## 2 Methods for Determining the Number of Power Line and Transformer Outages
### Factors Influencing the Time of Failure Removal
#### Failure Removal Time  
Based on the report of the Polish Energy Regulatory Authority and data available in the literature, it can be assumed that the average time to remove a failure of a transmission line in the Polish power grid is 14 h [16], while the average outage rate of 110 kV lines according to the same article is 1.7 outages per 100 km of line.  
In the case of the Chinese power grid, according to the work [119], the average time to repair a line is 10.5 h. According to [8] the outage rate of transmission lines in the Iranian transmission system is 0.61 outages per 100 km, with an average repair time of less than 8 h. According to [44], the average time to repair a line in Europe is less than 15 h, which corresponds to the values presented for Poland, while the average time to repair transmission lines for Canada and the USA is around 8 h, which is almost 2 times less time needed to repair the damage than in Europe.  
In [71] the authors obtained data for calculation purposes on transformers operating in the Egyptian Power System from 2002 to 2009. The number of transformers included in the calculations ranged from 223 transformers in 2002 to 292 transformers in 2009, which indicates that this network is similar in size to the Polish network, which has 213 system transformers. The results of the conducted studies show that the average time needed to repair a transformer without dividing into the type of damage was about 8 h in 2002, while in 2007, the average time needed to repair a single damage was 17 h, without dividing them into single damages. In the case of specifying the time needed to repair a specific damage, the most time was needed for Buchholz and pressure relief repair. In 2007, the repair time was 63 h, whereas the average repair time across all measured years was nearly 22 h. The smallest amount of time needed to repair a single failure was 50 min in 2007 to repair hot spots, while the average amount of time from all measurement years to repair this failure was 2 h.  
However, data available in the literature [8] regarding the Iranian power system indicate an average of less than 44 h needed to repair a network transformer.  
In [125] one can find detailed reliability calculations for the Polish power system in the 1990s. The authors obtained detailed data for the years 1995-1997. It can be seen that during these two years, there were 152 forced outages of 400 kV lines and 473 forced outages of 220 kV lines. In the case of network transformers, there were 85 forced outages and 709 planned outages. The authors also obtained information on the total duration of the network elements' inability to operate properly. Thus, in the case of network transformers, the average duration of an emergency shutdown for 400/220 kV transformers was 12 h per single failure, 12 h for 400/110 kV transformers, and 9 h for 220/110 kV transformers. In the case of HV transmission lines, the average time needed to repair forced shutdowns of 400 kV lines was 15 h per single shutdown, while for 220 kV lines, it was 13 h. Thesecalculations are based on actual data because the authors received data from the Polish Power System Operator.  
Averaging all results, the average time needed to restore a transmission line in the Polish Power System can be assumed to be 14 h, while the time needed to repair an HV/HV transformer failure can be assumed to be 11 h.