# Operational Performance and Degradation of PV Systems Consisting of Six Technologies in Three Climates

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## Abstract

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## 1. Introduction

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- Reading in available input data;
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- Data filtering;
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- Selection of performance metric;
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- Possible correction and data aggregation;
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- Application of the statistical method to calculate the final PLR.

_{t}is the data, S

_{t}is the seasonal component, T

_{t}is the trend-cycle component, and ε

_{t}is the remainder, all at period t. The “seasonality” component is a repeated pattern observed between regular intervals due to seasonal factors such as the time of the day or the month of the year. Seasonality in weather data related to PV systems shows the regular variation in the environmental conditions such as the irradiance, the spectral content, the angle of incidence (θ), the ambient temperature (${\mathrm{T}}_{\mathrm{amb}}$), and wind speed (ν) [14]. Seasonality affects both c-Si and thin-film technologies, although c-Si technologies are more dependent on temperature changes and spectral effects [15]. The “trend” component shows the overall increasing or decreasing slope of the metric over time. The “remainder” component is the activity that is not explained by the trend or the seasonal value. The remainder is also expressed as the “error”, “residual”, or “irregular” component.

## 2. Experimental Set-up

^{2}per year. The PV systems are located in Bolzano, Italy (EURAC), Pekanbaru, Indonesia (OTH Amberg-Weiden, maintained by UIN Suska Riau University), Cirata, Indonesia (PJB), and Alice Springs, Australia (Desert Knowledge Australia Solar Center (DKASC), maintained by Ekistica). The PV systems are located at the Southern hemisphere, with the highest irradiation of around 2245 kWh/m

^{2}/year, near the equator (around 1700 kWh/m

^{2}/year), and the Northern hemisphere, with the lowest irradiation (1400 kWh/m

^{2}/year).

^{2}is represented by several terms. They are beam or direct normal irradiance (DNI), diffuse horizontal irradiance (DHI), and ground-reflected irradiance on a horizontal surface (E

_{g}). The sum of all irradiances is global horizontal irradiance (GHI). On the plane of array (POA), also in W/m

^{2}, we use the in-plane terms, namely, in-plane global irradiance (G

_{POA}), in-plane beam irradiance (${\mathrm{G}}_{{\mathrm{b}}_{\mathrm{POA}}}$), in-plane diffuse irradiance (${\mathrm{G}}_{{\mathrm{d}}_{\mathrm{POA}}}$), and in-plane ground-reflected irradiance (${\mathrm{G}}_{{\mathrm{r}}_{\mathrm{POA}}}$). The terms used for irradiation in Watt-hours/m

^{2}are horizontal irradiation (H

_{h}) and POA irradiation (H

_{i}), which are the irradiance aggregated. Other important variables include T

_{amb}in °C, module temperature (T

_{m}) in °C, and wind speed (ν) in m/s.

_{POA}, is mandatory for PR calculation. If G

_{POA}was not available, it could be estimated from the global horizontal irradiance, GHI, using available decomposition and transposition models. Various empirical decomposition models that are commonly used have been tested by [38]. In general, they are used to estimate the diffuse horizontal irradiance, DHI, from measured GHI. Thereby, both parameters have the following relation.

_{s}is the solar elevation angle (°). All decomposition models use at least the clearness index, ${\mathrm{k}}_{\mathrm{t}}$, as input for computing ${\mathrm{k}}_{\mathrm{d}}$, while the other models require additional variables such as elevation angle, ambient temperature, or relative humidity (RH). All models can estimate both DHI and DNI effectively [38]. In this work, we use the Erbs decomposition model [39] due to simplicity because it requires only ${\mathrm{k}}_{\mathrm{t}}$ as the input variable to compute ${\mathrm{k}}_{\mathrm{d}}$.

_{POA}using Equation (4).

^{2}. Albedo is close to zero when the surface is very dark, and albedo is 1 when the surface is bright white, metallic, or a mirror. A ground albedo value of 0.2 is widely accepted and is used in the modeling of PV systems [40].

_{m}, was not available, it can be estimated using the Sandia module temperature model shown in Equation (7).

