# Comparison of FCS-MPC Strategies in a Grid-Connected Single-Phase Quasi-Z Source Inverter

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## Abstract

**:**

## 1. Introduction

## 2. Single-Phase Quasi-Z Source Inverter

#### 2.1. Shoot-Through Mode Operation

#### 2.2. Non-Shoot-Though Mode Operation

#### 2.3. Model with Conditional Variable

## 3. Two FCS-MPC Alternatives in SP-qZSI

#### 3.1. Formulation of the FCS-MPC Strategies to Be Used

#### 3.2. Classic FCS-MPC for SP-qZSI

#### 3.3. Proposed FCS-MPC for an SP-qZSI

## 4. Simulation Results

#### 4.1. qZSI Operating with the Classic Control

#### 4.2. qZSI Operating with the Proposed Control

#### 4.3. Performance Comparison

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

- Colli, V.; Cancelliere, P.; Marignetti, F.; Di Stefano, R. Voltage control of current source inverters. IEEE Trans. Energy Convers.
**2006**, 21, 451–458. [Google Scholar] [CrossRef] - Xie, H.; Angquist, L.; Nee, H.P. Design Study of a Converter Interface Interconnecting Energy Storage with the DC Link of a StatCom. IEEE Trans. Power Deliv.
**2011**, 26, 2676–2686. [Google Scholar] [CrossRef] - Ko, S.H.; Lee, S.; Dehbonei, H.; Nayar, C. Application of voltage- and current-controlled voltage source inverters for distributed generation systems. IEEE Trans. Energy Convers.
**2006**, 21, 782–792. [Google Scholar] [CrossRef] - Ahmed, H.F.; Cha, H.; Kim, S.H.; Kim, H.G. Switched-Coupled-Inductor Quasi-Z-Source Inverter. IEEE Trans. Power Electron.
**2016**, 31, 1241–1254. [Google Scholar] [CrossRef] - Peng, F.Z. Z-source inverter. IEEE Trans. Ind. Appl.
**2003**, 39, 504–510. [Google Scholar] [CrossRef] - Anderson, J.; Peng, F. Four quasi-Z-Source inverters. In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June 2008; pp. 2743–2749. [Google Scholar] [CrossRef]
- Liu, Y.; Abu-Rub, H.; Ge, B. Z-SourceQuasi-Z-Source Inverters: Derived Networks, Modulations, Controls, and Emerging Applications to Photovoltaic Conversion. IEEE Ind. Electron. Mag.
**2014**, 8, 32–44. [Google Scholar] [CrossRef] - Ayad, A.; Karamanakos, P.; Kennel, R. Direct Model Predictive Current Control Strategy of Quasi-Z-Source Inverters. IEEE Trans. Power Electron.
**2017**, 32, 5786–5801. [Google Scholar] [CrossRef] - Vazquez, S.; Leon, J.I.; Franquelo, L.G.; Rodriguez, J.; Young, H.A.; Marquez, A.; Zanchetta, P. Model Predictive Control: A Review of Its Applications in Power Electronics. IEEE Ind. Electron. Mag.
**2014**, 8, 16–31. [Google Scholar] [CrossRef] - Karamanakos, P.; Liegmann, E.; Geyer, T.; Kennel, R. Model Predictive Control of Power Electronic Systems: Methods, Results, and Challenges. IEEE Open J. Ind. Appl.
**2020**, 1, 95–114. [Google Scholar] [CrossRef] - Gajanayake, C.J.; Vilathgamuwa, D.M.; Loh, P.C. Development of a Comprehensive Model and a Multiloop Controller for Z-Source Inverter DG Systems. IEEE Trans. Ind. Electron.
**2007**, 54, 2352–2359. [Google Scholar] [CrossRef] - Ellabban, O.; Van Mierlo, J.; Lataire, P. A DSP-Based Dual-Loop Peak DC-link Voltage Control Strategy of the Z-Source Inverter. IEEE Trans. Power Electron.
**2012**, 27, 4088–4097. [Google Scholar] [CrossRef] - Bakeer, A.; Magdy, G.; Chub, A.; Vinnikov, D. Predictive control based on ranking multi-objective optimization approaches for a quasi-Z source inverter. CSEE J. Power Energy Syst.
**2021**, 7, 1152–1160. [Google Scholar] [CrossRef] - Abu-Rub, H.; Iqbal, A.; Moin Ahmed, S.; Peng, F.Z.; Li, Y.; Baoming, G. Quasi-Z-Source Inverter-Based Photovoltaic Generation System with Maximum Power Tracking Control Using ANFIS. IEEE Trans. Sustain. Energy
**2013**, 4, 11–20. [Google Scholar] [CrossRef] - Hou, T.; Zhang, C.Y.; Niu, H.X. Quasi-Z source inverter control of PV grid-connected based on fuzzy PCI. J. Electron. Sci. Technol.
