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Forecasting degradation rates of different photovoltaic systems using Robust Principal Component Analysis and ARIMA
Abstract and Figures
Degradation rates based on forecasting of performance ratio, Rp, time series are computed
and compared with actual degradation rates. A three year forecasting of monthly Rp, measured
from PV connected systems of various technologies is performed using the seasonal ARIMA
(SARIMA) time series model. The seasonal ARIMA model is estimated using monthly Rp measured
over a 5 year period and based on this model forecasting is implemented for the subsequent
three years. The degradation rate at the end of the forecasting period, eighth year, is computed
using a robust principal component analysis (RCPA) based methodology. The degradation rates
obtained for various (PV) systems are then compared to the ones obtained using the actual eight
year data.
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... The estimation of PLR provides the capability of determining the decay of output power of a PV system over its lifetime [2], [3]. Different statistical and comparative approaches have been reported in literature for PLR estimation including linear regression (LR), classical seasonal decomposition (CSD), year-on-year (YoY), robust principal component analysis (RPCA) and seasonal auto regressive integrated moving average (SARIMA) methods [1], [4]. ...
... Even though, different approaches have been reported in the literature, the selection of the most robust methodology for PLR estimation is an area that is not fully explored. Up to date, a standardised PLR estimation method does not exist [1]- [5], mainly due to the lack of a statistically significant model that can accurate capture the behaviour of the performance ration time series [2], [6]. ...
... Three of them were based on information criterions, namely the Akaike Information Criterion (AIC), the modified AIC for small sample size (AICc) and the Bayesian Information Criterion (BIC). The fourth one was based on an empirical methodology , referred as empirical criterion (EC) in this paper, by utilising the autocorrelation function (ACF), partial ACF (PACF) and residuals analysis [2]. Then, the RPCA method was used to estimate the PLR based on the forecasted PR values. ...
In this paper, an optimal methodology for forecasting the performance loss rate (PLR) of photovoltaic (PV) systems is presented using robust principal component analysis (RPCA) and seasonal auto regressive integrated moving average (SARIMA) methods. The SARIMA models were identified based on four different criterions (i.e., information and empirical criterions) using three different cases for the values of the seasonal and non-seasonal differencing orders of the models. The SARIMA models were used to forecast the performance ratio (PR) time series of fielded PV systems. Then, the RPCA method was used to estimate the PLR based on the forecasted PR values. The results demonstrated that the forecasted PLR values using the different cases and criteria were in good agreement with the PLR values extracted from actual field data, exhibiting absolute error (AE) below 1.03%/year. Therefore, the RPCA method can be used to estimate the PLR, even when using forecasted PR values. Moreover, for almost all PV systems, the models with the lower p-values yielded lower values for the RMSE between the actual and forecasted PR time series. The optimal methodology was finally chosen based on a comparative analysis focusing on the forecasting occuracy of both PR and PLR, statistical significance, and method’s simplicity.
... The second-order kinetic model, which was proposed subsequently [15], cannot be generalized to different ambient temperatures. To adapt the non-linear characteristics of a degradation trajectory, there have been some studies on the generalized exponential model [16], inverse power law model [17], autoregressive integrated moving average model [18], grayscale model [19], and other degradation modelling methods based on mathematical analysis models. Compared with the traditional dynamic model, mathematical analysis degradation models can improve the estimation accuracy of nonlinear degradation processes. ...
... Therefore, formula (19) should be excluded and the choice should be made among the other three formulas when making maintenance plans. In addition, formulas (18) and (20) are the research results for 500 kV reactors and 33/11 kV distribution transformers, respectively, but the research result of formula (17) comes from transmission transformers, which is highly similar to the application scenario of this paper. Therefore, it is recommended to adopt formula (17) when formulating the preventive maintenance plan of the transformer insulation. ...
Abstract This study is for the case where the available data of power transformer oil–paper insulation is limited to a small amount furfural data, to solve the problems in oil–paper insulation degradation modelling, such as few samples available, unknown function form of the degradation process, differences of individual transformers among degradation processes, and commonality of degradation trends. A power transformer oil–paper insulation degradation modelling and prediction method based on functional principal component analysis (FPCA) is proposed. First, discrete furfural data of oil–paper insulation degradation are converted into continuous functional data, and the common degradation information of transformers is extracted based on functional time warping technology. Second, the principal components of insulation degradation are extracted based on FPCA method, and the difference of degradation information of individual transformers is obtained by analysing the differential of principal component scores. Subsequently, power transformer oil–paper insulation degradation model is constructed, and finally, the degradation model is updated based on Bayesian theory and the oil–paper insulation degradation is predicted. The example results show that compared with traditional transformer oil–paper insulation degradation modelling method, the proposed method has obvious superiority in model accuracy.
