energies Article A Bayesian Model to Forecast the Time Series Kinetic Energy Data for a Power System Ashish Shrestha 1, * , Bishal Ghimire 2 and Francisco Gonzalez-Longatt 1   Citation: Shrestha, A.; Ghimire, B.; Gonzalez-Longatt, F. A Bayesian Model to Forecast the Time Series Kinetic Energy Data for a Power System. Energies 2021, 14, 3299. https://doi.org/10.3390/en14113299 Academic Editor: Wajiha Shireen Received: 3 May 2021 Accepted: 2 June 2021 Published: 4 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Electrical Engineering, Information Technology and Cybernetics, University of South-Eastern Norway, 3918 Porsgrunn, Norway; F.Gonzalez-Longatt@usn.no 2 Department of Electrical and Electronics Engineering, Kathmandu University, Dhulikhel 45200, Nepal; bishalghimire1997@gmail.com * Correspondence: Ashish.Shrestha@usn.no Abstract: Withthe massive penetration of electronic power converter (EPC)-based technologies, numerous issues are being noticed in the modern power system that may directly affect system dynamics and operational security. The estimation of system performance parameters is especially important for transmission system operators (TSOs) in order to operate a power system securely. This paper presents a Bayesian model to forecast short-term kinetic energy time series data for a power system, which can thus help TSOs to operate a respective power system securely. A Markov chain Monte Carlo (MCMC) method used as a No-U-Turn sampler and Stan’s limited-memory Broyden– Fletcher–Goldfarb–Shanno (LM-BFGS) algorithm is used as the optimization method here. The concept of decomposable time series modeling is adopted to analyze the seasonal characteristics of datasets, and numerous performance measurement matrices are used for model validation. Besides, an autoregressive integrated moving average (ARIMA) model is used to compare the results of the presented model. At last, the optimal size of the training dataset is identified, which is required to forecast the 30-min values of the kinetic energy with a low error. In this study, one-year univariate data (1-min resolution) for the integrated Nordic power system (INPS) are used to forecast the kinetic energy for sequences of 30 min (i.e., short-term sequences). Performance evaluation metrics such as the root-mean-square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and mean absolute scaled error (MASE) of the proposed model are calculated here to be 4.67, 3.865, 0.048, and 8.15, respectively. In addition, the performance matrices can be improved by up to 3.28, 2.67, 0.034, and 5.62, respectively, by increasing MCMC sampling. Similarly, 180.5 h of historic data is sufficient to forecast short-term results for the case study here with an accuracy of 1.54504 for the RMSE. Keywords: time series model; Bayesian model; ARIMA model; performance matrix; power system dynamics 1. Introduction With the increasing concern over clean and sustainable energy and rapid growth in electronic power converter (EPC)-based technologies, modern power systems are experi- encing vast transformation in all sectors, including generation, transmission, distribution, and even utilization. The generation sector is presently integrating EPC-based renewable energy resources (RESs), including photovoltaic panels and wind turbines, whereas the control mechanisms of other sectors are dependent on EPCs. At the same time, the propor- tion of synchronous generators is reducing in modern power systems, and synchronous generators are considered to be the main source of system inertia. In comparison to the conventional operation mode, the huge penetration of EPC-based technologies presents several changes in the operating dynamics of a modern power system. The major change is a significant drop in system inertia, which may directly affect the frequency quality, and operational security of power supply [1,2]. Frequency quality has an important role Energies 2021, 14, 3299. https://doi.org/10.3390/en14113299 https://www.mdpi.com/journal/energies