# Uncertainty Analysis of Energy Production for a 3 × 50 MW AC Photovoltaic Project Based on Solar Resources

Authors: Irfan Jamil; Jinquan Zhao; Li Zhang; Syed Furqan Rafique; Rehan Jamil
Journal: International Journal of Photoenergy
 (2019)

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## Abstract

Access to solar energy is a prerequisite to remedy CO2 and improve the standard of human living. Green solar energy is only an immediate solution to add its zero emission profile and provide carbon footprint reduction benefits. This energy does not emit greenhouse gases which means it is a renewable free source of energy when producing electricity. The purpose of this paper is to investigate the accurate annul energy production data reducing uncertainty in solar energy estimates. This work investigated the solar energy assessment taking into account a detailed solar resource and energy production assessment for a 3 × 50 MW PV project with uncertainty analysis. The authors defined a total uncertainty of energy production which is estimated at 9.5% for one year and 8.9% for ten years as well as future variability of 3.4% for one year and 1.1% for ten years. The annual power degradation and expected energy production over the plant lifespan at dissimilar 99%, 90%, 75%, 60%, 50%, and 25% probability of surplus are also observed in this paper.


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## Body

## 1. Introduction

Pakistan is confronting issues of acute shortage of electricity and energy supply demand. About 43% of the total population of Pakistan lives without access to electricity, and approximately 50,000 villages are completely detached from the national grid [1]. The GoP has tasked the province’s energy department for the provision of a requisite institutional framework to end the shortage of energy supply. The energy department’s domain, inter alia, includes the generation of electricity by exploring especially indigenous resources, including solar, wind, biomass, and hydro. A master plan was developed by the GoP to issue many LOIs to solar energy developers for the development of large-scale solar power plants because PV technology is a promising application of renewable energy, widely used in urban and remote areas [2]. Within the master plan, first step is an overview of solar information, investigating the resources, rights and general information. According to the PV installation environment, PV power-generating systems are divided into on-grid-connected and off-grid-connected PV systems. The original concept of the master plan is acquired to install an on-grid-connected project and grid-connected solar PV system which is the fastest-growing power-generating technology today [3, 4]. In this case, an installed capacity of 3 × 50 MW is selected, which would be able to produce electricity energy for about 150,000 homes during peak daytime hours [5]. Through this project, the authors intend to create awareness amongst the general public for the use of renewable energy resources to reduce the burden on the national grid and to improve environmental conditions of the province. In the development of PV projects, the major area of risk is quantifying the expected annual energy production and uncertainty analysis whereas the most significant driver is the uncertainty in solar irradiance. Solar project developers require reasonable information in energy yield predictions in order to reduce the cost of financing systems, to understand the PV modeling uncertainty [6]. The flow of energy yield in the PV modeling chain is also discussed further. For this purpose, a feasibility study of a project was performed with the aim of performing the following tasks:
(i)
Review different solar resources and evaluation of energy production of 3 × 50 MW with respect to uncertainty analysis
(ii)
Provision of the requirements of the photovoltaic systems to meet the identified design profiles and equipment selectionThe following uncertainly/elements and assemblies are subject to investigation as preparatory work.


### 1.1. Uncertainty in the PV Modeling Chain

Different performance models are applied in the industry to anticipate the measure of energy amount that the PV system can produce. These diverse models can differ significantly in their underlying mathematical formulations, in the numerical approach, and in the amount of data (assumptions) required for the simulation. The different steps in the PV modeling chain are subject to uncertainties as shown in Figure1. The uncertainties affect different steps of the whole PV system parameters such as on meteorological, irradiation, PV module temperature, PV array, and inverter. The uncertainties on the environmental conditions are moderately larger while assessing the PV energy yield [7].Figure 1
Different steps in the PV modeling chain.


### 1.2. Technical/Financial Risk Factors

The technical risk factors in solar power generation depend on the perspective of the different stakeholders and their physical liability in the socioeconomic sector. When they start the development of renewable energy technology, they go over technical and financial risk assessments in terms of the technology they applied. Herein, we take into consideration technical risk factors for 3 × 50 MW which are an important uncertainty for identification from the perspective of solar developers [8]. The uncertainly of solar resource has great impact on financial risk factors. To manage the financial risk assessment of an investment in a grid-connected PV system, the uncertainty quantification of solar energy yield calculation is identified, which is an important case based on the energy flow in the PV modeling chain. These uncertainties in solar resources are subjected to climate variability (σClim), irradiation quantification (σIrr), conversion to the plane-of-array (σPOA−conv), temperature modeling (σTmp), PV array modeling (σPVarr), inverter modeling (σInv), PV field-related uncertainties (σFld), DC cabling (σC−DC), AC cabling (σC−AC), and availability (σAv) highlighted in the different steps of the main energy conversion in a PV system. Thus, given the parameters in Figure 2, if we maintain with correct quantification all uncertainties in the PV system modeling, then the financial risk assessment will allow the developers and investors to contain this factor [7].Figure 2
Energy yield flow in PV modeling chain parameters are subjected to uncertainties.


### 1.3. PV Yield Assessment

We used the PVsyst package along with internal tools to calculate an energy yield assessment and expected production, which gives the right input data for the PV system [9].


### 1.4. Project Profile

Pakistan lies at a high potential solar radiation belt, and the land is available in large-scale magnitude for the development of solar power projects. The 3 × 50 MW site has an evacuation facility of 220 kV grid and is located 115 km northeast of Karachi, Pakistan, near the town of Thano Bula Khan and Nooriabad, Sindh. The 3 × 50 MW site is composed of three (3) identical projects which are located in combination in the same parcel of land side by side. Based on land coordinates, the site has a rich sun-radiation impact [5]. The physical condition of the project land can be viewed in Figure 3.Figure 3
Physical condition of site/land milestone.The site coordinates with latitude and longitude are given below in Table1.Table 1
3 × 50 MW project site coordinates.
Location: Karachi, Pakistan
Latitude
25°19′9.1″N
Land coordinates
Longitude
68°4′20.3″E
Elevation
Approximately 112 m above sea level


