Electrical – How to run a fridge on off grid system

You are describing a Solar Hybrid SOMETHING that may or may not exist in todays vast Marketplace? Step back and revisit a Block Diagram of a Complete Solar Panel Whole House System. You describe several Blocks or Components of the complete system and seem to want all of them in one Device which may be possible today but not practical for the DIY person that dwells within you. It is my impression your main question is of a "Charge Controller" who's function is to charge your Battery using your Solar Panels as the Charging Power Source. Todays Charge Controllers decide for you when the Mains need to take over, when the Battery is fully charged by the Solar Panels, and also when to divert the Solar Panels output to a Dump Load if and when your Batteries are completely charged. The Inverter is the expensive item who's sole purpose in life is to Convert the DC Battery Voltage to a usable AC Voltage ( not necessary for LIGHTING Circuits ONLY ) and Current your household appliances will agree with exactly like your Mains Power from your local Utility Company 230 VAC at 50 Hz I suspect. In an effort to thoroughly answer your question in the form of a recommendation.... Do not look for a single Component that "does it all", if it fails you will loose everything. Rather purchase a quality Charge Controller, a quality Inverter of size and capability to handle your entire anticipated Load, which will indeed be expensive! Most of all, read up / study the topic and fully understand what each individual Block or Component of the Basic,Entire System is responsible for and mostly how they interact to form a Complete System before making any investment. Read, understand, and then make an informed decision / plan to purchase equipment.

The typical PV installation is either classified as "off grid" or "on grid".

The off grid version charges batteries from the solar panels via a DC bus and an inverter converts the DC bus to AC to supply the facility loads. There is no interconnect between utility company provided mains and the solar system. These systems are often used when utility company energy is not available or it is prohibitively expensive to install and operate.

The on grid version is the most common form. Here a number of solar panels are wired in series and connected to an inverter. The inverter converts the DC bus from the panels to AC. The inverter monitors the utility company AC line and syncs its frequency and phase to the AC line. If the AC mains fail, the inverter has protection circuits so that it drops off of the AC line to avoid causing harm to power line workers, etc. Many installation codes still require a separate mains disconnect switch, however. This type of system supplies all of its energy back to the power utility and the facility loads remain connected to the utility. This essentially allows the solar produced energy to offset the purchased energy.

An on grid system can include any number of inverters to reach the desired energy capacity. No special connections are required as they are typically paralleled on the utilities side and connected to a unique string of solar panels on the DC side.

Either style of system can employ MPPT (Maximum Power Point Tracking). This is a technique that extracts the maximum power available from the solar panel under the current sunlight conditions. Some newer systems put small MPPT trackers in place for every solar panel or a small collection of panels with the promise of further optimizing the total solar panel array power when some panels are shaded by a tree or cloud for example.

A few on grid system offer an accessory connection to the inverter for a few kW of power to provide a limited form of backup for the facility when the mains fail. This is rarely sufficient to power all facility loads.