# A Modular Multilevel Converter with an Advanced PWM Control Technique for Grid-Tied Photovoltaic System

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## Abstract

**:**

## 1. Introduction

- low output voltage THD,
- low injected grid current THD,
- low inverter power loss, and
- high DC bus voltage utilization.

## 2. The MMC Inverter-Based Grid-Tied PV System

## 3. Existing and Proposed PWM Techniques

#### 3.1. Existing PWM Techniques

#### 3.2. Proposed PWM Technique

_{a}, s

_{b}, and s

_{c}are the three phase sinusoidal signals, and can be expressed by Equations (1)–(3).

_{1}of lower amplitude is generated, which is expressed by Equation (4).

_{2}, is generated by binding V

_{1}in a region, where the maximum amplitude of the signal is 0.11 C, and the minimum amplitude is −0.11 C. The following equations explains the relation mathematically.

_{a}, S

_{b}, and S

_{c}are the modulating signals of the proposed switching technique for a three-phase MMC inverter.

## 4. Inverter Control for Grid Synchronization

_{d}and Iq) and the reference currents (${I}_{d}^{\ast}$ and ${I}_{q}^{\ast}$) is then passed through the proportional-integral (PI) controllers, and the inverter reference voltage direct axis component (${V}_{d}^{\ast}$) and the inverter reference voltage quadrature axis component (${V}_{q}^{\ast}$) are determined. After that, the direct and quadrature axis components of the reference inverter voltage are converted into three-phase reference voltages, which are then added to the common mode signal to form the proposed modulating signal. Finally, the modulating signals are compared to the high-frequency carrier signals to produce the gate pulses for the MMC inverter.

## 5. Performance Evaluation

#### 5.1. Loss Evaluation of the MMC Inverter

_{cond}) + Switching loss (P

_{SL}).

_{dcl}), switch conduction loss (P

_{scl}), and total conduction loss (P

_{con}) are calculated [9].

_{F}, i

_{c}, and v

_{ce}are the voltage drop of antiparallel diode, collector current, and collector–emitter voltage drop, respectively.

_{on}) and switch turn-off loss (E

_{off}) are evaluated using the collector current characteristics curve taken from the datasheet of the IGBT module. The total switching loss (P

_{SL}) is calculated using Equation (15). In addition, using diode switch current and reverse recovery characteristics curve of the IGBT, diode switching loss (E

_{rec}) is calculated [9]. If N be the number of IGBTs, total diode switching loss (P

_{rrL}) can be calculated using Equation (16).

_{F}is the forward diode current and N = 24 for 3-phase 5-level MMC inverter. Figure 12 depicts various loss components with the proposed TSCMPWM technique.

#### 5.2. THD Profile of the MMC Inverter for Modulation Region Variation

#### 5.3. Dynamic Response of Inverter

#### 5.3.1. Sudden Load Change Response

#### 5.3.2. Voltage Sag/Swell Response

_{d}(direct axis component of grid voltage) and V

_{q}(quadrature axis component of grid voltage) are also modified due to the change in voltage amplitude, and the inverter modifies the modulation index accordingly. The inverter decreases its modulation index when voltage sags occur, and when voltage swells occur, the inverter raises its modulation index to cope with the grid voltage. Figure 15b depicts the zoomed inverter output phase voltage during sag and swell with the variation of the modulation index.

#### 5.3.3. Response of Grid Current during Fault

#### 5.3.4. Comparative Analysis

## 6. Experimental Validation

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Modulating signals with the modulation techniques: (

**a**) sine pulse width modulation (SPWM), (

**b**) third harmonic-injected PWM (THPWM), (

**c**) conventional space vector PWM (CSVPWM), (

**d**) third harmonic sixty-degree PWM (THSDPWM), (

**e**) thirty-degree bus clamping PWM (TDBCPWM) and (

**f**) sixty-degree bus clamping PWM (SDBCPWM).

**Figure 3.**Inverter line voltage with modulation techniques: (

**a**) SPWM, (

**b**) THPWM, (

**c**) CSVPWM, (

**d**) THSDPWM, (

**e**) TDBCPWM, and (

**f**) SDBCPWM.

**Figure 4.**Inverter line voltage total harmonic distortions (THDs) with the modulation techniques: (

**a**) SPWM, (

**b**) THPWM, (

**c**) CSVPWM, (

**d**) THSDPWM, (

**e**) TDBCPWM, and (

**f**) SDBCPWM.

**Figure 5.**Proposed triangle saturated common mode pulse width modulation (TSCMPWM) modulating signal.

**Figure 6.**Proposed TSCMPWM modulating signal generation technique: (

**a**) step by step procedure and (

**b**) flowchart/algorithm.

**Figure 7.**Illustration of gate pulse generation scheme using proposed TSCMPWM technique for 5-level MMC inverter (only modulating signal, Sa is shown here to demonstrate the system for better view).

