Impact of stochastic loads and generations on power system transient stability

Randomness in physical systems is usually ultimately attributed to external noise. Dynamic systems are driven not only by our own control inputs, but also disturbances which cannot be modeled deterministically. A linear system model is justifiable for a number of reasons, often such a model is adequate for the purpose at hand, and when non-linearities do exist, the typical engineering approach is to linearize about some nominal point or trajectory to achieve a perturbation or error model. However, in order for the resulting model to fit data generated by the real world, these disturbances need to be modeled stochastically. The traditional approach to power system stability studies is based on a deterministic transient energy function. However, such a deterministic analysis does not provide a realistic evaluation of system transient performance where the intermittency and variability of energy production associated with any renewable technology needs to be reflected and accurately modeled in system stability and performance assessments. In the papers that make up this dissertation, the random variations of system components is modeled by a Gaussian stationary process (white noise) with constant spectral density and the effect on the stability of the power system is examined. The stochastic perturbation of power loads has a significant effect on the transient stability of the power system. The load behavior is found in the random effect of system parameter arising from cumulative impacts of a number of independent events. The random load characteristic is considered to develop a structure-preserved power system transient stability using stochastic energy functions. The stochastic power system stability was analyzed both through the stochastic Lyapunov function and numerically using the Euler- Maruyama method --Abstract, page iv