  Using the multi-band $d-p$ model and unrestricted Hartree-Fock approximation
we investigate the electronic structure and spin-orbital order in
three-dimensional VO$_3$ lattice. The main aim of this investigation is testing
if simple $d-p$ model, with partly filled $3d$ orbitals (at vanadium ions) and
$2p$ orbitals (at oxygen ions), is capable of reproducing correctly nontrivial
coexisting spin-orbital order observed in the vanadium perovskites. We point
out that the multi-band $d-p$ model has to include partly filled $e_g$ orbitals
at vanadium ions. The results suggest weak self-doping as an important
correction beyond the ionic model and reproduce the possible ground states with
broken spin-orbital symmetry on vanadium ions: either $C$-type alternating
orbital order accompanied by $G$-type antiferromagnetic spin order, or $G$-type
alternating orbital order accompanied by $C$-type antiferromagnetic spin order.
Both states are experimentally observed and compete with each other in YVO$_3$
while only the latter was observed in LaVO$_3$. Orbital order is induced and
stabilized by particular patterns of oxygen distortions arising from the
Jahn-Teller effect. In contrast to time-consuming \textit{ab-initio}
calculations, the computations using $d-p$ model are very quick and should be
regarded as very useful in solid state physics, provided the parameters are
selected carefully.
