research article computational techniques for autonomous … · 2019. 7. 31. · issues, generation...

Research ArticleComputational Techniques for Autonomous Microgrid LoadFlow Analysis

M. Venkata Kirthiga and S. Arul Daniel

Department of Electrical and Electronics Engineering, National Institute of Technology, Tiruchirappalli 620015, India

Correspondence should be addressed to M. Venkata Kirthiga; [email protected]

Received 25 January 2014; Accepted 17 March 2014; Published 11 May 2014

Academic Editors: Q. Guo and B. Zhang

Copyright © 2014 M. V. Kirthiga and S. A. Daniel. This is an open access article distributed under the Creative CommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

This paper attempts at developing simple, efficient, and fast converging load flow analysis techniques tailored to autonomousmicrogrids. Two modified backward forward sweep techniques have been developed in this work where the largest generatoris chosen as slack generator, in the first method and all generator buses are modeled as slack buses in the second method.The second method incorporates the concept of distributed slack bus to update the real and reactive power generations in themicrogrid. This paper has details on the development of these two methodologies and the efficacy of these methods is comparedwith the conventional Newton Raphson load flow method. The standard 33-bus distribution system has been transformed into anautonomous microgrid and used for evaluation of the proposed load flow methodologies. Matlab coding has been developed forvalidating the results.

1. Introduction

Aggregation of generating units and loads, at medium andlow voltage levels, forms small power islands called micro-grids.Most researchers concentrate on the design and controlaspects of these microgrids with respect to the resourceavailability and dispatchability of power to the loads. Designissues, generation planning, and economic dispatch in anautonomous microgrid need dedicated and robust powerflow computations. Load flow analysis of an autonomousmicrogrid is necessary for ascertaining the adequacy of sup-ply from DGs without compromising the voltage profile andto determine the state of the system.

Different load flow techniques adopted in the literatureare classified into three categories, namely, direct meth-ods, Newton Raphson (NR) based methods, and backwardforward sweep based methods. Direct methods involveimpedance matrix where the numbering of nodes and linesdecides the efficacy and convergence criteria. Chen et al.proposed a rigid power flow method based on seriesimpedance model [1] and Carpaneto et al. suggested a lossallocation technique, based on decomposition of the branch

currents [2]. Tedious computation is the basic drawback inthese methods.

NR method was used in certain methodologies to deter-mine the bus voltages and power flows in distributionnetworks. AmodifiedNewtonmethod had been discussed byZhang and Cheng [3] and as an extension Teng and Chang[4] suggested a novel fast three phase load flow analysis forunbalanced radial distribution systems. Bijwe and Kelapure[5] proposed a nondivergent load flow analysis based onNR method. NR-based method was extended to unbalancedsystems by Zimmerman andChiang [6] and further improve-ments of the computational efficiency of NR-based algo-rithms were also attempted in the literature [7]. Garcia et al.[8] suggested a load flow algorithmbased on current injectiontechnique inwhich generator connected busesweremodelledas either PV or PQ buses. Most NR-based methods present ahigh convergence rate but fail to exploit the system topology.

In this context, researchers started exploiting the radialtopology of distribution systems, resulting in the develop-ment of backward forward sweep based load flow analysis [9].Breaking of loops and application of the equivalent currentinjection (ECI) method to the break points was adopted by

Hindawi Publishing CorporationISRN Power EngineeringVolume 2014, Article ID 742171, 12 pageshttp://dx.doi.org/10.1155/2014/742171

2 ISRN Power Engineering

Cespedes [10] and was further extended to three-phase radialdistribution systems by Cheng and Shirmohammadi [11].Modified backward forward sweep method was introducedby Chang et al. [12]. Later, data structure and object orientedapproaches were incorporated with the modified backwardforward sweep method to formulate a load flow analysissuitable to both radial and weakly meshed systems [13, 14].All these works focused on the distribution systems withoutany DGs and hence adopted the substation feeder as the slackbus. Basu et al. [15] attempted an NR-based load flow formicrogrids, where the largest generator is assigned as theslack generator but did not exploit the system topologyexplicitly.

In all the earlier works, a single bus has been considered asthe slack bus where the single slack generator is considered toshare the total losses in the system thereby getting overloaded.Though analytically this consideration is acceptable, in apractically competitive environment with many owners, itbecomes inevitable to clearly identify the contribution ofeach generator towards load, power flows, and losses. Thesegenerators’ contributions would vary depending upon theirrespective locations and network parameters. Kirschen et al.and Strbac et al. [16, 17] introduced the concept of “domains”and “commons” of individual generators in a microgrid.Yan [18] suggested the concept of modified slack bus basedon participation factor of generators. Distributed slack busmodel has been extended with Newton iterative method andthe effect of participation of generators with respect to theloads and losses were discussed by Tong and Miu [19–21].All these works focus mainly on the impact of participationfactor but not on maintaining the slack bus voltage constant.