**2021**, 19, 100021. [Google Scholar] [CrossRef] - Mosalam, H.A.; Amer, R.A.; Morsy, G. Fuzzy logic control for a grid-connected PV array through Z-source-inverter using maximum constant boost control method. Ain Shams Eng. J.
**2018**, 9, 2931–2941. [Google Scholar] [CrossRef] - Shinde, U.K.; Kadwane, S.G.; Gawande, S.P.; Reddy, M.J.B.; Mohanta, D.K. Sliding Mode Control of Single-Phase Grid-Connected Quasi-Z-Source Inverter. IEEE Access
**2017**, 5, 10232–10240. [Google Scholar] [CrossRef] - Bagheri, F.; Komurcugil, H.; Kukrer, O.; Guler, N.; Bayhan, S. Multi-Input Multi-Output-Based Sliding-Mode Controller for Single-Phase Quasi-Z-Source Inverters. IEEE Trans. Ind. Electron.
**2020**, 67, 6439–6449. [Google Scholar] [CrossRef] - Rostami, H.; Khaburi, D.A. Neural networks controlling for both the DC boost and AC output voltage of Z-source inverter. In Proceedings of the 2010 1st Power Electronic & Drive Systems & Technologies Conference (PEDSTC), Tehran, Iran, 17–18 February 2010; pp. 135–140. [Google Scholar] [CrossRef]
- Rastegar Fatemi, M.J.; Mirzakuchaki, S.; Rastegar Fatemi, S.M.J. Wide-Range Control of Output Voltage in Z-source Inverter by Neural Network. In Proceedings of the 2008 International Conference on Electrical Machines and Systems, Wuhan, China, 17–20 October 2008; pp. 1653–1658. [Google Scholar]
- Xu, Y.; He, Y.; Li, S. Logical Operation-Based Model Predictive Control for Quasi-Z-Source Inverter without Weighting Factor. IEEE J. Emerg. Sel. Top. Power Electron.
**2021**, 9, 1039–1051. [Google Scholar] [CrossRef] - Bakeer, A.; Ismeil, M.A.; Orabi, M. A Powerful Finite Control Set-Model Predictive Control Algorithm for Quasi Z-Source Inverter. IEEE Trans. Ind. Inform.
**2016**, 12, 1371–1379. [Google Scholar] [CrossRef] - Liu, Y.; Abu-Rub, H.; Xue, Y.; Tao, F. A Discrete-Time Average Model-Based Predictive Control for a Quasi-Z-Source Inverter. IEEE Trans. Ind. Electron.
**2018**, 65, 6044–6054. [Google Scholar] [CrossRef] - Baier, C.R.; Villarroel, F.A.; Torres, M.A.; Pérez, M.A.; Hernández, J.C.; Espinosa, E.E. A Predictive Control Scheme for a Single-Phase Grid-Supporting Quasi-Z-Source Inverter and Its Integration with a Frequency Support Strategy. IEEE Access
**2023**, 11, 5337–5351. [Google Scholar] [CrossRef] - Diaz-Bustos, M.; Baier, C.R.; Torres, M.A.; Melin, P.E.; Acuna, P. Application of a Control Scheme Based on Predictive and Linear Strategy for Improved Transient State and Steady-State Performance in a Single-Phase Quasi-Z-Source Inverter. Sensors
**2022**, 22, 2458. [Google Scholar] [CrossRef] [PubMed] - Rodriguez, J.; Cortes, P. Model Predictive Control. In Predictive Control of Power Converters and Electrical Drives; John Wiley & Sons: Hoboken, NJ, USA, 2012; pp. 31–39. [Google Scholar] [CrossRef]
- Khan, W.A.; Ebrahimian, A.; Iman Hosseini S., S.; Abarzadeh, M.; Weise, N.; Al-Haddad, K. A Generalized Analytical Tuning Approach for Model Predictive Controlled Grid-Tied Converters Under Wide Range of Grid Inductance Variation. IEEE Access
