  We summarize several semi-phenomenological approaches to estimate the
internal energy of one-component-plasma (OCP) in two (2D) and three (3D)
dimensions. Particular attention is given to a hybrid approach, which
reproduces the Debye-H$\ddot{\text{u}}$ckel asymptote in the limit of weak
coupling, the ion sphere (3D) and ion disc (2D) asymptotes in the limit of
strong coupling, and provides reasonable interpolation between these two
limits. More accurate ways to estimate the internal energy of 2D and 3D OCP are
also discussed. The accuracy of these analytic results is quantified by
comparison with existing data from numerical simulations. The relevance of the
KTHNY theory in locating melting transition in 2D OCP is briefly discussed.
