A method of controlling a refrigerant chiller system is particularly suited for chillers where the water being chilled (or some other liquid) flows through the chiller's evaporator at a flow rate that is variable and is not directly known. To effectively control the chiller and maintain the temperature of the water leaving the evaporator at a desired target temperature, the cooling capacity of the chiller's evaporator is estimated based the degree of valve opening of an expansion valve, a pressure differential across the expansion valve, and a change in enthalpy per unit mass of the refrigerant flowing through the evaporator. In some embodiments, the chiller system includes multiple refrigerant circuits that are hermetically isolated from each other.