To realize environmental benefits and well progress carbon emission permits trading system, a first and important problem needed to be settled is how to set the initial allocation approaches. A general equilibrium analysis method is utilized to an allocation model which is based on "grandfathering" under cap control, in order to find out the optimal equilibrium conditions that content the maximization of both society and enterprises' benefits in open and closed trading systems. Analysis shows that, in two systems, it is never optimal taking enterprises' historical output as a reference factor, and that taking enterprises' historical emission can be optimal only in closed system and only for a narrow class of allocation mechanisms. Instead, by utilizing exogenous factors that are irrelevant with enterprises' output or emission one can achieve social optimum and equilibrium in two trading systems.