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Reconfiguration of Primary Distribution Network with Several Independent Power Sources
2019 Workshop Control of Smart Gridon and Renewable Energy Systems 2019 IFAC IFAC Workshop on 2019 IFAC Workshop on 2019 IFAC Workshop on Control of and Renewable Energy Jeju, Korea, JuneGrid 10-12, 2019 Control of Smart Smart Grid and RenewableAvailable Energy Systems Systems online at www.sciencedirect.com Control of Smart Smart Grid and Renewable Energy Energy Systems Systems Control of and Renewable Jeju, Korea, June 10-12, 2019 2019 Workshop on Jeju, IFAC Korea, JuneGrid 10-12, 2019 Jeju, Korea, June 10-12, 2019 Jeju, Korea, June 10-12, 2019 Control of Smart Grid and Renewable Energy Systems Jeju, Korea, June 10-12, 2019
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IFAC PapersOnLine 52-4 (2019) 437–442 Reconfiguration of Primary Distribution Network with Several Independent Power Reconfiguration of Primary Distribution Network with Several Independent Power Sources Reconfiguration of Primary Distribution Network with Several Independent Power Sources Reconfiguration of Primary Distribution Network with Several Independent Power Sources , , Sources Eugene Boloev*,, **, Lyudmila Semenova* Irina Golub*, **, Oleg Voitov*, **, , , ,
Oleg Voitov* **, Eugene Boloev* **, Lyudmila Semenova* Irina Golub*,, **, Boloev* Irina **, Oleg Oleg Voitov* Voitov*,, **, **, Eugene Eugene Boloev*,, **, **, Lyudmila Lyudmila Semenova* Semenova* Irina Golub* Golub* **, , , *Melentiev Energy Systems Institute, **, of Siberian Branch of Russian Academy of Science **, Oleg Voitov* Eugene Boloev* **, Lyudmila Semenova* Irina Golub* *Melentiev Siberian Branch of Academy *Melentiev Energy Energy Systems Institute of Siberian Branch of Russian Russian Academy of of Science Science RussiaSystems (Tel: +7Institute (3952) of 424 700; e-mail: golub@ isem.irk.ru) *Melentiev Energy Systems Institute of Siberian Branch of Russian Academy of Science Russia (Tel: +7 (3952) 424 700; e-mail: golub@ isem.irk.ru) Russia (Tel: +7 (3952) 424 700; e-mail: golub@ isem.irk.ru) **Irkutsk National Research Technical University *Melentiev Energy Systems Siberian Branch ofUniversity Russian Academy of Science Russia (Tel: +7Institute (3952) of 424 700; e-mail: golub@ isem.irk.ru) **Irkutsk Research Technical **Irkutsk National Research Technical University (Tel: +7 National (3952) 405 127; e-mail: [email protected]) Russia (Tel: +7 (3952) 424 700; e-mail: golub@ isem.irk.ru) **Irkutsk National Research Technical University (Tel: +7 +7 (3952) (3952) 405 405 127; 127; e-mail: e-mail: [email protected]) [email protected]) (Tel: (Tel: +7 National (3952) 405 127; e-mail: [email protected]) **Irkutsk Research Technical University (Tel: +7 (3952) 405 127; e-mail: [email protected]) Abstract: We solve the problem of reconfiguration of a primary distribution network with feeders Abstract: We solve solve the problem of of reconfiguration of a primary distribution network with feeders Abstract: We problem of distribution network with powered from independent A high-performance algorithm is applied to reconfigure the Abstract: We several solve the the problem sources. of reconfiguration reconfiguration of aa primary primary distribution network with feeders feeders powereddistribution from several independent sources. A high-performance high-performance algorithm is applied applied to reconfigure reconfigure the powered from several independent sources. A algorithm is to the primary network by the loss minimization criterion. The algorithm constructs the maximum powered from several independent sources. A high-performance algorithm is applied to reconfigure the Abstract: We solvenetwork the problem reconfiguration of a primary distribution networkthe with feeders primary distribution distribution network by theofloss loss minimization criterion. The algorithm algorithm constructs the maximum primary by the minimization criterion. The constructs maximum spanning tree on the network graph and determines the composition of branches of independent loops. primary distribution by thesources. loss minimization The algorithm constructs the maximum powered from several independent A high-performance algorithm is applied to reconfigure the spanning tree on on thenetwork network graph and determines thecriterion. composition of determining branches of independent independent loops. spanning tree the network graph and determines the composition of branches of The information on the distribution network topology features allows the variants loops. of tie spanning tree on the network graph and determines the composition of branches of independent loops. primary distribution network by the loss minimization criterion. The algorithm constructs the maximum The information on the distribution network topology features allows determining the variants of tie The information distribution topology allows determining of tie switches that mayonbethe used to restorenetwork the power supplyfeatures at an emergency outage of the any variants sectionalizing spanning tree on the network graph and determines the composition of branches of independent loops. The information on the distribution network topology features allows determining the variants of tie switches that may be used to restore the power supply at an emergency outage of any sectionalizing switches be used to restore power supply at in anthe emergency of anyhave sectionalizing switch andthat anymay circuit breaker, and thethe subsystems of trees network, outage whose loads no reserve The information onbethe distribution network topology features allows determining variants of tie switches that used to restore the power supply at in anthe emergency outage of the anyhave sectionalizing switch and anymay circuit breaker, andofthe the subsystems of trees trees in the network, whose loads have no reserve reserve switch and any circuit breaker, and of network, whose no power supply. The efficiency thesubsystems offered algorithm is verified by the loads coincidence of the switches that may be used to restore the power supply at an emergency outage of any sectionalizing switch and any circuit breaker, and the subsystems of trees in the network, whose loads have no reserve power supply. results The efficiency efficiency ofitsthe the offered algorithm is network verifiedregarded by the the ascoincidence coincidence of the the power supply. The offered verified by of reconfiguration obtained onof basis for thealgorithm distributionis a test one with switch and any circuit breaker, and the subsystems of trees in the network, whose loads have nowith reserve power supply. The efficiency ofits the offered algorithm is network verified by the as coincidence of the the reconfiguration results obtained on its basis for the distribution network regarded as a test one with the reconfiguration results obtained on basis for the distribution regarded a test one results obtained results for thisobtained networkonbyitsother methods. The algorithm efficiency is as alsoa test illustrated by the an reconfiguration basis for thealgorithm distribution regarded one with power supply. The efficiency of offered is network verified by the coincidence ofby results obtained obtained for this network by the other methods. The algorithm algorithm efficiency is also also illustrated by an an results this network by other methods. The efficiency is illustrated example of a realfor municipal distribution network. results obtained for this network by other methods. The algorithm efficiency is also illustrated by an reconfiguration obtained on its basis for the distribution network regarded as a test one with the example of aa real realresults municipal distribution network. example of municipal distribution network. example of adistribution real municipal distribution results for thisnetwork, network by other methods. The algorithm is also illustrated bytree, an © 2019,obtained IFAC (International Federation ofnetwork. Automatic Control) Hosting byefficiency Elsevier Ltd. All rights reserved. Keywords: sectionalizing switches, tie switches, reconfiguration, spanning Keywords: distribution network, sectionalizing switches, tie tie switches, switches, reconfiguration, reconfiguration, spanning spanning tree, tree, example ofgeneration. adistribution real municipal distribution network. switches, Keywords: network, sectionalizing renewable Keywords: distribution Keywords: distribution network, network, sectionalizing sectionalizing switches, switches, tie tie switches, switches, reconfiguration, reconfiguration, spanning spanning tree, tree, renewable generation. generation. renewable renewable Keywords: distribution network, sectionalizing switches, tie switches, reconfiguration, spanning tree, renewable generation. generation. renewable generation. colony algorithms (see Abdelaziz et al. (2012); Chang 1. INTRODUCTION colony algorithms (see Abdelaziz et al. (2012); Chang colony algorithms (see Abdelaziz et (2012); (2008)), harmony search Kavousi-Fard et al. 1. INTRODUCTION colony algorithms (see algorithms Abdelaziz (see et al. al. (2012); Chang Chang 1. INTRODUCTION (2008)), harmony search algorithms (see Kavousi-Fard et al. (2008)), harmony search algorithms (see Kavousi-Fard et al. (2014b)) and particle swarm optimization algorithm (see 1. INTRODUCTION Reconfiguration of a primary distribution network is one of (2008)), harmony search algorithms (see Kavousi-Fard etWu al. colony algorithms (see Abdelaziz et al. (2012); Chang (2014b)) and particle swarm optimization algorithm (see Wu (2014b)) and particle swarm optimization algorithm (see Wu and Tsai (2011)). However, the complexity of present-day Reconfiguration of a primary distribution network is one of 1. INTRODUCTION Reconfiguration of a primary distribution network is one of (2008)), the major problems. Numerous algorithms have been (2014b)) and particle swarm optimization algorithm (see Wu harmony search algorithms (see Kavousi-Fard et al. Tsai However, complexity of Reconfiguration of a primary distribution network is one of and and Tsai (2011)). (2011)). However, the complexity of present-day present-day heuristic algorithms hinders the their use in real time, this the major Numerous algorithms have been the major inproblems. problems. Numerous algorithms have been developed the world, and new algorithms, reconfiguration and Tsai (2011)). However, the complexity of present-day (2014b)) and particle swarm optimization algorithm (see Wu heuristic algorithms hinders their use in real time, this heuristic algorithms hinders their use time, Reconfiguration of a primary distribution network is one of especially the major in Numerous algorithms have been concerns large systems. developed inproblems. the world, and new algorithms, reconfiguration algorithms hinders their use in in real real time, this this developed the world, and algorithms, reconfiguration criteria, new conditions and new constraints are steadily offered heuristic and Tsai (2011)). However, the complexity of present-day especially concerns large systems. especially concerns large systems. the major problems. Numerous algorithms have been developed in the world, and new algorithms, reconfiguration criteria, new conditions and constraints are steadily offered criteria, new conditions and constraints are steadily offered especially concerns large systems. for its solution. Reconfiguration is possible by virtue of a heuristic algorithms hinders their voltages use in and real currents time, this Besides the admissibility of nodal in criteria, new conditions and new constraints are steadily offered developed in the world, and algorithms, reconfiguration for its solution. possible by virtue of aa especially Besides the admissibility of nodal and currents for its solution. Reconfiguration is possible by virtue of concerns large systems. weakly closed Reconfiguration topology of a is primary medium-voltage Besides the admissibility of nodal voltages voltages and currents in in the feeder sections to be considered during reconfiguration for its solution. Reconfiguration is possible by virtue of a criteria, new conditions andof constraints are medium-voltage steadily offered Besides the admissibility of nodal voltages and currents in weakly closed topology aa primary the feeder sections to be considered during reconfiguration weakly closed topology of primary medium-voltage feeder sections to be considered during reconfiguration distribution network and to simplify the model of the network the radial topology including all the nodes of the distribution weakly closed topology of a isprimary medium-voltage feeder sections to be of considered during reconfiguration for its solution. Reconfiguration possible by virtue of a the the admissibility nodal and currents in distribution network