The authors have therefore developed two load flowmethodologies dedicated for autonomous microgrids, basedon backward forward sweep algorithm. The first methodadopts a single slack bus (bus to which largest generator isconnected) with all the other DG connected buses modelledas PQ injection buses. The second method incorporates thedistributed slack bus technique in the backward forwardsweep algorithm, where all generator buses are modelled asslack buses. Contributions of the generators towards total sys-tem losses and loads are utilized to update the real and reac-tive power generations, in the second method. The efficacyof the proposed techniques has been investigated using thestandard 33-bus distribution system [22, 23] transformed toan autonomousmicrogrid.The results are also comparedwiththat obtained using NR method.

The paper is organized as follows: introduction followedby modified backward forward sweep based load flow tech-nique with single slack bus in Section 2 and distributed slackbus based backward forward sweep load flow technique inSection 3. A case study illustrating the proposed method-ologies is dealt in Section 4 and a detailed comparison ofdifferent load flow methods adopted is shown in Section 5.The paper concludes with Section 6.

2. Modified Backward-Forward Sweep BasedLoad Flow Analysis

Thebasic backward forward sweep technique has beenmodi-fied to suit the load flow analysis of a sustainable autonomousmicrogrid.

ViIbr𝑘

Rij + Xij

DG Vj

Ish𝑗Iload𝑗

Ibr(𝑘−1)

Figure 1: Steady state representation of a branch “𝑘” between 𝑖th and𝑗th buses of a microgrid.

2.1. Backward Sweep Technique. The steady state equivalentcircuit representation of a branch “𝑘” between the buses “𝑖”and “𝑗” of microgrid is considered as shown in Figure 1 andthe currents are computed using the following:

𝐼br𝑘 = 𝐼br(𝑘−1) − 𝐼𝑗, (1)

where

𝐼𝑗 = 𝐼𝑔𝑗− (𝐼sh𝑗 + 𝐼load𝑗) , (2)

𝐼load𝑗 = conj(𝑆load𝑗

𝑉𝑗

) . (3)

All branch and node currents are computed using (1)–(3),respectively, in each of the iterations.The effect of introducinggenerators in distributed systems is incorporated in (2),where positive sign is assigned to the injected generator cur-rent and negative sign for the current components drawn bythe load and compensating devices. This polarity assignmentincorporates the effect of DGs penetrated in the system;namely, the net current injected at any 𝑗th bus with a DGattains a positive sign and without DG attains a negative sign.This is automatically reflected in bus voltages computed inthe forward sweep. Modifications incorporated in the con-ventional backward sweep technique is reflected in (2).

2.2. Forward Sweep Technique. Since the effect of addition ofDGshas been incorporated in the backward sweep, there is nomodification required in the forward sweep. Hence, the basicforward sweep is performed, as shown in the following:

𝑉𝑖 = 𝑉𝑗 + 𝐼br𝑘 (𝑅𝑖𝑗 + 𝑋𝑖𝑗) . (4)

The polarity assignment adopted for the current injec-tions facilitates appropriate bus voltage computations. Thisincludes the effect of voltage modifications automatically onforward sweep computations. The bus to which the largestgenerator is connected is considered the slack bus and henceits voltage alone is maintained at 1+𝑗0. All other bus voltagesare computed using (4).

2.3. Algorithm for Modified Backward/Forward Sweep Tech-nique. Modified backward forward sweep based load flowanalysis is formulated as follows.

(i) System data, including the connected load and net-work parameters, are taken.

ISRN Power Engineering 3

(ii) A flat voltage profile of 1 + 𝑗0 is adopted initially forall the buses. The tolerance value is defined and theconvergence criterion is fixed as

𝑉𝑖𝑘− 𝑉𝑖𝑘−1< tolerance, (5)

where 𝑘 denotes the iteration count.(iii) The largest generator is assigned as the slack genera-

tor.(iv) The load current at any𝑗th bus (node) is computed

using (3).(v) Backward sweep is performed and all the node and

branch currents of the microgrid are determinedusing (1)–(3).

(vi) Voltage at the slack bus is fixed at 1 + 𝑗0 and theforward sweep is performed to compute the voltage ofall the other buses starting from the slack bus using(4).

(vii) The iterations are continued till the convergencecriterion (5) is satisfied.

(viii) On satisfying the convergence criterion, system lossesare computed.

2.4. Significance and Limitations of theMethod. Theproposedload flow analysis is found to own certain significant featuresas well as limitations in comparison with the NR method.

2.4.1. Significance of Modified Backward Forward Sweep LoadFlow Method

(i) The radial topology of the system is exploited indetermining the bus voltages and the branch currents.

(ii) Computational procedure is very simple and dealswith only KCL and KVL avoiding complex equationsand matrix manipulations.

