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Summary

The Transformer Loss Model calculates power dissipation in step-up using a quadratic loss equation derived from no-load and full-load loss specifications. This model is shared by both transformers (array level) and 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.

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Inputs

NameSymbolUnitsDescription
Power InputPinP_{in}WAC power into the transformer
Transformer RatingPratedP_{rated}kVA (MV) / MVA (HV)Transformer nameplate capacity
No-Load LossLNLL_{NL}%No-load loss as a percentage of PratedP_{rated}
Full-Load LossLFLL_{FL}%Load-dependent (winding) loss as a percentage of PratedP_{rated}

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Outputs

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

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Detailed Description

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Loss Components

The input percentages are first converted from percentages to fractions (÷100\div 100) and the transformer rating is converted to VA (×1000\times 1000 for MV, ×106\times 10^6 for HV). The absolute loss values are then: LNL,abs=LNL×PratedL_{NL,abs} = L_{NL} \times P_{rated} LFL,abs=(LNL+LFL)×PratedL_{FL,abs} = (L_{NL} + L_{FL}) \times P_{rated} 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.

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Quadratic Loss Equation

The physical loss model states that total transformer loss is the sum of a constant no-load term and a winding term proportional to the square of the loading fraction: Ltrans=LNL,abs+LFLPrated Pout2L_{trans} = L_{NL,abs} + \frac{L_{FL}}{P_{rated}}\, P_{out}^2 Since Pout=Pin−LtransP_{out} = P_{in} - L_{trans}, the output power appears on both sides. Substituting: Ltrans=LNL,abs+LFLPrated(Pin−Ltrans)2L_{trans} = L_{NL,abs} + \frac{L_{FL}}{P_{rated}} \left( P_{in} - L_{trans} \right)^2 Expanding and rearranging yields a quadratic equation in LtransL_{trans}. Both roots are real and positive; the smaller root is the physically meaningful solution (the larger root exceeds PinP_{in}): Ltrans=12 LFL(Prated+2 LFL Pin−Prated2+4 LFL Prated (Pin−LNL,abs))L_{trans} = \frac{1}{2\, L_{FL}} \left( P_{rated} + 2\, L_{FL}\, P_{in} - \sqrt{P_{rated}^2 + 4\, L_{FL}\, P_{rated}\, (P_{in} - L_{NL,abs})} \right) The output power is: Pout=Pin−LtransP_{out} = P_{in} - L_{trans} If LFL=0L_{FL} = 0 the transformer is treated as lossless (Ltrans=0L_{trans} = 0).

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Nighttime Disconnect

When is enabled and any in an array triggers it (see Inverter Operating Regions for disconnect triggers), the MV transformer no-load loss is set to zero, effectively disconnecting it from the grid and eliminating standby core losses. For HV transformers, disconnect cascades from the array level: if any inverter in the plant triggers disconnect, all HV transformer no-load losses are set to zero. Additionally, plant output after HV equipment is set to zero if any inverter in the plant triggers disconnect.

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Application Points

This model is applied at two levels in the prediction:

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References

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