What is the Thévenin equivalent of the mains power supply?
Impedance depends on frequency. Assume 50 or 60 Hz unless otherwise noted.

Impedance is typically in the 0.1 - 0.5 Ohm range at the home switchboard with the latter being unusually high and under 0.1 Ohm not uncommon in well provided systems with short feeders.

Note that a resistance of 0.1 Ohm will drop 10 V at 100 A
As a percentage of Voltage on a 230 VAC circuit that's 10/230 = 4.3%. 

Main impedance meter slide show.  


They note in slide 27 that NFPA-70 suggests 5% drop at farthest outlet. 5% at 110 VAC = 5.5V.
At say 20A load that's a maximum R of 5.5 V/20 A = 0.275 Ohm at the furthest outlet!


ZM-100 mains impedance meter manual note typical result on page 1-8 of 0.l24 Ohms at 60 Hz (rising to 0.52 Ohms at 1 kHz.) . This diagram is simply meant to show effects of frequency but also shows what they consider a useful value for an example. The metter considers > 0.99 and &lt; 0.01 Ohms as faults.

Mains quality perspective here - around 0.1 Ohm mainly resistive for practical purposes in many cases. YMMV.

Quality discussion - useful 

HiFi user perspective here



Notes:

Thevenin Voltage = Voc = nominal mains Voltage (110 VAC, 230 VAC, ...)

Thevenin current = Isc.
You do not usually run a mains outlet at anything like Isc!.  

For practical purposes Zth (Thevenin impedance) will be nearly pure resistive. At the power entry point to a home switchboard short circuit current is liable to be of the order of hundreds of amps.
For eg 460 A at 230 V, R = V/I = 0.5 Ohms.
Lower is better and usual.

Maximum power transfer occurs when Vout = 0.5 x Voc and you don't even run a mains outlet anywhere near that heavily loaded ! - and Isc is MUCH greater again.
 Comment: Possibly the device that comes closest in formal use to maximum power transfer conditions is an arc welder and similar - a very special case.

To specify Thevenin impedance for a mains power supply you need to specify point of measurement, as the result varies substantially. Example ponts may be  


Just on consumer size of pole-fuse or feed point to consumer's individual circuit.
At home switchboard mains supply point 
In switchboard on load side of fuse of circuit breaker.
At wall outlet or light socket
At end of an extension cord.


Depending on aim of exercise - assume 0.1 Ohm at switch board input at 50 Hz will probably be an OK starting point in many cases.