Linear/quadratic programming-based optimal power flow using linear power flow and absolute loss approximations

This paper presents novel methods to approximate the nonlinear AC optimal power flow (OPF) into tractable linear/quadratic programming (LP/QP) based OPF problems that can be used for power system planning and operation. We consider a linear power flow and branch flow approximation and derive a power loss approximation in the form of absolute value functions that are suitable to cover a broader operating range. The key ideas are (1) to capture power losses and power flows in the full decision variable domain, (2) to combine these approximations to recast the nonlinear constraints of the OPF problem into linear ones, and (3) to solve the approximate OPF problem with off-the-shelf solvers in a non-iterative fashion. In this way, the problem complexity can be reduced significantly. In detail, we present four OPF approximation methods, in which we relax the absolute power loss functions as linear constraints. In a comprehensive case study the usefulness of our OPF methods is analyzed and compared with an existing OPF relaxation and approximation method. As a result, the errors on voltage magnitudes and angles are reasonable, while obtaining near-optimal results for typical scenarios. We find that our methods reduce significantly the computational complexity compared to the nonlinear AC-OPF making them a good choice for power system planning purposes.