# VSG Control for Cascaded Three-Phase Bridge Based Battery Inverter

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Carrier Phase-Shifted-Distributed PWM for Cascaded Three-Phase Bridge Inverter

_{km}, which can be defined as:

_{DC}, −V

_{DC}, 0, V

_{DC}, and 2V

_{DC}), and its amplitude is 2V

_{DC}. The equivalent circuit of a two-stage, five-level cascaded, three-phase bridge converter can be seen in Figure 2, where A–C are the three-phase grid-connected output of the cascaded three-phase bridge inverter, A1–C3 represents the output end of each bridge arm in the cascaded three-phase bridge inverter.)

_{kNn}(k = a, b, and c, and n = 1, 2, and 3) is the current of the kth submodule.

_{a}

_{3}, i

_{b}

_{1}, and i

_{c}

_{2}is 0, that is, i

_{a}

_{3}+ i

_{b}

_{1}+ i

_{c}

_{2}= 0.

_{kNn}(k = a, b, and c and n = 1, 2, and 3) is the voltage from k

_{n}to the neutral point N

_{n}of the power supply, and v

_{NOn}(n = 1, 2, and 3) is the voltage from point N

_{n}to the load neutral point O. R = R

_{f}+ R

_{s}, where R

_{s}is the equivalent resistance of the power device and R

_{L}is the equivalent resistance of the synchronous filter inductor.

_{a}, u

_{b}, and u

_{c}. The carrier wave is triangular wave m

_{1}, m

_{2}, and m

_{3}, and its phase lag is T

_{s}/3 (T

_{s}is the triangular carrier period). The carrier phase-shifted PWM modulation applies a plurality of triangular carriers with the same amplitude and phase lag at a certain angle to compare with the modulated wave. The generated PWM pulses control each switching device of the multilevel inverter, respectively. The CPS-PWM method is usually applied in the cascade H-bridge inverter, and the cascade H-bridge inverter under the CPS-PWM control method can achieve very good output characteristics.

_{s}/3 in phase sequence, and the carrier signal on the corresponding bridge arm in each module lag (or lead) T

_{s}/3 in phase sequence, by which the CPSD-PWM can balance carrier signal distribution. The CPSD PWM can be divided into two types depending on the carrier’s selected form. One can be described as u

_{al-N1}, which is obtained from u

_{a}and m

_{1}, u

_{bl-N1}, which is obtained from u

_{b}and m

_{1}, u

_{a2-N2}, which is obtained from u

_{a}and m

_{2}, and u

_{b2-N2}, which is obtained from u

_{b}and m

_{3}. This modulation method is allocated according to the lag T

_{s}/3, which belongs to the class I strategy of CPSD PWM. The other modulation method is allocated according to lead T

_{s}/3, which is named the class II strategy of CPSD PWM. Compared with traditional CPS-PWM, CPSD-PWM mode has a larger cumulative carrier signal difference and is center symmetric, which is more suitable for the cascaded three-phase bridge inverter and effectively improves the three-phase output symmetry of cascaded multilevel inverters. Based on the topological characteristics of a cascaded three-phase bridge inverter circuit, the output power of each phase is provided by a multiphase DC input unit. Therefore, the cascaded three-phase bridge inverter system based on CPSD-PWM control technology proposed in this paper can effectively improve the output symmetry of the three-phase inverter and the balance of three-phase power generation, and even realize the adaptive balance of three-phase output power through the mutual transmission of power generation between different units, which will significantly improve the stability and reliability of the microgrid system.

_{c}is the carrier angular frequency and ω

_{s}is the fundamental angular frequency.

_{ao}(x,y) can be expressed as a summation of harmonic components:

_{00}is the DC offset. A

_{0n}and B

_{0n}are fundamental components and base-band harmonics. A

_{m0}and B

_{m0}are carrier harmonics. A

_{mn}and B

_{mn}are side-band harmonics.

^{j}

^{nθ}are added into the expression of each harmonic component for CPSD-PWM, which makes CPSD-PWM have smaller components on the carrier harmonics and side-band harmonics. CPSD-PWM can improve the unbalance of three-phase output, and compared with the traditional CPS-PWM, the CPSD-PWM is more suitable for cascaded three-phase bridge multilevel inverters.