**2022**, 10, 108261–108275. [Google Scholar] [CrossRef] - Gonzalez-Prieto, A.; Martin, C.; González-Prieto, I.; Duran, M.J.; Carrillo-Ríos, J.; Aciego, J.J. Hybrid Multivector FCS–MPC for Six-Phase Electric Drives. IEEE Trans. Power Electron.
**2022**, 37, 8988–8999. [Google Scholar] [CrossRef] - Ramírez, R.O.; Baier, C.R.; Villarroel, F.; Espinoza, J.R.; Pou, J.; Rodríguez, J. A Hybrid FCS-MPC with Low and Fixed Switching Frequency without Steady-State Error Applied to a Grid-Connected CHB Inverter. IEEE Access
**2020**, 8, 223637–223651. [Google Scholar] [CrossRef] - Ali, M.; Hafeez, G.; Farooq, A.; Shafiq, Z.; Ali, F.; Usman, M.; Mihet-Popa, L. A Novel Control Approach to Hybrid Multilevel Inverter for High-Power Applications. Energies
**2021**, 14, 4563. [Google Scholar] [CrossRef] - Favato, A.; Carlet, P.G.; Toso, F.; Torchio, R.; Bolognani, S. Integral Model Predictive Current Control for Synchronous Motor Drives. IEEE Trans. Power Electron.
**2021**, 36, 13293–13303. [Google Scholar] [CrossRef] - Liu, X.; Qiu, L.; Wu, W.; Ma, J.; Fang, Y.; Peng, Z.; Wang, D. Neural Predictor-Based Low Switching Frequency FCS-MPC for MMC with Online Weighting Factors Tuning. IEEE Trans. Power Electron.
**2022**, 37, 4065–4079. [Google Scholar] [CrossRef] - Kaymanesh, A.; Chandra, A.; Al-Haddad, K. Model Predictive Control of MPUC7-Based STATCOM Using Autotuned Weighting Factors. IEEE Trans. Ind. Electron.
**2022**, 69, 2447–2458. [Google Scholar] [CrossRef] - Geyer, T.; Karamanakos, P.; Kennel, R. On the benefit of long-horizon direct model predictive control for drives with LC filters. In Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, USA, 14–18 September 2014; pp. 3520–3527. [Google Scholar] [CrossRef]
- Geyer, T.; Quevedo, D.E. Performance of Multistep Finite Control Set Model Predictive Control for Power Electronics. IEEE Trans. Power Electron.
**2015**, 30, 1633–1644. [Google Scholar] [CrossRef] - Tregubov, A.; Karamanakos, P.; Ortombina, L. Long-Horizon Robust Direct Model Predictive Control for Medium-Voltage Induction Motor Drives with Reduced Computational Complexity. IEEE Trans. Ind. Appl.
**2023**, 59, 1775–1787. [Google Scholar] [CrossRef] - Karamanakos, P.; Geyer, T. Guidelines for the Design of Finite Control Set Model Predictive Controllers. IEEE Trans. Power Electron.
**2020**, 35, 7434–7450. [Google Scholar] [CrossRef] - Dragičević, T. Model Predictive Control of Power Converters for Robust and Fast Operation of AC Microgrids. IEEE Trans. Power Electron.
**2018**, 33, 6304–6317. [Google Scholar] [CrossRef] - Young, H.A.; Marin, V.A.; Pesce, C.; Rodriguez, J. Simple Finite-Control-Set Model Predictive Control of Grid-Forming Inverters with LCL Filters. IEEE Access
**2020**, 8, 81246–81256. [Google Scholar] [CrossRef] - Duan, X.; Kang, L.; Zhou, H.; Liu, Q. Multivector Model Predictive Power Control with Low Computational Burden for Grid-Tied Quasi-Z-Source Inverter without Weighting Factors. IEEE Trans. Power Electron.
**2022**, 37, 11739–11748. [Google Scholar] [CrossRef] - Baier, C.R.; Flores, C.; Diaz, M.A.; Torres, M.A.; Pou, J.; Melín, P.; Espinosa, E. Reducing losses in the shoot-through state of a single-phase quasi-z-source inverter. In Proceedings of the 2017 IEEE International Telecommunications Energy Conference (INTELEC), Broadbeach, QLD, Australia, 22–26 October 2017; pp. 444–449. [Google Scholar] [CrossRef]
- Li, Y.; Jiang, S.; Cintron-Rivera, J.G.; Peng, F.Z. Modeling and Control of Quasi-Z-Source Inverter for Distributed Generation Applications. IEEE Trans. Ind. Electron.
**2013**, 60, 1532–1541. [Google Scholar] [CrossRef] - Ayad, A.; Hanafiah, S.; Kennel, R. A Comparison of Quasi-Z-Source Inverter and Traditional Two-Stage Inverter for Photovoltaic Application. In Proceedings of the PCIM Europe 2015; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Nuremberg, Germany, 19–20 May 2015; pp. 1–8. [Google Scholar]
- Hussain, A.; Sher, H.A.; Murtaza, A.F.; Javadi, A.; Al-Haddad, K. Transformerless Three Phase Variable Output Voltage DC/AC Standalone Power Converter Using Modified Restrictive Control Set Model Predictive Control. IEEE J. Emerg. Sel. Top. Power Electron.
**2020**, 8, 3772–3783. [Google Scholar] [CrossRef]

