# Allocation of 0.4 kV PTL Sectionalizing Units under Criteria of Sensitivity Limits and Power Supply Reliability

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Impact of Power Line Sectionalizing on Power Supply Reliability

#### 1.2. Allocation Problem of Sectionalizing Units within Electrical Networks

#### 1.3. Article Relevance, Contribution and Organization

## 2. Design of Sectionalizing Devices

- Two-way communication between SU and a network dispatcher;
- Constant monitoring of voltage and current parameters;
- Control of the vacuum contactor KM1 for automated (or remote) switching SU power circuits;
- Implementation of automatic (or remote) input or inhibit input of a reserve to an emergency PTL section (when using SU as a recloser);
- Automatic (or remote) control of automatic reclosing function;
- Providing an understandable interface and output of all information on a display for service personnel.

- Changes in current and voltage parameters;
- Position of vacuum contactor;
- Successful implementation of automatic reclosing function;
- Fact and duration of voltage interruption in circuits under monitoring.

## 3. Methodology for SU Allocation in 0.4 kV PTLs Based on Criteria of Sensitivity Limits and PS Reliability

#### 3.1. Criterion of Sensitivity Limits against Single-Phase SC

- ${U}_{Ph}$ is phase voltage, V;
- ${Z}_{\mathrm{T}}$ is impedance of a transformer feeding the PTL, Ohm;
- ${R}_{0Ph}$ is specific active resistance of the phase wire, Ohm/km;
- ${R}_{0N}$ is specific active resistance of the neutral wire, Ohm/km;
- ${X}_{0PhN}$ is specific inductive resistance of the phase-zero loop, Ohm/km;
- and ${\mathrm{I}}_{sens.}$ is current according to the sensitivity condition, A.

#### 3.2. Criterion for Power Supply Reliability Improvement

- To calculate the total number of hours of PS interruptions due to failures on PTL sections before SU. This time ${T}_{{\displaystyle \sum}li}$ (h/year) is determined by equation:$${T}_{{\displaystyle \sum}li}={{\displaystyle \sum}}_{i=1}^{n}\left(\frac{{\mathrm{T}}_{Rli}\times {\omega}_{0li}\times {l}_{i}}{100}\right),$$
- ${l}_{i}$ is length of the ith PTL section, km;
- ${\mathrm{T}}_{Rli}$ is average PS restoration time for the ith PTL section, h;
- and ${\omega}_{0li}$ is failure flow for the ith PTL section per 100 km, year
^{−1}.

- 2.
- To determine the total number of hours of PS interruptions from failures on PTL sections after SU:$${T}_{{\displaystyle \sum}lj}={{\displaystyle \sum}}_{j=1}^{m}\left(\frac{{\mathrm{T}}_{Rlj}\times {\omega}_{0lj}\times {l}_{j}}{100}+\frac{{\mathrm{T}}_{RSU}\times {\omega}_{0SU}}{100}\right),$$
- ${\mathrm{T}}_{RSU}$ is average restoration time for SU, h;
- ${\mathrm{T}}_{Rlj}$ is average restoration time for the jth PTL section, h;
- ${\omega}_{0lj}$ is failure flow at the jth PTL section per 100 km, year
^{−1}; - ${\omega}_{0SU}$ is failure flow at SU per 100 pcs, year
^{−1}; - and ${l}_{j}$ is the length of the jth PTL section after SU, km.

^{−1}.

- To determine the total number of hours of emergency outages within the entire PTL in the absence of SU ${T}_{{\displaystyle \sum}L}$ (h/year):$${T}_{{\displaystyle \sum}L}={\displaystyle \sum}_{i=1}^{n}\left(\frac{{\mathrm{T}}_{Rli}\times {\omega}_{0li}\times {l}_{i}}{100}\right)+{\displaystyle \sum}_{j=1}^{m}\left(\frac{{\mathrm{T}}_{Rlj}\times {\omega}_{0lj}\times {l}_{j}}{100}\right)$$
- 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:$${D}_{l}={{\displaystyle \sum}}_{g=1}^{k}\left({S}_{0g}\times \Delta {W}_{lg}\right)={{\displaystyle \sum}}_{g=1}^{k}\left({S}_{0g}\times \frac{{P}_{Mlg}\times {T}_{Mlg}\times {T}_{{\displaystyle \sum}L}}{8760}\right),$$
- ${S}_{0g}$ 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.

