ABSTRACT
Photovoltaic (PV) systems are an indispensable source of renewable energy supply for both commercial and domestic use in many developing countries including Kenya. However, it remains difficult to fully integrate solar energy into the power grid. This is because solar energy is intermittent and highly dependent on weather conditions. Therefore, proper modelling and assessment of the influence of environmental parameters on the PV system performance is essential. In this study, a detailed performance analysis of a 1.5 kW PV system was done to study the effect of selected weather parameters on the power output. A weather station was setup on the site to provide real-time measurements of the ambient temperature and relative humidity. Solar irradiance was measured using a HT304N reference cell and the PV module temperature measured using a HT instrument PT300N temperature sensor. A current - voltage values of the solar PV system were obtained using a current- voltage solar (I-V) analyzer. Data collection was done daily between 10:00 a.m. to 3:00 p.m. EAT at 30 minutes’ interval for a period of 21 days. Data analysis and visualization was performed using the R –software statistical package and Origin 9.1 software. An interactive application based on the single diode model was also developed and the results compared to measured data. The results obtained show that the ambient temperature increases with increasing solar irradiance with correlation coefficient (P) of 0.53 and Adj R2 of 0.27 showing a weak relationship. It was also noted that relative humidity varies inversely with solar irradiance with a correlation coefficient P of -0.50 and Adj R2 of 0.27. Relative humidity and ambient temperature exhibited a strong negative relationship yielding a correlation of -0.94 and Adj R2 of 0.90. It was also noted that the ambient temperature had a relatively strong linear relationship with module temperature having a correlation P of 0.84 and Adj R2 of 0.71. The study further showed that maximum PV power output varies linearly with solar irradiance with strong positive relationship evidenced by a correlation P of 0.99 and Adj R2 of 0.98. However, the PV system efficiency was noted to decrease with increasing solar irradiance with a negative correlation P of-0.85 and Adj R2 of 0.72. Series resistance was found to have a strong negative non-linear relationship with solar irradiance with Adj R2 of 1 while shunt resistance decreased non-linearly with solar irradiance of Adj R2 of 0.64. The open circuit voltage was found to vary inversely with the module temperature with correlation P of -0.50 and low Adj R2 of 0.25 indicating a weak relationship. The maximum power and module temperature exhibited a positive linear relationship with P of 0.70 and Adj R2 of 0.49. It was established that the module temperature decreased with the efficiency of the PV system with P of -0.87 and Adj R2 of 0.76. Due to the high correlation between ambient temperature, solar irradiance, relative humidity, module temperature principal component analysis (PCA) was done to remove redundant information. Support Vector regression (SVR) and random forest regression (RFR) models were therefore trained, tested and validated using data obtained from PCA to forecast real-time PV power output. SVR model employing leave one out cross validation technique (LOOCV) yielded the best model compared to 𝑘-fold and CV (Random resampling) cross validation techniques with root mean square (RMSE) of 40.4, Adj R2 of 0.98 and mean absolute error (MAE) of 29.01 on training dataset and RMSE of 45.10, Adj R2. of 0.97 and MAE of 29.27 on testing dataset. RFR model employing LOOCV yielded best model 𝑘-fold and CV (Random resampling) cross validation techniques with RMSE of 65, Adj R2 of 0.95 and MAE of 51.8 on training dataset whereas for testing set RMSE of 94, Adj R2 of 0.87, MAE of 68 were obtained. The trained models were further evaluated using validation dataset, SVR model outperformed RFR with RMSE of 43.16, Adj R2 of 0.97 and MAE of 32.57 compared to RMSE of 86, Adj R 2 of 0.90 and MAE of 69 obtained from RFR model. Furthermore, an app for carrying out real-time 1.5 kW PV power output prediction based on the SVR model was developed in this study. This research work therefore demonstrates that variability of solar irradiance, ambient temperature and relative humidity have significant effect on the performance of solar PV systems and must be considered when predicting PV power output. This is a significant step towards realizing a site-specific and dynamic solar PV performance analysis and forecasting technique.
