# Finding the Best Programmable PWM Pattern for Three-Level Active Front-Ends at 18-Pulse Connection

^{*}

## Abstract

**:**

## 1. Introduction

- recovering electricity to the grid when braking;
- maintaining zero shift of the fundamental current harmonic with respect to the input voltage;
- compensating for the reactive power at the grid connection point;
- using programmed PWMs in order to comply with the low and medium-frequency voltage and current quality standards [5].

- using multipulse connection to the grid based on multiwinding phase-shift transformers [8];
- use of programmed PWM voltage waveforms to eliminate or mitigate selected harmonics, i.e., Selective Harmonic Elimination PWM and Selective Harmonic Mitigation PWM [9];
- use of passive L and LCL filters to filter out higher harmonics on the AFE AC side [10];
- connecting MV regenerative ASD to a separate substation.

## 2. Statement of Problem, Goals and Objectives

## 3. Object of Research

#### 3.1. Specifications of the Object

#### 3.2. 18-Pulse Connection

_{AB}, U′

_{BC}, U′

_{CA}equals 1 p.u. The angle between the vectors U′

_{BC}and –U″

_{CA}equals that between the line ac and the vector U

_{BC}(Figure 2c), which is 120°. Then, the angle DBO equals 40°. Now let us draw the perpendicular line DO to the segment BC and analyze resultant triangle DOC:

#### 3.3. Three-Level Active Front-End

_{1}–VT

_{12}, 12 flyback diodes VD

_{1}–VD

_{12}, 6 clamped diodes VD

_{1c}–VD

_{6c}and two full capacitances С

_{dc1}and С

_{dc2}. The total of u

_{dc1}and u

_{dc2}determines the DC link voltage u

_{dc}. Only two of the four switches in each bridge leg can be ‘on’ at a time; they connect the potentials u

_{dc1}and u

_{dc2}to the load phase. The switching order depends on the modulation algorithm (signals S

_{a1–4}, S

_{b1–4}and S

_{c1–4}), which further determines the three-phase AFE PWM voltage waveform (u

_{a}, u

_{b}and u

_{c}). Mathematical description of three-phase AFEs follows well-known methodology and will not be covered herein.

#### 3.4. Programmed Pulse-Width Modulation (PWM)

_{swave}is the average semiconductor switching frequency and f is the AFE voltage frequency.

_{n}и b

_{n}are Fourier series coefficients.

_{n:}

_{n}is the level of the nth harmonic, M is the modulation index and α

_{k}is the switching angle number ranging from 1 to n.

_{max}, which can be found by the formula

_{a}, this method runs in increments of 0.01 from 0 to 1. After a suitable initial value is given, one switching pattern can be achieved.

- 5, 7, 17, and 19 in Pattern 1 (250 Hz);
- 17 and 19 in Pattern 2 (150 Hz);
- 17, 19, 35, and 37 in Pattern 3 (250 Hz);
- 5, 7, 17, 19, 35, and 37 in Pattern 4 (350 Hz).

## 4. Control System

_{аbc}and voltage signals u

_{аbc}are measured at the primary side of the T

^{0°}, T

^{20}

^{°}, T

^{−20}

^{°}phase-shift transformers. This is possible thanks to the absence of other power-consuming equipment. Figure 6 uses the following notation: T

^{0°}, T

^{20°}, T

^{−20°}are phase-shift transformers; PLL

^{0°}, PLL

^{20°}, PLL

^{−20°}are units that synchronize voltages to the secondary windings of phase-shift transformers; i

_{аbc}and u

_{аbc}are the measured instantaneous phase currents and values on the primary side of the phase-shift transformers in abc coordinates; θ is the grid voltage space vector angle; θ

^{0°}, θ

^{20}

^{°}, θ

^{−20°}are the calculated voltage space vectors for the secondary windings of phase-shift transformers; i

_{dq}are measured instantaneous phase currents and values on the primary side of the phase-shift transformers in dq0 coordinates; i

_{dq}

^{0°}, i

_{dq}

^{20}

^{°}, i

_{dq}

^{−20°}are the measured instantaneous phase currents of AFEs in dq0 coordinates; i