- ${S}_{0y}$ is specific damage from electricity undersupply for the yth consumer after SU, USD/kWh;
- $\Delta {W}_{ly}$ is electricity undersupply for the yth consumer, kWh/year;
- ${P}_{Mly}$ is maximum load of the yth consumer, kW;
- ${T}_{Mly}$ is usage time of maximum load by the yth consumer, h/year;
- and $q$ is the number of consumers connected to PTL after SU, pcs.

- 3.
- To calculate the effect of sectionalization ${E}_{s}$ (USD/year) for each intended installation location of SU:$${E}_{s}=\frac{{D}_{l}\times {T}_{{\displaystyle \sum}lj}}{{\mathrm{T}}_{{\displaystyle \sum}L}}$$
- 4.
- To determine scheduled downtime ${T}_{sc.d.}$ (h/year):$${T}_{sc.d.}={\displaystyle \sum}{T}_{sc.i}\times {m}_{i},$$${m}_{i}$ is number of scheduled repairs during the repair cycle for the ith network element.
- 5.
- To determine damage ${D}_{{\displaystyle \sum}l.sc.d}$ 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):$${D}_{{\displaystyle \sum}l.sc.d}={\displaystyle \sum}_{g=1}^{k}\left({S}_{0g.sc.d}\times \Delta {W}_{lg.sc.d}\right)={\displaystyle \sum}_{g=1}^{k}\left({S}_{0g.sc.d}\times \frac{{P}_{Mlg}\times {T}_{Mlg}\times {T}_{sc.d}}{8760}\right),$$
- ${S}_{0g.sc.d}$ 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.

- 6.
- To determine damage ${\mathrm{D}}_{lj{\displaystyle \sum}sc.d}$ caused by scheduled repairs at PTL sections after SU (USD/year):$${\mathrm{D}}_{{\displaystyle \sum}lj.sc.d}={{\displaystyle \sum}}_{y=1}^{q}\left({S}_{0y.sc.d}\times \Delta {W}_{ly.sc.d}\right)={{\displaystyle \sum}}_{y=1}^{q}\left({S}_{0y.sc.d}\times \frac{{P}_{Mly}\times {T}_{Mly}\times {T}_{lj.sc.d.}}{8760}\right),$$
- ${S}_{0y.sc.d}$ is specific damage from electricity undersupply for the yth consumer during scheduled repairs of PTL, USD/kWh;
- $\Delta {W}_{ly.sc.d}$ is electricity undersupply for the yth consumer during scheduled repairs, kWh/year;
- ${P}_{Mly}$ is maximum load of the yth consumer, kW;
- ${T}_{Mly}$ is usage time of maximum load by the yth 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.

- 7.
- To calculate the effect of sectionalization for each intended installation location of SU from reducing scheduled PTL repairs ${E}_{s.sc.d}$ (USD/year):$${E}_{s.sc.d}=\frac{{D}_{{\displaystyle \sum}l.sc.d}\xb7{T}_{lj.sc.d.}}{{T}_{sc.d}}$$
- 8.
- To calculate the cumulative effect of sectionalizing for each intended location ${E}_{s\Sigma}$ (USD/year):$${E}_{\Sigma s}={E}_{s}+{E}_{s.sc.d}$$
- 9.
- To calculate the annual economic effect from SU installation $G$ (USD/year):$$G={E}_{\Sigma s}-\left({\mathrm{C}}_{op}+{\mathrm{p}}_{n}\xb7{\mathrm{C}}_{cap}\right)\xb7{N}_{c}$$
- ${\mathrm{C}}_{op}$ is operating cost of servicing SU, USD/year;
- ${\mathrm{p}}_{n}$ is standard effectiveness ratio of capital investment. ${\mathrm{p}}_{n}$ 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. ${\mathrm{p}}_{n}$ can be set based on the desired payback period defining as: ${\mathrm{p}}_{n}$ = 1/Payback period;
- ${\mathrm{C}}_{cap}$ 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.

