Embodiments of the disclosure includes operating a power grid, including: generating, by a power management system of the power grid, a power grid resource allocation profile indicative of an operation of the power grid constrained by operational information of the power grid; generating a difference between a value of upper bounds from a plurality of obtained convergence paths and a value of lower bounds from the obtained convergence paths, the obtained convergence paths being based on a plurality of different initial conditions for the generated power grid resource allocation profile; and generating a resource allocation schedule for power grid resources operating within the power grid if the generated difference is smaller than a pre-determined threshold, the resource allocation schedule corresponding to a convergence path associated with the value of the upper bounds, the resource allocation schedule being configured to be received at the power grid resources.