Network Recon guration for Load Balancing in Distribution ... · The electrical power distribution systems consists of group of in- ... have been used for loss reduction using di

Network Reconfiguration for LoadBalancing in Distribution System withDistributed Generation and Capacitor

Placement by Gravitational SearchAlgorithm

D. Mahesh Kumar,Assoc. Prof., Dept. of EEE,ALITS,Ananthapuramu, A.P

Dr. S. Suresh Reddy,Professor,Head, Dept. of EEE,

NBKRIST, Vidyanagar,Kota Mandal Nellore (dt), A.P

Dr.P.Sujatha,Professor,Dept. of EEE,

JNTUCEA,Ananthapuramu, A.P

April 18, 2018

Abstract

This paper presents an efficient algorithm for optimiza-tion of radial distribution systems by a network reconfigu-ration to balance feeder loads and eliminate overload condi-tions. The system load-balancing index is used to determinethe loading conditions of the system and maximum systemloading capacity. The index value has to be minimum inthe optimal network reconfiguration of load balancing. Amethod based on swarm intelligence is proposed. The par-ticle swarm algorithm is employed to search for the optimalnetwork reconfiguration. The system load-balancing index

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International Journal of Pure and Applied MathematicsVolume 118 No. 24 2018ISSN: 1314-3395 (on-line version)url: http://www.acadpubl.eu/hub/Special Issue http://www.acadpubl.eu/hub/

is used to determine the loading conditions of the systemfeeders and maximum system loading capacity. The indexvalue has to be minimum in the optimal network recon-figuration of load balancing. The GSA algorithm is em-ployed to search for the optimal network reconfigurationin the premises of DG units and shunt capacitors. Thismethod presents low computational effort and is able tofind good quality configurations when compared with exist-ing TABU search method. Simulation results for a radial 41and 69-bus system with distributed generations and capac-itors placement are presented and compared with TABUsearch method. The simulation results show that the op-timal on/off patterns of the switches can be identified togive the best network reconfiguration involving balancingof feeder loads while respecting all the constraints.

1 Introduction

The electrical power distribution systems consists of group of in-terconnected radial circuits and have a number of constrains likeradial configuration, all loads served, coordinated operation of overcurrent protective devices, and voltage drop within limits etc. Eachfeeder in the distribution system has a different mixture of commer-cial, residential and industrial type loads, with daily load variations.There are several operational schemes in electrical distribution sys-tems; one of them is distribution network reconfiguration. Thereare some normally closed and normally opened switches (section-alizing and the switches) in a distribution feeder . Network recon-figuration is very important for operating the distribution system.Generally, power distribution network reconfiguration provides ser-vices to as many customers as possible following fault coding andduring planned outage for maintenance purposes with system lossminimization and load Balancing of the network.

Network reconfiguration problem is a complex non-linear combi-national problem due to non-differential status of switches and thenormally open tie switches, determined to satisfy system require-ment. From optimization point of view, the reconfiguration methodhave been used for loss reduction using different techniques on theother hand from service restoration point of view, the reconfigura-

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International Journal of Pure and Applied Mathematics Special Issue

tion allows to relocate loads by using an appropriate sequence ofswitching operations with operating constraints taken into account.

Network reconfiguration of an electrical distribution system isan operation to alter the topological structure of distribution sys-tem by changing status (open/closed) of sectionalizing and tie switches.By transferring loads from the heavily loaded feeders to the rela-tively lightly loaded feeders, the network reconfiguration can bal-ance feeder loads and eliminate overload conditions. The systemload-balancing index (LBI) is used to determine the loading con-ditions of the system and maximum system loading capacity. Theindex value has to be minimum in the optimal network reconfigu-ration of load balancing.

2 POWER FLOW EQUATIONS

Power flow in a electrical power distribution network can be de-scribed by a set of recursive equations called distribution flow branchequations that uses the real and reactive power and voltage at thesending end of a branch to express the same quantities at the re-ceiving end of the branch. A simple radial distribution network isshown in figure 2.1

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Fig 2.1 single line diagram of main feeder.

