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AC Power Electromagnetics

Solve PDEs that model harmonic electrical fields in conductors

The AC power electromagnetics problems are found when studying motors, transformers, and conductors carrying alternating currents. The Helmholtz's equation

·(1μEc)+(jωσω2ε)Ec=0

describes the propagation of plane electromagnetic waves in imperfect dielectrics and good conductors (σ » ωε). Here, ω is the angular frequency, ε is the coefficient of dielectricity, µ is the magnetic permeability, and σ is the conductivity. Complex permittivity εc is εc = ε-/ω. The conditions at material interfaces with abrupt changes of ε and µ are typical for the variational formulation and do not require special attention.

The boundary conditions associated with AC power electromagnetics are a Dirichlet boundary condition, specifying the value of the electric field Ec on the boundary, and a Neumann condition, specifying the normal derivative of Ec. This is equivalent to specifying the tangential component of the magnetic field Ht=jωn·(1μEc).

For details, see AC Power Electromagnetics Equations.

Apps

PDE ModelerSolve partial differential equations in 2-D regions

Topics

Programmatic Workflow

Wave Equation on Square Domain

Use command-line functions to solve a wave equation.

Scattering Problem

Use command-line functions to compute reflected waves from an object illuminated by incident waves.

PDE Modeler App Workflow

Wave Equation on Square Domain: PDE Modeler App

Use the PDE Modeler app to solve a wave equation.

Scattering Problem: PDE Modeler App

Use the PDE Modeler app to compute reflected waves from an object illuminated by incident waves.

Skin Effect in Copper Wire with Circular Cross Section

Analyze the skin effect produced by AC current carried by a copper wire with circular cross section.

Algorithms and Other Theory

AC Power Electromagnetics Equations

Equations used by the PDE Modeler app in the AC Power Electromagnetics mode.