# Determination of loss-minimum configuration with mathematical optimality in a three-sectionalized three connected distribution feeder network

Yasuhiro Hayashi, Junya Matsuki, Shinji Ishikawa, Hirotaka Takano, Eiji Muto, Naoki Kobayashi

Research output: Contribution to journalArticle

### Abstract

In a distribution system, in order to enhance the reliability of power supply, the distribution feeder is divided into several sections by installing sectionalizing switches, and then each of the sectionalized sections is connected to a different feeder. For example, one feeder is divided into three sections by two sectionalizing switches, and then each of the divided sections is connected to the other feeder through sectionalizing switch. Since a distribution system with many feeders has many sectionalizing switches, the system configuration is determined by states (opened or closed) of sectionalizing switches. Usually, a power utility tries to obtain distribution loss-minimum configuration among large numbers of configuration candidates. However, it is very difficult to determine the loss-minimum configuration such that the mathematical optimality is guaranteed, because it is well known that determination of a distribution system's configuration is to decide whether each sectionalizing switch is opened or closed by solving a combinatorial optimization problem. In this paper, the authors propose a determination method of loss-minimum configuration by which the mathematical optimality is guaranteed for a three-sectionalized three-connected distribution feeder network. A problem to determine the loss-minimum configuration is formulated as a combinatorial optimization problems with four operational constraints (1 feeder capacity, 2 voltage limit, 3 radial structure, and 4 three-sectionalization). In the proposed method, after picking up all partial configurations satisfied with radial structure constraint by using enumeration method, optimal combination of partial configurations is determined under the other operational constraints by using conventional optimization method. Numerical simulations are carried out for a distribution network model with 140 sectionalizing switches in order to examine the validity of the proposed algorithm in comparison with one of conventional meta-heuristics (tabu search).

Original language English 56-65 10 Electrical Engineering in Japan (English translation of Denki Gakkai Ronbunshi) 167 1 https://doi.org/10.1002/eej.20530 Published - 2009 Apr 15 Yes

### Fingerprint

Switches
Combinatorial optimization
Tabu search
Electric power distribution
Computer simulation
Electric potential

### Keywords

• Combinatorial optimization problem
• Distribution system
• Enumeration method
• Loss-minimum configuration
• Sectionalizing switch
• Three-sectionalized three-connected feeder network

### ASJC Scopus subject areas

• Electrical and Electronic Engineering
• Energy Engineering and Power Technology

### Cite this

Determination of loss-minimum configuration with mathematical optimality in a three-sectionalized three connected distribution feeder network. / Hayashi, Yasuhiro; Matsuki, Junya; Ishikawa, Shinji; Takano, Hirotaka; Muto, Eiji; Kobayashi, Naoki.

In: Electrical Engineering in Japan (English translation of Denki Gakkai Ronbunshi), Vol. 167, No. 1, 15.04.2009, p. 56-65.

Research output: Contribution to journalArticle

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AB - In a distribution system, in order to enhance the reliability of power supply, the distribution feeder is divided into several sections by installing sectionalizing switches, and then each of the sectionalized sections is connected to a different feeder. For example, one feeder is divided into three sections by two sectionalizing switches, and then each of the divided sections is connected to the other feeder through sectionalizing switch. Since a distribution system with many feeders has many sectionalizing switches, the system configuration is determined by states (opened or closed) of sectionalizing switches. Usually, a power utility tries to obtain distribution loss-minimum configuration among large numbers of configuration candidates. However, it is very difficult to determine the loss-minimum configuration such that the mathematical optimality is guaranteed, because it is well known that determination of a distribution system's configuration is to decide whether each sectionalizing switch is opened or closed by solving a combinatorial optimization problem. In this paper, the authors propose a determination method of loss-minimum configuration by which the mathematical optimality is guaranteed for a three-sectionalized three-connected distribution feeder network. A problem to determine the loss-minimum configuration is formulated as a combinatorial optimization problems with four operational constraints (1 feeder capacity, 2 voltage limit, 3 radial structure, and 4 three-sectionalization). In the proposed method, after picking up all partial configurations satisfied with radial structure constraint by using enumeration method, optimal combination of partial configurations is determined under the other operational constraints by using conventional optimization method. Numerical simulations are carried out for a distribution network model with 140 sectionalizing switches in order to examine the validity of the proposed algorithm in comparison with one of conventional meta-heuristics (tabu search).

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