## 4. Case Study for SU Allocation in 0.4 kV PTLs According to the Developed Methodology

#### 4.1. Determination of SU Maximum Distance According to Criterion of Sensitivity Limits against Single-Phase SC

^{2}. The length of PTLs with branch lines is 1.85 km.

#### 4.2. Determination of SU Installation Location According to Criterion for Power Supply Reliability Improvement

#### 4.3. Effect of Sectionalization in the Event of Unstable Failure

- t
_{obt. infor.}is time interval to obtain information about a failure, h; - t
_{rec. infor.}is time interval to recognize information about a failure, h; - t
_{repair}is time interval to repair failed equipment, h; - and t
_{harmonize}is time interval to connect repaired equipment including activities to harmonize connection, h.

_{obt. infor}.=1.01 h, t

_{rec. infor.}= 2.94 h, t

_{repair}=1 h, and t

_{harmonize}= 0.33 h.

- 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;
- 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);

- Time to repair failed equipment was absent, since a repair team only re-switched the device on manually, and it turned out to be successful;
- Time to harmonize the connection of repaired equipment to PS network and the connection itself equaled to no more than 0.05 h.

#### 4.4. Effect of Sectionalization in the Event of Stable Failure

#### 4.5. Effect of Sectionalization and Automatic Reclosing in the Event of Unstable Failure

_{obt. infor.}), time for recognizing information (t

_{rec. infor.}), and time for connecting the repaired equipment (t

_{harmonize}). If the PTL failure is unstable, PS restoration time could be reduced to the value of recloser time delay of SU contactor (in the experimental sample it is set equal to 0.5 min, or 0.0083 h), that is:

#### 4.6. Effect of Sectionalization and Automatic Reclosing in the Event of Stable Failure

- t
_{obt. infor.1}is time interval to obtain information about a failure by a sensor; - t
_{obt. infor.2}is time interval to obtain information about a failure by a signaling unit of dispatcher room; - and t
_{obt. infor.3}is time interval to obtain information about a failure by a dispatcher.

_{obt. infor.1}and t

_{obt. infor.2}depend on the applied data transmission method, for example, for the GPRS data transmission technology, together, they will be less than one second (0.0002 h) [44]. The time interval t

_{obt. infor.3}depends on the mode of information display to a dispatcher and includes the time required for a dispatcher to notice a message and read it. According to study [45], when equipping a dispatcher room with a SCADA system, this time interval is no more than 15 s (0.0042 h). Hence, time for receiving information about failure in the considered case would be 0.0044 h, and therefore, the power supply restoration time would be:

#### 4.7. Payback of Capital Investment in SU Installation

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Photos of sectionalizing units installed in Orel electrical networks [37].

