Admissible Unit Range of Plug-and-Play Distributed Energy Resource (DER) Systems Under Delay: A Scalable Design Framework

What the math gives to ML

The paper provides a constructive scalability mechanism for plug-and-play systems with variable unit count: normalize delay and aggregate loop gain, compute a stability boundary, impose an operational lower bound, and map the resulting feasible gain interval to an admissible number of connected units. Its transferable asset is the prediction that adding individually stable modules can destabilize an aggregate system, while delay can produce a non-monotonic feasible-capacity curve because implementation delay changes the effective loop gain. A neural analogue is a plug-and-play residual architecture whose number of blocks, experts, or graph updates is selected using measured latency and an aggregate Jacobian-gain budget rather than unconstrained stacking.