Quasi-Instantaneous Battery End-of-Discharge Time Prognosis with Non-Stationary Autoregressive Exogenous Inputs
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Published
Mar 1, 2026
David Acuña-Ureta
Diego Fuentealba-Secul
https://orcid.org/0000-0001-9958-2351
Diego Fuentealba-Secul
Abstract
Reliable automation of engineering systems consider the implementation of condition monitoring routines to make decisions that can be carried out either manually, or through control loops. In recent years, great efforts have been made to incorporate prognostics into decision making, primarily through heuristic or data-driven approaches. However, being effective and efficient in this task is quite difficult. On one hand, it takes time to compute predictions, which makes prognostics-informed control unfeasible in real-time. On the other hand, until very recently, prognostics lacked a solid theoretical foundation to provide formalism and mathematical guarantees on prediction convergence. The concept of near-instantaneous prognosis was recently introduced, enabling prognostic analysis in nonlinear dynamical systems with maximal performance and stochastic convergence guarantees, under the assumption that future exogenous inputs follow strictly stationary stochastic processes. In this article, near-instantaneous prognosis is revisited to predict the End-of-Discharge time of batteries in which the discharge current, interpreted as exogenous input, is modeled as an autoregressive stochastic process. Furthermore, the strict stationarity condition is relaxed giving rise to a new variant presented as quasi-instantaneous prognosis, seeking to generalize this approach by removing this restrictive hypothesis in order to broaden its range of applications, especially in electrical engineering, such as in solar and wind resource prediction, or energy demand forecasting, to name some examples.
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Keywords
Batteries, Condition monitoring, End-of-Discharge time, Event prognostics, Monte Carlo simulations, Time-of-Event
References
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Acuña-Ureta, D. E., & Orchard, M. E. (2022). Near-instantaneous battery End-of-Discharge prognosis via uncertain event likelihood functions. ISA Transactions.
Acuña-Ureta, D. E., Orchard, M. E., & Wheeler, P. (2021). Computation of time probability distributions for the occurrence of uncertain future events. Mechanical Systems and Signal Processing, 150.
Ahmed Murtaza, A., Saher, A., Hamza Zafar, M., Kumayl Raza Moosavi, S., Faisal Aftab, M., & Sanfilippo, F. (2024). Paradigm shift for predictive maintenance and condition monitoring from industry 4.0 to industry 5.0: A systematic review, challenges and case study. Results in Engineering, 24, 102935. doi: https://doi.org/10.1016/j.rineng.2024.102935
Alabi, T. M., Aghimien, E. I., Agbajor, F. D., Yang, Z., Lu, L., Adeoye, A. R., & Gopaluni, B. (2022). A review on the integrated optimization techniques and machine learning approaches for modeling, prediction, and decision making on integrated energy systems. Renewable Energy, 194, 822-849. doi: https://doi.org/10.1016/j.renene.2022.05.123
Amini, M., Karabasoglu, O., Ilić, M. D., Boroojeni, K. G., & Iyengar, S. S. (2015). ARIMA-based demand forecasting method considering probabilistic model of electric vehicles’ parking lots. 2015 IEEE Power & Energy Society General Meeting, 1-5. doi: https://doi.org/10.1109/PESGM.2015.7286050
Amini, M. H., Kargarian, A., & Karabasoglu, O. (2016). ARIMA-based decoupled time series forecasting of electric vehicle charging demand for stochastic power system operation. Electric Power Systems Research, 140, 378-390. doi: https://doi.org/10.1016/j.epsr.2016.06.003
Biggio, L., & Kastanis, I. (2020). Prognostics and health management of industrial assets: Current progress and road ahead. Front. Artif. Intell., 3(578613).
Bougerol, P., & Picard, N. (1992). Strict stationarity of generalized autoregressive processes. The Annals of Probability, 20(4), 1714–1730.
Brockwell, P. J., & Lindner, A. (2010). Strictly stationary solutions of autoregressive moving average equations. Biometrika, 97(3), 765–772.