### 1.5. Solar Resource Assessment

The solar energy resource assessment is the key role in the development of large scale-sized solar projects [10, 11]. The best way to determine the solar irradiation and temperature data at a particular site is by measuring different parameters of interest with the appropriate instruments at the location of the site. On-site measured irradiance data is not available at the project site. Therefore, several meteorological databases with different quality of data have been used to determine the long-term annual irradiation at the project site [12]. The authors consulted several weather databases as well as data supplied by the client and have obtained irradiation and temperature data from the ones listed in Table 2. The absence of usable on-site irradiance and temperature measurements introduces additional uncertainty in the solar resource assessment.Table 2
List of meteorological databases consulted for the project.
Database
Range
Stations
NASA-SSE
Worldwide
Satellites (1 degree longitude × 1 degree latitude mesh grid)
Meteonorm
—
8,055 weather stations
GeoModelSolarGIS
—
Satellite-derived solar radiation and meteorological data


#### 1.5.1. NASA’s Surface Meteorology and Solar Energy Server (NASA-SSE)

NASA-SEE can provide the monthly average values from 22 years of collecting data. Irradiation data for global horizontal, diffuse horizontal, and direct normal are provided for the specific coordinates of the site [13]. Table 3 presents the monthly values of global horizontal irradiation (GHI) and ambient temperature obtained from the site.Table 3
Monthly values from NASA-SSE.
Location
Project site
Global horizontal irradiation (keh/m2)
Temperature (°C)
Period
1983-2005
1983-2005
January
118
17.6
February
127
19.9
March
164
24.7
April
189
28.3
May
207
30.4
June
201
30.2
July
179
29
August
168
28.3
September
159
28.2
October
146
27.9
November
188
23.9
December
111
19.4
Total
1887
25.7


#### 1.5.2. Meteonorm

Meteonorm is primarily a method for the calculation of solar radiation on arbitrarily orientated surfaces at any specific location [14]. The Meteonorm database is mainly based on the GEBA ground stations and interpolates between the ground stations which we used to estimate the irradiation at the project site [12]. The results of Meteonorm were extrapolated from the Karachi weather station located 105 km from the project site. The coordinates, elevation, and climatic distance are provided in Table 4 below.Table 4
The coordinates of the Meteonorm stations and climatic distance to the site.
Latitude (degree)
Longitude (degree)
Elevation (m)
Climate distance (km)
Karachi weather station
24.9° N
67.0° E
22
105Tables5 and 6 present the average monthly values of the GHI and ambient temperature obtained from Metronome for the project location and the Karachi weather station as well as the period of record of each data, respectively.Table 5
Monthly values of GHI and temperature from Meteonorm from the project site.
Location
Project site
GHI (kWh/m2) (interpolated)
Temperature (°C) (interpolated)
Period
1986-2005
2000-2009
Jan
128
18.2
Feb
130
21.4
Mar
164
26.0
Apr
177
29.6
May
189
31.9
Jun
183
32.5
Jul
161
31.1
Aug
162
29.9
Sep
177
29.9
Oct
158
28.7
Nov
129
24.2
Dec
115
19.6
Total
1873
26.9Table 6
Monthly values of GHI and temperature from the Meteonorm from the nearest weather station.
Location
Nearest weather station
GHI (kWh/m2) (interpolated)
Temperature (°C) (interpolated)
Period
1986-2005
2000-2009
Jan
126
19.5
Feb
127
22.4
Mar
164
26.4
Apr
184
29.4
May
192
30.8
Jun
181
31.5
Jul
148
30.2
Aug
148
29.1
Sep
168
29.3
Oct
160
29.0
Nov
125
25.2
Dec
112
20.9
Total
1835
27.0


#### 1.5.3. SolarGIS

We procured SolarGIS irradiance and temperature data from GeoModel which includes 15 years of meteorological history at the project site. Table7 presents the average monthly values of the GHI and ambient temperature obtained from SolarGIS for the project location including the period of record [15]. From this data set, the interannual variability of the project site was calculated to be 3.4%.Table 7
Monthly values of GHI and temperature from SolarGIS.
GHI (kWh/m2)
Temperature (°C)
Period
1999-2013
1999-2013
Jan
134
18.5
Feb
153
22.7
Mar
197
26.0
Apr
215
32.3
May
227
34.2
Jun
204
33.7
Jul
180
33.7
Aug
179
31.1
Sep
179
31.0
Oct
172
30.0
Nov
136
25.8
Dec
122
20.5
Total
2098
28.3


### 1.6. Solar Resource Assessment Results

In the absence of an on-site solar monitoring station, the irradiation data sources referred to present several drawbacks. When compared to a high-quality on-site monitoring station, the data sources are lacking accuracy in terms of spatial distance, spatial resolution, or temporal resolution. It should be noted that there are no measured solar radiation data within 25 km of the project site. The GoP and the relevant department are known in this concept and are relying on satellite data to manifest the solar resource assessment studies. We have analyzed each available GHI data source and utilized the data sources to estimate the global horizontal radiation and temperature for the project site. This is because the energy yield of the project site is directly related to the availability of GHI [16]. A summary of the decision-making process is given briefly below.
(i)
The measured data is not available near the project site, but data from surrounding databases have been considered
(ii)
NASA-SSE predicts irradiation data at the project site; however, the data are coarse in spatial resolution with relatively high uncertainty (10%)
(iii)
Meteonorm results are based on extrapolation of data from a weather station located 105 km from the project. The irradiation data have an uncertainty of 11% and with an interannual variability of 4.5%
(iv)
SolarGIS data are provided at the project site using satellite data interpolated by the GeoModel algorithm which typically has an uncertainty between 3.5% and 7.0%. The irradiation data for the project site has an estimated uncertainty of 6.0% with a calculated interannual variability of 3.4% [5]Based on the conclusions above, SolarGIS irradiation has been retained for the analysis based on its lower relative uncertainty, the long period of record, and the representativeness of the project site. The authors consider this source as the best available source of irradiation data for the site and suitable at this stage in the development of the project. Based on its experience, PV projects have progressed through project development using modeled solar resource data with a similar level of uncertainty as the SolarGIS data chosen for this project site.


## 1.1. Uncertainty in the PV Modeling Chain

Different performance models are applied in the industry to anticipate the measure of energy amount that the PV system can produce. These diverse models can differ significantly in their underlying mathematical formulations, in the numerical approach, and in the amount of data (assumptions) required for the simulation. The different steps in the PV modeling chain are subject to uncertainties as shown in Figure1. The uncertainties affect different steps of the whole PV system parameters such as on meteorological, irradiation, PV module temperature, PV array, and inverter. The uncertainties on the environmental conditions are moderately larger while assessing the PV energy yield [7].Figure 1
Different steps in the PV modeling chain.


