  We investigate the $u=1/2$ [$\mathcal{O}(\Lambda_{\rm QCD})$] and $u=3/2$
[$\mathcal{O}(\Lambda_{\rm QCD}^3)$] renormalons in the static QCD potential in
position space and momentum space using the OPE of the potential-NRQCD
effective field theory. This is an old problem and we provide a formal
formulation to analyze it. In particular we present detailed examinations of
the $u=3/2$ renormalons. We clarify how the $u=3/2$ renormalon is suppressed in
the momentum-space potential in relation with the Wilson coefficient $V_A(r)$.
We also point out that it is not straightforward to subtract the IR renormalon
and IR divergences simultaneously in the multipole expansion. Numerical
analyses are given, which clarify the current status of our knowledge on the
perturbative series. The analysis gives a positive reasoning to the method for
subtracting renormalons used in recent $\alpha_s(M_Z)$ determination from the
QCD potential.
