google search term: trigeneration
Cogeneration (CHP-combined heat + power) and trigeneration (CCHP-combined cooling, heat, power) plants have been well researched, and many are in operation today in industrial applications. They have been proven to work best with gas turbines and ammonia absorption chillers in medium to large to gargantuan scale systems. Cities and districts with utility-provided DHW are by far the largest and most experienced group of experts using combined systems. Not surprisingly, most of these users are in Europe and nations previously ruled by the British empire.
From a provider's point of view, it makes good sense:
powerwaterheat.com has a good website that explores the tip of the iceberg of this subject. They build and sell medium and small scale units that can work anywhere.
By and large, the cooling system portion of micro-chp systems has not been exploited. The majority of small systems are built as temporary systems for remote work camps or disaster relief operations. For this purpose, space cooling is not considered important.
ORNL and the DOE have been attacking this idea for decades.
http://web.ornl.gov/info/ornlreview/...2/text/gas.htm