## 1.2. Technical/Financial Risk Factors

The technical risk factors in solar power generation depend on the perspective of the different stakeholders and their physical liability in the socioeconomic sector. When they start the development of renewable energy technology, they go over technical and financial risk assessments in terms of the technology they applied. Herein, we take into consideration technical risk factors for 3 × 50 MW which are an important uncertainty for identification from the perspective of solar developers [8]. The uncertainly of solar resource has great impact on financial risk factors. To manage the financial risk assessment of an investment in a grid-connected PV system, the uncertainty quantification of solar energy yield calculation is identified, which is an important case based on the energy flow in the PV modeling chain. These uncertainties in solar resources are subjected to climate variability (σClim), irradiation quantification (σIrr), conversion to the plane-of-array (σPOA−conv), temperature modeling (σTmp), PV array modeling (σPVarr), inverter modeling (σInv), PV field-related uncertainties (σFld), DC cabling (σC−DC), AC cabling (σC−AC), and availability (σAv) highlighted in the different steps of the main energy conversion in a PV system. Thus, given the parameters in Figure 2, if we maintain with correct quantification all uncertainties in the PV system modeling, then the financial risk assessment will allow the developers and investors to contain this factor [7].Figure 2
Energy yield flow in PV modeling chain parameters are subjected to uncertainties.


## 1.3. PV Yield Assessment

We used the PVsyst package along with internal tools to calculate an energy yield assessment and expected production, which gives the right input data for the PV system [9].


## 1.4. Project Profile

Pakistan lies at a high potential solar radiation belt, and the land is available in large-scale magnitude for the development of solar power projects. The 3 × 50 MW site has an evacuation facility of 220 kV grid and is located 115 km northeast of Karachi, Pakistan, near the town of Thano Bula Khan and Nooriabad, Sindh. The 3 × 50 MW site is composed of three (3) identical projects which are located in combination in the same parcel of land side by side. Based on land coordinates, the site has a rich sun-radiation impact [5]. The physical condition of the project land can be viewed in Figure 3.Figure 3
Physical condition of site/land milestone.The site coordinates with latitude and longitude are given below in Table1.Table 1
3 × 50 MW project site coordinates.
Location: Karachi, Pakistan
Latitude
25°19′9.1″N
Land coordinates
Longitude
68°4′20.3″E
Elevation
Approximately 112 m above sea level


## 1.5. Solar Resource Assessment

The solar energy resource assessment is the key role in the development of large scale-sized solar projects [10, 11]. The best way to determine the solar irradiation and temperature data at a particular site is by measuring different parameters of interest with the appropriate instruments at the location of the site. On-site measured irradiance data is not available at the project site. Therefore, several meteorological databases with different quality of data have been used to determine the long-term annual irradiation at the project site [12]. The authors consulted several weather databases as well as data supplied by the client and have obtained irradiation and temperature data from the ones listed in Table 2. The absence of usable on-site irradiance and temperature measurements introduces additional uncertainty in the solar resource assessment.Table 2
List of meteorological databases consulted for the project.
Database
Range
Stations
NASA-SSE
Worldwide
Satellites (1 degree longitude × 1 degree latitude mesh grid)
Meteonorm
—
8,055 weather stations
GeoModelSolarGIS
—
Satellite-derived solar radiation and meteorological data


### 1.5.1. NASA’s Surface Meteorology and Solar Energy Server (NASA-SSE)

NASA-SEE can provide the monthly average values from 22 years of collecting data. Irradiation data for global horizontal, diffuse horizontal, and direct normal are provided for the specific coordinates of the site [13]. Table 3 presents the monthly values of global horizontal irradiation (GHI) and ambient temperature obtained from the site.Table 3
Monthly values from NASA-SSE.
Location
Project site
Global horizontal irradiation (keh/m2)
Temperature (°C)
Period
1983-2005
1983-2005
January
118
17.6
February
127
19.9
March
164
24.7
April
189
28.3
May
207
30.4
June
201
30.2
July
179
29
August
168
28.3
September
159
28.2
October
146
27.9
November
188
23.9
December
111
19.4
Total
1887
25.7


### 1.5.2. Meteonorm

Meteonorm is primarily a method for the calculation of solar radiation on arbitrarily orientated surfaces at any specific location [14]. The Meteonorm database is mainly based on the GEBA ground stations and interpolates between the ground stations which we used to estimate the irradiation at the project site [12]. The results of Meteonorm were extrapolated from the Karachi weather station located 105 km from the project site. The coordinates, elevation, and climatic distance are provided in Table 4 below.Table 4
The coordinates of the Meteonorm stations and climatic distance to the site.
Latitude (degree)
Longitude (degree)
Elevation (m)
Climate distance (km)
Karachi weather station
24.9° N
67.0° E
22
105Tables5 and 6 present the average monthly values of the GHI and ambient temperature obtained from Metronome for the project location and the Karachi weather station as well as the period of record of each data, respectively.Table 5
Monthly values of GHI and temperature from Meteonorm from the project site.
Location
Project site
GHI (kWh/m2) (interpolated)
Temperature (°C) (interpolated)
Period
1986-2005
2000-2009
Jan
128
18.2
Feb
130
21.4
Mar
164
26.0
Apr
177
29.6
May
189
31.9
Jun
183
32.5
Jul
161
31.1
Aug
162
29.9
Sep
177
29.9
Oct
158
28.7
Nov
129
24.2
Dec
115
19.6
Total
1873
26.9Table 6
Monthly values of GHI and temperature from the Meteonorm from the nearest weather station.
Location
Nearest weather station
GHI (kWh/m2) (interpolated)
Temperature (°C) (interpolated)
Period
1986-2005
2000-2009
Jan
126
19.5
Feb
127
22.4
Mar
164
26.4
Apr
184
29.4
May
192
30.8
Jun
181
31.5
Jul
148
30.2
Aug
148
29.1
Sep
168
29.3
Oct
160
29.0
Nov
125
25.2
Dec
112
20.9
Total
1835
27.0


