The ever-increasing penetration of renewable energy resources (RESs) in power distribution networks has brought, among others, the challenge of maintaining the grid voltages within the secure region. Employing droop voltage regulators on the RES's inverters is an efficient and low-cast solution to reach this objective. However, fixing droop parameters or optimizing them only for overvoltage conditions does not provide the required robustness and optimality under changing operating conditions. In this article, a convex optimization approach is proposed for reconfiguring P-V and Q-V droop regulators during online operation. The objective is to minimize power curtailment, power losses, and voltage deviation subject to electrical security constraints. This enables to optimally operate the grid with high RES penetration under variable conditions while preserving electrical security constraints (e.g., current and voltage limits). As a first contribution, a mixed-integer linear model of the droop characteristics is developed. According to this model, a droop-regulated generation unit is represented as a constant-power generator in parallel with a constant-impedance load. As a second contribution, a modified augmented relaxed optimal power flow (MAR-OPF) formulation is proposed to guarantee that the electrical security constraints are respected in the presence of constant-impedance loads in the network. Sufficient conditions for the feasibility of the MAR-OPF solution are provided. Those conditions can be checked a priori and are valid for several real distribution networks. Furthermore, an iterative approach is proposed to derive an approximate solution to the MAR-OPF that is close to the global optimal one. The performance of the MAR-OPF approach and the accuracy of the proposed model are evaluated on standard 34- and 85-bus test networks.