GridStabilityControl
Recognition Science encodes grid stability controls as an inductive type with five constructors corresponding to inertia, primary frequency response, voltage support, demand response, and storage dispatch. Energy systems modelers cite this enumeration to fix configDim at five. The inductive declaration automatically provides decidable equality and finite type structure for subsequent cardinality proofs.
claimLet $C$ be the inductive type of grid stability controls generated by the constructors inertia, primary frequency response, voltage support, demand response, and storage dispatch.
background
The module on Grid Stability Controls from configDim posits that electric grid stability is achieved through exactly five canonical controls when the configuration dimension equals five. These controls correspond to rotational buffering via inertia, fast governor response via primary frequency response, reactive power management via voltage support, load-side control via demand response, and temporal energy shifting via storage dispatch. This enumeration supports the Recognition Science derivation of physical systems from the forcing chain and phi-ladder structures.
proof idea
The declaration is a direct inductive definition that lists the five constructors and derives DecidableEq, Repr, BEq, and Fintype.
why it matters in Recognition Science
The type feeds the cardinality theorem gridStabilityControl_count establishing five controls and the certification structure GridStabilityControlsCert. It realizes the energy depth of the framework by specifying the control space dimension as five, consistent with the configDim parameter in the model. The declaration closes the enumeration without open scaffolding.
scope and limits
- Does not assign numerical parameters or transfer functions to individual controls.
- Does not derive stability criteria or dynamical equations for the grid.
- Does not connect to specific values of phi or other constants from the Recognition Science units.
- Does not address interactions between the controls.
formal statement (Lean)
19inductive GridStabilityControl where
20 | inertia
21 | primaryFrequencyResponse
22 | voltageSupport
23 | demandResponse
24 | storageDispatch
25 deriving DecidableEq, Repr, BEq, Fintype
26