A Combinatorial Procedure to Determine the Full Range of Potential Operating Scenarios for a Dam System

  • Leanna M. KingEmail author
  • Andre Schardong
  • Slobodan P. Simonovic


Traditional dam safety assessment tends to place the focus on estimating the probabilities of failure for the system based on a few subjectively-chosen operating scenarios. The techniques used to assess these systems rely on linear chains of events and are incapable of considering component interactions, feedbacks and non-linear behaviour. This paper uses a systems approach to develop a new technique that puts possibilities first and is capable of generating an exhaustive list of potential component operating state scenarios for the system. The scenarios can then be simulated using a Monte-Carlo approach to determine a wide range of system behaviour (outcomes) for each scenario, taking into account component interactions and feedbacks. A component operating states database is presented where the system can be broken down into various levels of detail and the operating states and causal factors for each component can be defined. The Cartesian product of each operating state set is used to derive the full range of potential operating scenarios, with each scenario consisting of a single operating state for every component in the system. The list of scenarios can be used as an input to a simulation model which can then be run many times for each scenario, using Monte-Carlo inputs which vary the timing and severity of events as well as the inflows. The approach for automated scenario generation is demonstrated on a simple and complex representation of a hydropower system and the scenarios are generated and counted. Results show that increasing system complexity results in exponentially increasing numbers of potential operating scenarios, with the simple system having a total of 1.1 × 106 operating states in comparison to the complex system which has 1.83 × 1027. The approach presented in this paper (a) reduces the subjectivity associated with traditional dam safety assessments through automated scenario generation, and (b) improves the ability to understand component interaction and feedbacks by describing a Monte Carlo simulation approach which can be used for scenario simulation. By understanding how the system responds to the full range of potential operating conditions, dam owners and asset managers can make informed decisions relating to the improvement of operating strategies and implementation of system upgrades.


Hydropower Dam safety Systems approach Monte-Carlo simulation Combinatorics 



The authors would like to thank the National Science and Engineering Research Council and BC Hydro for their support of this research through the Collaborative Research and Development Grant. Thanks to Des Hartford and Derek Sakamoto from BC Hydro for their input and guidance.

Compliance with Ethical Standards

Conflict of Interest


Supplementary material

11269_2018_2182_MOESM1_ESM.xlsx (35 kb)
ESM 1 (XLSX 34 kb)


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Civil and Environmental EngineeringThe University of Western OntarioLondonCanada

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