# Reliability of Supply and the Impact of Weather Exposure and Protection System Failures +
## 2 Failure Bunching and Protection System Failures  
Harsh weather has long been known to cause common cause failures within short periods of time, often termed failure bunching. One way of incorporating such effects is to use multi-state Markov models or similar approximate methods when calculating reliability, another is to utilize Monte Carlo simulation techniques [3; 19; 20]. In [19], the effect of failure bunching due to wind exposure is captured using historical failure data and a Bayesian updating scheme to estimate annual wind dependent failure rates of transmission lines. The annual failure rate is then spread out in time by combining fragility curve modeling and a dataset of historical wind speeds for the lines in question. This results in hourly time-series of wind dependent failure probability for the lines. This approach has been applied to create similar time-series of failure probability due to other weather effects such as icing and lightning, which is further used together with a Monte Carlo-based tool to calculate system consequences in terms of interrupted power and interruption costs in [21]. In [10] an analytical technique is used to calculate time-series of expected unavailability of transmission lines due to wind conditions, instead of using a Monte Carlo approach. For each hour, the probability of failure of the transmission line is paired with a distribution of outage duration. An iterative algorithm then appends the probability of the component being unavailable due to a failure at a specific time for a given number of hours ahead in time. A contingency enumeration approach, defining outage combinations as cut-set structures [22; 23] is used together with the time-series of expected unavailability of transmission lines to calculate annual Energy Not Supplied (ENS) for the system. In this paper, a failure of a component is understood as a loss of ability to perform as required, leading to a fault, where the former is understood as an event, while the latter is understood as a state [24]. An outage is understood as the loss of ability of a component to deliver power, which may or may not cause an interruption of service to customers [25]. A contingency is understood as an outage occurrence of a single system component, or the concurrent outage of two or more system components [24]. A set is sometimes used interchangeably with a contingency. A cut-set is understood as a contingency which causes end-user consequences in terms of interrupted power. A cut-set is said to be minimal if the set cannot be reduced without loosing its status as a cut-set [26]. Protection systems are expected to be both dependable and secure [6; 17]. Missing operation of the protection system occurs if it fails to react appropriately to a situation it is designed to respond to and would be a shortfall of the dependability of the system. Similarly would an unwanted operation occur if the protection system reacts to conditions it is not designed to react to, and is a shortfall of the security of the system [17]. This corresponds to the protection system misoperation types defined in [27]. Protection systems have previously been incorporated in power systems reliability analysis in multiple ways, such as through Markov models [14; 16] and approximate methods [17; 28]. Dependability and security were the basis in [17] to construct different scenarios in which protection system reliability can cause a transmission line to be isolated from the network. This gave rise to four fault types [17]: Fault type 1 (FT1) is the failure rate of the transmission line in focus. Fault type 2 (FT2) represents failures due to the spontaneous unwanted operation of a line's own protection system. Fault type 3 (FT3) is explained by a situation where a failure occurs on a neighboring line but is not correctly cleared due to missing operation of the neighboring line's protection system, and thus causes the line in focus to be isolated from the system.