... Recent studies focused on deseasonalization techniques such as CSD and STL in order to reduce seasonal fluctuations [4,7,19,28]. Other studies focused on reducing and extracting the underlying structure of the data (components that show the most substantial variance in the data) by applying the RPCA to calculate the degradation rate [1,8,31]. Another estimation technique is the YOY (that identifies the median slope among all lines passing through the data points) which has been proposed as an alternative to regressive models [37,38]. ...
... A variety of statistical techniques for calculating the long-term R D , namely OLS, CSD, YOY, STL, ARIMA, and RCPA [1,4,7,8,19,28,31,37,38], were applied to the constructed monthly PR synthetic time series of the test-bench PV system. The best ARIMA model (derived by the "auto.arima" ...
Accurate quantification of photovoltaic (PV) system degradation rate (RD) is essential for lifetime yield predictions. Although RD is a critical parameter, its estimation lacks a standardized methodology that can be applied on outdoor field data. The purpose of this paper is to investigate the impact of time period duration and missing data on RD by analyzing the performance of different techniques applied to synthetic PV system data at different linear RD patterns and known noise conditions. The analysis includes the application of different techniques to a 10-year synthetic dataset of a crystalline Silicon PV system, with emulated degradation levels and imputed missing data. The analysis demonstrated that the accuracy of ordinary least squares (OLS), year-on-year (YOY), autoregressive integrated moving average (ARIMA) and robust principal component analysis (RPCA) techniques is affected by the evaluation duration with all techniques converging to lower RD deviations over the 10-year evaluation, apart from RPCA at high degradation levels. Moreover, the estimated RD is strongly affected by the amount of missing data. Filtering out the corrupted data yielded more accurate RD results for all techniques. It is proven that the application of a change-point detection stage is necessary and guidelines for accurate RD estimation are provided.
... A summary of current deep learning-based techniques for predicting wind and solar power was published by Wang et al [9]. Some scientists use factual techniques to predict Solar Power generation, such as Autoregressive Moving Normal (ARMA) [10], Autoregressive Incorporated Moving Normal (ARIMA) [11], and Autoregressive Moving Normal Model with Exogenous Data Sources (ARMAX) [12]. However, these models are insufficient to increase the nonlinear time series data of SPG's forecasting precision. ...
Prediction of Solar power generation plays an important role to improve the efficiency ofeconomic dispatch function and reduce the dependence on fossil fuels and help in the energy managementsystem. For time series solar energy prediction multiple models were introduced but these model trains arebased on yearly historical data. A big data collection containing many missing values makes these modeltraining more complicated that’s why In this paper, an efficient energy prediction model is proposed for theprediction of time series solar energy based on short predicted weather training data. Two complimentarymodels are based on linear regression and a knowledge based neural network is exploited to predict futuresolar power, with offline training. The LR is structured under the direction of the proposed input methodparameter selection and used when training data is enough. KBNN is used for existing advantagespredictive models are also very important when training data is not enough. According to test findings usingreal data sets. An LR model can deal effectively with linear data, but a KBNN model can cope effectivelywith nonlinear behavior. Additionally, the results demonstrate the effectiveness of LR showing a correlationcoefficient (R2) is 98% with a root mean square error of 45 and KBNN shows a correlation coefficient (R2)is 99% with a root mean square error of 44 in providing a reliable version, The results additionally showthe functionality of LR and KBNN in imparting a dependable version, especially when the short trainingdataset is available.
... ARIMA is also one of the most popular statistical methods, which is used; for PV systems; not only to assess the degradation of performance, but also to forecast the variation of performances in the future [26], [27]. Here, we are interested in the assessment of the degradation of the array yields of the two technologies under study. ...
