# Optimization-Based Capacitor Balancing Method with Customizable Switching Reduction for CHB Converters

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fundaments and Strategy

#### 2.1. Variables and Constraints

#### 2.2. Transition Commutations

#### 2.3. Objective Function for Switching Losses Reduction

#### 2.4. Integration and Interaction with Other Objectives

#### 2.4.1. Combination with DC-Link Voltage Objective

#### 2.4.2. Combination with DC-Link Ripple Reduction

- If both ${B}_{Akj}$ and ${B}_{Bkj}$ are high (relative to other benefit values), then there is a significant benefit in having a high value of ${U}_{kj}$. In the optimal solution, the module would probably be high-saturated;
- If both ${B}_{Akj}$ and ${B}_{Bkj}$ are low (i.e., if they have a big negative value), then there is a significant benefit in having a low value of ${U}_{kj}$. In the optimal solution, the module would probably be low-saturated;
- If ${B}_{Akj}$ is significantly lower than ${B}_{Bkj}$ (the opposite cannot occur), then there is a significant benefit in setting ${U}_{kj}$ to a particular voltage ${U}_{kj}^{*}$, which depends on the module’s desired active power. The module would probably modulate this voltage ${U}_{kj}^{*}$ through PWM. This third case only occurs when the power control and ripple reduction objective is selected for the corresponding module (${G}_{Pkj}\ne 0$); otherwise, ${B}_{Akj}={B}_{Bkj}$.

- Voltage control only: ${G}_{Vkj}>0;{G}_{Pkj}={G}_{Skj}=0$;
- Voltage control and ripple reduction: ${G}_{Vkj}>0;{G}_{Pkj}0;{G}_{Skj}=0$;
- Power control only (for batteries): ${G}_{Pkj}>0;{G}_{Vkj}={G}_{Skj}=0$;
- Voltage control and switching reduction: ${G}_{Vkj}>0;{G}_{Skj}0;{G}_{Pkj}=0$.

## 3. Materials and Methods

#### 3.1. Materials

#### 3.2. Methods

- Calculate ${B}_{Akj}$ and ${B}_{Bkj}$ as in (22) and (23);
- Obtain ${U}_{kj}$ as follows;

- 4.
- Update ${\delta}_{kj}$ for the next control cycle as in (26).

