arXiv:2611.06146v1 Announce Type: new Abstract: We study the coordination of primary and secondary frequency regulation by grid-forming battery energy storage systems in islanded microgrids. We formulate the coordination as a multi-period bilevel program, in which the upper level schedules secondary regulation setpoints and each lower level computes primary regulation decisions. Using the lower-level Karush-Kuhn-Tucker conditions, we obtain an exact single-level reformulation with complementarity constraints. To address the numerical difficulties introduced by these constraints, we develop a continuation method that couples the complementarity relaxation parameter with the interior-point barrier parameter and warm-starts successive stages. Under the stated boundedness assumptions and with vanishing subproblem residuals, we prove that every accumulation point is feasible and satisfies a first-order stationarity condition for the reformulated problem (C-stationarity). Numerical results for an islanded microgrid show that the proposed method reduces solution time by 89.3% and peak frequency deviation by 0.53% relative to conventional Scholtes relaxation.