the desired number of levels of the inverter’s outputvoltage can be achieved. A TMS320F2812 DSP optimized theperformance of the inverter. The less THD in the seven-levelinverter compared with that in the five- and three-level invertersis an attractive solution for grid-connected PV inverters.

RAHIM et al.: SINGLE-PHASE SEVEN-LEVEL GRID-CONNECTED INVERTER FOR PHOTOVOLTAIC SYSTEM 2443

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Nasrudin A. Rahim (M’89–SM’08) was born inJohor, Malaysia, in 1960. He received theB.Sc.(Hons.) and M.Sc. degrees from the Universityof Strathclyde, Glasgow, U.K., and the Ph.D. degreefrom Heriot–Watt University, Edinburgh, U.K.,in 1995.

He is currently a Professor with the Department ofElectrical Engineering, University of Malaya, KualaLumpur, Malaysia, where he is also the Directorof the Center of Research for Power Electronics,Drives, Automation and Control. His research inter-

ests include power electronics, real-time control systems, and electrical drives.Prof. Rahim is a Fellow of the Institution of Engineering and Technology,

U.K., and the Academy of Sciences Malaysia. He is also a Chartered Engineer.

Krismadinata Chaniago (S’09) received the B.Eng.degree from Andalas University, Padang, Indonesia,in 2000 and the M.Eng. degree from the Bandung In-stitute of Technology, Bandung, Indonesia, in 2004.

He is a Lecturer in electrical engineering withPadang State University, Padang, and since 2006, hehas been a Research Engineer with the Center ofResearch for Power Electronics, Drives, Automationand Control, Faculty of Engineering, University ofMalaya, Kuala Lumpur, Malaysia. His research in-terests are power electronics control and renewable

energy.

Jeyraj Selvaraj received the B.Eng.(Hons.) degreefrom Multimedia University, Cyberjaya, Malaysia,in 2002, the M.Sc. degree in power electron-ics and drives jointly from the University ofBirmingham, Birmingham, U.K., and the Universityof Nottingham, Nottingham, U.K., in 2004, and thePh.D. degree from the University of Malaya, KualaLumpur, Malaysia, in 2009.

He is currently with the Center of Research forPower Electronics, Drives, Automation and Control,Faculty of Engineering, University of Malaya. His

research interests are single- and three-phase multilevel inverters, digital PIcurrent-control techniques, photovoltaic inverters, and dc–dc converters.