Abstract: Distributed generation (DG) are small scale power producers close to end user of power. This is having are many technical, economic and environmental benefits. By appropriate placement of DGs at optimum location with optimum size, benefits of DG can be maximized. In this paper the optimal capacity of distributed generation (DG) plant in a microgrid is determined to minimize the cost function. Two different cases are considered to solve the cost function. In first case it is assumed that installation cost of DG unit is stable and based on the constraints of the capacity limit of DG, linear mathematical model is developed. Here the method is applied on diesel, wind and solar power unit. In second case uncertainty is considered in installation cost of DG. To deal with this uncertainty fuzzy logic is used and membership function made which defuzzified by three different methods and converted into linear mathematical programming. And both the cases are compared and found that FLP is better than simple linear programing.

Keywords: Distributed generation (DG), Microgrid (MG), Fuzzy linear programming (FLP), Linear programming (LP), Defuzzification.