TABLE OF CONTENTS
DECLARATION i
DEDICATION ii
ACKNOWLEGMENTS vi
ABSTRACT vii
LIST OF ABBREVIATIONS AND SYMBOLS ix
LIST OF TABLES xiii
LIST OF FIGURES xiv
CHAPTER ONE: INTRODUCTION
1.1 : Background of the study 1
1.1.1 : Solar Energy in Kenya 2
1.2 : Statement of the Problem 4
1.3 : Objectives 4
1.3.1 : Main Objective 4
1.3.2 : Specific Objectives 4
1.4 : Justification and Significance of the study 4
CHAPTER TWO: LITERATURE REVIEW
2.0 : Chapter overview 6
2.1 : PV Power forecasting methods 6
2.2 : Advances in PV power forecasting 7
CHAPTER THREE: THEORETICAL FRAMEWORK
3.0 : Chapter overview 11
3.1 : Solar radiation 11
3.2 : Solar cells 13
3.2.1 : External solar cell parameters 14
3.3 : The Equivalent circuit 16
3.4 : Exploratory data analysis (EDA) 19
3.4.1 : Principal Component Analysis (PCA) 20
3.5 : Machine learning techniques 21
3.5.1 : Support vector machines 22
3.5.2 : Random Forest Regression 24
3.6 : Accuracy Metrics for the evaluation of prediction models 25
CHAPTER FOUR: MATERIALS AND METHODS
4.0 : Chapter Overview 26
4.1 : Experimental setup 26
4.1.1 : PV Module Station 27
4.1.2 : Weather station setup 32
4.1.3 : Curve modelling 33
4.2 : Data preprocessing and analysis 33
4.3 : Machine learning (ML) 33
CHAPTER FIVE: RESULTS AND DISCUSSION
5.0 : Chapter Overview 35
5.1 : Variation of weather parameters within three weeks 35
5.1.1 : The variation of ambient temperature with solar irradiance 38
5.1.2 : The variation of solar irradiance with relative humidity 39
5.1.3 : The variation of ambient temperature with relative humidity 40
5.1.4 : The variation of ambient temperature with module temperature 42
5.2 : Effect of solar irradiance on the performance of the PV system 43
5.2.1 : Effect of solar irradiance on the maximum power 43
5.2.2 : Effect of solar irradiance on the short circuit current 44
5.2.3 : Effect of solar irradiance on the series resistance 45
5.2.4 : Effect of solar irradiance on the shunt resistance 46
5.2.5 : Effect of solar irradiance on the PV system efficiency 47
5.3 : Effect of module temperature on performance of the PV system 48
5.3.1 : Effect of module temperature on the maximum power 48
5.3.2 : Effect of module temperature on the open circuit voltage 49
5.3.3 : Effect of module temperature on the PV System efficiency 50
5.4 : Effect of relative humidity on the performance of a PV system 51
5.4.1 : Effect of relative humidity on the maximum power output 51
5.4.2 : Effect of relative humidity on the PV system efficiency 53
5.5 : Principal Component Analysis 54
5.6 : Random Forest Regression 56
5.7 : Support Vector Regression 59
5.8 : Model Validation 62
5.9 : Power forecast application based on the 1.5kW PV Solar system 65
5.10 : I-V curve application 67
CHAPTER SIX: CONCLUSIONS AND RECOMMENDATIONS
6.1 : Conclusions 72
6.2 : Recommendation for further work 73
REFERENCES 74
APPENDICES 79
Journal paper submitted to the Ethiopian journal of science and technology 102
LIST OF ABBREVIATIONS AND SYMBOLS
ARIMA Autoregressive Integrated Moving Average
ANN Artificial neural networks
ambtemp Ambient Temperature
Adj R2 Adjusted R Squared
AM Air Mass
app Application
𝐵 Zenith angle
CV Cross Validation
DC Direct current
DI Diffuse Horizontal Irradiance
DN Direct Normal Irradiance
𝐸𝑔 Energy band gap
EAT East Africa Time
FF Fill Factor
FiTs Feed-In Tariffs
𝐺 Irradiance at STC
𝐺𝑎 Measured irradiance
GE Mean-Squared Generalization Error
GI Global Horizontal Irradiance
Hum Relative Humidity
Im Maximum current
Isc Short-circuit current
IEA International Energy Agency
IES International Educational Services (UK)
Iv Output current
𝐼𝑑 Diode current
Ids Dark Saturation Current
Isa Saturation current
Ip Photo generated current
𝐼𝑅𝑝 Current through the parallel resistor
𝐼𝑣 Output current
I-V Current-Voltage
𝑘 Boltzmann Constant
KNN k Nearest Neighbor
𝑘𝑖 Temperature Coefficient short circuit current
𝑘𝑣 Temperature Coefficient Open circuit current
KRR Kernel ridge regression
LLAR Linear regression-time series model
modtemp Module Temperature
MIN Minimize
MAE Mean Absolute Error
ML Machine Learning
MW Megawatt
MoE Ministry of Energy
𝑛 Ideality factor
𝜼 Efficiency
𝑁𝑠 Number of cells connected in series
NWP Numerical Weather Prediction
NGO’s Non- Governmental Organization
P Pearson’s correlation Coefficient
PC1 First Principal Component
PC2 Second Principal Component
PC’s Principal Components
PCA Principal Component Analysis
PV Photovoltaic
P-V Power-Voltage
