Lagrange Multiplier Based Solution for Optimizing DG Sizes in Distribution Networks

Integration of Distributed Generation (DG) has occupied a great interest in modern power engineering due to its significant merits over the conventional power generation techniques. However, several aspects such as climatic conditions, land and fuel availability, DG location and DG size need to be carefully considered to harness the best results from integrating DG units for power networks. Among them, sizing of DG units has taken a prominent place as it affects the network operation as well as the cost aspect. Optimizing the sizes of prospective DG units that are intended to be integrated for a given network will facilitate in gaining the expected merits such as minimizing active power losses and voltage deviations without causing any stability, protection and power quality issue. The existing methodologies for determining optimal DG sizes are rather sophisticated. This paper presents a robust mathematical solving approach based on Lagrange Multiplier Method (LMM) for determining the optimal DG sizes for minimizing the active power losses and voltage deviations. The problem is formulated and solved as a multi objective function. Validation of the proposed mathematical solution strategy was tested using the IEEE-6 and IEEE-33 standard test bus systems. Results demonstrate the effectiveness of the proposed methodology.