Probability of failure of overloaded lines in cascading failures

• Blackouts in transmission power systems are due to cascading failures.
• Outages of overloaded lines are main contributors to cascading failures.
• The probability of line tripping as a function of the overload must be modeled.
• Previous models do not rely on empirical evidence or detailed analysis.
• This paper proposes a simple model backed up by a detailed analysis.

Power grids are vulnerable to cascading failures, as shown by previous blackouts or major system disturbances. Line outages due to overload are often the main contributors to the cascading failures leading to these undesired situations. Indeed, the more a line is overloaded, the larger is its sagging, and hence the probability that it will be tripped. It is necessary to quantify in a realistic way the probability of trip as a function of the load in order to compute a good estimation of the frequency of dangerous cascading outages. Several models were proposed for this purpose, but none of them is backed up by empirical evidence or detailed analysis. This paper studies factors that could affect the probability of trip as a function of load, and it computes this probability for two different test systems using a temperature simulation based methodology, called dynamic PRA level-I analysis. This paper then compares existing modelings of this probability to these results. This comparison shows that all modelings used in the literature are not always convenient. We finally propose a simple model that can be adopted in probabilistic risk assessment of cascading failures.