DC Grids provide a feasible and promising solution for renewable energy integration. To address the power fluctuation issues caused by the volatility and intermittency of renewable energy and the randomness of loads

the DC system needs to update the operating points of voltage source converters (VSCs) based on optimal power flow (OPF) results to maintain stable and economical operation. However

the traditional OPF methods are computationally inefficient and unsuitable for real-time control of DC systems. Therefore

this paper proposes a linear OPF of DC grids considering VSC control characteristics. First

an OPF model for DC grids is formulated with the objectives of minimizing voltage deviation

power losses

and dispatch deviations. Second

the power flow equality constraints and optimization objectives are partially linearized. Subsequently

the DC grid OPF model is fully linearized using the Lagrange multipliers and the generalized VSC control characteristics

obtaining the optimal operating points for the VSCs. Finally

the effectiveness of the proposed linear OPF for DC grids is validated using the Cigre B4 DC test system. Compared with conventional OPF

in a 10-node DC grid

the proposed linear OPF improves computation speed by over 100 times and saves more than 99% of computation time while keeping the error within 3%.