Examination of Three Different ACOPF Formulations With Generator Capability Curves

This paper examines three different formulations of AC optimal power flow problem and compares performance of well-established general-purpose optimization algorithms for each, over different initial conditions. Polar power-voltage, rectangular power-voltage, and rectangular current-voltage are formulated to evaluate ACOPF solution characteristic. The formulation here maintains line flows as explicit variables and employs summations of these quantities to impose conservation conditions at each node. Two representations of line thermal limits are considered, one using real power (to allow comparisons to dc power flow approximations), and a more physically based ampacity limit using current magnitude. Nonlinear generator capability curves are represented (“D-curves”), including options to allow active and reactive limits dependent on generator voltage. A uniform objective function is used throughout, that of minimizing quadratic generator operating cost curves. Numerical performance case studies are performed for these formulations over six different classes of initial conditions, evaluating computational time and also robustness of convergence.