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But I am unsure about the output voltages from transformer. Comparing the ground wire (green) to the two 24 VAC wires (black), found one wire with 24 VAC. The other wire was 0 VAC. Question, should both wires have 24 VAC?>
Well, the answer is no. There should be 24 VAC on one terminal only. The terminal that reads 0 VAC is the common neutral for the controller power and valves coils. As you may know, that green wire is the equipment grounding conductor for the safety system in your building wiring. In the transformer you have a three pin connection that plugs into the 120 VAC power outlet. The center pin is the green conductor and is connected inside the transformer to the common of the stepdown output side. This provides safety grounding for the controller as well as the coils.
Hope that this helps some.