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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:
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For an unbalanced line, Tv is the solution of the following equation:
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Where lambda is a diagonal matrix containing the eigenvalues of the matrix product ZY.
For a balanced line:
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Calculate three mode currents using a single phase line equation (represent each mode).
Convert three modes current into three-phase currents.
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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:
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where
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