To overpower the sun you will first need lots of power.
We normally use an Elinchrom Ranger RX speed on full power with an A head and a Deep octa or open reflector (depending on the look you want).
It all depends on how bright the sun is of course, at the evening you can do the same with a lot less power.
Also see what you want to do, you can make day into almost night with enough power, but most of the time it's much nicer to balance the sun and the model, see two examples.
Both shot during almost midday with the Ranger RX speed.
Using leaf shutterlenses in a MF system like the RZ67Pro from Mamiya or Hasselblad helps ALOT, being able to sync at 1/400 will give you much more control over the ammount of sunlight being blocked.
With a normal DSLR you are often limited to 1/125 or 1/160 for studio strobes.
I will be explaining the techniques on the Los Angeles workshops in June by the way.