> ## Documentation Index
> Fetch the complete documentation index at: https://docs.plantpredict.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Transformer Loss Model

export const Transformers = () => <Tooltip tip="Devices connecting two AC circuits at different voltages; losses comprise constant no-load (core) and load-dependent (winding) components.">
    transformers
  </Tooltip>;

export const NighttimeDisconnectCap = () => <Tooltip tip="Operational mode that disconnects transformers and zeroes plant output when inverters are in shutdown or low-power regions.">
    Nighttime Disconnect
  </Tooltip>;

export const HV = () => <Tooltip tip="High Voltage: portion of a plant's electrical infrastructure connecting it to the utility grid via step-up transformers and transmission lines.">
    HV
  </Tooltip>;

export const MV = () => <Tooltip tip="Medium Voltage: electrical infrastructure between inverter output and the plant collection point, including step-up transformers and AC cabling.">
    MV
  </Tooltip>;

export const Inverter = () => <Tooltip tip="Power electronics device that sets the operating point on the DC array's I-V curve and converts DC to AC for grid injection.">
    inverter
  </Tooltip>;

## 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

| Name                   | Symbol      | Units               | Description                                                  |
| ---------------------- | ----------- | ------------------- | ------------------------------------------------------------ |
| **Power Input**        | $P_{in}$    | W                   | AC power into the transformer                                |
| **Transformer Rating** | $P_{rated}$ | kVA (MV) / MVA (HV) | Transformer nameplate capacity                               |
| **No-Load Loss**       | $L_{NL}$    | %                   | No-load loss as a percentage of $P_{rated}$                  |
| **Full-Load Loss**     | $L_{FL}$    | %                   | Load-dependent (winding) loss as a percentage of $P_{rated}$ |

***

## Outputs

| Name                 | Symbol      | Units | Description                         |
| -------------------- | ----------- | ----- | ----------------------------------- |
| **Power Output**     | $P_{out}$   | W     | AC power after transformer losses   |
| **Transformer Loss** | $L_{trans}$ | W     | Power dissipated in the transformer |

***

## Detailed Description

### Loss Components

The input percentages are first converted from percentages to fractions ($\div 100$) and the transformer rating is converted to VA ($\times 1000$ for MV, $\times 10^6$ for HV). The absolute loss values are then:

$$
L_{NL,abs} = L_{NL} \times P_{rated}
$$

$$
L_{FL,abs} = (L_{NL} + L_{FL}) \times P_{rated}
$$

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.

### 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:

$$
L_{trans} = L_{NL,abs} + \frac{L_{FL}}{P_{rated}}\, P_{out}^2
$$

Since $P_{out} = P_{in} - L_{trans}$, the output power appears on both sides. Substituting:

$$
L_{trans} = L_{NL,abs} + \frac{L_{FL}}{P_{rated}} \left( P_{in} - L_{trans} \right)^2
$$

Expanding and rearranging yields a quadratic equation in $L_{trans}$. Both roots are real and positive; the smaller root is the physically meaningful solution (the larger root exceeds $P_{in}$):

$$
L_{trans} = \frac{1}{2\, L_{FL}} \left( P_{rated} + 2\, L_{FL}\, P_{in} - \sqrt{P_{rated}^2 + 4\, L_{FL}\, P_{rated}\, (P_{in} - L_{NL,abs})} \right)
$$

The output power is:

$$
P_{out} = P_{in} - L_{trans}
$$

If $L_{FL} = 0$ the transformer is treated as lossless ($L_{trans} = 0$).

### Nighttime Disconnect

When <NighttimeDisconnectCap /> is enabled and any <Inverter /> in an array triggers it (see [Inverter Operating Regions](../inverter-models/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.

### 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 Aggregation and AC Losses](array_level_losses).
* **HV Transformer** (plant level): applied after block aggregation, in user-defined sequence with transmission lines. See [Plant-Level Aggregation and AC Losses](plant_level_losses).

***

## References

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