### 1.5.3. SolarGIS

We procured SolarGIS irradiance and temperature data from GeoModel which includes 15 years of meteorological history at the project site. Table7 presents the average monthly values of the GHI and ambient temperature obtained from SolarGIS for the project location including the period of record [15]. From this data set, the interannual variability of the project site was calculated to be 3.4%.Table 7
Monthly values of GHI and temperature from SolarGIS.
GHI (kWh/m2)
Temperature (°C)
Period
1999-2013
1999-2013
Jan
134
18.5
Feb
153
22.7
Mar
197
26.0
Apr
215
32.3
May
227
34.2
Jun
204
33.7
Jul
180
33.7
Aug
179
31.1
Sep
179
31.0
Oct
172
30.0
Nov
136
25.8
Dec
122
20.5
Total
2098
28.3


## 1.5.1. NASA’s Surface Meteorology and Solar Energy Server (NASA-SSE)

NASA-SEE can provide the monthly average values from 22 years of collecting data. Irradiation data for global horizontal, diffuse horizontal, and direct normal are provided for the specific coordinates of the site [13]. Table 3 presents the monthly values of global horizontal irradiation (GHI) and ambient temperature obtained from the site.Table 3
Monthly values from NASA-SSE.
Location
Project site
Global horizontal irradiation (keh/m2)
Temperature (°C)
Period
1983-2005
1983-2005
January
118
17.6
February
127
19.9
March
164
24.7
April
189
28.3
May
207
30.4
June
201
30.2
July
179
29
August
168
28.3
September
159
28.2
October
146
27.9
November
188
23.9
December
111
19.4
Total
1887
25.7


## 1.5.2. Meteonorm

Meteonorm is primarily a method for the calculation of solar radiation on arbitrarily orientated surfaces at any specific location [14]. The Meteonorm database is mainly based on the GEBA ground stations and interpolates between the ground stations which we used to estimate the irradiation at the project site [12]. The results of Meteonorm were extrapolated from the Karachi weather station located 105 km from the project site. The coordinates, elevation, and climatic distance are provided in Table 4 below.Table 4
The coordinates of the Meteonorm stations and climatic distance to the site.
Latitude (degree)
Longitude (degree)
Elevation (m)
Climate distance (km)
Karachi weather station
24.9° N
67.0° E
22
105Tables5 and 6 present the average monthly values of the GHI and ambient temperature obtained from Metronome for the project location and the Karachi weather station as well as the period of record of each data, respectively.Table 5
Monthly values of GHI and temperature from Meteonorm from the project site.
Location
Project site
GHI (kWh/m2) (interpolated)
Temperature (°C) (interpolated)
Period
1986-2005
2000-2009
Jan
128
18.2
Feb
130
21.4
Mar
164
26.0
Apr
177
29.6
May
189
31.9
Jun
183
32.5
Jul
161
31.1
Aug
162
29.9
Sep
177
29.9
Oct
158
28.7
Nov
129
24.2
Dec
115
19.6
Total
1873
26.9Table 6
Monthly values of GHI and temperature from the Meteonorm from the nearest weather station.
Location
Nearest weather station
GHI (kWh/m2) (interpolated)
Temperature (°C) (interpolated)
Period
1986-2005
2000-2009
Jan
126
19.5
Feb
127
22.4
Mar
164
26.4
Apr
184
29.4
May
192
30.8
Jun
181
31.5
Jul
148
30.2
Aug
148
29.1
Sep
168
29.3
Oct
160
29.0
Nov
125
25.2
Dec
112
20.9
Total
1835
27.0


## 1.5.3. SolarGIS

We procured SolarGIS irradiance and temperature data from GeoModel which includes 15 years of meteorological history at the project site. Table7 presents the average monthly values of the GHI and ambient temperature obtained from SolarGIS for the project location including the period of record [15]. From this data set, the interannual variability of the project site was calculated to be 3.4%.Table 7
Monthly values of GHI and temperature from SolarGIS.
GHI (kWh/m2)
Temperature (°C)
Period
1999-2013
1999-2013
Jan
134
18.5
Feb
153
22.7
Mar
197
26.0
Apr
215
32.3
May
227
34.2
Jun
204
33.7
Jul
180
33.7
Aug
179
31.1
Sep
179
31.0
Oct
172
30.0
Nov
136
25.8
Dec
122
20.5
Total
2098
28.3


## 1.6. Solar Resource Assessment Results

In the absence of an on-site solar monitoring station, the irradiation data sources referred to present several drawbacks. When compared to a high-quality on-site monitoring station, the data sources are lacking accuracy in terms of spatial distance, spatial resolution, or temporal resolution. It should be noted that there are no measured solar radiation data within 25 km of the project site. The GoP and the relevant department are known in this concept and are relying on satellite data to manifest the solar resource assessment studies. We have analyzed each available GHI data source and utilized the data sources to estimate the global horizontal radiation and temperature for the project site. This is because the energy yield of the project site is directly related to the availability of GHI [16]. A summary of the decision-making process is given briefly below.
(i)
The measured data is not available near the project site, but data from surrounding databases have been considered
(ii)
NASA-SSE predicts irradiation data at the project site; however, the data are coarse in spatial resolution with relatively high uncertainty (10%)
(iii)
Meteonorm results are based on extrapolation of data from a weather station located 105 km from the project. The irradiation data have an uncertainty of 11% and with an interannual variability of 4.5%
(iv)
SolarGIS data are provided at the project site using satellite data interpolated by the GeoModel algorithm which typically has an uncertainty between 3.5% and 7.0%. The irradiation data for the project site has an estimated uncertainty of 6.0% with a calculated interannual variability of 3.4% [5]Based on the conclusions above, SolarGIS irradiation has been retained for the analysis based on its lower relative uncertainty, the long period of record, and the representativeness of the project site. The authors consider this source as the best available source of irradiation data for the site and suitable at this stage in the development of the project. Based on its experience, PV projects have progressed through project development using modeled solar resource data with a similar level of uncertainty as the SolarGIS data chosen for this project site.


