Abstract: Electronic controller apparatus for automatically controlling and managing load demand and operation of energy-consuming equipment powered by alternating electrical power current, whereby feedback signals from a vapor compression evaporator or other source, and possibly other physical signals, are used to supplement the pre-fixed, learned, or default settings to optimize compressor operation (run time) in cooling and refrigeration equipment, and thereby to improve heat transfer in the evaporator. The effect is to improve the Energy Efficiency Ratio (EER), Seasonal Energy Efficiency Ratio (SEER), and Coefficient of Performance (COP) for the unit, and provide other advantages and improvements. In gas-, oil-, and propane-fired HVAC&R heating systems, the apparatus can also optimize burner operation and thereby improve heat transfer across the burner heat exchanger. HVAC&R systems that incorporate the demand controller and methods of their operation also are provided.