Abstract: To explore Braess paradox phenomenon in an interconnected power grid, a second order Kuramoto-like phase oscillator model is applied to model dynamics of the power grid. The two subnets are connected by the largest degree nodes to build an interconnected power grid. As power transmission between two subnets occurs, new transmission lines are added in the two subnets repectively to explore the probability of Braess paradox phenomenon and analyze the reasons. It is found that as the power transmission between the two subnets reaches a critical value, synchronizability of the power receiving subnet is much better than that of the power supply subnet. The probability of Braess paradox caused by adding a new transmission line in the power supply subnet is much higher than that caused by adding a new transmission line in the power receiving subnet. The phenomena are analyzed in depth by defining subnet order parameter. This study is important for the topology optimization of a interconnected power grid.