The building space cooling is accounting for a significant portion of global energy use, and it is essential to enhance chiller efficiency for energy reduction and climate change mitigation. Chiller systems with multiple compressors provide the flexibility to meet varying cooling demands. The load-sharing strategy controls how the cooling load is distributed among the compressors. The load-sharing strategy optimization can significantly affect the chiller overall power consumption. This paper presents a mathematical analysis of the power consumption of centrifugal compressors under specific ambient temperatures. The influence of the inlet guide vane and the variable frequency drive efficiency on the compressor power consumption are considered and discussed briefly. An optimal load-sharing strategy for commonly used systems with identical compressors is proposed. Additionally, the scenarios involving a mix of different compressors are investigated. To validate the proposed strategies, a case study using the established performance data of a commercial centrifugal compressor is conducted. The case study results align with the mathematical analysis and the proposed strategy. This study provides valuable insights for designing and managing efficient chiller systems.