*Article* **Electrochemical Cell Loss Minimization in Modular Multilevel Converters Based on Half-Bridge Modules**

**Gianluca Brando 1,\*, Efstratios Chatzinikolaou 2, Dan Rogers 2 and Ivan Spina 1**


**\*** Correspondence: gianluca.brando@unina.it; Tel.: +39-0817683233

**Abstract:** In the developing context of distributed generation and flexible smart grids, in order to realize electrochemical storage systems, Modular Multilevel Converters (MMCs) represent an interesting alternative to the more traditional Voltage Source Inverters (VSIs). This paper presents a novel analytical investigation of electrochemical cell power losses in MMCs and their dependence on the injected common mode voltage. Steady-state cell losses are calculated under Nearest Level Control (NLC) modulation for MMCs equipped with a large number of half-bridge modules, each directly connected to an elementary electrochemical cell. The total cell losses of both a Single Star MMC (SS-MMC) and a Double Star MMC (DS MMC) are derived and compared to the loss of a VSI working under the same conditions. An optimum common mode voltage injection law is developed, leading to the minimum cell losses possible. In the worst case, it achieves a 17.5% reduction in cell losses compared to conventional injection laws. The analysis is experimentally validated using a laboratory prototype set-up based on a two-arm SS-MMC with 12 modules per arm. The experimental results are within 2.5% of the analytical models for all cases considered.

**Citation:** Brando, G.; Chatzinikolaou, E.; Rogers, D.; Spina, I. Electrochemical Cell Loss Minimization in Modular Multilevel Converters Based on Half-Bridge Modules. *Energies* **2021**, *14*, 1359. https://doi.org/10.3390/en14051359

Academic Editor: Jinliang Yuan

Received: 21 January 2021 Accepted: 24 February 2021 Published: 2 March 2021

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**Copyright:** © 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/).

**Keywords:** lithium batteries; los minimization; Modular Multilevel Converters; optimization methods
