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Closed-form methods for system reliability assessment of power distribution systems

Funding: National Science Foundation
Collaborators: Dr. Javier Rojo,
Rice University

The increased susceptibility of lifeline systems to failure due to aging and external hazards requires efficient methods to quantify their reliability and related uncertainty. Monte Carlo simulation techniques for network-level reliability and uncertainty assessment usually require large computational experiments. Also, available analytical approaches apply mainly to simple network topologies, and are limited to providing average values, low order moments, or confidence bounds of reliability metrics. This study introduces a closed form technique to obtain the entire probability distribution of a reliability metric of customer service availability (CSA) for generic radial lifeline systems. A special case of this general formulation reduces to a simple sum of products equation, for which a recursive algorithm that exploits its structure is presented. This special-case algorithm computes the probability mass function (PMF) of CSA for systems with M elements in O(M3) operations, relative to conventional O(2M) operations, and opens the possibility of finding recursive algorithms for the general radial case. Parametric models that approximate the CSA metric are also explored and their errors quantified. The proposed radial topology reliability assessment tools and resulting probability distributions provide infrastructure owners with critical insights for informed operation and maintenance decision making under uncertainty. 

Closed-form Methods
Typical 38-node basic radial topology of power systems at the distribution level.


  • Dueñas-Osorio, L. and J. Rojo, (2010).  "Reliability assessment of radial lifeline systems."  Computer-Aided Civil and Infrastructure Engineering, in press, DOI: 10.1111/j.1467-8667.2010.00661.x.
  • Dueñas-Osorio, L.*, and J. Rojo, (2009). "Probability models for the reliability metrics of practical power distribution networks." Proceedings of the 10th International Conference on Structural Safety and Reliability (ICOSSAR), Osaka, Japan, September 12-17, 2009.