Two-Layer HVDC Frequency Coordination with Local Energy Constraints and Planned Support Withdrawal

Finite-energy frequency support through multiple high-voltage direct-current (HVDC) links requires coordination of power delivery, device constraints, and support withdrawal, because maximizing the initial response can exhaust a source too early or deepen the frequency minimum after support ends. This paper develops a two-layer method that separates the energy supplied to a synchronous system by asynchronously connected sources from the power redistributed inside it by embedded links. A local scalar projection enforces the present source and capacitor constraints at every converter, with explicit conditions for discrete invariance, bounded-error sampled execution, finite-rate withdrawal, and the capacitor discharge time. A causal regional linear program allocates support over time and constrains the frequency response after the scheduled withdrawal; its feasibility condition is derived in terms of the remaining source energy, and late calculations or expired instructions revert to local frequency response. In a two-area benchmark with 900 MJ of source energy and a 20 MW internal transfer limit, 5 Hz coordination reduces the maximum frequency depression by 17.38% and 13.83% relative to independently searched static gains, and three-phase average-value electrical realization retains 16.57% and 13.25%. In 70 newly executed plant-perturbation cases with load damping, governor, secondary, inertia, and tie-line parameters varied by up to 20%, the controller improves on fixed droop in every case and on the searched static gains in 63, without device-limit violations; in a three-area extension with three stations the reductions are 6.60% to 17.55% relative to searched static gains and 38.04% to 42.05% relative to fixed droop. Measured calculation times identify the linear program as the only real-time bottleneck and quantify how its size grows with the number of areas and stations.