This paper develops a detailed equivalent model for modular multilevel converters with partially-integrated battery energy storage. The proposed model gains computational efficiency in two ways. Firstly, it markedly reduces the large number of nodes in the conventional switching model of the converter, thereby shrinking the size of its admittance matrix. Secondly, it avoids computationally expensive re-triangularization of the admittance matrix during the normal operation of the converter and restricts it only to the rare occasions of converter blocking. Mathematical derivation of the model is carried out using differential equations of the converter. The computational efficiency and accuracy of the proposed model are confirmed by comparison of the results from its implementation in the PSCAD/EMTDC simulator against conventional detailed switching models and measurements from a single-phase scaled-down laboratory setup. This paper also shows a case study wherein a converter with partially-integrated batteries is included in the CIGRE B4-5 benchmark system.