## 4 Case Study for SU Allocation in 0.4 kV PTLs According to the Developed Methodology
### Effect of Sectionalization in the Event of Unstable Failure  
The trial operation of the SU without automatic reclosing function in the Mezenka electric grid since 2015 has confirmed the high reliability of the equipment. During the operation of SU, there have been no observed malfunctions or failures. So, 3 weeks after the installation of SU in Mezenka village (17 November 2015), a short circuit occurred at the PTL section behind the SU. As a result, the SU was triggered, preventing the disconnection of consumers connected before it. Power supply restoration time was 0.83 h from the moment a dispatcher received information about the outage. The volume of liquidated electricity undersupply during the outage was 20 kWh for consumers S1-S29; the effect of liquidated damage from electricity undersupply for these consumers was USD32 when a specific damage value is USD 1.6 (RUB 120) per kWh, according to [41]. Electricity undersupply for consumers S30-S43 amounted to 6 kWh per 0.83 h. The damage from the undersupply, respectively, was USD 9.6. The damage proved to be unstable, and manual re-switching the SU on was successful. It should be noted that a week before the SU installation, a 0.4 kV power transmission line was also disconnected. In that case, all consumers connected to the PTL were de-energized, since the AS at the beginning of PTL had been triggered. The outage was also 0.8-1 h.  
The damage from electricity undersupply in the described case was taken from the technical reports of power grid company. The damage was calculated according to the methodology lying in the determination of power supply restoration time from the moment a dispatcher receives information about the shutdown. However, the actual damage was underestimated due to the fact that the time interval from the moment of the shutdown itself and the moment when the consumer reports it to a dispatcher is not taken into account in the methodology. According to our previous research [42], the power supply restoration time \(\mathfrak{t}_{\text{restor. }}\) (h) can be disaggregated into the following constituents:  
\[\mathfrak{t}_{\text{restor.}}\ =\ \mathfrak{t}_{\text{obt.infor.}}+\mathfrak{t}_{ \text{rec.infor.}}+\mathfrak{t}_{\text{repair}}+\mathfrak{t}_{\text{ harmonize}}, \tag{14}\]  
where  
\(\mathfrak{t}_{\text{obt.infor. }}\) is time interval to obtain information about a failure, h;  
\(\mathfrak{t}_{\text{rec.infor. }}\) is time interval to recognize information about a failure, h;  
\(\mathfrak{t}_{\text{repair}}\) is time interval to repair failed equipment, h;  
and \(\mathfrak{t}_{\text{harmonize}}\) is time interval to connect repaired equipment including activities to harmonize connection, h.  
The numerical values of these constituents have been deduced using the methods of expert assessments and analyzing statistical data provided by the electric grids of Orelregion, Russia [43]. So, we have obtained t\({}_{\text{bdt. infor. }}\)=1.01 h, t\({}_{\text{rec. infor. }}\) = 2.94 h, t\({}_{\text{repair}}\) =1 h, and t\({}_{\text{harmonic}}\) = 0.33 h.  
In the case of SU disconnection in Mezenka village, power supply restoration time was 0.83 h, and it included the time interval from the moment a dispatcher obtained information on a failure to the moment where disconnected consumers were energized. The constituents of PS restoration time were as follows:  
1. Time to obtain information on a failure, i.e., the time interval from the moment of the beginning of PS outage to the moment local residents reported this fact to a dispatcher, is not known;
2. Time to recognize information on a failure was approximately 0.1-0.15 h and included time intervals on: * Recognition of information about the failure place received during communication with a consumer and on making decision by a dispatcher (0.1-0.15 h);
* Preparation of a repair brigade for departure and reaching the failure place (amounted to 0.8 h);
* Inspection of SU (roughly 0.05-0.1 h);
* Search for the location of PTL failure (equal to 0 h, because the damage was unstable);
3.