  In this work the behavior of power corrections to Adler finction in operator
product expansion (OPE) is studied, in particular the possible contribution of
operator of dimension 2. The OPE terms of dimension 4 and 6 are taken into
account. Various experimental data on reactions of $e^+e^-$-annihilation to
pion channels ($\pi^+\pi^-$, $2\pi^+2\pi^-$, $\pi^+\pi^-2\pi^0$,
$3\pi^+3\pi^-$, $2\pi^+2\pi^-2\pi^0$) are used. The high-precision fits of the
experimental data are obtained and used. The method based on Borel transform of
Adler function is applied. It is shown that the contribution of operator of
dimension 2 is negative being compatible to zero at three standard deviations
level. The strong (anti)corellation between short string and local gluon
condensate is found.
