  A statistical study is carried out on the photospheric magnetic
nonpotentiality in solar active regions and its relationship with associated
flares. We select 2173 photospheric vector magnetograms from 1106 active
regions observed by the Solar Magnetic Field Telescope at Huairou Solar
Observing Station, National Astronomical Observatories of China, in the period
of 1988-2008, which covers most of the 22nd and 23rd solar cycles. We have
computed the mean planar magnetic shear angle (\bar{\Delta\phi}), mean shear
angle of the vector magnetic field (\bar{\Delta\psi}), mean absolute vertical
current density (\bar{|J_{z}|}), mean absolute current helicity density
(\bar{|h_{c}|}), absolute twist parameter (|\alpha_{av}|), mean free magnetic
energy density (\bar{\rho_{free}}), effective distance of the longitudinal
magnetic field (d_{E}), and modified effective distance (d_{Em}) of each
photospheric vector magnetogram. Parameters \bar{|h_{c}|}, \bar{\rho_{free}},
and d_{Em} show higher correlation with the evolution of the solar cycle. The
Pearson linear correlation coefficients between these three parameters and the
yearly mean sunspot number are all larger than 0.59. Parameters
\bar{\Delta\phi}, \bar{\Delta\psi}, \bar{|J_{z}|}, |\alpha_{av}|, and d_{E}
show only weak correlations with the solar cycle, though the nonpotentiality
and the complexity of active regions are greater in the activity maximum
periods than in the minimum periods. All of the eight parameters show positive
correlations with the flare productivity of active regions, and the combination
of different nonpotentiality parameters may be effective in predicting the
flaring probability of active regions.
