1. Introduction
In a fast-changing global energy market, the demand for electricity is rising more than ever. According to IEA’s semiannual Electricity Market Report, the global electricity demand has risen 6% in 2021, largest increase in percentage terms since 2010 [
1]. The gradual electrification of transport sector also will add stress to utility markets specifically in isolated grids. Solar energy technologies (photovoltaics (PV), solar collectors) are particular interest to North Cyprus due to the global horizontal irradiation (GHI) reaching 5.5 kWh/m
2 [
2]. The cumulative global installed PV capacity is estimated to reach 760 GW, with an additional capacity of 130 GW in 2020, passing cumulative global installed Wind capacity for the first time [
3]. Similarly cumulative installed PV capacity in North Cyprus has reached 95 MW by the end of 2021, reaching 25% of the total installed conventional capacity and the total electricity generation from photovoltaics has exceeded 10% of the total electricity generation [
4].
With the increased cumulative installed PV capacity, the island’s isolated grid is facing severe issues. Alongside the voltage rise issues in low voltage grid due to concentrated PV installations in some areas, the lack of demand for electricity specially in late April is the main limitation for PV integration. Considering island’s limited grid capacity, the ability to predict the decline in power output from photovoltaics over the time holds significant importance for maximizing the renewables share in energy mix.
Over the years, two terms used to represent the decline in power output of a PV system over the time degradation rate and performance loss rate (PLR) often represented with a unit of %/year. PLR incorporates both reversible components i.e., soiling, shading, degradation in balance of system (BOS) components and irreversible components, and material degradation of modules [
5], while the degradation rate only incorporates the irreversible component. Performance metrics used for degradation/PLR determination in the literature may be broadly categorized into three based on the monitored parameters; namely electrical parameters, regression models and normalized ratings. Based on the selected performance metric, it is either called performance loss rates (PLRs) or degradation rates of PV module or system [
6]. Generally, the assessment of short circuit current I
sc, open-circuit voltage V
oc, fill factor FF and efficiency analysis leads determination of degradation rates since both indoor and outdoor analysis technique allows for the cleaning of module prior to parameter measurements. This is followed by a comparison of instantaneous measured parameters to the nameplate of module for determining the power reduction. On the other hand, Regression models and normalized ratings are based on the field data. Field data provides aggregated values, includes soiling, shading, module mismatch in addition to the degradation of PV modules, therefore represented by performance loss rate. Degradation/PLR determined by field measurements do not provide any information related to degradation modes. The severity of degradation/PLR of field aged PV systems is highly dependent on external conditions such as solar radiation, temperature, wind speed, humidity and soiling and evidenced by the observed degradations such as delamination, glass breakage, busbar failure, broken interconnect, front surface discoloration, moisture ingress, reduced interlayer adhesion, diode failure, hotspots, corrosion, contact stability, cracked cells etc. [
7,
8,
9,
10,
11,
12,
13]. In addition to external conditions, it is also dependent on PV technology [
14], data quality [
15], filtering steps [
15], aggregation period [
16], performance metric [
17], and statistical approaches [
14,
17]. On the other hand, accelerated indoor aging tests conducted in a controlled environment provide flexibility for determining the impact of parameters on degradation rates such as irradiation, temperature etc. Various procedures including damp-heat (DH), thermal cycling (TC), UV exposure, mechanical load etc. are developed to mimic real environmental conditions for testing the degradation rate of PV modules [
6].
Various studies have reported PLR/Degradation rate for both natural and induced aged PV modules. Khan et al., conducted TC stress test composed of 200 cycles by varying temperature between −40 °C to 85 °C for PV modules, one fixed on a concrete slab, protecting the back surface of PV module while the other was left unprotected under controlled environment. Results suggested power loss for the reference PV module was approximately 3%, while concrete insulated PV modules only experienced a power loss of around 2% [
18]. Kyranaki et al., conducted experimental study to investigate the front and read side corrosion mechanisms by subjecting 3 set of c-si mini modules, one set of full module structure of glass-EVA-cell-EVA-backsheet being the control and the other two sets having either front or rear side exposed to damp-heat conditioning under 85% relative humidity (RH) and 85 °C. Results revealed that for the front side exposure Pmax was observed to drop by an average of 4.65%. On the other hand, for the rear-side exposed PV cells Pmax dropped by 9.3% while maximum power output of full modules degraded by 5.6%. Front side corrosion was the dominant form of degradation mode, mostly on the fingers and busbars and less on solder of the ribbons [
19]. Wu et al., conduced statistical analysis studies on UV induced degradation rate of polysilicon modules tested based on IEC 61215:2005. Results suggested after 3000 kWh/m
2 UV exposure, 95% of the tested modules did not exceed 8% degradation rate. Concluding, UV-induced degradation should not exceed 8% after 25 years of exposure [
20].
