| Title |
Investigation of Mathematical Models for Power System Analysis and Optimal Dispatch with Droop-Controlled Inverters |
| Authors |
임성수(Seong-Su Lim) ; 김경훈(Gyeong-Hun Kim) ; 이진오(Jin-Oh Lee) |
| DOI |
https://doi.org/10.5370/KIEE.2026.75.5.1029 |
| Keywords |
Dead-band; Droop-Controlled Inverters; Mixed-integer linear programming; Optimal power flow; Power flow; Power flow |
| Abstract |
Inverter-based resources are rapidly increasing across distribution networks, so steady-state analysis and operational optimization must faithfully capture their grid-support behavior, especially Volt-Var droop with a dead-band. However, the deadband creates a non-differentiable point at the boundary, which can delay or derail Newton-Raphson power flow (PF) convergence. In optimal power flow (OPF), the droop relation follows different rules across regions, and it cannot be posed directly with conditional statement inside an optimization model. To address these issues, the PF model smooths the dead-band boundary with a circular and cubic spline, and uses an analytic Jacobian to achieve reliable convergence. The OPF model expresses the droop relation through linear equality and inequality constraints, selecting the active region with binary variables so the formulation remains a mixed-integer linear programming without conditional statement. This paper validates the proposed models through case studies with multiple inverters, confirming stable PF convergence, plausible reactive-power sharing, and economically coherent dispatch, while quantifying how the dead-band width and droop slope influence voltage profiles and operating cost. |