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UCM | Line Model

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UCM | Line Model

Line Model

Conversion from 3 coupled phases into 3 decoupled modes

In a three-phase line, each phase is mutually coupled with other phases. To facilitate the line simulation, the EMTP uses a technique to convert a mutually coupled three-phase line into 3 decoupled, single-phase lines representing 3 decoupled modes.


In HYPERSIM®, lines are modeled as follows:

  • Get three phase node voltages at each terminal K and M,
  • Convert three phase voltages into three-mode voltages:


For an unbalanced line, Tv is the solution of the following equation:

Where lambda is a diagonal matrix containing the eigenvalues of the matrix product ZY.

Conversion from Three Coupled Phases into Three Uncoupled Modes

For a balanced line:


Calculate three mode currents using a single phase line equation (represent each mode).

Convert three modes current into three-phase currents.


Inject phase current to terminal nodes K and M.

Model of single-phase line


Each mode (0, 1, 2) can then be represented as shown in **. The current sources in this figure are given as:

where