PLR/degradation rates studies for modules exposed to outdoor conditions presented in literature are summarized in
Table 1. Based on location, capacity, monitoring duration, module type, the performance metric, implemented methodology and statistical approach are also presented.
Some of the conclusions that could be drawn from these studies are: Quansah et al., studied various systems in different climate categories of Ghana and reported higher degradation in humid environment [
21]. Frick et al., compared degradations rate between Germany and Cyprus. Higher degradation rates are reported in Cyprus, having relatively warmer climatic conditions compared to Germany [
15]. Ingenhoven et al., made a comparative study between Italy and Australia. Degradation rates reported in Italy was higher even though the system in Australia receiving 845 kWh/m
2 higher irradiation, concluding degradation rates are dependent on-site conditions as well [
22]. Reported degradation rate comparisons between polycrystalline and monocrystalline suggests no distinct superiority of one technology over another [
23,
24,
25]. On the other hand, Phinikarides et al., concluded that different PV technologies (i.e., thin film, crystalline etc.) has different degradation rates under same outdoor conditions [
14]. It is also found that different statistical approaches generate different degradation rates [
14,
26]. Data quality and filtering steps hold significant importance. Quality data combined with the good filtering approach yielded comparable to indoor measurements [
15]. Aggregation period has an impact on degradation rates. Comparison of monthly and daily degradation rates suggested daily analysis yielded lower degradation rates [
16]. Carigiet et al., conducted a comparative study between PR corrected to standard testing conditions and indoor sun simulator and reported PR
stc method results was twice of the sun simulator results [
27]. After the literature survey, it could be concluded that side by side performance loss rate comparison of PV systems is limited to smaller capacities and the same tilt angle, orientation and installation environment. The objective of this paper is to investigate the PLR of three different PV systems with a total capacity of 1045 kW
p, poly-crystalline silicone (p-Si) PV modules at inverter level, operated within 2 km with various tilt angles, orientations, installation types and installation environment in order to:
Test the applicability of meteorological data gathered from the meteorological station for modelling module temperature and in-plane irradiation;
Investigate the impact of selected performance metrics and statistical approaches on PLR results;
Provide direct comparison of PLR of PV modules and inverters from the same manufacturers under various installation environments, tilt angles and orientations.
3. Methodology
The general pipeline used for the assessment of PLRs of a PV system often involves following steps: data gathering, filtering, performance metric selection and statistical approach [
5]. The selected performance metric is deterministic on required parameters [
22,
33,
34]. For this analysis, the three performance metric is used as described in
Section 3.4. These metrics requires measured data of AC power, in-plane irradiation, module temperature, wind speed and ambient temperature. As on-site measurements of the aforementioned parameters are not present for the analyzed systems, in-plane irradiation and module temperature are modelled with the data acquired from the nearest meteorological station located within 6 km of installation location and compared with a nearby on-site meteorological station, equipped with sunny sensor box acquiring in-plane irradiation, module temperature, wind speed and ambient temperature. Detailed description of in plane irradiation and module temperature modelling described in
Section 3.1 and
Section 3.2, respectively, followed by filtering steps (
Section 3.3), performance metrics (
Section 3.4) and lastly statistical approaches (
Section 3.5) utilized for the PLR determination.
3.1. Modelling In-Plane Irradiaiton
Venues selected for the analysis has different orientation and tilt angle as summarized in
Table 2. Due to differences in orientation and tilt angle incident irradiation on module surfaces varies for each installation [
35]. In-plane irradiation measurements are not present for the systems analyzed therefore in-plane irradiation is modelled by using global horizontal irradiation (GHI) data acquired from the government owned meteorological station located within 6 km. Modelled irradiation data is further compared with a recently installed on-site meteorological station data available from June 2021 until April 2022 and applicability of the data from the government-owned meteorological station is tested. A brief description of the pathway for modelling in-plane irradiation by using GHI data is summarized in
Figure 1 below [
36].
Initially, hourly GHI data gathered from meteorological station separated to its components as direct and diffuse radiation by using decomposition model proposed by Tapakis et al. This model is selected in this study due to the fact that it is proposed based on 10 years data collected from Athalassa’s Nicosia Cyprus actinometric station. Its accuracy is tested against 23 decomposition model and found to be the best performing model [
37]. The governing model equations provided below.
where,
is the ratio of diffuse irradiation
to global horizontal irradiaiton
and clearness index
, ratio of
to extrateressial irradiaiton
)
.
Equations (1)–(3) presented above evaluates diffuse component
of the
based on various clearness index
. Beam component
Ib of
is then simply the subtraction of
from the
.
is decomposed into its components as
and
, then further used in transposition models for determining global tilted irradiance (
).
It is a combination of of direct tilted (
), diffuse tilted (
) component and reflected component (
) given by the Equation (4) [
36].