Pi Incident Power
Pm Maximum power
q Charge of an electron
Rs Series resistance
Rp Shunt resistance
R2 Coefficient of determination
RMSE Root Mean Square
RBNN Radial basis neural network
RF Random Forest
RFR Random Forest Regression
RES Renewable Energy Sources
SVM Support Vector Machines
SVR Support Vector Regression
STC Standard testing conditions
𝑇 Temperature at STC
𝑇𝑎 Ambient Temperature
𝑇𝑚 Module Temperature
UI User Interface
UK United Kingdom
Vt Thermal Voltage at STC
𝑉𝑡𝑛 Thermal Voltage at module temperature
𝑉𝑜𝑐 Open-circuit voltage
Vm Maximum Voltage
𝜎𝑎,𝑏 Standard Deviation
LIST OF TABLES
Table 4.1: The technical specifications of the 250W solar module used in the experiment at Standard testing conditions (Solinic East Africa.Limited, 2017) 27
Table 5.1: Summary of power output, solar irradiance, module temperature, ambient temperature and relative humidity for the three weeks 36
Table 5.2: Correlation matrix showing correlation between the measured weather parameters 54
Table 5.3: : Correlation matrix showing correlation between the four principal components 55
Table 5.4: Performance evaluation of RFR training data set and test dataset based on k-fold, “LOOCV” and CV (Random resampling) employed 57
Table 5.5: Performance evaluation of SVR training data set and test dataset based on k-fold, “LOOCV” and CV (Random resampling) employed. 60
Table 5.6: Comparison of performance of RFR and SVR based on performance on validation dataset. 63
LIST OF FIGURES
Figure 1.1: Map showing the PV potential power generated from 1994-2018 in Kenya (Solargis, 2019). 2
Figure 3.1: Illustration of air mass, AM0 outside the earth’s atmosphere, AM1 at the earth’s surface for normal incidence, AM1.5 at earth’s surface at zenith of 48.2 and AM 2.0 on the earth’s surface at zenith of 60.1 (Jeong, 2021) 12
Figure 3.2: Solar spectra: the blackbody, AM0 spectrum and the AM1.5 spectra (Zeman, et al., 2014) 13
Figure 3.3: Illustration of Solar cell and PV module (a) solar cell (b) PV module (Zeman, et al., 2014). 14
Figure 3.4: I-V characteristic curve of a PV module (Elkholy and El-ela, 2019) 16
Figure 3.5: Equivalent single diode model (Elkholy and El-ela, 2019) 17
Figure 3.6: Schematic showing a one-dimensional Support vector regression model showing hyperplane, ε – deviation and ξ is the deviation from the margin (Kleynhans et al., 2017) 23
Figure 4.1: Image of the 1.5kW PV Module station 26
Figure 4.2: Front view of the HT304 Standard Cell with two Si-Cells (a), Back view of the HT304N attached to the back frame of PV module using the stirrup and screws (b) 28
Figure 4.3: Temperature sensor PT300N attached with adhesive tape at the back of a solar module. 29
Figure 4.4: Solar Current –Voltage (I-V) 400 analyzer from HT instruments 30
Figure 4.5: An image of the Top View Software displayed on Computer monitor when connected to the Solar I-V 400 analyzer 31
Figure 4.6: A picture of the portable Weather station and a radio-controlled monitor displaying real time weather data is also shown. 32
Figure 4.7: A Block diagram showing the different Machine learning techniques used in this study 34 Figure 5.1: Illustration of minimum, 1st quartile, median, 3rd quartile and maximum 35
Figure 5.2: Variation of average daily solar irradiance with the day 37
Figure 5.3: Variation of average daily relative humidity with the day. 37
Figure 5.4: Variation of average daily ambient temperature with the day. 38
Figure 5.5 :Variation of ambient temperature with solar irradiance 39
Figure 5.6: Variation of solar irradiance with relative humidity. 40
Figure 5.7: Variation of ambient temperature with relative humidity 41
Figure 5.8: Variation of module temperature with ambient temperature 42
Figure 5.9: Variation of the maximum PV power with solar irradiance 43
Figure 5.10: Variation of short circuit current with solar irradiance 44
Figure 5.11: Variation of series resistance with solar irradiance 45
Figure 5.12: Variation of shunt resistance with solar irradiance 46
Figure 5.13: Variation of module efficiency with solar irradiance 47
Figure 5.14: Variation of maximum power with module temperature 48
Figure 5.15: Variation of open circuit voltage with module temperature 50
Figure 5.16: Variation of module efficiency with module temperature 51
Figure 5.17: Variation of maximum power with relative humidity 52
Figure 5.18: Variation of module efficiency with relative humidity. 53