The real and reactive power flow in the line between i+1 andnth buses are

Pi+1 = Pi − PLi+1 −Ri,i+1[(P 2

i +Q2i )

|Vi|2] (1)

Qi+1 = Qi −QLi+1 −Ri,i+1[(P 2

i +Q2i )

|Vi|2] (2)

The magnitude of the voltage at bus i+1 can be calculated as

|Vi+1|2 = |Vi|2−2(Ri,i+1·Pi+Xi,i+1·Qi)+(R2i,i+1+X2

i,i+1)[(P 2

i +Q2i )

|Vi|2]

(3)

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The power loss of the line section connecting buses i and i+1may be determined as

Ploss(i, i+ 1) = Ri,i+1[(P 2

i +Q2i )

|Vi|2] (4)

Where Pi is the active power at bus i Qi is the reactive powerat bus i Ri,i+1 is the resistance of line section between buses i andi+1 Xi,i+1 is the reactance of line section between buses i and i+1Vi is the voltage at bus i Gravitational search algorithm In thissection, we introduce our optimization algorithm based on the lawof gravity. In the proposed algorithm, agents are considered as ob-jects and their performance is measured by their masses. All theseobjects attract each other by the gravity force, and this force causesa global movement of all objects towards the objects with heaviermasses. Hence, masses cooperate using a direct form of commu-nication, through gravitational force. The heavy masses whichcorrespond to good solutions move more slowly than lighter ones,this guarantees the exploitation step of the algorithm.

In GSA, each mass (agent) has four specifications: position,inertial mass, active gravitational mass, and passive gravitationalmass. The position of the mass corresponds to a solution of theproblem, and its gravitational and inertial masses are determinedusing a fitness function. In other words, each mass presents a so-lution, and the algorithm is navigated by properly adjusting thegravitational and inertia masses. By lapse of time, we expect thatmasses be attracted by the heaviest mass. This mass will presentan optimum solution in the search space. The GSA could be con-sidered as an isolated system of masses. It is like a small artificialworld of masses obeying the Newtonian laws of gravitation andmotion. More precisely, masses obey the following laws: Law ofgravity: each particle attracts every other particle and the gravi-tational force between two particles is directly proportional to theproduct of their masses and inversely proportional to the distancebetween them, R. We use here R instead of R2, because accordingto our experiment results, R provides better results than R2 in allexperimental cases.

Law of motion: the current velocity of any mass is equal to thesum of the fraction of its previous velocity and the variation in thevelocity. Variation in the velocity or acceleration of any mass is

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equal to the force acted on the system divided by mass of inertia.To see how the proposed algorithm is efficient some

remarks are noted: Each agent could observe the performanceof the others, and hence the gravitational force is an information-transferring tool.

Due to the force that acts on an agent from its neighborhoodagents, it can see space around itself. A heavy mass has a largeeffective attraction radius and hence a great intensity of attraction.Therefore, agents with a higher performance have a greater gravi-tational mass. As a result, the agents tend to move toward the bestagent.

The inertia mass is against the motion and make the mass move-ment slow. Hence, agents with heavy inertia mass move slowly andhence search the space more locally. So, it can be considered as anadaptive learning rate. Gravitational constant adjusts the accuracyof the search, so it decreases with time (similar to the temperaturein a Simulated Annealing algorithm).

GSA is a memory-less algorithm. However, it works efficientlylike the algorithms with memory. Our experimental results showthe good convergence rate of the GSA.

Here, we assume that the gravitational and the inertia massesare the same. However, for some applications different values forthem can be used. A bigger inertia mass provides a slower mo-tion of agents in the search space and hence a more precise search.Conversely, a bigger gravitational mass causes a higher attractionof agents. This permits a faster convergence.

PROBLEM FORMULATION AND OBJECTIVE FUNC-TION Problem Formulation Load balancing index representsthe degree of loading among feeders. The aim of this work is tominimize the Loading Balance Index (LBI) that represents the de-gree of non-uniformity of loading among the feeders, mathemati-cally LBI can be written as

MinLBI =∑

kεB

Lk[Ik,tImaxk

] (5)

Where, B is the list of branches that forms the loops Lk is the lengthof the line branch k Ik,t is the current though of branch k for feederreconfiguration pattern t Imaxk is the maximum current carryingcapacity of branch k The above objective function is subjected to

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following constraints:1. Power flow equations2. Bus voltage Constraint:The voltage magnitude constraint i.e the voltage at each and

every bus should be within the specified minimum and maximumlimits mathematically (6) Where Vmin and Vmax are the minimumand maximum allowable voltages. In this work 0.9 p.u. and 1.05p.u. are taken as minimum and maximum allowable voltages.

3. Feeder capability constraint: The magnitude of the currentthrough all the line sections should be within the tolerable limitsof the respective section i.e.

