Intensional Maxwellian Formalism in Power Electronics: Causal Octonion Control of Distributed Multi-Phase Converters

Conventional power electronics rely on extensional mathematics, where physical phenomena are treated as memoryless, state-independent variables. This paper introduces a two-layer intensional formalism for the control of multi-phase Maximum Power Point Tracking (MPPT) converters, restoring James Clerk Maxwell’s original hypercomplex architecture. The first layer utilizes non-associative octonion algebra (O) to act as a hidden causal memory, accumulating material fatigue, thermal drift, and magnetic core saturation, enforcing the intensional axiom where the identity of origin alters the value (x * x != x^2). The second layer computes observable control parameters via tensor calculus (T_mu_nu). The causal history from the octonion layer is projected into the observable tensor layer exclusively through the octonion associator [X, Y, Z], which precisely quantifies the physical energy loss and material non-linearity. Implemented on a standard 170 MHz Cortex-M4 microcontroller running at a fixed 30 kHz frequency, the architecture evaluates 4 critical causal associators per micro-cycle, consuming only 42.3% of the CPU instruction time. Furthermore, this intensional framework inherently resolves the distributed consensus problem, enabling sensorless, wire-free phase-locking of a converter swarm via discrete Frequency Shift Keying over the shared DC bus.