To answer your question "I would like to know whether I have modeled it correctly or not. ":
Sure, you can also use UC_COMNET, if you only want to constrain the emissions over the full model horizon. TIMES by default multiplies the coefficients by the duration of each period, if the constraint is cumulative. I am not able to spot any problems in your constraint, and so it should indeed work for that purpose. But you also said "the model didn't optimize", which I don't really understand...
Sure, you can also use UC_COMNET, if you only want to constrain the emissions over the full model horizon. TIMES by default multiplies the coefficients by the duration of each period, if the constraint is cumulative. I am not able to spot any problems in your constraint, and so it should indeed work for that purpose. But you also said "the model didn't optimize", which I don't really understand...