(iii) The convergence rate is very high such that thealgorithm converges in two to three iterations for anysize of the system.

(iv) The algorithm does not require bus impedance oradmittance matrices.

2.4.2. Limitations of Modified Backward Forward Sweep LoadFlow Method. An initial guess of the real and reactive powerinjections is required at all the generator buses and hencethis is obtained by performing NR method in this work.This is essential to calculate the current injections during thebackward sweep.

3. Distributed Slack Bus Based LoadFlow Analysis

A new load flowmethodology based on distributed slack bustechnique has also been proposed for radialmicrogrids in thispaper.

3.1. Distributed Slack Bus Technique. In single slack busmodel, the generator connected to the slack bus alone isconsidered to take up the complete losses in the system, incontrary to the actual practice. In this method, all the genera-tors capable of supplying real and reactive powers are consid-ered to be slack generators with constant voltage magnitudeand angle, with varying real and reactive powers. Moreover,these generator buses, modeled as slack buses, are consideredto share the system demand and distribution losses indifferent proportionswith respect to real and reactive powers.

3.2. Disadvantages of Single Slack Bus Model. The followingare the noticeable limitations of single slack busmodel in loadflow analysis.

(i) In a radial system, the real power losses in the systemwould be higher if a single generator is committedto compensate the total system losses. This is suitablefor a nonautonomous microgrid as the substationfeeder also takes a share of the total losses but in anautonomous microgrid a single generator would beunnecessarily taxed to supply the total losses.

(ii) As the largest generator alone is considered as theslack bus and all other generator injections are fixed,there is always a chance for over voltage at thegenerator buses due to fixed real and reactive powerinjections by the generators in view of satisfying thedemand constraint alone.

(iii) On blackouts or line outages, intentional islanding ofthe microgrids to supply reliable and uninterruptedpower supply to select customers becomes difficult asthe demand constraint would not be satisfied whenthe slack generator gets isolated.

3.3. Domains and Commons of Generators. The distributedslack bus technique aims at distributing both the system loadsand losses to all the generators. Hence, to determine the realand reactive power generations of the generators, the actualcontributions of each generator towards the real and reactivepower flows, loads, and losses in the system are determinedusing the “domains” and “commons” of the generators.

The “domain” of a generator helps to identify which busesand hence loads are supplied from a generator and also thefarthest point till which the power injected by a generatorreaches. The “domain” of a generator is defined as the set ofbuses and branches supplied by the generator in the literature.The “domain” of a generator is determined after identifyingthe positive power flow direction on the microgrid. For twodirectly connected buses, 𝑖 and 𝑗,

(i) if Real(𝑉𝑖 × 𝐼∗𝑖 ) − Real(𝑉𝑗 × 𝐼

∗𝑗 ) ≥ 0, then positive real

power flows from bus 𝑖 to bus 𝑗;(ii) if Imag(𝑉𝑖 × 𝐼

∗𝑖 ) − Imag(𝑉𝑗 × 𝐼

∗𝑗 ) ≥ 0, then positive

reactive power flows from bus 𝑖 to bus 𝑗.

The positive real and reactive power flows are decidedby the loads and the network parameters and are used toupdate real and reactive power generations. Further, certain


loads would be supplied power by more than one generatorin a microgrid. Thus, “domains” of different generators oftenintersect and they have branches or loads in common. A“common” is defined as a set of contiguous buses suppliedby the same generators [19–21]. Based on the principle ofproportionality [20], that is, the proportion of loss and loadssupplied by different generators to a “common” is the sameas the proportion of positive real power injected by the gen-erators to this “common,” the proportion of loads and lossesof a “common” is assigned to the corresponding generator“domain.”Thus, all loads and losses in a network are assignedto individual generators using a directed graph. Thesecommons are interconnected through “links” connecting twoor more “commons” and there can be more than one linkconnecting two “commons.”

3.4. Contribution and Participation Factor of Generators.An oriented state graph is drawn identifying the generator“domains” and “commons” to compute howmuch a generatorcontributes to the loads and flows in the “commons” and“links” which are located “downstream.”The inflow of a “com-mon” is defined as the amount of power flowing into a “com-mon” either from generators connected to buses of this “com-mon” or across links from other “commons.” Similarly, theoutflow of a “common” is the amount of power flowing acrosslinks into other “commons” or consumed by loads connectedto buses of the “common.”

