A rotational transform for reducing large circuits preserving a regional centroid

A rotational transform is described that has been developed to reduce a large linear electrical system into an equivalent system of reduced size. The transform is a power-invariant transform not unlike n-port reduction. However, where n-port reduction will eliminate nodes (or loops) entirely from a circuit, this reduction instead will replace these nodes (loops) with a single equivalent node (loop). The significance of the transform is found in the usefulness of the equivalent node. The voltage magnitude and angle are open to free choice, and this choice can be judiciously made to preserve desired properties of the reduced regions of the circuit.<>