## 4. Tests and Results

## 5. Discussion

- Modules for reactive power compensation, whose DC-link typically includes only capacitors, can afford a higher ripple. In these modules, ${G}_{Vkj}$ should be relatively high to ensure balance, and ${G}_{Pkj}$ should be left null. ${G}_{Skj}$, which is expected to have a medium value, can be selected according to the affordable extra ripple, possibly using the estimation given by (16);
- Modules connected to photovoltaic panels cannot afford that much ripple. For these modules, ${G}_{Vkj}$ is the most important gain and should have the highest value. As long as the ripple is small, a low value of ${G}_{Skj}$ may be acceptable. If the ripple is unacceptable, then a low value of ${G}_{Pkj}$ may be used instead. It is also possible to leave both ${G}_{Skj}$ and ${G}_{Pkj}$ to 0;
- In modules with ultracapacitors, the DC-link voltage is more stable, but the ultracapacitors can suffer from the current ripple. In this case, ${G}_{Skj}$ must be null to prevent damage. ${G}_{Pkj}$ should be the dominant gain to prevent current ripple and allow the module to respond quickly to power demand. ${G}_{Vkj}$ should have a relatively low value, but it should not be null to prevent the ultracapacitors from discharging over time;
- Finally, modules with batteries are typically controlled using power or current set points instead of voltage set points. ${G}_{Pkj}$ is the appropriate gain for controlling such power or current reference. The other gains should be null.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- 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] - Rodriguez, J.; Lai, J.-S.; Peng, F.Z. Multilevel inverters: A survey of topologies controls and applications. IEEE Trans. Ind. Electron.
**2002**, 49, 724–738. [Google Scholar] [CrossRef][Green Version] - Rodriguez, J.; Bernet, S.; Wu, B.; Pontt, J.; Kouro, S. Multilevel voltage-source-converter topologies for industrial medium-voltage drives. IEEE Trans. Ind. Electron.
**2007**, 54, 2930–2945. [Google Scholar] [CrossRef] - Carrasco, J.M.; Franquelo, L.G.; Bialasiewicz, J.T.; Galvan, E.; PortilloGuisado, R.; Prats, M.A.M.; Leon, J.I.; Moreno-Alfonso, N. Power-electronic systems for the grid integration of renewable energy sources: A survey. IEEE Trans. Ind. Electron.
**2006**, 53, 1002–1016. [Google Scholar] [CrossRef] - Yu, Y.; Konstantinou, G.; Townsend, C.D.; Aguilera, R.P.; Agelidis, V.G. Delta-Connected Cascaded H-Bridge Multilevel Converters for Large-Scale Photovoltaic Grid Integration. IEEE Trans. Ind. Electron.
**2017**, 64, 8877–8886. [Google Scholar] [CrossRef][Green Version] - Nasiri, M.R.; Farhangi, S.; Rodríguez, J. Model Predictive Control of a Multilevel CHB STATCOM in Wind Farm Application Using Diophantine Equations. IEEE Trans. Ind. Electron.
**2019**, 66, 1213–1223. [Google Scholar] [CrossRef] - Tafti, H.D.; Maswood, A.I.; Konstantinou, G.; Townsend, C.D.; Acuna, P.; Pou, J. Flexible Control of Photovoltaic Grid-Connected Cascaded H-Bridge Converters during Unbalanced Voltage Sags. IEEE Trans. Ind. Electron.
**2018**, 65, 6229–6238. [Google Scholar] [CrossRef] - Ni, Z.; Narimani, M. A New Fast Formulation of Model Predictive Control For CHB STATCOM. In Proceedings of the IECON 2019—45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 14–17 October 2019; pp. 3493–3498. [Google Scholar] [CrossRef]
- Rodriguez, E.; Farivar, G.G.; Beniwal, N.; Townsend, C.D.; Tafti, H.D.; Vazquez, S.; Pou, J. Closed-Loop Analytic Filtering Scheme of Capacitor Voltage Ripple in Multilevel Cascaded H-Bridge Converters. IEEE Trans. Power Electron.