The Proportionality Principle States. For a given “common,” ifthe proportion of inflow which can be traced to generator“𝑖” is “𝑥,” then the proportion of the load and outflow ofthis “common” which can be traced to generator “𝑖” is also“𝑥.” First the root nodes or root “commons” are identified(“commons” in which the generators are present) and thecontribution by a generator to its encircled “common” isconsidered 100%. As a next step the contribution of anygenerator “𝑚” to a “common” “𝑛” is computed as shown inthe following:

𝐶𝑚𝑛 =∑𝑛𝑐𝑛=1 𝐹𝑚𝑝𝑛

𝐼𝑛

, (6)

where

𝐹𝑚𝑝𝑛 = 𝐶𝑚𝑝 × 𝐹𝑝𝑛

𝐼𝑛 =

𝑛 ln∑

𝑝=1

𝐹𝑝𝑛.

(7)

After computing contributions of the generators to the“commons,” the participation factor of a generator towards

real and reactive power loads and losses in every “common”is determined using the following:

𝐾𝑔𝑚𝑛loss𝑝 =∑𝑛𝑐𝑛=1 𝐶𝑚𝑛 × Com𝑛loss𝑝𝑃loss

𝐾𝑔𝑚𝑛load𝑝 =∑𝑛𝑐𝑛=1 𝐶𝑚𝑛 × Com𝑛load𝑝𝑃load

𝐾𝑔𝑚𝑛loss𝑞 =∑𝑛𝑐𝑛=1 𝐶𝑚𝑛 × Com𝑛loss𝑞𝑄loss

𝐾𝑔𝑚𝑛load𝑝 =∑𝑛𝑐𝑛=1 𝐶𝑚𝑛 × Com𝑛load𝑞𝑃load

.

(8)

These contributions and participation factors are usedfor updating the real and reactive power generations of thegenerators.

3.5. Algorithm for Distributed Slack Bus BasedLoad Flow Technique

(1) System data, location, and rating of DGs in the auto-nomous microgrid, load data, and convergence limitare determined.

(2) A preliminary load flow analysis (NR technique) isperformed.

(3) Initially a flat voltage profile of 1N 0∘ is considered forall buses.

(4) One complete backward sweep is performed startingfrom the terminal buses of the system, with thegenerator buses operated at 1N 0∘ using (1)–(3)

(5) Slack bus voltages are kept constant (1N 0∘) andthe forward sweep is performed starting from everygenerator bus and proceeding towards each terminalbus using (4).

(6) There are as many forward sweeps as that of numberof generators and the reversal of current direction ona distributor/lateral is an indication for starting a freshsweep.

(7) Power flows on the distributors and the total real andreactive power losses in the system are determined.

(8) “Domains” and “commons” of the generators aredetermined separately by accounting positive real andreactive power flows on laterals.

(9) As per the proportionality principle, the contributionof real and reactive power of each generator to each“common” is determined using (6)-(7).

(10) After determining the contributions, the participa-tion of each generator to share the loads and lossesin a “common” are determined using (8).


(11) The actual real and reactive powers to be generated byeach generator according to the participation factorsdetermined are computed as follows:

𝑃𝑔𝑖= 𝑃𝑔𝑖load+ 𝑃𝑔𝑖loss,

𝑄𝑔𝑖= 𝑄𝑔𝑖load

+ 𝑄𝑔𝑖loss,

(9)

where

𝑃𝑔𝑖load=

𝑛𝑐

∑

𝑛=1

𝐾𝑔𝑖𝑛 load𝑝∗ 𝑃load,

𝑃𝑔𝑖loss=

𝑛𝑐

∑

𝑛=1

𝐾𝑔𝑖𝑛 loss𝑝∗ 𝑃loss,

𝑄𝑔𝑖load=

𝑛𝑐

∑

𝑛=1

𝐾𝑔𝑖𝑛 load𝑞∗ 𝑄load,

𝑄𝑔𝑖loss=

𝑛𝑐

∑

𝑛=1

𝐾𝑔𝑖𝑛 loss𝑞∗ 𝑄loss.

(10)

(12) The demand constraints as shown in the following arechecked:

𝑛𝑔

∑

𝑖=1

𝑃𝑔𝑖= (𝑃load + 𝑃loss) ,

𝑛𝑔

∑

𝑖=1

𝑄𝑔𝑖= (𝑄load + 𝑄loss) .

(11)

(13) The iterative procedure (steps 4 to 12) is repeated tillthe tolerance limit (12) is satisfied:

𝑉𝑖𝑘− 𝑉𝑖𝑘−1< tolerance, (12)

where 𝑘 indicates the iteration count.(14) The final updated real and reactive powers to be

generated by each of the generators is computed as thesolution of the load flow analysis. The voltage profileand the losses corresponding to the final solution aretabulated.

3.6. Significance and Limitations of the Proposed Method.The proposed load flow analysis is found to possess certainsignificant features as well as limitations in comparison withthe standard NR method of load flow analysis.

3.6.1. Significance of Distributed Slack Bus BasedLoad Flow Method

(i) The proposedmethod exploits the system topology todetermine bus voltages and power generations.

(ii) No power factor controller is required. The real andreactive powers, generated by the DGs, are allowed tovary (practically feasible).

