In this note, it is shown that a three-machine power system with 2 PV and 1 slack busses can be modelled by using two Single Machine Infinite Bus models. It was found that a relation between the active powers of the two models at final resulted equations maintains interaction between two SMIB models. It provides a theoretical background to understand dynamic behavior of such power networks.

In power system dynamic analysis, computation of eigenvalues of state equations for various active dispatched powers is important. This concept provides a better understanding of the system dynamic behavior. In this paper, an approximate equation extraction technique is proposed for fast computation of real-part of the most critical eigenvalue of New England 39-bus power system. Simulation by using MATLAB PSAT toolbox is carried out as a source of the initial data for finding a proper approximate function and also its verification. As an application example, the obtained polynomial approximate function has been applied to small signal stability constrained optimal power flow by using GAMS optimization package. The obtained polynomial function can be used with various optimization criteria in the valid interval of the approximation. Also this polynomial function can be re-used when generation cost functions are changed, without need for a new dynamic analysis. All of the dynamic analyses by PSAT toolbox are performed by using automatic intermediate codes cooperating with functions and variables of the PSAT toolbox and handy registration of numbers is avoided.

In power systems dynamic analysis, one of the well-known used toolboxes is Power System Analysis Toolbox (PSAT). In order to easy cooperate with this toolbox, custom codes are required to do complicated optimization computations automatically and without much effort by the user. In this article, a simple code was proposed for this aim. It can be a base technique to write user defined optimization programs to be run fast and reliable without difficulties of handy manipulation of numbers by the user, especially for Small Signal Stability Constrained Optimal Power Flow (SSSC-OPF) optimizations.