Abstract-In the deregulated environment of power systems, the transmission networks are often operated close to their maximum capacity to achieve transfer of power. Besides, the operators must operate the system to satisfy its dynamic stability constraints under credible contingencies. This paper provides a method using trajectory sensitivity to reschedule power generation to ensure system stability for a set of credible contingencies while satisfying its economic goal. System modeling issue is not a limiting concern in this method, and hence the technique can be used as a preventive control scheme for system operators in real time.

Parameters of power system models can never be known exactly. Yet dynamic security assessment relies upon the simulations derived from those uncertain models. This paper proposes an approach to quantifying the uncertainty in simulations of power system dynamic behaviour. It is shown that trajectory sensitivities can be used to generate an accurate first order approximation of the trajectory corresponding to a perturbed parameter set. The computational cost of obtaining the sensitivities and perturbed trajectory is minimal. Therefore it is feasible to quickly generate many approximate trajectories from a single nominal case. To quantify the effect of parameter uncertainty on the nominal case, parameter sets are randomly generated according to their underlying statistical distribution. An approximate trajectory is obtained for each set. The collection of trajectories provides a bound within which the actual system dynamic behaviour should lie.

Trajectory sensitivity analysis (TSA) has been applied in control system problems for a long time in such areas as optimization and adaptive control. Applications in power systems in conjunction with Lyapunov/transient energy functions first appeared in the 1980s. More recently, TSA has found applications on its own by defining a suitable metric on the trajectory sensitivities with respect to the parameters of interest. In this chapter we present theoretical as well as practical applications of TSA for dynamic security applications in power systems. We also discuss the technique to compute critical values of any parameter that induces stability in the system using trajectory sensitivities.

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