_{m}were implemented using PVLIB Python, initiated by Sandia National Laboratories and developed by the PVLIB community [43]. PVLIB calculations are documented on Sandia’s PV Performance Modelling Collaborative (PVPMC).

_{a}, of PV arrays and the temperature coefficient of the maximum output power (γ

_{Pmp}) of the PV modules. γ

_{Pmp}indicates how strongly the PV array power output depends on the cell temperature. It is a negative number because power output decreases with increasing cell temperature.

## 3. Methods

#### 3.1. Data Preparation

^{2}and above 1500 W/m

^{2}. For T

_{amb}, only values between −40 and 60 °C were used. For the module temperature, T

_{m}, values between T

_{amb}and T

_{amb}plus 30 °C were included [49]. Wind speed values, ν, between 0 to 30 m/s were included. (2) The data were thoroughly checked to ensure consistency and to detect gaps. Duplicates in the data were detected and removed. (3) Further general outlier removal was applied based on predefined criteria depending on the characteristic of the data. If a variable value, X, minus the population mean, μ, is greater than two times the standard deviation, σ, then that specific X value is an outlier, and it will be excluded.

#### 3.2. Calculation of the Performance Ratio

_{A}, and Equation (10) for the system level, PR. In this work, we use PR as one of the performance matrices to be evaluated.

_{A}, is the amount of energy produced by the array, E

_{dc}, from each installed rated power, P

_{0}, over the analysis period. Y

_{A}is equivalent to the number of hours over which the PV array produces its rated power and is defined by Equation (11).

_{r}, is the total amount of available in-plane solar irradiance in kWh/m

^{2}, H

_{i}, divided by the reference irradiance, G

_{ref}, of 1000 W/m

^{2}(Equation (12).

_{f}, is the annual, monthly, or daily net AC energy output in kWh, E

_{ac}, of the PV system per installed rated power, P

_{0}, given by Equation (13).

_{stc.}, and annual-averaged temperature-corrected PR, PR

_{ann.}. For the calculation of PR

_{stc.}and PR

_{ann.}, the temperature coefficient of maximum power (γ

_{Pmp}) is a critical component.

#### 3.3. Calculation of the Performance Loss Rate Using Linear Regression and STL

_{ann.}time series using linear regression. With the second approach, the calculation of PLR involved three main steps. First, the decomposition of continuous monthly PR time-series into its components using STL (see Equation (1)). We used the annual-averaged temperature-corrected PR, PR

_{ann.}, as the base data from which the PLR was calculated. PR

_{ann.}was calculated using Equation (14) [50].

_{ac}is the measured AC electrical generation (kWh).

_{t}using a locally weighted polynomial fitting. The STL decomposition results in the “trend”, “seasonal”, and “residual” components of the original temperature-corrected PR time series. STL has been implemented in other PV performance studies using the software R [1,6,19,36]. Other studies such as [36,51] have also applied STL without mentioning the tools used to implement it in the analysis of PV systems’ time-series. In this work, the STL algorithm was implemented using a Python library named STLDecompose [52], according to the LOESS smoothing method [18]. The annual analysis period of 12 months is used, which represents the number of months in a year. To accommodate strong annual periodicity within the years of daily observations, if needed, a period of 365 days would be appropriate.

_{t}, of the temperature-corrected PR follows, using Equation (15).

_{t}, and b is the T

_{t}-intercept. The final PLR value, in percentage, is the rate of change, either positive or negative, of the regression of the trend component. From the regression parameters, the relative PLR is computed using Equation (16) [53].

#### 3.4. Calculation of the Performance Loss Rate Using the YoY Approach

## 4. Results and Discussion

#### 4.1. Performance Ratio

_{stc.}in orange, and PR

_{ann.}in green. Scatter plots are the actual values, and the lines are the 30-day averaged values. As shown, the PR and PR

_{ann.}values are close together while the PR

_{stc.}values are higher, about 0.1.

_{stc.}value. The right green plot is the PR

_{ann.}value. As shown, the mean values of PR were slightly higher than PR

_{ann.}, with around a 0.4% difference. However, PR

_{ann.}had a narrower standard deviation by 30% compared to the standard deviation of PR because its seasonal variations due to the temperature effect had been reduced using annual-averaged temperature values. The PR

_{stc.}values were always the biggest among the two other PRs (around 10% higher) because they were estimated with an STC temperature of 25 °C.

