Conservative Linear Line Flow Constraints for AC Optimal Power Flow

The AC optimal power flow problem is a nonconvex optimization problem that is difficult to solve quickly and reliably for large-scale grids. To enable the application of efficient and robust solution algorithms, various linear approximations of the nonlinear system model are used. However, this may lead to solutions that are AC suboptimal or even infeasible. This paper proposes new linearization techniques for constructing accurate line flow constraints that reduce the complexity of the AC optimal power flow problem without compromising the solution quality. In particular, it investigates the shape of the nonlinear constraints in polar coordinates and presents methods for producing conservative linear approximations with a desired accuracy. Numerical experiments are performed on systems with 118, 300 and 1354 buses. Obtained results indicate that the proposed formulation leads to a significant decrease in the computation time while at the same time providing high quality approximations of the exact line flows.