to simplify model of network the radial including all the nodes of the distribution distribution network and to simplify the model of the network the radial topology including all the nodes of the distribution network istopology the main constraint for voltages application heuristic relay protection fromand heavy currents the it operates asthe radial. The Besides distribution network and to simplify the model of the network the radial topology including all the nodes of the of distribution weakly closed topology of a primary medium-voltage the feeder sections to be considered during reconfiguration network is the main constraint for application of heuristic relay protection from heavy currents it operates as radial. The network is the main constraint for application of heuristic relay "radial" protection from heavytocurrents it operates as radial. term corresponds the network comprising all The the algorithms. distribution network toto simplify the model ofasthe network the main constraint for nodes application heuristic relay protection fromand heavy currents it operates radial. the radialistopology including all the of the of distribution algorithms. term corresponds the comprising all the algorithms. term "radial" "radial" corresponds to the network network comprising all The the network nodes, but containing no loops. algorithms. network is the main constraint for application of heuristic relay protection from heavy currents it operates as radial. The term "radial" corresponds to the network comprising all the In the algorithm of network reconfiguration by the active nodes, nodes, but but containing containing no no loops. loops. In the algorithm of network reconfiguration by the active algorithms. In the algorithm of network reconfiguration by the active term "radial" corresponds to the network comprising all the nodes, but containing no loops. power loss minimization criterion (see Golub et al. Under normal operation conditions, the network topology is In the algorithm of network reconfiguration by the(2017)), active power loss minimization criterion (see Golub et al. (2017)), Under normal operation conditions, the network topology is power loss minimization criterion (see Golub et al. (2017)), nodes, but containing no loops. the use of algorithms to construct a maximum spanning tree Under normal operation conditions, the network topology is changed to reduce energy and voltage losses, improve power loss minimization criterion (see Golub et al. (2017)), Under normal operation conditions, the network topology is In algorithm of network by the of active the use of to construct aa maximum spanning tree changed to reduce energy and voltage losses, improve the the use of algorithms algorithms toand construct maximum spanning tree (see Mainika (1981)) toreconfiguration determine branches the changed to reduce energy and voltage losses, improve reliability, balance load and generation by opening the changed tobalance reduce energy and voltage losses, improve the use of algorithms to construct a maximum spanning tree power loss minimization criterion (see Golub et al. (2017)), (see Mainika (1981)) and to determine branches of the Under normal operation conditions, the network topology is reliability, load and generation by opening the (see Mainika (1981)) and to determine branches of the loops by their chords (see Happ (1971)), which reliability, closed balance load and generation normally sectionalizing switch andbyby opening closing the independent (see Mainika (1981)) and to calculation determine branches of the the use of algorithms to construct a(see maximum spanning tree reliability, balance load and generation by opening the independent loops by their chords Happ (1971)), which changed reduce energy and voltage losses, improve normally closed sectionalizing switch and by closing independent loops by their chords (see Happ (1971)), which are included in the steady state program, excludes normally to closed sectionalizing switch and by closing the open tie switch. The network reinforcement to independent loops by their chords (see Happ (1971)), which (see Mainika (1981)) and to determine branches of normally closed sectionalizing switch and by closing the are included in the steady state calculation program, excludes reliability, balance load and generation by opening open tie switch. The network reinforcement to are included in the steady state calculation excludes the need to trace network radiality. Theprogram, basic idea of the the normally open tie switch. The network reinforcement to improve its reliability is the important among the included in thethe steady state calculation program, excludes normally open tiesectionalizing switch. Themost network reinforcement to are independent loops by their chords (see Happ (1971)), which the need to trace the network radiality. The basic idea the normally closed switch and by closing the improve its reliability is the most important among the need toistrace the network basicinidea ofopen the algorithm to achieve that radiality. the powerThe losses the of improve its reliability is the most important among the reconfiguration criteria (see Kavousi-Fard et al. (2014a)). The improve its reliability is the most important among The the the need should tois trace the network radiality. The basicin idea ofopen the are included in the steady state calculation program, excludes algorithm to achieve that the power losses the normally open tie switch. The network reinforcement to reconfiguration criteria (see Kavousi-Fard et al. (2014a)). algorithm is to achieve that the power losses in the open network be close to those in the closed network. In reconfiguration criteria (see Kavousi-Fard al. (2014a)). use of distributed generation sources, foretthis purpose, The is a algorithm is to achieve that the power losses in the open the need to trace the network radiality. The basic idea of the reconfiguration criteria (see Kavousi-Fard et al. (2014a)). The network should be close to those in the closed network. improve its reliability is the most important among the use of distributed generation sources, for this purpose, is a network should be close to those in the closed network. In (see Golub et al. (2017)), such a condition is shown to be use of distributed generation sources, for this purpose, is a new feature which should be considered in the network should be close to those in the closed network. In In that the losses incurrents the to open use of feature distributed generation sources, for purpose, isthe a algorithm (see et (2017)), such aa power condition shown be reconfiguration criteria (see Kavousi-Fard etetthis al. (2014a)). The new which should be considered in (see Golub Golub ettoal. al.achieve (2017)), such condition is of shown to be met, if the isspanning tree with a minimum sumis in new feature which should be considered in the reconfiguration algorithms (see Bernardon al. (2014)). Yet, new feature which should be considered in the (see Golub et al. (2017)), such a condition is shown to be network should be in close to those in the closed met, if the the spanning tree with minimum sum of ofnetwork. currents In in use of distributed generation sources, for this purpose, is a met, reconfiguration algorithms (see Bernardon et al. (2014)). Yet, if spanning tree with aanetwork. minimum sum currents in the chords is found a closed reconfiguration algorithms (see Bernardon et al. (2014)). Yet, the main objective of reconfiguration is the fastest restoration reconfiguration algorithms (see Bernardon etfastest al. (2014)). Yet, met, if the is spanning tree with anetwork. minimum sumis of currents in (see Golub et al. (2017)), such a condition shown to be the chords found in a closed new feature which should be considered in the the main objective of reconfiguration is the restoration the chords is found in a closed network. thepower main objective is theoffastest restoration of supply toofa reconfiguration maximum number consumers at an the chords is found in a closed network. met, if the spanning tree with a minimum sum of currents in the main objective of reconfiguration is the fastest restoration reconfiguration algorithms (see Bernardon et al. (2014)). Yet, A feature of the reconfiguration algorithm is ignoring the of power supply to a of maximum number of consumers at an of power supply to maximum number of consumers at emergency shutdown the sectionalizing by closing feature of the reconfiguration algorithm is ignoring the of power supply toofaa reconfiguration maximum number ofswitch consumers at an an A the chords is found in a closed network. A feature of the reconfiguration algorithm is ignoring the the main objective is the fastest restoration information on the initial composition of the normally open emergency shutdown of the sectionalizing switch by closing emergency shutdown of the switch by A feature ofonthe reconfiguration algorithm isnormally ignoring the the tie switch. composition emergency shutdown the sectionalizing sectionalizing by closing closing information the initial composition ofthethe thebeginning normallyofopen open of supply to a of maximum number ofswitch consumers at an information tie switches on thatthe areinitial regarded closed atof the the tie thepower tie switch. switch. information on the initial composition of the normally A feature of the reconfiguration algorithm is ignoring the switches that are at of tie switches that are regarded regarded closed at the the beginning beginning ofopen the the switch. emergency shutdown of the sectionalizing algorithm run. Then, at each ofclosed the iterations, whose number Thetieheuristic optimization algorithms switch found by theclosing most tie tie switches that are regarded closed at the beginning of the information on the initial composition of the normally open at each of the iterations, whose number The optimization algorithms found most algorithm run. Then, at each of the whose number the tieheuristic switch. is equal torun. the Then, number independent loops in the network The heuristic optimization algorithms found the thecriteria. most algorithm common application among different reconfiguration algorithm run. Then, at of each ofclosed the iterations, iterations, whose number tie switches that are regarded at loops the beginning of the The heuristic optimization algorithms found thecriteria. most is equal to the number of independent in the network common application among different reconfiguration is equal to the number of independent loops in the network graph, the load flow is calculated, the maximum spanning common application among different reconfiguration criteria. They include genetic algorithms (see Guimaraes et al. is equal to the number of independent loops in the network common application among different reconfiguration criteria. algorithm run. Then, at each of the iterations, whose number graph, the load flow is calculated, the maximum spanning The heuristic optimization algorithms found the most They include genetic algorithms (see Guimaraes et al. graph,whose the load flow is calculated, maximum spanning tree branch weights are the current magnitudes is They include genetic algorithms (see Guimaraes et al. (2010)), tabu search algorithms (see Junior et al. (2014)), They include genetic algorithms (see Guimaraes et ant al. graph, the flow is maximum to load thebranch number ofcalculated, independent loops in the spanning network treeequal whose branch weights are the current magnitudes is common application among different reconfiguration criteria. (2010)), search (see et ant tree whose weights are current magnitudes is (2010)), tabu tabu search algorithms algorithms (see Junior Junior et al. al. (2014)), (2014)), ant is tree whose branch weights are the current magnitudes is the load flow is calculated, maximum spanning (2010)),include tabu search algorithms (see Junior et al. (2014)), They genetic algorithms (see Guimaraes et ant al. graph, Copyright © 2019, 2019 IFAC 472 Hosting tree whose branch weights are current magnitudes is 2405-8963 © IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. (2010)), tabu search algorithms (see Junior et al. (2014)), ant Copyright © 2019 IFAC 472 Copyright 2019 responsibility IFAC 472Control. Peer review© of International Federation of Automatic Copyright ©under 2019 IFAC IFAC 472 Copyright © 2019 472 10.1016/j.ifacol.2019.08.249 Copyright © 2019 IFAC 472
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constructed, and the chord with a minimum current is opened. Thus, as a result of the first reconfiguration step that is the least complex a new composition of the open chords corresponding to tie switches is determined. At this new composition, the network power losses, as a rule, are essentially lower than those in the chords corresponding to the initial composition of tie switches.