## 3. Virtual Synchronous Generator Control Strategy for Cascade Three-Phase Bridge Inverters

_{m}and T

_{e}are the mechanical torque and electromagnetic torque, and P

_{m}and P

_{e}are the mechanical power and electromagnetic power. ω

_{0}is the angular velocity, which corresponds to the reference frequency.

_{e}is equivalent to VSG output power. Then the T

_{m}and T

_{e}can be approximately expressed as:

_{abc}and i

_{abc}are the terminal voltage and stator current of each phase winding in the generator, and i

_{f}is the rotor excitation current. R is the resistance of the armature winding, L

_{s}is the stator inductance, and M

_{f}is the mutual inductance of the stator windings and rotor windings.

_{a}is equivalent electronic armature resistance, and X

_{d}is synchronous reactance.

- (1)
- Active power-frequency control

_{ref}and ω

_{ref}are the VSG’s reference power and reference angular frequency, respectively.

_{m}is the output active power of the inverter, P

_{ref}is the reference active power, and ω is the angular frequency of the inverter output.

- (2)
- Reactive power–voltage control

_{ref}is the reference voltage, and U is the output voltage.

_{q}is the droop coefficient of reactive power–voltage characteristics. Q

_{ref}is the reference reactive power, and Q is the actual reactive power.

_{p}and K

_{i}are the parameters of the PI controller.

_{ω}, J, and D. Therefore, both J and D need synchronous, comprehensive optimization to achieve the best system performance.

_{q}, which can be calculated according to the typical parameter of synchronous generators with the same power capacity as the virtual synchronous generator. Thus, the key control parameters of a cascaded three-phase bridge inverter based on the VSG control strategy are designed.

## 4. Simulation and Experimental Results

- (1)
- Simulation in the island mode

- (2)
- Simulation in the grid-connected mode

_{ref}= 100 kW, Q

_{ref}= 0 var, and the grid-connected voltage is 220 V in the initial state. At 0.5 s, the reference power increases to P

_{ref}= 110 kW and Q

_{ref}=0 var. Simulation results of phase voltage and current at 0–0.5 s are shown in Figure 12.