Figure 5.19: PCA biplot showing score plot and loadings plot between the three clusters of power; low, medium and high-power output 56
Figure 5.20: Measured power output against predicted power output by Random regression model model (RFR)for the training dataset. 58
Figure 5.21: Measured power output against predicted power output by RFR for the testing dataset. 58
Figure 5.22: Measured power output against predicted power output by Support vector regresssion model (SVR) for the training dataset. 61
Figure 5.23: Measured power output against predicted power output by SVR model for the testing dataset. 62
Figure 5.24: Measured power output against predicted power output by RFR model for validation dataset. 64
Figure 5.25: Measured power output against predicted power output by SVR model for validation dataset 65
Figure 5.26: Power Forecast application user interface with input buttons, submit button and PV Output power 66
Figure 5.27: I-V curve shinny app user interface display showing the input parameters numeric input buttons and submit button for execution 67
Figure 5.28: Current-Voltage, Power-Voltage plots image from the I-V curve application 68
Figure 5.29: I-V curves for varying irradiance at a constant module temperature of 25℃ 69
Figure 5.30: I-V curve at varying module temperature with a constant irradiance of 1000W/m2 70
Figure 5.31: I-V curves of the simulated and measured at a solar irradiance 1117.5 W/m2 and at a module temperature 42.8℃ 71
CHAPTER ONE
INTRODUCTION
1.1 : Background of the study
Availability of sufficient, affordable and reliable energy is crucial for the wholesome development of any nation. Due to the ever-increasing world population together with advances in global technology with high power requirements, the world’s energy consumption is anticipated to rise by over 50% by the year 2050 (IEA, 2019).
To date, fossil fuels are the world's primary source of energy contributing about 85% of the world's energy budget (Lenzmann and Carol, 2016). Fossil fuels, therefore play a key role in the world economy and industrial development. However, they are non-renewable, unsustainable and their combustion has detrimental effects to the environment by contributing to a rise in atmospheric greenhouse gases, destruction of ecosystems, change in weather patterns, rising sea level and melting of glaciers (IES, 2019). It is for this reason, the United Nations has called for adoption of sustainable and renewable sources of energy.
Kenya’s economic growth has led to a rise in the demand for electricity from 1802 MW in 2018 to 1912MW in 2019. Demand for energy has been rising steadily by 3.6% annually (Africa Energy Series, 2020). 74.5% of Kenya’s energy demand is provided by wind, hydropower, solar and geothermal power which are all renewable energy sources with fossil fuel only supplying 25.5% to the energy mix. Majority of the power is derived from hydropower supplying approximately 677MW followed by geothermal 670 MW of the total 2.7GW installed capacity (Africa Energy Series, 2020). Hydropower capacity is adversely affected by long periods of drought which have been experienced since 2015 (Africa Energy Series, 2020). Geothermal power has great potential of providing up to 10 GW power (Achieng et al., 2012). However, rising investment charges, land disputes, lack trained personnel, huge grid infrastructural investment hinder its full exploitation (Samoita et al., 2020).
The focus of renewable energy has shifted to solar energy due to its abundance and availability. There are two types of solar technology in use today namely photovoltaics and thermal collectors. Photovoltaics are highly popular source of renewable energy especially off grid areas. Moreover, they require low maintenance, require short construction time and are pollution free energy (Goswami, 2017).
1.1.1 : Solar Energy
Kenya receives a lot of solar radiation due to its equatorial location. Kenya experiences an average of 5-7 hours of peak sunshine with average daily insolation of between 4-6 kW/m2. More specifically, the Northern parts and along the Lake Victoria basin generally receive higher and more consistent solar irradiance (Mark et al., 2009). Solar irradiation drops to less than 3.5 kWh/m2/day in populous regions near Nairobi, Mt Kenya, and the Aberdares, between the months of May and August (Mark et al., 2009).
Figure 1.1: Map showing the PV potential power generated from 1994-2018 in Kenya (Solargis, 2019).
