## 2 Design of sectionalizing Devices
### Criterion for Power Supply Reliability Improvement
To calculate the effect of sectionalization \(E_{s}\) (USD/year) for each intended installation location of SU:  
\[E_{s}\ =\ \frac{D_{l}\times T_{\sum{lj}}}{\text{T}_{\sum{L}}t} \tag{7}\]  
To determine scheduled downtime \(T_{sc.d. }\) (h/year):  
\[T_{sc.d.}\ =\ \sum T_{sc.i}\times m_{i}, \tag{8}\]  
where \(T_{sc.i}\) is average scheduled downtime for the \(i\)th network element, h; \(m_{i}\) is number of scheduled repairs during the repair cycle for the \(i\)th network element. To determine damage \(D_{\sum{l},sc.d}\) caused by scheduled repairs for PTL both without sectionalizing when servicing at any point and with sectionalizing when servicing at PTL section before SU (USD/year):  
\[D_{\sum{l},sc.d}\ =\ \sum_{g\ =\ 1}^{k}\left(S_{0g,sc.d}\times\Delta W_{lg,sc.d}\right)\ =\ \sum_{g\ =\ 1}^{k}\left(S_{0g,sc.d}\times\frac{P_{Mlg}\times T_{Mlg}\times T_{sc.d}}{8760} \right), \tag{9}\]  
where  
\(S_{0g,sc.d}\) is specific damage from electricity undersupply for the gth consumer during scheduled repairs of PTL, USD/kWh;  
\(\Delta W_{lg,sc.d}\) is electricity undersupply for the gth consumer during scheduled repairs, kWh/year;  
\(P_{Mlg}\) is maximum load of the gth consumer, kW;  
\(T_{Mlg}\) is usage time of the maximum load by the gth consumer, h/year;  
\(T_{sc.d}\) is scheduled downtime for the whole PTL, h/year;  
and \(k\) is number of consumers connected to PTL, pcs. To determine damage D\({}_{lj\sum{sc.d}}\) caused by scheduled repairs at PTL sections after \(SU\) (USD/year):  
\[\text{D}_{\sum{lj},sc.d}\ =\ \sum_{g\ =\ 1}^{q}\left(S_{0y,sc.d}\times \Delta W_{lg,sc.d}\right)\ =\ \sum_{g\ =\ 1}^{q}\left(S_{0y,sc.d}\times T_{Mly}\times T_{lj,sc.d}\right)\, \tag{10}\]  
where  
\(S_{0y,sc.d}\) is specific damage from electricity undersupply for the yth consumer during scheduled repairs of PTL, USD/kWh;  
\(\Delta W_{lg,sc.d}\) is electricity undersupply for the \(y\)th consumer during scheduled repairs, 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;  
\(T_{lj,sc.d. }\) is planned downtime for the PTL after SU, h/year;and \(q\) is number of consumers connected to PTL after SU, pcs. * To calculate the effect of sectionalization for each intended installation location of SU from reducing scheduled PTL repairs \(E_{s.sc.d}\) (USD/year): \[E_{ssc.d}\ =\ \frac{D_{\Sigma\_1 sc.d}\cdot T_{\_1 jsc.d.}}{T_{\_ \_1 sc.d}}\] (11)
* To calculate the cumulative effect of sectionalizing for each intended location \(E_{\_}{\Sigma}\) (USD/year): \[T_{\sum lj}\ =\ \sum_{j\ =\ 1}^{m}\left(\frac{\mathrm{T}_{Rlj}\times\omega_{0 lj}\times l_{j}}{100}+\frac{\mathrm{T}_{RSU}\times\omega_{0 SU}}{100}\right)\,\]0 (12)
* To calculate the annual economic effect from SU installation \(G\) (USD/year): \[T_{\sum lj}\ =\ \sum_{j\ =\ 1}^{m}\left(\frac{\mathrm{T}_{Rlj}\times\omega_{0 lj}\times l_{j}}{100}+\frac{\mathrm{T}_{RSU}\times\omega_{0 SU}}{100}\right)\,\]1 (13) where C\({}_{\_}{op}\) is operating cost of servicing SU, USD/year; p\({}_{\_}{n}\) is standard effectiveness ratio of capital investment. p\({}_{\_}{n}\) is taken in the range 0.1...0.3 [39]. For the energy industry, it usually equals 0.125, which corresponds to a payback period of 8 years, although PJSC ROSSETI [40] accepts a payback period of up to 10 years. p\({}_{\_}{n}\) can be set based on the desired payback period defining as: p\({}_{\_}{n}\) = 1/Payback period; C\({}_{\_}{cap}\) is capital cost of SU implementation, USD; and \(N_{\_}c\) is the number of SUs (if there are several _SUs_ in a power line), pcs. Sectionalizing units can be installed at all intended installation locations, for which G \(\geq\) 0. The only limitation is that it is necessary to fulfill the first criterion, that is, to fulfill sensitivity limits against single-phase SC current.