The following investigation describes the method used in minimizing the power consumption of multiple chiller systems by determining not only the most efficient combination of chillers in the system but also the optimal operating levels of each chiller making up the combination. The general mathematical formulation for a system of N chillers with arbitrary performance characteristics is solved and applied to the special case of chillers having parabolic performance characteristics. The analysis is then applied to various two and six chiller systems using performance characteristics of centrifugal chillers in order to show the optimal operating conditions and to illustrate the potential energy savings of multiple chiller systems compared to a single chiller system. The effects of various combinations of chillers and the effects of entering condenser water temperature are systematically investigated. A particular six chiller combination, corresponding to portions of the existing chiller systems at Virginia Tech, is also investigated. / Master of Science