Skip to main content

​
Summary

The Transformer Loss Model calculates power dissipation in step-up transformers using a quadratic loss equation derived from no-load and full-load loss specifications. This model is shared by both MV transformers (array level) and HV transformers (plant level). It accounts for constant no-load (core) losses and load-dependent (winding) losses that scale with the square of the loading fraction.

​
Inputs

NameSymbolUnitsDescription
Power InputPinP_{in}WAC power into the transformer
Transformer RatingSratedS_{rated}kVATransformer nameplate capacity
No-Load LossLNLL_{NL}—No-load loss as a fraction of SratedS_{rated}
Full-Load LossLFLL_{FL}—Full-load loss as a fraction of SratedS_{rated} (incremental, added to LNLL_{NL})

​
Outputs

NameSymbolUnitsDescription
Power OutputPoutP_{out}WAC power after transformer losses
Transformer LossLtransL_{trans}WPower dissipated in the transformer

​
Detailed Description

​
Loss Components

The no-load and full-load loss fractions are converted to absolute power values: LNL,abs=LNL×SratedL_{NL,abs} = L_{NL} \times S_{rated} LFL,abs=(LNL+LFL)×SratedL_{FL,abs} = (L_{NL} + L_{FL}) \times S_{rated} The load-dependent loss component is the difference between full-load and no-load losses: Lload=LFL,abs−LNL,absL_{load} = L_{FL,abs} - L_{NL,abs} No-load losses represent core magnetization losses that are present whenever the transformer is energized, regardless of loading. Load-dependent losses represent resistive (I²R) winding losses that increase with the square of the current.

​
Quadratic Loss Equation

The transformer loss is computed from the quadratic relationship between input power and dissipated power: Ltrans=12 Lload(Srated2+2 Lload Pin−SratedSrated2+4 Lload (Pin−LNL,abs))L_{trans} = \frac{1}{2\, L_{load}} \left( S_{rated}^2 + 2\, L_{load}\, P_{in} - S_{rated} \sqrt{S_{rated}^2 + 4\, L_{load}\, (P_{in} - L_{NL,abs})} \right) This equation is derived from the standard transformer equivalent circuit, where total loss equals the sum of a constant no-load term and a term proportional to the square of the load fraction. The quadratic formulation accounts for the fact that as load increases, the additional winding losses also reduce the power available at the output. The output power is: Pout=Pin−LtransP_{out} = P_{in} - L_{trans}

​
Guard Conditions

The quadratic model requires non-zero load losses to avoid division by zero:
  • Version 3: both LNL>0L_{NL} > 0 and LFL>0L_{FL} > 0 are required.
  • Version 4+: only LFL≥0.0001L_{FL} \geq 0.0001 is required (allows zero no-load loss).
When the guard condition is not met, the transformer is treated as lossless (Ltrans=0L_{trans} = 0).

​
Nighttime Disconnect

When nighttime disconnect is triggered (all inverters in the array are in shutdown or low-power regions), the no-load loss is set to zero for MV transformers, effectively disconnecting the transformer from the grid and eliminating standby core losses. HV transformer nighttime behavior depends on whether any array in the plant triggers disconnect.

​
Application Points

This model is applied at two levels in the prediction:
  • MV Transformer (array level): applied after auxiliary load deductions, before AC collection losses. See Array-Level AC Losses.
  • HV Transformer (plant level): applied after block aggregation, in user-defined ordinal sequence with transmission lines. See Plant-Level AC Losses.

​
References

  • IEEE Std C57.12.00. IEEE Standard for General Requirements for Liquid-Immersed Distribution, Power, and Regulating Transformers.