Analysis, and Modelling of Photo-Voltaic Systems

Monitoring of plant parameters is essential to ensure smooth and efficient functioning of a power plant. Any outage leads to both energy and financial loss.

Context

Causes for disruption or reduction in energy generation can be both avoidable and unavoidable in nature. Therefore, it is imperative to distinguish between the two and take appropriate steps to rectify preventable causes immediately. This can be done by continuously analyzing the data and comparing it with the historical data to check for any deviation in trends. These deviations could be seasonal, due to natural causes (unavoidable), or any other fault.

Analytics is a powerful tool that can assist in identifying these causes. In addition, it can provide good insight into various unavoidable reasons. As a result, long-term planning can be done, and steps can be taken to mitigate the impact of inevitable causes. This project attempts to understand the role of analytics in analyzing the parameters of a solar power plant and develop a mathematical model using past data through linear regression. This model would help in predicting energy generation.

The analysis of the project has been done using the guidelines provided in the report of Task-13 of the photovoltaic power system team of the International Energy Agency. Data for various plants were analyzed, and weekly trends were studied. Analysis of these trends helped develop a process that would assist in identifying the cause of deviation from the regular operation. It is a potent tool to help the analyst and the operator identify anomalies.

Key terms

Since the project is specific to the solar industry following are a few important terms that need to be discussed:

• Irradiation is the solar power received by the earth's surface. It is measured in W/m² (watt per meter square).

• Generation is the actual energy generated by a power plant. It is measured in kWh (kilowatt hour).

• Kilowatt peak (kWp) is the maximum power a module can generate under STC.

• Standard Test Condition (STC) is the ideal test condition under which the module will exhibit maximum efficiency. It is the condition when the ambient temperature is at 25°C and irradiation is at 1000 W/m². Standard Test Conditions help create uniform test conditions under which a consistent comparison of PV modules can be made.

• Performance ratio (PR) indicates the plant's performance. It is the ratio of actual generation and the energy that could have been generated theoretically by the solar module at a particular irradiation level. It is calculated by the below-mentioned formula. PR= (Actual generation)/(Irradiation * Area of the module * No of modules * Efficiency of the module) Ideally, this ratio should be 100%. But it is typically in the range of 82%-86%. If this ratio is too high or too low, it indicates abnormal operation or fault. It could also mean that some shading or near shading effect diminishes the plant performance and reduces generation. Other deficiencies like array performance, inverter performance, inverter shutdown, etc., can be easily captured through this. Further study of data and trend observation can help the operator identify the array or the inverter in which performance is not optimal.

• Stamps are the data points of various parameters of a PV plant plotted on a graph.

• System yield is the instantaneous value of power generated by a PV system and the kilowatt peak of the installed capacity. System yield is another important parameter of a PV plant. It is the ratio of power generated by the array and the maximum power that could be generated by a solar module as per the installed capacity.

Research

Rooftop solar PV plants are still in an early stage of maturity in India. During the project, the report published by Task 13 of the IEA PV Power Systems program was thoroughly studied, and the findings were incorporated into the research. The report gives a comprehensive guideline for the analytical assessment of the performance of a solar PV plant. It also describes how to prepare stamps and interpret the physical relationships between various parameters of a PV plant. By conducting periodic linear regression of the plant parameters and comparing the coefficients of the obtained equations, the behavior of the plant can be analyzed.

These linear relationships are characteristic of energy conversion steps to be monitored. For practical application, these relationships are identified periodically; that is, regression lines of recent samples are compared to the historical lines. These should be then regularly updated, which further helps in identifying trends or sudden changes. Over a more extended period, these models depict the functional properties of the components of the system. These plots help identify and interpret operational problems and highlight design flaws in the system. The application of these models helps in identifying the following indicators of the operation of the different energy conversion steps or sub-systems:

• If regression lines do not change significantly over time, it indicates that the properties of the system have remained constant.

• If regression lines change over time, it indicates a trend-wise change in system parameters.

• If the new samples show sudden and significant deviation from the regression lines, it hints toward exceptional operating points.

• If the samples show regular deviation from the regression lines, it hints towards some design flaw.

System-level performance can be monitored using solar irradiance and energy generation data. Module temperature is an additional valuable component. Further detailed analysis of the thermal behavior of the module and array level performance can be done using other parameters like ambient temperature and PR at the array level. System voltage and module temperature can be studied to understand the more specific thermal behavior of the module. Any effect that may occur between the PV module and the inverter would cause DC voltage to deviate from its characteristic linear voltage-temperature trend. The effect of wind speed can also be demonstrated at this level.

Problem statement

• To develop a tool that would help in preparing a baseline using historical data and comparing plant performance in future

• To develop a mathematical model using linear regression and historical data to help predict future energy generations

Methodology

SPSS Statistics software was used to prepare a mathematical model that would help predict the generation from the solar power plant. Initially, only solar irradiance was considered as the input variable. A model was obtained by using the data from the first year. Then this model was tested on the data for the second year by comparing the actual energy value generated with the model's predicted value. Percentage error between the actual and the generated value was calculated. It was observed that the percentage error was too high. Module temperature was also added to the mathematical model, and again the model was tested against historical data from the second year. Hence, an iterative method was adopted wherein parameters were added gradually, and the error was checked. Further, the data points where the irradiation level was too low and the deviation observed was high were eliminated based on solar irradiation (Gi) (Gi>500 W/m²).

