> ## 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 (DC 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 (DC 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, per-year schedule, or annual steps). This page documents the two DC-applied models and the optional DC-applied <LeTID /> model. For AC-applied degradation, see [Degradation Losses (AC Applied)](../ac-losses/degradation_ac_applied).

## Inputs

| Name                             | Symbol                 | Units    | Description                                            |
| -------------------------------- | ---------------------- | -------- | ------------------------------------------------------ |
| **DC Operating Power**           | $P_{DC}$               | W        | DC power from DC field aggregation, before degradation |
| **Energization Date**            | $t_0$                  | datetime | Block energization date (system commissioning)         |
| **Linear Degradation Rate**      | $r_{deg}$              | %/year   | Annual degradation rate                                |
| **Non-Linear Degradation Rates** | $[r_0, r_1, ..., r_n]$ | %/year   | Per-year degradation rates starting at year 0          |
| **LeTID Annual Rates**           | $[l_0, l_1, ..., l_n]$ | %/year   | Per-year LeTID rates starting at year 0                |
| **Current Timestamp**            | $t$                    | datetime | Simulation timestamp for the current timestep          |

***

## Outputs

| Name                  | Symbol       | Units | Description                                                  |
| --------------------- | ------------ | ----- | ------------------------------------------------------------ |
| **Degraded DC Power** | $P_{DC,deg}$ | W     | DC power after degradation, passed to operating-region logic |
| **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 DC or Non-Linear DC degradation is selected, degradation is applied to the aggregated DC power after DC field aggregation and before the inverter determines its operating region. Because the inverter sees the already-degraded DC power, DC-applied degradation can affect the <Clipping /> behavior: a system that clips in early years may stop clipping as modules degrade.

AC-applied degradation models, by contrast, are applied after inverter conversion and do not affect clipping behavior. Before the <EnergizationDate />, the system is not yet commissioned, so all models set $P_{DC,deg} = 0$.

### No DC Degradation (None, Linear AC, Stepped AC)

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

$$
U_{deg} = 0
$$

$$
P_{DC,deg} = P_{DC}
$$

### Linear DC Degradation

Linear 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:

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

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

### Non-Linear DC Degradation

Non-linear degradation specifies a separate rate $r_i$ for each year $i$ of operation, always starting from the energization date (no delayed onset option). Elapsed time $\Delta t$ is normalized to a 365-day year by subtracting leap days from the total elapsed time. The cumulative degradation sums all complete years plus a pro-rated portion of the current year:

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

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

**Example:** $t_0$ = January 1, 2027 00:00 and $t$ = March 15, 2033 00:00. There are 2265 elapsed days, with $n_{leap} = 2$ (February 29 in 2028 and 2032). Then $\Delta t = (2265 - 2)/365 = 6.2$, so $\lfloor \Delta t \rfloor = 6$ and the pro-rated fraction is $0.2 + 2/365 \approx 0.205$. The cumulative degradation is $U_{deg} = r_0 + r_1 + r_2 + r_3 + r_4 + r_5 + 0.205 \times r_6$.

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

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

### 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 and are applied at the same level (DC for Linear DC/Non-Linear DC, AC for Linear AC/Stepped AC). The algorithm uses the same cumulative approach as Non-Linear DC degradation:

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

where $\Delta t$, $\lfloor \Delta t \rfloor$, and $n_{leap}$ follow the same definitions as for Non-Linear DC degradation.

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

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

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

***

## 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)