IEEE-Compliant Electrical Engineering Calculators

Full IEEE 1584-2018 empirical model. Calculates incident energy, PPE category, and arc flash boundary for all five electrode configurations across the 208 V–15 kV range. Includes 3-D surface visualisation, sensitivity table, and citable output.

Full ANSI/IEEE point-to-point method (IEEE 551-2006 / IEEE 141-1993). Calculates symmetrical and asymmetrical fault currents, X/R ratio, peak Kp factor, and equipment duty for utility + transformer + cable systems. Supports 3-phase, SLG, LL, and DLG faults with motor contribution.

A rigorous treatment of electromagnetism as differential geometry. Maxwell's equations as dF = 0 and d⋆F = J on any manifold, the six validity regimes, regime boundaries as Morse critical points, and the Berry phase as holonomy of the electromagnetic connection.

Decomposes all 46 branch flows in the IEEE 39-bus New England test system into tree (scheduled) and loop (circulating) components using the 8 fundamental cycles of the network's cycle space. Visualises the holonomy of the voltage angle connection and identifies dominant circulating cycles. No free web tool exists for this.

Computes the weighted graph Laplacian of the IEEE 39-bus New England test system, extracts the Fiedler value (algebraic connectivity λ₂) and Fiedler vector via Jacobi eigendecomposition, and ranks all 46 N-1 contingencies by their impact on network connectivity. Visualises the natural partition, identifies islanding contingencies, and shows how the bisection boundary shifts under each outage. No equivalent free browser tool exists.

Checks the Heaviside distortionless condition (R/L = G/C) for any RLGC transmission line, designs Pupin loading coils (inductance per coil, spacing, cutoff frequency), and plots attenuation and phase velocity vs frequency for original, loaded, and ideal distortionless lines. Covers the 1858 KR problem, Heaviside's 1887 derivation, and Pupin's 1900 patent. No equivalent free browser tool exists.

Demonstrates that arc flash energy (IEEE 1584-2018), fault current decomposition (Fortescue), loop flows (Kirchhoff cycle space), algebraic connectivity (Fiedler/Cheeger), regime boundaries (Morse), and transmission line propagation (Heaviside/Atiyah-Singer) are six orthogonal measurements of the same admissible state space boundary ∂𝒜. The Atiyah-Singer index theorem (1963) is the keystone: the analytical index of the propagation operator equals the topological index of the network manifold.