_{ann.}. However, when the temperature is closer to STC, p-Si modules performed better than CdTe modules. In addition, the performance range of p-Si modules is smaller than CdTe modules. A similar comparison was observed for mono-Si and a-Si modules in terms of STC temperature; the mono-Si modules had a higher PR than a-Si while their PR and PR

_{ann.}were relatively similar.

_{ann.}, the p-Si system in climate Cfb of Italy has a higher performance of 0.84 than those in climates BWh (Australia) and Af (Indonesia) with the same value of 0.81. In contrast, PR

_{stc.}in climates BWh and Af were slightly higher than those in climate Cfb. The reason for this is because the average temperature in climates BWh and Af are closer to 25 °C.

#### 4.2. Performance Loss Rate Calculation Using LR and STL

_{ann.}time-series, their fitting lines, and trend components. As shown, the data do not have the same length, ranging from two to nine years. The grey lines are PR

_{ann.}, also shown in blue lines for PV systems with data less than a five-year period. The dashed orange lines are the applied linear regression fits of PR

_{ann.}, and the green lines are the STL-extracted “trend” component of the PR

_{ann.}time-series. For almost all systems, the difference between the regression fits with the trends is very small, which means that the STL method is useful for an accurate calculation of changes in performance.

#### 4.3. Comparison of PLR Values Using STL and YoY

_{amb}in Bolzano, Alice Springs, and Indonesia during their corresponding reporting periods were, respectively, 13, 26, and 31 °C. Moreover, calculations using the clear sky model showed different results, where the lowest PLR was in the BWh climate at −0.4%/year, followed by climate Af at −1.29%/year, and the highest rate was in the climate of Cfb at −1.41%/year. It has to be kept in mind, however, that clear sky modeling of irradiance data will inevitably result in higher uncertainties. It is usually used to cross-compare the quality of measured irradiance and as an alternative if no or corrupted irradiance measurements are available.

_{ann.}values of all systems fall between 76% and 88%, while the values of PR

_{stc.}are slightly higher. According to [56], the typical PR of present PV systems ranges from 80% to 90%. For most of the PV systems, the relative values of PLR using STL are smaller compared to the sensor-based PLR values using YoY, with a significant difference ranging from −12% to −20% for mono-Si in Alice Springs and −13% to −60% for p-Si in the same location. The differences in degradation values retrieved from STL and YoY were caused by the underlying differences in the methods themselves. The PLR using STL was calculated based on a decomposition of the temperature corrected PR while the YoY-based PLR was calculated using the differences in daily instances of PR and renormalized energy using PVWatts.

## 5. Conclusions

- The annual-averaged temperature-corrected performance ratio, PR
_{ann.}, with an average value of all systems from each technology. The CIGS system performed best with an average PR value of 0.88 ± 0.04. The least performing technology was the a-Si PV systems, with an average PR value of 0.78 ± 0.05. The p-Si systems in climate Cfb of Italy had a higher average PR of 0.84 than those operating in climates BWh (Australia) and Af (Indonesia), with the same value of 0.81. - Performance loss rates based on the STL approach. For almost all systems, the use of STL for the calculation of PLR is helpful, especially if monitoring data of high quality was not available. The p-Si systems show the lowest PLR among the technologies with an average PLR value of −0.6%/year. The strongest performance loss was experienced by a-Si modules at −1.58%/year.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

No. | City | Climate | Technology | PR | PR_{stc.} | PR_{ann.} | PLR (%/year) YoY | PLR (%/year) STL | |
---|---|---|---|---|---|---|---|---|---|

Sensor | Clear Sky | Relative | |||||||

1 | Alice Springs | BWh | a-Si | 0.78 ± 0.05 | 0.82 ± 0.05 | 0.78 ± 0.05 | −1.63 | −1.22 | −1.58 |

2 | Alice Springs | BWh | HIT | 0.86 ± 0.04 | 0.91 ± 0.03 | 0.86 ± 0.03 | −1.07 | −0.12 | −1.01 |

3 | Alice Springs | BWh | CIGS | 0.88 ± 0.04 | 0.96 ± 0.03 | 0.88 ± 0.03 | −1.20 | −0.17 | −0.80 |

