Application of the Trajectory Sensitivity Theory to Small Signal Stability Analysis

The security assessment of power systems represents one of the principal studies that must be carried out in energy control centers. In this context, small-signal stability analysis is very important to determine the corresponding control strategies to improve security under stressed operating conditions of power systems. This chapter details a practical approach for assessing the stability of power system’s equilibrium points in real time based on the concept of trajectory sensitivity theory. This approach provides complementary information to that given by selective modal analysis: it determines how the state variables linked with the critical eigenvalues are affected by the system’s parameters and also determines the way of judging how the system’s parameters affect the oscillatory behavior of a power system. The WSCC 9-bus and a 190-buses equivalent system of the Mexican power system are used to demonstrate the generality of the approach as well as how its application in energy management systems is suitable for power system operation and control

“SECURITY IMPROVEMENT OF POWER SYSTEMS BY USING TRAJECTORY SENSITIVITY APPROACHES”

The security assessment of power systems represents one of the principal studies that must be carried out in energy control centers. The major computational burden on security as- sessment is spent in the security evaluation of the critical contingencies. In this research several approaches are proposed to improve the dynamic security of power systems. These approaches are based on quantifying the parameters influence on the angular stability of the power systems via the trajectory sensitivities obtained with respect to the system parameters. In order to implement these approaches a digital program of transient stability was devel- oped in language C++ by following an Object Oriented Programming philosophy (OOP). The power system is represented by means of Differential-Algebraic Equation (DAE) systems, and the angular stability model is based on the power balance formulation. The transient stability solution uses the Simultaneous Implicit method (SI) of integration, which consists of implicitly integrating the differential equations, so that the resulting algebraized set of equations is solved together with the existent algebraic set of equations under a unified frame of reference. Furthermore, sparsity and pre-ordering techniques were considered in order to achieve a very important reduction in the computational burden. The efficient assessment of the parameter influence is accomplished by implementing the Staggered Direct Method (SDM), which consists of the analytical computation of the linear Trajectory Sensitivities (TS) at each time step of integration. The solution then requires only one forward/backward substitution at each integration step. This method is straightforwardly extended in order to compute a sensitivity function matrix obtained with respect to multiple system parameters at the same simulation