A V Karmanov (National University of Oil and Gas “Gubkin University”) :
Articles:
004.052 Modeling the risk of a complex energy system
Karmanov A. V. (National University of Oil and Gas “Gubkin University”), Orlova K. P. (National University of Oil and Gas “Gubkin University”), Serkin V. E. (National University of Oil and Gas “Gubkin University”)
doi: 10.18698/2309-3684-2025-4-108123
The article discusses some features of the functioning of a complex energy system (hereinafter referred to as the system), which operates based on long-term contractual obligations and has a finite set of states forming a single ergodic class. One such feature is the occurrence of various "negative" events—incidents—during system operation, which form a random point process over time. The flow of incidents is assessed in terms of technological risk, where this risk is understood as the average monetary damage per unit of time associated with incident mitigation and their consequences. The sources of incidents include: 1) the random process of failures and recoveries of the system's elements and its subsystems, and 2) gross violations of system operation rules. When an incident occurs, the system's operational mode typically changes, which in turn alters the probabilities of subsequent incidents. However, these changes in incident probabilities often cannot be described analytically. In many cases, though, it is possible to specify a range to which these changes belong.Two mathematical models are used to describe technological risk:The first model is a regular homogeneous semi-Markov process, which allows for risk calculation when changes in the system's operational mode do not affect the probabilities of subsequent incidents. In this model, risk is a specific type of functional representing the average accumulated income per unit of time. Over prolonged system operation, this risk becomes stationary. A formula and calculation procedure for stationary risk are provided, along with an illustrative example.The second model is a semi-Markov process with incomplete information, generalizing the first model and used for risk assessment under the following conditions: 1) incident occurrence alters the system's operational mode, changing the probabilities of subsequent incidents; 2) an analytical description of these probability changes is unknown, but certain ranges to which they belong are known. In this model, incomplete information consists of these ranges, leading to an interval estimate of stationary risk. The structure of incomplete information allows for the formulation of two optimization problems to calculate the lower and upper bounds of this interval estimate. A method and iterative procedures for solving these optimization problems are described, along with an example demonstrating their application for calculating the interval estimate of stationary risk.
Карманов A.B., Орлова К.П., Серкин В.Е. Моделирование риска сложной энергетической системы. Математическое моделирование и численные методы, 2025, № 4, с. 108–123.