This article presents a constrained model predictive control (MPC) strategy for a three-phase low-capacitance static compensator (LC-StatCom) with delta configuration. The controller consists of an outer loop that provides dynamic references for the active grid current component and the circulating current; whereas, the inner predictive loop minimizes the quadratic error of state variables subject to operating limit conditions, thus providing optimal control signals that produce a fast response while guaranteeing the prescribed safe operating limit conditions. The article also proposes an enhanced discrete-time model, which uses intersample values, that improves the accuracy of the model predictions when the sampling rate is not high enough to assume constant state variables. As a result, it facilitates the implementation of MPC on less powerful processors compared to the conventional modeling. The proposed control is especially suited for the LC-StatComs since it incorporates analytical computation of desired steady-state trajectories, which takes into account the induced oscillation on the capacitor voltages that are inherent to the LC-StatComs. The proposed approach has been verified by simulation and experimentally with a laboratory prototype.