Ik ≤ Imaxk , Kε [1, 2, 3....l] (6)

Where Imaxk is the maximum current capability of branch k Foreach possible network reconfiguration condition and DG placementthe voltages at all the nodes and currents through all the line sec-tion are calculated by using forward/backward sweep load flow tech-nique.

4. Radial configuration format: In a practical distribution net-work when we increase the number of switches then the numberof possible switching operations will be numerous. Consequentlyselecting the proper switches for network reconfiguration will be-come a tedious decision making and time consuming procedure forsystem engineers. Furthermore network reconfiguration problemwill be more difficult task as the electrical distribution systems aremostly configured in radial for proper relay coordination and pro-tection.

In this work the main problem studied is to find optimal networkreconfiguration for a radial distribution system with capacitor andDG placement. This will balance feeder loads and eliminate overload conditions. Where LBI is the load balancing index and it is tobe minimized. A minimum load balancing indicates balanced feederloads. It is minimized effectively by using GSA technique. Also acomparison is made between TABU search and GSA methods.

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3 Results & Analysis

The test systems for the case study are IEEE 69 BUS and IEEE41 BUS radial distribution systems. The cases considered for eachtest system are five and are listed below.

Case-1: Original configuration of the system without DG andcapacitors

Case-2: Optimal Configuration of the system without DG unitsand shunt capacitors

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Case-3: Optimal configuration with DG units and without shuntcapacitors

Case-4: Optimal configuration without DG units and with shuntcapacitors

Case-5: Optimal configuration with DG units and shunt capac-itors

Case study for Load balancing in distribution system

Example - 1An IEEE-69 bus system shown in figure 4.6 consisting of 69

buses, 68 lines with a total real power load of 3801.89 kW and totalreactive power load of 2594.9 KVAR. The line and load data for thissystem is given appendix A3, A4. The simulation results for theoriginal configuration without using DG units and shunt capacitorsare given in Table 4.7. It is observed that the total loss in thesystem is 224.68 kW, value of LBI is 2.949 and minimum voltageis observed to be 0.909 p.u.

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IEEE 69 Bus System

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Simulation results of IEEE 69 Bus system for OriginalConfiguration of the System without DG and Capacitors

In case-2, the proposed GSA is used to find the optimal net-work reconfiguration that gives us the sectionalizing switches to beopened without using DG units and shunt capacitors. Table 4.8shows the simulation results for case-2, from which it has been ob-served that the value of LBI has been reduced from 2.949 to 1.901,losses are also reduced from 224.68 kW to 98.48 kW. Convergencecharacteristics of GSA for this case are given in figure 4.7.

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Simulation results of IEEE-69 Bus system for case II

In case-3, four DG units of 100 kW, 200kW, 300 and 400 kW areconnected at the bus numbers 46, 35, 14 and 53 respectively beforegoing to search for optimal network reconfiguration. The proposedGSA here also is used to find the optimal network reconfigurationthat gives us the sectionalizing switches to be opened without usingshunt capacitors. Table 4.9 shows the simulation results for case-3,from which it has been observed that the value of LBI has beenreduced from 1.901 to 1.601, losses are also reduced from 98.48 kWto 80.48KW.

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Simulation results of IEEE-69 Bus system for case III

In case-4, four capacitor banks of rating 100 kVar, 200kVar , 300kVar and 400 kVar are connected at bus numbers 24, 45, 49 and61 respectively before going to search for optimal network reconfig-uration. The proposed GSA here also is used to find the optimalnetwork reconfiguration that gives us the sectionalizing switches tobe opened. Table 4.10 shows the simulation results for this case,from which it has been observed that the value of LBI has beenchanged from 1.601 to 1.611 and the losses are changed from 80.48kW to 83.64kW. Convergence characteristics of GSA for this caseare given in

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Simulation results of IEEE-69 Bus system for case IV

In case-5, four capacitor banks of rating 100 kVar, 200kVar , 300kVar and 400 kVar are connected at bus numbers 24, 45, 49 and 61respectively and four DG units of 100 kW, 200kW, 300 and 400 kWare connected at the bus numbers 46, 35, 14 and 53 respectivelybefore going to search for optimal network reconfiguration. Theproposed GSA here also is used to find the optimal network recon-figuration that gives us the sectionalizing switches to be opened.Table 4.11 shows the simulation results for case-5, from which ithas been observed that the value of LBI has been changed from1.611 to 1.311 and the losses are changed from 83.64 kW to 70.23kW.

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Table 4.11 Simulation results of IEEE-69 Bus system for case V

From the above simulation results it is observed that for case-2, case-4 and case-5 the power losses and LBI has reduced whencompared to case-1.