Cesar, W., Priyasta, D., Aji, P., Melyana, M., Suprianto, A., Nami, O. F., & Riza, R. (2025). A hybrid ARIMA and DNN approach with residual learning for electric vehicle charging demand forecasting. TELKOMNIKA (Telecommunication Computing Electronics and Control), 23(6), 1555–1565.
Chen, Z., Sun, H., Dong, G., Wei, J., & Wu, J. (2019). Particle filter-based state-of-charge estimation and remaining-dischargeable-time prediction method for lithium-ion batteries. Journal of Power Sources, 414, 158-166. doi: https://doi.org/10.1016/j.jpowsour.2019.01.012
Daigle, M. J., & Goebel, K. (2013). Model-based prognostics with concurrent damage progression processes. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 43(3), 535-546.
Dang, L., Yang, J., Liu, M., & Chen, B. (2024). Differential equation-informed neural networks for state-of-charge estimation. IEEE Transactions on Instrumentation and Measurement, 73, 1-15. doi: https://doi.org/10.1109/TIM.2023.3334377
Deng, Y., Barros, A., & Grall, A. (2014). Calculation of failure level based on inverse first passage problem. In 2014 reliability and maintainability symposium (p. 1-6). doi: https://doi.org/10.1109/RAMS.2014.6798459
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Fink, O., Wang, Q., Svensén, M., Dersin, P., Lee, W.-J., & Ducoffe, M. (2020). Potential, challenges and future directions for deep learning in prognostics and health management applications. Engineering Applications of Artificial Intelligence, 92, 103678.
García Bustos, J. E., Baeza, C., Brito Schiele, B., Rivera, V., Masserano, B., Orchard, M. E., Burgos-Mellado, C., & Perez, A. (2025). A novel data-driven framework for driving range prognostics in electric vehicles. Engineering Applications of Artificial Intelligence, 142, 109925. doi: https://doi.org/10.1016/j.engappai.2024.109925
Ghazal, T. M., Noreen, S., Said, R. A., Khan, M. A., Siddiqui, S. Y., Abbas, S., Aftab, S., & Ahmad, M. (2022). Energy demand forecasting using fused machine learning approaches. Intelligent Automation & Soft Computing, 31(1), 539–553. doi: https://doi.org/10.32604/iasc.2022.019658
Jinsong, Y., Shuang, L., Diyin, T., & Hao, L. (2017). Remaining discharge time prognostics of lithium-ion batteries using dirichlet process mixture model and particle filtering method. IEEE Transactions on Instrumentation and Measurement, 66(9), 2317-2328. doi: https://doi.org/10.1109/TIM.2017.2708204
Khalid, A., & Sarwat, A. I. (2021). Unified univariate-neural network models for Lithium-Ion battery State-of-Charge forecasting using minimized Akaike information criterion algorithm. IEEE Access, 9, 39154-39170. doi: https://doi.org/10.1109/ACCESS.2021.3061478
Khalid, A., Sundararajan, A., & Sarwat, A. I. (2019). An ARIMA-NARX model to predict Li-Ion state of charge for unknown charge/discharge rates. In 2019 ieee transportation electrification conference (itec-india) (p. 1-4). doi: https://doi.org/10.1109/ITEC-India48457.2019.ITECINDIA2019-1
Kim, Y., Son, H., & Kim, S. (2019). Short term electricity load forecasting for institutional buildings. Energy Reports, 5, 1270-1280. doi: https://doi.org/10.1016/j.egyr.2019.08.086
Kim, Y., & Kim, S. (2021). Forecasting charging demand of electric vehicles using time-series models. Energies, 14(5). doi: https://doi.org/10.3390/en14051487
Klump, A., & Kolb, M. (2023). Uniqueness of the inverse first-passage time problem and the shape of the shiryaev boundary. Theory of Probability & Its Applications, 67(4), 570-592. doi: https://doi.org/10.1137/S0040585X97T991155
Lefebvre, M. (2026). On an inverse first-passage problema for jump-diffusion processes. Mathematics, 14(1). doi: https://doi.org/10.3390/math14010087
Maden, A. H., & Arabacı, H. (2024). Effects of discharge cut-off voltage level on available battery charge capacity and battery life. International Journal of Data Science and Applications, 7(1), 1–12.
