The converter station serves as the core of direct current (DC) transmission project, and the control of the total electric field (TEF) on the ground within DC yard is crucial to environmental protection. Given the complex geometric structures of the busbars within the DC yard, a solution to two large-scale 3D fields must be solved to obtain the TEF. To reduce computational complexity, previous studies have focused on single busbar, overlooking the impact of other ones, and relied on 2D TEF calculation methods and empirical corrections for busbar selection. This paper proposes a fast upstream finite element method (FUFEM) for the 3D TEF of complex busbars. The validity of this method is verified using the analytical solution of concentric spheres. Through numerical experiments, the numerical performance of this method is analyzed, and the ground TEF distribution of II-shaped busbars is calculated. The results show that compared to the commonly-used sequential upstream finite element method (SUFEM), this FUFEM achieves approximately 50 times faster computation speed. When the busbars are in a dry and clean state, the high-value regions of TEF in the ground TEF distribution exhibit an elliptical shape. However, when the busbars are in a wet state, corona discharge occurs at the ends of all busbars, shifting the high-value regions of TEF from the center to both ends, forming a heart-shaped pattern. In this state, the maximum value of the ground TEF increases by about 70% compared to when the busbars are dry and clean.