How to generate 6 phase shifted (60 degrees between each) PWM Signals?
The extra 3 phases is unusual, which makes this a harder selection task. However the microcontroller requirements for a suitable inverter are straightforward. You need a system that has 6 center-aligned PWM outputs, all sharing the same time-base, and preferably with complementary outputs.
The time-base requirement is an absolute one for SVM, otherwise the PWM switching phase alignment won't be guaranteed. SVM also requires center aligned PWM generation, so you'll need to check for that option as well. You may be able to get away with using two separate timer sources with center aligned PWM, if there is an option to synchronize them and you have a stable shared clock source. STM32 has microcontrollers (i.e. STM32F7) with synchronizable time-bases, and center aligned PWM options.