### How are the apparent power parameters calculated?

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These are the different Apparent Power variables which can be selected in the flexible data page of a transformer or line. Using the transformer as an example:

m:Smax:bushv (Maximum power)

m:Ssum:bushv (Total Apparent Power)

m:S:bushv (Apparent Power)

Smax is calculated as:

Smax = sqrt(3) * | Imax (bus index) | * Un (bus index),

where

Imax (bus index) = current in kA of the corresponding side of the element, and

Un (bus index) = nominal voltage of the busbar in kV (of the corresponding side).

For a normal load flow, with the Low Voltage Analysis option not selected, Imax will be the same as I.

For a balanced load flow calculation, Ssum and S (i.e. apparent power) are both the same:

Ssum = sqrt(3)* | (I’ (bus index) * Ul (bus index)) |,

where

I’ (bus index) = complex current in kA of the corresponding side (but conjugate), and

Ul (bus index) = line-line voltage at bus in kV (of corresponding side)

Ssum = | Sa + Sb + Sc |

where

Sa = (Ia’ (bus index) * Ua (bus index)) -> apparent power of phase A (complex)

Sb = (Ib’ (bus index) * Ub (bus index)) -> apparent power of phase B (complex)

Sc = (Ic’ (bus index) * Uc (bus index)) -> apparent power of phase C (complex)

and

Ia, Ib, Ic are the phase currents in kA of corresponding side, and

Ua, Ub, Uc are the line-to-ground voltages at bus in kV (of corresponding side)

The apparent power of each phase is given by:

S:A = |Sa|

S:B = |Sb|

S:C = |Sc|

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