(iii) The method deals with only KCL and KVL avoidingcomplex equations and matrix manipulations.

(iv) The domain margin of each generator is obtainedwhich would help in pricing issues of autonomousmicrogrids.

(v) The algorithm does not require the formation of busimpedance or admittance matrix.

3.6.2. Limitations of Distributed Slack Bus BasedLoad Flow Method

(i) Initial real and reactive power injections are requiredat all the generator buses to calculate the currentinjections during the backward sweep. Hence, anyother standard load flow analysis is required at theinitial stage.

(ii) Forward sweep for a system with many generatorsneeds more computations since it has as many num-bers of sweeps as that of the generator buses.

(iii) Real and reactive power contributions need to becomputed to determine the updated real and reactivepower generations by the DGs. This increases thecomputational time.

3.6.3. Deliverables of the Proposed Load Flow Methodology.The proposed distributed slack bus based load flow analysisfor an autonomous microgrid is suitable for the followingapplications:

(i) to realize the actual scenario of load and loss sharedamong different generators in an autonomous micro-grid;

(ii) to schedule the different generators in a microgrid forselected customers;

(iii) to decide the tariff in an autonomous microgrid,where the different generators in the microgrid areowned by different companies;

(iv) to avoid pessimistic conclusions on the size of thelargest generator unlike in the case of single slack busbased analysis;

(v) this methodology can be used as a base case loadflow analysis for sizing of DGs in an autonomousmicrogrid.

4. Case Study

The standard 33-bus distribution system [22, 23], with ademand of 3.715MW and 4.456MW in summer and winter,respectively, has been considered for the validation of theproposed methodologies. This distribution system has beentransformed into a sustainable autonomous microgrid oninclusion of optimally sized DGs at optimal locations, asshown in Figure 2. The sizing details of the generators aregiven in Table 1. A base power of 100MVA and base voltageof 12.66 kV are adopted, respectively.


1 2 3 4 5 6 7 16 17 188 9 121110 13 14 15

19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

DG1 DG

2

DG3

Figure 2: One line diagram of the 33-bus autonomous microgrid.

Domain 2

Domain 3

Domain 1

1 2 3 4 5 6 7 16 17 188 9 121110 13 14 15

19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

DG1 DG2

DG3

Figure 3: Domains of the generators w.r.t. real power flows in the microgrid for winter demand.

Table 1: Optimal size of the distributed generators in the 33-busautonomous microgrid.

Bus number Rating/size of the generatorReal power rating in

MWReactive power rating in

MVAr3 1.90 1.189 0.95 0.5931 1.69 1.04

The load flow results for the 33-bus microgrid, obtainedby implementing the proposed load flow techniques, namely,modified backward forward sweep and distributed slack busbased load methodologies, are compared with that of thestandard NR method of load flow. The load flow has beenperformed for both the summer and winter demands ofthe system and the voltage variations are tabulated in Table 2.The existing backward forward sweep techniques are suitablefor radial distribution systems with a feeder node serving asa reference. However, in this work since the feeder is absent

the existing method is modified with the node having thelargest capacity as the slack (reference) node and the load flowis performed.

Table 2 shows evidently that the voltage at all the busesis found to be in close proximity with that obtained byNR methodology. Similarly the losses are compared andpresented in Table 3.

The real and reactive power losses are found to becomparable to that of the standard NR method. However,losses are found to be slightly more in distributed slack busbased method than the single slack bus model, as the sitingand sizing of DGs connected in the system have been deter-mined with single slack bus model. Real power “domains”and “commons,” for the winter demand, are shown in Figures3 and 4 and a similar analysis is also done for reactive powerflows. The details of the contributions and participationfactors of the generators for real and reactive power flows aretabulated in Table 4 for the winter demand of the system.

Table 4 shows clearly the procedure of determining thereal and reactive power generations in the microgrid usingthe distributed slack bus based load flow analysis.


Table2:Com

paris

onof

busv

oltagesfor

different

operatingcond

ition

softhe

33-bus

microgrid.

Busn

umber

Basic

backwardforw

ardsw

eep

metho

d:distrib

utionsyste

mwith

noDG

New

tonRa

phsonmetho

dapplied

to33-bus

autono

mou

smicrogrid

Backwardforw

ardsw

eepmetho

dappliedto

33-bus

autono

mou

smicrogrid

Distrib

uted

slack

busb

ased

metho

dappliedto

33-bus

autono

mou

smicrogrid

Summer

demand

voltage

inp.u.

Winterd

emand

voltage

inp.u.

Summer

demand

voltage

inp.u.

Winterd

emand

voltage

inp.u.

Summer

demand

voltage

inp.u.

Winterd

emand

voltage

inp.u.

Summer

demand

voltage

inp.u.

Winterd

emand

voltage

inp.u.