Orchard, M. E., & Vachtsevanos, G. J. (2009). A particle-filtering approach for on-line fault diagnosis and failure prognosis. Trans. Inst. Meas. Control 2009, 31(3-4), 221-246.
Pola, D. A., Navarrete, H. F., Orchard, M. E., Rabié, R. S., Cerda, M. A., Olivares, B. E., Silva, J. F., Espinoza, P. A., & Pérez, A. (2015). Particle-filtering-based discharge time prognosis for lithium-ion batteries with a statistical characterization of use profiles. IEEE Transactions on Reliability, 64(2), 710-721.
Quiñones, F., Milocco, R. H., & Real, S. G. (2018). Remaining discharge-time prediction for batteries using the Lambert function. Journal of Power Sources, 400, 256-263.
Rana, M. M., Uddin, M., Sarkar, M. R., Meraj, S. T., Shafiullah, G., Muyeen, S., Islam, M. A., Jamal, T. (2023). Applications of energy storage systems in power grids with and without renewable energy integration — a comprehensive review. Journal of Energy Storage, 68, 107811. doi: https://doi.org/10.1016/j.est.2023.107811
Salminen, P. (1988). On the first hitting time and the last exit time for a Brownian motion to/from a moving boundary. Advances in Applied Probability, 20(2), 411–426.
Saxena, A., Celaya, J., Roychoudhury, I., Saha, S., Saha, B., & Goebel, K. (2012). Designing data-driven battery prognostic approaches for variable loading profiles: Some lessons learned. European Conference of the Prognostics and Health Management Society.
Sbarufatti, C., Corbetta, M., Giglio, M., & Cadini, F. (2017). Adaptive prognosis of lithium-ion batteries based on the combination of particle filters and radial basis function neural networks. Journal of Power Sources, 344, 128-140.
Schacht-Rodríguez, R., Ponsart, J.-C., García-Beltrán, C. D., & Astorga-Zaragoza, C. M. (2018). Prognosis & health management for the prediction of UAV flight endurance. IFAC-PapersOnLine, 51(24), 983-990.
Shamsi, M., & Cuffe, P. (2022). Prediction markets for probabilistic forecasting of renewable energy sources. IEEE Transactions on Sustainable Energy, 13(2), 1244-1253. doi: https://doi.org/10.1109/TSTE.2021.3112916
Siegert, A. J. F. (1951). On the first passage time probability problem. Physical Review, 81(4), 617-623.
Steinstraeter, M., Buberger, J., & Trifonov, D. (2020). Battery and heating data in real driving cycles. IEEE Dataport. Retrieved from https://dx.doi.org/10.21227/6jr9-5235 doi: https://doi.org/10.21227/6jr9-5235
Vachtsevanos, G., & Zahiri, F. (2022). Prognosis: Challenges, precepts, myths and applications. 2022 IEEE Aerospace Conference (AERO), 1-13.
Van den Bergh, K., Hytowitz, R. B., Bruninx, K., Delarue, E., Dhaeseleer, W., & Hobbs, B. F. (2017). Benefits of coordinating sizing, allocation and activation of reserves among market zones. Electric Power Systems Research, 143, 140-148. doi: https://doi.org/10.1016/j.epsr.2016.10.012
Vollenbröker, B. K. (2011). Strictly stationary solutions of multivariate ARMA and univariate ARIMA equations (Unpublished doctoral dissertation). Technische Universität Braunschweig.