## 2. Uncertainty Methodology

Solar resource assessment with uncertainly analysis is required to know the mechanism of uncertainty methodology. The methodology of the uncertainty of solar recourse is associated with a modeling chain in which the uncertainty term in this paper refers to the RMSE classified as the estimation of a quantity. The RMSE is framed by a systematic part such as MBE and another nonsystematic part “σ.” The σ is the standard deviation of the error which represents random contributions to the error around the mean value [17]. The term accuracy measures RMSE, MBE, and MAE are normalized over the average value of θ̿i which are described as PRMSE, PBME, and PMAE, respectively; θ̇i is the actual quantity, θ¯i is the estimated quantity, and P variable is the number of samples which are defined below.
(1)RMSE=1P∑1Pθi¯−θ̇i2,MBE=1P∑1Pθi¯−θ̇i,MAE=1P∑1Pθi¯−θ̇i.Then,(2)RMSE2=MBE2+σ2.After that,(3)θi¯¯=1P∑1Pθ̇i.Here, these values are normalized over the average value(4)PRMSE=RMSEθi¯¯,PBME=MBEθi¯¯.(N) is presented herein as normalized:(5)PMAEN=MAEGI~.Here, we define the combination of uncertainty.The overall role of propagation of uncertaintiesUx and Uy for a given function fx,y can be computed in equation (6) when we assume the independent variables or neglecting correlations. The equation Uc is an estimation of the standard deviation of the function fx,y, accepting that Ux and Uy are small compared to the partial derivatives. The combined standard uncertainty Uc is computed using equation (7) based on uncertainty sources which shall be considered independent. In this way, combined expanded uncertainty U→will be calculated by multiplying the combined standard uncertainty Uc with a coverage factor presented in equation (8). We assume the 96% confidence interval of Gaussian distribution, and then this coverage factor CovFactor is 1.97. Therefore, the final equation to find the expanded uncertainty U→is obtained in equation (9) [18].
(6)Uc=∂f∂x2⋅Ux2+∂f∂y2⋅Uy2,(7)Uc=RNorma/22+RUnib/32+⋯P+SystNormc22+SystUnid22+⋯.Then, according to equation (7) and CovFactor,
(8)U→=CovFactor⋅Uc.Here,CovFactor=1.97 (coverage factor).
(9)U→=1.97⋅Uc,whereinUc = combined uncertaintyU→ = expanded uncertaintyP = number of samplesRNorma = normally distributed random componentsRUnib = uniformly distributed random componentsSystNormc = normally distributed systematic componentsSystUnid = uniformly distributed systematic components


## 3. Results and Discussion

### 3.1. PV Energy Production

The main simulation results of the energy production produce 80085 MWh/year, and the performance ratio (PR) of 77.62% is obtained for 1 × 50 MW from 3 × 50 MW. These are three (3) 50 MW AC solar projects located adjacent to the same extended piece of land with a combined AC capacity of 150 MW. Therefore, each 50 MW is identical from 3 × 50 MW, and the (1) 50 MW size is executed for the simulation in this paper. The energy assessment result through simulation is shown in Table8.Table 8
Energy assessment results through simulation.
Software
PVSYST V6.47
Project
3 × 50 MW solar PV power project
Aggregate power
50 MW (1 × 50 MW)
Data sources
Meteonorm 7.1 [2001-2010]Sat=56%
Land coordinates
Longitude 68°4.2′, north latitude 25°19.2′, altitude 70 m
Legal time
Time zone TU + 5
Mounting structure
Fixed tile
PV system grid-connected
PV field orientation
PV modules
PV array
Inverter
User’s needs
Tilt 20°, azimuth 0°
Model JKM300P-72Jinko Solar
No. of module 166680
Model TC 1000KS
Unlimited load (grid)
Pnom
Pnom total
Pnom
300 Wp
50004 kWp
1000 kW AC
Inverter pack
No. of units: 50.0, Pnom total: 50000 kW AC
PV modules
8334 strings of 20 modules in series, 50004 kWp total
Area
323069 m2
Production
80085 MWh/year
PR
77.62% (performance ratio)
No shading field defined


#### 3.1.1. Loss Diagram

According to the simulation result of the loss diagram in Figure3, PV facility defined loss factors such as module quality of +0.3%, module degradation loss of −1.0%, soiling of −0.3%, mismatch of −0.1, cabling (ohmic wiring loss) of -0.1%, inverter efficiency of −2.1%, transformer of −1.1%, system availability of 0.0%, and grid availability and parasitic [18, 19]. Based on the PV correction, the array nominal energy is defined as 9723 MW/h at an STC efficiency of 15.47% as well as array virtual energy at MPPT which is calculated at 83704 MW/h. Before the final energy is injected into the grid, available energy at the inverter output side is assumed significant in whole losses in the PV system; therefore, the energy in the inverter output is calculated as 81938 MW/h. The final energy is injected into grid 80085 MW/h which predicts the estimated Figure 4 after all losses behavior done.Figure 4
Simulation results of losses over the whole year at the PV facility.The results of Figures5–8 show the energy flow in the PV system defining the losses at each step and setting the benchmark of energy. Figures 9 and 10 show the energy injected into the grid monthly based on the daily input/output energy diagram.Figure 5
First month values of horizontal global irradiation and global incident in coll. plane.Figure 6
First month effective energy at the output of the array and array virtual energy at MPPT.Figure 7
First month of global inverter loss and available energy at inverter output.Figure 8
First month AC ohmic loss and external transformer loss.Figure 9
Daily input/output energy diagram.Figure 10
Energy injected into the grid monthly.


### 3.2. Uncertainty Analysis

The uncertainty of the final result is a consequence of the uncertainty of solar radiation in this case (global horizontal irradiation), the inaccuracies of the simulation procedure itself (a choice of model), and uncertainties associated with external influences (shading, soiling, deviation of components from specification, inverter losses, cabling losses, etc.).


