This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Reliability Engineering and System Safety

A three-stage resilience analysis framework for urban infrastructure systems

Performance assessment of topologically diverse power systems subjected to hurricane events

Multi-phase assessment and adaptation of power systems resilience to natural hazards

Energy infrastructures are perceived continuously vulnerable to a range of high-impact low-probability (HILP) incidents—e.g., earthquakes, tsunamis, floods, windstorms, etc.—the resilience to which is highly on demand. Specifically suited to battery energy storage system (BESS) solutions, this paper presents a new resilience-driven framework for hardening power distribution systems against earthquakes. The concept of fragility curve is applied to characterize an earthquake hazard, assess its impact on power distribution systems, and estimate the unavailability of the network elements when exposed to extreme earthquakes. A new metric is defined to quantify the network resilience taking into account the uncertain nature of such HILP events. A linear programming optimization problem is formulated to determine the capacity and location of the BESSs for enhanced resilience against earthquakes. Efficacy of the proposed framework is numerically analyzed and verified through application to a real-world distribution power grid.

Energy Storage Planning for Enhanced Resilience of Power Distribution Networks Against Earthquakes

Dealing with the transmission network of electric power systems, this paper identifies the sequential failures of receiving station components under a severe earthquake. Such failures progressively degrade the power network performance, potentially leading to a network blackout. Hence, in this paper, these components are incorporated into the network systems analysis taking their seismic vulnerability into consideration in the form of fragility curves for the evaluation of the network performance under seismic conditions. Specifically, most critical to the operation of transmission network, transformers, disconnect switches, circuit breakers and buses are integrated into the systems analysis, exploring the possibility of progressive failures of these components. The scenarios of these component failures can make it possible to estimate quantitatively direct cost of damage, emergency repair and restoration, and duration of power interruption and attendant economic losses and societal disruption. Copyright © 2006 John Wiley & Sons, Ltd.

X. Jin

Papers

Seismic performance of electric transmission network under component failures