Walker, E., Rayman, S., & White, R. E. (2015). Comparison of a particle filter and other state estimation methods for prognostics of lithium-ion batteries. Journal of Power Sources, 287, 1-12.
Wang, W., Yuan, B., Sun, Q., & Wennersten, R. (2022). Application of energy storage in integrated energy systems — a solution to fluctuation and uncertainty of renewable energy. Journal of Energy Storage, 52, 104812. doi: https://doi.org/10.1016/j.est.2022.104812
Wang, Y., & Chen, Z. (2020). A framework for state-of-charge and remaining discharge time prediction using unscented particle filter. Applied Energy, 260.
Wang, Y., Gao, G., Li, X., & Chen, Z. (2020). A fractional-order model-based state estimation approach for lithium-ion battery and ultra-capacitor hybrid power source system considering load trajectory. Journal of Power Sources, 449, 227543. doi: https://doi.org/10.1016/j.jpowsour.2019.227543
Wang, Y., Tian, J., Sun, Z., Wang, L., Xu, R., Li, M., & Chen, Z. (2020). A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems. Renewable and Sustainable Energy Reviews, 131, 110015. doi: https://doi.org/10.1016/j.rser.2020.110015
Wazirali, R., Yaghoubi, E., Abujazar, M. S. S., Ahmad, R., & Vakili, A. H. (2023). State-of-the-art review on energy and load forecasting in microgrids using artificial neural networks, machine learning, and deep learning techniques. Electric Power Systems Research, 225, 109792. doi: https://doi.org/10.1016/j.epsr.2023.109792
Xiong, R., Cao, J., Yu, Q., He, H., & Sun, F. (2017). Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access, 6, 1832-1843.
Yohai, V. J., & Maronna, R. A. (1977). Asymptotic behavior of least-squares estimates for autoregressive processes with infinite variances. The Annals of Statistics, 5(3), 554–560.
Zhang, X., Wang, Y., Liu, C., & Chen, Z. (2017). A novel approach of remaining discharge energy prediction for large format lithium-ion battery pack. Journal of Power Sources, 343, 216-225.
Zhang, Y., Xiong, R., He, H., & Pecht, M. G. (2019). Lithium-ion battery remaining useful life prediction with Box–Cox Transformation and Monte Carlo simulation. IEEE Transactions on Industrial Electronics, 66(2), 1585-1597.
Acuña-Ureta, D. E., & Orchard, M. E. (2022). Near-instantaneous battery End-of-Discharge prognosis via uncertain event likelihood functions. ISA Transactions.
Acuña-Ureta, D. E., Orchard, M. E., & Wheeler, P. (2021). Computation of time probability distributions for the occurrence of uncertain future events. Mechanical Systems and Signal Processing, 150.
Ahmed Murtaza, A., Saher, A., Hamza Zafar, M., Kumayl Raza Moosavi, S., Faisal Aftab, M., & Sanfilippo, F. (2024). Paradigm shift for predictive maintenance and condition monitoring from industry 4.0 to industry 5.0: A systematic review, challenges and case study. Results in Engineering, 24, 102935. doi: https://doi.org/10.1016/j.rineng.2024.102935
Alabi, T. M., Aghimien, E. I., Agbajor, F. D., Yang, Z., Lu, L., Adeoye, A. R., & Gopaluni, B. (2022). A review on the integrated optimization techniques and machine learning approaches for modeling, prediction, and decision making on integrated energy systems. Renewable Energy, 194, 822-849. doi: https://doi.org/10.1016/j.renene.2022.05.123
Amini, M., Karabasoglu, O., Ilić, M. D., Boroojeni, K. G., & Iyengar, S. S. (2015). ARIMA-based demand forecasting method considering probabilistic model of electric vehicles’ parking lots. 2015 IEEE Power & Energy Society General Meeting, 1-5. doi: https://doi.org/10.1109/PESGM.2015.7286050
Amini, M. H., Kargarian, A., & Karabasoglu, O. (2016). ARIMA-based decoupled time series forecasting of electric vehicle charging demand for stochastic power system operation. Electric Power Systems Research, 140, 378-390. doi: https://doi.org/10.1016/j.epsr.2016.06.003
Biggio, L., & Kastanis, I. (2020). Prognostics and health management of industrial assets: Current progress and road ahead. Front. Artif. Intell., 3(578613).
