Multi terminal DC (MTDC) has become a competitive cross-regional high-power transmission technology, but there has been little research on its complete mathematical model because of its structural complexity. A true bipolar hybrid bridge modular multi-level converter (MMC) is an important part of ultra-high voltage MTDC. If its mathematical model still adopts the simple half-bridge MMC, electrical connection on the AC side of the true bipolar MMC cannot be reflected. Also, the rationality of extending the 0-1 binary switching function of the half-bridge MMC model to the hybrid bridge has yet to be proven. To solve the above-mentioned problems in MTDC modeling, Kun-Liu-Long DC project is taken as an example. First, the complete mathematical model of the true bipolar hybrid bridge MMC is deduced, and the quasi-steady state and lumped parameter approximation of conventional HVDC converter stations and DC transmission lines are carried out. Then, both accuracy and complexity are considered to establish a practical engineering model of MTDC under a DC fault. Finally, the DC unipolar ground fault is calculated and analyzed using the proposed model. Compared with the calculation results of PSACD, the validity of the proposed model is verified. This work is supported by the Science and Technology Project of China Southern Power Grid Co., Ltd. (No. ZBKJXM20180635).