As the value of solar irradiation increases, the graph tends to be more linear. Energy generation is also more reliable at higher irradiation levels. Further, season-wise data were selected for analysis. Here, the data points for the monsoon months were eliminated because the generation from a PV plant gets very erratic during these months due to cloud cover. This helped in reducing the percentage error to 11.26%. In addition, this study helped identify the data points where the deviation from the regression line was too high. These data points were removed from the research, and the models developed were tested on these data sets. This helped improve the prediction of energy generation, and the percentage error was brought down to 6.66%. The equation and reference of SPSS have been provided in the results section.

Results/Analysis and Implications

The mathematical model obtained from the analysis can be described by the following equation:

Equation 1

Y= Min (1.375 + 45.827 * X1 - 0.004 * X2), 5)

Where,
Y is the generation (in kWh)
X1 is the solar energy (in kWh/m²)
X2 is module temperature (in °C)

An upper limit of 5kWh has been kept due to the capacity and the design of the inverters. For every 5 minute block the maximum energy that can be generated by the inverters installed at the plant can never exceed 5kWh.

This model was obtained by conducting linear regression in SPSS software. The analysis was done on the first year data and the model thus obtained was tested on the second year data. The model was accurate in predicting in generation with a percentage error of 6.66%. Other information obtained from the analysis is given below:

The analysis done on various PV plant parameters based on the procedure discussed above helped in identifying the following possible reasons due to which generation loss may be observed:

• Cloud cover

• Inverter outage or defective strings

• Soiling of the PV modules

• Partial or complete shadowing effect due to any temporary structures or vegetation growth

• Loose connection of sensors

• Power limitation due to inverter under sizing

a) System Generation vs Irradiation

The data points are very close to the trend line for weeks 1 & 4, which shows a routine operation for the plant. But the data points are more scattered for weeks 2, 3, and 6. One reason for these wider scatter could be fluctuations in the irradiance level throughout the day. Further confirmation was made by studying the time stamp of the graphs of individual days of the week. It was observed that the drop and rise in the output yield were low compared to the same for solar irradiance. This could be caused by some passing clouds on these days. Further, when the data points of these days were removed, a much narrower scatter plot was observed, which was very similar to weeks 1 & 4.

A unique trend line can also be observed in this graph. The scatter plot is wide for week 5, and many data points are much below the data points for other weeks. The trend line also has a much lower slope, indicating a lower average PR for the week. This graph can help in revealing much information about the performance of a PV power plant.

b)Influence of Module Temperature on Performance Ratio

The relationship between PR and temperature of the module describes similar causes of deviation in the operating characteristics, as shown by the relationship between system generation and irradiation. However, the module temperature is also considered in this analysis. It complements the previous study's inferences and this additional parameter.

The trend lines for weeks 1 & 2 show a longer tail than the other weeks, so the PR can be good even at a lower heat. This data set is for March when the average ambient temperature is less than in April. Hence, these two weeks have a longer tail. The trend line for week 5 can be seen significantly deviating from other lines. This further confirms that some fault occurred in the plant this week. The trend lines for additional weeks appear to vary from one another at lower temperatures but appear to converge at higher temperatures.

c) System Generation vs Irradiation (for specific inverter)

This analysis is similar to the one done in point (a) above. It is beneficial in identifying the inverter or the array with the actual problem. Here, it can be clearly observed that the inverter generated little power from many data points. Upon closer inspection, it was found that the inverter did not function during the four days of this week. The same data analysis from other inverters produced similar results in analyzing the whole system. This study is also valuable for identifying whether all the inverters show similar average PR as the system or a few inverters show better average PR than others.

Conclusions

The analytical process developed in this report could be beneficial in identifying possible reasons which affect the generation of a PV plant. Any deviation in the trend line could indicate the plant is not operating correctly, and suitable corrective actions may be required. The stamps provide a visual representation of the data, and many deviations can be easily spotted through inspection. When these stamps are studied together, one by one possibility of a fault can be eliminated, and the exact reason can be investigated. The analysis at level one is sufficient for concluding a satisfactory plant operation. Analysis at level two helps determine the array or the inverter where the fault occurred, and generation loss was observed. Although this analysis is at level three, it can help capture some significant minute deviations in the system. The mathematical model can help predict the energy generation for one of the company's plants. But the process developed would assist in developing better and more effective models for other power plants in the future.

Recommendations

As more and more data becomes available, it would increase our understanding of the system and our ability to predict the generation from our plant. Monitoring power plants is a continuous process that must be followed diligently to avoid any loss of generation and revenue. For this purpose, other stamps must be regularly created and compared with the historical data. Hence, an essential recommendation for the operational analytics team would be to continuously add trend lines based on new regression for each week for documentation purposes of plant operation and comparing data obtained in the future with these baselines. If any fault occurs in the system in the future, a tool would be ready at the team's disposal to identify it and take corrective actions. Another recommendation is that analysis should be done level-wise to check for optimum plant operation. Weekly trend lines should be generated for all the levels. This should create a baseline for all the direct and derived parameters.

References

Journals, Reports and external books:

• 1.Woyte, A.; Richter, M.; Moser, D.; Reich, N.; Green, M.; Mau, S.; Beyer, H.G.(2014),Analytical Monitoring of Grid-connected Photovoltaic Systems, Report IEA-PVPS T13-03: 2014 International Energy Agency

• Marcos, J.; Marroyo, L.; Lorenzo, E.; García M. (2012),Power output fluctuations in large PV plants,International Conference on Renewable Energies and Power Quality

Online resources:

• http://www.amplussolar.com

• http://www.iea-pvps.org/

• http://www.samlexsolar.com/

• http://www.cea.nic.in/

• http://ecotec-energy.com/

• http://sinovoltaics.com/

• http://www.eia.gov/

• https://www.grow-trees.com/

• http://www.uhbvn.com/

• http://www.mahadiscom.in/

Tools used: Excel, IBM SPSS Statistics, SQL