CPU frequency always at the maximum

I have a new Acer Aspire laptop (bought in February, now running Xubuntu 17.04), and when the power is plugged in, the CPU frequency is always 3.5 GHz, but when it is not plugged in, 2.7 GHz. So it saves some power.

It would be great if this could be automatically adjusted, as with 2.7 GHz, the battery is drained in just 2 hours.

My old laptop (with Xubuntu 16.04, also an Acer Aspire) automatically throttled down to 400 MHz when idle.

Edit 4: I have removed the previous edits, and my handmade logging tool caught an instance of this happening:

Tue Apr 18 12:56:36 2017 CPU MHz:               651.190
Tue Apr 18 12:56:46 2017 CPU MHz:               3491.186
Tue Apr 18 12:56:56 2017 CPU MHz:               984.484
Tue Apr 18 12:57:06 2017 CPU MHz:               799.871
Tue Apr 18 12:57:16 2017 CPU MHz:               3499.859
Tue Apr 18 12:57:26 2017 CPU MHz:               3499.859
Tue Apr 18 12:57:36 2017 CPU MHz:               3499.859
Tue Apr 18 12:57:46 2017 CPU MHz:               3500.036

...continuing with 3499.xxx and 3500.xxx, and very rarely 34xx.xxx.

After carefully comparing the pstree output with wdiff, I have not seen any different processes running before and after it happens.