This paper presents an analytic approach for defining optimal operation decisions for a power generation unit (PGU) in combined heating and power (CHP) systems. The system is optimized with respect to cost, and the independent variables are the thermal load and the electric load. Linear programming is a common tool used to find the optimal PGU operation for a given combination of thermal and electric loads, but these methods are more computationally intensive than the analytical approach proposed in this paper. The analytic process introduced in this paper shows that the optimal PGU operation for all possible thermal and electric loads can be decided by simple and explicit equations even when the efficiency of the PGU is allowed to vary with PGU loading. Moreover, the analysis reveals that for all possible load conditions, the optimal CHP system operation is based on either following the electric load (FEL) or following the thermal load (FTL) strategies. The cost ratio, i.e., the ratio of the electricity price to the fuel price, is introduced as the key parameter used for making optimal decisions. Cost ratios in Chicago, IL and Philadelphia, PA are used as case studies to show the effect that different cost ratios have on the optimal operation decisions for each possible input load.

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