11

10.9982

0.9979

0.9986

0.9983

0.9986

0.9983

20.9971

0.9964

0.9982

0.9979

0.9986

0.9983

0.9986

0.9983

30.9829

0.9792

1.000

1.0000

1.0000

1.0000

1.0000

1.0000

40.9755

0.9701

0.9991

0.9996

0.9990

0.9995

0.9990

0.9752

50.9681

0.9611

0.9985

0.9996

0.9982

0.9994

0.9982

0.9751

60.9497

0.9386

0.9972

0.9999

0.9966

0.9993

0.9918

0.9750

70.9462

0.9343

0.9974

0.9994

0.9967

0.9988

0.9918

0.9744

80.9413

0.9284

0.9981

0.9991

0.9971

0.9984

0.9972

0.9740

90.9351

0.9208

1.000

91.0

010

1.000

01.0

002

1.000

01.0

000

100.9292

0.9136

0.9955

0.9946

0.9945

0.9937

0.9946

0.9935

110.9284

0.9126

0.9947

0.9936

0.9937

0.9927

0.9938

0.9930

120.9269

0.9107

0.9934

0.9920

0.9923

0.9910

0.9924

0.9908

130.9208

0.9033

0.9877

0.9852

0.9866

0.9842

0.9867

0.9840

140.9185

0.9005

0.9856

0.9828

0.9845

0.9816

0.9846

0.9814

150.9171

0.8988

0.9843

0.9812

0.9832

0.9800

0.9832

0.9798

160.9157

0.8971

0.9830

0.9797

0.9819

0.9785

0.9820

0.9783

170.9137

0.8946

0.9811

0.9775

0.9800

0.9762

0.9801

0.9760

180.9131

0.89

380.98

060.9768

0.97

940.97

550.97

950.97

5319

0.9965

0.9958

0.9977

0.9973

0.9981

0.9976

0.9981

0.9977

200.9929

0.9915

0.9942

0.9930

0.9945

0.9933

0.9945

0.9934

210.9922

0.9906

0.9935

0.9922

0.9938

0.9925

0.9938

0.9925

220.99

160.98

990.99

280.99

140.99

320.99

170.99

320.99

1823

0.9794

0.9749

0.9965

0.9958

0.9965

0.9958

0.9965

0.9958

240.9727

0.9669

0.9900

0.9881

0.9899

0.9879

0.9899

0.9879

250.96

940.96

280.98

680.98

420.98

670.98

400.98

670.98

4026

0.9477

0.9362

0.9972

1.0005

0.9966

1.0000

0.9917

0.9756

270.9452

0.9331

0.9973

1.0016

0.9966

1.0010

0.9918

0.9767

280.9337

0.9191

0.9975

1.0062

0.9968

1.0053

0.9919

0.9811

290.9255

0.9091

0.9980

1.0102

0.9973

1.0091

0.9924

0.9850

300.9220

0.9047

0.9991

1.0133

0.9984

1.0121

0.9935

0.9881

310.9178

0.8996

1.0056

1.0252

1.004

81.0

238

1.000

01.0

000

320.9169

0.8985

1.004

81.0

242

1.004

01.0

228

0.9992

0.9990

330.9166

0.89

811.0

045

1.0239

1.0037

1.022

50.99

890.99

87


Table3:Com

paris

onof

realandreactiv

epow

erlosses

inthe3

3-bu

smicrogrid.

Losses

Basic

backwardforw

ardsw

eep

metho

d:distrib

utionsyste

mwith

noDG

New

tonRa

phsonmetho

dappliedto

33-bus

autono

mou

smicrogrid

Distrib

uted

slack

busb

ased

metho

dappliedto

33-bus

autono

mou

smicrogrid

Mod

ified

backwardforw

ardsw

eep

metho

dappliedto

33-bus

autono

mou

smicrogrid

Summer

demand

Winterd

emand

Summer

demand

Winterd

emand

Summer

demand

Winterd

emand

Summer

demand

Winterd

emand

Realpo

wer

losses

inkW

202.68

301.4

523.52

45.1

27.62

52.27

27.54

51.14

Reactiv

epow

erlosses

inkV

Ar

135.14

201.1

18.21

36.3

21.57

42.55

21.5

41.54


Table4:Con

tributionandparticipationfactorso

fthe

generators.

