# Analysis of the Power System Stability Under Uncertainty

Monday, February 22, 2016 - 2:45pm - 3:30pm

Lind 305

Alexandre Tartakovsky (Pacific Northwest National Laboratories)

We study the effect of the uncertainty of wind power on the angular stability of power systems, including a single-machine, infinite-bus (SMIB) system, and a three-generator, nine-bus multi-machine system, which are subject to a self-clearing three-phase fault. Probability density function (PDF) and Monte Carlo (MC) methods are used to calculate the PDFs of states and the probability of the systems successfully clearing the fault as a function of the clearing time and the stochastic properties of the wind power fluctuations, namely the variance and correlation time of the fluctuations. Simulation results for both systems exhibit a significant effect of stochastic resonance between the system's small-signal fluctuation oscillation frequency around the synchronous equilibrium and the correlation time of the wind power fluctuations, amplifying generator state¹s fluctuations and decreasing the probability of successfully clearing the fault. This resonance effect is analytically verified by studying the dependence of the power system state¹s probability density function on the stochastic properties of the wind power fluctuations. For the multi-machine

power system, we study the effect of the ratio of renewable-to-total

generated power on the system¹s transient stability properties. We find that the probability of successfully clearing the three-phase faults considered

decreases with increasing renewable-to-total power ratio. We also define

stochastic critical clearing times as function of the desired confidence of

successfully clearing the fault.

power system, we study the effect of the ratio of renewable-to-total

generated power on the system¹s transient stability properties. We find that the probability of successfully clearing the three-phase faults considered

decreases with increasing renewable-to-total power ratio. We also define

stochastic critical clearing times as function of the desired confidence of

successfully clearing the fault.