supply, but combining the source nodes into one node results in a loop, whose one branch, for example, branch 3-4, is selected as a chord. In a four-source scheme, the spanning tree allows choosing only one chord, for example, chord 1112, but combining the power sources – one chord in each of the four loops. The proposed modification of the reconfiguration algorithm consists in the initial modeling of a distribution network with several power sources in the form of a single-source network followed by the use of the reconfiguration algorithm developed by the authors earlier (see Golub et al. (2017)).
At the second reconfiguration step, we study the possibility to decrease the network power losses by replacing the chords, opened at the first step, with spanning tree branches in the loops connected with the chords. This is achieved by the following operations: each chord opened at the first step is sequentially closed, the composition of branches of the loop connected with the chord is determined, and the load flow is calculated. Then, the nodes with a degree higher than two are fixed in the closed loop left and right of the chord nodes, a sequential disconnection of the branches between such nodes is simulated. For each disconnection, the load flow is calculated, and the total losses are determined. The previous chord or a new one with minimum total losses is opened. If there are no nodes with a degree higher than two in the loop, disconnection of all the loop branches is simulated. The most important characteristic of our reconfiguration algorithm is a high speed of the solution at a high accuracy of the load flow calculation.
In a real distribution network, tie switches for several feeders connected to one power source are installed between the nodes of the feeder and the nodes of different feeders. In the case of several power sources, tie switches are also installed between the feeder nodes powered from different sources. Reconfiguration of such a network can lead to a new radial topology of individual feeders. The paper is arranged as follows. In Section 2, we prove the efficiency of the offered reconfiguration algorithm for a test distribution network with two independent power sources. The efficiency is verified by the coincidence of the reconfiguration results obtained by the authors with the results obtained by other methods (see Xingquan et al. (2018)), including the case of the test network with distributed generation sources.
Such an algorithm, as shown in (see Golub (2018a)), enables us to successfully solve the distribution network reconfiguration problem, even if the latter has renewable generation sources.
In Section 3, the reconfiguration problem is solved for a real municipal distribution network with several feeders powered from six independent sources. The reconfiguration is shown to reduce power losses in the network, and to decrease loads of the most loaded feeders.
However, if some feeder of the distribution network is powered from two independent power sources, such as primary transformer substations, the algorithm of constructing a maximum spanning tree does not allow identifying such a feeder as a loop and selecting a chord in it that corresponds to a tie switch. This situation can be excluded if, before using the reconfiguration algorithm, all power supply nodes of feeders are combined into one balancing node, as shown in Fig. 1, assuming the voltages in these nodes to be the same.
In Section 4, we analyze the problems of reliable power supply to the distribution network consumers, determination loads, whose provision is reserved, at least, by one tie switch, and determination of subsystems of the trees, whose loads have no backup power source. 2. ILLUSTRATION OF THE RECONFIGURATION ALGORITHM To illustrate the efficiency of the offered reconfiguration algorithm, we use the primary 11.4 kV distribution network of the Taiwan electric company, Fig. 2. The distribution network comprises two subsystems receiving power from two sources (see Wu et al. (2010); Wang and Cheng (2010)). This network contains 11 feeders, 83 normally closed sectionalizing switches and 13 normally open tie switches, 5 of which (1-5) allow combining two subsystems of the distribution network which are powered from two sources into one node.
Fig. 1. Schemes of distribution networks with two and four power sources before (a, b) and after (c, d) combining the sources into one. Dashed lines show the chords corresponding to the tie switches.
Subsystem 1 includes feeders 1-6, subsystem 2 - feeders 7-11. Tie switch 6 mutually reserves the power supply of feeders 2 and 6, tie switch 7 mutually reserves the power supply to part of the consumers of feeders 5 and 6. Switches 8-10 reserve the power supply to part of the consumers of feeders 4 and 5. Tie switches 11-13 mutually reserve the
Such, construction of a spanning tree and selection of tie switches are exemplified by the feeder with a bilateral power supply and the four-source loop. The spanning tree will include all the nodes in the feeder with bilateral power 473
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power supply to part of the consumers of feeders 3-4, 2-3, and 7-8, respectively.
439
Power losses (kW)
(2018)). After adding the sources, the power losses in the initial open network decreased to 427.980 kW, whereas in the network with the closed tie switches, the losses dropped to 377.285 kW. Already at the first reconfiguration step, we determined the basic optimal switchings, and only one switching was corrected at the second step, Fig. 4. The symbols shown on the horizontal axis are similar to the symbols in Fig. 3.
Fig. 2. Distribution network scheme in which the power supply nodes of two subsystems of feeders 1-6 and 7-11 are combined into one node. Dashed lines show the branches with tie switches, B1-B11- circuit breakers.
Fig. 4. Change in total power losses and in composition of the branches with tie switches at the first (a) and second (b) reconfiguration steps in a network with renewable generation sources.
When opening all the tie switches in Fig. 2, feeders 1-11 operate independently, and the total power losses, in this case, equal 532.002 kW. When closing all the tie switches, the losses decrease to 462.679 kW. Fig. 3 illustrates the process of change in power losses owing to the network reconfiguration. The numbers of iterations, which is equal to the number of independent loops in the network with closed tie switches, are indicated above the horizontal axis of Fig.3, the line a below the axis contains the chords selected at each iteration at the first reconfiguration step, and the chords specified at the second reconfiguration step are given in the line b.
The obtained optimal composition of tie switches differs from that obtained in (see Xingquan et al. (2018)): the composition includes chord 12-13, instead of chord 13-76 in our solution. At the same time, replacement of chord 13-76 with chord 12-13 in our solution led to an increase in the losses from 383.128 kW to 383.17 kW. We perform an additional analysis of the reconfiguration results without distributed generation.
Number of nodes
Analysis of the load flow obtained as a result of reconfiguration shows that it allowed decreasing the total power losses, changing the number of nodes in the feeders and balancing the feeder loads and power losses. Figs. 5 - 7 present the plots confirming such conclusions.
Fig. 3. Change in total power losses and in composition of the branches with tie switches at the first (a) and second (b) reconfiguration steps in a network without renewable generation sources. Fig. 3 also shows that, already at the first step of reconfiguration, a new composition of the open chords (open tie switches) with the power losses of 471.727 kW was obtained. At the second step, only 5 reconfigurations were performed, and the composition of tie switches completely coincided, according to (see Xingquan et al. (2018)), with the composition of tie switches providing minimum losses. In our calculations, the losses equal 469.879 kW after the second reconfiguration step.
Fig. 5. Number of nodes in feeders before (a) and after (b) reconfiguration. 4000 a
b
3000 2000 1000
To prove the efficiency of the applied reconfiguration algorithm for the network with distributed generation sources, such sources were added to nodes 7, 12, 19, 28, 34, 71, 75 and 79 in accordance with the information on their allocations and generating capacities of the sources for the Taiwan network (see Xingquan et al.
1
2
3
4
5
6 7 feeder
8
9
10
11
Fig. 6. Change in total loads of feeders before (a) and after (b) reconfiguration.
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Upon closing all the tie switches, the power losses in the network decreased from 2133.3 kW to 1657.1 kW, and combining the feeder power sources into one led to a decrease in the number of nodes to 277 in the network scheme. The plots in Fig. 9 illustrate the process of the further loss change at the first and second reconfiguration steps related to determination and correction of the chords of 50 loops. At the first step related to selection of the initial composition of tie switches, the losses increase from 1657.9 kW to 1736.0 kW, and at the second correcting reconfiguration step the losses decrease to 1731.7 kW.
