  This paper discusses the modeling of inverters used in distributed energy
resources in steady state. Modeling the interaction between distribution grids
and inverter-based resources is crucial to understand the consequences for the
network's operational and planning processes. This work highlights the
limitations of existing models and emphasizes the need for better
representations of inverters and their control laws in decision-making
contexts. Improved steady-state grid-following and grid-forming inverter models
are presented, including both three-leg and four-leg converter variants. The
advantages of these improved models in mathematical optimization contexts are
showcased by investigating the power quality improvement capabilities of the
inverters. Numerical studies integrating the proposed inverter models in a
four-wire unbalanced optimal power flow engine are presented, and trade-offs
between modeling detail and computational intensity are illustrated.