The prediction of performance of photovoltaic technologies is crucial, not only to improve the reliability and durability of these technologies but also to increase the confidence of investors and consumers in them. The accurate calculation of the degradation rate DR (%) in real operating conditions under specific climatic stresses is, therefore, paramount. The present study provides a comparison of performance losses of two silicon PV technologies installed on the rooftop of the Higher School of Technology in Laâyoune-Morocco. The two systems are a polycristalline array (pc-Si: 1.82 kWp) and an amorphous array (a-Si: 1.55 KWp), which are grid connected. In the light of related performance gathered over three-year, the degradation rates of the two systems were estimated using four statistical methods under the open-source software R. The techniques engaged in this paper are: classical seasonal decomposition (CSD), holt-winters (HW), autoregressive integrated moving average (ARIMA), and seasonal and trend decomposition by LOESS (STL). The results obtained using those methods show that DR(%) varies between 0.39% and 0.99% for pc-Si and between 0.29% and 0.64% for a-Si. The analysis of degradation accuracy shows that STL and CSD techniques provide results with high accuracy than ARIMA and HW for the two systems. The present study adds to knowledge on PV degradation under the subtropical desert climate of Laâyoune.
... Various statistical forecasting models have been developed by the researcher such as Auto Regressive Moving Average (ARMA) [5], Auto Regressive Integrated Moving Average (ARIMA) [6], Autoregressive integrated moving average with exogenous inputs (ARMAX) [7] and statistical time series model [8] which supports linear data, but it doesn't give promising results for non-linear data. Various methods have been presented in the literature to handle non-linear data such as optimization algorithm, Machine learning, fuzzy based system and hybridization of the algorithms. ...
Forecasting Solar Power is an important aspect for power trading company. It helps in energy bidding, planning and control. The challenge in forecasting is to predict non-linear data, which can be fulfilled by Computation technique and Machine Learning model. To further enhance the ML model optimization technique is used for training. Artificial Neural Network (ANN) is used as a ML model and optimization-based model is developed named as Optimized Artificial Neural Network (OANN). This paper also presents how the computation technique is incorporated in machine learning model, and a comparison is shown between these two models. Two OANN models are developed based on Crow Search Algorithm (CSA-ANN) and Seagull Optimization Algorithm (SOA-ANN). These models are forecasted for a day ahead, three days ahead and a week ahead solar power generation by considering time, irradiation and temperature as input parameter for the model. ANN gives best result for short-term prediction but unable to predict for mid-term and long-term prediction. This demerit of ANN is overcome by SOA-ANN, which is measured with statistical parameters such as Mean Absolute Error (MAE), Mean Square Error (MSE), Mean Absolute Percentage Error (MAPE) and Co-relation of determination (R ² ). The percentage improvement of SOA-ANN is obtained with these statistical parameter as 6.54%, 16.05%, 1.67% and 3.61%. The results associated with CSA-ANN is not much efficient as SOA-ANN, but it can predict better for low frequency values, but its overall performance is poor. SOA-ANN exhibit improved performance over ANN and CSA-ANN for forecasting.
... Such process allows to increase the estimation accuracy of d PVG Daily for the rest of the day (from two hours after sunrise time to sunset time). The Auto-Regressive Integrated Moving Average (ARIMA) model is used to perform PVG Short-Term (ST) forecasting thanks to its approved use and good accuracy [22][23][24][25][26][27][28]. ARIMA is an extended part of the ARMA method known as AR integrated MA. ...