Power losses (kW)
150 a
b
100 50 0
1
2
3
4
5
6 7 feeder
8
9
10
11
Power losses (kW)
Fig. 7. Change in total power losses of feeders before (a) and after (b) reconfiguration. 3. ILLUSTRATION OF THE RECONFIGURATION ALGORITHM BY EXAMPLE OF REAL DISTRIBUTION NETWORK We conducted the study similar to that for the Taiwan network for the real municipal 6 kV distribution network with 282 nodes, 326 branches with sectionalizing switches, 50 branches with tie switches. The loading transformers are installed at 189 network nodes. Thus, the calculation scheme of the municipal distribution network differs from the Taiwan network in addition of the transformers, which leads to a necessity of including the transformer losses into their estimation during the reconfiguration. In total, there are 15 feeders in the network. Schematically, Fig. 8 shows the feeders that are powered from 6 independent sources. Feeders 1, 7, 8, 9 and 11 are powered from the first source, feeders 3, 4, 5, 6, 10 and 12 – from the second source, and feeders 2, 13, 14 and 15 – from sources 3-6.
Fig. 9. Change in total power losses at the first (a) and second (b) reconfiguration steps. Fig. 10 presents the structural scheme of the network after the reconfiguration, during which only 19 switches changed their status from the normally closed to normally open. Of them, 2 switches belong to feeders 4 and 9, and the remaining 17 tie switches are shown in the scheme by dashed lines.
Fig. 10. Structural scheme of the distribution network after reconfiguration, solid lines between the feeders correspond to tie switches which coincide with tie switches in the initial scheme, and dashed ones – to tie switches obtained after reconfiguration.
Fig. 8. Initial structural scheme of the distribution network with feeders and branches between them with tie switches. Numerals on the branches indicate their number. Fig. 8 presents only 42 branches out of 50 branches with tie switches, since the 8 remaining tie switches belong to feeders: 2, 8, 9 and 10 have one switch each, and feeders 4 and 14 have 2 switches each. Two tie switches 8-11 and 9-11, as is shown in Fig. 8, combine feeders powered from the first source and seven tie switches 5-6, 6-12, 10-12, 3-6 (two branches) and 3-10 (two branches) combine feeders powered from the second source. The other 35 tie switches combine the feeders powered from different sources.
Power losses (kW)
As a result of reconfiguration the number of nodes in the feeders changed, Fig.11.
In the initial network with open tie switches, in which each feeder operates independently and is powered from the connected source, the power losses equal 2133.3 kW in the 6.2 kV power sources at the total load equal to 47074.0 kW for the maximum load condition.
Fig. 11. Number of nodes in feeders before (a) and after (b) reconfiguration. For example, there were 13 nodes in feeder 6 before reconfiguration, and 14 nodes after reconfiguration, the 475
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Table 1 for the Taiwan network, received after reconfiguration, provides the variants of the tie switches that can be used to restore the power supply after opening one of 11 circuit breakers. The last column presents the minimum losses in the network after opening the circuit breaker and closing the tie switch indicated in bold. For example, at emergency shutdown of B1 or B8 in the same independent loop: B1, 1-… -4, 4-5, 5-6, 6-7, 7-60, 60-… -56, B8, power supply can be restored by closing the tie switch corresponding to chord 6-7 of this loop. The total losses after restoration, when circuit breaker B1 is open, are lower than those, when the tie switch corresponding to chord 55-54 of the loop is closed: B1, 1-… -4, 4-5, 5-55, 55-54, 54 -53, 53… -47, B7.
number of nodes in feeder 10 before and after reconfiguration changed from 28 to 14. The appearance of two new branches 6-10 with tie switches between feeders 6 and 10 can be commented as follows. As a result of the reconfiguration, three nodes, let us call them 1, 2, 3, united by branches 1-2 and 2-3 with sectionalizing switches belonged to feeder 10. After reconfiguration node 2 shifted to feeder 6 and nodes 1 and 3 remained in feeder 10. The number of nodes in feeder 6 increased, and two branches 6-10 with tie switches appeared between feeders 6 and 10, Fig. 10.
Power losses (kW)
The load redistribution, connected with changes in the number of nodes in the feeders, led to an essential decrease of power losses in feeder 10, Fig. 12.
Analysis of the spanning tree and its chords enables us to determine subsystems of the trees, whose loads can be covered only from one source. In the presented example, an emergency outage of one of branches 7-8, 7-9, or 7-10 will lead to power supply violation for nodes 8, 9, or 10, with 300.0 kW each, and an emergency outage of branch 20-21 in will lead to power supply violation for four tree nodes 21, 22, 23, and 24, with the total load of 550.0 kW.
Fig. 12. Change in total power losses of feeders before (a) and after (b) reconfiguration.
The estimation of the reliability of power supply to feeders in the municipal distribution network after closing all tie switches and combining all power sources into one showed that to restore the power supply at an emergency outage of circuit breaker, the number of variants of tie switches for different feeders ranged from 1 to 14, as shown in Fig.13, plot a.
4. ANALYSIS OF POWER SUPPLY RELIABILITY
Number of variants
The reconfiguration algorithm based on constructing a spanning tree on the network graph and determining the composition of independent loop branches by the tree chords enables us to determine the variants of tie switches that may be used to restore power supply at an emergency outage of any sectionalizing switch (Golub et al. (2018b)), as well as any circuit breaker. Since the same branch of the spanning tree can be in several loops, the power supply in case of emergency outage of the sectionalizing switch or circuit breaker can be restored by closing any tie switch connected with it by the common loop. The minimum power losses in the network after the reconfiguration may be a criterion for selecting the tie switch.
Fig. 13. Number of tie switch variants for power supply to feeders at opening a circuit breaker (a), and maximum total load of subsystems without reserve supply (b).
Table 1. Variants of tie switches to be used to restore power supply at an emergency outage of the circuit breakers Circuit breakers B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11
Variants of tie switches 1 6-7 11-43 14-18 16-26 28-32 11-43 54-55 6-7 71-72 12-13 82-83
2 54-55 12-13 16-26 28-32 33-34 33-34 61-62 61-62
3
4
14-18 82-83 38-39
71-72
38-39
41-42
41-42
441
Load of subsystems
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The estimation of the power supply reliability enabled us to determine that out of 189 load nodes, the power supply to 88 consumers with the total power of 33253.4 kW was reserved, at least, by one tie switch, and the supply to 101 consumes with the total power of 13521.1 kW had no reserve supply.
Power losses (kW) 603.37 481.44 528.43 518.82 553.24 490.62 802.93 593.48 544.54 536.72 767.03
The subsystems of the trees, whose loads have no reserve power supply, are determined by the following actions. The branches of the loops and the branches that are chords of these loops are excluded from the list of network graph branches. The remaining branches are ordered by decreasing power flows in them and the subsystems of spanning trees, which comprise one through several branches, are constructed. For each subsystem with unilateral power supply, we determine the total load and the subsystem with the maximum total load. The plot b in Fig. 13 characterizes the subsystem with the maximum total load for each feeder. 476
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As an illustration, Fig. 14 shows the scheme of feeder 12 of the municipal distribution network before reconfiguration, in which we indicated eight subsystems of trees with the loads that have no reserve power supply. At an emergency outage of the branch with maximum power flow at the head section of the subsystem tree, such branches in Fig.14 are shown by the dashed-doted lines, the power supply of the subsystem will be violated. Feeder 12 consists of 8 subsystems, 6 of which consist of only one branch, one subsystem includes two branches, and the subsystem with the maximum total load contains 14 consumers. The branches shown by the dashed lines in Fig. 14 correspond to the tie switches connecting feeder 12 to feeders 2, 6, 7, 8, 9, 10, 13, 14, and 15, Fig. 8.