Realpo

wer

distrib

utionpertaining

tothew

interd

emandof

thes

ystem

Generatorsa

ndtheirb

uslocatio

nsCom

mon

Con

tributionof

the

generatortothe

realpo

werloadof

thec

ommon

inkW

Con

tributionof

the

generatortothe

realpo

wer

losses

ofthec

ommon

inkW

Link

Con

tributionof

the

generatortothe

realpo

wer

losses

onthelinks

inkW

Con

tributionof

the

generatortothetotal

realpo

werloadof

the

syste

min

kW

Con

tributionof

the

generatortothetotal

realpo

wer

losses

ofthes

ystem

inkW

Participationfactor

oftheg

enerator

tothetotalrealpo

wer

load

inthes

ystem

Participationfactor

oftheg

enerator

tothetotalrealpo

wer

losses

inthes

ystem

G1at3rd

bus

C11776

15.21

L10.2

1854

15.41

0.4159

0.30

C2—

—L2

—C3

——

L3—

C4—

—L4

—C5

77.97

——

—

G2at9thbu

s

C1—

—L1

—

938

12.16

0.2104

0.2355

C2810

11.77

L20.39

C3—

—L3

—C4

128

—L4

—C5

——

——

G3at31stbu

s

C1—

—L1

—

1666

24.05

0.3737

0.46

C2—

—L2

—C3

1488

23.83

L30.09

C4112.0

—L4

0.13

C566

.02

——

—Re

alpo

wer

generatio

nof

G1is1870k

W,G

2is950k

W,and

G3is1690

kW,respectively

Reactiv

epow

erdistrib

utionpertaining

tothew

interd

emandof

thes

ystem

Generatorsa

ndtheirb

uslocatio

nsCom

mon

Con

tributionof

theg

enerator

tother

eactivep

ower

load

ofthe

common

inkV

AR

Con

tributionof

theg

enerator

tother

eactivep

ower

losses

ofthe

common

inkV

AR

Link

Con

tributionof

theg

enerator

tother

eactivep

ower

losses

onthelinks

inkV

AR

Con

tributionof

the

generatortothetotal

reactiv

epow

erload

ofthes

ystem

inkV

AR

Con

tributionof

the

generatortothetotal

reactiv

epow

erlosses

ofthes

ystem

inkV

AR

Participationfactor

oftheg

enerator

tothetotalreactiv

epo

wer

load

inthe

syste

m

Participationfactor

oftheg

enerator

tothetotalreactiv

epo

wer

losses

inthe

syste

m

G1at3rd

bus

C11092

15.66

L10.51

1160

18.97

0.4203

0.452

C2—

—L2

—C3

——

L3—

C438.2

—L4

2.8

C530.0

——

—

G2at9thbu

s

C1—

—L1

—

574

90.2079

0.2144

C2492

8.97

L20.03

C3—

—L3

—C4

81.8

—L4

—C5

——

——

G3at31stbu

s

C1—

—L1

—

1026

140.3718

0.3336

C2—

—L2

—C3

972

12.6

L31.4

C4—

—L4

—C5

54.0

——

—Re

activ

epow

ergeneratio

nof

G1is1179k

VAR,

G2is583k

VAR,

andG3is1104

0kVA

R,respectiv

ely


Link 3: 7-8 Link 2: 9-8

Link 4: 5-4

Link 1: 3-4 Common 5

Common 2

Common 3

Common 1

1 2 3 4 5 6 7 16 17 188 9 121110 13 14 15

19 20 21 22

23 24 25 26 27 28 29 30 31 32 33

DG1 DG2

DG3

Common 4

Figure 4: “Commons” of the generators in the microgrid w.r.t the real power flows for winter demand.

0.85

0.87

0.89

0.91

0.93

0.95

0.97

0.99

1.01

1.03

1 6 11 16 21 26 31

Bus v

olta

ge m

agni

tude

(p.u

.)

Bus number

No DGNR method

Modified backward/forward sweep methodDistributed slack bus method

Figure 5: Comparison of voltage profile for summer demand of the33-bus microgrid.

5. Comparison of the Proposed Methods

5.1. Comparison of Voltage Profile. The voltage profile for the33-bus microgrid (shown in Figure 1) on implementation ofthe proposed methodologies (Table 2) is compared with thatof the standardNRmethod results for realizing the efficacy ofthe proposed algorithms. This comparison, for summer andwinter demands, is shown in Figures 5 and 6, respectively.

Figure 5 depicts that the voltage profiles obtained by NRmethod and modified backward forward sweep methods arein close agreement, since the generators are modeled as PQinjection machines. Since the real and reactive power gener-ations at all the generators are fixed, the voltage at 31st bus(generator bus) is found to rise above 1 p.u.On the other hand,the voltage profile obtained by distributed slack bus basedmethod is found to be almost flat and the maximum voltagedoes not exceed 1 p.u. at any bus.

5.2. Comparison of Distribution Losses. The distributionlosses for the 33-bus microgrid (shown in Figure 1) obtained

0.85

0.87

0.89

0.91

0.93

0.95

0.97

0.99

1.01

1.03

1 6 11 16 21 26 31

Volta

ge m

agni

tude

(p.u

.)