**Figure 8.**(

**a**) Output line voltage with TSCMPWM scheme, (

**b**) frequency spectra of line voltage with TSCMPWM scheme, and (

**c**) frequency spectra of line voltage with THPWM scheme.

**Figure 10.**Comparisons of the MMC inverter line voltage THDs for the existing and the proposed TSCMPWM techniques.

**Figure 11.**Control scheme for the MMC inverter-based grid-tied PV system with the implementation of the proposed TSCMPWM technique.

**Figure 12.**Power loss analysis against modulation index variation for the proposed TSCMPWM technique.

**Figure 13.**Converter output voltage profiles with the variation of modulation region for different PWM schemes: (

**a**) SPWM, (

**b**) THPWM, (

**c**) CSVPWM, (

**d**) THSDPWM, (

**e**) TDBCPWM, (

**f**) SDBCPWM, and (

**g**) proposed TSCMPWM.

**Figure 16.**Fault response in inverter current: (

**a**) fault is applied in phase “a” and “b” (

**b**) fault is applied in phase “b” and “c” (

**c**) fault is applied in phase “c” and “a,” and (

**d**) fault is applied in phase “a,” “b,” and “c.”

**Figure 17.**Inverter power loss for different PWM techniques with the variation of modulation index at 2 kHz carrier frequency.

**Figure 19.**At steady-state condition: (

**a**) proposed TSCMPWM modulating signals, (

**b**) three-phase line–line PWM voltages before filter, and (

**c**) three-phase load currents after filter.

Switching Techniques | Mathematical Expressions |
---|---|

SPWM | ${S}_{1}=A\mathrm{sin}\left(\omega t+\theta \right)$ $\left[{S}_{1a}\text{\hspace{1em}}{S}_{1b}\text{\hspace{1em}}{S}_{1c}\right]=\left[{S}_{{1}_{\theta =0\xb0}}\text{\hspace{1em}}{S}_{{1}_{\theta =-120\xb0}}\text{\hspace{1em}}{S}_{{1}_{\theta =120\xb0}}\right]$ |

THPWM | $B=kA\mathrm{sin}\left(3\omega t\right)$ ${S}_{2}=A\mathrm{sin}\left(\omega t+\theta \right)+B$ $\left[{S}_{2a}\text{\hspace{1em}}{S}_{2b}\text{\hspace{1em}}{S}_{2c}\right]=\left[{S}_{{2}_{\theta =0\xb0}}\text{\hspace{1em}}{S}_{{2}_{\theta =-120\xb0}}\text{\hspace{1em}}{S}_{{2}_{\theta =120\xb0}}\right]$ |

CSVPWM | ${S}_{3}=\frac{2}{\sqrt{3}}\text{}[\mathrm{A}\text{}\mathrm{sin}\left(\omega t+\theta \right)]-\frac{1}{2}\left\{\mathrm{max}\left({S}_{1a},{S}_{1b},{S}_{1c}\right)\right\}+\frac{1}{2}\left\{\mathrm{min}\left({S}_{1a},{S}_{1b},{S}_{1c}\right)\right\}$ $\left[{S}_{3a}\text{\hspace{1em}}{S}_{3b}\text{\hspace{1em}}{S}_{3c}\right]=\left[{S}_{{3}_{\theta =0\xb0}}\text{\hspace{1em}}{S}_{{3}_{\theta =-120\xb0}}\text{\hspace{1em}}{S}_{{3}_{\theta =120\xb0}}\right]$ |

THSDPWM | ${X}_{1}={S}_{1}$ $=0.76A(when{S}_{1}0.76A)$ $=-0.76A(when{S}_{1}-0.76A)$ ${S}_{4}={X}_{1}=\mathrm{B}$ $\left[{S}_{4a}\text{\hspace{1em}}{S}_{4b}\text{\hspace{1em}}{S}_{4c}\right]=\left[{S}_{{4}_{\theta =0\xb0}}\text{\hspace{1em}}{S}_{{4}_{\theta =-120\xb0}}\text{\hspace{1em}}{S}_{{4}_{\theta =120\xb0}}\right]$ |

TDBCPWM | ${S}_{5}=A\mathrm{sin}\left(\omega t+\theta \right)+{f}_{1}\left(\alpha \right)\left\{{V}_{c}-\mathrm{max}\left({S}_{1a},{S}_{1b},{S}_{1c}\right)\right\}+{f}_{2}\left(\alpha \right)\left\{-{V}_{c}-\mathrm{min}\left({S}_{1a},{S}_{1b},{S}_{1c}\right)\right\}$ Where, ${f}_{1}\left(\alpha \right)=0(when0\xb0\alpha 60\xb0)$ $=1(when60\xb0\alpha 120\xb0)$ ${f}_{2}\left(\alpha \right)=1(when0\xb0\alpha 60\xb0)$ $=0(when60\xb0\alpha 120\xb0)$ $\left[{S}_{5a}\text{\hspace{1em}}{S}_{5b}\text{\hspace{1em}}{S}_{5c}\right]=\left[{S}_{{5}_{\theta =0\xb0}}\text{\hspace{1em}}{S}_{{5}_{\theta =-120\xb0}}\text{\hspace{1em}}{S}_{{5}_{\theta =120\xb0}}\right]$ |

