Recently there have been an advance in the fabrication of the periodic arrays of pinning sites. The arrays with triangular, square, and rectangular geometries have been fabricated using either microholes or blind holes and magnetic dots. We calculate analytically the critical persistent current for the case of the matching field (when number of vortices is equal to that of the pinning centers) using a simple variational method in the framework of Ginzburg-Landau equations. It is shown that the vortex cores are deformed and displaces in the current carrying state. Displacement of the centers of the vortices with respect to pinning centers and structure of these states is determined.The dependence of the persistent current on the vortex displacement is linear at small displacements and approaches its maximum (the critical current) at about half of the maximal displacement. The coefficient in the linear part is the Laboucsh constant which is calculated.