Bus number

No DGNR method

Modified backward/forward sweep methodDistributed slack bus method

Figure 6: Comparison of voltage profile for winter demand of the33-bus microgrid.

from the proposed methodologies (Table 3) are comparedwith the results of standard NR method. This comparisonof real and reactive power losses for summer and winterdemands is shown in Figures 7 and 8. Since the comparisonis made for the generators sized using single slack bus model,the losses are found to be slightly high for the distributed slackbus based load flow analysis.

6. Conclusions

This paper has suggested two backward/forward sweepbased load flow methodologies dedicated for autonomousmicrogrids. One method focuses on single slack bus modelwhereas the other method incorporates distributed slackbus technique into the sweep algorithm. Both the proposedmethodologies exploit the radial structure of microgridsand the possibility of operating synchronous generators tosupply varying real and reactive power outputs at constant


0

50

100

150

200

250

300

1 2 3 4

Loss

(kW

), (k

VAR)

Type of load flow analysis

a

a a a

b

b b b

(1) No DG (2) Newton Raphson method(3) Modified backward and forward

(4) Distributed slack bus method

(a) Real power loss(b) Reactive power loss

sweep method

Figure 7: Comparison of losses for summer demand of the 33-busmicrogrid.

0

50

100

150

200

250

300

1 2 3 4

Loss

(kW

), (k

VAR)

a

a

a a

b

b b b

Type of load flow analysis

(1) No DG (2) Newton Raphson method(3) Modified backward and forward

(4) Distributed slack bus method

(a) Real power loss(b) Reactive power loss

sweep method

Figure 8: Comparison of losses for winter demand of the 33-busmicrogrid.

voltage magnitude and angle has been verified.The proposedmethodology has been validated on a 33-bus autonomousmicrogrid. It is found that the proposed techniques are onpar with the standard Newton Raphson load flow techniqueboth in convergence and accuracy points of view. Further,the distributed slack bus based load flow technique formsthe basis for fixation of tariff in a deregulated environmentby identifying the individual contributions of the DGs in thesystem.

List of Symbols

𝐶𝑚𝑛: Contribution of𝑚th generator towards𝑛th common (p.u.)

Com𝑛load𝑝 : Real power load in 𝑛th common (p.u.)Com𝑛loss𝑝 : Real power loss in 𝑛th common (p.u.)Com𝑛load𝑞 : Reactive power load in 𝑛th common (p.u.)Com𝑛loss𝑞 : Reactive power loss in 𝑛th common (p.u.)

𝐹𝑚𝑝𝑛: Contribution of𝑚th generator through𝑝th link to 𝑛th common (p.u.)

𝐹𝑝𝑛: Power flow contributed by pth link to 𝑛thcommon (p.u.)

𝐼br𝑘 : Branch current for the branch “𝑘” (p.u.)𝐼𝑔𝑗

: Generator injected current at 𝑗th bus (p.u.)𝐼𝑗: Net current injected at 𝑗th bus (p.u.)𝐼load𝑗 : Load current drawn from the 𝑗th bus

(p.u.)𝐼𝑛: Total power inflow into 𝑛th common (p.u.)𝐼sh𝑗 : Shunt compensation current injected at

𝑗th bus (p.u.)𝐾𝑔𝑚𝑛load𝑝 : Participation factor of𝑚th generator for

real power load in 𝑛th common𝐾𝑔𝑚𝑛loss𝑝 : Participation factor of𝑚th generator for

real power loss in 𝑛th common𝐾𝑔𝑚𝑛load𝑞: Participation factor of𝑚th generator for

reactive power load in 𝑛th common𝐾𝑔𝑚𝑛loss𝑞 : Participation factor of𝑚th generator for

reactive power loss in 𝑛th commonnc: Number of commonsng: Number of generatorsnln: Number of links connected to any 𝑛th

common𝑃𝑔𝑖

: Total real power generated by 𝑖thgenerator (kW)

𝑃𝑔𝑖load: Total real power load supplied by 𝑖th

generator (kW)𝑃𝑔𝑖loss

: Total real power load supplied by 𝑖thgenerator (kW)

𝑃load: Total real power load (kW)𝑃loss: Total real power loss (kW)𝑄𝑔𝑖

: Total reactive power generated by 𝑖thgenerator (kVAR)

𝑄𝑔𝑖load: Total reactive power load supplied by 𝑖th

generator (kVAR)𝑄𝑔𝑖loss

: Total reactive power load supplied by 𝑖thgenerator (kVAR)

𝑄load: Total reactive power load (kVAR)𝑄loss: Total reactive power loss (kVAR)𝑅𝑖𝑗: Resistance of the distributor between

buses “𝑖” and “𝑗” (p.u.)𝑆load𝑗 : Apparent load power at 𝑗th bus (p.u.)𝑉𝑗: Voltage at 𝑗th bus (p.u.)𝑋𝑖𝑗: Reactance of the distributor between buses

“𝑖” and “𝑗” (p.u.).

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

References

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