4 | Alice Springs | BWh | mono-Si | 0.79 ± 0.03 | 0.86 ± 0.02 | 0.79 ± 0.02 | −0.91 | −0.19 | −0.80 |

5 | Alice Springs | BWh | mono-Si | 0.76 ± 0.04 | 0.85 ± 0.02 | 0.76 ± 0.02 | −0.50 | +0.29 | −0.41 |

6 | Alice Springs | BWh | mono-Si | 0.79 ± 0.05 | 0.87 ± 0.05 | 0.79 ± 0.04 | −1.62 | −0.93 | −1.30 |

7 | Alice Springs | BWh | CdTe | 0.76 ± 0.05 | 0.80 ± 0.05 | 0.76 ± 0.05 | −1.85 | −1.55 | −2.20 |

8 | Alice Springs | BWh | CdTe | 0.84 ± 0.03 | 0.88 ± 0.03 | 0.84 ± 0.03 | −1.10 | −0.32 | −0.95 |

9 | Alice Springs | BWh | CdTe | 0.87 ± 0.03 | 0.92 ± 0.02 | 0.87 ± 0.02 | −1.19 | −0.60 | −0.38 |

10 | Alice Springs | BWh | p-Si | 0.86 ± 0.03 | 0.95 ± 0.01 | 0.86 ± 0.01 | −0.47 | +0.33 | −0.19 |

11 | Alice Springs | BWh | p-Si | 0.78 ± 0.04 | 0.94 ± 0.03 | 0.78 ± 0.02 | −1.12 | −0.36 | −0.97 |

12 | Alice Springs | BWh | p-Si | 0.78 ± 0.03 | 0.87 ± 0.02 | 0.78 ± 0.02 | −0.64 | +0.09 | −0.56 |

13 | Cirata | Af | p-Si | 0.81 ± 0.03 | 0.90 ± 0.03 | 0.81 ± 0.03 | n.a | n.a. | −0.60 |

14 | Pekanbaru | Af | p-Si | 0.85 ± 0.02 | 0.93 ± 0.02 | 0.85 ± 0.02 | −1.60 | −1.29 | −0.62 |

15 | Bolzano | Cfb | p-Si | 0.84 ± 0.04 | 0.89 ± 0.03 | 0.84 ± 0.03 | −0.80 | −1.41 | −0.77 |

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**Figure 1.**The geographical distribution of the photovoltaic (PV) systems, climate locations, and annual global irradiation on a horizontal surface (kWh/m

^{2}/year). The map is based on [37], irradiation data are obtained from Global Solar Atlas 2.0, a free, web-based application developed and operated by Solargis s.r.o. on behalf of the World Bank Group, with funding provided by the Energy Sector Management Assistance Program (ESMAP). For additional information: https://globalsolaratlas.info.

**Figure 3.**The period of data availability for each PV system; green: data is available, red: data is not available.

**Figure 4.**Examples of the degradation rate of a copper indium gallium selenide (CIGS) PV system from Site 27 in Alice Springs. The degradation calculation based on (

**a**) measurement sensors, and (

**b**) a clear sky model.

**Figure 6.**Box plots of the performance ratio of each PV system. Left/blue: PR, middle/orange: temperature-corrected PR by STC, right/green: annual-averaged temperature-corrected PR. Numbers at the upper right corners in the boxes indicate the duration of the analyzed data in the number of years.

**Figure 8.**Annual-averaged monthly temperature-corrected performance ratios, PR

_{ann.}, of the PV systems (grey or blue lines), their linear fit (dashed orange line), and trend components (green line) over the monitoring period. Numbers at the top right of the charts indicate the lengths of the data in years.

