The diagram looks measleading to me. It makes it appear that MPPT is a certain hardware block that power goes through. MPPT is rather a method of controlling DC-DC converter. Also DC-AC followed by AC-DC converter is usually not the most efficient way to convert the power.
Look at the
buck DC-DC converter. They have a decent explanation on how it works. Now, instead of the input voltage source, connect a solar panel and a capacitor in parallel. Connect the battery as the load. When the battery is connected, the output capacitor is not really needed, so you may remove it.
The MPPT controller is concerned about two entities - Vs - voltage at the panel (and capacitor), and Vb - voltage at the battery.
See what happens when the switch is off. Panel is charging the capacitor, so Vs increases (and will increase until it reaches panel open cirtcuit voltage - Voc). The current into pattery (if there was any stored in the inductor) decreases and as a result Vb decreases.
Now when you turn the switch on. Battery strat dischaging the capacitor, so Vs decreases, but the current through the inductor into the battery increases and then Vb increases too.
Battery is usually charged in four stages.
1. Bulk stage occurs at the beginning when battery is discharged.
The goal of the MPPT controller is to get as much energy as possible. To do this, it must keep Vs as close to the optimum MP point as possible. We will set aside how this point is found (In the simplest form, you just use the panel specification). The MP point occurs at certain voltage called Vmp. Total power is equal to V x I. Vs higher than Vmp will decrease production because of lower current. Vs lower than Vmp will decrease production because of lower voltage.
So, the goal of MPPT controller is to keep Vs as close to Vmp as possible. This can be done by manipulating the switch. When Vs > Vmp, you turn the switch on. When Vs < Vmp, you turn the switch off. Of course, you use some hysteresis.
2. Absorption stage occurs later when battery voltage reaches pre-set Vabs voltage.
The goal of the MPPT controller is not to let Vb rise above Vabs, which would overcharge, or could even destroy the battery. This can be done by manipulating the same switch. When Vb < Vabs, you turn the switch on. When Vb > Vabs, you turn the swith off. Hysteresis is needed too. While you're doing this, Vs naturally slides up above Vmp limiting the production to what is needed.
3. Float stage occurs when battery is fully charged.
You could turn the charger off completely, but there could be loads on the batteries (inverter, lights etc.), and it's better to keep the charger on to support these loads instead of discharging the batteries. This is done by maintaining batteries at a constant Vfloat voltage, which is slightly higher than resting voltage for fully charged batteries.
The goal of MPPT controller is to keep Vb as close to Vf as it can. When Vb < Vfloat, you turn the switch on. When Vb > Vfloat, you turn the swith off. Hysteresis ...
4. Off stage occurs during the night.
Panels must be disconnected from the controller to avoid draining batteries through the panels. Usually a separate relay is used.
Combining stages.
The three day stages can work using the same algorithm. You have a maximum voltage Vmax, which is set to Vabs during bulk and absorption stages, and to Vfloat during the float stage. If ((Vs > Vmp) AND (Vb < Vmax)) you turn the switch on, otherwise, you turn it off. In the simplest form, this can be done with two comparators and a logic gate.
Of course, there are more complicated MPPT controllers, but the concept is the same.