It is a well-known fact that a power system contains many sources of uncertainties. These uncertainties coming from the loads, the renewables, the model and the measurement, etc, are influencing the steady state and dynamic response of the power system. Facing this problem, traditional methods, such as the Monte Carlo method and the Perturbation method, are either too time consuming or suffering from the strong nonlinearity in the system. To solve these, this Dissertation will mainly focus on developing the polynomial chaos based method to replace the traditional ones. Using it, the uncertainties from the model and the measurement are propagated through the polynomial chaos bases at a set of collocation points. The approximated polynomial chaos coefficients contain the statistical information. The method can greatly accelerate the calculation efficiency while not losing the accuracy, even when the system is highly stressed. In this dissertation, both the forward problem and the inverse problem of uncertainty quantification will be discussed. The forward problems will include the probabilistic power flow problem and statistical power system dynamic simulations. The generalized polynomial chaos method, the adaptive polynomial chaos-ANOVA method and the multi-element polynomial chaos method will be introduced and compared. The case studies show that the proposed methods have great performances in the statistical analysis of the large-scale power systems. The inverse problems will include the state and parameter estimation problem. A novel polynomial-chaos-based Kalman filter will be proposed. The comparison studies with other traditional Kalman filter demonstrate the good performances of the proposed Kalman filter. We further explored the area dynamic parameter estimation problem under the Bayesian inference framework. The polynomial-chaos-expansions are treated as the response surface of the full dynamic solver. Combing with hybrid Markov chain Monte Carlo method, the proposed method yields very high estimation accuracy while greatly reducing the computing time. For both the forward problem and the inverse problems, the polynomial chaos based methods haven shown great advantages over the traditional methods. These computational techniques can improve the efficiency and accuracy in power system planning, guarantee the rationality and reliability in power system operations, and, finally, speed up the power system dynamic security assessment. / PHD / It is a well-known fact that a power system state is inherently stochastic. Sources of stochasticity include load random variations, renewable energy intermittencies, and random outages of generating units, lines, and transformers, to cite a few. These stochasticities translate into uncertainties in the models that are assumed to describe the steady-sate and dynamic behavior of a power system. Now, these models are themselves approximate since they are based on some assumptions that are typically violated in practice. Therefore, it does not come as a surprise if recent research activities in power systems are focusing on how to cope with uncertainties when dealing with power system planning, monitoring and control. This Dissertation is developing polynomial-chaos-based method in quantifying, and managing these uncertainties. Three major topics, including uncertainty quantification, state estimation and parameter estimation are discussed. The developed method can improve the efficiency and accuracy in power system planning, guarantee the rationality and reliability in power system operations in dealing with the uncertainties, and, finally, enhancing the resilience of the power systems.