This paper proposes an optimal power flow (OPF) algorithm based on quadratic modeling and incremental loading of the network. The proposed OPF algorithm is robust and highly efficient for large-scale power systems. Robustness is achieved by the design of the algorithm to operate on infeasible but optimal points and move towards the feasible and optimal operating point. Efficiency is achieved by (a) the design of the algorithm to include mainly the active constraints and therefore reducing the problem size and (b) quadratic modeling that provides faster solution times of the network update solutions. The algorithm guarantees a solution. In case that an optimal solution does not exist, it provides the best solution, the constraints that cannot be satisfied and the remedial actions necessary to satisfy the operating constraints. Numerical examples indicate that the proposed algorithm converges fast and the convergence speed is not affected by system size.