Electromagnetic Transients (EMT)

This directory documents electromagnetic transient (EMT) model specifications and reusable operators in instantaneous phase coordinates.

Note

The formulation supports \(N\) phases; initial development targets three phases.

Conventions

  • \(N\) denotes a phase or output dimension, \(K\) a conductor or input dimension, \(M\) a mode count, and \(Q\) a pole count.

  • Corresponding calligraphic symbols denote index sets, such as \(\mathcal{M}\) for modal indices and \(\mathcal{Q}\) for pole indices.

  • Equations use SI units unless a model states otherwise.

  • Time derivatives are written explicitly as \(\mathrm{d}(\cdot)/\mathrm{d}t\).

  • Current injection terms are written as positive into buses.

  • \(\mathrm{j}\) denotes the imaginary unit and is not used as an index.

  • The Model Variables section lists DAE variables owned directly by the model. Each scalar internal variable corresponds to one local residual row; external variables are owned elsewhere. Submodel-owned variables are not repeated by the parent.

  • Wiring introduces aliases or derived signals, not DAE variables or residual rows. Ports and monitors may expose either without changing ownership.

  • Equation headings follow the assembled DAE row classification; connected models may add derivative terms to a residual that contains none locally.

Assembly

Bus voltage is algebraic unless a connected model contributes a voltage derivative to the bus current-balance.

Initialization

EMT models are initialized using real-valued, instantaneous phase-coordinate quantities in \(\mathbb{R}^N\). RMS or phasor calculations, when used by an upstream initialization workflow, are outside the EMT model specification.

Initial differential states, algebraic variables, derivatives, and discrete inputs must be consistent with the assembled EMT equations at \(t_0\). Models that require additional history document that requirement locally.

Contents

References