Synchronism versus stability in power systems: Frequency dependent loads

In this work, considerations about current power system modeling methods, related to transient stability analysis are presented. It is shown that the swing equations do not present equilibrium solutions if damping coefficients are neglected. It is not possible to characterize the stability of the power system in the Lyapunov sense due to some structural problems. Those structural problems are made clear using power mismatch concepts. Stability studies using one machine as reference (OMR) and the center of angle as reference (COA) are in fact equivalent and do not eliminate the aforementioned structural problems. A possible solution for these difficulties is developed, that is, modeling the system loads as frequency dependent. A structure preserving model with the loads as frequency dependent is presented. In the presence of these loads the system can reach equilibrium solutions in velocities other than the synchronous frequency. The equilibrium frequency is calculated through the solution of a structure preserving power flow added to the equation of equilibrium frequency.