Bougerol, P., & Picard, N. (1992). Strict stationarity of generalized autoregressive processes. The Annals of Probability, 20(4), 1714–1730.
Brockwell, P. J., & Lindner, A. (2010). Strictly stationary solutions of autoregressive moving average equations. Biometrika, 97(3), 765–772.
Cesar, W., Priyasta, D., Aji, P., Melyana, M., Suprianto, A., Nami, O. F., & Riza, R. (2025). A hybrid ARIMA and DNN approach with residual learning for electric vehicle charging demand forecasting. TELKOMNIKA (Telecommunication Computing Electronics and Control), 23(6), 1555–1565.
Chen, Z., Sun, H., Dong, G., Wei, J., & Wu, J. (2019). Particle filter-based state-of-charge estimation and remaining-dischargeable-time prediction method for lithium-ion batteries. Journal of Power Sources, 414, 158-166. doi: https://doi.org/10.1016/j.jpowsour.2019.01.012
Daigle, M. J., & Goebel, K. (2013). Model-based prognostics with concurrent damage progression processes. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 43(3), 535-546.
Dang, L., Yang, J., Liu, M., & Chen, B. (2024). Differential equation-informed neural networks for state-of-charge estimation. IEEE Transactions on Instrumentation and Measurement, 73, 1-15. doi: https://doi.org/10.1109/TIM.2023.3334377
Deng, Y., Barros, A., & Grall, A. (2014). Calculation of failure level based on inverse first passage problem. In 2014 reliability and maintainability symposium (p. 1-6). doi: https://doi.org/10.1109/RAMS.2014.6798459
Dong, G., Shen, F., Sun, L., Zhang, M., & Wei, J. (2025). A bayesian inferred health prognosis and state of charge estimation for power batteries. IEEE Transactions on Instrumentation and Measurement, 74, 1-12. doi: https://doi.org/10.1109/TIM.2024.3497053
Dong, G., Wei, J., Chen, Z., Sun, H., & Yu, X. (2017). Remaining dischargeable time prediction for lithium-ion batteries using unscented kalman filter. Journal of Power Sources, 364, 316-327. doi: https://doi.org/10.1016/j.jpowsour.2017.08.040
El-Afifi, M. I., Eladl, A. A., Sedhom, B. E., & Hassan, M. A. (2025). Enhancing EV charging station integration: A hybrid ARIMA-LSTM forecasting and optimization framework. IEEE Transactions on Industry Applications, 61(3), 4924-4935. doi: https://doi.org/10.1109/TIA.2025.3540788
Fink, O., Wang, Q., Svensén, M., Dersin, P., Lee, W.-J., & Ducoffe, M. (2020). Potential, challenges and future directions for deep learning in prognostics and health management applications. Engineering Applications of Artificial Intelligence, 92, 103678.
