Equivalent-circuit models of the lithium-ion battery are still used as the basic model towards existing energy-storage-side simulation when researching power systems. This single type of battery model will inevitably lead to a serious simulation accuracy reduction for the multi-type hybrid energy storage and the new energy-storage system. Considering the influence of temperature on the battery model, this manuscript adjusts the model parameters and structure on the basis of the classical Thevenin model, and proposes a temperature compensation model to achieve temperature adaptation. In addition, the impact of noise on state-of-charge estimation is reduced by introducing an Adaptive Extended Kalman Filter (AEKF) algorithm into the model. The temperature compensation model combined with the AEKF algorithm possesses a good temperature adaptability and a high accuracy towards the state-of-charge for six types of energy-storage batteries: the lithium iron phosphate battery, the lithium titanate battery, the NCM ternary lithium-ion battery, the sodium-ion battery, the solid-state lithium-ion battery and the super-capacitor. Based on this model, the intensive simulation research on the six types of energy-storage batteries is conducted. This Equivalent-circuit model library can realize the joint allocation and management towards different types of battery models during the energy-storage-system simulation.