**2020**, 35, 8819–8832. [Google Scholar] [CrossRef] - Ge, X.; Gao, F. Flexible Third Harmonic Voltage Control of Low Capacitance Cascaded H-Bridge STATCOM. IEEE Trans. Power Electron.
**2018**, 33, 1884–1889. [Google Scholar] [CrossRef] - Gómez, P.J.; Galván, L.; Galván, E.; Carrasco, J.M.; Vázquez, S. Optimal Switching Sequence Model Predictive Control for Single-Phase Cascaded H-Bridge. In Proceedings of the IECON 2021—47th Annual Conference of the IEEE Industrial Electronics Society, Toronto, ON, Canada, 13–16 October 2021; pp. 1–6. [Google Scholar] [CrossRef]
- Raveendran, V.; Andresen, M.; Buticchi, G.; Liserre, M. Thermal Stress Based Power Routing of Smart Transformer With CHB and DAB Converters. IEEE Trans. Power Electron.
**2020**, 35, 4205–4215. [Google Scholar] [CrossRef] - Rahman, S.; Meraj, M.; Iqbal, A.; Prathap-Reddy, B.; Khan, I. A Combinational Level Shifted and Phase Shifted PWM Technique for Symmetrical Power Distribution in CHB Inverters. IEEE J. Emerg. Sel. Top. Power Electron.
**2021**. [Google Scholar] [CrossRef] - Steimel, A. Electric railway traction in Europe. IEEE Ind. Appl. Mag.
**1996**, 2, 6–17. [Google Scholar] [CrossRef] - Song, K.; Konstantinou, G.; Mingli, W.; Acuna, P.; Aguilera, R.P.; Agelidis, V.G. Windowed SHE-PWM of interleaved four-quadrant converters for resonance suppression in traction power supply systems. IEEE Trans. Power Electron.
**2017**, 32, 7870–7881. [Google Scholar] [CrossRef][Green Version] - Leon, J.I.; Dominguez, E.; Wu, L.; Marquez Alcaide, A.; Reyes, M.; Liu, J. Hybrid Energy Storage Systems: Concepts, Advantages, and Applications. IEEE Ind. Electron. Mag.
**2021**, 15, 74–88. [Google Scholar] [CrossRef] - Gomez-Merchan, R.; Vazquez, S.; Alcaide, A.M.; Tafti, H.D.; Leon, J.I.; Pou, J.; Rojas, C.A.; Kouro, S.; Franquelo, L.G. Binary Search Based Flexible Power Point Tracking Algorithm for Photovoltaic Systems. IEEE Trans. Ind. Electron.
**2021**, 68, 5909–5920. [Google Scholar] [CrossRef] - Romero-Cadaval, E.; Spagnuolo, G.; Franquelo, L.G.; Ramos-Paja, C.A.; Suntio, T.; Xiao, W.M. Grid-Connected Photovoltaic Generation Plants: Components and Operation. IEEE Ind. Electron. Mag.
**2013**, 7, 6–20. [Google Scholar] [CrossRef][Green Version] - Monopoli, V.G.; Alcaide, A.M.; LEON, J.I.; Liserre, M.; Buticchi, G.; Franquelo, L.G.; Vazquez, S. Applications and Modulation Methods for Modular Converters Enabling Unequal Cell Power Sharing: Carrier Variable-Angle Phase-displacement Modulation Methods. IEEE Ind. Electron. Mag.
**2021**. [Google Scholar] [CrossRef] - Gong, R.; Xue, B.; Liu, J.; Zhang, X. Power balance modulation strategy for hybrid cascaded H-bridge multi-level inverter. Electron. Eng.
**2021**, 1–10. [Google Scholar] [CrossRef] - Ye, M.; Ren, W.; Chen, L.; Wei, Q.; Song, G.; Li, S. Research on Power-Balance Control Strategy of CHB Multilevel Inverter Based on TPWM. IEEE Access
**2019**, 7, 157226–157240. [Google Scholar] [CrossRef] - Neyshabouri, Y.; Chaudhary, S.K.; Teodorescu, R.; Sajadi, R.; Iman-Eini, H. Improving the Reactive Current Compensation Capability of Cascaded H-Bridge Based STATCOM Under Unbalanced Grid Voltage. IEEE J. Emerg. Sel. Top. Power Electron.
