Multiple chiller systems are widely utilized for space cooling in industrial and commercial buildings. Good chiller control methods could offer benefits to users for more energy savings. Matching the anticipated cooling load and achieving higher coefficient of performance (COP) are the main objectives of multiple chiller capacity control strategies. With this as a main motivation, a dynamic model of compressor refrigeration chiller (CRC) and design of a closed loop PI controller for single CRC and multiple CRC systems are presented in this thesis. The dynamic model of vapor compressor refrigeration system includes thermostat expansion valve, evaporator, compressor, compressor motor, and condenser. The model equations were solved and open loop simulations were made to evaluate the time response characteristics of each component and whole chiller system under varying cooling load. A PI controller was designed and output responses of supply water temperatures, refrigerant mass flow rate and compressor motor rotor speed were studied.