Transposition models have the same formula for
and
Ir components
, only representation of
varies based on the model used. The models generally classified based on representation of
as isotropic and anisotropic. Isotropic models assume uniform distribution of
over the sky dome. On the other hand, anisotropic models includes circumsolar irradiation, sky conditions and horizon brightening [
36,
38]. The governing components of
is given below and summary of angle and their representative symbols is presented in
Table 4 [
38].
Direct tilted (
) component
where
is the ratio of beam radiation on tilted surface to that on a horizontal surface and represented by
.
Reflected () component
The reflected component of irradiation on tilted surface is assumed to be isotropic and is dependent on GHI, albedo and tilt angle represented by the following equation [
39,
40,
41,
42]
where albedo, (
) is estimated as a constant 0.2 [
38].
Diffuse tilted components ()
Two transposition models are proposed for the estimating the diffuse component specific to Cyprus [
43,
44] isotropic Badescu model [
45] and anisotropic Temps-Coulson model [
46]. In this analysis, four more models are used in addition to the two aforementioned models, namely isotropic Liu & Jordan [
47] and the three anisotropic model Hay model [
48], Klutcher model [
49] and Reindl model [
50]. The governing equations are provided below.
Klutcher model
where
Reindl Model
Diffuse tilted component is evaluated for each model by using the governing equations given above and combined with direct tilted component and reflected component to generate in-plane irradiation specific to each model. Furthermore, modelled in-plane irradiation is compared with the on-site data acquired by Sunny SensorBox (SMA Solar Technology AG, Niestetal, Germany). The performance of models is evaluated based on the root mean squared error (RMSE) and mean bias error (MBE) and R
2 value [
51]. RMSE and MBE are computed as:
where,
is the modelled irradiation and
is the measured data.
3.2. Modelling Module Temperature
Alongside the incident irradiation, power output of PV modules is also temperature dependent. Manufacturers generally provide the effect of temperature as %/°C on parameters such as Pmax, Voc and Isc. Depending on the selected performance metric module temperature or cell temperature needs to be modelled since direct measurements are not available [
21,
23]. The module temperature model selection procedure is provided in
Figure 2.
Various models are proposed in literature for determining module temperature
. Three arbitrarily selected model is provided below [
52].
Initially wind speed (v), ambient temperature () and in plane irradiation data acquired from a nearby on-site station substituted into models provided above. The models result compared with on-site measured module temperature data. Performance of each model is evaluated based on RMSE Equation (14) and MBE Equation (15) as provided earlier. Among the tested models, the best performing model is selected and its accuracy further tested with wind speed and ambient temperature data acquired from the meteorological station coupled with modelled in-plane irradiation. The performance of selected model with meteorological data further tested on RMSE and MBE.
3.3. Filtering
The filtering step holds significance importance, specifically when modelling in plane irradiance from the global horizontal irradiation values acquired from the nearby station. Poor or variable solar resource conditions biasing data needs to be removed. Lindig et al., suggested the applied filter highly performance metric and statistical model dependent [
53]. Furthermore, the filter choice is highly correlated with the outcome of the analysis, inappropriate filtering will yield wrong outcomes [
6]; moreover, it provides depth to the analysis and may reveal practical issues such as inverter clipping [
33]. IEC61724-3 suggests that the filtering criteria might change based on the local conditions and might yield better results.
In this study, two widely accepted filters are applied to the data; an irradiance low threshold filter of 200 W/m
2 is applied to in plane irradiation and high threshold is set to 1200 W/m
2. The low threshold filter is set to remove nighttime data and low irradiance periods. With the high threshold filter, measurement errors are omitted [
22].
Another filter introduced for the dataset is the statistical filter. In-plane irradiation is modelled from GHI from a nearby station; therefore, some discrepancy might occur due to variation in irradiation. Therefore, a high filter (HF) and a variable low filter (LF) are set to maintain the power-irradiance relationship. Both filters are based on the measured irradiance and PV production correlation. The high filter is based on the fact that inverter production cannot be higher than maximum theoretical PV production.
For the low filter, the accuracy of the modelled monthly irradiation values is used as a guide. Generally, results suggested that from May to October, the in-plane irradiation has higher accuracy compared to rest of the year. Therefore, two different low filters arbitrarily set; LF
low is set for HF × 0.5 for May to October. LF
high is set for HF × 0.7 for November to April. LF
low also showed variability between venues in order to account for the variability in temperature variations and soiling effect.
3.4. Metrics
Various performance metrics were utilized for determining PLR at system level [
12,
15,
22]. Metrics used in this study are the performance ratio (PR), temperature corrected performance ratio (TCPR) and weather corrected performance ratio (NRELPR). Performance ratio PR is the most popular metric and is the ratio of the final energy yield of the system (kWh/kWp) to the reference yield (kWh/kW) described by the IEC 61724. In essence, it is an optimal performance parameter that represents the ability of a PV system to capture energy from the available in-plane irradiation under real life conditions and given by the following equation [
28].
where
is the PV array output for a given period (day, month or year)
is the nominal power of the system,
is the inplane irradiation for a given period (day, month or year),
is the reference radiation 1 kW/m
2.
