## 2 Design of sectionalizing Devices
### Criterion for Power Supply Reliability Improvement  
Although the sensitivity criterion limits the possibility of choosing SU places by the distance from a transformer substation (TS), it is not the only selection criterion. The second criterion is to improve power supply reliability for consumers. This criterion depends on the configuration of the sectionalized PTL and the distribution of the load along it. In the case of sectionalizing, PS reliability increases for consumers connected to PTL section before SU. To determine the installation location of SU in terms of PS reliability, it is necessary to use the following methodology. 1. To calculate the total number of hours of PS interrupptions due to failures on PTL sections before SU. This time \(T_{\sum li}\) (h/year) is determined by equation: \[T_{\sum li}\ =\ \sum_{i\ =\ 1}^{n}\left(\frac{\mathrm{T}_{Rli}\times\omega_{0 li}\times l_{i}}{100}\right)\,\] (2) where \(l_{i}\) is length of the \(i\)th PTL section, km; T\({}_{Rli}\) is average PS restoration time for the \(i\)th PTL section, h; and \(\omega_{0 li}\) is failure flow for the \(i\)th PTL section per 100 km, year\({}^{-1}\). The values of failures flow and average PS restoration time for power lines are taken according to statistical data or literature sources. 2. To determine the total number of hours of PS interrupptions from failures on PTL sections after SU: \[T_{\sum lj}\ =\ \sum_{j\ =\ 1}^{m}\left(\frac{\mathrm{T}_{Rlj}\times\omega_{0 lj}\times l_{j}}{100}+\frac{\mathrm{T}_{RSU}\times\omega_{0 SU}}{100}\right)\,\] (3) where \(\mathrm{T}_{RSU}\) is average restoration time for SU, h; T\({}_{Rlj}\) is average restoration time for the jth PTL section, h; \(\omega_{0 lj}\) is failure flow at the jth PTL section per 100 km, year\({}^{-1}\); \(\omega_{0 lSU}\) is failure flow at \(SU\) per 100 pcs, year\({}^{-1}\); and \(l_{j}\) is the length of the jth PTL section after SU, km. The average restoration time of SU is determined on the basis of experimental data on SU maintenance and amounts to 1 h. The parameter of SU failures flow per 100 pcs is taken to be 2 year\({}^{-1}\). 1. To determine the total number of hours of emergency outages within the entire PTL in the absence of SU \(T_{\sum L}\) (h/year): \[T_{\sum L}\ =\ \sum_{i\ =\ 1}^{n}\left(\frac{\mathrm{T}_{Rli}\times\omega_{0 li}\times l_{i}}{100}\right)+\sum_{j\ =\ 1}^{m}\left(\frac{\mathrm{T}_{Rlj}\times\omega_{0 lj}\times l_{j}}{100}\right)\] (4)
2. The damage caused by emergency outages for the year is calculated as follows. Failures on any PTL section without sectionalization and failures on PTL sections before SU with sectionalization are equivalent since they lead to a power failure for all consumers. Damage in these situations \(D_{l}\)(USD/year) is determined as follows: \[D_{l}\ =\ \sum_{g\ =\ 1}^{k}\left(S_{0g}\times\Delta W_{lg}\right)\ =\ \sum_{g\ =\ 1}^{k}\left(S_{0g}\times\frac{P_{Mlg}\times T_{Mlg}\times T_{\sum L}}{8760} \right)\,\] (5) where \(S_{0g}\) is specific damage from electricity undersupply for the gth consumer, USD/kWh; \(\Delta W_{lg}\) is electricity undersupply for the gth consumer, kWh/year; \(P_{Mlg}\) is maximum load of the gth consumer, kW;\(T_{Mlg}\) is usage time of maximum load by the gth consumer, h/year; and \(k\) is the number of consumers connected to PTL, pcs. In case of failures on PTL sections after SU, damage D\({}_{lj\sum}\) (USD/year) is determined by:  
\[\text{D}_{\sum{lj}}\ =\ \sum_{g\ =\ 1}^{q}\left(S_{0y}\times\Delta W_{ly} \right)\ =\ \sum_{g\ =\ 1}^{q}\left(S_{0y}\times\frac{P_{Mly}\times T_{Mly}\times T_{\sum{lj}}}{8760} \right), \tag{6}\]  
where  
\(S_{0y}\) is specific damage from electricity undersupply for the \(y\)th consumer after SU, USD/kWh; \(\Delta W_{ly}\) is electricity undersupply for the \(y\)th consumer, kWh/year;  
\(P_{Mly}\) is maximum load of the \(y\)th consumer, kW;  
\(T_{Mly}\) is usage time of maximum load by the \(y\)th consumer, h/year;  
and \(q\) is the number of consumers connected to PTL after SU, pcs.