How does "delta"-like three phase power source avoid short circuit?
From Alternating Current Machines-Synchronous Machines



If you did this with batteries, you would have a big problem (your short circuit concern), but a delta (or wye) takes advantage of the phase shift of 120\$^o\$.  

$$ \vec {V_A} = 450\ \angle  0 ^o\ V$$
$$ \vec {V_B} = 450\ \angle  120 ^o\ V$$
$$ \vec {V_C} = 450\ \angle  -120 ^o\ V$$

If you do vector addition around the loop, the sum of the voltages equals 0.

$$ \vec {V_A} + \vec {V_B} + \vec {V_C} = 0$$

No voltage, so no current circulates around delta. All current flow out to loads.  

There is a cavaet if one of the windings is connected incorrectly. 

Image on left shows installation of generator in delta.  Before connecting up last connection, voltmeter is used to ensure voltage is 0.  If one of the windings was connected backwards, the net voltage would be 900V, which would burn out the low impedance windings in a short circuit.