A battery management unit for a battery system with a conductor or busbar, the battery management unit comprising: a printed circuit board and a fluxgate current sensor, the fluxgate current sensor comprising: a magnetic core with a through-hole; at least one excitation winding (320 A); at least one compensation winding (320 B); a sensor electronics; wherein the at least one excitation winding (320 A) is wound around the magnetic core and the at least one compensation winding (320 B) is wound around the magnetic core; wherein the sensor electronics is configured to measure the magnetization of the excitation winding(s) (320 A), to generate a driving signal for driving the compensation winding(s) (320 B) such that the magnetic flux in the magnetic core is cancelled out by the current in the compensation winding(s) (320 B), to generate a current flowing through the compensation winding(s) (320 B) according to the driving signal, and to generate an output signal corresponding to the magnitude of an electric current I P flowing through the through-hole of the magnetic core; and the battery management unit being characterized in that the magnetic core, the excitation winding(s) (320 A), the compensation winding(s) (320 B), and the sensor electronics are each integrated into the printed circuit board; and wherein the magnetic core is arranged so on the printed circuit board that the battery management unit is mountable such into the battery system that the conductor or busbar of the battery system passes through the through-hole of the magnetic core. a printed circuit board and a fluxgate current sensor, the fluxgate current sensor comprising: a magnetic core with a through-hole; at least one excitation winding (320 A); at least one compensation winding (320 B); a sensor electronics; wherein the at least one excitation winding (320 A) is wound around the magnetic core and the at least one compensation winding (320 B) is wound around the magnetic core; wherein the sensor electronics is configured to measure the magnetization of the excitation winding(s) (320 A), to generate a driving signal for driving the compensation winding(s) (320 B) such that the magnetic flux in the magnetic core is cancelled out by the current in the compensation winding(s) (320 B), to generate a current flowing through the compensation winding(s) (320 B) according to the driving signal, and to generate an output signal corresponding to the magnitude of an electric current I P flowing through the through-hole of the magnetic core; and a magnetic core with a through-hole; at least one excitation winding (320 A); at least one compensation winding (320 B); a sensor electronics; wherein the at least one excitation winding (320 A) is wound around the magnetic core and the at least one compensation winding (320 B) is wound around the magnetic core; wherein the sensor electronics is configured to measure the magnetization of the excitation winding(s) (320 A), to generate a driving signal for driving the compensation winding(s) (320 B) such that the magnetic flux in the magnetic core is cancelled out by the current in the compensation winding(s) (320 B), to generate a current flowing through the compensation winding(s) (320 B) according to the driving signal, and to generate an output signal corresponding to the magnitude of an electric current I P flowing through the through-hole of the magnetic core; and the battery management unit being characterized in that the magnetic core, the excitation winding(s) (320 A), the compensation winding(s) (320 B), and the sensor electronics are each integrated into the printed circuit board; and wherein the magnetic core is arranged so on the printed circuit board that the battery management unit is mountable such into the battery system that the conductor or busbar of the battery system passes through the through-hole of the magnetic core.