Comparative analysis of loss-aware optimal power flow considering droop-controlled inverters

The rapid integration of renewable energy sources into distribution networks necessitates advanced voltage regulation strategies, such as smart inverter Volt-VAR droop control with dead-bands. However, conventional linearized optimal power flow (OPF) models frequently overlook network losses, resulting in suboptimal reactive power allocation. This study presents a comparative analysis of three loss-aware OPF formulations tailored for inverter-dominated grids employing piecewise linear droop control. The iterative mixed-integer linear program (MILP) linearizes quadratic loss terms using successive Taylor expansions within a trust-region framework. The mixed-integer quadratically constrained quadratic program (MIQCQP) relaxes nonconvex loss equalities into convex quadratic inequalities, incorporating a reactive loss penalty. The two-stage MILP + AC-OPF enforces the full nonlinear AC power flow equations as optimization constraints. These formulations are evaluated on a combined IEEE 30-bus and 33-bus transmission–distribution system under four scenarios that vary photovoltaic (PV) capacity, flexible AC transmission system (FACTS) device availability, and inverter reactive power limits, and on a modified 250-bus T118D4 system with 40 PV inverters. The iterative MILP and MIQCQP converge to nearly identical generation costs. The AC-OPF achieves 1.0–2.3% lower generation costs and 5–20% lower reactive power losses through different reactive power allocations. All three formulations yield AC-feasible dispatches, but their reactive power allocations differ substantially, highlighting that AC feasibility alone does not ensure dispatch optimality. On T118D4, the MIQCQP more closely reproduces the AC-OPF voltage and reactive power dispatch, whereas the iterative MILP solves faster, revealing a tradeoff between agreement with the AC-OPF benchmark and computational efficiency.