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MV Transformers connected in cascade

In the present time, PVsyst supposes that each MV transformer is connected to a common point (input of the HV inverter or injection point) by an individual cable ("star" connexion). You have to specify the sizes (length and section) of this cable.

Transformers in cascade

In some installations, the MV transformers are connected in cascade on a single bus line, up to the injection point.

Transfos in cascade

This configuration is not yet implemented in PVsyst. As a workaround, we have to evaluate the global ohmic loss with this configuration, and define the wire lengths of the PVsyst model in such a way that the simulation calculates the same losses.

Global ohmic loss calculation

Remember that for a single conductor, the ohmic loss is calculated as \(PLoss = Resistance * Current²\) where \(Resistance[ohm] = rho[ohm·mm²/m] / section[mm2] * length [m]\)

Let us call:

  • ResL = rho / section [ohm/m], the linear resistance,
  • Length1 = length from the transfo #1 to the transfo #2
  • Length2 = length from the transfo #2 to the transfo #3
  • Length3 = length from the transfo #3 to the injection point
  • I1, I2, I3 the currents out of each transfo,

Then the loss in each section is:

  • \(Ploss1 = ResL1 * Length1 * I1²\)
  • \(Ploss2 = ResL2 * Length2 * (I1 + I2)²\)
  • \(Ploss3 = ResL2 * Length3 * (I1 + I2 + I3)²\)

=> PLosstotal, the global loss is the sum of these 3 contributions.

Simplification

Now for a better understanding of the issues, let's suppose that the currents and the cable sections are identical.

  • \(PLoss_{total} = ResL * (Length1 * I1² + Length2 * 4 * I1² + Length3 * 9 * I1²)\)
  • \(PLoss_{total} = ResL * (Length1 + Length2 * 4 + Length3 * 9) * I1²\)

(and so on if more than 3 transfos, with the square of the upstream number of transfos).

Ohmic loss in PVsyst calculation

Now we should ensure that the calculation of PVsyst leads to the same loss:

\(PLoss_{TotPVSyst} = ResL * (Length1_{PVS} + Length2_{PVS} + Length3_{PVS}) * I1²\)

If the currents and sections are the same, there is no constraint for the allocation of a part of the loss to a given transformer. You can do what you want as long as

\((Length1_{PVS} + Length2_{PVS} + Length3_{PVS}) = (Length1 * 1 + Lenght2 * 4 + Lenght3 * 9)\)

The easiest choice (without significant meaning) could be to allocate identical lengths:

\(Length1_{PVS} = (Length1 * 1 + Lenght2 * 4 + Lenght3 * 9) / 3\)

Intuitively, when we have a long line for the section 3 up to the injection, if we neglect Length1 and Length2, this would mean that the loss attributed to each transformer is the third of the Length3 line.

You can of course do the same calculation explicitly with the real data of your system (different currents and sections).

NB: Here the cable section has to be sized for the global current of all transformers. For sparing material, the cable section in the first and second intervals could be lower. However this is not possible in the present version of PVsyst: as the lines are "independent" up to the injection, all the sections are supposed identical.

If you have several transformer groups, each connected to the injection point by a single line, you should apply the same procedure to each group.

Future versions

This calculation should be done in detail in a future version of PVsyst. This requires that we explicitly define a list of transformers, in order to identify the upstream currents.