**2020**, 8, 1466–1476. [Google Scholar] [CrossRef] - Aguilera, R.P.; Acuna, P.; Rojas, C.A.; Konstantinou, G.; Pou, J. Instantaneous Zero Sequence Voltage for Grid Energy Balancing Under Unbalanced Power Generation. In Proceedings of the 2019 IEEE Energy Conversion Congress and Exposition (ECCE), Baltimore, MD, USA, 29 September–3 October 2019; pp. 2572–2577. [Google Scholar] [CrossRef]
- Montero-Robina, P.; Alcaide, A.M.; Dahidah, M.; Vazquez, S.; Leon, J.I.; Konstantinou, G.G.; Franquelo, L.G. Feedforward Modulation Technique for More Accurate Operation of Modular Multilevel Converters. IEEE Trans. Power Electron.
**2022**, 37, 1700–1710. [Google Scholar] [CrossRef] - Behrouzian, E. Operation and Control of Cascaded H-Bridge Converter for STATCOM Application. Ph.D. Thesis, Chalmers University, Gothenburg, Sweden, 2016. [Google Scholar]
- Marquez, A.; Leon, J.I.; Monopoli, V.G.; Vazquez, S.; Liserre, M.; Franquelo, L.G. Generalized Harmonic Control for CHB Converters with Unbalanced Cells Operation. IEEE Trans. Ind. Electron.
**2020**, 67, 9039–9047. [Google Scholar] [CrossRef] - Alcaide, A.M.; Leon, J.I.; Portillo, R.; Yin, J.; Luo, W.; Vazquez, S.; Kouro, S.; Franquelo, L.G. Variable-Angle PS-PWM Technique for Multilevel Cascaded H-Bridge Converters with Large Number of Power Cells. IEEE Trans. Ind. Electron.
**2021**, 68, 6773–6783. [Google Scholar] [CrossRef] - Liserre, M.; Buticchi, G.; Leon, J.I.; Alcaide, A.M.; Raveendran, V.; Ko, Y.; Andresen, M.; Monopoli, V.G.; Franquelo, L. Power Routing: A New Paradigm for Maintenance Scheduling. IEEE Ind. Electron. Mag.
**2020**, 14, 33–45. [Google Scholar] [CrossRef] - Gómez, P.J.; Galván, L.; Galván, E.; Carrasco, J.M. Energy Storage Systems Current Ripple Reduction for DC-Link Balancing Method in Hybrid CHB Topology. In Proceedings of the IECON 2020 the 46th Annual Conference of the IEEE Industrial Electronics Society, Singapore, 18–21 October 2020; pp. 1808–1813. [Google Scholar] [CrossRef]
- De Alvarenga, M.B.; Pomilio, J.A. Modulation strategy for minimizing commutations and capacitor voltage balancing in symmetrical cascaded multilevel converters. In Proceedings of the 2011 IEEE International Symposium on Industrial Electronics, Gdansk, Poland, 27–30 June 2011; pp. 1875–1880. [Google Scholar] [CrossRef]
- Bassi, H.M. A New PWM Technique for Cascade H-Bridge with Reduced Switching Losses. In Proceedings of the 2019 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), Sochi, Russia, 25–29 March 2019; pp. 1–5. [Google Scholar] [CrossRef]
- Kim, S.-M.; Lee, E.-J.; Lee, J.-S.; Lee, K.-B. An Improved Phase-Shifted DPWM Method for Reducing Switching Loss and Thermal Balancing in Cascaded H-Bridge Multilevel Inverter. IEEE Access
**2020**, 8, 187072–187083. [Google Scholar] [CrossRef] - Islam, M.T.; Fayek, H.H.; Rusu, E.; Rahman, M.F. A Novel Hexagonal-Shaped Multilevel Inverter with Reduced Switches for Grid-Integrated Photovoltaic System. Sustainability
**2021**, 13, 12018. [Google Scholar] [CrossRef] - Galván, L.; Gómez, P.J.; Galván, E.; Carrasco, J.M. Optimization-Based Capacitor Balancing Method with Selective DC Current Ripple Reduction for CHB Converters. Energies
**2022**, 15, 243. [Google Scholar] [CrossRef] - Galván, L.; Galván, E.; Carrasco, J.M. Optimal Modulation Method for DC-Link Control in Cascaded H-Bridge Multilevel Converters. In Proceedings of the IECON 2019—45th Annual Conference of the IEEE Industrial Electronics Society, Lisbon, Portugal, 14–17 October 2019; pp. 5763–5768. [Google Scholar] [CrossRef]