_{dq}

_{ref}

^{0°}, i

_{dq}

_{ref}

^{20}

^{°}, i

_{dq}

_{ref}

^{−20°}are the configured phase currents of AFEs in dq0 coordinates; u

_{dq}

^{0°}, u

_{dq}

^{20°}, u

_{dq}

^{−20°}are the measured instantaneous phase voltages of AFEs in dq0 coordinates; u

_{dc}

^{0}

^{°}, u

_{dc}

^{20°}, u

_{dc}

^{−20°}are the measured instantaneous voltages of DC link capacitors in AFEs; u

_{dc}

_{ref}

^{0}

^{°}, u

_{dc}

_{ref}

^{20}

^{°}, u

_{dc}

_{ref}

^{−20°}are the configured AFE DC link capacitor voltages; m

^{0°}, m

^{20°}, m

^{−20°}are the AFE modulation indices; α

^{0°}, α

^{20°}, α

^{−20°}are the phase shifts between secondary windings of phase-shift transfers and phase voltages of AFEs; L

_{AFE}is the AFE input inductance; L

_{load}is the FC input inductance; LPF are lowpass filters.

_{pdc}and K

_{idc}, as well as the parameters of the current vector PI controller K

_{pi}and K

_{ii}in the orthogonal dq0 axes.

## 5. Simulation Results and Discussion

_{aAFE}in the secondary winding of one of the three phase-shift transformers. Analysis of the data produced calculations of the total harmonic distortions (THD) and individual harmonic factors for up to the 50th i

_{aAFE}harmonic.

_{aAFE}to have ~30% THD in Patterns 1 and 4, which is about 1.5 times less than in Patterns 2 and 3. This is because that the individual harmonic factors of i

_{aAFE}harmonics 5 and 7 have the greatest effect in the visible spectrum. Apparently, eliminating harmonics 35 and 37 (Patterns 3 and 4) results in no significant improvement in the harmonic spectrum of i

_{aAFE}. The reason is that the inductive reactance of the AFE input is sufficient to passively filter out the harmonics on this order.

_{ag}drawn from the grid by the three three-level AFEs in an 18-pulse connection. Figure 8c clearly shows that the THD of i

_{ag}has the best value (3.66%) in Pattern 3, which is 1.39% less than in the case of the recommended Pattern 1 (see Figure 8a). The reason is that 18-pulse connection filters out harmonics of secondary-winding currents except 18n ± 1 (n = 1, 2, …, ∞).

_{ag}in the recommended Pattern 1 (harmonics 5, 7, 17, and 19 eliminated) is not far below that in Pattern 3. Compared to Patterns 2 (Figure 8b) and 4 (Figure 8d), the quality of i

_{ag}in Pattern 1 has better THDs and individual harmonic factors for up to the 50th harmonic.

