An air conditioning system that comprises a controller that is in electrical communication with a compressor, a condenser fan, a temperature sensor that measures the temperature of the ambient air, a temperature sensor that measures the temperature of a condenser coil of the air conditioning system, and a low pressure switch (LPS) that measure the pressure of a refrigerant disposed within the air conditioning system. An algorithm resident on the controller controls the controller to enter a low ambient cooling mode when the temperature of the ambient air is less than a set temperature. The algorithm further controls the controller so that a minimum and/or maximum cycling frequency is imposed on the condenser fan. The algorithm further controls the controller so that the controller does not respond to an LPS trip during the early part of a cooling cycle under low outdoor temperature conditions, which might not accurately indicate a system fault, but still shuts down the compressor in response to an LPS trip under conditions that truly indicate a system fault.