Derivation of diode voltage in three phase full wave diode rectifier
Ok, so the derivation was found with hint from Tony Stewart Sunnyskyguy EE75.

As always in analysing eletrical circuits we use KVL.
From picture in question we can write two equations


First we write the equation of conductiong path $$ u_{rs}-L_i\frac{di_0}{dt}-v_{D1}-L_0\frac{di_0}{dt}-v_0-v_{D5}-L_i\frac{di_0}{dt}=0 $$
$$ \frac{di_0}{dt}=\frac{u_{rs}-v_0}{2L_i+L_0} $$
Next we can write equation for non conducting path from point \$t\$ to point \$r\$ ignoring \$v_0\$ and we get $$ u_{st}-v_{D6}-L_i\frac{di_0}{dt}=0$$
with putting two equations together we get $$ v_{D6} = u_{st} + \frac{L_i}{2L_i+L_0} (u_{rs}-v_0) $$