_{abAFE}has a subpar value (29.70%) in Pattern 1, and an increase of 3–5% from Patterns 2, 3 and 4 (see Figure 8b,c). However, this does not cause significant issues with the AFE current as shown in Figure 7 and Figure 8.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Abu-Rub, H.; Bayhan, S.; Moinoddin, S.; Malinowski, M.; Guzinski, J. Medium-Voltage Drives: Challenges and existing technology. IEEE Power Electron. Mag.
**2016**, 3, 29–41. [Google Scholar] [CrossRef] - Jing, T.; Maklakov, A.S. A Review of Voltage Source Converters for Energy Applications. In Proceedings of the Ural Conference on Green Energy (UralCon) 2018 International, Chelyabinsk, Russia, 4–6 October 2018; pp. 275–281. [Google Scholar]
- Franquelo, L.G.; Rodriguez, J.; Leon, J.I.; Kouro, S.; Portillo, R.; Prats, M.A.M. The age of multilevel converters arrives. IEEE Ind. Electron. Mag.
**2008**, 2, 28–39. [Google Scholar] [CrossRef] [Green Version] - Kouro, S.; Rodriguez, J.; Wu, B.; Bernet, S.; Perez, M. Powering the Future of Industry: High-Power Adjustable Speed Drive Topologies. IEEE Ind. Appl. Mag.
**2012**, 18, 26–39. [Google Scholar] [CrossRef] - Leon, J.I.; Vazquez, S.; Franquelo, L.G. Multilevel Converters: Control and Modulation Techniques for Their Operation and Industrial Applications. Proc. IEEE
**2017**, 105, 2066–2081. [Google Scholar] [CrossRef] - Perez, M.A.; Bernet, S.; Rodriguez, J.; Kouro, S.; Lizana, R. Circuit Topologies Modeling Control Schemes and Applications of Modular Multilevel Converters. Power Electron. IEEE Trans.
**2015**, 30, 4–17. [Google Scholar] [CrossRef] - De Caro, S.; Foti, S.; Scimone, T.; Testa, A.; Cacciato, M.; Scarcella, G.; Scelba, G. THD and efficiency improvement in multi-level inverters through an open end winding configuration. In Proceedings of the Energy Conversion Congress and Exposition (ECCE), Milwaukee, WI, USA, 18–22 September 2016; pp. 1–7. [Google Scholar]
- Nikolaev, A.A.; Bulanov, M.V.; Shakhbieva, K.A. Development of Improved PWM Algorithm of Active Rectifier with Function of Resonant Phenomena Adaptation in Electrical Networks of Medium Voltage. In Proceedings of the 2020 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), Sochi, Russia, 18–22 May 2020; pp. 1–6. [Google Scholar]
- Marquez Alcaide, A.; Leon, J.I.; Laguna, M.; Gonzalez-Rodriguez, F.; Portillo, R.; Zafra-Ratia, E.; Vazquez, S.; Franquelo, L.G.; Bayhan, S.; Abu-Rub, H. Real-Time Selective Harmonic Mitigation Technique for Power Converters Based on the Exchange Market Algorithm. Energies
**2020**, 13, 1659. [Google Scholar] [CrossRef] [Green Version] - Saleem, M.; Choi, K.-Y.; Kim, R.-Y. Resonance damping for an LCL filter type grid-connected inverter with active disturbance rejection control under grid impedance uncertainty. Int. J. Electr. Power Energy Syst.
**2019**, 109, 444–454. [Google Scholar] - Paice, D.A. Multipulse Methods and Transformers. In Power Electronics Converter Harmonics: Multipulse Methods for Clean Power; Wiley-IEEE Press: Hoboken, NJ, USA, 1996; pp. 25–37. [Google Scholar]
- Kornilov, G.P.; Nikolaev, A.A.; Khramshin, T.R. Mathematical Modeling of the Metallurgical Plants’ Electrotechnical Complexes; Nosov Magnitogorck State Technical University: Magnitogorsk, Russia, 2012. [Google Scholar]
- Hoevenaars, A.; Farbis, M.; McGraw, M. Active Harmonic Mitigation: What the Manufacturers Don’t Tell You. IEEE Ind. Appl. Mag.
**2020**, 26, 41–51. [Google Scholar] [CrossRef] - Kouro, S.; Malinowski, M.; Gopakumar, K.; Pou, J.; Franquelo, L.G.; Wu, B.; Rodriguez, J.; Pérez, M.A.; Leon, J.I. Recent Advances and Industrial Applications of Multilevel Converters. Ind. Electron. IEEE Trans.
**2010**, 57, 2553–2580. [Google Scholar] [CrossRef] - Nabae, A.; Takahashi, I.; Akagi, H. New neutral-point-clamped PWM inverter. IEEE Trans. Ind. Appl.
**1981**, IA-17, 518–523. [Google Scholar] [CrossRef] - Yan, Q.; Wu, X.; Yuan, X.; Geng, Y. An Improved Grid-Voltage Feedforward Strategy for High-Power Three-Phase Grid-Connected Inverters Based on the Simplified Repetitive Predictor. IEEE Trans. Power Electron.
**2016**, 31, 3880–3897. [Google Scholar] [CrossRef] [Green Version] - Napoles, J.; Leon, J.I.; Portillo, R.; Franquelo, L.G.; Aguirre, M.A. Selective Harmonic Mitigation Technique for High-Power Converters. IEEE Trans. Ind. Electron.
