The increase in the penetration rate of renewable energy exacerbates the rise in system short-circuit level. Thus, short-circuit constraints (SCCs) are crucial in the co-optimization of transmission and generation expansion planning. The deregulated environment further complicates this process by assigning responsibilities for transmission and generation to separate market entities. This paper proposes a multi-period co-optimization method of transmission and wind turbine generation expansion planning to address this challenge. The transmission expansion planning (TEP) problem limits the short-circuit level, which could be elevated by lines, synchronous generators, and wind turbine generators. The method is formulated as a tri-level mixed-integer linear programming (MILP) problem, where an equilibrium problem with equilibrium constraints is formed at the second and third levels. This problem is restructured into a MILP problem with Nash equilibrium conditions via complementarity problem reformulation. We propose an iterative algorithm targeting the SCCs to solve it. The effectiveness of the proposed method is validated on the IEEE 24-bus reliability test system through comparisons with three existing TEP methods, analyzing the impact of SCCs and generation expansion planning on TEP and the system operating cost under a deregulated environment.