reduction using the hyper-cube ant colony optimisation algorithm. IET Generation, Transmission & Distribution, 6 (2), 176-187. Bernardon, D., et al. (2014). Real-time reconfiguration of distribution network with distributed generation. Electric Power Systems Research, 107, 59-67. Chang, C.-F. (2008). Reconfiguration and capacitor placement for loss reduction of distribution systems by ant colony search algorithm. IEEE Transactions on Power System, 23 (4), 1747-1755. Golub, I.I., et al. (2017). Method of Distribution Network Reconfiguration at Daily Operation Scheduling. Acta Energetica, 31(2), 57-62. Golub, I.I., et al. (2018a). Reconfiguration of Distribution Network with Renewable Generation. Energy Systems Research, 1 (1), 74-83. Golub, I.I., et al. (2018b) Minimizing the number of remotely controlled switches when the planning the reconfiguration of a primary distribution network. E3S Web of Conferences, 58, 7. Guimaraes, M.A.N., et al. (2010). Distribution systems operation optimisation through reconfiguration and capacitor allocation by a dedicated genetic algorithm. IET Generation, Transmission & Distribution, 4 (11), 1213-1222. Happ, H. H., (1971) Diakoptics and networks. New York and London. Academic press. Junior, B.R.P., et al. (2014). Multiobjective multistage distribution system planning using tabu search. IET Generation, Transmission & Distribution, 8(1), 35-45. Kavousi-Fard, A., Niknam, T., and Khosravi, A. (2014). Multi-objective probabilistic distribution feeder reconfiguration considering wind/power plants. International Journal of Electrical Power & Energy Systems, 55, 680-691. Kavousi-Fard, A., Niknam, T. and Khooban, M.H. (2014) Intelligent stochastic framework to solve the reconfiguration problem from the reliability view. IET Science, Measurement & Technology, 8 (5), 245-259. Mainika, E. (1978) Optimization algorithms for networks and graphs. New York . M. Dekker. Wang, C. and Cheng, H.Z. (2010) Optimization of network configuration in large distribution systems using plant growth simulation algorithm. IEEE Transactions on Power Systems, 23(1), 119-126. Wu, Y.K., et al. (2010). Study of reconfiguration for the distribution system with distributed generators. IEEE Transactions on Power Delivery, 25(3), 1678-1685. Wu, W.C., and Tsai, M.S. (2011). Application of enhanced integer coded particle swarm optimization for distribution system feeder reconfiguration. IEEE Transactions on Power Systems, 26(3), 1591-1599. Xingquan J., et al. (2018). Distribution network reconfiguration based on vector shift operation. IET Generation, Transmission & Distribution, 12(13), 33393345
Fig. 14. Scheme of feeder 12 of the municipal distribution network. 5. CONCLUSIONS We propose a modification of the reconfiguration algorithm based on the methods of constructing a maximum spanning tree and determining by the tree chords the composition of branches of independent loops in a primary distribution network, whose feeders are powered from several independent sources. The algorithm efficiency is verified by the calculations for the network regarded as a test one, and for a real municipal distribution network. We illustrate that reconfiguration makes it possible to reduce the power losses in the whole network and to balance the total loads and power losses in feeders by changing the number of nodes in them, which has not been analyzed earlier. The reconfiguration algorithm can also be applied to analyze the power supply reliability at an emergency outage of any sectionalizing switch, as well as any circuit breaker, and to determine the subsystems of trees in the network scheme without reserve power supply. ACKNOWLEDGMENT This study was supported by the project III.17.4.2 of the fundamental research program SB RAS, reg. No. AAAAA17-117030310438-1. REFERENCES Abdelaziz, A.Y., Osama, R.A., and El-Khodary, S.M. (2012). Reconfiguration of distribution systems for loss 477
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IFAC PapersOnLine 52-4 (2019) 437–442 Reconfiguration of Primary Distribution Network with Several Independent Power Reconfiguration of Primary Distribution Network with Several Independent Power Sources Reconfiguration of Primary Distribution Network with Several Independent Power Sources Reconfiguration of Primary Distribution Network with Several Independent Power Sources , , Sources Eugene Boloev*,, **, Lyudmila Semenova* Irina Golub*, **, Oleg Voitov*, **, , , ,
Oleg Voitov* **, Eugene Boloev* **, Lyudmila Semenova* Irina Golub*,, **, Boloev* Irina **, Oleg Oleg Voitov* Voitov*,, **, **, Eugene Eugene Boloev*,, **, **, Lyudmila Lyudmila Semenova* Semenova* Irina Golub* Golub* **, , , *Melentiev Energy Systems Institute, **, of Siberian Branch of Russian Academy of Science **, Oleg Voitov* Eugene Boloev* **, Lyudmila Semenova* Irina Golub* *Melentiev Siberian Branch of Academy *Melentiev Energy Energy Systems Institute of Siberian Branch of Russian Russian Academy of of Science Science RussiaSystems (Tel: +7Institute (3952) of 424 700; e-mail: golub@ isem.irk.ru) *Melentiev Energy Systems Institute of Siberian Branch of Russian Academy of Science Russia (Tel: +7 (3952) 424 700; e-mail: golub@ isem.irk.ru) Russia (Tel: +7 (3952) 424 700; e-mail: golub@ isem.irk.ru) **Irkutsk National Research Technical University *Melentiev Energy Systems Siberian Branch ofUniversity Russian Academy of Science Russia (Tel: +7Institute (3952) of 424 700; e-mail: golub@ isem.irk.ru) **Irkutsk Research Technical **Irkutsk National Research Technical University (Tel: +7 National (3952) 405 127; e-mail: [email protected]) Russia (Tel: +7 (3952) 424 700; e-mail: golub@ isem.irk.ru) **Irkutsk National Research Technical University (Tel: +7 +7 (3952) (3952) 405 405 127; 127; e-mail: e-mail: [email protected]) [email protected]) (Tel: (Tel: +7 National (3952) 405 127; e-mail: [email protected]) **Irkutsk Research Technical University (Tel: +7 (3952) 405 127; e-mail: [email protected]) Abstract: We solve the problem of reconfiguration of a primary distribution network with feeders Abstract: We solve solve the problem of of reconfiguration of a primary distribution network with feeders Abstract: We problem of distribution network with powered from independent A high-performance algorithm is applied to reconfigure the Abstract: We several solve the the problem sources. of reconfiguration reconfiguration of aa primary primary distribution network with feeders feeders powereddistribution from several independent sources. A high-performance high-performance algorithm is applied applied to reconfigure reconfigure the powered from several independent sources. A algorithm is to the primary network by the loss minimization criterion. The algorithm constructs the maximum powered from several independent sources. A high-performance algorithm is applied to reconfigure the Abstract: We solvenetwork the problem reconfiguration of a primary distribution networkthe with feeders primary distribution distribution network by theofloss loss minimization criterion. The algorithm algorithm constructs the maximum primary by the minimization criterion. The constructs maximum spanning tree on the network graph and determines the composition of branches of independent loops. primary distribution by thesources. loss minimization The algorithm constructs the maximum powered from several independent A high-performance algorithm is applied to reconfigure the spanning tree on on thenetwork network graph and determines thecriterion. composition of determining branches of independent independent loops. spanning tree the network graph and determines the composition of branches of The information on the distribution network topology features allows the variants loops. of tie spanning tree on the network graph and determines the composition of branches of independent loops. primary distribution network by the loss minimization criterion. The algorithm constructs the maximum The information on the distribution network topology features allows determining the variants of tie The information distribution topology allows determining of tie switches that mayonbethe used to restorenetwork the power supplyfeatures at an emergency outage of the any variants sectionalizing spanning tree on the network graph and determines the composition of branches of independent loops. The information on the distribution network topology features allows determining the variants of tie switches that may be used to restore the power supply at an emergency outage of any sectionalizing switches be used to restore power supply at in anthe emergency of anyhave sectionalizing switch andthat anymay circuit breaker, and thethe subsystems of trees network, outage whose loads no reserve The information onbethe distribution network topology features allows determining variants of tie switches that used to restore the power supply at in anthe emergency outage of the anyhave sectionalizing switch and anymay circuit breaker, andofthe the subsystems of trees trees in the network, whose loads have no reserve reserve switch and any circuit breaker, and of network, whose no power supply. The efficiency thesubsystems offered algorithm is verified by the loads coincidence of the switches that may be used to restore the power supply at an emergency outage of any sectionalizing switch and any circuit breaker, and the subsystems of trees in the network, whose loads have no reserve power supply. results The efficiency efficiency ofitsthe the offered algorithm is network verifiedregarded by the the ascoincidence coincidence of the the power supply. The offered verified by of reconfiguration obtained onof basis for thealgorithm distributionis a test one with switch and any circuit breaker, and the subsystems of trees in the network, whose loads have nowith reserve power supply. The efficiency ofits the offered algorithm is network verified by the as coincidence of the the reconfiguration results obtained on its basis for the distribution network regarded as a test one with the reconfiguration results obtained on basis for the distribution regarded a test one results obtained results for thisobtained networkonbyitsother methods. The algorithm efficiency is as alsoa test illustrated by the an reconfiguration basis for thealgorithm distribution regarded one with power supply. The efficiency of offered is network verified by the coincidence ofby results obtained obtained for this network by the other methods. The algorithm algorithm efficiency is also also illustrated by an an results this network by other methods. The efficiency is illustrated example of a realfor municipal distribution network. results obtained for this network by other methods. The algorithm efficiency is also illustrated by an reconfiguration obtained on its basis for the distribution network regarded as a test one with the example of aa real realresults municipal distribution network. example of municipal distribution network. example of adistribution real municipal distribution results for thisnetwork, network by other methods. The algorithm is also illustrated bytree, an © 2019,obtained IFAC (International Federation ofnetwork. Automatic Control) Hosting byefficiency Elsevier Ltd. All rights reserved. Keywords: sectionalizing switches, tie switches, reconfiguration, spanning Keywords: distribution network, sectionalizing switches, tie tie switches, switches, reconfiguration, reconfiguration, spanning spanning tree, tree, example ofgeneration. adistribution real municipal distribution network. switches, Keywords: network, sectionalizing renewable Keywords: distribution Keywords: distribution network, network, sectionalizing sectionalizing switches, switches, tie tie switches, switches, reconfiguration, reconfiguration, spanning spanning tree, tree, renewable generation. generation. renewable renewable Keywords: distribution network, sectionalizing switches, tie switches, reconfiguration, spanning tree, renewable generation. generation. renewable generation. colony algorithms (see Abdelaziz et al. (2012); Chang 1. INTRODUCTION colony algorithms (see Abdelaziz et al. (2012); Chang colony algorithms (see Abdelaziz et (2012); (2008)), harmony search Kavousi-Fard et al. 1. INTRODUCTION colony algorithms (see algorithms Abdelaziz (see et al. al. (2012); Chang Chang 1. INTRODUCTION (2008)), harmony search