**2010**, 57, 2315–2323. [Google Scholar] [CrossRef] - Pérez-Basante, A.; Ceballos, S.; Konstantinou, G.; Pou, J.; Kortabarria, I.; de Alegría, I.M. A Universal Formulation for Multilevel Selective-Harmonic-Eliminated PWMWith Half-Wave Symmetry. IEEE Trans. Power Electron.
**2019**, 34, 943–957. [Google Scholar] [CrossRef] - Al-Hitmi, M.; Ahmad, S.; Iqbal, A.; Padmanaban, S.; Ashraf, I. Selective Harmonic Elimination in a Wide Modulation Range Using Modified Newton–Raphson and Pattern Generation Methods for a Multilevel Inverter. Energies
**2018**, 11, 458. [Google Scholar] [CrossRef] [Green Version] - Aguilera, R.P.; Lezana, P.; Konstantinou, G.; Acuna, P.; Wu, B.; Bernet, S.; Agelidis, V.G. Closed-loop SHE-PWM technique for power converters through Model Predictive Control. In Proceedings of the Industrial Electronics Society IECON), Yokohama, Japan, 9–12 November 2015; pp. 5261–5266. [Google Scholar]
- Leon, J.I.; Kouro, S.; Franquelo, L.G.; Rodriguez, J.; Wu, B. The Essential Role and the Continuous Evolution of Modulation Techniques for Voltage-Source Inverters in the Past Present and Future Power Electronics. Ind. Electron. IEEE Trans.
**2016**, 63, 2688–2701. [Google Scholar] [CrossRef] - Zhang, Y.; Hu, C.; Wang, Q.; Zhou, Y.; Sun, Y. Neutral-Point Potential Balancing Control Strategy for Three-Level ANPC Converter Using SHEPWM Scheme. Energies
**2019**, 12, 4328. [Google Scholar] [CrossRef] [Green Version] - Cheng, J.; Chen, D.; Chen, G. Modeling and Compensation for Dead-Time Effect in High Power IGBT/IGCT Converters with SHE-PWM Modulation. Energies
**2020**, 13, 4348. [Google Scholar] [CrossRef] - Steczek, M.; Jefimowski, W.; Szeląg, A. Application of Grasshopper Optimization Algorithm for Selective Harmonics Elimination in Low-Frequency Voltage Source Inverter. Energies
**2020**, 13, 6426. [Google Scholar] [CrossRef] - Maklakov, A.S.; Radionov, A.A.; Gasiyarov, V.R. Power factor correction and minimization THD in industrial grid via reversible medium voltage AC drives based on 3L-NPC AFE rectifiers. In Proceedings of the IECON Proceedings (Industrial Electronics Conference), Florence, Italy, 23–26 October 2016; pp. 2551–2556. [Google Scholar]
- Zhang, W.; Li, X.; Qiao, J.; Liu, X. Research on DC Voltage Utilization Ratio of Inverter SHEPWM Control Method Based on Immune Algorithm. In Proceedings of the 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 11–14 August 2019; pp. 1–5. [Google Scholar]
- Siddique, M.D.; Mekhilef, S.; Shah, N.M.; Momon, M.A.; Mustafa, A. SHEPWM Based New Hybrid Multilevel Inverter Topology with Reduced Switch Count. In Proceedings of the 2019 21st European Conference on Power Electronics and Applications (EPE ‘19 ECCE Europe), Genova, Italy, 3–5 September 2019; pp. 1–9. [Google Scholar]
- Wu, W.; Liu, W.; Wang, J.; Zhou, X. Inner Relationship between SHEPWM and SVPWM in Tri-level Converter. In Proceedings of the 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA), Xi’an, China, 19–21 June 2019; pp. 793–798. [Google Scholar]
- Liu, C.; Wang, Y.; Wang, J.; Yu, X.; Zhou, L.; Xu, J. A hybrid PWM strategy based on SVPWM and SHEPWM for high-power drive system. In Proceedings of the 2021 6th Asia Conference on Power and Electrical Engineering (ACPEE), Chongqing, China, 8–11 April 2021; pp. 1413–1417. [Google Scholar]
- Yang, Y.; Tang, Y.; Li, Y. Dead-Time Elimination Method of High Frequency Inverter with SHEPWM. In Proceedings of the 2019 14th IEEE Conference on Industrial Electronics and Applications (ICIEA), Xi’an, China, 19–21 June 2019; pp. 457–461. [Google Scholar]
- Shahmi Bin Bimazlim, M.A.; Ismail, B.; Aihsan, M.Z.; Khodijah Mazalan, S.; Muhammad Azhar Walter, M.S.; Khairul Hafizi Rohani, M.N. Comparative Study of Optimization Algorithms for SHEPWM Five-Phase Multilevel Inverter. In Proceedings of the 2020 IEEE International Conference on Power and Energy (PECon), Penang, Malaysia, 7–8 December 2020; pp. 95–100. [Google Scholar]
- Steczek, M.; Chudzik, P.; Szeląg, A. Application of a Non-carrier-Based Modulation for Current Harmonics Spectrum Control during Regenerative Braking of the Electric Vehicle. Energies
**2020**, 13, 6686. [Google Scholar] [CrossRef]