SDBCPWM | ${S}_{6}=A\mathrm{sin}\left(\omega t+\theta \right)+{f}_{2}\left(\alpha \right)\left\{{V}_{c}-\mathrm{max}\left({S}_{1a},{S}_{1b},{S}_{1c}\right)\right\}+{f}_{1}\left(\alpha \right)\left\{-{V}_{c}-\mathrm{min}\left({S}_{1a},{S}_{1b},{S}_{1c}\right)\right\}$ $\left[{S}_{6a}\text{\hspace{1em}}{S}_{6b}\text{\hspace{1em}}{S}_{6c}\right]=\left[{S}_{{6}_{\theta =0\xb0}}\text{\hspace{1em}}{S}_{{6}_{\theta =-120\xb0}}\text{\hspace{1em}}{S}_{{6}_{\theta =120\xb0}}\right]$ |

**Table 2.**Inverter line voltage total harmonic distortions (THDs) for different existing switching techniques.

PWM Techniques | SPWM | THPWM | CSVPWM | THSDPWM | TDBCPWM | SDBCPWM |
---|---|---|---|---|---|---|

THD (%) | 25.54 | 17.22 | 18.43 | 22.24 | 19.80 | 22.02 |

**Table 3.**Line voltage THDs of different pulse width modulation (PWM) techniques for carrier frequency variation.

Line Voltage THDs (%) for Different Carrier Frequencies (C. F.) with Modulation Index = 1 | ||||
---|---|---|---|---|

PWM Technique | C.F. = 1 kHz | C.F. = 2 kHz | C.F. = 3 kHz | C.F. = 4 kHz |

SPWM | 25.49 | 25.54 | 25.57 | 25.48 |

THPWM | 17.20 | 17.22 | 17.19 | 17.24 |

CSVPWM | 18.37 | 18.43 | 18.33 | 18.46 |

THSDPWM | 25.49 | 22.24 | 25.57 | 25.48 |

TDBCPWM | 19.76 | 19.80 | 19.75 | 19.84 |

SDBCPWM | 21.91 | 22.02 | 21.91 | 21.98 |

TSCMPWM | 13.06 | 13.00 | 13.11 | 13.07 |

Line Voltage THDs (%) for Different Modulation Indexes (M.I.) with Carrier Frequency = 2 kHz | ||||
---|---|---|---|---|

PWM Technique | M.I. = 0.7 | M.I. = 0.8 | M.I. = 0.9 | M.I. = 1.0 |

SPWM | 28.04 | 29.72 | 28.71 | 25.54 |

THPWM | 36.28 | 33.04 | 26.55 | 17.22 |

CSVPWM | 37.13 | 34.15 | 27.99 | 18.43 |

THSDPWM | 37.14 | 35.05 | 29.83 | 22.24 |

TDBCPWM | 32.65 | 29.79 | 25.64 | 19.80 |

SDBCPWM | 25.23 | 26.52 | 25.69 | 22.02 |

TSCMPWM | 24.50 | 19.54 | 14.48 | 13.00 |

Line Voltage THDs (%) | ||||||
---|---|---|---|---|---|---|

PWM Technique | 5 Level | 7 Level | 9 Level | 11 Level | 13 Level | 15 Level |

SPWM | 25.54 | 14.94 | 12.28 | 8.63 | 7.71 | 5.95 |

THPWM | 17.22 | 11.89 | 9.48 | 7.40 | 6.14 | 5.47 |

CSVPWM | 18.43 | 13.36 | 10.55 | 8.75 | 7.35 | 6.28 |

THSDPWM | 22.24 | 16.81 | 12.51 | 9.87 | 8.54 | 7.33 |

TDBCPWM | 19.80 | 11.65 | 9.53 | 8.36 | 6.38 | 5.18 |

SDBCPWM | 22.02 | 11.47 | 10.11 | 7.83 | 6.90 | 5.07 |

TSCMPWM | 13.00 | 9.463 | 8.03 | 5.90 | 4.89 | 4.52 |

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**MDPI and ACS Style**

Haq, S.; Biswas, S.P.; Hosain, M.K.; Rahman, M.A.; Islam, M.R.; Jahan, S.
A Modular Multilevel Converter with an Advanced PWM Control Technique for Grid-Tied Photovoltaic System. *Energies* **2021**, *14*, 331.
https://doi.org/10.3390/en14020331

**AMA Style**

Haq S, Biswas SP, Hosain MK, Rahman MA, Islam MR, Jahan S.
A Modular Multilevel Converter with an Advanced PWM Control Technique for Grid-Tied Photovoltaic System. *Energies*. 2021; 14(2):331.
https://doi.org/10.3390/en14020331

**Chicago/Turabian Style**

Haq, Safa, Shuvra Prokash Biswas, Md. Kamal Hosain, Md. Ashib Rahman, Md. Rabiul Islam, and Sumaya Jahan.
2021. "A Modular Multilevel Converter with an Advanced PWM Control Technique for Grid-Tied Photovoltaic System" *Energies* 14, no. 2: 331.
https://doi.org/10.3390/en14020331