Statistical Analysis of Resilience Distribution and Application to Rural Electric Distribution System subjected to Hurricane Wind

Abstract

Several mathematical frameworks and models are proposed to quantify the resilience of power systems against hurricane events. However, these frameworks contribute to the urban area's large-scale transmission system or networked power delivery system. They are barely applicable to the rural power distribution system, whose intrinsic properties vary distinctively compared to an urban area. These inherent properties such as less robustness due to the high vulnerability of aged wooden poles, topology characterization as a set of linear subsystems that emanate from one power substation and individually feature zero redundancy and cascading effect, and slow recovery due to low socio-economic resources and geospatially sparse customers make it less resilient. This study thus proposes a fully probabilistic and analytical measurement framework for assessing the resilience of linear power distribution systems affected by hurricane wind. The proposed framework includes the mechanical analysis of coupled wooden-pole and feeder-line as a system unit, the definition of component restoration and system-level recovery functions, and a new resilience measure termed the total mean system-resilience (TMSR). Numerical experimentation is provided that validates the effectiveness and the analytical tractability of the framework. The insight that how physical aging, local resourcefulness, and spatial sparseness interplay and affect the system resilience is shed quantitatively. On the other hand, from a critical synthesis of the existing literature towards several quantitative resilience measures or ambiguously termed metrics frameworks for quantifying the resilience of civil infrastructure, the author found informational inadequacy on taking objective decisions such as resilience acceptance or parameter strengthening prioritization. Two ingrained drawbacks of such measurements are lack of theoretical basis in 1. Discriminating relatively how a parametric infrastructure system is more resilient than a different one or the same one subject to some changed conditions and, 2. answering which input parameter is most influential while assessing the resilience measure. This study thus explores and suggests several statistical tools such as 1. A nonparametric approach to perform sensitivity analysis of each input parameter to output resilience and check for the robustness of the proposed resilience assessment framework. 2. Copula-based dependence analysis to determine the most influential parameter and tail dependencies of the resilience measure with each input parameter. 3. Information-theoretic distance measures termed Resilience Distance (RD) measures to characterize how a system evolves as a function of system variables from the realm of materials, hazards, or socioeconomic resourcefulness. 4. Nonparametric two-sample test to check if the calculated resilience can be accepted when compared to targeted resilience of the same system. Numerical evaluation is conducted using these statistical tools on the proposed probabilistic resilience assessment framework of stochastically modeled rural electrical distribution system, and numerical measures show that the proposed statistical analysis of the resilience distribution can be a possible objective decision-making tool.