In this case seems that problem is theoretically simple.-BLDC is not 3-phase generator ?
=SYCHRONJUSE is better, but PRICY ! (f.e. EMRAX motores)
However when you really try to produce it and connect it into existing electric propulsion system you will face a lot of problems.
I know only few really flying electric airplanes with range extender.
C42 from Toni Roth
Unfortunatelly "Hybrid C42" reported a lot of problems....
Toni Roth has produced a hybrid version of the Comko Ikarus C42 with up to five hours endurance using a Swiss engine/generator and HPD55 motor.
e-Genius.... but I don´t know if they flown it already with range extender.
Diamond DA40 Hybrid
Test flown, but no more news....
Diamond Aircraft Industries GmbH in collaboration with Siemens AG is pleased to announce the first flight of a jointly developed multi-engine hybrid electric aircraft, commenced on the 31st of October 2018 at Diamond Aircraft’s headquarters in Wiener Neustadt, Austria.
Non of this projects is reporting some long flights or news. So as I wrote - range extending on board generator seems to be simple, but it is not