- (3)
- Experimental results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Antarasee, P.; Premrudeepreechacharn, S.; Siritaratiwat, A.; Khunkitti, S. Optimal Design of Electric Vehicle Fast-Charging Station’s Structure Using Metaheuristic Algorithms. Sustainability
**2023**, 15, 771. [Google Scholar] [CrossRef] - Abud, T.P.; Augusto, A.A.; Fortes, M.Z.; Maciel, R.S.; Borba, B.S.M.C. State of the Art Monte Carlo Method Applied to Power System Analysis with Distributed Generation. Energies
**2023**, 16, 394. [Google Scholar] [CrossRef] - Rehman, H.; Tariq, M.; Sarwar, A.; Alhosaini, W.; Hossain, M.A.; Batiyah, S.M. Single-Phase Fault Tolerant Multilevel Inverter Topologies—Comprehensive Review and Novel Comparative Factors. Energies
**2022**, 15, 9319. [Google Scholar] [CrossRef] - Mohammed, M.F.; Qasim, M.A. Single Phase T-Type Multilevel Inverters for Renewable Energy Systems, Topology, Modulation, and Control Techniques: A Review. Energies
**2022**, 15, 8720. [Google Scholar] [CrossRef] - Shieh, J.-J.; Hwu, K.-I.; Li, Y.-Y. Analysis and Modeling of a Single-Power-Source T-Type 7-Level Single-Phase DC-AC Inverter with Voltage Gain of 3. Energies
**2022**, 15, 7894. [Google Scholar] [CrossRef] - Samadaei, E.; Salehi, A.; Iranian, M.; Pouresmaeil, E.; Single, D.C. Source Multilevel Inverter with Changeable Gains and Levels for Low-Power Loads. Electronics
**2020**, 9, 937. [Google Scholar] [CrossRef] - Li, T.; Shi, Y. Power Quality Management Strategy for High-Speed Railway Traction Power Supply System Based on MMC-RPC. Energies
**2022**, 15, 5205. [Google Scholar] [CrossRef] - Salem, M.; Richelli, A.; Yahya, K.; Hamidi, M.N.; Ang, T.-Z.; Alhamrouni, I. A Comprehensive Review on Multilevel Inverters for Grid-Tied System Applications. Energies
**2022**, 15, 6315. [Google Scholar] [CrossRef] - Islam, R.; Rafin, S.M.S.H.; Mohammed, O.A. Comprehensive Review of Power Electronic Converters in Electric Vehicle Applications. Forecasting
**2023**, 5, 22–80. [Google Scholar] [CrossRef] - Eswar, K.N.D.V.S.; Doss, M.A.N.; Vishnuram, P.; Selim, A.; Bajaj, M.; Kotb, H.; Kamel, S. Comprehensive Study on Reduced DC Source Count: Multilevel Inverters and Its Design Topologies. Energies
**2023**, 16, 18. [Google Scholar] [CrossRef] - Rojas, C.A.; Kouro, S.; Inzunza, R.; Mitsugi, Y.; Alcaide, A.M. Harmonic Impedance Model of Multiple Utility-Interactive Multilevel Photovoltaic Inverters. Energies
**2022**, 15, 9462. [Google Scholar] [CrossRef] - Ahmed, S.; Saqib, M.A.; Kashif, S.A.R.; Hashmi, K.; Aymen, F.; AboRas, K.M.; Jasińska, L.; Leonowicz, Z. A Modified Multi-Level Inverter System for Grid-Tied DES Applications. Sustainability
**2022**, 14, 16545. [Google Scholar] [CrossRef] - Anand, V.; Singh, V.; Sathik, M.J.; Almakhles, D. A Generalized Switched-Capacitor Multilevel Inverter Topology with Voltage Boosting Ability and Reduced Inrush Current. Energies
**2022**, 15, 9158. [Google Scholar] [CrossRef] - Chappa, A.; Rao, K.D.; Dawn, S.; Ustun, T.S. Development of an Enhanced Selective Harmonic Elimination for a Single-Phase Multilevel Inverter with Staircase Modulation. Electronics
**2022**, 11, 3902. [Google Scholar] - Corzine, K.; Familiant, Y. A new cascaded multilevel H-bridge drive. IEEE Trans. Power Electron.
**2012**, 17, 125–131. [Google Scholar] [CrossRef] - Dahidah, M.S.A.; Konstantinou, G.S.; Agelidis, V.G. Selective harmonic elimination pulse-width modulation seven-level cascaded H-bridge converter with optimized DC voltage levels. IET Power Electron.
**2018**, 5, 852–862. [Google Scholar] [CrossRef] - Carrara, G.; Gardella, S.; Marchesoni, M.; Salutari, R.; Sciutto, G. A new multilevel PWM method: A theoretical analysis. IEEE Trans. Power Electron.
**1992**, 7, 497–505. [Google Scholar] [CrossRef] - Liang, Y.; Nwankpa, C.O. A new type of STATCOM based on cascading voltage-source inverters with phase-shifted unipolar SPWM. Ind. IEEE Trans. Appl.
**1999**, 35, 1118–1123. [Google Scholar] [CrossRef] - Leon, J.I.; Vazquez, S.; Sanchez, J.A.; Portillo, R.; Franquelo, L.G.; Carrasco, J.M.; Dominguez, E. Conventional space-vector modulation techniques versus the single-phase modulator for multilevel converters. IEEE Trans. Ind. Electron.
**2010**, 57, 2473–2482. [Google Scholar] [CrossRef] - Li, X.; Song, Q.; Li, J.; Liu, W. Capacitor voltage balancing control based on CPS-PWM of modular multilevel converter. In Proceedings of the 2011 IEEE Energy Conversion Congress and Exposition, Phoenix, AZ, USA, 17–22 September 2011; pp. 4029–4034. [Google Scholar]
- Ghias, A.M.; Pou, J.; Ciobotaru, M.; Agelidis, V.G. Voltage balancing strategy for a five-level flying capacitor converter using phase disposition PWM with sawtooth-shaped carriers. In Proceedings of the 2012-38th Annual Conference on IEEE Industrial Electronics Society, Montreal, QC, Canada, 25–28 October 2012; pp. 5013–5019. [Google Scholar]
- Yang, Z.; Zhao, J.; Nil, X.; Lu, J.; Chen, B. Research on eliminating common-mode voltage of cascaded medium-voltage variable frequency driver with phase-difference SVPWM. In Proceedings of the 2007 European Conference on Power Electronics and Applications, Aalborg, Denmark, 2–5 September 2007; pp. 1–10. [Google Scholar]
- Zambroni de Souza, A.C.; Santos, M.; Castilla, M.; Miret, J.; Garcia de Vicuna, L.; Marujo, D. Voltage security in AC microgrids: A power flow-based approach considering droop-controlled inverter. IET Renew. Power Gener.
**2015**, 9, 954–960. [Google Scholar] [CrossRef] [Green Version] - Ackermann, T.; Andersson, G.; Soder, L. Distributed generation: A definition. Electr. Power Syst. Res.
**2011**, 57, 195–204. [Google Scholar] [CrossRef] - Guo, F.; Wen, C.; Mao, J. Distributed Secondary Voltage and Frequency Restoration Control of Droop-controlled Inverter-based Microgrids. IEEE Trans. Ind. Electron.
**2015**, 62, 4355–4364. [Google Scholar] [CrossRef] - Zhong, Q.C.; Nguyen, P.L.; Ma, Z.; Sheng, W. Self-Synchronized Synchronverters: Inverters Without a Dedicated Synchronization Unit. IEEE Trans. Power Electron.
**2014**, 29, 617–630. [Google Scholar] [CrossRef]