algorithms (see Kavousi-Fard et al. (2008)), harmony search algorithms (see Kavousi-Fard et al. (2014b)) and particle swarm optimization algorithm (see 1. INTRODUCTION Reconfiguration of a primary distribution network is one of (2008)), harmony search algorithms (see Kavousi-Fard etWu al. colony algorithms (see Abdelaziz et al. (2012); Chang (2014b)) and particle swarm optimization algorithm (see Wu (2014b)) and particle swarm optimization algorithm (see Wu and Tsai (2011)). However, the complexity of present-day Reconfiguration of a primary distribution network is one of 1. INTRODUCTION Reconfiguration of a primary distribution network is one of (2008)), the major problems. Numerous algorithms have been (2014b)) and particle swarm optimization algorithm (see Wu harmony search algorithms (see Kavousi-Fard et al. Tsai However, complexity of Reconfiguration of a primary distribution network is one of and and Tsai (2011)). (2011)). However, the complexity of present-day present-day heuristic algorithms hinders the their use in real time, this the major Numerous algorithms have been the major inproblems. problems. Numerous algorithms have been developed the world, and new algorithms, reconfiguration and Tsai (2011)). However, the complexity of present-day (2014b)) and particle swarm optimization algorithm (see Wu heuristic algorithms hinders their use in real time, this heuristic algorithms hinders their use time, Reconfiguration of a primary distribution network is one of especially the major in Numerous algorithms have been concerns large systems. developed inproblems. the world, and new algorithms, reconfiguration algorithms hinders their use in in real real time, this this developed the world, and algorithms, reconfiguration criteria, new conditions and new constraints are steadily offered heuristic and Tsai (2011)). However, the complexity of present-day especially concerns large systems. especially concerns large systems. the major problems. Numerous algorithms have been developed in the world, and new algorithms, reconfiguration criteria, new conditions and constraints are steadily offered criteria, new conditions and constraints are steadily offered especially concerns large systems. for its solution. Reconfiguration is possible by virtue of a heuristic algorithms hinders their voltages use in and real currents time, this Besides the admissibility of nodal in criteria, new conditions and new constraints are steadily offered developed in the world, and algorithms, reconfiguration for its solution. possible by virtue of aa especially Besides the admissibility of nodal and currents for its solution. Reconfiguration is possible by virtue of concerns large systems. weakly closed Reconfiguration topology of a is primary medium-voltage Besides the admissibility of nodal voltages voltages and currents in in the feeder sections to be considered during reconfiguration for its solution. Reconfiguration is possible by virtue of a criteria, new conditions andof constraints are medium-voltage steadily offered Besides the admissibility of nodal voltages and currents in weakly closed topology aa primary the feeder sections to be considered during reconfiguration weakly closed topology of primary medium-voltage feeder sections to be considered during reconfiguration distribution network and to simplify the model of the network the radial topology including all the nodes of the distribution weakly closed topology of a isprimary medium-voltage feeder sections to be of considered during reconfiguration for its solution. Reconfiguration possible by virtue of a the the admissibility nodal and currents in distribution network to simplify model of network the radial including all the nodes of the distribution distribution network and to simplify the model of the network the radial topology including all the nodes of the distribution network istopology the main constraint for voltages application heuristic relay protection fromand heavy currents the it operates asthe radial. The Besides distribution network and to simplify the model of the network the radial topology including all the nodes of the of distribution weakly closed topology of a primary medium-voltage the feeder sections to be considered during reconfiguration network is the main constraint for application of heuristic relay protection from heavy currents it operates as radial. The network is the main constraint for application of heuristic relay "radial" protection from heavytocurrents it operates as radial. term corresponds the network comprising all The the algorithms. distribution network toto simplify the model ofasthe network the main constraint for nodes application heuristic relay protection fromand heavy currents it operates radial. the radialistopology including all the of the of distribution algorithms. term corresponds the comprising all the algorithms. term "radial" "radial" corresponds to the network network comprising all The the network nodes, but containing no loops. algorithms. network is the main constraint for application of heuristic relay protection from heavy currents it operates as radial. The term "radial" corresponds to the network comprising all the In the algorithm of network reconfiguration by the active nodes, nodes, but but containing containing no no loops. loops. In the algorithm of network reconfiguration by the active algorithms. In the algorithm of network reconfiguration by the active term "radial" corresponds to the network comprising all the nodes, but containing no loops. power loss minimization criterion (see Golub et al. Under normal operation conditions, the network topology is In the algorithm of network reconfiguration by the(2017)), active power loss minimization criterion (see Golub et al. (2017)), Under normal operation conditions, the network topology is power loss minimization criterion (see Golub et al. (2017)), nodes, but containing no loops. the use of algorithms to construct a maximum spanning tree Under normal operation conditions, the network topology is changed to reduce energy and voltage losses, improve power loss minimization criterion (see Golub et al. (2017)), Under normal operation conditions, the network topology is In algorithm of network by the of active the use of to construct aa maximum spanning tree changed to reduce energy and voltage losses, improve the the use of algorithms algorithms toand construct maximum spanning tree (see Mainika (1981)) toreconfiguration determine branches the changed to reduce energy and voltage losses, improve reliability, balance load and generation by opening the changed tobalance reduce energy and voltage losses, improve the use of algorithms to construct a maximum spanning tree power loss minimization criterion (see Golub et al. (2017)), (see Mainika (1981)) and to determine branches of the Under normal operation conditions, the network topology is reliability, load and generation by opening the (see Mainika (1981)) and to determine branches of the loops by their chords (see Happ (1971)), which reliability, closed balance load and generation normally sectionalizing switch andbyby opening closing the independent (see Mainika (1981)) and to calculation determine branches of the the use of algorithms to construct a(see maximum spanning tree reliability, balance load and generation by opening the independent loops by their chords Happ (1971)), which changed reduce energy and voltage losses, improve normally closed sectionalizing switch and by closing independent loops by their chords (see Happ (1971)), which are included in the steady state program, excludes normally to closed sectionalizing switch and by closing the open tie switch. The network reinforcement to independent loops by their chords (see Happ (1971)), which (see Mainika (1981)) and to determine branches of normally closed sectionalizing switch and by closing the are included in the steady state calculation program, excludes reliability, balance load and generation by opening open tie switch. The network reinforcement to are included in the steady state calculation excludes the need to trace network radiality. Theprogram, basic idea of the the normally open tie switch. The network reinforcement to improve its reliability is the important among the included in thethe steady state calculation program, excludes normally open tiesectionalizing switch. Themost network reinforcement to are independent loops by their chords (see Happ (1971)), which the need to trace the network radiality. The basic idea the normally closed switch and by closing the improve its reliability is the most important among the need toistrace the network basicinidea ofopen the algorithm to achieve that radiality. the powerThe losses the of improve its reliability is the most important among the reconfiguration criteria (see Kavousi-Fard et al. (2014a)). The improve its reliability is the most important among The the the need should tois trace the network radiality. The basicin idea ofopen the are included in the steady state calculation program, excludes algorithm to achieve that the power losses the normally open tie switch. The network reinforcement to reconfiguration criteria (see Kavousi-Fard et al. (2014a)). algorithm is to achieve that the power losses in the open network be close to those in the closed network. In reconfiguration criteria (see Kavousi-Fard al. (2014a)). use of distributed generation sources, foretthis purpose, The is a algorithm is to achieve that the power losses in the open the need to trace the network radiality. The basic idea of the reconfiguration criteria (see Kavousi-Fard et al. (2014a)). The network should be close to those in the closed network. improve its reliability is the most important among the use of distributed generation sources, for this purpose, is a network should be close to those in the closed network. In (see Golub et al. (2017)), such a condition is shown to be use of distributed generation sources, for this purpose, is a new feature which should be considered in the network should be close to those in the closed network. In In that the losses incurrents the to open use of feature distributed generation sources, for purpose, isthe a algorithm (see et (2017)), such aa power condition shown be reconfiguration criteria (see Kavousi-Fard etetthis al. (2014a)). The new which should be considered in (see Golub Golub ettoal. al.achieve (2017)), such condition is of shown to be met, if the isspanning tree with a minimum sumis in new feature which should be considered in the reconfiguration algorithms (see Bernardon al. (2014)). Yet, new feature which should be considered in the (see Golub et al. (2017)), such a condition is shown to be network should be in close to those in the closed met, if the the spanning tree with minimum sum of ofnetwork. currents In in use of distributed generation sources, for this purpose, is a met, reconfiguration algorithms (see Bernardon et al. (2014)). Yet, if spanning tree with aanetwork. minimum sum currents in the chords is found a closed reconfiguration algorithms (see Bernardon et al. (2014)). Yet, the main objective of reconfiguration is the fastest restoration reconfiguration algorithms (see Bernardon etfastest al. (2014)). Yet, met, if the is spanning tree with anetwork. minimum sumis of currents in (see Golub et al. (2017)), such a condition shown to be the chords found in a closed new feature which should be considered in the the main objective of reconfiguration is the restoration the chords is found in a closed network. thepower main objective is theoffastest restoration of supply toofa reconfiguration maximum number consumers at an the chords is found in a closed network. met, if the spanning tree with a minimum sum of currents in the main objective of reconfiguration is the fastest restoration reconfiguration algorithms (see Bernardon et al. (2014)). Yet, A feature of the reconfiguration algorithm is ignoring the of power supply to a of maximum number of consumers at an of power supply to maximum number of consumers at emergency shutdown the sectionalizing by closing feature of the reconfiguration algorithm is ignoring the of power supply toofaa reconfiguration maximum number ofswitch consumers at an an A the chords is found in a closed network. A feature of the reconfiguration algorithm is ignoring the the main objective