Assuming the cabinet is adequately insulated and the
refrigeration equipment is sized to suit the
project, then your suspicion regards voltage drop (power supply) could be correct and the cause of the poor performance.
Power supply issues are the most common cause of 12 / 24VDC refrigeration system failures.
You may check and the
compressor is running, but does it continue running to complete the
cooling cycle or not?
To explain: The MDM (motor driver module ... black box) at the
compressor monitors and protects against low / high voltage, over load, over heat etc and these 'fail safes' are auto resetting so you can have a situation where a poor power supply can allow the comp to run for a short period, cut off prematurely then start again etc. Effectively running in increments and therefore not performing correctly.
To check:
Using a good multi-meter connected to the negative and positive terminals (- & +) on the MDM read the voltage before and when the compressor starts or attempts to start.
The voltage reading with no load, before the compressor starts is meaningless but do note that no-load voltage.
Next, continue to
monitor the voltage as the compressor starts or attempts to start. If this voltage drops away by say a volt or more or below 10.9 volts then that is confirmation that most likely the power supply is the problem .