When thinking about efficiency one must look at the whole system or the whole home and not just an individual device or appliance.  Over the past 120 years, almost all power came from the AC grid, or from an AC generator to simulate the grid.  Comparing the efficiency of one Appliance to another was simple enough.  Consequently, the big yellow stickers required by the Department of Energy to be displayed on all appliances so when you're shopping at a big box store you know exactly how much that Appliance will cost you in energy each year.

With the advent of solar primarily, but also all forms of non-grid dependent energy self-production including wind, hydro, geothermal, bio-digesters, hydrogen fuel cells, and generators, it becomes imperative to design and analyze the energy efficiency of the complete system from energy production source to load, and methods of energy storage which is always required or used in some form.

30% = Solar Panel --> DC 3ft --> AC Microinverter 10% loss -- AC 50 ft -->  AC Breaker Panel -- AC 50 Ft --> DC Converter 10%-50% loss --> DC Load

Solar Panel --DC 3ft --> AC Microinverter 10% loss -- AC 50 ft --> AC Breaker Panel --AC/DC Battery Charger 10% Loss --> Battery --> AC Inverter 10% --> AC 50 Ft --> DC Bridge Rectifier 10% --> Variable Speed AC Inverter 20% loss --> AC Compressor Load

Refrigerators or Heat Exchangers / Air Conditioners with "inverter" technology use inverters to convert AC power into DC, but they're not strictly DC refrigerators. The term "inverter" refers to the technology that allows the compressor to vary its speed, enhancing efficiency and reducing wear. This is achieved by using a rectifier to convert AC to DC, and then an inverter to convert it back to AC, but at a variable frequency to control the compressor's speed. 

Inverter refrigerators, while efficient, involve 15% to 30% energy loss during AC-to-DC and back-to-AC conversion. Generally, inverter technology can achieve efficiencies between 85-95% in the AC-to-DC conversion, and similar efficiency in DC-to-AC conversion. However, factors like the quality of the inverter and the specific application can affect the overall efficiency.

• AC to DC Conversion: a Full Wave Bridge Rectifier converts the alternating current (AC) from the power grid into direct current (DC). High-quality rectifiers can achieve efficiencies around 85-90%. 
• DC to AC Conversion: The inverter then converts the DC back into AC with a variable frequency and voltage, allowing an AC compressor to operate at different speeds. Inverters are generally 85-95% efficient.
• Variable Speed Inverter: Inverter technology uses a variable speed drive (VSD) to control the AC compressor speed, allowing it to adjust the cooling output based on the cooling demand like a DC compressor which are naturally variable speed. This can result in energy savings compared to traditional on/off AC compressors, even with the required 15% to 30% energy loss from AC-to-DC back-to-AC conversion. 
• This makes a DC-Direct appliance with a DC compressor 15% to 30% more efficient than even the best AC Appliance with inverter technology, and 50% to 100% more efficient than an appliance using a traditional on/off AC compressor.
• Overall Efficiency: The efficiency of the entire system is a combination of the rectifier, inverter, and compressor efficiencies, as explained in this ScienceDirect article "A Comparative analysis of system efficiency for AC and DC residential power distribution paradigms" about system efficiency. While the individual components are generally efficient, some energy is lost during each conversion.

Recently an engineer from a manufacturer that has won national awards for their new ultra-high efficiency AC hydronic water chiller for smaller residential deployments said they could not see sufficient efficiency improvements to justify switching to a 48v DC compressor within their chiller.  Hydronic heating and cooling systems are well known to be the most energy-efficient but are more complex. Think old classic boilers and radiators. However complexity means more cost to design, build, and much higher labor cost to install and maintain. Further, the system's efficiency can be seriously impaired by simple installation mistakes.   Consequently, the US HVAC industry moved away from hydronic for smaller residential Heating and Cooling many decades ago except for large expensive projects on large buildings.  So any company that can  solve the complexity problem of smaller residential hydronic systems is deserving of awards!  But I asked myself, if this engineer couldn't see the bigger picture, how do I explain this to you in a way that is so simple, that anyone without any technical expertise will understand.