Performance ratio is prone to variations in ambient temperature. Power output of the PV modules are dependent on the ambient temperature based on their temperature coefficient. Dependency on temperature introduces high seasonal variations during the computation of performance ratio. The temperature-corrected performance ratio suggested by [
28,
30,
31,
34] introduces additional parameters that normalize the variations due to the operating temperature. The removal of seasonality due to the temperature variations favored the PRSTC for the degradation analysis [
18]. The temperature-corrected performance ratio suggested by IEC 61724 is given by the following equation.
is the PV array output for a given period (hour, day, month or year), is the nominal power of the system, is the in-plane irradiation for a given period (hour, day, month or year), is the reference radiation 1 kW/m2, is the PV module temperature coefficient of power (%/°C, negative in sign), : is the module temperature for a given period (hour, day, month or year), : is the reference module temperature STC, 25 °C.
Another methodology is developed by National Renewable Energy Laboratory. It is aimed to have a better representation of a weather corrected PR. This methodology incorporates the weather-related effects including ambient temperature, wind and irradiation.
The Weather corrected PR is estimated by the following equation [
27,
34].
The main difference between weather corrected performance ratio and IEC 61724 is the accommodation of normalization parameters. The formula suggested by IEC724 was based on the module temperatures while formula suggested by NREL uses the cell temperature equation as follow
where
is the module back temperature and can be evaluated by
where
conduction/convection heat transfer coefficient °C.m
2/kW. WS is the wind m/s. The coefficients (a, b and ΔTcnd) are the empirical coefficients and recommended by King, Boyson, and Kratochvill (2004) [
54] for a Glass/cell/polymer sheet module type in a free ventilation installation is −2,81, −0.0455 and 3, respectively. Average irradiance weighted cell temperature is calculated from the following equation.
(Average irradiance-weighted cell temperature from one year of weather data using the project weather file, = calculated cell operating temperature for each hour, = POA irradiance for each hour, J is each hour of the year (8760 h total).
3.5. Statistical Approach
Various statistical methods are proposed for the PLR calculations. In this study, three statistical methods are coupled with the performance metrics for determining PLR, namely seasonal trend decomposition by LOESS (STL), Classical Seasonal Decomposition (CSD), and Year on year (YOY) analysis.
The CSD method introduced in 1920s forms the basis of time series decomposition techniques. The main objective of decomposition models is to remove the seasonality from the data such that the trend can be seen more clearly. Even some of the normalized metrics used in this study accounts the variability of temperature, however, the soiling effect perseveres. Classical decomposition models represented below in Equation (26).
where
is the time series,
is the trend,
is the seasonal and
is the residual component. The trend is obtained from the original data with a centered 12 month moving average. The seasonality component is obtained by subtracting the trend from the original data. Each month is averaged across the year; the combined seasonal component and the trend are extracted from the original time series to find the residual components [
17,
53]. The seasonal component is assumed to be constant over the years and due to the twelve months centered moving average; the first and last six months are not included in computation [
53,
55].
STL is a robust algorithm used for decomposition of time series. Similarly to CSD, STL also separates time series to three components: seasonal, trend and reminder. The seasonal component is a recurring pattern present in data. Once determined, it is removed from the time series data to eliminate the seasonal component. Dissimilar to the centered moving average for extracting trend in CSD method, the trend is extracted from locally weighted polynomial fitting in STL [
17,
53,
56]. The remainder of the component is obtained by subtracting the trend and the seasonal component. STL method is more prone to outliers, outages and missing data due to its locally formed trend.
STL and CSD analysis are conducted by using the python package ‘statmodels’ to analyze monthly data of metrics [
57]. Annual degradation rates were evaluated by applying the linear regression on the trend of both CSD and STL.
Once the slope (a) and the intercept (b) are extracted yearly relative PLR is calculated by the following equation
. and the uncertainty is of PLR is calculated by the following equation [
53].
where a and b are the fitting coefficients of the linear regression,
the variances of fitting coefficients and
the standard deviation of PLR.
Lastly, YoY method proposed by Hasselbrink et al., as a comparative method different than the statistical analysis. This was further developed by Jordan et al., for the assessment of daily metrics. YoY method evaluates the rate of change for two points in subsequent years based on the duration taken into account (monthly, weekly and daily). This procedure is repeated for every point of throughout the monitoring period. Furthermore, a distribution of rate of changes are generated and median of this distribution, representing the performance loss rate of the system [
33,
58]. Median value provides more robust analysis due to the reduction in impact of outliers over the mean value [
15].