| CPC H02J 7/0014 (2013.01) [B60L 58/22 (2019.02); H02J 7/0024 (2013.01); H02J 7/0048 (2020.01); H01M 10/441 (2013.01)] | 20 Claims |

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1. A battery system comprising:
a first positive terminal;
a second positive terminal;
a negative terminal;
switches;
first, second and third battery modules, wherein each of the first, second, and third battery modules includes three strings of battery cells that are configured to, at different times be:
connected in series and to the first positive terminal via first ones of the switches;
connected in parallel and to the second positive terminal via second ones of the switches; and
disconnected from both of the first and second positive terminals; and
a switch control module configured to:
determine state of charges (SOCs) of the strings of battery cells, respectively;
determine, using model predictive control, periods of phases, respectively, to balance SOCs of the first, second, and third battery modules;
determine, using model predictive control, periods for the strings, respectively, including setting one of the periods for one of the strings to be included in at least two of the phases;
selectively actuate the switches based on the periods of the phases and the periods for the strings of battery cells,
wherein the switch control module is configured to:
during a first phase:
connect the strings of battery cells of the first battery module in series and to the first positive terminal; and
connect the strings of battery cells of the second and third battery modules in a parallel mode and to the second positive terminal;
during a second phase:
connect the strings of battery cells of the first and third battery modules connected in parallel and to the second positive terminal; and
connect the strings of battery cells of the second battery module in series and to the first positive terminal; and
during a third phase:
connect the strings of battery cells of the first and second battery modules in parallel and to the second positive terminal; and
connect the strings of battery cells of the third battery module in series and to the first positive terminal.
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