Department of Mathematics
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Item Time Series Auto-Regressive Integrated Moving Average Model for Renewable Energy Forecasting(Springer, 2020-07) Pasari, SumantaDue to the rapid pace of industrialization and growing demand for energy consumption, forecasting of renewable energy has become an inevitable focus of many recent studies. In this paper, our aim is to develop a univariate auto-regressive integrated moving average (ARIMA) model to forecast daily and monthly wind speed and temperature based on 15 years (2000–2014) of hourly data at Charanka Solar Park, Gujarat. To check the stationarity of time series, Dickey fuller test and rolling statistics plots are employed. Autocorrelation and partial autocorrelation plots are used to determine potential models, whereas Akaike information criterion (AIC) and Bayesian information criterion (BIC) are utilized to establish ARIMA (2, 1, 2) model. After rigorous training, model performance is validated using root means square (RMS) errors. The entire methodology is implemented in python using pandas for data exploration, and stats and scikit-learn libraries for model building and validation. On comparing results based on the log-likelihood, AIC and BIC values, we conclude that the ARIMA model provides better accuracy to the wind power forecasting as compared to solar power on the selected dataset.Item Statistical Analysis and Forecasting of Wind Speed(IEEE, 2022) Pasari, SumantaEnergy plays a vital role in urbanization and industrialization. Wind energy is highly valuable and accurate forecasts can help determine the best locations to set up windmills. Using a dataset comprising wind speeds from 15 years (2000–2014) within two locations of Rajasthan, namely Jaipur and Jaisalmer, we present a detailed statistical analysis including distribution analysis and forecasting using Moving Average (MA), Auto-Regressive (AR), Auto-Regressive Moving Average (ARMA), Auto-Regressive Integrated Moving Average (ARIMA) and Seasonal Auto-Regressive Integrated Moving Average (SARIMA). We show empirically why SARIMA is the best model and why the former four models are inadequate when it comes to forecasting wind speeds.Item Efficacy and application of the window-sliding ARIMA for daily and weekly wind speed forecasting(AIP, 2022-10) Pasari, SumantaAccurate forecasting of renewable energy resources has a deep societal and environmental impact. In this work, we investigate the efficacy and applicability of the Window-Sliding ARIMA (WS-ARIMA) method for daily and weekly forecasting of wind speed. The WS-ARIMA technique with a fixed or variable window length belongs to the class of adaptive models. Particularly, the sliding windows of fixed length are popular in the areas of finance, energy, and traffic management, where the dataset of necessity exhibits a seasonal pattern. To carry out the proposed analysis, the following processes were done: (1) we first perform a stationarity test on the wind speed data and observe weak stationarity; (2) we then apply a grid search method to obtain the optimal parameters of the ARIMA model; (3) we implement the WS-ARIMA method for both daily and weekly wind speed data and compare the results with the conventional ARIMA model, and (4) finally, we perform a residual analysis as a post processing step to examine any systematic bias in the implemented models. The experimental results based on 15 years (2000–2014) of daily and weekly wind speed data collected at four different locations in India reveal that the WS-ARIMA method consistently outperforms the conventional ARIMA method. The inclusion of window sliding in ARIMA has resulted in the overall RMSE reduction up to 75% in daily wind speed data and 50% in the weekly data. Therefore, we recommend the WS-ARIMA model as one of the potential techniques in wind speed forecasting at daily and weekly time horizons.Item Exploration of Solar Irradiance in Thar Desert Using Time Series Model(Springer, 2023) Pasari, SumantaThe present study concentrates on the exploration of solar irradiance in the Thar desert at eight selected locations, including Bhadla and Dhirubhai Ambani solar parks. For this, we first perform daily, weekly, and monthly solar irradiance prediction using five time-series models, namely AR, MA, ARMA, ARIMA, and seasonal ARIMA (SARIMA). The dataset of necessity includes hourly solar irradiance values of 21 yr (2001–2021) from NASA’s power project. As these time series models turn out to be inadequate to capture seasonality across temporal resolution, we additionally implement the window sliding ARIMA (WSARIMA) and LSTM to incorporate possible nonlinearity and seasonality in the dataset. Based on the three standard indicators, namely RMSE, MAPE, and MAE, we observe that LSTM outperforms other models at daily and weekly time resolution, whereas ARMA turns out to be the best on monthly dataset. The emanated results suggest that all locations reveal a high potential for harnessing solar power. The present analysis, therefore, enables solar irradiance exploration in the Thar desert through different time series models.