Authors - Kunam Subba Reddy, Mangavarapu Jahnavi, Kotte Hima Teja, Shaik Kathamma Basheerun, Nama Adarsh Abstract - Proper estimation of battery state of charge (SOC), state of health (SOH) and state of power (SOP) are vital to safe and efficient operation of photovoltaic (PV)-battery energy storage systems, particularly at highly dynamic profiles in which both charging and discharging is taking place. In this paper, a clear comparative analysis of classical, model-based, and machine-learning-based estimation techniques is performed in terms of a similar 24-h ultra-challenging PV + load current profile, simulating realistic residential microgrids operation. The test profile involves strong directions of current swings, partial charging, and long constant-power discharge, and temperature change. The estimators are implemented and benchmarked such as open-circuit-voltage (OCV)-based SOC estimation, linear Kalman filter (KF), extended Kalman filter (EKF), unscented Kalman filter (UKF), basic machine learning (ridge regression) and support vector machine (SVM). Each of the methods is compared to a high-fidelity model of an electro-thermal battery with capacity degradation and resistance increase with age and temperature. The accuracy of SOC tracking, SOH estimation error, and SOP tracking capability are discussed. It is found that the OCV-based method fails when the loading is dynamic which makes the SOC about constant and SOP highly conservative. KF and EKF are much better SOC trackers but they have greater deviation at high SOC and near bottom-of-discharge. ML and SVM estimators based on Ridge-regression show high SOC accuracy in the entire profile and UKF shows the best overall trade off between SOC accuracy, SOH tracking as well as SOP estimation strength when resistance varies with temperature and with age. The paper discusses the relevance of the collaborative consideration of SOC, SOH, and SOP and shows the advanced filters and ML models can significantly increase the performance of PV-battery applications that require tough operating conditions.