is the fastest restoration information on the initial composition of the normally open emergency shutdown of the sectionalizing switch by closing emergency shutdown of the switch by A feature ofonthe reconfiguration algorithm isnormally ignoring the the tie switch. composition emergency shutdown the sectionalizing sectionalizing by closing closing information the initial composition ofthethe thebeginning normallyofopen open of supply to a of maximum number ofswitch consumers at an information tie switches on thatthe areinitial regarded closed atof the the tie thepower tie switch. switch. information on the initial composition of the normally A feature of the reconfiguration algorithm is ignoring the switches that are at of tie switches that are regarded regarded closed at the the beginning beginning ofopen the the switch. emergency shutdown of the sectionalizing algorithm run. Then, at each ofclosed the iterations, whose number Thetieheuristic optimization algorithms switch found by theclosing most tie tie switches that are regarded closed at the beginning of the information on the initial composition of the normally open at each of the iterations, whose number The optimization algorithms found most algorithm run. Then, at each of the whose number the tieheuristic switch. is equal torun. the Then, number independent loops in the network The heuristic optimization algorithms found the thecriteria. most algorithm common application among different reconfiguration algorithm run. Then, at of each ofclosed the iterations, iterations, whose number tie switches that are regarded at loops the beginning of the The heuristic optimization algorithms found thecriteria. most is equal to the number of independent in the network common application among different reconfiguration is equal to the number of independent loops in the network graph, the load flow is calculated, the maximum spanning common application among different reconfiguration criteria. They include genetic algorithms (see Guimaraes et al. is equal to the number of independent loops in the network common application among different reconfiguration criteria. algorithm run. Then, at each of the iterations, whose number graph, the load flow is calculated, the maximum spanning The heuristic optimization algorithms found the most They include genetic algorithms (see Guimaraes et al. graph,whose the load flow is calculated, maximum spanning tree branch weights are the current magnitudes is They include genetic algorithms (see Guimaraes et al. (2010)), tabu search algorithms (see Junior et al. (2014)), They include genetic algorithms (see Guimaraes et ant al. graph, the flow is maximum to load thebranch number ofcalculated, independent loops in the spanning network treeequal whose branch weights are the current magnitudes is common application among different reconfiguration criteria. (2010)), search (see et ant tree whose weights are current magnitudes is (2010)), tabu tabu search algorithms algorithms (see Junior Junior et al. al. (2014)), (2014)), ant is tree whose branch weights are the current magnitudes is the load flow is calculated, maximum spanning (2010)),include tabu search algorithms (see Junior et al. (2014)), They genetic algorithms (see Guimaraes et ant al. graph, Copyright © 2019, 2019 IFAC 472 Hosting tree whose branch weights are current magnitudes is 2405-8963 © IFAC (International Federation of Automatic Control) by Elsevier Ltd. All rights reserved. (2010)), tabu search algorithms (see Junior et al. (2014)), ant Copyright © 2019 IFAC 472 Copyright 2019 responsibility IFAC 472Control. Peer review© of International Federation of Automatic Copyright ©under 2019 IFAC IFAC 472 Copyright © 2019 472 10.1016/j.ifacol.2019.08.249 Copyright © 2019 IFAC 472
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constructed, and the chord with a minimum current is opened. Thus, as a result of the first reconfiguration step that is the least complex a new composition of the open chords corresponding to tie switches is determined. At this new composition, the network power losses, as a rule, are essentially lower than those in the chords corresponding to the initial composition of tie switches.
supply, but combining the source nodes into one node results in a loop, whose one branch, for example, branch 3-4, is selected as a chord. In a four-source scheme, the spanning tree allows choosing only one chord, for example, chord 1112, but combining the power sources – one chord in each of the four loops. The proposed modification of the reconfiguration algorithm consists in the initial modeling of a distribution network with several power sources in the form of a single-source network followed by the use of the reconfiguration algorithm developed by the authors earlier (see Golub et al. (2017)).
At the second reconfiguration step, we study the possibility to decrease the network power losses by replacing the chords, opened at the first step, with spanning tree branches in the loops connected with the chords. This is achieved by the following operations: each chord opened at the first step is sequentially closed, the composition of branches of the loop connected with the chord is determined, and the load flow is calculated. Then, the nodes with a degree higher than two are fixed in the closed loop left and right of the chord nodes, a sequential disconnection of the branches between such nodes is simulated. For each disconnection, the load flow is calculated, and the total losses are determined. The previous chord or a new one with minimum total losses is opened. If there are no nodes with a degree higher than two in the loop, disconnection of all the loop branches is simulated. The most important characteristic of our reconfiguration algorithm is a high speed of the solution at a high accuracy of the load flow calculation.
In a real distribution network, tie switches for several feeders connected to one power source are installed between the nodes of the feeder and the nodes of different feeders. In the case of several power sources, tie switches are also installed between the feeder nodes powered from different sources. Reconfiguration of such a network can lead to a new radial topology of individual feeders. The paper is arranged as follows. In Section 2, we prove the efficiency of the offered reconfiguration algorithm for a test distribution network with two independent power sources. The efficiency is verified by the coincidence of the reconfiguration results obtained by the authors with the results obtained by other methods (see Xingquan et al. (2018)), including the case of the test network with distributed generation sources.
Such an algorithm, as shown in (see Golub (2018a)), enables us to successfully solve the distribution network reconfiguration problem, even if the latter has renewable generation sources.
In Section 3, the reconfiguration problem is solved for a real municipal distribution network with several feeders powered from six independent sources. The reconfiguration is shown to reduce power losses in the network, and to decrease loads of the most loaded feeders.
However, if some feeder of the distribution network is powered from two independent power sources, such as primary transformer substations, the algorithm of constructing a maximum spanning tree does not allow identifying such a feeder as a loop and selecting a chord in it that corresponds to a tie switch. This situation can be excluded if, before using the reconfiguration algorithm, all power supply nodes of feeders are combined into one balancing node, as shown in Fig. 1, assuming the voltages in these nodes to be the same.
In Section 4, we analyze the problems of reliable power supply to the distribution network consumers, determination loads, whose provision is reserved, at least, by one tie switch, and determination of subsystems of the trees, whose loads have no backup power source. 2. ILLUSTRATION OF THE RECONFIGURATION ALGORITHM To illustrate the efficiency of the offered reconfiguration algorithm, we use the primary 11.4 kV distribution network of the Taiwan electric company, Fig. 2. The distribution network comprises two subsystems receiving power from two sources (see Wu et al. (2010); Wang and Cheng (2010)). This network contains 11 feeders, 83 normally closed sectionalizing switches and 13 normally open tie switches, 5 of which (1-5) allow combining two subsystems of the distribution network which are powered from two sources into one node.
Fig. 1. Schemes of distribution networks with two and four power sources before (a, b) and after (c, d) combining the sources into one. Dashed lines show the chords corresponding to the tie switches.
Subsystem 1 includes feeders 1-6, subsystem 2 - feeders 7-11. Tie switch 6 mutually reserves the power supply of feeders 2 and 6, tie switch 7 mutually reserves the power supply to part of the consumers of feeders 5 and 6. Switches 8-10 reserve the power supply to part of the consumers of feeders 4 and 5. Tie switches 11-13 mutually reserve the
Such, construction of a spanning tree and selection of tie switches are exemplified by the feeder with a bilateral power supply and the four-source loop. The spanning tree will include all the nodes in the feeder with bilateral power 473
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power supply to part of the consumers of feeders 3-4, 2-3, and 7-8, respectively.
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(2018)). After adding the sources, the power losses in the initial open network decreased to 427.980 kW, whereas in the network with the closed tie switches, the losses dropped to 377.285 kW. Already at the first reconfiguration step, we determined the basic optimal switchings, and only one switching was corrected at the second step, Fig. 4. The symbols shown on the horizontal axis are similar to the symbols in Fig. 3.
Fig. 2. Distribution network scheme in which the power supply nodes of two subsystems of feeders 1-6 and 7-11 are combined into one node. Dashed lines show the branches with tie switches, B1-B11- circuit breakers.
Fig. 4. Change in total power losses and in composition of the branches with tie switches at the first (a) and second (b) reconfiguration steps in a network with renewable generation sources.
When opening all the tie switches in Fig. 2, feeders 1-11 operate independently, and the total power losses, in this case, equal 532.002 kW. When closing all the tie switches, the losses decrease to 462.679 kW. Fig. 3 illustrates the process of change in power losses owing to the network reconfiguration. The numbers of iterations, which is equal to the number of independent loops in the network with closed tie switches, are indicated above the horizontal axis of Fig.3, the line a below the axis contains the chords selected at each iteration at the first reconfiguration step, and the chords specified at the second reconfiguration step are given in the line b.
The obtained optimal composition of tie switches differs from that obtained in (see Xingquan et al. (2018)): the composition includes chord 12-13, instead of chord 13-76 in our solution. At the same time, replacement of chord 13-76 with chord 12-13 in our solution led to an increase in the losses from 383.128 kW to 383.17 kW. We perform an additional analysis of the reconfiguration results without distributed generation.
Number of nodes
Analysis of the load flow obtained as a result of reconfiguration shows that it allowed decreasing the total power losses, changing the number of nodes in the feeders and balancing the feeder loads and power losses. Figs. 5 - 7 present the plots confirming such conclusions.
Fig. 3. Change in total power losses and in composition of the branches with tie switches at the first (a) and second (b) reconfiguration steps in a network without renewable generation sources. Fig. 3 also shows that, already at the first step of reconfiguration, a new composition of the open chords (open tie switches) with the power losses of 471.727 kW was obtained. At the second step, only 5 reconfigurations were performed, and the composition of tie switches completely coincided, according to (see Xingquan et al. (2018)), with the composition of tie switches providing minimum losses. In our calculations, the losses equal 469.879 kW after the second reconfiguration step.
