Title: Statistical Estimation of Uncertainties in Power System Adequacy Studies

Date: 7/27/2021

Abstract: Power system adequacy studies are concerned with the estimation of unlikely events, usually by means of Monte Carlo simulation. In this presentation, I will present two challenges that arise when estimating the sampling uncertainty in this context. First, the case of (very) rare events is considered, when very small numbers of relevant samples are available. A computational resampling approach is described that can reliably generate (conservative) Bayesian credible intervals for quantities of interest, such as means or quantiles. Second, a case of ‘inverse’ uncertainty quantification is discussed: the estimation of capacity values (reliability contribution of resources), which are the solution of a stochastic root finding problem. Common pitfalls for generating credible intervals for these capacity values are discussed, alongside possible solutions.

Title: Applications of Polynomial Chaos Expansion-based Methods in Power System Probabilistic Security Assessments

Date: 7/27/2021

Abstract: The ever-increasing integration of renewable energy sources and new forms of load demand introduces a growing uncertainty level to power systems, which greatly affect various security properties of a system. In this talk, I will present some recent works of my group in utilizing polynomial chaos expansion (PCE)-based methods in power system probabilistic security assessments including probabilistic power flow solutions, available transfer capability assessments, and economic dispatch. In contrast to Monte Carlo-based simulations that require a large number of scenarios and model evaluations, the polynomial chaos expansion method can build a surrogate model for assessing the model response (e.g., probabilistic power flow solution) from a small number of scenarios and model evaluations, which thus saves huge computational efforts. I will also introduce the efforts to relax the assumption of knowing marginal distributions of random variables required in PCE. Insights for decision-making to reduce the negative impacts of uncertainty on power system security will also be discussed.

Title: Optimization-based Approaches to Uncertainty Propagation in Power-system Models

Date: 7/27/2021

Abstract: This talk will overview optimization-based strategies to propagate input and parametric uncertainty to the solution of two classical problem setups in power-system analysis: i) the power flow problem, and ii) differential-algebraic equation (DAE) models for power-system dynamics. For the power-flow setting, the approach is based on maximizing and minimizing quadratic approximations of the power-flow states as a function of the uncertainties subject to inequality constraints that capture all possible values the uncertain elements can take. The formulated quadratic programs are non-convex in general, and we adopt the Alternating Direction Method of Multipliers to solve them. For the DAE models, our approach is based on a second-order Taylor-series approximation of the state trajectories as a function of the uncertainties. A key contribution in this regard is the derivation of a DAE model that governs the second-order trajectory sensitivities of states to uncertainties in the model. Bounds on the states are then obtained by solving semidefinite programs, where the objective is to maximize/minimize the Taylor-series approximations subject to constraints that describe the uncertainty space.

Title: Applications of Probabilistic Methods in Power System Reliability Assessment utilized in Power Industry

Date: 7/27/2021

Abstract: The applications of probabilistic methods can provide points of view from power system planners and operators, focusing on the frequency and duration of system problems, or from customers focusing on the impact of system uncertainty and unreliability. This presentation introduces two typical probabilistic reliability methods which are widely used in power industry: (1) probabilistic reliability assessment and (2) substation reliability assessment. The probabilistic reliability assessment is applied to calculate reliability indices, provide weak point analysis (i.e., components most affected by outages) and compare different operating conditions and planning alternatives. Substation reliability assessment can augment substation design principles to evaluate the reliability of a substation in terms of probabilistic indices (e.g., frequency and duration of load curtailments) and compare alternative substation configurations.