Bifurcation analysis of static unbalanced power networks with distributed generation

Voltage stability has been well investigated for the traditional power system using bifurcation analysis: saddle-node bifurcation (SNB) and hopf bifurcation (HB). This paper studies the impacts of distributed generators (DGs) on the voltage stability of power system. The bifurcations analysis is applied on the steady state three-phase load-flow Jacobian-matrix of unbalanced distribution system. The analysis of the eigenvalues is used to study distribution system behavior under different operating conditions. 10-bus radial distribution system is used as the study system. Different case studies and loading scenarios are presented to trace the eigenvalues of the Jacobian-matrix. The eigenvalues were calculated and the worst point, which is the nearest point to the imaginary axis, was registered for every case. The loci of these points with different load unbalance and location of DGs were plotted. Maximum loading point (MLP) was calculated at different ratings and locations of DGs. Results show that bifurcation analysis can clearly explain the voltage stability of the distribution systems. It also, explains the effect of introducing DGs on the voltage stability of the unbalanced distribution systems. Distribution of the eigenvalues helps in choosing the best location and rating of the required DGs.