The accurate forecast of the photovoltaic generation (PVG) process is essential to develop optimum installation sizing and pragmatic energy planning and management. This paper proposes a PVG forecast model for a PVG/ Battery installation. The forecasting strategy is built on a Medium-Term Energy Forecasting (MTEF) approach refined dynamically every hour (Dynamic Medium-Term Energy Forecasting (DMTEF)) and adjusted by means of a Short-Term Energy Forecasting (STEF) strategy. The MTEF predicts the generated energy for a day ahead based on the PVG of the last 15 days. As for STEF, it is a combination between PVG Short-Term (ST) forecasting and DMTEF methods obtained by selecting the least inaccurate PVG estimation every 15 minutes. The algorithm results are validated by measures taken on a 3 KWp standalone PVG/Battery installation. The proposed approaches have been integrated into a management algorithm in order to make a pragmatic decision to ensure load supply considering relevant constraints and priorities and guarantee the battery safety. Simulation results show that STEF provides accurate results compared to measures in stable and perturbed days. The NMBE (Normalized Mean Bias Error) is equal to -0.58% in stable days and 26.10% in perturbed days. © This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Forecasting Solar Power is an important aspect for power trading companies. It helps in energy bidding, planning, and control. The challenge in forecasting is to predict nonlinear data, which can be fulfilled by the computation technique and machine learning model. ML models have high accuracy for time-series forecasting, but their accuracy is poor for nonlinear forecasting. To enhance the ML model for nonlinear prediction, an optimization algorithm is used for training. This paper presents how the computation technique is incorporated into the machine learning model and compared it with the conventional model. CSA-ANN and SOA-ANN models are developed and forecast solar power for a-day-ahead, three-day-ahead, and a week-ahead solar power generation by considering time, irradiation, and temperature as input parameters for the model. The models are compared with ANN, DE-ANN, and PSO-ANN since these models are widely used. Upon comparison, ANN gives the best result for short-term prediction but is unable to predict midterm and long-term predictions, whereas this problem is overcome by SOA-ANN, which is done by changing its training algorithm, and its performance is measured via statistical parameters such as MAE, MSE, MAPE, and R2. The percentage improvement of SOA-ANN is obtained with these statistical parameters as 6.54%, 16.05%, 1.67%, and 3.61%. Hence, SOA-ANN gives best result as compared to other models.
This paper proposes to enhance the execution requirements of the solar photovoltaic (PV) street lighting system in Kuwait. A strength, weakness, opportunity and threat (SWOT) analysis was performed to recognise the elements needed for feasibility analysis followed by analysing the economic and environmental viability. The cost analysis shows that in a year, 18,770,072.56 m³ of natural gas and 4,939,492.779 gallons of fossil fuel can be saved from the installation. Hence, the cost of lowering carbon dioxide (CO2) is directly proportional to the cost of conserved energy resources since emissions from generation stations are reduced by 132,37vc8,406 kg of CO2. The payback period of 3 years and price decrease ratio of 13% shows that this system is economically and environmentally viable.
This paper provides a review of methodologies for measuring the degradation rate, RD, of photovoltaic (PV) technologies, as reported in the literature. As presented in this paper, each method yields different results with varying uncertainty depending on the measuring equipment, the data qualification and filtering criteria, the performance metric and the statistical method of estimation of the trend. This imposes the risk of overestimating or underestimating the true degradation rate and, subsequently, the effective lifetime of a PV module/array/system and proves the need for defining a standardized methodology. Through a literature search, four major statistical analysis methods were recognized for calculating degradation rates: (1) Linear Regression (LR), (2) Classical Seasonal Decomposition (CSD), (3) AutoRegressive Integrated Moving Average (ARIMA) and, (4) LOcally wEighted Scatterplot Smoothing (LOESS), with LR being the most common. These analyses were applied on the following performance metrics: (1) electrical parameters from IV curves recorded under outdoor or simulated indoor conditions and corrected to STC, (2) regression models such as the Photovoltaics for Utility Scale Applications (PVUSA) and Sandia models, (3) normalized ratings such as Performance Ratio, RP, and PMPP/GI and, (4) scaled ratings such as PMPP/Pmax, PAC/Pmax and kWh/kWp. The degradation rate results have shown that the IV method produced the lowest RD and LR produced results with large variation and the largest uncertainty. The ARIMA and LOESS methods, albeit less popular, produced results with low variation and uncertainty and with good agreement between them. Most importantly, this review showed that the RD is not only technology and site dependent, but also methodology dependent.
Grid-connected photovoltaic (PV) systems have become a significant constituent of the power supply mix. A challenge faced by both users and suppliers of PV systems is that of defining and computing a reliable metric of annual degradation rate while in service. This paper defines a new measure to calculate the degradation rate of PV systems from the PV field measured performance ratio (PR). At first, the PR time series is processed by conventional principal component analysis, which yields seasonality as the dominant data feature. The environment, operating conditions, uncertainty, and hardware used for monitoring influence the outdoor measurements unpredictably. These influences are viewed as perturbations that render the dominant feature obtained by PCA unsuitable to be used in a degradation rate definition. Robust principal component analysis (RPCA) is proposed to alleviate these effects. The new measure is defined as the area enclosed by the time series of the corrected by the RPCA annual monthly PR values. The degradation rates obtained for different technologies are compared with those obtained in previous studies. The results have shown that the degradation rates estimated by RPCA were in good agreement with previous investigations and provided increased confidence due to mitigation of uncertainty.
