For most, it seems the reason to use multiphase is to smooth out the DC going to the batteries once rectified. For this reason, many designs wire their coils for 3 (and some up to 5) phases. This smooth output helps batteries last longer.
However, transmitting multiple phases ineveitably involves more wires, more losses, or less flexibility. You must either put your batteries next to your wind generator, transmit DC and put up with losses, or run enough wires for each of the phases you generate.
What is the reason others, like power companies, prefer multiphase? They are not charging batteries. They don't want to run more wires than they have to. Power companies typically generate and transmit no more than 3 phases.
I submit that the real benefits of multiphase are in alternator design and efficiency. Furthermore, I submit that most designs fail to take advantage of this efficiency.
Here is my understanding of the benefit of 3-phase design. With a single phase, you have a coil of wire passing a magnet. One leg of the coil produces a positive voltage. The other, negative. This produces a full sine wave, or one phase. However, with the physical constraints of this design, there must be space within the coil of wire that is basically wasted. No current is produced as this empty space passes the magnet.
Here's where other phases come in. When we instead take two coils, placing the leg of one within the empty space of the other (and vice-versa), we have effectively increased the efficiency of our design. We now generate twice as much power in only 33% more space, with only an investment in more copper (not magnets). This is a 2 phase design.
Is there reason to go beyond 2 phases? Perhaps to help satisfy the original reason for using multiphase in axial flux alternators, to smooth the output to the batteries. There may also be geometric reasons for adding more phases to the arrangement.
Thoughts? Additions? Criticisms?