**Figure 1.**Topology diagram of a typical cascaded three-phase bridge battery power generation system. (A–C are the three-phase grid-connected output of the inverter. O represents the neutral point of a three-phase network. A1–C3 represents the output end of each bridge arm in the cascaded three-phase bridge inverter.)

**Figure 5.**Output voltage of cascaded three-phase bridge inverters by SPWM and CPSD-PWM. (

**a**) SPWM and (

**b**) CPSD-PWM.

**Figure 9.**Simulation result of the inverter by VSG control in the island operation mode: (

**a**) phase voltage and (

**b**) phase current. (Red, black and blue are simulation waveforms of phase A, phase B and phase C respectively).

**Figure 11.**(

**a**) Simulation results of active power and reactive power. (

**b**) Simulation results of frequency.

**Figure 20.**Experimental results of voltage and current in three phases: (

**a**) voltage in three phases and (

**b**) current in three phases. (Red, blue and black are simulation waveforms of phase A, phase B and phase C respectively).

Line Voltage | Phase Current | ||||||
---|---|---|---|---|---|---|---|

Modulation Strategy | Phase | Fundamental Amplitude (V) | THD (%) | Three-Phase Asymmetry (%) | Fundamental Amplitude (A) | THD (%) | Three-Phase Asymmetry (%) |

CPS-PWM | A | 380.1 | 43.40 | 1.24 | 8.039 | 1.37 | 1.22 |

B | 372.6 | 44.72 | 7.894 | 1.17 | |||

C | 380.1 | 43.40 | 7.894 | 1.17 | |||

CPSD-PWM | A | 381.8 | 43.10 | 0.01 | 8.039 | 1.37 | 0.01 |

B | 381.8 | 43.10 | 8.039 | 1.32 | |||

C | 381.8 | 43.09 | 8.038 | 1.42 |

Circuit Parameters | Value | Control Parameters | Value |
---|---|---|---|

DC bus voltage of submodule | 350 V | Virtual inertia | 0.8 kg·m^{2} |

Peak phase voltage | 311 V | Damping coefficient | 4 N·m·s/rad |

Rated frequency | 50 Hz | Reactive droop coefficient | 500 |

Inverter-side inductance | 5 mH | Proportionality coefficient of current loop | 20.3 |

Filter capacitance | 5 μF | Integration coefficient of the current loop | 562.21 |

Proportionality coefficient of the voltage loop | 0.05 | ||

Integration coefficient of the voltage loop | 8.9 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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**

Qi, X.; Zheng, J.
VSG Control for Cascaded Three-Phase Bridge Based Battery Inverter. *World Electr. Veh. J.* **2023**, *14*, 203.
https://doi.org/10.3390/wevj14080203

**AMA Style**

Qi X, Zheng J.
VSG Control for Cascaded Three-Phase Bridge Based Battery Inverter. *World Electric Vehicle Journal*. 2023; 14(8):203.
https://doi.org/10.3390/wevj14080203

**Chicago/Turabian Style**

Qi, Xiaojing, and Jianyong Zheng.
2023. "VSG Control for Cascaded Three-Phase Bridge Based Battery Inverter" *World Electric Vehicle Journal* 14, no. 8: 203.
https://doi.org/10.3390/wevj14080203