García Bustos, J. E., Baeza, C., Brito Schiele, B., Rivera, V., Masserano, B., Orchard, M. E., Burgos-Mellado, C., & Perez, A. (2025). A novel data-driven framework for driving range prognostics in electric vehicles. Engineering Applications of Artificial Intelligence, 142, 109925. doi: https://doi.org/10.1016/j.engappai.2024.109925
Ghazal, T. M., Noreen, S., Said, R. A., Khan, M. A., Siddiqui, S. Y., Abbas, S., Aftab, S., & Ahmad, M. (2022). Energy demand forecasting using fused machine learning approaches. Intelligent Automation & Soft Computing, 31(1), 539–553. doi: https://doi.org/10.32604/iasc.2022.019658
Jinsong, Y., Shuang, L., Diyin, T., & Hao, L. (2017). Remaining discharge time prognostics of lithium-ion batteries using dirichlet process mixture model and particle filtering method. IEEE Transactions on Instrumentation and Measurement, 66(9), 2317-2328. doi: https://doi.org/10.1109/TIM.2017.2708204
Khalid, A., & Sarwat, A. I. (2021). Unified univariate-neural network models for Lithium-Ion battery State-of-Charge forecasting using minimized Akaike information criterion algorithm. IEEE Access, 9, 39154-39170. doi: https://doi.org/10.1109/ACCESS.2021.3061478
Khalid, A., Sundararajan, A., & Sarwat, A. I. (2019). An ARIMA-NARX model to predict Li-Ion state of charge for unknown charge/discharge rates. In 2019 ieee transportation electrification conference (itec-india) (p. 1-4). doi: https://doi.org/10.1109/ITEC-India48457.2019.ITECINDIA2019-1
Kim, Y., Son, H., & Kim, S. (2019). Short term electricity load forecasting for institutional buildings. Energy Reports, 5, 1270-1280. doi: https://doi.org/10.1016/j.egyr.2019.08.086
Kim, Y., & Kim, S. (2021). Forecasting charging demand of electric vehicles using time-series models. Energies, 14(5). doi: https://doi.org/10.3390/en14051487
Klump, A., & Kolb, M. (2023). Uniqueness of the inverse first-passage time problem and the shape of the shiryaev boundary. Theory of Probability & Its Applications, 67(4), 570-592. doi: https://doi.org/10.1137/S0040585X97T991155
Lefebvre, M. (2026). On an inverse first-passage problema for jump-diffusion processes. Mathematics, 14(1). doi: https://doi.org/10.3390/math14010087
Maden, A. H., & Arabacı, H. (2024). Effects of discharge cut-off voltage level on available battery charge capacity and battery life. International Journal of Data Science and Applications, 7(1), 1–12.
Orchard, M. E., & Vachtsevanos, G. J. (2009). A particle-filtering approach for on-line fault diagnosis and failure prognosis. Trans. Inst. Meas. Control 2009, 31(3-4), 221-246.
Pola, D. A., Navarrete, H. F., Orchard, M. E., Rabié, R. S., Cerda, M. A., Olivares, B. E., Silva, J. F., Espinoza, P. A., & Pérez, A. (2015). Particle-filtering-based discharge time prognosis for lithium-ion batteries with a statistical characterization of use profiles. IEEE Transactions on Reliability, 64(2), 710-721.
Quiñones, F., Milocco, R. H., & Real, S. G. (2018). Remaining discharge-time prediction for batteries using the Lambert function. Journal of Power Sources, 400, 256-263.
Rana, M. M., Uddin, M., Sarkar, M. R., Meraj, S. T., Shafiullah, G., Muyeen, S., Islam, M. A., Jamal, T. (2023). Applications of energy storage systems in power grids with and without renewable energy integration — a comprehensive review. Journal of Energy Storage, 68, 107811. doi: https://doi.org/10.1016/j.est.2023.107811
Salminen, P. (1988). On the first hitting time and the last exit time for a Brownian motion to/from a moving boundary. Advances in Applied Probability, 20(2), 411–426.
Saxena, A., Celaya, J., Roychoudhury, I., Saha, S., Saha, B., & Goebel, K. (2012). Designing data-driven battery prognostic approaches for variable loading profiles: Some lessons learned. European Conference of the Prognostics and Health Management Society.
Sbarufatti, C., Corbetta, M., Giglio, M., & Cadini, F. (2017). Adaptive prognosis of lithium-ion batteries based on the combination of particle filters and radial basis function neural networks. Journal of Power Sources, 344, 128-140.
Schacht-Rodríguez, R., Ponsart, J.-C., García-Beltrán, C. D., & Astorga-Zaragoza, C. M. (2018). Prognosis & health management for the prediction of UAV flight endurance. IFAC-PapersOnLine, 51(24), 983-990.
