Abstract: To explore a better power grid structure and reduce the probability of Braess paradox. In this paper, the second order Kuramoto-like phase oscillator model is used to reasonably model the power grid, and several networks are generated by ER random model in which the number of network nodes and links is the same as IEEE14, IEEE30, and IEEE39, respectively. By increasing the number of generator nodes and changing the position of generators in the random network, the occurrence probability of Braess paradox caused by a new adding transmission lines in the different power grid is studied. Study shows that appropriately increasing the number of generator nodes in the power grid can reduce the probability of the Braess paradox in the power grid, and taking large-degree nodes as generator nodes is beneficial to improve the power grid synchronizability and reduce the probability of Braess paradox. This study has certain guiding significance for the topology design and optimization of the power grid.