Harmonic optimal power flow with transformer excitation

Harmonics pose significant challenges to the operation of power systems, and active filters are a key technology to mitigate impacts. When there are multiple active filters in a network, they can be coordinated to achieve specific goals, e.g., provide maximal compensation at the point of common coupling. Mathematical optimization of power systems with representation of harmonics, i.e., harmonic optimal power flow, is a framework that develops solutions to such decision problems. This paper presents a formulation for harmonic optimal power flow in the rectangular current-voltage variable space, and solves it as a continuous nonlinear optimization problem. A key novelty of this work is the detailed treatment of transformers, and transformer harmonics due to saturation. Normally, transformer excitation is modeled in the time domain, so the inclusion of these effects in frequency-domain optimization models poses a nontrivial challenge, which is addressed here through a conversion to empirical multivariate nonlinear continuous functions (splines). The model is demonstrated numerically on a real-world test case.