This work aims to elucidate notions concerning the ideal operation and greenhouse gas (GHG) emissions benefits of combined heat and power (CHP) systems by investigating how various metrics change as a function of the GHG emissions from the underlying electricity source, building use type and climate. Additionally, a new term entitled "CHP Attributable" reductions is introduced to quantify the benefits from the simultaneous use of thermal and electric energy, removing benefits achieved solely from fuel switching and generating electricity more efficiently. The GHG emission benefits from implementing internal combustion engine, microturbines, and phosphoric acid (PA) fuel cell based CHP systems were evaluated through an optimization approach considering energy demands of prototypical hospital, office, and residential buildings in varied climates. To explore the effect of electric GHG emissions rates, the ideal operation of the CHP systems was evaluated under three scenarios: "High" GHG emissions rates, "Low" GHG emissions rates, and "Current" GHG emissions rate for a specific location. The analysis finds that PA fuel cells achieve the highest GHG emission reductions in most cases considered, though there are exceptions. Common heuristics, such as electric load following and thermal load following, are the optimal operating strategy under specific conditions. The optimal CHP capacity and operating hours both vary as a function of building type, climate and GHG emissions rates from grid electricity. GHG emissions reductions can be as high as 49% considering a PA fuel cell for a prototypical hospital in Boulder, Colorado however, the "CHP attributable reductions are less than 10%. (C) 2016 Elsevier Ltd. All rights reserved.