Problems with controlling 24VAC 3way valve (with arduino)
Generally 0-10Vdc controlled valves are two-way not three-way. I mean 2 way electrically, but they say 3 way mechanically, meaning 3 ports. (SPDT action)

They are usually optoisolated drivers to switch the solenoid powered by a floating transformer both isolated from grid AC and requires no SMPS DC supply (for this purpose) and no ground connection to the supply output, except a DC ground between Valve and logic driver of Arduino.  (Verify with a diode test and DMM.)

Thus because the user has a choice of using 0 to 10Vdc voltage control (isolated from 24Vac) or 50 Ohm current control using 5V logic direct drive. (which is what I think you mean by 50% ... of 10Vdc.)

Most CMOS now is 50 Ohms in 5Vmax logic and 25 Ohms in 3.3V max logic. This drives about 10-20 mA in current mode thru the IR optoisolated valve control input often with a small current limiting R. 


(5-1.2V)/20mA = 190 Ohms ... subtract 50 gives Rs = 170 Ohms


examples

http://electricoperatedvalve.m.sell.everychina.com/p-104817047-3-4-inches-0-10v-0-20ma-three-way-mixing-proportional-control-ball-valve.html

http://www.axiomatic.com/10vdc-din-controller.pdf (linear)

The SMPS is NOT needed at all for the valve and may be floating output for other circuits isolated both from the 24Vac and the 5Vdc logic.  If powering the SMPS from the same 24Vac transformer used by the valve, then the VA rating must be capable of supplying VA output requirements for both.

Now getting back to your "three-way" title. Thus implies tertiary logic levels for forward, reverse and center OFF using 0mA 5mA and 10mA.

Please confirm 3 way valve with specsheet. But may be terminology for 3 port connection with a 2way solenoid. i.e. SPDT