Investigation of voltage stability in three-phase unbalanced distribution systems with DG using modal analysis technique

Because of the slow expansion of distribution systems, fast growth of load, and increased penetration level of distribution generation (DG), voltage stability becomes an important issue for the proper operation of distribution systems. In this work modal analysis technique was extended to three-phase unbalanced distribution systems to analyze voltage stability problem. Netwon-Raphson algorithm with power mismatch in polar representation was adopted to find the three-phase power flow solution, and its Jacobian matrix was used for three-phase modal analysis technique. This technique was applied to IEEE 13-node test feeder. Several case studies were performed to investigate the impact of unbalance loading degree and DG power output on voltage stability problem. It was found that both would influence not only the maximum loadability of the system but also the location of the weak buses, weak branches and suitable locations to provide reactive power support.