#### 3.2.1. Uncertainty Analysis of the Irradiation Data

Variability of the global horizontal irradiation is not negligible; at this site, the interannual variability of 3.4% of the project area has been calculated based on 15 years of monthly GI data from SolarGIS. In addition to the yearly variability of GHI, we have estimated an uncertainty of 6.0%~6.1% to account for any error in the modeled GHI data. This uncertainty considers the modeling accuracy of GHI data for the project site considering the vendor validation results of the model within this region.(1) Uncertainty of the Simulation. The main sources of uncertainties, excluding the variability of the global horizontal irradiation, are as shown in Table 9.Table 9
The above sources assessed for the project and are presented in the table.
Source of uncertainty in the simulation
Estimated uncertainty standard deviation
Irradiation on the tilted plane
3.0%
Shading/soiling/snow
2.5%
Reflection and spectral losses
1.5%
Deviation from STC
4.0%
Module power tolerance
2.0%
Module mismatch
1.0%
Cabling losses
0.8%
MPPT tracking
0.5%
Inverter losses
1.5%
Total
6.4%(2) Total Uncertainty. The future variability of GHI should be added to the above uncertainties, in order to obtain the total uncertainty in the solar energy assessment. The one-year or ten-year periods are typically under consideration. It is assumed that all errors are independent and that the Gaussian distribution is applicable. Table 10 resumes the uncertainty figures considered for the project.Table 10
The uncertainty figures considered for the project.
PV plant
Simulation uncertainty (%)
Solar resource uncertainty (%)
6.4%
6.1%
Future variability (%)
Total uncertainty (%)
1 year
10 years
1 year
10 years
3.4%
1.1%
9.5%
8.9%The total uncertainty of the energy production estimate could be reduced by considering an on-site solar monitoring station with irradiance data measured for a minimum period of one year. The confidence limits for probabilities of exceeding 99%, 90%, 75%, 60%, and 50% for the one year and ten years are provided in Table11 for each layout in downside scenarios. Additionally, we have an “upside” probability exceeding 25% in Table 11.Table 11
Confidence limits for the PV layout of PV plant 1- and 10-year periods, without power degradation.
Probability of exceedance (%)
1 year
10 years
Net energy output (MWh/annum)
Capacity factor (%/annum)
Net energy output (MWh/annum)
Capacity factor (%/annum)
99
86,683
15.3%
88,146
15.5%
90
97,700
17.2%
98,506
17.4%
75
104,101
18.3%
104,525
18.4%
60
108,542
19.1%
108,701
19.1%
50
111,213
19.6%
111,213
19.6%
25
118,325
20.8%
117,900
20.8%
Total
104,761
18.4%
104,832
18.5%The capacity factor of a PV plant is defined as the ratio of the actual energy produced over a period of time, to the hypothetical maximum possible, which refers to running full time at a rated power [19–21].


### 3.3. Power Degradation and Production

The degradation factors based on the PV module manufacturer’s warranty are typically pessimistic, and a more realistic approach on the temperature of the photovoltaic module has an adverse effect on the performance of photovoltaic modules [22]. If degradation is less, then good performance depends on the environmental conditions and seasons of the year. Previous research depicts that modules of different technologies have shown par. It has to be based on both the track record and existing information regarding each technology of the PV module’s manufacture. For that purpose, the polycrystalline silicon technology track record is taken into consideration. Ideally, module degradation would be further investigated during the technical due diligence process for the project, and the analysis of the specific datasheet would be reviewed by the module manufacturer. The authors have considered the PV module technology track record. Based on this review, the authors applied a linear factor of 0.75% to account for annual degradation due to long-term mechanisms. The degradation factor at the end of a single year is applied at the beginning of the same year, based on a pragmatic approach [5]. As a result, the PR for each single year is demonstrated in Table 12. The resulting production figures for a one-year period, with corresponding performance ratios, are also presented in Table 12. In order to reduce the minimum degradation factor in PV panels, a regular cleaning mechanism is required to enhance the good production [23]. The PV module degradation losses can reach 5% with a lifespan of 20~25-year warranty period [19, 24].Table 12
Performance ratio and net energy output (MWh/year) for one-year periods.
Year
PR (%)
P25
P50
P75
P90
P99
1
77.6
122750
115383
108006
101365
90064
2
77.2
121870
114549
107225
100632
89414
3
76.80
121099
113715
106444
99899
88764
4
76.20
120102
112881
105663
99166
88114
5
75.90
119214
112047
104882
98433
87464
6
75.50
118326
111213
104101
97700
86683
7
75.10
117438
110379
103320
96967
86033
8
74.50
16550
109545
102539
96234
85383
9
73.90
15663
108711
10 1759
95502
84733
10
73.40
14775
107877
10 0978
94769
84083
11
72.80
13888
107042
100197
94036
83433
12
72.20
13000
106208
99416
93,303
82782
13
71.70
12113
105374
98636
92571
82132
14
71.10
11225
104540
97855
91838
81482
15
70.50
10338
103706
97074
91105
80832
16
70.00
9451
102872
96293
90372
80182
17
69.40
8563
102038
95513
89640
79532
18
68.80
7676
101204
94732
88907
78882
19
68.30
6788
100370
93951
88174
78232
20
67.70
5901
99536
93170
87441
77581
21
67.10
5013
98701
92390
86709
76931
22
66.60
4126
97867
91609
85976
76281
23
66.00
3239
97033
90828
85243
75631
24
65.40
2351
96199
90047
84510
74981
25
64.90
1464
95365
89267
83778
74331
Total
71.54
40116.9
105374.2
94341.5
92570.8
82158.4


## 3.1. PV Energy Production

The main simulation results of the energy production produce 80085 MWh/year, and the performance ratio (PR) of 77.62% is obtained for 1 × 50 MW from 3 × 50 MW. These are three (3) 50 MW AC solar projects located adjacent to the same extended piece of land with a combined AC capacity of 150 MW. Therefore, each 50 MW is identical from 3 × 50 MW, and the (1) 50 MW size is executed for the simulation in this paper. The energy assessment result through simulation is shown in Table8.Table 8
Energy assessment results through simulation.
Software
PVSYST V6.47
Project
3 × 50 MW solar PV power project
Aggregate power
50 MW (1 × 50 MW)
Data sources
Meteonorm 7.1 [2001-2010]Sat=56%
Land coordinates
Longitude 68°4.2′, north latitude 25°19.2′, altitude 70 m
Legal time
Time zone TU + 5
Mounting structure
Fixed tile
PV system grid-connected
PV field orientation
PV modules
PV array
Inverter
User’s needs
Tilt 20°, azimuth 0°
Model JKM300P-72Jinko Solar
No. of module 166680
Model TC 1000KS
Unlimited load (grid)
Pnom
Pnom total
Pnom
300 Wp
50004 kWp
1000 kW AC
Inverter pack
No. of units: 50.0, Pnom total: 50000 kW AC
PV modules
8334 strings of 20 modules in series, 50004 kWp total
Area
323069 m2
Production
80085 MWh/year
PR
77.62% (performance ratio)
No shading field defined