Long-term reliability is critical to the cost effectiveness and commercial success of photovoltaic (PV) products. Today most PV modules are warranted for 25 years, but there is no accepted test protocol to validate a 25-year lifetime. The qualification tests do an excellent job of identifying design, materials, and process flaws that are likely to lead to premature failure (infant mortality), but they are not designed to test for wear-out mechanisms that limit lifetime. This paper presents a method for evaluating the ability of a new PV module technology to survive long-term exposure to specific stresses. The authors propose the use of baseline technologies with proven long-term field performance as controls in the accelerated stress tests. The performance of new-technology modules can then be evaluated versus that of proven-technology modules. If the new-technology demonstrates equivalent or superior performance to the proven one, there is a high likelihood that they will survive versus the tested stress in the real world.
We evaluate and compare several forecasting techniques using no exogenous inputs for predicting the solar power output of a 1 MWp, single-axis tracking, photovoltaic power plant operating in Merced, California. The production data used in this work corresponds to hourly averaged power collected from November 2009 to August 2011. Data prior to January 2011 is used to train the several forecasting models for the 1 and 2 h-ahead hourly averaged power output. The methods studied in this work are: Persistent model, Auto-Regressive Integrated Moving Average (ARIMA), k-Nearest-Neighbors (kNNs), Artificial Neural Networks (ANNs), and ANNs optimized by Genetic Algorithms (GAs/ANN). The accuracy of the models is determined by computing error statistics such as mean absolute error (MAE), mean bias error (MBE), and the coefficient of correlation (R2) for the differences between the forecasted values and the measured values for the period from January to August of 2011. This work also addresses the accuracy of the different methods as a function of the variability of the power output, which depends strongly on seasonal conditions. The findings show that the ANN-based forecasting models perform better than the other forecasting techniques, that substantial improvements can be achieved with a GA optimization of the ANN parameters, and that the accuracy of all models depends strongly on seasonal characteristics of solar variability.
A brief discussion of Statistical Quality Control Charting procedures is first presented with special reference to the relevance of the objectives and assumptions. An approach to the design of discrete feedforward and feedback control schemes, which are of great importance for example, in the chemical industry, is then given. This approach to control employs discrete stochastic and dynamic models discussed in Part I of this paper (Box and Jenkins, 1968) and has a close link with the forecasting problems discussed there. The control algorithms obtained are ideally suited to discrete digital computer control. However, for common simple situations the algorithms may be represented by suitable charts or nomograms which may be employed to obtain improved manual control. The paper ends with a discussion of a problem typical of that arising in the parts manufacturing industry.
For a large scale implementation of photovoltaics (PV) in the urban environment, building integration is a major issue. This includes installations on roof or facade surfaces with orientations that are not ideal for maximum energy production. To evaluate the performance of PV systems in urban settings and compare it with the building user’s electricity consumption, three-dimensional geometry modelling was combined with photovoltaic system simulations. As an example, the modern residential district of Scharnhauser Park (SHP) near Stuttgart/Germany was used to calculate the potential of photovoltaic energy and to evaluate the local own consumption of the energy produced.
For most buildings of the district only annual electrical consumption data was available and only selected buildings have electronic metering equipment. The available roof area for one of these multi-family case study buildings was used for a detailed hourly simulation of the PV power production, which was then compared to the hourly measured electricity consumption. The results were extrapolated to all buildings of the analyzed area by normalizing them to the annual consumption data. The PV systems can produce 35% of the quarter’s total electricity consumption and half of this generated electricity is directly used within the buildings.
Long-term reliability is critical to the cost effectiveness and commercial success of photovoltaic (PV) products. Today most PV modules are warranted for 25 years, but there is no accepted test protocol to validate a 25-year lifetime. The qualification tests do an excellent job of identifying design, materials, and process flaws that are likely to lead to premature failure (infant mortality), but they are not designed to test for wear-out mechanisms that limit lifetime. This paper presents a method for evaluating the ability of a new PV module technology to survive long-term exposure to specific stresses. The authors propose the use of baseline technologies with proven long-term field performance as controls in the accelerated stress tests. The performance of new-technology modules can then be evaluated versus that of proven-technology modules. If the new-technology demonstrates equivalent or superior performance to the proven one, there is a high likelihood that they will survive versus the tested stress in the real world.