**Figure 1.**Single-phase inverter quasi-Z source: (

**a**) SP-qZSI connected to the network, (

**b**) shoot-through mode of operation, (

**c**) non-shoot-through mode of operation.

**Figure 6.**Response of the classic FCS-MPC scheme to a reference step of 200 W to 600 W: (

**a**) response of the current of the inductor ${i}_{L1}$ with a horizon ${N}_{p}=1$, (

**b**) response of the current of the inductor ${i}_{L1}$ with a horizon ${N}_{p}=10$, (

**c**) voltage response of the capacitor ${v}_{C1}$ with a horizon ${N}_{p}=1$, (

**d**) voltage response of the capacitor ${v}_{C1}$ with a horizon ${N}_{p}=10$, (

**e**) response of the output current ${i}_{o}$ with a horizon ${N}_{p}=1$, (

**f**) response of the output current ${i}_{o}$ with a horizon ${N}_{p}=10$.

**Figure 7.**Response of the proposed FCS-MPC scheme to a reference step of 200 W to 600 W: (

**a**) response of the current of the inductor ${i}_{L1}$ with a horizon ${N}_{ac}=1$ and ${N}_{dc}=1$, (

**b**) response of the current of the inductor ${i}_{L1}$ with a horizon ${N}_{ac}=1$ and ${N}_{dc}=10$, (

**c**) voltage response of the capacitor ${v}_{C1}$ with a horizon ${N}_{ac}=1$ and ${N}_{dc}=1$, (

**d**) voltage response of the capacitor ${v}_{C1}$ with a horizon ${N}_{ac}=1$ and ${N}_{dc}=10$, (

**e**) response of the output current ${i}_{o}$ with a horizon ${N}_{ac}=1$ and ${N}_{dc}=1$, (

**f**) response of the output current ${i}_{o}$ with a horizon ${N}_{ac}=1$ and ${N}_{dc}=10$.

**Figure 8.**Performance analysis between the classic FCS-MPC vs. the proposed FCS-MPC strategies: (

**a**) total harmonic distortion, (

**b**) simulation times.

MPC Strategy Type | Advantages | Disadvantages | References |
---|---|---|---|

Hybrid MPC | - Fast dynamic response - Near-zero steady-state error | - Processing load could be significant for long prediction horizons - Parameters tuning might be more complex. | [28,29,30] |