### 3.1.1. Loss Diagram

According to the simulation result of the loss diagram in Figure3, PV facility defined loss factors such as module quality of +0.3%, module degradation loss of −1.0%, soiling of −0.3%, mismatch of −0.1, cabling (ohmic wiring loss) of -0.1%, inverter efficiency of −2.1%, transformer of −1.1%, system availability of 0.0%, and grid availability and parasitic [18, 19]. Based on the PV correction, the array nominal energy is defined as 9723 MW/h at an STC efficiency of 15.47% as well as array virtual energy at MPPT which is calculated at 83704 MW/h. Before the final energy is injected into the grid, available energy at the inverter output side is assumed significant in whole losses in the PV system; therefore, the energy in the inverter output is calculated as 81938 MW/h. The final energy is injected into grid 80085 MW/h which predicts the estimated Figure 4 after all losses behavior done.Figure 4
Simulation results of losses over the whole year at the PV facility.The results of Figures5–8 show the energy flow in the PV system defining the losses at each step and setting the benchmark of energy. Figures 9 and 10 show the energy injected into the grid monthly based on the daily input/output energy diagram.Figure 5
First month values of horizontal global irradiation and global incident in coll. plane.Figure 6
First month effective energy at the output of the array and array virtual energy at MPPT.Figure 7
First month of global inverter loss and available energy at inverter output.Figure 8
First month AC ohmic loss and external transformer loss.Figure 9
Daily input/output energy diagram.Figure 10
Energy injected into the grid monthly.


## 3.1.1. Loss Diagram

According to the simulation result of the loss diagram in Figure3, PV facility defined loss factors such as module quality of +0.3%, module degradation loss of −1.0%, soiling of −0.3%, mismatch of −0.1, cabling (ohmic wiring loss) of -0.1%, inverter efficiency of −2.1%, transformer of −1.1%, system availability of 0.0%, and grid availability and parasitic [18, 19]. Based on the PV correction, the array nominal energy is defined as 9723 MW/h at an STC efficiency of 15.47% as well as array virtual energy at MPPT which is calculated at 83704 MW/h. Before the final energy is injected into the grid, available energy at the inverter output side is assumed significant in whole losses in the PV system; therefore, the energy in the inverter output is calculated as 81938 MW/h. The final energy is injected into grid 80085 MW/h which predicts the estimated Figure 4 after all losses behavior done.Figure 4
Simulation results of losses over the whole year at the PV facility.The results of Figures5–8 show the energy flow in the PV system defining the losses at each step and setting the benchmark of energy. Figures 9 and 10 show the energy injected into the grid monthly based on the daily input/output energy diagram.Figure 5
First month values of horizontal global irradiation and global incident in coll. plane.Figure 6
First month effective energy at the output of the array and array virtual energy at MPPT.Figure 7
First month of global inverter loss and available energy at inverter output.Figure 8
First month AC ohmic loss and external transformer loss.Figure 9
Daily input/output energy diagram.Figure 10
Energy injected into the grid monthly.


## 3.2. Uncertainty Analysis

The uncertainty of the final result is a consequence of the uncertainty of solar radiation in this case (global horizontal irradiation), the inaccuracies of the simulation procedure itself (a choice of model), and uncertainties associated with external influences (shading, soiling, deviation of components from specification, inverter losses, cabling losses, etc.).


### 3.2.1. Uncertainty Analysis of the Irradiation Data

Variability of the global horizontal irradiation is not negligible; at this site, the interannual variability of 3.4% of the project area has been calculated based on 15 years of monthly GI data from SolarGIS. In addition to the yearly variability of GHI, we have estimated an uncertainty of 6.0%~6.1% to account for any error in the modeled GHI data. This uncertainty considers the modeling accuracy of GHI data for the project site considering the vendor validation results of the model within this region.(1) Uncertainty of the Simulation. The main sources of uncertainties, excluding the variability of the global horizontal irradiation, are as shown in Table 9.Table 9
The above sources assessed for the project and are presented in the table.
Source of uncertainty in the simulation
Estimated uncertainty standard deviation
Irradiation on the tilted plane
3.0%
Shading/soiling/snow
2.5%
Reflection and spectral losses
1.5%
Deviation from STC
4.0%
Module power tolerance
2.0%
Module mismatch
1.0%
Cabling losses
0.8%
MPPT tracking
0.5%
Inverter losses
1.5%
Total
6.4%(2) Total Uncertainty. The future variability of GHI should be added to the above uncertainties, in order to obtain the total uncertainty in the solar energy assessment. The one-year or ten-year periods are typically under consideration. It is assumed that all errors are independent and that the Gaussian distribution is applicable. Table 10 resumes the uncertainty figures considered for the project.Table 10
The uncertainty figures considered for the project.
PV plant
Simulation uncertainty (%)
Solar resource uncertainty (%)
6.4%
6.1%
Future variability (%)
Total uncertainty (%)
1 year
10 years
1 year
10 years
3.4%
1.1%
9.5%
8.9%The total uncertainty of the energy production estimate could be reduced by considering an on-site solar monitoring station with irradiance data measured for a minimum period of one year. The confidence limits for probabilities of exceeding 99%, 90%, 75%, 60%, and 50% for the one year and ten years are provided in Table11 for each layout in downside scenarios. Additionally, we have an “upside” probability exceeding 25% in Table 11.Table 11
Confidence limits for the PV layout of PV plant 1- and 10-year periods, without power degradation.
Probability of exceedance (%)
1 year
10 years
Net energy output (MWh/annum)
Capacity factor (%/annum)
Net energy output (MWh/annum)
Capacity factor (%/annum)
99
86,683
15.3%
88,146
15.5%
90
97,700
17.2%
98,506
17.4%
75
104,101
18.3%
104,525
18.4%
60
108,542
19.1%
108,701
19.1%
50
111,213
19.6%
111,213
19.6%
25
118,325
20.8%
117,900
20.8%
Total
104,761
18.4%
104,832
18.5%The capacity factor of a PV plant is defined as the ratio of the actual energy produced over a period of time, to the hypothetical maximum possible, which refers to running full time at a rated power [19–21].


