If you follow the model steps and select only the field you want in the "Export Feature Attribute to ASCII", it should only export that particular field (plus x and y, which you can remove by editing that tool's script).
So, say you have a table with 20 fields... you can apply your filter (where some attribute = "P-1 Feeder"), then select only the [TWACs_Number] field in the fields list within the "Export Feature Attribute to ASCII" tool. When you export, you should only have a CSV with the [TWAVs_Number] field and all of its attributes, where the feeder assignment = "P-1 Feeder".
I was able to get this to work both with making a feature layer, and by skipping this step (making a feature selection update, like in the model).