A system for storing and cooling milk comprising a cooling tank provided to store milk, a first sensor provided to monitor a filling level of milk in the cooling tank, a temperature sensor for sensing a temperature of the milk in the cooling tank, and a cooling arrangement for cooling the milk in the cooling tank comprising a cooling device, a second sensor, and a control device, wherein - the cooling device comprises an evaporator, a compressor connected with its suction side to the evaporator, a condenser connected to the high pressure side of the compressor, and an expansion valve interconnected between the condenser and the evaporator, thereby forming a closed circuit, in which a refrigerant can be circulated; - the evaporator is in heat exchange contact with at least a portion of the bottom surface of the cooling tank; - the compressor has a varying capacity, which can be controlled; - the second sensor is provided to monitor a parameter indicative of the pressure or temperature at the suction side of the compressor or in the evaporator; and - the control device is operatively connected (i) to the first sensor to receive the monitored filling level of milk in the cooling tank, (ii) to the second sensor to receive the monitored parameter, and (iii) to the compressor to control the capacity thereof in response to the monitored filling level of milk in the cooling tank and the monitored parameter, characterized in that - the compressor is a capacity modulated scroll compressor, wherein the capacity is controllable by means of changing the modulation of the compressor; and - the control device is configured to control the capacity of the compressor by means of changing the modulation of the compressor such that the pressure or temperature at the suction side of the compressor or in the evaporator is regulated towards a first desired value (P 1TH) when the monitored filling level of milk in the cooling tank is below a first threshold level (L1 TH), and towards a second desired value (P 2TH), when the monitored filling level of milk in the cooling tank is above the first threshold level, but below a second threshold level (L2 TH), wherein the second desired value is lower than the first desired value, and - wherein the control device is configured to control the compressor in response to the sensed temperature when the monitored filling level of milk in the cooling tank is above the second threshold level. - the cooling device comprises an evaporator, a compressor connected with its suction side to the evaporator, a condenser connected to the high pressure side of the compressor, and an expansion valve interconnected between the condenser and the evaporator, thereby forming a closed circuit, in which a refrigerant can be circulated; - the evaporator is in heat exchange contact with at least a portion of the bottom surface of the cooling tank; - the compressor has a varying capacity, which can be controlled; - the second sensor is provided to monitor a parameter indicative of the pressure or temperature at the suction side of the compressor or in the evaporator; and - the control device is operatively connected (i) to the first sensor to receive the monitored filling level of milk in the cooling tank, (ii) to the second sensor to receive the monitored parameter, and (iii) to the compressor to control the capacity thereof in response to the monitored filling level of milk in the cooling tank and the monitored parameter, characterized in that - the compressor is a capacity modulated scroll compressor, wherein the capacity is controllable by means of changing the modulation of the compressor; and - the control device is configured to control the capacity of the compressor by means of changing the modulation of the compressor such that the pressure or temperature at the suction side of the compressor or in the evaporator is regulated towards a first desired value (P 1TH) when the monitored filling level of milk in the cooling tank is below a first threshold level (L1 TH), and towards a second desired value (P 2TH), when the monitored filling level of milk in the cooling tank is above the first threshold level, but below a second threshold level (L2 TH), wherein the second desired value is lower than the first desired value, and - wherein the control device is configured to control the compressor in response to the sensed temperature when the monitored filling level of milk in the cooling tank is above the second threshold level.