MPC with integral action | - Help to mitigate the effects of non-idealities | - Processing load could be significant for long prediction horizons - The THD values might be higher than those in a hybrid MPC - The dynamic response is no longer as fast | [29,31] |

MPC with techniques to reduce the number of solution | - Contribute to reducing the processing load | - Relative difficulty in implementation | [36,40] |

With tuning techniques for the weighting factors | - Low complexity in parameter tuning - Improved system performance | The processing load could be significant | [32,33] |

N° | State | ${\mathit{s}}_{1}$ | ${\mathit{s}}_{2}$ | ${\mathit{s}}_{3}$ | ${\mathit{s}}_{4}$ | ${\mathit{S}}_{\mathit{ST}}$ | ${\mathit{S}}_{\mathit{AC}}$ | ${\mathit{v}}_{\mathit{ac}}$ | ${\mathit{i}}_{\mathit{ac}}$ |
---|---|---|---|---|---|---|---|---|---|

1 | nSTS${}^{+}$ | 1 | 0 | 0 | 1 | 1 | 0 | $+{v}_{dc}$ | $+{i}_{ac}$ |

2 | nSTS${}^{-}$ | 0 | 1 | 1 | 0 | −1 | 0 | $-{v}_{dc}$ | $-{i}_{ac}$ |

3 | nSTS${}^{0}$ | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |

4 | nSTS${}^{0}$ | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |

5 | STS | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

6 | STS | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |

7 | STS | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |

Variables | Description | Values |
---|---|---|

${v}_{in}$ | Input voltage | 70 V |

${L}_{1}\phantom{\rule{3.33333pt}{0ex}}\&\phantom{\rule{3.33333pt}{0ex}}{L}_{2}$ | Inductances of the quasi-Z network | 1.5 mH |

${C}_{1}\phantom{\rule{3.33333pt}{0ex}}\&\phantom{\rule{3.33333pt}{0ex}}{C}_{2}$ | quasi-Z network capacitances | 1000 μF |

${L}_{f}$ | Output inductive filter inductance | 15 mH |

r | Resistance associated with ${L}_{f}$ | 0.01 $\mathrm{\Omega}$ |

${f}_{o}$ | Output frequency | 50 Hz |

${v}_{g}$ | Grid voltage | 45 V |

${P}_{o}^{ref}$ | Reference power 1st step | 200 W |

${P}_{o}^{ref}$ | Reference power 2nd step | 600 W |

${v}_{C1}^{ref}$ | Voltage reference | 150 V |

Variables | Description | Values |
---|---|---|

${f}_{s}$ | Sample frequency | 20 kHz |

${\lambda}_{i}$ | Weighting factor for inductor current ${L}_{1}$ | 1.6 |

${\lambda}_{v}$ | Weighting factor for capacitor voltage ${C}_{1}$ | 1.9 |

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## Share and Cite

**MDPI and ACS Style**

Saavedra, J.L.; Baier, C.R.; Marciel, E.I.; Rivera, M.; Carreno, A.; Hernandez, J.C.; Melín, P.E.
Comparison of FCS-MPC Strategies in a Grid-Connected Single-Phase Quasi-Z Source Inverter. *Electronics* **2023**, *12*, 2052.
https://doi.org/10.3390/electronics12092052

**AMA Style**

Saavedra JL, Baier CR, Marciel EI, Rivera M, Carreno A, Hernandez JC, Melín PE.
Comparison of FCS-MPC Strategies in a Grid-Connected Single-Phase Quasi-Z Source Inverter. *Electronics*. 2023; 12(9):2052.
https://doi.org/10.3390/electronics12092052

**Chicago/Turabian Style**

Saavedra, Jorge L., Carlos R. Baier, Esteban I. Marciel, Marco Rivera, Alvaro Carreno, Jesús C. Hernandez, and Pedro E. Melín.
2023. "Comparison of FCS-MPC Strategies in a Grid-Connected Single-Phase Quasi-Z Source Inverter" *Electronics* 12, no. 9: 2052.
https://doi.org/10.3390/electronics12092052