**Figure 9.**Performance loss rate of the PV systems using STL. (

**a**) Grouped by module technologies, (

**b**) grouped by climate. Left: relative values, right: absolute values.

**Figure 10.**Performance loss rate of the PV systems using YoY. (

**a**) Grouped by module technologies, (

**b**) grouped by climate. Left: based on monitoring sensors, right: based on the clear sky model.

Location | Module Types | Temp. Coeff. of Power, γ_{Pmp}(%/K) | Rated d.c. Power, P_{0}(kWp) | Inverter | Tilt Angle (°) | Array Orientation (°) | Array Area, A_{a}(m ^{2}) | ||
---|---|---|---|---|---|---|---|---|---|

Country, City | Climate Class | Description | |||||||

Italy, Bolzano | Cfb | Temperate, no dry season, warm summer | p-Si (210W) | −0.457 | 4.20 | SMA SB 4000TL | 30 | 188.50 | 29.70 |

Indonesia, Pekanbaru | Af | Tropical, rainforest | p-Si (PS 220-6P-S) | −0.490 | 1.76 | SMA SB1700 | 10 | 180.00 | 13.14 |

Indonesia, Cirata | Af | Idem | p-Si (ASL-M100E) | −0.480 | 5.00 | SMA SMC 5000 | 10 | 15 | 33.50 |

Australia, Alice Springs | BWh | Arid, desert, hot/Site 8 | p-Si (BP 3165) | −0.50 | 4.95 | SMA SMC 6000A | 20 | 0 | 37.75 |

BWh | Idem/Site 11 | p-Si (BP 3165) | −0.50 | 4.95 | Idem | 20 | 0 | 37.75 | |

BWh | Idem/Site 34 | p-Si (WSP-240P6) | −0.45 | 5.28 | Idem | 20 | 0 | 36.59 | |

BWh | Idem/Site 8 | a-Si (G-EA060) | −0.230 | 6.00 | Idem | 20 | 0 | 95.04 | |

BWh | Idem/Site 17 | HIT (HIP-210NKHE5) | −0.30 | 6.30 | SMA SMC 7000TL | 20 | 0 | 37.83 | |

BWh | Idem/Site 27 | CIGS (SL1-85) | −0.38 | 5.61 | SMA SMC 6000A | 20 | 0 | 49.48 | |

BWh | Idem/Site 7 | CdTe (FS-272) | −0.250 | 6.96 | Fronius Primo 6.0 | 20 | 0 | 69.12 | |

BWh | Idem/Site 23 | CdTe (CX-50) | −0.250 | 5.40 | SMA SMC 6000A | 20 | 0 | 77.76 | |

BWh | Idem/Site 28 | CdTe (FS-387) | −0.250 | 5.60 | Idem | 20 | 0 | 46.08 | |

BWh | Idem/Site 10 | mono-Si (SPR-215-WHT-I) | −0.38 | 5.81 | Idem | 20 | 0 | 33.59 | |

BWh | Idem/Site 12 | mono-Si (BP 4170N) | −0.50 | 5.10 | Idem | 20 | 0 | 37.81 | |

BWh | Idem/Site 13 | mono-Si (TSM-175DC01) | −0.45 | 5.26 | Idem | 20 | 0 | 38.37 |

Climate | Country | PR | PR_{stc.} | PR_{ann.} |
---|---|---|---|---|

BWh | Australia | 0.81 ± 0.03 | 0.92 ± 0.02 | 0.81 ± 0.02 |

Af | Indonesia | 0.81 ± 0.03 | 0.90 ± 0.03 | 0.81 ± 0.03 |

Cfb | Italy | 0.84 ± 0.04 | 0.89 ± 0.03 | 0.84 ± 0.03 |

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**MDPI and ACS Style**

Kunaifi, K.; Reinders, A.; Lindig, S.; Jaeger, M.; Moser, D.
Operational Performance and Degradation of PV Systems Consisting of Six Technologies in Three Climates. *Appl. Sci.* **2020**, *10*, 5412.
https://doi.org/10.3390/app10165412

**AMA Style**

Kunaifi K, Reinders A, Lindig S, Jaeger M, Moser D.
Operational Performance and Degradation of PV Systems Consisting of Six Technologies in Three Climates. *Applied Sciences*. 2020; 10(16):5412.
https://doi.org/10.3390/app10165412

**Chicago/Turabian Style**

Kunaifi, Kunaifi, Angèle Reinders, Sascha Lindig, Magnus Jaeger, and David Moser.
2020. "Operational Performance and Degradation of PV Systems Consisting of Six Technologies in Three Climates" *Applied Sciences* 10, no. 16: 5412.
https://doi.org/10.3390/app10165412