Kenya’s solar market is among the most well-established in Africa with its roots extending to as early as the 1970’s with PV sales estimated at more than 1.2 MW market per year (Mark et al., 2009). The PV market has grown steadily for the past ten years at over 10 % annually. Kenya's total installed PV capacity is 100MW. This capacity is projected to grow yearly by 15% (Samoita et al., 2020).
The solar energy market is composed of tourism , telecom off-grid (community and household) and small-scale business electrification. In the late 1980’s, off-grid household electrification kicked off in the most densely inhabited rural areas with television signals. In the early to mid-1990’s coffee and tea “boom period” small-scale farmers from remote areas started purchasing residential solar electric systems. Off-grid household market is highly competitive and mature, however concerns of sub- standard quality of components and poor installation practices have recently risen (Mark et al.,2009). Off-grid community/ institutional systems include many active NGO’s, schools, churches missions, hospitals and other amenities that provide services to remote areas e.g. West Pokot also use solar power to operate their project. The tourism market includes game parks, hotels that are off-grid in the tourism industry while the telecom market is primarily made up of the mobile networks that use solar powered base stations.
The Kenyan government has also implemented policies such as Feed-In tariffs and 2006 Power Act No.12 that encourages the utilization of renewable energy sources (RES) to improve electricity generation in the country (Ministry of Energy, 2012). Feed-in tariffs (FiTs) are a policy that forces power providers to sell electricity generated by renewables at a predetermined rate. These government efforts have led to increase in PV system installations all over the country such as the largest solar farm of 55 MW in Garissa.
Solar power generation by PV depends heavily on weather variability. Due to the fluctuating weather conditions the question of reliability of solar power and its ability to satisfy the demand for energy remains an important unsolved problem in solar energy research. In this study a detailed analysis of the effect of relative humidity, solar irradiance ,ambient temperature and module temperature on the performance of a 1.5 kW solar PV system was performed. Machine learning- based predictive models to predict PV power output under varying weather conditions were built.
1.2 : Statement of the Problem
Solar PV systems have a huge potential for generating vast amounts of electric power, but their performance and power output is often highly variable, and heavily dependent on fluctuations in solar irradiance and other weather conditions. The inherent fluctuating nature of solar power sources poses a major challenge in the quest to fully integrate solar energy power plants into existing power grids without compromising on the stability of the power output. Therefore, as the number of solar PV systems and solar grid connected solar power plants installations increase, there is an urgent need to carry out research aimed at developing techniques and models with the capability of performing accurate real-time site-specific performance analysis and power output forecasting.
This research work aimed at carrying out detailed analysis and modelling of the effect of fluctuating weather parameters and solar irradiance on the performance of a 1.5 kW solar PV system, as well as develop a machine learning- based technique for performing real-time solar PV power system performance under varying weather conditions.
1.3 : Objectives
1.3.1 : Main Objective
To perform detailed analysis and modelling of PV solar systems performance using real-time observations and weather data as well as building a flexible and adaptable solar PV power forecasting model employing machine learning techniques.
1.3.2 : Specific Objectives
The specific objectives of this study were:
1. To obtain real time measurements of solar irradiance, relative humidity, module temperature and ambient temperature for analysis.
2. To obtain real time performance data of 1.5 kW PV solar system for analysis.
3. To model the 1.5 kW PV system performance (I-V curve and power output) and develop a forecasting model based on machine learning techniques.
1.4 : Justification and Significance of the study
The fast-increasing worldwide installation and use of solar PV systems has made it necessary to carry out research aimed at developing accurate and site-specific techniques and systems able to carry out real-time PV system performance analysis and output power forecasting. Particularly, solar energy stability is highly affected by variations in solar irradiance and various weather parameters. Most solar panels are flash tested at 1000 W/m2, 25°C Air mass 1.5 which are unrealistic owing the fact that these conditions during outdoor operations nearly never occur.
Furthermore, solar energy is highly intermittent and heavily depended on weather fluctuations, proper energy budgeting and planning, requires the development of reliable predictive and forecasting models able to provide accurate performance forecasts and modelling information for PV solar systems power output. This has the advantage of improving stability in power supply by providing predictions in PV power systems generation that are crucial for system controllers and future energy planning.
Research aimed at developing accurate PV systems power analysis and prediction models is therefore crucial in helping realize value and maximize returns from investments in Kenya's solar energy sector and therefore help reduce the existing barriers to the effective contribution of solar power to the national grid as well as domestic consumption. This research work is an endeavor in that direction
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