> ## 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.

# Degradation Losses (AC Applied)

export const EnergizationDate = () => <Tooltip tip="Date when a PV system block is first connected to the grid; reference point for degradation calculations.">
    energization date
  </Tooltip>;

export const Clipping = () => <Tooltip tip="Condition where DC power exceeds the inverter's rated AC capacity; the inverter moves off the maximum power point to limit output.">
    clipping
  </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>;

export const LeTID = () => <Tooltip tip="Light and Elevated Temperature Induced Degradation: partially reversible efficiency loss from carrier-induced defects at elevated temperatures.">
    LeTID
  </Tooltip>;

## Summary

Degradation Losses (AC Applied) model the time-dependent reduction in PV system output due to module aging and performance decline. PlantPredict offers five degradation models—None, Linear DC, Non-Linear DC, Linear AC, and Stepped AC—differing in where the loss is applied (DC power upstream of the <Inverter /> vs. AC power downstream of the inverter) and how the rate evolves over time (constant, continuous, or annual steps). This page documents the two AC-applied models and the optional AC-applied <LeTID /> model. For DC-applied degradation, see [Degradation Losses (DC Applied)](../inverter-models/degradation_dc_applied).

## Inputs

| Name                        | Symbol                 | Units    | Description                                    |
| --------------------------- | ---------------------- | -------- | ---------------------------------------------- |
| **AC Power**                | $P_{AC}$               | W        | AC power from inverter efficiency model        |
| **Energization Date**       | $t_0$                  | datetime | Block energization date (system commissioning) |
| **Linear Degradation Rate** | $r_{deg}$              | %/year   | Annual degradation rate (linear or stepped)    |
| **LeTID Annual Rates**      | $[l_0, l_1, ..., l_n]$ | %/year   | Per-year LeTID rates starting at year 0        |

***

## Outputs

| Name                  | Symbol       | Units | Description                   |
| --------------------- | ------------ | ----- | ----------------------------- |
| **Degraded AC Power** | $P_{AC,deg}$ | W     | AC power after degradation    |
| **Degradation Loss**  | $L_{deg}$    | W     | Power loss due to degradation |
| **LeTID Loss**        | $L_{LeTID}$  | W     | Power loss due to LeTID       |

***

## Detailed Description

### Application Point

When Linear AC or Stepped AC degradation is selected, degradation is applied to AC power at the array level, after summing inverter outputs and before auxiliary loads and transformer losses. Because degradation is applied after inverter conversion, AC-applied models do not affect <Clipping /> behavior—unlike DC-applied models, which reduce the power the inverter sees and can change the operating point as modules age (see [Degradation Losses (DC Applied)](../inverter-models/degradation_dc_applied)).

Before the <EnergizationDate />, the system is not yet commissioned, so all models set $P_{AC,deg} = 0$.

### No AC Degradation (None, Linear DC, Non-Linear DC)

When None, Linear DC, or Non-Linear DC degradation is selected, no AC-level degradation is applied:

$$
U_{deg} = 0
$$

$$
P_{AC,deg} = P_{AC}
$$

### Linear AC Degradation

Linear AC degradation applies a constant annual rate $r_{deg}$ over the system lifetime. Degradation accumulates from the energization date $t_{onset} = t_0$ when First Year Degradation is enabled, or from $t_{onset} = t_0 + 1$ year when disabled. The degradation coefficient is:

$$
U_{deg} = r_{deg} \cdot \Delta t
$$

where $\Delta t = \max(t - t_{onset},\, 0)$ is the elapsed time expressed as a fractional number of years (using an 8760-hour year). The degraded power is:

$$
P_{AC,deg} = (1 - U_{deg}) \times P_{AC}
$$

$$
L_{deg} = P_{AC} - P_{AC,deg} = U_{deg} \times P_{AC}
$$

### Stepped AC Degradation

Stepped AC degradation applies the same constant annual rate $r_{deg}$ but in discrete annual increments rather than continuously. Degradation onset follows the same First Year Degradation logic as Linear AC: $t_{onset} = t_0$ when First Year Degradation is enabled, or $t_{onset} = t_0 + 1$ year when disabled. The degradation coefficient is:

$$
U_{deg} = r_{deg} \times \left\lceil \frac{\Delta h}{8760} \right\rceil
$$

where $\Delta h$ is the number of hours since $t_{onset}$ ($\Delta h = (t - t_{onset}) \times 24$ if $t > t_{onset}$, $\Delta h = 0$ otherwise) and $\lceil \cdot \rceil$ denotes the ceiling function (round up to the nearest integer). Because of the ceiling, each degradation step takes effect at the start of the year—the first step applies immediately once $t > t_{onset}$. With First Year Degradation enabled, the system degrades from the moment of energization. Versions 3–4 used a floor function ($\lfloor \cdot \rfloor$) instead, which deferred each step to the end of the year.

The degraded power is:

$$
P_{AC,deg} = (1 - U_{deg}) \times P_{AC}
$$

$$
L_{deg} = P_{AC} - P_{AC,deg} = U_{deg} \times P_{AC}
$$

### Light and Elevated Temperature Induced Degradation (LeTID)

<LeTID /> is an additional degradation mechanism that can be enabled independently of the primary degradation model. Unlike conventional degradation, LeTID is partially reversible—modules typically degrade over the first few years of operation, then partially recover (Repins et al., 2020). Per-year rates $l_i$ can therefore be negative in later years to capture this recovery.

LeTID losses are reported separately from primary degradation. When Linear AC or Stepped AC degradation is selected, LeTID is applied at the AC level. The algorithm uses the same cumulative approach as Non-Linear DC degradation (see [DC degradation](../inverter-models/degradation_dc_applied)):

$$
U_{LeTID} = \sum_{i=0}^{\lfloor \Delta t \rfloor - 1} l_i + \left( \Delta t - \lfloor \Delta t \rfloor + \frac{n_{leap}}{365} \right) \times l_{\lfloor \Delta t \rfloor}
$$

where $\Delta t$ is the elapsed time in fractional years (with leap days excluded from the year length), $\lfloor \Delta t \rfloor$ is the number of complete years elapsed, and $n_{leap}$ is the count of February 29th occurrences between $t_0$ and $t$. The first term sums the rates of all complete years; the second term pro-rates the current year's rate.

$$
L_{LeTID} = U_{LeTID} \times P_{AC}
$$

When both primary degradation and LeTID are active, their losses are additive:

$$
P_{AC,deg} = P_{AC} - L_{deg} - L_{LeTID}
$$

***

## References

* Jordan, D. C., & Kurtz, S. R. (2013). *Photovoltaic degradation rates—an analytical review.* Progress in Photovoltaics: Research and Applications, 21(1), 12–29. DOI: [10.1002/pip.1182](https://doi.org/10.1002/pip.1182)
* Repins, I., et al. (2020). *Light and elevated temperature induced degradation (LeTID) in a utility-scale photovoltaic system.* IEEE Journal of Photovoltaics, 10(4), 1084–1092. DOI: [10.1109/JPHOTOV.2020.2989168](https://doi.org/10.1109/JPHOTOV.2020.2989168)
* Kersten, F., Engelhart, P., et al. (2015). *Degradation of multicrystalline silicon solar cells and modules after illumination at elevated temperature.* Solar Energy Materials and Solar Cells, 142, 83–86. DOI: [10.1016/j.solmat.2015.06.015](https://doi.org/10.1016/j.solmat.2015.06.015)