Connect an additional wire to HVAC system where all the terminals are full

After looking closely at the images you've supplied, this is what it appears is going on in the last photo.

From what I know about HVAC systems, I would guess a broader view of the system would look something like this.

• The transformer supplies power to the thermostat through the RED wire.
• The BLUE wire serves as the COOL call from the thermostat.
• The BLUE wire connects to the WHITE wire, which is connected to the coil of the contactor in the condensing unit.
• The GREEN wire is the other side of the contactor coil.
• The GREEN wire connects to the BROWN wire, which is the other side of the transformer (C).

When the thermostat calls for COOL, the BLUE wire is energized. This energizes the WHITE wire leading to the contactor, which pulls the contactor closed. The GREEN wire connects to the BROWN wire, which leads back to the transformer, thus completing the circuit.

Therefore, if you want to use the YELLOW wire as C. You should include it in the twist-on wire connector with the GREEN and BROWN wire.

You'll just want to make sure the transformer is sized properly to supply the additional current draw of the thermostat.

If it were me, I'd rewire it so that the YELLOW wire was the COOL call, and the BLUE wire was C. As that's a more common color coding.

Since in your case, one side of the transformer is grounded. You can simply use a fork or ring terminal, to connect the C wire to the chassis. Though it appears there's already a wire that's attached to ground, and comes right over near the thermostat wiring. I'd just put my C wire in with the other two wires, in that twist-on wire connector near the bottom of the photo.