Summary: Motivated by the holographic principle, it has previously been suggested that the dark energy (DE) density can be inversely proportional to the area \(A\) of the event horizon of the Universe. However, this kind of model would have a casuality problem. In this work, we study the power-law entropy-corrected holographic DE (PLECHDE) model in the non-flat Friedmann-Robertson-Walker universe, with the future event horizon replaced by the average radius of the Ricci scalar curvature. We derive the equation of state parameter \(\omega_\Lambda\), the deceleration parameter \(q\) and the evolution of energy density parameter \(\Omega'_D\) in the presence of interaction between DE and dark matter. We consider the correspondence between our Ricci-PLECHDE model and the modified Chaplygin gas and the tachyon, K-essence, dilaton and quintessence scalar fields. The potential and dynamics of the scalar field models have been reconstructed according to the evolutionary behaviour of the interacting entropy-corrected holographic DE model.