**Table 1.**Maximum distance from TS with a 250 kVA transformer to SU when PTL wires are of different cross-sections.

${\mathit{I}}_{\mathit{s}\mathit{e}\mathit{n}\mathit{s}.},\mathrm{A}.$ | ${\mathit{U}}_{\mathit{P}\mathit{h}},\mathbf{V}$ | ${\mathit{L}}_{\mathit{m}\mathit{a}\mathit{x}}\mathbf{for}\mathbf{ABS}2\phantom{\rule{0ex}{0ex}}3\times 35\phantom{\rule{0ex}{0ex}}+1\times 50,\mathbf{km}$ | ${\mathit{L}}_{\mathit{m}\mathit{a}\mathit{x}}\mathbf{for}\mathbf{ABS}2\phantom{\rule{0ex}{0ex}}3\times 50\phantom{\rule{0ex}{0ex}}+1\times 50,\mathbf{km}$ | ${\mathit{L}}_{\mathit{m}\mathit{a}\mathit{x}}\mathbf{for}\mathbf{ABS}2\phantom{\rule{0ex}{0ex}}3\times 50+\phantom{\rule{0ex}{0ex}}1\times 70,\mathbf{km}$ | ${\mathit{L}}_{\mathit{m}\mathit{a}\mathit{x}}\mathbf{for}\mathbf{ABS}2\phantom{\rule{0ex}{0ex}}3\times 70+\phantom{\rule{0ex}{0ex}}1\times 70,\mathbf{km}$ | ${\mathit{L}}_{\mathit{m}\mathit{a}\mathit{x}}\mathbf{for}\mathbf{ABS}2\phantom{\rule{0ex}{0ex}}3\times 70\phantom{\rule{0ex}{0ex}}+1\times 95,\mathbf{km}$ | ${\mathit{L}}_{\mathit{m}\mathit{a}\mathit{x}}\mathbf{for}\mathbf{ABS}2\phantom{\rule{0ex}{0ex}}3\times 95+\phantom{\rule{0ex}{0ex}}1\times 95,\mathbf{km}$ |
---|---|---|---|---|---|---|---|

48 | 220 | 2.65 | 2.96 | 3.29 | 3.72 | 4.03 | 4.43 |

75 | 220 | 1.69 | 1.89 | 2.11 | 2.38 | 2.58 | 2.84 |

96 | 220 | 1.32 | 1.48 | 1.64 | 1.86 | 2.01 | 2.21 |

120 | 220 | 1.06 | 1.18 | 1.32 | 1.49 | 1.61 | 1.77 |

150 | 220 | 0.85 | 0.95 | 1.05 | 1.19 | 1.29 | 1.41 |

189 | 220 | 0.67 | 0.75 | 0.83 | 0.95 | 1.02 | 1.12 |

240 | 220 | 0.53 | 0.59 | 0.66 | 0.74 | 0.80 | 0.88 |

300 | 220 | 0.42 | 0.47 | 0.52 | 0.59 | 0.64 | 0.70 |

375 | 220 | 0.34 | 0.38 | 0.42 | 0.47 | 0.51 | 0.56 |

480 | 220 | 0.26 | 0.29 | 0.33 | 0.37 | 0.40 | 0.44 |

600 | 220 | 0.21 | 0.23 | 0.26 | 0.29 | 0.32 | 0.35 |

750 | 220 | 0.17 | 0.19 | 0.21 | 0.23 | 0.25 | 0.28 |

960 | 220 | 0.13 | 0.14 | 0.16 | 0.18 | 0.20 | 0.22 |

1200 | 220 | 0.10 | 0.11 | 0.13 | 0.14 | 0.16 | 0.17 |

1500 | 220 | 0.08 | 0.09 | 0.10 | 0.11 | 0.12 | 0.14 |

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**MDPI and ACS Style**

Vinogradova, A.; Vinogradov, A.; Bolshev, V.; Izmailov, A.; Dorokhov, A.; Bukreev, A.
Allocation of 0.4 kV PTL Sectionalizing Units under Criteria of Sensitivity Limits and Power Supply Reliability. *Appl. Sci.* **2021**, *11*, 11608.
https://doi.org/10.3390/app112411608

**AMA Style**

Vinogradova A, Vinogradov A, Bolshev V, Izmailov A, Dorokhov A, Bukreev A.
Allocation of 0.4 kV PTL Sectionalizing Units under Criteria of Sensitivity Limits and Power Supply Reliability. *Applied Sciences*. 2021; 11(24):11608.
https://doi.org/10.3390/app112411608

**Chicago/Turabian Style**

Vinogradova, Alina, Alexander Vinogradov, Vadim Bolshev, Andrey Izmailov, Alexey Dorokhov, and Alexey Bukreev.
2021. "Allocation of 0.4 kV PTL Sectionalizing Units under Criteria of Sensitivity Limits and Power Supply Reliability" *Applied Sciences* 11, no. 24: 11608.
https://doi.org/10.3390/app112411608