Fig. 5. Number of nodes in feeders before (a) and after (b) reconfiguration. 4000 a
b
3000 2000 1000
To prove the efficiency of the applied reconfiguration algorithm for the network with distributed generation sources, such sources were added to nodes 7, 12, 19, 28, 34, 71, 75 and 79 in accordance with the information on their allocations and generating capacities of the sources for the Taiwan network (see Xingquan et al.
1
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6 7 feeder
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9
10
11
Fig. 6. Change in total loads of feeders before (a) and after (b) reconfiguration.
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Upon closing all the tie switches, the power losses in the network decreased from 2133.3 kW to 1657.1 kW, and combining the feeder power sources into one led to a decrease in the number of nodes to 277 in the network scheme. The plots in Fig. 9 illustrate the process of the further loss change at the first and second reconfiguration steps related to determination and correction of the chords of 50 loops. At the first step related to selection of the initial composition of tie switches, the losses increase from 1657.9 kW to 1736.0 kW, and at the second correcting reconfiguration step the losses decrease to 1731.7 kW.
Power losses (kW)
150 a
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Fig. 7. Change in total power losses of feeders before (a) and after (b) reconfiguration. 3. ILLUSTRATION OF THE RECONFIGURATION ALGORITHM BY EXAMPLE OF REAL DISTRIBUTION NETWORK We conducted the study similar to that for the Taiwan network for the real municipal 6 kV distribution network with 282 nodes, 326 branches with sectionalizing switches, 50 branches with tie switches. The loading transformers are installed at 189 network nodes. Thus, the calculation scheme of the municipal distribution network differs from the Taiwan network in addition of the transformers, which leads to a necessity of including the transformer losses into their estimation during the reconfiguration. In total, there are 15 feeders in the network. Schematically, Fig. 8 shows the feeders that are powered from 6 independent sources. Feeders 1, 7, 8, 9 and 11 are powered from the first source, feeders 3, 4, 5, 6, 10 and 12 – from the second source, and feeders 2, 13, 14 and 15 – from sources 3-6.
Fig. 9. Change in total power losses at the first (a) and second (b) reconfiguration steps. Fig. 10 presents the structural scheme of the network after the reconfiguration, during which only 19 switches changed their status from the normally closed to normally open. Of them, 2 switches belong to feeders 4 and 9, and the remaining 17 tie switches are shown in the scheme by dashed lines.
Fig. 10. Structural scheme of the distribution network after reconfiguration, solid lines between the feeders correspond to tie switches which coincide with tie switches in the initial scheme, and dashed ones – to tie switches obtained after reconfiguration.
Fig. 8. Initial structural scheme of the distribution network with feeders and branches between them with tie switches. Numerals on the branches indicate their number. Fig. 8 presents only 42 branches out of 50 branches with tie switches, since the 8 remaining tie switches belong to feeders: 2, 8, 9 and 10 have one switch each, and feeders 4 and 14 have 2 switches each. Two tie switches 8-11 and 9-11, as is shown in Fig. 8, combine feeders powered from the first source and seven tie switches 5-6, 6-12, 10-12, 3-6 (two branches) and 3-10 (two branches) combine feeders powered from the second source. The other 35 tie switches combine the feeders powered from different sources.
Power losses (kW)
As a result of reconfiguration the number of nodes in the feeders changed, Fig.11.
In the initial network with open tie switches, in which each feeder operates independently and is powered from the connected source, the power losses equal 2133.3 kW in the 6.2 kV power sources at the total load equal to 47074.0 kW for the maximum load condition.
Fig. 11. Number of nodes in feeders before (a) and after (b) reconfiguration. For example, there were 13 nodes in feeder 6 before reconfiguration, and 14 nodes after reconfiguration, the 475
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Table 1 for the Taiwan network, received after reconfiguration, provides the variants of the tie switches that can be used to restore the power supply after opening one of 11 circuit breakers. The last column presents the minimum losses in the network after opening the circuit breaker and closing the tie switch indicated in bold. For example, at emergency shutdown of B1 or B8 in the same independent loop: B1, 1-… -4, 4-5, 5-6, 6-7, 7-60, 60-… -56, B8, power supply can be restored by closing the tie switch corresponding to chord 6-7 of this loop. The total losses after restoration, when circuit breaker B1 is open, are lower than those, when the tie switch corresponding to chord 55-54 of the loop is closed: B1, 1-… -4, 4-5, 5-55, 55-54, 54 -53, 53… -47, B7.
number of nodes in feeder 10 before and after reconfiguration changed from 28 to 14. The appearance of two new branches 6-10 with tie switches between feeders 6 and 10 can be commented as follows. As a result of the reconfiguration, three nodes, let us call them 1, 2, 3, united by branches 1-2 and 2-3 with sectionalizing switches belonged to feeder 10. After reconfiguration node 2 shifted to feeder 6 and nodes 1 and 3 remained in feeder 10. The number of nodes in feeder 6 increased, and two branches 6-10 with tie switches appeared between feeders 6 and 10, Fig. 10.
Power losses (kW)
The load redistribution, connected with changes in the number of nodes in the feeders, led to an essential decrease of power losses in feeder 10, Fig. 12.
Analysis of the spanning tree and its chords enables us to determine subsystems of the trees, whose loads can be covered only from one source. In the presented example, an emergency outage of one of branches 7-8, 7-9, or 7-10 will lead to power supply violation for nodes 8, 9, or 10, with 300.0 kW each, and an emergency outage of branch 20-21 in will lead to power supply violation for four tree nodes 21, 22, 23, and 24, with the total load of 550.0 kW.
Fig. 12. Change in total power losses of feeders before (a) and after (b) reconfiguration.
The estimation of the reliability of power supply to feeders in the municipal distribution network after closing all tie switches and combining all power sources into one showed that to restore the power supply at an emergency outage of circuit breaker, the number of variants of tie switches for different feeders ranged from 1 to 14, as shown in Fig.13, plot a.
4. ANALYSIS OF POWER SUPPLY RELIABILITY
Number of variants
The reconfiguration algorithm based on constructing a spanning tree on the network graph and determining the composition of independent loop branches by the tree chords enables us to determine the variants of tie switches that may be used to restore power supply at an emergency outage of any sectionalizing switch (Golub et al. (2018b)), as well as any circuit breaker. Since the same branch of the spanning tree can be in several loops, the power supply in case of emergency outage of the sectionalizing switch or circuit breaker can be restored by closing any tie switch connected with it by the common loop. The minimum power losses in the network after the reconfiguration may be a criterion for selecting the tie switch.
Fig. 13. Number of tie switch variants for power supply to feeders at opening a circuit breaker (a), and maximum total load of subsystems without reserve supply (b).
Table 1. Variants of tie switches to be used to restore power supply at an emergency outage of the circuit breakers Circuit breakers B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11
Variants of tie switches 1 6-7 11-43 14-18 16-26 28-32 11-43 54-55 6-7 71-72 12-13 82-83
2 54-55 12-13 16-26 28-32 33-34 33-34 61-62 61-62
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4
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71-72
38-39
41-42
41-42
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The estimation of the power supply reliability enabled us to determine that out of 189 load nodes, the power supply to 88 consumers with the total power of 33253.4 kW was reserved, at least, by one tie switch, and the supply to 101 consumes with the total power of 13521.1 kW had no reserve supply.
Power losses (kW) 603.37 481.44 528.43 518.82 553.24 490.62 802.93 593.48 544.54 536.72 767.03
The subsystems of the trees, whose loads have no reserve power supply, are determined by the following actions. The branches of the loops and the branches that are chords of these loops are excluded from the list of network graph branches. The remaining branches are ordered by decreasing power flows in them and the subsystems of spanning trees, which comprise one through several branches, are constructed. For each subsystem with unilateral power supply, we determine the total load and the subsystem with the maximum total load. The plot b in Fig. 13 characterizes the subsystem with the maximum total load for each feeder. 476
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As an illustration, Fig. 14 shows the scheme of feeder 12 of the municipal distribution network before reconfiguration, in which we indicated eight subsystems of trees with the loads that have no reserve power supply. At an emergency outage of the branch with maximum power flow at the head section of the subsystem tree, such branches in Fig.14 are shown by the dashed-doted lines, the power supply of the subsystem will be violated. Feeder 12 consists of 8 subsystems, 6 of which consist of only one branch, one subsystem includes two branches, and the subsystem with the maximum total load contains 14 consumers. The branches shown by the dashed lines in Fig. 14 correspond to the tie switches connecting feeder 12 to feeders 2, 6, 7, 8, 9, 10, 13, 14, and 15, Fig. 8.
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Fig. 14. Scheme of feeder 12 of the municipal distribution network. 5. CONCLUSIONS We propose a modification of the reconfiguration algorithm based on the methods of constructing a maximum spanning tree and determining by the tree chords the composition of branches of independent loops in a primary distribution network, whose feeders are powered from several independent sources. The algorithm efficiency is verified by the calculations for the network regarded as a test one, and for a real municipal distribution network. We illustrate that reconfiguration makes it possible to reduce the power losses in the whole network and to balance the total loads and power losses in feeders by changing the number of nodes in them, which has not been analyzed earlier. The reconfiguration algorithm can also be applied to analyze the power supply reliability at an emergency outage of any sectionalizing switch, as well as any circuit breaker, and to determine the subsystems of trees in the network scheme without reserve power supply. ACKNOWLEDGMENT This study was supported by the project III.17.4.2 of the fundamental research program SB RAS, reg. No. AAAAA17-117030310438-1. REFERENCES Abdelaziz, A.Y., Osama, R.A., and El-Khodary, S.M. (2012). Reconfiguration of distribution systems for loss 477