Economic load dispatch (ELD) is a complicated issue, when renewable energy sources are also considered with thermal power generation systems. It becomes challenging and difficult to find the optimum solution at lower fuel costs, in order for generated power to meet the active power load demand. This paper primarily focuses on the modeling of ELD for solar power plants synchronized with Thermal power plants. In this paper, the purposed optimization method used is Genetic algorithm (GA). According to which, all thermal generators in the system will supply output power at lowest fuel rate however satisfying the system limitations. Minimum fuel cost of a generator will be calculated by using generator characteristic curve for all generators present in the system. With the help of GA, achievable range for best solution is attained while restricting the output power of thermal generators. Proposed system priority to achieve is solar at first and generators on second such that generator or combination of generators resulting in lowest cost will be on second priority. Simulations on various test systems were performed including one with six thermal generators and the other with six thermal generators and solar power system. By using MATLAB the proposed problem is simulated.