Low Charge and the Pressure Enthalpy Diagram

I’ll start this discussion with a plot of the system design perimeters. I do this a lot because if you don’t know how the system is supposed to operate, you can’t know when something is broke!
Our unit is an air cooled 134a cycle with 10 degrees of superheat and 9 degrees of sub-cooling. The saturation temperature of the evaporator is 45 degrees Fahrenheit, and the saturation temperature of the condenser is 120 degrees F.
The system capacity is 36,000 Btu/hour, or three tons. Below is the cycle plotted and some of the system characteristics calculated from the information on the diagram.

There a varying degrees of low system charge, very low system charge will freeze the coil up and have ice hanging off the suction line. This condition doesn’t require much diagnostic effort, if the filter is okay, and the blower is okay, then low charge is probably it, and then you find the leak.
The low charge condition that’s tough to find is one that leads to capacity problems with no other apparent symptoms. This condition leads to very high energy costs and should be corrected as soon as its determined.
Refrigerant mass flow multiplied by the heat of compression and divided by 42.43 is the compressor horse power, so, (9.8 X 35)/42.43 = 8 horse power. To find the compressor amp draw, we multiply horse power by 746 (watts per horse power) and divide by the (volts X Efficiency X power factor). Efficiency and power factor can be considered 1 for most circumstances, so, (8 X 746) / 220 volts = 27.4 amps we would expect to see on a single-phase unit compressor.
Next, we plot the low charge conditions against the design conditions. The plot will look like low load or low ambient, but one thing to remember is that low load and low ambient have ample cooling capacity, where low charge everything is low (pressures, capacity, sub-cooling) but two characteristics, the heat in the compressor and out.
The superheat with an expansion valve system will be elevated depending on the extent of undercharge since the valve will try to compensate for the high suction line temperature. On fixed metering devices, such as pistons and capillary tubes, the superheat will be notably high.
I have plotted a cycle of the same unit during the same operating conditions but the unit is under charged. 

The sub-cooling dropped to 1 degree and the suction superheat bumped up to 13 degrees. The compressor superheat (discharge temperature minus the saturation temperature) also increased from 108 to 111 degrees.
The evaporator enthalpy dropped to 60 Btu/pound lowering the net refrigeration effect and the inlet volume to the compressor changed to .99 cubic foot per pound.
The volume of flow, 8.7 cfm, calculated on the first diagram, is the compressors physical displacement because that was the design flow at the design inlet volume. If we divide the fixed volume of 8.7 by our new suction density of .99, the mass flow is reduced to 8.7/.99 = 8.78 pounds per minute of refrigerant flow. 11% lower.
The new mass flow multiplied by the lower evaporator enthalpy, 8.78 X 60 Btu/pound = 527 Btu/minute. There is 200 Btu/min in a ton of cooling, so, 527/200 = 2.6 Tons of cooling 14% less cooling than the 3-ton design. That’s enough to cause problems.
The compressor is running hotter because the gas coming back to it is hotter. The pressure ratio dropped down some so there is a little less work going on.
The heat of compression, 33 Btu/pound, multiplies by the new flow, 8.78 pounds per minute, divided by 42.43 is 6.8 horse power. Finding the new motor current, (6.8 X 746)/220 = 23 amps, about 5 amps less than the fully charged system.