**Figure 2.**Winding connections in phase-shift transformers. (

**a**) +20° winding circuit; (

**b**) +20° primary voltage vector diagram; (

**с**) +20° secondary voltage vector diagram; (

**d**) −20° winding circuit; (

**e**) −20° primary voltage vector diagram; (

**f**) −20° secondary voltage vector diagram.

**Figure 5.**Calculations of four AFE switching patterns. (

**a**) Pattern 1 with harmonics 5, 7, 17 and 19 eliminated. (

**b**) Pattern 2 with harmonics 17 and 19 eliminated. (

**c**) Pattern 3 with harmonics 17, 19, 35 and 37 eliminated. (

**d**) Pattern 4 with harmonics 5, 7, 17, 19, 35 and 37 eliminated.

**Figure 7.**Oscillograms of rated AFE current i

_{aAFE}in the secondary winding of a single phase-shift transformer. (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; (

**d**) Pattern 4.

**Figure 8.**Oscillograms of the rated phase current i

_{ag}drawn from the grid by the three three-level AFEs. (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; (

**d**) Pattern 4.

**Figure 9.**Oscillograms of the line AFE voltage u

_{abAFE}. (

**a**) Pattern 1; (

**b**) Pattern 2; (

**c**) Pattern 3; (

**d**) Pattern 4.

U_{r}, V | I_{r}, А | f_{r}, Hz | P_{r}, MW | cos(φ) | R_{l}, mOhm | L_{l}, mH |
---|---|---|---|---|---|---|

3300 | 2460 | 10 | 12 | 1 | 9.54 | 32.15 |

U_{r}, V | I_{r}, А | U_{dc}_{r}, V | f_{sw}, Hz | P_{r}, MW | Efficiency_{r}, % | C_{dc}, µF |
---|---|---|---|---|---|---|

3300 | 800 | 5020 | 350 | 8.4 | 97 | 6341.54 |

S_{r}, kVAR | U_{1r}, V | U_{2r}, V | I_{1r}, А | I_{2r}, А | U_{sc}, % | ∆P_{sc}, kW | ∆P_{nl}, kW |
---|---|---|---|---|---|---|---|

5700 | 10,000 | 3300 | 329.1 | 997.2 | 16 | 55 | 4.9 |

K_{pdc} | K_{idc} | K_{pi} | K_{ii} |
---|---|---|---|

0.5 | 20 | 1.5 | 25 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Maklakov, A.S.; Jing, T.; Radionov, A.A.; Gasiyarov, V.R.; Lisovskaya, T.A.
Finding the Best Programmable PWM Pattern for Three-Level Active Front-Ends at 18-Pulse Connection. *Machines* **2021**, *9*, 127.
https://doi.org/10.3390/machines9070127

**AMA Style**

Maklakov AS, Jing T, Radionov AA, Gasiyarov VR, Lisovskaya TA.
Finding the Best Programmable PWM Pattern for Three-Level Active Front-Ends at 18-Pulse Connection. *Machines*. 2021; 9(7):127.
https://doi.org/10.3390/machines9070127

**Chicago/Turabian Style**

Maklakov, Alexander S., Tao Jing, Andrey A. Radionov, Vadim R. Gasiyarov, and Tatyana A. Lisovskaya.
2021. "Finding the Best Programmable PWM Pattern for Three-Level Active Front-Ends at 18-Pulse Connection" *Machines* 9, no. 7: 127.
https://doi.org/10.3390/machines9070127