Abstract: With the development of energy networks, power grid and transportation systems have gradually integrated. To study the interaction mechanism of the coupled networks and describe the equilibrium state achieved by their interaction, a unified mathematical theoretical framework for the research of the equilibrium description of the coupled power-traffic networks was proposed based on the theory of variational inequality in a creative way. In terms of mathematical modeling, the mixed user equilibrium state at the traffic network side was defined firstly. Secondly, a variational inequality with second-order conical constraints was proposed to describe the optimal power flow problem of the distribution network. On this basis, a unified variational inequality mathematical framework was established for describing the network equilibrium state of coupled power-traffic networks. In order to qualitatively analyze the equilibrium solution of coupled networks, a theoretical method for studying the existence and uniqueness of the equilibrium solution was given based on the variational inequality framework. Finally, to solve the complicated network equilibrium problem effectively, a projection-contraction algorithm based on relaxation improvement was designed, and the optimality and convergence of the algorithm were proved by the properties of variational inequality. The effectiveness of the proposed models, frameworks and algorithms has been verified by the simulation method.