Loadability Limits Under Periodic Load Forcing

Abstract

The static loadability limit, defined as the demand at which the equilibrium equations lose their solution, is the standard basis for interconnection screening of large new loads. This letter shows that when part of the demand varies periodically, as for data-center loads, the steady state is a forced periodic orbit whose loadability limit differs from the static one. The classical optimization argument is extended directly from equilibria to fixed points of the period map. At the limit, the monodromy matrix acquires a Floquet multiplier at +1, so the generic instability is a cyclic fold of the orbit rather than a saddle-node of equilibria. The limit is therefore a function of the forcing frequency, which no static computation can capture. Additionally, with the network Jacobian turning singular along the cycle, singularity-induced instability is extended to orbits. On a four-bus test system, a static margin of 2.5 p.u. shrinks to 0.53 p.u. near the swing frequency, the instability mechanism switches from voltage collapse to a rotor-angle fold, and cold starts fail at amplitudes where the orbit still exists. A static analysis reproduces none of these effects.