This purpose of this paper is to propose a methodology for optimal generating operation in power system to minimize the cost of generation subject to not only system constraints but also regional $CO_2$ emission constraints. To solve this ELD problem calculated range limit on minimum and maximum power outputs by regional Equal Generator how each regional capacity is connected into one and expressed Equal Fuel Cost Function considering regional $CO_2$ emission constraints. Accordingly, being modified regional load, new power outputs considering regional $CO_2$ emission constraints were calculated by ELD. The proposed model for evaluating availability is tested on IEEE RTS(Reliability Test System)-24 in detail.