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 vaiy 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, ¡L 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.
An optimal sizing method is developed in this work based on an analytical scheme for determining optimal operation decisions. Using the analytic optimal operation scheme allows for a more thorough optimal sizing method because of the minimal computational effort required as compared to mixed integer programming approaches. For example, an optimal sizing method based on this approach can more feasibly consider several years of weather data and the range of likely fuel/electricity costs for the term of operation of the PGU. The optimal sizing method in this work takes advantage of this efficient optimal operation scheme and provides a robust optimal solution with respect to weather and fuel/electricity cost uncertainty. A case study of a medium sized office building is carried out by testing the algorithm for a range of 20 commercially available diesel engine PGUs.
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