Example - 2An IEEE-41 bus system shown in figure 4.1 consisting of 41

buses, 40 lines with a total real power load of 4635 kW and totalreactive power load of 3250 KVAR. The line and load data for thissystem is given appendix A1, A2.

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IEEE 41 Bus Systems Simulation Results for originalConfiguration of the system without DG and Capacitors

The simulation results for the original configuration withoutusing DG units and shunt capacitors are given in Table 4.2. It isobserved that the total loss in the system is 239.83 kW, value ofLBI is 2.96 and minimum voltage is observed to be 0.92p.u.

In case-2, the proposed GSA is used to find the optimal net-work reconfiguration that gives us the sectionalizing switches to

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be opened without using DG units and shunt capacitors. Table4.3 shows the simulation results for case-2, from which it has beenobserved that the value of LBI has been reduced from 2.96 to 2,losses are also reduced from 239.83 kW to 100.12 kW. Convergencecharacteristics of GSA for this case are given in figure.

Simulation results of IEEE 41 Bus system for case II

In case-3, three DG units of 100 kW, 200kW and 300 kW areconnected at the bus numbers 18, 33 and 41 respectively beforegoing to search for optimal network reconfiguration. The proposedGSA here also is used to find the optimal network reconfigurationthat gives us the sectionalizing switches to be opened without usingshunt capacitors. Table 4.4 shows the simulation results for case-3,from which it has been observed that the value of LBI has beenreduced from 2.00 to 1.628, losses are also reduced from 100.12 kWto 87.65 KW. Convergence characteristics of GSA for this case aregiven in figure 4.3.

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Simulation results of IEEE 41 Bus system for case III

In case-4, three capacitor banks of rating 100 kVar, 200kVarand 300 kVar are connected at bus numbers 8, 30, 38 respectivelybefore going to search for optimal network reconfiguration. Theproposed GSA here also is used to find the optimal network recon-figuration that gives us the sectionalizing switches to be opened.Table 4.5 shows the simulation results for case-4, from which it hasbeen observed that the value of LBI has been changed from 1.628to 1.637 and the losses are changed from 87.65 kW to 90.239kW.Convergence characteristics of GSA for this case are given in

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Simulation results of IEEE 41 Bus system for case IV

In case-5, three capacitor banks of rating 100 kVar, 200kVar and300 kVar are connected at bus numbers 8, 30, 38 respectively andthree DG units of 100 kW, 200kW and 300 kW are connected atthe bus numbers 18, 33 and 41 respectively before going to searchfor optimal network reconfiguration. The proposed GSA here alsois used to find the optimal network reconfiguration that gives us thesectionalizing switches to be opened. Table 4.6 shows the simulationresults for case-5, from which it has been observed that the value ofLBI has been changed from 1.637 to 1.39 and the losses are changedfrom 90.239kW to 67.65kW. Convergence characteristics of GSA forthis case are given in figure 4.5.

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Simulation results of IEEE 41 Bus system for case V

From the above simulation results it is observed that for case-2, case-4 and case-5 the power losses and LBI has reduced whencompared to case-1.

4 Conclusions:

Here the test results for two examples is presented for the proposedOptimal Network Reconfiguration of a distribution system with DGunits and shunt capacitors by GSA and are discussed. The optimal

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network reconfiguration, Losses, LBI, convergence Characteristicsand voltage profile for five cases are presented. In this work Net-work configuration with DG and capacitor placement method inradial distribution systems based on gravitational search algorithmis proposed and tested on two examples viz., IEEE-41 and IEEE-69 Bus radial distribution system. For each system five cases areconsidered as mentioned in chapter 4. For each case load balancingindex (L.B.I), power losses and voltages at each bus are calculated.From the above calculations it is observed that proper network re-configuration with DG and capacitor placement in the distributionsystem reduces the load balancing index (L.B.I), eliminates overload conditions, reduces power loss and also improves the voltageprofile.

Test results indicate that the method can identify the most ef-fective network reconfiguration for improvement in load balancing.It is found that the optimal or near optimal configuration for loadbalancing also reduce losses and improves the voltage profile ofthe network while satisfying all the constraints. Simulations forthe test systems demonstrated the potential of use of the proposedGSA technique that can be a useful tool for distribution systemsplanning and operation.

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Network Recon guration for Load Balancing in Distribution ... · The electrical power distribution systems consists of group of in- ... have been used for loss reduction using di