## 3.2.1. Uncertainty Analysis of the Irradiation Data

Variability of the global horizontal irradiation is not negligible; at this site, the interannual variability of 3.4% of the project area has been calculated based on 15 years of monthly GI data from SolarGIS. In addition to the yearly variability of GHI, we have estimated an uncertainty of 6.0%~6.1% to account for any error in the modeled GHI data. This uncertainty considers the modeling accuracy of GHI data for the project site considering the vendor validation results of the model within this region.(1) Uncertainty of the Simulation. The main sources of uncertainties, excluding the variability of the global horizontal irradiation, are as shown in Table 9.Table 9
The above sources assessed for the project and are presented in the table.
Source of uncertainty in the simulation
Estimated uncertainty standard deviation
Irradiation on the tilted plane
3.0%
Shading/soiling/snow
2.5%
Reflection and spectral losses
1.5%
Deviation from STC
4.0%
Module power tolerance
2.0%
Module mismatch
1.0%
Cabling losses
0.8%
MPPT tracking
0.5%
Inverter losses
1.5%
Total
6.4%(2) Total Uncertainty. The future variability of GHI should be added to the above uncertainties, in order to obtain the total uncertainty in the solar energy assessment. The one-year or ten-year periods are typically under consideration. It is assumed that all errors are independent and that the Gaussian distribution is applicable. Table 10 resumes the uncertainty figures considered for the project.Table 10
The uncertainty figures considered for the project.
PV plant
Simulation uncertainty (%)
Solar resource uncertainty (%)
6.4%
6.1%
Future variability (%)
Total uncertainty (%)
1 year
10 years
1 year
10 years
3.4%
1.1%
9.5%
8.9%The total uncertainty of the energy production estimate could be reduced by considering an on-site solar monitoring station with irradiance data measured for a minimum period of one year. The confidence limits for probabilities of exceeding 99%, 90%, 75%, 60%, and 50% for the one year and ten years are provided in Table11 for each layout in downside scenarios. Additionally, we have an “upside” probability exceeding 25% in Table 11.Table 11
Confidence limits for the PV layout of PV plant 1- and 10-year periods, without power degradation.
Probability of exceedance (%)
1 year
10 years
Net energy output (MWh/annum)
Capacity factor (%/annum)
Net energy output (MWh/annum)
Capacity factor (%/annum)
99
86,683
15.3%
88,146
15.5%
90
97,700
17.2%
98,506
17.4%
75
104,101
18.3%
104,525
18.4%
60
108,542
19.1%
108,701
19.1%
50
111,213
19.6%
111,213
19.6%
25
118,325
20.8%
117,900
20.8%
Total
104,761
18.4%
104,832
18.5%The capacity factor of a PV plant is defined as the ratio of the actual energy produced over a period of time, to the hypothetical maximum possible, which refers to running full time at a rated power [19–21].


## 3.3. Power Degradation and Production

The degradation factors based on the PV module manufacturer’s warranty are typically pessimistic, and a more realistic approach on the temperature of the photovoltaic module has an adverse effect on the performance of photovoltaic modules [22]. If degradation is less, then good performance depends on the environmental conditions and seasons of the year. Previous research depicts that modules of different technologies have shown par. It has to be based on both the track record and existing information regarding each technology of the PV module’s manufacture. For that purpose, the polycrystalline silicon technology track record is taken into consideration. Ideally, module degradation would be further investigated during the technical due diligence process for the project, and the analysis of the specific datasheet would be reviewed by the module manufacturer. The authors have considered the PV module technology track record. Based on this review, the authors applied a linear factor of 0.75% to account for annual degradation due to long-term mechanisms. The degradation factor at the end of a single year is applied at the beginning of the same year, based on a pragmatic approach [5]. As a result, the PR for each single year is demonstrated in Table 12. The resulting production figures for a one-year period, with corresponding performance ratios, are also presented in Table 12. In order to reduce the minimum degradation factor in PV panels, a regular cleaning mechanism is required to enhance the good production [23]. The PV module degradation losses can reach 5% with a lifespan of 20~25-year warranty period [19, 24].Table 12
Performance ratio and net energy output (MWh/year) for one-year periods.
Year
PR (%)
P25
P50
P75
P90
P99
1
77.6
122750
115383
108006
101365
90064
2
77.2
121870
114549
107225
100632
89414
3
76.80
121099
113715
106444
99899
88764
4
76.20
120102
112881
105663
99166
88114
5
75.90
119214
112047
104882
98433
87464
6
75.50
118326
111213
104101
97700
86683
7
75.10
117438
110379
103320
96967
86033
8
74.50
16550
109545
102539
96234
85383
9
73.90
15663
108711
10 1759
95502
84733
10
73.40
14775
107877
10 0978
94769
84083
11
72.80
13888
107042
100197
94036
83433
12
72.20
13000
106208
99416
93,303
82782
13
71.70
12113
105374
98636
92571
82132
14
71.10
11225
104540
97855
91838
81482
15
70.50
10338
103706
97074
91105
80832
16
70.00
9451
102872
96293
90372
80182
17
69.40
8563
102038
95513
89640
79532
18
68.80
7676
101204
94732
88907
78882
19
68.30
6788
100370
93951
88174
78232
20
67.70
5901
99536
93170
87441
77581
21
67.10
5013
98701
92390
86709
76931
22
66.60
4126
97867
91609
85976
76281
23
66.00
3239
97033
90828
85243
75631
24
65.40
2351
96199
90047
84510
74981
25
64.90
1464
95365
89267
83778
74331
Total
71.54
40116.9
105374.2
94341.5
92570.8
82158.4


## 4. Conclusion

The authors evaluated the energy yield assessment with a study of different solar resources, which is based on uncertainty analysis for acquiring the final selection of the equipment and technology choice. Based on the total estimated production by simulation, the performance ratio of 77.62% and CF of 18.2% are calculated. However, based on the total uncertainty analysis, the net energy output/year and capacity factor/year are calculated at P99, P90, P75, P60, P50, and P25 and are presented in Table11. We applied a linear factor of 0.75% to account for the annual degradation (1~25 years) at the different probability of exceedance due to the long-term mechanisms applied. As a result, total PR% and total production at P25, P50, P75, P90, and P99 are calculated and presented in Table 12. In these results, we found that the PV plant is still achievable and the system can inject the target production into the grid, which will be given less PR shortfall against liquidated damages and fulfill the requirements of the power warranty.



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*Source: 1056735-2019-02-04.xml*