This paper proposes a detailed equivalent model for electromagnetic transient simulation of a modular multilevel converter with embedded battery energy storage in its submodules. The model offers an accuracy identical to that of a detailed switching model (DSM), while it markedly reduces the computational complexity of simulations. This is achieved by modeling each multivalve as a Thevenin equivalent considering the full dynamics of each constituent submodule, which results in a significant reduction in the number of switchable nodes in the converter model and hence the dimensions of the systems admittance matrix. The paper presents the mathematical development of the model and validates it against detailed switching models through several case studies. Experimental results from a scaled-down laboratory setup are also presented for further verification.