**Figure 1.**Schematic of the CHB topology. The figure also shows the nomenclature considered in this paper, including the sign criteria and the ordering of the subscripts.

**Figure 3.**General control scheme. The proposed upgrade is applied to the balancing method in the modulation layer.

**Figure 4.**First test results, without switching reduction or power following objectives: (

**a**) DC-link voltage ripple (25 V/dv) vs. time (50 ms/div); (

**b**) Modules output voltages for 2.5 grid periods.

**Figure 5.**Second test results, with small gain for switching reduction on all modules (${G}_{Skj}=0.01$): (

**a**) DC-link voltage ripple (25 V/dv) vs. time (50 ms/div); (

**b**) Modules output voltages for 2.5 grid periods.

**Figure 6.**Third test results, with greater gain for switching reduction on all modules (${G}_{Skj}=0.1$): (

**a**) DC-link voltage ripple (25 V/dv) vs. time (50 ms/div); (

**b**) Modules output voltages for 2.5 grid periods.

**Figure 7.**Fourth test results, with switching penalization on half of the modules (${G}_{Sk2}=0.1$): (

**a**) DC-link voltage ripple (25 V/dv) vs. time (50 ms/div); (

**b**) Modules output voltages for 2.5 grid periods.

**Figure 8.**Fifth test results, with ripple penalization on the other half of the modules (${G}_{Pk1}=0.1$): (

**a**) DC-link voltage ripple (25 V/dv) vs. time (50 ms/div); (

**b**) Modules output voltages for 2.5 grid periods.

**Figure 9.**Sixth test results, each phase contains one module with ripple penalization (${G}_{Pk1}=0.1$) and another with switching penalization (${G}_{Sk2}=0.1$ ): (

**a**) DC-link voltage ripple (25 V/dv) vs. time (50 ms/div); (

**b**) Modules output voltages for 2.5 grid periods.

Magnitude | Value |
---|---|

Nominal phase-to-phase RMS voltage | 400 V |

Nominal RMS phase current | 30 A |

Type of transistors | IGBT |

Phase inductance (L) | 6 mH |

$\mathrm{Modules}\mathrm{DC}-\mathrm{link}\mathrm{capacitance}({C}_{kj}\forall k,j$) | 4.1 mF |

Modules maximum DC-link voltage | 800 V |

Modulation carrier signal frequency | 2 kHz |

Control frequency | 4 kHz |

Module | Phase 1 | Phase 2 | Phase 3 |
---|---|---|---|

First | Yellow | Green | Purple |

Second | Blue | Red | Orange |

Test | Phase 1 | Phase 2 | Phase 3 | |||
---|---|---|---|---|---|---|

Module 1 | Module 2 | Module 1 | Module 2 | Module 1 | Module 2 | |

1 | 12.5 | 12.5 | 12.5 | 10 | 12.5 | 17.5 |

2 | 15 | 12.5 | 12.5 | 12.5 | 17.5 | 12.5 |

3 | 32.5 | 30 | 30 | 30 | 32.5 | 32.5 |

4 | 15 | 22.5 | 12.5 | 22.5 | 12.5 | 22.5 |

5 | 0 * | 7.5 | 0 * | 7.5 | 0 * | 7.5 |

6 | 3.75 | 15 | 2.5 | 15 | 3.75 | 12.5 |

Test | Phase 1 | Phase 2 | Phase 3 | |||
---|---|---|---|---|---|---|

Module 1 | Module 2 | Module 1 | Module 2 | Module 1 | Module 2 | |

1 | 690 | 1100 | 1200 | 810 | 835 | 875 |

2 | 780 | 740 | 750 | 815 | 960 | 690 |

3 | 820 | 610 | 610 | 770 | 605 | 870 |

4 | 1220 | 200 | 1285 | 190 | 1460 | 200 |

5 | 1980 | 780 | 1960 | 790 | 1990 | 785 |

6 | 1950 | 280 | 1940 | 230 | 1950 | 270 |

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

© 2022 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**

Galván, L.; Gómez, P.J.; Galván, E.; Carrasco, J.M.
Optimization-Based Capacitor Balancing Method with Customizable Switching Reduction for CHB Converters. *Energies* **2022**, *15*, 1976.
https://doi.org/10.3390/en15061976

**AMA Style**

Galván L, Gómez PJ, Galván E, Carrasco JM.
Optimization-Based Capacitor Balancing Method with Customizable Switching Reduction for CHB Converters. *Energies*. 2022; 15(6):1976.
https://doi.org/10.3390/en15061976

**Chicago/Turabian Style**

Galván, Luis, Pablo J. Gómez, Eduardo Galván, and Juan M. Carrasco.
2022. "Optimization-Based Capacitor Balancing Method with Customizable Switching Reduction for CHB Converters" *Energies* 15, no. 6: 1976.
https://doi.org/10.3390/en15061976