Shamsi, M., & Cuffe, P. (2022). Prediction markets for probabilistic forecasting of renewable energy sources. IEEE Transactions on Sustainable Energy, 13(2), 1244-1253. doi: https://doi.org/10.1109/TSTE.2021.3112916
Siegert, A. J. F. (1951). On the first passage time probability problem. Physical Review, 81(4), 617-623.
Steinstraeter, M., Buberger, J., & Trifonov, D. (2020). Battery and heating data in real driving cycles. IEEE Dataport. Retrieved from https://dx.doi.org/10.21227/6jr9-5235 doi: https://doi.org/10.21227/6jr9-5235
Vachtsevanos, G., & Zahiri, F. (2022). Prognosis: Challenges, precepts, myths and applications. 2022 IEEE Aerospace Conference (AERO), 1-13.
Van den Bergh, K., Hytowitz, R. B., Bruninx, K., Delarue, E., Dhaeseleer, W., & Hobbs, B. F. (2017). Benefits of coordinating sizing, allocation and activation of reserves among market zones. Electric Power Systems Research, 143, 140-148. doi: https://doi.org/10.1016/j.epsr.2016.10.012
Vollenbröker, B. K. (2011). Strictly stationary solutions of multivariate ARMA and univariate ARIMA equations (Unpublished doctoral dissertation). Technische Universität Braunschweig.
Walker, E., Rayman, S., & White, R. E. (2015). Comparison of a particle filter and other state estimation methods for prognostics of lithium-ion batteries. Journal of Power Sources, 287, 1-12.
Wang, W., Yuan, B., Sun, Q., & Wennersten, R. (2022). Application of energy storage in integrated energy systems — a solution to fluctuation and uncertainty of renewable energy. Journal of Energy Storage, 52, 104812. doi: https://doi.org/10.1016/j.est.2022.104812
Wang, Y., & Chen, Z. (2020). A framework for state-of-charge and remaining discharge time prediction using unscented particle filter. Applied Energy, 260.
Wang, Y., Gao, G., Li, X., & Chen, Z. (2020). A fractional-order model-based state estimation approach for lithium-ion battery and ultra-capacitor hybrid power source system considering load trajectory. Journal of Power Sources, 449, 227543. doi: https://doi.org/10.1016/j.jpowsour.2019.227543
Wang, Y., Tian, J., Sun, Z., Wang, L., Xu, R., Li, M., & Chen, Z. (2020). A comprehensive review of battery modeling and state estimation approaches for advanced battery management systems. Renewable and Sustainable Energy Reviews, 131, 110015. doi: https://doi.org/10.1016/j.rser.2020.110015
Wazirali, R., Yaghoubi, E., Abujazar, M. S. S., Ahmad, R., & Vakili, A. H. (2023). State-of-the-art review on energy and load forecasting in microgrids using artificial neural networks, machine learning, and deep learning techniques. Electric Power Systems Research, 225, 109792. doi: https://doi.org/10.1016/j.epsr.2023.109792
Xiong, R., Cao, J., Yu, Q., He, H., & Sun, F. (2017). Critical review on the battery state of charge estimation methods for electric vehicles. IEEE Access, 6, 1832-1843.
Yohai, V. J., & Maronna, R. A. (1977). Asymptotic behavior of least-squares estimates for autoregressive processes with infinite variances. The Annals of Statistics, 5(3), 554–560.
Zhang, X., Wang, Y., Liu, C., & Chen, Z. (2017). A novel approach of remaining discharge energy prediction for large format lithium-ion battery pack. Journal of Power Sources, 343, 216-225.
Zhang, Y., Xiong, R., He, H., & Pecht, M. G. (2019). Lithium-ion battery remaining useful life prediction with Box–Cox Transformation and Monte Carlo simulation. IEEE Transactions on Industrial Electronics, 66(2), 1585-1597.
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